A simple open-system model is used to evaluate the effect of groundwater flow on borosilicate glass dissolution. With appropriate assumptions, the mass balance equation is: dc/dt=R-kfc;R=k(ceq-c)
where c is the concentration of dissolved species i, t is time, kf is the flushing frequency (i.e., volumetric flow rate divided by fixed pore volume), and R is the normalized rate of dissolution. A first-order dependence of R on departure of c from the equilibrium saturation concentration, Ceq, is also assumed. Results from steady-state (dc/dt = 0; c = css = constant) static and dynamic flow tests on a borosilicate glass at 90°C were used to calculate R and the dissolution rate constant, k, as a function of flow rate. The calculated results of the model are in good agreement with independent measurements.
There are three important conclusions. First, even the slowest flow rate used (0.1 ml/hr) corresponds to a high flow rate with respect to the intrinsic dissolution rate of the glass and expected repository flow conditions. Second, previous release models that scale radionuclide release rate directly to solubility concentration may overestimate release at high flow rates. This is because previous models fail to account for the pronounced decrease in steady-state solution concentration at the solid interface with increasing flow rate. Third, increased flow rate accelerates the glass dissolution rate without changing the reaction mechanism. This effect is attributable to constant replenishment of undersaturated solution at the glass surface and an apparent increase in the dissolution rate constant with increasing flow rate.