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2026-03-09
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Abstract
Multiphase flow in porous media underpins a wide range of subsurface engineering applications, such as petroleum recovery, CO2 sequestration, and groundwater remediation—by describing how two immiscible fluids (e.g. water and oil, or gas and liquid) migrate through a porous rock matrix [74]. Extending Darcy's law to each phase requires introducing saturation-dependent relative permeabilities https://www.w3.org/1998/Math/MathML" display="inline">kr,α(S), which capture the reduction in effective permeability due to the presence of another fluid, and capillary pressure https://www.w3.org/1998/Math/MathML" display="inline">pc(S), which embodies interfacial forces arising from pore geometry and fluid–fluid tension [75, 76, 77]. These constitutive functions give rise to hysteresis during drainage and imbibition, a hallmark of two-phase displacement in porous media [78].
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Numerical Methods in Porous Media MATLAB® and Python Approaches