Evaluation of productivity index in unconventional reservoir systems: An extended Distributed Volumetric Sources method

Horizontal drilling and hydraulic fracturing technologies make the production of unconventional reservoirs practically and economically feasible. The combination of these two techniques leads to complex well-reservoir systems. Distributed Volumetric Source (DVS) can be utilized as an effective methodology to evaluate the production of hydrocarbons from a complex configuration of fractured/non-fractured wells (both vertical and horizontal) in a well-reservoir system. This study modifies the DVS method through generalizing the solution for different boundary conditions and improving the accuracy of the method at the infinite acting conditions. The DVS method is introduced as an appropriate replacement to the influence function in the common/conventional Multi-Well Productivity Index (MPI) method because of its capability to capture the production mechanisms and production index over both transient and pseudo-steady state regimes, by employing a single influence function so that the internal well fluid flow can be coupled to the fluid flow in the reservoir. The horizontal well still remains a challenging configuration. It is found that the impact of the well penetration ratio on the productivity of horizontal well during the production time can be properly modeled by the DVS method. Due to the low precision of the common (original version of) DVS method at early times, a new solution method based on Fourier integral is proposed and the accuracy is systematically examined. Hence, DVS is employed to circumscribe the infinite-acting response of this well configuration. Finally, a new methodology is proposed to optimize the design of Multi-Fractured Horizontal Well (MFHW). According to the output of this study, the extended DVS procedure offers a better plan in terms of technical and economic aspects to design MFHW, compared to conventional solution techniques.