Unsaturated hydro-mechanical–chemical constitutive coupled model based on mixture coupling theory: Hydration swelling and chemical osmosis

Abstract

Very low permeability soils and rocks may act as actual semi-permeable membranes and also have the potential to swell if they contain clay minerals. This study extends Mixture Coupling Theory for unsaturated, very low permeability swelling rock, based on non-equilibrium dynamics and Biot's elasticity, and develops new advanced coupled mathematical formulations, by including unsaturated chemical osmosis and hydration swelling. Helmholtz free energy has been used to derive the link between solid deformation and multiphase transport. Darcy's law has been extended and the influence of swelling on stress and strain has been included. The mathematical formulation shows that swelling capacity may have a strong influence on the deformation of host rock in the chemical osmosis process, which is demonstrated by a numerical simulation of two representative cases. Important engineering applications of this model and analysis are highlighted.

A new matrix for multiphase couplings in a membrane porous medium

“…In this illustration, the multiphases include water, heat, and chemicals. When a water pressure gradient ( grad p ), a chemical mass fraction gradient ( grad c ), and a temperature gradient ( grad T ) are applied across the mixture in a porous medium, the following situations are involved: (1) The pressure gradient causes the water molecules to migrate (usually from high pressure to lower pressure) with a mass flux of u = − ( k / v ) grad p , in which k is the permeability of the porous medium, v is the viscosity of the fluid, and u is the Darcy flux; (2) This water flow will be affected simultaneously by the chemical ( J = ρ f D grad c , where ρ f is the fluid mass density, D is the diffusion coefficient, and J is the diffusion flux) and thermal ( , in which λ is the thermal conduction coefficient and is the thermal flux) transport flows, and vice versa; (3) The secondary or tertiary coupled driving force may become the major driving force of the flow in some circumstances (eg, grad c becomes the major driving force of water flow rather than grad p for chemical osmosis in a membrane porous medium); (4) Overall, the 3 flows (water, chemical, and thermal) and 3 driving forces ( grad p , grad c , and grad T ) present a 3 × 3 matrix describing the cross‐couplings between each other (Figure ), which is the realistic condition of the multiphase porous medium system. Extensive experiments have been conducted in recent decades, but little has been achieved regarding theoretical development in a strict mathematical way.…”

Mathematical model of coupled dual chemical osmosis based on mixture-coupling theory

“…Solutes in the subsurface, which are influenced by this process, originate from a diverse range of sources and industrial applications, including carbon geological storage and nuclear waste disposal. Single chemical osmosis has been studied within nuclear waste disposal and Darcy's Law has been extended accordingly [2,3]. However, dual coupled chemical osmosis, the influence of sorption, and its subsequent effect on solid consolidation has not received any attention.…”

“…A comprehensive review of this approach has been completed by Atkin and Craine [19]. This approach has the difficulties of obtaining information on the interaction between the phases as discussed by Rajagopal [15]; and (3) Mixture-Coupling theory approach, which combines the advantages of both former approaches, provides a smooth link between geophysics and geochemistry [3,[20][21][22][23].…”

“…As the name Modified Mixture Theory does not fully describe the core of this approach, and also does not make clear distinctions from other "Modified Mixture Theory" such as [27], it is necessary to rename it as Mixture Coupling Theory [3], in this case, the coupling of both fluids and solids as multiphases is specifically addressed (with consideration of secondary phases arising from chemical reaction between groundwater and soils or rock in the future).…”

“…Mixture theory has difficulties in obtaining information on the interactions between solid/fluid phases, and also to deal with the coupling of chemicals [12,13]. Mixture Coupling Theory has successfully overcome the challenges that the above domain approaches face, and has generated more advanced constitutive coupled equations for multiphase flow in deformable porous media [3,25,29].…”