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ChE 4162 CRYSTALLIZATION EXPERIMENT – Salicylic Acid Crystallization Revised 1Feb2012 Note: Read your assignment first. Not all sections below are relevant to all assignments. Introduction The processing of biochemicals and pharmaceuticals is just as important to Chemical Engineering today as petrochemical production and oil refining. Such processing involves operations such as crystallization, ultracentrifugation, membrane filtration, preparative chromatography and several others, all of which have in common the need to separate large from small molecules, or solid from liquid. Of these, crystallization is the most important from a tonnage standpoint; it is commonly employed in the pharmaceutical, chemical and food processing industries. Important biochemical examples include chiral separations (Wibowo et al., 2004), purification of antibiotics (Genck, 2004), separation of amino acids from precursors (Takamatsu and Ryu, 1988), and many other pharmaceutical (Wang and Berglund, 2000; Kim et al., 2003), food additive (Hussain et al., 2001; Gron et al., 2003) and agrochemical (Lewiner et al., 2002) purifications. The control of crystal morphology and size distribution is critical to overall process economics, as these factors determine the costs of downstream processing operations such as drying, filtration, and solids conveying. If you are unfamiliar with crystallization, you should consult a specialized textbook or Chapter 27 of your Unit Operations textbook (McCabe et al., 2005). Our experimental crystallization apparatus enables study of key facets of crystallization: (a) effects of key parameters such as supersaturation and cooling/heating rates on solids content, morphology and crystal size distribution; (b) on-line control of crystallization processes. The different classifications of crystallization include cooling, evaporative, pH swing and chemical modification. While an on-line video microscope is widely used in actual crystallization processes to monitor morphology and size distribution (Barrett, 2003), such an instrument is at present beyond our budget (cost ~$80 K), so we use an offline microscope to measure from 10-1000 crystal sizes, a typical size range for crystallizations of biologicals. The current experiment is a “chemical modification” crystallization, generating salicylic acid (precursor of aspirin) crystals from the rapid reaction of aqueous solutions of sodium salicylate (NaSAL) and H2SO4 (Franck et al., 1988). The byproduct sodium sulfate remains (mostly) soluble. This “chemical” crystallization has many facets in common with crystallizations of other biologicals such L-ornithine-L-aspartate (LOLA), used to treat chronic liver failure (Kim et al., 2003). However, whereas the precursor Lornithine hydrochloride costs >$300/kg and is difficult to recycle, we buy sodium salicylate for ~$50/kg, and the salicylic acid can be reused by rinsing and draining out the byproduct sodium sulfate, and then reacting the salicylic acid with dilute NaOH solution (usually 0.25 N) in the product tank, followed by recycle.
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System Overview The crystallization apparatus consists of two feed tanks, three variable speed (peristaltic) pumps, a crystallizer, a circulating bath for temperature control, power controller, product tank, and a makeup tank for feed regeneration. There are pH and temperature probes on the crystallizer. There is also a UV/VIS spectrophotometer for offline analysis of dissolved salicylate concentration, along with miscellaneous other instruments, valves and variable speed agitators. A complete list of the equipment tag designations can be found below. The crystallization itself takes place in a baffled ~5 L glass vessel equipped with an air-driven agitator, thermocouple, pH probe, sampling port and extra ports. Temperature is controlled by a thermostated bath and power controller with its own thermocouple. Air is supplied to the agitator after filtering. The crystallizer normally does not require cleaning. If you are told to clean it, use soap and hot water and rinse with DI (deionized) water. This is true as well for all other glassware used in this experiment. To disassemble the crystallizer, remove the agitator unit with an Allen wrench, remove all probes and place them on Kimwipes (remove pH probe slowly and carefully - easy to break). Rinse the pH probe with DI water only and put it in either DI water or buffer solution. Leave everything else on a CLEAN (e.g., Kimwipe) surface. Then disconnect the overflow line and feed lines (quick connect fittings) and lift the internals from the glass vessel. There are organic (sodium salicylate, NaSAL) and acid (sulfuric acid, 0.25 M = 0.50 N) solutions fed to the crystallizer, and a base (sodium hydroxide, 0.25 N) solution fed to the product tank from a base makeup tank. Water can be fed to the makeup tank from the city water supply. The NaSAL can be added to the feed tank from either a bottle of the pure solid or by recycle of used NaSAL solution from the product tank. You should wear latex gloves when handling NaSAL, salicylic acid or their solutions. Sodium hydroxide is available as a 50 wt% solution which should be handled with neoprene gloves and added to a large volume of water in the makeup tank to create the desired molarity solution. Sulfuric acid (0.25 M, 0.5 N) is available from a large tank near the center of the U.O. lab and can be handled with latex gloves. Basic physical properties of the key chemicals can be found in crystallizer.xls. Typical pH values for both NaSAL solutions and saturated salicylic acid slurries can also be found there. These values were measured using the same probe used in the crystallizer. Operating the Crystallization Experiment Understanding Experion PKS Control System Terminology In Honeywell‟s Experion PKS, each process variable is represented by an entity called a Control Module (CM). Each CM is a collection of Function Blocks (FB). And each FB consists of many values called parameters. Within a CM (and sometimes between CM‟s), the FB‟s are “wired” together in various ways to monitor and control the process. Desired values of many parameters may be entered via the computer keyboard.
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The purpose of the next few paragraphs is to explain how to use Experion to run this equipment. Now, on a PC loaded with Honeywell Station software, log on using your normal ID, password and domain. Open the Honeywell Station software by navigating to Start>All Programs>Honeywell Experion PKS>Client Software>Station. A message block saying Unable to connect Attempt to reconnect may appear. If it does, click Cancel. From the program menu, select Station>Connect. The Connect pop-up appears. Select the Connection Name for the workstation at which you are working (given on front of the PC chassis), then click the Connect button. If your ID is in the system, the Station program full menu will appear. From the Unit item on the menu, select CRU. The CRU P&ID schematic will appear. This schematic is much like a P&ID (Process and Instrumentation
Diagram), and the crystallizer is controlled from it. There is also a schematic which shows trends of the analog values associated with the unit. On the main schematic, each measurement transmitter and continuous controller is represented by a circle containing its tagname. The first letter of the tagname indicates the type of measurement: A for analyzer (pH in this case), T for temperature, L for level, or F for flow. There are also five device controllers (sometimes called discrete controllers): solenoid valves which either start/stop the flow in a line, or switch the flow from one line to another. When you click on a circle representing any measurement or continuous controller, or a square representing a solenoid valve, a faceplate will appear in the lower right corner of the schematic. It contains the tagname, engineering units, description, and PV for transmitters. For continuous and discrete controllers, additional values and controls are available (see below). To change an analog value from a schematic or from a faceplate, single click the value (if change is allowed, its background color will change), and then enter the new desired value. To change the mode of a continuous controller, use the combo box labeled MD near the bottom of its faceplate (more about controller modes below). To change the output of a device controller, use the OP radio buttons on the right side of its faceplate. At the start of a run, all continuous controllers should be in manual mode (signified by yellow backgrounds in the circles), and all solenoids should be either closed or in recycle (signified by the green backgrounds in the squares). Now open the Product Recycle Solenoid (D401) for practice (click on the solenoid valve on the left side of the schematic, and then click on the upper OP radio button on the right side of the faceplate). Notice that the solenoid valve changed from green (representing closed) to blue (representing changing positions) to red (representing open) when you open the valve. When you close the solenoid, the color sequence will be from red to blue to green. You may not see the blue state because the solenoid changes very quickly. A transmitter‟s most important value is the measurement of the process variable itself, abbreviated as PV. This value is shown in cyan (light blue) near the circle. Controllers have several additional values, the most important of which is the setpoint or SP. This is just like the speed setting on a cruise control - the controller will manipulate its output (the throttle position in this case) to move the PV to the SP and hold it there. The SP (in green) and the PV (in cyan) are shown near the circle representing
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the controller. The OP always has units of percent (0-100%) and the SP has the same engineering units as the PV. On the crystallizer, pH is measured in pH units, flow rates are measured in ml/min, levels are measured in percent full, and temperatures are measured in degrees C. When the controller mode is MANual, the OP is held until the operator changes it. If you want to change the OP, simply click the OP in the faceplate, type in the new value, and press ENTER. The new OP will be held until you change it again. Note that you can change an OP only while a controller is in MAN. For practice, click the NaSAL flow rate controller (to call up its faceplate) and change the output to 50%, then to 100%, and back to -6% (-6% is known as “tight shutoff” in the PKS system). Notice the small bar under the control valve on the schematic – its length is proportional to the output. When the mode is not MAN, the controller uses the PV, SP and tuning constants to calculate a new OP. When the mode is AUTOmatic, you may enter a new SP to be used for control. Note that changing an SP affects the OP only while a controller is in AUTO. Notice that the circle representing a continuous controller is filled with a background color, which indicates the current mode of the controller - yellow means the mode is MAN, and .white means the mode is AUTO. Display Navigation When you logged into Flex Station, you used an item from the menu bar to call up the main PDU schematic. There are several additional ways to go from one display to another. For example, you can enter the tagname of a CM in the Command field at the top of the screen and press F12 to call up the detail display. Try it with your bath temperature controller (T401). For continuous and discrete controllers, the detail display has 7 tabs, and for a measurement, only three. Most of the toolbar buttons are used for navigation – some require a name or number to be entered, and some go directly to the display. Most of the same functions are on the function keys. For example, to return to the previous display, click , or press F8. To return to the display before that, do it again. From most displays (both system displays and custom schematics such as CRU), double clicking any value associated with a CM will take you to its detail display. From a detail display, click or press F2 to return to the main CRU schematic. On most custom schematics there may also be buttons to quickly get you from one display to another. Understanding Trend Schematics There is a button on the main PDU schematic to call up trends. The top button displays the PVs of the four pairs of cascaded controllers. The next displays the tower temperature profile, pressure drop and flows into the tower. The third displays other miscellaneous temperatures, etc. Click the Trend Cascades button. At the bottom of the trend is the legend with all the tag.block.parameters associated with the traces. The checkboxes in the Pen column indicate which traces are currently on the trend. Click on the chart area of the trend and a white hairline cursor
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appears on the chart and the values at the hairline cursor appear in the Reference Value column of the legend. Along the bottom of the chart area is a horizontal scroll bar which allows you to scroll the chart area back and forth. Along the left axis are the low and high range of the selected trace These allow you to change the range of the trace for the selected parameter. Practice by changing the range of one of the level controllers to 20-80. Immediately above the left side of the chart area is a combo box which allows you to select one of the traces (you may also click anywhere on the line for this trace in the legend area). When you select an active trace, it is highlighted (thicker) in the chart area. Above the right side of the chart area is the Period combo box which allows you to select how much data (timewise) is displayed in the chart area. To the right of that is the Interval combo box which allows you to select the interval between points in the chart area. Practice changing to a different period and interval. Leave the period set to 1 day and the interval at 1 minute for now. For practice, scroll back until some variation in some of the traces appears. Notice that the timestamps below the chart area change as you scroll. Find some local max or min in one of the traces and click or drag the hairline to it. Now change the period back to one hour and notice that the cursor is centered on (or at least near) the local max or min. If necessary, move the hairline so it is exactly on the peak or valley and notice that the values, as well as the date and time, are shown in the Reference Value column in the legend. Now return the trend to the current time by clicking . All changes you make to the trend can be saved by clicking the familiar Windows Save icon just above the right end of the chart area next to the word (Modifed). Saving Data into Excel Successful completion of the objectives of this experiment will require analysis of a great deal of data. To collect this data, an Excel workbook containing a Visual Basic Add-In is provided. In Windows Explorer, navigate to C:\Program Files\Honeywell\Experion PKS\client\UOLABSpreadSheets\snr and double click on CRURecorder.xls. The workbook will open with a Start button,
the experiment name, a collection frequency Combo Box, and a Stop button on the top line. Click on the Start button, and the workbook will start collecting the relevant data at the specified collection frequency. These data will be extremely useful in analyzing your results. While the workbook is collecting data, it may be scrolled, but you should not attempt to do anything else in this instance of Excel until after you click on the Stop button. If you do, the collector may stop and you may lose valuable data. When you finish a run, click on the Stop button and cut or copy whatever data you need to your daily workbook in a separate instance of Excel. Let the workbook collect data while you finish reading this introduction.
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Tag Descriptions with Engineering Units TagName Description A401 Reactor pH D401 Product Recycle Solenoid D402 Product Drain Solenoid D403 Product Water Supply Solenoid D404 NaSAL Feed Solenoid D405 H2SO4 Feed Solenoid F404 NaSAL Flow Rate Control F405 H2SO4 Flow Rate Control L403 Product Tank Level T401 Reactor Temperature T402 Bath Temperature Control
EngrUnit pH Open/Closed Open/Closed Open/Closed Recycle/Feed Recycle/Feed ml/min ml/min Percent Deg C Deg C
Operating the Crystallizer 1. Be sure the crystallizer is full to the overflow level, with either water or salicylic acid slurry (in crystallization literature, the slurry is often called “magma”). Turn on agitator for the crystallizer. Turn on thermostated bath and pimps. Set the temperature controller to AUTO and the setpoint to the desired T. The control T (process variable) for the T-controller is the bath T, not the crystallizer T. The crystallizer T will probably end up at 2-3ºC below the setpoint, so adjust the setpoint accordingly. 2. The default setting on the 3-way valves for the feed tanks is recycle. Leave them in recycle for now. Set the pump speeds using the interface (e.g., 30% open). 3. Verify that the feed pumps are operating. Sometimes the tubing at a pump heads will leak. In this case the tubing must be replaced. Find Mr. Perkins. Raise the pump output as necessary to achieve desired flow rate. 4. After making up your solutions, run the pumps in recycle for a few minutes to ensure homogeneity in the tank. 5. Confirm that the product tank is not full and that the drain valve is closed. 6. Switch to feed mode on both 3-way valves. This is time zero for an experiment. 7. Periodically check the overflow line. Under certain conditions it may block up. If so, squeeze the flexible tubing connecting the crystallizer and product tank, and use a spatula or piece of steel tubing to ream out the line entering the product tank. Samples can be collected from this entrance, or directly from the crystallizer through the sample port using a wide-mouth pipette. Shutting Down the Crystallizer 1. To shut down the system, set the 3-way valves to recycle, set the pump outputs to 0%, return the T-controller to MAN at 0% output, and shut off the pumps, agitators and thermostated bath.
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2. If using the spectrophotometer, remember to shut off the lamps. Recycling NaSAL If your assignment calls for using recycled material, you must convert salicylic acid back to NaSAL in the product tank. With the agitator off, let as much as possible of the salicylic acid settle to the bottom of the tank. Drain off the liquid into the plastic bottles provided; filter out the salicylic acid from this solution using the large Buchner funnel provided. Return this acid to the product tank. The filtrate can be discarded to the floor drain with wash water. Estimate the amount of solid acid in the product tank, then add about half the (estimated) required amount of 0.25 N NaOH from the makeup tank. Turn on the agitator for a few minutes to homogenize. Sample the liquid and check the pH. Repeat this process until the pH is in the 8.0-8.5 range. At this time all or almost all of the salicylic acid should have disappeared. If not, continue agitation/ addition of small amounts of 0.25 NaOH. Prior to recycle, take your final sample from the product tank, dilute appropriately, and determine its NaSAL concentration by UV/Vis (see below). Then calculate how much fresh NaSAL solid must be added to the feed tank after you recycle some or all of the product tank contents. You can store excess recycle solution in the plastic bottles provided. Be sure to label properly and give the NaSAL concentration on the label. Using the spectrophotometer Dissolved NaSAL and salicylic acid concentrations can be measured simultaneously by UV/Vis spectroscopy. An on- and off-line analyzer probe (Ocean Optics UV dip probe) is provided for this purpose. This probe must be handled with care. Nothing should ever enter the liquid tip of the probe except the (diluted) process fluid or distilled water for cleaning. The probe should not be placed on a dirty surface. The probe is normally mounted near the crystallizer. The absorbances of dissolved salicylate and salicylic acid can be assumed additive (why?). Be sure to turn off the lamps at the end of a lab period, to prolong their life. The Ocean Optics spectrometer itself resides in a module (connected to the PC through a USB port) near the experiment. Fiber-optic cables transmit the radiation from the DT1000 source to the dip probe and the detected signal to the PC. 1. Ensure that USB communication from the Crystallizer spectrometer is enabled. To do this, first locate the SX Virtual Link icon on the desktop, as shown in Figure 1. Double-click that icon. Doing so will display the main application window for the SX Server Link application, as shown in Figure 2. If everything is powered up and working in the field, this display should show two Ocean Optics USB 2000 devices, one for the Permeameter (given by location 2.41.3) and one for the Crystallizer (given by location 2.41.0). If these do not appear on this display, disconnect and reconnect the power to the field USB hub. After the hub completes its self-test cycle, these two devices should appear on this display. If not, contact the lab coordinator.
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Figure 1. Locating the SX Virtual Link application icon.
Figure 2. SX Virtual Link main application screen.
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2. With the SX Virtual Link application window still open, select the desired Ocean Optics device by clicking on the item with 2.41.3 on its link. Then click the leftmost of the two round buttons on the bottom of the window. This is the connect button. The Available wording on the item in question should change to You are Connected. And the right arrow head should change to a green check mark. The instrument is now connected to the network. See Figure 3 for what this should now look like.
Figure 3. SX Virtual Link application showing Connected Permeameter USB device.
At the end of use on any lab day, disconnect the USB connection by clicking the rightmost of the two round buttons on the bottom of the window. This will disconnect the USB connection from YOUR computer and allow the Ocean Optics to be used by the next team. Please be sure to perform this disconnect operation as no other computer will be able to connect to the Permeameter spectrophotometer until your connection is closed! 3. The SpectraSuite© icon may appear on the desktop. If not, go to directory C:\Program Files\Ocean Optics\SpectraSuite\spectrasuite\bin\ and start the SpectraSuite application file. Locate and have available the SpectraSuite© Spectrometer Operating Software- Installation and Operating Manual at the imbedded link here, or in your folder, or at www.oceanoptics.com. On the website, select
Technical, then Operating Instructions, then Software Operation. The instructions apply to our USB 2000 model.
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4. Switch on both the UV and VIS lamps on the source. The red light at the top will come on when the UV lamp is warmed up and ready for a test. (Be sure to turn the lamps off at the end of the lab period.) Set the acquisition mode to Scope. 5. Open or create a dark file. The dark file must be compatible with the current „Integration time‟, „Scans to Average‟, „Boxcar width‟, and the cursor wavelength selected on the acquisition software. Typical settings are integration time = 200 ms, scans to average = 10, and boxcar width of 2 to 3. NOTE: The Strobe/Lamp, Electric dark correction, Nonlinearity correction, and Stray Light correction must be enabled! 6. Store a reference file using the background test fluid - DI water in a test tube. The reference file is important. If you don‟t see zero absorbance (in the desired spectral range) with the probe in the reference fluid after saving the reference file, clean the probe further and try a cleaner test tube. A good way to check if the probe is clean is to put it back in the reference fluid.. NOTE: Every time a setting (above) is changed, you “must” create a new dark and reference file! 7. Switch from Scope to Absorbance mode. For NaSAL solutions, you should see absorbance at <400 nm, usually two peaks. A wavelength near the second peak (~300 nm) is usually adequate for quantification. For some old data on these solutions, see crystallizer.xls. 8. Note that quantification is only possible if NaSAL/salicylic acid solutions follow the Beer-Lambert law (absorbance in the “linear region”). For the salicilate ion, this region is A < ~0.9-1. Examining the data in crystallizer.xls, this criterion suggests that you MUST dilute NaSAL solutions (with DI water) to ~0.05 g/L or less in order to quantify them. Then you quantify the unknown solutions by comparing to the absorbance of an appropriately diluted standard solution: Cu/Cs = Au/As Where C is concentration, A absorbance, “u” an unknown, and “s” a standard solution of NaSAL. Note that BOTH “u” and “s” must show absorbance inside the linear range. The absorbance at the cursor is read at the bottom left corner of the display. 9. In spectroscopy, the absorbance depends on a couple of factors. First, the type of chemicals, second the concentration. Third, the path length in the fluid, which in turn depends on what probe tip is installed. We have 10 mm, 5 mm, and 2 mm tips. I suggest sticking with the current (10 mm) tip, because it‟s easiest to clean.
Spectrophotometer Trouble-Shooting Tips
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1) Daily standard checks must be made prior to operation of the unit. A 0.05 g/L NaSAL solution with DI water should be prepared for this purpose. With the integration time set at 200 milliseconds, number of averages at 10, and the wavelength at 297 nm, the absorbance should read 0.46. The spectrum should not vary more than 0.05 Abs. If you cannot achieve this reading, then something is “WRONG” and you must find the trouble before you can successfully use the unit. 2) The following are possible problems: a) The probe window is coated with something other than the standard. Clean the glass with a soft cloth. Wash with DI water, shake off excess water and insert the probe in your sample again with some stirring. b) The lamp has failed and its raw signal intensity is < 1000 in the Scope mode. c) The optical fiber connecting the probe to the USB 2000 unit is broken or frayed. d) Your sample has become turbid due to contamination. See Mr. Perkins for a replacement probe if no other problem can be found. 3) Never let the PC go into standby or hibernation mode as the USB communication will be lost when this occurs. To correct, go to START then CONTROL PANEL then POWER OPTIONS. “System Standby” and “System Hibernate” should be set to “Never”. 4) Is “remote access to this PC” enabled? Run Network Set-up Wizard to set. 5) Make sure that your references are stored in “temp” in the OceanOptics directory. Be sure the file is not set to “Read Only”. 6) Check the size and pH of your standard. An acidic solution will under-represent 260-280 nm by 0.2 to 0.3 absorbance units, while a basic solution will overrepresent the absorbance by 0.2 to 0.3 units. 7) Obtaining an unusual spectrum can be the result of detector saturation. This can be caused when you have to select too high an integration time due to a dirty sample window. Try cleaning the probe. 8) A “ragged” spectrum can be caused by insufficient light intensity reaching the spectrophotometer. This could be caused by a weak lamp. Gravimetric analysis for salicylic acid The salicylic acid concentration can also be determined gravimetrically. Sample from either the entrance of the product tank or, with the agitator on and using a widemouth pipette, from the sample port of the crystallizer. Use labeled 15 mL test tubes to collect the samples. Centrifuge for 5 min. Then decant most of the water (without losing many crystals); this liquid can be used for NaSAL spectrophotometric analysis. Dry the test tubes upright in the Blue M oven at 60ºC, for two days if possible. Weigh, clean out the tubes, re-dry and re-weigh. Alternative procedures may also be part of your assignment. Size determination of salicylic acid crystals The crystals are typically needle shaped. The key dimension is length. The length distribution of a representative sample can be determined microscopically. Turn
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on the light of the Wild microscope. The reticle in the left lens contains 12 major divisions (120 minor divisions) at 1 mm/division at 1x magnification. The lenses are 10x, and the magnification of the objective is selected by lining up the number with the black dot. Total magnification = (lens) x (objective). Use a microscope slide to mount your samples. It‟s OK to dry the samples first. Theories of Crystal Growth Your Unit Operations textbook (McCabe et al., 2005) discusses both common mechanisms for initially generating (“nucleating”) crystals, but only heterogeneous nucleation takes place here. It is the more common mechanism. Both existing crystals and other solid surfaces such as the agitator can catalyze heterogeneous nucleation. If n is the number density of crystals (mol/volume), then the nucleation rate B0 is often expressed as initial growth in the key linear dimension (L) per unit time (t) times the number density of just-formed crystals (n0). The subsequent growth rate G is expressed as dL/dt. An example of L would be the radius for a spherical crystal. The relation between B and G is then by definition: B0 = n0 G
(1)
where n0 is the number density for just-formed crystals. The birth rate can be empirically correlated with key physical and operational parameters by (Garside, 1985): B0 = KB F(geometry) Cb Mj Nh
(2)
where C is the supersaturation (liquid concentration of solute is excess of equilibrium solubility), N is stirrer speed, and Mj is the jth moment of the crystal size distribution. For typical agitated crystallizers, j and h are both ~3, and the geometry function is: F(geometry) = p Ds5/V
(3)
where p is propeller pitch, Ds is stirrer diameter, and V is liquid volume. The crystal growth rate is primarily a function of supersaturation, and is usually correlated as: G = kg
Cg
(4)
This can in turn be written in terms of series mass transfer and kinetic resistances as is done in your textbook (McCabe et al., 2005). The powers b and g are system specific. The ratio of the two, b/g, is often called the “relative kinetic order”, i. Because B0 and G both depend upon C, if C is constant at constant T, N, geometry etc. (as is possible for a MSMPR, or perfectly stirred tank, crystallizer), then B0 and G can be related: B0 = KR Gi
(5)
Other examples of such correlations for specific crystallizers are given in your textbook. Note that the power “i” in these correlations varies between 2.8 and 6. Because the number density n is a probability density function with respect to L, then n dL/( n dL) represents the fraction of crystals at a particular value L to L+dL. Let this fraction be called . Then a mass balance on the fraction in any control volume gives:
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Amount of
accumulated = flow of in – flow of out + generated per time by birth + gained per time by growth – lost per time by growth.
This type of mass balance, where the conserved quantity is a fraction (a “probability”) is called a “population balance”. The population balance is needed here because ultimately we are interested in finding the number density n (or itself). The last two terms give (how?): - (G‟ ), where G‟ is the normalized growth function. Often the mass balance is written in terms of n, not . We can convert to n and simplify the population balance for the crystallizer by the following steps: (a) Multiply all terms by ( n dL)/dL . (b) Recognize that the birth function only applies to n0, so in general for n we can set it = 0 (it becomes an initial condition for the equation, n = n0 at L = 0). (c) Recognize that flow of
is given by
Q/V, where Q is volumetric flow rate.
The final result is:
n t
n Qin V
n Q out V
(G n) L
(6)
For an MSMPR crystallizer there is no accumulation, Qin = Qout, and, because we are perfectly mixed, G is a constant. So the general population balance becomes:
dn dL
n Gτ
(7)
Where is the space time (V/Q). Using the initial condition and eq. (1) this is easily solved to give: n = (B0/G) exp[-L/(G )]
(8)
Eq. (8) predicts an exponential distribution for the number density produced in an MSMPR distribution, with an average L = G .
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References P. Barrett, Chem. Eng. Prog., August 2003, pp. 26-32. R. Franck, R. David, J. Villermaux and J.P. Klein, Chem. Eng. Sci., 43, 69-77 (1988). J. Garside, Chem. Eng. Sci., 40, 3-26 (1985). W.J. Genck, Chem. Eng. Prog., Oct. 2004, pp. 26-32. H. Gron, A. Borissova and K.J. Roberts, Ind. Eng. Chem. Res., 42, 198-206 (2003). K. Hussain, G. Thorsen and D. Malthe-Sorenssen, Chem. Eng. Sci., 56, 2295-2304 (2001). Y. Kim, S. Haam, Y.G. Shul, W.-S. Kim, J.K. Jung, H.-C. Eun and K.-K. Koo, Ind. Eng. Chem. Res., 42, 883-889 (2003). F. Lewiner, G. Fevotte, J.P. Klein and F. Puel, Ind. Eng. Chem. Res., 41, 1321-1328 (2002). McCabe, W.L., Smith, J.C., and Harriott, “Unit Operations of Chemical Engineering”, 7th Ed., McGraw-Hill, New York, 2005, ch. 27. S. Takamatsu and D.D.Y. Ryu, Biotechnol. Bioeng., 32, 184-191 (1988). F. Wang and K.A. Berglund, Ind. Eng. Chem. Res., 39, 2101-2104 (2000). C. Wibowo, L. O‟Young and K.M. Ng, Chem. Eng. Prog., Jan. 2004, pp. 30-39.
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APPENDIX – USE OF JASCO UV/VIS SPECTROPHOTOMETER Only use the Jasco if you are specifically instructed to do so. The Jasco is a research grade UV/VIS spectrometer of high spectral resolution. The switch for the unit is on the right side. The external power supply does not have to be turned on. The sample cuvette goes in the front compartment, the reference cuvette in the rear. Be sure the cuvettes are clean both inside and outside. After starting the ”Spectrum Manager” program from the start menu, click on ”spectrum measurement”. Select ”Parameters” to set the mode (e.g., ABSORBANCE), response (e.g., MEDIUM), bandwidth, scan speed etc. You can also load a parameter file. I set one up called ”std” that has standard parameters (except the wavelengths) that will work OK for most samples. The machine goes to the start wavelength and you select ”START” from the menu to collect data. Analysis is done by selecting ”Spectral Analysis”. Select ”processing”, then ”peak find” then ”execute”, and it will give the wavelength and intensity (absorbance). You can also select ”other”, then ”comment” to add comments to the file. When done processing, select ”save as” to overwrite the original file with the processing info. While there are also ”baseline correction” and ”smoothing” routines under ”processing”, these are not necessary. It automatically supplies some baseline correction based on a ”baseline” file which is the last one taken. It is not necessary to run a baseline test unless you see something wrong in your spectra – consult the Instructor. Turn the machine off at the end of the day, to conserve the lamps.
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