Nonlinear Adsorption of Uranyi: Analytical Modeling of Liner Migration

Abstract

This paper is concerned with establishing the breakthrough time for leachate to migrate out of waste facilities containing large quantities of low‐level, radioactive uranium. The impoundments have clay liners which adsorb uranyl cations dissolved in the leachate. A nonlinear isotherm, derived from a consideration of the phenomenological basis and chemical kinetics of the adsorption process, is used in conjunction with a time‐dependent, one‐dimensional species transport equation to develop a mathematical expression for the retarded migration time interval. The nonlinear transport equation is identical to one occurring in theoretical gas dynamics for the description of shock waves, and whose solution is well‐known. Results indicate that large breakthrough time‐interval errors can arise if a linear isotherm is used to model the adsorption process, particularly if leachate concentrations along the floor of the pit are near saturation. Conversely, at dilute concentrations, computations based on the linear isotherm underpredict the time interval required for the onset of leakage. The underprediction is acceptable from an engineering viewpoint because environmental protection afforded by the liner is not overstated.