AN ANALYTICAL SOLUTION TO THE SOLUTE TRANSPORT-EQUATION WITH RATE-LIMITED DESORPTION AND DECAY

An analytical solution is derived for the advection-dispersion equation with rate-limited desorption and first-order decay, using an eigenfunction integral equations method. The model equations represent one-dimensional solute transport in a homogeneous isotropic porous medium where the porous medium is saturated with the aqueous solution. The flow field is uniform. Rate-limited desorption is described as a first-order process where the rate is proportional to the difference in concentration between the sorbed phase and the aqueous phase. The solution was verified for the limiting case of equilibrium desorption using the solution of van Genuchten and Alves (1982). Example calculations are presented to show the effect of the desorption rate, decay rate, and distribution coefficient on the rate of contaminant removal from both the aqueous and sorbed phases of a groundwater aquifer. The solution quantifies the expected results, where the larger the desorption and decay rate and the smaller the distribution coefficient, the faster the rate of contaminant removal from the aqueous and sorbed phases.