Pore pressure profiles in fractured and compliant rocks1

Fluid permeability in fractured rocks is sensitive to pore-pressure changes. This dependence can have large effects on the flow of fluids through rocks. The authors define the permeability compliance [gamma] = 1/k([partial derivative]k/[partial derivative]p[sub p])[sub pc], which is the sensitivity of the permeability k to the pore pressure p[sub p] at a constant confining pressure p[sub c], and solve the specific problems of constant pressure at the boundary of a half-space, a cylindrical cavity and a spherical cavity. The results show that when the magnitude of permeability compliance is large relative to other compliances, diffusion is masked by a piston-like pressure profile. The authors expect this phenomenon to occur in highly fractured and compliant rock systems where [gamma] may be large. The pressure profile moves rapidly when fluids are pumped into the rock and very slowly when fluids are pumped out. Consequently, fluid pressure, its history and distribution around injection and production wells may be significantly different from pressures predicted by the linear diffusion equation. The propagation speed of the pressure profile, marked by the point where [partial derivative]p[sub p]/[partial derivative]x is a maximum, decreases with time approximately as [radical]t, and the amplitude of the profile also dissipates with timemore » (or distance). The effect of permeability compliance can be important for fluid injection into and withdrawal from reservoirs. For example, excessive drawdown could cause near-wellbore flow suffocation. Also, estimates of the storage capacity of reservoirs may be greatly modified when [gamma] is large. The large near-wellbore pressure gradients caused during withdrawal by large [gamma] can cause sanding and wellbore collapse due to excessive production rates.« less