A model of hindered solute transport in a poroelastic shale

Abstract

Theories for the transport of solvent and solute through an imperfect semi-permeable membrane are used as the basis for a model of transport through shale. The flow of solute is reduced, relative to that of solvent, by a transmission coefficient λ ≼ 1. In this model, it is assumed that the chemical composition of the pore fluid has no direct effect upon the swelling of the shale, other than via the thermodynamic pressure p . Invasion is governed by a pair of coupled diffusion equations. There is an initial, rapid diffusion of pressure, leading to a swelling pressure (1-λ) RT ∆ x / V w , where RT ∆ x / V w is the van’t Hoff osmotic pressure difference due to a change in solute mole fraction ∆ x . A subsequent slow diffu­sion process, dominated by diffusion of the solute, then occurs. A change in solute concentration has been assumed to have no direct effect upon the rock, and ultimately has no effect upon the pore pressure and stress. Nevertheless, imperfect exclusion of solute can lead to transient changes in pore pressure which might destabilize the shale before the final steady state is achieved. This is demonstrated by a poroelastic analysis of pressure and solute diffusion into rock surrounding a wellbore.