Probability density functions for advective-reactive transport in divergent flow

Much of stochastic subsurface hydrology deals with low-order ensemble moments (i.e., mean and variance) of concentration. While useful for gaining physical insight into the effects of heterogeneity on contaminant migration, such analyses are often inadequate for predicting rare events that are described by the tails of statistical distributions. We derive a deterministic equation for the probability density function (PDF) for the concentration of a chemically reactive solute advected by divergent flow. The solute undergoes a heterogeneous chemical reaction with a solid phase in the presence of advection due to extraction/injection from a point source. This allows us to quantify uncertainty associated with spatially varying reaction rate constants for both linear and nonlinear reactions.