A Mathematical Model for Fracture Networks with Considering Fracture Propagation and Closure in Shale

Abstract

This study develops a semi-analytical model for fracture networks with considering fracture propagation and closure. To consider the volumetric fracturing, Warren-Root dual-porosity model is used to divide the reservoir into a fracture system and a matrix system. In addition, the discrete secondary fractures connected by hydraulic fractures are also taken into account. After model solution, it is found that flow stages of the theoretical well test curve of the multi-stage fractured horizontal well in shale reservoirs can be divided into: stage before the fracture closes, stage after the fracture closes, supply flow stage between secondary fractures and hydraulic fractures, linear flow stage, early dual radial flow stage, interporosity flow stage, late dual radial flow, and pseudo radial flow. The pressure and pressure conduction curves coincide with a straight line with a slope of 1 at stage before the fracture closes, which is similar to the wellbore storage effect. The shape of the derivative curve of dimensionless pressure and dimensionless pressure is similar to the behaviour of variable well-storage, during stage after the fracture closes. At the supply flow stage, there is a slight “dip”, which means that the reservoir fluid is supplied from the secondary fractures activated by fracturing to the main hydraulic fractures.