Surrogate-Assisted Multiobjective Optimization of a Hydraulically Fractured Well in a Naturally Fractured Shale Reservoir with Geological Uncertainty

Hydraulic fracturing is the most widely used technology for the commercial exploitation of shale-gas reservoirs, yet still faces high cost and development risk caused by many inestimable and uncertain geological parameters in shale reservoirs. Optimally designing the hydraulic fracturing considering the geological uncertainty is an essential topic, and also a computationally expensive problem, which still has not obtained enough investigation. Facing this urgent requirement, a novel surrogate-assisted multiobjective optimization (MOO) framework is proposed for the hydraulically fractured well optimization in shale-gas reservoirs with geological uncertainty. A shale-gas-production numerical model is illustrated using the embedded discrete-fracture model (EDFM), in which a set of stochastic power-law distributed natural-fracture (NF) models are generated to describe the geological uncertainty. To fully grasp the expected economical revenue and the development risk, the MOO strategy is applied, in which the expected value and standard deviation of the net present values (NPVs) are regarded as the objective functions; a Pareto-ranking scheme is adopted to search for the Pareto front (PF) that satisfies both objectives. In addition, a state-of-the-art hybrid multiobjective particle-swarm optimization (HMOPSO) algorithm is developed, which couples the synthetic advantages of multiobjective particle-swarm optimization (MOPSO) and the nondominated sorting genetic algorithm II (NSGA-II) and presents a higher accuracy and efficiency than both of them. Furthermore, a Gaussian-process Kriging model is adopted as the surrogate model to replace the time-consuming numerical simulation caused by the geological uncertainty; it is then integrated with the HMOPSO to construct a surrogated-assisted HMOPSO, which helps to increase the optimization efficiency and accuracy of the computationally expensive problem. Finally, the superiority of the HMOPSO against the traditional algorithms is validated using several benchmark functions, and the surrogated-assisted HMOPSO is performed into a hydraulic-fracture (HF)-well MOO example in a shale-gas reservoir with geological uncertainty. The PF is obtained, which provides a set of tradeoff solutions for designers.