Pressure transient analysis for vertical fractured wells with fishbone fracture patterns

Many diagnostic technologies have proven that complex fracture pattern would be generated during the operation of fracture treatment for vertical well. However, there had been very little research reported on fishbone fracture pattern for vertical well, which is one of the typical fracture geometries. To analysis the pressure behavior of this kind fracture pattern, a semi-analytical method is proposed and some typical fracture patterns are compared in this work. Based on the theory of superposition, the physical model is divided into two sub-systems: (a) a formation/fracture sub-system and (b) a fracture sub-system. A flexible discretization and coupling method is developed to investigate irregular fracture geometry and non-orthogonal between two fractures. The mathematical model is solved in the Laplace domain and the Stehfest inversion algorithm is applied to determine the corresponding pressure distribution in the real-time domain. Type curves are generated and flow regimes are identified. Sensitivity analysis and actual field case are conducted. It is found that there are five flow regimes, they are bilinear flow, flow feed, fracture linear flow, formation linear flow, bi-radial flow and pseudoradial flow. The pressure depletion decreases with increase of the number, length and conductivity of secondary fractures, and their effect on contribution of primary fracture have a similar tendency. Effects of Inclined angle between secondary and primary fractures on pressure transit behavior occurs during flow feed and later regimes, while fractures pattern with different geometries can influence all the flow regimes. The derived analytical pressure transient solution may provide a theoretical basis for the analysis of the pressure transient behavior of the fishbone fracture pattern in a vertical well.