Management of Commercially Generated Radioactive Waste - U.S. ...

P.1.1.1 Use of Solubility Data
P.2
Chemical weathering and alteration are most often the result of the interaction between
an electrolyte aqueous solution and the various minerals being weathered. Several factors
are important in determining the mobility of elements via weathering ionic solutions. One
group of factors is related to the overall physical properties of the "weathering system,"
i.e., of the hydrologic system and the host mineral assemblage. For example, the flow rate
of solution through a permeable system is determined by Darcy's Law:
S k u
u = - (pg + VP) v -=
where u = fluid flux vector (g/cm 2 /sec)
S= true fluid velocity (cm/sec)
= gravity force vector (cm/sec
k = permeability of the rock assemblage (cm
P = viscosity of the fluid (cm 2 /sec)
P = density of 3 the fluid ) (g/cm
P = pressure (bars)
0= porosity of rock.
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Clearly, then, the water flow depends on gravity and the pressure gradient at the given
locality (a property of the hydrologic system as a whole) as well as on the porosity and
permeability of the rock assemblage in the locality, and the density and viscosity of the
fluid.
The hydrodynamic equations, which incorporate Darcy's Law, allow us to calculate the
hydrodynamic mobility of a given cation or anion in solution from its original location
within a given mineral of the weathered rock to its place of deposition such as a sedimen-
tary deposit, rivers, oceans or the biosphere. We can obtain absolute flux rates for a
given ion (i.e., moles/cm2/sec), however; only iff we know its concentration in the percolating
solution.
The magnitude of the concentration of a given element in a solution that is in contact
with a weathering mineral assemblage is the central element used in establishing the intrin-
sic stability of a particular nuclear waste element-containing mineral to alteration and
weathering. This concentration is generally a function of time, since it is kinetically
controlled. Nevertheless, almost all geochemical work on the mobility of elements via solu-
tions has applied a thermodynamic and not a true kinetic approach. Whether true thermodynamic
equilibrium is reached between solution and a particular mineral depends, among other
things, on how long they are in contact (i.e., the flow rate); this concept often appears
as the ambiguous "water-rock ratio" in the literature. It seems likely that under most cir-
cumstances the concentration of an element in a'weathering solution will be kinetically con-
trolled. Unfortunately, there is a dire need for suitable kinetic data. The kinetic
factors involved in the time dependence of the concentration, which may keep the concentration
well below the thermodynamic limit, will be discussed below.
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