Preview only show first 10 pages with watermark. For full document please download

AES/PE/10-34 Evaluation of post-fracture production in tight gas reservoirs: The impact of unconventional reservoir behaviour on production and well test interpretation. November 3rd, 2010 L.F. van Zelm MSc. Petroleum Engineering – Thesis report - L.F. van Zelm 2 MSc. Petroleum Engineering – Thesis report - L.F. van Zelm Title : Evaluation of post-fracture production analysis in tight gas reservoirs: The impact of unconventional reservoir behaviour on production and well test interpretation. Author : L.F. van Zelm Date : November 3rd, 2010 Professor : Prof. dr. W.R. Rossen Supervisors : Prof. dr. W.R. Rossen Dr. C.J. de Pater Committee Members : Prof. dr. W.R. Rossen Dr. C.J. de Pater Prof. dr. P.L.J. Zitha Dr. ir. C.W.J. Berentsen TA Report number : AES/PE/10-34 Postal Address : Section for Petroleum Engineering Department of Applied Earth Sciences Delft University of Technology P.O. Box 5028 The Netherlands Telephone : (31) 15 2781328 (secretary) Telefax : (31) 15 2781189 Copyright ©2010 Section for Petroleum Engineering All rights reserved. No parts of this publication may be reproduced, stored in a retrieval system, or transmitted, In any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of the Section for Petroleum Engineering. 3 MSc. Petroleum Engineering – Thesis report - L.F. van Zelm 4 MSc. Petroleum Engineering – Thesis report - L.F. van Zelm Abstract Worldwide rising gas demand is creating new opportunities for low-permeability gas reservoirs to be exploited with large hydraulic fracturing campaigns. These so-called tight gas reservoirs have been subject of much research over the past three decades, primarily because it is difficult to optimize recovery. In this thesis, post-fracture production of tight gas reservoirs is simulated and interpreted through well test analyses. The focus lies on the impact of unconventional reservoir behaviour, specifically the impact of leakoff water on gas production and assessing the accuracy of post-fracture evaluation using production data and well tests. Specific characteristics of tight gas reservoirs, such as high capillary pressure, a ‘permeability jail’, and reservoir heterogeneity, may invoke phase trapping mechanisms that could potentially harm gas production. The ‘permeability jail’ is a hypothesis that gas-water relative permeability functions include a large saturation range with little or no fluid mobility, caused by the complex pore-structure of tight gas sandstone reservoirs. This thesis presents reservoir simulations of both the short and the long-term gas and water production, performed with a commercial numerical simulator. Simulations show that high capillary pressures alone do not harm gas production significantly. Assuming a permeability jail in lower-permeability reservoir zones in a heterogeneous reservoir results in an extended cleanup period and a reduction in total recoverable gas. This result is comparable to the simulation of mechanical or chemical damage to the reservoir surrounding the fracture, or so-called fracture face damage. With mechanical or chemical damage, the water production is impaired initially and slowly recovers with time. This distinguishes this type of damage from a permeability jail, which shows rapid water flow-back of approximately 50% of the leakoff water. Finally, the impact of leakoff water on a permeability jail is severe. Therefore, it is advisable to control leakoff during the treatment. The simulation output data is analyzed with a commercial pressure transient analysis software package. The well test analyses show that a heterogeneous reservoir with permeability jail damage can also be interpreted as a homogeneous reservoir with either a very short or low-conductivity fracture: all three hypotheses fit the well-test data. This confirms that well tests may be inconclusive for distinguishing among these cases. Subsequent performed simulations show that reduction in fracture length does not extend the initial cleanup period, but strongly correlates with a shift of the production decline curve to lower gas rates. A reduced fracture length and damage from leakoff and a permeability jail are therefore distinguishable. On the other hand, it’s difficult to separate production results for a model with a low-conductivity fracture from a model with permeability jail damage: both show strongly reduced initial gas rates and followed by long cleanup periods. Water production can be used to discriminate between a fracture with reduced permeability and reservoir damage, however. This allows for a correct diagnosis and appropriate actions to be taken to optimize subsequent fracture treatments. 5 MSc. Petroleum Engineering – Thesis report - L.F. van Zelm 6 MSc. Petroleum Engineering – Thesis report - L.F. van Zelm Preface / Acknowledgements This report presents my final thesis work of the MSc. Petroleum Engineering, as part of the section Petroleum Engineering at the department of Geotechnology of the Delft University of Technology. This thesis work is performed in close cooperation StrataGen Delft, an engineering consulting company. StrataGen offers a broad range of services, including fracture and reservoir studies, fracture treatment design and onsite treatment supervision. I would like to thank Prof. dr. W.R. Rossen deeply for his guidance during this project, his expertise on reservoir engineering and his out-of-the-box thinking on hydraulic fracturing operations and simulations. Furthermore, I would like to thank him greatly for helping me to structure my thesis report by providing many edits and comments until the last moment. I owe my gratitude to my supervisor dr. Hans de Pater, manager of StrataGen Delft, for the possibility to do my research on this very interesting topic in cooperation with StrataGen. Furthermore, I am very grateful for all his advise and that he has been willing to share his knowledge and expertise with me. Special thanks goes out to Josef Shaoul, for all his support on the various software programmes I needed for this thesis and for sharing his ideas and expertise on hydraulic fracturing with me. I would like to thank him for always being open to questions and his enthusiasm in helping me to tackle various problems. Also, I would like to thank Bart, Winston and Marcello for the many tips and tricks on fracturing, the oil industry and other important things in life over the last year. I very much enjoyed working with you! I would like to thank my committee members, Prof. dr. Pacelli Zitha and dr. ir. Cas Berentsen, for their interest in my work and their willingness to be part of my graduation committee. Last, but certainly not least: I would like to deeply thank my family and friends for their support, understanding, believe, love, enjoyable reliefs and laughter! 7 MSc. Petroleum Engineering – Thesis report - L.F. van Zelm 8 MSc. Petroleum Engineering – Thesis report - L.F. van Zelm Table of Contents Abstract ..................................................................................................................5 Preface / Acknowledgements .................................................................................7 Table of Contents....................................................................................................9 1 Introduction.................................................................................................. 11 1.1 Problem statement and objectives......................................................... 11 1.2 State-of-the-art of tight gas stimulation and evaluation........................... 12 1.2.1 Water blocking principle ................................................................ 12 1.2.2 Fracture damage and cleanup ........................................................ 13 1.2.3 Well test analysis .......................................................................... 13 1.3 Thesis structure................................................................................... 14 2 Theory........................................................................................................... 15 2.1 Single phase gas flow .......................................................................... 15 2.2 Multiphase (gas-water) flow ................................................................. 17 2.2.1 Relative permeability ..................................................................... 17 2.2.2 Fluid saturations and capillary pressure........................................... 17 2.3 Characterization of tight gas reservoirs.................................................. 19 2.3.1 Rock properties............................................................................. 19 2.3.2 Phase trapping and the ‘permeability jail’ ........................................ 20 2.3.3 Capillary pressure ......................................................................... 22 2.3.4 Heterogeneity............................................................................... 22 2.4 Well test analysis................................................................................. 23 2.4.1 Dimensionless variables ................................................................. 23 2.4.2 Theory of buildup analysis ............................................................. 24 2.4.3 Analysis plots................................................................................ 24 2.4.4 Hydraulic fracture evaluation: procedure and accuracy ..................... 27 3 Modelling of Tight Gas Reservoirs................................................................. 28 3.1 Simulation Model Setup........................................................................ 28 3.1.1 Tight gas properties ...................................................................... 28 3.1.2 Well, hydraulic fracture and grid properties ..................................... 31 3.1.3 Base case initiation........................................................................ 34 3.2 Tight-gas capillary pressure .................................................................. 36 3.2.1 The impact of capillary pressure on gas production .......................... 36 3.2.2 Capillary end effect and its water block potential ............................. 40 3.3 Permeability jail................................................................................... 49 3.4 Heterogeneity model............................................................................ 54 3.4.1 Heterogeneity model: preparation .................................................. 54 3.4.2 Heterogeneity model: production simulation.................................... 61 3.4.3 Heterogeneity modelling results: cleanup period .............................. 65 3.4.4 Heterogeneity modelling results: long-term production..................... 68 3.4.5 Heterogeneity modelling results: impact of injected water ................ 72 3.4.6 Controlling damage from leakoff water ........................................... 74 9 MSc. Petroleum Engineering – Thesis report - L.F. van Zelm 4 Well Test Interpretation of Simulation Results............................................. 76 4.1 Well test preparation ........................................................................... 76 4.2 Well test results................................................................................... 77 4.2.1 Pre-fracture well test ..................................................................... 77 4.2.2 Post-fracture well test ................................................................... 78 4.3 Well test interpretation and implications ................................................ 82 4.4 Closing the circle: using well test results................................................ 85 5 Conclusion and Recommendations ............................................................... 91 5.1 Conclusions......................................................................................... 91 5.2 Recommendations ............................................................................... 94 6 Bibliography.................................................................................................. 95 6.1 Books and articles ............................................................................... 95 6.2 Software and internet ........................................................................ 100 7 Nomenclature ............................................................................................. 102 8 Appendix - Flow calculations in simulator .................................................. 103 9 Appendix - Modelling hysteresis effect ....................................................... 105 10 Appendix – Equilibrium Sw profile: a spreadsheet calculation.................. 107 11 Appendix - Hydraulic Fracture Design and Simulation ............................. 110 12 Appendix - Grid refinement options ......................................................... 112 13 Appendix - Reservoir model test runs ...................................................... 115 14 Appendix - Simulation of fluid leakoff process ......................................... 117 10 MSc. Petroleum Engineering – Thesis report - L.F. van Zelm 1 Introduction 1.1 Problem statement and objectives Worldwide rising gas demand is creating new opportunities for low-permeability gas reservoirs to be exploited. These so-called tight gas reservoirs have been subject of much research over the past three decades, primarily because it is difficult to optimize recovery. Economic development of tight gas reservoirs is only possible through the use of well stimulation techniques, mainly hydraulic fracturing, in vertical or horizontal wells. Hydraulic fracturing is the technique of pumping fluid with sand or ceramic proppant into the reservoir, where the downhole pumping pressure exceeds the formation stress. This will cause the formation to break and split in the direction perpendicular to the minimum stress. The fracture will improve the well productivity by creating a conductive channel that provides much better contact between well and reservoir (Economides and Nolte 2000). The production enhancement for any well, whether oil or gas, can be simulated with use of combined reservoir and fracture simulators. In general, the well productivity increase can be calculated to a certain degree. For tight gas wells, the improved well productivity is nevertheless generally overestimated by simulation programs using fracture characteristics estimated from fracture simulation software (Cramer 2005). Several factors may result in the unrealistic forecasting of the production. One issue is that in tight reservoirs, it is very difficult to measure kh and reservoir pressure (Britt et al. 2004), which are needed for basic flow calculations and are crucial for evaluating stimulation success. The problem arises because it takes a long time to measure these parameters in well tests. Furthermore, in tight gas reservoirs an additional problem is to evaluate the performance to optimize the stimulation. Estimating productivity after stimulation requires pre-determined or estimated values for fracture geometry (length-width-height) and conductivity, all which are hard to quantify without an accurate estimate of the kh. A second cause for the underperformance is the strong and long-lasting cleanup that is often observed in tight gas reservoir with a hydraulic fracture. The cleanup of a well is the initial period (a few days) in which gas rates are slowly increasing over time, instead of starting with peak production. An extended cleanup, up to weeks or months, can be caused by fracture face damage, water blockage in the reservoir, fluid leakoff behaviour, fracture gel cleanup in the fracture or a combination of these effects. Generally, the influence of each of the individual factors remains an ‘unanswered question’ (Wang et al. 2009). Over the past decades, many researchers have focused on the influence of these mechanisms for the well’s potential is significantly affected. A brief review of the most important findings is included in section 1.2. The thesis objectives are to research proposed ideas on phase trapping mechanisms, such as relative permeability reduction and the effect of heterogeneity in fracture face cleanup. Secondly, to build a reservoir simulation model to test proposed ideas and to perform postfracture analysis on modelled production data. In this analysis, the objective is to test whether the input data for the reservoir simulation (reservoir and hydraulic fracture properties) can be obtained from the well test results. It will also be tested how unique and accurate the solution is. The aim is to improve the understanding and interpretation of the impact of unconventional fluid behaviour on production and well test analysis. 11 MSc. Petroleum Engineering – Thesis report - L.F. van Zelm 1.2 State-of-the-art of tight gas stimulation and evaluation 1.2.1 Water blocking principle During the fracturing process, water invades the formation and remains there until production starts and the cleanup commences. Then, if pressure drawdown overcomes capillary pressure within the reservoir, some or all of the water returns to the fracture. This water can also remain trapped in the pores of the reservoir by capillary forces and it can negatively affect well productivity (Mahadevan et al. 2009). This process is called water blocking. Holditch (1979) explored various factors affecting water blocking and gas flow from hydraulically fractured wells. He shows that if formation damage is present due to fluid invasion and capillary pressures exceed pressure drawdown, the damaged zone acts as a pressure sink to attract and trap water. This causes the relative permeability of gas to be reduced and hence influences the production dramatically. A limitation is that this work addresses uniform reservoir only. Cramer (2005) shows that the production reduction from water blocking can be expressed as an additional skin which is added to the existing skin factors in a producing well, and is defined as a function of hydraulic fracture length, damagezone width and the ratio of undamaged permeability and the permeability in the damaged zone. He calculates dramatically reduced well productivity. The impact of the combined effects of damaged zones surrounding the hydraulic fracture and water blockage is recognized and tested widely by many authors. Apart from previously referenced work, Settari et al. (2002) shows that water blockage alone is not a major cause of concern in gas wells, but in combination with absolute permeability damage can cause serious productivity reduction. Recently, Friedel (2004) also concludes that the so-called hydraulic damage, caused by increased water saturation and relative permeability effects in the vicinity of the fracture, has less impact on production than reduction of porosity and permeability surrounding the fracture (mechanical damage) caused by the fracturing process. As shown in the referenced papers, many different causes can be found for the reduction in production by the water invasion in the formation. In this thesis, the focus will be on damage caused by the invasion of leakoff water into the reservoir surrounding the hydraulic fracture. Some factors seem to be important in this process, such as capillary pressures, initial water saturations and pressure drawdown. But also wettability of the reservoir rock (Bang et al. 2008) may play an important role in this process. The increased focus on reservoir properties and their importance to describe gas recovery and post-fracture production results is also noted by Rickman and Jaripatke (2010). Water block mechanisms, such as high capillary pressures, are taken into consideration for the simulation models. More details are provided in the specific sections of this thesis (chapter 3). 12 MSc. Petroleum Engineering – Thesis report - L.F. van Zelm 1.2.2 Fracture damage and cleanup The fluid used in hydraulic fracturing operations contains apart from water certain polymer additives, which are mainly responsible for viscosifying the fluid, proppant transport, and fluid-loss control. The main design criterion for fracturing fluids is viscosity (Economides and Nolte 2000). After the proppant placement, ideally the polymer should degrade chemically and be produced back through the well. If this does not happen, severe damage within the fracture can occur. This is referred to in the industry as a slow or incomplete fracture cleanup. A proper cleanup of the fracture after the pumping stage is important for determining the fracture properties and estimating the long-term well performance (Montgomery et al. 1990). Tight gas wells with an infinite-conductivity fracture should show a high initial production peak, followed by a steep decline in rate. This so-called hyperbolic decline curve is typical for tight gas reservoirs, compared to more common exponential decline (Holditch 2006). In some producing wells, a slowly increasing production plateau has been observed, which may be the result of the viscous gels remaining in the proppant pack. When gel remains in the fracture, a reduction up to 80% in initial gas rate can be seen (Voneiff et al. 1996). In order to simulate this kind of behaviour, one must represent the flow of three phases: gas, formation/fracturing water and unbroken gel (Wang et al. 2009). Multiphase flow and the gel remaining in the fracture are important factors affecting fracture cleanup and it should be taken into account when simulating the well productivity of tight gas wells with special focus on the role of the fracture itself. The simulations in this thesis will only be performed with two phases present: gas and water. The water represents both the initial reservoir water and the leakoff fluid. When referred to ´the cleanup period´, this then refers to the initial gas rate reduction caused by the water phase only (see section 1.2.1 for examples). This thesis does not include research on fracture damage. However, low-conductivity (e.g. unbroken gels) and short (e.g. poorly placed proppant) fractures are taken into consideration during the post-fracture evaluation (chapter 4). 1.2.3 Well test analysis For many years, the most common way to obtain important reservoir properties is to perform a well test analysis. Early interpretation methods, such as semi-log or log-log pressure plots, were limited to the estimation of well performance, near-wellbore effects or assumptions of reservoirs with homogeneous properties (Gringarten 2006). With the introduction of the pressure-derivatives plot by Bourdet et al (1989), the analysis of well tests changed dramatically, allowing for heterogeneous reservoirs, limited wellbore entry and boundary effects. Where early pressure-analysis methods recorded the movement of a pressure wave through the reservoir, the pressure derivative can reveal much more detail. By definition, the pressure derivative is more sensitive to changes that occur in the movement of this wave and therefore it is capable of detecting changing patterns in the reservoir. This results in different patterns for different scenarios, which can be recognized on specific log-log plots. Examples are boundary dominated flow, wellbore storage dominated flow, early flow times (transient), infinite reservoir (radial flow), (in)finite hydraulic fracture, and many more. 13 MSc. Petroleum Engineering – Thesis report - L.F. van Zelm For conventional reservoirs, this practice has been proved to be simple, effective and inexpensive. Nevertheless, in low-permeability formations, the use of tests such as Pressure Buildup (PBU) analysis are mostly inadequate, mainly due to operational aspects (Cipolla and Mayerhofer 1998). PBU tests require a long shut-in period to obtain pseudo-radial flow from which permeability can be calculated using a log-log plot. In low-permeability formations with long hydraulic fractures this flow transition might take months or years, as proved by Gringarten et al. (1974) and Cinco-Ley et al. (1978). This will make the operation expensive and therefore mostly unwanted by operators. Furthermore, research shows (Montgomery et al. 1990) that conventional PBU analysis methods will, at best, provide only fair to poor results in low permeability reservoirs. Additional variables, such as low conductivity in the fracture, formation damage in the fracture, water invasion of the reservoir and natural fractures networks, tend to complicate the results of these analyses further. This makes it hard to obtain a unique solution to the problem, which is necessary for the appropriate actions to be taken. Chapter 4 focuses on well test analyses (PBU) performed on the simulated production data. Several scenarios are analyzed and the accuracy of the outcome is tested. Focus lies on the interpretation of multiphase fluid flow, complicated reservoir behaviour and fracture damage. For a good post-fracture production analysis, it’s crucial to obtain the basic reservoir and fracture properties. 1.3 Thesis structure This thesis consists of 4 main chapters, starting with the introduction to the general problem statement and objectives of thesis in chapter 1. Next, chapter 2 provides the theoretical background on fluid flow in a reservoir towards a hydraulically fractured well, the characteristics of tight gas reservoirs and the basics of well test analysis. The next two sections (chapter 3 and 4) both discuss specific parts of the thesis problem. Chapter 3 provides the reservoir model used in the numerical production simulations of this thesis. The first section (3.1) describes the model setup, followed by a presentation of the simulation results of high capillary pressures and the effect of phase relative permeability reduction on gas and water production (section 3.2 and 3.3). Finally, section 3.4 introduces a heterogeneous reservoir model to more realistically simulate specific tight gas reservoir properties and the impact of water invasion around the hydraulic fracture. Chapter 4 focuses on well test analyses performed in the models of chapter 3 and shows the obtained results. It’s shown that these may lead to various interpretations, regarding the state of the reservoir and the hydraulic fracture. The implications are discussed subsequently. Chapter 5 concludes with the main findings of the thesis and provides recommendations for fracture treatments in tight gas reservoirs and ideas for further research. Finally, after the thesis bibliography (chapter 6), a total of 7 appendices are included in the back of this thesis report (chapters 7 to 14). These chapters provide background information on the simulations and elaborate on decisions made in the process. 14 MSc. Petroleum Engineering – Thesis report - L.F. van Zelm 2 Theory This chapter describes the theoretical background of gas flow in the reservoir and gas production. The formulas are from Hagoort (1988). The first section (2.1) discusses singlephase flow and the introduction of the hydraulic fracture into the model. Multiphase (gaswater) flow (section 2.2) requires an update of the inflow equation and the introduction of additional parameters. The water phase is introduced and the corresponding multiphase equations are presented. The second part of this chapter (section 2.3) discusses the specific properties of tight gas reservoirs and introduces complications related to the standard fluid flow equations. This introduction will be the base of the tight gas modelling in chapter 3. Finally, this chapter concludes with the theory of well test analyses (section 2.4), which will be used in the postfracture analyses in chapter 4. 2.1 Single phase gas flow Production from gas bearing formations in the subsurface occurs through the flow of gas towards the well. A pressure difference between the bottom of the well and the reservoir causes flow of the gas into the wellbore. The pressure near the wellbore rapidly decreases towards the wellbore pressure. The initial decrease in pressure is referred to as the ‘transient period’. The pressure wave continues outward through the reservoir, until a pressure boundary is ‘felt’. After this period pressure declines with time at a uniform rate throughout the reservoir and flow is stabilized. This is named either ‘steady state’ or ‘pseudo-steady state’, depending on whether the boundary is perfectly transparent (steady state) or sealing (pseudo-steady state) (Lake 2003). Single-phase flow in a porous medium is described by two equations: Darcy’s Law (Eq. 2-1) and mass conservation (Eq. 2-2). Darcy’s Law is valid in the absence of inertial effects and neglecting gravity and the mass conservation is for an infinitesimal Cartesian volume element at steady-state. k q u = = − grad ( P ) A µ Eq. 2-1 δ δ δ ( ρ ux ) + ( ρu y ) + ( ρ u y ) = div( ρ u ) = 0 δx δy δy Eq. 2-2 These equations can be combined into a working gas radial inflow well equation (Eq. 2-3) under assumptions of pseudo-steady state and isotropic and uniform reservoir properties. The individual steps and elaborate discussions are found in Hagoort (1988) and will not be thoroughly discussed here. Subscript r is used here for reference state of the gas. q= 2π kH ( mR − mbh ) 3   ( µ B ) r  ln( Re / Rw ) − + stot  4   Eq. 2-3 15 MSc. Petroleum Engineering – Thesis report - L.F. van Zelm Under certain circumstances, the assumption of steady state is not applicable to describe the flow of gas in reservoirs. Especially in low-permeability gas formations, transient flow can dominate much of the life of a well (Wattenbarger et al. 1969). A good mathematical approximation is achieved with the pseudo-steady state equation for the inflow of gas into the wellbore and a skin factor combining any flow resistance in the near-wellbore area (stot). The basic properties of gas depend on pressure and can therefore not be assumed constant throughout production. This requires introducing a quantity called pseudo pressure (AlHussainy et al. 1966). Pseudo pressure (Eq. 2-4) can be calculated from (reference) pressure and the property state at this reference pressure. m( p ) = 1 (ρ / µ ) r p ∫ ( ρ / µ )dP Eq. 2-4 pr So far, the radial inflow equation (Eq. 2-3) has not considered flow into a hydraulic fracture. To do so, the radius of the well is replaced by the so-called ‘effective wellbore radius r’w to account for the increased fracture inflow area. Prats (1961) was the first to introduce this term and showed that for an infinite-conductivity fracture the following relation applies, where xf is the fracture half-length: Eq. 2-5 R ' = 0.5 x w f Combining this with Eq. 2-3, the equation for gas flow into a hydraulically fractured well is as follows: q= 2π kh(mR − mbh ) 3   ( µ B )r ln( Re / Rw' ) − + s frac  4   Eq. 2-6 where R’w is effective wellbore radius after stimulation and sfrac is the skin resulting from damage to the fracture face and damage to the fracture, e.g. reduction of permeability. Eq. 2-6 assumes (pseudo-) radial single-phase gas flow in the reservoir towards the well. Initially a fractured well shows strong transient flow behaviour, which includes a period of linear flow, which gradually changes to radial flow. In low-permeability reservoirs, this transition can take a very long time. The rate given by Eq. 2-6 is therefore a theoretical value, which can only be used for comparing rates at longer simulation times and not in the early transient period of the well. Chapter 13 (Appendix for reservoir model test runs) discusses the validation of the numerical simulator by comparing the simulated rate with the calculated rate using Eq. 2-6. 16 MSc. Petroleum Engineering – Thesis report - L.F. van Zelm 2.2 Multiphase (gas-water) flow Section 2.1 provides an introduction to the flow of gas in the reservoir towards the hydraulic fracture and then into the wellbore. Throughout the whole derivation single-phase flow is assumed. Both initial formation water and invading fracturing fluid can lead to a systematically different and more complex behaviour of gas flow in the reservoir. This section focuses on the theory behind these important multiphase phenomena that need to be taken into consideration for the modelling of gas production in tight gas reservoirs. 2.2.1 Relative permeability The introduction of the water phase into the system has an impact on both the material balance and the flow through the reservoir. Therefore, the mass balance equation and Darcy’s Law need to be updated. Darcy’s Law for a single phase α in a multiphase system, is uα = − kkrα µα grad ( Pα ) Eq. 2-7 Laboratory experiments are used to determine the relative permeabilities of gas and water as functions of water saturations. When experimental data is lacking, some empirical relations are available. The most widely used relations for relative permeabilities are the Brook-Corey relations (Brooks and Corey 1964). Many studies refer to the use of these correlations in calculating the relative permeabilities for a given system. For this study, the relations used are presented in section 3.1.1. 2.2.2 Fluid saturations and capillary pressure Throughout section 2.1 steady state is assumed. In order to describe the multiphase flow processes that occur during fracturing-fluid invasion of the formation and later gas production, this assumption has to be relaxed. Multiphase flow in reservoirs is described in detail by Dake (1978). In multiphase flow, the two phases require a separate approach with respect to flow and mass conservation. It’s therefore necessary to introduce the phase saturations; water saturation Sw and gas phase Sg. The sum of Sw and Sg is 1. This now allows one to calculate a mass balance per phase. The simulator works with discretized forms of the mass balance and fluid flow equations to allow the solution to be solved numerically. More detail on the use of the flow equations in Eclipse 100 (Schlumberger 2009) is provided in chapter 7 (Appendix for flow calculations). 17 MSc. Petroleum Engineering – Thesis report - L.F. van Zelm A second parameter needed to correctly model the flow of gas and water, is the capillary pressure Pc. The capillary pressure is defined by Eq. 2-8 Pc = Pnw − Pw The most common form of the capillary-pressure function is from Leverett (1941), introducing a dimensionless J-function. The capillary pressure is a function of the interfacial tension (σ), the contact angle between rock and fluid (θ), the porosity (φ) and the function J(Sw). φ  Pc = σ cos(θ )   J ( S w ) k Eq. 2-9 This relation reveals that for tight gas reservoirs with generally smaller pores, the capillary pressure is high. This will be discussed in more detail in 2.3.3. 18 MSc. Petroleum Engineering – Thesis report - L.F. van Zelm 2.3 Characterization of tight gas reservoirs This section presents an overview of rock properties of low-permeability rocks, which dominates the flow behaviour of tight gas reservoirs. In particular, this section discusses capillary pressure, the ‘permeability jail,’ and reservoir heterogeneity, which are the focus of much of this thesis. 2.3.1 Rock properties Many authors have focused on classifying and determining the various types of tight gas sands in the US, after the immense potential became more evident in the last decades. Spencer (1985) describes the geological aspects of tight gas reservoirs in the Rocky Mountain Region. He states that there are generally 4 types of reservoir: marginal marine blankets, shallow marine blankets, lenticular fluvial reservoirs and finally chalk reservoirs, each with specific lateral reservoir continuity (Holditch 2006). As an example, Table 2-1 below presents an overview of general properties of some reservoirs located in the Rocky Mountains (Shanley et al. 2004), one of the most thoroughly studied regions of low-permeability reservoirs worldwide. Property Porosity Permeability (Klinkenberg corrected) Stressed permeability (Klinkenberg corrected) Water saturation (producible range) Irreducible water Pore type Pore-throat description Description 5-10% 0.1 – 10 mD 0.001 – 10 mD <50% 20 – 40% Slot pores dominated permeability Micro- to nanopore throats Table 2-1 rock property values, tight sands in Rocky Mountains region (Shanley et al. 2004). Overall, tight sandstones have low porosity, which is a result of heavy compaction; pores present are of micrometer to nanometer-size. Rushing et al. (2008) states that ‘the low permeabilities and porosities associated with tight gas sands can be attributed directly to a large distribution of small and very small pores and/or a very tortuous system of pore throats connecting these pores’. Byrnes (1996) describes the reservoir characteristics of the typical low-permeability sandstones found in the Rocky Mountains, and comments that ‘the influence of confining stress on permeability can be attributed primarily to the decrease in size of the pore throats that connect the larger pores, which result in permeability decreases of 10 to 40 times’. An example is shown in Fig. 2-1. 19 MSc. Petroleum Engineering – Thesis report - L.F. van Zelm Fig. 2-1 Thin section of slot and fracture porosity in Deep Basin of Canada (Aguilera 2008). 2.3.2 Phase trapping and the ‘permeability jail’ A number of authors argue that the complex pore structure of tight-gas reservoirs, dominated by slot pores and sheet-like pore throats and high effective overburden stress, gives rise to specific issues concerning multiphase flow. This complex structure may form a potential damage to gas production, for example by phase trapping. Bennion (2009) describes favourable and unfavourable pore structures for phase trapping. He concludes that a pore structure in which most of the effective permeability is contained in a relatively small fraction of the pore space, which consists of interconnected meso- or macropores or small fractures, is not sensitive to water-based phase trapping. They have a rather large ‘capacity’ to store the water without it blocking the main pores. A structure of a more uniform distribution of micro-pores (1-10 µD) will, by a slight increase in water saturation, result in the clogging of most of the pores with water and thus a reduction in effective permeability to gas throughout the whole pore structure. A pore structure that consists of narrow pore throats, he argues, is susceptible to this kind of behaviour. Apart from phase trapping, the high effect stresses in the rock may impact the permeability to fluids so severely that classical theories for multiphase flow are no longer applicable. The relative permeabilities to both water and gas can be so low that neither phase has significant relative permeability over some range of saturations. This idea is named the ‘permeability jail’ (Shanley et al. 2004). 20 MSc. Petroleum Engineering – Thesis report - L.F. van Zelm Fig. 2-2 The relative permeability and capillary pressure in low-permeability gas reservoirs (Shanley et al. 2004). Fig. 2-2 illustrates this concept for relative permeability and capillary pressure functions. In some tight gas formations water ceases to flow at a ‘critical’ water saturation that is substantially greater than connate water saturation. Normally, field observations of low water production would imply that the reservoir is at irreducible saturation, and one would expect gas to flow freely, but it does not. Second, the lowered permeability causes the two phases to increasingly interfere in the restricted flow paths of the rock pore space. Sgc increases toward initial water saturation. This region of saturations where neither phase has significant relative permeability is named ‘permeability jail’. Cluff and Byrnes (2010) also discuss the existence of a permeability jail in low-permeability reservoir rocks, where the water is trapped by the high capillary pressure and thereby reduces the permeability to gas significantly. Although hard laboratory evidence in the form of published studies is missing, the authors believe that multiple gas-brine drainageimbibition hystereses can cause this typical fluid behaviour. This form of hysteresis is believed to occur in lithologies with complex pore geometries, as presented for example by Bennion (2009). 21 MSc. Petroleum Engineering – Thesis report - L.F. van Zelm Gdanski and Walters (2010) demonstrate the impact of relative permeability functions on gas and fracture treatment water production in low-permeability gas reservoirs. The ‘poorquality matrix rel-perms’ are referred to as ‘rel-perm jail’ and not considered to be typical drainage relative permeability functions. Nevertheless, the authors also believe that indeed multiple hystereses may cause strong relative permeability reduction. Britt and Schoeffler (2009) describe the permeability jail as ‘extremely important for reservoir and petrophysical assessment of resource quality’. Contrary, Blasingame (2008) refers to it as ‘a provocative study with regard to their concept of capillarity controlled production’, but he also states that ‘the reality of poor well performance is explained […] by the concept of permeability jail, but there are other specific factors influencing flow at the reservoir scale’. The area of repeated hysteresis and the impact on low-permeability gas reservoirs is a topic that requires much more study. For example, at the time of this writing, the Ecole Centrale de Lille (2010) has a research position open for petrophysical analysis at micro-pore scale, for normal analysis method often fail to result in consequent output. The geology department of the University of Utah (2010) works on a project which aims at the interplay between multiphase flow and hydraulic fracture models in tight gas reservoirs, also specifically naming ‘permeability jail’ as an important research topic. Although the idea for the existence of a ‘permeability jail’ has so far not been proven in any laboratory tests, this thesis will investigate this phenomenon as part of the post-fracture production analysis of tight gas reservoirs. 2.3.3 Capillary pressure Low-permeability reservoirs have small pores, and under stress ‘pore throats decrease in diameter by up to 50% to 70%’ (Byrnes 1996). Eq. 2-9 illustrates the relation between low permeability and capillary pressure. For a quick order-of-magnitude calculation, assume cos(θ) = 1 = J(Sw). For a tight-gas sandstone, common values for interfacial tension, porosity and permeability are respectively 50 mN/m, 0.05 and 0.001 mD (= 1 x 10-18 m2), which gives a reference capillary pressure of 111 bars. Because, according to Eq. 2-9 capillary pressure is proportional with the inverse of the square root of the permeability, a higher permeability implies significantly lower capillary pressure. This thesis investigates the impact of capillary pressure on post-fracture production. 2.3.4 Heterogeneity Reservoirs are heterogeneous both vertically and laterally. Barree (2009) states that in some reservoirs a large part of the fracture face contacts low-permeability regions with high capillary pressures. Other higher-permeability regions have lower capillary pressure and allow gas to flow freely, at higher velocity. Section 3.4 discusses the influence of heterogeneity in more detail. 22 MSc. Petroleum Engineering – Thesis report - L.F. van Zelm 2.4 Well test analysis The success of a hydraulic fracture in a tight gas reservoir is determined by the increase in gas production as a result of an increased effective wellbore radius. The extent of the improvement can be predicted with reservoir simulations, which require a few important input parameters. Amongst other methods, well test analyses can provide these parameters (pressure and permeability) prior to the fracture treatment. An example is a Pressure Buildup (PBU) test. A post-fracture well test analysis can also determine fracture half-length for further production forecasting. This thesis focuses on the use and accuracy of the PBU test in tight gas reservoirs, by analyzing the production results of a numerical reservoir simulation model. This section introduces the theory of these tests and discusses the procedure and accuracy of a PBU test. 2.4.1 Dimensionless variables In well test analysis, often the use of dimensionless variables aids the search for the unknown reservoir parameters (Horne 1995). Using dimensionless variables reduces the amount of unknowns and provides a solution for any system of units. The variables used are pressure, time and radius. The dimensionless pressure is defined as (SI units): pD = 2π kh ( m( pi ) − m( pwf ) ) QBµ Eq. 2-10 The dimensionless time is as follows: tD = kt Φµ ct rw2 Eq. 2-11 Finally, the dimensionless radius is: rD = r rw Eq. 2-12 For the analysis of hydraulically fractured wells, the dimensionless time is mostly re-written to obtain the fracture half-length xf instead of the wellbore radius. By applying Eq. 2-13, the resulting dimensionless time is derived as shown in Eq. 2-14. rw2 x 2f Eq. 2-13 kt Φµ ct x 2f Eq. 2-14 tD,x f = tD tD,x f = 23 MSc. Petroleum Engineering – Thesis report - L.F. van Zelm 2.4.2 Theory of buildup analysis Buildup tests and analyses are based on the theory of superposition, which uses the principle that a linear combination of particular solutions is also a solution. This is a wellknown and widely applicable theory in science and engineering (Horne 1995). For a buildup test it means that the well is controlled at two different rates over two pre-defined period of time, whereby the second rate is set to zero. Superposing the two pressure solutions results in a pressure response that can be analyzed by various methods, including a Horner plot. The simulations in this thesis can accurately control bottomhole rate or pressure and will allow a proper analysis to be made. A few important assumptions are made and should be taken into account when examining the results. First, the analysis of the PBU is based on single-phase flow (gas only) and therefore a combined inflow of liquid and gas may cause divergence from the solution. Other assumptions behind the PBU theory include infinite drainage area, homogeneous and isotropic reservoir, slightly compressible fluids and constant fluid and rock properties. These assumptions do not necessarily match the conditions in the simulator. Finally, the theoretical model assumes radial flow, while in hydraulically fractured wells in low permeability formations this may take much longer than an average well test last. The calculated properties from a PBU are therefore possibly inaccurate. Nevertheless, the absence of other quick, cheap and practical methods make a PBU test still widely used in the field and therefore useful to include in this thesis as the method of post-fracture analysis. 2.4.3 Analysis plots A standard method to analyze the pressure behaviour in a well during a pressure buildup (PBU) test is to perform a type curve match on a log-log plot. By matching the data to a type curve, reservoir parameters are estimated from plotted curves with known properties. Dimensionless time and pressure are linear functions of ‘real’ time and pressure and can hence be derived from a match. This method assumes pseudo-radial or radial flow and is incorrect for other flow regimes. When plotted on a log-log basis, the difference between the log functions and the actual data is a constant amount, as shown by Eq. 2-15 and Eq. 2-16 (Horne 1995). For example, from the pressure match a good estimate for kH can be obtained, when the rate q, formation volume factor B and the viscosity μ are known.  2π kH  log ∆m( p ) = log m( pD ) − log    qB µ   k  log t = log t D − log  2   Φµ ct rw  Eq. 2-15 Eq. 2-16 In a medium permeability reservoir without a hydraulic fracture, the first part of the pressure response is dominated by wellbore storage. Later in time, the pressure wave is stabilized in the reservoir and the response defines radial inflow into the well. The radial flow is seen in a horizontal line in the derivative plot. Fig. 2-3 shows a typical pressure response for such reservoir. 24 MSc. Petroleum Engineering – Thesis report - L.F. van Zelm A fractured well produces a different pressure response due to the high permeability in the fracture, thereby usually diminishing any apparent wellbore effect. Therefore, a log-log plot will display significantly different features, where two main cases are most apparent (Horne 1995). For this, first, the principle of fracture conductivity is introduced (Eq. 2-17). The fracture conductivity (CfD or FCD) provides a measurement for the fluid handling capacity of the hydraulic fracture and is an important design criterion in fracture treatments (Economides and Nolte 2000). C fD = kf w kx f Eq. 2-17 A finite-conductivity fracture will exhibit linear flow through the fracture, with a resulting pressure drop over the total fracture half-length (Cinco-Ley et al. 1978), and linear flow in the reservoir towards the fracture. The observed flow regime is referred to as bilinear flow and may also represent the cleanup period of the fracture. An infinite-conductivity fracture shows no gradient of pressure in the fracture and only linear flow towards the fracture from the reservoir, and thus the flow regime is named linear flow. This can be seen as a ‘cleaned up’ fracture. Mostly, the linear flow regime is preceded by bilinear flow, after which finally radial flow may occur. Fig. 2-3 Typical log-log plot (pseudo pressure (psi2/cp) versus dt (hr)) for mediumpermeability reservoir without a hydraulic fracture (Cipolla and Mayerhofer 1998). In the most ideal cases, these flow regimes show typical responses in a pressure derivative plot. Of course, field examples may display more complicated pressure behaviour, which need computer-aided matching processes to obtain a good match (Cipolla and Mayerhofer 1998). In Fig. 2-4 the pressure response of a high-conductivity fracture is presented, showing a characteristic ½ slope of the pressure derivative on the log-log plot. The half slope originates from the pressure drop which is related to the square of the fracture dimensionless time. The finite-conductivity fracture with bilinear flow is noticeable as a line with a ¼ slope, as shown in Fig. 2-5. Again the slope on the log-log plot is determined by the relation between the pressure and the time, with time now raised to the power of ¼. 25 MSc. Petroleum Engineering – Thesis report - L.F. van Zelm Fig. 2-4 Typical log-log plot (pseudo pressure (psi2/cp) versus dt (hr)) for high-conductivity fracture in a low-permeability reservoir (Cipolla and Mayerhofer 1998). Fig. 2-5 Typical log-log plot (pseudo pressure (psi2/cp) versus dt (hr)) finite-conductivity fracture in low-permeability reservoir (Cipolla and Mayerhofer 1998). 26 MSc. Petroleum Engineering – Thesis report - L.F. van Zelm 2.4.4 Hydraulic fracture evaluation: procedure and accuracy In the following section, an overview is given of the general workflow for determining some important parameters for the evaluation of the hydraulic fracture. To get an idea of the time involved in these tests, a brief overview of a standard well test schedule in tight gas reservoirs in Alberta (Canada) is given. Before the hydraulic fracture is created in the reservoir, often a PBU is performed right after drilling and completing the well. This test can provide the reservoir permeability and the reservoir pressure uniquely. This is common practice in oil and gas fields around the world, although in tight gas formations it causes severe operational issues. The well needs to be shut-in for a long time to reach (pseudo-) radial flow to determine the reservoir properties. For example, for a typical tight gas well with a hydraulic fracture with half-length of 100 ft, in a reservoir with permeability of 0.01 mD, porosity of 0.15, gas viscosity of 0.03 cp and total compressibility of 1.0 x 10-4 psi-1, it may take 213 days to reach pseudo-radial flow (Cheng et al. 2007). It is clear that this is rather expensive for the operator. Nevertheless, the importance of the test is well recognized, for the determination of the virgin reservoir permeability and pressure is not again so easily determined as in this phase of the characterization and evaluation process. After a hydraulic fracture is placed in the reservoir, some basic parameters are needed for a proper evaluation of the treatment. A well test (PBU) can provide information on fracture length (effective/productive) and fracture conductivity and can confirm the reservoir pressure and permeability obtained from a pre-frac PBU test. Nevertheless, without either input for pressure or permeability, the analysis is non-unique for fracture length. This is related to the use of 2 equations (Eq. 2-10 and Eq. 2-14) to calculate 3 unknowns (pressure, permeability and effective half-length). This is a parametric equation, and cannot be solved uniquely. Without a fracture, the wellbore radius is known, and the remaining 2 unknowns can be solved for with the 2 equations Independent input to the post-fracture analysis is therefore essential at this stage. Reservoir pressure and permeability can be obtained from field analogues, which can provide some guidance to the results. Permeability can also be obtained from logging or core samples. Although, high pressure compaction at reservoir conditions, or an unexpected permeability jail will also limit the use of core analyses as a trustful source of information for permeability. Finally, the fracture half-length can also be determined from the fracture design process before the actual treatment takes place. In essence, it’s one of the main design criteria. Nevertheless, there’s a rather important difference between the two estimated fracture half-lengths. The fracture model mainly predicts the pumped or created half-length; the production analysis shows the effective or productive half-length. It has been reported that the effective half-length can decrease up to only 5% of the modelled fracture half-length due to width loss, complicated fracture cleanup, and multiphase effects (Barree et al. 2003b). Assuming a value of fracture half-length based on fracture design or treatment, therefore, is not completely accurate to production analysis. For a proper analysis of post-fracture gas production, the understanding of the theory and possible resulting inaccuracies of well test analysis in tight gas is crucial. This thesis will discuss the possible impact of these complicated processes on field development plans or subsequent fracture campaigns. 27 MSc. Petroleum Engineering – Thesis report - L.F. van Zelm 3 Modelling of Tight Gas Reservoirs This chapter discusses the results of the post-fracture production simulations of tight gas reservoirs, whereby special attention is given to different phase trapping mechanisms. The first section (3.1) introduces the base case simulation model, including reservoir, hydraulic fracture and grid properties. The specific tight gas reservoir properties are highlighted in detail (3.1.1), for it’s an important part of the simulations. Next, variations in capillary pressure (section 3.2) and a ‘permeability jail’ (section 3.3) are presented. Each section introduces the specific adjustments made in the setup of the model regarding fluid, rock, grid or fracture properties. This is followed by presenting the modelling result. The final section of this chapter (section 3.4) introduces a new reservoir model with a different grid and fracture properties. The aim of this model is to allow for heterogeneity modelling with separate relative-permeability and capillary-pressure functions assigned to different rock type classes. An extensive discussion on the results is presented (3.4.2 to 3.4.6). All simulations in this thesis are performed with the commercial numerical reservoir simulator Eclipse 100 (Schlumberger 2009). 3.1 Simulation Model Setup 3.1.1 Tight gas properties The base case model is designed to capture the typical characteristics of a producing tight gas field. The following parameters are chosen (Table 3-1). Reservoir properties Model size (L - W - H) 250 – 20 – 100 m Depth top reservoir 2800 m Reservoir pressure 250 bar Reservoir permeability 0.001 mD Water saturation 0.40 Porosity 5.0 % Table 3-1 Reservoir properties of base scenario model. Chapter 1 explains that a reservoir is classified as a tight gas field if it’s not economically producible without the use of a hydraulic fracture. The model has a permeability of 1 x 10-3 mD or 1 µD. The base case model is uniform in all its properties, and the horizontal and vertical permeabilities are both 1 µD. For 1-µD reservoirs the porosity is generally between the 4 and 10%, as is shown in studies on the MesaVerde Basin (Byrnes et al. 2009). The base case model has therefore porosity of 5% and this is uniform throughout the reservoir. In the simulations in Section 3.4 the assumption of homogeneous reservoir properties is relaxed. 28 MSc. Petroleum Engineering – Thesis report - L.F. van Zelm Hydrostatic pressure is taken as a rough predictor of pressure at the depth of the reservoir, which gives an initial pressure of 250 bars. It’s not possible to talk about a ‘typical pressure’ for tight gas reservoirs, for many variations exist worldwide (Holditch 2006). Tight gas reservoirs can be deep or shallow, high-pressure or low-pressure, high-temperature or lowtemperature, and heterogeneous, relatively homogeneous or naturally fractured. A uniform water saturation of 0.4 is assumed throughout the reservoir, and gravity/capillary effects in the vertical direction are not factored into the initial water distribution. The reservoir gas PVT properties are taken from a study of a tight gas reservoir at similar pressure and temperature (Shaoul et al. 2009). The viscosity (Fig. 3-2) and the gas formation volume factor (Fig. 3-1) are presented below as functions of pressure. Fig. 3-1 Gas formation volume factor used in this study. Fig. 3-2 Gas viscosity used in this study. The relative permeabilities for water and gas used in this study are shown in Fig. 3-3. The gas relative permeability is based on a study on the tight gas reservoirs of the MesaVerde Basin in United States (Byrnes 2009). From this elaborate study, I selected the function corresponding to the base case permeability of 1 x 10-3 mD. For validation purposes, a fit of krg is made with an extended Corey relation (Eq. 3-1) for which the input parameters are taken from another tight gas study (Cluff and Byrnes 2010). The connate water saturation for krg (Swc,kr) and the critical gas saturation gas (Sgc) are determined from the permeability of the reservoir model, following equations provided by the authors. For calculation of the gas relative permeability, I used Swc,kr to establish the point at which the gas relative permeability curve reaches it maximum. Fig. 3-3 shows the match between the curve from the Corey relation and the base case functions. p q  ( S w − S wc ,kr )    ( S w − S wc , kr )   krg = 1 −    * 1 −  − − − (1 S S ) (1 S )     gc wc , kr  wc , kr    Eq. 3-1 Fitting property Value Unit Swc,kr 0.0 (-) Sgc 0.3 (-) p 1.7 (-) q 2.0 (-) Table 3-2 Fitting parameters to Corey extended relative permeability function. 29 MSc. Petroleum Engineering – Thesis report - L.F. van Zelm I have chosen the water relative permeability curve for the base case scenario to match the data used in a recent study of tight gas reservoir modelling (Wills 2009), which includes a study on the influence of water. In low-permeability sandstones, the general trend is that the lower the absolute permeability, the more reduction in gas relative permeability is caused by the presence of a given saturation of water (Jones and Owens 1980). The authors contend that this caused by the sheet-like tabular structure of the pore-throats in combination with the strong water-wet behaviour, trapping water and blocking the flow to gas (Cluff and Byrnes 2010). Therefore krw takes a low value at Sgc and generally low values over the complete saturation range. The connate water saturation Swc is different than the endpoint of the krg curve, but represents the water trapping in the small pores, and results in a higher residual (or connate) water. The choice for the water relative permeability curve, including Swc,kr has a great influence of the overall mobility of the two phases present. The result of these equations and parameter values is that any water in the pore space interferes with gas flow and greater gas saturation is needed to establish a connective path to allow a given amount of gas production. When initial water saturation approaches (1-Sgc), there is hardly any permeability to gas. Fig. 3-3 Relative permeability functions of the base case scenario including a match for the krw obtained by Corey’s formula. 30 MSc. Petroleum Engineering – Thesis report - L.F. van Zelm The base case model uses a lower capillary pressure function than expected in a reservoir with permeability of 1 µD (see Fig. 3-4). The capillary pressure function corresponds to a permeability of 0.05 mD calculated by Eq. 2-9, a higher permeability than the base case permeability. I choose this capillary pressure function in order to neglect any possible blockage of the gas flow or capillary suction of the water into the reservoir from the fracture. As a result, in the base case drawdown easily overcomes the capillary pressure, and gas can be produced without hindrance. Fig. 3-4 Capillary pressure curve used in the base case model. 3.1.2 Well, hydraulic fracture and grid properties The static features of the reservoir model (production well, hydraulic fracture and grid) are specifically chosen for this study. This section briefly introduces the chosen options; a more detailed description is provided in the appropriate appendices at the end of the thesis report (chapters 11, 12, 13 and 14). The length of the well from surface to the top of the reservoir is 2800 m, after which the reservoir continues for 100 m. The well has a production tubing of inner diameter 7.67 cm (3 inch). Initially, we assume that the well is perforated over an interval of 80 m for the fracturing treatment, but during modelling of the production period, this is adjusted (see chapter 12 for additional discussion). The hydraulic fracture is designed and analyzed using FracproPT (Carbo Ceramics 2007), a hydraulic fracture software tool. The model requires the input of a simplified 2D reservoir model. The model consists of a layer cake model of a homogenous, uniform sandstone with a 100 meters net pay height confined by shale layers, which are not considered as part of the reservoir and thus is not included in the model. 31 MSc. Petroleum Engineering – Thesis report - L.F. van Zelm After the design, the fracture treatment can be simulated (Crocket et al. 1986) and the resulting fracture dimensions are imported into a 3D numerical simulator (Behr et al. 2003). Here we use Eclipse 100 (Schlumberger 2009). Table 3-3 shows a brief overview of the fracture treatment and the resulting fracture dimensions. The fracture covers the complete height of the reservoir and extends with a propped fracture half-length of 117 meters into the reservoir. The resulting dimensionless fracture conductivity is calculated by FracproPT (Carbo Ceramics 2007) from the fracture properties (Table 3-3) with the use of Eq. 2-17. The created fracture has a CfD of 2444, and thus can be considered infinitely conductive (Economides and Nolte 2000). More detail on the input data, the fracture treatment and output files are presented in chapter 11 (Appendix on hydraulic fracture design and simulation). Property Value Unit Property Value Unit Fracture half-length Xf 131 m Propped half-length 117 m Total fracture height 118 m Total propped height 105 m Max. fracture height 0.33 cm Avg. fracture width 0.25 cm Total clean fluid pumped 244.3 m³ Total proppant 98006.1 kg pumped Table 3-3 Overview of fracture treatment data and the resulting fracture dimensions as computed by FracproPT (Carbo Ceramics 2007). In any reservoir model, the grid-block size and simulation time step are the most important parameters controlling the stability and accuracy of the numerical solution method (see chapter 8 for more information). The introduction of a hydraulic fracture requires a special grid to model the complex fluid behaviour in and around the fracture. The grid blocks of the fracture are upscaled and, on the other hand, the reservoir grid blocks in the fracture face are refined. Finally, for simulation purposes, only ¼ of the model modelled. Due to this symmetry, the simulated well rates are 25% of the actual values and the well is located in the corner grid block. In this study, the fracture is modelled with a row of grid blocks with a width of 50 cm (ydirection), which represents ½ of one fracture wing and thus ¼ of the hydraulic fracture. The actual width of the fracture created is 0.25 cm. Too-small grid blocks within the fracture slows down the model (Friedel 2004). In order to model the same fracture storage space and transmissibility as in the real fracture, the porosity and permeability of the fracture is scaled down proportionately, by a factor of 300. This procedure is standard in hydraulic fracture modelling and results in sufficiently accurate simulations (Shaoul et al. 2006). This grid contains a refinement in the y-direction, the direction perpendicular to the fracture length. Here, the fluids flow from the lower permeability matrix, where pressure and saturation changes are small, into the high-permeability fracture. This discontinuity requires sufficient grid resolution, and therefore smaller grid blocks and small time steps, especially early in production. A fine grid is also needed to capture the fracture-face cleanup period accurately. If too-large grid blocks are present in the fracture face, the water imbibition does not increase Sw significantly and results in only minor impact on the gas relative permeability. It’s assumed that capturing this effect with a grid refinement is important in the analysis of the cleanup period (Gdanski et al. 2006). On the other hand, smaller grid blocks increase simulation times. The initiation of the leakoff water around the fracture prior to the production simulation is discussed in section 3.1.3. 32 MSc. Petroleum Engineering – Thesis report - L.F. van Zelm This refinement can be modelled by two approaches; a refinement of a part of the reservoir host grid and a so-called Local Grid Refinement (LGR), whereby a second and more refined grid is placed inside the host grid. In this thesis, the host grid refinement is chosen for the reservoir model (Fig. 3-5). This refinement option allows us to more closely examine the process of water invasion and potential blockage around the fracture. More detail is provided in chapter 12 (Appendix on grid refinement options), presenting some simulations (single- and multiphase) to test the accuracy and speed of the refinement options. Concluding on these results, chapter 12 discusses the decision for the host grid refinement in favour of the LGR. Fig. 3-5 Host grid refinement in the reservoir model. The fracture is located in the first row of grid blocks starting at the well location (0,0) and the fracture face refinement extents perpendicular to the fracture. The same level of grid refinement extends beyond the end of the fracture to the edge of the reservoir model (see chapter 12 for more detail on the grid). Fig. 3-6 Host grid refinement in the reservoir model, zoomed in close to the fracture. 33 MSc. Petroleum Engineering – Thesis report - L.F. van Zelm 3.1.3 Base case initiation To this point, the base case model has been set up with dynamic properties (section 3.1.1) and static features (section 3.1.2). Before the model is used for the modelling of postfracture gas production, it’s compared to an analytical solution. This should confirm the initial flow period of the well and test the simulation outcome for accuracy. A detailed description and a discussion on the results are provided in chapter 13 (Appendix for reservoir model test runs). For the base case model, it’s important that the analysis confirms a long transient period in the reservoir. The understanding of this is important in this thesis, especially in the well test analysis (chapter 4). One final aspect of the base case model remains to be specified: the initial zone of increased water saturation around the fracture as a result of the fracture treatment. It’s expected that when the simulation is started, the initial gas rate is influenced by this leakoff water. This is the so-called cleanup phase; a delay in the maximum gas rate. The water rate is in decline from the beginning of the production phase. After some time, the gas rate enters the transient period and dominates the flow into the hydraulic fracture and the wellbore. To examine fracture and fracture face cleanup, it’s important to properly model how, when and where the fluid moves into the reservoir during the hydraulic fracture treatment. There are two methods to simulate leakoff behaviour. First method is to determine the fluid distribution during the fracturing simulation in the separate software programme FracproPT (Carbo Ceramics 2007) and to export this model into a reservoir simulator for further simulations (named “leakoff model” in this thesis). Or, the second method is to simulate an injection period prior to production in the reservoir simulator itself. For this thesis, I chose the second approach, i.e. injection of the treatment volume to simulate the water invasion into the fracture face. Appendix G (chapter 14) provides more insight into the assumptions of the two models and shows the result of a test simulation. Although the leakoff model is suitable and very accurate for long-term production forecasts, the injection method is more applicable for the use in this thesis. The model in FracproPT (Carbo Ceramics 2007) does not allow for specific heterogeneity in the reservoir, which could influence the water distribution. Second, fluid and rock properties such as capillary pressure or relative permeabilities cannot be changed in FracproPT (Carbo Ceramics 2007) to test whether it will influence the fluid distribution in the fracture face and hence the cleanup phase. The injection of water gives rise to an imbibition process near the fracture face, which results in possible hysteresis effects. Hysteresis is named as a possible cause for the existence of a permeability jail (section 2.3.2), but it introduces more complexity and uncertainty in the model. First, the model is not initialized with experimental data, so there’s no imbibition curve available. Modelling this thus introduces another unknown variable. Second, the modelling of hysteresis in the numerical simulator (Schlumberger 2009) is rather complex and is not considered to be part of this thesis and therefore not studied in detail. For the base case scenario and subsequent simulations, hysteresis is therefore not taken into consideration; more detail and an extensive discussion on the effects is provided in chapter 9 (Appendix for hysteresis effect modelling). The gas and water production profiles and a 3D-image of the pressure response of the base case model are presented in Fig. 3-7 and Fig. 3-8. 34 MSc. Petroleum Engineering – Thesis report - L.F. van Zelm Fig. 3-7 Base case model production overview: gas (red) and water (blue) rate and cumulative gas (green). Note: the model is ¼ symmetry. Fig. 3-8 Base case pressure response after 2 years of production. The well is produced at a pressure of 150 bars; the reservoir is initially at 250 bars. 35 MSc. Petroleum Engineering – Thesis report - L.F. van Zelm 3.2 Tight-gas capillary pressure Holditch (1979) describes the possible impact of capillary pressure in the reservoir on the flow of fluids and gas towards the hydraulic fracture. His conclusion is that ‘generally no gas block occurs by capillary pressure only, if the rock permeability is not damaged’, but ‘gas production can be impaired if the applied pressure drawdown is lower than the capillary pressures’. Capillary pressure can prevent water flowback to the fracture, but also drive water imbibition further into the reservoir, away from the fracture, and thus reduce the water blockage of gas flow. Mahadevan et al. (2009) state that evaporation and capillary suction are the two major cleanup mechanisms in tight gas reservoirs. They conclude that when comparing the two, capillary suction results in faster recovery of the gas relative permeability surrounding the fracture. This ultimately reduces the water blockage impact near the hydraulic fracture. This section evaluates the effect of the higher capillary pressures expected at low absolute permeability. 3.2.1 The impact of capillary pressure on gas production Holditch (1979) shows a variety of capillary pressure curves in his classic investigation, including a ‘representative low-permeability reservoir’ with capillary pressure ranging from 200 to 600 psi (14 – 40 bars) over the saturation range. With scaling function Eq. 2-9, this can be calculated back to a 20 µD reservoir rock. He also performs calculation on the effect of a damaged zone around the fracture in a more porous (porosity 0.12) and permeable (k = 0.28 mD) reservoir. The capillary pressure functions for this damaged zone vary from 40 to 200 psi (or 2 – 14 bars), representing a small permeability reduction as can be calculated from Eq. 2-9. In this thesis, the scaling parameter is also used to link the capillary pressure to the reservoir water saturation. As a result of the lower permeability (1 µD) and porosity (0.05), the capillary pressures are much higher than used in the Holditch’ study (1979), approximately 100 bars over the saturation range. Second, the data from the MesaVerde tight gas basin (Byrnes et al. 2009) suggests that capillary pressure is larger in tight-gas sandstones than suggested simply by the lower permeability. Fig. 3-9 shows data for a permeability of 1 µD, or 1 x 10-3 mD. It should be noted that these capillary pressures are for a mercury-air system fluid pair, and need to be scaled down by a factor of 0.15 for hydrocarbon-brine capillary pressure using appropriate data (Jennings et al. 1971). Specifically, the Purcell equation (1949) is used to relate the values for the two systems: Pcres = Pclab ( σ cos θ res ) σ cos θlab Eq. 3-2 The resulting capillary pressure curve for the high capillary pressure scenario is presented in Fig. 3-10, with the base case capillary pressure for comparison. 36 MSc. Petroleum Engineering – Thesis report - L.F. van Zelm Fig. 3-9 Reference data set from MesaVerde study. Fig. 3-10 Capillary pressures used in the base case and high capillary pressure scenario. Fig. 3-11 shows the results of the simulated water invasion and production of gas for the two capillary pressure regimes (Fig. 3-10) and one scenario with zero capillary pressure. Some obvious differences are present during the cleanup period. First, the higher the capillary pressure, the higher is the initial gas peak (Fig. 3-12). Second, after approximately 10-12 days of production the gas rates of the three scenarios converge, with the high-Pc case outperforming the other two cases by a small margin. Finally, there’s a large contrast in the water production of the various models (Fig. 3-13); no water is backproduced in the case with the largest Pc. Because all reservoir, fracture and fluid properties are the same among the cases, the capillary pressure is the cause of differences between the gas and water rates. When examining the water-saturation profile in the reservoir near the hydraulic fracture for the two extreme cases of large capillary pressure and no capillary pressure (Fig. 3-14 and Fig. 3-15), it’s possible to relate this to the observed gas rates. In the high capillary pressure case, a large capillary pressure gradient pulls water phase into the reservoir, as reported by Mahadevan et al (2009). Furthermore, the high pressure gradient draws out the water that is initially present in the fracture and leaves the fracture grid blocks at Swc, where the case without capillary pressure produces back significant amounts of water. This explains the observation that the high capillary pressure scenario has more water in the invaded zone surrounding the hydraulic fracture. During the first days, as presented in Fig. 3-14, the high water saturation around the fracture, reduces the gas relative permeability and thus hinders gas production. After 6 months of simulated production both scenarios have strongly reduced water saturations around the fracture (Fig. 3-15 – note change of scale), either by production or by further imbibition into the reservoir and thus the impact on the gas rate is limited. 37 MSc. Petroleum Engineering – Thesis report - L.F. van Zelm Fig. 3-11 Cleanup gas rate comparison (¼ symmetry model) of three scenarios: base case scenario, and high and no capillary pressure regimes. Fig. 3-12 Detailed gas rate of the first hours; the high peak of the high capillary pressure scenario is clearly visible. Note change of scale with Fig. 3-11. Fig. 3-13 Total water production in the first 100 days of the three scenarios presented. The pink curve is along the horizontal axis (no water produced). 38 MSc. Petroleum Engineering – Thesis report - L.F. van Zelm Fig. 3-14 Comparison of water saturation near Fig. 3-15 Comparison of water saturation near the fracture face for two capillary pressure the fracture face for two capillary pressure scenarios after a few days. scenarios after 6 months of production. Note change of scale with Fig. 3-14. Simulation Scenario (Base Case = 1.00) Cumulative Water Production (-) 2 months Cumulative Water Production (-) 2 yrs Cumulative Gas Production (-) 2 months Cumulative Gas Production (-) 2 yrs Base Case 1.00 1.00 1.00 1.00 No capillary pressure 1.07 1.52 1.01 0.99 High capillary pressure 0.03 0.01 0.95 1.01 Table 3-4 Gas and water production overview of the different scenarios related to the reservoir capillary pressure regime as discussed in this section. The cumulative production over time is presented in Table 3-4, which reveals that long-term production is not much impacted by the change in assumptions about capillary pressure in the reservoir. For the short-term cleanup effect, modest differences are observed. It’s important to realize that the capillary pressure function in the low-Pc and zero-Pc cases is not consistent with the low reservoir permeability and the Leverett J-function (Eq. 2-9). The high capillary pressure case is most representative of tight gas reservoirs. The production table also shows water production for the two scenarios; the high-capillary-pressure scenario back-produces virtually no water from the reservoir. This lack of water production is demonstrated by other authors, e.g. Soliman and Hunt (1985). In a later section (3.2.2), a more thorough investigation is presented on the water production in hydraulically fractured reservoirs. The tests performed in this section show the effect of the capillary pressure on post-fracture gas production. The main conclusion is that capillary pressures alone not impact the gas productivity severely and that the amount back-produced water is strongly reduced with high capillary pressures. The results could be used as analogue for the use of chemical additives to reduce surface tensions between gas and water, as described by Gdanski (2007). 39 MSc. Petroleum Engineering – Thesis report - L.F. van Zelm 3.2.2 Capillary end effect and its water block potential A component of the capillary effects discussed in the previous section is the capillary end effect. The capillary end effect is described in the literature (Huang and Honarpour 1996) as a result of the discontinuity of capillarity at the outlet end of a core sample. The capillary pressure differential is related to the gas and water phase pressure differentials, as displayed in the formula below. Eq. 3-3 ∆P = ∆P − ∆P cap gas water At an interface of two different porous media, a change in capillary-pressure functions occurs. This step in the capillary pressure causes large capillary pressure gradient over that interface. A result of this gradient is a reduced flow of water across the interface and hence the water saturation rises towards the discontinuity. In the limit of an extremely abrupt transition, no flow of wetting phase (water) across the interface is possible unless the capillary pressures on both sides of the interface are equal. If the capillary pressure on the downstream side is zero (as at the outlet of a core in a core flood, or a wellbore in the field), the capillary pressure in the formation at the interface must be zero also for water to flow across the interface. This phenomenon causes problems in small-scale core flood experiments at the outlet of the sample and is called the capillary end effect. For reservoir engineering purposes, the capillary end effect is relevant at large permeability discontinuities in the reservoir, where water is present on both sides. For the type of simulations in this thesis, the change in permeability and capillary pressure functions between the reservoir and the fracture may give rise to this effect. Here the fracture face between the reservoir rock and the proppant-filled fracture is the location of the discontinuity. Section 3.2.1 examines the capillary pressure effect in the full reservoir model; in this section the focus is more specifically on the discontinuity at the fracture face. The simulations of the base case model show an increased water saturation in the formation around the fracture as a result of water invasion (chapter 14). This high Sw reduces the gas flow slightly, but forms no permanent ‘water block’ in the base case. The high water saturations in the base case decrease over time due to water production into the wellbore or imbibe into the reservoir, depending on the capillary pressures. This is not specifically a capillary end effect. If water is produced, that should imply that capillary pressures at the fracture face is almost zero, or that the pressure gradient caused by the bottomhole pressure is large enough to overcome the capillary pressure gradient. This latter condition is complicated by the fact that the simulator calculates pressure gradient numerically, and therefore will the magnitude of the capillary pressure gradient at the fracture face depend on grid block size. 40 MSc. Petroleum Engineering – Thesis report - L.F. van Zelm This section reports on simulations that investigate the following issues: - Is there a steep increase in Sw visible in simulations and does the size of the grid have an influence? - Is the Sw profile dependent on the magnitude of capillary pressures in the reservoir? - What is the possible effect of the increased saturation near the fracture face; i.e. is the gas transmissibility reduced in the fracture face because of the capillary effect? - Does the simulator validate the principle that water is produced only when the applied pressure gradient is larger than the gradient of the capillary pressure? Many papers discuss the effect of capillary pressures and the end effect on gas production in low-permeability reservoirs with hydraulic fractures. I present a brief overview of the most important findings below. First, Mahadevan et al. (2009) use their simulator to focus on the effect of capillary suction on the gas production. Their results show an increase in Sw near the fracture face. Moreover, they conclude that higher capillary pressure in the reservoir, thereby creating more capillary suction pulling water into the formation away from the fracture, is beneficial for the prevention of a water block near the fracture face. Friedel (2004) too shows the presence of the steep saturation gradient near the fracture face (Fig. 3-16). He comments that the affected zone is no more than 1 cm wide and depends on capillary forces in the reservoir and the ratio of gas and water rates. He concludes that by itself the zone does not impact the gas production and that the numerical simulator is capable of solving for this discontinuity. Gaupp et al. (2005) studied the Rotliegendes Tight Gas Formation in North-Germany. There, a capillary end effect is observed in the post-fracture production and it impacts the permeability to gas locally. They conclude that proper numerical simulation of these phenomena requires the use of ‘ultra-fine’ discretization of the near-fracture region. Finally, Gdanski et al. (2005) comments that his simulations show increased water saturations near the fracture, where it ‘pooled’ against the fracture face discontinuity. He concludes that the water saturation would remain increased near the face, until the gas relative permeability is reduced to a level where the pressure drop is large enough to overcome the capillary pressure discontinuity. If this does not occur, the high value of Sw can cause a permanent reduction in gas production. Fig. 3-16 Saturation distribution around fracture (Friedel, 2004). 41 MSc. Petroleum Engineering – Thesis report - L.F. van Zelm With these observations regarding the water saturation profile and capillary pressure distribution along the hydraulic fracture face, we consider the process of water invasion, imbibition further from the fracture, and back-production into the fracture in more detail. We assume that during leakoff a certain volume of water enters the formation. The water saturation around the fracture increases, and the distance of the invaded zone is determined by the initial water saturation, formation porosity, relative permeabilities (i.e., the final water saturation) and the total leakoff volume. The water saturation profile is at maximum saturation at the fracture, and decreases with distance from the fracture because of capillary suction. During the process capillary pressure equality applies at the fracture face, and presumably capillary pressure increases with distance into the formation. Depending on the capillary pressure and relative permeabilities in the reservoir, the water will then either be back-produced, imbibe further away into the reservoir, or remain trapped. High capillary pressures imply water flow in the opposite direction of the gas during production, i.e. into the reservoir. A small capillary pressure will allow water to be backproduced into the fracture. The change in saturation profile with permeability and time can be seen in Fig. 3-16 from Friedel (2004). To investigate these issues, I performed a sensitivity study with different grid properties to see more detail in water saturation close to the fracture face. First, I adjusted the 1st row of grid blocks adjacent to the fracture, which are at maximum water saturation (1-Sg,r) shortly after the injection period. I split this row into 100 grid blocks of 0.004 ft (or 0.12 cm). To create a smooth transition at the fracture face discontinuity, I also adjusted the original fracture grid block of 1.640 ft (or 50 cm) into 100 grid blocks. This allows for more gradual saturation and pressure variation in the fracture. Apart from adjusted grid block sizes, the simulations in this chapter also include a variety of capillary-pressure functions (Table 3-5). The use of the base case capillary pressures represents a medium to low-permeability rock type; the high capillary pressure scenario represents a poor (tight) reservoir rock (Fig. 3-10). I examine the amount of water close to the fracture, water production and the effect of the water block surrounding the fracture. Reservoir rock type Capillary pressure range (bar) Scenarios tested - fine grid - base case grid - fine grid Medium 0 – 25 (low) - base case grid Table 3-5 Capillary pressure regimes tested for capillary end effect. Poor 0 – 2000 (high) 42 MSc. Petroleum Engineering – Thesis report - L.F. van Zelm Fig. 3-17 Water saturation profile over time in the grid block adjacent to the fracture face; dark blue is the fine grid, light blue the base case grid; shown are two months of simulation for the medium reservoir rock. Fig. 3-18 Water saturation profile over time in the grid block adjacent to the fracture face; dark blue is the fine grid, light blue the base case grid; shown are two months of simulation for the poor reservoir rock. The first comparison is the water saturation over time in the first reservoir grid block adjacent to the fracture face, for the both rock types, either with or without the fine grid. Fig. 3-17 shows the medium-quality reservoir, Fig. 3-18 represents the poor-quality rock with much higher capillary pressures. The figures show that the more refined grids have higher water saturations adjacent to the fracture over the period of 2 months. This partly reflects averaging over the grid blocks. With the finer grid, the saturation is that of a zone 0.12 cm thick; for the coarser grid, the saturation is of a zone 100 times thicker. The high capillary pressure scenario shows a strong decline in water saturation in the first grid block with time, for both grids. This can be explained by capillary suction of water into the reservoir. This effect is not sensitive to grid refinement near the fracture face. Fig. 3-19, Fig. 3-20, Fig. 3-21 and Fig. 3-22 show water saturation profiles in the formation near the fracture (which is off to the left in these plots) for the four different scenarios. The various curves represent various times through the simulation, starting right after the water invasion (dark blue), and respectively after 5 (light blue) and 15 days (pink) of production. Fig. 3-20 and Fig. 3-22 show the result of the models with the normal grid, clearly showing a profile with abrupt changes in saturation moving into the reservoir. This grid is used in the base case model of this thesis. In contrast, Fig. 3-19 and Fig. 3-21 show a more gentle slope in the Sw profile. The differences between the two reservoir rock types, and thus the capillary pressure, are important. Fig. 3-21 is the scenario with low capillary pressures and water production, and shows a rapid decline of Sw in the fracture face. But there’s also a clear distinct steep increase in Sw towards the fracture face in the final reservoir grid blocks adjacent the fracture. This is not visible in the coarser grid, neither in the poorer rock type. This shows good agreement with the example of Friedel’s simulation (2004) in Fig. 3-16, where the higher-permeability rock (thus low capillary pressure) also reveals this steep slope in Sw. This is the 1-cm capillary end effect he refers to in his paper. Nevertheless, in the poor rock, the capillary end effect can be masked by the high Sw in much larger part of the reservoir. 43 MSc. Petroleum Engineering – Thesis report - L.F. van Zelm Fig. 3-19 Sw profile perpendicular to the fracture (which is off plot to left) for poor rock and fine grid; shown are 3 moments during the simulation. Fig. 3-20 Sw profile perpendicular to the fracture (which is off plot to left) for poor rock and base case grid; shown are 3 moments during the simulation. Fig. 3-21 Sw profile perpendicular to the Fig. 3-22 Sw perpendicular to the fracture fracture (which is off plot to left) for (which is off plot to left) profile for medium medium rock and fine grid; shown are 3 rock and base case grid; shown are 3 moments during the simulation. moments during the simulation. 44 MSc. Petroleum Engineering – Thesis report - L.F. van Zelm Now that the presence of a capillary end effect is shown to appear in a simulation model with low capillary pressure and very fine grid, two important questions remain. - Is this steep water saturation profile realistic or a simulation artefact? - Does this small zone of high capillary pressure affect the flow of gas and water around the fracture? If the saturation profile is realistic and a result of the multiphase flow equations and capillary pressures, it can be approached in spreadsheet calculation with a 1D – model. Mahadevan and Sharma (2003) state that the nature of the saturation profile is related to the shape of the capillary pressure. Chapter 10 describes the spreadsheet calculation in detail, including the equations and assumptions used. In particular, the calculation assumes that gas flows at a fixed volumetric rate in the vicinity of the fracture, and the water saturation is at equilibrium: that is, the capillary-pressure gradient in the water just balances the pressure gradient in the gas, leaving zero pressure gradient for the water. Although the calculated profile does not match the conditions in the reservoir, it provides some guidance in examining the simulations. The static saturation profile in the mediumquality reservoir rock (Fig. 3-23) shows a similar steep increase in Sw close to the fracture face, as in the simulation. The water distribution visible in the simulation models is therefore reasonable, based on the theoretical saturation distribution, and not a result of a miscalculation in the simulator. For a detailed discussion, including a comparison of the scale of the profile compared with the simulation, see chapter 10. Fig. 3-23 Water saturation profile from 1D flow calculation – medium reservoir rock with low capillary pressure. The final issues regarding the capillary end effect in the models are related to the flow of gas and water in the model. It needs to be testes if the gas production is affected by the increased water saturation in the very fine grid. For water it’s important to understand if it flows into the fracture over the capillary discontinuity. Before this can be properly examined, it’s important to refer again to chapter 7, where a description of the flow calculations by upstream weighing is presented. Upstream weighing calculates the flow of a phase from grid block i to grid block n by the pressure difference and the fluid properties of grid block i. 45 MSc. Petroleum Engineering – Thesis report - L.F. van Zelm Fig. 3-24 shows gas production rate for the low-capillary pressure (medium rock) case. There’s some difference in gas production rates based on level of grid refinement, but only in the first 4 days of production. This can be the result of higher water saturations in the grid blocks adjacent to the fracture in the fine grid model compared (Fig. 3-17). Fig. 3-24 Gas rate overview of the two models in the first days of production: base case grid (red) and fine grid (green). Second, the reduction of relative permeability close to the fracture is different per grid. To determine whether this reduction impacts the gas flow towards the fracture, it’s important to calculate the transmissibility. The transmissibility coefficient is described as follows: ∆T =  kkrg 1  ∆krg ∆λ = ∆ ∼ ∆x  B µ x  ∆x Eq. 3-4 Many of these input parameters are considered constant such as absolute permeability, or assumed to be relatively constant (Bµ). The transmissibility is therefore strongly related to the relative permeability of the gas phase. Table 3-6 shows the transmissibility over a zone of 0.5 m for both grids, related to the reduction in relative permeability and hence a negative value. The calculation is performed for the low-capillary pressure (medium rock) case, which shows a clear capillary end effect (Fig. 3-21). Start production After 10 days After 1 month (10-3 mD/m) (10-3 mD/m) (10-3 mD/m) Fine grid -0.34 -0.34 - .34 Base case grid -0.37 -0.26 -0.25 Table 3-6 Transmissibility over time for a 0.5 m invaded zone in the fracture face area for the two grid sizes. 46 MSc. Petroleum Engineering – Thesis report - L.F. van Zelm Figures Fig. 3-19 up to Fig. 3-22 present the variation in water saturation for the first grid blocks and indicate a large Sw contrast per grid size. Table 3-6 shows a reduction in transmissibility with time for the base case grid to 0.25 x 10-3 mD/m, where the fine grid remains to see a transmissibility reduction of 0.34 x 10-3 mD/m over the investigated zone. This seems to be rather significant, but most of the difference in transmissibility occurs in a thinner zone (< 1 cm). Although the process of gas flow in a reservoir can be considered like electrical series circuits, where the total resistance is the sum of all separate resistances, the large transmissibility reduction in the final 1 cm does not harm the gas rate significantly. Over time, the fine grid model has a gas flow rate in the grid block adjacent the fracture of just a few percentages lower than in the base case grid. When the cumulative gas totals are compared, only a small difference (0.5%) is showing after 1 month whereby the base case grid is more favourable. In conclusion, the fine grid is more precise in the representation of the capillary end effect, whereby a thin zone of high water saturation and decreased capillary pressure and gas relative permeability is seen. But the impact on the flow of gas into the fracture is not significant, accounting for only a few percent deviation on the long-term production forecast. The final comments on the behaviour of capillary pressures are related to how much water is produced in a 1 month period in all scenarios, after the injection of 50 m3 at the start of the simulation. It’s examined if the simulator is capable of properly modelling the movement of the water and gas phase. Water production High Pc - Fine Grid High Pc - Normal Grid 4 days cleanup (m3) 0 0.03 1 month production (m3) 0 0.03 Low Pc - Fine Grid 21.86 32.98 Low Pc - Normal Grid 18.23 36.4 Table 3-7 Water production after 4 days of cleanup and 1 month of total production. Table 3-7 presents an overview of water production, with the water volumes in cubic meters. Only with the medium reservoir rock model, i.e. with low capillary pressure, is there a substantial water production. Fig. 3-25 shows that the capillary pressure is almost zero after the injection, due to the high Sw, and increasing to a maximum of 2 bars. The poor rock with high capillary pressures shows high capillary pressures in the first reservoir grid block (Fig. 3-25). This is not overcome by the pressure gradient created by the well and breaches the idea that no capillary pressure difference may exist at the boundary during the simultaneous flow of water and gas. Hence no water is flowing over the fracture face discontinuity into the hydraulic fracture. 47 MSc. Petroleum Engineering – Thesis report - L.F. van Zelm Fig. 3-25 Capillary pressure in the first grid block adjacent the fracture. Low Pc means medium reservoir model, and High Pc poor reservoir model, i.e. steep Pc(Sw) function. In the first 50 cm of the reservoir, the wellbore pressure creates a pressure drawdown in both models of approximately 75-90 bars, where the capillary pressure gradient in the low and high capillary pressure model is respectively 4 and 170 bars. This observation is important, for it proves that in the poor rock indeed no water flows over the fracture discontinuity when capillary pressure gradient is too large. The low capillary pressures in the medium reservoir rock of just a few bars can easily be overcome by the pressure drawdown, which hence explains the water production. Concluded is that a very fine grid model is needed to model the specific capillary end effect, on top of a more gentle increase in Sw after water injection. This is shown in both a 1D spreadsheet calculation and in the production simulations. However, the capillary end effect is only present in a very thin zone along the hydraulic fracture interface and does not affect the gas rate over a longer production period. Hence, this effect alone does not cause a water block to gas flow. Furthermore, low-permeability reservoirs with high capillary pressure in the rock matrix can prevent any water, both from the reservoir and from the fracture treatment, from being produced. 48 MSc. Petroleum Engineering – Thesis report - L.F. van Zelm 3.3 Permeability jail The ‘permeability jail’ is introduced in section (2.3.2). The relative-permeability and capillarypressure curves are presented there in accordance with the theory provided by Shanley et al. (2004) and Cluff and Byrnes (2010). This section discusses two permeability-jail scenarios where the mobilities of gas and water are modelled differently. The reservoir is assumed to be homogeneous with respect to permeability, porosity and initial water saturation, using the properties provided in Section 3.1.1. The first scenario is the total permeability jail, where the relative permeability curves of the fluids do not intersect and where within a region of width 0.2 in water saturation no fluids are mobile at all. This represents the state of very poor reservoir rocks with extremely low permeability, which Shanley et al. (2004) describe to be present in some reservoirs worldwide. To be able to represent this scenario, both the water and gas relative permeability curves have been shifted across the water saturation range as in Fig. 3-26. At the initial reservoir water saturation (Sw = 0.4) gas is mobile, while water is totally immobile. Fig. 3-26 Water and gas relative permeability curves of the total permeability jail, after Shanley et al. (2004). Fig. 3-27 Water and gas relative permeability curves of the small permeability jail, after Shanley et al. (2004). Fig. 3-28 Capillary pressure functions for the two permeability jail models. 49 MSc. Petroleum Engineering – Thesis report - L.F. van Zelm The second scenario is named the small permeability jail and is based on low, but finite fluid mobility in the jail saturation range, or jail zone. The relative permeability curves are constructed to have a permeability reduction of at least 98% across the jail zone. This is in line with data presented by Cluff and Byrnes (2010), who refer to a jail of width 0.3 in water saturation for a rock with absolute permeability of 1 µD. Fig. 3-27 shows a reduction over a width 0.25 in Sw. Finally, the capillary pressures are very high; around 250 bars across the jail zone for the total permeability jail and lower for the small permeability jail; around 20 bars across the jail zone (Fig. 3-28). The two permeability scenarios are tested in two separate simulations with a homogeneous reservoir model including a hydraulic fracture as presented in section 3.1.2. In the simulations, the complete reservoir is modelled either as total permeability jail or as small permeability jail respectively. After the injection period, the well is opened to flow at a bottom hole pressure (BHP) of 150 bars and allowed to flow with this pressure constraint for 2 years. The results of the simulations are shown in Table 3-8 and Fig. 3-29. The base case model (section 3.1) is included for comparison and discussion of the results. In this and similar tables below, gas and water production rates are normalized by their values in the base case. Fig. 3-29 Gas rate comparison of the base case model and the two relative permeability jail scenarios: Small permeability jail (green) with an extended cleanup and total permeability jail (pink) (pink lies on the horizontal axis (no production)). 50 MSc. Petroleum Engineering – Thesis report - L.F. van Zelm Simulation Scenario (Base Case = 1) Base Case Small permeability jail Cumulative Water Production (-) 1 month Cumulative Water Production (-) 2 yrs Cumulative Gas Production (-) 1 month Cumulative Gas Production (-) 2 yrs 1 1 1 1 0.40 0.51 0.10 0.38 Total permeability jail <0.001 <0.001 <0.001 <0.001 Table 3-8 Production overview of the two permeability jail scenarios compared with the base case model. Table 3-8 shows that the total permeability jail lives up to its expectations; hardly any reservoir fluids are produced in two years of production. The water injection and the resulting increased water saturations around the fracture apparently reduce the gas mobility completely. During this time, the simulator has great trouble with converging towards a condition that satisfies the reservoir flow and well equations. This problem can be explained by examining the numerical solution method used by the Eclipse 100 software (Schlumberger 2009) to solve the flow of the two phases in the reservoir grid blocks. At initial reservoir water saturation, gas is mobile, but the relative permeability to water is zero in the reservoir and thus no water can move. When the water injection commences, a water pressure gradient is created from the fracture grid block to the adjacent first reservoir grid block. Due to the upstream weighing method used in the Eclipse simulator (Schlumberger 2009), the fluid properties needed to calculate the flow from the fracture grid block into the first reservoir grid block, are derived from the fracture grid block. This is explained in more detail in chapter 7. Because the water phase is mobile in the fracture (at Sw = 1.0), the water will move into the first grid block adjacent the fracture. The numerical problems will now emerge, because in the reservoir grid block neither the gas nor water can initially move out of this grid block, as governed by their relative permeability functions, to create space for this additional water. This contradiction causes abnormal saturations to be reported in the grid block where the water wants to enter. This continues until Sw exceeds Swc,kr in that grid block and the water will be mobile and can move freely to the next grid block. With the water, also the ‘problem’ moves towards this grid block. The result is that grid blocks in the fracture face area are at high water saturation and krg is completely reduced to zero. The latter is a result of the gas relative permeability functions illustrated in Fig. 3-26; it prevents any gas flow in this zone upon reversal of the flow when production is started unless Sw decreases. The water around the fracture remains present throughout the whole simulation. The simulator has much trouble with the combination of the fluid immobility over a large saturation range and the high capillary pressures. Only minor movement of the water phases is reported in the simulation and the result is that no water is back-produced through the fracture into the well (Table 3-8). The gas phase in the grid blocks in the rest of the reservoir, still at the initial value of Sw and thus mobile, can move towards the fracture by the pressure gradient. But no fluid movement occurs in the grid blocks of the invaded zone and therefore the zone is permanently blocked to gas flow. The result is that no gas is produced, as presented in Table 3-8. 51 MSc. Petroleum Engineering – Thesis report - L.F. van Zelm In conclusion, the relative permeability functions of the total permeability jail describe that at the initial reservoir water saturation, gas is mobile and can be produced water-free. It’s with the injection of water, that numerical problems occur. Solutions to phase saturations and pressures are not always physically correct in the fracture face grid blocks at all times due water invasion and the resulting extreme simulation conditions. The numerical simulator allows water to move slowly after the initial period of invasion of the reservoir, but no gas is allowed to move during flowback. Despite the numerical instability of this scenario, the observation of the water bank appears to be similar to, though more extreme than, the well-known ‘water blockage’ by reservoir permeability impairment as presented by Holditch (1979). He describes a water block as a situation where ‘the water mobility is low due to reduced absolute permeability and increased capillary pressure, so that fracture fluids remain immobile around the fracture’. This occurs with the total permeability jail, except that water is not trapped by reduced absolute permeability, but by a strong reduction of relative permeabilities in combination of high capillary pressures. Second, at these high water saturations, the gas is immobile. Nevertheless, the approach of modelling the total permeability jail uniformly throughout a reservoir, is not realistic. The concept of a total permeability jail is extended to the lowpermeability zones of heterogeneous reservoirs in section 3.4. It’s expected to be more realistically modelled if only occurring in a small part of the reservoir, similar to very poor reservoir rock, shaly or non-pay sections. The second variation on the permeability jail concept, the small permeability jail, represents a tight gas reservoir with a relative permeability reduction of at least 99% across the jail zone (Fig. 3-27). This means that compared to the total permeability jail both fluids are mobile across the jail and is a more realistic variation on the permeability jail concept. The capillary pressure in the matrix is around the 20 bars. The result of this modification is that after invasion, water moves more deeply into the matrix surrounding the fracture, at lower Sw than with the total permeability jail. Second, and more important, due to lower capillary pressures and the improved krw, the water is mobile in the invaded zone. When backproduction is started by opening the well, the water moves back into the fracture and is produced through the wellbore. This results in a Sw reduction near the fracture face, and the gas phase is mobile as described by the gas relative permeability in Fig. 3-27. Fig. 3-29 reveals an initial dip in gas production and a slow rise to a maximum over some 200 days. Thereafter gas production is still substantially reduced compared to the base case, which shows a minor water impact in the first 2 days (Fig. 3-7). Table 3-8 shows that over the first month of production there’s a reduction in gas production of 90%. This effect is caused by both the reduction in the gas relativepermeability function in comparison to the base case scenario, and the decreased water mobility around the fracture (which prevents more-rapid cleanup and gas flow). As shown in Table 3-8, approximately 60% less water is produced after 1 month of cleanup. With the total permeability jail, no water is produced due to the combination of high capillary pressure in the reservoir (this represents a very poor reservoir rock) and the large saturation range with no fluid mobility to either phase. 52 MSc. Petroleum Engineering – Thesis report - L.F. van Zelm When the mobility of the two fluids is increased over the jail saturation, the water is more mobile as mentioned above. The water production in Table 3-8 also shows this. In the invaded zone, the water retains a larger fraction of its base-case mobility than the gas: the water production after 1 month is relatively closer to its base-case value than is the gas production (0.4 versus 0.1). To recapitulate: for the total permeability jail, water invasion is modelled by the numerical solution method used in Eclipse (Schlumberger 2009). Whether this numerical method is accurate for this case is beyond the scope of this thesis, but it’s a stable numerical solution method used in many routine simulations (Schlumberger 2009). Nevertheless, the solution method has trouble handling the immobility of the fluids over such a large saturation range. The model predicts water to invade the reservoir grid blocks near the fracture and remain present around the fracture due to a strongly impaired water flow caused by reduced relative permeability. Moreover, the gas mobility also remains also zero and no gas is produced. Finally, the total permeability jail is not considered realistic to be modelled uniformly in a homogeneous model. In the small permeability jail, the water phase is more mobile. It’s produced through the fracture back into the wellbore. This reduces the Sw near the fracture over time, and allows gas to reach the fracture through the invaded zone, albeit with a lower rate and with a longer cleanup period compared to the base case scenario. This long cleanup can possibly explain observations made in the field (Wang et al. 2009). Furthermore, the water production is impaired in both scenarios due to the reduction in relative permeability and the increased capillary pressures in the reservoir. Nevertheless, in the small permeability jail the water is relatively mobile and thus an increased water-gas production ratio is observed in the initial cleanup period. Therefore, for the homogeneous reservoir model, it can be concluded that the small permeability jail is a possible explanation to the gas production impairment often seen in tight gas reservoirs. In another section (3.4), a heterogeneous model including the permeability jail of both types will be tested to extend these findings. 53 MSc. Petroleum Engineering – Thesis report - L.F. van Zelm 3.4 Heterogeneity model In many reservoir engineering studies the aim is to best replicate the lateral and small scale variations in layers and subsurface formations of a particular area of interest. The models used are therefore equipped to capture the heterogeneous nature of the reservoir, for which the input for the permeability and porosity distributions is taken from logs, core or geological models. For the production analysis of hydraulically fractured tight gas reservoir, the reservoir model used is often homogeneous or consisting of a layer-cake reservoir with uniform layer properties, because detailed geological data and broadly applicable property relations are often not available (Rushing et al. 2008). This section examines if the simplification of the reservoir model with respect to the geology is an acceptable assumption for modelling hydraulically fractured tight gas reservoirs. The hypothesis is that the combination of low porosity areas along the hydraulic fracture, abnormal fluid behaviour and high capillary pressure result in fully water saturated areas which hinder the gas flow from the reservoir towards the fracture. This blockage can result in a reduction in effective fracture half-length, which is an important parameter to understand in post-fracture production analysis. It can dramatically impact both the fracture and reservoir cleanup period and the long-term gas production. Second, it may result in better insight in the behaviour of tight gas reservoirs to water invasion following a fracture treatment. A detailed description and initiation of the model is given, the results are presented and concluded with some finals remarks. All the data and results presented in this chapter are valid for the parameters chosen and under acknowledgement of the assumptions made during the process. 3.4.1 Heterogeneity model: preparation To generate a heterogeneous permeability field, a new full field model is created in a geological modelling software programme (Schlumberger 2009). The model is divided into 20 layers with height of 5 meters of each: in total, 40 by 40 by 10 grid blocks (representing a region of 250 by 250 by 100 m). Furthermore, at this point the model is still unrefined near the wellbore. Multiple cases are examined to probe the effect of heterogeneity. The permeability field of the heterogeneous model is constrained to be comparable to the permeability of the homogeneous scenario using a logarithmic Gaussian distribution function. The criteria for this match are both an approximation of the average permeability throughout the whole field and in the first row of grid blocks in the reservoir (fracture face). During the tests, the maximum and minimum values of permeability are constrained to respectively 0.1 mD and 1.0 x 10-6 mD and the property is modelled to behave logarithmically. I used two statistical methods to assign the permeability spatial distribution; a logarithmic Gaussian and a Spherical distribution (Schlumberger 2009). These two distributions have specific variograms that determine the amount of permeability variation allowed over a specific distance (spatial dependence or variability) in the model. The two distributions functions are chosen to test the difference between the two, although it’s expected that the differences in range is more influential. 54 MSc. Petroleum Engineering – Thesis report - L.F. van Zelm Fig. 3-30 Example of variogram, displaying the range, sill and the nugget effect (WaveMetrics 2010). A variogram is created by plotting the semivariance versus the separation distance of a data set. An example is shown below in Fig. 3-30, where three important features are shown on the graph. The range is the point where the curve flattens, indicating the distance over which no more correlation between two data points exist. Decreasing the range reduces the maximum correlation length and shortens the distance over which permeability varies. The maximum variance is the sill, which is enforced at 1.0, because Petrel (Schlumberger 2009) uses a unit sill thereby making the variogram independent on scale. Smaller or large values for the sill may indicate a spatial trend, which is not intended in this model (Schlumberger 2009). Finally, the ‘jump’ in the semivariance at the origin of the graph is referred to as the nugget effect. The nugget effect is commonly present in measured data, where it either represents an error in the measurement due to sparse sampling, or in reservoir modelling it can relate to variation smaller than the grid size used. If larger grid blocks are chosen, one can increase the nugget and thereby acknowledge this artefact in the model. For this model, the nugget is set to zero; adjacent grid blocks can have similar permeability. For the theoretical background on the statistical methods behind the heterogeneity model, see Deutsch and Journel (1998). The two models prepared for the heterogeneity study have the following specifications (Table 3-9) in order to represent generic tight sand gas reservoirs, albeit, as mentioned, no standard tight reservoirs exist. The following models are created to examine the effect of heterogeneity on the production period following a hydraulic fracturing treatment. Some generic features are included, but it’s not a detailed reservoir model or an analogue of a specific producing tight gas reservoir. The first model (H-Fluvial) contains sediment bodies modelled with the maximum and minimum range of respectively 75 and 25 m. The thickness of these bodies is controlled by the vertical range, which in this scenario is 10 m. This results in a model with strong correlation over small lengths, but less correlation at points further spread out. Geologically this can be interpreted as more and larger concentrated flow bodies and barriers and can therefore be classified as fluvial systems with lenticular shapes (Spencer 1985). The model is therefore named H-Fluvial throughout the rest of the thesis. 55 MSc. Petroleum Engineering – Thesis report - L.F. van Zelm The second model, with longer major and minor range has long sediment packages with improved horizontal continuity in high-permeability flow bodies. Of course, low permeability layers also may form continuous flow barriers throughout the model. By the description of Spencer (1985) this could be classified as marine blanket reservoirs, as for example as the Frontier formation in the Greater Green River Basin in the United States Rocky Mountains. In this thesis, this model is referred to as H-Marine. Name H-Fluvial H-Marine Variogram type Gaussian Spherical Major range (m) 75 250 Minor range (m) 25 50 Vertical range (m) 10 25 Azimuth 0⁰ / -90⁰ 0⁰ / -90⁰ Sill 1.0 1.0 Nugget 0 0 Table 3-9: Specific details of the geostatistical variogram used to create multiple heterogeneity realizations. For each of the models, also two variations in the azimuth are generated: a model with the major direction of the flow bodies towards (0⁰) and parallel (-90⁰) to the hydraulic fracture. In the simulations, it’s examined if this has any impact on flow behaviour at short and longer times, where it’s expected that if the flow bodies are directed towards the fracture result in higher cumulative production due to the increased drainage area (Gatens et al. 1991). These models are referred to in this thesis as respectively H-Fluvial and H-Marine, with major range perpendicular to the fracture. The rotated models, with major range parallel to the fracture, are named respectively H-Fluvial-90 and H-Marine-90. Fig. 3-31 shows the H-Marine-90 model with long sediment bodies along the fracture face. The figure is shown to give an indication of the variation in permeability in the models, rather than to provide a detailed overview of the permeability per grid block. Fig. 3-31 Permeability distribution of H-Marine model; a side view of the fracture face shows the long sediment bodies along the fracture. 56 MSc. Petroleum Engineering – Thesis report - L.F. van Zelm The spatial permeability distributions are generated in Petrel (Schlumberger 2009). The resulting overall log-normal permeability distribution is shown in Fig. 3-32 below. Here the permeability is plotted as function of the inverse log, which allows for easy grouping of the rock type classes. Fig. 3-32 Permeability distribution of the H- Fig. 3-33 Porosity distribution of the HFluvial model; the x-axis is the inverse Fluvial model; the porosity is derived from logarithmic of k in mD. the permeability distribution. The porosity Φ is not modelled in Petrel (Schlumberger 2009), but is related to the permeability (k in mD) by the following equation (Eq. 3-5), whereby k0 is taken as a reference permeability of 1 mD. The scaling is done to match the porosity for the base case scenario permeability. The resulting porosity distribution is shown above in Fig. 3-33, after all negative or zero values have been automatically edited to 1 x 10-5. The other initial reservoir parameters are similar to the base case scenario of section 3.1.1: water saturation of 0.4 and a reservoir pressure of 250 bars for all reservoir grid blocks of the model. k  log   + 4.5 k φ = 0.1  0  2.5 Eq. 3-5 The resulting models used in this thesis are presented in Table 3-10 and are used to examine the effects of the heterogeneity on cleanup and production phase. The average kH is based on the arithmetic averaged permeability of the complete model as results from the geostatistical method. The two permeability distribution directions (0° and -90°) generated by the geostatistical analysis are used to specifically test the impact of the fracture placement in the reservoir with respect to the local geology. Model Arithmetic Spherical Gaussian Flow bodies Flow bodies averaged heterogeneity heterogeneity towards along distribution distribution reservoir fracture fracture kH (md.m) Homogeneous 0.1 H-Fluvial 0.079 X X H-Fluvial-90 0.079 X X H-Marine 0.075 X X Table 3-10 Details of the simulation models: one homogeneous and three heterogeneous models in total. 57 MSc. Petroleum Engineering – Thesis report - L.F. van Zelm After the specification of the reservoir properties, the hydraulic fracture is introduced into the model in a different manner than in the previous models of section 3.1.2. The hydraulic fracture is now modelled completely into two directions from the wellbore through the reservoir and located in the centre of the model instead of in a corner grid block. This results in a newly created full field model which is needed for a detailed production analysis with a well test later on in this thesis (chapter 4). This analysis requires a full 360° pressure and rate response around the hydraulic fracture and therefore does not work with ¼ symmetry models. The fracture is modelled as a row of grid blocks of width 33 cm with an upscaled porosity of 5.9 x 10-3 to preserve storage capacity of the fracture. Furthermore, the fracture has an upscaled permeability of 500 mD to maintain transmissibility in the grid, and a half-length of 100 meters. This results in a high-conductivity fracture. The relative-permeability and capillary pressure functions of the hydraulic fracture are as described in chapter 11. Once all properties are assigned to the grid blocks, a double refinement is put into the model to capture the fluid flow behaviour near the wellbore and the hydraulic fracture (Fig. 3-34). Again, note that the hydraulic fracture now extends in two and the refinement into four directions, contrary to as what is shown in Fig. 3-5 and Fig. 3-6. First, the row of grid blocks of the fracture is adjusted to match the fracture model as described above. Next to the fracture there are four rows of very fine (10 cm) grid blocks to capture small changes in Sw and Pc. Moving away from the fracture, the size of the grid blocks is slowly increased with a maximal enlargement of 1.3 per next grid block to maintain a stable solution. Fig. 3-34 Top view of the grid around the well in the heterogeneity scenario models; the hydraulic fracture is now completely modelled and located in the centre of the model. The two fracture wings in this top view extend from top to bottom in this figure with the upscaled fracture and the more refined fracture face grid blocks. 58 MSc. Petroleum Engineering – Thesis report - L.F. van Zelm The final properties needed are the relative-permeability and capillary-pressure functions in the model. In the simulations of this chapter, I will use two scenarios of each model presented in Table 3-10; one including normal relative-permeability and capillary-pressure functions (see section 3.1.1) and one using permeability jail functions. The homogeneous model has either the normal relative-permeability and capillary-pressure functions or the small permeability jail functions (section 3.3) assigned to all reservoir grid blocks. For the heterogeneous model, it’s necessary to divide the model grid blocks into various rock type classes according to the permeability variation. Each of these classes is assigned a specific set of saturation, rock deformation and PVT functions in order to best capture the effects of heterogeneity on all these properties. I have chosen to divide the full range of permeabilities in the reservoir into 5 different classes, each with different relativepermeability and capillary-pressure functions. Rock type class 6 is used for the properties of the hydraulic fracture. Fig. 3-35 shows the distribution of the various classes in the reservoir along the hydraulic fracture. Fig. 3-35 Side view of the rock type classes distribution in the first row of grid blocks in reservoir along the hydraulic fracture in the model H-Fluvial; in Fig. 3-34 this would be the first row on the right side of the fracture. The refinement in the y-direction is also clearly visible. 59 MSc. Petroleum Engineering – Thesis report - L.F. van Zelm Rock Permeability range Presence Permeability jail functions (mD) in model Type Class (%) 1 < 1.0x10-4 4 Poor rock ; total permeability jail 2 1.0x10-4 <> 3.5x10-4 24 Tight sand ; small permeability jail -4 -3 3 3.5x10 <> 1.0x10 43 Tight sand ; small permeability jail 4 1.0x10-3 <> 3.5x10-3 25 Tight sand ; small permeability jail 5 > 3.5x10-3 4 Low permeability sand ; normal functions Table 3-11: Rock type classes in the heterogeneous model with their normal relativepermeability and capillary-pressure and permeability jail functions. Table 3-11 presents the 5 classes for the heterogeneous model with permeability jail functions with increasing permeability and fluid mobility, but with similar PVT and rock deformation properties. The lowest class with permeability smaller than 0.1 µD is characterized as very tight sand (poor rock or non-pay section), and is therefore assigned with the total permeability jail (section 3.3) in all its grid blocks. Furthermore, these grid blocks have high capillary pressures (100-300 bars). The permeability in the next three classes are in range of the homogeneous model (0.1-3 µD) and the fluid behaviour is therefore described by the small permeability jail, keeping water and gas still slightly mobile in the jail. The capillary pressures in these classes are moderately high, with values ranging between 10 and 150 bars. This setup makes comparison to the homogeneous model possible and can show the impact of the heterogeneity in the model. Finally, rock type class number 5 includes the highest permeabilities, which is up to the maximum value of 0.1 mD. Here relative permeability curves and capillary pressures are as described in section 3.1.1. Finally, for the heterogeneous models with normal relative-permeability and capillarypressure functions, all the above presented rock type classes are assigned with the normal functions as in rock type class 5. The only difference between the homogeneous model is thus the permeability variation. For the permeability jail models, the homogeneous model is assigned with small permeability functions in all reservoir grid blocks, and the heterogeneous model as described in Table 3-11. 60 MSc. Petroleum Engineering – Thesis report - L.F. van Zelm 3.4.2 Heterogeneity model: production simulation This section introduces the first simulation results of the homogeneous and heterogeneous models. First, the models with normal relative-permeability and capillary-pressure functions are tested and compared, both before and after a correction for the reservoir arithmetic averaged kH (Table 3-10). Finally, the impact of the permeability jail relative-permeability and capillary-pressure functions on gas and water production is shown, which results in the research questions for the following sections of this chapter. All simulations start with an injection period of 24 hours in which 100 m3 is injected to simulate the leakoff process during the fracture treatment. The well is then shut-in for 1 day to simulate the complete process of fracturing, retrieval of downhole tools and preparing site of production. The production phase has a short initial rate constraint to control the flow towards the well and continues with a BHP constraint 150 bars throughout the rest of the simulation. The following two figures show the results of the first simulation, which is used to compare the two models and to comment on possible differences. Fig. 3-36 presents the early production period, including a distinct short period of fracture face cleanup, and Fig. 3-37 shows the long-term cumulative gas production of the two scenarios. Note the change of xaxis scale in both figures (days and years). Fig. 3-36 Cleanup rates of the homogeneous Fig. 3-37 Comparison between the longand heterogeneous H-Fluvial model, with term total cumulative gas of the matching generic saturation functions. homogeneous and heterogeneous H-Fluvial model. At first sight, the cleanup phase gas rate shows a very good match, with the same maximum gas rate and subsequent decline. Over two years, the production of the homogeneous model starts to exceed the heterogeneous model. To examine if this is related to the permeability and porosity distribution of the heterogeneous model, I use the results after a correction for the average permeability in the model as presented by the kH values (see Table 3-10). 61 MSc. Petroleum Engineering – Thesis report - L.F. van Zelm The results are presented in Table 3-12, and show a different outcome than outlined in Fig. 3-36 and Fig. 3-37. The cleanup gas production in the H-Fluvial model is significantly higher than in the homogeneous model when corrected for the kH. After one month and two years, this difference is still present; only after 10 years is the production of the models is similar. This effect is caused by variations in permeability around the hydraulic fracture in the heterogeneous models. Local high-permeability zones are controlling the short term production in favour of the low-permeability zones. To calculate the ultimate production recovery of the gas in the models, I used an approximation by taking the production after 50 years to compare with the Gas Initially In Place (GIIP). After this period, one can assume that the well has had its most economical period and would probably already have been abandoned due to increasing operational costs. The simulation of the homogeneous model results in an ‘ultimate’ recovery (UR) of 30.8%. The two heterogeneous models (H-Fluvial and H-Marine) have a simulated UR of resp. 26.2 and 25.5% (see Table 3-12). So although the corrected production totals are very similar, the recovery of the models is different after 50 years of production. Nevertheless, for field economics the production after a specific period is a more interesting figure, for it governs the cash flow; ultimate recovery is only a snapshot of the gas produced versus the remaining gas in the reservoir. In conclusion, the gas production of the homogeneous model and the two heterogeneous models, both with normal relative-permeability and capillary-pressure functions and no permeability jail, can be explained by the variation in permeability (kH) in the models. Second, heterogeneity can cause an increase in the short term gas (and water) production if local higher-permeability zones are present. Cleanup 1 month 2 years 10 years gas gas gas gas production production production production (-) (-) (-) (-) Homogeneous 0.1 1.00 1.00 1.00 1.00 H-Fluvial 0.079 1.27 1.25 1.13 1.02 H-Marine 0.075 1.05 1.11 1.10 1.00 Table 3-12 Production overview of the homogeneous and heterogeneous models; the data is corrected for average kH in the model. Simulation Scenario kH (mD.m) Fig. 3-38 and Fig. 3-39 show the injected and subsequently produced water per rock type class for the homogeneous and heterogeneous H-Fluvial model with normal relativepermeability and capillary-pressure functions. Here, the water volume is scaled with the pore volume (PV) of the 5 rock type classes. The sum of the injected volume is therefore not 100 m3, but results in a dimensionless factor. The volumetric scaling is calculated as follows (Eq. 3-6): Vscaled = PVrock type PVtotal = Vrock type Vtotal Φ rock type Eq. 3-6 62 MSc. Petroleum Engineering – Thesis report - L.F. van Zelm The result for the homogeneous model requires some more explanation, since the nature of the model states that there’s no difference in permeability and therefore no differences in rock types. Grid blocks here are assigned to the rock types according to the distribution of rock types at the same positions as in the heterogeneous model. This assignment and the adjustment using Eq. 3-6 normalizes for position along the fracture and frequency of occurrence of the various rock types in the heterogeneous model. The homogenous model shows a rather uniform water injection per rock type. The small difference is related to the position of the grid blocks; rock type 1 and 5 are located respectively more at the far end or the top of the fracture wings and therefore less water invades these classes during the injection process. During a real-life hydraulic fracture pumping treatment the leakoff is also not uniform, with most water leaking off close to the wellbore due to highest pressure difference there. The variation in leakoff volume along the fracture is therefore realistic. In the heterogeneous H-Fluvial model most water accumulates in the higher-permeability rocks (type 4 and 5) and no water is injected into rock type 1. Zone 4 has accumulated relatively most of the injected water, which is caused by the favourable location of that rock type along the fracture face. A more detailed inspection of the water production in both models shows, upon reversal of the flow, relatively uniform movement of the water in the homogeneous model. Only rock type 1 shows an unexpected large production, but this could be related to the relatively small sample size. In the H-fluvial model, the high-permeability zones (rock type 4 and 5) produce more water than the other, lower-permeability zones. Finally, after 4 days of cleanup, the total water production of both models is the same after correction for average kH. Fig. 3-38 Distribution of the injected water volume over the 5 rock type classes in the model in the homogeneous and H-Fluvial model. Fig. 3-39 Classification of the origin of the water flow during the first 4 days of production per rock type class in the homogeneous and H-Fluvial model. In conclusion, the comparison between the homogeneous and heterogeneous models with normal relative-permeability functions (i.e., those without a relative permeability jail) shows a match for both the cleanup and long-term water and gas production when corrected for a arithmetically averaged reservoir kH. The early production is dominated by the fracture face area and local variations in permeability can have a significant impact on the gas production. This is can be economically interesting for field development. Finally, the two model types show the same response to the injected leakoff fluid, which causes only a small reduction in gas production in the first days of production. 63 MSc. Petroleum Engineering – Thesis report - L.F. van Zelm Next, the impact of relative permeability jail on the homogenous and the heterogeneous HFluvial is examined. Fig. 3-40 presents the gas production impairment in the cleanup period for the homogeneous and heterogeneous (H-Fluvial) model. The damage appears to be significant and can be economically very important. The focus in the remainder of this chapter is on the following issues regarding the presence of a relative permeability jail: - what causes the gas rate to be reduced? - is the effect of the fluid leakoff on gas production more severe? - what is the effect of introducing heterogeneity in the model? - are there zones surrounding the fracture or elsewhere in the reservoir of high water saturation, and/or where no flow occurs? - is the effective fracture length or area reduced by any fluid retention? During the following discussions in sections 3.4.3 to 3.4.6, thee heterogeneous models (HFluvial and H-Fluvial-90 and H-Marine) are used in the analysis of the issues raised above. These models are more realistic representations of the subsurface, and allow for assigning specific properties to specific parts of the reservoir as explained in section 3.4.1. Fig. 3-40 Cleanup gas rate comparison between the homogeneous and H-Fluvial model; shown are the scenarios without and with the permeability jail. 64 MSc. Petroleum Engineering – Thesis report - L.F. van Zelm 3.4.3 Heterogeneity modelling results: cleanup period The first period of production is the period where most impairment is seen in the gas rate and is often referred to as the cleanup period of a well. During the cleanup, it’s therefore important to focus on the effect of the additional water that is introduced by the hydraulic fracture treatment. The hypothesis is that the severe damage observed in the field is caused by the leakoff fluid in combination with the relative permeability jail. A heterogeneous model (H-Fluvial) can simulate this in parts along the fracture face. An often-heard explanation is that the leakoff fluid can only cause problems around the hydraulic fracture if mechanical damage is simultaneously occurring during the fracture treatment process (Holditch (1971); Friedel (2004)). We examine whether relative-permeability effects of liquid near the fracture face could cause damage similar to that ascribed to mechanical damage. This section starts with a close look at the water in the fracture face after the injection period ends of the heterogeneous H-Fluvial model. As described in section 3.4.1, the initial water saturation is 0.4 throughout the reservoir and with the normal relative-permeability functions (section 3.1.1) and permeability jail functions (section 3.23.3), this means it’s immobile. On the other hand, the injected leakoff water is mobile and can be produced back through the hydraulic fracture. As shown in Fig. 3-41, the H-Fluvial model with normal relative-permeability and capillary-pressure functions shows a gradual increase of water production in the scenario with zones of increasing permeability. The gas flow in this scenario is also distributed according to the absolute permeability of the regions. Introducing the permeability jail in the low-permeability rock type classes (type 1 to 4) causes a large difference in the water production. First, in the H-Fluvial the total amount of water produced after 4 days falls to 64% with the permeability jail, leaving more potentially harmful water surrounding the fracture. Fig. 3-41 shows that hardly any water is produced from the rock type classes affected by the permeability jail; almost all the water flows from rock type 5 (81%). The other heterogeneity models show the same pattern in the water production; a reduction of 55% of total water produced is seen in the H-Fluvial-90 model, where rock type class 5 contributes 56% of the total water. The high-permeability rock class of H-Marine model is responsible for the majority of the water production during the cleanup, more than 80%. Also here the total amount of water produced is reduced to half. Fig. 3-41 Detailed overview of the origin of the water produced over a period of 4 days during the cleanup of the fracture and fracture face in model H-Fluvial. 65 MSc. Petroleum Engineering – Thesis report - L.F. van Zelm To fully understand the cleanup in the heterogeneous models, the impact of changed water distribution on the gas production is examined. Fig. 3-40 shows a significant reduction in the gas rates when a permeability jail is introduced, but it does not discriminate between the various permeability zones. Fig. 3-42 Detailed overview of the origin of the total gas produced over a period of 4 days during the cleanup of the fracture and fracture face. Fig. 3-43 Detailed overview of the origin of the gas produced over a period of 4 days during the cleanup of the fracture and fracture face, but now scaled according to Eq. 3-6. In Fig. 3-42, total gas production in the first 4 days of production is allocated by rock type. The figure presents the total gas and the rock type from which it’s produced, where clearly the difference in total amount between the two scenarios is visible. The large contribution of rock classes 3 and 4 in the normal relative-permeability and capillary-pressure functions is striking. This pattern is not visible in the permeability jail and requires more explanation. Fig. 3-43 presents more detail into the gas production: the large contribution of rock classes 3 and 4 is completely related to scaled pore volume distribution as governed by Eq. 3-6. Generally, the higher permeability of the rock matrix, the higher the contribution of total gas flow into the hydraulic fracture. For the permeability jail scenario, rock class 5 is the dominant gas supplier. This doesn’t come to a surprise considering the relative-permeability and capillary-pressure functions of that class, but nevertheless the complete dependency is interesting. What’s more important, is the strong decline in gas production from the other zones, especially zone 4. The zones are almost completely blocked and do not contribute to the total gas production in the short term. For the other heterogeneity models, the same dependency on rock type 5 modelled with the permeability jail is seen. Model H-Fluvial-90 and H-Marine show respectively a net reduction of gas production of 85% and 83%, and with a contribution of 74% and 81% of rock type 5. 66 MSc. Petroleum Engineering – Thesis report - L.F. van Zelm Rock type class 1, modelled as total permeability jail, does not contribute to the total gas production. The numerical method used in the simulations is discussed in the description of the permeability jail model (section 3.23.3), where it’s stated that the upstream weighing allows the injected water to enter a grid block with a total permeability jail due to the properties of the fracture grid block. In the heterogeneous model, rock type 1 is in total jail and the grid blocks adjacent the fracture indeed take up some leakoff water. Nevertheless, because of the small storage capacity and transmissibility compared to the other rock type classes, Sw never reaches the critical flowing saturation in these grid blocks. Therefore there’s neither water (Fig. 3-41) nor gas production (Fig. 3-43). It should now be noted that there seems to be a strong connection between the poor leakoff fluid retrieval and the gas production of a zone, with rock type class 4 as a clear example. In other words, the leakoff water seems to result in more impairment to gas flow in regions of the reservoir where a permeability jail is present. Fig. 3-44 below shows the reduction of the gas relative permeability in a grid block of model H-Fluvial adjacent to the fracture where the permeability falls in the rock type class 3. The reduction seems to be a combined effect of the leakoff water increasing the Sw and the permeability jail reducing the krg directly. This leads to two questions; is damage by leakoff water permanent or will it resolve with time, and second can we prevent this type of gas flow impairment by controlling our leakoff fluid during the hydraulic fracture treatment? The second issue will be discussed in later phase of this chapter (3.4.6); first a closer look is taken at the gas production after approximately 2 years of production. Fig. 3-44 Gas relative permeability in the first week compared with normal relative permeability (green) and permeability jail functions (red). 67 MSc. Petroleum Engineering – Thesis report - L.F. van Zelm 3.4.4 Heterogeneity modelling results: long-term production Section 3.4.3 demonstrates that the effect of the relative permeability jail on the short term cleanup of the fracture and the fracture face is significant. The overall gas permeability is reduced in most rock type classes of the reservoir, and the gas well rates are significantly lower. Second, most of the leakoff fluid is not produced back shortly after opening of the flow through the hydraulic fracture and into the wellbore. When liquid remains trapped near the fracture, the gas flow is additionally impaired. This section focuses on whether the gas flow remains impaired also for the long term and what the effect of the heterogeneity is. Results are presented for two years production, all scaled according to Eq. 3-6, including a detailed analysis of where (through which rock type class) the gas enters the fracture. A comparative overview of 10 years of production is also given to provide better insight to gas reserves present and possible economic consequences of typical tight-gas flow behaviour. Fig. 3-45 shows the production of each of the rock type classes after approximately two years. The figure shows gas-rate impairment per rock type similar to that in the short-term gas production. With normal saturation functions (no permeability jail) most gas flows into the fracture through high-permeability rock type 5, accounting for approximately 50% of the gas flow into the fracture. With the permeability jail, one observes the same apparent reduction in gas flow in permeability regions 1 to 4 as seen in the analysis of the short term production. The difference in gas production after two years is now 42%. And again, while rock type 5 represents only some 4% of the total reservoir, is responsible for 72% of the flow towards the fracture. Fig. 3-46 shows similar results for the H-Marine model; an overall reduction in gas production of 44%, with a larger percentage of the gas (80%) entering the fracture from region 5. Fig. 3-45 Scaled production of the H-Fluvial model, with specified origin of each of the rock types classes. Fig. 3-46 Scaled production of the H-Marine model, with specified origin of each of the rock types classes. 68 MSc. Petroleum Engineering – Thesis report - L.F. van Zelm After two years of production gas flow is still hindered by the gas relative permeability reduction in combination with the water trapped in the lower-permeability zones of the reservoir. The permeability jail saturation functions decrease the overall gas cumulative production over 2 years by 42%, which is significant for this most important economic period of a well. Table 3-13 presents an overview of the gas production at different times and the ‘ultimate’ gas recovery after 50 years. The impact of the relative permeability jail is clearly visible on the short term production, as discussed in section 3.4.3. After 10 years of production this effect is smaller. But with a reduction for the homogeneous and heterogeneous model of respectively 35% and 33% compared to normal relative-permeability and capillary-pressure functions, it is still economically significant. 4 days 1 month 2 years 10 years Simulation gas gas gas gas production production production production Scenario kH (Hom = 1.0) (-) (-) (-) (-) (mD.m) Homogeneous 0.100 1.00 1.00 1.00 1.00 H-Fluvial 0.079 1.27 1.25 1.13 1.02 H-Marine 0.075 1.05 1.11 1.10 1.00 Perm Jail Simulations Homogeneous 0.100 0.10 0.12 0.50 0.65 H-Fluvial 0.079 0.18 0.33 0.65 0.67 H-Marine 0.075 0.17 0.29 0.63 0.63 Table 3-13 Production comparison between the various models simulated in this thesis; the results have been corrected for kH and normalized to the homogeneous model with normal relative permeability functions for comparison. Simulation Scenario Homogeneous H-Fluvial H-Marine Perm Jail Simulations Homogeneous H-Fluvial H-Marine Normalized 50 years gas production (-) 1.00 Numeric 50 years gas production (m3) 1.13 x 107 Model GIIP (m3) 50 years “recovery” (%) 3.67 x 107 31 3.48 x 10 7 26 3.31 x 10 7 26 9.14 x 10 6 1.00 8.45 x 10 6 0.75 8.52 x 106 3.67 x 107 23 0.68 6.11 x 10 6 3.48 x 10 7 18 5.36 x 10 6 3.31 x 10 7 16 1.02 0.63 Table 3-14 Normalized (and kH corrected) and numeric gas production after 50 years, GIIP and 50 years “recovery” presented for the various models simulated in this thesis. 69 MSc. Petroleum Engineering – Thesis report - L.F. van Zelm Table 3-14 shows the gas production after 50 years, both as a normalized (and kH corrected) and the numeric gas volume. The heterogeneous models remain at the same normalized production level as after 10 years (Table 3-13) for the scenario with normal relativepermeability and capillary-pressure functions. The simulations with the modelled permeability jail only show improvement in the homogeneous model over the additional production period of 40 years; the heterogeneous models remain at the same normalized productivity. This proofs again that, when corrected for kH, the production of the homogeneous and heterogeneous models are similar throughout the production life, even at the long term. Table 3-14 also presents the Gas Initially in Place (GIIP) of the various models. The GIIP is a function of the average porosity (pore space) and gas saturation of the models, and is therefore slightly different for the homogeneous and heterogeneous models. The porosity of the heterogeneous models is determined from the permeability by Eq. 3-5, and is therefore distributed differently in the model. The GIIP can be combined with the numeric gas production volumes to calculate a “recovery” after 50 years, or ‘ultimate recovery’ (UR). Table 3-13 shows that the recovery is much affected by the permeability jail in both the homogeneous and the heterogeneous reservoirs. For the homogeneous reservoir there is a reduction of 8% in total producible gas after 50 years, which accounts for a significant economic depreciation of the gas field. The heterogeneous models show a lower UR of resp. 18 and 16% for the H-Fluvial and H-Marine models. This caused by the lowered normalized and kH corrected gas production after 50 years; resp. 0.68 and 0.63 compared to 0.75 for the homogeneous model. Thus, the permeability jail reduces the recoverable gas in the whole model and it specifically impacts the lower-permeability rock classes of heterogeneous models. During the first month of production, the heterogeneous H-Fluvial model with permeability jail produces more than twice as much gas than the homogeneous model, as shown in Fig. 3-47. This can be explained by earlier observations of the significant contribution of rock type class 5 in this model, and the limited hindrance the leakoff water imposes on this rock type. After 2 years of production there is still more production in the two heterogeneous models with permeability jail compared to the homogeneous model; only after 10 years does the homogeneous model produce as much as the other models. Fig. 3-47 Normalized gas production of the homogeneous and the two heterogeneous models, all modelled with the permeability jail functions. 70 MSc. Petroleum Engineering – Thesis report - L.F. van Zelm The reason for this change is related to heterogeneous nature of the models. The higherpermeability rock (rock class 5) is not affected by the permeability jail and produce gas at high rates for short periods, after which a strong decline is seen. Because the other (lower) permeability regions only contribute with small discharges, the cumulative gas profile will show strong curvature at early times and will flatten with time. The same pattern is seen in the cumulative gas curve of H-Marine. The homogeneous model is uniformly affected by the gas permeability reduction and the water blockage, thus shows a lower gas rate during cleanup and a slow decline throughout the field life. A potential blockage to gas flow at the rock face is therefore either present or not present, and the degree of damage throughout the reservoir is therefore also uniform. The heterogeneous model has zones of very low gas and water mobility, and higherpermeability rock classes that supply ample gas production in the early field life and thus resulting in a better cleanup. But the blocked zones of lower permeability still impact longterm production. Because some variation in grain size and pore distribution is to be expected (Fig. 3-48) and moreover some parts of the reservoir might have responded differently to diagenesis throughout their burial history (Claverie and Hansen 2009), the proposed heterogeneous model attempts to represent this. Moreover, the application of the heterogeneous model best captures the true impact of the relative permeability jail saturation functions. It shows that regions of lower permeability and porosity can cause natural traps for leakoff water introduced by the fracturing process. Both the short term and long-term gas production is impacted and the impact can be quite severe. Fig. 3-48 Permeability distribution in four common productive tight sandstone gas formations in Texas (Holditch 2006). The Cleveland and Wilcox Lobo data lie on nearly on the same trend. 71 MSc. Petroleum Engineering – Thesis report - L.F. van Zelm 3.4.5 Heterogeneity modelling results: impact of injected water In the discussions in this chapter so far it is shown that the introduction of the relative permeability jail in different permeability regions of a heterogeneous reservoir causes severe impairment to the gas production of a hydraulically fractured well. In the simulations the fracture treatment is simulated by an injection of a total amount of 100 m3 over a period of 24 hours, followed by a 24 hours shut in. The injected water and its damage potential have up to now not been considered separately, but more as a starting condition for our simulations. As shown in the section 3.4.4, the long-term gas production is still impacted by the mobility of the water in the reservoir. In this section, I test the effect of the leakoff fluid is on the gas production over time and whether the leakoff fluid has an impact on the UR, if it only impacts the cleanup period. Table 3-15 presents an overview of the cumulative gas production volumes at four times during production. In contradiction to the previous table with production data, the gas cumulative totals are now normalized with respect to the heterogeneous model with normal relative-permeability and capillary-pressure functions (no permeability jail) and the injection of 100 m3 water to represent the leakoff volume. Simulation Scenario (H-Fluvial Normal = 1.00) Cleanup 1 month 2 years 10 years gas gas gas gas production production production production (-) (-) (-) (-) H-Fluvial Normal kri-Pc 1.00 1.00 1.00 1.00 H-Fluvial Perm Jail 0.14 0.27 0.58 0.66 H-Fluvial - No Leakoff 1.76 1.07 1.01 1.00 H-Fluvial Perm Jail - No Leakoff 1.33 0.80 0.72 0.69 H-Fluvial - 99% Face Damage 0.07 0.06 0.30 0.56 Table 3-15 Normalized gas production overview of the heterogeneous H-Fluvial model: with or without the permeability jail and the injection of 100 m3 water. Final entry is the H-Fluvial model with 99% permeability reduction in the fracture face. The second row of Table 3-15 shows the effect of the permeability jail. The next two rows present the scenarios in which in the water injection period is skipped. The effect of leakoff water on gas production modelled in the conventional way (H-Fluvial – No Leakoff) is rather severe in the cleanup phase, but quickly diminishes. More interesting for this study is the fourth row which shows the effect of the leakoff fluids to a reservoir with a permeability jail present. Where the leakoff fluid reduces gas production during cleanup by 43% with normal relative-permeability functions (comparing H-Fluvial Normal kri-Pc to H-fluvial - No Leakoff: 1.00 v. 1.76), its impact on the permeability jail is 89% (comparing H-Fluvial Perm Jail to H-Fluvial Perm Jail - No Leakoff: 0.14 v. 1.33). This is caused by the strong reduced krg at high Sw in the permeability jail. After one month, the reduction caused by the leakoff fluid in combination with the permeability jail is still very significant (comparing 0.27 to 0.80), while H-Fluvial with normal relative-permeability and capillary-pressure functions shows just minor hindrance by the additional water phase (comparing 1.00 to 1.07). At longer production times, the impact of the leakoff fluid on the permeability jail slowly diminishes and but still impacts the gas production nevertheless after 10 years (comparing 0.69 to 0.66). 72 MSc. Petroleum Engineering – Thesis report - L.F. van Zelm It can therefore be concluded that the total leakoff volume still impacts production after many years of production when a permeability jail is present. The observation of long-term production impairment caused by water invasion combined with the permeability jail is very similar to what other authors have presented regarding mechanical damage (clay swelling, fines migration) in combination with high capillary pressures near the hydraulic fracture (Friedel (2004); Holditch (1979); Gdanski et al. (2005)). As a comparison, therefore, the final entry in Table 3-15 which shows the impact of a 99% reservoir permeability reduction in a heterogeneous model (to 0.01 µD) in a zone of 30 cm surrounding the fracture, following an idea of Holditch (1979). The capillary pressure in this zone is equal to the reservoir capillary pressure, so the blockage effect is only related to a reduction in absolute permeability. Also in this scenario, the most severe impact is at early production times (comparing 1.00 to 0.07), where the combined effect of both absolute and relative permeability of gas reduction occurs. Nevertheless, some differences are seen in these two types of damage models, especially in the water production. In the heterogeneity models with the permeability jail most water is produced rapidly during the cleanup from the high-permeability zones, after which the water production almost falls to zero (Fig. 3-49). This is due to the permeability jail, which traps water in the pores of the poorer (lower permeability) rock type classes. Also, the leakoff water is very mobile at high Sw in the permeability jail and can thus be produced back during the cleanup period. In the simulation with a mechanically damaged zone, the water production is more evenly distributed over time and continues for a much longer period. Also more water is produced back after the injection period, as seen in Fig. 3-49. Gdanski et al. (2005) provides a far more detailed discussion on the effect of a zone of reduced permeability around the fracture and the impact on water and gas production. He reports a decrease in gas production and a significant increase in water production over time when a damaged zone with increased capillary pressures is present around the fracture. This confirms the reported high water production in Fig. 3-49. Fig. 3-49 Water production comparison between three heterogeneous models: H-Fluvial Normal kri-Pc, H-Fluvial Perm Jail and H-Fluvial - 99% Face Damage. 73 MSc. Petroleum Engineering – Thesis report - L.F. van Zelm In conclusion, fracture face permeability reduction has long been considered (Friedel (2004); Holditch (1979); Gdanski et al. (2005)) as a potential damage mechanism in tight gas reservoirs. Sections 3.4.3 and 3.4.4 show that permeability jail also has the potential to cause large reductions in gas rate for both short and long term and hence could explain field observations of unexpected impaired gas production. This section discusses the water production as a potential discriminating factor between the two types of damage. It´s observed that the permeability jail mostly impacts the gas permeability, and mobile water is quickly produced during the cleanup period. Fracture face damage causes slow water cleanup, but can eventually lead to more water production at longer production times. Finally, it´s shown that the impact of the leakoff water on the gas production is rather severe and provides additional reduction, especially when a permeability jail is present. The potential gas rate improvement is interesting and therefore discussed in the next section. 3.4.6 Controlling damage from leakoff water Section 3.4.5 above describes the potential damage caused by water leaked off during the fracture treatment in reservoirs with a permeability jail or with mechanical damage. It’s shown that some resemblance exists when the gas production is examined after the injection of a large amount of water. In chapter 4 the well test results are discussed for several damage scenarios, which include a discussion of possible observed behaviour. Here, I briefly discuss proposed methods to reduce the amount of leakoff water lost to the formation in a fracturing treatment. Gas production impairment can be caused by both a reduction in absolute and relative permeability, as governed by Darcy’s Law. Water can reduce the absolute permeability by swelling of clays in the reservoir. This can even lead to a ‘total permeability block’ around the fracture (Bennion et al. 1996). In addition, simulation results in this thesis shows that a permeability jail is capable of strong reduction of krg when the fracture face consists of regions of increased Sw. An obvious potential remedy for this type of damage is to reduce the amount of water leakoff during a fracture treatment. This issue has been discussed over the years, but using water as main component of fracturing fluids is by far the most economical solution. Some large horizontal well multiple stage hydraulic fracturing campaigns in the shale basins of the USA require up to millions of litres of fracturing fluid. Replacing the water with oil-based fracturing fluids is a proposed method (Bennion et al. 2006) to reduce the impact on watersensitive reservoirs. Nevertheless, it’s generally more expensive and has strong environmental impact. Recently, various service companies have introduced new technologies that use either high-pressured nitrogen or carbon dioxide gas as carrier for the proppant, e.g. VaporFrac (BJ Services), ThermaFOAM CO2 (Schlumberger) or MISCO2 Frac (Halliburton). These new type of fracturing fluids cause no water imbibition into the reservoir and therefore reduce the impact of phase trapping by either a permeability jail or reservoir damage. 74 MSc. Petroleum Engineering – Thesis report - L.F. van Zelm This thesis focuses on gas production impairment as a result of specific properties of tight gas reservoirs, and not as a result of permeability damage by fracturing treatments. I demonstrate the impact of capillary pressures and the capillary end effect (section 3.2 and 3.2.2) and introduce the relative permeability jail in a heterogeneous model (section 3.4) to aid the understanding of long cleanup periods and gas rate reduction in tight gas reservoirs. Considering that both effects are properties of reservoirs with a permeability jail, it raises the question whether this can be altered or if these reservoirs are not to be considered as potential reserves. Both these properties are a result of the physical interaction between rock and fluid, and are based on physical and chemical principles. Penny et al. (2006) discuss the use of surfactants as additives in fracture treatment fluids for low-permeability shale reservoirs. These microemulsions alter the rock-fluid interfacial tension, decreasing capillary pressures and the end effect by 50% and increasing krg substantially. Their results show a 50% increase in water production and 30 to 40% increased gas production. This is confirmed by other research, such as Rickman and Jaripatke (2010). Parekh and Sharma (2004) state that the alteration of strongly water-wet reservoir rock to intermediate-wet enhances the cleanup of the fracture face after a hydraulic fracture treatment. As a result better gas production is seen. It seems that the use of these chemicals would allow a reduction of the impact of the permeability jail to a certain extent, of course depending on the initial saturation state of the reservoir and the relative permeability curves. If the mobility of the water-phase can be improved, then gas can flow more easily through the pores and hence result in higher gas production. This resembles a change from a total permeability jail to the small permeability jail as shown in section 3.3. Moreover, this remedy is especially valuable to improve the relative permeability of a fluid, and not the absolute permeability of the reservoir. Damage caused by clay swelling or fines migration as shown in section 3.4.5 does not benefit. The effect of this treatment can hence be tested accordingly. In the next chapter, an overview is presented of the post-fracture analysis with well testing methods. It is examined if a distinction between damage to the fracture and the reservoir can be made, in order to find a solution for the correct problem. 75 MSc. Petroleum Engineering – Thesis report - L.F. van Zelm 4 Well Test Interpretation of Simulation Results The previous chapter (chapter 3) focuses on modelling hydraulic fractured reservoirs including the introduction of a permeability jail into the reservoir. The production results show an extended cleanup period. So far, the analysis only focuses on the forward modelling of these reservoirs generating pressure and gas-water rate profiles. The outcome of these simulations can be used for two types of analysis. First, history matching is based on matching the simulator output with the observed data over a period of production by adjusting various input parameters. Examining the impact of each of the parameters may then lead to a better understanding of the well, hydraulic fracture and reservoir. A problem is that this process is not unique, for some parameters are correlated, resulting in a possible solution rather than necessarily the true solution. A second method, as introduced in section 2.4, is to perform a well test analysis in the simulation models. A common test is a Pressure Buildup (PBU) test; this simulates a shut-in and following pressure increase. As the theory predicts, it should be possible to obtain the basic reservoir parameters from this type of tests. Nevertheless, the introduction of the hydraulic fracture makes the solution often non-unique. Assumption is that we use a simple, uniform model and investigate the validity of the matched parameters for heterogeneous reservoirs. This section describes the set up of the PBU analysis performed in the various models from section 3.4. The analysis results in values of the basic reservoir properties, which are compared to the original model input. The accuracy of these results is important to a discussion of the value of the post-fracture production evaluation, specifically if leakoff and permeability jail are detected. 4.1 Well test preparation To simulate a PBU test, the simulation is set up for a production period of 2 weeks followed by a shut-in of 1 month. Long test periods (flow and shut-in) are necessary to improve the quality of the PBU results (Garcia et al. 2006). The data is recorded every time step (minute) to provide high quality data for calculating the pressure derivative. The data is then loaded into a commercial pressure transient analysis software programme, Saphir (Kappa Engineering 2009), which analyses the data with pre-determined plots. I found that controlling the well by a constant pressure constraint during production results in difficulty with acquiring an acceptable solution for both fracture length and reservoir pressure. The theoretical background of the PBU analysis is based on the principle of superposition, which is based on two constant-rate periods of which the latter is the shut-in (gas rate = zero). Nevertheless, for many gas wells, pressure constraints are the method of production control, and this is rather unfavourable for a PBU test. A constant pressure implies a varying rate, which requires the superposition of the rate to be calculated at each time step. The accumulation of errors may lead to the unsatisfactory results as observed. 76 MSc. Petroleum Engineering – Thesis report - L.F. van Zelm Therefore, I simulated a second round of tests with constant rate during the initial two-week production period, and followed by 4-week shut in. In total 4 unfractured models and 6 models with a hydraulic fracture were tested. The pre-fractured models are included to complete the full circle of production analysis usually performed in tight gas reservoirs. Prefracture test are used to obtain the basic reservoir properties, which can then be used for treatment design. During the discussion of the results, it’s important to understand the expected and desired accuracy of the results for fracture length and reservoir permeability. In the field, due to various reasons as discussed by Lolon et al. (2003), the effective fracture length is often reduced by 50% or more compared to the created length. Therefore a match for fracture length can be considered accurate, if it results within a 10% margin of the actual (model) input value. More accuracy is in the field practically impossible and therefore not necessary in these analyses. Second, the equations Eq. 2-10 and Eq. 2-14 provide solutions to permeability and fracture length, but these are both dependent on the initial (and possibly unknown) reservoir pressure. During the analysis, the reservoir pressure is therefore taken as input in order to reduce the uncertainty. 4.2 Well test results 4.2.1 Pre-fracture well test Before discussing any of the simulation models of section 3.4, the results of the unfractured models are presented in Table 4-1. The models are the same as used in the simulations of chapter 3 and are highlighted in Table 3-10 with properties as discussed in section 3.1.1 for the normal relative-permeability and capillary-pressure functions and section 3.4.1 for the permeability jail functions; the only difference is the removal of the hydraulic fracture in the model. For clarity, the data of the initial homogeneous model with hydraulic fracture is included to examine the accuracy. The reported kH consists of the height of the total paylayer (100 m) and the permeability to gas (krg multiplied with reservoir permeability of 1 µD). At the initial water saturation, for the normal relative-permeability results in krg = 0.2 and the relative permeability jail in krg = 0.1. Details of model Homogenous Normal kri and Pc Homogenous Perm Jail Pre-frac Homogeneous Normal kri and Pc Pre-frac H-Fluvial Normal kri and Pc kH (µD.m) 20 10 0.846 1.92 Error (%) -96% -90% Pre-frac Homogeneous Perm Jail 0.464 -95% Pre-frac H-Fluvial Perm Jail 0.99 -90% Table 4-1 Results of pressure buildup analyses of the pre-fracture models. 77 MSc. Petroleum Engineering – Thesis report - L.F. van Zelm The resulting kH for the pre-fracture scenarios show a general poor match with the model input values, for which two possible causes can be found. First, no radial flow is achieved despite the rather long shut-in period, as shown in the pressure derivative plots of the homogeneous (Fig. 4-1) and H-Fluvial (Fig. 4-2) with normal relative-permeability and capillary-pressure functions. The two plots never reach the time where the pressure derivative line (in red) stabilises horizontally. The outcome of the analysis is therefore nonunique, as explained in section 1.2.3 and can be incorrect for kH (Garcia et al. 2006). Second, the reported kH for the fractured models assumes correctly a height of the total pay-layer, but this total height is not sensed in the pre-frac scenario. The permeability estimate from the reported kH is therefore wrong and misleading. It’s therefore better to refer to the reported kH from the software itself instead. The practical implications of these results are discussed in a later part of this chapter (section 4.3). Gas potential [psi2/cp] Gas potential [psi2/cp] The kH of both H-Fluvial scenarios is significantly higher than the homogeneous model. This is an interesting result, because the models match overall fracture permeability in the wellbore area. Apparently, a long shut-in of 4 weeks in low-permeability reservoirs only senses the local permeability close to the well, which can vary to a certain extent. I highlight the influence of local permeability variations in the analysis of the initial production period (section 3.4.3). 1E+8 1E+7 1E+6 1E-3 0.01 0.1 1 10 100 1E+8 1E+7 1E+6 1E-3 0.01 0.1 Time [hr] Log-Log plot: m(p)-m(p@dt=0) and derivative [psi2/cp] vs dt [hr] Fig. 4-1 Pressure derivative plot of the prefracture homogeneous model with normal relative-permeability and capillary-pressure functions. 1 10 100 Time [hr] Log-Log plot: m(p)-m(p@dt=0) and derivative [psi2/cp] vs dt [hr] Fig. 4-2 Pressure derivative plot of the prefracture H-Fluvial model with normal relative-permeability functions. and capillary-pressure 4.2.2 Post-fracture well test Next, the results of the well test analyses on the hydraulically fractured wells are presented. In total 6 different models are evaluated: the homogeneous and H-Fluvial models as described in Table 3-13, and two scenarios without water injection (“No Leakoff”) as described in Table 3-15 of section 3.4.5. Fig. 4-3 and Fig. 4-4 present obtained results for permeability and fracture length matches for all models. The results are normalized to the model input values, thus a result of 1.0 is a good match. The initial pressure and reservoir height are fixed input parameters during these analyses. 78 MSc. Petroleum Engineering – Thesis report - L.F. van Zelm Both the homogeneous and heterogeneous models show fairly accurate results for the important parameters for the post-fracture analysis of tight gas wells, except when the permeability jail is modelled. The models without water injection produce almost no water, and the good match is as expected. For with leakoff water and modelled with normal relative-permeability and capillary-pressure functions, the resulting match for fracture length and reservoir permeability are very well within the error margin of the analysis method. The injected leakoff fluid apparently does not cause major errors in the final solution. This is a very encouraging result and confirms that despite simplifying assumptions (section 2.4) a match can be obtained for low permeability hydraulic fractured gas wells. Of course, this is achieved with a known initial reservoir pressure. The results of two scenarios are included below for illustration, and show good matches for the log-log (Fig 4-5 and Fig. 4-6) and history plots (Fig. 4-7 and Fig. 4-8) obtained by the well test analysis software (Kappa Engineering 2009). I have used these two plot types for the iterative matching process during the analyses. Fig. 4-3 Results of post-fracture PBU analyses for permeability to gas for the models with normal relative-permeability and capillary-pressure functions. Fig. 4-4 Results of post-fracture PBU analyses for fracture length of all models. Again, note the poor match for the permeability jail models. 79 Gas po tential [psi2/cp] Gas potential [psi2/cp] MSc. Petroleum Engineering – Thesis report - L.F. van Zelm 1E+8 1E+7 1E+6 1E-3 0.01 0.1 1 10 1E+8 1E+7 1E+6 1E-3 100 Time [hr] 0.01 0.1 1 10 100 Time [hr] 3000 2000 1000 Pre ssure [p sia] Pressure [psia] Fig 4-5 Pressure derivative plot of the H- Fig. 4-6 Pressure derivative plot of the Fluvial model with normal saturation homogeneous model with normal functions, but excluding the injection of saturation functions. fluids. 3300 2800 Fig. 4-7 PBU history match plot of the H- Fig. 4-8 PBU history match plot of the model with normal Fluvial model with normal saturation homogeneous saturation functions. functions, but excluding the injection of fluids. Fig. 4-9 shows the pressure-derivative plot of the homogeneous model with normal saturation functions including the representative specialized lines for the ¼ and ½ slope for the two fluid-flow periods in the model. The fracture is initially filled with water and therefore does not provide enough conductivity to the gas, which results in a ¼ slope at early test times. The ¼ slope is always present in a hydraulic fracture analysis, though sometimes not visible due to a short duration. In Fig. 4-9, the ¼ slope is present for the first hour approximately. At later times, a ½ slope would have been expected to represent the highly conductive fracture present in the model, but no good match is obtained. This simulation shows that after a few months gas production, still a small pressure drop is visible in the fracture. The missing of the linear flow is therefore expected in the PBU analysis. Furthermore, the pressure derivative curve does not show the characteristic flat line representing radial flow. For these types of wells it’s not expected to see radial flow at such a time scale, as highlighted in section 2.4.4. Nevertheless, this means that the analysis is non-unique. 80 Gas potential [psi2/cp] MSc. Petroleum Engineering – Thesis report - L.F. van Zelm 1E+8 1E+7 1E+6 1E-3 0.01 0.1 1 10 100 Time [hr] Fig. 4-9 Homogeneous model pressure derivative plot including specialized lines for detecting the ¼ and ½ slope, representing respectively the two flow periods within the fracture: bilinear flow (dark line) for the early times and linear flow (green line) expected for the flow in a highly conductive fracture. G a s p o te n tia l [p s i2 /c p ] G a s p o te n tia l [p si2 /cp ] The relative permeability jail scenarios for the homogeneous and H-Fluvial reservoirs show extended and complicated cleanup behaviour during the production simulation (see chapter 3) and it´s expected that causes problems for the PBU analyses as well. The matches for the reservoir permeability (Fig. 4-3) and fracture length (Fig. 4-4) show that both parameters clearly deviate from the input values. The fitted reservoir permeability is far higher than the expected input value; but a much-shorter fracture half-length is inferred, as short as just a few meters. With the observed strong reduction in productivity of the well, we did not expect a long fracture anyhow. 1E+8 1E+7 1E+6 0.01 0.1 1 10 Time [hr] 100 1E+8 1E+7 1E+6 1E-3 0.01 0.1 1 10 100 Time [hr] Fig. 4-10 Pressure derivative plot of the Fig. 4-11 Pressure derivative plot of the Hhomogeneous model modelled with a Fluvial model modelled with a relative relative permeability jail. permeability jail. Fig. 4-10 and Fig. 4-11 show the pressure derivative plots for the two scenarios including a relative permeability jail, whereby especially the homogeneous model shows a distorted pressure curve. This distortion is caused by the inability of the pressure wave to move through the reservoir due to the impaired gas relative permeability around the fracture. It’s therefore difficult to match this curve with a standard model provided by the well test software. The heterogeneous model shows a slightly less distorted and possibly more realistic results. Nevertheless, both clearly deviate from the scenarios with normal saturation functions. 81 MSc. Petroleum Engineering – Thesis report - L.F. van Zelm 4.3 Well test interpretation and implications The next step in the well test analyses is to interpret the results and comment on the accuracy and uniqueness. Because the PBU is performed with known input parameters, it’s one can identify incorrect interpretations and the implications for a possible next fracture treatment. The pre-frac PBU tests show that radial flow is not reached and that makes the results nonunique. As a result, the output kH deviates significantly from the model input value for kH. Also the unknown H causes a large uncertainty in the results. In my models, I could examine the investigation radius of the pressure wave during the test period, which is of course impossible in a real well. If from logging while drilling or core tests, a net-pay of 100 m is detected, one obtains a too low kH and ends up with a far too low permeability. This can affect subsequent decisions in the field development process or can even lead to abandonment of the well due to insufficient proven reservoir quality. The pre-frac permeability to gas in a low-permeability or tight reservoir should therefore always be backed-up with a second independent source of information, as explained in section 2.4.4. The PBU results for the fractured wells show a clear distinction between the scenarios with normal (Fig 4-5 and Fig. 4-6) and permeability jail relative-permeability and capillarypressure functions (Fig. 4-10 and Fig. 4-11). The two results are discussed separately in this section, starting with the results for the normal saturation functions. The interpretation of the simulation with normal fluid behaviour (with or without) leakoff water causes no interpretation problems. The plots of Fig 4-5 and Fig. 4-6 show a good match, and the slope clearly indicates the presence of a hydraulic fracture. When these results are compared with an example of a fractured well in a tight gas field in Texas (Fig. 4-12), much resemblance is seen. From this PBU analysis, the fracture was believed to be long and highly conductive. The input values of the thesis scenarios indeed also represent a long and conductive fracture. It’s therefore concluded that a PBU analysis in a hydraulic fractured tight reservoir can result in a good estimate when either no water leaks off into the reservoir, or the fluid behaviour allows for rapid cleanup and minor damage to the fracture face. Moreover, the results in Fig. 4-3 and Fig. 4-4 show that the estimates for permeability and fracture length are very accurate, when the pressure is known. Fig. 4-12 Example of PBU test performed in tight gas field in Texas, interpreted as a long and conductive fracture (Cipolla and Mayerhofer 1998). 82 MSc. Petroleum Engineering – Thesis report - L.F. van Zelm Fig. 4-13 Example of PBU test performed in tight gas field in Texas, interpreted as a long fracture with very low-conductivity (Cipolla and Mayerhofer 1998). For the analysis of the permeability jail PBU results, this accuracy is not to seen at all. The matches on the log-log and history plots are all poor and the resulting fracture lengths and reservoir permeabilities are inaccurate compared to the input values. In practice, this interpretation could results in false conclusions. This section discusses some possible next (wrong) steps in the interpretation of the PBU test results. Fig. 4-13 shows an example of a fractured well in a tight gas field in Texas (Cipolla and Mayerhofer 1998) for which the PBU output resulted in a long fracture with very low conductivity. The shape of the pressure derivative shows much resemblance with Fig. 4-11 and can possibly reveal similar problems. The authors considered excessive fracture fluid damage, poor proppant placement or slower fracture cleanup. Only after testing the example well again after 3 years of production, where a high-conductivity fracture was seen, it was concluded that the problem was a slow fracture cleanup. Analyzing the H-Fluvial permeability jail scenario as a low-conductivity fracture in the well test software results in a fair match on the log-log plot and on the history plot for the buildup period only. The resulting output parameters are a fracture half-length of 139 m, a permeability of 2.4 x 10-4 mD and a conductivity of 0.035 mD per meter. Thus the PBU analysis results in a longer fracture with too low a conductivity in a reservoir with a fairly accurate permeability compared to the actual model. In Fig. 4-11, a ¼ slope seems to appear at later times, indicating a low-conductivity fracture. The extended cleanup period due to the permeability jail can apparently easily be identified as fracture cleanup when the well test is performed before production has commenced. This suggests that modifications are made to the treatment in subsequent fracturing stages, or future wells, which will enhance the gel breaking or cleanup in the fracture, while the actual problem lies in the reservoir response to excessive leakoff of water. Without a re-test after some time, it’s apparently difficult to distinguish fracture damage or reservoir cleanup. This is an important conclusion, indicating that an interpretation of a well test can be inconclusive with respect to the type of damage. 83 MSc. Petroleum Engineering – Thesis report - L.F. van Zelm A second way to interpret the outcome of the PBU analysis is to set the permeability during the matching process at the expected value, as if accurately determined by pre-fracture well tests, core measurements or previous experience in the area of interest. This is the absolute reservoir permeability multiplied by the relative permeability at initial water saturation, resulting in a value of 0.2 µD. The software programme can then iterate only on fracture half-length until a match is obtained. This analysis assumes that no damage occurs to the fracture itself and the high design fracture conductivity is achieved. The homogeneous permeability jail model shows a match with a fracture half-length of 6 m; the H-Fluvial permeability jail model reports fracture half-lengths of 26 m for 0.2 µD. As Fig. 4-10 shows, the homogeneous perm jail model shows deviant pressure response as a result of the zone of increased water saturation around the fracture. This is because the entire formation is affected by the permeability jail so that the fluid movement is totally impaired. Even a poor match in the well test analysis can therefore only be obtained by using a very short fracture length, i.e. only 6 m. For the H-Fluvial model the solution of a fracture of length 26 m length is more realistic. This solution can therefore invoke a false test interpretation of a strongly reduced fracture length, while the permeability jail is the actual cause of the poor test response. The fracture only appears to be reduced. The reverse process, i.e. setting the fracture length and iterating for reservoir permeability, is not a very common practice, but is useful to bound the ranges of the solution space of the results. Nevertheless, the analysis yields in no match for either model after numerous iterations in the software programme on both history and pressure derivative plots. This result implies that it´s impossible to match the behaviour with long effective hydraulic fractures. If this would be the result of a well test in a real tight gas reservoir, the effective fracture appears to be short. Whether this is caused by ineffective fracture cleanup cannot be determined. This is an important and difficult issue. A shorter created fracture can be the result of poor proppant placement as suggested by Cipolla and Mayerhofer (1998) or the creation of multiple fractures, which requires the engineer to focus on the treatment schedule, or fluids and proppant used. These scenarios require a different solution. An independent measurement could possibly verify if the created fracture length is indeed reduced, for example micro-seismic monitoring during the fracture treatment. Nevertheless, if the fracture treatment schedule design is based on experience, and the treatment execution shows no problems, another interpretation is that the fracture appears to be shorter. A reduction in effective fracture length can result if along a fracture the inflow for gas is reduced, as is the hypothesis for the permeability jail models. Section 3.4 indeed shows that certain areas along the fracture have a strongly impaired contribution to the total gas inflow, especially as a result of the leakoff water. It also describes possible remedies to prevent the impact of a reduction in fluid mobility by the use of surfactants. Penny et al. (2005) describe the use of surfactants can increase the flow area after damage has occurred due to phase trapping. They reach this conclusion from a production analysis in a Barnett shale well, which showed signs of increased effective fracture length after the use of surfactants. Although not concluded from a well test, this result nevertheless provides insight into the possibility of a permeability jail to reduce the effective fracture length in heterogeneous models. 84 MSc. Petroleum Engineering – Thesis report - L.F. van Zelm This leads to an interesting conclusion on the use of well tests in post-fracture production analysis of low permeability gas wells. I have demonstrated that a PBU match results in good matches for hydraulic fractures in reservoirs governed by normal fluid saturations. The simplified approach to reservoir response used by well test analysis software is capable of handling a cleanup from leakoff water injection. Second, the use of the heterogeneous model with no permeability jail does not cause any serious trouble; despite that local permeability variations may influence the pressure response. The presence of a relative permeability jail severely impairs the fluid mobility surrounding the fracture and the PBU analysis is much more complicated. A good match is impossible, and the result for reservoir permeability and fracture half-length are incorrect. The homogeneous perm jail model shows more reduction in gas rate (section 3.4) and also results in a poorer match on reservoir permeability and fracture half-length. The permeability jail modelled in a heterogeneous reservoir also results in incorrect estimates, though the error in fracture half-length is less severe. Moreover, if iteration is performed on fracture half-length only, a much shorter fracture is estimated. Considering that frequently the effective fracture is found to be much shorter than the created length, this is a dangerous conclusion. The fluid response to a relative permeability jail may lead to a false interpretation of a PBU, and mistakenly report a shorter fracture length. This can have great consequences for possible further well stimulation treatments to the well and further field development. 4.4 Closing the circle: using well test results Section 4.3 concludes that it’s hard to determine the origin of the damage to gas flow in specific cases through well tests. A simulation of production provides a possible solution. Specifically, this section compares gas production of fractures with low conductivity or reduced fracture length with the observed production from the scenarios with and without a permeability jail. Fig. 4-3 and Fig. 4-4 show that a conductive and long fracture does not give unexpected results for fracture length and reservoir permeability in a PBU in a reservoir with normal saturation functions. On the other hand, when a permeability jail is modelled, the results become very inaccurate and the best matches are for short fracture lengths. This result is now used in the production simulations and compared to the other scenarios. Fig. 4-14 shows the early production of 5 different scenarios of the homogeneous model: specifically the permeability jail and the scenarios with normal relative-permeability and capillarypressure functions, both used in the analysis of section 3.4. Finally, three scenario of reduced fracture length, resp. 45, 30 and 6 meters with normal relative-permeability and capillary-pressure functions. The homogeneous model is used for modelling convenience in this section, although the response of the heterogeneous model is more realistic. Nevertheless, the impact of the permeability jail is rather similar (Fig. 3-36) and the normalized production matches. Hence the homogeneous model is applicable for this comparison and a discussion on the different scenarios. 85 MSc. Petroleum Engineering – Thesis report - L.F. van Zelm Fig. 4-14 Gas rate profile of early production period of various scenarios, including reduced fracture half-lengths. Fig. 4-15 Gas rate profile of early production period of various scenarios, including reduced fracture permeability. 86 MSc. Petroleum Engineering – Thesis report - L.F. van Zelm The permeability jail scenario (green line) with the half-length of 100 m is interpreted in the well test as a fracture with a fracture half-length of 6 m, and indeed shows some resemblance in the first 10 days. Both scenarios result in low rates for gas after an initial small peak. Nevertheless, the short fracture retains a low gas rate due to the decreased drainage area, while the permeability jail shows signs of cleanup and improving rates. If somewhat longer fractures (30 and 45 m half-length) are modelled, a very short cleanup period is seen. After approximately 2 months of production, the gas rate of the two scenarios matches the permeability jail scenario. Section 4.3 also shows that the H-Fluvial reservoir with a permeability jail can be interpreted as a long fracture, but with a lower conductivity. The gas production is therefore simulated for 4 scenarios with lower-conductivity fractures and compared to the production of the model with and without a permeability jail. Again, the homogeneous permeability jail model (Fig. 4-10) is used for modelling convenience instead of the heterogeneous model; this model has a base case fracture permeability of 500mD. The other scenarios consist of fractures with reduced fracture permeability to respectively 150, 50, 10 and 5 mD. The production simulation results of long fractures with reduced permeability are presented in Fig. 4-15. All scenarios have apparent cleanup periods, increasing in time and magnitude as the fracture permeability is reduced. This confirms earlier findings on the importance of fracture conductivity on the cleanup of fracture fluids (Wang et al. 2009). Second, the scenario with a fracture of permeability of 5 mD in the fracture (yellow line), resulting in an interpretation of a low-conductivity fracture, shows much resemblance with the permeability jail scenario (light green line) during the cleanup period including a gas rate increase over time. The well tests also present a match for a long but low-conductivity fracture with the permeability jail in the heterogeneous H-Fluvial model. Production analysis (Fig. 4-15) apparently does not provide better discrimination between these cases. Homogeneous simulation scenarios (Normalized) 1 year gas production (-) Normal saturation functions (kri and Pc) 1.00 Permeability jail 0.40 Fracture with 6 m half-length 0.10 Fracture with 30 m half-length 0.34 Fracture with 45 m half-length 0.46 Fracture permeability 150 mD – infinite conductive 0.99 Fracture permeability 50 mD – infinite conductive 0.95 Fracture permeability 10 mD – high conductivity 0.74 Fracture permeability 5 mD – low conductivity 0.57 Table 4-2 Gas production overview after 1 year simulation of various scenarios. Table 4-2 presents simulation results of 1 year production of all fracture damage scenarios and a few interesting characteristics of the scenarios appear. The production impairment for the first scenarios in the table (shorter fractures) seems to be rather proportional to the reduction in the fracture length. The permeability jail showed a more severe cleanup initially, but results in more gas production after one year. The fracture with 6 m fracture half-length produces the least gas, as a result of the small drainage area. 87 MSc. Petroleum Engineering – Thesis report - L.F. van Zelm It can be concluded that there are some features which help to discriminate between a permeability jail and a reduction in apparent fracture length. Most significant is strong correlation of a shift in production decline curve to lower gas rates with reduced fracture length, rather than an extended and more severe cleanup period with gas rates improving over time. A reduction of fracture length results in a smaller drainage area rather than a reduction in fluid flow capacity. So, though the two types of damage give similar results in well test analysis, they do not match in production simulation performed with a numerical reservoir simulator. In real field examples, this different behaviour can help to diagnose the cause for the gas production impairment. On the other hand, it’s very hard to distinguish damage from a permeability jail from reduction in fracture permeability. First, a good match is obtained in a well test analysis for the permeability jail with model including a low-conductivity fracture due to the reduced capacity of fluid flow handling in the fracture. Second, it’s observed that the lower the conductivity, the more apparent the fracture cleanup period. At some point, it even resembles the strong cleanup seen in the permeability jail scenario and the 1-year production results also are similar. Because a reduction in fracture conductivity is common, it’s a problem that is shows close resemblance with the permeability jail. Moreover, it requires a totally different approach for optimizing treatments. To properly evaluate the post-fracture production of a hydraulically fractured well and distinguish between a lowconductivity fracture and a relative permeability reduction, it’s necessary to find some discriminating factor. We consider next water production. Simulation Cleanup 1 month water 1 year water Scenario water production production production (Homogeneous = 1.00) (-) (-) (-) Homogeneous Normal 1.00 1.00 1.00 Homogeneous Perm Jail 0.45 0.51 0.52 H-Fluvial Normal 1.28 1.25 1.25 H-Fluvial Perm Jail 0.58 0.77 0.78 Fracture Perm – 150 mD 0.80 0.98 1.02 Fracture Perm – 50 mD 0.51 0.85 0.98 Fracture Perm – 10 mD 0.14 0.44 0.72 Fracture Perm – 5 mD 0.08 0.30 0.61 Table 4-3 Water production of various simulation models, including homogeneous models with strong reduced fracture permeability. Table 4-3 provides an overview of the water production of the homogeneous and H-Fluvial model and the homogeneous models of Table 4-2 with reduced fracture permeability. Because the homogeneous models have a slightly higher average kH throughout the reservoir, the results for H-Fluvial have been normalized accordingly (section 3.4.2) to allow for proper comparison. The hydraulic fractures with permeabilities of 150 and 50 mD can still be considered infinitely conductive and show a no resemblance with the permeability jail when comparing gas production. (Fig. 4-15 and Table 4-2). It is Interesting that the water production during cleanup of the 50 mD fracture is nevertheless similar to the permeability jail models. Section 3.3 also shows that the water mobility is less impaired by the permeability jail than the gas mobility. 88 MSc. Petroleum Engineering – Thesis report - L.F. van Zelm This difference in water production becomes even more prominent when examining the low-conductive fractures, with strongly reduced water production. The water production of the permeability jail models stabilizes after approximately a few weeks. The same holds for the more conductive fractures, that produce the mobile water around the fracture within a few months. On the contrary, the low-conductivity fractures still produce significant amounts of water after 1 year and approach (H-Fluvial) or exceed (homogeneous reservoir) the reported water production in a permeability jail. Another way of presenting this data is by a cross-plot of water and gas production for three times during the production period (Fig. 4-16). Here, the H-Fluvial Normal is the model with normal relative-permeability and capillary-pressure functions (as described in section 3.1.1) to which all other models are normalized for comparison for both water and gas production. In the figure, the orange dot represents this model at position (1,1) in the top right corner. The permeability jail model (blue dot) is the obvious outlier in all three plots, representing a relatively more water than gas production. This makes the water production a discriminating factor and aids the post-fracture production analysis significantly. Secondly, the permeability jail model matches the gas production of the 50 mD scenario during the cleanup period, but over time resembles more the gas production of the very low-conductivity fracture. Fig. 4-16 Three cross-plots plotting gas and water production. Both the water and gas production is normalized to the H-Fluvial Normal model. This leads to the conclusion that the reduction in fracture conductivity impairs the ability of the fracture to conduct the reservoir fluids to the wellbore, whether gas or water. For the gas phase, this results in an apparently extended cleanup period for low-conductivity fractures and an increase in gas rate with time. The water production is equally hindered by an extended cleanup period. This is a large contrast with the permeability jail models in this thesis, which shows a more strongly impaired gas than water production. A cross-plot such as Fig. 4-16 can assist in this procedure and the shown trends can result in an improved interpretation of post-fracture production analysis in tight gas reservoirs. 89 MSc. Petroleum Engineering – Thesis report - L.F. van Zelm If low-conductivity fractures are the result of poorly broken fracturing fluid and remaining gel residues, the fracture conductivity sometimes improves over time as shown by the example in Fig. 4-13. The comparisons in Fig. 4-16 are therefore even more interesting. A fracture with very low conductivity initially produces less gas and water than expected, but the gas rate gradually improves over time. Or as Fig. 4-16 displays it, the point of the graph will move towards the top of the graph with time. On the contrary, if the lower than expected gas production is combined with relatively high water production, it’s possibly caused by a permeability jail. But now the gas production impairment will remain present throughout the well’s lifetime. No remedy for a permeability jail at full reservoir scale is available, only surfactants can provide possible local improvement. It can therefore be concluded that the production of relatively more water than gas is less desirable from a tight-gas production standpoint. Finally, to conclude the evaluation of the post-fracture gas production, Table 4-4 shows the effect of the injection of leakoff water on the reduced fracture conductivity fracture models and the response when action are taken to control such leakoff. The results for the heterogeneous models with or without a permeability jail are shown as well in Table 3-15 and are repeated for convenience. The scenarios without leakoff represent a fracture treatment without the use of water, as discussed in section 3.4.6. Important is that the normalized gas production of the permeability jail model shows a far more significant increase in the early gas production than the low-conductivity fracture models; even the reference model is surpassed (comparing 1.33 to 1.00). The low-conductivity fracture models also show an increased gas production due to the removal of the water (respectively 0.43 v. 0.03 and 0.26 v. 0.02), but it’s apparent that another damage factor is present in the model. Nevertheless, as in the H-Fluvial models, the additional gas production caused by the removal of leakoff water is more apparent in the early production times than after 1 year of production (comparing 0.43 v. 0.03 to 0.74 v. 0.64 for the 10 mD fracture). Simulation Cleanup 1 month gas 1 year gas Scenario gas production production production (H-Fluvial= 1.00) (-) (-) (-) H-Fluvial Normal 1.00 1.00 1.00 H-Fluvial Normal - no leakoff 1.76 1.07 1.02 H-Fluvial Perm Jail 0.15 0.27 0.52 H-Fluvial Perm Jail - no leakoff 1.33 0.79 0.73 Fracture Perm – 10 mD 0.03 0.17 0.64 Fracture Perm – 10 mD - no leakoff 0.43 0.53 0.74 Fracture Perm – 5 mD 0.02 0.08 0.49 Fracture Perm – 5 mD - no leakoff 0.26 0.38 0.63 Table 4-4 Gas production of various simulation models, including homogenous models with strong reduced fracture permeability. 90 MSc. Petroleum Engineering – Thesis report - L.F. van Zelm 5 Conclusion and Recommendations 5.1 Conclusions Chapter 3 introduces the reservoir base-case simulation model to research the impact of unconventional reservoir behaviour and water leakoff on gas production. The main findings are as follows. Capillary pressures in tight gas reservoirs are very high, due to correlation with low porosity and permeability. Simulations show that these high capillary pressures alone do not have a large effect on the gas production. On the other hand, water production is strongly reduced. The specific impact of the capillary end effect is considered by using different grid refinements around the fracture. With a very fine grid, the capillary end effect is visible at the fracture face discontinuity. Nevertheless, the resulting high water saturations have little impact on long-term gas production. Simulations of a total permeability jail (relative permeability functions with a large range of saturations with zero mobility of both gas and water) in a homogeneous reservoir show complete blockage to water and gas flow and high water saturations around the fracture following the injection period. This case showed many convergence errors in the numerical solution of the simulator. Therefore this case is dropped from further consideration in this thesis, in favour of more-realistic models of a total permeability jail modelled in parts of a heterogeneous reservoirs, representing poor-reservoir rock, shaly or non-pay sections. We define a small permeability jail as a case with a range of saturations with near-zero mobility of gas and water. The simulation results for a homogenous reservoir with a small permeability jail show a significant initial reduction in gas rate and a slow recovery over time (a "cleanup" effect). The leakoff water in the fracture face is mobile and an increased watergas production ratio is observed. A heterogeneous model is created to model specific fluid transport properties in regions of low and high permeability. Specifically, for the case of ‘permeability jail’ in the heterogeneous reservoir, we assign a total permeability jail to rock type classes with the lowest permeability, a small permeability jail to intermediate-permeability rock classes, and normal relative-permeability and capillary-pressure functions to rock with the highest permeabilities. A comparison between the homogeneous and heterogeneous models with normal relative-permeability functions (i.e., those without a relative permeability jail) shows a match for both the cleanup and long-term water and gas production when corrected for reservoir-average kH. The early production is dominated by the fracture face area and local variations in permeability can have a significant impact on the gas production. Including the permeability jail in the heterogeneous model as described above, results in strongly reduced gas production compared to the normal relative-permeability functions. The higherpermeability rock classes, with no jail, supplies ample gas in early field life and reduces the overall cleanup effect. The long-term gas production is impacted by the permeability jail, however; a 60-70% reduction over 10 years and 70-75% reduction over 50 years of gas production. The remainder of chapter 3 focuses on a heterogeneous reservoir, and ‘permeability jail’ means a jail assigned for rock type classes according to permeability, as defined in the previous paragraph. 91 MSc. Petroleum Engineering – Thesis report - L.F. van Zelm The effect of the leakoff water on gas production is examined separately by removing the water-injection period prior to production. The improvement in gas production with leakoff water eliminated is significant during the cleanup period, for both the normal relativepermeability and capillary-pressure functions (+76%) and the permeability-jail functions (+850%). Nevertheless, the impact of the leakoff water on gas production diminishes over time and is negligible after 1 year of production. For the fracture treatment, it is advised to control leakoff or use surfactants to improve local relative permeability for it can improve the well’s potential significantly during the early production period. The heterogeneous model with a permeability jail is compared to a simulation of a heterogeneous model with additional mechanical or chemical damage, modelled as a 30 cm thick zone with permeability reduced by 99% (to 0.01 µD) along the entire face of the hydraulic fracture. Gas production is strongly impaired and shows close resemblance with the permeability jail. Water production is different between the two cases, however. With the permeability jail, the water phase is relatively mobile at high Sw, resulting in high water flow-back rates. The damaged zone impairs the fluid flow of both phases towards the fracture and therefore low water rates are observed. Thus one can distinguish between a permeability jail and chemical or mechanical damage (as modelled here) by examining water production during the cleanup period. Chapter 4 focuses on the interpretation of Pressure Buildup (PBU) tests performed on the models of chapter 3. Second, this chapter discusses the accuracy of post-fracture production analysis using a PBU test. The tests are simulated with an initial production period of 2 weeks, followed by a 1-month shut-in. The main conclusions are as follows. The PBU tests performed on unfractured homogeneous and heterogeneous reservoir models show that no radial flow is detected and no match with conventional type curves (pressure derivative, or log-log plots) is obtained. The results are therefore non-unique and inaccurate. Second, the full net-pay height is not sensed in the well test duration, and thus the reservoir height estimate is unreliable. This results in large errors for the final kH measurement. An independent second source of information is needed to confirm reservoir permeability or pressure. With a hydraulic fracture, the analysis of the models with normal relative-permeability and capillary-pressure functions, both with and without simulated leakoff water, result in good matches on the log-log plots. Although radial flow is not detected, the fit for fracture and reservoir properties is accurate. Second, heterogeneity does not result in inaccuracies, although the well-test theory assumes homogeneous reservoirs. The models with permeability jail damage show a disturbed pressure response, for both the homogeneous and heterogeneous models. The results cannot be fitted with type-curves and the obtained reservoir and fracture properties are not matching the model values; the best match incorrectly implies a very short hydraulic fracture. A fair match is obtained assuming a low-conductivity fracture instead. Without some way to distinguish between a short fracture, a fracture with internal damage, and a permeability jail, appropriate actions cannot be taken to optimize subsequent fracture treatments. 92 MSc. Petroleum Engineering – Thesis report - L.F. van Zelm Production simulations with the numerical simulator over longer periods than a well test show that short fractures, modelled in a homogeneous model for simulation convenience, impact the drainage area and a shift in decline curve to lower gas rates. Short fractures do not extend the cleanup period as does a permeability jail, and this difference allows for discrimination between a short fracture and a permeability jail. On the other hand, reduced gas production in the simulations of homogenous models with low-conductivity fractures resemble the extended cleanup observed with a permeability jail. Differences in water production, however, allow for discrimination between a fracture with damaged internal permeability and a fracture with a permeability jail. Low-conductivity fractures have impaired flow capacity for both phases, and the water production is therefore reduced along with gas. On the other hand, the permeability jail reduces gas flow much more than water. With the aid of a normalized water-gas production cross-plot, it’s possible to distinguish between the two cases. 93 MSc. Petroleum Engineering – Thesis report - L.F. van Zelm 5.2 Recommendations Some recommendations for future fracture treatment procedures and further research are presented in this section. - The permeability jail concept should be further explored. Laboratory experiments are needed to verify the presence of a permeability jail in low-permeability sandstones, e.g. by simulations of multiple drainage and imbibition cycles under ambient conditions. Hysteresis is mentioned as a possible cause for the existence of a permeability jail. - The leakoff of large volume of water should be controlled during fracture treatments in tight-gas reservoirs. The use of non-aqueous fracture fluids is a possibility. - The use of surfactants is recommended to improve the relative phase permeability in the fracture vicinity. This will increase the cleanup of the leakoff water and improve gas flow in the fracture face. - During the cleanup period of a well, following the fracture treatment, water monitoring allows for proper evaluation of back-produced water. If chemical analysis is performed on this water, it can be tested whether it’s formation or fracture treatment water. This could provide insight in the cleanup phase and the mobility of the water phase in the reservoir. Second, it can help to discriminate between types of damage, if present, as explained in this thesis. - After a treatment, fracture fluid components (e.g. gels) can break down slower than designed. When the production period is started, the fracture is then assumed to be low-conductive. Over time, nevertheless, the remaining residues can dissolve and the fracture regains it infinite conductivity. Fracture conductivity is thus not a constant factor throughout production. Simulations with fracture conductivity improvement over time can therefore be more realistic. This can be modelled, for example, by changing the transmissibility of fracture grid blocks throughout the simulation. Or a third phase can be introduced with specific properties, such as very low viscosity. It can subsequently be examined if with this model the cleanup period is different: more or less initial gas rate reduction, shorter or longer affected and water production. 94 MSc. Petroleum Engineering – Thesis report - L.F. van Zelm 6 Bibliography 6.1 Books and articles • • • • • • • • • Aguilera, R. 2008. Role of Natural Fractures and Slot Porosity on Tight Gas Sands. Paper SPE 114174 presented at SPE Unconventional Reservoirs Conference, Keystone, Colorado, 10-12 February. DOI: 10.2118/114174-MS. Al-Hussainy, R., Ramey Jr, H.J. and Crawford, P.B. 1966. The Flow of Real Gases Through Porous Media. J Pet Technol 18 (5): 624-636. SPE-1243-A-PA. DOI: 10.2118/1243-A-PA. Bang, V., Pope, G.A. and Sharma, M.M. 2008. A New Solution to Restore Productivity of Gas Wells With Condensate and Water Blocks. Paper SPE 116711 presented at SPE Annual Technical Conference and Exhibition, , Denver, Colorado, 21-24 September. DOI: 10.2118/116711-MS. Barree, R.D., Cox, S.A., Barree, V.L. and Conway, M.W. 2003. Realistic Assessment of Proppant Pack Conductivity for Material Selection. Paper SPE 84306 presented at SPE Annual Technical Conference and Exhibition, Denver, Colorado, 5-8 October. DOI: 10.2118/84306-MS. Barree, R.D., Cox, S.A., Gilbert, J.V., Dobson, M. 2003. Closing the Gap: Fracture Half-length from Design, Buildup, and Production Analysis. Paper SPE 84491 presented at SPE Annual Technical Conference and Exhibition, Denver, Colorado, 5-8 October. DOI: 10.2118/84491-MS. Barree, R.D. 2009. Unconventional reservoir stimulation, presentation, May 2009, http://barree.net/C12%20%20Damage%20and%20Water%20Block%20during%20Production.pdf (assessed 14 December 2009). Behr, A., Mtchedlishvili, G., Friedel, T. and Haefner, F. 2003. Consideration of Damaged Zone in Tight Gas Reservoir Model with Hydraulically Fractured Well. Paper SPE 82298 presented at SPE European Formation Damage Conference, The Hague, Netherlands, , 13-14 May. DOI: 10.2118/82298-MS. Bennion, D.B. and Thomas, F.B. 2005. Formation Damage Issues Impacting the Productivity of Low Permeability, Low initial Water Saturation Gas Producing Formations. Journal of Energy Resources Technology 127: 240-247. DOI: 10.1115/1.1937420. Bennion, D.B., Thomas, F.B., Bietz, R.F. 2006. Low Permeability Gas Reservoirs: Problems, Opportunities and Solutions for Drilling, Completion, Stimulation and Production. Paper SPE 35577 presented at SPE Gas Technology Symposium, Calgary, Alberta, Canada, 28 April-1 May. DOI: 10.2118/35577-MS. Bennion, D.B., Thomas, F.B., Schulmeister, B. 1996. Water and Oil Base Fluid Retention in Low Permeability Porous Media – an Update. Paper 2006-136 presented at Petroleum Society’s 7th Canadian International Petroleum Conference (57th Annual Technical Meeting), Calgary, Alberta, Canada, June 13 – 15. 95 MSc. Petroleum Engineering – Thesis report - L.F. van Zelm • • • • • • • • • • • • • Blasingame, T.A. 2008. The Characteristic Flow Behavior of Low-Permeability Reservoir Systems. Paper SPE 114168 presented at SPE Unconventional Reservoirs Conference, Keystone, Colorado, 10-12 February. DOI: 10.2118/114168-MS. Bourdet, D., Ayoub, J.A. and Pirard, Y.M. 1989. Use of Pressure Derivative in WellTest Interpretation. SPE Form Eval 4 (2): 293-302. DOI: 10.2118/12777-PA. Britt, L.K. and Schoeffler, J. 2009. The Geomechanics of a Shale Play: What Makes a Shale Prospective! Paper SPE 125525 presented at SPE Eastern Regional Meeting, Charleston, West Virginia, 23-25 September. DOI: 10.2118/125525-MS. Britt, L.K., Jones, J.R., Heidt, J.H., Adil, I., Kelly, P., Sparkes, D., and Collin, B. 2004. Application of After-Closure Analysis Techniques to Determine Permeability in Tight Formation Gas Reservoirs. Paper SPE 90865 presented at SPE Annual Technical Conference and Exhibition, Houston, Texas, 26-29 September. DOI: 10.2118/90865MS. Brooks, R.H., and Corey, A.T., 1964. Hydraulic properties of porous media. Hydr. Pap 3, Colorado State University. Byrnes, A.P. 1996. Reservoir Characteristics of Low-Permeability Sandstones in the Rocky Mountains. The Mountain Geologists 34 (1): 39-51. Byrnes, A.P., Cluff, R.M. and Webb, J.C. 2009. Analysis Of Critical Permeablity, Capillary Pressure And Electrical Properties For Mesaverde Tight Gas Sandstones From Western U.S. Basins. Final report, DE-FC26-05NT42660. Cheng, Y., Lee, W.J. and McVay D.A. 2007. A New Approach for Reliable Estimation of Hydraulic Fracture Properties in Tight Gas Wells. Paper SPE 105767 presented at SPE Hydraulic Fracturing Technology Conference, College Station, Texas, 29-31 January. DOI: 10.2118/105767-MS. Cinco-Ley, H., Samaniego, V.F., Dominguez, A.N. 1978. Transient Pressure Behavior for a Well With a Finite-Conductivity Vertical Fracture. SPE J 18 (4): 253-264. SPE6014-PA. DOI: 10.2118/6014-PA. Cipolla, C.L., Mayerhofer, M. 1998. Understanding Fracture Performance by Integrating Well Testing & Fracture Modeling. Paper SPE 49044 presented at SPE Annual Technical Conference and Exhibition, New Orleans, Louisiana, 27-30 September. DOI: 10.2118/49044-MS. Claverie, M. and Hansen, S.M. 2009. Mineralogy, Fracture and Textural Analysis for Formation Evaluation in Tight Gas Reservoirs. Paper IPTC 13832 presented at International Petroleum Technology Conference,Doha, Qatar, , 7-9 December. DOI: 10.2523/13832-MS. Cluff, R.M. and Byrnes, A.P. 2010. Relative permeability in tight gas sandstyone reservoirs – the permeability jail model. Paper presented at PWLA 51st Annual Logging Symposium, Perth, Australia, 19-23 June. Cramer, D.D. 2004. Analyzing Well Performance in Hydraulically Fractured Gas Wells: Non-Ideal Cases. Paper SPE 90777 presented at the SPE Annual Technical Conference and Exhibition, Houston, Texas, 26-29 September. DOI: 10.2118/90777MS. 96 MSc. Petroleum Engineering – Thesis report - L.F. van Zelm • • • • • • • • • • • • • • • Cramer, D.D. 2005. Fracture Skin: A Primary Cause of Stimulation Ineffectiveness in Gas Wells. Paper SPE 96869 presented at SPE Annual Technical Conference and Exhibition, Dallas, Texas, 9-12 October. DOI: 10.2118/96869-MS. Crockett, A.R., Okusu, N.M. and Cleary, M.P. 1986. A Complete Integrated Model for Design and Real-Time Analysis of Hydraulic Fracturing Operations. Paper SPE 15069 presented at SPE California Regional Meeting, Oakland, California, 2-4 April. DOI: 10.2118/15069-MS. Dake, L.P. 1978. Fundamentals of Reservoir Engineering. Amsterdam: Elsevier. Daneshy, A. A. 2010. Why care about treatment fluid recovery?. E&P Magazine 2010 (6). Deutsch, C.V. and Journel, A.G.1998. GSLIB: Geostatistical Software Library and User's Guide (Applied Geostatistics Series), second edition. New York: Oxford University Press. Economides, M.J. and Nolte, K.G. 2000. Reservoir Stimulation, 3rd edition. Chichester: John Wiley and Sons. Ehrl, E. and Schueler, S.K. 2000. Simulation of a Tight Gas Reservoir with Horizontal Multifractured Wells. Paper SPE 65108 presented at SPE European Petroleum Conference, Paris, France, 24-25 October. DOI: 10.2118/65108-MS. Friedel, T. 2004. Numerical Simulation of Production from Tight-Gas Reservoirs by Advanced Stimulation Technologies. PhD dissertation, TU Bergakademie Freiberg, Freiberg, Germany. Garcia, J.P., Pooladi-Darvish, M., Brunner, F., Santo, M. and Mattar, M. 2006. Well Testing of Tight Gas Reservoirs. Paper SPE 100576 presented at SPE Gas Technology Symposium, Calgary, Alberta, Canada, 15-17 May. DOI: 10.2118/100576-MS. Gatens, J.M., Lee, W.J., Hopkins, C.W. and Lancaster, D.E. 1991. The Effect of Permeability Anisotropy on the Evaluation and Design of Hydraulic Fracture Treatments and Well Performance. Paper SPE 21501 presented at SPE Gas Technology Symposium, Houston, Texas, 22-24 January. DOi: 10.2118/21501-MS. Gaupp, R., Liermann, N. and Pusch, G. 2005. Adding Value through Integrated Research to Unlock the Tight Gas Potential in the Rotliegendes Formation of Northern Germany. Paper SPE 94354 presented at SPE Europec/EAGE Annual Conference, Madrid, Spain, 13-16 June. DOI: 10.2118/94354-MS. Gdanski, R. 2007. Modeling the Impact of Capillary Pressure Reduction by Surfactants. Paper SPE 106062 presented at International Symposium on Oilfield Chemistry, Houston, Texas, 28 February-2 March. DOI: 10.2118/106062-MS. Gdanski, R. Fulton, D. and Shen, C. 2006. Fracture face skin evolution during cleanup. Paper SPE 101083 presented at 2006 SPE Annual Technical Conference and Exibition, San Antonio, Texas, September 24-27. DOI: 10.2118/101083-MS. Gdanski, R. and Walters, H. 2010. Impact of fracture conductivity and matrix relative permeability on load recovery. Paper SPE 133057 presented at SPE Annual Technical Conference and Exhibition, Florence, Italy, 19-22 September. DOI: 10.2118/133057MS. Gdanski, R., Weaver, J., Slabaugh, B., Walters, H. and Parker, M. 2005. Fracture Face Damage—It Matters. Paper SPE 94649 presented at SPE European Formation 97 MSc. Petroleum Engineering – Thesis report - L.F. van Zelm • • • • • • • • • • • • • • • • Damage Conference, Sheveningen, The Netherlands, 25-27 May. DOI: 10.2118/94649-MS. Gringarten, A.C. 2006. From Straight Lines to Deconvolution: The Evolution of the State of the Art in Well Test Analysis. Paper SPE 102079 presented at SPE Annual Technical Conference and Exhibition, San Antonio, Texas, 24-27 September. DOI: 10.2118/102079-MS. Gringarten, A.C., Ramey Jr, H.J. and Raghavan, R. 1974. Unsteady-State Pressure Distributions Created by a Well With a Single Infinite-Conductivity Vertical Fracture. SPE J 14 (4): 347-360. SPE-4051-PA. DOI: 10.2118/4051-PA. Hagoort, J. 1988. Fundamentals of Gas Reservoir Engineering. Amsterdam: Elsevier. Holditch, S.A. 1979. Factors Affecting Water Blocking and Gas Flow From Hydraulically Fractured Gas Wells. J Pet Technol 31 (12): 1515-1524. SPE-7561-PA. DOI: 10.2118/7561-PA. Holditch, S.A. 2006. Tight Gas Sands. J Pet Technol 58 (6): 86-93. SPE-103356-MS. DOI: 10.2118/103356-MS. Holditch, S.A. and Morse, R.A. 1976. The Effects of Non-Darcy Flow on the Behavior of Hydraulically Fractured Gas Wells. J Pet Technol 28 (10): 1169-1179. SPE-5586-PA. DOI: 10.2118/5586-PA. Horne, R.N. 1995. Modern Well Test Analysis: A Computer-Aided Approach. Palo Alto, California: Petroway. Huang, D.D. and Honarpour, M.M. 1996. Capillary End Effects in Coreflood Calculations. Paper 9634 presented at 1996 International Symposium of the Society of Core Analysts, Montpellier, France, September 8-10. Jennings Jr, H.Y. and Newman, G.H. 1971. The effect of temperature and pressure on the interfacial tension of water against methane-normal decane mixtures. SPE J 11 (2): 171-175. DOI: 10.2118/3071-PA. Jones, F.O. and Owens, W.W. 1980. A Laboratory Study of Low-Permeability Gas Sands. J Pet Technol 32 (9): 1631-1640. SPE- 7551-PA. DOI: 10.2118/7551-PA. Killough, J.E. 1976. Reservoir Simulation With History-Dependent Saturation Functions. Soc Pet Eng AIME J 16 (1): 37-48. Lake, L. and M.P. Walsh. 2004. Primary Hydrocarbon Recovery. Amsterdam: Elsevier. Leverett, M.C. 1941. Capillary Behavior in Porous Solids. Petr Trans AIME 142: 152169. SPE 941152-G. Lolon, E.P., McVay, D.A. and Schubarth, S.K. 2003. Effect of Fracture Conductivity on Effective Fracture Length. Paper SPE 84311 presented at SPE Annual Technical Conference and Exhibition, Denver, Colorado, 5-8 October. DOI: 10.2118/84311-MS. Mahadevan, J. and Sharma, M.M. 2003. Cleanup of Water Blocks in Low Permeability Formations. Paper SPE 84216 presented at SPE Annual Technical Conference and Exhibition, Denver, Colorado, 5-8 October. DOI: 10.2118/84216-MS. Mahadevan, J., Duc, L. and Hoang, H. 2009. Impact of Capillary Suction on Fracture Face Skin Evolution in Waterblocked Wells. Paper SPE 119585 presented at SPE Hydraulic Fracturing Technology Conference, The Woodlands, Texas, 19-21 January. DOI: 10.2118/119585-MS. 98 MSc. Petroleum Engineering – Thesis report - L.F. van Zelm • • • • • • • • • • • • Mohan, J., Pope, G.A. and Sharma, M.M. 2006. Effect of Non-Darcy Flow on Well Productivity in a Hydraulically Fractured Gas/Condensate Well. Paper SPE 103025 presented at SPE Annual Technical Conference and Exhibition, San Antonio, Texas, USA, 24-27 September. DOI: 103025-MS Montgomery, K.T., Holditch, S.A.; Berthelot, J.M. 1990. Effects of Fracture Fluid Invasion on Cleanup Behavior and Pressure Buildup Analysis. Paper SPE 20643 presented at SPE Annual Technical Conference and Exhibition, New Orleans, Louisiana, 23-26 September. DOI: 10.2118/20643-MS. Parekh, B. and Sharma, M.M. 2004. Cleanup of Water Blocks in Depleted LowPermeability Reservoirs. Paper SPE 89837 presented at SPE Annual Technical Conference and Exhibition, Houston, Texas,26-29 September. DOI: 10.2118/89837MS. Penny, G., Pursley, J.T. and Holcomb, D. 2005. The Application of Micro-emulsion Additives in Drilling and Stimulation Results in Enhanced Gas Production. Paper SPE 94274 presented at SPE Production Operations Symposium, Oklahoma City, Oklahoma, 16-19 April. DOI: 10.2118/94274-MS. Penny, G.S., Pursley, J.T. and Clawson, T.D. 2006. Field Study of Completion Fluids To Enhance Gas Production in the Barnett Shale. Paper SPE 100434 presented at SPE Gas Technology Symposium, Calgary, Alberta, Canada, 15-17 May. DOI: 10.2118/100434-MS. Prats, M. 1961. Effect of Vertical Fractures on Reservoir Behaviour - Incompressible Fluid Case. SPE J 1 (2): 105-118. SPE-1575-G. DOI: 10.2118/1575-G. Purcell, W.R. 1949. Capillary Pressures - Their Measurement Using Mercury and the Calculation of Permeability Therefrom. Petr Trans AIME 186: 39-48. SPE 949039-G. Rickman, R.D. and Jaripatke, O. 2010. Optimizing Micro-emulsion/Surfactant Packages for Shale and Tight-Gas Reservoirs. Paper SPE 1131107 presented at SPE Deep Gas Conference and Exhibition, Manama, Bahrain, 24-26 January. DOI: 10.2118/131107-MS. Rushing, J.A., Newsham, K.E. and Blasingame, T.A. 2008. Rock Typing-Keys to Understanding Productivity in Tight Gas Sands. Paper SPE 114164 presented at SPE Unconventional Reservoirs Conference, Keystone, Colorado, 10-12 February. DOI: 10.2118/114164-MS. Settari, A., Sullivan, R.B. and Bachman, R.C. 2002. The Modelling of the Effect of Water Blockage and Geomechanics in Waterfracs. Paper SPE 77600 presented at SPE Annual Technical Conference and Exhibition, San Antonio, Texas, 29 September-2 October. DOI: 10.2118/77600-MS. Shanley, K.W., Cluff, R.M. and Robinson, J.W. 2004. Factors controlling prolific gas production from low-permeability sandstone reservoirs: Implications for resource assessment, prospect development, and risk analysis. AAPG Bulletin 88 (8): 10831121. DOI: 10.1306/03250403051. Shaoul, J.R., Behr, A. and Mtchedlishvili, G. 2006. Automatic generation of 3D reservoir simulation input files directly from a fracture simulation model. OIL and GAS European Magazine 4: 176-182. SPE 99 MSc. Petroleum Engineering – Thesis report - L.F. van Zelm • • • • • • • • • Shaoul, J.R., De Koning, J., Chapuis, C. and Rochon, J. 2009. Successful Modelling of Post-Fracture Cleanup in a Layered Tight Gas Reservoir. Paper SPE 122021 presented at 8th European Formation Damage Conference, Scheveningen, The Netherlands, 27-29 May. DOI: 10.2118/122021-MS. Soliman, M.Y. and Hunt, J.L. 1985. Effect of Fracturing Fluid and Its Cleanup on Well Performance. Paper SPE 14514 presented at SPE Eastern Regional Meeting, Morgantown, West Virginia, 6-8 November. DOI: 10.2118/14514-MS. Spencer, C.H. 1985. Geologic Aspects of Tight Gas Reservoirs in the Rocky Mountain Region. J Pet Technol 37 (7): 1308-1314. SPE-11647-PA. DOI: 10.2118/11647-PA. Spencer, C.W. 1985. Geologic Aspects of Tight Gas Reservoirs in the Rocky Mountain Region. J Pet Technol 37 (7): 1308-1314. SPE-11647-PA. DOI: 10.2118/11647-PA. Von Schroeter, T., Hollaender F. and Gringarten, A.C. 2001. Deconvolution of Well Test Data as a Nonlinear Total Least Squares Problem. Paper SPE 71574 presented at SPE Annual Technical Conference and Exhibition, New Orleans, Louisiana, 30 September-3 October. DOI: 10.2118/71574-MS. Voneiff, G.W., Robinson, B.M. and Holditch, S.A. 1996. The Effects of Unbroken Fracture Fluid on Gaswell Performance. SPE Proj & Fac 11(4): 223-229. SPE-26664PA. DOI: 10.2118/26664-PA. Wang, J., Holditch, S.A., McVay, D. 2009. Modelling Fracture Fluid Cleanup in Tight Gas Wells. Paper SPE 119624 presented at SPE Hydraulic Fracturing Technology Conference, The Woodlands, Texas, 19-21 January. DOI: 119624-MS. Wattenbarger, R.A. and Ramey Jr., H.J. 1969. Well Test Interpretation of Vertically Fractured Gas Wells. J Pet Technol 21 (5): 625-632. SPE-2155-PA. DOI: 10.2118/2155PA. Wills, H.A. 2009. 3D Numerical Investigation of hydraulic fracture cleanup processes. PhD dissertation, Colorado School of Mines, Golden, Colorado, USA. 6.2 Software and internet • • • • • • BJ Services. VaporFrac, http://www.bjservices.com/website/index.nsf/WebPages/Shale-Papers-ExpandableSection/$FILE/VaporFrac%20Stimulation%20Services.pdf (accessed 12 September 2010.) CarboCeramics. Carbo-Prop, http://www.carboceramics.com/CARBO-PROP/ (assessed 9 September 2010). Eclipse 100, 2009. Houston, Texas: Schlumberger Information Solutions. Ecole Centrale de Lille. PhD Proposal 2010, http://csc-centrale.eclyon.fr/sujets/PhD_Proposal_CSC2010_ECLille_LML_Skoczylas.pdf (assessed 14 July 2010). FracproPT, 2007. Houston: Carbo Ceramics - GTI. Halliburton. MISCO2 Frac, http://www.halliburton.com/ps/default.aspx?pageid=475&navid=104&prodid=PRN: :IQTUARO62 (accessed 12 September 2010.) 100 MSc. Petroleum Engineering – Thesis report - L.F. van Zelm • • • • • Petrel, 2009. Houston, Texas: Schlumberger Information Solutions. Saphir, 2009. Paris, France: Kappa Engineering. Schlumberger. ThermaFOAM CO2, http://www.slb.com/services/stimulation/tight_gas_stimulation/thermafoam.aspx (accessed 12 September 2010.) University of Utah, Utah Geological Survey, Golder and Associates and Itasca. Inc. Research proposal, http://geology.utah.gov/emp/tightgas/pdf/tightgas_soa.pdf (assessed 14 July, 2010). WaveMetrics. Image Interpolation software, http://www.wavemetrics.com/products/igorpro/imageprocessing/imagetransforms /imageinterpolation.htm, (assessed 18 October, 2010). 101 MSc. Petroleum Engineering – Thesis report - L.F. van Zelm 7 Nomenclature Symbol A B C H J k L m(p) P p/q PV Q q R s t T u w W x ϴ σ φ ρ µ λ Unit Description m2 m m2 m Pa Pa m3 m3/s m S m2/m m/s m m m ° N/m kg/m3 Pa.s m2/Pa.s Cross section area Formation volume factor Conductivity Height / thickness Leverett J-function Permeability Length model (x-direction) Pseudo-pressure Pressure Corey coefficients Pore volume Volumetric flow rate Corey coefficient Radius Skin Time Transmissibility Volumetric velocity Fracture Width Width model (y-direction) Distance Contact angle Interfacial tension Porosity Density Viscosity Mobility Subscript Description bh c D f g gc irr lab nw R r res tot w wc α Bottomhole Capillary Dimensionless Fracture Gas Critical gas Irreducible Laboratory Non-wetting Reservoir Relative Reservoir Total Water / wetting Connate water Phase α 102 MSc. Petroleum Engineering – Thesis report - L.F. van Zelm 8 Appendix - Flow calculations in simulator Eclipse (Schlumberger 2009) uses by default a fully implicit method to calculate the changes in pressure and saturation over time. Implicit calculation of properties takes the state of the property into consideration at both the current time and the next time step. The method is therefore relatively stable, but can be time-consuming. The equations used by Eclipse (Schlumberger 2009) are explained briefly in this appendix. The starting equation is the mass balance equation solved for pressure and saturation implicitly. In Eclipse (Schlumberger 2009), the solution vector is referred to as X, the residual vector as R and the Jacobian J. Here X is defined as:  Po    X = Sw  Sg    Eq. 8-1 Next comes solution for oil pressure Po and the saturations for water and gas. For this research, the primary parameter is not of use. The residual vector looks like:  Ro    R =  Rw   Rg    Eq. 8-2 Each of these non-linear residuals is examined separately, by the following equation: R fl = dM t + F ( Pt , St ) + Q( Pt , St ) dt Eq. 8-3 With Rfl dM F Q = non-linear residual, for each cell and each fluid = mass, per unit surface density, accumulated during time step dt = net flow rate into neighbouring grid blocks = net flow rate into wells during the time step The Jacobian is calculated by taking the derivative of the R to X, thereby creating a matrix where the residuals are evaluated for all saturations and pressures. The goal of the numerical method is to approach R = 0, by taking ‘small enough time steps’ throughout the simulation. This can be accomplished by reducing the error in the mass balance solution and the maximum saturation normalized residual, which is related to the change in saturation per grid cell. In order to solve for the mass balance implicitly, the following equations for a gas-water system are used (Eq. 8-4 and Eq. 8-5). 103 MSc. Petroleum Engineering – Thesis report - L.F. van Zelm dM = M t + dt − M t Eq. 8-4  Sw  B  w M = PV *    Sg     Bg  Eq. 8-5 With M t dt PV Bw Bg = mass or volume of cell = time = time change (time step) = cell pore volume = water formation volume factor = gas formation volume factor For the calculation of the flow, not only the time step is important, but also the location of the grid blocks and in which direction the equation is solved using down- or upstream weighing. The flow rate F into cell i from neighbouring cell n is calculated by the following equation:  kro   Bo µo  Fni = Tni  0    Rs kro  Bo µo  0 krw Bw µ w 0 Rv krg   Bg µ g      dPoni  0  *  dPwni    dPgni  krg   Bg µ g  U Eq. 8-6 For the system under review in this thesis, the equation will simply be reduced to:   0  Fni = Tni  0   0   0 krw Bw µ w 0   0      dPoni  0  *  dPwni    dPgni  krg   Bg µ g  U Eq. 8-7 where Fni Tni dPαni = flow rate from cell n into cell i = transmissibility between cell n and cell i = phase α potential difference between the cells The transmissibility term is a function of pressure and the fluid properties. Furthermore, the subscript U in the formula stands for upstream weighing, which refers to the numerical calculation method used in Eclipse (Schlumberger 2009). When dP is positive, the phase flow occurs from cell n to into cell i the fluid properties in cell n are used for the flow calculations. This is important in some of the simulations of this thesis. As mentioned, the pressure is evaluated in both cells, and its differential determines the flow directions. Finally, the total flow rate is calculated by the summation of the individual cells in each direction. 104 MSc. Petroleum Engineering – Thesis report - L.F. van Zelm 9 Appendix - Modelling hysteresis effect Injection of liquid into a gas reservoir introduces the possibility of relative permeability hysteresis to occur after the fluid invasion has taken place. Hysteresis is the process that determines the relative permeability of a certain path as a function of the saturation path and history. Basically, as a porous medium experiences a change in saturation (e.g. by water imbibition due to injection), the reverse process will not follow the same relative permeability curves. There has been much discussion on the effect on hysteresis and its impact on the post-fracture gas production. In section 2.3.2 it is explained as a possible cause for the existence of a ‘permeability jail’. The exact origin of this effect is not part of the problem statement of this thesis and is not discussed. Furthermore, in post-fracture production analysis (Friedel 2004), the hysteresis of the relative permeabilities is not taken into consideration. This section discusses the differences in the results for the cleanup period and long-term production when hysteresis is considered. The reservoir simulator Eclipse allows one to simulate the hysteresis effect using the model of Killough (1976). This model allows the input of multiple relative permeability curves to describe imbibition and drainage processes. The imbibition curves for the gas relative permeability and the capillary pressure are presented in Fig. 9-1 and Fig. 9-2. The drainage curves are the relative permeability and capillary pressure curves used in the base case in the thesis, as shown in section 3.1.1 (Fig. 3-3 and Fig. 3-4). Fig. 9-1 The drainage and imbibition curves Fig. 9-2 The drainage and imbibition curves for the gas relative permeability used in the for the capillary pressure used in the hysteresis model. hysteresis model. During water injection, Sw increases in grid blocks close to the fracture blocks, and the capillary pressure and relative permeability are now determined by the imbibition curves. This continues until the maximum Sw is reached in the grid block. When the flow direction is reversed upon opening of the well, the water saturation will start to decrease in each of the grid blocks and gas starts to flow. This is a drainage process and thus requires the drainage curves as presented in Fig. 9-1 and Fig. 9-2. The Killough model creates an interpolated curve between the imbibition and the drainage curve starting at the current value of Sw decreasing to the residual gas saturation. This method, therefore, uses a slightly different gas relative permeability during production than the input drainage curve. This provides an additional complexity to the permeability that is assigned to the gas phase at a specific Sw. For this thesis, it’s chosen not to thoroughly investigate this complexity and the possibilities of this method. 105 MSc. Petroleum Engineering – Thesis report - L.F. van Zelm The gas production profile with and without hysteresis is shown in Fig. 9-3. The cleanup phase reflected in the initial gas rate reduction is much more apparent with hysteresis. Only after some 15 days of production does the gas rate catch up with the case excluding the hysteresis effect. As can be interpreted from Fig. 9-1, the new interpolated permeability curve is always below the initial drainage curve, and thus providing less permeability to the gas phase. In both models the water phase is in exponential decline from the beginning of the field life, where initially rates up to 30 m3 per day are reached. With hysteresis, a total of 50 m3 is recovered after approximately 1 year, at which point the water rate is almost zero. For injection without hysteresis, slightly less water is produced, 44 m3 after 1 year. The injected volume is 61 m3, so not all fluid is produced back. The difference in fluid recovery is related to the capillary pressures in the two models, which shows an average lower capillary pressure when hysteresis is modelled. Lower capillary allows more water to be produced back into the fracture. If more water is produced and water saturation near the fracture falls, the gas also becomes more mobile. The slightly increased gas rate at longer times (20+ days) as seen in Fig. 9-3 can be possibly explained by this. In conclusion, there are some differences in the two models, but both predict a cleanup effect and similar gas rates. Because of the complexity in the relative permeability and capillary pressure functions used in the hysteresis model, we do not use the hysteresis model in this thesis. Further and more thorough investigation is needed in the possibilities to use hysteresis in the model. Fig. 9-3 Production profile after water injection showing the gas and water rates. Two models are presented: with and without hysteresis. 106 MSc. Petroleum Engineering – Thesis report - L.F. van Zelm 10 Appendix – Equilibrium Sw profile: a spreadsheet calculation In order to compare the saturation profiles shown in the simulations of section 3.2 to capillary equilibrium, a spreadsheet calculation has been performed. This calculation provides insight in the relation between the capillary pressure and water distribution in the reservoir near a hydraulic fracture. References to rock types and capillary pressure regimes in the model in this appendix are similar to those outlined in section 3.2. The spreadsheet is a 1D – model, from the fracture on the left side at x = 0.5 m, extending into the reservoir. The gas flow is controlled by Darcy’s Law under the assumption that water is immobile (i.e., at capillary equilibrium), and thus the pressure gradient in the gas phase is equal to the capillary-pressure gradient. This allows the capillary pressure to be calculated as follows: ∆Pc ( S w ) = µ g ug kkrg ( S w ) ∆x Eq. 10-1 with ug ∆x = gas superficial velocity = calculation steps Important considerations include the following: - the calculation assumes static equilibrium solution, not dynamic behaviour as is seen in the simulations. - water flow occurs in the simulations: water can produced or imbibe further into the reservoir. - the total amount of water given by Eq. 10-1 may not correspond to the actual volume of water invading the formation. The input data for the flow calculations are taken from the simulations in section 3.2 in order to represent as closely as possible the saturation profile from the simulation models. Darcy’s Law requires specification of reservoir permeability, gas viscosity and the gas superficial velocity. Furthermore, the calculation requires gas relative permeability and capillary pressure as functions of water saturation relations. The capillary pressure regimes (low and high) are the same as the two scenarios presented in Fig. 3-10 as the base case and high scenarios. The relative permeability curves are the same as in the base case (Fig. 3-3). Finally, water saturation at the fracture face (x = 0.5 m) is set at Sw = 0.699, representing nearly zero capillary pressure, as required if water flows back into the fracture. The additional parameters in Eq. 10-1 are the gas superficial velocity and the distance increment ∆x. 107 MSc. Petroleum Engineering – Thesis report - L.F. van Zelm Fig. 10-1 Water saturation profile along the fracture face into the reservoir – poor reservoir rock with high capillary pressures Fig. 10-2 Water saturation profile along the fracture face into the reservoir – medium reservoir rock with low capillary pressures Fig. 10-1 and Fig. 10-2 show the saturation profiles near the fracture face for both models. The results shown are calculated with an average gas velocity of 5 m3/day or 3.6 x 10-5 m/s which is a good reference velocity for the early production period. A very small step size ∆x is needed to calculate a smooth profile, especially for the low permeability rock model; I use a step ∆x of 1.0 x 10-9, increasing to 1.0 x 10-4 in approximately 100 steps. The mediumpermeability rock model has an initial step ∆x of 1.0 x 10-7 at the rock face, increasing to 1.0 x 10-4 further from the fracture. The low capillary pressure profile (Fig. 10-2) extends further into the reservoir, which is a result of lower pressure gradient in this case, with higher absolute permeability. This is contrary to what Friedel (2004) shows (Fig. 3-16), where the higher permeability (lower Pc) scenario has a small zone of water invasion during production. This is also seen in the simulation results in Fig. 3-19 to Fig. 3-22. The profiles do match the simulation results in the early production, because the initial amount of water is not the same. Furthermore, the high capillary pressure in the poor reservoir rock model drains water out of the fracture, whereby a large inflow of water is created into the reservoir and thus more invasion into the reservoir. It can therefore be stated the 1D approach with a simple spreadsheet calculation predicts a saturation profile based on assumptions of capillary equilibrium in the water phase, zero capillary pressure at the fracture face, and a fixed gas superficial velocity toward the fracture. These assumptions used do not allow simple comparison with the simulations in Eclipse (Schlumberger 2009). At a point in the simulation when injected water is produced, the condition of zero Pc applies, and the model may predict a correct saturation profile if the water in the formation is close to capillary equilibrium. 108 MSc. Petroleum Engineering – Thesis report - L.F. van Zelm Finally, Fig. 10-3 and Fig. 10-4 show the possible impact of the large predicted increase in water saturation, taken from the 1D flow spreadsheet exercise. The gas relative permeability (Fig. 10-3) and its inverse (Fig. 10-4) are plotted over the same distance as the saturation profile for the medium-permeability formation. Close to the fracture the resistance to gas flow is steeply increases, which is caused by the capillary end effect. The additional resistance for gas flow can be approximated by taking the integral of the resistance to gas flow with position close the fracture. The logarithmic scale of Fig. 10-4 may under-represent this resistance, which increases the resistance over a zone of 10 cm wide by more than a factor of 250. Nevertheless, results in section 3.2.2 shows that the gas flow in only slightly impaired and not completely blocked by this additional resistance. Second, the transmissibility is only affected over a short distance. Fig. 10-3 Plot of gas relative permeability as calculated from 1D Darcy’s Law in a medium- permeability rock. Fig. 10-4 Plot of resistance to flow (inverse of krg) as calculated from 1D Darcy’s Law in a medium-permeability rock. 109 MSc. Petroleum Engineering – Thesis report - L.F. van Zelm 11 Appendix - Hydraulic Fracture Design and Simulation The hydraulic fracture is designed and analyzed in FracproPT (Carbo Ceramics 2007), a software tool for hydraulic fracture treatments. The software uses a simplified 2D reservoir model and treatment details such as total proppant and fluid used, as input for calculation of the fracture dimensions. The calculation of the fracture in FracproPT (Carbo Ceramics 2007) is based on literature (Crocket et al. 1986) and is governed by volume of fluid, rate and pressure of injection, the leakoff to the formation and the properties of the rock. The latter two are defined as defaults in the fracturing software for the rock types used. FracproPT (Carbo Ceramics 2007) has an option to convert the 2D fracture model into 3D simulator input files (Behr et al. 2003). These files can then be loaded into the dynamic reservoir model in Eclipse (Schlumberger 2009) and used for reservoir modelling and production forecasting. The following table (Table 11-1) provides more detail on the lithology and a selection of the reservoir rock properties used in the calculations. The yellow highlighted zone is the net-pay reservoir layer. Top of Stress Young's Stress Poisson's Permeability Layer # Lithology zone Gradient modulus (bar) ratio (mD) (m (bar/m) (bar) 1 Shale 2700 458.1 0.1697 4.1x105 0.25 1x10-8 5 2 Shale 2750 469.9 0.1697 4.1x10 0.25 1x10-8 3 Shale 2790 474.2 0.1697 4.1x105 0.25 1x10-8 5 4 Sandstone 2800 399.7 0.1402 3.4x10 0.20 1x10-3 5 5 Shale 2900 492.8 0.1697 4.1x10 0.25 1x10-8 5 6 Shale 2910 495.8 0.1697 4.1x10 0.25 1x10-8 Table 11-1 Layer properties in the reservoir, used for the design of the hydraulic fracture. Layer 4 in yellow is the main target layer of the reservoir, with a height of 100 meters. The resulting dimensions and the total fluid and proppant are listed in section 3.1.2 (Table 3-3). A total of 244 m3 fluid is pumped, including the pad, slurry and final flush. The pad is the initial volume of fluid (here 50 m3) without proppant injected to create width and length in the fracture (Economides and Nolte 2000). Next in the treatment is the slurry, which carriers the proppant into the fracture and is the part of the treatment that last the longest and uses most fluid (182 m3). The slurry can contain a gel and is used for transport of the proppant through the wellbore into the hydraulic fracture, where its high viscosity should help place all the proppant evenly throughout the fracture. The decision on the density of the slurry is crucial for the execution of the hydraulic fracture treatment (Economides and Nolte 2000). Finally, the flush is used to clean the wellbore of any remaining proppant. Fig. 11-1 shows a side view of the fracture in FracproPT (Carbo Ceramics 2007), including the width and proppant concentration after complete closure. Note that the vertical and horizontal scales are not matching; the fracture is actually almost round. 110 MSc. Petroleum Engineering – Thesis report - L.F. van Zelm Width Profile (cm) TVD(m) 1 0 Fracture Conductivity (mD·m) 1 25 50 75 2800 Layer Properties 100 125 150 Fracture Length (m) 131.4 Propped Length (m) 116.6 Total Fracture Height (m) 118.5 Total Propped Height (m) 105.2 Fracture Top Depth (m) 2787.5 Fracture Bottom Depth (m) 2906.0 Average Fracture Width (cm) 0.247 Dimensionless Conductivity 2444.521 Rocktype Stress (b... 450 700 Permeabi... TVD(m) Shale Sandstone 2850 2800 2850 2900 Shale 2900 Fracture Conductivity (mD·m) 0 54 108 162 216 270 324 378 432 486 540 Fig. 11-1 Side view of propped hydraulic fracture, as presented after the treatment design in FracproPT (Carbo Ceramics 2007). Finally, to model the flow permeability function. The laboratory tests by Barree provides high performance Ceramics. in the fracture properly, the simulator requires a relativefollowing figure (Fig. 11-2) shows the curves taken from et al. (2003a) for CarboProp 20/40 mesh proppant, which in low- to moderate-permeability wells, according to Carbo Finally, in the hydraulic fracture, near-zero capillary pressure is assumed for to the high permeability of the proppant pack. Fig. 11-2 Relative permeabilities for the hydraulic fracture in the model (Barree et al. 2004). 111 MSc. Petroleum Engineering – Thesis report - L.F. van Zelm 12 Appendix - Grid refinement options This appendix describes the tests that were conducted to select the grid option, and includes a general discussion of the two grid options. Two approaches for refining a grid are common in reservoir simulations; a refinement of a part of the reservoir host grid and a so-called Local Grid Refinement (LGR), whereby a second and more refined grid is placed inside the host grid around the hydraulic fracture. The first option requires a grid refinement in the near-fracture area to be created separately in the reservoir simulator and the properties for the hydraulic fracture need to be updated accordingly (Ehrl and Schueler 2000). This is nevertheless a time-consuming task and often results in the assumption of constant properties to speed up the model preparation (Shaoul et al. 2006). The second option is to create a built-in additional grid, a LGR, which contains the hydraulic fracture including detailed property description and a fluid distribution in the reservoir (Behr et al. 2003). The output of the hydraulic fracture simulator used in this thesis (Carbo Ceramics 2007), produces its output in the LGR format which can be used by many commercial simulators. This method has one major advantage, especially in large reservoir simulations, where it can refine a smaller part of the model instead of refinements in the complete model over a specific direction. This is best illustrated in Fig. 12-1 and Fig. 12-2, where the host grid refinement stretches out through the complete reservoir. Fig. 12-1 LGR model refinement model. Fig. 12-2 Host grid refinement. Two simulations were run to test the speed and accuracy of the two grids, introducing more complexity in each simulation. First, a single-phase run was simulated; the model contains only gas. Second, the water phase was introduced by an initial water saturation (Sw = 0.4) and a water relative permeability function (Fig. 3-3). This option does not take into account the leakoff as a result of the fracturing process. This issue is dealt with separately in section 3.1.3. 112 MSc. Petroleum Engineering – Thesis report - L.F. van Zelm For proper modelling of multiphase flow, the well connections opened for flow need to be reduced in order to control the water flow into the wellbore. The modelling software is not capable of simulating the independent inflow of water into the wellbore at multiple locations. Probably the cause is to be found in the low flow velocities in the well. The water probably flows downward within the wellbore and reappears in grid blocks lower in the well. The symptom is that the wellbore equations are not solved within an acceptable amount of iterations. The simulation performance is tested by looking at the total amount of grid blocks in the model, the total simulation time and cumulative production for 1 year. For clarity, the refinement of the two models near the fracture is the same, only the host grid refinement extends the refinement further out into the model (Fig. 12-2). Table 12-1 provides an overview of the results, where the gas production is normalized at 100 for the single-phase LGR run. Together with Fig. 12-3 and Fig. 12-4, it reveals that for the prediction of total volumes and rates, there’s no significant difference between the two refinement options. The difference in cumulative production between the local grid refinement is small and the host grid refinement is both the single phase and multiphase scenario. Simulation method Local Grid Host grid (full field results) Refinement (LGR) refinement Total amount of grid blocks 18,064 21,120 Single phase Simulation time (s) 101 61 Normalized cum. gas production 100 100.08 Multi phase Simulation time (s) 164 (+62%) 86 (+40%) Normalized cum. gas production 33.20 33.23 Normalized cum. water production 100 100 Table 12-1 Overview of grid sensitivity study performed on two grid model options frequently used in the post-fracture production analysis of low-permeable reservoirs. The gas production is normalized at 100 for the single-phase LGR run. There is, however, a difference in the simulation time required to obtain the results. The LGR option has fewer grid blocks, but it takes more time to run the simulation. The reduction in calculation speed might be related to matching the boundary conditions of both grids throughout the simulation. Additional time required to perform the simulation also applies with two phases present, where the LGR has to update the boundary conditions of the two grids with the more complicated two-phase pressure and flow equations. For modelling production in hydraulically fractured wells, both models are accurate and show no difference in both water and gas production. There is however, a difference in total simulation time, whereby the LGR is slower. 113 MSc. Petroleum Engineering – Thesis report - L.F. van Zelm Fig. 12-3 Production profile single phase, comparison per grid option (¼ symmetry model rates). Here the Red line lies underneath green line. Fig. 12-4 Cumulative production multi phase, comparison per grid option (¼ symmetry model volumes). Here the green line lies underneath the red line. 114 MSc. Petroleum Engineering – Thesis report - L.F. van Zelm 13 Appendix - Reservoir model test runs A single-phase run is used to test the model. The reservoir contains only gas and no reservoir water is present. Furthermore, no permeability damage or fluid invasion is present. The rest of the model, e.g. grid dimension, well, fracture and gas properties, are the same as in the base case model described in section 3.1. To analyze the outcome of the simulations I compare it to the analytical solution calculated from Eq. 13-1. This equation uses reservoir and fluid properties as input (Table 13-1). The effective wellbore radius is calculated with the relation of Prats (1961) because the hydraulic fracture is assumed infinitely conductive (Eq. 2-5). This results in rw’ = 60 meters, which is half of the fracture half-length. q= 2π kh(mR − mbh ) 3   ( µ B )r ln( Re / Rw' ) − + s frac  4   Eq. 13-1 Average Properties k 1.0 x 10-18 m2 H 117 m Re 25 m Rw’ 60 m Sfrac 0 Xf 120 m Table 13-1 Properties used for the analytical calculation of the gas rate. Finally, there are two parameters in the equation that require some more explanation, namely the gas pseudo pressure and the reference PVT properties. As explained in the theory presented in section 2.1, the changing pressures in the reservoir, the fracture and near the wellbore require constant updating of the gas properties, which are highly variable with pressure. A general approach is used, where the PVT properties are evaluated at reservoir and bottomhole pressure and averaged accordingly. This is line with the theory presented by Hagoort (1988), where a straight-line relation between m(p) and p is assumed. Fig. 13-1 shows that this assumption can be made for two pressure ranges in the reservoir. The condition at the bottomhole is approached with the match of the lower pressure range; the gas properties at the outer edge of the reservoir are approached with the second trend line. These two lines are used separately in the calculation, because for the calculation of 1 year production, the two pressures remain almost constant. The intersection of the two lines does therefore not influence the measurements. 115 MSc. Petroleum Engineering – Thesis report - L.F. van Zelm Fig. 13-1 The straight-line relationship between pressure and the product of two gas properties (viscosity and formation volume factor) used in the analytical solution. Fig. 13-2 shows the simulated gas rate versus the analytical solution calculated from Eq. 13-1. Apparent is the transient flow period in the simulated gas rate, which predicts very high initial rates. This period is dominated by linear flow towards the fracture and therefore does not allow for comparison with the analytical radial flow gas rate. After one year of production, the analytical production forecast matches the simulated rate. This implies that radial flow is established in the simulation and the outcome can be approached with the pseudo-steady state radial inflow equations. This approach seems therefore be valid for gas rate production at late times. Second, this result validates the outcome of the simulation prior to modelling more complex scenarios. Fig. 13-2 Single phase gas rate comparison with theoretical value for a full field simulation. 116 MSc. Petroleum Engineering – Thesis report - L.F. van Zelm 14 Appendix - Simulation of fluid leakoff process The base case model is initialised with the leakoff water modelled by injection of the total fluid pumped in the fracture treatment. As explained in section 3.1.3, another option for leakoff water modelling is available. This appendix demonstrates possible differences between the two and comment on the final choice made for this thesis. The first method (leakoff model) is based on the use of a separate fracturing modelling software programme which predicts the saturation profile around the fracture. This is done by including fracture propagation and coefficients for leakoff and wall-building for each reservoir layer (Behr et al. 2003). The underlying assumption is one-dimensional plug-flow (or Buckley-Leverett flow) of the treatment water into the reservoir normal to the hydraulic fracture face. This method is the default method in FracproPT (Carbo Ceramics 2007) and will be referred to as the ‘leakoff model’ method throughout this section. After the hydraulic fracture is generated in FracProPT and the leakoff saturation distribution is determined, a grid is exported into the reservoir simulator (LGR) including the appropriate permeabilities, porosities and increased water saturation defined per grid block. The part of the fracture filled with proppant is at water saturation Sw = 1. The remaining leaked off water is distributed in the reservoir along the fracture, with the first row of grid blocks initialized at maximum water saturation (Sw = 0.7). Depending on the total amount of water that leaks off, the next grid blocks either have increased water saturations or are at initial Sw (= 0.4). This process continues until there is only enough water to saturate one column of grid blocks at Sw between 0.4 and 0.7. This fluid distribution is solely based on a material balance, and not controlled by relative permeabilities or capillary pressures. The leakoff model method, used by FracproPT (Carbo Ceramics 2007), allows the user to simulate a fracture treatment and generate a leakoff water distribution in the grid blocks near the fracture face. The grid blocks with increased Sw have reduced gas permeability upon opening of the well and this results in a short, but still apparent, cleanup period. The injection method, chosen in this thesis, is based on simulating the leakoff of fracturing fluid separate of the fracturing process by water injection prior to the production simulation using the reservoir simulator Eclipse (see similar work in Gdanski et al. 2005; Wang et al. 2009). In this case, the fracture dimensions are set at the start of the simulation as simulated by a separate fracture treatment programme (e.g. FracproPT by Carbo Ceramics). The correct permeabilities and porosities are again included in the grid, and Sw is initially 0.4 throughout the formation. The total leakoff volume is then derived from the total fluids pumped during the treatment minus the fluids that remain in the fracture. This volume is injected through the well and static fracture into the reservoir. For this simulation, the total clean volume of the fracture treatment is 244 m3, of which 61 m3 is injected, due to the ¼ symmetry of the model. This injection method is a simplification of the true process, but results in a method capable of examining the effect of leakoff on the cleanup process (Soliman and Hunt 1985). For this thesis, it’s important to be able to influence the fluid leakoff process. 117 MSc. Petroleum Engineering – Thesis report - L.F. van Zelm Although the injection method has a few advantages over importing a grid with a predetermined fluid distribution, it’s important to compare the results for both water and gas production. The model is setup with the properties of the base case scenario, including the relative-permeability (Fig. 3-3) and capillary-pressure functions (Fig. 3-4), the initial Sw of 0.4 and the hydraulic fracture properties (section 3.1.2). Fig. 14-1 Gas production shortly after the well has started producing gas. The water invasion causes a reduction in the expected gas rate in the first few days. Fig. 14-1 shows the cleanup period of both leakoff modelling methods. The leakoff model used by FracproPT (Carbo Ceramics 2007) has an increasing gas rate up to 3 days, after which the expected hyperbolic decline is seen. The injection method starts with a high peak followed by a strong reduction. This difference is related to the water saturation in the first grid blocks adjacent the fracture after the shut-in period. Fig. 14-2 shows the injection method and Fig. 14-3 the leakoff model. The injection method spreads out the water more evenly, also governed by the presence of capillary pressures in the reservoir, whereby the water saturation is generally lower close to the fracture in comparison to the leakoff model. Second, the leakoff model initiates a higher Sw at the tip of the fracture, which is not simulated with an injection. A part of the leakoff water volume is therefore located at a different location in the reservoir at the start of the production. 118 MSc. Petroleum Engineering – Thesis report - L.F. van Zelm Fig. 14-2 Water distribution around fracture after the injection and shut-in period in the injection model. Note the scale: the y-direction perpendicular to the fracture is enlarged far clarity. Fig. 14-3 Water distribution around fracture after shut-in period in the leakoff model by FracproPT (Carbo Ceramics 2007). Note the scale: the y-direction perpendicular to the fracture is enlarged far clarity. 119 MSc. Petroleum Engineering – Thesis report - L.F. van Zelm Simulation scenario production comparison (fluid injection = 1) Fluid injection (Eclipse) Water Production 2 months (m3) 1.0 Water Production 2 yrs (m3) 1.0 Gas Production 2 months (m3) 1.0 Gas Production 2 yrs (m3) 1.0 Leakoff model (FracproPT) 0.80 0.73 0.97 0.98 Table 14-1 Production comparison of total water and gas produced after 2 months and 2 years. Table 14-1 compares gas production for the two models over a longer period than the cleanup period. Some deviation in the cumulative gas production can be seen, although just a few percent after two months. More apparent is the change in water production, although the total water in place in the model is matching. This is probably related to the distribution of the leakoff water at the tip of the fracture as shown in Fig. 14-3. This part of the LGR is initialized with an elevated Sw, but the fracture does not extend that far, thereby not creating a drawdown to produce the water. It’s not investigated if this is realistic or not, but it can explain the observed differences. In conclusion, for the modelling of the cleanup period there are some difference apparent in the gas and water production. This is directly related to the distribution of the water around the fracture. It is difficult to predict which method is more realistic, for the leakoff process cannot be monitored in the subsurface. It is apparent that the leakoff in these scenarios only influences the short-term production, because the long-term gas production is matching. With this observation and the arguments stated above, the injection method is chosen for the rest of the simulations in chapter 3. 120

Similar Pages

Rating

Date

Size

Views

Categories

Share

Transcript

Forgot your password?.