These two models can accurately estimate the
MODELING
chemical composition (Fig. 7) and unfrozen water
(Fig. 8) of seawater at least down to 30C. At low-
Solutes in saline environments play a critical role
in defining freezing and thawing of these systems.
er temperatures some discrepancies exist [e.g., Mg
A few mathematical models have been developed
concentrations (Fig. 7) and unfrozen water (Fig. 8)].
that explicitly consider the effect of solutes on
Given the difficulties in making experimental mea-
freezethaw processes. These models can be divid-
surements at low temperatures, it is impossible with
ed into three classes:
the presently available data to determine whether
Chemical thermodynamic equilibrium;
the model or the experimental measurements are
Solute segregation at the waterice interface;
most accurate at low temperatures (Marion and
and
Grant 1994). Note that even at temperatures as low
as 50C, a small fraction of seawater (0.3%) re-
Solute segregation in soil systems.
Classical chemical thermodynamic models only
mains unfrozen. The importance of salt precipita-
provide information on the states of systems at
tion during the freezing process is demonstrated
equilibrium; they do not describe the pathways to
for Na and Cl salts (Fig. 9), where only 0.3% of Na
the equilibrium states. Their utility depends on how
and 4.5% of Cl remain in the solution phase at
50C.
well natural systems that are constantly fluctuat-
ing can be approximated by the equilibrium states.
These papers make it clear that to accurately
Spencer et al. (1990) developed a chemical thermo-
interpret or model solute effects during freezing
dynamic model (SpencerMllerWeare model)
and thawing of saline solutions such as seawater,
valid over the temperature range of 60 to +25C,
we need accurate chemical thermodynamic data on
for the system Na-K-Ca-Mg-Cl-SO4-H2O. This
mineral solubilities at subzero temperatures.
model is parameterized with data from pure bina-
Apparently the databases for handling chloride
ry and ternary salt solutions. This model predicts
salts down to the eutectic temperature of seawater
(54C) are adequate (Spencer et al. 1990, Marion
the formation of ice and the precipitation of 15 chlo-
ride and sulfate salts, which allows the accurate
and Grant 1994). However, there are problems in
prediction of the freezing point and chemical com-
modeling some sulfate salts at subzero tempera-
position of simple and complex solutions, includ-
tures, which may be due to poor-quality solubility
ing seawater. Marion and Grant (1994) have
data, to lack of data for some salts such as CaSO4
developed a Fortran version of the SpencerMller
and perhaps to an inadequate solution-phase model
Weare model called FREZCHEM. The FREZCHEM
for concentrated sulfate solutions (Bukshtein et al.
model has two reaction pathways:
1953, Linke 1965, Spencer et al. 1990, Marion and
Freezing at variable temperature and fixed
Grant 1994). The quantity and quality of data for
water; and
the bicarbonate and carbonate salts of Na, K, Ca
Evaporation at variable water and fixed tem-
and Mg at subzero temperatures are even more
perature.
sparse (Bukshtein et al. 1953). More research is clear-
0
Experimental Model
10
Cl
Na
Mg
Ca
20
30
40
50
Figure 7. Concentrations of major sea-
0
2
4
6
8
water constituents during freezing.
Molality (mol kg 1)
15
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