Integrated optimization design for horizontal well spacing and fracture stage placement in shale gas reservoir

Highlights

• A novel integrated optimization design method for shale gas is established.

• The multi-fidelity support vector regression is proposed to assist well spacing and fracture optimization.

• This method provides a fast optimization approach for shale gas well space and fracture scheme.

Abstract

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.

Introduction

In the past ten years, the demand for fossil energy resources has increased sharply. The international energy association reports that the global demand of fossil energy in 2040 will be approximately seven percent more than it was in 2019 (IEA, 2020). Development of unconventional natural gas resources is a promising way to ensure energy security and overcome energy shortages. With the advent of hydraulic fracturing technique and multiple well drilling from one platform technology, some countries such as America, Canada, and China have successfully developed commercial shale gas resources in the past years (Rahmanifard and Plaksina, 2018; Yu et al., 2019; Lu et al., 2019a, 2019b; Sherratt et al., 2021). However, the high fracturing cost poses a great challenge to the economic development of shale gas reservoirs (Zhang and Sheng, 2021a). Therefore, it is necessary to find accurate and optimal well spacing and fracture solutions so as to achieve maximum developmental benefits and gas recovery (Cho, 2001; Yao et al., 2021).

Establishing an accurate and efficient optimization framework for integrating horizontal well spacing and fracture stage placement in shale gas reservoirs can help in obtaining suitable schemes for increasing developmental benefits and gas recovery. Accurate fracture characterization and reservoir modeling technology are vital tools for horizontal well spacing and fracture stage placement optimization in shale gas reservoir (Wang and Chen, 2019a; Shang et al., 2021). Due to the sophisticated seepage mechanisms and fractures distribution in ultralow permeability shale reservoirs, numerical simulation technique is frequently used to simultaneously characterize various mechanisms and different-scale fractures during production simulation (Zhang et al., 2020, Zhang et al., 2021; Feng et al., 2018, Feng et al., 2021). Thus, it is a suitable tool for objectives evaluation in the process of well spacing and fracture optimization (Xu et al., 2018). On the other hand, nature-inspired algorithms which can be easily combined with any complex engineering problem is suitable for shale gas optimization (Rahmanifard and Plaksina, 2018; Wang and Chen, 2019b; Yao et al., 2021; Zhang and Sheng, 2021a). Thus, numerical simulation model and nature-inspired algorithm are the two key techniques for horizontal well spacing and fracture stage placement integration optimization in shale gas reservoirs.

Numerical simulation based horizontal well spacing and fracture optimization design has gained significant attention in the past decade (Rafiee et al., 2012; Gordeliy and Peirce, 2013; Yu and Sepehrnoori, 2013; Jahandideh and Jafarpour., 2016; Rammay and Awotunde, 2016; Suarez and Pichon, 2016; Liu and Forouzanfar, 2018; Zhang et al., 2019; Li et al., 2021). More specifically, Ma et al. (2015) compared the performance of three frequently-used algorithms called SPSA, GA, and CMA-ES on integrated well placement and hydraulic fracture optimization of unconventional gas reservoirs. Yang et al. (2017) combined the fast marching method (FMM) and genetic algorithm (GA) for hydraulic fracture optimization design. Rahmanifard and Plaksina (2018) applied an analytical model and three algorithms to accelerate the optimization process of shale gas fracture stage placement. Wang and Chen (2019b) optimized hydraulic fracture parameters and well placement simultaneously using the generalized differential evolution algorithm and the net present value (NPV) was set as the objective. Zhang and Sheng (2020) considered stimulated reservoir volume (SRV) and modified the particle swarm optimization (PSO) algorithm for horizontal well fracturing of shale gas reservoirs. Furthermore, Zhang and Sheng (2021b) conducted a complex fracture network simulation and optimization using numerical method and the modified neural network algorithm. It is obvious that these researches have achieved great success in the optimization of well spacing and fracture stage placement. Nevertheless, all of these researches were conducted by running numerical simulation models during the entire optimization process. This is time-consuming and cannot meet the requirement for fast and optimal well spacing and fracture stage placement scheme decision-making. In summary, these optimization techniques are not adequate in terms of obtaining an optimization scheme in a short time and this significantly affects the development efficiency of shale gas reservoirs. For this purpose, it is necessary to propose an efficient and reliable optimization method to satisfy industrial and commercial shale gas production requirements.

Surrogate-assisted technique, which uses simple-yet-vigorous machine learning models to substitute expensive numerical simulation models for accelerating the evaluation process of objective functions, is a potential method to address this issue (Wang et al., 2020). With the development of computational intelligence technology, numerous machine learning models such as artificial neural network (ANN) (Liu and Reynolds, 2021), support vector regression (SVR) (Guo and Reynolds, 2018), radial basis function (RBF) (Wang et al., 2021), and Gaussian process regression (GPR) (Zhang et al., 2019) have been successfully used as surrogate models in the development of oil and gas resources. These studies have fully demonstrated the feasibility of applying surrogate-assisted techniques in the field development of oil and gas resources. Meanwhile, the application of surrogate-assisted technique to integrate optimization design for horizontal well spacing and fracture stage placement is far from enough. Besides, most of the previous surrogate models used for oil and gas development adopted single fidelity samples only to establish the surrogate model. This makes it difficult to balance the computational burden of sampling and the evaluation accuracy of the surrogate model.

In general, the accuracy of the surrogate model is highly dependent on the number of samples obtained (Chen et al., 2020). To this end, collecting only high fidelity (HF) samples requires significant computing resources, while employing only low fidelity (LF) samples will lead to inaccurate predictions. For this reason, multi-fidelity (MF) surrogate model(Tyan et al., 2015), which adopts samples from different fidelities, is the most suitable way to balance the computational burden of sampling and evaluation accuracy of the surrogate model (Yin et al., 2021). In the MF surrogate model, a large number of LF samples are used to approximate the trend of the model, while a small number of HF samples are adopted to correct the errors (Wang et al., 2022). In this way, the MF surrogate model achieves the goal of reducing computational burden and increasing the evaluation accuracy simultaneously. Despite the discussed researches, research on horizontal well spacing and fracture stage placement integration optimization in shale gas reservoirs using the MF surrogate model is scarce.

Following the above discussion, an efficient and reliable optimization method based on MF support vector regression (MFSVR) surrogate model is proposed in this study so as to lessen the computational burden of the optimization process. The uniqueness of the MFSVR model is that the LF and HF samples are mapped to a high dimension space by a kernel function. To improve the performance of the MFSVR model, the particle swarm optimization (PSO) algorithm is adopted to search the optimal combination of the hyper-parameters. In addition, a comparative research was conducted between this MFSVR method and other traditional optimization methods. The rest of this study is organized as follows. The optimization model of well spacing and fracture stage placement including optimization variables and objective functions, as well as their related terminologies, are presented in section 2. In section 3, the multi-fidelity surrogate support vector regression model, the quality metrics of the multi-objective optimization, and the workflow of the proposed WSF-MFSVR method are discussed. The properties of the WSF-MFSVR method as well as the computational results from the two cases are investigated in section 4. Then, the discussions of this study are presented in section 5. In section 6, the conclusions of this research and prospects for future work are presented.