Abstract
Reservoir permeability and stress heterogeneous distribution leads to different hydraulic fractures length and angle. Gas reservoirs heterogeneous characteristics leads that well is not the center of the circle high-permeability region after large-scale fracturing. Traditional pressure transient model cannot be used in this case. When horizontal well length is relatively small, radial composite model can be used to simulate wellbore pressure. Therefore, the aim of this paper is to present a semi-analytical mathematical model of the off-center fractured horizontal well with circle high-permeability region. The coupling approach of hydraulic fracture and matrix model is employed to solve mathematical model. The wellbore pressure transient solution can be obtained by the Laplace transform, Gauss elimination and the Stehfest numerical inversion. The results shown that wellbore pressure response curve of this model includes eleven flow regimes. When well is not the reservoirs center, an obvious derivative curve “upwards” will emerge after inner radial flow regime, which is different from previous fractured horizontal well model. Hydraulic fractures properties and geometries distribution has obvious influence on derivative curves characteristic of early regime. Off-center distance and reservoirs properties has distinct influence on derivative curves characteristic of middle regime. This semi-analytical mathematical model can provide guide on high-permeability region depiction, hydraulic fracture, and reservoirs parameter inversion.
