Permeability models for heated saturated igneous rocks

Abstract

This paper is concerned with the heating effects in saturated, cracked granitic rocks. A model is constructed which permits permeability to be derived as a function of temperature. Granites have generally a low permeability so that the fluid response is considered to be undrained. Heating produces a fluid pressure rise. As long as the resulting deformation is reversible, cracks open elastically, and the rock behavior is described by thermoporoelasticity. If the confining pressure is constant, the fluid pressure derivative dp/dT depends essentially on the solid bulk modulus K5, on the thermal expansion coefficient αm, and on the initial crack aspect ratio A0. Irreversible deformations, i.e., crack propagation, take place when tensional stresses at the crack tip exceed the rock strength. This occurs at a critical temperature Tc which is controlled by dp/dT. Tc depends (1) on boundary conditions (constant confining pressure or constant bulk deformation), (2) on rock properties (solid bulk modulus Ks and thermal expansion coefficient αm) and most of all on crack aspect ratio. Tc is rather high for very thin cracks and low for high aspect ratio cracks. A model is developed in order to describe permeability and connected porosity evolution as temperature increases: at temperatures higher than Tc, cracks propagate step by step. The results of the modeling suggest that permeability is controlled by several effects. The balance of these is variable. On one hand, when crack propagation occurs, crack closure occurs simultaneously so that permeability decreases. On the other hand, connectivity is improved by the crack propagation process and this produces a permeability increase. The overall permeability increase is expected to cover at the most 2 orders of magnitude.