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Physics-informed neural networks (PINN) have recently become attractive for solving partial differential equations (PDEs) that describe physics laws. By including PDE-based loss functions, physics laws such as mass balance are enforced softly in PINN. This paper investigates how mass balance constraints are satisfied when PINN is used to solve the resulting PDEs. We investigate PINN's ability to solve the 1D saturated groundwater flow equations (diffusion equations) for homogeneous and heterogeneous media and evaluate the local and global mass balance errors. We compare the obtained PINN's solution and associated mass balance errors against a two-point finite volume numerical method and the corresponding analytical solution. We also evaluate the accuracy of PINN in solving the 1D saturated groundwater flow equation with and without incorporating hydraulic heads as training data. We demonstrate that PINN's local and global mass balance errors are significant compared to the finite volume approach. Tuning the PINN's hyperparameters, such as the number of collocation points, training data, hidden layers, nodes, epochs, and learning rate, did not improve the solution accuracy or the mass balance errors compared to the finite volume solution. Mass balance errors could considerably challenge the utility of PINN in applications where ensuring compliance with physical and mathematical properties is crucial. [ABSTRACT FROM AUTHOR]

Reduced-order modeling is a promising approach, as many phenomena can be described by a few parameters/mechanisms. An advantage and attractive aspect of a reduced-order model is that it is computational inexpensive to evaluate when compared to running a high-fidelity numerical simulation. A reduced-order model takes couple of seconds to run on a laptop while a high-fidelity simulation may take couple of hours to run on a high-performance computing cluster. The goal of this paper is to assess the utility of regression-based reduced-order models (ROMs) developed from high-fidelity numerical simulations for predicting transient thermal power output for an enhanced geothermal reservoir while explicitly accounting for uncertainties in the subsurface system and site-specific details. Numerical simulations are performed based on equally spaced values in the specified range of model parameters. Key sensitive parameters are then identified from these simulations, which are fracture zone permeability, well/skin factor, bottom hole pressure, and injection flow rate. We found the fracture zone permeability to be the most sensitive parameter. The fracture zone permeability along with time, are used to build regression-based ROMs for the thermal power output. The ROMs are trained and validated using detailed physics-based numerical simulations. Finally, predictions from the ROMs are then compared with field data. We propose three different ROMs with different levels of model parsimony, each describing key and essential features of the power production curves. The coefficients in the proposed regression-based ROMs are developed by minimizing a non-linear least-squares misfit function using the Levenberg–Marquardt algorithm. The misfit function is based on the difference between numerical simulation data and reduced-order model. ROM-1 is constructed based on polynomials up to fourth order. ROM-1 is able to accurately reproduce the power output of numerical simulations for low values of permeabilities and certain features of the field-scale data. ROM-2 is a model with more analytical functions consisting of polynomials up to order eight, exponential functions and smooth approximations of Heaviside functions, and accurately describes the field-data. At higher permeabilities, ROM-2 reproduces numerical results better than ROM-1, however, there is a considerable deviation from numerical results at low fracture zone permeabilities. ROM-3 consists of polynomials up to order ten, and is developed by taking the best aspects of ROM-1 and ROM-2. ROM-1 is relatively parsimonious than ROM-2 and ROM-3, while ROM-2 overfits the data. ROM-3 on the other hand, provides a middle ground for model parsimony. Based on R 2 -values for training, validation, and prediction data sets we found that ROM-3 is better model than ROM-2 and ROM-1. For predicting thermal drawdown in EGS applications, where high fracture zone permeabilities (typically greater than 10 −15 m 2 ) are desired, ROM-2 and ROM-3 outperform ROM-1. As per computational time, all the ROMs are 10 4 times faster when compared to running a high-fidelity numerical simulation. This makes the proposed regression-based ROMs attractive for real-time EGS applications because they are fast and provide reasonably good predictions for thermal power output. [ABSTRACT FROM AUTHOR]

During hydraulic fracturing millions of gallons of water are typically injected at high pressure into deep shale formations. This water can be housed in fractures, within the shale matrix, and can potentially migrate beyond the shale formation via fractures and/or faults raising environmental concerns. We describe a generic framework for producing estimates of the volume available in fractures and undamaged shale matrix where water injected into a representative shale site could reside during hydraulic fracturing, and apply it to a representative site that incorporates available field data. The amount of water that can be stored in the fractures is estimated by calculating the volume of all the fractures associated with a discrete fracture network ( DFN) based on real data and using probability theory to estimate the volume of smaller fractures that are below the lower cutoff for the fracture radius in the DFN. The amount of water stored in the matrix is estimated utilizing two distinct methods-one using a two-phase model at the pore-scale and the other using a single-phase model at the continuum scale. Based on these calculations, it appears that most of the water resides in the matrix with a lesser amount in the fractures. [ABSTRACT FROM AUTHOR]

In this paper, we apply the thermodynamic framework recently put into place by Rajagopal and co-workers, to develop rate-type models for viscoelastic fluids which do not possess instantaneous elasticity. To illustrate the capabilities of such models, we make a specific choice for the specific Helmholtz potential and the rate of dissipation and consider the creep and stress relaxation response associated with the model. Given specific forms for the Helmholtz potential and the rate of dissipation, the rate of dissipation is maximized with the constraint that the difference between the stress power and the rate of change of Helmholtz potential is equal to the rate of dissipation and any other constraint that may be applicable such as incompressibility. We show that the class of models that are developed exhibit fluid-like characteristics, when none of the material moduli that appear in the model are not zero, and are incapable of instantaneous elastic response. They also include Maxwell-like and Kelvin–Voigt-like viscoelastic materials (when certain material moduli take special values). [ABSTRACT FROM AUTHOR]

This paper presents a physics-informed machine learning (ML) framework to construct reduced-order models (ROMs) for reactive-transport quantities of interest (QoIs) based on high-fidelity numerical simulations. QoIs include species decay, product yield, and degree of mixing. The ROMs for QoIs are applied to quantify and understand how the chemical species evolve over time. First, high-resolution datasets for constructing ROMs are generated by solving anisotropic reaction–diffusion equations using a non-negative finite element formulation for different input parameters. The reactive-mixing model input parameters are: time-scale associated with flipping of velocity, spatial-scale controlling small/large vortex structures of velocity, perturbation parameter of the vortex-based velocity, anisotropic dispersion contrast, and molecular diffusion. Second, random forests, F-test, and mutual information criterion are used to evaluate the importance of model inputs/features with respect to QoIs. We observed that anisotropic dispersion contrast is the most important feature and time-scale associated with flipping of velocity is the least important feature. Third, Support Vector Machines (SVM) and Support Vector Regression (SVR) are used to construct ROMs based on the model inputs. The constructed SVR-ROMs are then used to predict scaling of QoIs. We also present estimates and inequalities on the QoIs, which inform that the species decay, mix, and produce in an exponential fashion. These inequalities also inform that a radial basis function is the most suitable kernel for the SVM/SVR models for QoIs. It is observed that R 2 -score for SVR-ROMs on unseen data is greater than 0.9, implying that the SVR-ROMs are able to predict the reaction–diffusion system state reasonably well. Finally, in terms of the computational cost, the proposed SVM-ROMs are O (1 0 7) times faster than running a high-fidelity finite element simulation for evaluating QoIs. This makes the proposed ML-based ROMs attractive for reactive-transport sensing and real-time monitoring applications as they are significantly faster yet reasonably accurate. • ML-ROMs are built to predict reactive-mixing under heterogeneity and anisotropy. • Accuracy of our ROMs on unseen data is greater than 90%. • Proposed ROMs are ≈ 1 0 7 times faster than high-fidelity numerical simulations. [ABSTRACT FROM AUTHOR]

Abstract: High‐fidelity, predictive fluid flow simulations of the interactions between the rising thermal plumes from forced air warming blower and the ultra‐clean ventilation air in an operating room (OR) are conducted to explore whether this complex flow can impact the dispersion of squames to the surgical site. A large‐eddy simulation, accurately capturing the spatiotemporal evolution of the flow in 3 dimensions together with the trajectories of squames, is performed for a realistic OR consisting of an operating table (OT), side tables, surgical lamps, medical staff, and a patient. Two cases are studied with blower‐off and blower‐on together with Lagrangian trajectories of 3 million squames initially placed on the floor surrounding the OT. The large‐eddy simulation results show that with the blower‐off, squames are quickly transported by the ventilation air away from the table and towards the exit grilles. In contrast, with the hot air blower turned on, the ventilation airflow above and below the OT is disrupted significantly. The rising thermal plumes from the hot air blower drag the squames above the OT and the side tables and then they are advected downwards toward the surgical site by the ventilation air from the ceiling. Temporal history of the number of squames reaching 4 imaginary boxes surrounding the side tables, the OT, and the patient's knee shows that several particles reach these boxes for the blower‐on case. [ABSTRACT FROM AUTHOR]

Fractures form the main pathways for flow in the subsurface within low-permeability rock. For this reason, accurately predicting flow and transport in fractured systems is vital for improving the performance of subsurface applications. Fracture sizes in these systems can range from millimeters to kilometers. Although modeling flow and transport using the discrete fracture network (DFN) approach is known to be more accurate due to incorporation of the detailed fracture network structure over continuum-based methods, capturing the flow and transport in such a wide range of scales is still computationally intractable. Furthermore, if one has to quantify uncertainty, hundreds of realizations of these DFN models have to be run. To reduce the computational burden, we solve flow and transport on a graph representation of a DFN. We study the accuracy of the graph approach by comparing breakthrough times and tracer particle statistical data between the graph-based and the high-fidelity DFN approaches, for fracture networks with varying number of fractures and degree of heterogeneity. Due to our recent developments in capabilities to perform DFN high-fidelity simulations on fracture networks with large number of fractures, we are in a unique position to perform such a comparison. We show that the graph approach shows a consistent bias with up to an order of magnitude slower breakthrough when compared to the DFN approach. We show that this is due to graph algorithm's underprediction of the pressure gradients across intersections on a given fracture, leading to slower tracer particle speeds between intersections and longer travel times. We present a bias correction methodology to the graph algorithm that reduces the discrepancy between the DFN and graph predictions. We show that with this bias correction, the graph algorithm predictions significantly improve and the results are very accurate. The good accuracy and the low computational cost, with O(104) times lower times than the DFN, makes the graph algorithm an ideal technique to incorporate in uncertainty quantification methods. [ABSTRACT FROM AUTHOR]

Analysis of reactive-diffusion simulations representing complex mixing processes requires a large number of independent model runs. For each high-fidelity model simulation, the model inputs are varied and the predicted mixing behavior is represented by temporal and spatial changes in species concentration. It is then required to discern how the model inputs (such as diffusivity, dispersion, anisotropy, and velocity field properties) impact the mixing process. This task is challenging and typically involves interpretation of large model outputs representing temporal and spatial changes of species concentration within the model domain. However, the task can be automated and substantially simplified by applying Machine Learning (ML) methods. In this paper, we present an application of an unsupervised ML method (called NTF k) using Non-negative Tensor Factorization (NTF) coupled with a custom clustering procedure based on k -means to reveal the temporal and spatial features in product concentrations. An attractive and unique aspect of the proposed ML method is that it ensures the extracted features are non-negative, which is important to obtain a meaningful deconstruction of the mixing processes. The ML methodology is applied to a large set of high-resolution finite-element model simulations representing anisotropic reaction-diffusion processes in perturbed vortex-based velocity fields. The applied finite-element method ensures that spatial and temporal species concentration are always non-negative, even in the case of high anisotropic contrasts. The simulated reaction is a fast irreversible bimolecular reaction A + B → C , where species A and B react to form species C. The reactive-diffusion model input parameters that control mixing include properties of the velocity field (such as vortex structures), anisotropic dispersion, and molecular diffusion. We demonstrate the applicability of the ML feature extraction method to produce a meaningful deconstruction of model outputs to discriminate between different physical processes impacting the reactants, their mixing, and the spatial distribution of the product C. The presented ML analysis allowed us to identify additive temporal and spatial features that characterize mixing behavior. The application of the proposed NTF k approach is not limited to reactive-mixing. NTF k can be readily applied to any observed or simulated datasets that can be represented as tensors (multi-dimensional arrays) and have separable latent signatures or features. • NTF k provides an elegant way to extract hidden features in irreversible fast bimolecular reaction-diffusion systems. • Features extracted using NTF k are non-negative which is an important constraint to ensure physically meaningful decomposition of the reactive-mixing process. • Added benefit of our method is data compression along with minimal loss of information. [ABSTRACT FROM AUTHOR]

We present the description of a fully coupled simulator FEHM for modeling coupled thermo-hydro-mechanical (THM) processes in geomedia. The coupled equations for fluid flow and energy transport are implemented using finite volume whereas Galerkin finite element method is used for mechanical force balance. The simulator is designed to address spatial scales on the order of tens of centimeters to tens of kilometers, and time scales on the order of hours to tens of years. The governing coupled nonlinear equations are solved using a Newton-Rapshon scheme with analytically or numerically computed Jacobians. A suite of models is available for coupling flow and mechanical deformation via permeability-deformation relationships. The coupled simulator is verified by comparing with several analytical solutions developed for this purpose. A subset of the simulator capabilities is benchmarked against commercially available simulators. We also demonstrate a good match with data from Desert Peak geothermal field in Nevada, USA. This validation required the use of a shear failure model with non-linear permeability-stress relationship. In addition, we present another application involving fluid injection into an inclined fault zone using a non-orthogonal grid with stress-dependent Young's modulus and permeability. [ABSTRACT FROM AUTHOR]

Quantitative predictions of natural and induced phenomena in fractured rock is one of the great challenges in the Earth and Energy Sciences with far‐reaching economic and environmental impacts. Fractures occupy a very small volume of a subsurface formation but often dominate fluid flow, solute transport and mechanical deformation behavior. They play a central role in CO2 sequestration, nuclear waste disposal, hydrogen storage, geothermal energy production, nuclear nonproliferation, and hydrocarbon extraction. These applications require predictions of fracture‐dependent quantities of interest such as CO2 leakage rate, hydrocarbon production, radionuclide plume migration, and seismicity; to be useful, these predictions must account for uncertainty inherent in subsurface systems. Here, we review recent advances in fractured rock research covering field‐ and laboratory‐scale experimentation, numerical simulations, and uncertainty quantification. We discuss how these have greatly improved the fundamental understanding of fractures and one's ability to predict flow and transport in fractured systems. Dedicated field sites provide quantitative measurements of fracture flow that can be used to identify dominant coupled processes and to validate models. Laboratory‐scale experiments fill critical knowledge gaps by providing direct observations and measurements of fracture geometry and flow under controlled conditions that cannot be obtained in the field. Physics‐based simulation of flow and transport provide a bridge in understanding between controlled simple laboratory experiments and the massively complex field‐scale fracture systems. Finally, we review the use of machine learning‐based emulators to rapidly investigate different fracture property scenarios and accelerate physics‐based models by orders of magnitude to enable uncertainty quantification and near real‐time analysis.Plain Language Summary: Some of the greatest challenges currently facing humanity have roots in the Earth and Energy Sciences. Policymakers rely on scientific research to answer questions related to the transition to green renewable energy, mitigate the climate crisis, and ensure global stability with reliable energy and water resources. A common thread in addressing these societal issues with far‐reaching economic and environmental impacts is the prediction of flow and transport in subsurface systems in the Earth, particularly in fractured rock. The need to predict, optimize and ultimately control fractured subsurface systems is an increasingly important topic, with 80% of the US energy resources and 50% of its drinking water supply coming from the subsurface. In this review, we describe the state‐of‐the‐art research on flow and transport in fracture systems and the path forward for the integration of field observations, laboratory experiments, predictive modeling, and uncertainty quantification to enable more efficient and environmentally prudent usage of critical subsurface resources.Key Points: Understanding and predicting fractured systems requires integrating field and lab experiments, simulation and uncertainty quantificationDensely monitored field sites and in situ lab experiments provide quantitative measures of flow and transport that can constrain modelsPhysics‐based models with machine‐learning emulators enable uncertainty quantification of flow and transport in complex fracture networks [ABSTRACT FROM AUTHOR]

• Machine learning (ML) can understand reactive-mixing phenomena. • ML predicts quantities of interest (QoIs) of reactive-mixing phenomena. • 20 Machine learning emulators are used to predict reactive-mixing phenomena. • Linear and Bayesian emulators predict QoIs with accuracy <80%. • Ensemble and MLP ML emulators predict QoIs with accuracy >99%. Mixing phenomena are important mechanisms controlling flow, species transport, and reaction processes in fluids and porous media. Accurate predictions of reactive mixing are critical for many Earth and environmental science problems such as contaminant fate and remediation, macroalgae growth, and plankton biomass growth. To investigate the evolution of mixing dynamics under different scenarios (e.g., anisotropy, fluctuating velocity fields), a finite-element-based numerical model was built to solve the fast, irreversible bimolecular reaction-diffusion equations to simulate a range of reactive-mixing scenarios. A total of 2,315 simulations were performed using different sets of model input parameters comprising various spatial scales of vortex structures in the velocity field, time-scales associated with velocity oscillations, the perturbation parameter for the vortex-based velocity, anisotropic dispersion contrast (i.e., ratio of longitudinal-to-transverse dispersion), and molecular diffusion. The outputs comprised concentration profiles of reactants and products. The inputs and outputs from these simulations were concatenated into feature and label matrices, respectively, to train 20 different machine learning (ML) models intended to emulate system behavior. These 20 ML emulators, based on linear methods, Bayesian methods, ensemble learning methods, and multilayer perceptrons (MLPs), were trained to classify the state of mixing and predict three quantities of interest (QoIs) characterizing species production, decay (i.e., average concentration, square of average concentration), and degree of mixing (i.e., variances of species concentration). Unsurprisingly, linear classifiers and regressors failed to reproduce the QoIs; however, ensemble methods (classifiers and regressors) and the MLP model accurately classified the state of reactive mixing and the QoIs. Among ensemble methods, random forest and decision-tree-based AdaBoost faithfully predicted the QoIs. At run time, trained ML emulators produced results ≈ 10 5 times faster than the finite-element simulations. Due to their low computational expense and high accuracy, ensemble and MLP models are excellent emulators for these numerical simulations and great utilities in uncertainty quantification exercises, which can require 1,000s of forward model runs. [ABSTRACT FROM AUTHOR]

Clinical studies have suggested that myocardial iron is a risk factor for left ventricular remodeling in patients after myocardial infarction. Ferroptosis has recently been reported as a mechanism of iron-dependent nonapoptotic cell death. However, ferroptosis in the heart is not well understood. Mechanistic target of rapamycin (mTOR) protects the heart against pathological stimuli such as ischemia. To define the role of cardiac mTOR on cell survival in iron-mediated cell death, we examined cardiomyocyte (CM) cell viability under excess iron and ferroptosis conditions. Adult mouse CMs were isolated from cardiac-specific mTOR transgenic mice, cardiac-specific mTOR knockout mice, or control mice. CMs were treated with ferric iron [Fe(III)]-citrate, erastin, a class 1 ferroptosis inducer, or Ras-selective lethal 3 (RSL3), a class 2 ferroptosis inducer. Live/dead cell viability assays revealed that Fe(III)-citrate, erastin, and RSL3 induced cell death. Cotreatment with ferrostatin-1, a ferroptosis inhibitor, inhibited cell death in all conditions. mTOR overexpression suppressed Fe(III)-citrate, erastin, and RSL3-induced cell death, whereas mTOR deletion exaggerated cell death in these conditions. 2',7'=-Dichlorodihydrofluorescein diacetate measurement of reactive oxygen species (ROS) production showed that erastin-induced ROS production was significantly lower in mTOR transgenic versus control CMs. These findings suggest that ferroptosis is a significant type of cell death in CMs and that mTOR plays an important role in protecting CMs against excess iron and ferroptosis, at least in part, by regulating ROS production. Understanding the effects of mTOR in preventing iron-mediated cell death will provide a new therapy for patients with myocardial infarction. [ABSTRACT FROM AUTHOR]

Despite the impact that hydraulic fracturing has had on the energy sector, the physical mechanisms that control its efficiency and environmental impacts remain poorly understood in part because the length scales involved range from nanometres to kilometres. We characterize flow and transport in shale formations across and between these scales using integrated computational, theoretical and experimental efforts/methods. At the field scale, we use discrete fracture network modelling to simulate production of a hydraulically fractured well from a fracture network that is based on the site characterization of a shale gas reservoir. At the core scale, we use triaxial fracture experiments and a finite-discrete element model to study dynamic fracture/crack propagation in low permeability shale. We use lattice Boltzmann pore-scale simulations and microfluidic experiments in both synthetic and shale rock micromodels to study pore-scale flow and transport phenomena, including multi-phase flow and fluids mixing. A mechanistic description and integration of these multiple scales is required for accurate predictions of production and the eventual optimization of hydrocarbon extraction from unconventional reservoirs. Finally, we discuss the potential of CO2 as an alternative working fluid, both in fracturing and re-stimulating activities, beyond its environmental advantages. [ABSTRACT FROM AUTHOR]

• A numerical simulation was carried out to generate mineral-trapping data due to CO 2 injection in a sandstone reservoir. • An unsupervised machine learning tool called non-negative matrix factorization with k-means clustering was used to analyze the data. • We identified injection-, short-, mid-, and long-term reaction stages. • Calcite, dolomite, siderite, clinochlore, kaolinite, Na+, K+, Ca2+, Mg2+, and aq. CO 2 play major role in mineral trapping. Discovery of hidden geothermal resources is challenging. It requires the mining of large datasets with diverse data attributes representing subsurface hydrogeological and geothermal conditions. The commonly used play fairway analysis approach typically incorporates subject-matter expertise to analyze regional data to estimate geothermal characteristics and favorability. We demonstrate an alternative approach based on machine learning (ML) to process a geothermal dataset from southwest New Mexico (SWNM). The study region includes low- and medium-temperature hydrothermal systems. Several of these systems are not well characterized because of insufficient existing data and limited past explorative work. This study discovers hidden patterns and relations in the SWNM geothermal dataset to improve our understanding of the regional hydrothermal conditions and energy-production favorability. This understanding is obtained by applying an unsupervised ML algorithm based on non-negative matrix factorization coupled with customized k -means clustering (NMF k). NMF k can automatically identify (1) hidden signatures characterizing analyzed datasets, (2) the optimal number of these signatures, (3) the dominant data attributes associated with each signature, and (4) the spatial distribution of the extracted signatures. Here, NMF k is applied to analyze 18 geological, geophysical, hydrogeological, and geothermal attributes at 44 locations in SWNM. Using NMF k , we find data patterns and identify the spatial associations of hydrothermal signatures within two physiographic provinces (Colorado Plateau and Basin and Range) and two sub-regions of these provinces (the Mogollon-Datil volcanic field and the Rio Grande rift) in SWNM. The ML algorithm extracted five hydrothermal signatures in the SWNM datasets that differentiate between low (<90°C) and medium (90-150°C)-temperature hydrothermal systems. The algorithm also suggests that the Rio Grande rift and northern Mogollon-Datil volcanic field are the most favorable regions for future geothermal resource discovery. NMF k also identified critical attributes to identify medium-temperature hydrothermal systems in the study area. The resulting NMF k model can be applied to predict geothermal conditions and their uncertainties at new SWNM locations based on limited data from unexplored regions. The code to execute the performed analyses as well as the corresponding data can be found at https://github.com/SmartTensors/GeoThermalCloud.jl. [ABSTRACT FROM AUTHOR]