Graph Convolutional Networks for Simulating Multi-phase Flow and Transport in Porous Media

Numerical simulation of multi-phase fluid dynamics in porous media is critical for many subsurface applications. Data-driven surrogate modeling provides computationally inexpensive alternatives to high-fidelity numerical simulators. While the commonly used convolutional neural networks (CNNs) are powerful in approximating partial differential equation solutions, it remains challenging for CNNs to handle irregular and unstructured simulation meshes. However, subsurface simulation models often involve unstructured meshes with complex mesh geometries, which limits the application of CNNs. To address this challenge, here we construct surrogate models based on Graph Convolutional Networks (GCNs) to approximate the spatial-temporal solutions of multi-phase flow and transport processes. We propose a new GCN architecture suited to the hyperbolic character of the coupled PDE system, to better capture the saturation dynamics. Results of 2D heterogeneous test cases show that our surrogates predict the evolutions of the pressure and saturation states with high accuracy, and the predicted rollouts remain stable for multiple timesteps. Moreover, the GCN-based models generalize well to irregular domain geometries and unstructured meshes that are unseen in the training dataset

Artificial intelligence methods for oil and gas reservoir development: Current progresses and perspectives

Artificial neural networks have been widely applied in reservoir engineering. As a powerful tool, it changes the way to find solutions in reservoir simulation profoundly. Deep learning networks exhibit robust learning capabilities, enabling them not only to detect patterns in data, but also uncover underlying physical principles, incorporate prior knowledge of physics, and solve complex partial differential equations. This work presents the latest research advancements in the field of petroleum reservoir engineering, covering three key research directions based on artificial neural networks: data-driven methods, physics driven artificial neural network partial differential equation solver, and data and physics jointly driven methods. In addition, a wide range of neural network architectures are reviewed, including fully connected neural networks, convolutional neural networks, recurrent neural networks, and so on. The basic principles of these methods and their limitations in practical applications are also outlined. The future trends of artificial intelligence methods for oil and gas reservoir development are further discussed. The large language models are the most advanced neural networks so far, it is expected to be applied in reservoir simulation to predict the development performance.Document Type: PerspectiveCited as: Xue, L., Li, D., Dou, H. Artificial intelligence methods for oil and gas reservoir development: Current progresses and perspectives. Advances in Geo-Energy Research, 2023, 10(1): 65-70. https://doi.org/10.46690/ager.2023.10.0

Physics-informed Neural Networks for Solving Inverse Problems of Nonlinear Biot's Equations: Batch Training

In biomedical engineering, earthquake prediction, and underground energy harvesting, it is crucial to indirectly estimate the physical properties of porous media since the direct measurement of those are usually impractical/prohibitive. Here we apply the physics-informed neural networks to solve the inverse problem with regard to the nonlinear Biot's equations. Specifically, we consider batch training and explore the effect of different batch sizes. The results show that training with small batch sizes, i.e., a few examples per batch, provides better approximations (lower percentage error) of the physical parameters than using large batches or the full batch. The increased accuracy of the physical parameters, comes at the cost of longer training time. Specifically, we find the size should not be too small since a very small batch size requires a very long training time without a corresponding improvement in estimation accuracy. We find that a batch size of 8 or 32 is a good compromise, which is also robust to additive noise in the data. The learning rate also plays an important role and should be used as a hyperparameter.Comment: arXiv admin note: text overlap with arXiv:2002.0823

Deep learning based liquid level extraction from video observations of gas-liquid flows

The slug flow pattern is one of the most common gas–liquid flow patterns in multiphase transportation pipelines, particularly in the oil and gas industry. This flow pattern can cause severe problems for industrial processes. Hence, a detailed description of the spatial distribution of the different phases in the pipe is needed for automated process control and calibration of predictive models. In this paper, a deep-learning based image processing technique is presented that extracts the gas–liquid interface from video observations of multiphase flows in horizontal pipes. The supervised deep learning model consists of a convolutional neural network, which was trained and tested with video data from slug flow experiments. The consistency of the hand-labelled data and the predictions of the trained model have been evaluated in an inter-observer reliability test. The model was further tested with other data sets, which also included recordings of a different flow pattern. It is shown that the presented method provides accurate and reliable predictions of the gas–liquid interface for slug flow as well as for other separate flow patterns. Moreover, it is demonstrated how flow characteristics can be obtained from the results of the deep-learning based image processing technique

Machine Learning Methods and Computationally Efficient Techniques in Digital Rock Analysis

Digital Rock Analysis involves (1) 3D X-ray CT imaging and processing, (2) identifying and segmenting the minerals, and (3) performing flow simulation to obtain upscalable petrophysical parameters. Limitations exist at each step, primarily: (1) the resolution and Field of View (FOV), (2) bias and accuracy of identification and segmentation, and (3) the accuracy and computational intensity of direct simulation. These limitations are surpassed with machine learning and efficient simulation techniques. Super Resolution Convolutional Neural Networks (SRCNNs) and Enhanced Deep Generative Adversarial Networks (EDSRGANs) are shown in 2D and 3D to compensate for resolution-FOV limitations. SRCNNs boost resolution and recover edge sharpness, while EDSRGANs also recover texture. The noise reduction of SRCNNs precondition for image segmentation. Physical accuracy measured by phase topology and permeability achieves the closest match with EDSRGAN. Generalisation with augmentation shows high adaptability to noise and blur. Regenerated under-resolution features and comparison with SEM images shows consistency with underlying geometry. A custom formulated Deep CNN, U-ResNet and other networks are trained to perform 3D multi-mineral segmentation to eliminate user-bias, manual tuning, and algorithmic limitations inherent in traditional methods. U-ResNet performs most accurately and reliably, achieving the highest voxelwise accuracy and most consistent physical accuracy measured by calculating the topology of segmented mineral phases and comparing single and multi-phase direct flow simulations. Several techniques are proposed for efficient single and multi-phase flow at steady-state conditions. Single-phase flow in large images can be estimated using a Dual Grid Domain Decomposition (DGDD) that significantly reduces memory computational requirements, allowing workstations to solve supercomputer size problems. Multi-phase flow can be accelerated with a Morphologically Coupled Multi-phase Lattice Boltzmann Method (MorphLBM), rapidly computing capillary dominated flows, typically 5x faster using a Shell Aggregation morphing method. A U-net CNN can also rapidly estimate steady-state velocity fields, used as-is or as preconditioner in direct LBM simulation (ML-LBM). Similarly, the same acceleration procedure can also be coupled to Pore Network Models and Semi-Analytical Solvers to form accelerated direct simulation techniques. At each step of the Digital Rock workflow, machine learning methods and efficient techniques enhance results past physical limits and/or boost performance of traditional techniques

Machine Learning-based Generalized Multiscale Finite Element Method and its Application in Reservoir Simulation

In multiscale modeling of subsurface fluid flow in heterogeneous porous media, standard polynomial basis functions are replaced by multiscale basis functions, which are used to predict pressure distribution. To produce such functions in the mixed Generalized Multiscale Finite Element Method (GMsFEM), a number of Partial Differential Equations (PDEs) must be solved, leading to significant computational overhead. The main objective of the work presented in this thesis was to investigate the efficiency of Machine Learning (ML)/Deep Learning (DL) models in reconstructing the multiscale basis functions (Basis 2, 3, 4, and 5) of the mixed GMsFEM. To achieve this, four standard models named SkiplessCNN models were first developed to predict four different multiscale basis functions. These predictions were based on two distinct datasets (initial and extended) generated, with the permeability field being the sole input. Subsequently, focusing on the extended dataset, three distinct skip connection schemes (FirstSkip, MidSkip, and DualSkip) were incorporated into the SkiplessCNN architecture. Following this, the four developed models - SkiplessCNN, FirstSkipCNN, MidSkipCNN, and DualSkipCNN - were separately combined using linear regression and ridge regression within the framework of Deep Ensemble Learning (DEL). Furthermore, the reliability of the DualSkipCNN model was examined using Monte Carlo (MC) dropout. Ultimately, two Fourier Neural Operator (FNO) models, operating on infinite-dimensional spaces, were developed based on a new dataset for directly predicting pressure distribution. Based on the results, sufficient data for the validation and testing subsets could help decrease overfitting. Additionally, all three skip connections were found to be effective in enhancing the performance of SkiplessCNN, with DualSkip being the most effective among them. As evaluated on the testing subset, the combined models using linear regression and ridge regression significantly outperformed the individual models for all basis functions. The results also confirmed the robustness of MC dropout for DualSkipCNN in terms of epistemic uncertainty. Regarding the FNO models, it was discovered that the inclusion of a MultiLayer Perceptron (MLP) in the original Fourier layers significantly improved the prediction performance on the testing subset. Looking at this work as an image (matrix)-to-image (matrix) problem, the developed data-driven models through various techniques could find applications beyond reservoir engineering