Mathematical Modeling of Electrokinetic Transport and Enhanced Oil Recovery In Porous Geo-Media - Electrokinetics for Petroleum and Environmental Engineers - page 185

where, T e is the volumetric charge density of the soil medium (CL -3 ), and
C p is the electrical capacitance per unit volume (Farad.L -3 ). The equation
describes the rate of change in the electrical potential required to maintain
electrical neutrality of the medium. For zero net change in charge, zero
electric capacitance ( C p ) is assumed for the soil.

5.3.5 Geochemical Reactions

In equation 5.20, reactive transport of charged species is controlled by
rates of geochemical reactions ( R ). Electrolysis reactions at the electrodes
significantly affect the pH and chemistry conditions at the boundaries
(Alshawabkeh, 1996; Cao, 1997). The chemistry boundary conditions results
in a complex system of geochemical reactions that include sorption, redox,
and precipitation/dissolution reactions. The term could be written as:

p
=+ +

s aq

(5.22)

RRR R
i i i i

where, R i s represents the sorption term, R i aq is aqueous reactions terms,
and R i p represents precipitation/dissolution reactions. Two approaches have
been developed and used to describe chemical reactions in the literature
including (i) the instantaneous equilibrium approach, and (ii) the kinetics
approach (Kirkner and Reeves, 1988; Davis and Kent, 1990; Alshawabkeh
and Acar, 1992, 1996; Stumm and Morgan, 1995; Cao, 1997). In the instan-
taneous equilibrium reactions species concentrations reach equilibrium
instantaneously whereas in kinetic reactions approach concentrations in
solution vary with time until they reach equilibrium (Acar et al., 1997).
For several species, chemical reactions have been found to vary with time
before reaching equilibrium. The kinetics approach is expected to be more
realistic for modeling these reactions. However, one could assume chemi-
cal reactions reach equilibrium at a very short time (relative to transport
time) and can use instantaneous equilibrium. Different geochemical mod-
els exist and one could incorporate these models for predicting rates of
geochemical reactions during electric field applications. In the following
section an overview of these reactions is provided.

5.3.5.1 Sorption reaction

The following general term is considered for sorption evaluation:

r ∂

∂

S
t

r ∂

∂

S
t

∂
∂

C
t

s

i = 1,2,…N (5.23)

R =

i

=

i i

i

n n