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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 199 records · Page 11
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

A buoyancy–shear–drag-based turbulence model for Rayleigh–Taylor, reshocked Richtmyer–Meshkov, and Kelvin–Helmholtz mixing

A phenomenological turbulence model for Rayleigh–Taylor, reshocked Richtmyer–Meshkov, and Kelvin–Helmholtz instability-induced mixing is developed using a general buoyancy–shear–drag model. Analytic solutions to the simplified model equations corresponding to each instability are derived separately, which are then used to calibrate the model coefficients to predict specific values of the mixing layer growth parameters and exponents. The buoyancy-shear–drag equations for the bubble and spike mixing layer widths are then solved numerically, and a turbulent diffusivity (or viscosity) is constructed dimensionally as the product of the mixing layer width, h, and its time-derivative, dh/dt. Surrogate turbulent fields are then constructed by multiplying a presumed, approximate self-similar spatial profile by appropriate functions of h and dh/dt. Using several simplifying approximations, the turbulent diffusion equations satisfied by the mean mass fraction and mean shear velocity are solved analytically in a reference frame moving with the mean advection velocity, and it is shown that the mean fields evolve in space and time as expected. The explicit modeling and solution of turbulent transport equations (e.g., for the turbulent kinetic energy and its dissipation rate or a lengthscale) are not required. By using separate equations for the bubble and spike evolution, the model naturally captures the asymmetry induced by an increasing density contrast between the heavy and light fluids. The model also includes molecular dissipation and diffusion, and therefore, can describe transition to fully-developed turbulence if the initial turbulent diffusivity/viscosity is much smaller than the molecular diffusivity/viscosity. This model is applied to constant-acceleration Rayleigh–Taylor, impulsively reshocked Richtmyer–Meshkov, and variable-density Kelvin–Helmholtz mixing layers to demonstrate its utility. It is shown that the numerical solutions of the model calibrated using specific values of the instability growth parameters and exponents: (1) produces mixing layer widths in agreement with the expected self-similar growth power laws; (2) gives spatiotemporal profiles of turbulent fields that are expected and consistent with previous results; (3) predicts the expected power-law growths and decays of the spatially-integrated turbulent fields, and; (4) gives spatiotemporal profiles of the mean fields that are expected and consistent with previous results. This relatively simple model can be implemented numerically, and is expected to be useful for fundamental as well as astrophysical and inertial confinement fusion applications.

42 ENGINEERING↗
DOE OSTI2021

WKB Estimate of Bilayer Graphene’s Magic Twist Angles

We report that graphene bilayers exhibit zero-energy flatbands at a discrete series of magic twist angles. In the absence of intrasublattice interlayer hopping, zero-energy states satisfy a Dirac equation with a non-Abelian SU(2) gauge potential that cannot be diagonalized globally. We develop a semiclassical WKB approximation scheme for this Dirac equation by introducing a dimensionless Planck’s constant proportional to the twist angle, solving the linearized Dirac equation around AB and BA turning points, and connecting Airy function solutions via bulk WKB wave functions. We find zero-energy solutions at a discrete set of values of the dimensionless Planck’s constant, which we obtain analytically. Our analytic flatband twist angles correspond closely to those determined numerically in previous work.

36 MATERIALS SCIENCE↗
DOE OSTI2020

An extended trajectory-mechanics approach for calculating two-phase flow paths

A technique originating in quantum dynamics is used to derive a trajectory-based, semi-analytical solution for two-phase flow. The partial differential equation governing the evolution of the aqueous phase is equivalent to a family of ordinary differential equations defined along a path through the porous medium. The trajectories may be found by solving the differential equations directly or by post-processing the output of a numerical solution to the full set of governing equations. The trajectories, which differ from conventional streamlines, are found to bend downward in response to gravitational forces. The curvature is more pronounced as the dip of the porous layer containing the flow increases. Subtle changes in the relative permeability curve can lead to significant variations in the trajectories. The ordinary differential equation for the trajectory provides an expression for the travel time along the path. The expression produces a semi-analytical approximation to the model parameter sensitivities, the partial derivatives of the travel times with respect to changes in the permeability model. The semi-analytical trajectory-based sensitivities generally agree with those computed using a numerical reservoir simulator and a perturbation approach. The sensitivities are useful in tomographic imaging algorithms designed to estimate the spatial variation in permeability within a porous medium using multiphase observations.

58 GEOSCIENCES↗
DOE OSTI2021

An Analytic Benchmark for Neutron Boltzmann Transport with Downscattering—Part I: Flux and Eigenvalue Solutions

Computing in the energy dimension is one of the greatest challenges confronting present-day deterministic neutron transport solvers. Accurately resolving the neutron flux as neutrons downscatter across resonances in the nuclear cross sections currently requires considerable computing power and suffers from approximation errors. Flux uncertainty resulting from the uncertainty of the resonance structure is the single-largest cause of reactivity uncertainty. Any additional reference solution for the critical neutron downscattering problem with resonance phenomena would be a boon to verification and validation of neutronics codes. This paper establishes a benchmark to verify the accuracy of neutron transport criticality solvers along the energy dimension. For the first time, the analytic solution of the flux amplitude is derived in the particular case of an infinite homogeneous medium with isotropic scattering in the center of mass and an arbitrary number of no-threshold, neutral particle reaction resonances (e.g., radiative capture, fission, and resonance scattering). Furthermore, original analytic expressions are established to quantify the discrepancy between the ψ k (E) and ψ α (E) flux amplitudes, respective solutions of the multiplication factor k, or the exponential time-evolution frequency α eigenproblems. The physical study of these relations led to analysis of their first-order relative difference near the criticality condition α=0. Finally, numerical solutions are provided to a benchmark problem constituted of the first resonance of 239 Pu, the 6.67-eV resonance of 238 U, and a scattering isotope with a flat cross section, allowing for the computational verification of the energy resolution of current neutron transport criticality codes. Through these novel results, this analytic benchmark can serve as a reference to verify the energy resolution and sensitivity analysis of neutron transport criticality calculations.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

Vacuum magnetic fields with exact quasisymmetry near a flux surface. Part 1. Solutions near an axisymmetric surface

While several results have pointed to the existence of exactly quasisymmetric fields on a surface (Garren & Boozer, Phys. Fluids B, vol. 3, 1991, pp. 2805–2821; 2822–2834; Plunk & Helander, J. Plasma Phys. , vol. 84, 2018, 905840205), we have obtained the first such solutions using a vacuum surface expansion formalism. We obtain a single nonlinear parabolic partial differential equation for a function $\eta$ such the field strength satisfies $B = B(\eta )$ . Closed-form solutions are obtained in cylindrical, slab and isodynamic geometries. Numerical solutions of the full nonlinear equations in general axisymmetric toroidal geometry are obtained, resulting in a class of quasihelical local vacuum equilibria near an axisymmetric surface. The analytic models provide additional insight into general features of the nonlinear solutions, such as localization of the surface perturbations on the inboard side. The local solutions thus obtained can be continued globally only for special initial surfaces.

Physics↗
DOE OSTI2022

Efficient co-solution of time step size and independent state in simulations of fluid-driven fracture propagation with embedded meshes

Here we present an efficient time-continuation scheme for fluid-driven fracture propagation problems in the extended finite element method framework. The approach applies a monolithic solution strategy to a fully coupled and implicit approximation of hydro-mechanical systems in conjunction with simultaneous linear elastic propagation of multiple fractures. At the end of each time step, the process ensures that the weakest fracture tip is in an equilibrium propagation regime. Furthermore, the solution process provides an initialization procedure for the newly created fracture spaces and an a priori estimate of the stress intensity factor growth rate, improving simulation robustness, and efficiency. The solution process is validated using the Kristianovich-Geertsma-de Klerk analytical solution under the toughness- and viscosity-dominated regimes. It is also extended to and demonstrated on problems with multiple fractures undergoing simultaneous propagation with stress shadow interactions. Numerical examples demonstrate that the solution process can reduce the required computational cost by one order of magnitude compared to other existing methods.

42 ENGINEERING↗
DOE OSTI2020

Thermal transport exceeding bulk heat conduction due to nonthermal micro/nanoscale phonon populations

While classical size effects usually lead to a reduced effective thermal conductivity, we report here that nonthermal phonon populations produced by a micro/nanoscale heat source can lead to enhanced heat conduction, exceeding the prediction from Fourier's law. We study nondiffusive thermal transport by phonons at small distances within the framework of the Boltzmann transport equation (BTE) and demonstrate that the transport is significantly affected by the distribution of phonons emitted by the source. We discuss analytical solutions of the steady-state BTE for a source with a sinusoidal spatial profile, as well as for a three-dimensional Gaussian “hot spot,” and provide numerical results for single crystal silicon at room temperature. If a micro/nanoscale heat source produces a thermal phonon distribution, it gets hotter than that predicted by the heat diffusion equation; however, if the source predominantly produces low-frequency acoustic phonons with long mean free paths, it may get significantly cooler than that predicted by the heat equation, yielding an enhanced heat transport beyond bulk heat conduction.

42 ENGINEERING↗
DOE OSTI2020

Modeling of resistive plasma response in toroidal geometry using an asymptotic matching approach

The method of solving linear resistive plasma response, based on the asymptotic matching approach, is developed for full toroidal tokamaks by upgrading the Resistive DCON code [A.H. Glasser, Z.R. Wang and J.-K. Park, Physics of Plasmas, \textbf{23}, 112506 (2016)]. The derived matching matrix, asymptotically matching the outer and inner regions, indicates that the applied three dimension (3-D) magnetic perturbations contribute additional small solutions at each resonant surface due to the toroidal coupling of poloidal modes. In contrast, the resonant harmonic only affects the corresponding resonant surface in the cylindrical plasma. Since the solution of ideal outer region is critical to the asymptotic matching and is challenging to be solved in the toroidal geometry due to the singular power series solution at the resonant surfaces, systematic verification of the outer region $\Delta^\prime$ matrix is made by reproducing the well known analytical $\Delta^{\prime}$ result in [H.P. Furth, P.H. Rutherford and H. Selberg, The Physics of Fluids, \textbf{16}, 1054-1063 (1073)] as well as by making a quantitative benchmark with the PEST3 code [A. Pletzer and R.L. Dewar, J. Plasma Physics, \textbf{45}, 427-451 (1991)]. Finally, the reconstructed numerical solution of resistive plasma response from the toroidal matching matrix is presented. Comparing with the ideal plasma response, the global structure of the response can be affected by the small finite island at the resonant surfaces.

MHD simulation↗
DOE OSTI2020

Entanglement properties of disordered quantum spin chains with long-range antiferromagnetic interactions

Entanglement measures are useful tools in characterizing otherwise unknown quantum phases and indicating transitions between them. Here we examine the concurrence and entanglement entropy in quantum spin chains with random long-range couplings, spatially decaying with a power-law exponent $\textit{α}$. Using the strong disorder renormalization group (SDRG) technique, we find by analytical solution of the master equation a strong disorder fixed point, characterized by a fixed point distribution of the couplings with a finite dynamical exponent, which describes the system consistently in the regime $α > \frac{1}{2}$ . A numerical implementation of the SDRG method yields a power-law spatial decay of the average concurrence, which is also confirmed by exact numerical diagonalization. However, we find that the lowest-order SDRG approach is not sufficient to obtain the typical value of the concurrence. We therefore implement a correction scheme which allows us to obtain the leading-order corrections to the random singlet state. This approach yields a power-law spatial decay of the typical value of the concurrence, which we derive both by a numerical implementation of the corrections and by analytics. Next, using numerical SDRG, the entanglement entropy (EE) is found to be logarithmically enhanced for all $\textit{α}$, corresponding to a critical behavior with an effective central charge $\textit{c}$ = ln(2), independent of $\textit{α}$. This is confirmed by an analytical derivation. Using numerical exact diagonalization (ED), we confirm the logarithmic enhancement of the EE and a weak dependence on $\textit{α}$. For a wide range of partition size $\textit{l}$, the EE fits a critical behavior with a central charge close to $\textit{c}$ = 1, which is the same as for the clean Haldane-Shastry model with a power-law-decaying interaction with $\textit{α}$ = 2. Only for small $l \ll L$, in a range which increases with the number of spins N, we find deviations which are rather consistent with the strong disorder fixed point central charge $\textit{c}$ = ln(2). Furthermore, we find using ED that the concurrence shows power-law decay, albeit with smaller power exponents than obtained by SDRG. Finally, we also present results obtained with DMRG and find agreement with ED for sufficiently small $\textit{α}$ < 2, whereas for larger $\textit{α}$ DMRG tends to underestimate the entanglement entropy and finds a faster decaying concurrence.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Local Lagrangian reduced-order modeling for the Rayleigh-Taylor instability by solution manifold decomposition

The Rayleigh-Taylor instability is a classical hydrodynamic instability of great interest in various disciplines of science and engineering, including astrophysics, atmospheric sciences and climate, geophysics, and fusion energy. Analytical methods cannot be applied to explain the long-time behavior of the Rayleigh-Taylor instability, and therefore, numerical simulation of the full problem is required. However, in order to capture the growth of amplitude of perturbations accurately, both the spatial and temporal discretizations need to be extremely fine for traditional numerical methods, and long-time simulation may become prohibitively expensive. In this paper, we propose efficient reduced order model techniques to accelerate the simulation of the Rayleigh-Taylor instability in compressible gas dynamics. Here, we introduce a general framework for decomposing the solution manifold to construct the temporal domain partition and temporally-local reduced order model construction with varying Atwood number. We propose two practical approaches in this framework, namely decomposition by physical time and by penetration distance. Numerical results are presented to examine the performance of the proposed approaches.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Accelerating magnonic simulations with the pseudospectral Landau-Lifshitz equation

The pseudospectral Landau-Lifshitz (PS-LL) model can describe atomic-scale magnetic exchange interactions within a continuum framework. This is achieved by employing a convolution kernel that models the nonlocal interaction in a grid-independent manner. Even though the PS-LL was originally introduced to address atomic exchange, any nonlocal kernel can be modeled. In the field of magnonics, the dipole field is fundamental to describe the dispersion relation of magnons, the quasiparticle representation of angular momentum. Because dipole-dipole interactions are long-range, numerical approaches typically rely on convolutions. Here, we demonstrate that the PS-LL model can be used to perform magnonic simulations with a single convolution kernel derived from analytical solutions. We demonstrate a twofold increase in computational speed compared with the full dipole calculation. This approach is valid insofar as the excitations are linear, which is typically the case for magnons. Our results have the potential to accelerate magnonic research, particularly for the inverse design method, where several simulations must be performed to achieve the desired outcome.

Mathematics and computing↗
DOE OSTI2023

Analytic insights into nonlocal energy transport: Steady state Fokker Planck theory in arbitrary Z plasmas

The generation of energetic electrons in laser fusion in an important issue. The electrons may either arise from a laser plasma instability, or from the uncoupled high temperature tail of a Maxwellian distribution. To study these in a laser fusion context, it is important to find a method accurate enough to be useful, and simple enough to be incorporated into a radiation hydrodynamics numerical simulation, the main workhorse for studying the laser fusion target. That is why analytic insights become important, they allow one to simplify the Fokker Planck theory so that a solution of it can be incorporated into a radiation hydrodynamic simulation. This work develops and analyzes a steady state Fokker Planck theory for plasmas of arbitrary Z. It develops a method of solving the simplified Fokker Planck method with a technique called sparse eigenfunction analysis. As a result, this method appears to work reasonably well when compared to the experimental results from the Rochester/NIF on plastic spherical targets with and without a silicon layer.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Scaling Field-Theoretic Simulation for Multicomponent Mixtures with Neural Operators

Multicomponent polymer mixtures are ubiquitous in biological self-organization but are notoriously difficult to study computationally. Plagued by both slow single molecule relaxation times and slow equilibration within dense mixtures, molecular dynamics simulations are typically infeasible at the spatial scales required to study the stability of mesophase structure. Polymer field theories offer an attractive alternative, but analytical calculations are only tractable for mean-field theories and nearby perturbations, constraints that become especially problematic for fluctuation-induced effects such as coacervation. Here, we show that a recently developed technique for obtaining numerical solutions to partial differential equations based on operator learning, neural operators, lends itself to a highly scalable training strategy by parallelizing per-species operator maps. We illustrate the efficacy of our approach on six-component mixtures with randomly selected compositions and that it significantly outperforms the state-of-the-art pseudospectral integrators for field-theoretic simulations, especially as polymer lengths become long.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

A phase-field model of quasi-brittle fracture for pressurized cracks: Application to UO 2 high-burnup microstructure fragmentation

Here, in this paper, we present a phase-field model of quasi-brittle fracture with pressurized cracks, with dedicated applications for polycrystalline materials. The model is formulated as a minimization problem within the variational framework. The external work done by pressure on the crack surfaces is included in the objective function. Several careful modeling choices lead to a regularization-length-independent critical strength. The model is constructed to give a softening response with an underlying linear traction-separation law. The pressure-dependent softening response and the regularization of the prescribed pressure are demonstrated with a (quasi) one-dimensional numerical analysis. In a two-dimensional numerical analysis under plane strain assumptions, the critical stress corresponding to crack propagation (as predicted by our quasi-brittle fracture model) is compared with linear elastic fracture mechanics (LEFM) analytical solutions. Our model is further utilized to simulate fission-gas-induced fragmentation of the UO 2 high-burnup structure (HBS). Simulation results show that pressurized bubbles can cause crack nucleation and propagation, and that the bubble size and the surrounding external pressure affect the critical pressure corresponding to crack nucleation. Simulations of a partial HBS at different recrystallization stages show that different grain structures (due to recrystallization) also influence crack paths and fragmentation morphology.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Coupled Lattice Boltzmann Modeling Framework for Pore-Scale Fluid Flow and Reactive Transport

In this paper, we propose a modeling framework for pore-scale fluid flow and reactive transport based on a coupled lattice Boltzmann model (LBM). We develop a modeling interface to integrate the LBM modeling code parallel lattice Boltzmann solver and the PHREEQC reaction solver using multiple flow and reaction cell mapping schemes. The major advantage of the proposed workflow is the high modeling flexibility obtained by coupling the geochemical model with the LBM fluid flow model. Consequently, the model is capable of executing one or more complex reactions within desired cells while preserving the high data communication efficiency between the two codes. Meanwhile, the developed mapping mechanism enables the flow, diffusion, and reactions in complex pore-scale geometries. We validate the coupled code in a series of benchmark numerical experiments, including 2D single-phase Poiseuille flow and diffusion, 2D reactive transport with calcite dissolution, as well as surface complexation reactions. The simulation results show good agreement with analytical solutions, experimental data, and multiple other simulation codes. In addition, we design an AI-based optimization workflow and implement it on the surface complexation model to enable increased capacity of the coupled modeling framework. Compared to the manual tuning results proposed in the literature, our workflow demonstrates fast and reliable model optimization results without incorporating pre-existing domain knowledge.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

How machine learning can extend electroanalytical measurements beyond analytical interpretation

Electroanalytical measurements are routinely used to estimate material properties exhibiting current and voltage signatures. Analysis of such measurements relies on analytical expressions of material properties to describe the experiments. The need for analytical expressions limits the experiments that can be used to measure properties as well as the properties that can be estimated from a given experiment. Such analytical relations are essentially solutions of the physics-based differential equations (with properties as coefficients) describing the material behavior under certain specific conditions. In recent years, a new machine learning-based approach has been gaining popularity wherein the differential equations are numerically solved to interpret the electroanalytical experiments in terms of corresponding material properties. Since the physics-based differential equations are solved, one can additionally estimate underlying fields, e.g., concentration profile, using such an approach. To exemplify the characteristics of such a machine learning assisted interpretation of electroanalytical measurements, we use data from the Hebb–Wagner test on a magnesium spinel intercalation host. In conclusion, as compared to the traditional analytical expression-based interpretation, the emerging approach decreases experimental efforts to characterize relevant material properties as well as provides field information that was previously inaccessible.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Quarterly Research Performance Progress Report (Q8)

As part of Task 1, we have started by testing our modeling capabilities by reproducing isothermal DFIT simulations presented in the literature. Once satisfied with the results we have started by targeting the modeling of the DFITs at conducted at well 58-32. We have a identified a specific test (cycle 4 in zone 2) as the most interesting to be model with GEOS hydraulic fracturing module. Thus, we have first produced results with an isothermal model and adjusted model parameters to get a satisfying match with field pressure data. The, we have added thermal effects and compared the modeling results with and without thermal effects to estimate how thermal effects may influence test interpretation. Models seem to suggest that, for small volumes of fluid, thermal effects are moderate. In Task 2, we have adapted GEOS phase-field formulation to be able to simulate near-wellbore hydraulic fracture nucleation and propagation. We have devised a novel formulation that, compared to other existing ones, incorporates rock strengths. We have submitted a journal publication about our work. We are currently employing this phase-field formulation to model the experiments taking place at U Pitt and help us understand the effect of various parameters. In Task 3, we have built a model of the region surround well 16A and have started modeling stage 3 stimulation because of its simpler planar geometry. After calibrating simulation parameters using known analytical solutions, we have simulated the stage 3 stimulation using our isothermal hydraulic fracturing module, varying the permeability field, the stress conditions including different physics to get a better understanding of the numerical challenges and of the effects of varying these parameters on the simulation results. In Task 4 laboratory experimentation, a set of specialized drilling and injection tools has been customized and constructed to accommodate an inclined well with an orientation of up to 30 degrees relative to material anisotropy or principal stress axes. These inclined samples have also undergone thermal stress and hydraulic fracturing at a temperature of 190 degrees Celsius. Furthermore, both vertical and deviated sampling testing setups enable an extended analysis of post-peak pressure behaviors, facilitating post-test pressure analyses such as the G-function, step rate, and fracture reopening measurements. Thus, the key components of in-situ stress estimation can be extracted and validated through our experiment, providing a solid foundation for validating existing in-situ stress estimation theories or proposing new ones. Simultaneously, we are integrating computer vision techniques with traditional experimental fracture observation methods such as multi-overcore/slicing and water-penetration fracture observation. This combination will prove beneficial in populating the hydraulic fracture patterns database, generated under challenging EGS conditions. This approach aims to deepen our understanding of the complexities in EGS reservoirs and pave the way for future data-driven investigations. Additionally, PITT has also equipped the ELE International compression machine, which is now prepared for conducting indirect tensile and fracture toughness tests. These tests will aid in characterizing how rock fabrics influence the resulting fracture patterns. Additionally, we have completed the required personnel training and gained access to Scanning Electron Microscopy (SEM) and Energy Dispersive Spectroscopy (EDS) for conducting more detailed characterization and analysis of rock fabrics, as well as the examination of thermal and hydraulically induced fracture patterns. Thus, the PITT team has effectively demonstrated the capabilities of our experimental apparatuses in exploring the thermal effects, well deviation angles, material anisotropy, and operational choices (such as circulation rate, injection fluid viscosity, and injection rate) and their impact on pressure responses and fracture trajectories under the Utah FORGE conditions.

15 GEOTHERMAL ENERGY↗
DOE OSTI2022

CO 2 zonal injection rate allocation and plume extent evaluation through wellbore temperature analysis

Temperature analysis during a pause in injection operations, known as warmback analysis, has been used in the petroleum industry for evaluating the injection conformance and estimating the location of the flooded front in applications, such as waterflooding oil reservoirs. Here in this work, methods are introduced to extend the application of temperature warmback analysis to estimate the zonal CO 2 injection rate and zonal CO 2 plume extent during geologic CO 2 storage in a saline aquifer. First, novel analytical solutions are developed to model transient temperature in the aquifer during the injection and subsequent shut-in periods considering two-phase flow (gaseous CO 2 and aqueous brine) conditions in the aquifer. The solution involves a discretization of the aquifer into regions; the energy and mass conservation equations for the regions are solved simultaneously considering appropriate boundary conditions at the interfaces. Two solutions techniques are presented: multi-region and three-region solutions. Inverse models are developed accordingly to evaluate the injection profile and estimate the extent of the plume front in the reservoir during the injection period. The multi-region solution results in an inversion approach that requires regression analysis. However, the three-region formulation results in a simple graphical technique for inverse modeling. The analytical solutions are validated against a thermally coupled reservoir simulation tool using different synthetic cases for CO 2 injection in deep saline aquifers. The results of the developed solutions provide a good match with numerical results during forward and inverse modeling.

54 ENVIRONMENTAL SCIENCES↗