Continuous time random walk and multirate mass transfer modeling of sorption

Abstract

Abstract We address the question of how to relate between macroscopic transport behaviors of passive and sorbing (reactive) tracers in heterogeneous media. We use continuous time random walk (CTRW) and multirate mass transfer (MRMT) approaches for this purpose. In the framework of CTRW, we formulate the sorption process using a ‘sticking’ rate and a ‘sticking’ time distribution and derive a relation between the distributions of the sorbing and non-sorbing tracer in terms of these quantities. In the MRMT approach, the medium is divided into mobile and immobile regions with diffusive mass transfer between them. The mobile and immobile zones are characterized by different sorption properties. The relations between sorbing and passive tracer distributions derived within the two modeling frameworks turn out to be equivalent. Thus, both approaches show different aspects of the same transport behavior of a sorbing tracer and so lead to a deeper understanding of the underlying processes and the governing transport equations.