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DOE OSTI2021

Physics-Informed Machine Learning Models for Predicting the Progress of Reactive-Mixing

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 simu-lations. 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-di?usion equations using a non-negative finite element formulation for di?erent 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 strength/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 strength/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 R2-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(107) 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.

Mudunuru, Maruti K.↗

DOE OSTI2025

Coupled Hydrological-Thermal-Biogeochemical Modeling for Predicting Arctic Carbon Emissions (CH4PACE)

The Arctic, with nearly 1,700 billion metric tons of carbon stored in its soils, is experiencing significant warming trends that raise concerns about the potential release of greenhouse gases, particularly methane. This report investigates the conversion of carbon stored in Arctic soils and permafrost into methane and its subsequent atmospheric release over the coming decades. Recent data indicate a rise in global methane concentrations, highlighting the importance of understanding the mechanisms of methane generation under anaerobic conditions prevalent in thawing permafrost. Our study employs a multi-faceted approach that integrates fieldwork, benchtop experiments, and numerical simulations to explore the subsurface hydrological-thermal-biogeochemical systems influencing methane emissions. We focus on the relationship between microbial activity in decomposing organic matter under oxygen-limited conditions and the transport of methane out of these saturated wetland soils. Key hydrological parameters, including permeability, porosity, and thermal conductivity, were measured on soil samples from Fairbanks, Alaska, and used to parameterize PFLOTRAN, a coupled hydrological-thermal-reactive transport simulator. Our model enables prediction of the evolution of the active layer and its impact on methane production and release. Our findings underscore the critical need for a mechanistic understanding of methane dynamics in permafrost environments to improve predictions of methane emissions in Earth systems models.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2020

Exploring an ‘ideal hill': how lithology and transport mechanisms affect the possibility of a steady state during weathering and erosion

We introduce a model of chemical reaction within hills to explore how evolving porosity (and by inference, permeability) affects flow pathways and weathering. The model consists of hydrologic and reactive-transport equations that describe alteration of ferrous minerals and feldspar. These reactions were chosen because previous work emphasized that oxygen- and acid-driven weathering affects porosity differently in felsic and mafic rocks. A parameter controlling the order of the fronts is presented. In the absence of erosion, the two reaction fronts move at different velocities and the relative depths depend on geochemical conditions and starting composition. In turn, the fronts and associated changes in porosity drastically affect both the vertical and lateral velocities of water flow. For these instances, estimates of weathering advance rates based on simple models that posit unidirectional constant-velocity advection do not apply. In the model hills, weathering advance rates diminish with time as the Darcy velocities decrease with depth. The system can thus attain a dynamical steady state at any erosion rate where the regolith thickness is constant in time and velocities of both fronts become equal to one another and to the erosion rate. The slower the advection velocities in a system, the faster it attains a steady state. For example, a massive rock with relatively fast-dissolving minerals such as diabase -- where solute transport across the reaction front mainly occurs by diffusion -- can reach a steady state more quickly than granitoid rocks in which advection contributes to solute transport. The attainment of a steady state is controlled by coupling between weathering and hydrologic processes that force water to flow horizontally above reaction fronts where permeability changes rapidly with depth and acts as a partial barrier to fluid flow.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2021

Toward more mechanistic representations of biogeochemical processes in river networks: Implementation and demonstration of a multiscale model

A recently introduced multiscale model for representing the effects of small-scale hyporheic-zone biogeochemical processes is extended from the reach scale to river network scales. The model uses advection-dispersion-reaction equations for the channel network and one-dimensional advection-reaction subgrid models for the hyporheic zone. We summarize implementation in the integrated surface/subsurface hydrology modeling system Amanzi-ATS. The extension uses topologically defined meshes to represent stream/river networks and associates a hyporheic subgrid model with each channel grid cell. Biogeochemical reaction modeling capability residing in community software is accessed through an application programming interface. The implementation is verified against independent numerical solutions on a single reach. Mesh convergence studies show that commonly used semi-distributed representations can introduce significant spatial discretization error. Denitrification of farm runoff in a subbasin of the Portage River Basin in Ohio, USA is used to demonstrate the general-purpose reactive transport capability.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2021

SISGR: Chemomechanics of Far-From-Equilibrium Interfaces (COFFEI)

Portable, reliable, and deployable devices for energy storage and conversion require fundamental changes in design of solid-state composites comprising ceramics and metals. These materials comprise the electrodes and electrolytes of next-generation solid-oxide fuel cells and all solid-state batteries, forming solid-state functional composites. The advent of solid-state batteries – which replace liquid electrolytes with solid electrolytes capable of lithium ion transport for reliable energy storage in portable batteries – and the increased demand space for all solid-state fuel cells capable of oxygen reduction at intermediate temperatures remain important challenges for improved material stability and decreased system cost. However, little is understood about three fundamental facets of materials that enable such solid-state energy applications. First, how do such materials deform, fracture, or delaminate under operando conditions? Second, how does such mechanical deformation limit or facilitate electronic and ionic transport within and across such material interfaces? Third, how we can predictably design interface-rich composites to engineer both structural and electrochemical stability? This COFFEI Group comprised expertise from Materials Science & Engineering and Nuclear Science & Engineering to integrate unique in situ experiments, simulations, and fabricated interfaces that address these fundamental questions in solid-state interfaces of nanoscale composites that will guide solid-state electrochemistry, transport kinetics, and mechanical deformation for nonstoichiometric materials that enable such applications. In particular, we built on COFFEI’s understanding of chemomechanical coupling among defect concentrations, ionic transport, electron transport, and stored elastic energy that is particularly acute in the far-from-equilibrium conditions typical of energy device applications. By tailoring our focus to solid-state interfaces, we addressed these important issues by (a) developing and applying advanced in situ and ex situ characterization tools to characterize model materials and interfaces synthesized with molecular-level control, under both laboratory-controlled and extreme environments representative of energy device operation; and (b) employing computational modeling and simulation frameworks to predict transport mechanisms, reactivity and stability of these model materials and interfaces under significant chemical strains typical of energy device operation. Recent progress provided insights to additional materials systems and electrochemomechanical fatigue and fracture that were not fully envisioned when the program was initiated. Specifically, in the final three years of COFFEI we pursued two integrated thrusts, with complementary focus. Thrust I focused on failure-resistant electrochemomechanical composites, while Thrust II focused on strain-modulated conductivity and reactivity across interfaces. In contrast to our initial COFFEI focus, these thrusts concentrated wholly on solid-state material interfacial interactions and included greater integration of multiscale visualization including in situ electron microscopy of strained structures/interactions and mesoscale simulations. Successful development of functionally superior and long-lived battery and fuel cell systems and stress adaptable oxides requires a deeper, fundamental understanding of the coupling among the historically important subfields of solid-state electrochemistry, transport kinetics, and mechanical deformation for nonstoichiometric metal oxide electrodes. In this program, the understanding and the application of chemomechanical coupling of defect concentrations, ionic transport, electro-catalytic activity and stored elastic energy, particularly acute in the far-from-equilibrium conditions typical of energy device applications, are being refined and implications for device operation clarified, including for miniaturized solid-state batteries and fuel cells.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Resolving experimental biases in the interpretation of diffusion experiments with a user-friendly numerical reactive transport approach

The reactive transport code CrunchClay was used to derive effective diffusion coefficients (D e ), clay porosities (ε), and adsorption distribution coefficients (K D ) from through-diffusion data while considering accurately the influence of unavoidable experimental biases on the estimation of these diffusion parameters. These effects include the presence of filters holding the solid sample in place, the variations in concentration gradients across the diffusion cell due to sampling events, the impact of tubing/dead volumes on the estimation of diffusive fluxes and sample porosity, and the effects of O-ring-filter setups on the delivery of solutions to the clay packing. Doing so, the direct modeling of the measurements of (radio)tracer concentrations in reservoirs is more accurate than that of data converted directly into diffusive fluxes. While the above-mentioned effects have already been described individually in the literature, a consistent modeling approach addressing all these issues at the same time has never been described nor made easily available to the community. A graphical user interface, CrunchEase, was created, which supports the user by automating the creation of input files, the running of simulations, and the extraction and comparison of data and simulation results. While a classical model considering an effective diffusion coefficient, a porosity and a solid/solution distribution coefficient (D e –ε–K D ) may be implemented in any reactive transport code, the development of CrunchEase makes it easy to apply by experimentalists without a background in reactive transport modeling. CrunchEase makes it also possible to transition more easily from a D e –ε–K D modeling approach to a state-of-the-art process-based understanding modeling approach using the full capabilities of CrunchClay, which include surface complexation modeling and a multi-porosity description of the clay packing with charged diffuse layers.

58 GEOSCIENCES↗

DOE OSTI2021

A micromechanical hydro-mechanical-damage coupled model for layered rocks considering multi-scale structures

An anisotropic Hydro-Mechanical-Damage coupled model was established in the framework of thermodynamics for saturated layered rocks, which contain arbitrarily-distributed cracks of smaller scales and orientated bedding planes of much larger scales. Here, the proposed model considers the anisotropic damage growth and frictional sliding of cracks and shear sliding and dilatancy of bedding planes, as well as the interaction between cracks and bedding planes. Numerical implementation of the nonlinear coupled model was developed based on TOUGHREACT, which is a well-established simulator for multiphase fluid flow and reactive transport analysis. The proposed model was first validated with laboratory water injection test results on rock blocks, and then used to study the effects of injection rates, in situ stresses and bedding planes on fluid injection processes at the field scale, demonstrating the importance to consider the variation of multi-scale structures for better understanding the coupled Hydro-Mechanical responses in layered rocks.

58 GEOSCIENCES↗

DOE OSTI2026

Stochastic fracture generation and thermo-hydro-mechanical modeling in an equivalent continuum framework for enhanced geothermal systems

Enhanced geothermal systems (EGS) involve fracturing low permeability material to establish well connectivity and then injecting and circulating fluid into the fractured subsurface for geothermal power production. Changes in fracture aperture from contraction of the cooling matrix rock may alter network connectivity and risk thermal short-circuiting. Thermo-hydro-mechanical (THM) models are a useful tool to study these processes. However, as fracture networks are complex, and data may be limited, fracture networks in THM models are often stochastically generated. Given reliance on stochastic fracture networks and THM modeling to represent the subsurface and assess productivity of EGS, increased understanding of the influence of such statistically derived fracture networks on flow and heat transport in THM models is needed. Here, a new fracture process model is developed in the reactive transport code PFLOTRAN to stochastically generate fracture families and simulate changes in fracture aperture over time due to temperature changes of the rock matrix. Sixty-four different fracture networks ranging from well to poorly-connected, are modeled in PFLOTRAN with and without mechanical processes (THM vs TH). Results indicate that for well-connected fracture networks, thermal short-circuiting is less of a concern due to the abundance of available alternative flowpaths. For poorly-connected fracture networks, inclusion of mechanical processes showed steep thermal drawdown coincident with increase in fracture aperture along developing colder flowpaths, demonstrating the risk of thermal short-circuiting. Simulations with additional, larger fractures engineered to establish connectivity in a poorly-fractured subsurface, indicate that while stochastic variation of fracture orientation of the background network had limited influence, such variation in the engineered fractures significantly affected flow and heat transport.

Discrete fracture networks (DFN)↗

DOE OSTI2020

Modeling the impact of riparian hollows on river corridor nitrogen exports, Frontiers in Water: Dataset

This package contains all reactive transport simulation outputs used in "Modeling the impact of riparian hollows on river corridor nitrogen exports" (Rogers, D.B., et al., 2021). The simulation outputs reflect hydrological and biogeochemical behavior of a single, generalized riparian hollow located in the intra-meander region of a sub-alpine floodplain under transient hydrological conditions. The context for, purpose of, and conclusions drawn from this model are detailed in Rogers, D.B., et al., 2021.The .zip file contains simulation outputs for each of the five time periods analyzed (see metadata for specific dates), with each folder representing one continuous simulation period. Within each folder are the raw simulation outputs, which are comprised of hundreds of files. Files ending in ".vtk" are best visualized and analyzed using ParaView (https://www.paraview.org). All other files are best viewed or analyzed using R. For a detailed description of the meaning of each file, refer to the ".fls" file located in each folder.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2023

Management and International Sorption Model Collaboration (M4SF-23LL010302062-NEA-TDB)

This progress report (Level 4 Milestone Number M4SF-23LL010302062) summarizes research conducted at Lawrence Livermore National Laboratory (LLNL) within the Crystalline International Collaborations Activity Number SF-23LL01030206. The activity is focused on our long-term commitment of engaging our partners in international nuclear waste repository research. This includes participation in the Nuclear Energy Agency Thermochemical Database (NEA-TDB) Project and development of methodologies for integrating US and international thermodynamic databases for use in SFWST Generic Disposal System Assessment (GDSA) efforts. A continuing focus for FY23 efforts has been to support the US participation in the NEA-TDB effort (Mavrik Zavarin replaced Cindy Atkins-Duffin on the NEA-TDB Management Board (MB) and Executive Group (EG)) and developing mechanisms for integration of NEA-TDB thermochemical data with LLNL’s SUPCRTNE thermodynamic database that supports the SFWST GDSA activities. This effort is coordinated with the Argillite work package SUPCRTNE database development efforts. The goal is to provide a downloadable database that will be hosted on a LLNL website which integrates NEA-TDB data into the LLNL SUPCRTNE database where appropriate. As part of our international activities, we continue our effort to integrate international sorption databases into L-SCIE (Zavarin et al., 2022b). We presented opportunities to include sorption in the next phase of NEA-TDB efforts at the April 2023 EG meeting in Paris. FY23 efforts focused on ensuring interoperable database development across multiple international database development activities. The overall goal is to produce an open source database that can be shared and integrated with multiple nuclear waste programs internationally and harness modern data science workflows and algorithms to incorporate these new approaches into reactive transport and performance assessment models. In collaboration with our Helmholtz Zentrum Dresden Rossendorf partners, we recently demonstrated the power of FAIR open source databases by fitting iron oxide (hydrous ferric oxide, goethite, hematite, and magnetite) protolysis constants to all available L-SCIE data. The results were submitted as a manuscript to J. Colloid Interface Science. This work will inform future metal sorption studies on a variety of iron oxides in order to discern the most appropriate acidity constants and surface complexation modeling constructs to account for pH-dependent mineral surface charge behavior. This work also explored automated surface complexation model development workflows in order to generate higher throughput model input files for a more facile incorporation into GDSA activities.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗

DOE OSTI2021

Simulation of hardened cement degradation and estimation of uncertainty in predicted failure times with peridynamics

Modeling the degradation of cement-based infrastructure due to aqueous environmental conditions continues to be a challenge. In order to develop a capability to predict concrete infrastructure failure due to chemical degradation, here we created a chemomechanical model of the effects of long-term water exposure on cement paste. The model couples the mechanical static equilibrium balance with reactive–diffusive transport and incorporates fracture and failure via peridynamics (a meshless simulation method). The model includes fundamental aspects of degradation of ordinary Portland cement (OPC) paste, including the observed softening, reduced toughness, and shrinkage of the cement paste, and increased reactivity and transport with water induced degradation. This version of the model focuses on the first stage of cement paste decalcification, the dissolution of portlandite. Given unknowns in the cement paste degradation process and the cost of uncertainty quantification (UQ), we adopt a minimally complex model in two dimensions (2D) in order to perform sensitivity analysis and UQ. We calibrate the model to existing experimental data using simulations of common tests such as flexure, compression and diffusion. Then we calculate the global sensitivity and uncertainty of predicted failure times based on variation of eleven unique and fundamental material properties. We observed particularly strong sensitivities to the diffusion coefficient, the reaction rate, and the shrinkage with degradation. Also, the predicted time of first fracture is highly correlated with the time to total failure in compression, which implies fracture can indicate impending degradation induced failure; however, the distributions of the two events overlap so the lead time may be minimal. Extension of the model to include the multiple reactions that describe complete degradation, viscous relaxation, post-peak load mechanisms, and to three dimensions to explore the interactions of complex fracture patterns evoked by more realistic geometry is straightforward and ongoing.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Geologic Disposal Safety Assessment (GDSA) Biosphere Model Development

The Spent Fuel and Waste Science and Technology Campaign of the U.S. Department of Energy Office of Nuclear Energy, Office of Spent Fuel and Waste Disposition is conducting research and development on geologic disposal of spent nuclear fuel and high-level nuclear waste. This work includes the Geologic Disposal Safety Assessment (GDSA) program which is charged with development of generic deep geologic repository concepts and system performance assessment models. One part of the GDSA framework is the development of a biosphere model capable of assessing doses to potential receptors exposed to radionuclides released from geologic disposal sites. As part of the GDSA framework, a biosphere model compatible with the PFLOTRAN massively parallel subsurface flow and reactive transport code is under development. The PFLOTRAN model provides the radionuclide source term for the biosphere model. The GDSA Biosphere model then assesses the potential movement of radionuclides through the surface biosphere and the subsequent exposure to a human receptor living in the biosphere. The biosphere model includes pathways originating from the groundwater as well as pathways originating from surface water bodies that have a water exchange with a contaminated groundwater body. The pathways for human exposure include consumption of drinking water, irrigated crops, meat animals, aquatic vegetation, and animals, etc.; external exposure from irrigated ground surfaces, surface water bodies, recreational activities, etc.; and inadvertent exposures such as ingestion of contaminated soils or shower water, etc. The GDSA Biosphere model was designed to be flexible and generic in order to accommodate a variety of different sites and climate states. This presentation will present the on the purpose, design, and development progress of the GDSA Biosphere Model.

GDSA, biosphere, repository↗

DOE OSTI2021

Numerical study of the chemo-mechanical behavior of FEBEX bentonite in nuclear waste disposal based on the Barcelona expansive model

Experimental studies show that compacted bentonite used as a backfill material for nuclear waste repository experiences strong coupling between chemical and mechanical processes. Here, we use a dual-structure expansive soil model, referred to as the Barcelona Expansive Model (BExM), to predict the behavior of bentonite buffer in subsurface emplacement tunnels for high-level radioactive waste. After emplacement, the bentonite is subjected to complex and coupled Thermal-Hydraulic-Mechanical-Chemical (THMC) processes. The BExM constitutive model is implemented in a multi-phase reactive transport and geomechanics simulator, TOUGHREACT-FLAC3D, and the model is verified with one benchmark test on FEBEX bentonite. We utilize a one-way Chemo-Mechanical (C-M) coupling approach, in which chemical changes affect the mechanical behavior of bentonite through the BExM linked with the evolution of mass fraction of smectite, exchangeable cation concentration, and ionic strength via osmotic suction. The parameters of the new coupled model for FEBEX bentonite are calibrated against a series of laboratory experiments with various salinity solutions. Finally, coupled THMC modeling is conducted for a generic argillite repository with bentonite buffer under high temperature, focusing on the long-term chemical change and its effect on the mechanical process.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

DOE OSTI2023

Simulation of gallium nitride vertical fin-shaped field effect transistor for use as thermal neutron detector

Through the use of a radiation detection system simulation framework, a gallium nitride vertical fin-shaped field effect transistor (FinFET) was studied for output response when utilized as a thermal neutron detector. The FinFET was assumed to had been backfilled with boron carbide, reactive to thermal neutrons. The GaN FinFET was modeled with radiation transport from MCNP, and the electronic transport from COMSOL Multiphysics. Fabricated FinFET devices (not neutron reactive) were tested to aid in the tuning of the COMSOL FinFET model. Through time-depenent studies, the drain current response pulse to simulated ionization due to single events lead to building of a database of device responses to radiation. By integrating the current pulses over time, the induced charge was calculated. Using the results of the radiation transport PTRAC file in combination with the induced charge database, an integrated charge spectrum was calculated.

Davidson, Bryce L.↗

DOE OSTI2024

A mineral precipitation model based on the volume of fluid method

A novel volume of fluid method is presented for mineral precipitation coupled with fluid flow and reactive transport. The approach describes the fluid-solid interface as a smooth transitional region, which is designed to provide the same precipitation rate and viscous drag force as a sharp interface. Specifically, the governing equation of mineral precipitation is discretized by an upwind scheme, and a rigorous effective viscosity model is derived around the interface. The model is validated against analytical solutions for mineral precipitation in channel and ring-shaped structures. It also compares well with interface tracking simulations of advection-diffusion-reaction problems. Here, the methodology is finally employed to model mineral precipitation in fracture networks, which is challenging due to the low porosity and complex geometry. Compared to other approaches, the proposed model has a concise algorithm and contains no free parameters. In the modeling, only the pore space requires meshing, which improves the computational effciency especially for low-porosity media.

58 GEOSCIENCES↗

DOE OSTI2020

A review of spatial Markov models for predicting pre-asymptotic and anomalous transport in porous and fractured media

Heterogeneity across a broad range of scales in geologic porous media often manifests in observations of non-Fickian or anomalous transport. While traditional anomalous transport models can successfully make predictions in certain geological systems, increasing evidence suggests that assumptions relating to independent and identically distributed increments constrain where and when they can be reliably applied. A relatively novel model, the Spatial Markov model (SMM), relaxes the assumption of independence. The SMM belongs to the family of correlated continuous time random walks and has shown promise across a wide range of transport problems relevant to natural porous media. It has been successfully used to model conservative as well as more recently reactive transport in highly complex flows ranging from pore scales to much larger scales of interest in geology and subsurface hydrology. In this review paper we summarize its original development and provide a comprehensive review of its advances and applications as well as lay out a vision for its future development.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2021

A Review of Lattice-Boltzmann Models Coupled with Geochemical Modeling Applied for Simulation of Advanced Waterflooding and Enhanced Oil Recovery Processes

To maintain economic profit and improve the oil production efficiency after the primary and secondary production phase, advanced waterflooding techniques such as low salinity waterflooding in carbonate reservoirs have been investigated in numerical simulations, laboratory experiments, and field pilot tests. Multiple underlying mechanisms have been proposed based on these studies, and they are still under debate. Various numerical modeling approaches are introduced, but there exists a lack of a pore-scale comprehensive modeling scheme to fully understand the processes. Lattice-Boltzmann method (LBM) is a type of numerical fluid flow modeling technique that shows capabilities and flexibilities in modeling pore-scale fluid flow to integrate physical–chemical processes within complex structures. The intrinsic feature of LBM makes it a promising framework for simulating advanced waterflooding due to its flexibility, accuracy, and parallel efficiency. LBM works either by itself for solving reactive transport problems or by coupling with a third-party reaction solver. This review mainly introduces the LBM fluid flow and reactive transport capabilities and the concept and modeling approaches to simulate advanced waterflooding techniques. Meanwhile, an evaluation of the coupled LBM models for enhanced oil recovery (EOR) simulations is discussed with future research challenges and directions concluded.

02 PETROLEUM↗

DOE OSTI2023

Automated Symbolic Upscaling: 2. Model Generation for Extended Applicability Regimes

Abstract In this second part of the two paper series, we detail an algorithmic procedure for systematically implementing the generalized closure form strategy presented in Part 1. This strategy extends the applicability of homogenized models with respect to classical homogenization theory, as demonstrated in Part 1 where upscaled models are rigorously derived in moderately reactive physical regimes. After encoding the algorithm into Symbolica, an automated upscaling framework, we upscale two reactive mass transport problems and numerically validate the resulting nonlinear homogenized models by showing the absolute error estimates predicted by homogenization theory are satisfied. In both problems, nontrivial closure forms and closure problems are automatically formulated using the encoded strategy with no human interaction, nor prior knowledge regarding the closure required for the systems. We hope these demonstrations spark further interest in automated analytical frameworks for multiscale modeling, as such capabilities are invaluable for generating rigorous multiscale models of complex phenomena in porous media.

Pietrzyk, Kyle↗