Hot fluid migration in compressible saturated porous media

Abstract

Solutions for heat and pressure transfer in compressible thermoporoelastic, fluid-saturated media are presented. A hot and pressurized fluid reservoir is envisaged, which comes into contact with a cold, saturated half-space; the boundary between them is either pervious or impervious. In the 1-D problem, two coupled non-linear equations are obtained for the temperature and pressure fields, which are solved employing the self-similarity method. The thermally induced pressure in the half-space is found to be generally relevant for low-/intermediate-permeability media. In the pervious boundary problem, the thermal interaction gives rise to a striking effect in low-permeability materials: the induced pressure increases away from the boundary, up to a maximum, before declining to vanishingly small values further away; a backflow is driven by the reverse pressure gradient, from the point of maximum towards the reservoir. The same effect is present, although to a lesser extent, in intermediate-permeability materials, saturated with liquid water, under low boundary pressures. In the impervious boundary problem, the thermally induced pressure is relevant even for high-permeability media. The temperature field is affected by fluid flow only in the pervious boundary problem, for high-permeability media, saturated with low-viscosity fluids, subjected to high overpressure over the boundary. The conductive approximation (which is obtained after neglecting the advection and the dissipation terms in the heat transfer equation) is found to be applicable even to high-permeability rocks under the impervious boundary conditions. Even if the previous conclusions are not strictly applicable to problems with different geometries, the present solutions seem to bear important consequences on fluid-migration mechanisms in volcanic areas, where the backflow identified in low-permeability media seems to be a viable mechanism for water enrichment by magma ascending through a dyke or emplaced in a magma chamber surrounded by colder, water-saturated, low-permeability rocks. Pore pressure and temperature can be also very effective in providing rock deformation: depending on the rock type and boundary conditions, either the pore-pressure contribution or the thermal contribution may be dominant. Inflation episodes, which are often observed in volcanic areas, can be interpreted in a similar way. Thermoporoelastic effects might also be relevant in fault regions after the sudden frictional heating of water embedded between fault surfaces. The theory may be also applied (e.g. Mc Tigue 1986) to the modelling of areas of nuclear waste disposal.