Analytical model for pressure and rate analysis of multi-fractured horizontal wells in tight gas reservoirs

Multi-fractured horizontal wells (MFHWs) are effective for developing unconventional reservoirs. A complex fracture network around the well and hydraulic fractures form during fracturing. Hydraulic fractures and fracture network are sensitive to the effective stress. However, most existing models do not consider the effects of stress sensitivity. In this study, a new analytical model was established for an MFHW in tight gas reservoirs based on the trilinear flow model. Fractal porosity and permeability were employed to describe the heterogeneous distribution of the complex fracture network. The stress sensitivity of fractures was also considered in the model. Pedrosa substitution and perturbation method were applied to eliminate the nonlinearity of the model. Analytical solutions in the Laplace domain were obtained using Laplace transformation. The model was then validated and applied. Finally, sensitivity analyses of pressure and rate were discussed. The presented model provides a new approach to estimate the effect of fracturing. It can also be utilized to recognize formation properties and forecast the dynamics of pressure and the production of tight gas reservoirs.