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CRYSTALLIZATION IN A STIRRED TANK REACTOR

Introduction

Stirred Tank Reactor (STR) of sizes ranging from 10 liters to 100,000 liters is thetraditional "work horse" in various fine chemicals and pharmaceutical operations. STRsare frequently employed for mixing and gas-liquid contacting. Most of the operationscarried out in a properly baffled cylindrical vessels equipped with an agitator dependprimarily on high rates of fluid shear, high fluid recirculation rates due to the impellers onthe agitators, or a combination of both. For example, emulsification processes requireprimarily a high intensity of the shearing action to reduce droplet size, and high rates ofheat transfer depend upon large flow rates of the fluid past the heated surfaces. Chemicalreactions require both large flow rates to distribute reactant streams throughout the vesseland a high intensity of turbulence to aid the mixing of the reactant streams to the desireddegree of completeness on a molecular level. Turbulence is also needed to enhance masstransfer between gas and liquid inside a STR (or bioreactor) for various biologicalprocesses. For example, oxygen transfer is enhanced in a stirred reactor (usually called afermentor or bioreactor) for various biological processes.

Theory

The concept of mechanical agitation imparted to Newtonian fluids was advancedby Rushton et al (1950). They found that the power absorption can be characterized by adimensionless power number. This dimensionless number Np represents the ratio ofexternal force exerted to the inertial force imparted to the fluid.

NP g

N Dpo c

i

= =3 5ρExternal forceInertial force

1

where

Np is the power number (dimensionless),

P0 is the external power from the agitator in g-cm/sec,

gc is the Newton conversion factor in cm/sec2,

N is the impeller rotational speed in sec-1,

Di is the impeller diameter in cm,

ρ is the density of the fluid in g/cm3.

Fluid motion in an agitated vessel can also be characterized similar to that forfluid flow in a pipe, using a dimensionless number, NRe which depicts the ratio of inertialforce to the viscous force for the fluids in motion. The NRe for a stirred tank reactor isdefined as:

NN Di

Re = =ρ

µ

2 Inertial forceViscous force

2

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where

NRe is the impeller Reynolds number (dimensionless),

µ is the viscosity of the fluid in g/cm-sec.

Rushton et al. (1950) were able to demonstrate experimentally that the powernumber (Np) is correlated to the Reynolds number (NRe) over a wide range of operatingconditions. The Np is also dependent on the number and the types of impellers used. Itshould also be clear that these STR's are fully baffled and thus the Froude number onpower absorption has been neglected.

Fig 1 Relationship of Power number to Reynolds Number of non-gassed Newtonianfluid.

Power (P0) is the rate of doing work or the rate of energy flow. The traditionalunit of power is the horsepower, HP (550 ft lbf/sec) which is related to the SI system by 1HP = 745.7 W. Table 1 shows the power requirements for some typical applications.

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Table 1: Suggested Horsepower Requirements (HP/1000 gal) in STRs.

Agitation type HP Application

Mild 0.5-2 Mixing, blending

Medium 2-5 Heat transfer, suspension, gas absorption

Turbulent 5-10 Reactions, emulsification, suspension of devices

Mixing Time

Many different kinds of reactors may exhibit non-uniform characteristics. Whilesmall STRs (<500 L) are essentially well mixed, larger STRs (> 5000 L) are usuallypoorly mixed. For example, differences in dissolved oxygen levels can be readily shownin the larger STRs.

Using dimensional analysis techniques, Fox and Gex (1956) have been able towork out a correlation for time to mix a solution on a molecular scale

f t ND g D Yt m i i= ( ) =2 2 3 1 6 1 2 3 2/ / / / Constant for NRe > 105 3

Where ft is a mixing function, tm is the experimentally observed molecular mixingtime, Y is the liquid depth and T is the tank diameter.

For geometrically similar vessels equation 3 reduces to

t

t

N D

N Dm

m

s i

l i

1

2

41

42

1 6

=

/

4

where tm1 and tm2 represent mixing time for large and small reactors respectively.

Since geometrically similar reactors with same volumetric agitated input (i.e.P/Di

3 = constant)

t

t

D

Dm

m

i

i

1

2

1

2

11 18

=

/

5

As expected, the mixing time increases with increasing scale.

Despite its intrinsic limitation, mixing time is still the most commonly usedparameter to quantify the mixing behavior of a reactor. Many attempts have been madeto correlate the mixing time in unaerated mixing vessels to the impeller speed and thegeometry of vessels and stirrers. For a low-viscosity medium, the mixing time in stirredtanks with standard geometry is not too far away from what can be predicted based on theinformation in the literature. The following is an example of the correlation (Riet andTremper, 1991).

N tN

T

Dp i95 1 3

1 33

% /

/

=

NRe > 104 6

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t95% is the time span to reach 95% homogeneity, N is the rotation speed (sec-1), Np is thepower number, T is the tank diameter, Di is the impeller diameter (m).

The mixing time for multiphase systems is less understood. Riet (1991)concluded that aeration would lead to approximately a doubling of the mixing timecompared to unaerated conditions at the same stirrer speed, while others concluded themixing time actually decreased under aerated conditions. Therefore the mixing time forunaerated conditions can only be used as a first approximation.

Crystals and Crystallization

A crystal is the most highly organized particular matter of non-living origin. It ischaracterized by an orderly 3 dimensional lattice made of either atoms, ions or molecules.Crystal formation is an important unit operation in various fine chemical andpharmaceutical industries. Crystallization occurs when the molecular species reachabove saturation, which is the maximum concentration of solutes (So) which isthermodynamically stable in solution. Saturation is the result of phase equilibria fromequal chemical potentials between the solid crystal phase and the mother liquor. In manycases, solutions can contain more solute than that present in saturation. Suchsupersaturated solutions are thermodynamically unstable. Yet, they are often metastableand remain unaltered for long periods of time. Precipitation is quite similar tocrystallization with a major difference in that crystallization yields particles of well-defined shape and size, while precipitation results in amorphous solids of ill-definedshape and size.

The main objective of a crystallization process is to produce crystals withproperties such as crystal size distribution (CSD), shape and purity. The CSD is oftendetermined by the rates of nucleation, attrition and breakage, agglomeration and growth.Batch and continuous crystallization are usually done in a stirred reactor and is a relativesimple operation in which a clear, warm, concentrated solute solution near its solubilitylimit is manipulated (such as cooling) slowly until small crystals are formed. These smallcrystals are often induced by adding “seeds” or smaller crystals. After crystallization, thecrystal product is recovered by filtration or centrifugation from mother liquor. Scaletranslation of crystallization is often difficult because large scale crystallization occurs inreactors of ill-defined geometry, with simultaneous mass and heat transfer in a multiphase, multi component system that is also thermodynamically unstable. It is alsoprofoundly affected by small trace impurities.

The primary and secondary nucleation rates (Bp, Bs) are often described by powerlaws:

B K Cp pn p= ∆

B K t W Cs sns= ( ) ∆

Kp and Ks are constants. The secondary nucleation rate constant Ks is a functionof time. W is the magma density and ∆C is the degree of supersaturation.

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One unique characteristics of the crystal quality is the distribution of the crystalsizes during this crystallization process or CSD. A typical crystal size distribution can berelated to a population density (Randolph and Larson, 1988). The population balancescan be solved using method of moments, which is based on the evaluation of the timevariations of the crystal size distribution moments. Other methods are based on a sizediscretization of the population balances or method of classes (Marchal et al, 1988,Rawlings et al, 1993). It consists of integrating the population balance equation along thesize. Several measurement techniques for on-line crystal size distribution are available.Image analyses and microscopy will be used in this lab to determine the crystal size andits distribution.

The size distribution and concentration of crystals vary within an agitatedsuspension. In batch crystallization, often the optimal agitation is the minimum stirringrate needed to keep all crystals just suspended from the bottom. At such conditions, ahomogeneous suspension is not necessarily obtained, but especially axial variations inparticle concentration and size distribution are significant. The hydrodynamics varysignificantly in an agitated vessel. The local energy dissipation rate may vary by twoorders of magnitude and the highest values are found close to the agitator. Previousresults indicate that the rate of secondary nucleation is approximately proportional to themean specific power input to the fluid (Garside and Davey, 1980). It is thus likely thatthe rate of secondary nucleation may vary significantly within the reactor and thus affectthe crystal quality.

Model System: L-glutamic acid and crystal formation.

L-glutamic acid, a common natural amino acid will be used as a model crystal inthis experimental investigation. We are interested in examining the crystal sizedistribution in a well-agitated stirred tank reactor. The quality of these crystals will bedependent on the processing conditions during the batch crystallization. Polymorphismexists in L-glutamic acid crystals where the α form is a coarse pyramidal crystal, whilethe β form crystal usually has shapes like needles or leaflets with a high moisture content(Sugita, 1988). You are being asked to develop an experimental protocol to obtainconsistently good quality α form crystal using pH neutralization in the stirred reactorbased on your understanding of the crystallization process.

The experiments have to be carried out by collecting as much information on boththe liquid and solid phases. For the liquid phase, the pH and the conductivity of thesolution should be monitored during crystallization while for the solid phase, the finalamount of the crystal formed and the crystal size distribution should be determined.After mixing and establishing equilibria, the conductivity of the solution first remainsconstant but decreases after the induction period with corresponding increases in the

amount of crystals in the solution. Owing to the high ionic conductivity of H+ and theconductivity of the solution can be safely assumed to be proportional to the concentration

of H+ ions. Therefore, H+ ions and afterwards, all other chemical species present in thestirred reactor can be estimated due to mass conservation and equilibrium relationships.Thus, the supersaturation should be known as a function of time. Crystal size distribution

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(CSD) can be estimated by taking a representative sample from the reactor at the end ofthe experiment. The crystals can be filtered out and viewed with a microscope. Acharacteristic size L should be estimated through multiple measurements and estimationof a shape factor (Jones et al, 1986).

Equipment Description

A 10 liter stirred tank reactor (STR) donated by Dow-Elanco (Harbor Beach,Michigan) has been modified with the necessary computer and process instrumentationand data acquisition systems to evaluate its performance. This modification is based on afinancial contribution from Abbott Laboratories (N. Chicago, Ill.). Figure 2 shows aschematic diagram of the reactor setup.

Filt

er

Flowmeter

Water supply

Syringevalve

Airsupply

Rotameter

STR Vessel

Heating Coil/Baffles

Fro

m th

erm

osta

t

To

ther

mos

tat

Bottom drain

Topdrain

Propeller

Quick-connect

Fig 2: Stirred Tank Reactor Diagram

The CSTR reactor consists of a glass cylindrical vessel 9 inches internal diameterand 12 inches high. The CSTR is equipped with the following equipment andinstrumentation:

1. Top-entry variable-speed agitator, with a 4-inch diameter 3-blade marine propeller.

2. Integral internal coil/baffles for heating purposes and efficient mixing.

3. Resistance Temperature Detector (RTD) for reaction temperature monitoring.

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4. Conductivity probe and pH probe to monitor the conductivity and pH of the reactorcontents

5. Feed flow meter

6. Tachometer to measure agitation speed

7. Current meter to measure the power used by the agitator motor.

8. Two feed inlet ports (one ear the top, one near the bottom)

9. Two air inlet ports (one above the liquid, one just below the propeller).

10. Two product discharge ports (one from the top, one from the bottom).

EXPERIMENTAL PROCEDURES

Use of Personal Protection Equipment (PPE)

Safety glasses must be worn at all times in the laboratory.

When handling corrosive liquids (such as Sulfuric Acid solutions) appropriaterubber gloves should be used. N-Dex nitrile rubber gloves are provided for this purpose.

When handling a container of more than 1-liter of Concentrated Sulfuric Acid(30% or higher). A chemical resistant apron, face shield and heavy resistant glovesshould be used.

I. Equipment Start-up:

The reactor needs to be plugged into a 208-volt electric outlet and the additionalinstrumentation for data acquisition needs to be plugged into a 110-volt electric outlet(the display on the conductivity transmitter lights-up when the instrumentation is on).

Reactor Agitator: A knob located in the control panel is used to control the agitatorspeed. The agitator speed is displayed in the built-in tachometer. Note that the motorwill overheat and shutdown if it is operated at currents above 2.5 amps. The load of themotor varies with RP, liquid viscosity, density, impeller type, gas-liquid ratio, etc. Theuser must be careful to monitor the motor current usage during operation to preventoverload. Currently there is a single 4-inch propeller installed. A second 4-inchpropeller and two 4-inch flat-blade impellers are also available.

Water flow: Water feed rate can be controlled with a valve located prior to the waterinlet filter, and it can be introduced into the reactor trough one of two possible locations.One enters at the top, near the liquid surface, the other at a position near the bottom of thevessel. A tee in the water feed-line is fitted with a valve with a syringe adapter. Thisport can be used to introduce an additional component in the feed stream.

Air flow: The air feed to the reactor can be controlled with the valve located at the top ofthe air rotameter. A tee in the air line allow the air to be introduced into the reactor attwo locations. The top location (above the water surface) can be used by opening thepinch-clamp on the plastic hose directing air to the appropriate port. Closing the pinch-

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clamp forces the air to flow through the dip-tube located directly below the lowerimpeller.

Product Discharge: The product from the reactor can be discharged from the bottom ofthe tank or from the top. The bottom drain can be opened by loosening the pinch-clamplocated on the plastic tube that discharges the bottom of the reactor to the drain. The topdrain can be activated by introducing a positive air pressure into the reactor and allowingthe liquid to overflow through the siphon tube located at the top of the reactor.

Temperature Control: The temperature can be controlled from the thermostaticallycontrolled recirculating water to the internal coils. The maximum possible watertemperature in the recirculation loop is 60 °C. The maximum temperature achievable inthe reactor is determined by the heat load, heat-loses and heat-transfer characteristic ofthe internal coil.

II Data Acquisition and Data Logging

A computer is connected to the reactor hardware and instrumentation for Datalogging purposes. The IBM compatible computer uses “LABTECH CONTROL”software (produced by Laboratory Technologies Corporation, Wilmington MA), tocontrol the process and display all the information received from the sensors. Thisinformation can be stored in user-configured data files, which can be stored in thecomputer hard disk or in floppy diskettes provided by the user.

The analog signals from each one of the instruments are converted to equivalentanalog signals ranging from 0 to 5 volts. These signals are then used by the analog-to-digital (A/D) conversion card in the computer to generate a digital signal that is read bythe computer. The CONTROL program converts the digital signal (in volts) to the valueof the measured variables in the desired engineering units (i.e. l/min., degrees C, etc.).

Data File Storage

A file named “RTDnnn.XLS” is generated every time the data acquisitionprogram is invoked. The “nnn” indicate the numerical order of the file and it isincremented by one each time a new file is saved. Flow rate, conductivity, temperature,RPM, current to the agitator motor and time values are stored in this file every 15seconds. Note that the data written to the file are not the actual readings at every 15-second mark; instead, they are the calculated average of the values read over the previous15 seconds. To stop the data acquisition program, simply select “Exit” from theapplication “File” menu.

If a faster rate of data acquisition is desired, click-hold on the “FASTACQUISITION” toggle switch (located on the lower-right corner of the Process Controlscreen) until it changes status from the OFF to the ON position. While this switch is inthe ON position, all values are recorded every second, and stored in a file named“FASTnnn.XLS”. It is recommended that this be used only when necessary since it willcreate very large data files in a relatively short period of time.

To retrieve these files at the end of your work, double-click on the “DATA” iconin the “STIRRED TANK REACTOR” Folder. The files list can be sorted by date with

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the most recently created file at the top of the list. Your files can be recognized by theircreation date and time.

When you are done with the computer, please double-click on the “Shut Down”icon on the “Start” menu.

III. Monitoring Reactor Conditions.

CONTROL operates under Microsoft WINDOWS® 95 operating system. Tostart the program, turn the computer on if it is not already. The computer is notconnected to the network, so click "Cancel" in the "Enter network password" dialog box.Double-click on the “STIRRED TANK REACTOR” folder if it is not open already. Thisfolder contains icons for the CONTROL set-up, the 5 calibration files, a file to reset thecalibration and a folder for the storage of the data from the experimental runs. Beforeeach lab session, be sure to double-click on the “reset calibration” icon to erase anychanges that the previous lab group may have made. In order to start the data acquisitionprogram double-click on the "REACTOR" icon. A product identification screen and theCONTROL setup will start the data acquisition and control functions.

The program produces a window that displays the values for all the sensor outputson the right-hand side of the screen, and analog traces for the sensor outputs on the left-hand side of the screen.

When you are finished using the computer please do not shut it down. There is ananti-virus program which is set to run every night at midnight and the computer must beleft on for this event.

IV. Sensor Calibration

The electronic signals produced by the flow meters, RTDs, etc., are converted to astandard voltage signal and sent to the computer. The sensor calibration is done bymeans of a regression (either linear or non-linear) between the variable measured (flowrate or temperature) and the voltage signal produced by the sensor. These calibrationscan be implemented with the computer by means of a polynomial fit. For sensors with alinear response, a 1st. order polynomial is sufficient for the calibration. For sensors with anon-linear response, a higher order polynomial will be required. The softwareimplements polynomial fits using:

y a a V a V a V a V a Vnn= + + + + + +0 1 2

23

34

4 ..... 6

where:

y = Variable being monitored (temperature, flow, etc.)

V = Volts produced by the measuring instrument (flow meter,RTDs, etc.)

ao, a1, a2, ... , an = correlation constants

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All calibrations can be implemented in this manner. For example, an instrumentthat has a linear relationship between the monitored variable and the voltage produced,can be calibrated with:

y a a V= +0 1 7

This has the same form as equation 6 where: a a a an2 3 4 0= = = = =..... .Similarly for any ith. order polynomial (i ≤ 10 in the current data acquisition setup) canbe implemented by setting aj = 0 (where j>i).

Several instruments have been calibrated and fitted with an equation. Theparameters ai for each instrument calibration are located in text files with the same nameas the instrument, and can be edited by double clicking on the file icon1. These filesconsist of 11 numbers in a column where a0 is at the top, and a10 is at the bottom. Table2 shows the units for each of the calibrations and the sensor range:

Table 2: Sensor calibration ranges

Variable CalibrationRange

Units

Conductivity: 0 - 9.99 mS

Motor Current 0 - 4.2 Amps

Rotation speed: 0 - 550 RPM

Temperature: 0 - 100 °C

The flow meter and pH transmitter need to be calibrated.

Calibration of the pH Electrode

In order to calibrate the pH electrodes, a two-point calibration is generally carriedout with the help of two standard buffer solutions of known pH. This type of calibrationgenerally produces a straight-line correlation between the pH electrode response to the H+

ion concentration and the transmitter output. Note that this will not correct for any non-linearity of the electrode response. Standard buffer solutions of pH 7 and 4 are providedfor this calibration.

In order to calibrate the pH electrode/transmitter pair between pH 7 and 4, use thefollowing procedure: 1 To edit the calibration files, double-click on the file icon and enter the ai numbers in the appropriatepositions (note that each one of these files has to have 11 numbers in a single column or an error messagewill be generated during data acquisition). Save each file by selecting “Save” from the “File” menu, andexit the text editor by selecting “Exit” from the “File” menu.

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1. Fill a 250-ml beaker with 200 ml of DI water and rinse the pH electrode.

2. Fill a 50 ml beaker with Standard buffer pH = 7. Insert the pH electrode in the beakeruntil the pH reading is stable. Mild agitation with a stirring plate and magnet may beuseful.

3. Once the reading is stable, adjust the "CALIB" screw in the transmitter until the pHvalue of 7 registers in the transmitter display.

4. Rinse the pH electrode with DI water.

5. Fill a 50 ml beaker with Standard buffer pH = 4. Insert the pH electrode in the beakeruntil the pH reading is stable.

6. Once the reading is stable adjust the "SLOPE" screw in the transmitter until the pHvalue of 4 registers in the transmitter display.

Note: pH 7 is the neutral point for the slope of the pH transmitter. That means that thepH reading at 7 should not change when adjusting the “SLOPE” screw. If calibration atpoints other than pH 7 and 4 is desired (i.e. between pH 8 and 10 or between pH 4 and1);use the buffer closer to pH 7 in step 2, the buffer farthest from pH 7 in step 5, and repeatsteps 1 to 6 until both pH readings match the pH of the buffer solutions.

pH Electrode StorageWhen all your daily experiments have been completed the pH electrodes must be

stored in pH 7 buffer solution.

Calibration of the pH Transmitter and Flow meterThe pH tranmitter generates a current signal which is converted to a voltage

sisgnal and sent to the computer. The flow meter generates a pulse that in turn isconverted to a voltage signal. This signal is sent to the computer. A calibration is neededto convert these voltage signals to pH units and flow units.

Procedure:

1. Turn the computer ON and double-click on each one of the pH and flowcalibration files icons (located in the “LABTECH CONTROL” group window) toascertain that the parameter values are a1 1= , anda a a a a0 2 3 4 10 0= = = = = =..... (edit the files if they are not)

2. Double-click on the “STR”. If conditions shown in step 1 are met, then the pHand flow values displayed and saved to the file by this setup represent the directinstruments output and have units of VOLTS.

3 . Make several measures of pH values displayed by the transmitter and thecorresponding voltages sent to the computer. Create a table correlating pHdisplayed vs. volts. Note that both pH calibrations (pH electrode/transmitter andComputer Data Acquisition) can be performed simultaneously to save both timeand buffer solutions

4. Make several measurements of flow rates and the corresponding voltages sent tothe computer. Create a table correlating Flow vs. volts.

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5. Plot the pH values against the voltage for the pH transmitter, plot the flow ratevalues against the voltage and conduct appropriate curve fits, using either yourcalculator, Delta-Graph, Excel or other programs, or graph paper, pencil and ruler.Calculate the parameters ai in equation 6 (or equation 7 for linear relationships)for each the pH transmitter and the flow meter.

6. Enter the values for the parameters ai in each of the calibration files. To do this,double-click on the file icon and enter the ai numbers in the appropriate positions(note that each one of these files has to have 11 numbers in a single column or anerror message will be generated during data acquisition). Save each file byselecting “Save” from the “File” menu, and exit the text editor by selecting “Exit”from the “File” menu. Once this is done for all calibration files, the computer willdisplay and store the sensor data in the appropriate engineering units (such as pHunits and l/min).

Once the calibration procedure is completed, dispose of all used buffer solutions.NEVER return used solutions to the original container.

Residence Time and Mixing Time Characterization.

Section 8 of this manual include theory on residence time distribution and suggestmethod to characterize the residence time frequency function of a stirred tank utilizing astep function on the concentration of the feed. A similar method can be used here todetermine the residence time frequency function by applying a pulse function in theconcentration of the feed (Fogler Chapter 13). Mixing times can be analyzed in a similarmanner during batch operation of the reactor.

References

Rushton, J. H., E. W. Costich, and H. J. Everet, “Power Characteristics of MixingImpellers I and II,” Chem. Eng. Progr., 46, 395 and 467 (1950)

Fox, E. A. and Gex,V. E. AIChE Journal 2:539 (1956)

Fogler, H. S. Elements of Chemical Reaction Engineering, Chapter 13.Prntice-Hall,Englewood Clifs, New Jersey (1986)

Randolph, A.D. and M.A. Larson. Theory of Particulate Processes. 2nd edition ,

Academic Press, New York, 1988.

Marchal P., David, R., Klein, J.P., and Villermaux, J., “Crystallization and PrecipitationEngineering - I. An Efficient Method for Solving Population Balance in Crystallizationwith Agglomeration” Chem. Eng. Sci., 43:59- 67, 1988.

Rawlings, J.B., S.M. Miller and W.R. Witkowski. “Model Identification and control ofsolution Crystallization Processes: A Review” Ind. Eng. Chem. Res. 32:1275-1296,1993.

Garside, J. and R.J. Davey. “Secondary Contact Nucleation: Kientics, Growth and Scale-Up” Chem Eng Commun., 4:393, 1980.

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Y. H. Sugita. “Polymorphism of L-Glutamic acid Crystals and Inhibitory Substance for βTransition in beet Molasses” Agric. Biol. Chem. 52:3081-3085, 1988.

Jones, A.G., Budz, J. and J.W. Mullin. “Crystallization Kinetics of Potassium Sulfate inan MSMPR Agitated Vessel” AIChE J. 32:2002-2008, 1986.

Riet,K. and Tramper, J. 1991. “Basic Bioreactor Design”, (Marcel Dekker, New York).

Henry Y. Wang, Pablo La Valle, January 7, 2002