Global Buckley-Leverett theory for multicomponent flow in fractured media: Isothermal equation-of-state coupling and dynamic capillarity

Abstract

We present an isothermal Global Buckley--Leverett framework for multicomponent, multiphase flow in porous and fractured media that retains the interpretability of classical Buckley--Leverett while incorporating essential physics: equation of state-based phase behavior, multicomponent Maxwell--Stefan diffusion, dynamic capillarity, stress-sensitive permeability, and non-Darcy fracture flow. The formulation yields a single global-pressure equation driving the total Darcy flux and an exact fractional-flow decomposition of phase velocities with buoyancy and capillary drifts; inertial effects enter as per-phase damping that renormalizes mobilities. Crucially, the combination of Maxwell--Stefan diffusion and dynamic capillarity renders transport pseudo-parabolic, resolving the loss of strict hyperbolicity that plagues three-phase Buckley--Leverett and ensuring a well-posed initial-value problem. In practice, each time step solves the scalar global-pressure equation, reconstructs phase fluxes via the split, and advances strictly conservative component balances; axisymmetric (cylindrical) forms for radial injection with vertical buoyancy are provided. The model reduces exactly to classical Buckley--Leverett when added physics are disabled, making it a practical backbone for carbon storage, geothermal exchange, and contaminant transport in fractured, compositionally complex reservoirs.