Lawrence Berkeley National Laboratory

Quick estimates of fluid-induced subsurface deformation are helpful to assess the land uplift/subsidence and to reveal precursors of induced seismicity. Here, we adopt the inclusion theory and Green's function to develop a closed-form solution in a half space for the poroelastic response of a reservoir compartmentalized by an intersecting fault that can be offset and either permeable or impermeable. Simulated results reveal that (1) fault permeability mainly impacts the spatial distribution of displacement while its effect on displacement magnitude is small; (2) ground displacement slightly increases with fault dip while slightly decreases with increasing fault offset; in contrast, reservoir geometry shows a stronger effect than fault geometry: the ground displacement is proportional to the vertical and lateral depth ratios, defined as the ratios of reservoir thickness (h) and width (w) to reservoir depth (D), respectively; (3) the maximum vertical displacement is the double of the horizontal one regardless of fault permeability, fault and reservoir geometries, and mechanical parameters. Comparing the solution in a half space with that in a full space shows that neglecting the free surface underestimates the poroelastic displacement in the overburden. The validity of full-space solutions can be assessed with the product of the lateral and vertical depth ratios, i.e., wh/D2. The full-space solutions become valid when wh/D2 decreases to an intrinsic threshold. This threshold may range from 0.01 to 0.02 for displacement, and its specific value depends on the field background and demands of projects, but can be estimated based on our solution. It is larger for stress than for displacement, and wh/D2 ≤ 0.1 is recommended as a general condition for neglecting the free-surface effects on induced stress. The analytical solution represents a useful tool for estimating ground deformation and for gaining insights of reservoir and fault geometries by analyzing surface deformation patterns.