Analytical solution for solute transport with depth-dependent transformation or sorption coefficients

Reaction processes in soils, such as degradation and sorption, are often strongly depth dependent. Microbial activity and organic matter, which play an important role in reaction processes, are mostly confined to the top few decimeters of the soil. The purpose of this paper is to analyze the effects of space-dependent reaction coefficients on transport of solutes through soil. We derive an analytical solution of the advection-dispersion equation with depth-dependent transformation or sorption coefficients. The solution is obtained in Laplace space and is inverted numerically. Breakthrough curves and concentration profiles of degrading and sorbing chemicals are presented to illustrate the influence of spatially variable reactions. It is demonstrated that the concentration profiles for depth-dependent reactions vary between the two extreme cases of no and constant reactions, depending on how fast the reactions cease with increasing depth. The results emphasize the relevance of depth-dependent transformation and sorption to transport of chemicals in soils. It is further shown that depth-dependent sorption may cause a bimodal depth profile, even under steady state water flow regimes.