Deep learning for size-agnostic two-phase flow simulation with realistic pore structures and rock-fluid properties

Abstract

The study of pore-scale flow in porous media is essential across numerous fields, including petroleum engineering, environmental science, chemical engineering, and biomedicine. Recently, deep learning techniques have shown significant potential in enhancing pore-scale flow modelling. However, existing research predominantly addresses single-phase flow, and studies focusing on the prediction of two-phase flow fields remain sparse. Current deep learning research in two-phase flow typically involves simplified pore structures, limited training datasets, and fixed rock-fluid and flow parameters. In this work, I develop deep neural networks as data-driven proxy models for generating phase distributions during a two-phase, capillary-dominated drainage process, where a non-wetting phase invades a wetting-phase-saturated porous rock. My approach integrates complex Computerised Tomography (CT) images and incorporates pixel size (i.e., imaging resolution), interfacial tension, contact angle (wettability), and capillary pressure as direct inputs. Leveraging these capabilities, I showcase several real-world applications of the trained models. First, I construct an extensive and diverse dataset by subsampling both synthetic and real rock images. Next, an efficient morphology-based drainage simulator is developed, providing phase distributions for each sub-image. I evaluate various deep learning architectures and analyse their accuracy and adherence to physical principles. A recurrent encoder-decoder model outperforms the commonly used U-Net in capturing phase connectivity, though it exhibits flow-direction bias and high computational demands. I subsequently introduce a hybrid transformer-convolutional neural network that performs drainage based solely on pore size, with phase connectivity enforced as a post-processing step. This approach facilitates inference for images of various sizes and accommodates any fluid inlet-outlet configuration. The trained models exhibit high efficiency and accuracy across unseen and larger sandstone and carbonate images. I further validate the models against data from microfluidic experiments and Lattice-Boltzmann (LBM) simulations, demonstrating similar capillary pressure curves and phase distributions with significantly faster performance. These models can replace slow direct simulations or costly experiments, generate finer pressure steps between existing results, and serve as data validation tools. They deliver results in seconds to minutes with minimal preprocessing across a range of realistic rock types, rock-fluid properties, resolutions, and image sizes. I show that the final deep learning models can integrate with an efficient optimiser to estimate wettability if phase distributions are already available. I apply this inverse-problem technique to determine the average contact angle from an LBM-generated phase distribution image in a core-scale Bentheimer sandstone, where supercritical CO2 displaces brine. This scenario has applications in CO2 sequestration. I find that the model achieves results comparable to the GPU-accelerated LBM method, 5,000 times faster. I then generate phase distributions over 101 pressure steps and build the complete capillary pressure curve in minutes. Through these studies, it becomes clear that the developed models can be seamlessly integrated into downstream workflows to provide further insight into pore-scale flow.James Watt Scholarshi