•TgNN model trained with data while being guided by theory of the underlying problem.•TgNN achieves better predictability, reliability, and generalizability than DNN.•TgNN tested for cases with ...changed BCs, noisy data or outliers, and engineering controls.
Active researches are currently being performed to incorporate the wealth of scientific knowledge into data-driven approaches (e.g., neural networks) in order to improve the latter’s effectiveness. In this study, the Theory-guided Neural Network (TgNN) is proposed for deep learning of subsurface flow. In the TgNN, as supervised learning, the neural network is trained with available observations or simulation data while being simultaneously guided by theory (e.g., governing equations, other physical constraints, engineering controls, and expert knowledge) of the underlying problem. The TgNN can achieve higher accuracy than the ordinary Deep Neural Network (DNN) because the former provides physically feasible predictions and can be more readily generalized beyond the regimes covered with the training data. Furthermore, the TgNN model is proposed for subsurface flow with heterogeneous model parameters. Several numerical cases of two-dimensional transient saturated flow are introduced to test the performance of the TgNN. In the learning process, the loss function contains data mismatch, as well as PDE constraint, engineering control, and expert knowledge. After obtaining the parameters of the neural network by minimizing the loss function, a TgNN model is built that not only fits the data, but also adheres to physical/engineering constraints. Predicting the future response can be easily realized by the TgNN model. In addition, the TgNN model is tested in more complicated scenarios, such as prediction with changed boundary conditions, learning from noisy data or outliers, transfer learning, learning from sparse data, and engineering controls. Numerical results demonstrate that the TgNN model achieves much better predictability, reliability, and generalizability than DNN models due to the physical/engineering constraints in the former.
CO2 capture and geologic sequestration is one of the most promising options for reducing atmospheric emissions of CO2. Its viability and long-term safety, which depends on the caprock’s sealing ...capacity and integrity, is crucial for implementing CO2 geologic storage on a commercial scale. In terms of risk, CO2 leakage mechanisms are classified as follows: diffusive loss of dissolved gas through the caprock, leakage through the pore spaces after breakthrough pressure has been exceeded, leakage through faults or fractures, and well leakage. An overview is presented in which the problems relating to CO2 leakage are defined, dominant factors are considered, and the main results are given for these mechanisms, with the exception of well leakage. The overview includes the properties of the CO2–water/brine system, and the hydromechanics, geophysics, and geochemistry of the caprock-fluid system. In regard to leakage processes, leakage through faults or fracture networks can be rapid and catastrophic, whereas diffusive loss is usually low. The review identifies major research gaps and areas in need of additional study in regard to the mechanisms for geologic carbon sequestration and the effects of complicated processes on sealing capacity of caprock under reservoir conditions.
Solar energy constitutes an effective supplement to traditional energy sources. However, photovoltaic power generation (PVPG) is strongly weather-dependent, and thus highly intermittent. ...High-precision forecasting of PVPG forms the basis of the production, transmission, and distribution of electricity, ensuring the stability and reliability of power systems. In this work, we propose a deep learning based framework for accurate PVPG forecasting. In particular, taking advantage of the long short-term memory (LSTM) network in solving sequential-data based regression problems, this paper considers the specific domain knowledge of PV and proposes a physics-constrained LSTM (PC-LSTM) to forecast the hourly day-ahead PVPG. It aims to overcome the shortcoming of recent machine learning algorithms that are applied based only on massive data, and thus easily producing unreasonable forecasts. Real-life PV datasets are adopted to evaluate the feasibility and effectiveness of the models. Sensitivity analysis is conducted for the selection of input feature variables based on a two-stage hybrid method. The results indicate that the proposed PC-LSTM model possesses stronger forecasting capability than the standard LSTM model. It is more robust against PVPG forecasting, and more suitable for PVPG forecasting with sparse data in practice. The PC-LSTM model also demonstrates superior performance with higher accuracy of PVPG forecasting compared to conventional machine learning and statistical methods.
•Domain knowledge of PV is firstly considered into the deep-learning model.•A two-stage hybrid method is proposed to select the input feature variables.•PC-LSTM is more robust against PV power output forecasting than the basic LSTM.•PC-LSTM has advantages in the forecasting of PV power generation with sparse data.
To supplement missing logging information without increasing economic cost, a machine learning method to generate synthetic well logs from the existing log data was presented, and the experimental ...verification and application effect analysis were carried out. Since the traditional Fully Connected Neural Network (FCNN) is incapable of preserving spatial dependency, the Long Short-Term Memory (LSTM) network, which is a kind of Recurrent Neural Network (RNN), was utilized to establish a method for log reconstruction. By this method, synthetic logs can be generated from series of input log data with consideration of variation trend and context information with depth. Besides, a cascaded LSTM was proposed by combining the standard LSTM with a cascade system. Testing through real well log data shows that: the results from the LSTM are of higher accuracy than the traditional FCNN; the cascaded LSTM is more suitable for the problem with multiple series data; the machine learning method proposed provides an accurate and cost effective way for synthetic well log generation.
In this study, we propose an ensemble long short‐term memory (EnLSTM) network, which can be trained on a small data set and process sequential data. The EnLSTM is built by combining the ensemble ...neural network and the cascaded LSTM network to leverage their complementary strengths. Two perturbation methods are applied to resolve the issues of overconvergence and disturbance compensation. The EnLSTM is compared with commonly used models on a published data set and proven to be the state‐of‐the‐art model in generating well logs. In the case study, 12 well logs that cannot be measured while drilling are generated based on the logs available in the drilling process. The EnLSTM is capable of reducing cost and saving time in practice.
Plain Language Summary
A novel neural network, called EnLSTM, is proposed by combining the ensemble neural network, which has good performance on small‐data problems, and the cascaded long short‐term memory network, which is effective at processing sequential data. The EnLSTM's capability of processing sequential data based on a small data set is especially suitable for generating synthetic well logs. In addition, two perturbation methods are used to ensure that the EnLSTM can be fully trained in practice. In the experiments, the EnLSTM achieved the current best results on a published well log data set, and its application value is verified in a case study.
Key Points
We proposed an ensemble long short‐term memory (EnLSTM) network to process sequential data based on a small dataset
The EnLSTM solved a well log generation problem with higher prediction accuracy than the previously best model on a published dataset
The EnLSTM accurately generated 12 hard‐to‐measure well logs based on LWD logs, resulting in a reduction of cost and time in practice
Uncertainty is ubiquitous with multiphase flow in subsurface rocks due to their inherent heterogeneity and lack of
in-situ
measurements. To complete uncertainty analysis in a multi-scale manner, it ...is a prerequisite to provide sufficient rock samples. Even though the advent of digital rock technology offers opportunities to reproduce rocks, it still cannot be utilized to provide massive samples due to its high cost, thus leading to the development of diversified mathematical methods. Among them, two-point statistics (TPS) and multi-point statistics (MPS) are commonly utilized, which feature incorporating low-order and high-order statistical information, respectively. Recently, generative adversarial networks (GANs) are becoming increasingly popular since they can reproduce training images with excellent visual and consequent geologic realism. However, standard GANs can only incorporate information from data, while leaving no interface for user-defined properties, and thus may limit the representativeness of reconstructed samples. In this study, we propose conditional GANs for digital rock reconstruction, aiming to reproduce samples not only similar to the real training data, but also satisfying user-specified properties. In fact, the proposed framework can realize the targets of MPS and TPS simultaneously by incorporating high-order information directly from rock images with the GANs scheme, while preserving low-order counterparts through conditioning. We conduct three reconstruction experiments, and the results demonstrate that rock type, rock porosity, and correlation length can be successfully conditioned to affect the reconstructed rock images. The randomly reconstructed samples with specified rock type, porosity and correlation length will contribute to the subsequent research on pore-scale multiphase flow and uncertainty quantification.
Despite the variety of studies that have investigated the development of fracture networks during kerogen maturation in organic‐rich shale, the fracture interaction modes and generation mechanisms in ...three‐dimensions are not yet fully understood. In this study, we introduce a novel numerical approach to model the evolution of fracture swarms with three‐dimensional nonplanar geometries. This model enables precise simulation of the propagation, interplay, and coalescence of the fracture swarms with variable apertures and geometries via solving fluid flow, fracture growth, and stress interference. Our results suggest five basic fracture interaction modes between neighboring fractures. The evolving fracture swarms exhibit simultaneous, alternant, and differential growth characteristics at different development phases. We also elucidate the mechanical mechanisms that determine the evolution of three‐dimensional curved fracture swarms. This work yields an improved understanding of fluid‐driven fracture swarms' development in organic‐rich shale due to rapid fluid generation.
Plain Language Summary
Rapid pressure increase due to fluid generation or fluid injection in pores of rock may promote the extension of multiple fractures, which is a common issue involved in natural geological processes and geo‐resources development. However, how the grown fractures interact with each other in three‐dimensions and why these fractures tend to develop into curved, interconnected geometries remain poorly understood. Here, we introduce a novel computer algorithm to accurately simulate the growing process of three‐dimensional fracture arrays with evolving fracture apertures and geometries. It is found that there are five basic fracture interaction modes that support the fracture arrays to form complex geometry and topology in three‐dimensions during fluid generation in shale rock. Through modeling, we also demonstrate how the stress in shale rock governs the growth of fracture arrays. This study results in a better understanding of fracture generation and oil/gas transport in unobservable subsurface rock.
Key Points
Development of three‐dimensional nonplanar fracture swarms due to kerogen maturation in organic‐rich shale is numerically simulated
Five basic fracture interaction modes are proposed to understand the patterns of geomechanically grown fracture swarms in three‐dimensions
Mechanical mechanisms that determine the simultaneous, alternant, and differential growth of curved fracture swarms are elucidated
•Rock permeability can be evaluated rapidly by the convolutional neural network.•Physical information improves the performance of the convolutional neural network.•Physical information reduces the ...number of samples required.•Physical information is helpful for out-of-range problems.•Transfer learning can be applied in the case of out-of-range problems.
Permeability is one of the most important properties in subsurface flow problems, which measures the ability of rocks to transmit fluid. Normally, permeability is determined through experiments and numerical simulations, both of which are time-consuming. In this paper, we propose a new effective method based on convolutional neural networks with physical information (CNNphys) to rapidly evaluate rock permeability from its three-dimensional (3D) image. In order to obtain sufficient reliable labeled data, rock image reconstruction is utilized to generate sufficient samples based on the Joshi-Quiblier-Adler method. Next, the corresponding permeability is calculated using the Lattice Boltzmann method. We compare the prediction performance of CNNphys and convolutional neural networks (CNNs). The results demonstrate that CNNphys achieves superior performance, especially in the case of a small dataset and an out-of-range problem. Moreover, the performance of both CNN and CNNphys is greatly improved combined with transfer learning in the case of an out-of-range problem. This opens novel pathways for rapidly predicting permeability in subsurface applications.
An efficient method for uncertainty analysis of flow in random porous media is explored in this study, on the basis of combination of Karhunen‐Loeve expansion and probabilistic collocation method ...(PCM). The random log transformed hydraulic conductivity field is represented by the Karhunen‐Loeve expansion and the hydraulic head is expressed by the polynomial chaos expansion. Probabilistic collocation method is used to determine the coefficients of the polynomial chaos expansion by solving for the hydraulic head fields for different sets of collocation points. The procedure is straightforward and analogous to the Monte Carlo method, but the number of simulations required in PCM is significantly reduced. Steady state flows in saturated random porous media are simulated with the probabilistic collocation method, and comparisons are made with other stochastic methods: Monte Carlo method, the traditional polynomial chaos expansion (PCE) approach based on Galerkin scheme, and the moment‐equation approach based on Karhunen‐Loeve expansion (KLME). This study reveals that PCM and KLME are more efficient than the Galerkin PCE approach. While the computational efforts are greatly reduced compared to the direct sampling Monte Carlo method, the PCM and KLME approaches are able to accurately estimate the statistical moments and probability density function of the hydraulic head.
A systematic investigation of multiscale pore structure in organic‐rich shale by means of the combination of various imaging techniques is presented, including the state‐of‐the‐art ...Helium‐Ion‐Microscope (HIM). The study achieves insight into the major features at each scale and suggests the affordable techniques for specific objectives from the aspects of resolution, dimension, and cost. The pores, which appear to be isolated, are connected by smaller pores resolved by higher‐resolution imaging. This observation provides valuable information, from the microscopic perspective of pore structure, for understanding how gas accumulates and transports from where it is generated. A comprehensive workflow is proposed based on the characteristics acquired from the multiscale pore structure analysis to simulate the gas transport process. The simulations are completed with three levels: the microscopic mechanisms should be taken into consideration at level I; the spatial distribution features of organic matter, inorganic matter, and macropores constitute the major issue at level II; and the microfracture orientation and topological structure are dominant factors at level III. The results of apparent permeability from simulations agree well with the values acquired from experiments. By means of the workflow, the impact of various gas transport mechanisms at different scales can be investigated more individually and precisely than conventional experiments.
Key Points:
A combination of various imaging techniques is applied to investigate the multiscale pore structure in organic‐rich shale
The pores, which appear to be isolated, are connected by smaller pores resolved by higher‐resolution imaging
A multilevel simulation workflow is proposed to simulate the gas transport process, which agrees well with the experimental result
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