Baixe Basic-Solar-Pond-Model and Material Balance e outras Notas de estudo em PDF para Engenharia Química, somente na Docsity!
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.
138 SALTS & BRINES '
system i s s t e a d y - s t a t e , t h e inventory change is n e a r zero. I n t h e model developed i n t h i s paper, s t e a d y s t a t e w i l l b e 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
B R I N € DENSITY (concentration 1
FIGURE m
EXIT AND FEED BRINES
The c o n c e n t r a t i o n of e i t h e r t h e e x i t o r f e e d b r i n e s w i l l almost always b e known. The concen- t r a t i o n of t h e f e e d 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 c o n c e n t r a t i o n such a s ocean b r i n e o r w e l l b r i n e. By knowing t h e f e e d b r i n e concentra- t i o n s , t h e e x i t b r i n e can b e c a l c u l a t e d. T h i s e x i t b r i n e now becomes t h e f e e d t o t h e second pond, e t c.
Sometimes it is n e c e s s a r y t o s t a r t w i t h t h e l a s t pond of a system and work backwards. I n such a c a s e , t h e end b r i n e c o n c e n t r a t i o n i s known o r assumed. The c o n c e n t r a t i o n of t h e f e e d b r i n e need-
ed t o make t h e r e q u i r e d e x i t b r i n e is t h e n c a l c u - l a t e d. This newly c a l c u l a t e d f e e d b r i n e now be- comes t h e e x i t b r i n e of t h e n e x t t o l a s t pond. T h i s same c a l c u a t i o n i s made s t e p p i n g backwards t o t h e n e x t pond i n s e r i e s u n t i l t h e c o n c e n t r a t i o n of t h e r e s e r v e b r i n e is reached. The mass of b r i n e f e d t o t h e pond i s g i v e n t h e symbol Tn, and t h e mass o u t i s shown a s T ( n + l ).
SALT DEPOSITS
The s a l t s d e p o s i t e d i n a pond system may be simple t o complex. The s i m p l i s t system is a no s a l t d e p o s i t. The f i r s t phase of c o n c e n t r a t i n g ocean b r i n e i s a n 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 o n l y one m i n e r a 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 c o n c e n t r a t e d Great S a l t Lake b r i n e i n c l u d e H a l i t e , Epsomite, M i r a b i l i t e , Leonite, Schoenite, K a i n 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 b e included i n t h e pond model. L e t Sn be t h e symbol f o r t h e s a l t tonnage d e p o s i t e d i n pond number N. S u b s c 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 a n e o u s l y. 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 c a p t u r e d t n t h e v o i d s p a c e between s a l t c r y s t a l s. Each s a l t h a s i t s c h a r a c t e r i s t i c v o i d volume. H a l i t e , f o r example, w i l l c a p t u r e about 35% v o i d. A d e p o s i t of c a r n a l l i t e may c o n t a i n over 50% void. Some s a l t s c o n t a i n 90% v o i d. Of c o u r s e t h e v o i d 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 b a l a n c e c a l c u a t i o n , t h e volume i s t r a n 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 e n t r a i n e d i n t h e d e p o s i t. I f a d e p o s i t c o n t a i n s 25% e n t r a i n - ment, t h e n 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 c a p t u r e d i n s a l t d e p o s i t Snl is (Sn,)(I1), where I1 i s t h e entrainment f a c t o r of s a l t s p e c i e s 1.
LEAKAGE
A l l s o l a r ponds l e a k. I n some, l e a k a g e is n e g l i g i b l e , b u t i n o t h e r s it may b e t o o h i g h t o o p e r a 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 t h a n. O 1 i n c h p e r day l e v e l from l e a k a g e a l o n e. R a t e s of .04 o r h i g h e r 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 l e a k a g e r a t e s from s o l a r ponds is a s c i e n c e of i t s own and w i l l n o t b e d i s c u s s e d f u r - t h e r h e r e. Leakage must b e 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 i n c h per day v a l u e w i l l b e used. The symbol f o r l e a k - a g e i s "L".
DEVELOPMENT OF THE MODEL
F i g u r e I shows t h e b a s i c p a r a m e t e r s of t h e model. F i g u r e 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 streams and t h e i r a s s o c i a t e d 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 e n g i n e e r may want t o c a l c u l a t e t h e pond a r e a r e q u i r e d t o produce a s p e c i f i e d tonnage of s a l t. I n a n o t h e r c a s e , only a s p e c i f i e d a r e a may b e a v a i l a b l e f o r s o l a r ponding and t h e e n g i n e e r wants t o determine how much s a l t can be produced from t h a t a r e a.
F i g u r e V shows a simple, b u 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 a d y - s t a t e and t h e r e f o r e , t h e inventory streams a r e n o t shown. As a n example, suppose it i s d e s i r e d t o produce y t o n of sodium c h l o r i d e from a pond system having t h e f o l l o w i n g parameters:
FEED STREAM Component WeightIFraction Symbol
Sodium 0.0333 Na 1
C h l o r i n e 0.0856 c
Water 0.869 H
EXIT STREAM
Component ~ e i g h t / F r a c t i o n Symbol
Sodium 0. C h l o r i n e 0.156 C l n Water 0.780 H
Leakage Rate = .02 i n c h e s per day Evaporation =. 2 i n c h p e r day Time P e r i o d = 30 days
An example of t h e pond model w i l l b e used t o f i n d t h e a r e a r e q u i r e d t o make y t o n sodium c h l o r - i d e over t h e 30 day p e r i o d and t o f i n d how much end b r i n e (T2) w i l l b e produced.
From F i g u r e V a m a t e r i a l b a l a n c e is made. S i n c e o n l y 3 parameters a r e unknown, A, S and T2, t h e n o n l y t h r e e e q u a t i o n s need b e s e t up.
Mass Balance T 1 = E + T 2 + S + S I + L
C h l o r i n e Balance TICll = T2C12 + S(.607) + SIC12 + L(C12)
TN b - b T(N + I 1 POND N
WHERE:
A = P O N D A R E A TN = POND F E E D B R I N E
E = EVAPORATION TN+I = D I S C H A R G E B R I N E
I = ENTRAINMENT FACTOR VON = BEGINNING INVENTORY
N = POND NUMBER VIN = F I N A L 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
SOLAR POND MODELING
f u n c t i o n of temperature and f e e d 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 e v a p o r a t e s b
and c o n c e n t r a t e s can e a s i l y b e e v a l u a t e d i n t h e Use of t h e s t a p l e pond model d e s c r i b e d i n t h i s l a b o r a t o r y i f proper p r e c a u t i o n s a r e taken. paper can h e l p a n e n g i n e e r c r i t i q u e a proposed
F i g u r e V I shows a t y p i c a l c o n c e n t r a t i o n p a t h of sodium c h l o r i d e i n Great S a l t Lake b r i n e. The e q u a t i o n 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 ( f e e d b r i n e ) 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 e r r o n e o u s l y choose, say, P o i n t A t o be t h e f i n a l b r i n e c o n c e n t r a t i o n and f o r c e t h e pond model t o comply w i t h 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 n a c c u r a t e and m i s l e a d i n g.
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 a d t o o p t i m i z a t i o n of a pond system and p r o v i d e t h e t o o l s n e c e s s a r y 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 e a d y i n o p e r a t i o n. 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 i n c l u d e non-steady-state c o n d i t i o n s , ground b r i n e exchange phenomena and changing b r i n e t e m p e r a t u r e s.
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 b e known.
- B r i n e c o n c e n t r a t i o n p a t h a s water i s evaporated.
- P o s s i b l e s a l t s p e c i e s t h a t may c r y s t a l - l i z e (phase c h e m i s t r y ). 3. Leakage r a t e s.
- Entrainment F a c t o r.
- Evaporation 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 v a l u - a b l e d e s i g n 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 l o w streams. Under s p e c i a l c o n d i t i o n s even e v a p o r a t i o n r a t e s , leakage r a t e s , and some b r i n e c o n c e n t r a t i o n s can b e c a l c u l a t e d.
REFERENCES
l. B u t t s , David S., Theory of S e q u e n 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, e v a p o r a t i o n and entrainment f a c t o r s a r e d i f f i c u l t t o o b t a i n. I f t h e y 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 b e known t o a r r i v e a t v a l i d c o n c l u s i o n s.
