Modeling Kinetic Adsorption in Porous Media by a Two-State Random Walk Particle Method

In this paper, a stochastic approach to address linear kineticadsorption mechanisms using a two-state particle tracking random walktheory is presented. During reactive solute transport in porous mediumparticles are assigned two states: Either mobile (free) or immobile(adsorbed). By studying the exchange of particles’ states, the mechanismof adsorption can be better understood. The kinetics of theparticles is modeled with a Markov chain characterized by a transitionprobability matrix between the two states. The concept of exchange ofparticle states of the solute particles is more fundamental than that ofrelaxing the probability with a retardation factor and it is of great significancein modeling various reactive transport mechanisms. A computercode (called ADS_2D) has been developed to perform numericaladsorption experiments. It has been shown from the experiments thatadsorption with slow kinetics can not adequately be modeled using aretardation factor. The fundamental analytical solution deviates fromthe numerical solution, particularly the spreading of the solute plume.This is due to the fact that the fundamental analytical solution does nottake into account the extra dispersion due to the kinetic reaction