Chapter 10 - Fractional-order derivatives for multiphase flow in porous media
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2025-02-01
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This chapter explores the application of fractional-order derivatives in modeling multiphase flows in porous media. When dealing with anomalous diffusion and nonlocal effects, traditional models often fall short of accurately capturing the complex dynamics of fluid flow in such media. Incorporating fractional-order derivatives can provide a more comprehensive representation of these processes. The chapter presents fractional-order models for multiphase flow in porous media. We derive the fractional multiphase continuity equation using the Caputo derivative and discuss the fractional-order Darcy's law, which incorporates spatial and temporal memory effects. A case study on countercurrent imbibition illustrates the practical application of these models. Additionally, we examine the modeling of flow in fractured porous media and the dual-continuum models used to describe such systems. A case study about the analytical solution of the fractional groundwater model for density-independent flow in a uniformly homogeneous aquifer. The chapter also includes a detailed model of two-phase flows in fractured porous media, which is often used in reservoir simulation.
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Fractional Modeling of Fluid Flow and Transport Phenomena