Equivalent force convolution method for solving stress induced by oil and gas reservoir development

Abstract Stress sensitivity is an important factor affecting the seepage mechanism of oil and gas reservoirs. Accurate simulation of reservoir development must comprehensively consider the mechanical properties of fluids and rocks. Since the reservoir is located in a semi-infinite formation, its induced deformation will inevitably propagate infinitely outward. However, the current various solution methods cannot fully characterize the influence of the semi-infinite formation. This study proves through detailed mechanical derivation that the effects of fluid seepage and impermeable boundaries inside the reservoir on formation deformation are equivalent to the effects of external forces inside the reservoir and at the reservoir boundary on formation deformation. The concepts and calculation methods of seepage equivalent force and boundary equivalent force were established for the first time. The effective force is decided by the pore pressure gradient, the mass of liquid and the elasticity of the rock. The induced distortion can be calculated by means of the convolution of equivalent force and Green’s function, which is equivalent force convolution. Based on the theory of equivalent force convolution, the paper analyses the stress in two cases: when the pressure does not reach the side of the reservoir, or when the limited disk storage is exhausted. The results indicate that if the pressure does not reach the side of the oil field, the reservoir will be compressed due to the reduction of the pore pressure. When the reservoir is depleted, the strain inside the reservoir is also compressive strain, and the deformation distribution inside the reservoir is relatively uniform. The closer to the lateral boundary, the more severe the horizontal compression, and the lighter the vertical compression. This method is applicable to any reservoir shape and pressure distribution, can accurately solve the deformation state at any position, fully consider the half-space formation, and ensure the same accuracy of far-field and near-field solutions, providing a new solution to the induced reservoir geotechnical problems in oil and gas reservoir development.