Semianalytical solutions for fluid flow in rock joints with pressure‐dependent openings

Abstract

[1] If fluid is injected into joints in rock masses, the pressure required might result in changes in the joint space between rock blocks that accommodate the fluid transport. At one extreme, very low injection rate and pressure, the joint space is unaffected, and the fluid pressure follows the usual law of linear diffusion. At the opposite extreme, very high injection rates, as used, for example, during hydraulic fracturing, the pressure is so high as to overcome the original Earth stress holding the rock blocks in contact. They ''lift off,'' resulting in huge changes in joint space, and the flow equation then becomes so nonlinear that pressure pulses are no longer transmitted in a smooth, diffusive manner but more like a propagating shock wave. In between these extremes, at more modest pressure, the result is not liftoff, but nevertheless, the effective stress tending to close the joint space is reduced; this space dilates, and the effective permeability and storativity of the joint will increase. While the pressure wave will not propagate quite as sharply as it does for liftoff, nonlinearities greatly influence the results, exhibiting behavior far from that predicted by linear diffusion.

Estimating permeability from quasi-static deformation: Temporal variations and arrival-time inversion

“…That is, there may be coupling between deformation and flow properties. Such coupling might occur when the CO 2 is channeled into a narrow fault zone (Murphy et al 2004). …”

Matrix permeability of reservoir rocks, Ngatamariki geothermal field, Taupo Volcanic Zone, New Zealand

“…Natural macro-fractures within a geothermal system, resulting from unconformities, cooling joints, and tectonic stress discontinuities, strongly control fluid flow due to their high permeability (Murphy et al 2004), and generally control the permeability in geothermal systems (Jafari and Babadagli 2011). Testing of macro-fracture permeability is usually done in situ with injection flow rate tests used to identify areas of high permeability associated with fractured zones (Watson 2013).…”

On the propagation of a quasi‐static disturbance in a heterogeneous, deformable, and porous medium with pressure‐dependent properties

“…This situation is similar to that studied by Wu and Pruess [2000] and Murphy et al [2004], where the governing equation for fluid pressure is generalized to allow for pressure-dependent coefficients. Then the product term " P " U in equation (46) vanishes.…”

“…Rather, because of the complexity of the problem, most investigations have utilized numerical methods [Raghavan et al, 1972;Noorishad et al, 1984;Rutqvist et al, 1998]. A handful of analytical studies have focused on the governing equation for fluid pressure with pressure-dependent coefficients [Wu and Pruess, 2000;Murphy et al, 2004]. However, these studies do not explicitly include the equation governing displacements in the porous solid, thus neglecting the full coupling of deformation to fluid pressure.…”

“…A number of investigators have considered poroelastic media, for which the solid component behaves in a linear elastic manner [Biot, 1941;Levy, 1979;Burridge and Keller, 1981;Segall, 1985;Wang, 2000;Vasco, 2009]. However, it is widely recognized that in many situations the material and flow properties may depend upon both the solid deformation and the fluid pressure [Nelson and Baron, 1971;Raghavan et al, 1972;Biot, 1973;Samaniego et al, 1977;Walsh and Brace, 1984;Gobran et al, 1987;Bethke and Corbet, 1988;Goddard, 1990;Zimmerman, 1991;Wu and Pruess, 2000;Bemer et al, 2001;Shapiro, 2003;Makse et al, 2004;Murphy et al, 2004;Cappa et al, 2006;Daley et al, 2006;Cheng and Abousleiman, 2008;Vasco and Minkoff, 2009;Liu et al, 2009], resulting in nonlinear governing equations.…”