NONLINEAR SEEPAGE MODEL FOR MULTIPLE FRACTURED HORIZONTAL WELLS WITH THE EFFECT OF THE QUADRATIC GRADIENT TERM

Abstract

The multiple fractured horizontal well (MFHW) has been extensively employed to develop oil and gas reservoirs, especially in the development of low permeability reservoirs. Many types of seepage models have been proposed to investigate the pressure responses of MFHWs in different reservoir scenarios. However, to our knowledge, all of the proposed models for MFHWs are inconsistent with the principle of the mass conservation because the quadratic gradient term in the nonlinear partial differential equation (PDE) is neglected for the sake of simplicity. This paper establishes a nonlinear seepage model for an MFHW in an infinitely large underground porous-media formation. All of the terms in the nonlinear PDE are retained. The transformed pressure and flow rate function are first introduced to obtain the linearized point source model, and then the Laplace transform, principle of superposition, numerical discrete method, and Stehfest numerical inversion are taken to solve the nonlinear seepage model for MFHWs. Type curves of the transient pressure for an MFHW are plotted and the main flow regimes are observed. The effects of the nonlinearity on the transient pressure and flow-rate density distribution in fractures are qualitatively and quantitatively analyzed. The nonlinear model presented is consistent with material balance, and thus it can be used to obtain more accurate transient pressure in MFHWs.