FREZCHEM2
A Chemical Thermodynamic Model for
Electrolyte Solutions at Subzero Temperatures
MIKHAIL V. MIRONENKO, STEVEN A. GRANT, GILES M. MARION, AND RONALD E. FARREN
static and only explicitly recognizes a few chemi-
INTRODUCTION
cal interactions, such as ion-pair formation. This
The FREZCHEM model was developed by Mar-
is why the system under consideration is very
ion and Grant (1994) to calculate chemical equilib-
simple from the viewpoint of chemical interac-
ria among aqueous electrolyte solutions, ice, and
tions, but it is very complex from the viewpoint of
salts. The model applies the Pitzer equations for
the influence of activity coefficients on the behav-
calculation of aqueous species and water activi-
ior of the Gibbs energy function.
ties. To find chemical equilibrium, this program
solves sequentially a set of nonlinear equations
MATHEMATICAL ALGORITHM
that includes both solid-phase deposition and ion-
pair formation using an individual subroutine for
The system under investigation consists of the
every reaction. FREZCHEM uses data on constants
following components: 1) solid salts of fixed
of chemical reactions and Pitzer equation parame-
chemical composition and pure ice (so-called
ters published by Spencer et al. (1990). The results
one-component phases), and 2) aqueous solu-
of modeling show good agreement both with
tions consisting of water and dissolved electro-
experimental data and with the results of the
lytes. The applied algorithms of chemical equilib-
SpencerMllerWeare model. However, the
ria computation will be described in terms of
FREZCHEM model has some limitations. One is
these components.
convergence problems at high ionic strengths (>15
The equilibrium composition of the system at
molal) and at junctions, where new phases begin
constant T, P, and specified bulk composition
to precipitate. Another is that addition of any new
may be found by minimizing the Gibbs energy
substance into this model requires changes not
function of the system under balance restrictions.
only in data but also in the program code.
The objective of this report is the further devel-
Local minimum computation
opment of the chemical thermodynamic model
Local minimum is considered as an equilibri-
FREZCHEM to make it more reliable, universal,
um composition of the system, in which all exist-
and flexible. The point calculation reliability was
ing phases are specified before computation. The
improved by applying the Gibbs energy minimi-
Gibbs energy function of the system that contains
zation approach to computing equilibrium. The
M solids and aqueous solution (water and J spe-
thermodynamic information needed for com-
cies) is as follows:
putations is separated from the calculating rou-
M
J
tines. That allows components to be added to the
G
= ∑ k nk + w nw + ∑ j n j
g=
0
system without code changes and the program
RT k =1
j =1
code to be applied for other chemical systems. It
should be noted that the Pitzer approach describes
where G = free energy of the system,
most interactions in aqueous solution as electro-
n = the molal quantity of components,
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