Anirban Chakraborty

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.

Simulations of two-phase flow in heterogeneous porous media are crucial for several applications, such as CO2 sequestration, efficient oil and gas recovery, and groundwater pollution remediation. Modeling of two-phase flow systems becomes very challenging when capillary heterogeneity and hydraulic discontinuities are considered. Traditional models use numerical techniques such as finite difference, finite element, and finite volume for solving the partial differential equations of the system. Although numerical methods have been shown to produce reliable solutions for complex flow problems, they can become computationally expensive. This emphasizes the high computational demand for solving the inverse problem. The use of DNNs (deep neural networks) has become more common in predicting subsurface flow behavior. DNNs is a data-driven approach that enables the learning of a system by linking input and output parameters and provides fast predictions of dynamic, complex systems. Nevertheless, when data is extremely scarce, particularly in subsurface systems, standard DNNs are unable to yield robust results. Recent advancements enable the integration of physical constraints as partial differential equations (PDEs) into the DNNs scheme. Such a class of deep learning techniques is generally referred to as physics-informed neural networks (PINNs). PINNs are also capable to provide forward solutions for PDEs. In this work, we examined PINNs' capabilities to provide forward solutions of a 1D steady-state two-phase flow with capillary heterogeneity at the sub-core scale. Here, we trained a PINNs system that incorporates high variability in the hydraulic properties and boundary conditions implemented as input parameters. We compared the PINNs results with numerical solutions to test the efficiency of the developed PINNs system. Results have shown that the trained PINNs system could reproduce both capillary pressure and phase saturation profiles for altering fractional flows, injection rates, hydraulic properties, and domain lengths with high accuracy and within a single training. Training the extended PINNs system was obtained in a few hours, and the post-trained system provided unlimited solutions for variable structures and boundary conditions within a few seconds.

Increasing pollution in the environment, particularly for groundwater, has been an issue of great concern for decades. Thus, proper management strategies need to be adopted for reclamation of such polluted groundwater aquifers. Success of these reclamation strategy relies on the precision with which the pollution source characteristics (location of sources, release flux histories, and the starting times of pollutant sources) are identified. In clandestine scenarios of groundwater pollution where neither the location nor starting times of pollutant sources are known, it is impossible to decide where to install a monitoring well. Therefore, an optimally designed pollutant data monitoring plan is needed to reduce the time and cost of monitoring and simultaneously achieve greater accuracy in identification of source characteristics. To address this issue, a principal component analysis (PCA)-based methodology is proposed to design an efficient well network for identifying unknown characteristics of pollutant sources (UCPS). PCA is applied to reduce the dimensionality of a dataset comprising a large number of interrelated variables, thus reducing the uncertainty due to ambivalent source characteristics.

Large numbers of untreated toxic wastes are often buried underground, as a method of disposal. Such methods of clandestine disposal have led to widespread pollution of groundwater resources. These methods of wastes disposal are often adopted to avoid the cost incurred in proper treatment of the waste and untraceability of such clandestine disposals. However, the effect of such disposals manifests in form of groundwater pollution, which if left unchecked would potentially pollute the entire aquifer. Such polluted aquifers need to be reclaimed by implementing proper remediation techniques. However, the effectiveness of any remediation technique would depend on the precise knowledge of the unknown pollutant source/s characteristics, in terms of their Numbers, their Locations and their Release Flux history referred to as NLRF. This study presents a noble technique for simultaneously estimating the unknown number of clandestine pollutant sources, their locations along with their release flux history. Simulated Annealing (SA) is used in Linked Simulation Optimization (LSO) based framework. In this developed methodology, the number of sources and their respective locations and release flux histories are treated as unknown decision variables, and are estimated simultaneously along with the source release flux history.

Groundwater pollution is the biggest threat to sustainability of groundwater resources and even more difficult to detect in case of clandestine sources. At the time when pollution is first detected in randomly located sparse wells, very little is known about the pollution sources. Finding the precise locations of clandestine sources of pollution and their release flux history is the biggest challenge and often termed as a problem belonging to the class of environmental forensics. In this study, two linked simulation optimization–based novel techniques are developed to estimate locations and release flux history from clandestine point sources of groundwater pollution. Simulation model is clubbed with optimization solver to determine the locations and release flux histories of groundwater pollution sources by minimizing the residual error between observed and simulated concentration values. Simulated annealing (SA) and particle swarm optimization (PSO) are used as optimization algorithms. A detailed comparative analysis of these two meta-heuristic optimization algorithms in minimizing the residual error is presented in this study. The performance evaluation of both the algorithms in identifying the sources locations and release flux history is carried out for two synthetic cases and a real-life scenario of groundwater pollution in an aquifer in New South Wales, Australia, which has not been attempted in the past. The results of source location identification and release flux history show the selective applicability of each algorithm in solving real-life scenarios of groundwater pollution.