A Perturbation Boundary Element Model to Simulate Nonplanar Fracture Networks in Shale Gas Reservoirs

摘要

In reality, hydraulic fracturing creates unstructured fracture networks in which nonplanar fractures with varying fracture width exist. Pressure and rate transient analysis for such a complex fracture network is quite challenging. We proposed a perturbation boundary element model to handle the nonplanar varying-width fractures within non-orthogonal fracture network considering stress-sensitivity effect. Line source function is obtained by solving the reservoir flow equation. Hydraulic fractures are represented explicitly and divided into small elements. We established governing equations for each fracture segment in local coordinate system, with sufficient flexibility to set up each segment with different fracture width, permeability and orientation. The stress-dependent fracture permeability is adopted to account for the effect of stress sensitivity. Pedrosa's transformation and a perturbation technique are employed to solve the nonlinear diffusivity equations. Superposition principle is employed to obtain the pressure responses in shale formations. We performed case studies which compared two fractured horizontal wells, one with three constant-width fractures and another with three varying-width elliptical fractures. We found that the difference of well performance decreases with fracture conductivity increasing. It shows that pressure behavior is strongly dependent on the fracture geometry. The nonplanar fracture geometry and stress sensitivity have negative effects on well performance.