A thermodynamically consistent theory of multicomponent porous media: finite-deformation mechanics, compositional flow, electrostatics, reactions, and phase transformations

John T. Foster 

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.