Global Buckley-Leverett theory 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 pseudoparabolic, 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.