Estimating sub-core permeability using coreflood saturation data: a coupled physics-informed deep learning approach

Estimating multiphase flow properties, particularly permeability, is critical for addressing critical challenges in subsurface engineering applications such as CO2 sequestration, efficient oil and gas recovery, and groundwater contaminant remediation. At the sub-core scale, accurate determination of permeability is vital for understanding flow dynamics and reservoir characterization. However, traditional estimation methods, which rely heavily on numerical simulations, are computationally expensive and time-intensive, limiting their scalability for large-scale or real-time applications. Deep Neural Networks (DNNs) have emerged as a promising alternative due to their ability to learn complex input-output relationships, enabling rapid predictions. Despite their potential, standard data-driven deep neural networks (DNNs) encounter substantial challenges when data availability is limited, often resulting in suboptimal performance and unreliable predictions. Additionally, these models heavily rely on the quality of the measurements, making them sensitive to noise and inaccuracies in the dataPhysics-Informed Neural Networks (PINNs), a class of DNNs that incorporate physical laws as soft constraints, have demonstrated exceptional robustness in addressing inverse problems under data-scarce conditions. By embedding the governing equations into the learning process, PINNs bridge the gap between data-driven and physics-based modeling approaches. Nevertheless, the application of PINNs to inverse problems is often scenario-specific, requiring retraining when transitioning to new conditions or settings. While recent studies have begun leveraging PINNs as surrogate models to efficiently solve forward problems across varying conditions, their full potential in generating datasets for coupled systems remains underexplored. In this study, we present an innovative framework that integrates a PINNs-based surrogate model with a data-driven DNN to accurately and efficiently estimate a 1D heterogeneous permeability profile using sub-core saturation measurements. The surrogate PINNs system was pre-trained to solve a 1D steady-state two-phase flow problem, incorporating capillary pressure heterogeneity and spanning a wide range of flow conditions. This pre-trained PINNs system was subsequently employed to generate an extensive dataset for training a DNN, which establishes a direct mapping between permeability, flow conditions, and measured saturations at the sub-core level. By coupling these two systems, our approach enables the rapid prediction of permeability profiles based on observed flow conditions and saturation measurements, bypassing the computational burden of traditional numerical simulations. The coupled framework demonstrated remarkable accuracy and robustness, achieving average misfits below 1% when validated against actual permeability profiles. Its computational efficiency also facilitated the development of a stochastic extension, allowing the system to handle noisy or contaminated data while quantifying uncertainties. This enhanced solution, capable of delivering results in less than 15 seconds, significantly improves the reliability and applicability of the method for real-world scenarios. Furthermore, the approach successfully reconstructed 1D permeability structures from 3D datasets and generated 1D saturation profiles under varying conditions, achieving an average misfit of approximately 3%. These findings highlight the potential of integrating PINNs with data-driven models for high-fidelity, efficient estimation of flow properties in heterogeneous systems. The proposed method offers a powerful tool for advancing subsurface flow characterization, with broad implications for both scientific research and practical applications.