Horizontal well drilling and hydraulic fracturing technologies play an essential role in improving gas recovery from shale reservoirs. However, they are expensive technologies and resource intensive production strategies. Optimization design of horizontal well spacing and fracture stage placement helps in striking a balance between gas production and economic benefits. However, previous researches relied mainly on numerical simulation technique which is computationally expensive and time-consuming. To reduce the computational burden, a novel multi-fidelity support vector regression (MFSVR) surrogate model assisted horizontal well spacing and fracture stage placement integrated optimization method, namely WSF-MFSVR, is proposed in this study. In the WSF-MFSVR method, both low-fidelity (LF) and high-fidelity (HF) numerical simulation models were applied to establish the multi-fidelity (MF) surrogate model so as to lessen the computational burden and guarantee its quality. In order to enhance the evaluation accuracy, the particle swarm optimization (PSO) algorithm was adopted to find the optimal hyper-parameters of the MFSVR model. Two cases with different wells and fracture types based on the shale gas reservoir with Barnett shale properties were employed to verify the WSF-MFSVR method. The results indicated that a combination of 300 H F and 3500 LF samples was the most suitable for establishing the MFSVR model to approximate the numerical simulation model. In terms of computational efficiency, the WSF-MFSVR method was about 50 times faster than the HF numerical simulation model-based method. Furthermore, the relative hyper-area difference (RHD) and overall spread (OS) of the WSF-MFSVR method were similar to that of the HF numerical simulation model-based method. However, the RHD and OS of the WSF-MFSVR method were superior to that of the LF numerical simulation model-based and single-fidelity support vector regression model-assisted methods. The data of these indexes quantitatively showed the superior convergence and diversity of the final optimal solutions obtained by WSF-MFSVR method.

水平井钻井和水力压裂技术在提高页岩气藏采收率方面发挥着重要作用。然而，它们是昂贵的技术和资源密集型生产策略。水平井间距和压裂段布置的优化设计有助于在产气和经济效益之间取得平衡。然而，以往的研究主要依赖于数值模拟技术，计算量大且耗时。为了减少计算负担，一种新颖的多保真支持向量回归（MFSVR）本文提出了替代模型辅助水平井间距与裂缝段位布置一体化优化方法，即WSF-MFSVR。在WSF-MFSVR方法中，同时应用低保真（LF）和高保真（HF）数值模拟模型建立多保真（MF）代理模型，以减轻计算负担并保证其质量。为了提高评估精度，采用粒子群优化（PSO）算法寻找MFSVR模型的最优超参数。基于页岩气使用具有 Barnett 页岩特性的储层来验证 WSF-MFSVR 方法。结果表明，300 H F 和 3500 LF 样本的组合最适合建立 MFSVR 模型以逼近数值模拟模型。在计算效率方面，WSF-MFSVR 方法比基于 HF 数值模拟模型的方法快约 50 倍。此外，WSF-MFSVR 方法的相对超面积差 (RHD) 和整体扩散 (OS) 与基于 HF 数值模拟模型的方法相似。然而，WSF-MFSVR 方法的 RHD 和 OS 优于基于 LF 数值模拟模型和单保真支持向量回归模型辅助的方法。