Well-logging is an important formation characterization and resource evaluation method in oil and gas exploration and development. However, there has been a shortage of well-logging data because Well-logging can only be measured by expensive and time-consuming field tests. In this study, we aimed to find effective machine learning techniques for well-logging data prediction, considering the temporal and spatial characteristics of well-logging data. To achieve this goal, the convolutional neural network (CNN) and the long short-term memory (LSTM) neural networks were combined to extract the spatial and temporal features of well-logging data, and the particle swarm optimization (PSO) algorithm was used to determine hyperparameters of the optimal CNN-LSTM architecture to predict logging curves in this study. We applied the proposed CNN-LSTM-PSO model, along with support vector regression, gradient-boosting regression, CNN-PSO, and LSTM-PSO models, to forecast photoelectric effect (PE) logs from other logs of the target well, and from logs of adjacent wells. Among the applied algorithms, the proposed CNN-LSTM-PSO model generated the best prediction of PE logs because it fully considers the spatio-temporal information of other well-logging curves. The prediction accuracy of the PE log using logs of the adjacent wells was not as good as that using the other well-logging data of the target well itself, due to geological uncertainties between the target well and adjacent wells. The results also show that the prediction accuracy of the models can be significantly improved with the PSO algorithm. The proposed CNN-LSTM-PSO model was found to enable reliable and efficient Well-logging prediction for existing and new drilled wells; further, as the reservoir complexity increases, the proxy model should be able to reduce the optimization time dramatically.

Oil production from tight oil reservoirs has become economically feasible because of the combination of horizontal drilling and multistage hydraulic fracturing. Optimal fracture design plays a critical role in successful economical production from a tight oil reservoir. However, many complex parameters such as fracture spacing and fracture half-length make fracturing treatments costly and uncertain. To improve fracture design, it is essential to determine reasonable ranges for these parameters and to evaluate their effects on well performance and economic feasibility. In traditional analytical and numerical simulation methods, many simplifications and assumptions are introduced for artificial fracture characterization and gas percolation mechanisms, and their implementation process remains complicated and computationally inefficient. Most previous studies on big data-driven fracturing parameter optimization have been based on only a single output, such as expected ultimate recovery, and few studies have integrated machine learning with evolutionary algorithms to optimize fracturing parameters based on time-series production prediction and economic objectives. This study proposed a novel approach, combining a data-driven model with evolutionary optimization algorithms to optimize fracturing parameters. We established a significant number of static and dynamic data sets representing the geological and developmental characteristics of tight oil reservoirs from numerical simulation. Four production-prediction models based on machine-learning methods—support vector machine, gradient-boosted decision tree, random forest, and multilayer perception—were constructed as mapping functions between static properties and dynamic production. Then, to optimize the fracturing parameters, the best machine-learning-based production predictive model was coupled with four evolutionary algorithms—genetic algorithm, differential evolution algorithm, simulated annealing algorithm, and particle swarm optimization—to investigate the highest net present value (NPV). The results show that among the four production-prediction models established, multilayer perception (MLP) has the best prediction performance. Among the evolutionary algorithms, particle swarm optimization (PSO) not only has the fastest convergence speed but also the highest net present value. The optimal fracturing parameters for the study area were identified. The hybrid MLP-PSO model represents a robust and convenient method to forecast the time-series production and to optimize fracturing parameters by reducing manual tuning.

Reservoir lithology identification is the basis for the exploration and development of complex lithological reservoirs. Efficient processing of well-logging data is the key to lithology identification. However, reservoir lithology identification through well-logging is still a challenge with conventional machine learning methods, such as Convolutional Neural Networks (CNN), and Long Short-term Memory (LSTM). To address this issue, a fully connected network (FCN) and LSTM were coupled for predicting reservoir lithology. The proposed algorithm (LSTM-FCN) is composed of two sections. One section uses FCN to extract the spatial properties, the other one captures feature selections by LSTM. Well-logging data from Hugoton Field is used to evaluate the performance. In this study, well-logging data, including Gamma-ray (GR), Resistivity (ILD_log10), Neutron-density porosity difference (DeltaPHI), Average neutron-density porosity(PHIND), and (Photoelectric effect) PE, are used for training and identifying lithology. For comparison, seven conventional methods are also proposed and trained, such as support vector machines (SVM), and random forest classifiers (RFC). The accuracy results indicate that the proposed architecture obtains better performance. After that, particle swarm optimization (PSO) is proposed to optimize hyper-parameters of LSTM-FCN. The investigation indicates the proposed PSO-LSTM-FCN model can enhance the performance of machine learning algorithms on identify the lithology of complex reservoirs.

An important problem in machine learning theory is to understand the approximation and generalization properties of two-layer neural networks in high dimensions. To this end, researchers have introduced the Barron space $\mathcal{B}_s(Ω)$ and the spectral Barron space $\mathcal{F}_s(Ω),$ where the index $s ∈ [0, ∞)$ indicates the smoothness of functions within these spaces and $Ω ⊂ \mathbb{R}^d$ denotes the input domain. However, the precise relationship between the two types of Barron spaces remains unclear. In this paper, we establish a continuous embedding between them as implied by the following inequality: For any $\delta∈ (0, 1),s ∈ \mathbb{N}^+$ and $f : Ω\mapsto \mathbb{R},$ it holds that $$\delta||f||_{\mathcal{F}_{s−\delta}(Ω)}\lesssim_s||f||_{\mathcal{B}_s(Ω)}\lesssim_s||f||_{\mathcal{F}_{s+1}(Ω).}$$ Importantly, the constants do not depend on the input dimension $d,$ suggesting that the embedding is effective in high dimensions. Moreover, we also show that the lower and upper bound are both tight. COPYRIGHT: © Global Science Press