Pressure Transient Behaviors of Vertical Fractured Wells With Asymmetric Fracture Patterns

It is well proven that hydraulic fracturing may cause a complex fracture network or an asymmetric fracture pattern. This study aims to develop a model to analyze the pressure transient behaviors for asymmetric fracture patterns. Some physical models were built to describe the asymmetric of fracture length and conductivity. In order to solve the model, each fracture was discreted to several segments and each segment was treated as a line source. According to theory of superposition, we coupled the flow rate and pressure in the boundaries and the middle point of segments. After a Laplace transform to the mathematical model, the flow rate of each line source can be calculated. We used Stehfest inversion algorithm to determine the simulation results in a real-time domain. The calculation results show that the asymmetry of fracture patterns or properties can make a significant change in pressure and derivation curves. If only primary fracture is considered, it is difficult to differentiate the flow period. If the fracture patterns contain several secondary fractures, the derivation curve shows an obvious pseudo-radial flow in the early period.