Pressure Transient Behavior of Horizontal Wells Intersecting Multiple Hydraulic Fractures in Naturally Fractured Reservoirs

Abstract

In this study, we present a mesh-free semi-analytical technique for modeling pressure transient behavior of continuously and discretely hydraulically and naturally fractured reservoirs for a single-phase fluid. In our model, we consider a 3D reservoir, where each fracture is explicitly modeled without any upscaling or homogenization as required for dual-porosity media. Fractures can have finite or infinite conductivities, and the formation (matrix) is assumed to have a finite permeability. Our approach is based on the boundary element method. The method has advantages such as the absence of grids and reduced dimensionality. It provides continuous rather than discrete solutions. The uniform-pressure boundary condition over the wellbore is used in our mathematical model. This is the true physical boundary condition for any type of well, whether fractured or not, provided that the friction pressure drop in the wellbore is small and the fluid is Newtonian. The method is sufficiently general to be applied to many different well geometries and reservoir geological settings, where the spatial domain may include arbitrary fracture and/or fault distribution, a number of horizontal wells with and without hydraulic fractures, and different types of outer boundaries. The model also applies to multistage hydraulically fractured horizontal wells in homogenous reservoirs. More specifically, it is applied to investigate the pressure transient behavior of horizontal wells in continuously and discretely naturally fractured reservoirs, including multistage hydraulically fractured horizontal wells. A number of solutions have been published in the literature for horizontal wells in naturally fractured reservoirs using the conventional dual-porosity models that are not applicable to many of these reservoirs that contain horizontal wells with multiple fractures. Most published solutions for fractured horizontal wells in homogenous and naturally fractured reservoirs ignore the presence of the wellbore and the contribution to flow from the formation directly into the unfractured horizontal sections of the wellbore. Therefore, some of the flow regimes from these solutions are incorrect or do not exist, such as fracture-radial flow regime. In our solutions, all or some of multistage hydraulic fractures may intersect the natural fractures, which is very important for shale gas and oil reservoir production. The number and type of fractures (hydraulic or natural) intersecting the wellbore and with each other are not limited in both homogeneous and naturally fractured reservoirs. Our solutions are compared with a number of existing solutions published in the literature. Example diagnostic derivative plots are presented for a variety of horizontal wells with multiple fractures in homogenous and naturally fractured reservoirs.