Poroelastic Solution for the Nonlinear Injectivity of Subsurface Rocks With Strain‐Induced Permeability Variations

Abstract

Fluid injection in porous rock occurs in a variety of hydrogeological operations including wastewater disposal, CO2 sequestration, enhanced oil recovery, and geothermal energy extraction. Influx of fluid into the host rock is usually accompanied by induced permeability enhancement due to increased pore fluid pressure and consequent dilation of the pore volume. The effect would, in turn, enhance the well injectivity index. This paper presents an analytical solution to the nonlinear problem of underground fluid injection in a disk‐shaped reservoir while accounting for the induced permeability enhancement. The host rock permeability is considered to depend on the rock total stress and pore fluid pressure. For this purpose, the rock stress is formulated as a nonlocal function of disturbances in the pore fluid pressure using the fundamental solution for a nucleus of strain in an elastic half space. Alongside, the nonlinear fluid transport equation that incorporates stress‐sensitive rock permeability is analytically solved using a perturbation technique. The good match with finite difference solution to the same problem verifies the validity and accuracy of the perturbation solution. Parametric study on a test case problem is conducted to examine the influence of different parameters on well injectivity. Findings reveal the higher vulnerability of shallower host reservoirs to stress‐induced permeability variations. The effect of rock poroelastic properties on fluid transport process is discussed.

Well Injectivity during CO2 Geosequestration: A Review of Hydro-Physical, Chemical, and Geomechanical Effects

“…Furthermore, due to the nonlocal dependence of permeability on pore pressure, the well injectivity enhancement will be more pronounced in shallow host formations. 63 In addition, heterogeneity in permeability can strongly affect the injectivity of wellbores through impacting the effective permeability anisotropy, sweep efficiency, diffusive mixing, convective mixing, viscous effects, and the density-driven flow of scCO 2 in aquifer systems. 44,64,65 Heterogeneity might occur due to the existence of even small spatial lenses of tight rocks penetrated through sandstones, scouring, and changes in clay content, bedding planes, or diagenetic features.…”

“…Besides, the controversies might stem from the time-dependent nature of the permeability and injectivity of wellbores, that is to say that longer injection times lead to enhanced permeability and injectivity. Furthermore, due to the nonlocal dependence of permeability on pore pressure, the well injectivity enhancement will be more pronounced in shallow host formations …”

Modelling of fluid pressure migration in a pressure sensitive fault zone subject to cyclic injection and implications for injection-induced seismicity

“…Katayama et al 2018;De Barros et al 2022). The fluid diffusion process is nonlinear because the local fault permeability is a function of local fluid pressure (Pedrosa 1986;Zhang & Mehrabian 2020. Particularly, pore pressure increase reduces the effective stress and thus increases the permeability along the fault, which in turn affects the fluid diffusion and the associated seismic hazard.…”