Abstract
The technique of stimulated reservoir volume (SRV) is becoming a key measure to enhance vertical well productivity and ultimate recovery in tight oil reservoirs. After the SRV treatment, micro-seismic monitoring strongly shows approximate rectangle stimulated reservoir volumes with a single bi-wing fracture are generated. However, most published works on the pressure transient of vertically fractured wells assumed that the SRV is an approximate circle, and few works have been done to rectangle SRV.
In this paper, a new analytical pressure transient solution for vertically fractured wells (VFW), with rectangle SRV and a single bi-wing fracture, is derived under constant rate. First, a two-region composite model is established to model the VFW. The inner region is considered as rectangle dual-porosity with a single bi-wing fracture. In addition, this model also considers other multiple factors including stress-sensitivity effect of permeability, unsteady cross flow between matrix and fractures. Then, the trilinear flow model proposed by Brown is extended to handle the rectangle boundary and bi-wing fracture; the Pedrosa's perturbation and Laplace transformation are applied to solve the non-linear equation, and the Kazemi's method is adopted to simulate the unsteady cross flow, and the pressure equation for VFW is solved. After that, this analytical solution is applied to the real cases from Ordos Basin reservoir to conduct equation validation. Finally, sensitivity studies are conducted to evaluate the effect of some critical parameters on pressure behavior of VFW.
The results of verification show there are great agreements. Results from this study show that the special flow regimes for a VFW in tight oil reservoirs includes (1) linear flow for the effect of bi-wing fracture conductivity, (2) SRV width effect flow, (3) inner boundary-dominated flow. The linear flow is stronger with the increase of bi-wing fracture length, bi-wing fracture conductivity, and SRV width. As the permeability of SRV increases, the inner boundary-dominated flow becomes more obvious. In addition, the SRV linear flow is stronger with the increase of SRV volume.
This work provides significant references for reservoir engineers in pressure transient analysis as well as fracturing evaluations of vertically fractured wells in the tight oil reservoirs.
