Transient pressure response of fractured horizontal wells in tight gas reservoirs with arbitrary shapes by the boundary element method

Horizontal wells and hydraulic fracturing are the key techniques to develop tight gas reservoirs efficiently, but the related researches on the pressure of such wells in arbitrary shaped reservoirs are rare. On this background, this paper extends the boundary element method (BEM) into application to study a multiple fractured horizontal well (MFHW) in arbitrary shaped tight gas reservoirs. By discretizing the outer boundary as well as the fractures, the boundary integral equation can be derived through coupling the fundamental solution of the Helmholtz equation with the dimensionless diffusivity equation. Thereafter, the coefficient matrix, including the fluxes and pressure on the boundaries, can be assembled, and the bottomhole pressure can be computed simultaneously. In this study, by comparison with some semi-analytical solution cases, the accuracy of the results from the BEM was validated. Also, the pressure response and its derivative type curves for a MFHW in an elliptical drainage area were also analyzed, and the effects of reservoir shape, fracture number together with fracture distribution on type curves were examined, respectively. The results suggest that the reservoir shape has a weak effect on the type curves for a MFHW in a large drainage area. If the reservoir size is not large enough comparing to the size of MFHW, the effects of boundary shape could become more obvious and the pressure wave would propagate to the closer boundary (i.e., the minor axis is small) in a relatively short time, which leads to earlier boundary reflection flow period.