Equivalent force model of deformation induced by oil and gas reservoir development and its volume boundary element method solution

To address the issue that traditional finite element methods cannot fully consider the semi-infinite earth strata and have lower solution accuracy, a new equivalent force model for induced deformation during oil and gas reservoir development is derived from the perspective of semi-infinite strata. A brand-new volume boundary element numerical method solution has been developed and verified and tested. The influences of internal flow and flow boundary of the reservoir on strata deformation are equivalent to the impacts on strata deformation when external forces act at the interior and boundary of the reservoir, respectively. Calculation methods for the flow equivalent force and boundary equivalent force are provided. The deformation solution at any point in the strata can be obtained through the convolution of flow equivalent forces, boundary equivalent forces and Green's functions. After discretization, the deformation solution at any point in the strata can be obtained by multiplying the grid boundary equivalent forces, grid flow equivalent forces with their corresponding grid boundary sources and grid volume sources respectively, and then summing them up. This numerical method is termed the Volumetric Boundary Element Method (VBEM). Compared with traditional commercial simulators, VBEM fully considers the effects of reservoir flow boundaries, pore pressure gradient fields within the reservoir, and fluid mass changes within pores on formation deformation. It eliminates the need for meshing outside the reservoir, achieves significantly improved solution accuracy, and provides a new technical framework for simulating deformation induced by reservoir development.