Abstract In the last decades, natural gas from unconventional reservoirs has become a major portion of total gas supply due to advances in horizontal well drilling and multi-stage hydraulic fracturing as well as reduction of operational costs and capital expenditures. However, hydraulic fracturing technique is a still costly and resource intensive production strategy that requires optimal planning to conform to the best safety practices and to obtain the highest returns on investments. Thus, the proposed fast and reliable hydraulic fracture (HF) placement optimization technique based on physics and analytical equations is the key tool to balance between gas production costs and anticipated revenues. 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.

中文翻译：

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快速分析方法和人工智能优化技术在页岩气藏水力压裂阶段布置中的应用

摘要 近几十年来，由于水平井钻井和多级水力压裂技术的进步以及运营成本和资本支出的降低，非常规油气藏天然气已成为天然气供应总量的重要组成部分。然而，水力压裂技术仍然是一种成本高昂且资源密集型的生产策略，需要优化规划以符合最佳安全实践并获得最高投资回报。因此，所提出的基于物理和分析方程的快速可靠的水力压裂 (HF) 布置优化技术是平衡天然气生产成本和预期收入的关键工具。在这项研究中，我们开发了一个分析模型，其中使用伪压力方法的修正 Wattenbarger 板模型被集成到作为目标函数的净现值 (NPV) 中。我们考虑四个决策变量，包括 HF 级数、HF 间距、HF 半长和井眼间距，并使用三种随机无梯度优化方法（即遗传算法 (GA)、差分进化 (DE) 和粒子群优化） (PSO)) 以优化具有 Barnett 页岩特性的合成页岩气储层模型的目标函数。为了验证得到的最优解的准确性，我们对每种随机优化方法进行了四次试验，100代，种群规模为20。结果表明，PSO发现的NPV的最佳总体值为1.7%和7。分别比 DE 和 GA 获得的高 6%。此外，PSO 具有最快的收敛速度（50 代），与其他方法所需的计算时间相比至少节省 10% 的计算时间，并且在所有试验中得到相同的最优解。最后，考虑生产初期的双线性流动、生产后期的非线性流动以及分析模型中的重力效应，仍是该领域未来研究的开放领域。