A mathematical model for consolidation in a thermoelastic aquifer due to hot water injection or pumping

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Abstract
A mathematical model is developed for the areal distribution of fluid pressure, temperature, land subsidence, and horizontal displacements due to hot water injection into thermoelastic confined and leaky aquifers. The underlying assumption is that the aquifer is thin in relation to the horizontal distances of interest, and hence all dependent variables of interest are average (over the thickness) values. The solid matrix is assumed to be thermoelastic. Following the development of three‐dimensional conservation of mass and energy equations and equilibrium equations in terms of horizontal and vertical displacements, the mathematical model is derived by averaging the three‐dimensional model over the vertical thickness of the aquifer, subject to conditions of plane total stress. The effects of viscous dissipation and compressible work have been included in the formulation. The resulting averaged coupled equations are in terms of pore water pressure, temperature, and vertical and horizontal displacements which are functions of x, y, and t only. The equations are nonlinear and have to be solved simultaneously due to the coupling that exists among them. Equations and appropriate boundary conditions in radial coordinates have also been presented for an example of a single injecting (or pumping) well.