This work studied the transport phenomena in the soil of the Gramacho MSW landfill located in Rio de Janeiro, Brazil. A model was proposed to determine the mass transfer rate of the leachate contaminant ions to the soil particles. Previous researchers have focused on the diffusion and sorption phenomena using simple relations that do not completely explain the data of overall mass transfer obtained by laboratory experiments. Thus, this work proposes a modified rate equation implemented into MPHMTP software that takes into account the combined mechanisms of advection and diffusion in the leachate and sorption at the particle surface followed by diffusion in the interior of the soil particle. The model predictions were compared with laboratory-measured data and presented better agreement compared to those obtained using the commercial POLLUTE software.