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Uncertain Predictions of Flow and Transport in Random Porous Media: The Implications for Process Planning and Control

Abstract : Traditional predictions of flow and transport in porous media are based on mass balance equations in the form of partial differential equations (PDEs), where the flux at every point is defined by Darcy's law, q = -K(del)h, i.e., the flux is proportional to hydraulic head gradient, where K is the hydraulic conductivity of the medium (a tensor or a scalar; essentially, a material property); it is further assumed that Darcy's law applies to transient multiphase flow in three dimensions. The solutions of these PDEs constitute groundwater models, oil reservoir simulators, geothermal models, and models of flow and transport in soils/vadosezone. Due to the similarity between the linear Darcy's law and Ohm's law in electricity, Fourier law in heat conduction, and Hooke's law in elasticity, such models (or PDE solutions) are similar and commonly interchangeable between these fields.