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Experimental Study and Theoretical Approach of Cooling Surfaces Fouling in Industrial Crystallizers
0263±8762/97/$07.00+ 0.00 Institution of Chemical Engineers
EXPERIMENTAL STUDY AND THEORETICAL APPROACH OF COOLING SURFACES FOULING IN INDUSTRIAL CRYSTALLIZERS S. BRIANCËON, D. COLSON and J. P. KLEIN Laboratoire d’Automatique et de Ge nie des Proce de s ( LAGEP) , UniversiteÂClaude Bernard Lyon 1, Villeurbanne, France
F
ouling of cooling surfaces of industrial crystallizers is a major problem which reduces the productivity of installations. This phenomenon, which results from the surface temperature being lower than that of the bulk so as to allow heat transfer, is essentially initiated by primary heterogeneous nucleation. The experimental setup has been designed to study the in¯ uence of di erent parameters such as suspension ¯ ow velocity, temperatures, the nature and the ® nish of the deposit surface, as well as the nature of the product which crystallizes. The conditions of the appearance of a crystalline layer and its subsequent growth are studied simultaneously by measuring the inlet and outlet temperatures of the two ¯ uids which leads to calculation of the degradation of overall heat transfer coe cient and, more directly, by physically measuring the evolution in time of the thickness pro® le. Keywords: fouling; crystallisation; heterogeneous nucleation; crystal deposit; heat exchange surface; roughness
INTRODUCTION Encrustation is the industrial term used to describe the progressive fouling of cooling crystallizers. This phenomenon is particularly troublesome for the productivity of installations and incurs heavy economic penalties. Fouling of heat transfer surfaces is a problem inherent in many of the unit operations of chemical engineering and has been studied especially in the ® eld of heat exchangers1. However, during cooling crystallization, fouling is favoured by the very nature of the process. Indeed, near the exchange surfaces, the bulk temperature is the lowest in the crystallizer. Supersaturation which leads to crystallization is at its maximum value at the wall and nucleation preferentially occurs there leading to the growth of a crystalline layer that increases the thermal resistance of the system. Fouling is in¯ uenced by a great number of parameters, on the one hand by physical ones such as ¯ ow velocity near the wall, temperature and the chemical nature and surface ® nish of the wall. On the other hand, the chemical concentration of the di erent compounds (solute, solvent, impurities) has to be taken into account. The great number of these parameters and their interdependence explain the di culties encountered when predicting fouling by a theoretical approach. That is the reason why this phenomenon is essentially represented by empirical laws for each particular case. This allows optimal operating conditions and technical solutions to be obtained which avoid, or at least reduce, fouling, for a speci® c process2 . The objective of this work is to understand the mechanisms involved in fouling and to generalize the
empirical laws. The ® nal aim is to provide solutions to reduce and control fouling, without carrying out experimental work which could prove too unwieldy. EXPERIMENTAL SETUP Description The experimental setup shown in Figure 1 comprises two main elements: a stirred tank with an external jacket (1) and an annular crystallizer (4). The bulk solution is prepared in the tank and its temperature is kept constant and adjustable by means of the hot water circuit, the temperature of which is ® xed by the thermostated bath (5). The crystallizer is composed of two concentric tubes, the suspension ¯ owing through the annular space and cooling water counter¯ owing in the inner tube. The inlet temperature of the coolant is controlled by the temperature programmer in the water tank (6). During a run, the suspension ¯ ows axially through the annular space, its inlet temperature and ¯ owrate being kept constant at chosen values. Initially, the two liquids are at thermal equilibrium; then, the inlet temperature of the coolant decreases slowly with a linear slope. The crystalline layer grows around the inner tube when the wall temperature reaches a critical value, and can be observed visually through the glass outer tube. Measurements The inlet and outlet temperatures of the suspension (respectively T 1 and T 3 ) and of the cooling water (T 2 and T 4 ) are measured continuously by Pt 100 probes and 147
148
BRIANCËON et al.
Figure 1. Experimental setup.
recorded by a data acquisition system. The accuracy of the measurement is 1/100ÊC for T 2 and T 4 and 1/10ÊC for T 3 and T 1. Other measurements have been carried out to characterize the formation and the evolution of the deposit. The ® rst one concerns the appearance of the ® rst crystals on the heat exchange surface. The latter begins at the top of the crystallizer (outlet of the suspension), creating a crystallization front which then spreads along the tube under the in¯ uence of the increasing temperature di erence between the two ¯ uids. Simultaneously, crystals already formed keep growing, leading to the radial and axial development of the layer, the axial one increasing the propagation rate of the front. Visual observations of the displacement of this front have resulted in relationships such as t0 = f (z) or z0 = f (t ), t0 being the time required for ® rst crystals to appear at position z, or z0 being the position where crystals ® rst appear at time t. The thickness pro® le has been measured at the end of each run. To do this, the inner tube is carefully removed, and the deposit is collected after having been sliced into 0.05 metre long elements. Each element is then weighed before and after drying, thus allowing the evaluation of layer thickness and porosity pro® les along the tube. Furthermore, this kind of test has been repeated under identical conditions but for di erent time periods. From this, it is possible to derive the experimental evolution of the deposit thickness versus time for each product for temperature and velocity conditions previously de® ned.
the crystallizer. It represents the supersaturation at this point, assuming that the suspension is still saturated at T 3 . (T 4 - T2) is the cooling water temperature change ·along the crystallizer which is proportional to the heat ¯ ux exchanged through the surface.
Figure 2a. Evolution of temperature versus time.
RESULTS Temperature Curves An example of curves obtained from the collected data is given in Figure 2. Figure 2a shows the evolution of temperature versus time, from which it is possible to plot (T 3 - T 2) versus (T 4 - T 2), see Figure 2b.
(T 3 - T 2) measures the temperature di erence ·between bulk solution and cooling water at the top of
Figure 2b. Evolution of temperature di erences.
Trans IChemE, Vol 75, Part A, February 1997
FOULING OF COOLING SURFACES IN INDUSTRIAL CRYSTALLIZERS
149
The operating conditions of the test represented in Figure 2 are as follows: product: Adipic Acid; inner tube: stainless steel; cooling rate: - 2ÊC h- 1; temperature T 1 = 35ÊC velocity u = 0.73 m s- 1 coolant ¯ ow rate: 700 l h- 1 . These curves are composed of three parts: The initial phase (I) is the beginning of the run, before ·crystallization occurs; the data can be represented by a straight line. The second phase (II) represents the temperature ·changes during the growth of the layer. The last phase (III) corresponds to an equilibrium, ·when the deposit has reached a limiting thickness. Theoretically this phase is represented by a straight line too (as in phase I) because heat transfer coe cient is constant. The slope of this line is greater than the initial one, corresponding to a lower coe cient. In fact, this line is observed for only half of the experimental runs. The transition between phases (I) and (II) is marked by a return point which we could call the apparent critical point, because it is deduced from the observed thermal e ect. This point is ® rst considered as representative of the beginning of fouling and it allows us to calculate an apparent critical di erence of temperature between bulk and wall (T 3 - T ps )c. The evolution of this parameter D T c is measured as a function of the following variables: temperature and velocity of suspension, as well as nature and surface ® nish of the inner tube and the chemical product. Evolution of the Crystalline Layer Figure 3 shows the change with time of position z0 at which crystals ® rst appear, as described below. The subsequent calculation requires a relationship between time and position which is of the form: t0 = t01 + t02 exp (- (z/ k )).
Figure 4. Thickness pro® les at di erent times.
The position z = 1m marks the top of the crystallizer which corresponds to the suspension outlet and also to the deposit initiation position. At the bottom of the tube, between z = 0 and z = 0.3 m, the layer is usually thinner. This is due on the one hand to a longer t0 (z) time, and on the other hand to reentrainment of the crystals by the ¯ ow of suspension entering this area. MODELS The crystallizer is an annular counter¯ ow heat exchanger which can be described by two types of energy balances: overall balance gives a relation between the inlet ·andThe outlet temperatures of the two ¯ uids, (T T ) and
(T 4 - T 2).
3
-
1
erentialbalanceson each length element dz take ·intoThedi account the evolution of the temperature di erence
with: t01 = 44.6 min t02 = 58.5 min k = 0.383 m- 1 Thickness pro® les measured under identical conditions but at di erent times are represented in Figure 4.
between bulk and coolant along the crystallizer. The thermal balances embody not only the constant process parameters such as mass ¯ ow rates and speci® c heat but also some time dependent and space dependent terms (temperature, heat exchange surface and coe cient, crystallization ¯ ow).
Figure 3. Position of the crystallization front versus time. n measured; ÐÐ model.
Figure 5. Calculated and experimental curves.
Trans IChemE, Vol 75, Part A, February 1997
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BRIANCËON et al.
Initial Phase As long as no deposit occurs, the heat ¯ ow because of crystallization is nonexistent; moreover, the overall heat transfer coe cient Hg and exchange surface area S are constant. The integration of the di erential balances in along the length of the tube leads to the following relationship: (T 3 - T 2) = A(T4 - T 2) + B The coe cients A and B being constant before crystallization, this relation is linear and represents the ® rst part (I) of the temperature curves (Figure 2b). In this relationship, the only unknown is the overall heat transfer coe cient of the system before encrustation, Hg0 . This can be calculated from the slope A: 1 1 A= . SH g0 . mc cpc - ms cps m and cp are respectively mass ¯ ow rate and speci® c heat of the ¯ uids. Index c is used for coolant and s for suspension.
(
)
Crystallization Phase During this phase, the overall heat exchange coe cient Hg varies continuously with the thickness of the deposit, for three reasons: The crystalline layer creates an additional thermal ·resistance which increases with the thickness e. The deposit thickness narrows the suspension cross ·section, thus increasing the velocity. The ® lm heat
transfer coe cient at the interface of solid/bulk varies with the velocity. · The area of the exchange surface is slightly modi® ed. Moreover, the crystallization heat ¯ ux is no longer zero and varies according to the mass ¯ ow of crystallization. Considering a non uniform thickness along the tube, all the terms of the energy balances become time and space dependent, and analytical integration is now impossible. The numerical calculation needs the de® nition of a thickness evolution model. Fouling is usually supposed to be the result of a deposition process accompanied by a removal one3 due to the shearing o by the ¯ uid and the erosion of the layer. The thickness
evolution is then represented by an exponential curve, the thickness reaching a limiting value e* when the rate of the solids removed from the surface equals that of deposition4. Taking into account the experimental observations, parametric identi® cation is based on the following model: e = e* 1 - exp - D(t - t0(z)
[
[
]]
The expression t0 = f (z) is measured during the test. Energy balances are solved by an iterative calculation, for change in time (index i ) and, for each time step, in space (index j):
Calculation of thickness e(i, j ) at any time i and any ·position z( j ) Calculation of the exchange coe cients and of the ·layer thermal resistance of crystallization ¯ ow · Calculation erential balance at index j links the elements j and ·j +Di 1 Temperatures at the crystallizer limits are linked together through the overall energy balance. This calculation method gives temperatures T 1 , T 2, T 3, T 4 at any time and allows the curves of calculated temperature di erences to be drawn (see Figure 5). Although the calculated curve coincides very well with the experimental one for the temperature di erences, this is not the case for the time at which crystallisation begins, which does not appear in Figure 5. Experience shows that the ® rst crystals are formed after a time shorter than that corresponding to the apparent critical point. The moment when crystals ® rst appear is shown in Figure 5 by t0i . The identi® cation between calculated and experimental temperature curves has led us to introduce a delay of 14 minutes in the expression t0 = f (z) to make the two critical points ® t. Thus, there is a delay between the time when the deposit actually appears and the time needed for the detection of its thermal e ect. In fact, the temperature di erence D T c observed visually is lower than that measured by the apparent critical point. This thermal delay is sometimes mentioned in fouling studies and it corresponds to a transition period during which the fouling resistance is negative5. This can be explained by the fact that the ® rst crystals behave as
Figure 6. Simulation of the thermal delay. n experiment.
Trans IChemE, Vol 75, Part A, February 1997
FOULING OF COOLING SURFACES IN INDUSTRIAL CRYSTALLIZERS roughness elements which can increase the ® lm heat transfer coe cient. It is well established that increasing the roughness of an exchange surface enhances heat transfer6 . Di erent correlations are proposed in the literature7- 11 for the estimation of this in¯ uence, which depends on the nature of the roughness (size, shape and distribution of roughness elements). Using this property of the exchange surface, it is possible to simulate the delay between the e ective appearance of crystals and the apparent critical point. Figure 6 shows curves that have been calculated with an enhancement of 50% of the ® lm heat transfer coe cient applied from the nucleation of crystals until they reach a critical size corresponding to a limiting value of thickness e I for each length element. This value of 50% is an average value of enhancements calculated from the di erent literature correlations. The curves in Figure 6 are calculated by using the experimental expression of t0 = f (z), without introducing any delay. Fitting is then done based on the value of the limiting thickness e I . This value corresponds on the one hand to a decrease of roughness due to the ® lling up of cavities leading to a smoother surface, and on the other hand to a su cient mass of solids deposited for the layer resistance to become dominant. CONCLUSION The fouling tests already carried out with two chemicals allow us to bring out the in¯ uence of the operating conditions on the initiation of fouling. The visual observations of the initial phase of the process lead us to make a distinction between a point corresponding to the real appearance of crystals and the apparent critical point inferred from the degradation of heat exchange. The model that has been developed describes the di erent phases of the fouling process. It allows us to obtain the overall heat transfer coe cient of the clean system (without crystallization) on the one hand, and an
Trans IChemE, Vol 75, Part A, February 1997
151
evolution of the layer thickness pro® le in time during the crystallization phase on the other hand. The transition period is also represented by a temporary enhancement of the heat exchange coe cient. This model of thickness evolution has now to be compared with the crystallization kinetics of the chemicals studied, and linked with physical parameters characterizing the deposit layer (porosity, cohesion) and its interactions with the wall and the suspension. REFERENCES 1. Shock, R. A. W., 1983, Encrustation of crystallisers, J Sep Proc Technol, 4(1): 1±13. 2. Troup, D. H. and Richardson, J. A., 1978, Scale nucleation on a heat transfer surface and its prevention, Chem Eng Commun, 2: 167±180. 3. Epstein, N., 1983, Thinking about heat transfer fouling, Heat Transfer Eng, 4(1): 43±56. 4. Krause, S., 1993, Fouling of heat transfer surface by crystallisation and sedimentation, Int Chem Eng, 33(3): 355±401. 5. Crittenden, B. D. and Alderman, N. J., 1992, Mechanismby which foulingcan increaseoverallheat transfer coe cients, Heat Transfer Eng, 13(4): 32±41. 6. Walker, R. A. and Bott, T. R., 1964, E ect of surfaceroughnesson convective heat transfer, Int J Heat and Mass Transf, 7: 653±663. 7. Dipprey, D. F. and Sabersky, R. H., 1963, Heat and momentum transfer in smooth and rough tubes at variousPrandtl numbers, Int J Heat and Mass Transf, 6: 329±353. 8. Gomelauri, V., 1964, In¯ uence of two dimensional arti® cial roughness on convective heat transfer, Int J Heat and Mass Transf, 7: 653±663. 9. Kolar, V., 1965, Heat transfer in turbulent ¯ ow of ¯ uids through smooth and rough tubes, Int J Heat and Mass Transf, 8: 639±653. 10. Smith, J. W. and Epstein, N., 1957, E ect of wall roughness on convectiveheat transfer in commercial pipes, AIChE J, 3: 242±248. 11. Walker, R. A. and Bott, T. R., 1973, E ect of surfaceroughnesson heat transfer in exchanger tubes, The Chemical Engineer, March, 151±156.
ADDRESS Correspondence concerning this paper should be addressed to Dr S. BriancËon, LAGEP, UniversiteÂClaude Bernard Lyon 1, CPE-Lyon, URA-CNRS D1328, Villeurbanne, France.
0263±8762/97/$07.00+ 0.00 Institution of Chemical Engineers
EXPERIMENTAL STUDY AND THEORETICAL APPROACH OF COOLING SURFACES FOULING IN INDUSTRIAL CRYSTALLIZERS S. BRIANCËON, D. COLSON and J. P. KLEIN Laboratoire d’Automatique et de Ge nie des Proce de s ( LAGEP) , UniversiteÂClaude Bernard Lyon 1, Villeurbanne, France
F
ouling of cooling surfaces of industrial crystallizers is a major problem which reduces the productivity of installations. This phenomenon, which results from the surface temperature being lower than that of the bulk so as to allow heat transfer, is essentially initiated by primary heterogeneous nucleation. The experimental setup has been designed to study the in¯ uence of di erent parameters such as suspension ¯ ow velocity, temperatures, the nature and the ® nish of the deposit surface, as well as the nature of the product which crystallizes. The conditions of the appearance of a crystalline layer and its subsequent growth are studied simultaneously by measuring the inlet and outlet temperatures of the two ¯ uids which leads to calculation of the degradation of overall heat transfer coe cient and, more directly, by physically measuring the evolution in time of the thickness pro® le. Keywords: fouling; crystallisation; heterogeneous nucleation; crystal deposit; heat exchange surface; roughness
INTRODUCTION Encrustation is the industrial term used to describe the progressive fouling of cooling crystallizers. This phenomenon is particularly troublesome for the productivity of installations and incurs heavy economic penalties. Fouling of heat transfer surfaces is a problem inherent in many of the unit operations of chemical engineering and has been studied especially in the ® eld of heat exchangers1. However, during cooling crystallization, fouling is favoured by the very nature of the process. Indeed, near the exchange surfaces, the bulk temperature is the lowest in the crystallizer. Supersaturation which leads to crystallization is at its maximum value at the wall and nucleation preferentially occurs there leading to the growth of a crystalline layer that increases the thermal resistance of the system. Fouling is in¯ uenced by a great number of parameters, on the one hand by physical ones such as ¯ ow velocity near the wall, temperature and the chemical nature and surface ® nish of the wall. On the other hand, the chemical concentration of the di erent compounds (solute, solvent, impurities) has to be taken into account. The great number of these parameters and their interdependence explain the di culties encountered when predicting fouling by a theoretical approach. That is the reason why this phenomenon is essentially represented by empirical laws for each particular case. This allows optimal operating conditions and technical solutions to be obtained which avoid, or at least reduce, fouling, for a speci® c process2 . The objective of this work is to understand the mechanisms involved in fouling and to generalize the
empirical laws. The ® nal aim is to provide solutions to reduce and control fouling, without carrying out experimental work which could prove too unwieldy. EXPERIMENTAL SETUP Description The experimental setup shown in Figure 1 comprises two main elements: a stirred tank with an external jacket (1) and an annular crystallizer (4). The bulk solution is prepared in the tank and its temperature is kept constant and adjustable by means of the hot water circuit, the temperature of which is ® xed by the thermostated bath (5). The crystallizer is composed of two concentric tubes, the suspension ¯ owing through the annular space and cooling water counter¯ owing in the inner tube. The inlet temperature of the coolant is controlled by the temperature programmer in the water tank (6). During a run, the suspension ¯ ows axially through the annular space, its inlet temperature and ¯ owrate being kept constant at chosen values. Initially, the two liquids are at thermal equilibrium; then, the inlet temperature of the coolant decreases slowly with a linear slope. The crystalline layer grows around the inner tube when the wall temperature reaches a critical value, and can be observed visually through the glass outer tube. Measurements The inlet and outlet temperatures of the suspension (respectively T 1 and T 3 ) and of the cooling water (T 2 and T 4 ) are measured continuously by Pt 100 probes and 147
148
BRIANCËON et al.
Figure 1. Experimental setup.
recorded by a data acquisition system. The accuracy of the measurement is 1/100ÊC for T 2 and T 4 and 1/10ÊC for T 3 and T 1. Other measurements have been carried out to characterize the formation and the evolution of the deposit. The ® rst one concerns the appearance of the ® rst crystals on the heat exchange surface. The latter begins at the top of the crystallizer (outlet of the suspension), creating a crystallization front which then spreads along the tube under the in¯ uence of the increasing temperature di erence between the two ¯ uids. Simultaneously, crystals already formed keep growing, leading to the radial and axial development of the layer, the axial one increasing the propagation rate of the front. Visual observations of the displacement of this front have resulted in relationships such as t0 = f (z) or z0 = f (t ), t0 being the time required for ® rst crystals to appear at position z, or z0 being the position where crystals ® rst appear at time t. The thickness pro® le has been measured at the end of each run. To do this, the inner tube is carefully removed, and the deposit is collected after having been sliced into 0.05 metre long elements. Each element is then weighed before and after drying, thus allowing the evaluation of layer thickness and porosity pro® les along the tube. Furthermore, this kind of test has been repeated under identical conditions but for di erent time periods. From this, it is possible to derive the experimental evolution of the deposit thickness versus time for each product for temperature and velocity conditions previously de® ned.
the crystallizer. It represents the supersaturation at this point, assuming that the suspension is still saturated at T 3 . (T 4 - T2) is the cooling water temperature change ·along the crystallizer which is proportional to the heat ¯ ux exchanged through the surface.
Figure 2a. Evolution of temperature versus time.
RESULTS Temperature Curves An example of curves obtained from the collected data is given in Figure 2. Figure 2a shows the evolution of temperature versus time, from which it is possible to plot (T 3 - T 2) versus (T 4 - T 2), see Figure 2b.
(T 3 - T 2) measures the temperature di erence ·between bulk solution and cooling water at the top of
Figure 2b. Evolution of temperature di erences.
Trans IChemE, Vol 75, Part A, February 1997
FOULING OF COOLING SURFACES IN INDUSTRIAL CRYSTALLIZERS
149
The operating conditions of the test represented in Figure 2 are as follows: product: Adipic Acid; inner tube: stainless steel; cooling rate: - 2ÊC h- 1; temperature T 1 = 35ÊC velocity u = 0.73 m s- 1 coolant ¯ ow rate: 700 l h- 1 . These curves are composed of three parts: The initial phase (I) is the beginning of the run, before ·crystallization occurs; the data can be represented by a straight line. The second phase (II) represents the temperature ·changes during the growth of the layer. The last phase (III) corresponds to an equilibrium, ·when the deposit has reached a limiting thickness. Theoretically this phase is represented by a straight line too (as in phase I) because heat transfer coe cient is constant. The slope of this line is greater than the initial one, corresponding to a lower coe cient. In fact, this line is observed for only half of the experimental runs. The transition between phases (I) and (II) is marked by a return point which we could call the apparent critical point, because it is deduced from the observed thermal e ect. This point is ® rst considered as representative of the beginning of fouling and it allows us to calculate an apparent critical di erence of temperature between bulk and wall (T 3 - T ps )c. The evolution of this parameter D T c is measured as a function of the following variables: temperature and velocity of suspension, as well as nature and surface ® nish of the inner tube and the chemical product. Evolution of the Crystalline Layer Figure 3 shows the change with time of position z0 at which crystals ® rst appear, as described below. The subsequent calculation requires a relationship between time and position which is of the form: t0 = t01 + t02 exp (- (z/ k )).
Figure 4. Thickness pro® les at di erent times.
The position z = 1m marks the top of the crystallizer which corresponds to the suspension outlet and also to the deposit initiation position. At the bottom of the tube, between z = 0 and z = 0.3 m, the layer is usually thinner. This is due on the one hand to a longer t0 (z) time, and on the other hand to reentrainment of the crystals by the ¯ ow of suspension entering this area. MODELS The crystallizer is an annular counter¯ ow heat exchanger which can be described by two types of energy balances: overall balance gives a relation between the inlet ·andThe outlet temperatures of the two ¯ uids, (T T ) and
(T 4 - T 2).
3
-
1
erentialbalanceson each length element dz take ·intoThedi account the evolution of the temperature di erence
with: t01 = 44.6 min t02 = 58.5 min k = 0.383 m- 1 Thickness pro® les measured under identical conditions but at di erent times are represented in Figure 4.
between bulk and coolant along the crystallizer. The thermal balances embody not only the constant process parameters such as mass ¯ ow rates and speci® c heat but also some time dependent and space dependent terms (temperature, heat exchange surface and coe cient, crystallization ¯ ow).
Figure 3. Position of the crystallization front versus time. n measured; ÐÐ model.
Figure 5. Calculated and experimental curves.
Trans IChemE, Vol 75, Part A, February 1997
150
BRIANCËON et al.
Initial Phase As long as no deposit occurs, the heat ¯ ow because of crystallization is nonexistent; moreover, the overall heat transfer coe cient Hg and exchange surface area S are constant. The integration of the di erential balances in along the length of the tube leads to the following relationship: (T 3 - T 2) = A(T4 - T 2) + B The coe cients A and B being constant before crystallization, this relation is linear and represents the ® rst part (I) of the temperature curves (Figure 2b). In this relationship, the only unknown is the overall heat transfer coe cient of the system before encrustation, Hg0 . This can be calculated from the slope A: 1 1 A= . SH g0 . mc cpc - ms cps m and cp are respectively mass ¯ ow rate and speci® c heat of the ¯ uids. Index c is used for coolant and s for suspension.
(
)
Crystallization Phase During this phase, the overall heat exchange coe cient Hg varies continuously with the thickness of the deposit, for three reasons: The crystalline layer creates an additional thermal ·resistance which increases with the thickness e. The deposit thickness narrows the suspension cross ·section, thus increasing the velocity. The ® lm heat
transfer coe cient at the interface of solid/bulk varies with the velocity. · The area of the exchange surface is slightly modi® ed. Moreover, the crystallization heat ¯ ux is no longer zero and varies according to the mass ¯ ow of crystallization. Considering a non uniform thickness along the tube, all the terms of the energy balances become time and space dependent, and analytical integration is now impossible. The numerical calculation needs the de® nition of a thickness evolution model. Fouling is usually supposed to be the result of a deposition process accompanied by a removal one3 due to the shearing o by the ¯ uid and the erosion of the layer. The thickness
evolution is then represented by an exponential curve, the thickness reaching a limiting value e* when the rate of the solids removed from the surface equals that of deposition4. Taking into account the experimental observations, parametric identi® cation is based on the following model: e = e* 1 - exp - D(t - t0(z)
[
[
]]
The expression t0 = f (z) is measured during the test. Energy balances are solved by an iterative calculation, for change in time (index i ) and, for each time step, in space (index j):
Calculation of thickness e(i, j ) at any time i and any ·position z( j ) Calculation of the exchange coe cients and of the ·layer thermal resistance of crystallization ¯ ow · Calculation erential balance at index j links the elements j and ·j +Di 1 Temperatures at the crystallizer limits are linked together through the overall energy balance. This calculation method gives temperatures T 1 , T 2, T 3, T 4 at any time and allows the curves of calculated temperature di erences to be drawn (see Figure 5). Although the calculated curve coincides very well with the experimental one for the temperature di erences, this is not the case for the time at which crystallisation begins, which does not appear in Figure 5. Experience shows that the ® rst crystals are formed after a time shorter than that corresponding to the apparent critical point. The moment when crystals ® rst appear is shown in Figure 5 by t0i . The identi® cation between calculated and experimental temperature curves has led us to introduce a delay of 14 minutes in the expression t0 = f (z) to make the two critical points ® t. Thus, there is a delay between the time when the deposit actually appears and the time needed for the detection of its thermal e ect. In fact, the temperature di erence D T c observed visually is lower than that measured by the apparent critical point. This thermal delay is sometimes mentioned in fouling studies and it corresponds to a transition period during which the fouling resistance is negative5. This can be explained by the fact that the ® rst crystals behave as
Figure 6. Simulation of the thermal delay. n experiment.
Trans IChemE, Vol 75, Part A, February 1997
FOULING OF COOLING SURFACES IN INDUSTRIAL CRYSTALLIZERS roughness elements which can increase the ® lm heat transfer coe cient. It is well established that increasing the roughness of an exchange surface enhances heat transfer6 . Di erent correlations are proposed in the literature7- 11 for the estimation of this in¯ uence, which depends on the nature of the roughness (size, shape and distribution of roughness elements). Using this property of the exchange surface, it is possible to simulate the delay between the e ective appearance of crystals and the apparent critical point. Figure 6 shows curves that have been calculated with an enhancement of 50% of the ® lm heat transfer coe cient applied from the nucleation of crystals until they reach a critical size corresponding to a limiting value of thickness e I for each length element. This value of 50% is an average value of enhancements calculated from the di erent literature correlations. The curves in Figure 6 are calculated by using the experimental expression of t0 = f (z), without introducing any delay. Fitting is then done based on the value of the limiting thickness e I . This value corresponds on the one hand to a decrease of roughness due to the ® lling up of cavities leading to a smoother surface, and on the other hand to a su cient mass of solids deposited for the layer resistance to become dominant. CONCLUSION The fouling tests already carried out with two chemicals allow us to bring out the in¯ uence of the operating conditions on the initiation of fouling. The visual observations of the initial phase of the process lead us to make a distinction between a point corresponding to the real appearance of crystals and the apparent critical point inferred from the degradation of heat exchange. The model that has been developed describes the di erent phases of the fouling process. It allows us to obtain the overall heat transfer coe cient of the clean system (without crystallization) on the one hand, and an
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evolution of the layer thickness pro® le in time during the crystallization phase on the other hand. The transition period is also represented by a temporary enhancement of the heat exchange coe cient. This model of thickness evolution has now to be compared with the crystallization kinetics of the chemicals studied, and linked with physical parameters characterizing the deposit layer (porosity, cohesion) and its interactions with the wall and the suspension. REFERENCES 1. Shock, R. A. W., 1983, Encrustation of crystallisers, J Sep Proc Technol, 4(1): 1±13. 2. Troup, D. H. and Richardson, J. A., 1978, Scale nucleation on a heat transfer surface and its prevention, Chem Eng Commun, 2: 167±180. 3. Epstein, N., 1983, Thinking about heat transfer fouling, Heat Transfer Eng, 4(1): 43±56. 4. Krause, S., 1993, Fouling of heat transfer surface by crystallisation and sedimentation, Int Chem Eng, 33(3): 355±401. 5. Crittenden, B. D. and Alderman, N. J., 1992, Mechanismby which foulingcan increaseoverallheat transfer coe cients, Heat Transfer Eng, 13(4): 32±41. 6. Walker, R. A. and Bott, T. R., 1964, E ect of surfaceroughnesson convective heat transfer, Int J Heat and Mass Transf, 7: 653±663. 7. Dipprey, D. F. and Sabersky, R. H., 1963, Heat and momentum transfer in smooth and rough tubes at variousPrandtl numbers, Int J Heat and Mass Transf, 6: 329±353. 8. Gomelauri, V., 1964, In¯ uence of two dimensional arti® cial roughness on convective heat transfer, Int J Heat and Mass Transf, 7: 653±663. 9. Kolar, V., 1965, Heat transfer in turbulent ¯ ow of ¯ uids through smooth and rough tubes, Int J Heat and Mass Transf, 8: 639±653. 10. Smith, J. W. and Epstein, N., 1957, E ect of wall roughness on convectiveheat transfer in commercial pipes, AIChE J, 3: 242±248. 11. Walker, R. A. and Bott, T. R., 1973, E ect of surfaceroughnesson heat transfer in exchanger tubes, The Chemical Engineer, March, 151±156.
ADDRESS Correspondence concerning this paper should be addressed to Dr S. BriancËon, LAGEP, UniversiteÂClaude Bernard Lyon 1, CPE-Lyon, URA-CNRS D1328, Villeurbanne, France.