Global Buckley--Leverett for Multicomponent Flow in Fractured Media: Isothermal Equation-of-State Coupling and Dynamic Capillarity

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.