How to Design Fractional Crystallization Processes - Industrial

Design of the Separation System. Gautham Parthasarathy ... Improving Product Recovery in Fractional Crystallization Processes: Retrofit of an Adipic A...
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How to Design Fractional Cryst alIization Processes hen a chernical engineer is asked to design a dis-

W tillation process for separating a complex mixture of components, he goes about it systematically a n d confidently. H e can recognize many different cases, or configurations of equilibrium lines, and knows holv to deal with each. Considerable ingenuity niay be required, hut the engineer knows the "tricks of 1 he trade" a n d how to attack the probleiii. Faced with a mixture of components to separate by fractional crystallization, however, he usually has litrle to fall back on except intuition and inspiration. Fractional crystallization is not more complicated than distillation, but the engineer has not been taught any principles from which to recognize foriiial similarity in different examples. And he seldom has any stock of standard process solutions for given cases when he meets them. Design of even moderately complicated fractional crystallization processes is recognized as beyond the ordinary skill of a chemical engineer-"one versed in the art"-in that they can usually be patented. But rational principles and a bag of tricks d o exist for fractional crystallization. With these in mind a process designer knows in advance what to look for in a phase diagram, a n d what to do when he finds it. H e can move ahead as deliberately as if he were treating a distillation problem rather than having to look for inspiration. This paper focuses upon a set of systematized procedures by which ideal equilibrium processes can be generated from solubility data. There is not space in a 6

INDUSTRIAL A N D ENGINEERING CHEMISTRY

single article to ireat also the manifold problems cncountered in reducing a n ideal process concept to a practical a n d economical flowsheet. But a proces? must be conceived in principle before it can he reduced to practice, a n d i t is in the original conception of processes that iiiost engineers have least background. T h e paper is divided into three sections, corresponding to handling three, four, and n coinpoiicnts, respectively. Since a three-component system is a special case of a four-component one, a n d both are special cases of n com.ponent systeiiis, this necessitates passing from special to general cases, with repetition of basic ideas in progressively more generalized forin. But with each increase in the number of components, the abstractness and difficulties of representation a n d ireatiiient increase greatly. T h e paper is arranged this way primarily so that an engineer faced with a specific fractional crystallization problem need go into the subject only as deeply as necessary to solve his problem. H e won't have to cross niountains to climb a foothill.

THREE-COMPONENT SYSTEMS Fractional crystallization processes are worked out graphically in practice, since solubility data arc highly empirical at this time. Graphical methods are uscd to represent the system, its equilibria, and the results of various process manipulations. \-Ve now start laying the foundation for graphical treatment in terms of the three-component systems being considered here.

BRYANT FITCH

Paper focuses on a set of systematized procedures by which ideal equilibrium processes can be generated from solubility data

Composition plots. T h e composition of a threecompoiient system has two degrees of freedom, and can be represented in a two-dimensional coordinate system or graph. If the coiiiponents are designated respectively A , B, and S, YoA can be plotted against YoB. T h e content of the third constituent, S, is always deterB S = 100%. Any mined by the condition A weight units may be used. I n this paper we use simple wt % extensively (weight of a given component per 100 weights in total system). Equivalent wt % is used occasionally (equivalent weights of a given coniponent per 100 equivalent weights of all coiiiponents in system). Other coniposition ratios might be used, such as granis per 100 grams solvent, grams per 100 grains “free” solvent, or grams per gram of key component other than solvent. Such plottings are in some cases very convenient, but are not fundamentally different from percentage plots. Concentration plots (grams per liter) are not suitable because they d o not perinit use of constructions to be described below. Composition coordinates may be either rectilinear or skewed. A percentage plot will be bounded by a right triangle in rectilinear coordinates (Figure 1). If the axes are 60” apart a n d the scale modules are equal, the familiar equilateral triangular plot appears (Figure 2). It has no functional advantages over one using rectilinear coordinates, being just a linear transformation from it. T h e two can be used interchangeably ( 9 ) )a n d we will use them that way.

+ +

Figure 1. Plotting composition potnt in right angle coordinates

I t will be convenient to think of compositions as being represented by vectors, a n d coordinate axes as bases for vector spaces. T h u s point p (Figures 1 a n d 2) represents the sum of a constituent vector iii the A direction representing the yo of component A , a n d one in the B direction representing the yGof B. Iii this view coordinate axes are simply guidelines showing the direction a n d scale iiiodules of A a n d B vectors. Such a view is perhaps overelegant for simple systems, but it brcoines useful in dealing with more complicated ones. VOL. 6 2

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S

Figure 2. Plotting composition point i n GO’ or t i i u y u l a i coordznatcs Figure 4. Construction “rajs”

i t follows algebraically that

Figure 3. “Center

of

grazlity” principle

Equations 1 and 2 may be interpreted as a material balance of two constituents or groups of constituents in systeiiis 1 a n d 2, coinbining to form system 3. A’s may be interpreted as weights of coiiiponent A ; C’s may be interpreted as hundred weights of coiiipoiients A B S. T h e n Equation 3 interprets as

+ +

Construction lines. If any two sb-stems 1 a n d 2, having compositions represented by p ( 1) a n d p ( 2 ) (Figure 3), are n i x e d to form another system 3, the composition of the new system, p ( 3 ) , will be on a straight line joining points p(1) a n d p ( 2 ) . This derives froni material balance, a n d holds also for the case that system 3 is split into systems 1 and 2. Such straight lines form the bases for all process constructions on a composition diagram. I t follows from the above that if solvent is added or subtracted from any system, the residue must plot soinewhere along a ray from the origin or solvent point. Such rays will be called “dilution rays.” Likewise, adding or subtracting solids A or B will move the system composition point along rays through points A or B, respectively, a n d these will be called “A rays” or “B rays” or “solid rays” (Figure 4). Material balances. hfaterial balance calculations are made from process constructions by the method known as “center of gravity” ( 9 ) , or “line segment ratio” (8), or “ratio scale moment” (5). For any case in which 8

INDUSTRIAL A N D E N G I N E E R I N G CHEMISTRY

total _ _ ~weight from system ~

2 -

total weight from system 1

%A in mixture 3 - G/CA in systein 1 _ _ _ ~ _ ~ _ ~ in system 2 - 7&4 in mixture 3 ~

~

(4)

T h e iiiatheniatical relationships are analogous to those of levers or moments. Material balances may be figured as though the line joining systeiiis 1 a n d 2 on the charl were a lever arm, with “basis” \%eights(\!eight of components comprised in the denominators of the composition ratios) contributed by the various systeins applied at their system points. T h e mixture will lie at the “center of gravity” of the contributing s) steiiis. Alternatively, moments may be taken around a n y one of the three s) stern points. T h e iiioinenls Contributed by the other two must be equal. Thus taking iiioiiients around point $ ( l ) (Figure 3) (total Meight in systeni 3) X (7&4 in sysieiii 3 -

Yc.4

in system 1) = (total weight froin sbsteiii 2) X (7cL4 in q s t e i i i 2

-

7i-Ain systein 1) (5)

If we wanted to calculate directly the distribution of coinponent B between the three systems, its weight would be put into the denominator of a composition ratio. Thus (wt B in system 3)

(g

x %A %B

)

in system 3 - __ in system 1

(wt B from system 2)

x

(E

__ in system

=

2 -

%A __ in system I ) %B

(6)

Equilibrium lines-The phase diagram. At equilibrium, a system of any given composition will be made u p of one or more phases. T h e phase diagram is a set of equilibrium cur\ es on a composition plot showing what these phases are. In fractional crystallization, equilibration is conceived to take place only if a solution phase is present. Therefore, the phase diagram is concerned mostly with compositions of the liquid phase, and is often called a “solubility diagram.” Various types of phase diagranis will be discussed iii inore detail in the sections that follow. Classification of phase systems. Fractional crystallization systems comprise solutes that are to be separated, and a solvent from which they are selectively crystallized. For verbal convenience the former will sometimes be called “salts,” a n d the latter “water,” letting these specific materials stand for their respective classes. Three basic types of systems are recognized : Type I : Solutes crystallize without forming either solid solutions or compounds among themselves (double salts). They may, however, form compounds with the solvent (hydrates) Type I1 : Solutes crystallize as compounds (double salts) T y p e 111: Solutes crystallize in solid solutions Space does not permit treatment of Type I11 systems in this paper. W e note, however, that the separation methods used in such systems are analogous to those for liquid-solid extraction. Type I Systems

T h e phase diagram for a Type I system at some temperature T ( 1 ) might appear as in Figure 5. Solutions plotting along curve a(1)-b(1) are saturated with respect to component A; those along b(1)-c(1) with component B. Systems plotting within the solution phase bounda-

Scientist, D o r r - O h e r Inc., International Headquarters, S t a m f o r d , Conn. 06904.

AUTHOR B r y a n t F i t c h i s Chief

Figure 5.

Typical solubility diagram-Type

I

ries S-a(1)-b(1)-c(1) consist of unsaturated solution a n d no solid phase. Systems plotting outside the boundaries comprise saturated solution a n d whatever solid phases must be split out to yield saturated solution as the residue. A-level separations. Any mixture of A a n d B having a ratio A / B different from that of point b ( 1 ) can be resolved a t temperature T(1) into a mixture of solution and a crop of crystalline A or B, whichever is in excess, by adding or evaporating solvent. Thus in Figure 6, solvent may be added to a mixture of solids plotting a t F, moving the system point along a dilution ray toward the origin or solvent point. With proper adjustment of solvent, the systcin can be brought to plot at point a on a tie line between the compositions of doubly saturated solution a t b(1) a n d that of the crystalline species A coiitaiiiiiig component A. (If A crystallizes in pure form its solids point will be at 100% A . If it crystallizes as a hydrate, its solids point will be less than 10070 A. If it is iiiipure, it will plot off the A axis.) After equilibration the system will consist of a phase of A solids, a n d a solution of composition b ( 1 ) . And while arranging to have the solution phase arrive at b(1) will give the greatest yield of crystalline A, dilution of the system to any point between a aiid c will result in a solution phase saturated with respect to A , a n d a solid phase of species A. System a can be reached by leaching solids with the appropriate amount of solvent, thus dissolving all B aiid as much A as is needed to form solution b ( l ) , leaving excess A undissolved. Alternatively, it can be reached by diluting to or beyond the point c to dissolve all solids, a n d then evaporating to system point, a, whereby excess A is recrystallized. O r , if the system initially contains excess solvent, it can be brought to point a by evaporation. Any route leaves a crop of solid phase A that can be physically separated, a n d a solution b(1) that must be fractionated. Such separation of a crop of one constituent is basic to all fractional crystallization processes, a n d will be called a n A-level separation. VOL. 6 2

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Figure 6. A-level separation

of finding a system in which all points along the polytherm have the same A I B ratio seem infinitesimal. Therefore, in principle, any Type I, three-coinponent system can be separated by fractional crystallization. For future identification, we call this cyclc a B-level separation. T o be econoiiiical, the basic cycle should have short dilution a n d evaporation vectors b(1)-a aiid b ( 2 ) - c so that there will be a m a l l amount of solvent to a d d and evaporate. I t should have long crystallization legs ab ( 2 ) and c-b(1) to give a high yield per cycle. Standard Type I process. T h e cycle just described depletes the system. Soiiic A aiid B are removed each cycle, a n d none are added back. A continuous or steady-state process is obtained by adding new feed each cycle in either step 1 or step 2 ; which process is better may be apparent in specific cases, but often will be determined by testing each possibility. Example I . Figure 8 shows process constructions for a system in which the doubly saturated points have [ A , B ] coordinates as follows:

b(1)

=

[ 2.8,

b(2)

=

[17.7, 15.01

24.21

Crystal crops are assumed to be iniperfectly separated, a n d will have the follov%ig coordinates : Crystal species A = [35.0,1.51 Crystal species B = [1.0, 95.01 Figure 7. B-level cjcle

T h e feed assumed for this example:

F

Basic Type I fractionation cycle. T h e solubility isotherm for another reiiiperature T ( 2 ) has bceii added in Figure 7. T h e doubly saturated point, b ( 2 ) , has rnoved to a lower A I ' B ratio than it had at T ( 1 ) . Therefore the following generalized cycle is possible : (1) Starting with solution a t b ( l ) , change the teiiiperature to T ( 2 ) a n d adjust the solvent concentration (in this example dilute) to reach system point a. This results in a n A-level separation yiclding b ( 2 ) solution a n d a crop of crystal species A . Separate crop of A . (2) Change temperature of solution b ( 2 ) to T ( 1 ) , adjust solvent concentration (in this example evaporate) to system point c. This makes a n A-lwei separation yielding a crop of solid phase B aiid a solution phase of composition b ( 1 ) . Separate the crop of B a n d recycle the solution to step 1. Existence of this cycle assures that we can fractionate any Type I, three-component system unless points b(1) a n d b ( 2 ) have the same A / B ratio. T h e chances 10

INDUSTRIAL A N D E N G I N E E R I N G CHEMISTRY

=

[30.0, 45.01

W e consider the process in which nc\v feed will be added in the path froiii operating point b ( 2 ) to b ( 1 ) . I n the forward path from b ( 1 ) t o b ( 2 ) , liquid phasc of coinposition b ( 1 ) is evaporated a t T ( 2 ) ,corresponding to vector b ( l ) - a . This causes a crop of spccics B to crystallizc, corresponding to vector a - b ( 2 ) . T h e return path coinprises adding a n amount of new feed corresponding to some vector b ( 2 ) - c , diluting to d, and crystallizing a crop of species A a t temperature T(1) to return the mother liquor composition to point b ( 1 ) . T h e composition of point c can be determined by material balance since the amount of either solute added per cycle iriust equal that removed. Material balance may be easily made as follows. Take 100 units of new feed as a basis:

(1) T h e solutes in new feed F are split ultimately into the solutes in crystal crop A plus those in crystal crop B. Substitutiiig appropriately in Equation 6, it will be found that 1.27 units of coriiponeiit B elid u p as impurities in crystal crop A. This leaves, by difference, 43.73 units for crystal crop B.

We)

Figure 8.

Type I process cycle

( 2 ) I n the path from b(1) to b ( 2 ) , the solutes in liquor b ( 1 ) are split into those in b ( 2 ) plus those in crystal crop B. T h e amount of component B in crystal crop B is now known. Again, making use of the method of ratios, it will be found that liquor b ( 2 ) must contain 4.33 units of component B. Suniniing B from B a n d b ( 2 ) gives 48.06 units for liquor b ( 1 ) . ( 3 ) From given compositions it is now easy to coniplete material balance calculations, including the amount of dilution or evaporation needed in each path. Composition of system point c is found by adding the coiiiponents in new feed to those in liquor b (2). I n the above example A is Na2C03, B is NaCl, and the temperatures are 0 ' a n d 30"C, respectively. T h e above exemplifies a standard process for separating the solutes of a three-component system. Construction of new feed vector. T h e length of the new feed vector b(2)-c in Figure 8 was found by making material balance calculation. I t is sometimes useful, particularly in preliminary considerations of processes, to determine it by construction. This is done as follows: Project compositions of feed a n d crystal crops along dilution rays to the line of zero solvent (Figure 9) establishing points F', A', a n d B'. (Note that each dilution ray is the locus of points with constant A / B ratio. T h e procedure will be called ratzo projection.) If new feed is to be added to solution b ( 2 ) , construct any vector that represents taking the system from the A / B ratio of b(1) to that of b ( 2 ) by crystallizing B'. I n Figure 9 it is a'-b(2). Construct a n A ' ray through the tail of this vector a n d a n F ' ray through its head. T h e two rays will intersect a t some point c', a n d the true point c, representing system composition after addition

of new feed, will fall a t the intersection of the dilution ray through c ' a n d a line joining b ( 2 ) a n d F. Example 2-special leach cycle. In example 1 both operating points b(1) and b ( 2 ) were doubly saturated. I n some important instances it is economical to accept less than the maximum crystal crop in each process cycle, a n d to choose a n operating point saturated with only the crystallizing phase. Figure 9 shows the 80" and 20" isotherms for the system KCl, NaCl, ILO. If liquor of composition b ( 2 ) is cooled to 20°C, it will yield a liquor of composition a a n d a crop of pure KCl. Instead of evaporating solution a to reach doubly saturated point b ( l ) , point a is itself taken as the operating point. T h e crystal crop of K C l is separated, the temperature of solution a is raised to 8 0 ° C ) a n d enough new feed is added to reach system point c. KC1 is leached from the new feed, leaving NaCl as its residue, a n d regeneratiny solution b ( 2 ) . T h e simple process triangle of Figure 10 corresponds to the five-vector cycle of Figure 9, with the two dilution ray vectors made null. This coiiimercially important leach cycle requires no evaporation or dilution. Type II Systems-Double

Salts

T h e solubility chart of a system in which some double salt AB f o r m will appear as in Figure 11. Solutions plotting along the isotherm a-b will be in equilibrium with solids B, as may be indicated by tie lines back to composition B . Along c-d they will be in equilibriuin with solids A. However, along b - 6 they will be in equilibriuni with the double salt AB. Subsidiary axes and systems. A dilution ray through solids point AB may be considered as a n A B axis, as valid and meaningful as the A or B axis. T h a t is, any composition plotting between the A and A B axes may be expressed just as well in terms of A and A B as it can in terms of A a n d B . For example, if A is Na2SOe, B is K2SO4, a n d A B is glaserite, 3 KzS04. N a 2 S 0 4 ,the coniposition of a system might be expressed equally well as 50% KzS04 a n d logo NazSOJ, or as 13.2% K z S 0 4a n d 46.8y0 glaserite. Put another way, a glaserite vector and a K 2 S 0 4 vector form the basis for a vector space representing system compositions. Therefore, the part of the diagram lying betweeii S-A and S-AB represents a system A , AB, S. Since no further double salts are formed between A a n d AB, it may b e considered a Type I system. Any system with a higher A I R ratio than that of double salt AB can, therefore, be fractionated into A a n d A B by Type I procedures. Likewise, that part of the diagram bounded by the A B a n d B axis also represents a Type I system, AB, B , S , a n d can be separated into pure phases of A B a n d B . These subsidiary systems will be called subsystems VOL. 6 2

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KCI

NaCl

(%)A Figure 9. Constiuctioii for neiI: b e d cector

A-AB a n d AB-B, the prcsence of S beiiig understood in all cases. C-level separation. \$’hat wc iiccd to find, then, is some ivay to break dolvii the double salt so as to produce a n A-enriched fraction lying \vel1 Tvithin the A-AB subsystem, and a B-enriclied residue lying as far as possible into the AH-H subsystem. Once this is done, each fraction caii be further processed by Type I procedures, as necessary, to recover some A, some B, arid some AB that caii be recycled. \$‘e \vi11 call such disproportioning of a double salt a ‘‘C-le\d separation.” Where the double-salt axis passes through the doublesalt isotheriii 6-6, as in Figure 11, the double salt is said to be congruently soluble-it is i n equilibr iurii with a solution having the saiiie A,!B ratio. This condition perinits no C-level separation siiicc a solution of AB, when evaporated, yields a n A B ratio i n both fractions. In order to make a C - l e d separation, it is necessary to find a teiiiperature or condition such thar a solid phase of one of the coiiiponents, such as B, is in cquilibriuin Lvith a solution lying in the other subsystcin A-AB. Example-the system M g S 0 4 , K~SO’I, HzO. T h e systeiii AfgSO;, KnSO.,, HzO is used to exemplify a Type 11 systeiii, i n part because it comprises hydrated solids a n d gives an exaiiiple of their treatment. Figure 12 is a three-diitiensional picture of the system, in which teiiiperature is added as a third variable a n d axis. T h e phase diagram a t 5OCC is showm in Figure 13. From a(50) a t composition [0:33.51 to b ( 5 O ) a t [4.74, 31.321, saturated solution is in equilibriuiii with hlgS0.I. 6 H 2 0 , whose coinposition l’ector is [0, 32.71. Froiii b(50) to c(50) a t [23.23, 11.081, it is in equilibrium with 12

INDUSTRIAL A N D ENGINEERING CHEMISTRY

Figure 70. M o d $ e d Tjpe I p o c e s s cjcle scparatioii of KC1 uncl ,YaCI

Fzgure 71.

Tlpicul solubilitj diagrum-Tjpe

I1

aslrakanite, Na2SO ’ ?\lgSO 4 HzO. whose composition vector is [42.5, 36.01. From ~(50)to d(50) at [31.7, 01,it is in equilibriuiii with NatSOd. No C-level split is possible ar this temperature because astrakanite is congruenrly soluble. The 25’C isotherms are as shown. ariioiig others, in Figure 14. T h e magnesium sulfate solid phase has become S l g S 0 4 . 7 € 1 9 0 ; the sodiuni sulfate solid phasc, T a , S O 1 10 H 2 0 . Astrakanite is still congruently

soluble. An isotherin offering a more favorable split is needed. T h e isotherms at 15’ a n d 0 ° C are also shown in Figure 14. At these temperatures, the astrakanite phase has disappeared. N a z S 0 4 10 . HzO remains as the sodium phase; M g S 0 4 . 7 H2O is the M g phase except possibly near O’C, where it is replaced by M g S 0 4 . 1 2 Hz0. I t is apparent that at either of these temperatures a n Na2S04-enriched phase (namely NazS04.10 HzO) can be crystallized far into the MgS04, astrakanite, H 2 0 subsystem Therefore, a good C-level split can be accomplished in this temperature range. Point b ( 5 0 ) a n d the b polytherni between the MgSO1. 7 H20 a n d Na2SOd.10 HzO fields arc plotted in Figure 15. A Type I separation cycle is not necessary in the Na2S04-astrakanite subsystem, because the C-leva1 split working to a point on the b ( 0 ) - b ( 1 5 ) polytherrii will yield a pure sodium sulfate phase (NazS04.10 H 2 0 ) directly. A good B-level separation is possible in the astrakanite-hlgSOe subsystem since points b ( 5 0 ) a n d b ( 0 ) or b ( 1 5 ) are not lined u p along a dilution ray. Therefore, subsystem astrakanite-MgS04 can be broken down. A full fractionation of the entire system is possible. A “basic Case I1 process cycle” is thcn as follows (Figure 15) :

BASICC ~ S I1 E PROCESS CYCLE Dilute recycled astrakanite (and any N a 2 S 0 4 (1) rich new feed) to system point e on a tie line between liquor b ( 0 ) a n d solids Na&30,.10 HzO. Cool to 0 ” C , crystallizing Glauber salt. Separate the solids as a product. (2) Evaporate liquor b ( 0 ) plus b(1) from step 3 to sonie point g, a d d hIgS04-rich feed to a system point f on a tie line between astrakanite a n d liquor b ( 5 0 ) , a n d equilibrate a t 50°C. Separate the astrakanite aiid recycle to step 1. ( T h e locations of pointsg a n d J must be found by material balance.) (3) Cool liquor b ( 5 0 ) , crystallizing MgS0’1.7 H20, until the solution phase reaches the b polytherin at some point b(1). Separate the M g S 0 4 . 7 HzO as product, a n d recycle liquor b ( 1 ) to step 2. T h e flowsheet would appear as in Figure 16. System with more than one double salt. More than one double salt is formed in some systems. A system with two double salts is represented by Figure 17. From a to b saturated solution is in equilibrium with a pure B phase. From b to c it is in equilibrium with a B-rich double salt BA, a n d from c to d with a n A-rich double salt AB. From d to e pure A phase is stable. This system breaks down into three Type I subsystems, B-BA, BA-AB, a n d AB-A. I t can also be divided into two overlapping Type I1 subsystems (more if there are more double salts), a n d this is the way it is treated. In Type I1 subsystem B-AB, double salt BA (and new

i;:

E20

10

10-

(%) No, SO,

Figure 12. System Na2SO4, MgSO4,HzO

feed if it plots in the subsystem) is broken down into pure B a n d double salt AB. In subsystem B.4-A the AB is split into some pure A, a n d some double salt BA, which is recycled back to the other subsystem. For complete fractionation, B-level separation must be possible in all Type I subsystems, aiid C-level ones must be available to split each of the double salts. Thus, a t the teinperature of Figure 17, fractionation is not possible because both double salts are congruently soluble a n d no C-level separations can be made. Some more favorable isotherms must be found. A process flowsheet for fractionation in a system of two double salts might be blocked out as shown in Figure 18.

BEWARE OF MINOR CONSTITUENTS I n practice, most input materials to a fractional crystallization process will contain minor impurities. None of the processes just described have provisions for

Figure 73. 50’ isotherms in systems NazSO4, MgSO4, HzO VOL.

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DECEMBER 1 9 7 0

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MgSO 4

n

out with the products. But the boundaries of the solution phase would be altered beyoiid any siniilarily to those for the pure system, a n d the process cycle would be greatly changed-usually for the worse. iVith its load of impurities, the liquid phase would take u p much less KCI, and thus the yield per cycle would bc greatly dccreased. Minor impurities can be dealt with in various w a y s :

H* Fagure 14. O’, 10’. and 20’ isotherms an sjstein Na2SO4. Mgs‘O4, HzO

(1) Operate with solution phase loaded to crystallization endpoint with minor constituents as described above. However, in this case be sure to use the major constituent solubilities arid phase diagram appropriate for this loaded liquid phase. T h e products will then contain the minor constituents as impurities. (2) Bleed off enough liquid phase to maintain iriiiior impurities in it a t a lo147 level. T h e products (theoretically) would then be free of minor impurities. T h e bleed solution could be taken as feed to another cycle operated as in (1). ( 3 ) Give the impurities full status as components, and treat the system as one of many components.

FOUR-COMPONENT SYSTEMS Representation

Faguie 15. Process constructions for scpaiuting l\‘a?SOi and iMgSO4

eliminating them. They will build u p in the liquid phase until it becomes saturated with respect to some solid phase or phases containing the minor impurities ; by then they will no longer be minor constituents iii the solution phase. For example, naturally occurring sylvinite (KC1 NaC1) contailis a t least minor amounts of M g + + a n d SO1-- salts. These will build u p in the leach liquor of Figure 10 until saturation with some salt such as glaserite, schoenite, leonite, kainite, or carnallite. Minor impurities Lvould then no longer be dissolved by the liquid phase in a leach cycle, or else would crystallize

+

14

INDUSTRIAL A N D ENGINEERING CHEMISTRY

T h e composition of three-coniponcnt systems can bc represented completely in the two degrees of freedom prokided on a piece of graph paper. Graphical representation of such systems can be comprehended intuitively. But the composition of a four-component system has three degrees of freedon], and requircs a three-dimensional model for complete representation. Since we propose to depict thc s)steiii with lines on a two-dimensional surface, we will have to rely on techniques involving less than complete representation. Engineers have much experience in representing threedimensional constructs on two-dimensional drawings. They easily surmount the formal difficulties and, indeed, are hardly aware of them. However, the formal difficulties exist a n d can be comprehended a t this level. And in systems of more than four coniponcnts the problem becomes complex. Therefore, we now consider more formally a n d theoretically, first, how many degrees of freedom a sys tern has and, second, how to handle them graphically. Classical phase rule. T h e classical phase rule, deduced from thermodynamic arguments, asserts that (Degrees of Freedom)

+ (Number of Phases)

=

(Number of Components)

+2

T h e “number of components” is usually defined as the niiniinurn set of chemical species necessary to express the ana1)sis of the system. \Ve will develop a less restricted view later. T h e phase rule assumes that pressure is one of the variables affecting the state of a system, a n d indeed, if

0

Attrakonitc Distdver

Na-Rich

5oo

Astrakanite

4

I

I

Liquor e

I

Mg-Rch

Crystallizer

A

S Astrakanite

Figure

77.

Typical solubility

diagram-two

double salts

LlqWrMl) MgS04.7H20 Crystallizer

-

Separate MgS04. 7H,O

-

pressure is not high enough, the solvent will form a vapor phase. I n fractional crystallization it is usually assumed that the pressure has some fixed value (such as 1 atm) high enough to prevent vaporization. Its exact value is not too important, since pressure norinally has a negligible effect on the solubility of solid-phase species. Under such conditions the systeni is said to be “condensed.” O n e of the degrees of freedom is used u p in specifying pressure, so for such systems a modified phase rule is sometimes written (Degrees of Freedom)

+ (Number of Phases) = (Number of Components)

+1

I n practice, one seldom thinks of the classical phase rule. In fractional crystallization, we focus attention on the composition of the solution phase, a n d this is what we plot in a phase or “solubility” diagram. I t follows from the phase rule that a solution phase of n components, present by itself in a condensed system, has n degrees of freedom. O n e of them is temperature; the remainder are composition coordinates. Every

solid phase additionally present reduces the degrees of freedom by one. “Conditions” and available degrees of freedom. T h e presence of solid phases is not the only thing that reduces the degrees of freedom available to the solution phase. As we have seen, specifying a fixed value for pressure reduces its degrees of freedoin by one. Specifying a fixed temperature (isotherm) reduces freedom by another degree. Anything that reduces by one the degrees of freedom available to the solution phase will be called a “condition” imposed on it. W e can therefore write for the solution phase in a condensed system Available Degrees of Freedom

=

Components

- Conditions

There are basically three types of conditions :

(1) Saturation with respect to any given solid phase. (2) Specified value for a n otherwisc independent variable. (3) Any general relationship or equation between independent variables. [This is analogous to the effect of simultaneous equations in reducing the nurnber of independent variables. For example, it might be reasonable a przorz to select the following components for a system: [Na+, Cl-, HZO]. As a three-coinponent reduced system, its solution phase should hake threc degrees of freedom. But for all practical purposes electric neutrality imposes the condition : (YoNa +/23) = (%‘oc1-/35.5). This condition reduces the degrees of freedom available to the classically expected two, namely temperature a n d ajoNaC1. Operating from this point of view we need not be classically precise in defining a n d specifying “components.” W e can use any VOL. 6 2

NO. 1 2

DECEMBER 1970

15

Feed if in Subsvstem A-AB

1

1 Subsystem A - A B

,A 1

Type1 Separation

I

,i

Feed if in Subsystem AB-EA

1 BA+

Subsystem AB-BA

~

I

I

I

Feed if in Subsystem B A - 8

Figure I S .

Subsystem E3A-B Sewrotion

Generalized proccssjowshcct f o r separation of components where tivo double salts are formed

set of chemical species into which a system can he resolved instead of rhe classical miniiiiuiu set. But then we must note all “conditions” bctween iiiciiibers of the selected set to arrive at available degrees of freedoin. ( T h e difference is purely procedural since the presence of a relationship between a set of constituents iniplies the existence of another set of one less iiieniber.) This point of view will be particularly convenient when we come to consider reciprocal salt pairs. ] Limitations of two-dimensional plots. All ise can dra\v on a solubility diagram are lines and points. Lines represent one degree of freedom regardless of the dimensions of the space in which they are drawn. (Only one coordinate along a line may be specified independently. T h e values of all others are then dependent upon the one.) Therefore, what \ve actually plot on a solubility diagram must represent the system with at least enough conditions imposed to leave only one degree of freedom. For exainple, in rhe three-component system of Figure 20, the isotherm a-d represents solution saturated with H a B 0 3 . T h e solution has three components, XanS04, H3B03, H 2 0 , a n d two conditions, namely fixed teiiiperature and a solid phase. Therefore, the line a--d represents, as is necessary, a relationship haviiig one degree of freedom. T h e solution phase alone, with two degrees of freedoin, can plot anywhere in the field bounded by isotherins a-d a n d d-h, as at point I ) for example. Thus two degrees of freedoin in a threecoriiponent system are represented by a n open area or field. In the four-component system of Figure 19, the isotheriii b-c (for example) represents the presence of solution and two solid phases, namely HaB03 a n d NaCl. Again, as expected, the line represents a situation with 16

&1

INDUSTRIAL A N D ENGINEERING CHEMISTRY

Figure 79. sjstem

TjFical solubility diagram for four-component T ~ p eI

one degree of freedom. T m o dcgrees of freedoni, M. hich ~ o u l result d from the presence of oiily one solid phase a t a fixed teniperature, are represented by surfaces bounded by lines--for example, the surface bounded b17 a-c-b-d represents solution H3BOd. Possible solution COIIIpositions, ivith three degrees of freedom, plot anywhere within the space bounded by the surface fields. In Figure 20 we are able to plot all the inforination w e need. 4 point, such asp, fully specifies the condition of the system, a n d in this case we see without ambiguity that it represents a n unsaturated solution phase. But what does point q in Figure 19 represent? \Ye can’t tell, and even gixren the information that its coordinates are [18.9,8.7, 10.31, we still can’t tell whether or not it

+

Figure 20.

Three-component system boundary to Figure 19

represents unsaturated solution, solution saturated with N a 2 S 0 4 , or solution plus a solid phase. T h e existing lines give us only the boundaries of the solution-NazS04 surface, a n d not its true position at points away from the boundaries. This loss in definition is inherent in the use of two-diinensional d i a g r a m to represent systems of three or more residual degrees of freedom. We have no way, on a two-diniensional diagram, to make a continuous plot showing a t all its points the location of a surface in a space of three or more diiiiensions. And the loss of definition becomes rapidly greater as the nuinbrr of degrees of freedom increase. T h e loss in definition inherent in two-diniensional plotting usually turns out not to be limiting. Data are rarely available to define the position of points on a phase surface away froiii boundary lines. In fact, it is usual in polycoriiponent systems to find data only for the points representing zero available degrees of freedomsuch as the lettered points in Figure 1 9 . Straight lines are drawn between points as representing approximately the “edges” of the phase diagram. From the foregoing it will be seen that a polytherln is a line (one degree of freedom) in a phase diagram having temperature as a residual variable; isotherms are lines for which the temperature is fixed. Projections. T h e standard engineering method of depicting three-dimensional objects is by projection. Thus Figure 19 is a n isometric projection of a space model. As noted, hohever, points in a n isometric projection cannot be resolved into their space coordinates. Where dimensions or coordinates must be scalable from the drawings or plots, it is conventional to use elevations, plans, and sections. All of these are projections of lines in a space structure d o ~ 7 none of the axes onto the plane defined by the other two. Most complete representation of a surface in three dimensions is by contour projection or mapping. As related to Figure 19, sections might be taken at a series of uniformly spaced NaCl concentrations, a n d projected down the NaCl axis onto the NazSOd-H3B03 plane. T h e result might appear as in Figure 21. (Curvature

% Figure 21. Representation uf three-dimensional solubiliti diagram by contour plotting

of lines is hypothetical. D a t a are available only for points or corners of the diagram.) A more useful approach for our purposes is to use “front a n d side elevations.” One projection is made lookiiig down the NaCl axis; the other, down the Na2SO1 axis. For graphical convenience the two projections are placed back to back, with a common axis, as shown in Figure 22. A pair of projections arranged this way will be called a Suhr diagram [after Henry Suhr who developed such projections, particularly for reciprocal salt pairs, a n d to whom the present work owes inuch]. It takes a little study to recognize that the areas to the left a n d right of the common H3B03 axis are separate projections. But corresponding points are found a t the same &Bo3 coordinate on each side. This arrangement is handy for making process constructions simultaneously in both projections. Ratio projection. A special sort of projection is much used for process design in multicomponent systems. T h e points and lines of the space model are projected out along dilution rays onto the plane of zero 70solvent. Figure 23 depicts the relationship of the space model to the zero Ye solvent plane, which is defined in space by the points for 10070 NaC1, lOOYe N a S 0 4 , a n d 10070 H3B03. Point b of the space model, for example, maps as point b’ on the ratio projection. Figure 24 shows the projection itself. Moving all points along dilution rays to the zero solvent plane is the process equivalent of removing all solvent from the system. T h u s Figure 24 shows compositions of each salt as a fraction of the total salts present, excluding solvent. T h e coordinates of points in the ratio projection are therefore easily calculated directly from solubility data. Ratio projections sacrifice all information on how soluVOL. 6 2

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DECEMBER 1970

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% H,BO, 30

I

Na, SO, NaCl

% NaCl

20

10

0

10

20

30 %Na2S3,

Figure 22. Representation of three-dimensional solubility daagram by Suhr projections

Figure 24. Crystallization path from composition ratio p to crystallization endpoint

following boundary c ’-b ’ toward the triply saturated cr) stallization endpoint b ’. By generalization from the abo\,e, it will be apparent that crystallization endpoint b’ can be reached, by crystallization of not more than two salts, from any other composition point on the diagram. T h e ainounts of each salt crystallized can be calculated from the equivalent construction vectors p-7 a n d r-b’. Figure 23. Relationship to three-dimensional solubilitj diagram to ratio projection

ble the salts arc, but show their relative proportions or ratio at each point; hence the name. T h u s from Figure 24, it is not possible to tell whether point p represents unsaturated solution, saturated solution, or a system of solution plus solid phases, since the projection gives no information on how much solvent is present. However, point p lies within the projecrion of the KaCl field. Therefore, if it is known to represcnt a solution phase, a n d solvent is evaporated, then the first solid phase that crystallizes will be NaC1. Crystallization paths. If solvent is removed from a liquid phase plotting initially a t point p in Figure 24, the first salt to crystallize will be NaC1. Constructions on any linear projection from a phase diagram onto a plane follow the same rules as they do in the phase diagram itself. Therefore, separation of NaCl from the liquid phase will cause its composition to move away from the NaCl point along a n NaCl ray in the ratio projection. It will follow crystallization path p-q. From q it will crystallize H 3 B 0 3 a n d NaCl paragenetically, 18

INDUSTRIAL A N D ENGINEERING CHEMISTRY

Type I Systems

This section will deal with four-coniponen~systeiiis in which no double salts or solid solutions are formed. It will show how to construct fractional crystallization processes, using ratio projections, by procedures formally identical to those used for three-component Type I systems. However, the added componenL gives inore room to manoeuver, a n d inore variations of the basic process are possible. At the same time, there will be added coriiplications in getting all constituents to balance in steady-state processes. W e start by describing the iiiost general basic cycle, a n d then treat modifications of it. Basic fractional crystallization cycle. Assume that at some temperature T(1) the crystallization endpoint on a ratio projection plots a t some point b ( 1 ) . At some other temperature T ( 2 ) , it plots a t another point 6(2). A t temperature 7’(2), there is a crystallization path from b ( 1 ) to b ( 2 ) in which, a t most, two of the solute components are crystallized. And a t temperature T ( 2 ) ,there is another crystallization path returning from b ( 2 ) to 6(1), in which a different pair of componeiits is crystallized. Therefore, there exists a cycle that separates the three salts of the four-component systeiii into two two-salt or three-component systems. The

two-salt systems can then each be fractionated into their components by procedures described earlier. Schematically :

Schema I (A (A

+ C + B)

+ c>

J.\k----J.

(A)

1 three-salt system

/\ (C

(C)

+ B)

2

two-salt systeins

(B)

3

one-salt components

Figure 25A shows such a cycle on a ratio projection from a generalized four-component system A-B-CSolvent. Construction vectors for the forward path are b(1)-u a n d a-b(2), showing crystallization of species C a n d B, respectively. For the return path, vectors b(2)-c and c-b(I) show crystallization of species C a n d A. T h e similarity of these constructions to those for a Type I, three-component systein should be apparent, particularly when replotted as in Figure 25B. T h e constructions of Figure 25R are the same as those of Figure 7, except that a salt (in this case species C) has taken the position of solvent in the diagram. T h e similarity is not coincidental. T h e three salts are being plotted graphically in exactly the same way as the two salts a n d solvent of a three-component system. And the constructions we are using derive solely from material balance, which is satisfied individually a n d in total by the three salts. Therefore, the constructions will be just as valid for a three-salt ratio projection as they are for a three-coniponent system. W h a t problem there is arises with the operating points. Operating points. An operating point must represent a completely fixed state of the system-one with no residual degrees of freedom. T h e state of the three salts will depend very much on how much solvent is associated with them. I n order to establish operating points on the ratio projection then, w e must impose enough conditions on the system so that when the two salt ratios represented by the axes of the ratio projection are fixed, there will be no residual degrees of freedoin, a n d thus the solvent ratio will also be fixed. T h e solution phase of a condensed four-coniponent system, by our relaxed rule, has four degrees of freedom. O n e is used u p by specifying the temperature of the operating points, leaving three. T w o more are consumed by the salt ratios we will plot. T h e one residual degree of freedom is used up by specifying that the operating points are saturated with at least one solid phase. Since the operating points will have zero residual degrees of freedom, the amount of solvent present will be fixed, even though not represented on the ratio projection plot. Modified cycles. A necessary condition for a pair of operating points is that each one can be reached along some crystallization or process path from the other. In the basic cycle, crystallization endpoints were specified since they can be reached by crystallization a t their respective temperatures from any other composition ratio

A

Figure 2.5. Basic B-levrl cycle for Jour-compnnerit Type I system. ( A ) I n triangular coordinates; ( B ) in rectangular. coordinates

point in the diagram. Such a pair alhiays satisfy the necessary condition. M’e now consider a modified cycle, in which a t least one of the operating points is not a crystallization endpoint. Figure 26 shows the saiiic crystallization endpoints b ( 1 ) and b ( 2 ) , but the phase diagraiii projcctioii has been added for T(1). Field a-b(l)-c-A shows salt ratios for which specks A will crystallize from solution. Crystallization endpoint solution b ( 2 ) lies 1% ithiii this field. If salt is crystallized at T(1) from a solution of composition ratio b ( 2 ) , i t will be species A, a n d the solution composition ratio \vi11 iiiove along path b ( 2 ) - e(1). When it reaches e ( l ) , species C also will start to crystallize, and the crysLallization path follows the phase diagram line c-e(1)-b(1) toward the crystallization endpoint b ( 1 ) . Point b ( 2 ) can be couplcd with any other point along the crystallization path b(2)-e(l)b ( l ) , and the pair will fulfill the necessary condition for operating points. Any such other point can be reached by crystallization VOL. 6 2

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DECEMBER 1970

19

Figure 26. C?jstul/izcttion pcith for Sepaiating compoficizt A in pure form

a t 7 ( 1 ) froiii point b ( 2 ) , and b ( 2 ) can be reached froin any point in the diagraiii by crystallization at T ( 2 ) . If we choose our T(1) operaiiiig point anpvhere between points h ( 2 ) and e ( l ) , a crop of pure species A will be obtained in one leg of rlic cycle. T h e modified cyclc, based on points e(1) a i d b ( 2 ) , is shoivii in Figure 27. I n the path froiii ~(1)to h ( 2 ) , a iiiixture of species B and C is crystallizcd. O n t h c return trip, A is crystallized alone. Complete fractionation would then follow the schema :

[Point e ( 1 ) iyould usually bc selwted as the operatiiig point because it ~ v o u l dyicld a larger crop of A per cycle than aiiy point along the path nearer b ( 2 ) . However, xve d o iiot yet know Tvhat adjustments in sol1,ent will be necessary to bring about crystallization of A . TVe know only that if the necessary evaporations or dilutions are iiiade a t ?"(I), \ve can ani\-c at any solution coinposition ratio along the path. A n operating point short of e ( 1 ) could coiicci\-ably involve iiiore ecoiioniical nianipulation of solvent. Thus in seine cases, cooling to T ( 1 ) alone lvithout aiiy ci.aporation or dilution could yield a solution ratio bethveen b (2) and e (1). ] Species A is iiot the only one that can be brought out separately in a cycle. Figure 28 shows how the phase diagram iiiight look a t teiiiperature T ( 2 ) . In this hypothetical case, b ( 1 ) falls within the field of species B a t temperature T ( 2 ) . A cycle can be built using point e ( 2 ) , iz-hich separates species B by itself. Salting-out cycles. Figure 29 shoivs a different sort of cycle based o n points b ( 1 ) and h ( 2 ) . The forward path, froin b ( 1 ) to h ( 2 ) , is a crystallization path as before. A mixture of species C and B are separated. 20

INDUSTRIAL A N D E N G I N E E R I N G CHEMISTRY

T h e return path, b(2)-c-b( l), involves crystallization of species A, but dissolution of B . Thus the cycle requires feeding back or recycling some of species B after it has been separated from C . TVe can control feedback of B to obtain a solution phase essentially saturated with it, without any excess. There will then remain no solid phase of species B after the return from b ( 2 ) to b ( l ) , a n d species A will be Crystallized by itself. In Figure 30, it is species A that is recycled, salting out species B in pure foriii. These cycles probably would have lirtle interest in theiiiselves, but when the basic fractionation cycles are expanded into continuous or steady-state process cycles by acldiLion of new feed a t soiiic point, salting-out paths beconie important. Process cycles. Continuous or steady-state processes are formed, as before, by introducing enough new feed into the return path of a fractionation cycle to make u p for separated components. T h e principal problem will be determining how much. T h e s a n e constructioiis can be used as for threecoiiiponeiit processes, letting one of the solutes take the place of solvent, a n d taking its vertex as the origin of the coordinate system. But which solute? T h e construction for new feed addition is valid if the solute that is crystallized or added in both forward a n d backward path takes the place of solvent. W e iiaiiie it the "pseudosolvent." A n y one of the three solutes might be chosen as the pseudosolvent, but the choice will affect what sort of cycle will be developed. Thus in Figure 25, coinponelit C is the pseudosolvent. I n Figure 29, based on the same operating points, B is the pseudosolvent, a n d in Figure 30, A . T h e coinposition of the new feed will also affect the type of cycle obtained. T h u s in Figure 25, the forward path comprises crystallization of C a n d B in a certain

Figure 21. B-level cycle fur crystallizing component A i n pure form

I

I

A

\

Figure 28. Crjistallization path for separnting component C in pure

Figure 30. Snltiizg-out cycle to yield C in pure form

form

A

B R Figure 29. Salting-out cycle to yield B in pure forni

ratio. If [he new feed contains a lower ratio of C / B than this, then a n aiiiouiit of new feed sufficient to replenish B will introduce less C than was reiiioved in the forward path. In such a case, species C would have to be added or recirculated into the return path. On the other hand, if sufficient feed is added to replenish C, there will be a n excess of B that will have to be crystallized on the return path. T h e pseudosolvent has changcd froin C to B. T o determine graphically which pair will crystallize in a process return path including new feed addition, project a line through the two operatiiig points to the axis representing iiiixtures of the two solutes crystallized in the forward path. I n Figure 31 this will be point R on the B-C axis. Draw a line through R a n d the opposite vertex-in this case line A-A. If the new feed composition plots on the B side of the line, this component will crystallize in the return path, a n d B is the pseudosolvent; if on the C side, C takes this role. T o make material balance, calculate a forward path (the one not including new feed addition) based on some basis quantity of solutes at the first operating point. T h e n a d d enough new feed at the second operating

Figure 3 I .

Constructions for identqjling pseudosolvent

point solution to replenish whichever of the components, depleted in the forward path, is not the pseudosolvent. Alternatively, the new feed vector can be coiistructed graphically, as shown in Figure 32 for the case of C as the pseudosolvent. New feed is projected to point I;’ oii the zero pseudosolvent linc. T h e nonpseudosolvcnt vector on the forward path is a-b(2). From the tail of this vector, a line a-A is drawn to the A species point. Froiii the head of the vector, a line is drawn to point F’. T h e iiitersection of these two lines, a t e, locates the pseudodilution ray C-e on which the new feed vector 6(2)-c terminates. I t will usually be dcsirable to follow Scheiiia 2, with one of the solid phases being separated by itself. This can be accomplished by choosing operating points for a forward path according to principles described for Figures 27 a n d 28. Alternatively, operating points can be selected so that the pseudosolvent vector of the return path is made null. This is done by choosing operating points so that line A-R (Figure 31) passes through point F’. This is illustrated in Figure 33, which shows the operating point a t b ( 1 ) a n d the solid phase boundaries for T ( 2 ) . Point e(2), on the B-C boundary, lined u p VOL. 6 2

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DECEMBER 1 9 7 0

21

A

along a ray from F' through point b ( l ) , is used as a second operating point. T h e ratio R of B C coniponents crystallized along the forward path is then made the same as that, F ' , existing in new feed. Since the return path comprises only dissolution of new feed with elimination of a solid phase of A , the latter is separated by itself in the return path. Solvent representation. Solvent disposition has thus far not been considered, and need not be in determining what fractional crystallization cycles are possible. But it does greatly affect the economy of a process, a n d the process engineer will usually want to display it graphically. I t can be done as follows. Ratio projection from a component point (such as the solvent point) eliminates that component from the basis. T h u s the ratio .4/(.4 B C) is used to represent a composition coordipate rather than A / ( A B C S). A solvent axis may be plotted on the same basis as S/(A B C) in a coordinate frame as shown in Figure 34, a n d a three-dirneiisiorial phase diagrarii can be plotted or mapped into the resulting coordinate system. T h e solvent point lies a t infinity on the S / ( A B C) axis, so ratio projection from it of the phase diagram onto the A-B-C plane will be the same thing as one down the solvent axis. T h e system can be represented by back to back elevations as shown in Figure 35. T h e triangle to the right of the vertical ( B ) axis is the ratio projection; the projection on the left shows solvent coinposition. In the phase diagram shown, A is Na2SO4, B is HaBOa, C is SaC1, a n d S is water. T h e phase diagram is a mapping into these coordinates of the 75" isotherm shown in Figures 19, 22, and 24. T h e crystallization endpoint b ( 3 5 ) is also plotted. \Ye note that crystallization endpoints b ( 7 5 ) a n d b(35) are (by fortunate coincidence) lined u p along a B ray, so this species (H3BO3) can he crystallized pure in going

+

+ +

+

+ + .+

.+

+

+

from b(75) to b(35). T h e solvent projection, however, shows that a short dilution vector, x - b ( 3 5 ) is needed to make the path. A complete process q d e is d r a n n i n both projections for dry feed of composition F. Point 3 , representing system composition after fecd addition, obviously has less solvent than would be required to take all constituents of the feed into solution, but component B will be leached from it. T h e sum of vectors representing removal of h a n d C frorii the system terminates on the solution side of b ( 7 5 ) at z , so that some evaporation is necessary to return to b(75). By adding solute with the new feed, which would not affect the ratio projection at all, new feed could be takcn into solution a n d subsequently recrystallized, if there were any reason to do so. Type II Systems

A

forward

/ .3 C , \ \

Figure 32. Process qcle f o r four-component Type I system 22

Figure 33. Mod$cd process f o r jour-component TJpe I sjistem, sepuruting A in pure form

INDUSTRIAL AND ENGINEERING C H E M I S T R Y

Systems that form solute compounds (double or triple salts) are handled on the ratio projection in a manner quite analogous to Type 11, three-component systems. T h e system is divided into two (three for triple salts) subsidiary systems. A C-levei separation is then sought that will break down the double salt into a solid phase of one of its solute components, a n d a solution phase within the subsystem comprising its other solute cornponent. T h e solution phase is then broken down into its subsystem components, including a crop of double salt that is recycled. W e demonstrate with the system NazS04, N a 2 C 0 3 ,NaCl, H 2 0 , which forms the double salt burkeite, whose composition we take as Na2C03.2 NasSOd. (H. B. Suhr has demonstrated, in a beautiful but unpublished solubility study, that there is a series of burkeites having different but definite rational Na2C03/Na2S04 mol ratios.] Ratio projections of the isotherms at O", S o , a n d 10°C are shown as solid lines in Figure 36; those for 35"

Type I1 processes are, therefore, possible and may be attractive. T h e process selected will depend on the composition of feed. For this example we will assume it contains a n equal mixture of its three salt components a n d 20Yc water. A C-level split of burkeite is possible over a wide range of NaCl concentrations. However, we choose to separate burkeite free of NaCl in the main process cycle because in the absence of NaCl we expect solubility of burkeite to be greater, a n d anticipate a more favorable water balance this way. W e then operate the main cycle to separate pure burkeite, a n d a mixture of NaCl a n d Na2C03. These primary splits could be broken down separately by threecomponent cycles, but this way we would be taking crops of NasCOa in two places, which seems a waste if it can be avoided. Therefore, we choose to make a C-level split on burkeite, taking the crop of Glauber salt as product, and recycling its NazCO3-enriched niother liquor back to the main cycle. Constructions for a main cycle are shown in Figure 38. I t also shows the b polytherm drawn through points b(O)-b(5)-b(lO). But in order to avoid clutter, the various solubility isotherms are omitted. To start, take the f(50) crystallization endpoint as a first operating point, then cool (always with appropriate adjustment of solvent) to crystallize sal soda at a ternperature such that the sal soda vector terminates at sonic point b ( x ) on the b polytherni. This yields a pure sodium carbonate solid phase, which is taken as a product. Solution b ( x ) , heated to the temperatures of Figure 37,

Figure 34. Coordinate framework for representing solvent content with ratio projection

and 50"C, in Figure 37. T h e dashed lines in Figure 36 are for 20". At the lower temperatures, the system behaves as Type I. I t could easily be fractionated, using principles already discussed. But assume we are looking for a better alternative. It is apparent that a good C-level separation of burkeite into Glauber salt, NazS04.10 HzO, a n d a solution well within the NaCl-Na2C03-burkeite subsysteni is possible over a wide range of conditions.

I

B

Figure 35. Process cycle with solvent projection VOL. 6 2

NO. 1 2

DECEMBER

1970

23

Figure 36. Ratio projection of system .Va2SO~..Tu2C03, -VaCl, H20, shoteitig Oo,5', 70' isotherms (20' isotherm dushed)

Figure 37. Ratio projection of sjstern Al-a?S04..YanCOa, lVaCI, H20. shorbing 35' and 50' isotherms 24

INDUSTRIAL AND ENGINEERING C H E M I S T R Y

Figure 38. Process coristructions in system NanSO4, N u z C O ~NaCl, , HnO in ratio projection

lies deep within the NaCl fields. Therefore, a substantial crop of NaCl can be crystallized by evapcration before the burkeire field is reached. W e will try to obtain enough of a crop of pure NaCl this way to satisfy material balance. T o d o so, a n NaCl vector starting a t b ( x ) must terininate a t some point y, such that the ratio of NaCl to Na2C03 removed in the total path from f(50) toy will be the sarne as that added in feed. Using the constructions of Figure 33, we project F onto the NaCl-Na2C03 axis to find point F’. Point F’ must represent the overall composition of the solids precipitated in going from point f ( S 0 ) to y, so a n F’ solids ray must pass through points J(50) a n d y. Therefore, to obtain the desircd material balance, pointy must be located a t the intersection of the F’ ray through point f ( S 0 ) , a n d a n NaC1-crystallization ray through point b ( x ) . Point y thus located turns out to fall within the NaCl field at both 35” (Figure 37) a n d 20” (Figure 36). Therefore liquor b ( x ) can be evaporated, in a solar pond if desired, to yield more than enough pure NaCl to satisfy material balance on the given feed. This step gives the NaCl product. From point y the process will comprise addition of new feed, incorporation of mother liquor returning from the C-level split, and crystallization of burkeite. Eiut all solutes removed as burkeite from the main cycle will return in C-level mother liquor, except the NazS04 crystallized in the C-level separation. Therefore, the net or “material balance” result of going from point y to f(S0) will be addition of new feed a n d withdrawal of the final crop of N a 2 S 0 4as Glauber salt. Constructions are derived solely from material balance. They can

be made for the net or equivalent process, a n d will serve to define the length of the new feed vector, y-z. This vector must terminate on a n NaZS04 ray returning to operating pointf(S0). T h e actual process comprises addition of C-level mother liquor a n d crystallization of burkeite to return from point z tof(50). C-level mother liquor composition will be adjusted to give favorable water balance, but assume at this stage it corresponds to d ( 2 0 ) . Point w is found as the intersection of a burkeite ray through f(50), with a d ( 2 0 ) ray through point z. T h e main process cycle, f(SO)-b(x)-y-t-w-f(50) is thus completed. So far, water balance has not been represented. In actual design for a n economical process, it would be kept in mind at all times. Figure 39 shows the process cycle of Figure 38 in rectangular coordinates, with HzO/ (NaC1 NaZC03 Na2S04) shown as a side projection. Construction lines a n d process vectors in the right or ratio projection side correspond to those of Figure 38. T h e projection of process vectors on the water projection are shown on the left. Starting a t point f(50), sal soda is removed to point b’ a t the same NaSC03 coordinate as b ( x ) . As will be seen, it takes a dilution vector b ’ - b ( x ) to make the path to b ( x ) . NaCl is then crystallized along a n NaCl ray to the N a 2 C 0 3 level of point y (off the diagram), a n d evaporation is necessary to bring it back to point y. T h e water level a t pointy has to be estimated by interpolation from phase diagrams, since it lies in the middle of a n NaCl field, but should be about as shown. From pointy, new feed is added along its ray to point t a t the proper NazC03 level, then liquor d ( 2 0 ) is added along its ray to point w,

+

+

VOL. 6 2

NO. 1 2 DECEMBER 1970

25

FiLFure39. Process constructions in system LTa2SOi, XaL'O3, n h C l , HzO in ratio and solvent projectioni

again a t the N a 2 C 0 3 coordinates established in the ratio projection. Froin point w burkeite is precipitatcd along a burkeite ray to the N a 2 C 0 3 level of J(50). A \very short dilutioii vector IS necessary to reach f(30) a n d close the cycle. At this point operating points niight bc adjusted to inipro\e the process, but this is beyond the scope of the present paper. T h e coiniiiercial "Soda Products" process a t T r o n a (I) is essentially this oiie with several adjustiimits a n d refinements (2, 3, 4, 7 1 ) . hlost iinportant, the sal soda end liquor at b ( x ) is discarded since its values d o not warrant the cost of evaporating it. T h u s the T r o n a process is not cyclical, a n d there is a n end liquor loss. Second, the dilution 1-ector froin b' to b ( x ) is cliniinated by stepwise cooling of the J ( 3 0 ) liquor to crystallize and separate a crop of NaCl before precipitation of sal soda. Furthermore, considerable advantage is taken of metastability as in most T r o n a processes (6,7).

a four-coinponent s>-stem,which is rationalized as follows There is no cornposition in an) solution of thcsc coiiiponents that cannot be expressed in tcriiis of three of the salts. T h u s in a n ) gi\en s)steiii, Rcactioii 7 inay be concci\ ed as going to completion to the riqht. Eirhcr N a N O a or KC1 \$ill be exhausted by thc reaction, leaving subs) stein KC1-KNO j-NaC1 if KC1 w a s i n excess, or subsystein Nah-03-KNOd-NaC1 if it was not. Since this q s t e n i has the saiiic residual degrees of freedom as a four-coriiponent one, i t iiiust he rcprescntable in the saiiie sort of coordinatc systems. l y e should then he able to plot isotheritis for a n entire q s t c i i i i n teriiis of three salt concentrations. But if so, hoii does the concentration of the fourth salt plot? Representations. I n Figure 40 we arbitraril) choosc wt "/;c KaC1, KC1, and K N 0 3 as the principal axes. Converting Equation 7 from mol weights to direct weights

I Reciprocal salt pairs occur when two coniponents of a systein can react. For example

101.1 g K N 0 3

85.0 g N a N 0 3

Reciprocal Salt Pairs-Type

NaN03

+ KCl

=

KK03

+ NaCl

or i"\;azCOa

+ Na2B407 + HsO = 2 NaHCOs

+ Na2B201

(8)

A system such as KaNOa, K C l , KKOy, NaC1, H20 may be considered, by our relaxed rule, to have fi\.e components a n d one condition, namely that defined by Equation 7. This leaves it Lvith the same residual degrees of freedom as the four-component systems prcviously discussed. Thermodynamically this makes it 26

INDUSTRfAL A N D ENGINEERING CHEMISTRY

+ 58.5 g NaCl

(9)

or

g NaN03 (7)

+ 74.6 g KC1 =

=

1.19 g KKOa

+ 0.69 g NaCl 0.88 g KC1

(10)

I n other words, to get a unit of NaN03, add 1.19 units of KNOB,0.69 units of NaCl, a n d subtrdct 0.88 units of KC1. On Figure 40, these are vector operations that can be plotted as shomn. This vector sum defines the direction a n d scale module of the N a N 0 3 axis. Positive quantities of T\-aNOawill plot v i t h an equivalent negative KC1 component. Put another way, the N a C 1 - N a h T 0 3 - K S 0 3 subsystem will plvl bclow the origin. T h e idea of a negative concentration of anything inay

boggle the mind. You can't subtract more KC1 than is present to get a negative concentration. But the negative representation means only subtracting it in amounts u p to as much as is created by metathesis from K N 0 3 a n d NaCl. A Suhr projection of the isotherms at 75°C is shown in Figure 41, a n d a ratio projection in Figure 42. A ratio projection as shown in Figure 42 does not fit graph paper very well, a t least through subsystem NaC1-KN03-NaN03. Something more syiiimetrical would be desirable. But as long as we stick to wt 70, a n d to 60" triangular coordinates for the principal subsystem, the N a N 0 3 point is fixed a t its inconvenient location. If we arbitrarily move it, there will be discontinuity in solubility curves a n d in construction lines in passing from one subsystem to the other. If a reniapping is made, it should be by a linear transformation. A more convenient diagram results if the principal axes of the ratio projection are transfornied to 45", a n d the scales from direct wt % to equivalent wt yo (equivalents of a component per 100 equivalents total solute components). After this transformation, the ratio projection will appear as in Figure 43. I n this convenient form it is well known as a Janecke plot or prqjection. D a t a can be plotted into a Janecke diagram in two ways. As a n example of the first way, the NaCl corner may be treated as the origin of a N o s - , K + coordinate system (the coordinate system ions being those not included in the salt a t the origin point). I n this example, the percentage fraction of anion equivalents that are N o s - is plotted as the abscissa; the percentage fraction

E X

U

-

0 Y

Figure 40. Location of fourth axis i n rec$rocal salt pair system

M ~ N ~ N O ,

Figure 41. Suhr projection of reciprocal salt pair system Kh'Os $. NaCl = h'aNO3 KCl

+

of cation equivalents that are K + as the ordinate. Alternatively, analyses may be given in ternis of any three of the salts; such as, for example, KCl, NaN03, a n d K N 0 3 . These three components identify a subsystein. O n e of the conipoiients, in this example, K N 0 3 , will be a t the right angle corner of the triangle representing the subsystem. Consider this corner as the origin of a coordinate system, a n d plot in terms of the other two components. Thus point a(75), Figure 43, might be plotted as 72.7Y0 N O 3 a n d 62.2% K on a n equivalent solvent-free basis, a n d these coordinates would be plottcd from the NaCl corner. Alternatively, it might be reported as 35% KNOa, 27.3% KC1, a n d 37.7y0 N a N 0 3 (on aii equivalent, solvent-free basis). I t would be plotted from the K N 0 3 corner with the coordinate 27.3% K C l measured to the left, a n d 37.7y0 NaNOa plotted down. Solute contents can be represented as needed by side projection exactly as in Figures 35 a n d 39. Process cycles-metathesis. Figure 43 shows isotherms for 25 " a n d 75 "C. I t will be apparent that solid phases of KC1 a n d N a N 0 3 cannot coexist in equilibrium with solution phases a t either temperature since their fields d o not abut a t any point. Reacting two such components to produce the other two by metathesis constitutes a simple special case problem. [This problem a n d this process have been well described by Purdon a n d Slater (70). They also describe the basic process for Type I, three-component systems. Their book is recommended reading, particularly for those seeking a lucid, elementary review of phase chemistry.] And one of the reasons that it is simple is that only two coniponents, in this case K N 0 3 a n d NaCI, have to be isolated in solid phases. I n Figure 43 there is a n overlap of product fields (KNO3 a n d NaC1) between the 25" a n d 75" isotherms. A process triangle can be constructed anywhere within this area consisting of three vectors. From some operating point a the system is cooled to 25", with appropriate adjustment of solvent, to crystallize a crop of K N 0 3 , which is removed as product. An equi-equivalent mixVOL. 6 2

NO. 1 2

DECEMBER 1970

27

KCI

KNO,

i

1

I

\ i

KCI FIELDS

KNO, FIELDS

75 I O C

,

/

I

/

,' ///

/f

1

NaCl FIELDS

75oc I NaN03 , FIELDS

25"c/

//

/

I

NaCl

NaNO3

43. Junecke projection--rutia projection i n eguiualent cooidinates, showing process cjcle f o r metathesis ~ ~ a 3 ,$.~ ECCl O KiYO3 ilhCl

Filurc

+

ture of NaNO3 a n d KC1, corresponding to point F, is then added to Inothcr liquor B . It carries the system to point c, which is found as thc inrcrscction of a n F ray through operaring point 0 , and a n NaCl ra)- through operating point a. T h e systeiii at c is tlien c\-aporated a n d equilibrated a t 75" to Crystallize NaC1 a n d return the liquor composition to point a. Operating points a .and b \vi11 be chosen to give most econoiiiical solvent nianagenient. Reacting KNO3 a n d NaCl to produce NaNOa a n d KC1 presents a inore general probleiii. (Thcrc Tvould be no coniiiiercial incentive to d o so; tve address the problem to illustrate a general solution.) T h e axis running betuxen the two reacting salt points divides tlie system into two subsysteins. In this example the NaC1-KN03 axis divides it into subsysteiiis K N 0 3 NaNOa-NaCl a n d KKO~-KCl-NaCl, respecti\-el>--. If a t any point a product salt field crosses this axis, tlie process is possible. In this example, the KC1 field crosses rhe NaCl-KN03 axis at 73"C, extending to point a(75). Therefore, a C-level split of a mixture of hTaC1and K N 0 3 is possible, producing a solid phase of KCl, and a liquid phase in the opposite subsystem. T h e first step of the process, then, is to react a n appropriate mixture of NaCl aiid I AVa, I C!, SO4, HnO, shou,ing 83" isotherms; all points saturated ivith ,Z'aCl. A r r o u show progressive crjstallization path f r o m composition of Great Salt Lake brine to crystallization endpoint

ration at the right places, the products viill be Na2S0., ( + N a C l ) , a n d a solution plotting on the KC1 boundary. Since the net result of the process sequence is separating Na2SOJ from GSL, the end solution will plot at point a (Figure 50) in line ctith the K a ~ S Oa. n~d GSL points. Part of the KC1 field boundary at 25" is also shown in Figure 50. Point a lies well within this field, so a crop of KC1 (+NaCl) can be obtained by cooling solution a to 25" a n d appropriately adjusting solvent. T h c h'aC1 crop can be separated a n d further fracKC1 tionated by standard methods. Mother liquor froin this operation would plot at point 6 . Solution 6 can be evaporated at 83" 10 crystallization endpoint W , precipitating a mixture of magnesium sulfate a n d carnallite. T h e solids can he separated a n d thrown back into the countercurrent conversion sequence. This will alter the steady-state location of points a a n d 6, but not enough to change the process in principle. Solution TV is highly concentrated in MgClz, a n d might be used as is. I t retains, however, all unprecipitated minor impurities, including boron a n d a certain amount of SOe, both harmful if the hfgCl2 is destined for electrolytic winning of magnesium metal. A s one tvay of purifying it (by purely fractional crystallization means), liquor W can be reacted with recycled KC1 to yield a crop of cari?allite a n d a mother liquor highly concentrated in impurities. This carnallite crop would be free of minor impurities, a n d also, it turns out, of SaC1. T h e purified crop of carnallite can easily be processed to recover K C l a n d a solution at G, which is MgCl2 contaminated only b y a small amount of KCl.

+

Na,SO,

FIELD

GLASERITE FIELD

Glaserite Polnt

Na, SO,

\ KC I

Nap SO4

KCi

Fzgure 49. Double ratio projection from system Mg, iVa, K , Cl, SO,, H2O showing 25’ isotherm; allpoints saturated with NuCl

Figure 50. Process constructions for separating NatSO,,, KCI, and MgClt

In the above we have roughly blocked out one possible process, based on some available data, for fractionating Great Salt Lake brine. While this process has been calculated in more detail, our purpose here is only to display a n d demonstrate the steps of conceptual design. We don’t know, after only this much work, whether the process promises to be economically attractive or practically operable. All we know is that, from a phase equilibrium standpoint, it is possible. Working out process details a n d material balances from this point may be complicated, but it falls within the routine knowhow of process engineers, a n d is “left as a n exercise for the student.”

because they might be economically attractive, but because solubility data happened to be readily available. No attention has been given to rates at which phase equilibrium might be attained, or to the process variations made possible by kinetics of approach to equilibrium. And n o consideration has been given to combinations of fractional crystallization with other separation steps such as flotation, classification, or thermal decomposition, for example. All these should be considered in solving a real, commercial problem. T h e approach given is not the only one possible. Those accustonied to dealing with fractional crystallization will probably use a collection of special-case methods, each perhaps more powerful in its range of applicability. But the generalized one given here will get the answers, a n d should serve the engineer without experience suddenly faced with a fractional crystallization problern-if he can find the necessary solubility data.

SUMMARY A systematized approach has been presented for conceptual design of fractional crystallization processes for systems in which the crystalline spccics d o not form solid solutions. Detailed procedures have been given for three-component (two-salt) systems. Four-component systems have been treated in a more generalized manner, but a t least most of the several alternative process steps a n d sequences have been demonstrated. T h e rangc of alternatives available for treating systems of more than four components is so great that detailed coverage is not possible in a single article. But a conceptual basis was developed during treatment of simpler systems, a n d the way to use it on more complex ones has been pointed out. M a n y things have not been covered at all. Little consideration has been given to what makes a