Porothermoelastic Analysis of the Response of a Stationary Crack Using the Displacement Discontinuity Method

Thermally induced volumetric changes in rock result in pore pressure variations, and lead to a coupling between the thermal and poromechanical processes. This paper examines the response of a fracture in porothermoelastic rock when subjected to stress, pore pressure, and temperature perturbations. The contribution of each mechanism to the temporal variation of fracture opening is studied to elucidate its effect. This is achieved by development and use of a transient displacement discontinuity (DD) boundary element method for porothermoelasticity. While the full range of the crack opening due to the applied loads is investigated with the porothermoelastic DD, the asymptotic crack opening is ascertained analytically. Good agreement is observed between the numerical and analytical calculations. The results of the study show that, as expected, an applied stress causes the fracture to open while a pore pressure loading reduces the fracture width (aperture). In contrast to the pore pressure effect, cooling of the crack surfaces increases the fracture aperture. It is found that the impact of cooling can be more significant when compared to that of hydraulic loading (i.e., an applied stress and pore pressure) and can cause significant permeability enhancement, particularly for injection/extraction operations that are carried out over a long period of time in geothermal reservoirs.

[1]  Masataka Tanaka,et al.  Boundary element method applied to 2-D thermoelastic problems in steady and non-steady states , 1984 .

[2]  D. F. McTigue,et al.  Thermoelastic response of fluid‐saturated porous rock , 1986 .

[3]  Euripides Papamichos,et al.  Conductive heat flow and thermally induced fluid flow around a well bore in a poroelastic medium , 1994 .

[4]  P. T. Delaney.  Rapid intrusion of magma into wet rock: Groundwater flow due to pore pressure increases , 1982 .

[5]  S. L. Crouch,et al.  Boundary element methods in solid mechanics , 1983 .

[6]  Emmanuel M Detournay,et al.  A direct boundary element method for plane strain poroelasticity , 1988 .

[7]  J. Roegiers,et al.  Thermoporoelastic modelling of wellbore stability in non-hydrostatic stress field , 1998 .

[8]  J. H. Curran,et al.  A Displacement Discontinuity Model For Fluid-saturated Porous Media , 1987 .

[9]  M. Biot.  General Theory of Three‐Dimensional Consolidation , 1941 .

[10]  J. Fredrich,et al.  Micromechanics of thermally induced cracking in three crustal rocks , 1986 .

[11]  A. Cheng,et al.  Transient boundary element formulation for linear poroelasticity , 1987 .

[12]  J. Sládek,et al.  Boundary integral equation method in thermoelasticity part III: uncoupled thermoelasticity , 1984 .

[13]  Ahmad Ghassemi,et al.  A transient fictitious stress boundary element method for porothermoelastic media , 2004 .

[14]  I. N. Sneddon.  The distribution of stress in the neighbourhood of a crack in an elastic solid , 1946, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[15]  Carlos Alberto Brebbia,et al.  Boundary Elements: An Introductory Course , 1989 .

[16]  Ahmad Ghassemi,et al.  Integral equation solution of heat extraction‐induced thermal stress in enhanced geothermal reservoirs , 2005 .

[17]  Emmanuel M Detournay,et al.  Plane strain analysis of a stationary hydraulic fracture in a poroelastic medium , 1991 .

[18]  A. Cheng,et al.  On singular integral equations and fundamental solutions of poroelasticity , 1998 .

[19]  A. Cheng,et al.  An integral equation solution for three‐dimensional heat extraction from planar fracture in hot dry rock , 2003 .

[20]  P. A. Domenico,et al.  Characterization of drained and undrained response of thermally loaded repository rocks , 1982 .

[21]  Herbert F. Wang.  Theory of Linear Poroelasticity with Applications to Geomechanics and Hydrogeology , 2000 .

[22]  J. Rice,et al.  Some basic stress diffusion solutions for fluid‐saturated elastic porous media with compressible constituents , 1976 .

[23]  M. Biot.  THEORY OF ELASTICITY AND CONSOLIDATION FOR A POROUS ANISOTROPIC SOLID , 1955 .

[24]  John P. Carter,et al.  Elastic consolidation around a deep circular tunnel , 1981 .

[25]  A two‐dimensional poroelastic displacement discontinuity method for hydraulic fracture simulation , 1989 .

[26]  Stephen J. Bauer,et al.  Thermal expansion and cracking of three confined water-saturated igneous rocks to 800°C , 1983 .