Nonisothermal global-pressure exactness in fractured multiphase flow with aperture feedback

Global-pressure formulations recast multiphase Darcy flow in terms of a single pressure driving the total flux. Their exact equivalence to phase-pressure formulations holds only when the constitutive data satisfy the compatibility conditions required for a total-differential structure and its generalized nonisothermal extension. Here, we derive the exactness criterion for temperature-dependent mobilities and capillary pressures. We show that equivalence depends on whether the mobility-weighted capillary contribution is path independent in the saturation–temperature domain, so that it can be absorbed into a scalar global pressure. This yields the classical compatibility conditions within the saturation sector and a distinct mixed saturation–temperature condition that arises only in nonisothermal settings. We then incorporate this structure into a reduced matrix–fracture model with heat transport, matrix–fracture thermal exchange, and evolving aperture. Numerical benchmarks recover the three regimes predicted by the theory: globally exact, exact on each fixed-temperature slice but not on the full saturation–temperature domain, and fully nonexact. In fractured systems, thermal forcing alone can drive transitions between these regimes, while aperture evolution changes the path through state space. When saturation-sector exactness is lost, a least-squares projection on fixed-temperature slices extracts the nearest gradient component of the mobility-weighted capillary field. This yields a conservative slice-wise scalar-pressure surrogate and a quantitative projection residual. The residual separates saturation-sector nonintegrability from the mixed saturation–temperature incompatibility that controls genuinely nonisothermal loss of exactness. The framework links nonisothermal exactness theory, fractured-flow dynamics, and conservative reduced closure in a global-pressure formulation.