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PDF methods for reactive transport in porous media

PDF methods for reactive transport in porous media

IAHS-AISH Publication 277(Pages 162-167

Reactive transport in porous media is described by (a system of) nonlinear differential equations. Typically, the parameters entering these equations are either under-specified by data (e.g. hydraulic conductivity, macroscopic velocity) or cannot be measured on a required scale in principle (e.g. the dynamic behaviour of interfacial surfaces between reacting components, pore-scale velocity). In recent decades stochastic methods, which treat such parameters as random fields, have emerged as powerful tools for dealing with the uncertainty inherent in modelling subsurface phenomena. Monte Carlo simulations and moment differential equations (MDE) methods are most often used in stochastic hydrogeology. The comparative strengths and weaknesses of both approaches are well understood. By contrast, so-called PDF approaches, which are based on deriving (conditional) probability density functions for the corresponding stochastic flow and transport equations, have received virtually no attention. Yet their advantages for analysing reactive transport remain to be demonstrated. Unlike most MDE approaches, they do not linearize the governing equations and they provide a natural framework for analysing rare events that are crucial for risk assessment studies. We use a perturbation closure to derive a general PDF equation for advective transport of a contaminant undergoing a heterogeneous, nonlinear chemical reaction. We conclude by solving this equation analytically for a batch system, which allows us to comment on the convergence of the solution.

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