Numerical simulation of multi-stage fractured horizontal well in low-permeable oil reservoir with threshold pressure gradient with moving boundary

Abstract

Abstract A stimulation technology of multi-stage fractured horizontal well is commonly used for enhancing the productivity in the development of low-permeable oil reservoirs. However, it is well known that the fluid flow in low-permeable oil reservoirs doesn t obey conventional Darcy s law, and the threshold pressure gradient exists; as a result, in fact, the model of multi-stage fractured horizontal well in low-permeable oil reservoirs belongs to a nonlinear moving boundary problem. And realization of the numerical simulation for the model is very complicated and difficult. It is significant to figure out the threshold pressure gradient effect on the numerical simulation results for the solution of actual engineering problems. In view of the concerns, based on the subsurface Darcy s flow module in COMSOL Multiphysics, an effective numerical simulation method is presented here: The non-Darcy kinematic equation at the full pressure gradient range is expressed at the interface of the gravitational acceleration vector in Darcy s law. Furthermore, the simulation method is strictly verified through the comparison with two analytical solutions for a one-dimensional case and a two-dimensional case (radial flow) respectively. Consequently, according to a constructed model, which can cover non-Darcy flow in the unstimulated reservoir area with threshold pressure gradient, Darcy s flow in the stimulated reservoir area and Darcy s flow in the main hydraulic fractures, the two-dimensional numerical simulation of the multi-stage fractured horizontal well in the low-permeable oil reservoir is realized just through the subsurface Darcy s flow module. Finally, through analyses and discussions on the numerical results for several designed simulation scenarios, some significant conclusions are obtained such as due to the threshold pressure gradient effect, there exists large undeveloped areas in low-permeable oil reservoirs, which don t change with the production time for the constant well production pressure condition; SRV fracturing can largely improve the utilization degree of the low-permeable reservoir area between the adjacent main hydraulic fractures at the early production period; it is very necessary to incorporate the threshold pressure gradient effect in the simulation for the optimal well spacing design in the development of low-permeable oil reservoirs.