Ind. Eng. Chem. Res. 1993,32, 1993-2005
1993
Process Designs for Fractional Crystallization from Solution Luis A. Cisternas'*+and Dale F. Rudd Department of Chemical Engineering, University
of
Wisconsin-Madison, Madison, Wisconsin 53706
Asystematic procedure is presented for the identification of alternative process designs for fractional crystallization from solution. We seek designs that involve low rates of recycle, evaporation, and dilution. Only a limited number of general process designs need be analyzed if the crystallizations are operated at hot and cold points of multiple saturation and if the salts are ordered so that the relative composition is greater at the cold point of multiple saturation than at the hot point of multiple Saturation. Multiple component systems with sufficiently temperature-dependent equilibria are examined which form (1) anhydrous and hydrated single salts; (2) anhydrous and hydrated, congruently soluble, multiple salts; and (3)anhydrous and hydrated, incongruently soluble, multiple salts. Further, we show that systems that form solid solutions and systems that do not have sufficiently temperature-dependentequilibrium can be considered as simple extensions of the general principles.
Introduction Fractional crystallization operations are deceptively simple methods of separating mixtures of salts that differ in solubility. The wide variety of industrial applications consist of sequences of heating, cooling, evaporating, diluting, and solids separating. However, we do not yet know how to sequence these simple operations to accomplish many important industrial separations. In fact, the legal system recognizes that the design of even moderately complicated fractional crystallization processes is beyond the ordmaryskill of "one versed in the art". For this reason, novel crystallization process designs usually can be patented. We present in Figure 1the types of solid/liquid phase equilibra considered in this paper (Fitch, 1970). Type I Solutes crystallize without forming either solid solutions or multiple-salt compounds among themselves. However, they may form compounds with the solvent. Type 11 Solutes may crystallizeas hydrated or anhydrous multiple salts. The multiple salts may be congruently or incongruently soluble. Type III Solutes crystallize as solid solutions. The general approach to process design taken in this paper is based on four simple observations. First, we recognize that the natural pictorial representation of the design problem is the phase equilibrium diagram. The process design, the material balances, and the phase equilibrium data simultaneously can be represented on the same diagram. Second, we recognize that in industrial practice a crystallizeris often operated as close as practical to hot or cold points of multiple saturation to maximize product recovery. Points of multiple saturation occur where the equilibrium solution is saturated in more than one salt. Third, we notice that, by the simple expedient of ordering the salts so that the relative composition at a cold point of multiple saturation is greater than the relative composition at a hot point of multiple saturation, the wide variety of designs can be reduced to a small number of equivalent general process designs with no loss of generality. Fourth, we notice that investment costs and operating costs of industrial crystallizer systems are increasing functions of the evaporation, dilution, and recycle rates. We seek the superior process designs that have low flow rates. Toward that end, we present the
* To whom correspondence should be directed.
+ Permanent address:
Departamento de Ingenierla Quhica, Universidad de Antofagasta, Antofagasta, Chile.
SALT 1
SOLVBKT
SALT
1
8
unslamtedsdvlim
b
EqdUkhmofaysfllsofmdtmdwmtedmhuh
c
ccu&emDfofoftwoslltsviithlohmmI.
d
EqdUkhmDfdDUblcmhviith~lCdsdvlim
e
f
Bqullibrhnnofsdidlohmmam~~a c o c x L a c n n ~ f t w ~ r O l l d ~ w i m ~ L
1
~
D
f
d
~
SALT 2
Figure 1. Solid/liquid phase equilibria considered in this paper.
completely solved material balance equations for all of the general process designs.
Type I: Anhydrous or Hydrated Single Salts Ternary Systems. A typical industrial operation is shown in Figure 2 on the ternary phase equilibrium diagram for a system which forms only single salts. In design IA, the feed F is mixed with solution at the hot point of multiple saturation H to form a solution at point d. Then, the solvent concentration is adjusted by evaporation to form point a. Upon cooling, the solution at point a forms an equilibrium mixture of a salt 2 and a solution at the cold point of multiple saturation C. The solvent concentration of the cold point of multiple saturation solution C is adjusted by evaporation to get point b, which upon heating forms an equilibrium mixture of salt 1 and a solution at the hot point of multiple saturation H. The solution H is recycled to complete design IA. In design IB, the feed F is mixed initially with solution at the cold point of multiple saturation C to initiate the crystallization cycle. For either processing cycle to function, the relative compositions of the solutions at the hot and cold points of multiple saturation H and C must differ. We define the relative composition R as the mass ratio of salt 1to salt 2. The relative compositionsevaluated at the hot and cold points of multiple saturation are denoted RH and RC, 0 1993 American Chemical Society
~
1994 Ind. Eng. Chem. Res., Vol. 32, No. 9, 1993 P
FEED F
Wt 1
SALT 2
HVmR4TIoN
EVAPORATION or DILUTION
WATER VAPOR
I
-
MI
SALT P
SALT 1
sP
EVAPORATION or DILUTION
DESIGN IA
M2
P salt I
TE,XE,F,
Figure 3. Design I for the separation of ternary system. WATER VAPOR
L5?
SEPARAnoN
DESIGN m Figure 2. Flow sheets and graphical representationfor separation of a ternary system.
respectively. These are the dilution rays that pass through the points of multiple saturation H and C. We adopt the convention that salt 1and salt 2 be selected so that the relative composition at saturation decreases as the temperature increases.
Table I. Keys for the Designs of Figure 3, Figure 9, and Figure 27 design ~
~
Symbol
IA
IB
P
2 1 C
1 2
H
H
C
Q
D E
Chart I. Mass Flows for Design Class I, Figure 3 recycle and internal flow rates
R~ > R~ On the ternary diagram, the dilution ray at the cold point of multiple saturation is above the dilution ray at the hot point of multiple saturation. This convention in no way restricts our analysis of crystallization process designs. However, this convention is critical to the reasoning which follows as we sort through the combinatorial problems which arise in the synthesis of crystallization system designs. A useful consequence of this convention is that salt 1is always separated at the hot temperature and salt 2 is always separated at the cold temperature. The general process design for all ternary systems with single-saltformation is shown in Figure 3. Table I provides the key for converting the general process design into the two specific designs IA and IB. In Figure 3, salt P and salt Q are anhydrous or hydrated product of the form salt PanpH20 and salt Q q H z O , respectively. If streams MI and M2 are positive, they represent dilution; if they are negative,they represent evaporation. Two general designs are possible depending on which solution is recycled. In design IA, the hot solution H is recycled whereas in design IB the cold so1ution.C is recycled. In design IA, a salt 2 product is separated first. In design IB, a salt 1product is separated first. Our solution to the mass balance for the general process design shown in Figure 3 is given in Chart I. Given are explicit equations for all of the internal and external flows. These general equations are a direct consequence of our
external fiow rates SQ = (%$~/MWQ + 1)fQ Sp (npl8IMWp + 1)fp M I Fa + S p - 1 - FR Mz FR + SQ- Fs
fundamental assumptions; namely, (1) the crystallizers operate at the hot point of multiple saturation H and the cold point of multiple saturation C, (2) the salts are named salt 1and salt 2 so that RC > RH,and (3) the salt products are single salts (hydrated or dehydrated). Some care must be taken with systems which form hydrated single salts. Depending on the composition of the other component and depending on the temperature, a salt may crystallize as either the anhydrous or hydrated salt. The general equations in Chart I apply, but the solid separated has to be selected carefully. Remember that salt 1always is separated at the hot temperature and salt 2 at cold temperature. Also, remember that the solid separated is the solid that is in equilibrium at the point of multiple saturation. For example, in the phase equilibrium shown in Figure 4a, salt 1 can precipitate as a hydrated salt or as an anhydrous salt depending on the composition of salt 2. In the cycle shown in Figure 4a, the salt 1is separated as an anhydrous substance because this is the form in equilibrium with salt 2. In phase equilibrium shown in Figure 4b, salt 1can precipitate as a hydrated salt or as an anhydrous salt depending on the temperature. In the cycle shown in Figure 4b, the salt 1is separated as
Ind. Eng. Chem. Res., Vol. 32, No. 9, 1993 1995 SALT I
SALT I
DILUTION
M I -1.68
X h
-
0.117
EVAPORATION
b
3
Figure 4. Partial cycleswhere salt 1 will crystallize as the anhydrous or aa a hydrated salt depending on (a) the composition of the other component and (b) the temperature. Table 11. Solubility Data for the System KCl-NaCl-H20 saturated solution, w t % temp, O C KCl NaCl solid phase R 0 7.28 22.40 KC1 + NaCl 3.08 10 8.71 21.60 KC1 + NaCl 2.48 20.03 20 10.19 KC1 + NaCl 1.97 30 11.70 20.25 KCl + NaCl 1.73 19.66 KC1 + NaCl 1.49 40 13.16 60 16.07 18.57 KCl+ NaCl 1.15 KC1 + NaCl 0.92 80 19.03 17.59 15.90 100 22.20 KC1 + NaCl 0.72 110 23.04 16.58 KC1 + NaCl 0.72 120 24.23 16.35 KC1 + NaCl 0.70
anhydrous substance because that salt forms at the hot temperature where salt 1 is separated. Example. Production of Potash from Sylvinite. Consider the production of potassium chloride from sylvinite (47.7% KC1, 56.6% NaC1). Data on phase equilibrium for the system KCl-NaCl-H20 from Linke and Seidell (1965) are given in Table 11. The relative saturation is computed in the last column. NaCl was chosen to be salt 1and KCl to be salt 2 so that the relative saturation decreases as temperature increases. The selection of the operating temperatures is made so that a significant difference in the relative saturation is achieved; the cold temperature of 30 "C to avoid refrigeration and the hot temperature of 100 "C since higher temperatures do not improve the difference in the relative saturation. Thus, TH = 100 "CyF = 30 "C,xlH = 0.159, qc= 0.2025, xzH = 0.222, xzC = 0.117, nl = 0, n2 = 0, f1 = 0.566, and f i = 0.427. The required material balances for the two process designs contained in Figure 3 are found in Chart I. design IA: M,= 1.68, M,= -1.68,
FR
= 2.51
design IB: M,= 0.27, M2 = -0.27, FR = 2.58 These two designs are shown in Figure 5. There is only a small difference in the recycle flow between design IA and design IB. Design IB has much less combined evaporation and dilution flows. It is clear from the mass flows that design IB is superior using the low flow criterion. Multicomponent Systems. We next show how to generate designs to separate an N-component system in two ( N - 1)-component systems. Again the operating points for the crystallizersarepoints of multiple saturation where the N-component solution is saturated with N - 1 components. The methods to be developed are similar to those used previously for ternary systems, only more variations are possible. Because the graphical representation of multicomponent systems is very complicated, the method will be explained in detail only for four-
-
Mz 0.27
CSEPARATION 5-a
I
x,: x,:
PI -2.51
--om o w DESIGN
&.OB3
x:.
IA
-0.117
DESIGN
m
Figure 5. Flow sheets for the extractivecrystallizationof potassium chloride from sylvinite. SALT 1
SALT 3
b
SALT 2
Figure 6. Four-component graphical representation and evaporationldilution path.
component systems. However, the method and equations developed apply in general to multicomponent systems. The Gibbs phase rule indicates that a four-component system containing a single phase has five degrees of freedom. By imposing the additional conditions of fixed temperature, fixed pressure, and saturation with at least one solid phase, a two-dimensional representation becomes possible. Figure 6 shows such a four-component system. All points on this diagram are saturated solutions. For example, region salt 1a-d-c represents a solution saturated with salt 1 as an equilibrium solid phase. Salt 1can be an anhydrous or hydrate salt. Isothermal evaporation of any initial solution must end in the point representing a solution saturated with the three substances. For example, isothermal evaporation/dilutionof solvent from the system corresponding to point e will crystallize salt 1until point f, where the solution will be saturated with salt 1and salt 3. On further evaporation or dilution, salt 1and salt 3 will precipitate paragenetically, and the composition of the mother liquor will move from f to point d. The lines e-g and g-d are used here to represent more clearly that salt 1and salt 3 are the salts crystallized. Further, these lines help us to distinguish precipitation steps from dissolution steps. All potential separations sequences for a system consisting of salt A, salt B, salt C, and a solvent are shown in Figure 7. However, only a few of these sequences will be feasible for a given system. In Figure 8a, the solution at point C is heated to the temperature of the point of multiple saturation H, and it is evaporated or diluted such that salt
1996 Ind. Eng. Chem. Res., Vol. 32, No. 9, 1993 FEED fl,
f, ,......f,
SEPARATION
**"
$1
B
Figure 7. Potential separation sequences for a four-component system. SALT 1 - C
SALT 1 - B
SALT I - C
TB,, ' X
F,
Figure 9. Design I for the separation of multicomponent single Salts.
SALT3-8
SALTZ-A
a
SALT3-C
SALT'Z-A
b
SALT3-A
SALTZ-B
Chart 11. Mass Balances for Design Class I, Figure 9 recycle and internal flow rates
C
Figure 8. Separation paths for a four-component system,
C and salt B are crystallized. Then, the solution at point H is cooled to the temperature of the point of multiple saturation C, and it is evaporated or diluted such that salts A and B are crystallized. This represents an AB/BC separation in which salt B is called the pseudosolvent. If salt C is used as pseudosolvent, as shown in Figure 8b, an AC/CB separation is not possible. If the solution at C is heated at the temperature of the point of multiple saturation H and is evaporated or diluted, salts C and B will be crystallized. However, when the solution at H is cooled at the temperature of the point of multiple saturation C and is evaporated or diluted, salt C will dissolve and salt A will be crystallized. This is a BC/A separation. Note that salt C is called a pseudosolvent because it participates in the dissolution or crystallization of other components. For example, the precipitation of salt A by the dissolution of salt C as the pseudosolvent is the common salting-out phenomena. Notice in Figure 8c that salt A is used as the pseudosolvent to salt out salt C during a C/AB separation. For any quaternary system there are three possible cycles, depending on which salt is considered to be the pseudosolvent. For each cycle, two designs are possible depending on which point of multiple saturation solution is recycled. Figure 9 shows the design to separate an N-component system into two (N- 1)-componentsystems. The solvent is the component N, salts 3 through N - 1are pseudosolvents (which can precipitate or dissolve), and salt 1and salt 2 are salt P or Q in Figure 9. The keys for this design are given in Table I. Chart I1 gives the mass flows for the design shown in Figure 9. Positive values of M I and M Zare dilutions, and negative values are evaporations. Positive values of sk (k = 3,4, ..., N - 1)are precipitations, and negative values are dissolutions. Note also in Chart I1 that the recycle flow depends only on the composition at the point of multiple saturations of salt 1 and salt 2. The following steps generate designs to separate a N-component system in two systems with at least (N1)-components:
(
f/ = z-$)FR%% k = 3,4,...,N- 1
N-1
M~= F, + S,
+ '&si-
1 - FR
N-l
(1)Select salt 1and salt 2 so that the relative saturation decreases as the temperature increases. (2) Determine the internal and external material flows using Table I and Chart I1 for Design IA and Design IB in Figure 9. Depending on the sign of MI and Mz,select dilution or evaporation. Depending on the sign of Sk (k = 3, 4, ..., N-11, select precipitation or dissolution. (3)Repeat steps 1 and 2 for all possible pairs of salts. For a four-component system, there are six different ways to separate the system into at least a three-component system. But since there are two ways to separate a threecomponent system into ita components, there are a maximum of 24 and a minimum of 12 possible flow sheeta to separate the four-component system into ita three salts. For five-component systems, the number of possible schemes to form the four salts is between 6912 and 1728. For each situation, it is possible to eliminate the schemes that require large evaporation, dilution, or recycle flows. Also, it is possible to eliminate schemes where valuable salts are used to salt out salts of little value merely by
Ind. Eng. Chem. Res., Vol. 32, No. 9,1993 1997 -3 8
m
-3
=3
m C
Figure 10. Separation cycles using operation points that are not points of multiple saturation. Table 111. Solubility Data for KNOa-NaC1-NaNOa-HZ0 System saturated solution, w t % temp,OC KN03 NaCl NaNOs solid phase 15.68 11.20 27.02 KNO3 + NaCl + NaN03 20 100 49.66 2.88 32.74 KNOa + NaCl + N d O 3 20 21.31 21.56 KNOs + NaCl 0.0 91 61.14 10.92 0.0 KNO3 + NaCl 0.0 13.80 30.34 NaCl + NaNOa 20 100 0.0 5.63 57.40 NaCl + NaNOs 20 17.13 0.0 42.03 KNOa + NaNOs 100 KNO3 + NaN03 48.1 0.0 36.7 Table IV. Material Balance Exam& Production of KNOI design salt3 d t P case FR Mi Mz saltingout 1 KNO3 IA 0.72 -0.11 -0.54 NaCl 2 KN03 NaCl IB 0.02 -0.66 0.01 NaCl KNOa IA 0.08 -0.54 -0.12 3 4 NaCl NaNO3 IB 1.44 -1.30 0.65 KNOs NaNOs KNO3 IA 0.35 -0.15 -0.51 KNO3 5 6 NaNOs NaCl IB 0.11 -0.70 0.04 NaCl
allowing the operation of crystallizers at other than point of multiple saturation. Figure 10 illustrates the use of modified operation points H’ and C’ to alter the crystallization phenomena. Example. Production of Potassium Nitrate. We seek to separate an aqueous solution of 19.8% potassium nitrate (valuableproduct), 11.5% sodium chloride (waste), and 3.37% sodium nitrate (valuableproduct). Equilibrium data from Linke and Seidell(1965)are shown in Table 111. Six possible ways to separate this system into at least three-component systems are shown in Table IV. Design 4 has high solventand recycle flows. In design 1,potassium nitrate, the valuable product, is used to salt out sodium chloride (a waste). Although it is possible to modify this scheme such that the salting-out step is eliminated (see Figure loa), this option is not interesting because of high recycle flow. Therefore, only the four designs in Figure 11are attractive. The total solvent flows are similar for designs 2,3,and 5 and a little higher for design 6. Design 6 can also be modified to eliminate the salting-out of NaC1.
Type 11: Anhydrous or Hydrated Multiple Salts Ternary Systems. Figure 12 shows phase diagrams for two ternary systems with double-salt formation. In
both cases there are three solid compounds: salt 1,salt 2, and the double salt. We divide the equilibrium diagram into two subdiagrams: salt 1-double salt and salt 2-double salt. We select a first salt to be precipitated and analyze the subsystem formed from this salt and the double salt as a single-salt ternary system. Then, we consider the remaining subsystem consisting of the double salt and the second salt. It is important to note that there is only one choice for the first salt. This choice depends on the characteristics of the phase diagram. The double salt formed in the system shown in Figure 12a is called congruently soluble because it is in equilibrium with solution having the same relative concentration. The double salt of Figure 12b is incongruently soluble. If the relative composition of the double salt is in between the relative compositions at the point of multiple saturation, the double salt is congruently soluble. Otherwise, the double salt is incongruently soluble. Ranges of temperature may exist where no double salt is formed. In such a case, two possible operation conditions can be considered. First, one operation point can be the point of multiple saturation at the temperature where no double salt is formed, and the other operation point can be the point of multiple saturation where double salt is formed. Second,the two operation points can be the point of multiple saturations where double salt is formed. These situations lead to different classes of crystallizationcycles. 1. Multiple Saturation without Double Salt. The method to be described next can be applied to congruent and incongruent systems. However, it is specially important for congruent systems, as such systems cannot be separated using two point of multiple saturations where the double salt is formed. The method begins with a search for a temperature where no double salt is formed. Figure 13 shows four different possible operations. Note that as before there is always a cycle between a hot temperature point of multiple saturation and a cold temperature point of multiple saturation. In Figure 13a,b, double salts do not form at the cold temperature, and in Figure 13c,d, double salts do not form at the hot temperature. In Figure 13a,c, the relative saturation at the point of multiple saturation without double-salt formation is not between the relative saturation of the point of multiple saturation with double-salt formation. A simple process cycle as discussed earlier is sufficient to separate the salts. In Figure 13b,d, the relative saturation at the point of multiple saturation without double-salt formation is between the values of the relative saturation of the two points of multiple saturation with double-salt formation. In such situations, a first cycle is need to precipitate the one salt and the double salt, and then a dilution of the double salt will produce the other salt and a solution to be recycled. The process cycles are shown in Figure 14a,b. Note that basically the cycles are the same as those for systems without double salt, with the addition of a dilution step. The keys for Figure 14a,b are given in Table V. Systems with two points of multiple saturation temperatures are distinguished by C1 and C2 (or H1 and H2) such that Rcl > RC2 (orRH1> ItH2).For each cycle,there are two possible designs because the feed can be mixed with either solution at the point of multiple saturations. For example, design IIAl and design IIBl are alternative flow sheets for the same system. The general material balance is given in Chart 111. The double salt is of the form rgSaltQ. rpSdtP%dH@.
1998 Ind. Eng. Chem. Res., Vol. 32, No. 9, 1993
c SEPARATION
I
ma (om)
WATER
C
(evllPorunoN1
W A r W (0.12)
d
Figure 11. Separation of a mixture of KN03, NaC1, and NaNOa: (a) design 2; (b) design 3; (c) design 5; (d) design 6. SALT I
SALT 1
SALT 1
SALT 1
b
SALT 2 SALT 1
SALT 2 SALT 1
d a
b
Figure 12. Phase diagrams for ternary system with double-salt formation: (a) congruently soluble, (b) incongruently soluble. DOUBLB SALT
The procedure below can be applied to congruent and incongruent systems where there is a cold or hot temperature point of multiple saturation without double salt. The steps are as follows: (1)Select two temperatures such that at one temperature no double salt is formed. (2) Select salt 1and salt 2 such that the relative composition at the double salt (RDS)and the relative compositions at the point of multiple saturations satisfy any of these conditions: (a) RC > RH1, (b) Rc2 > RH, (c) Rcl > RH > RDS, and (d) RDS> RC > RH2. (3)If situation a or b obtains, select the process cycle using the method of point 1. The number of hydrated molecules with which the salt crystallizes can be determined by
SALT 2
!%
SALT 2
Figure 13. Process cycles exploiting an end point without doublesalt formation.
remembering that salt 1 is always recovered at the hot temperature and salt 2 at the cold temperature. (4) If situation c or d obtains, select the designs given in Figure 14a and Figure 14b using Table V. That is, select design IIAl and design IIBl for situation d, and design IIA2 and design IIB2 for situation c. (5)Evaluate the mass balance
Ind. Eng. Chem. Res., Vol. 32, No. 9, 1993 1999 PEED
Table V. Keys for the Designs of Figure 14a,b design key P
Q D
E
Figure 14a IIAl IIA2 2 1 1 2 C H H2 c1
Figure 14b IIBl IIB2 1 2 2 1 H2 c1 C H
Chart 111. Mass Balance for Design 11, Figure l4a,b flow
design A1/A2
equation
BlJB2
AlJA2
B1/B2 SALT P, S,
Q , SQ
+(*SALT
RI
A1/A2
b BlJB2
Figure 14. (a) Design I1 A1 or A2. (b) Design I1 B1 or B2. SALT 1
SALT 1
AlJA2 BlJB2 SALT
AlJA2IBlJB2 AlJA2JBlJB2 AlJA2 B1/B2 All A2 B1/B2 AlJA2 BlIB2
for the two cases selected in the previous steps using the equations given in Chart 111. 2. Two Points of Multiple Saturationwith Double Salt. We now examine the situation where the two points of multiple saturation involve the formation of double salts. The double salt must be incongruently soluble. Figure 15 shows four different cycles. Note that in each case there is a cycle where one salt and the double salt are produced. The other salt is obtained by dilution of the double salt. Again, only one salt can be separated by dilution of the double salt. There are several possibilities for each case. For example, in Figure 15a only one cycle is possible between C1 and H1,but several combinations are possible for the separation of salt 2. These options are to use C2 as operation point and recycle solution C1 (as is shown in Figure 15a), use C2 as operation point and recycle solution H1,use H2 as operation point and recycle solution C1, and use H2 as operation point and recycle solution H1. The feed can be mixed either with solution C1 or H1;therefore, eight possible configurations are possible for the system in Figure Ma. Figure 16 gives the
SALT
2 SALT I
SALT 2 SALT I
c
SALT 2
d
SALT 2
Figure 15. Process cycles exploiting two end points with double salt.
basic process designs for the four structures shown in Figure 15. Table VI is the key for selecting the process designs in Figure 16. A procedure to generate the possible schemes follows: (1)Select two temperatures where the double salt is formed. Check that the double salt is incongruentlysoluble at the two temperatures; namely, that the relative saturation at the double salt ( R D S ) is not between the values of the relative saturation at the two points of multiple saturation. (2)Select salt 1 and salt 2 such that either Rcl > RH1> RD* (call this case 1)or RDS> Rc2 > RH2(call this case 2). (3) Select the possible schemes using Table VI and the following additional conditions:
2000 Ind. Eng. Chem. Res., Vol. 32, No. 9, 1993 FEED
I
iEVAFORATION or DILUTTON
1 EVAPORATION or DILUTION
or DILUTION
I
(+)22-
DOUBLE SALT
I DOUBLE SALT
a
C PEED
-A-
I
I 0
($>SALT
DILUTTON
0
DILUTION
Q , SQ
s,> DOUBLE SALT
b Figure 16. (a) Design I11 A1 or A2. (b)Design I11 B1 or B2. ( c ) Design I11 C1 or C2. (d) Design I11 D1 or D2.
case 1: Rc' if R"
> RH1> RDS > RC2,use design IIIAl and design IIIDl
if RH1> RH2,use design IIIA2 and design IIID2 if Rcl
> RC2,use design IIICl and design IIIBl
if Rc'
> RH2,use design IIIC2 and design IIIB2
case 2: RDS> Rc2 > RH2 if RH1> RC2,use design IIIA2 and design IIID2 if R"
> RH2,use design IIICB and design IIIB2
if Rcl > RC2,use design IIIAl and design IIIDl if Rc' > RH2,use design IIICl and design IIIBl As many as eight possible designs are possible. (4) Calculate the mass balance using the equations of Chart IV. Quaternary Systems. Two situationswill be analyzed next. First, we examine the situation in which one of the operation points is a point of multiple saturation where a double salt does not form. In the second situation, both operation points are points of multiple saturation where double salts form. 1. Multiple Saturationwithout Double Salt. Figure 17,Figure 18,and Figure 19show different cycles between two points of multiple saturation where one of the point of multiple saturations does not form a double salt. The condition that the relative saturation decreases as temperature increases has been applied to the operation point
Table VI. Keys for the Designs of Figure 16 (Design 111) A1 A2 B1 B2 C1 C2 D1 D2 Case 1 P 2 2 2 2 2 2 2 2 Q 1 1 1 1 1 1 1 1 C1 C1 H1 H1 H1 H1 D C1 C1 H1 C1 C1 E H1 H1 H1 C1 C1 F C2 H2 C2 H2 C2 H2 C2 H2 Case 2 P 1 1 1 1 1 1 1 1 6 2 2 2 2 2 2 2 2 D H2 H2 H2 H2 C2 C2 C2 C2 E C2 C2 C2 C2 H2 H2 H2 H2 C1 F C1 H1 H1 C1 H1 C1 H1
of multiple saturations. In cases a of Figure 17, 18, and 19, the double salt does not form at the cold temperature, whereas in cases b the double salt does not form a t the hot temperature. The double salt can be congruently or incongruently soluble. Figure 17a shows the case where RC > RH1, and Figure 17b shows the case where Rc2 > RH. For these designs, there is no precipitation of the double salt. The process cycles can be selected using the methods described for type I equilibrium. Figure 18shows the cases where the double salt is formed between salt 1 and salt 2. Salt 3 is thought to be a pseudosolvent because it can be precipitated or dissolved. For example, in Figure 18b salt 3 is added to the solution at C1 to salt out salt 1. Figure 18a represents the case where RDS > RC > RH2and Figure 18b the case where Rc' > RH > RDS. For these cycles, two flow sheet schemes are possible if the feed is mixed with any of the point of multiple saturation solutions. Figure 20 shows these flow sheet schemes, and Table VI1 is the key for the operation conditions.
Ind. Eng. Chem. Res., Vol. 32, No. 9,1993 2001 Chart IV. Mass Balance for Design 111, Figure 16a-d flow
design
SALT 1
SALT 1
eauation
A/C B/ D
A/ C fPmd
SALT 3
SALT 2
SALT
SALT 3
2
rpMWp- rQMWp.E/xt BID fPMWd
rpMWp- rQMWp.;/xp" A/B
b
1
Figure 17. Process cycles for double-saltquaternary system without precipitation of double salt. SALT I
SALT 1
C/D
A/B SALT
SALT 3
C/D
2
SALT
SALT 3
2
b
1
Figure 18. Process cycles for double-salt quaternary system with double salt formed for salt 1 and salt 2. BID
SALT I
SALT I
A/C
A/ C
BID
SALT 3
SALT 2
SALT3
DOVBLB
SALT2
SALT
A/B/ClD AlB/C/D A/B C/D A/B C/D A/B/C/D A/BlC/D
Figure 19 shows the case when the double salt is formed for either the salt 1and salt 3 or the salt 2 and salt 3. Note that the relative composition of the double salt (RDS)for Figure 19b is equal to zero. But for Figure 19a, RDSis indeterminate. For the purpose of this work, RDSin this situation will be defined as infinite. We do this so Figure 19a can represent the case where RDS> RC > RH2.Figure 19b illustrates the case where RC1 > RH> RDS. Again, two designs are possible for each cycle. The designs are the same as in Figure 20, but the double salt formed is different. The following procedure allows the generation of the possible crystallization systems: (1)Select two temperatures such that at one temperature there are no double salts formed. (2) Select one salt to be the pseudosolvent, called salt 3. Then select salt 1and salt 2 such that the relative saturation at the double salt (RDS)and the relative saturation factors at the points of multiple saturation meet any of these conditions: (a) RC
1
b
Figure 19. Process cycles for double-salt quaternary system with double salt formed for (a) salt 1 and salt 3 and (b) salt 2 and salt 3.
> RH1,(b) Rc2 > RH,(c) Rcl > RH > RDs, and (d) RDS > RC > RH2.If the double salt is formed with salt 1and salt 3, the following conditions must be met: R13' > R13" for situation a (if this condition is not satisfied, then consider situation d) and RDS> R1sH2for situation d. If the double salt is formed with salt 2 and salt 3, the followingconditions are also needed R32c2 > R32H for situation b (if this condition is not satisfied, then consider situation c) and R32c1> R32Dsfor situation c. (3)If situation a or b obtains, select the design given for type I equilibrium. (4) If situation c or d obtains, select the scheme given in Figure 20 using Table VII. The selection is design IVAl and design IVB2 for situation c and design IVBl and design IVA2 for situation d. If the double salt is formed between salt 1and salt 2, the following condition are also needed: for design IVAl and design IVB2, RF> RDS,and for design IVBl and design IVA2, RDS > RF. ( 5 ) Evaluate the mass balance for the two cases selected in the previous steps using the equations given in Chart V. In this chart, the column "key" is used to differentiate the cases where the double salt is formed between salt 1 and salt 2, and the case where the double salt is formed either with salt 3 and
2002 Ind. Eng. Chem. Res., Vol. 32, No. 9, 1993
Chart V. Mass Balance for Design IV, Figure 20a,b flow
~
{
bSakP k h l
Q 5 I\
0
.,a1 LL) P % I \ O
DESIGN A I m B I
%?
{
r.SakP+Y
Q
rrSakl %& Q
DESIGN AZ
5
9
0
am
-++
Table VII. Keys for Design IV, Figure 20a,b Figure 20a Figure 20b IVAl IVBl IVA2 IVB2 P 2 1 2 1 1 2 1 2 Q c1 H2 C H D E H C H2 c1
xsDF3- X a E F ~
fa - fs"
select key 1 2 2 3 4 4
(6) Select another salt to be salt 3 and repeat the previous steps until each salt has been salt 3. 2. Two Points of Multiple Saturation with Double Salt. In this situation, the cycles are similar to those in the previous case. For example, Figure 21 shows several cycles. In Figure 21a,b, the double salt is incongruent and only one cycle is possible. In Figure 21c,d, the double salt is congruently soluble and two cycles are possible. The flow sheet schemes for these cycles are shown in Figure 20. The steps for the generation of the flow sheets are as follows: (1) Select two temperatures a t which double salts form. (2) Select one salt to be the pseudosolvent called salt 3. Then select salt 1and salt 2 such that the relative saturation at the double salt (RDs)and the relative saturation at the point of multiple saturations reach any of these situations: (a) RC1 > RH1 > R D S and (b) R D S > R C 2 > RH2. If the double salt is formed with salt 1and salt 3, the following condition is also needed R13D8 > R 1 3 ~for 2 situation b. If the double salt is formed with salt 2 and salt 3, the following condition is also needed: R&1 > R32DS for situation a. Recognize that more of one situation is possible if the double salt is congruently soluble. (3) For any situation, select the scheme given in Figure 20 using Table VII. That is, select design IVAl and design IVBB for situation a, and select design IVBl and design IVA2 for situation b. If the double salt is formed between salt 1and salt 2, then the following conditions are also needed for design IVAl and design IVB2, RF > RDS,and for design IVBl and design IVA2, RDS> RF. (4) Evaluate the mass balance for the two cases selected in the previous steps using the equations
f Q'
salt 1or with salt 3 and salt 2. The following table helps to find the proper "key" to be used. and the double salt is salt 1 and salt 2 salt 1 and salt 3 salt 2 and salt 3 salt 1 and salt 2 salt 1 and salt 3 salt 2 and salt 3
equation
I\ 0
Figure 20. Design IV.
If design is IVAl or IVBl IVAl or IVBl IVAl or IVBl IVA2 or IVB2 IVA2 or IVB2 IVA2 or IVBS
key
a
.
.
This equation applied to Sa' and Sg".
given in Chart V. In this chart, the column "key" is used to differentiate the cases where the double salt is formed between salt 1and salt 2 and the case where the double salt is formed either with salt 3 and salt 1 or with salt 3 and salt 2. The following table helps to find the proper "key" to be used. If design is IVAl or IVBl IVAl or IVBl IVAl or IVBl IVA2 or IVBS IVA2 or IVBB IVA2 or IVB2
and the double salt is salt 1 and salt 2 salt 1 and salt 3 salt 2 and salt 3 salt 1 and salt 2 salt 1 and salt 3 salt 2 and salt 3
select key 1 2 2 3 4
4
(5) Now select another salt to be salt 3 and repeat the previous steps until each salt has been salt 3.
a
KL
SALT
b L
SALT 1
d
c
SALT 3
SALT 2
SALT 3
SALT 2
Figure 21. Process cycles for a double-salt quaternary system exploiting two end pointawith double salt (a,b)incongruentlysoluble, (c,d) congruently soluble.
Both procedures given in this section can be applied to systems where the solid phases form anhydrous salts or hydrated salts. The feed can be mixtures of solid salts or solutions. Always the solvent is considered as a component even when the feed does not contain it. There are some systems where more than one double salt is formed. It is possible to extend the method for these more complex situations, but several more possible operations must be considered. However, it may be possible to find some range of temperatures where this situation can be avoided. For example, the system lithium sulfate-sodium sulfatewater has two double salts at 45 "C, one of which disappears a t 40 "C. Example: Separation of the Double Salt Burkeite. Consider the production of sodium carbonate and sodium sulfate from the double salt Burkeite: Na&0~2NazSO.+ Several patented process designs have been proposed (Allen et al., 1931; Black et al., 1943; Black et al., 1944; Suhr and Fitch, 1946). Data for the phase diagram are available in Linke and Seidell(l965) and are shown in Table VI11 with the values of relative saturation added. Our selection of salt 1and salt 2 depends on temperature. The system does not form a double salt below 30 "C. Above 30 "C, the double salt Burkeite forms. The relative composition of Burkeite is RDS = 2.27. Note that the RDS is not between the values of the relative saturation where double salts form: the system is incongruently soluble. Also, notice that this result is independent of which salt is called salt 1 and which is called salt 2. Several process are possible for separating Burkeite. First, two temperatures can be selected such that double salts do not form, for example, 15 and 25 "C. This choice of temperature leads to design IA and design IB in Figure 3. However, design IB requires about 2 times the evaporation and dilution flows of design IA and about 4 times the recycle flow. Therefore, for these operation temperatures design IA is preferred, Figure 22. A second possibility is to choose a cold temperature where the double salt does not form and a hot temperature where the double salt forms, for example, 20 and 50 "C. This will give two schemes analogous to design IIAl and design IIBl in Figure 14. However, design IIBl involves less evaporation, dilution, and recycle, Figure 23. Finally, it is possible to choose both temperatures where the double salt forms, for example, 30 and 50 "C. This
Figure 23. Separation of Burkeite exploiting one end point without double salt. Design I1 B1. Table VIII. Points of Multiple Saturation for the System Sodium CarbonateSodium SulfateWater solution composition, temp, wt% O C NazCOs Na2SO4 solid phase R 15 12.3 8.0 Na2COvlOH20 + Na2SOplOHzO 0.65 20 14.95 11.2 Na2COvlOH20 + Na2SO4.1OH20 0.75 25 17.9 16.2 Na2COs~lOH20+ NafiO4.1OHzO 0.91 NazCOvlOH20 + Na~COs.2NafiO40.33 30 25.8 8.6 15.5 19.5 NazCOs.2Na&304 + Na2SO4 1.26 10.2 25.1 2.46 NazSO4 + NaflO4.lOH2O 50 29.7 5.5 NazCOvHzO + NqCOs.PNazSO4 0.19 11.4 22.2 NazCOs.2NaflO4 + NaflO4 1.95
gives eight schemes analogous to those shown in Figure 16. The feasible operation conditions are case 1in Table VI. Table IX gives the flow needed for the eight possibilities. Design IIIAl in Figure 24 and design IIIBl in Figure 25 involve the lowest evaporation, dilution, and recycle. It is not possible to distinguish between the four designs (Figure 22 through Figure 25) based only on material balance.
Extensions of Basic Principles It is now possible to relax some of the fundamental assumptions imposed earlier in this paper. For some systems, the value of the relative saturation does not
2004 Ind. Eng. Chem. Res., Vol. 32, No. 9, 1993 SALT I
SALT 1
SALT 1
PEED
9
1EVAPORATION
1
SWARATION
e c 30' C EVAPORATION
MI-0.38
BuRKEITe
-
-
hi) 2.88
bZW4
>
S a , - 1.17
SALT 2
s 1- 0.69 M,
M2-0.01
-
a
b
C
1.97
Figure 26. Phase diagram for system whose form is a solid solution in the whole range of concentration.
1
I
SALT 2
SALT 2
FEED I
I
BURKEnZ
Figure 24. Separation of Burkeite exploiting two end pointa with double salt. Design I11 A l . PEED
EVAPORATION
(?)--
I
TD
FRACTIONAL CRYSTALLIZATION
SALT Q
EVAPORATION
Figure 27. Scheme for the separationof a system with a solid solution that has a congruence point. I
9
Figure 25. Separation of Burkeite exploiting two end points with double salt. Design I11 B1. Table IX. Flows for the Cases Using Two Temperatures with Double Salt A1 A2 B1 B2 C1 C2 D1 D2 1.48 1.48 1.39 1.12 1.39 -0.38 -0.38 -0.20 0.01 0.01 0.01 2.88 2.88 12.54 1.97 11.63 2.15
F R ~ 1.48
Fm Mi
-Mz Ms -Md
1.48 1.12 -0.20 0.01 12.54 11.81
14.65 1.12 2.21 2.42 2.88 2.15
14.65 15.77 1.39 1.12 2.21 2.21 2.42 2.60 12.54 2.88 11.81 1.97
14.65 1.39 2.21 2.60 12.54 11.63
depend significantly on temperature, and excessively high flows obtain. Fortunately, this difficulty may be avoided by the simple expedient of adding an additional component which has the desired solubility properties. In addition, a few inorganic systems form solid solution in the whole range of temperature and concentration. With these systems, a countercurrent cascade must be used to obtain the desired fractionation. If we replace the single-stage crystallizer with the proper countercurrent cascaded crystallizer system, the basic principles can be applied directly to this unusual phase equilibrium. Insufficient Temperature Dependence. For systems in which the value of the relative saturation does not depend significantly on temperature, the internal flows become excessive. However, this difficulty may be avoided if an additional component can be found that has certain desirable solubility properties. For example, in a ternary system with constant relative saturation, a fourth component may be added as a pseudosolvent. This is analogous to the scheme shown in Figure 9, with the feed containing only salt 1 and salt 2. The fourth component, salt 3, is added to salt out either
salt 1 or salt 2. The required properties for the fourth component, salt 3, are as follows: (a) the relative saturation at the quaternary points of multiple saturation must be sufficiently temperature dependent to give low internal flows, (b) the salt must be inexpensive, ( c ) the subsystem (salt l-salt 3 or salt 2-salt 3) must be easy to separate, and (d) salt 3 must be a qualified crystal habit former. Solid Solutions. For systems which form a solid solution in the whole range of temperature and concentration, the methods of McCabe-Theile and PonchonSavarit may be used to determine the required number of equilibrium stages in the cascade (Fitch, 1976). Other systems may form solid solution in some ranges of temperature and concentration. It may be preferable to avoid the solid solution region in these cases. Consider the three ternary systems shown in Figure 26, which form solid solutions over the whole concentration range. In Figure 26a,b, the solid solution is formed continuously. In Figure 26c, there is adiscontinuity. Points s in Figure 26b,c are congruence points where the solids are in equilibrium with a solution with the same relative composition. For systems like that shown in Figure 26a, a singlestage crystallizer is replaced with a countercurrent cascade in which the more soluble salt moves in the direction of liquid flow and the less soluble salt moves in the direction of solid flow. For systems like Figure 26b and Figure 26c, the congruent points s mark the limit of enrichment possible by countercurrent fractional crystallization. However, a complete separation is possible by operating two cascades at different temperatures. Such a system is shown in Figure 27. The following procedure identifies schemes for the separations of two salts that form a solid solution: Select salt 1 and salt 2 so that the relative saturation at the congruent points decreases with temperature. Use
Ind. Eng. Chem. Res., Vol. 32, No. 9,1993 2005 the schemes in Figure 27,Table I, and the following rules: if RF > RC,select design IA if RF > RH,select design IB if RC > RF > RH,select both design IA and design IB
Nomenclature F = mass flow rates M = dilution and evaporation mass flow rate MW = molecular weight n = number of water molecules in hydrate salt R = relative composition factor r = stoichiometric coefficient S = salt mass flow rate T = temperature, "C x = mass fraction f = feed mass fraction Subscripts 1, 2, 3 = salt 1, 2, 3
DS = double salt P = salt P
...
Q = salt Q R = recycle Superscripts C = cool temperature point of multiple saturation D = cool or hot temperature point of multiple saturation E = cool or hot temperature point of multiple saturation F = feed H = hot temperature point of multiple saturation
Literature Cited Allen, W. H.; Gale, W. A.;Ritchie, C. F. U.S.Patent 1,836,426,1931. Black, L. G.; Fitch, E. B.; Suhr,H. B. U.S.Patent 2,309,569,1943. Black, L. G.; Fitch, E. B.; Suhr,H. B. U.S.Patent 2,348,164,1944. Fitch, B. How to Design Fractional Crystallization Processes. Ind. Eng. Chem. 1970,62,6. Fitch, B. Design of fractionalcrystallizationprocesses involving solid solutions. AIChE Symp. Ser. 1976,72,153. Linke, W. F.; Seidell,A. Solubilities of Inorganic and Metal Organic Compounds; AmericanChemicalSociety: Washington,D.C., 1965. Suhr, H. B.; Fitch, E. B. US. Patent 2,392,888,1946. Received for review December 10,1992 Revised manuscript received June 14, 1993 Accepted June 23, 1993.
Abstract published in Advance ACS Abstracts, August 15, 1993.
