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

An analytical solution is derived for the advection-dispersion equatio n with rate-limited desorption and first-order decay, using an eigenfu nction integral equations method. The model equations represent one-di mensional solute transport in a homogeneous isotropic porous medium wh ere the porous medium is saturated with the aqueous solution. The flow field is uniform. Rate-limited desorption is described as a first-ord er process where the rate is proportional to the difference in concent ration between the sorbed phase and the aqueous phase. The solution wa s verified for the limiting case of equilibrium desorption using the s olution of van Genuchten and Alves (1982). Example calculations are pr esented to show the effect of the desorption rate, decay rate, and dis tribution coefficient on the rate of contaminant removal from both the aqueous and sorbed phases of a groundwater aquifer. The solution quan tifies the expected results, where the larger the desorption and decay rate and the smaller the distribution coefficient, the faster the rat e of contaminant removal from the aqueous and sorbed phases.