Analysis of Sulfur Dioxide Wet Limestone Scrubbing Data from Pilot Plant Spray and TCA Scrubbers W. J. McMichael,’ L. S. Fan, and C. Y. Wen’ Department of Chemical Engineering, West Virginia University, Morgantown, West Virginia 26506
Experimental data from both small and largescale turbulent contacting absorbers (TCA) and spray columns used in the wet scrubbing of SO2 from flue gases have been analyzed to obtain the gas film mass transfer coefficients and the overall coefficients in the liquid film which includes chemical reaction in the liquid film. The scrubbing slurries investigated are recycled limestonemagnesium oxidewater slurries. The gas film coefficients for the spray and TCA scrubbers were calculated from data on SO2 scrubbing with sodium carbonate solutions. The overall mass transfer resistances in the liquid phase for both scrubbers were correlated in terms of the ratio of the gas film and liquid film mass transfer resistances. Over the range of variables studied and within the accuracy of the experimental data, the ratio of the resistances was found to be a function of only the scrubber type, the inlet SO2 partial pressure in the gas phase, and inlet pH and magnesium concentration of the scrubbing slurry. Specifically, it was found that the ratio of the gas and liquid film mass transfer resistances or the fraction to which SO2 removal is gas film controlled increases with increasing slurry pH and magnesium concentration and with decreasing SO2 partial pressure. The correlations for the gas film mass transfer coefficient and the ratio of mass transfer resistances developed in this paper can predict within 5% the experimentally observed SO2 removal efficiencies for widely differing size TCA and spray column scrubbers.
Introduction
Because of the EPA regulations on the emission of SO2 in stack gases much effort has gone into studying the scrubbing of SO2 from flue gases using limestone slurries. Two of the most promising scrubbers for carrying out the limestone scrubbing appear to be the turbulent contacting absorber (TCA) and the spray column. Several largescale scrubberholding tank recycle systems have been built and sponsored by the EPA to test the performance and reliability of these scrubbers. In this paper experimental data from the largescale TCA scrubber and spray column located a t the TVA Shawnee power station and the EPA TCA scrubber a t Research Triangle Park, North Carolina, are analyzed to obtain correlations which can be used to design and scaleup spray column and TCA scrubbers which utilize limestone slurries to scrub SO2 from flue gases. Scale drawings of the scrubbers to be considered in this paper are given in Figures 1, 2, and 3. In the TVA Shawnee TCA scrubber, as shown in Figure I,the scrubbing slurry is sprayed from a single arrangement of nozzles at the top of the column and falls through a series of grids and areas filled with low density packing spheres. Actually the TCA has been operated without the spherical packed pieces and in this situation the column is referred to as the “TCA without packing spheres.” Flue gas containing SO2 in concentrations up to 4500 ppm passes countercurrently t o the limestone slurry. The spray column with four spray headers shown in Figure 2 is slightly more complicated than the TCA without spheres in that the scrubbing slurry is sprayed a t four levels. However, as will be discussed later, this situation is easily handled and the column can be described mathematically in terms of the mass transfer coefficients for the TCA without packing spheres. In Figure 3 a scale drawing of the EPA/RTP TCA scrubber is given. The TVA Shawnee TCA and spray column treat flue gas a t a rate equivalent to a 10 MW power station and have crosssections which are square (5 f t edge) and circular (8 f t
’
U.S. Energy Research and Development Administration, Pitts burgh Energy Research Center, Pittsburgh, Pa. 15213
diameter), respectively. The EPA/RTP is approximately 9 in. in diameter. In subsequent sections a mathematical model is given which describes the absorption of SO2 by limestone slurries in a scrubber; parameters appearing in this model are evaluated from experimental data and correlated in terms of the operating parameters, and the experimentally observed SO2 removal efficiency is compared to the efficiency computed from the model. Mathematical Model of Spray and TVA Scrubbers
In the analysis and design of contacting devices used for the scrubbing of SO2 from flue gas with limestone slurries, the mass transfer coefficients, which describe the SO2 fluxes in the gas and liquid phases, should be known. The gas film mass transfer coefficients are relatively easily obtained from experimental data; on the other hand, the liquid film coefficient for physical absorption is difficult to determine due to chemical reactions which usually occur upon the absorption of a gas molecule into a liquid phase. In the present case, where the mechanism of the absorption of SO2 into limestone slurry is not completely understood, the liquid film mass transfer coefficient for physical absorption cannot be separated from the chemical effects associated with the absorption of SO2 into limestone slurry. Clearly this separation of the liquid film mass transfer coefficient for the TCA and spray columns into physical and chemical parts is desirable since it may result in a simplification of the data and lead to a general predictive model for SO2 absorption into limestone slurries. However, in the absence of this separation the liquid film resistance to the transfer of SO2 into limestone slurries, determined from experimental data, is correlated in terms of the ratio of the gas and liquid film mass transfer resistances. This ratio of the resistances appears to be only a function of the magnesium concentration and p H of the slurry, SO2 partial pressure in the gas phase, and type of scrubber within the accuracy of the experimental data. Gas and Liquid Film Mass Transfer Coefficients. For the TCA operating with packing spheres, the column can be divided into packed and unpacked sections, and separate mass transfer coefficimts can be used to describe the respective Ind. Eng. Chem., Process Des. Dev., Vol. 15, No. 3, 1976
459
GAS OUl
Making standard assumptions (see Fan, 1975) the molar flux of SO2 can be written as
CqEVmY 3EW'STER
"
:J 1
EFFLJENT
_ F I %n / I. ,
I
SLLRRY
Figure 1. Schematic of TVA Shawnee threebed TCA (Epstein
where H is the Henry's law constant defined by €'so2 = HCA. In eq 2 both 4 and Pso2* are functions of position in the column and both depend on the mechanism of SO2 absorption into recycled limestone slurries. For a calcium carbonate, calcium sulfite, carbon dioxide, sulfur dioxide, and water system a t equilibrium and a p H greater than 4.7, the equilibrium SO2 partial pressure of the aqueous system will usually be much less than the SO2 partial pressure found in the flue gas (Le., Pso2 >> Pso2* for pH >4.7). Thus Pso2* can be ignored relative to Pso2 in eq 2. The rate of SO2 absorption in a differential height of the scrubber, dZ, can then be written as
(1973a)).
~ G dPso2 =
PT
G A S CLl
_L DEMISTER W A S I i
dz
(+) 1 k,a
H 4kL"a
1
pso*
(3)
Equation 3 can be integrated over the height of the column section (from 21 to 2,) to give
DEW STER W A S H
where 4 and K c a are an average enhancement factor and average overall mass transfer coefficient, respectively, and U =2
GAS
h
+ EF'.UEY
SLJRR'
Figure 2. Schematic of TVA Shawnee spray tower (Epstein (1973a)). GAS O U T I
4 EFFLUEVT SLURRY
Figure 3. Schematic of the EPA/RTP Research TCA scrubber (Borgwardt (1972a)).
sections. The molar flux of SO2 across the gasliquid interface of a packed or unpacked section of a wet scrubber can be written in terms of the gas or liquid side resistance as
Nso2 = kg(Psoz  Psoi) = kLo4(CAi  C A ) (1) The enhancement factor, 4, takes into account the reaction of the diffusing HzS03 with components found in the liquid phase. 460
Ind. Eng. Chem., Process Des. Dev., Vol. 15,NO.3, 1976
2
 21.
Large values of the enhancement factor, 4,correspond to the gas film being the dominating resistance to the transfer of S02, and small values of the enhancement factor indicate that the liquid film resistance is important. If the gas and liquid film mass transfer coefficients for physical absorption can be calculated, it is possible to separate the liquid film mass transfer coefficient, h ~ ainto , a chemical reaction term (i.e., the enhancement factor, 4,) and the liquid film mass transfer coefficient for physical absorption, kLoa. However, for the Shawnee and EPA scrubbers being analyzed in this paper, it does not appear possible to calculate the liquid film mass transfer coefficients for physical absorption from the data reported. Thus, the separation of the liquid film mass transfer coefficient into chemical reaction and mass transfer effects cannot be made a t this time. The second equation of eq 4 can be rearranged to give
The overall coefficient, KGa, can be calculated from experimental data using the first equation of eq 4. The gas film mass transfer coefficient, k g a ,can be calculated by methods to be discussed below. The lefthand side of eq 5 (or the definition of R ) can be interpreted as the ratio of the gas and liquid film mass transfer resistances. The larger this ratio the more the SO2 transfer in the column is controlled by the gas film. As will be shown below, the ratio of resistances appears to be an effective method of correlating liquid film resistances. The gas side mass transfer coefficient in the Shawnee TCA operating without packing spheres has been reported by Epstein (1973a) as
kgSa= 0.00134G0.8L0.4
(6)
This correlation is based on experiments on SO2 absorption into sodium carbonate solutions which had pH values greater than 8.5.At these high pH values the transfer of ,902 into these solutions is essentially gas film controlled. The gas film mass transfer coefficient for the Shawnee TCA
operating without packing spheres can also be applied to the Shawnee spray column. This was verified using the data of Epstein et al. (1973) for a limestone depletion run in the Shawnee spray column in which the initial pH of the scrubbing slurry was 7.30. Assuming that a t this pH the SO2 absorption is gas film controlled and taking into consideration that the slurry is sprayed into Shawnee spray column a t four levels (see Fan (1975) for details), the gas film coefficient is calculated to be k,a = 1.65 X 105 gmol/cm3 atm s at a gas flow rate of G = 0.005 48 gmol/cm2 s and a total liquid rate of L = 0.652 g/cm2 s. The gas film coefficient calculated using gmol/cm3 Epstein’s correlation (eq 6) gives k 2 a = 1.75 X atm s under the same flow conditions. I t can be seen that Epstein’s correlation for the gas film coefficient in the Shawnee TCA operating without packing spheres can predict the gas film coefficient for the Shawnee spray very accurately, and in the absence of more data it is assumed that the gas film coefficient for both the Shawnee spray column and the TCA without packing spheres can be given by Epstein’s correlation (eq 6). The ratio of the mass transfer resistance of the gas film to that of the liquid film can be calculated for the Shawnee TCA without packing spheres and the Shawnee spray column with 4 spray headers from the data of Epstein (1973a) and Epstein et al. (1973). The values of R obtained for these scrubbers are shown indirectly in Figure 4. Here the ratio of the overall mass transfer coefficient, K c a , to the gas film coefficient, k , a , or R / ( R 1)is shown as a function of the inlet pH. (See Table 1.) Several data were excluded from Figure 4 because of the high pressure drops across the scrubber with respect to those normally found at given operating conditions. The normal pressure drop for spraytype scrubbers has been correlated by Fan (1975) as PN = 0.481G1.17L0.6Z, (7) It is evident from the data reported by Epstein et al. (1973) that higher than normal pressure drops across the scrubbers, due possibly to pressure drop associated with scale formation, greatly affects the SO2 scrubbing efficiency. However, the effect of the pressure drop on scrubbing efficiency has not been fully analyzed. The ratio of mass transfer resistances, R , was correlated in terms of inlet slurry pH for several reasons: (1)the inlet slurry pH was readily available; (2) the amount of SO2 absorbed per liter of slurry is relatively small and the slurry residence time fairly short and therefore, the average condition of the slurry in the scrubber could be reflected in its initial pH. For the spray type devices discussed above, the dependence of R on hydrodynamics could not be distinguished above the scatter of the data. The scatter in the data in Figure 4 could be due in part to the fact that the raw data used t o calculate the ratio of resistances, R , was reported in ranges and the average of the reported ranges was used to calculate the value of R. In Figure 4 it can be seen that the extrapolation of the straight line through the data points to a value of Rs/(R, 1) equal to 1 giving a pH of 7.2 as the pH above which the SO2 absorption is gas film controlled. This is in agreement with the
+
+
10 09 /
08
/ / /
07
/
/ /
06
a
?
’ /a
d . 04 .. 0 5
d L
0
.%
$ 0 3
rno ?L
02
,
I
I
60
! 1
I
70 PH
Figure 4. Ratio of the overall mass transfer coefficient for spray devices, K&, to the gas film coefficient,k;a, as a function of the pH of the scrubbing slurry at the inlet of the scrubber.
assumption that the SO2 absorption was gas film controlled at a pH of 7.3 in the case of the limestone depletion run for the Shawnee spray column discussed above. For the TCA operation with packing spheres the column must be divided into two sections: one corresponding to the section filled with packing spheres, and another where there are no packing spheres and the column behaves much like a spray device. This situation is illustrated in Figure 5 . The reason for this separation is that the packed and spray sections will have significantly different contacting mechanisms and consequently different mass transfer coefficients. Also this separation is desirable so that columns with different packing heights can be compared. An actual TCA scrubber can be made up of several stages such as the one shown in Figure 5 . In the development to follow it will be assumed that the overall gas side mass transfer coefficients for the spray sections are constant regardless of the position of the section in the column and that the height of the packed section in the fluidized state can be characterized by the height of the packed section without gas flow. Chen and Douglas (1968) have reported bed expansion for TCA scrubbers; however, their data were taken for gas velocities substantially lower than the gas velocities of interest in this paper. The integrated mass balance on SO2 in the TCA scrubber can be written as
Table I. Range of Data for the Shawnee Spray Column and TCA Operating Without Packing Spheres Used in Constructing Figure 4
Equipment and reference Spray column 4 spray headers, Epstein et al. (1973) TCA without packing spheres, Epstein (1973a)
pH
G , gmol/ L , g/cm2 Inlet slurry temp Inlet Pso2, AP, in. of cm2s S OF PPm HzO
5.300.00548 7.30 5.856.4 0.006870.01378
Mg concn in slurry, ppm
0.652
97113
17503187 Not reported
6 . 6
2 04
e
*
* 0

n u
:
e
e I
0 

e
'8
1
e
I
I
I
p H of t h e I n l e t S l u r r y
Figure 9. The preexponential function, A,, in the expression for R , the ratio of resistances, as a function of the pH of the inlet slurry for the packed section of TVA TCA and EPA TCA. Low magnesium concentration ([Mg] < 350 ppm). 2.Q
1
,
1 1 1 1
I
I
I
I
1.0
4

m


C +
n d
=
( 3 )e As
cs
=
1 . 0 , for Mg
A~
=
50.1 h4go'6682;
6.6 A, given by solid line in Figure 11 or by equations A, = 1.0; for [Mg] < 3600 PPm 1,= 2.2 X lo7 [Mg]* 06j; for [Mg] 2 3600 ppm K c P a = k,paR,/(l + R,)
A,l
A EPAIRTP TCA
2x102
k,pa = 0.00220~0 47.~0 51 (15) R , = (Ap/Ap)e330PS02'" A, given by solid line in Figure 9 or by the equations API = 0.308; for pH 56.0
.Q73a)
EPAIRTP Data ( s e e T a b l e I V f o r Range o f D i r a ) EP.A/RTP TCA H ' l t h o u t P a c k l n g S p h e r e s B o r p u a r d t ( 1 9 7 3 a 1973b. 1974b)
W [L
i
1
s,Ol
i
4 3
0 23
1
01
y *020
310 410 50 do 7; OESEWED PERCENT SO1 REMOVAL
810
L
Figure 12. Comparison of'the predicted and observed SO2 removal efficiencies for spraytype devices using limestone slurry as the scrubbing medium.
bing of S o p from flue gases is shown in Figures 12 and 13 for the spray and TCA devices, respectively. I t is interesting to note that the correlations used in simulating the data given in Figures 12 and 13 were developed from a combination of large and small scale scrubber data. However,
V
I
I
I
1 I1
1
 ,,
\In
I 9c
i
J
IL
Figure 13. Comparison of the predicted and observed SO2 removal efficiencies for TCA scrubbers using limestone slurry as the scrubbing medium.
it can be seen that the SO:! removal efficiencies predicted for both small and large scale spray and TCA columns with various packing depths compares favorably with the observed efficiencies. This fact gives added confidence t h a t the correInd. Eng. Chem., Process Des. Dev.. Vol. 15, No. 3, 1976
465
lations developed in this paper can be extrapolated to scrubbers of various sizes. Conclusions a n d Discussion In this paper a mathematical model which can simulate both large and small scale TCA scrubbers used for the scrubbing of SO2 from flue gases by limestone and limestonemagnesium oxide slurries has been proposed. The parameters which appear in this model have been evaluated from experimental data. The gas film mass transfer coefficients for the spray and packed sections of the TCA were obtained from the literature and calculated from experimental data, respectively. The liquid film resistances for both the spray and packed section were calculated from experimental data and correlated in terms of the ratio of the mass transfer resistance in the gas film to that in the liquid film as function inlet pH and magnesium concentration of the scrubbing slurry and inlet partial pressure of SO2 in the flue gas. Within the accuracy of the experimental data, the ratio of the mass transfer resistances appears to be independent of the gas and liquid flow rates. The temperature dependence of the ratio of resistances was not determined since the experimental data were available only in a narrow range of temperature. The ratio of the mass transfer resistances was found to have an exponential dependence on the SO2 partial pressure in the flue gas. According to this form (as given by eq 13) the ratio of the resistances approaches the value of the preexponential factor, A , as the SO2 partial pressure decreases to zero. Actually the ratio of the resistances should approach an infinite value as the SO2 partial pressure approaches zero because the SO2 transfer then becomes gas film controlled. The fact that eq 1 4 gives the incorrect low SO2 partial pressure asymptote points out two facts: (1)that with regard to slurry pH, gas composition, and gas and liquid flow rates the correlations developed in this paper should not extend outside the range of data from which they were determined, and (2) that more work is needed on the mechanism of SO2 absorption into limestone slurry and in determining liquid film mass transfer coefficients for physical absorption in TCA and spray scrubbers so that more general, predictive models of SO2 scrubbing with limestone slurries can be developed. However, the use of the correlations given in this paper for scaleup of TCA and spray scrubber systems appears warranted since the correlations have been shown capable of predicting the SO2 scrubbing efficiency of columns of widely differing size and over a wide range unexpanded packing heights. Although many assumptions were made in the analysis of the limestone scrubbers and scatter of the data can be seen in the derived correlations, these assumptions appear to have given rise to a satisfactory method of simulating the performance of both small and large scale TCA and spray column scrubbers in removing SO2 from flue gases using limestone or limestonemagnesium oxide slurries as the scrubbing medium. In most cases the calculated SO2 removal efficiency was within 5% of the experimentally observed efficiency, The scatter in the data in the figures presented in this paper arise from several sources. Probably the most important of these is that many of the data are taken from largescale units where the operating conditions and purity of reagents are difficult to control. Also a substantial number of the data were reported as averages over long periods of operation or reported in ranges and the averages over these ranges were utilized in the analysis. Nomenclature a = specific interfacial area available to mass transfer, cm1 A = preexponential factor in the expression for R defined by eq 13, dimensionless 466
Ind. Eny. Chem., Process Des. Dev., Vol. 15,No. 3, 1976
A,, A , = preexponential factor in the expression for R for the packed and spray sections, respectively, dimensionless CA = H2SO3 concentration in the bulk liquid phase, gmol/ cm3 CA~ = interfacial H2SO3 concentration, gmol/cm3 G = molar gas flow rate based on crosssectional area of the scrubber, gmol/cm2 s H = Henry's law constant, atm cm3/gmol k, = gas film mass transfer coefficient for physical absorption, gmol/cm2 atm s LO = liquid film mass transfer coefficient for physical absorption, cm/s KGU = average overall gas side mass transfer coefficient, gmol/cm3 atm s KG'U = overall gas side mass transfer coefficient for the packed section of the TVA, gmol/cm3 atm s k,pu = gas side mass transfer coefficient for the packed section, gmol/cm3 atm s K G , ~= overall gas side mass transfer coefficient for the spray section of the TCA, gmol/cm3 atm s kgsa = gas side mass transfer coefficient for the spray section, gmol/cm3 atm s kpaovera1l= gas film mass transfer coefficient defined by eq 12, gmol/cm3 atm s L = liquid flow rate based on crosssectional area of the scrubber, g/cm2 s Nsoz = molar flux of SOz, gmol/cm* s Psoz = partial pressure of SO2 in the bulk gas phase, atm Pso2: = interfacial partial pressure of S02, atm PsoZln= inlet partial pressure of SO2 in the bulk gas phase, atm Pso20Ut= outlet partial pressure of SO2 in the bulk gas phase, atm Psoz* = partial pressure of SO2 which can be maintained in equilibrium with the bulk liquid phase, atm PT = total pressure, atm R = ratio of the gas to liquid film mass transfer resistances, dimensionless R = average ratio of mass transfer resistances in TCA, dimensionless R,, R , = the value of R in the packed and spray sections, respectively, dimensionless T = liquid temperature, K z = height measured from gas inlet, cm ZT = total height of the transfer region, cm 2, = height of the ith position, cm 2, = height of the unixpanded packing in the TCA, cm 2, = height of the spray section in the TCA, cm
Greek Letters 4 = enhancement factor for mass transfer in the liquid film due to chemical reaction, dimensionless = average enhancement factor, dimensionless A P N = normal pressure drop across the spray column, in. of Hz0 A 2 = difference between height 2 2 and 21, cm As, A, = magnesium correction factor for A, and A,, dimensionless
6
L i t e r a t u r e Cited Borgwardt, R.. "Limestone Scrubbing of SO2 at EPA Pilot Plant", Report No. 1. (Aug 1972a). Borgwardt, R.. "Limestone Scrubbing of SOz at EPA Pilot Plant", Report No. 2 lSeot 1972bl. Boigwkrdt, R., "Limestone Scrubbing of SO2 at EPA Pilot Plant", Report No. 3 (Oct 1972~). Borgwardt, R., "Limestone Scrubbing of SO2 at EPA Pilot Plant", Report No. 4 (Nov 1972d). Borgwardt, R., "Limestone Scrubbing of SOz at EPA Pilot Plant", Report No. 7 (Feb 1973al. Boigwardt, R..'"Limestone Scrubbing of SO2 at EPA Pilot Plant", Report No. 11 (June 1973b). Borgwardt, R.. "Limestone Scrubbing of SO2 at EPA Pilot Plant", Report No. 12 (July 1 9 7 3 ~ ) . Borgwardt, R., "Limestone Scrubbing of SO2 at EPA Pilot Plant", Report No. 14 (Jan 1974a). Borgwardt, R., "Limestone Scrubbing of SOz at EPA Pilot Plant", Report No. 16 (June 1974b). Borgwardt, R., "EPA/RTP Pilot Studies Related to Unsatwated Operation of Lime
and Limestone Scrubbers", a paper presented at the EPA Flue Gas Desulfurization Symposium, Atlanta, Ga.. Nov 47, 1974c. Chen, B. H., Douglas, W. J. M., Can. J. Chem. Eng.,46, 245 (1968). Epstein. M.. "EPA Alkali Scrubbing Testing Facility: Sodium Carbonate and Limestone Test Results", report prepared by Bechtel for the EPA (Aug 1973a). Epstein. M., "EPA Alkali Scrubbing Test Facility at the TVA Shawnee Power Plant", Bechtel progress report prepared for the EPA for July 1, 1973 to Aug 1, 1973 (Aug 31, 1973b). Epstein, M., progress report for Oct 1, 1973 to Nov 1, 1973 (Nov 30, 1 9 7 3 ~ ) . Epstein. M., "EPA Alkali Scrubbing Test Facility: Limestone Wet Scrubbing Test Results", report prepared by Bechtel for the EPA (Jan 1974a). Epstein, M., "EPA Alkali Scrubbing Test Facility at the TVA Shawnee Power Plant", Bechtel progress report prepared for the EPA for Dec 1, 1973 to Jan 1, 1974 (Jan 31, 1974b). Epstein. M., progress report for Jan 1, 1974 to Feb 1, 1974 (Feb 28. 1 9 7 4 ~ ) . Epstein, M.. progress report for May 1. 1974 to June 1, 1974 (June 30, 1974d). Epstein. M.. progress report for June 1, 1974 to July 1, 1974 (July 31. 1974e). Epstein, M., progress report for July 1, 1974 to Aug 1, 1974 (Aug 31, 19741).
Epstein, M., Sybert, L., Wang. S.C.. Leivo, C. C.. Princiotta, F. T., "Scrubbing Test Facility at the TVA Shawnee Power Plant", a paper presented at the 66th Annual Meeting of the A.I.Ch.E., Philadelphia, Pa.. Nov 1973. Fan, L. S.,Ph.D. Dissertation, West Virginia University, 1975. Gleason, R. J. "Limestone Scrubbing Efficiency of Sulfur Dioxide in a Wetted Film Packed Tower in Series with a Venturi Scrubber", paper presented at the Second International Lime/Limestone Wet Scrubbing Symposium, New Orleans, La., Nov 812, 1971. Nannen, L. W., West, R. E., Kreith, F., J. Air. Pollut. ControlAssoc., 24, 29 (1974).
Received for review August 4 , 1975 Accepted March 3, 1976 T h e authors wish to express their gratitude to the Environmental Protection Agency for the support of this work under grant number EHSD7120 and to J. Orndorff and C. Y. Lin for help in preparing the manuscript.
COMMUNICATIONS
Design Considerations for a Multistage Cascade Crystallizer
Experimental approaches were examined for determining the maximum allowable crystal growth rate that can be achieved in the absence of nucleation. This information was considered essential for the design of a multistage continuous suspension crystallizer in which nucleation occurs only in the first stage. A singlestage crystallizer seeded continuously with monodisperse crystals was shown to be better suited than a multistage system for obtaining useful growth rate data.
Much work has been done over the past decade in understanding the crystallization process. The work of Randolph and Larson (1962) and Hulburt and Katz (1964) has provided useful techniques for interpreting crystal size distributions (CSD) from suspension crystallization processes. Many experiments have since made use of these techniques in the design and analysis of the continuous mixedsuspension, mixedproductremoval (CMSMPR) crystallizer. Steadystate experiments with a singlestage CMSMPR crystallizer provide size distribution data that are readily interpreted to give meaningful estimates of the growth and nucleation kinetics (Randolph and Larson, 1971). Crystallization is sometimes performed continuously in staged vessels such that the entire magma of one vessel discharges as feed to a subsequent vessel. The resulting CSD can be altered significantly in this cascade system under different operating strategies. Variations of this problem have been treated previously (Robinson and Roberts, 1957; Randolph and Larson, 1962, 1971; Randolph, 1965; Larson and Wolff, 1971; Njvlt, 1971). Randolph (1965) considered a twostage continuous cascade system with allocated production and retention times and indicated that the twostage system produces a considerably smaller and somewhat more uniform CSD than a single stage of equal total volume. Larson and Wolff (1971) studied mathematically the case where no nucleation occurs in the second stage and defined operating conditions necessary to obtain a given maximum allowable supersaturation (and hence, a given maximum permissible growth rate) without nucleation. These investigators considered an arbitrary choice of the limit of the metastable region where growth can occur without nucleation but suggested no method for determining this limit for a given system.
Larson and Garside (1973) discussed the need for knowing such a limit in the design of both batch and continuous crystallizers in which the suppression of nucleation is desired. Their analysis considered techniques for determining the maximum allowable supersaturation for a Class I (lowyield) crystallization system. However, for a Class I1 (highyield) system where the supersaturation generally cannot be measured, determination of the maximum growth rate is not nearly as straightforward. The purpose of this communication is to suggest an experimental approach for determining the maximum permissible growth rate (in the absence of nucleation) for all but the first stage of a multistage cascade system. The following discussion is especially useful f i r Class I1 systems in which the supersaturation cannot be determined experimentally.
TwoStage Cascade System Consider a cascade of two wellstirred stages operating with no seeding in the first stage. Under the assumptions of a sizeindependent growth rate (McCabe's AL.law), zerosize nuclei, and constant and equal input and output flowrates, the steadystate CSD for each of the two stages can be given (Randolph, 1965) as nl =
nlOeL/GiTi
(1)
The suspension density for each stage can be used as a constraint on the above two equations. Thus
MI =
som
pkvnlL3dL = 6phVnl0(G1T1)*
Ind. Eng. Chem., Process Des. Dev., Vol. 15, No. 3, 1976
(3) 467