The vaporization of a liquid front moving through a hot porous rock

Abstract

We develop an analytical model to describe the generation of vapour as water moves through a hot porous rock, as occurs in hot, geothermal reservoirs. Typically the isotherms in the liquid lag behind the water-vapour interface and so water is supplied to the interface at the interface temperature. This temperature is lower than that in the rock far ahead of the interface. Therefore, as the hot porous rock is invaded with water, it cools and the heat released is used to vaporize some of the water. At low injection rates, vapour formed from the injected liquid may readily move ahead of the advancing liquid-vapour interface and so the interfacial pressure remains close to that in the far field ahead of the interface. The mass fraction that vaporizes is then limited by the superheat of the rock. For larger injection rates, the interfacial vapour pressure becomes considerably greater than that in the far field in order to drive the vapour ahead of the moving interface. As a result, the interfacial temperature increases. The associated reduction in the thermal energy available for vaporization results in a decrease in the mass fraction of vapour produced.Since the vapour is compressible, the motion of the vapour ahead of the interface is governed by a nonlinear diffusion equation. Therefore, the geometry of injection has an important effect upon the mass fraction of water that vaporizes. We show that with a constant supply of water from (i) a point source, the mass fraction of water which vaporizes increases towards the maximum permitted by the superheat of the rock; (ii) a line source, a similarity solution exists in which the mass fraction vaporizing is constant; and (iii) a planar source, the liquid-vapour interface steadily translates through the rock with a very small fraction of the injected water vaporizing.

Instabilities during liquid migration into superheated geothermal reservoirs

“…As a result, the interfacial temperature Ti is also lower, and so, the amount of energy released by the hot rock as it is invaded by the liquid and cools to temperature Ti is greater. As a result, there is more energy available for vaporization [Woods and Fitzgerald, 1993].…”

Asymptotic analysis of a Hiemenz flow in a low-porosity medium with phase change

“…Vapour extraction from a water-saturated porous reservoir (Woods & Fitzgerald 1993;Tsypkin & Woods 2004), condensing flow of steam (Bergins, Crone & Strauss 2005), motion of aqueous saline solution through a low-permeability fracture (Tsypkin & Woods 2005), gas extraction from multilayered rocks (Farcas & Woods 2007) represent examples of geothermal applications of phase change in porous media.…”

Mathematical modeling of cold water injection into a depleted high-temperature geothermal reservoir

“…The problems associated with water injection into geothermal reservoirs were investigated by a number of authors using analytical and numerical methods [1][2][3][4][5][6][7][8]. Bodvarsson [1] found a solution of the traveling wave type for a flow with spherical symmetry, which enables one to estimate the volume of water injected into a geothermal reservoir.…”

“…The exactness of analytical solution was confirmed by results of numerical solutions. Woods and Fitzgerald [5][6][7] treated the radial problem on liquid motion in superheated fissured rocks and derived simple solutions and estimates providing an asymptotic description for two limiting cases at high and low rates of injection. Barmin and Tsypkin [8] derived a complete system of boundary conditions in the boiling front, which includes the laws of conservation for mass and energy and the Clausius-Clapeyron relation, and gave the solution to one-dimensional problem in a linear approximation for injection to low-permeability rocks.…”