-II 13-
I
PREDICTION OF THE CHEMICAL EVClLUTION
OF NATURAL WATERS
WRING EVAPORATION
Abdallah AL-DROUBI::
, Bertrand
FRITZ:: , Jean-Yves GAC':::
, Yves TARD?:
::Centre de Sédimentologie et de Géochimie de la Surface (CNRS)
Institut de Géologie, Université Louis Pasteur
1 , rue Blessig, 67084 Strasbourg - France
O.R.S.T.O.M., 24, rue Bayard, 75008, Paris - France
,..,
,.,.
Chemical evolution of natural waters concentrated by evaporation
Abstract can be predicted using a computer program designed to calculate the distribution of aqueous species and the precipitation of minerals on basis of equilibrium reactions. Total molality of elements, pH and alkalinity of solutions
fluctuate during the evaporation processes. These fluctuations can be interpreted by the use of the concept of generalized residual alkalinity.
I
1
t
I - A COMPUTER MODEL FOR WATER CONCENTUTION BY EVAPORATION
' I
A computer program called EVAPOR
calculates the evolution of the che-
mical composition of solutions submitted to evaporation, on the hasis of the
I
equilibrium reactions proposed by GARRELS and MACKENZIE (1967). The program and
, AL-DROUBI
e t ai!. (1976 a, 1976 ,
)
b
AL-DROUBI (1976) and CAC e t ai!.(1977), are applied to the Euphrate river (Syria).
Some of the results are presented in Fig. 1 and Table 1. Starting from the initial chemicalcomposition of the river, the model simulates a theoretical evaporathe model, already described by FRITZ (1975)
tion by successive small increments of concentration..At each step, ionic strength,
activity coefficients, activity of the free ions and complex aqueous species as
well as degree of the solution saturation with respect to salts, are computed.
,
After reaching saturation with respect to one mineral, the number of moles of
this mineral precipitated is then calculated as function of the concentration
t)
factor.
In Euphrate system, the following minerals are formed : calcite (Caco3)
, Mg-montmorillonite (Mg3Si4010(OH) 2)
, magnesite
(MgC03) , gypsum (Cas04 , 2H20)
c9
thenardite (Na2S04) and sylvite (KC1) for concentration factors respectively
equal to : I , 2, 3.5,
i
48.6,
3735 and 5680.
A s shown on Fig. 1, the sense of variation of alkalinity, pH, Ca, Mg or
SO4
in solution, can change with respect to concentration factor when the precipi-
tation of a new mineral occurs in the sequence. pH, for example increase after
precipitation of calcite, Mg-montmorillonite or gypsum but decreasesafter formation of magnesite or thenardite. Direction and magnitude of these variations
0. R.S.T.O.M.
Fonds DGcumeniaire
No:
3LrZ
CDk? 2
13
9
E* I
?
-II 14differ for each case analyzed.
II- PREDICTED CHEMICAL EVOLUTION. OF SOME NATURAL L'ATERS
Different natural waters were concentrated by simulated evaporation :
Euphrate (Syria), Jordan (Jordan), Chari (Chad) and sea water. Calculated chemical evolutions are schematically reported on Fig. 2, where changes of log total
molality O S elements (ordinates) are shown as function of log concentration factor (abscissae), with fC02 of initial water maintained constant : 10-2.36Sor
Euphrate,
for Jordan,
for Chari and
for sea water
.
Before concentration by evaporation, the relative amounts of anions and
cations in these four natural solutions are the following :
Euphrate river
Jordan river
Chari river
Sea water
:
:
:
:
HCO3 > Ca > Na > C1 > Mg > $04, K and 3Si02 < 4Mg
HCO3 > N a = Mg > Ca = C1 > K > SO4 and 3Si.02 < 4Mg
HCO3 > N a > Ca > Pig > K > C1 > SO4 and 3Si02 < 4Mg
C1 > Na > Mg > SOI+ > Ca > K > HCO; and 3siO2 < 4Mg
It,can be seen on Fig. 2 that before precipitation of the first mineral
the pH and all molalities increase with concentration factor. Therefore after
-formation of successive minerals, the pH, alkalinity and molalities may increase
slower or decrease and sometimes increase again. pH for example rises continuously even after precipitation of sylvite and trona (Jordan and Chari), falls after
the magnesite saturation point (Euplirqte an¿ sea water) and rises again after
gypsum precipitation (Euphrate). In the case of sea water, magnesium molality
increases continuously,but for Chari and Jordan it decreases after Mg-montmorillolonite and magnesite precipitations. Magnesium molality fluctuates frequently in
the case of the Euphrate. Such considerations can be emphasized for each element
involved. It is now tempting to consider an approach for predicting such patterns.
III- BEHAVIOUR OF ELEMENTS IN SOLUTION DURING PRECIPITATION OF SALTS
During evaporation, the behaviour of elements in solution after reaching
the saturation point with respect to a given salt is easily predictable, only
when the salt in question is a simple strong electrolyte. This is the case of
NaCl, for example ; total molality of Na or C1, written (Na) and (Cl), rise t o gether in solution until the saturation point with respect to halite. At this
point, three possibilities are offered, depending on the ratio
((Na)/(Cl) in the
initial solution. If (Na) > (Cl), (Na) will go on to increase and (Cl) to decrease as function of concentration factor ; if (Cl) > (Na),the contrary is observed. Molalities of Na and C1 will not change if they are equal in the initial
solution. This problem can simply be treated, using the mass action law and mass
balance equations, disregarding activity coefficients and complex aqueous species
I'
, @
-11 15-
If (Na::) and (Cl") are the molalities at a saturation point with respect
I
to NaCl, we have : (Na::) (Cl::)
=
Ksp
After a small step of evaporation, corresponding to a concentration factor of ( 1 + dS) and precipitation of dx moles of NaCl, it follows that :
(Na)
=
(Na::) ( 1 + dS)
-
dx ; (C1) = (Cl:') (l+dS)
-
dx,with : (Na) (Cl) = Ksp
The direction of variation of (Na) and (Cl) are given by the signs of :
I
i
!
1
By deriving the mass action law equation (Na)(Cl)
I
d(Na) + - - =1 d(C1)
0
(Na) d 5
(CI) d S
Ksp, we obtain :
=
I
!
L
,
!
j
If we have now a salt with three or more components, the expression of
the derivative is much more complicated. For a fictive NaKC12 salt, for example
the expressions calculated above would become :
I
1
I
i
i
i
.{
Thus, after reaching saturation point with respect to NaKC12, (Na) willgo on to
increase if (Na::) (I?) + (Na::) (Cl':) - 3 (K::) (Cl::) > O that is : (Na::) > 3(K::)+(cl;.)
(JG)
(C 1::)
i
I
i
l
1
4(Na::) (K::)
During the same time, (Cl) will continue to increase if (Cl;:) > (Na::) + (K::)
Prediction of such behaviour will be more accurate if calculations of
I
complex ions and activity coefficients are taken into account. However, when a
t i :
f
mineral precipitates, the higher the concentration of one of its components in
the initial solution, the greater the chance that the concentration of this components will rise during the evaporation steps.
I
In the case of calcium carbonate, the problem was approached by EATON
(1 950) and treated by EUGSTER ( 1 970). Van BEEK and Van BREEMEN ( 1 973) introduced
the concept of residual alkalinity for predicting the behaviour of alkalinity and
I
pH in alkali soils formation.
i
l
IV- GENERALIZED RESIDUAL ALKALINITY CONCEPT
AL-DROUBI (1976) extended the concept of residual alkalinity of Van BEEK and
Van BREEMEN ( 1 973).
Alkalinity of natural solutions can be defined as :
(Alk.)
=
(K)t + (Na),
+
í'(Calt + 2(Mg),
-
(Cl)t
-
2(S0,+)t
-II 16-
(Alk.1 = (HC03)t
+
2(C03)t
(OH)t
+
-
(H)
in which (HC03)t is the total molality, including the molality of the free ion
HCO; as well as the molality of complex bound HCO3, i.e. NaCOs, MgHCOS
CaHCO; etc
...
; Or (OH)t includes the molality of the free ion (OH)-
as molality of Mg(OH)+,
Ca(0H)'
etc
.. .
as well
( S T W and MORGAN, 1970).
Residual alkalinity for calcite, after reaching calcite saturation is
defined as :
(Res. Alk.) calcite
=
(Alk.)
-
2(Ca)t
Residual alkalinity for calcite and magnesite after precipitation of
these.two minerals is defined as :
(Res. Alk.) calcite + magnesite
=
(Alk.)
-
2(Ca)t
-
2(Mg)t
If fC02 is constant during the evaporation, the sign of residual alkalinity will determine :
a) the behaviour of calcium, pH and alkalinity during the precipitation of
calcite,
b) the behaviour of calcium,magnesium, pH and alkalinity during coprecipitation
of calcite and magnesite.
After precipitation of calcite, calcium concentration increases, pH and
alkalinity decrease,if (Res. Alk.) calcite is negative. If positive, calcium
concentration decreases, pH and alkalinity rise. At the stage of precipitation
of magnesite, after calcite, magnesium and calcium concentrations increase, pH
and alkalinity decrease if (Res. Alk.) calcite + magnesite is negative ; if
(Res. Alk.) calcitefmagnesite is positive, magnesium and calcium concentrations
decrease, pH and alkalinity rise together.
It must be emphasized that if the sign of (Res. Alk.) calcite is Bositive and the sign of (Res. Alk.) calcite + magnesite is negative, calcium concentration decreases after calcite precipitation but increases again after magnesite
precipitation. This is what happens in the case of the Euphrate river (Fig. 2)
-II
0
17-
Application to other binary s a l t s
When, a f t e r c a l c i t e and magnesite p r e c i p i t a t i o n , o t h e r s a i t s a r e formed,
i t can b e shown t h a t t h e above e x p r e s s i o n of R e s i d u a l A l k a l i n i t y is s t i l l v a l i d .
A f t e r r e a c h i n g s a t u r a t i o n p o i n t w i t h r e s p e c t t o gypsum, f o r example :
(Res. Alk.) magnesite
-
(Alk.)
“t
2(MgIt
(K)t
+
-
-
calcite
-t
2(Ca)t
-t
+ .Z(S04)t
gypsum =
=
(Cut
I f (Res. Alk.) i s p o s i t i v e , A l k a l i n i t y and pH w i l l i n c r e a s e , (Ca)t and (Mg)t
w i l l d e c r e a s e and by t h e way (SO4)t w i l l r i s e . I f n e g a t i v e , t h e o p p o s i t e evo
U-
t i o n i s observed.
I f , f o l l o w i n g gypsum, t h e n a r d i t e (Na2S04) p r e c i p i t a t e s :
(Res. Alk.) magnesite
i
i
!
(Alk.)
-
-
2(Mg)t
+ c a l c i t e + gypsum + t h e n a r d i t e
2(Ca)t + 2(SOq)t
t h e same r u l e can b e a p p l i e d i . e .
-
(Na)t = (K)t
-
=
(Cl)t
(Na)t w i l l i n c r e a s e i f (S04)t decreaseswhichhapper
when’(Res. Alk.) i s n e g a t i v e .
A f t e r h a l i t e (NaCl) p r e c i p i t a t i o n :
f
+ c a l c i t e + gypsum + t h e n a r d i t e + h a l i t e =
2(Mg)t - 2(CaIt + 2(SOq)t - (Na)t + (Cl), = (K)t
(Res. Alk.) magnesite
J
(Alk.)
i
-
I
The r e s i d u a l A l k a l i n i t y i s obviously p o s i t i v e ; i n t h i s c a s e (K&,(Cl& ,(S04& ,(Alk.)
and pH w i l l r i s e and (Na)t,
w i l l decrease.
(Ca)t and
F i n a l l y a f t e r s y l v i t e (KC1) p r e c i p i t a t i o n :
t
(Res. Alk.) magnesite + c a l c i t e + gypsum + t h e n a r d i t e + h a l i t e + s y l v i t e =
(Alk.)
-
2(Mg)t
-
2(Ca)t + 2(SOI,It
-
(Na)t: + (Cl.lt
-
Wt=
O
(Res. Alk.) i s e q u a l t o z e r o , a l k a l i n i t y , pH and c o n c e n t r a t i o n of o t h e r elements
i n s o l u t i o n w i l l n o t change and remain c o n s t a n t according t o t h e phase r u l e , t h e
I
number of phases which c o n t r o l t h e system becoming s u f f i c e n t l y h i g h .
Ilhen a s t r o n g e l e c t r o l y t e i s formed two p o s s i b i l i t i e s a r e o f f e r e d :
I
a)
i f any of t h e two components (anion o r c a t i o n ) was a l r e a d y involved i n a pre-
v i o u s p r e c i p i t a t i o n , t h e formation of t h e new m i n e r a l does n o t modify t h e R e s i <
dual Alkalinity ;
k
b)
when one of t h e two components (anion o r c a t i o n ) w a s a l r e a d y i n v o l v e d , t h e
t o t a l m o l a l i t y of t h e o t h e r must be added ( i f anion) o r sub-tracted
( i f cation)
from t h e p r e v i o u s R e s i d u a l A l k a l i n i t y , t o c a l c u l a t e t h e new one.
I f t h e s a l t formed i s a weak a c i d s a l t , t h e c o n c e n t r a t i o n of t h e c a t i o n
o n l y , must be s u b k . r a c t e d , t h e weak a c i d anion being a l r e a d y counted i n t h e
Alkalinity.
I
e
-II 18-
Derivative of A Z k a l i n i t y
A mathematical f o r m u l a t i o n i s now developped f o r t h e simple case of a
s o l u t i o n s a t u r a t e d w i t h r e s p e c t t o c a l c i t e and r e a c h i n g gypsum p r e c i p i t a t i o n
p o i n t , i n c o n d i t i o n s of fC02 f i x e d . Without t a k i n g i n t o account of a c t i v i t y coeff i c i e n t s and complex s p e c i e s , f o l l o w i n g e q u a t i o n s c a n b e d e r i v e d from t h e mass
b a l a n c e and t h e mass a c t i o n l a w e q u a t i o n s .
F o r a small s t e p of e v a p o r a t i o n (1
+ dS), dx and dy are r e s p e c t i v e l y
t h e number of moles of c a l c i t e and gypsum formed :
(Alk.) = ( 1 + dS)
-
+ (K::),
2 dx - 2 dy
-
-
+ 2(Mg::)t
2(S04::)t
-
-
dS
(Res. Alk.) c a l c i t e + gypsum = ( 1 + dc) [(Na::)
+ (K::)
(Res. Alk.) c a l c i t e + gypsum = ( 1 + dc) (Res. Alk.::)
d ( R e s . Alk.) c + g
dS
(1 + dc)
(-2 dy)
+ d t ) - 2 dx and d(A1k*) = (AIk.::)
(Alk.) = (Alkv) ( 1
+ 2(Ca::)t
(C1::)t]
2 dx
d5
+ 2 (Ng::)
- (Cl::)
t]
c a l c i t e + gypsum
c+g
= (RQs. Alk.::)
(:: s t a r s ' i n d i c a t e t h e i n i t i a l v a l u e s )
According now t o mass a c t i o n l a w f o r C O Z , HCOY, H 2 0 , CaC03 and
Caso4, 2H20
e q u i l i b r i u m r e a c t i o n , it comes :
Î
1. ] are confused w i t h t o t a l m o l a l i t i e s and combining t h e s e
If a c t i v i t i e s
e q u a t i o n w i t h t h e above ones, one h a s :
d (Alk.) _
dS
-
Because (Res. Alk.) c a l c i t e
d (Alk.)
d (Ca) [(HCO::)
d 6
\
1
2(Ca::)
+ gypsum
= (Alk.)
+ 4(CO::)
a
-
d S
(OH::)
>O
+
(H::)]
1
2 ( C a ) t t ~ ( S O G )i~t , comes :
d (Res. Alk.) c a l c i t e - t g y p s u m
dS
=
t
+
2 -d(Ca)
dS
2 d(SO4)
dS
j
. .
,.
.-.
, .,
.
.
-
.
.,
*".
.
a
-II 19-
1
t
and finally :
Y
I'
1
1
(Res. Alk.) calcite+gypsum.
I
b
bE
r
1
; fF
i
I
A
\
always positive
Thus, the derivative of Alkalinity has the sign of Residual Alkalinity defined
for the minerals involved.
Limitations for the use of Residual Alkalinity
Two major limitations were found in the use of Residual Alkalinity for
f
!
predicting behaviour of elements in solution when salts precipitate.
f
The first one comes from the direction of variation of Alkalinity in
i
I
connection with pH at constant fC02. The equilibrium HCOT + 'H
+ 2H'
2
C02+ H20
CO2 + H20 indicates that activities of HCOT or COS increases when
i
or CO:
f
pH ipcreases. Thereforein brines, because molalities can be very different from
f
activities, it is possible to find cases in which Alkalinity varies in a diffe-
I
rent direction of pH.
i
expression and the use of Residual Alkalinity become complex. This is, f,or exam-
t
i
Furthermore when the salts involved are of three or more components, the
ple, the case when dolomite or montmorillonite are the first minerals formed.
iI
t
4
i
CONCLUDING REMARKS
1
i
i-
l
During evaporation, concentration of soluble species can fluctuate, depending on the nature of salts precipitating and of the relative amount of these
species in solution. Prediction of such behaviour may be approached by the use
of Residual Alkalinity extended concept. However this method is limited to re-
i
latively simple cases. A computer approach seems then necessary to solve cor-
!
rectly the problem.
!
I
I
I
1
Table 1.
Chemical composition of Euphrate waters, (concentrations in moles/
kg H20, Alkalinity in meq/kg H20) before evaporation ( 1 ) and :l.fter evaporation
for a concentration factor of 5680 (2), maintaining fC02 = 10”2.36.
Conc.fact.
(1)
Alk
3.051
1
(2) 5680
15.28
SO4
c1
Na
K
0.701
O. 875
1.266
0.072
564.6
4969.9
5702.1
408.9
Ca
. .
Mg
Si02 I o n i c str.
1.270 0.725 0.115
0.007
0.89
5.19
1.3.
1.15
Fig. 1 - Evolution of chemical composition of solutions and amount of
salt precipitated during evaporation of
of concentration factor
(5).
Euphrate water, as function
-II 21-
calcite (Caco3)
Mgmontmor.(Mg,Si40,0 (OH),
Mg-montmor (Mg,Si,O&OH),
1 Il
1
..--._.-._
~
si02-=------l
,
log cmcantration factor
EVAPORATION OF CHARI WATER
EVAPORATION OF EUPHRATE WATER
Mg-montmor. (Mg,Si,0,0(01-&4)
I-!
.-.----"_I
calci te (Ca Co
magnesite (Mg CO,)
yg.-,
I
--- -..
h../
PSU m (Ca SO4 .2H201-
-- -
l-halite
(NaCl)-
-2-
.o
o
E
--
-----___
o
O
B
- ______--------
-2
-._.--_
sio,
'
-4:
EVAPORATION
Fig.2
-
log concentration factor
OF SEA WATER
*
--.
A
1
EVAPORATION
2
3
log concentration factor
OF JORDAN WATER
Schematic computed chemical evolution of Euphrate, Chari,
sea water and Jordan waters, during concentration by evaporation.
i
c
4
-II 22-
REFERENCES
AL-DROUBI A. (1976)
Géochimie des sels et des solutions concentrées par éva-
poration. Modgle thermodynamique de simulation. Application aux sols salés
du Tchad. Thèse Université Louis Pasteur, Strasbourg, et Sei. Ge'oZ. Me'm.
177 pp (in press).
AL-DROUBI
A.
, FRITZ, B.
and ,TARDY,Y. ( 1 976)
Equilibres entre minéraux et so-
lutions. Programmes de calcul appliqués à la prédiction de la salure des
sols et des doses optimales d'irrigation. Cah. ORSTOM, s6r. Pe'doZ. XIV,
13-38
-
AL-DROUBI A. , CHEVERRY, C. , FRITZ , B. and TARDY, Y.. ( I 976)
Géochimie des
eaux et des sels dans les sols des polders du lac Tchad : Application d'un
modèle thermodynamique de simulation de .l'é<aporation. Chm. Geol. 17, 165177.
BEEK C.G.E. Van and BREEMEN N. van (1973)
The alkalinity of alkali s o i l s .
J . S o i l S e i . 24, 129-136.
. f i
Significance of carbonates in irrigation waters. Soi2 S e i .
EATON F.M. (1950)
..
6 9 , 123-133.
EUGSTER H.P.
(1970)
Chemistry and origine of the brines of lake Magadi,
'
Kenya. MineraZ. Soc.Amer. Spec. Pap. 3, 213-235.
FRITZ B. (1975)
.
Etude thermodynamique et simulation des réactions entre mi-
néraux et solutions. Application à la géochimie des altérations et des
eaux continentales. S e i . @OZ.
Mgm. 4 1 , 1 5 2 pp.
j
GAC J.Y., AL-DROUBI A., FRITZ B. and TARDY Y. (1977)
Geochemical behaviour
of silica and magnesium during the evaporation of waters in Chad. Chem.
GeoZ. (in press).
-
,
GARRELS R.M. and MACKENZIE F,T. (1967)
Origin of the chemical compositions
of some springs and lakes. In : Equilibrium concept in natural water sys-
tems. Gould Ed. Amer. Chem. Soc. Ser. 67, 222-242.
STLJMM
W. and MORGAN J.J. (1970)
Aquatic chemistry. An introduction emphasi-
zing chemical equilibria in natural waters. Wiley- Interscience, 583 pp.
l
1
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Ø"