Application of fast analytical approach and AI optimization techniques to hydraulic fracture stage placement in shale gas reservoirs

In this study, we develop an analytical model in which the modified Wattenbarger slab model with the pseudo-pressure approach are integrated into the Net Present Value (NPV) as the objective function. We consider four decision variables including number of HF stages, HF spacing, HF half-length, and wellbore spacing and use three stochastic gradient-free optimization methods (i.e., genetic algorithm (GA), differential evolution (DE), and particle swarm optimization (PSO)) to optimize the objective function on a synthetic shale gas reservoir model with the Barnett Shale properties. To verify the accuracy of the obtained optimal solutions, we conduct four trials for each stochastic optimization method with 100 generations and the population size of 20. The results show that the best overall value of the NPV found by PSO are 1.7% and 7.6% higher than those obtained by DE and GA, respectively. Moreover, PSO has the fastest convergence rate (in 50 generations), saves at least 10% of the computational time in comparison to those required by other methods, and results in the same optimal solution in all trials. Finally, considering bilinear flow at the early stages of the production period, nonlinear flow at the late production time, and gravitational effects in the analytical model are still open areas for future research in this field.