EPA-R2 73-235
MAY 1973 Environmental Protection Technology Series
Cation Transport in Soils
and Factors Affecting
Soil Carbonate Solubility
Office of Research and Monitoring
U.S. Environmental Protection Agency
Washington, D.C. 20460
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RESEARCH REPORTING SERIES
Research reports of the Office of Research and
Monitoring, Environmental Protection Agency, have
been grouped into five series. These five broad
categories were established to facilitate further
development and application of environmental
technology. Elimination of traditional grouping
was consciously planned to foster technology
transfer and a maximum interface in related
fields. The five series are:
1. Environmental Health Effects Research
2. Environmental Protection Technology
3. Ecological Research
H. Environmental Monitoring
5. Socioeconomic Environmental studies
This report has been assigned to the ENVIRONMENTAL
PROTECTION TECHNOLOGY series. This series
describes research performed to develop and
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methodology to repair or prevent environmental
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pollution. This work provides the new or improved
technology required for the control and treatment
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standards.
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EPA-R2-73-235
May 1973
CATION TRANSPORT IN SOILS
and
FACTORS AFFECTING SOIL CARBONATE
SOLUBILITY
by
Jerome J. Jurinak
Sung-Ho Lai
John J. Has sett
Utah State University
Logan, Utah 84322
Project #13030 FDJ
Program Element #1B2039
Project Officer
Dr. James P. Law, Jr.
U. S. Environmental Protection Agency
Robert S. Kerr Environmental Research Laboratory
P. O. Box 1198
Ada, Oklahoma 74820
Prepared for
OFFICE OF RESEARCH AND MONITORING
U. S. ENVIRONMENTAL PROTECTION AGENCY
WASHINGTON, D. C. 20460
For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, D.C. 20402
Price $1.25 domestic postpaid or $1 QFO Bookstore
-------
EPA Review Notice
This report has been reviewed by the Environmental
Protection Agency and approved for publication.
Approval does not signify that the contents necessarily
reflect the views and policies of the Environmental Pro-
tection Agency, nor does mention of trade names or
commercial products constitute endorsement or
recommendation for use.
ENVIRONMENTAL PROTECTION AGENCY
11
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ABSTRACT
A predictive model of cation transport in soils was developed and
tested. This model involved the definition of the cation exchange
process in soil columns during the miscible displacement of cation
solutions. A mass balance equation was formulated which included a
general nonlinear exchange function. The solution of the equation
was accomplished by numerical methods. The method was applied
to the transport of cations through an exchanger using five different
types of exchange functions. The model was further tested by con-
ducting soil column studies where both homovalent and heterovalent
exchange occurred. The agreement between predicted cation trans-
port in soils and experimental data was good.
Laboratory studies were also conducted, using the carbonate saturo-
meter, to assess the effect of Mg ion on the solubility of calcareous
+2
materials. Carbonate solubility in the presence of Mg ion was found
to vary with the surface area of the solid phase, the mineralogy of the
carbonate material, and the degree of saturation of the water with
respect to a given carbonate mineral. Calcite generally increased in
+2
solubility, when Mg was present, in waters which were unsaturated
with respect to calcite. Carbonate material which contained magne-
sium as a constituent ion, e. g., dolomite, decreased solubility as
Mg concentration incre
with respect to dolomite.
Mg concentration increased in waters which were near saturation
111
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CONTENTS
Section
I Conclusions 1
II Recommendations 5
Part A-Model for Cation Transport in Soils 7
III Introduction 9
IV Theory and Application of Model 11
V Materials and Methods 27
VI Results and Discussion 31
Part B-Magnesium Ion Effect on Carbonate Solubility 51
VII Introduction 53
VIII Materials and Methods 57
IX The Carbonate Saturometer 6l
X Experimental Technique 65
XI Results and Discussion 67
XII References 75
XIII Publications and Patents 79
XIV Appendix 81
FORTRAN Program I 81
FORTRAN Program II 85
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FIGURES
No.
1 The five representative types of isotherms used in
the study. 16
2 The cation concentration profiles X(z, t) and Y(z, t)
computed from the Type I isotherm. 18
3 The cation concentration profiles X(z, t) and Y(z, t)
computed from the Type II isotherm. 19
4 The cation concentration profiles X(z, t) and Y(z, t)
computed from the Type III isotherm by numerical
and analytical methods. 20
5 The cation concentration profiles X(z, t) and Y(z, t)
computed from the Type IV isotherm. 21
6 The cation concentration profiles X(z, t) and Y(z, t)
computed from the Type V isotherm. 22
7 The normalized cation exchange isotherm of the
Mg -> Ca exchange for Yolo loam soil. The broken
line is the linear regression line. The solid line is
the modified Kielland function. 32
8 The normalized concentration profiles of the solution
phase for the three Yolo loam columns, including both
experimental and theoretical values calculated from the
linear exchange function (broken lines), and from the
modified Kielland function (solid lines). 33
VI
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FIGURES (Continued)
No. Page
9 The normalized concentration profiles of the adsorbed
phase for three Yolo loam columns, including both ex-
perimental and theoretical values calculated from the
linear exchange function (broken lines), and from the
modified Kielland function (solid lines). 34
10 The normalized cation exchange isotherm of the Mg -»
Ca exchange for Nibley clay loam soil with the modified
Kielland function shown by the solid line. 37
11 The normalized cation exchange isotherm of the Mg-»Ca
exchange for Hanford sandy loam soil with the modified
Kielland function shown by the solid line. 38
12 The normalized concentration profiles of the solution
phase for three Nibley clay loam columns. The experi-
mental values are represented by the points and the
theoretically computed values by the lines. 39
13 The normalized concentration profiles of the adsorbed
phase for three Nibley clay loam columns. The experi-
mental values are represented by the points and the
theoretically computed values by the lines. 40
14 The normalized concentration profiles of the solution
phase for three Hanford sandy loam columns. The exper-
imental values are represented by the points and the
theoretically computed values by the lines. 41
VII
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FIGURES (Continued)
No. Page
w
15 The normalized concentration profiles of the adsorbed
phase for three Hanford sandy loam columns. The
experimental values are represented by the points and
the theoretically computed values by the lines. 42
16 The reduced Na adsorption isotherm in Yolo loam
soil. The solid line is represented by Equation [17]. 45
17 The concentration profiles X (z, t) for the three
column experiments. 47
18 The concentration profiles Y (z, t) for the three
IN £L
column experiments. 48
19 Reaction vessel of carbonate saturometer. 64
20 Amount of carbonate dissolved or precipitated upon
equilibration of reagent grade calcite (T) with waters
containing variable amounts of Mg , in moles. 68
21 Amount of carbonate dissolved or precipitated upon
equilibration of Purecal U (U) with waters containing
variable amounts of Mg , in moles. 69
22 Amount of carbonate dissolved or precipitated upon
equilibration of Portneuf soil with waters containing
variable amounts of Mg , in moles. 70
23 Amount of carbonate dissolved or precipitated upon equi-
libration of Millville soil with waters containing variable
amounts of Mg , in moles. 71
viii
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TABLES
No. Page
1 The Column Parameters. 15
2 The Column and Soil Parameters for Miscible
Displacement Studies Involving Magnesium
Adsorption. 29
3 The Basic Column and Soil Parameters for Miscible
Displacement Studies Involving Sodium Adsorption. 30
4 Composition of the Four Waters Used in the "Carbonate
Saturometer. " Ionic Strength for all Waters was,
I = .05. 58
IX
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SECTION I
CONCLUSIONS
A valid predictive model was developed and tested to define the one-
dimensional transport of cations in soil columns undergoing miscible
displacement by various ionic solutions. The material balance equa-
tion used in the model was formulated to incorporate a nonlinear
equilibrium exchange function (isotherm equation). This study showed
that cation transport through soils was strongly dependent on the
equilibrium exchange function which defines a cation's reactivity with
the exchange complex of a given soil.
An important parameter in the equilibrium exchange function was the
^
separation factor a_, which measures the preference of the soil exchange
B
complex for some cation A over cation B. In terms of water quality,
when the value of the separation factor of a soil for a given cation > 1,
the cation will be effectively removed from percolating water and
irrigation return flow will contain only the cations for which it was
exchanged in the soil matrix. The model which was developed not
only predicts to what extent a cation will be removed from percolating
water in a given soil but when it will eventually make its appearance
in the return flow. Correspondingly, when a soil has a separation
factor < 1 for a cation in an irrigation water the cation essentially
moves with the percolating water and appears immediately in the
return flow although its concentration will be reduced from its inflow
value. The predictive model estimates the reduced concentration level
in the return flow.
This study showed that even when considering cation exchange between
+2 +2
similar cations as Mg and Ca the resulting isotherm is not linear,
-------
i. e., ce ^ 1. A general statement is that when considering a total
B
range of possible cation concentrations in soils, the exchange function
is nonlinear. However, depending on the portion of the isotherm util-
ized, the assumption of a linear exchange function may not be in great
error.
The predictive model developed for cation transport in soils, under
saturated flow conditions, has immediate utility in estimating the
quality of irrigation return flow, particularly with reference to soil
reclamation. In this case, the model can predict the concentration
of both Ca and Na in both the solution and exchanger phase and
allows the estimation of how much calcium treated water is required
to exchange and displace a given amount of sodium in the soil. In add-
ition, the model can predict the water composition change which can
occur during groundwater recharge or the rate of heavy metal accum-
ulation which can occur in a soil when subject to inputs of industrial
wastewater. This latter aspect is extremely critical when relating
industrial waste disposal to the water quality of receiving streams or
groundwater.
The second part of this study was concerned with the effect of Mg
ion concentration in soil water on the solubility of carbonate material
which exists in the matrix. The result in terms of water quality is
reflected in an increase or decrease in the total hardness of irrigation
return flow. To predict the Mg effect on return flow quality requires
some knowledge of the soil mineralogy.
When the soil carbonate is pure calcite (CaCO ) and the water is
unsaturated with respect to calcite, an increase in the Mg ion
concentration increases the solubility of calcite. The principle
mechanism accounting for this increase in calcite solubility is the
-------
+2
formation if ion-pairs involving the Mg ion. Thus, irrigating a soil
containing calcite with a water unsaturated relative to calcite and
+2
containing Mg , would result in an increase in total hardness of the
irrigation return flow.
When the solid phase carbonate in a given system contains Mg, e. g.
+2
dolomite, as one of its constituents, the presence of Mg ion in the
water reacts differently than when the carbonate is pure calcite. The
data show that, for water far enough removed from saturation with
respect to solid phase carbonate, the effect of increasing the concen-
+ 2
tration of Mg in solution will be to increase the amount of carbonate
dissolved. However, as the saturation of the water is approached and
+2
exceeded, the effect of Mg in solution will be to decrease the solu-
bility or increase the precipitation of the carbonate. The initial
increase in solubility is ascribed to the formation of ion-pairs
involving Mg . As the water becomes saturated, the reduction in
carbonate solubility is due to the common ion effect of Mg which
swamps the ion-pair effect. Under field conditions, a soil containing
dolomite or a Mg-calcite will enhance the precipitation of carbonate
from the percolating water as the Mg ion concentration in the water
increases. This effect exists if the water is near saturation or
+2 +2
supersaturated with respect to the carbonate. Thus, Ca and Mg
will be removed reducing the hardness of the return flow water. If
the irrigation water is far removed from saturation, in terms of the
soil carbonate material, the presence of Mg will increase the solu-
bility of carbonate increasing the hardness of return flow water relative
to the irrigation water.
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SECTION II
RECOMMENDATIONS
The results of this study show the feasibility of modeling cation
transport through soils under saturated flow conditions which allows
prediction of the cation composition of irrigation return flow. In
principle, the same procedure is adequate to allow predictive model-
ing of any soluble component that is added to the soil; i. e. , herbicides,
fertilizers, industrial waste, etc. For example, the modeling of
phosphorous or nitrogen movement in soils would produce data valuable
to the development of pollution abatement programs.
Since this initial study necessarily involved only controlled laboratory
column studies, the full assessment of the model requires expansion
into a lysimeter or field study where less control is present and more
approximations are required as program inputs. Most normal field
conditions involve unsaturated moisture flow; therefore, extension of
the model to include unsaturated conditions is a necessary requirement
to cover all field situations. Evaluation of multi-cation exchange and
soil layering effects must also be included to give the model additional
flexibility.
The data from the carbonate solubility study has shown that predicting
the effect of irrigation on the total hardness of return flow is not a
simple procedure even in refined systems. Chemical data of both the
water and soil are required to ascertain whether a given water will
dissolve soil carbonate material or whether carbonate will precipitate
from a solution. A factor which must be evaluated is the limit of
solubility that exists for natural soil carbonates because the data have
shown that soil carbonates do not react in the same manner as pure car-
bonate minerals.
-------
An important aspect of the carbonate precipitation-water quality
research should be concerned with the plant growth effect on carbonate
precipitation or dissolution from irrigation water. This aspect should
involve plant studies in greenhouse or field lysimeters. The objective
should be to show the importance of the plant as a sink for water
(salt-concentrating agent) and a source of CO. in determining how,
where, and to what extent carbonate is dissolved or formed from
irrigation water. The coupling of chemical water quality data with
evapotranspiration and soil CO partial pressure data from the
dt
lysimeters will provide valuable information concerning the effect of
irrigation of crops on the total hardness of irrigation return flow.
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PART A
MODEL FOR
CATION TRANSPORT IN SOILS
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SECTION III
INTRODUCTION
Cation adsorption in the soil system is important not only because
the soil can be used to modify water quality with respect to the cation
composition, but also because it provides a basis for study of water
quality treatment with respect to other chemical species which can be
adsorbed by soils and other adsorbents.
The cation adsorption operation in resin beds was studied by Hiester
and Vermeulen (1952) who used second order kinetics to define the rate
of cation exchange. They did not consider the fluid dispersion effect.
The same problem was studied by Lapidus and Amundson (1952). They
assumed an infinite rate of cation exchange and described the exchange
reaction by a linear exchange isotherm. A comparative study of different
models of cation adsorption operation was reported by Biggar and
Nielsen (1963). Additional studies of the dispersive convective flow
through an adsorbent bed were reported by Brenner (1962), Hashimoto
et al. (1964) and Lindstrom et al. (1967). Analytical solutions of the
material balance equation in the above studies were obtained for cer-
tain restricted cases.
In natural soil systems, because of the heterogeneous nature of the
pore sequences and slow rate of water flow, the fluid dispersion effect
becomes significant and must be considered. In addition, most cation
exchange reactions that occur in soil systems do not exhibit linear
isotherms. These complications make the analytical solution of the
cation adsorption problem formidable.
Biggar et al. (1966) applied the finite plate concept and adopted the
computation method developed by Dutt and Tanji (1962) to compare
-------
their numerical computation with the experimental data. The success
of the finite plate method depends on the empirical evaluation of the
theoretical plate height, which approximates the effects of non-
equilibrium condition, fluid dispersion and other disturbances in the
column operation. Their study not only included the non-constant
separation factor, but also showed the potential of using the numerical
method in solving the cation saturation problem in soil columns.
In this study, the finite difference method was applied to the solution
of the material balance equation (MBE). The MBE described the
dispersive convection flow of the chemical solution and the general
adsorption function. The numerical solutions obtained for different
adsorption functions show the effect of adsorption on the flow of cations
through the adsorbent columns. For linear adsorption, the numerical
solution was compared to the analytical solution used by Lindstrom
et al. (1967). This comparison provides a measure of the accuracy
of the numerical solution. To show the applicability of the numerical
solution, column experiments were also conducted involving sodium
ion adsorption by Yolo loam soil.
10
-------
SECTION IV
THEORY AND APPLICATION OF MODEL.
The theoretical prediction of one -dimensional cation adsorption in
soil columns involved the solution of a material balance equation with
given initial and boundary conditions. For the exchange reaction
A+ + BR ^B+ + AR [1]
where A and B are counter ions (adsorbates), and R is the cation
exchanger (adsorbent), the material balance equation fo.r the cation
A is
p q
D - - V = + -- - [2]
o ^ 2 o -, *... >,.
O Z OZ Ot Ot
where C is the concentration of the absorbate A in solution, q is
-t\. ./*
the amount of the adsorbate A adsorbed per unit weight of the exchanger,
z is the depth of the soil column along the direction of the fluid flow,
e is the pore fraction, p is the bulk density, t is time, V is the pore
velocity and D is the dispersion coefficient. Defining X A = C /C
} o v A A o
and YA = q . /Q where C and Q are the total cation concentration in
A A o
solution and the total cation adsorption capacity, respectively,
Equation [2] is reduced to
d2x Sx ox PQ oY
D - f- - V - - = - + -- [3]
The variables X. and Y are the reduced concentration of the solution
A A
phase and the adsorbed phase, respectively. They are both functions
of z and t.
11
-------
In this study, it is assumed that equilibrium exists between the cation
in solution and the cation adsorbed on the exchanger phase. Thus, at
given temperature there is a unique function to relate Y to X , which
J\. A.
is called an adsorption function, or adsorption isotherm. We can
express Y . in terms of X.
^ A A
- f(X ) [4]
and
dt dX dt
XTL
[5]
Substituting Equation [5] into Equation [3] and dropping the subscript,
understanding that we are dealing with the adsorbate A , we have
[6]
where
D
D(X) =
1 + r f (X)
o
[7]
V
V(X) =
i + --f (X)
o
and f ' (X) =. Hashimoto et al. (1964) called the term 1 + -- f ' (X)
dX eC,
the retardation factor. The terms D(X) and V(X) are defined as the
apparent dispersion coefficient and the apparent pore velocity, respect-
ively. They are functions of X.
12
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The initial and boundary conditions for the cation saturation operation
are:
X(z, 0) = 0 0 < z < L
X(0,t) = 1.0 t >0 [8]
sr (L, t) = 0 t > 0
where L is the length of the column.
The solution of Equations [6] and [8] is obtained by the finite difference
method.
Numerical Solution of Model
The partial differential terms in Equation [6] are approximated by the
finite differences as follows:
d X X. , . - 2X. . + X. , .
_ i+l, J i, J i-l, 3
ciz
dt
Az
X. , . - X.
i+l, j i-l, j
2Az
x. . , - x. .
1, J+'l 1, J
At
D(X) =D(X. .)
l> J
V(X) =V(X. .
Az is the depth increment, At is the time increment, i is the subscript
for the depth increment and j is the subscript for the time increment.
[9]
13
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Substituting Equations [9] into Equation [6] and rearranging the terms
we obtain
X
= At
D(X. .
A,2
) V(X. .)
2Az
X . -
2D(X .)
i,3
Az
1
At
fD(X. .)
Az
- x. . +
[10]
v(x. .;
1,3
2Az
X.
The initial and the boundary conditions are:
Xi, 0 = C
X
X
1.0
[11]
where i = 1, 2, . . . N; j = 1, 2, . . . M. (N and M are the last
number of subscript i and j, respectively. ) A FORTRAN program was
written to perform the computation of the algorithm in Equations [10]
and [11]. The computation was done by a Univac 1108 digital computer.
The numerical result obtained approximated the solution X(z, t). The
values of Y(z, t) were computed from the values of X(z, t) through the
adsorption function, Equation [4].
The numerical solution of this scheme was found to be stable when
the grid network spacing was chosen so that
0 <
At
(Az)
When this was not met, numerical oscillation occurred.
14
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The application of the numerical method for solution of the MBE in-
volving cation adsorption is illustrated by solving example problems.
We will take one set of soil column parameters, as shown in Table 1,
and solve the equation with five different types of adsorption isotherms
and examine the behavior of the concentration functions of the solution
phase X(z, t) and that of the adsorbed phase Y(z, t), obtained from the
solution in form of cation concentration profiles.
Table 1. The Column Parameters
ITEM
Pore velocity, V
Dispersion coefficient, D
Bulk density, p
Pore fraction, e
Cation adsorption capacity, Q
Total cation concentration, C
o
Column length, L
Pore volume
Depth increment used
Time increment used
UNIT
cm/hr
2
cm /hr
, 3
g/cm
meq/g
/ 3
meq/cm
cm
ml
cm
hr
VALUE
1. 50
1.50
1. 30
0.45
0. 25
0. 10
30.00
612.50
0. 50
0. 10
The behavior of the adsorption functions depend mainly on (1) the
type of adsorbent, (2) the adsorbate involved, and (3) the total concen-
tration of the adsorbate. The five adsorption functions selected for
this study are shown in Figure 1. They can be represented by a general
equation:
Y= [12]
X + (l
15
-------
Figure 1. The five representative types of isotherms used in
the study.
16
-------
_
where a (X) is a function called the separation factor defined by
A Y X
A A -p
Helfferich (1962) as a - rp . It described the relative distribu-
B Y_ A
B A
tion of the adsorbates between the adsorbent and the solvent. The sep
aration factor is either a constant or a function of the composition X.
For the exchange functions of Type I, II and III, as shown in Figure 1,
the separation factors are constant and have a value equal to 10, 0. 1
and 1.0, respectively. For the exchange functions of Type IV and V,
p^
a (X) is a function of X and can be represented as
B
exp [inK + c(l-2X)]
where K is the thermodynamic equilibrium constant and c is a propor-
tionality constant which accounts for adsorbate interaction. This ad-
sorption function is referred to as the Kielland function (Helfferich,
1962). The value of K for Type IV and Type V adsorption functions is
arbitrarily set equal to 1. 0 and the value of c is -1.0 and -f-1. 2,
respectively.
The solution of the MBE, in terms of X(z,t) and Y(z,t) for each ad-
sorption function, is presented in Figures 2 through 6 as concentration
profiles with time as a parameter.
Isotherm Shape
The isotherms or part of the isotherm in Figure 1 can be classified
according to the value of the separation factor:
17
-------
1.0
.8
.6
.2
X
Y
t =
10
15
20
DEPTH cm
25
30
Figure 2. The cation concentration profiles X(z, t) and Y(z, t)
computed from the Type I isotherm.
18
-------
10 15
DEPTH cm
Figure 3. The cation concentration profiles X(z, t) and Y(z, t)
computed from the Type II isotherm.
19
-------
Numerical
Analytical
10 15 20
DEPTH cm
25
30
Figure 4. The cation concentration profiles X(z, t) and Y(z, t)
computed from the Type III isotherm by numerical
and analytical methods.
20
-------
1.0
.8
.6
b
X 4
.2
.0
t=10
10 15 20
DEPTH cm
25
30
Figure 5. The cation concentration profiles X(z, t) and Y(z, t)
computed from the Type IV isotherm.
21
-------
10 15
DEPTH cm
20
25
30
Figure 6. The cation concentration profiles X(z, t) and Y(z, t)
computed from the Type V isotherm.
22
-------
(1) Convex isotherm a > 1
D
Type I 0. < X< 1.0
Type IV 0. < X < 0. 5
Type V 0. 5 < X< 1.0
(2) Concave isotherm a < 1
Type II 0. < X< 1.0
Type IV 0. 5 < X< 1. 0
Type V 0. < X < 0. 5
(3) Linear isotherm a - 1
Type III 0. < X < 1.0
Convex Isotherm. The fixed-bed adsorption of cations that exhibit
convex isotherms is characterized by (1) sharp concentration profiles,
(2) an approximately steady state advancement of the profiles, and
(3) the adsorbed phase profiles preceding the solution phase profiles.
These properties are shown in Figure 2; in Figure 5, when 0 < X, Y
< 0. 5; and in Figure 6, when 0. 5 < X, Y < 1. 0.
Two factors affecting dispersion are (1) the nature of the pore se-
quences in the matrix (physical dispersion) and (2) the shape of the
adsorption isotherm. For a convex isotherm f ' (X) is a decreasing
function of X while V and D are increasing functions of X, thus,
dispersion is suppressed. When the two factors balance each other,
the advancing profiles reach a steady state and assume parallel
positions as shown in Figure 2.
The separation factor for convex isotherms is greater than unity
(a >l. 0) which favors cation adsorption. Thus, the profile of the
B
23
-------
adsorbed phase advances ahead of the solution phase profile. This
operation is efficient in the removal of the adsorbate from the solvent.
Concave Isotherm. Fixed-bed cation adsorption described by a concave
isotherm is characterized by (1) increasingly diffused concentration
profiles, and (2) the lagging of the adsorbed phase profile behind the
solution phase profile. These features are shown in Figure 3; in
Figure 5 when 0. 5 < X, Y < 1. 0; and in Figure 6 when 0 < X, Y < 0. 5.
The f' (X) of a concave isotherm is an increasing function of X, and
V and D are decreasing functions of X. The result is an increase in the
spreading of the adsorbate along the direction of flow in addition to
physical dispersion. Rachinskii (1965) concluded that the dispersion
of the profiles due to the concavity of the isotherm is proportional to
1/2
t, while that due to physical dispersion is proportional to t . The
concavity of the isotherm is an important cause of dispersion as seen
by comparing Figure 3 with Figure 4. The latter figure only involves
A
physical dispersion. Since or,, < 1, the adsorption of the cation from
15
solution is not favored. Hence, the solution phase profile precedes
the adsorbed phase profile. The adsorption of Na in the Ca-soil
system is an example of this case. Experimental data are presented
later (Section VI).
Linear Isotherm. The linear isotherm is intermediate between the
convex and concave isotherms. Figure 4 shows the concentration
profiles for the linear isotherm case. Profile characteristics are:
(1) the dispersion of the profiles increase with time, and (2) the ad-
sorbed phase and solution phase profiles are identical.
The values of D and V are constant in a linear isotherm system, hence,
the solution of the MBE is the same as that involving nonadsorbed
24
-------
chemical species. However, the profile advancement, compared to that
of a nonadsorbed species is reduced by the retardation factor. Because
a = 1, there is an equal distribution of the adsorbate between phases.
B
Verification of the Numerical Solution
The numerical solution of the MBE was checked for accuracy, in the
linear isotherm case, by comparison with the analytical solution. The
analytical solution used was reported by Lindstrom et al. (1967) as:
C/C =1/2
'2
V
D
erfc
f D
f
V
I
r
z-Vt
Vt + z
ex]
4V2t '
3
DTT
1
zV
D
1/2
ex
erfc
P -
zH
z-Vt
1(4Dt)1/
-Vt 1
(4Dt)1/2/J
'2
[14]
The analytical and numerical solutions are shown in Figure 4. The
discrepancy between the two solutions of the MBE was less than 10
percent for all profiles. The accuracy of the numerical solution for
the other isotherm types should be comparable to that of the linear
case, although the concave isotherm may be more prone to numerical
error.
The error related to the numerical solution of the MBE is referred to
as "numerical dispersion" (Bredehoeft, 1971; Oster et al. , 1970;
Pinder and Copper, 1970). This error is largest when the pore velocity
is high. The discrepancy between the numerical and analytical solution
shown in Figure 4 is independent of time. The error is well confined
and is believed to originate during the early stages of computation when
the boundary singularity exists. During diffusive, convective flow
involving adsorption, the apparent pore velocity and apparent dispersion
25
-------
coefficient are both reduced by the retardation factor. This makes the
numerical scheme less vulnerable to numerical dispersion (Oster,
1971).
26
-------
SECTION V
MATERIALS AND METHODS
The columns used in this study consisted of eleven lucite rings, with
an inside diameter of 7. 6 cm, separated by rubter gaskets and joined
together with three threaded brass bars. The effluent end of the column
contained a porous plate inbedded in a lucite plate with an outlet at
the center.
The column was packed uniformly with soil to a depth of about 24 cm.
It was initially saturated with a 0. 1 _N_ CaCl_ solution until it reached
steady state with respect to the Ca ion. The miscible displacement
was conducted by adding 0. 1 N MgCl or 0. 1 N NaCl exchanging
L* ~~~~
solution. When a predetermined amount of the exchanging cation
solution had been added to the column, the flow was terminated and
the column sectioned into eleven portions. The soil solution in each
section was extracted and the soil air dried. The cations in the
extracts, and the exchangeable cations of the soil were determined
for each section.
The average interstitial flow velocity was used since only a slight
change of the flow rate was detected throughout the experiment. The
fluid dispersion coefficient was determined for each column before the
miscible displacement experiment by obtaining the chloride breakthrough
curve and applying the equation of Rifai et al. (1956) to calculate the
D/V ratio
D/V = \~^ [15]
4TTV ^S *
o o
27
-------
where L is the length of the column, V is the effluent volume at the
o
chloride concentration C/C = 0. 5, which is also the apparent pore
volume used in the study, and S is the slope of the breakthrough
curve at C/C = 0. 5. The column parameters for the experiments
are presented in Tables 2 and 3.
The exchange isotherm was obtained by plotting the normalized
concentration in the solution X against the normalized concentration
in the adsorbed phase Y obtained from each section of the column.
The exchange function was then obtained by fitting the experimental
value of X and Y into the Equatiqns [12] and [13].
The soils used in this study were Yolo loam and Hanford sandy loam
from California and Nibley clay loam from Utah. Three column
experiments, using different total volumes of miscible displacing
solution, were conducted with each' soil.
28
-------
tSJ
Table 2. The Column and Soil Parameters for Miscible Displacement Studies Involving Magnesium
Adsorption
Items
Flow velocity, V
Dispersion coefficient, D
Bulk density, p
Pore fraction,
Cation exchange capacity, Q
Total concentration, C
o
Column length, L
Total time, t
Pore volume, V
o
Total input volume
Total input volume (pore
Unit
cm/hr
cm /hr
g/cm
me/g
me /ml
cm
hr
ml
ml
volume)
Yolo Loam
Column
I
3. 936
1. 875
1. 284
0. 406
0.257
0. 105
24.7
14
455
1015
2.231
II
4.
2.
1.
0.
0.
0.
24
25
712
245
295
406
262
104
.7
455
21
4.
70
770
III
3. 688
1. 757
1.303
0.441
' 0. 274
0. 105
23. 6
40
472
2950
6. 248
Nibley Clay Loam Hanford Sandy Loam
Column Column
I
1. 043
1.268
1.332
0.446
0. 266
0. 107
23.5
20
475
430
0. 905
II
1.227
1.492
1. 332
0.446
0. 285
0. Ill
23.5
50
475
1240
2. 611
III
1. 974
1.471
1. 307
0.467
0. 308
0. Ill
23. 6
50
500
2090
4. 180
I
1.284
0, 316
1. 602
0. 358
0.057
0. 108
24. 0
15
390
313
0.803
II
1. 302
0. 327
1. 604
0. 351
0. 059
0. 108
24. 5
30
390
622
1.595.
Ill
1.452
0.481
1. 591
0. 378
0. 068
0. 107
22.6
43
388
1072
2. 763
-------
Table 3. The Basic Column and Soil Parameters for Miscible Displace-
ment Studies Involving Sodium Adsorption
Soil: Yolo Loam
Items
Pore velocity, V
Dispersion coefficient, D
Bulk density, p
Pore fraction, e
Cation adsorption capacity, Q
Total concentration, C
o
Column length, L
Total time, t
Pore volume
Total input volume
Total input volume
Unit
cm/hr
2
cm /hr
g/cm
meq/g
meq/ml
cm
hr
ml
ml
(pore volume)
1
7. 373
0.950
1.306
0.470
0.248
0. 106
23.0
4.0
490.0
628. 3
1.282
Column
2
3. 732
0.286
1.312
0.491
0. 250
0. 105
23. 1
10.0
515.0
832.0
1.616
3
5. 343
0.797
1.302
0.460
0.241
0. 105
23.0
10.0
480.0
1121.4
2.336
30
-------
SECTION VI
RESULTS AND DISCUSSION
Comparison of the Linear and the Nonlinear Models
The model of Lapidus and Amundson, which expressed the cation ex-
change isotherm as a linear function, i. e., Y = a + bx, is compared
to the nonlinear model in which the cation exchange function is expressed
by the nonlinear modified Kielland function, Equation [13], The pre-
dictions obtained from the two methods were compared to the experi-
mental data obtained from the soil columns.
The cation exchange isotherm of the Mg -*Ca exchange for Yolo loam
soil is presented in Figure 7. The broken line represents the linear
regression line of the experimental data in the form of Y = a + bx with
the value of a and b equal to . 04 and . 92, respectively. The solid
line represents the modified Kielland function expressed in Equations
[12] and [13] with InK and c equal to . 0855 and -. 475, respectively.
The results of the numerical computation for the value of X(z,t)
obtained from these two methods are presented as concentration pro-
files in Figure 8, along with the experimental results. The values
of Y(z,t) were obtained from the exchange functions using the computed
values of X(z, t). These results are presented in Figure 9, together
with the experimental results.
Figure 8 shows that the values computed from the nonlinear exchange
function agree with the experimental data better than those computed
from the linear function. This is particularly true in the higher con-
centration region where 0. 4 < X < 1.0. The exchange isotherm, in
Figure 7, also shows that the nonlinear form of the isotherm represents
31
-------
Experimental data ,
0.2 0.4 0.6 0.8 1-0
0.0
Figure 7. The normalized cation exchange isotherm of the Mg -» Ca
exchange for Yolo loam soil. The broken line is the
linear regression line. The solid line is the modified
Kielland function.
32
-------
10 15
Depth (cm)
20
25
Figure 8. The normalized concentration profiles of the solution phase
for the three Yolo loam columns, including both experimental
and theoretical values calculated from the linear exchange
function (broken lines), and from the modified Kielland
function (solid lines).
33
-------
0
10 15 20
Depth (cm)
Figure 9. The normalized concentration profiles of the adsorbed
phase for three Yolo loam columns, including both
experimental and theoretical values calculated from the
linear exchange function (broken lines), and from the
modified Kielland function (solid lines).
34
-------
the experimental values more closely than the linear form. The non-
linear fit is superior not only in the actual position of the isotherm
but also in the shape of the isotherm. It is emphasized that in the
theoretical computation, the slope of the isotherm f ' (X) is involved
in the evaluation of g (X. .), see Section IV, thus both the position
l> J
and the shape of the isotherm are important in obtaining the theore-
tical solution. Biggar and Nielsen (1963) concluded that one of the
reasons for the disagreement of the Lapidus and Amundson model
with experimental data could be due to an inadequate description of
the exchange function. This study gives evidence to support their
conclusion. The cation exchange theory dictates that the isotherm
must pass through the two points having the X and Y coordinates of
(0, 0) and (1,1). Only one straight line exists between these two
points, thus the linear isotherm is the line Y = X.
The linear isotherm may be expected in the situation where the soil
exhibits no preference for either of the cations involved in exchange,
e. g. , isotopic cation exchange. Another case may be when only a
trace of cation is introduced into the column and only a small portion
of the isotherm is involved in the computations, and a linear approx-
imation of this portion of the isotherm may be adequate. It is expected,
however, that nonlinear isotherms are normal in soil systems.
Results shown in Figure 9 also indicate that the Y(z,t) profiles compu-
ted with the nonlinear function agree with the experimental value better
than the ones calculated with the linear function. From the linear
exchange function the calculated value of Y varies between 0, 04 and
. 96 when X varies between 0. 0 and 1. 0. Thus, according to the linear
isotherm, the column can nev(
This is theoretically unsound.
isotherm, the column can never be saturated with either Mg or Ca
35
-------
Application of the Nonlinear Model to Mg ->Ca Exchange
The nonlinear method was ^Iso applied to the Mg -*Ca exchange for
Nibley clay loam and Hanford sandy loam. The Mg -* Ca cation ex-
change isotherms for the Nibley clay loam and the Hanford sandy loam
are presented in Figures 10 and 11, respectively. The experimental
data were fitted into the modified Kielland function with the values of
InK and c equal to . 4048 and -. 92, respectively, for the Nibley clay
and equal to .377 and -.725, respectively, for the Hanford sandy
loam. The normalized concentration profiles for the solution phase
X(z, t) and for the adsorbed phase Y(z, t) are presented in Figures 12
and 13, respectively, for the Nibley clay loam. The same data, for
Hanford sandy loam, are presented in Figures 14 and 15.
Figures 12 and 15 show that the agreement between the experimental
results and the theoretical computation is good both in the position and
shape of the profiles. However, a slight discrepancy was noted between
the experimental values and the computed values at the advancing front
of the profiles. This difference tended to increase with time. Discuss-
ion of i;hese data will be presented later.
Figure 11 shows that the Mg -»Ca exchange isotherm for Hanford
sandy loam at a total concentration of 0. 1 _N is nonlinear. The separa-
A
tion factor, a , is a function of the ionic composition. The modified
B
Kielland function closely represents the isotherm, except in the higher
concentration range.
Figure 14 shows that the agreement between the experimental and the
theoretical profiles is reasonable for the first two columns. For the
third column, the agreement is fair with respect to both the actual
position and the shape of the profiles. Similar observation can be
36
-------
1.0
0.8
0.6
0.4
0.2
0
0
n Experimental data
0.2 0.4 0.6
0.8
1.0
Figure 10. The normalized cation exchange isotherm of the
Mg -»Ca exchange for Nibley clay loam soil with
the modified Kielland function shown by the solid
line.
37
-------
1.0
0.8
0.6
0.4
0.2
Experimental data
0.2 0.4 0.6 0.8 1.0
Figure 11. The normalized cation exchange isotherm of the
Mg -« Ca exchange for Hanford sandy loam soil with
the modified Kielland function shown by the solid
line.
38
-------
10 15
Depth (cm)
20
25
Figure 12. The normalized concentration profiles of the solution
phase for three Nibley clay loam columns. The exper-
imental values are represented by the points and the
theoretically computed values by the lines.
39
-------
1.0
>r05
10 15 20
Depth (cm)
25
Figure 13. The normalized concentration profiles of the adsorbed
phase for three Nibley clay loam columns. The exper-
imental values are represented by the points and the
theoretically computed values by the lines.
40
-------
0
10 15
Depth (cm)
20
25
Figure 14. The normalized concentration profiles of the solution
phase for three Hanford sandy loam columns. The
experimental values are represented by the points
and the theoretically computed values by the lines.
41
-------
0
10 15
Depth (cm)
20
25
Figure 15. The normalized concentration profiles of the adsorbed
phase for three Hanford sandy loam columns. The
experimental values are represented by the points and
the theoretically computed values by the lines.
42
-------
made for the adsorbed phase profiles in Figure 15. The advanced front
of the experimental profiles, the low concentration range, is more
diffused than theoretically computed. This phenomenon, though less
severe, was also observed in the Yolo and Nibley columns. At least
two factors can contribute to this situation: (1) a non-equilibrium
process between the solution phase and the exchanger phase during
miscible displacement, (2) a change in the fluid dispersion during the
cation displacement process. In the model developed, fluid dispersion
is assumed constant and equal to the value determined by chloride
displacement.
The second-order kinetics of cation exchange as expressed by Hiester
and Vermuelen (1952) is
dS
- k[CA (Q-SA) - SA(Co-CA)] [16]
where k is the rate constant for adsorption, K is the exchange constant
for the reaction, S is the amount of cation adsorbed per unit mass of
A.
exchanger and C is the concentration of the exchanging cation solution.
.A.
The remaining variables have been defined earlier. At low concentrations
where S and C are small, Equation [16] can be approximated by
J\ J\
dS
-zr = kCAQ
dt A
Thus, the rate of cation exchange is a function of both the concentration
of the exchanging cation, C , and the cation exchange capacity, Q, of
.A.
the soil. Both Yolo loam and Nibley clay loam have Q values of about
25 me/lOOg while Hanford sandy loam has a Q value of about 6 me/lOOg.
Comparison of these data allows the conclusion to be made that, at a
43
-------
given value of C and k, the rate of exchange in he Hanford soil is
A.
significantly slower than in the other soils studied. Thus, the assump-
tion of equilibrium conditions in the Hanford soil probably has a lower
degree of validity than in the other soils. The study of Biggar and
Nielsen. (1963) using Oakley sand, with a Q value of 3. 75 me/100 g,
tends to corroborate the above conclusion. They showed that by
varying the flow velocity from 1. 77 cm/hr to 0. 194 cm/hr the dis-
crepancy between their experimental values and those predicted by
the model of Lapidus and Amundson was significantly reduced in the
region of C/C = 0. 5. The slower flow rate allowed equilibrium to be
o
more closely approximated, hence, compensating for the low Q value
of their soil. Thus, at low concentrations of the exchanging cation,
exchange equilibrium depends on both the flow velocity of the displace-
ment process and the Q value (CEC) of the soil.
Although the value of the dispersion coefficient is assumed invariant
during a miscible displacement experiment, the possibility exists that
the value does vary. However, the degree of variation, if it does occur,
is difficult to assess. The measurement of the dispersion coefficient
before and after miscible displacement may provide an estimate of the
degree of variability.
Application of the Nonlinear Model to Na -* Ca Exchange
The nonlinear model was applied to the heterovalent system involving
Na -» Ca exchange. The soil used in the column study was Yolo loam.
The experimental isotherm is given in Figure 16 and is classified as
a Type II isotherm (See Figure 1). It was found that the general non-
linear exchange function expressed in Equation [12] did not describe
the curve adequately. The function was modified, as shown by Lai
44
-------
1.0
.8
.6
.4
.2
.0
Experimental data
Figure 16. The reduced Na adsorption isotherm in Yolo loam
soil. The solid line is represented by Equation [17].
45
-------
(1970), to yield an exchange function which is written
v
Y = Cl 71
X + (1-X) [k1 + C(1-2X)] L J
where k1 and C were found to be 8. 0 and -4. 0, respectively, for the
Na -» Ca exchange. The modified exchange function is plotted as a
solid line in Figure 16. The modification fit the data reasonably
well. The modified exchange equation was used in solving the material
balance equation. The numerical solution of the material balance
equation along with the experimental data from three column experi-
ments are given in terms of X(z, t) and Y(z, t) in Figures 17 and 18,
respectively.
The sharp drop of the reduced concentration X at the profile front
(Figure 17) predicted by theory was not obtained experimentally. This
can be ascribed to the possibility that actual equilibrium was not
reached throughout the column, thus, the cation was allowed to travel
further down the soil column before it reached equilibrium with the ex-
changer phase. The result is a flatter profile at the advancing front
of the soil solution.
The deviation from theory of the reduced concentration in the exchanger
phase, Y(z,t) as shown in Figure 18, is not as marked. The reason
is that at low concentrations of Na in the percolating water, Y values
are relatively low and change less with X.
In the column studies, it was noted that the flow velocity decreased as
the amount of Na ion solution introduced in the column increased.
In the theoretical computation.an overall average flow velocity was
used. Hence, some of the deviation noted, in both Figures 17 and 18,
46
-------
1.0
.8
.6
Columns
o 1
2 Experimental Data
3
Numerical Results
10 15
DEPTH cm
20
25
Figure 17. The concentration profiles X (z, t) for the three
column experiments.
47
-------
Columns
o 1
2 Experimental Data
* 3
Numerical Results
25
Figure 18. The concentration profiles Y (z, t) for the three
column experiments.
48
-------
from theory may be attributed to this factor. For the heterovalent
system, the model developed in this study allowed reasonable pre-
diction of cation transport.
49
-------
PART B
MAGNESIUM ION EFFECT
ON CARBONATE SOLUBILITY
51
-------
SECTION VII
INTRODUCTION
The application of irrigation water to a soil can.result in either the
precipitation of carbonates from the water or the dissolution of
existing carbonate material in the soil matrix by the water. Either
of these reactions has a direct influence on the quality of water
returning to the stream. The solution of calcium and magnesium
carbonates not only affects the total salt load in the return flow, but
also adds to the total hardness of the water. Eldridge (i960) considers,
from the viewpoint of industrial and municipal pollution, the increase
in water hardness to be the most important single adverse effect con-
tributed by irrigation return flow to downstream use.
From agronomic considerations, carbonate precipitation, while re-
ducing the total salt load of the water, increases the sodium hazard
+2 +2
of return flow water by reducing the concentrations of Ca and Mg
ions in relation to the Na ion, Eaton (1950) was one of the first to
recognize the potential hazard and introduced the concept of residual
sodium carbonate. This was an attempt to estimate the sodium hazard
of the waters by assuming that all Ca and Mg ions precipitate in
-2
the presence of excess HCO and CO, ions. Recent studies
(Bower, Ogata, and Tucker, 1968; Doner and Pratt, 1969) have placed
more emphasis on the pertinent chemistry of calcium and magnesium
carbonate systems and how it relates to carbonate precipitation from
irrigation waters.
+2 +2
The effect of Mg ion is of particular interest since both Ca and
+2
Mg are usually linearly combined in predictive precipitation equations
(Eaton, 1970; Bower et al. , 1968) whereas, their chemistry is not
necessarily similar.
53
-------
Daviea (1962), Garrels and Christ (1965), and Nakayama (1968) have
shown that Mg and Ca ions readily form ion-pairs. The effect
of ion-pair formation on a CaCO solution is to increase the amount
of CaCO which will dissolve and to decrease the amount which will
precipitate as compared to a system without ion-pairs. The thermo-
dynamic solubility product constant for CaCO is still valid, but
increasing CaCO must dissolve to maintain a constant value for
the ion activity product. While ion-pairs involving Ca , HCO ,
and OH ions exist for waters in the absence of Mg ion, the addition
+2
of Mg ion results in increased ion-pair formation and, hence,
increased solubility of CaCO . In addition to Mg ion-pairs, the Mg
ion may also affect CaCO precipitation by inhibiting calcite nucleation.
The formation of a precipitate may be considered to consist of two
distinct processes, nucleation and crystal growth. The fact that
supersaturated solutions exist for definite periods of time suggests
that the process of initiating precipitation (nucleation) differs from
the process of continuing precipitation (crystal growth). Fisher (1962)
states that the distinction between the two reactions results from the
fact that in crystal growth the driving force is the difference in free
energy between the ions in the crystal lattice and the hydrated ions in
solution, while in nucleation no lattice and, hence, no lattice energy
exists.
+2
The effect of Mg ion on CaCO nucleation was first recognized by
L/eitmeier (1968) who found that Mg ion favored the precipitation of
aragonite over calcite (Bischoff, 1968). Doner and Pratt (1969) found
the CaCO precipitated and Mg was coprecipitated in the solid phase.
A
Bischoff (1968) showed that Mg ion inhibited the diagenetic aragonite
to calcite transformation by reacting with the calcite nuclei. He
54
-------
+2
postulated that the strongly hydrated Mg ion reduced the rate of
growth of calcite nuclei because of the rate-controlling dehydration
+2
of the Mg ion. After dehydration, however, the calcite lattice
+2
preferentially accepts the smaller Mg ion. The inhibition to
crystal transformation is overcome when sufficient calcite nuclei
+2
are present to reduce Mg ion concentration to a level at which new
+2
nuclei can form which do not contain Mg ion.
The Mg ion can also affect carbonate equilibrium by interacting with
the solid phase. Akin and Lagerwerff (1965) reported enhanced solu-
bility of CaCO precipitating from supersaturated solutions in the
presence of Mg and SO ions. They developed a theory of en-
hanced carbonate solubility based on the surface adsorption of Mg
and SO ions, and the constituent-ions of CaCO on the crystal
surface.
Weyl (1961) found that the slow kinetics of calcite dissolution in the
+2 +2
presence of Ca and Mg ions could not be explained by ion-pair
formation and concluded that the rate inhibiting mechanism was at the
solid-liquid interface. Chave and Schmalz (1966) found, using pH-
sensing techniques, that three factors (mineralogy, grain size, and
character) involving the solid phase controlled the interaction of the
carbonate crystal with the associated waters. They also found the
activities of magnesium calcites were four times greater than pure
calcite and that particles of calcite 10 cm in diameter have activities
more than eight times greater than 1 cm particles.
This report represents the results of a study to define the role of Mg
ion in the precipitation and dissolution of carbonates in systems which
contain excess solid carbonate.
55
-------
SECTION. VIII
MATERIALS AND METHODS
The studies consisted of equilibration of four series of artificial waters
(see Table 4) with four solid carbonates and the determination of the
amount of carbonate which dissolved or precipitated. Waters 1, 2, and
3 are undersaturated with respect to CaCO , while water 4 is super-
+2
saturated. The waters within each series were at constant Ca and
+2
HCO concentration, constant ionic strength, but varied in Mg ion
-3
concentration from 0 to 2 x 10 M. The waters were made from appro-
priate mixtures of NaCl, NaHCO , CaCl~, and MgCl_ solutions. Two
liters of each water were prepared fresh for each replication. It was
found that water 4, the supersaturated water, was stable for a period
of up to 48 hours. This stability or lack of precipitation is a function
of how supersaturated a water is, the greater the supersaturation the
shorter the period of time before nucleation occurs (Pytkowicz, 1965).
The four solid carbonate materials were: Mallinckrodt reagent grade
CaCO , lot TEJ (T), Purecal U (U) from the Wyandotte Chemical
Corp. , Millville loam soil, and Portneuf siltloam soil. T and U were
shown by X-ray diffraction techniques to be calcite. Surface area
measurements using stearic acid adsorption after the method of Suito
et al. (1955) showed T to have a surface area of ~0. 8 m /g and U to
have a surface area of -13. 5 m /g.
Millville soil is a highly calcareous soil (-45% CaCO equivalent) from
Northeastern Utah. X-ray diffraction showed the calcareous material
to be predominantly dolomite with a small amount of calcite present.
Portneuf is a calcareous loess soil (20% CaCO equivalent) from the
Snake River Valley in Southwestern Idaho. X-ray diffraction showed
57
-------
Table 4. Composition of the Four Waters Used in the "Carbonate
Saturometer. " Ionic Strength for all Waters was, I = . 05
Waters
1. a
b
c
d
e
f
2. a,
b
c
d
e
f
'
3. a
b
c
d
e
{
4. a
b
c
d
e
f
Ca+2
5.x 10"4
5 x 10~4
5 x 10"4
5 x 10"4
_4
5x10
5 x 10"4
-4
5x10
5xlO"4
-4
5 x 10
-4
5 x 10
_4
5 x 10
_4
5x10
_3
1x10
_3
1x10
_3
1 x 10
-3
1 x 10
_3
1x10
_3
1x10
_3
2 x 10
_3
2 x 10
-3
2 x 10
-3
2 x 10
-3
2 x 10
-3
2 x 10
HC03"
5 x 10"
5 x 10"4
5xlO"4
5 x 10"4
-4
5x10
5 x 10"4
-3
1 x 10
1 x 10"3
_3
1 x 10
-3
1 x 10
-3
1 x 10
-3
1 x 10
_3
1 x 10
_3
1x10
_3
1 x 10
j
1 x 10"
_3
1 x 10
_3
1 x 10
_3
2x 10
-3
2 x 10
-3
2x10
-3
2 x 10
_3
2x10
-3
2 x 10
Mg+2
0
5 x 10"5
2. 5 x 10"4
5 x 10"4
-3
1 x 10
2 x 10"3
0
5 x 10"5
-4
2. 5 x 10
-4
5x10
-3
1 x 10
_3
2 x 10
0
_5
5x10
_4
2. 5 x 10
-4
5x10
-3
1x10
_3
2x10
0
-5
5x10
-4
2.5 x 10
-4
5 x 10
-3
1 x 10
_3
2 x 10
58
-------
the calcareous material to contain about equal amounts of calcite and
dolomite. Approximately 0. 25 g of CaCO or 1 g of soil was equilibrated
with 100 ml of solution. Equilibrium was determined when a constant
pH value was obtained.
59
-------
SECTION DC
THE CARBONATE SATUROMETER
Any determination of carbonate solubility is complicated by the number
of system variables which cannot be experimentally measured.
Attempts to use the thermodynamic-derived constants for various
equilibria require that corrections be made for ion-pair formation,
the ionic strength and the deviation of the solid phase from its standard
state of unit activity.
To overcome these difficulties the "carbonate saturometer" method,
as developed by Weyl (1961) was used to measure carbonate solubility.
This method is based upon the fact that the pH of a solution changes
-2
when the CO ion is added or removed from solution. The reactions
involved are:
HC03" - H+ + C03~2 [1]
Ca+2 + C03"2 - CaC03 (s) [2]
Ca+2 + HCO " - H+ 4 CaCO (s) [3]
If the water is undersaturated with respect to a solid carbonate, the
-2 +
carbonate dissolves, yielding CO ions which combine with H ions,
thereby increasing the pH of the solution. If the water is supersaturated
with respect to a solid carbonate, the carbonate precipitates, HCO,
ions dissociate, the pH decreases. If the water is saturated with re-
spect to a. solid carbonate, the pH of the suspension remains the same.
The "carbonate saturometer" is calibrated for each water by comparing
the amounts of strong acid (+Z) or base (-Z) required to produce the
61
-------
same ApH as was produced by a standard addition of y1 moles of
bicarbonate. The calibration results in:
F(x) = -Z/y1 [4]
where F(x) is a function of apparent equilibrium constants, the hydro-
gen ion activity, and can be shown (Garrels and Christ, 1965) to be
equal to:
1 + 2K '/x
where x is the hydrogen ion activity, K ' and K ' are apparent equili
brium constants defined as:
x(HC03")
(H2C03) + (C02)
x(CO ~2)
(HC03~)
where the parentheses represent concentrations of the various ionic
species. Once this function is determined, the amount of carbonate y
precipitated can be calculated from:
-y = Z/[l - F(x)] [8]
where Z is the amount of strong acid (+Z) or base (- Z) required to
produce the same ApH as resulted upon equilibration of the water with
the solid carbonate. Approximately 0. 001 _N_ NaOH and HC1 is used to
calibrate the waters.
62
-------
A Heath pH recording electrometer Model EU-301-A was used to obtain
the necessary ApH measurements. The accuracy of the instrument was
found to be better than 0. 5% full scale (less than 0. 01 pH on a recorder
span of 2 pH units). All measurements were made in a reaction vessel
(Figure 19) using a calomel reference electrode and a Corning glass
electrode system. The equilibrium pH data were obtained at room
temperature (22 C) with the water at equilibrium with atmospheric
CO .
63
-------
Air hole -
Electrodes
Access hole
Figure 19. Reaction vessel of carbonate saturometer.
64
-------
SECTION X
EXPERIMENTAL TECHNIQUE
The description of the experimental method using the carbonate satur-
ometer is given. A 100 ml sample of a given water is pipetted into
the reaction vessel (see Figure 19) and aerated until a constant pH is
reached. The atmosphere above the water is flushed with N_ gas and
Ci
a slight positive pressure gradient of N between the reaction vessel and
o
the atmosphere is established. The water is titrated by adding 0. 25 ml
_3
increments of approximately 2x10 _N NaOH or HC1. The pH resulting
from the addition of each increment is recorded. The titration curve
which results is plotted as equivalents per liter vs pH.
A 100 ml subsample is taken from the same water sample and placed
into the reaction vessel and aerated to constant pH. As aeration is
_2
continued, 0. 5 ml increments of 1. 0 x 10 M NaHCO is added to
samples which are undersaturated with respect to calcium carbonate
or 0. 5 ml increments of 1. 0 x 10 M NaHCO is added to samples
which are supersaturated with calcium carbonate. The pH is allowed
to stabilize between additions of the NaHCO solutions. From the
initial acid or base titration curve the equivalents of titer required to
produce the same pH value that resulted from the addition of each
increment of bicarbonate is determined. From Equation [4], F(x) is
calculated for the water.
Another 100 ml subsample of water is taken and aerated to constant
pH. An excess (1-2 grams) of solid CaCO is added and the system
aerated to constant pH. From the initial acid or base titration data
the equivalents of titer required to produce the same pH value which
resulted from the addition of solid CaCO is determined. The amount
65
-------
of carbonate precipitated or dissolved, -y or + y, respectively, is then
calculated using Equation [8].
66
-------
SECTION XI
RESULTS AND DISCUSSION
The results of the "carbonate saturometer" studies are given in
Figures 20 to 23. The dissolution of solid carbonate in each water
+2
is plotted against the molar concentration of Mg in the water. Pos-
itive values of Y are obtained when carbonate dissolves in the water,
and negative values of Y indicate precipitation of carbonate. Each
data point is the average of at least three replications. The lines
drawn and the equations given are the result of linear regression
analysis.
Figure 20 shows the data obtained when calcite T was equilibrated with
the four waters. In all waters except water 3, the solubility of calcite
+2
increased as the Mg ion concentration increased. The effect of
+2
Mg in water 3 indicated no change or a slight decrease in solubility.
The general trend in carbonate solubility can be ascribed to increased
+2
ion-pair formation promoted by Mg , although the modified lattice
concept of calcite solubility as proposed by Akin and Lagerwerff (1965)
cannot be precluded. Where precipitation occurred (water 4) the in-
crease in carbonate solubility corroborates the findings of Dorter and
Pratt (1969).
Figure 21 shows the same study using calcite U as the solid phase. It
is noted that the solubility of calcite U (13. 5 m /g) is generally higher
in all waters than the solubility of calcite T (0. 8 m /g). These data
show the effect of surface area on calcite solubility and suggest the
possibility that calcite U is in a metastable phase. This supports the
conclusion of Chave and Schmalz (1966) who related carbonate solu-
bility with particle size. The solubility of calcite U, when equilibrated
67
-------
O
UJ
UJ
K
(L
§-'
^-2
8 -3
Q J
"
9 ,
x -4
CO
UJ
25
WATER ! Y = 1.38+.0019X
WATER 2A Y=1.27*.0016X
WATER 3A Y-0.59-.0004X
WATER 40 Y= -5.1 + .0091X
100
MffxlO!
200
Figure 20. Amount of carbonate dissolved or precipitated upon
equilibration of reagent grade calcite (T) with waters
+2
containing variable amounts of Mg , in moles.
68
-------
>
WATER
WATER.
WATER 3 A
WATER 40
Y=1.74+.0023X
Y=1.29-.0002X
V=-4.0-.C»16X
Figure 21, Amount of carbonate dissolved or precipitated upon
equilibration of Purecal U (U) with waters containing
+2
variable amounts of Mg , in moles.
69
-------
-
Q
UJ
WATER 1 Y=1.41+.0013X
WATER 2 A Y=1.43-.0007X
WATER 3 A Y-0.89-.0021X
WATER 4 0 Yc -.75-.0012X
25
100 .
M.xKT
200
Figure 22. Amount of carbonate dissolved or precipitated upon
equilibration of Portneuf soil with waters containing
variable amounts of Mg , in moles.
70
-------
WATER 1
WATER 2 A
WATER 3 A
WATER 4 0
Y=5.27t.0081X
Y=2.85-.0069X
Yc 145-.0054X
Y-0.67-.0437X
25
100
MgxlO!
200
Figure 23. Amount of carbonate dissolved or precipitated upon
equilibration of Millville soil with waters containing
variable amounts of Mg , in moles.
71
-------
with under saturated waters, followed.the same pattern as did calcite T.
However, when calcite U was equilibrated with supersaturated water
+2
4, Mg ' had no apparent effect on its solubility. The slight negative
slope of the regression line is not considered significant. Thus, the
type of calcite used in this study appears to affect its relationship with
Mg . The major difference found between the two calcite sources
is that the specific area of calcite U is 17 times greater than the
specific area of calcite T. This difference is reflected in the fact
+2
that the solubility of U is greater than T in water 4, when no Mg is
present. The data from the supersaturated system (Figure 21, water
4) suggest that, in the presence of an excessive number of possible
nucleation sites, the precipitation of carbonate effectively removed
Mg from solution and incorporated it into the newly formed carbonate
that had a Ca/Mg mole ratio of sufficient magnitude to stabilize the
solubility of calcite U (Doner and Pratt, 1969). The relatively high
+2
concentration of Ca in this system strengthens the possibility of
maintaining a high Ca/Mg mole ratio in the precipitated phase. The
+2
removal of Mg from solution also nullifies its ion-pair formation
capabilities. This study infers that increasing the amount of nucleating
surface essentially acts as a dilutent for Mg and is a factor in deter-
mining the solubility of CaCO precipitated from solution.
Figures 22 and 23 show how Mg ion concentration in water varies the
carbonate solubility in two calcareous soils. The Portneuf soil contains
about equal amounts of dolomite and calcite, while the Millville soil
is predominantly dolomite. When the soils were equilibrated with
water 1, they behave similar to the calcite material T and U, i. e. ,
+2
the presence of Mg increased the dissolution of solid carbonates in
the soil. Upon equilibration of the Portneuf and Millville soils with
undersaturated waters 2 and 3, the solubility of soil carbonates
72
-------
+2
decreased as the Mg ion concentration was increased. These data
are readily explained by the degree of saturation of waters. Water 1
is sufficiently undersaturated with respect to the carbonates in the
+2
soils that increasing the Mg ion concentration only resulted in add-
itional ion-pairs being formed, thus, increasing the solubility of the
soil carbonates. Waters 2 and 3 are closer to saturation; hence,
increasing the initial amount of Mg ion resulted in a decrease in
+2
solubility due to the common effect of Mg on the dolomite present
in the soils. The common ion effect can also be used to explain the
increase in precipitation noted when the soils are equilibrated with
the supersaturated water.
73
-------
SECTION XII
REFERENCES
1. Akin, G. W. , and J. V. Lagerwerff. 1965. Calcium carbonate
equilibria in solutions open to the air. IL Enhanced solubility
+2
of CaCO in the presence of Mg and SO . Geochimica et
5 ~r
Cosmochimica Acta 29:253-360.
2. Biggar, J. W. , and D. R. Nielsen. 1963. Miscible displacement:
V. Exchange processes. Soil Science Society of America Pro-
ceedings 27:623-627.
3. Biggar, J. W. , D. R. Nielsen, and K. K. Tanji. 1966. Comparison
of computed and experimentally measured ion concentrations in
soil column effluents. Transactions American Society of Agri-
cultural Engineers 9:784-787.
4. Bischoff, J. L. 1968. Kinetics of calcite nucleation, magnesium
ion inhibition and ionic strength catalysis. Journal of Geophysical
Research 73:3315-3322.
5. Bower, C. A. , G. Ogato, and J. M. Tucker. 1968. Sodium
hazard of irrigation waters as influenced by leaching fraction and
by precipitation or solution of calcium carbonate. Journal of
Soil Science 106:29-34.
6. Bredehoeft, J. D. 1971. Comment on 'Numerical solution to the
convective diffusion equation1 by C. A. Oster, J. C. Sonnichsen,
and R. T. Jaske. Water Resource Research 7:755-756.
75
-------
7. Brenner, H. 1962. The diffusion model of longitudinal mixing in
beds of finite length. Numerical values. Chemical Engineering
Science 17:229-243.
8. Chave, K. E. , and R. F. Schmalz. 1966. Carbonate-seawater
interactions. Geochimica et Cosmochimica Acta 30:1037-1048.
9. Davies, C. W. 1962. Ion Association. Butterworths, London.
190 p.
10. Doner, H. E. , and P. F. Pratt. 1969. Solubility of calcium car-
bonate precipitated in aqueous solutions of magnesium and sulfate
salts. Soil Science Society of America Proceedings 33:690-693.
11. Dutt, G.R., and K. K. Tanji. 1962. Predicting concentrations
of solutes in water percolated through a column of soil. Journal
of Geophysical Research 67:3437-3439.
12. Eaton, F. M. 1950. Significance of carbonates in irrigation
waters. Soil Science 69:123-133.
13. Eldridge, E. R. I960. Return irrigation waters characteristics
and effects. U.S. Department of Health, Education and Welfare,
Region IX, Portland, Oregon, May.
14. Fisher, R. B. 1962. Surface of precipitated particles. Record
of Chemical Progress 23:93-103.
15. Garrels, R. M. , and C. L. Christ. 1965. Solutions, Minerals
and Equilibria. Harper & Row, New York. p. 93-122.
76
-------
16. Hashimoto, I., K. B. Deshpande, and H. C. Thomas. 1964. Pec-
let numbers and retardation factors for ion exchange columns.
Industrial and Engineering Chemistry Fundamentals 3:213-218.
17. Helfferich, F. 1962. Ion Exchange. McGraw-Hill, New York.
18. Niester, N. K., and T. Vermeulen. 1952. Saturation performance
of ion-exchange and adsorption columns. Chemical Engineering
Progress 48:505-516.
19. Lai, Sung-Ho. 1970. Cation exchange and transport in soil
columns undergoing miscible displacement. PhD Dissertation,
Utah State University, Logan, Utah.
20. Lapidus, L. , and N. R. Amundson. 1952. Mathematics of ad-
sorption in beds. VL The effect of longitudinal diffusion in
ion-exchange and chromatographic columns. Journal of Physical
Chemistry 56:984-988.
21. Leitmeier, H. 1968. Die absatze des minerolwasers rohitsch-
saverbrunn steiermark. Cited by Bishoff, J. L. Journal of Geo-
physical Research 73:3315-3322.
22. Lindstrom, F. T. , R. Haque, V. H. Freed, and L. Boersma.
1967. Theory on the movement of some herbicides in soils.
Linear diffusion and convection of chemicals in soils. Environ-
mental Science and Technology 1:561-565.
23. Nakayama, K. S. 1968. Calcium activity, complex and ion-pair
in saturated CaCO solution. Soil Science 106:429-434.
77
-------
24. Oster, C. A. , J. C. Sonnichsen, and R. T. Jaske. 1970. Numer-
ical solution to the convective diffusion equation. Water Resource
Research 6:1746-1752.
25. Oster, C. A. 1971. Reply. Water Resource Research 7:757.
26. Finder, G. F. , and H. H. Cooper, Jr. 1970. A numerical
technique for calculating the transient position of the salt water
front. Water Resource Research 6:875-882.
27. Pytkowicz, R. M. 1965. Rates of inorganic calcium carbonate
nucleation. Science 146:196-199.
28. Rachinskii, V. V. 1965. The General Theory of Sorption Dyna-
mics and Chromatography. Translation from Russian. Consul-
tants Bureau. New York.
29. Rifai, M. N. E. , W. J. Kaufman, and D. K. Todd. 1956. Disper-
sion phenomena in laminar flow through porous media. Report
No. 3, Industrial Engineering Report Series 90, Sanitary Engin-
eering Research Lab, University of California, Berkeley.
30. Suito, E. , A. Masafumi, and T. Arakawa. 1955. Surface area
measurement of powder by adsorption in liquid phase (L). Bulletin
of the Institute of Chemical Research, Kyto, University, Japan,
33:1-7.
31. Weyl, P. K. 1961. The carbonate saturometer. Journal of Geo-
logy 69:32-44.
78
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SECTION XIII
PUBLICATIONS AND PATENTS
1. Hassett, J. J. 1970. Magnesium ion inhibition of calcium car-
bonate precipitation and its relations to water quality. PhD
Dissertetion, Utah State University, Logan, Utah.
2. Hassett, J. J. , and J. J. Jurinak. 1971. Effect of Mg ion on
the solubility of solid carbonates. Soil Science Society of America
Proceedings 35:403-406.
3. Hassett, J. J. , and J. J. Jurinak. 1971. Effect of ion-pair
formation on calcium and magnesium ion activities in aqueous
carbonate solutions. Soil Science 111:91-94.
4. Lai, Sung-Ho. 1970. Cation exchange and transport in soil
columns undergoing miscible displacement. PhD Dissertation,
Utah State University, Logan, Utah.
5. Lai, Sung-Ho, and J. J. Jurinak. 1972. One dimensional cation
saturation performance in a steady state flow through a soil
column: A numerical approach. Water Resources Research
8:99-107.
6. Lai, Sung-Ho, and J. J. Jurinak. 1971. Numerical approximation
of cation exchange in miscible displacement through soil columns.
Soil Science Society of America Proceedings 35:894-899.
7. Lai, Sung-Ho, and J. J. Jurinak. 1972. The transport of cations
in soil columns at different pore velocities. Soil Science Society
of America Proceedings 36:730-733.
79
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N XIV
I. The FORTRAN
the explicit
in cu solve the Equations [10] through []|J, by
' with a "Kielland" type exchange function.
C
c
c
c
c
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c
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c
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c
c
c
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c
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c
c
c
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c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
PURPOSE
TO SOLVE
BOUNDARY
PROCESS
DESCRIPTION
IDSET
SIGN
D
V
RO
Q
ALF
CO
HZ
HT
IT
IZ
N
KT
C
ALNK
T
X
YOX
INPUT
SIGN
D,VSRO,Q
HZ.HT.KX
C.ALNK
OUTPUT
SIGN
D.V.RO.Q
HZ.HT
C.ALNK
T,X(I)
YOX(I)
IKE MATERIAL BALANCE EQUATION, WHICH IS THE INITIAL
VrtlAlE PROBLEM THAT GOVERNS THE CATION TRANSPORT
IN THE STEADY DISPLACEMENT FLOW.
Of PARAMETERS
NUMBER OF DATA SET
DATA SET IDENTIFICATION AN ALPHANUMERIC
ARRAY
DISPERSION COEFFICIENT
INTERSTITIAL FLOW VELOCITY
BULK DENSITY
CATION EXCHANGE CAPACITY
PORE FRACTION
TOTAL CONCF-XTKATION
DEPTH INCREMENT
TIMS INCREMENT
OUTPUT CONTROL NUMBER
OUTPUT CONTROL NUMBER
TOTAL NUMBER OF THE DEPTH INCREMENT
TOTAL NUMBER OF THE TIME INCREMENT
CONSTANT IN KIELLAND FUNCTION
CONSTANT IN KIELLAND FUNCTION
ILME
SOLUTION CONCENTRATION AN ARRAY
EXCHANGER CONCENTRATION AN ARRAY
,ALF,CO
,N,IT,iZ
.ALF.CO
-------
c
C SUBROUTINE REQUIRED
C EXFCN
C
C METHOD
C AN EXPLICIT METHOD DESCRIBED IN THE TEXT
C
C
C MAIN PROGRAM
C
DIMENSION X(100), Y(100), YOX(IOO), SIGN(ll)
IDSET = 2
DO 10 ID = 1, IDSET
C
C INPUT OF BASIC DATA
C
READ(5,99) (SIGN(I), I = 1,11)
WRITE(6,199)(SIGN(I), I = 1,11)
READ(5,100) D,V,RO,Q,ALF,CO
READ(5,101) HZ,HT,MT,N,IT,IZ
WRITE(6,200) D,V,RO,Q,ALF,CO
WRITE(6,201) HZ.HT
NP1 = N + 1
NM1 = II - 1
DZ2 = D/(HZ*HZ)
VZ = V/(2.*HZ)
RQAC = (RO*Q)/(ALF*CO)
READ(5,102)C, ALNK
WRITE(6,202)C, ALNK
C
C SET THE TOP BOUNDARY AND INITIAL CONDITIONS
C
X(l) = 1.0
DO 1 I = 2, NP1
1 X(I) = 0.0
KN = 0
T = 0.0
C
C BEGIN THE COMPUTATION OF X(I)
C
DO 20 IIT = 1, MT
DO 30 I = 2, N
BOX = EXP(ALNK 4- C*(l. - 2.*X(I)))
FOX = ((1. + 2.*C*X(I)*(1. - X(I)))*EOX)/((X(I) +
4(1. - X(I))*EOX)**2)
FT - (1. + RQAC*FOX)/HT
Y(I) = ((DZ2 - VZ)*X(I + 1) - (2.*DZ2 - FT)*X(I)
&(DZ2 + VZ)*X(I - 1)
30 CONTINUE
82
-------
c
C EVALUATE THE BOTTOM BOUNDARY
C
Y(NP1) = Y(NM1)
DO 40 J = 2, NP1
40 X(J) = Y(J)
KN = KN + 1
T = T + HT
IF(KN.NE.IT) GO TO 20
C
C OUTPUT X(I)
C
WRITE(6,203) T, (X(I), I = 1, N, IZ)
C
C COMPUTE YOX(I) IN SUBROUTINE EXFCN
C
CALL EXFCN(X, C, ALNK, N, YOX)
C
C OUTPUT YOX(I)
C
WRITE(6,204) (YOX(I), I = 1, N)
KN = 0
20 CONTINUE
10 CONTINUE
C
99 FORMAT(11A4)
100 FORMAT(6F10.4)
101 FORMAT(2F10.4, 415)
102 FORMAT(2F10.5)
199 FORMAT(1H1, 10X, 11A4)
200 FORMAT(1H1, 14X, 'DISPERSION COEFFICIENT1, F15.6/15X,
S'FLOW VELOCITY'.F15.6/15X,'BULK DENSITY', F15.6/15X,
i'EXCHANGE CAPACITY', F15.6/15X, 'PORE FRACTION1, F15.6
&/15X, 'TOTAL CONCENTRATION', F15.6)
201 FORMAT (//14X, 'DEPTH INTERVAL',F15.6, 10X, 'TIME
&INTERVAL', F15.6)
202 FORMAT(1H1, 13X, 'CONSTANT C IS', F10.6, 'CONSTANT
&LN K IS', F10.6//)
203 FORMAT(1H , 14X, 'TIME IS', F10.2//(10F13.7))
204 FORMAT(//(10F13.7))
STOP
END
83
-------
c [[[
c
C SUBROUTINE EXFCN
C
C PURPOSE
C TO EVALUATE Y(I) AS A FUNCTION OF X(I)
C
C USAGE
C CALL EXFCN (X, C, ALNK, N, YOX)
C
C ..... ..... ..............................................
C
SUBROUTINE EXFCN (X, C, ALNK, N, YOX)
DIMENSION X(100), YOX(IOO)
DO 1 I = 1, N
1 YOX(I) = X(I)/(X(I) -(- (1. - X(I))*EXP(ALNK -I- C*(l.
-------
II. The FORTRAN program to solve the Equations [lQ] through
with a linear exchange isotherm.
c
c
c
c
c
c
c
c
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c
c
PURPOSE
TO SOLVE
THE MATERIAL BALANCE EQUATION THAT GOVERNS
THE CATION TRANSPORT WITH A LINEAR CATION EXCHANGE
FUNCTION
DESCRIPTION
D
V
RO
Q
ALF
ca
HZ
HT
MT
N
SLOPE
AINCP
X
T
FOX
INPUT
D, V, RO
OF PARAMETERS
DISPERSION COEFFICIENT
FLOW VELOCITY
BULK DENSITY
EXCHANGE CAPACITY
PORE FRACTION
TOTAL CONCENTRATION
DEPTH INCREMENT
TIME INCREMENT
NUMBER OF TIME INCREMENT
NUMBER OF THE DEPTH INCREMENT
THE CONSTANT OF THE EXCHANGE FUNCTION
THE CONSTANT OF THE EXCHANGE FUNCTION
SOLUTION CONCENTRATION
TIME
EXCHANGER CONCENTRATION
, Q, ALF, CO
HZ, HT, MT, N, IT, IZ
SLOPE, AINCP
OUTPUT
D, V, RO
HZ, HT
, Q, ALF, CO
SLOPE, AINCP
T, X(I)
FOX(I)
METHOD
THE EXPLICIT METHOD DESCRIBED IN THE TEXT WITH A LINEAR
EXCHANGE
FUNCTION
MAIN PROGRAM
DIMENSION X(100), Y(100), FOX(IOO)
C
C
INPUT BASIC
DATA
85
-------
READ(5,100) D, V, RO, Q, ALF, CO
READ(5,101) HZ, HT, MT, N, IT, IZ
WRITE(6,200) D, V, RO, Q, ALF, CO
WRITE(6,201) HZ, HT
READ(5,102) SLOPE, AINCP
WRITE(6,204) SLOPE, AINCP
NP1 = N + 1
NM1 = N - 1
DZ2 = D/(HZ*HZ)
VZ = V/(2.*HZ)
RQAC = (RO*Q*SLOPE)/(ALF*CO)
FT = (1. + RQAO/HT
C
C SET THE BOUNDARY AND THE INITIAL CONDITIONS
C
X(l) = 1.0
DO 1 I. « 2, NP1
1 X(I) = 0.0
KN = 0
T » 0.0
C
C BEGIN THE COMPUTATION OF X(I)
C
DO 20 IIT - 1, MT
DO 30 I = 2, N
Y(I) = ((DZ2 - VZ)*X(I + 1) - (2.*DZ2 - FT)*X(I) +
&(DZ2 + VZ)*X(I - 1))/FT
30 CONTINUE
Y(NP1) - Y(NM1)
DO 40 J = 2, NP1
40 X(J) - Y(J)
KN = KN + 1
T T + HT
IF(KN.NE.IT) GO TO 20
C
C OUTPUT OF X(I) AND FOX(I)
C
WRITE(6,203) T, (X(I), I = 1, N, IZ)
DO 50 I = 1, N
50 FOX(I) = AINCP + X(I)*SLOPE
WRITE(6,205) (FOX(I), I = 1, N, IZ)
KN = 0
20 CONTINUE
100 FORMAT(6F10.4)
101 FORMAT(2F10.4,4I5)
102 FORMAT(2F10.5)
200 FORMAT(1H1, 14X, 'DISPERSION COEFFICIENT1, F15.6/15X,
tfFLOW VELOCITY', F15.6/15X, 'BULK DENSITY', F15.6/
86
-------
&15X, 'EXCHANGE CAPACITY1, F15.6/15X, 'PORE FRACTION',
&F15.6/15X, 'TOTAL CONCENTRATION', F15.6)
201 FORMAT(//14X, 'DEPTH INTERVAL1, F15.6, 10X, 'TIME
{.INTERVAL1, F15.6)
203 FORMATUH , 14X, 'TIME IS', F10.2//(10F13.7))
204 FORMAT(1H1, 'SLOPE OF THE EXCHANGE FUNCTION IS', F10.6,
&' INTERCEPT IS', F10.6)
205 FORMAT(//(10F13.7))
STOP
END
87 ftU.S. GOVERNMENT PRINTING OFFICE: 1973 514-156/329 1-3
-------
SELECTED WATER
RESOURCES ABSTRACTS
INPUT TRANSACTION FORM
1. Report No.
4. Title CATION TRANSPORT IN SOIL S AND FACTORS
AFFECTING SOIL CARBONATE SOLUBILITY,
7. Author(s)
Jurinak, Jerome J. , Lai, Sung-Ho and Hassett, John J.
9. Organization
Utah State University, Logan, Utah 84322
3. Accession No.
w
5. Report Date
6.
8. Performing Organization
Report No.
10. Project No.
13030 FDJ
11. Contract I Grant No.
13030 FDJ
13. Type of Report and
Period Covered
12. Sponsoring Organization
15. Supplementary Notes
Environmental Protection Agency Report No. EPA-R2-73-235, May 1973
16. Abstract A predictive model of cation transport in soils undergoing miscible displace-
ment was developed and tested. A mass balance equation was formulated to include
a general nonlinear cation exchange function. The model was applied to the transport
of cations through an exchanger using five types of exchange functions. The model
was further tested by conducting soil column studies which involved both homovalent
and heterovalent exchange. Good agreement between experimental and predicted
data was obtained.
Laboratory studies were also conducted to assess the affect of Mg ion
on the solubility of calcareous materials. Solubility was found to vary with the surface
area and mineralogy of the carbonate material, and the degree of saturation of the
water with respect to a given carbonate mineral. In waters unsaturated with respect
+2 +2
to calcite, Mg generally increased the solubility of calcite. The presence of Mg
decreased the solubility of dolomite in waters which were near saturation with respect
to dolomite.
(Jurinak - Utah State)
na. Descriptors ion transport*, calcium carbonate *, soil leaching, cation exchange,
irrigation return flow, precipitation chemical, hardness (water).
17ft.Identifiers solute transport*, carbonate solubility*, miscible displacement,
carbonate saturometer.
17c. CO WRR Field & Group 0 5 B
18. Availability
19. Security Class.
(Report)
20. Security Class.
(Page)
21. No. of
Pages
Send To :
WATER RESOURCES SCIENTIFIC INFORMATION CENTER
U.S. DEPARTMENT OF THE INTERIOR
WASHINGTON. D. C. 20240
Abstractor jerOme J. Jurinak
22. Price
I i»*tit»tionUtah State University. Logan. Utah 84322
WRSIC 102 (REV. JUNE 1971)
GP 0 9 13.261
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