A new semi-analytical model for simulating the effectively stimulated volume of fractured wells in tight reservoirs

In this paper, a new semi-analytical model is presented for vertically fractured wells with stimulated reservoir volumes (SRV). Specifically, we employ fractal porosity and permeability to describe the heterogeneous distribution of porous media in a SRV. An approach is given for estimating the size and equivalent permeability of the fractal SRV for vertically fractured wells in tight reservoirs. The line source function, Laplace transformation, integral of the modified Bessel function and Stehfest numerical inversion algorithms are used to solve the composite model. Based on the Duhamel principle, the dimensionless pressure responses of tight oil and gas wells in the Laplace domain and time domain are obtained. Flow regime diagnostics of vertically fractured wells in tight reservoirs are characterized. Sensitivity analysis, including the effects of SRV parameters and fractal parameters on pressure responses and linear flow, are performed. The results show that seven primary regimes can be divided into pressure response curves. The size and equivalent permeability of the fractal SRV can be calculated by the dimensionless pressure derivative curves. In a complex fractal reservoir, the larger the connectivity index is and the smaller the fractal dimension is, the more significant the heterogeneity of the fractal SRV is and the larger the slopes of linear flow are, which leads to a smaller equivalent permeability of the fractal SRV radius. The presented model and the results in this paper can enrich the pressure transient analysis models for vertically fractured wells in unconventional reservoirs.