Nonisothermal global-pressure exactness in fractured multiphase flow with aperture feedback
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Date
2026-07
Publication Type
Journal Article
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yes
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Abstract
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.
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published
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Journal / series
Volume
38 (7)
Pages / Article No.
073357
Publisher
American Institute of Physics