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Solute transport with residence‐time‐dependent sink/source reaction coefficients

Solutes and colloids moving through porous media often undergo kinetic reactions, such as sorption or degradation. The kinetic reactions are mathematically described by rate laws and their associated rate coefficients. Rate coefficients are often considered to be time invariant, but there is experimental evidence that the coefficients may depend on the travel or residence time of the dissolved or suspended substance. In this paper we present a theoretical approach to describe transport with residence‐time‐dependent sink/source reaction coefficients. The solution to the transport problem with an arbitrary functional form for the reaction term is expressed in terms of the solution to the nonreactive transport problem. The solution is therefore independent of the nature of the transport process and independent of any specific representation of the reaction coefficients. Applications to a convective‐dispersive transport regime are given, and differences between time‐dependent and residence‐time‐dependent reaction coefficients are illustrated with solute breakthrough curves. Depending on the boundary conditions of a specific problem, time‐dependent and residence‐time‐dependent reaction coefficients can lead to very different transport behavior.