Geothermal heat extraction by water circulation through a large crack in dry hot rock mass

Abstract

SUMMARYOne proposed geothermal heat extraction scheme relies on water circulation in a large vertical crack created by hydraulic fracturing in a hot dry impermeable rock mass. Water flow, heat convection and crack opening widths are analysed by finite elements. Governing field equations of the problem are first set up rigorously and then various small terms are identified and neglected, retaining the effects of pressure gradient, buoyancy, velocity head (kinetic energy) and head loss due to viscous friction in the water flow equation, and the effects of heat convection in water and heat conduction in rock in the heat transfer equation. The finite element scheme for water flow is based on a variational principle that is typical for diffusion problems, and for heat transfer it is based on the method of least-square residuals. The system of differential equations is highly non-linear. The non-linear terms and coefficients are treated in the finite element analysis as constant; the finite element analysis of the steady-state pressures, fluxes and temperatures is then iterated, evaluating all non-linear terms and coefficients on the basis of the solution obtained in the previous iteration. Numerically calculated fields at various times after the start of cooling are presented. They indicate some features favourable for the geothermal scheme, such as formation of eddy currents, and downward flux of water toward hotter rock. However, other important questions would have to be solved to gain full understanding of this proposed geothermal scheme. INTRODUCflONIn one proposed scheme of heat extraction from hot dry rock geothermal reservoirs, a large vertical crack is to be induced by hydraulic fracturing from a borehole (Figure 1). The upper part of the crack is then intersected by a second borehole, and heat is extracted by circulating water through the crack. Influx of cold water is expected to cause secondary fracturing and large expansion of the region from which the heat can be withdrawn.Considerable interest has been recently shown in this scheme and various aspects of the problem have been studied. 1-3 One problem of particular interest is the circulation of water, heat convection and opening width of a single, main crack created by hydraulic fracture. This problem was analysed by McFarland 4 using a standard finite difference program for diffusion flows. The present paper deals with finite element analysis of the problem. Variations of the crack thickness due to temperature changes are taken into account, and differential equations describing the flow and heat convection in the crack more accurately than those used before are developed.

Initiation of parallel cracks from surface of elastic half-plane

“…When a floating sea ice plate is subjected to a vertical load, star-shaped cracks of finite length radiate suddenly from the loaded area when the applied load reaches a certain level. Spacing of thermal cracks produced in hot rock by circulation of cold water is important for the hot dry rock geothermal energy scheme [4]. In all these situations, cracks of macroscopic sizes form at a smooth surface.…”

On Heat and Mass Transfer within Thermally Shocked Region of Enhanced Geothermal System

“…As mentioned earlier, the occurrence of the thermal fractures in an EGS reservoir has been proven theoretically and experimentally [3,5,[13][14][15]. Their presence has also been acknowledged in induced seismicity studies in several operating geothermal sites [22].…”

“…Barr [14] investigated the branching of thermal fractures by examining the potential of crack propagation away from the surface of the primary fracture in a hot dry rock (HDR) system. Bažant and Ohtsubo [15] as well as Murphy [3] and Barr [14] show that, during the heat extraction process, a network of closely spaced thermal fractures, which resembles a "waffle" grid of grooves [2], is formed adjacent to the primary fractures. One of the common observations of these studies is that the growth patterns of thermal fractures are complex, particularly under the large thermal strain close to the surfaces of primary fractures.…”

An integral method for predicting hydraulic fracture propagation driven by gases or liquids

“…The fluid motion within the fracture is governed by conservation of mass and momentum, which may be expressed in the following one-dimensional form: a i a -(pw)+---(r"pwu)+2p0=0 at rn ax (5) in which p, u and w are density, longitudinal velocity, and aperture, each averaged over the cross section (so, w = w,n/4 for the envelope-shaped fracture which has an elliptical cross-section") and u is the local seepage velocity into the walls of the fracture. Depending upon the magnitude of the Reynolds number II/ = 0 2 ( : ) , rough-wall turbulence2'-22…”