PDF equations for advective–reactive transport in heterogeneous porous media with uncertain properties

We consider advective–reactive solute transport in porous media whose hydraulic and transport properties are uncertain. These properties are treated as random fields, which renders nonlinear advection–reaction transport equations stochastic. We derive a deterministic equation for the probability density function (PDF) of the concentration of a solute that undergoes heterogeneous reactions, e.g., precipitation or dissolution. The derivation treats exactly (without linearization) a reactive term in the transport equation which accounts for uncertainty (randomness) in both flow velocity and kinetic rate constants but requires a closure, such as a Large-Eddy-Diffusivity (LED) approximation used in the present analysis. No closure is required when reaction rates are the only source of uncertainty. We use exact concentration PDFs obtained for this setting to analyze the accuracy of our general, LED-based PDF equations.