A thermodynamically consistent theory of multicomponent porous media: finite-deformation mechanics, compositional flow, electrostatics, reactions, and phase transformations
Year: 2026
Type: preprint
Abstract: Reactive reservoir models must combine compositional flow, deformation, electrostatics, chemical reactions, and phase transformations without losing the thermodynamic origin of each term. This paper develops such a theory for multicomponent, multiphase porous media at finite deformation. Component mass conservation is first written on phase-attached material regions and then volume averaged, which separates molecular diffusion and mechanical dispersion from bulk phase motion. Mobile fluids and load-bearing multicomponent solids use the same phase/component variables. Solid composition can therefore change stress-free deformation, elasticity, plastic flow, and nonlinear Biot coupling. A fixed-pressure Legendre transform gives phase Biot coefficients at the current reacted state; an optional additive component specialization resolves those coefficients into component contributions. The derivation combines a constrained Hamilton-d'Alembert statement for the phase-coordinate balances with Onsager stationarity for dissipative saturation redistribution, reaction, and component-relative transport. Varying component material measures and phase Jacobians together produces the momentum carried by inserted mass and a generalized Darcy-like relative-flux law. The same calculation gives the composition restrictions, transfer-potential equations, and phase-transfer equilibrium conditions. Material-carried charge is tied directly to component mass. Traditional reaction affinities are sums of electrochemical potentials. Away from uniform temperature, charged transport instead keeps the temperature-weighted neutral-potential gradient separate from the electric field so that the force is independent of the arbitrary electric-potential level. The entropy inequality identifies admissible stress, pressure, reaction, drag, diffusion, dispersion, heat-transfer, and plastic-flow laws. A capillary-history state extends the interfacial energy to drainage-imbibition hysteresis, with its evolution restricted by the same dissipation inequality. An optional dynamic-capillary resistance relates the pressure lag to the skeleton-following saturation rate and supplies its d'Alembert work in the phase momentum balances. Standard compositional flow, black-oil flow, nonlinear poromechanics, and single-solid, single-fluid Biot theory follow as stated limits of the full solid-reference formulation.
DOI: 10.31223/x5051h
Author: John Foster
Language: English
Subfield: Computational Mechanics
Field: Engineering
Domain: Physical Sciences
Open Access status: green
Funder: U.S. Department of Energy
Awards: G3425315134, G6410433233, G8511067563
OpenAlex ID: W7221339370