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Improved Product Quality at a Cooling Crystallization Process by Measurement and Control of Supersaturation
0263±8762/97/$07.00+ 0.00 Institution of Chemical Engineers
IMPROVED PRODUCT QUALITY AT A COOLING CRYSTALLIZATION PROCESS BY MEASUREMENT AND CONTROL OF SUPERSATURATION M. KUÈHBERGER and A. MERSMANN Lehrstuhl B fuÈr Verfahrenstechnik, Technical University of Munich, Munich, Germany
A
new supersaturation measurement technique is presented, based on forced encrustation of a cooled sensor surface. After a short discussion of aspects of the control of supersaturation, the measurement principle is introduced. The relationship between encrustation mass and crystallization heat on the one hand and supersaturation on the other hand is explained. As a main point of this presentation the technical realization of the supersaturation sensor are shown. The explanation of the innovative sensor technique is split into two parts. First, the technical construction is shown and second the detection and analysis of the measuring signal is presented. The integration of the sensor into a control strategy is possible for laboratory experiments. As the experimental results show, supersaturation measurement for systems with a small metastable zone width, such as KNO3, can be carried out in a reliable and accurate way. Furthermore, the universal applicability for various readily soluble solutes poses no problem. Keywords: crystallization; supersaturation; encrustation; sensor; measurement; control
INTRODUCTION The product quality of inorganic or organic crystalline solids produced in the chemical and pharmaceutical industries is in¯ uenced by controlling the crystallization step as a very important chemical engineering process. As shown in Figure 1, there is a well known logical connection between the process parameter supersaturation (local and median values, D c or DÅ c respectively), the kinetic parameters nucleation rate B and growth rate G and the product quality, expressed in terms of CSD, purity, crystal shape, morphology and so on. In industry, the maximum pro® t can be found by plotting the curves of investment and operating costs against the supersaturation. As explained in Kind1, it is possible to ® nd an optimal supersaturation, combining these requirements. Therefore, supersaturation in industrial crystallizers must be measured and controlled as precisely as possible to keep this parameter in the optimal range. However, in industry the measurement of supersaturation is limited to a few alternatives, such as expensive density-meters and not very accurate viscosity-meters. For the highly soluble systems (c * > 0.1 mol l- 1) considered in this presentation, the metastable zone width in terms of subcooling is in the range of 4.0K to 0.1 K. Therefore, the optimal range of relative supersaturation r = D c/ c* is below 0.1. The method for measuring supersaturation and the technical details will be introduced in this paper.
PRINCIPLE OF MEASUREMENT Fundamental Measurement Method A crucial requirement an innovative supersaturation sensor has to meet is to detect the state of saturation or supersaturation before nucleation and crystal growth occur in the crystallizer. That is the only way to keep these two essential process parameters under control. Therefore, a precise state of thermodynamical instability has to be forced on the sensor, so that a measurable signal is created anticipating the prevailing supersaturation of a crystallization step. The method for the supersaturation measurement is based on the encrustation of a cooled sensor plate arranged in a solution with an unknown degree of supersaturation. Figure 2 describes the basics of the measurement idea based on the dependence between supersaturation, encrustation of a cooled surface and the crystallization heat. Under the assumption of a supersaturated solution (D cproc ) a temperature drop on a surface (equivalent to supersaturation D cSensor ) situated in this solution will cause an essential increase of supersaturation (D cmeasure ). After a short induction period, nucleation and crystal growth will start on the surface. The increase of encrustation thereby strongly depends on the supersaturation, as explained later. An increase of the subcooling value will cause an increasing supersaturation leading to a higher crystal mass on the surface (mcryst ). Further, the course of the crystallization heat with time (D H cryst ) depends on the increase of this 213
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Figure 1. Dependence of properties of a crystalline product on supersaturation.Interactionsamong variables in a crystallization process.
encrustation mass. This heat D Hcryst can be related to the change of the surface temperature with time and will therefore give information about the prevailing supersaturation in the process. Thus, the basic statement to the innovative sensor is: The prevailing supersaturation D cproc can be measured by detecting the behaviour of the temperature T surf (t) on a surface where encrustation is forced by cooling.
induction time. This induction time ti depends on the prevailing supersaturation D cSensor such that ti decreases with increasing D cSensor . The explanation for the beginning of nucleation on the surface and not in the solution surrounding the sensor wall can be found by looking at the free surface enthalpy of a critical nucleus for heterogeneous nucleation D Gc, het .
D Gc, het
=f
Ac c 3
CL
with f
=
(2 + cos H)(1 - cos H)2 4
Theoretical Background to the Measurement Method In Figure 3 the generation of a concentration gradient by exceeding the solubility limit and the process of encrustation is illustrated. The creation of a certain supersaturation D cSensor , the thermodynamic driving force of encrustation, is explained in Figure 3a. At the beginning of an experiment the concentration of the solution is adjusted to the solubility at bulk temperature. The pro® le of the solubility, shown in Figure 3a, depends on the pro® le of the temperature near the wall. The small decrease in the solution concentration will not occur before crystals grow on the sensor wall. Figure 3b describes the beginning of nucleation. The time between the beginning of cooling and the detection of the ® rst nucleus on the surface is called
As the surface nucleation enthalpy D Gc, het is smaller than the free nucleation enthalpy D Gc by the factor f , with 0 £ f £ 1, nucleation will start on foreign particles ® rst. If there are no impurities in the solution, the sensor surface represents the only foreign solid. The wetting angle H is formed between the foreign particle surfaces, e.g. the sensor surface, and the growing crystal. There is a certain dependence between the surface and lattice structure of this solid, the supersaturation of the solution and the growth of units forming the wetting angle H with the foreign surface2 . When the angle H is below 180°, the nucleation work is reduced by the wetting surface of the sensor. The factor f in equation (1) takes this reduction
Figure 2. Dependence between the tempeature measurement on a cooled surface and the prevailing supersaturation.
Figure 3. Measuremnt principle with cooled surface and its physical explanation. (a) concentration behaviour (b) induction time (c) kinetic of encrustation.
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Trans IChemE, Vol 75, Part A, February 1997
IMPROVED PRODUCT QUALITY AT A COOLING CRYSTALLIZATION PROCESS into account. c CL is the interfacial tension between nucleus and solution and A c the surface heterogeneous nucleus. In Figure 3c the growth of the crystal layer is shown. The increase of crystal mass with time is the most important parameter in order to determine supersaturation using the new sensor. The crystal layer growth depends on di usion and convection; that means that the growth is hardly in¯ uenced by the integration step. Therefore, the dependence between supersaturation and encrustation can be predicted qualitatively. With increasing concentration di erence, the transport of molecules is accelerated and the growth of crystal mass on the surface increases. The dependence of encrustation mass with time can be predicted as shown in Krause 3. The mass of solid deposited per unit area, mf, is a function of time and can be calculated from: dmf . . (2) m m dt = d - r In most cases of fouling or encrustation, the deposition process (index d) is accompanied by a removal process (index r). The removal is caused by tearing o crystal fragments, by erosion or dissolution. The encrustation, occurring during supersaturation measurements, takes place in a closed measuring cell without ¯ ow above the layer. Therefore no removal process occurs. The present investigation of encrustation resulted in the same asymptotic behaviour of crystal mass with time as described by Krause 3 for fouling with removal of crystal mass. The decreasing slope of the curve of crystal deposit in dependence of the encrustation time can be explained by the growth of the layer. The thicker the layer the better the thermal insulation. Therefore, the temperature at the interface between layer and solution is higher than the temperature on the Peltier-surface, supersaturation decreases with time and therefore the crystal growth slows down. The interfacial temperature can be calculated according to Grigull and Sander 4 under the assumption of nonsteady heat conduction with phase change e ect. The dependence of the mass of incrustation with time can be calculated from equation (3). The mass transfer coe cient at a semipermeable interface, k d, s , used generally for crystal growth, can be calculated according to Mersmann2 from the purely di usive or true mass transfer coe cient k d , as shown in equation (4). dmf . (3) m k (c c* ) dt = d = d, s - s kd (4) k d, s = (1 - w) The actual value of layer growth can be calculated from the increase of layer thickness or mass per unit time. As there are large di erences of temperature between sensor surface and solution in order to obtain high encrustation mass, the prevailing supersaturation on the surface is far beyond a metastable zone width. Therefore, dentritic growth of single crystals on the surface can be observed, and needles are formed. This high growth rate, however, supports the inclusion of solution in the layer. Trans IChemE, Vol 75, Part A, February 1997
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TECHNICAL REALIZATION OF THE SUPERSATURATION SENSOR Cooling Element The technical realization of the measuring necessitates an easy method of cooling and heating the sensor front plate. A Peltier-element (semiconductor unit) which must be supplied with constant direct current is very suitable for this purpose. If this current is kept constant with high accuracy (appr. 0.002% and smaller), the voltage depends only on the temperature di erence between both sides of the element. If the temperature on the heat removing side is kept constant while measuring, the voltage change can be used as a measure for a temperature change on the cooling side of the Peltier-element. This voltage change, therefore, can be used as a measuring signal for the increase of the crystal layer and determination of the supersaturation, as will be shown in the section on the measuring signal. The cooling power of the Peltier-element is determined by the quality of the heat exchanger on the heat removal side of the element5. Furthermore, the geometry of the element and the thermoelectric data play a role.
Sensor Surface The encrustation of the sensor is mainly in¯ uenced by the state (roughness, adsorption layer) of the surface. Unlike to industrial crytallizers, the surface of the sensor should favour encrustation, as high encrustation will lead to stable and reproducable measuring signals. As shown in the previous section on the principle of measurement, a rough surface will lead to higher crystal mass for a given time. Since the encrustation mass is the measure for supersaturation, the time for encrustation will determine the necessary measuring period. In the case of a suitable (rough) surface, the measuring time can be reduced. On the other hand, it is of the utmost importance to keep the surface in its original state in order to obtain stable and reproducable measuring signals, that means crystal layers. As rough surfaces tend to change their state with time, a surface has to be chosen which combines all aspects. The present investigations of di erent materials and surface states have shown that the use of the ceramic-surface of the Peltierelement as the sensor wall is the optimal compromise between short encrustation time and an easy way of restoring the original surface structure after each measurement. The macroscopic smooth surface can be cleaned in an optimal way with regard to time and original state, the microscopic roughness will accelerate the encrustation procedure. Figure 4 shows the supersaturation cell in detail, arranged in a batch - cooling crystallizer of a volume of 0.02 m3 with a marine type propeller and ba‚ es. The control of the crystallizer temperature can be done by regulating a thermostat with the computer. All the equipment for loading and unloading the cell with the solution of unknown supersaturation is mounted in the crystallizer. The electronic equipment for voltage measurement transfers the signal to the analysing computer used for control of the crystallizer.
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Mullin6 and Mersmann2 as
D Hcrys = - D Hi* D Hcrys = - f
Figure 4. Experimental device and the supersaturationsensor in detail.
Measuring Signal For the detection of the mass of the crystal layer growing on the cooled sensor surface, a Peltier-element is used. An electronic plot has been developed to enable both setting an accurate and very stable direct current and measuring thereby the voltage change of the Peltierelement. As will be explained in the section on di erent systems of crystallization, it is necessary to produce di erent cooling temperatures on the sensor surface in order to generate encrustation of di erent highly soluble systems in a reasonably short time. Therefore, the current supply has to be adjustable. KNO3 with a metastable zone width6 of 0.4 K at 25°C tends to high encrustation for a measuring period of about 300 s at a surface subcooling of 8 K. For this subcooling degree, a current of up to 1000 mA is su cient. For an aqueous KAI(SO)4)2 solution, the metastable zone width is 4 K at 25°C and the surface temperature has to be decreased by more than 30 K to obtain a reliable measuring signal. This can be obtained by a current of up to 3000mA. The actual measuring signal is the voltage change during the operation of the Peltier-element. The aim of the development is to measure the increase of crystal mass in-line with the crystallization process. Thereby the measurement technique will not disturb the growth of encrustation mass. The cooling power Qk of the Peltierelement is mainly in¯ uenced by the temperature di erence between the cooling side and the heat removal side of the Peltier-element, D T u o , and by the cooling side temperature T o , as shown in equation (5)5. In this equation n is the number of elements, I the current, R the resistance, k is the 1 q (5) Qk = n(eT o I - I 2 R - 2k D T u o ) 2 l coe cient of thermal conductivity, q the cross section of the element and l its length. Thus the dependence between voltage change and the surface temperature T o can be detected under the condition of a constant temperature on the backside of the Peltier-element, T u . During the growth of a crust on the cooled plate, the heat of crystallization is released. This phase transition heat leads to a temperature increase on the surface, which can be measured by the voltage change. The heat of crystallization D Hcrys can be calculated according to
é ù ë ( )û ï ï
d lna *i ½ * ½ for a i ® ai 1 d T
(6) (7)
Measurement of the temperature in this way enables the registration of the heat of crystallization all over the surface. Therefore, the measuring system produces a stable and reproducible signal. The measurement of surface temperature with small conventional probes (Pt100) will give scattering and therefore unreliable local information. The use of probes covering parts of the surface will disturb the encrustation process and thus the measuring signal. In Figure 5 the curve of the measuring signal is plotted against time to compare experiments with pure water (cooling down behaviour) with saturated KNO3 solution (cooling down and encrustation behaviour). Four time periods can be distinguished on the plot. Section 0: the behaviour of both systems is the same. The Peltier-element surface starts cooling, the surface temperature decreases, the temperature di erence D T u o rises and the measuring signal increases. Section I: The signal curve for the KNO3 solution begins to di er from that of water. This is the point of the end of the induction period. The supersaturation is rising up to a value where nucleation and crystal growth become detectable. First small crystals are produced and therefore crystallization heat is developed. The growth of single crystals is enhanced up to the point when a compact encrustation layer is formed. The heat of crystallization produced exceeds the cooling power of the Peltier-element. The measuring signal runs through the relative maximum. Section II: The signal passes through a relative minimum. More crystal mass is growing and the thickness of the layer increases. According to Krause 3 the encrustation mass show an asymptotic behaviour with time and the heat of crystallization is reduced. At this moment the cooling power of the Peltier-element is
Figure 5. Dependence of the measuring voltage signal versus time for four di erent periods.
Trans IChemE, Vol 75, Part A, February 1997
IMPROVED PRODUCT QUALITY AT A COOLING CRYSTALLIZATION PROCESS again su cient to cool the surface, and the measuring signal reaches the relative minimum. Section III: The curve of the measuring signal rises with a de® nite slope. In this section an almost constant layer thickness is obtained. As only little heat of crystallization is produced, the surface temperature is cooled down and the signal rises. Figure 6 give an example of the measuring signals received for di erent surface subcooling values. As the experiments are carried out with a saturated KNO3 solution at 25°C, varying the subcooling corresponds with the variation of supersaturation D cSensor . For higher sensor subcooling, such as 9.78 K, the encrustation of the surface takes place faster than for the lowest subcooling under investigation (6.64 K). The relative maximum as well as the relative minimum (according to section I and II, Figure 5) occur earlier and the time between both is shorter. This can only be explained by an increase of the heat of crystallization due to higher encrustation mass for increasing supersaturation. The di erence between the measuring signals now can be used in laboratory scale (see Figure 4) in connection with calibration lines to recalculate the supersaturation prevailing in the crystallizer (D cproc ). As the signal curves versus time di er with solubility and surface subcooling, an array of calibration measurements have to be placed on disposal for analysis purposes. To simplify the calibration measurement, the array can be calculated from a few essential calibration experiments. The following conclusions can be drawn from the experiments presented in Figure 6: mass as a measure for supersatura·tionThecanencrustation be detected due to the heat of crystallization released during encrustation and the resulting thermal e ects on the sensor surface. The measuring signal, the Peltier-element voltage, ·depends on the surface temperature. DIFFERENT SYSTEMS OF CRYSTALLIZATION The innovative measurement technique based on encrustation is especially suitable for highly soluble systems (c* ³ 0.1 mol l- 1 ), which are industrially crystallized at relative supersaturation r between 0.001 and 0.1. Experiments with di erent chemical systems are carried
Figure 6. Measuring signal of encrustation experiments with aqueous KNO3 solutions at di erent surface subcoolingvalues.
Trans IChemE, Vol 75, Part A, February 1997
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out, to prove the usability of the sensor for various applications. The aim of the experiments is to obtain detectable encrustation in a reasonable time (below 300 s). It can be shown that there are two crucial properties for encrustation, the slope of the solubility curve and the metastable zone width of the system. They have to match data which are suitable for the cooling principle, i.e. dc* / dq > 0.01kmol (m- 3 K - 1), D Tmet < 2.0 K. Experiments have been carried out to investigate the dependencebetween these two parameters and the encrustation behaviour. A measuring cell similar to that described above has been used to produce encrustation of di erent systems. The crystal layer produced by cooling was been removed and the mass of the layer measured by a balance. Figure 7 describes the results of these encrustation experiments. The solution was saturated at 40°C and the surface was subcooled for D T = 8 K. Curves are plotted for two di erent encrustation times (120 s, 300s). The di erent crystallizing systems have metastable zone widths in a range of 0.3 K up to 4.0K at a temperature of 25°C. As shown in Figure 7, the encrustation mass created in experiments with KNO3 is more than 100 times the mass of the KAl(SO4 ) 2 encrustation. As the subcooling span is kept constant, the following conclusion can be drawn from the results. The more the metastable zone is exceeded by the sensor subcooling, the larger is the encrustation mass. For the system H2 O-KNO3 the chosen subcooling of 8K is su cient to produce a measurable encrustation. For the system under investigation with the largest metastable zone width, the subcooling does not exceed the metastable zone far enough and no detectable crystal mass is obtained. Experiments with the sensor threw light on the encrustation behaviour of KAl(SO4 )2 . At a surface subcooling of below 20K, nucleation and crystal growth have been so slow that only a few single slowly growing crystals occurred but no compact layer at all has been produced. Therefore it is necessary to exceed the metastable zone far enough to produce a compact layer and a reproducible signal. As a rule an encrustation layer and a reliable signal can be obtained when the metastable zone width is at least exceeded by a factor of ten.
Figure 7. Dependence of encrustation mass on metastable zone width for di erent crystallizingsystems.
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CONTROL OF SUPERSATURATION In batch cooling crystallizers the generation of supersaturation depends on the cooling rate. Signi® cant improvement in the product CSD has been observed using an optimal cooling rate in comparison with linear cooling rate or a natural cooling rate. When dealing with continuous crystallizers, it is possible to obtain optimum supersaturation D copt resulting in a moderate nucleation rate and favourable growth rate by a proper residence time in combination with a constant cooling rate2. Nevertheless, there are major problems with the control of supersaturation when starting up a continuous industrial crystallizer. These crystallizers in some cases show a swinging behaviour in supersaturation during the process start and even during operation time. All these e ects can be controlled by an appropriate cooling course. However, the control of supersaturation requires a reliable and easy measurement of supersaturation. Running a batch crystallizer raises comparable problems. If the process is uncontrolled, the supersaturation will exceed the metastable limit and spontaneous nucleation and wall fouling result, leading to undesirable CSD, loss of product, and increased cycle time for cleaning2. Mayrhofer and Nyvlt7 , for example, have derived an analytic expression for the optimal temperature pro® le of a seeded and an unseeded batch crystallizer. However, in industry batch crystallizers are usually not operated at constant supersaturation because a programmed cooling process is too expensive and not reliable enough. Moreover, each precalculated temperature course has the problem that there is no possibility of responding to any disturbance. As supersaturation is the driving force in industrial crystallizers, every important in¯ uence and the resulting e ect must be observed and controlled. In industry temperature control is achieved by throttling the ¯ ow rate of steam-water mix to the crystallizer jacket. Under certain circumstances when large cooling rates are required, a refrigeration system may be necessary. Dealing with experiments at laboratory scale carried out with a crystallizer volume of about 20 litres the control of temperature is managed by thermostats. Therefore, the time delay of supersaturation measurement and thermostat reaction have to be taken into consideration. Gutwald8 managed the control of a cooling crystallizer based on concentration measurement by using a density meter. The prevailing concentration is thereby compared with an optimal value calculated from a ® xed optimal supersaturation. The temperature of the cooling circuit could be changed to control the process. The same control strategy is applicable for the new measurement technique. The only modi® cation is that the density meter is replaced by the supersaturation sensor. FINAL REMARKS The new inexpensive supersaturation measurement technique presented in this paper is suitable for highly soluble systems. An application of the sensor in industrial crystallizers has to be investigated to check the in¯ uence of disturbances or variation of operational
conditions on the measuring signal. In particular, the long-term stability of the voltage signal has to be tested. For systems with a metastable zone width of above 3 K, further research must be carried out to improve the reproducibility and the accuracy of the measuring signal. NOMENCLATURE Ac surface of critical nucleus, m2 ai activity of component i, a*i saturation activity of component i, c molar concentration, kmolm- 3 c* molar saturation concentration kmol m- 3 D c concentration driving force or supersaturation, kmolm- 3 e thermal force of Peltier element, VK - 1 f factor, D Gc,het free surface enthalpy of a critical nucleus, J mol- 1 D Hcrys heat of crystallization, J mol- 1 D Hi* di erent heat of solution, J mol- 1 I curent, A kd mass transfer coe cient, ms- 1 k d,s mass transfer coe cient at semiperm. interface, ms- 1 l length of Peltier element, m L 50 median crystal size, m md mass of deposit, kg mf fouling mass, kg mr mass of removal, kg n number of Peltier elements, q cross section area of Peltier, m2 Qk cooling power, W R electric resistance of Peltier element, V f ideal gas constant, J mol- 1 K- 1 t measuring time, s ti induction time, s To temperature of cooling side, K Tu temperature of heat removal side, K D T uo temperature di erence, K D T met metastable zone width, K U voltage, V w mass fraction, kgkg- 1 c CL interfacial tension, J m- 2 contact angle, 0 H q celsius temperature, °C r relative supersaturation, k coe cient of thermal conductivity, Wm- 1 k- 1
REFERENCES 1. Kind, M., 1989, UÈber die UÈbersaÈttigung waÈhrend der Kornkristallisation aus LoÈsungen, Thesis, (TU Munich). 2. Mersmann,A., 1995, CrystallizationTechnologyHandbook ( Marcel Dekker, New York) . 3. Krause, S., 1993, Fouling of heat transfer surfacesby crystallization and sedimentation, Int Chem Eng, 33: 355±401. 4. Grigull, U. and Sandner, H., 1979, WaÈrmeleitung (Springer Verlag, Berlin). 5. MuÈller H., 1963, Bermessung und Aufbau von Peltieraggregaten, KaÈltetechnik, 5: 137±143. 6. Mullin, J. W., 1993, Crystallization, 3rd ed. (Butterworth-Heinemann, Oxford). 7. Mayrhofer, B., Nyvlt, J. 1988, Programmed cooling of batch crystallizer, Chem Eng Process, 24: 217. 8. Gutwald, T., 1991, UÈ ber die Bestimmung kinetischer Parameter bei der diskontinuierlichen Kristallisation aus LoÈsungen, Thesis, (TU Munich).
ADDRESS Correspondence concerning this paper should be addressed to Dipl-Ing M. KuÈhberger, Lehrstuhl B fuÈr Verfahnenstechnik,Technical University of Munich, Arcisstrasse 21, 80333 Munich, Germany.
Trans IChemE, Vol 75, Part A, February 1997
0263±8762/97/$07.00+ 0.00 Institution of Chemical Engineers
IMPROVED PRODUCT QUALITY AT A COOLING CRYSTALLIZATION PROCESS BY MEASUREMENT AND CONTROL OF SUPERSATURATION M. KUÈHBERGER and A. MERSMANN Lehrstuhl B fuÈr Verfahrenstechnik, Technical University of Munich, Munich, Germany
A
new supersaturation measurement technique is presented, based on forced encrustation of a cooled sensor surface. After a short discussion of aspects of the control of supersaturation, the measurement principle is introduced. The relationship between encrustation mass and crystallization heat on the one hand and supersaturation on the other hand is explained. As a main point of this presentation the technical realization of the supersaturation sensor are shown. The explanation of the innovative sensor technique is split into two parts. First, the technical construction is shown and second the detection and analysis of the measuring signal is presented. The integration of the sensor into a control strategy is possible for laboratory experiments. As the experimental results show, supersaturation measurement for systems with a small metastable zone width, such as KNO3, can be carried out in a reliable and accurate way. Furthermore, the universal applicability for various readily soluble solutes poses no problem. Keywords: crystallization; supersaturation; encrustation; sensor; measurement; control
INTRODUCTION The product quality of inorganic or organic crystalline solids produced in the chemical and pharmaceutical industries is in¯ uenced by controlling the crystallization step as a very important chemical engineering process. As shown in Figure 1, there is a well known logical connection between the process parameter supersaturation (local and median values, D c or DÅ c respectively), the kinetic parameters nucleation rate B and growth rate G and the product quality, expressed in terms of CSD, purity, crystal shape, morphology and so on. In industry, the maximum pro® t can be found by plotting the curves of investment and operating costs against the supersaturation. As explained in Kind1, it is possible to ® nd an optimal supersaturation, combining these requirements. Therefore, supersaturation in industrial crystallizers must be measured and controlled as precisely as possible to keep this parameter in the optimal range. However, in industry the measurement of supersaturation is limited to a few alternatives, such as expensive density-meters and not very accurate viscosity-meters. For the highly soluble systems (c * > 0.1 mol l- 1) considered in this presentation, the metastable zone width in terms of subcooling is in the range of 4.0K to 0.1 K. Therefore, the optimal range of relative supersaturation r = D c/ c* is below 0.1. The method for measuring supersaturation and the technical details will be introduced in this paper.
PRINCIPLE OF MEASUREMENT Fundamental Measurement Method A crucial requirement an innovative supersaturation sensor has to meet is to detect the state of saturation or supersaturation before nucleation and crystal growth occur in the crystallizer. That is the only way to keep these two essential process parameters under control. Therefore, a precise state of thermodynamical instability has to be forced on the sensor, so that a measurable signal is created anticipating the prevailing supersaturation of a crystallization step. The method for the supersaturation measurement is based on the encrustation of a cooled sensor plate arranged in a solution with an unknown degree of supersaturation. Figure 2 describes the basics of the measurement idea based on the dependence between supersaturation, encrustation of a cooled surface and the crystallization heat. Under the assumption of a supersaturated solution (D cproc ) a temperature drop on a surface (equivalent to supersaturation D cSensor ) situated in this solution will cause an essential increase of supersaturation (D cmeasure ). After a short induction period, nucleation and crystal growth will start on the surface. The increase of encrustation thereby strongly depends on the supersaturation, as explained later. An increase of the subcooling value will cause an increasing supersaturation leading to a higher crystal mass on the surface (mcryst ). Further, the course of the crystallization heat with time (D H cryst ) depends on the increase of this 213
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KUÈHBERGER and MERSMANN
Figure 1. Dependence of properties of a crystalline product on supersaturation.Interactionsamong variables in a crystallization process.
encrustation mass. This heat D Hcryst can be related to the change of the surface temperature with time and will therefore give information about the prevailing supersaturation in the process. Thus, the basic statement to the innovative sensor is: The prevailing supersaturation D cproc can be measured by detecting the behaviour of the temperature T surf (t) on a surface where encrustation is forced by cooling.
induction time. This induction time ti depends on the prevailing supersaturation D cSensor such that ti decreases with increasing D cSensor . The explanation for the beginning of nucleation on the surface and not in the solution surrounding the sensor wall can be found by looking at the free surface enthalpy of a critical nucleus for heterogeneous nucleation D Gc, het .
D Gc, het
=f
Ac c 3
CL
with f
=
(2 + cos H)(1 - cos H)2 4
Theoretical Background to the Measurement Method In Figure 3 the generation of a concentration gradient by exceeding the solubility limit and the process of encrustation is illustrated. The creation of a certain supersaturation D cSensor , the thermodynamic driving force of encrustation, is explained in Figure 3a. At the beginning of an experiment the concentration of the solution is adjusted to the solubility at bulk temperature. The pro® le of the solubility, shown in Figure 3a, depends on the pro® le of the temperature near the wall. The small decrease in the solution concentration will not occur before crystals grow on the sensor wall. Figure 3b describes the beginning of nucleation. The time between the beginning of cooling and the detection of the ® rst nucleus on the surface is called
As the surface nucleation enthalpy D Gc, het is smaller than the free nucleation enthalpy D Gc by the factor f , with 0 £ f £ 1, nucleation will start on foreign particles ® rst. If there are no impurities in the solution, the sensor surface represents the only foreign solid. The wetting angle H is formed between the foreign particle surfaces, e.g. the sensor surface, and the growing crystal. There is a certain dependence between the surface and lattice structure of this solid, the supersaturation of the solution and the growth of units forming the wetting angle H with the foreign surface2 . When the angle H is below 180°, the nucleation work is reduced by the wetting surface of the sensor. The factor f in equation (1) takes this reduction
Figure 2. Dependence between the tempeature measurement on a cooled surface and the prevailing supersaturation.
Figure 3. Measuremnt principle with cooled surface and its physical explanation. (a) concentration behaviour (b) induction time (c) kinetic of encrustation.
(1)
Trans IChemE, Vol 75, Part A, February 1997
IMPROVED PRODUCT QUALITY AT A COOLING CRYSTALLIZATION PROCESS into account. c CL is the interfacial tension between nucleus and solution and A c the surface heterogeneous nucleus. In Figure 3c the growth of the crystal layer is shown. The increase of crystal mass with time is the most important parameter in order to determine supersaturation using the new sensor. The crystal layer growth depends on di usion and convection; that means that the growth is hardly in¯ uenced by the integration step. Therefore, the dependence between supersaturation and encrustation can be predicted qualitatively. With increasing concentration di erence, the transport of molecules is accelerated and the growth of crystal mass on the surface increases. The dependence of encrustation mass with time can be predicted as shown in Krause 3. The mass of solid deposited per unit area, mf, is a function of time and can be calculated from: dmf . . (2) m m dt = d - r In most cases of fouling or encrustation, the deposition process (index d) is accompanied by a removal process (index r). The removal is caused by tearing o crystal fragments, by erosion or dissolution. The encrustation, occurring during supersaturation measurements, takes place in a closed measuring cell without ¯ ow above the layer. Therefore no removal process occurs. The present investigation of encrustation resulted in the same asymptotic behaviour of crystal mass with time as described by Krause 3 for fouling with removal of crystal mass. The decreasing slope of the curve of crystal deposit in dependence of the encrustation time can be explained by the growth of the layer. The thicker the layer the better the thermal insulation. Therefore, the temperature at the interface between layer and solution is higher than the temperature on the Peltier-surface, supersaturation decreases with time and therefore the crystal growth slows down. The interfacial temperature can be calculated according to Grigull and Sander 4 under the assumption of nonsteady heat conduction with phase change e ect. The dependence of the mass of incrustation with time can be calculated from equation (3). The mass transfer coe cient at a semipermeable interface, k d, s , used generally for crystal growth, can be calculated according to Mersmann2 from the purely di usive or true mass transfer coe cient k d , as shown in equation (4). dmf . (3) m k (c c* ) dt = d = d, s - s kd (4) k d, s = (1 - w) The actual value of layer growth can be calculated from the increase of layer thickness or mass per unit time. As there are large di erences of temperature between sensor surface and solution in order to obtain high encrustation mass, the prevailing supersaturation on the surface is far beyond a metastable zone width. Therefore, dentritic growth of single crystals on the surface can be observed, and needles are formed. This high growth rate, however, supports the inclusion of solution in the layer. Trans IChemE, Vol 75, Part A, February 1997
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TECHNICAL REALIZATION OF THE SUPERSATURATION SENSOR Cooling Element The technical realization of the measuring necessitates an easy method of cooling and heating the sensor front plate. A Peltier-element (semiconductor unit) which must be supplied with constant direct current is very suitable for this purpose. If this current is kept constant with high accuracy (appr. 0.002% and smaller), the voltage depends only on the temperature di erence between both sides of the element. If the temperature on the heat removing side is kept constant while measuring, the voltage change can be used as a measure for a temperature change on the cooling side of the Peltier-element. This voltage change, therefore, can be used as a measuring signal for the increase of the crystal layer and determination of the supersaturation, as will be shown in the section on the measuring signal. The cooling power of the Peltier-element is determined by the quality of the heat exchanger on the heat removal side of the element5. Furthermore, the geometry of the element and the thermoelectric data play a role.
Sensor Surface The encrustation of the sensor is mainly in¯ uenced by the state (roughness, adsorption layer) of the surface. Unlike to industrial crytallizers, the surface of the sensor should favour encrustation, as high encrustation will lead to stable and reproducable measuring signals. As shown in the previous section on the principle of measurement, a rough surface will lead to higher crystal mass for a given time. Since the encrustation mass is the measure for supersaturation, the time for encrustation will determine the necessary measuring period. In the case of a suitable (rough) surface, the measuring time can be reduced. On the other hand, it is of the utmost importance to keep the surface in its original state in order to obtain stable and reproducable measuring signals, that means crystal layers. As rough surfaces tend to change their state with time, a surface has to be chosen which combines all aspects. The present investigations of di erent materials and surface states have shown that the use of the ceramic-surface of the Peltierelement as the sensor wall is the optimal compromise between short encrustation time and an easy way of restoring the original surface structure after each measurement. The macroscopic smooth surface can be cleaned in an optimal way with regard to time and original state, the microscopic roughness will accelerate the encrustation procedure. Figure 4 shows the supersaturation cell in detail, arranged in a batch - cooling crystallizer of a volume of 0.02 m3 with a marine type propeller and ba‚ es. The control of the crystallizer temperature can be done by regulating a thermostat with the computer. All the equipment for loading and unloading the cell with the solution of unknown supersaturation is mounted in the crystallizer. The electronic equipment for voltage measurement transfers the signal to the analysing computer used for control of the crystallizer.
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Mullin6 and Mersmann2 as
D Hcrys = - D Hi* D Hcrys = - f
Figure 4. Experimental device and the supersaturationsensor in detail.
Measuring Signal For the detection of the mass of the crystal layer growing on the cooled sensor surface, a Peltier-element is used. An electronic plot has been developed to enable both setting an accurate and very stable direct current and measuring thereby the voltage change of the Peltierelement. As will be explained in the section on di erent systems of crystallization, it is necessary to produce di erent cooling temperatures on the sensor surface in order to generate encrustation of di erent highly soluble systems in a reasonably short time. Therefore, the current supply has to be adjustable. KNO3 with a metastable zone width6 of 0.4 K at 25°C tends to high encrustation for a measuring period of about 300 s at a surface subcooling of 8 K. For this subcooling degree, a current of up to 1000 mA is su cient. For an aqueous KAI(SO)4)2 solution, the metastable zone width is 4 K at 25°C and the surface temperature has to be decreased by more than 30 K to obtain a reliable measuring signal. This can be obtained by a current of up to 3000mA. The actual measuring signal is the voltage change during the operation of the Peltier-element. The aim of the development is to measure the increase of crystal mass in-line with the crystallization process. Thereby the measurement technique will not disturb the growth of encrustation mass. The cooling power Qk of the Peltierelement is mainly in¯ uenced by the temperature di erence between the cooling side and the heat removal side of the Peltier-element, D T u o , and by the cooling side temperature T o , as shown in equation (5)5. In this equation n is the number of elements, I the current, R the resistance, k is the 1 q (5) Qk = n(eT o I - I 2 R - 2k D T u o ) 2 l coe cient of thermal conductivity, q the cross section of the element and l its length. Thus the dependence between voltage change and the surface temperature T o can be detected under the condition of a constant temperature on the backside of the Peltier-element, T u . During the growth of a crust on the cooled plate, the heat of crystallization is released. This phase transition heat leads to a temperature increase on the surface, which can be measured by the voltage change. The heat of crystallization D Hcrys can be calculated according to
é ù ë ( )û ï ï
d lna *i ½ * ½ for a i ® ai 1 d T
(6) (7)
Measurement of the temperature in this way enables the registration of the heat of crystallization all over the surface. Therefore, the measuring system produces a stable and reproducible signal. The measurement of surface temperature with small conventional probes (Pt100) will give scattering and therefore unreliable local information. The use of probes covering parts of the surface will disturb the encrustation process and thus the measuring signal. In Figure 5 the curve of the measuring signal is plotted against time to compare experiments with pure water (cooling down behaviour) with saturated KNO3 solution (cooling down and encrustation behaviour). Four time periods can be distinguished on the plot. Section 0: the behaviour of both systems is the same. The Peltier-element surface starts cooling, the surface temperature decreases, the temperature di erence D T u o rises and the measuring signal increases. Section I: The signal curve for the KNO3 solution begins to di er from that of water. This is the point of the end of the induction period. The supersaturation is rising up to a value where nucleation and crystal growth become detectable. First small crystals are produced and therefore crystallization heat is developed. The growth of single crystals is enhanced up to the point when a compact encrustation layer is formed. The heat of crystallization produced exceeds the cooling power of the Peltier-element. The measuring signal runs through the relative maximum. Section II: The signal passes through a relative minimum. More crystal mass is growing and the thickness of the layer increases. According to Krause 3 the encrustation mass show an asymptotic behaviour with time and the heat of crystallization is reduced. At this moment the cooling power of the Peltier-element is
Figure 5. Dependence of the measuring voltage signal versus time for four di erent periods.
Trans IChemE, Vol 75, Part A, February 1997
IMPROVED PRODUCT QUALITY AT A COOLING CRYSTALLIZATION PROCESS again su cient to cool the surface, and the measuring signal reaches the relative minimum. Section III: The curve of the measuring signal rises with a de® nite slope. In this section an almost constant layer thickness is obtained. As only little heat of crystallization is produced, the surface temperature is cooled down and the signal rises. Figure 6 give an example of the measuring signals received for di erent surface subcooling values. As the experiments are carried out with a saturated KNO3 solution at 25°C, varying the subcooling corresponds with the variation of supersaturation D cSensor . For higher sensor subcooling, such as 9.78 K, the encrustation of the surface takes place faster than for the lowest subcooling under investigation (6.64 K). The relative maximum as well as the relative minimum (according to section I and II, Figure 5) occur earlier and the time between both is shorter. This can only be explained by an increase of the heat of crystallization due to higher encrustation mass for increasing supersaturation. The di erence between the measuring signals now can be used in laboratory scale (see Figure 4) in connection with calibration lines to recalculate the supersaturation prevailing in the crystallizer (D cproc ). As the signal curves versus time di er with solubility and surface subcooling, an array of calibration measurements have to be placed on disposal for analysis purposes. To simplify the calibration measurement, the array can be calculated from a few essential calibration experiments. The following conclusions can be drawn from the experiments presented in Figure 6: mass as a measure for supersatura·tionThecanencrustation be detected due to the heat of crystallization released during encrustation and the resulting thermal e ects on the sensor surface. The measuring signal, the Peltier-element voltage, ·depends on the surface temperature. DIFFERENT SYSTEMS OF CRYSTALLIZATION The innovative measurement technique based on encrustation is especially suitable for highly soluble systems (c* ³ 0.1 mol l- 1 ), which are industrially crystallized at relative supersaturation r between 0.001 and 0.1. Experiments with di erent chemical systems are carried
Figure 6. Measuring signal of encrustation experiments with aqueous KNO3 solutions at di erent surface subcoolingvalues.
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out, to prove the usability of the sensor for various applications. The aim of the experiments is to obtain detectable encrustation in a reasonable time (below 300 s). It can be shown that there are two crucial properties for encrustation, the slope of the solubility curve and the metastable zone width of the system. They have to match data which are suitable for the cooling principle, i.e. dc* / dq > 0.01kmol (m- 3 K - 1), D Tmet < 2.0 K. Experiments have been carried out to investigate the dependencebetween these two parameters and the encrustation behaviour. A measuring cell similar to that described above has been used to produce encrustation of di erent systems. The crystal layer produced by cooling was been removed and the mass of the layer measured by a balance. Figure 7 describes the results of these encrustation experiments. The solution was saturated at 40°C and the surface was subcooled for D T = 8 K. Curves are plotted for two di erent encrustation times (120 s, 300s). The di erent crystallizing systems have metastable zone widths in a range of 0.3 K up to 4.0K at a temperature of 25°C. As shown in Figure 7, the encrustation mass created in experiments with KNO3 is more than 100 times the mass of the KAl(SO4 ) 2 encrustation. As the subcooling span is kept constant, the following conclusion can be drawn from the results. The more the metastable zone is exceeded by the sensor subcooling, the larger is the encrustation mass. For the system H2 O-KNO3 the chosen subcooling of 8K is su cient to produce a measurable encrustation. For the system under investigation with the largest metastable zone width, the subcooling does not exceed the metastable zone far enough and no detectable crystal mass is obtained. Experiments with the sensor threw light on the encrustation behaviour of KAl(SO4 )2 . At a surface subcooling of below 20K, nucleation and crystal growth have been so slow that only a few single slowly growing crystals occurred but no compact layer at all has been produced. Therefore it is necessary to exceed the metastable zone far enough to produce a compact layer and a reproducible signal. As a rule an encrustation layer and a reliable signal can be obtained when the metastable zone width is at least exceeded by a factor of ten.
Figure 7. Dependence of encrustation mass on metastable zone width for di erent crystallizingsystems.
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CONTROL OF SUPERSATURATION In batch cooling crystallizers the generation of supersaturation depends on the cooling rate. Signi® cant improvement in the product CSD has been observed using an optimal cooling rate in comparison with linear cooling rate or a natural cooling rate. When dealing with continuous crystallizers, it is possible to obtain optimum supersaturation D copt resulting in a moderate nucleation rate and favourable growth rate by a proper residence time in combination with a constant cooling rate2. Nevertheless, there are major problems with the control of supersaturation when starting up a continuous industrial crystallizer. These crystallizers in some cases show a swinging behaviour in supersaturation during the process start and even during operation time. All these e ects can be controlled by an appropriate cooling course. However, the control of supersaturation requires a reliable and easy measurement of supersaturation. Running a batch crystallizer raises comparable problems. If the process is uncontrolled, the supersaturation will exceed the metastable limit and spontaneous nucleation and wall fouling result, leading to undesirable CSD, loss of product, and increased cycle time for cleaning2. Mayrhofer and Nyvlt7 , for example, have derived an analytic expression for the optimal temperature pro® le of a seeded and an unseeded batch crystallizer. However, in industry batch crystallizers are usually not operated at constant supersaturation because a programmed cooling process is too expensive and not reliable enough. Moreover, each precalculated temperature course has the problem that there is no possibility of responding to any disturbance. As supersaturation is the driving force in industrial crystallizers, every important in¯ uence and the resulting e ect must be observed and controlled. In industry temperature control is achieved by throttling the ¯ ow rate of steam-water mix to the crystallizer jacket. Under certain circumstances when large cooling rates are required, a refrigeration system may be necessary. Dealing with experiments at laboratory scale carried out with a crystallizer volume of about 20 litres the control of temperature is managed by thermostats. Therefore, the time delay of supersaturation measurement and thermostat reaction have to be taken into consideration. Gutwald8 managed the control of a cooling crystallizer based on concentration measurement by using a density meter. The prevailing concentration is thereby compared with an optimal value calculated from a ® xed optimal supersaturation. The temperature of the cooling circuit could be changed to control the process. The same control strategy is applicable for the new measurement technique. The only modi® cation is that the density meter is replaced by the supersaturation sensor. FINAL REMARKS The new inexpensive supersaturation measurement technique presented in this paper is suitable for highly soluble systems. An application of the sensor in industrial crystallizers has to be investigated to check the in¯ uence of disturbances or variation of operational
conditions on the measuring signal. In particular, the long-term stability of the voltage signal has to be tested. For systems with a metastable zone width of above 3 K, further research must be carried out to improve the reproducibility and the accuracy of the measuring signal. NOMENCLATURE Ac surface of critical nucleus, m2 ai activity of component i, a*i saturation activity of component i, c molar concentration, kmolm- 3 c* molar saturation concentration kmol m- 3 D c concentration driving force or supersaturation, kmolm- 3 e thermal force of Peltier element, VK - 1 f factor, D Gc,het free surface enthalpy of a critical nucleus, J mol- 1 D Hcrys heat of crystallization, J mol- 1 D Hi* di erent heat of solution, J mol- 1 I curent, A kd mass transfer coe cient, ms- 1 k d,s mass transfer coe cient at semiperm. interface, ms- 1 l length of Peltier element, m L 50 median crystal size, m md mass of deposit, kg mf fouling mass, kg mr mass of removal, kg n number of Peltier elements, q cross section area of Peltier, m2 Qk cooling power, W R electric resistance of Peltier element, V f ideal gas constant, J mol- 1 K- 1 t measuring time, s ti induction time, s To temperature of cooling side, K Tu temperature of heat removal side, K D T uo temperature di erence, K D T met metastable zone width, K U voltage, V w mass fraction, kgkg- 1 c CL interfacial tension, J m- 2 contact angle, 0 H q celsius temperature, °C r relative supersaturation, k coe cient of thermal conductivity, Wm- 1 k- 1
REFERENCES 1. Kind, M., 1989, UÈber die UÈbersaÈttigung waÈhrend der Kornkristallisation aus LoÈsungen, Thesis, (TU Munich). 2. Mersmann,A., 1995, CrystallizationTechnologyHandbook ( Marcel Dekker, New York) . 3. Krause, S., 1993, Fouling of heat transfer surfacesby crystallization and sedimentation, Int Chem Eng, 33: 355±401. 4. Grigull, U. and Sandner, H., 1979, WaÈrmeleitung (Springer Verlag, Berlin). 5. MuÈller H., 1963, Bermessung und Aufbau von Peltieraggregaten, KaÈltetechnik, 5: 137±143. 6. Mullin, J. W., 1993, Crystallization, 3rd ed. (Butterworth-Heinemann, Oxford). 7. Mayrhofer, B., Nyvlt, J. 1988, Programmed cooling of batch crystallizer, Chem Eng Process, 24: 217. 8. Gutwald, T., 1991, UÈ ber die Bestimmung kinetischer Parameter bei der diskontinuierlichen Kristallisation aus LoÈsungen, Thesis, (TU Munich).
ADDRESS Correspondence concerning this paper should be addressed to Dipl-Ing M. KuÈhberger, Lehrstuhl B fuÈr Verfahnenstechnik,Technical University of Munich, Arcisstrasse 21, 80333 Munich, Germany.
Trans IChemE, Vol 75, Part A, February 1997