Chapter 13

BASIC SOLAR POND MODELING AND MATERIAL BALANCE TECHNIQUES

David S. Butts Great Salt Lake Minerals & Chemicals Corporation

Ogden, Utah

ABSTRACT

There are many solution mining operations that use solar ponds as a mineral recovery step. Other locations in the world are now under investigation to recover minerals by solution mining but require the cheap energy of solar ponds to make the recovery viable.

This paper shows a step-by-step material balance system that can be used in both simple and complex solar ponds. Use of this system will help the engineer determine if solar ponding efficiency can be improved or if solar ponding will work at all with a given set of conditions.

Even the most complicated solar pond can be reduced to six flow streams. These are (1) feed, (2) exit, (3) leakage, (4) entrainment, (5) salts, and (6) evaporation. The equations developed in this paper will allow the solar pond engineer to easily evaluate the effect of each of the flow streams on the mineral production of a pond or pond complex.

SOLAR POND MODELING

INTRODUCTION EVAPORATION The high c o s t of f o s s i l f u e l s o r t h e l a c k of i t

a l t o g e t h e r have caused many new e v a p o r i t e ven tu r e s t o i n v e s t i g a t e s o l a r energy.

One proven s o l a r energy a p p l i c a t i o n is evapor- a t i o n of water from s o l a r ponds and numerous in- d u s t r i e s a r e c u r r e n t l y i n v e s t i g a t i n g p r o j e c t s t h a t r e q u i r e s o l a r ponds i n a minera l p rocess ing se- quence. Many of t h e s e p r o j e c t s a r e q u i t e l a r g e . Egypt is i n v e s t i g a t i n g Lake Qarun, China is de- veloping t h e Tsaidam Basin, Jordan and I s r a e l a r e e xp lo i t i ng t h e Dead Sea, and C h i l e i s u s ing t h e sun a t t h e Sa l a r de Atacama. I n v e s t i g a t i o n s f o r s o l a r ponding systems a r e a l s o being conducted a t t h e Sa l t on Sea, ~ o l i v i a ' s Alto Plano, Botswana, Tunis ia , Saudia Arabia, I n d i a , Mexico and many more.

BACKGROUND

I n 1965, 66 and 67, Great S a l t Lake Minera l s and Chemicals Corporat ion spent cons ide r ab l e t ime and money t o i n v e s t i g a t e t h e u s e of s o l a r ponds t o s e p a r a t e minera l s and water from t h e potassium s u l f a t e contained i n t h e Great S a l t Lake b r i ne . Engineers working on t h e p r o j e c t found t h a t t h e r e was l i t t l e advanced technology a v a i l a b l e i n t h e des ign and opera t ion of a do l a r pond system. What technology was a v a i l a b l e was l i m i t e d t o pro- duc t ion of t h e r e l a t i v e l y s imple sodium c h l o r i d e c r y s t a l l i z a t i o n pond system and ocean b r i n e s . More advanced technology had t o be developed from sc r a t ch .

Th i s paper d e a l s wi th a s imple step-by-step pond modeling program t h a t l a t e r l e d t o much more advanced technology and understanding of comp- l i c a t e d s o l a r pond systems such a s s equen t i a l pond theory. ' BASICS

A l l s o l a r pond systems can be descr ibed by t h e model shown i n F igure I. A b r i e f d e s c r i p t i o n of each of t h e f low streams shown i n t h e f i g u r e w i l l be given t o f a m i l i a r i z e t h e r eade r w i th t h e terms used and t o provide some background. The f i g u r e shows only one pond. I n most systems t h e r e i s more than one pond and t h e e x i t b r i n e of one pond becomes t h e feed b r i n e t o t h e next . Evaporat ion i s a f unc t i on of t h e concen t r a t i on of t h e begin- ning and ending inventory , and of meteoro logica l c ond i t i ons . The s a l t depos i t i s a f unc t i on of b r i n e concen t r a t i on , temperature and evapora t ion .

Entrainment i s t h e b r i n e cap tured i n t h e vo id s between s a l t c r y s t a l s . A l l s a l t s have a charac t - e r i s t i c void volume. Sodium c h l o r i d e ha s a 35% void volume f o r example.

Leakage is t h e l o s s of b r i n e through porous d i k e s o r seepage down v e r t i c a l l y through t h e pond f l o o r . A m a t e r i a l ba lance around t h e pond system must a l s o i nc lude changes of b r i n e volume ( in- ven tory) and changes i n concen t r a t i on . Each of t h e s e b a s i c parameters wil!. 1.e d i s r u s s d in t h e develogm'e?t ofs.w-ojltiflp pond model.

FEED BRINE

I POND I I

BEGINNING INVEWORY SALT INVQ NTORY +

LEAKAGE 1 SOLAR POND FLOW STREAMS

FIGURE I

There a r e a few assumptions t h a t w i l l b e made h e r e without formal proof , bu t which need a t l e a s t some b r i e f explana t ion . One i s t h a t a t any given t ime, t h e e n t i r e pond concen t r a t i on is i d e n t i c a l t o t h e e x i t b r i n e concen t r a t i on . It is n o t t h e aver - age concen t r a t i on of t h e f e ed b r i n e and e x i t b r i n e . The o the r assumption is t h a t t h e pond is a t s teady- s t a t e having cons t an t b r i n e depth and concentra- t i o n . This assamption w i l l e l im ina t e t h e begin- n ing and ending inventory s tream i n t h e model.

Before s e t t i n g up t h e model, each stream w i l l b e b r i e f l y d i scussed i n more d e t a i l .

EVAPORATION

Figure I1 shows some t y p i c a l l y shaped curves . Each concen t r a t i on ha s i t s own p a r t i c u l a r evap- o r a t i o n r a t e . Once a p l o t of evapora t ion curves has been made, equa t ions can be e s t a b l i s h e d f o r u s e i n t h e pond model. F igure 111, f o r example, shows t h e evapora t ion r a t e a s a f unc t i on of con- c e n t r a t i o n f o r t h e month of J u l y . S imi l a r l y , t h e evapora t ion r a t e equa t ions f o r a l l months of t h e year can be e s t ab l i shed . The symbol "E" w i l l be used t o r ep r e sen t evapora t ion i n t h e model. Nor- mally, t h e va lue of E can be represen ted by a l i n e a r equa t ion a s i l l u s t r a t e d .

The a c t u a l v a l u e s of E a t a s p e c i f i c l o c a t i o n r e q u i r e c a r e f u l planning t o e s t a b l i s h . The me- thods used t o d e f i n e evaporat ion w i l l n o t be ex- p la ined i n t h i s paper except t o say t h a t t ime (over a y e a r ) , money, exper ience and some good ins t rumenta t ion a r e needed.

INVENTORY

The beginning and ending inventory of a pond need t o be considered i n t h e c r i t i c a l s t a r t up phase of a pond system. The pond system a t Great S a l t Lake Minera l s and Chemicals Corpora t ion re - qu i red 3 y e a r s t o bu i l d a working inventory of b r i n e be fo r e f u l l production was r e a l i z e d . Af t e r t h i s i n i t i a l s t a r t up phase i s over and t h e

138 SALTS & BRINES '85

system i s s t e ady - s t a t e , t h e inventory change is near zero. I n t h e model developed i n t h i s paper , s t e ady s t a t e w i l l be assumed.

- -

J F M A M J J A S O N D T I M E O F YEAR

EVAPORATION RATE CURVES

FIGURE Il

GROSS EVAPORATION FOR JULY

I 1.20 1.25 1.30 1.35

BRI N € DENSITY (concentration 1

FIGURE m EXIT AND FEED BRINES

The concent ra t ion of e i t h e r t h e e x i t o r f e ed b r i n e s w i l l a lmost always b e known. The concen- t r a t i o n of t h e feed t o t h e f i r s t pond is t h e re- s e m e b r i n e concen t r a t i on such a s ocean b r i n e o r we l l b r i ne . By knowing t h e f eed b r i n e concentra- t i o n s , t h e e x i t b r i n e can be ca l cu l a t ed . Th i s e x i t b r i n e now becomes t h e f eed t o t h e second pond, e t c .

Sometimes it is necessary t o s t a r t w i th t h e l a s t pond of a system and work backwards. I n such a case , t h e end b r i n e concen t r a t i on i s known o r assumed. The concen t r a t i on of t h e f e ed b r i n e need-

ed t o make t h e r equ i r ed e x i t b r i n e is then ca lcu- l a t e d . This newly c a l c u l a t e d f eed b r i n e now be- comes t h e e x i t b r i n e of t h e nex t t o l a s t pond. This same ca l cua t i on i s made s tepping backwards t o t h e nex t pond i n s e r i e s u n t i l t h e concen t r a t i on of t h e r e s e rve b r i n e is reached. The mass of b r i n e f ed t o t h e pond i s g iven t h e symbol Tn, and t h e mass ou t i s shown a s T(n+l ) .

SALT DEPOSITS

The s a l t s depos i ted i n a pond system may be s imple t o complex. The s i m p l i s t system is a no s a l t depos i t . The f i r s t phase of concen t r a t i ng ocean b r i n e i s an example where no s a l t s c r y s t a l - l i z e . Many s o l a r pond systems c r y s t a l l i z e on ly one minera l such a s h a l i t e o r s i l v i t e . S t i l l o t h e r s c r y s t a l l i z e many mixed s a l t s . S a l t s pre- c i p i t a t i n g from concent ra ted Great S a l t Lake b r i n e inc lude H a l i t e , Epsomite, M i r a b i l i t e , Leonite , Schoenite , Ka in i t e , C a r n a l l i t e and B i s c h o f i t e t o mention a few. Each s a l t must be included i n t h e pond model. Le t Sn be t h e symbol f o r t h e s a l t tonnage depos i ted i n pond number N . Subsc r i p t s 1, 2, 3 , ---- r e p r e s e n t t h e s p e c i e s of s a l t . Suppose a pond c r y s t a l l i z e d two s a l t s s i m - u l t aneous ly . Then Snl would be t h e tonnage of t h e f i r s t and Sn2 i s t h e tonnage of t h e second.

ENTRAINMENT

A s each of t h e s a l t s c r y s t a l l i z e , some of t h e b r i n e i s cap tured t n t h e vo id space between s a l t c r y s t a l s . Each s a l t ha s i t s c h a r a c t e r i s t i c vo id volume. H a l i t e , f o r example, w i l l c a p t u r e about 35% void . A depos i t of c a r n a l l i t e may con t a in over 50% void. Some s a l t s con t a in 90% vo id . Of course t h e vo id is f i l l e d ' w i t h b r i n e . I n t h e

, m a t e r i a l ba lance c a l c u a t i o n , t h e volume i s t r an s - l a t e d i n t o weight f r a c t i o n of b r i n e en t r a ined i n t h e depos i t . I f a d e p o s i t c o n t a i n s 25% en t r a in - ment, then 100 pounds of d e p o s i t w i l l have 25 pounds of b r i n e and 7 5 pounds of s a l t . The r a t i o of b r i n e t o s a l t i n t h e d e p o s i t i s c a l l e d t h e entrainment f a c t o r . Thus, t h e entrainment f a c t o r i n t h e preceding example is 25/75 o r .333. The amount of b r i n e cap tured i n s a l t d e p o s i t Snl is (Sn,)(I1) , where I1 is t h e entrainment f a c t o r of s a l t spec i e s 1.

LEAKAGE

A l l s o l a r ponds l e ak . I n some, leakage is n e g l i g i b l e , bu t i n o t h e r s it may be too h igh t o ope ra t e a s o l a r pond system. A t i g h t pond i s one t h a t would l o s e l e s s than . O 1 i n ch per day l e v e l from leakage a lone . Rates of .04 o r h igher a r e u s u a l l y considered i n t o l e r a b l e . The methods of determining leakage r a t e s from s o l a r ponds is a s c i ence of i t s own and w i l l n o t b e d i scussed f u r - t h e r he r e . Leakage must be accounted f o r i n t h e pond model, however. For i l l u s t r a t i o n , .02 inch per day va lue w i l l b e used. The symbol f o r l eak- age i s "L" . DEVELOPMENT OF THE MODEL

F igu re I shows t h e b a s i c parameters of t h e model. F igure I V shows t h e n e x t s t e p i n expand-

SOLAR POND MODELING

ing t h e model t o show a l l p o s s i b l e s treams and t h e i r a s soc i a t ed symbols and nomenclature.

The method of handling t h e model now depends on what is wanted. I n one c a s e a p r o j e c t engineer may want t o c a l c u l a t e t h e pond a r e a r equ i r ed t o produce a s p e c i f i e d tonnage of s a l t . I n ano the r c a se , only a s p e c i f i e d a r e a may be a v a i l a b l e f o r s o l a r ponding and t h e engineer wants t o determine how much s a l t can be produced from t h a t a r ea .

F igure V shows a s imple, bu t t y p i c a l c a s e of a pond t h a t d e p o s i t s only one s a l t . The pond i s assumed t o be a s t e ady - s t a t e and t h e r e f o r e , t h e inventory s treams a r e n o t shown. As an example, suppose it i s d e s i r e d t o produce y ton of sodium c h l o r i d e from a pond system having t h e fo l lowing parameters:

FEED STREAM Component WeightIFract ion Symbol

Sodium 0.0333 Na 1 Chlor ine 0.0856 c11 Water 0.869 H201

EXIT STREAM Component ~ e i g h t / F r a c t i o n Symbol

Sodium 0.0219 Chlor ine 0.156 C l n Water 0.780 H202

Leakage Rate = .02 inches per day Evaporat ion = . 2 inch pe r day Time Per iod = 30 days

An example of t h e pond model w i l l be used t o f i n d t h e a r e a requi red t o make y ton sodium chlor - i d e over t h e 30 day per iod and t o f i n d how much end b r i n e (T2) w i l l be produced.

From F igu re V a m a t e r i a l ba lance is made. S ince on ly 3 parameters a r e unknown, A, S and T2, then only t h r e e equa t ions need be s e t up.

Mass Balance T 1 = E + T 2 + S + S I + L

Chlor ine Balance TICll = T2C12 + S(.607) + SIC12 + L(C12)

TN b - b T(N + I 1 POND N

WHERE:

A = POND A R E A TN = POND F E E D B R I N E

E = EVAPORATION TN+I = DISCHARGE BRINE

I = ENTRAINMENT FACTOR VON = BEGINNING INVENTORY

N = POND NUMBER VIN = FINAL INVENTORY

SN = SALT DEPOSIT OF SPECIES

A L L STREAMS ARE IN WEIGHT UNITS. NUMBERS REPRESENT SALT SPECIES

BASIC POND M O D E L

FIGURE IP

SALTS & BRINES '85

Water Balance (TI) (H201)= E +TL(~IZOZ)+SI(HZ~Z)+L(H~~Z)

But evapora t ion = .2 inch lday and t o t a l water evaporated from a r e a "A" over 30 days is (675) (A) tons . Likewise, t h e t o n s l o s t t o leakage is (83) A. The entrainment f a c t o r f o r NaCl is .333. As- sume f o r a b a s i s t h a t 100 ton of feed i s t h e weight of Tz. The t h r e e equa t i ons now become:

Mass 100 = 675A+T2+S+S(.333)+83A

Chlor ine 100(.0856)=~~(.156)+~(.607)+~(.333)

(.156)+838(.156)

Water 100(.869)=675~+~~(.78)+~(.333)(.78) +83A(. 78)

These equa t ions a r e solved simultaneously and A = .0974 a c r e s

Tz= 16.7 t o n s end b r i n e

S = 7.12 t ons sodium c h l o r i d e TMe t o t a l a r e a needed t o make Y t ons of s a l t i s

(A) x (YIS) = ( . 0974 ) (~ /7 .12 ) a c r e s . ~ / ~ i s t h e s c a l e up f a c t o r . The t o t a l t o n s of feed b r i n e needed i s (100) (Yl7.12).

I f 2C;OOO ton of s a l t i s t o be made, then a 274 a c r e pond w i l l be needed. The pond f eed b r i n e tonnage w i l l b e 281,000 ton and t h e end b r i n e w i l l be 46,910 ton .

The model can now b e used f o r s e n s i t i v i t y t e s t s and numerous s p e c i a l c a se s . As an example, suppose t h a t t h e leakage is zero. What w i l l be t h e e f f e c t ?

I n t h e m a t e r i a l ba lance equa t ion l e t L = 0. Solving t h e equa t ion s e t :

A = .0975 T2 = 24.63 S = 7.15

Note t h a t t h e v a l u e of A and S is t h e same wi th o r without leakage. Only t h e amount of end b r i n e i s a f f e c t e d by leakage . I f end b r i n e is de- s i r e d , then leakage ha s a s i g n i f i c a n t impact on production. I f s a l t d e p o s i t is t h e only concern, then leakage h a s l i t t l e impact. The no leakage c a s e w i l l produce n e a r l y 50% more b r i ne .

60.7 O l e C I

BASIS: TI c 100 UNKNOWNS ARE A,S and T p

EXAMPLE OF A ONE SALT DEPOSIT

FIGURE Y

feed and end b r i n e s and o n t h e accuracy of t h e evaporat ion r a t e . Most b r i n e c o n s t i t u e n t s can be analyzed q u i t e a ccu ra t e ly . I f a b r i n e c o n t a i n s only NaCl, then obviously on ly one s a l t can c r y s t a l - l i z e . The m a t e r i a l ba lance equa t ion can be based on mass, water and sodium. I f another c o n s t i t u e n t is p r e sen t , say SO4, then a second s a l t may c y r s t a l l i z e , Na2S04, and another equa t ion can a l s o be w r i t t e n around t h e SO balance. There w i l l a l -

4 most always be enough s e p a r a t e i ons i n t h e b r i n e , t o a l low f o r t h e r equ i r ed number of m a t e r i a l ba l -

ance equa t ions .

~ a - r e must b e taken i n t h e assumption of t h e s a l t s t h a t c r y s t a l l i z e d . Th i s r e q u i r e s i nves t i ga - t i o n s of phase chemistry. Some bench s c a l e t e s t s may be necessary i f chemical phase da t a a r e no t a v a i l a b l e . Na SO may c r y s t a l l i z e i n s e v e r a l phases. One miy he t h e anhydrous form o r it could c r y s t a l l i z e a s Glauber ' s S a l t ( m i r a b i l i t e ) , Na SO .10H20.

2 4

As t h e b r i n e s become more complicated, so do t h e p o s s i b l e combinations of s a l t depos i t s . The f i v e ion system K, Na, Mg, SO4, and C 1 can c r y s t a l l i z e 18 o r more d i f f e r e n t s a l t s , depending on concen t r a t i ons and tempera tures . While t h e a n a l y s i s of t h e b r i n e is s t r a i g h t forward and r e l - a t i v e l y easy , t h e s a l t a n a l y s i s i s d i f f i c u l t .

MULTIPLE SALT DEPOSIT Leon i t e (M~SOI, 'KZSOI, '~HZ~) and Schoeni te (MgS01,'KzS01,'6Hz0) a r e nea r imposs ib le t o i d e n t i f y from each o t h e r by ion a n a l y s i s a lone . A mixture

I f it is expected t h a t more than one s a l t of s i l v i t e and epomite (MgS04*7HzO) is d i f f i c u l t t o spe c i e s w i l l be c r y s t a l l i z e d , then i t i s a s imple i d e n t i f y from a K a i n i t e s a l t (KC12MgS0,-4~20). ma t t e r t o s e t up one more m a t e r i e l ba lance equa- t i o n . Each a d d i t i o n a l s a l t spec i e s c r y s t a l l i z -

Many s t u d i e s have been made on b r i n e chemis t ry and

ing w i l l r e q u i r e one more equa t ion . The en t r a in - u s u a l l y phase r e l a t i o n s can be found i n t h e l i t e r a -

ment f a c t o r f o r each spec i e s should be used. I f t u r e . I f no t , then bench o r f i e l d t e s t s must be

t h e f a c t o r s a r e n o t known, then they must be es- made. X-ray def r a c t ion , pe t rog raph i c and micro- scopic i d e n t i f i c a t i o n of each s a l t s p e c i e s may b e t imated. Most f a c t o r s run between .3 and .5. necessary .

Use .4 i f no d a t a i s a v a i l a b l e . Some minera l s such a s m i r a b i l i t e (Na2S0,. 10HzO) o r bischof f i t e BRINE CONCENTRATION PATH (MgClZ.6H2O) have h igh f a c t o r s of 2 o r 3 . Each b r i n e has i t s c h a r a c t i s t i c concen t r a t i on

pa th . This pa th must a l s o be e s t a b l i s h e d be fo r e

The accuracy of t h e m a t e r i a l ba lance equa t ion t h e pond model can be f u l l y used. The pa th is i s dependent on a c c u r a t e chemical a n a l y s i s of t h e n o t s u b j e c t t o c o n t r o l a t w i l l . The pa th i s a

SOLAR POND MODELING

f unc t i on of temperature and f eed b r i n e concentra- SUMMARY t i o n . The chemistry of t h e b r i n e a s i t evapora tes b and concen t r a t e s can e a s i l y be eva lua ted i n t h e Use of t h e s t a p l e pond model descr ibed i n t h i s l a bo ra to ry i f proper p r ecau t i ons a r e taken. paper can he lp an engineer c r i t i q u e a proposed

F igure V I shows a t y p i c a l concen t r a t i on pa th of sodium c h l o r i d e i n Great S a l t Lake b r i n e . The equa t ion f o r t h e l i n e can b e e s t a b l i s h e d and used i n t h e pond model. The beginning b r i n e ( feed b r i ne ) and t h e f i n a l b r i n e ( e x i t b r i n e ) must f a l l on l i n e . One may er roneous ly choose, say, Po in t A t o be t h e f i n a l b r i n e concen t r a t i on and f o r c e t h e pond model t o comply w i th a m a t e r i a l balance. The end r e s u l t s w i l l b e i naccu ra t e and mis lead ing .

EXIT B R I N E CONCENTRATION

system o r e v a l u a t e an e x i s t i n g one. Use of t h e model w i l l l e ad t o op t im iza t i on of a pond system and provide t h e t o o l s necessary f o r s e n s i t i v i t y a n a l y s i s . The model can be used t o understand t h e complexity of s o l a r ponding and a i d i n c o n t r o l of a system a l r eady i n ope ra t i on . Once t h e model i s used t o a i d a p r o j e c t engineer t o understand t h e b a s i c s of s o l a r ponding, more advanced models can be made t o inc lude non-steady-state cond i t i ons , ground b r i n e exchange phenomena and changing b r i n e tempera tures .

EVAPORATIO N O F BR l N E + NaCl CONCENTRATION PATH

FIGURE PI

PRECAUTIONS I N USING THE MODEL

Proper u s e of t h e model r e q u i r e s t h a t t h e f o l - lowing be known.

1. Br ine concen t r a t i on pa th a s water i s evaporated.

2. P o s s i b l e s a l t spec i e s t h a t may c r y s t a l - l i z e (phase chemis t ry) .

3 . Leakage r a t e s . 4. Entrainment Fac tor . 5. Evaporat ion r a t e s a s a f u n c t i o n of con-

c e n t r a t i o n .

Manipulation of t h e mozel can r e s u l t i n va lu- a b l e des ign parameters and understanding of t h e s e n s i t i v i t y of s o l a r ponding t o i t s f low streams. Under s p e c i a l cond i t i ons even evapora t ion r a t e s , leakage r a t e s , and some b r i n e concen t r a t i ons can be c a l c u l a t e d .

REFERENCES

l . B u t t s , David S. , Theory of Sequen t i a l Pond Systems, P r e p r i n t No. 84-318, SME-AIME F a l l Meeting, Oct. 24-26, 1984, Denver, Colorado.

Leakage, evapora t ion and entrainment f a c t o r s a r e d i f f i c u l t t o ob t a in . I f they a r e a l l e s t i - mated, e r r o r s w i l l occur. These parameters must be known t o a r r i v e a t v a l i d conc lus ions .