Search NASA⌕ Search

SEARCH · Search NASA

Results for “transient storage model”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Transient Storage Model Parameter Optimization Using the Simulated Annealing Method

Hyporheic exchange in streams is critical to ecosystem functions such as nutrient cycling along river corridors, especially for slowly moving or small stream systems. The transient storage model (TSM) has been widely used for modeling of hyporheic exchange. TSM calibration, for hyporheic exchange, is typically used to estimate four parameters, including the mass exchange rate coefficient, the dispersion coefficient, stream cross-sectional area, and hyporheic zone cross-sectional area. Prior studies have raised concerns regarding the non-uniqueness of the inverse problem for the TSM, that is, the occurrence of different parameter vectors resulting in TSM solution that reproduces the observed in-stream tracer break through curve (BTC) with the same error. This leads to practical non-identifiability in determining the unknown parameter vector values even when global-optimal values exist, and the parameter optimization becomes practically non-unique. To address this problem, we applied the simulated annealing method to calibrate the TSM to BTCs, because it is less susceptible to local minima-induced non-identifiability. A hypothetical (or synthetic) tracer test data set with known parameters was developed to demonstrate the capability of the simulated annealing method to find the global minimum parameter vector, and it identified the “hypothetically-true” global minimum parameter vector even with input data that were modified with up to 10% noise without increasing the number of iterations required for convergence. The simulated annealing TSM was then calibrated using two in-stream tracer tests conducted in East Fork Poplar Creek, Tennessee. In conclusion, simulated annealing was determined to be appropriate for quantifying the TSM parameter vector because of its search capability for the global minimum parameter vector.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

Seasonal Performance Characterization of a Gen3 Particle-Based Concentrating Solar Plant With a Spatially Resolved Transient Thermal Storage Model

Particle-based Gen3 Concentrating Solar Power (CSP) can be paired with high-temperature power cycles (>700 °C) and can have built-in long duration (≥10 hours) thermal energy storage if the working particles are stored properly in thermal energy storage bins. Although high-temperature and long-duration thermal energy storage can mitigate daily intermittencies in solar irradiation, seasonal variability in local meteorological conditions can still have a significant impact on the overall performance of CSP systems. Aside from daily cloud coverage affecting incident solar radiation, wind speed and ambient temperature are also significant variables regarding system heat attenuation, component efficiency, and overall solar conversion efficiency. In this work, we present simulation results for a Gen3 CSP prototype system in operation over four weeks throughout the year in Albuquerque, NM. The meteorological conditions are taken directly from the TMY3 data at the Albuquerque International Sunport, where the hourly Direct Normal Irradiation (DNI), wind speed, and ambient temperature are of particular interest. An investigation of the sensitivity of individual components like storage and ducting to the local meteorological conditions is provided and extended to the overall performance of the CSP system. The results from this study show that the particle inlet temperature at the particle-to-sCO2 heat exchanger can change as fast as 30 °C/min under standard operation in a passive mode.

Plewe, Kaden (ORCID:0000000286826879)↗
DOE OSTI2024

Mechanistic definition and prediction of the mass exchange coefficient between rivers and hyporheic zones: The $α$ of two $Ω$s

Solute transport in interconnected rivers and hyporheic zones is typically modeled through dual-domain models where first-order solute mass transfer between the two domains, Ω R and Ω HZ , is represented by a coefficient α. The transient storage model (TSM) is an example of such an approach. In practice, α is determined by fitting the tails of solute tracer breakthrough curves using a TSM. This approach has led to ambiguity regarding α’s physical meaning and transferability. Here, in this work, we investigated the physical basis for α and tested it with virtual experiments through the fully coupled multiphysics model hyporheicFoam for the Ω R – Ω HZ system. hyporheicFoam explicitly simulated coupled flow and solute transport over a kilometer with centimeter-scale resolution. Model results were analyzed to calculate α following its theoretical definition directly. Using the determined α within a TSM enables accurate reproduction of solute transport, underscoring α’s physical relevance and precision.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

Transient Physical Modelling for the Coupling of a High Temperature Gas Reactor with Thermal Energy Storage

Improving the flexibility of nuclear reactors to meet fluctuating demand on grids with high renewable energy generation penetration is key to improving reactor economics. Economic optimization using the code HERON gives maximum profit of coupling high temperature gas reactors (HTGRs) to thermal energy storage (TES) systems in the configuration shown in Figure 1 when following the demand in Figure 3. We look to model the physics of operation for a HTGR-TES using the HYBRID library in the code Modelica.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2022

Multilevel Analysis, Design, and Modeling of Coupling Advanced Nuclear Reactors and Thermal Energy Storage in an Integrated Energy System

This report discusses the different options for coupling thermal energy storage (TES) systems to advanced nuclear power plants (A-NPPs) in order to enable flexible and hybrid plant operation. An advanced light-water reactor (A LWR), a high-temperature gas-cooled reactor (HTGR) and a liquid-metal fast reactor (LMFR) were selected as the initial use cases for demonstrating a thermally balanced energy storage coupling design for thermal power extraction. The models presented herein showcase several design considerations, focusing on optimal deployment methodologies for achieving steady-state and transient-state operation with minimum disruption to the nuclear power cycle. This first part of the study presents steady-state models developed using Aspen HYSYS®, with the thermal energy bypass for NPP-TES coupling being varied at up to 50%. The various components were sized using the Aspen Process Economic Analyzer (APEA) and Aspen Exchanger Design and Rating (EDR), when applicable. Cost functions from these models were developed using the latest publicly available data obtained from APEA V11. The TES-coupled A-NPP steady-state models and cost functions then provided a baseline for dynamic operation and process optimization by using Idaho National Laboratory (INL)’s Framework for Optimization of Resources and Economics (FORCE) tools. A stochastic optimization of the various energy storage systems coupled to the A-NPPs was then performed using the Risk Analysis Virtual Environment (RAVEN) and its dispatch optimization plugin, the Holistic Energy Resource Optimization Network (HERON). The signal processing and synthetic history capabilities of RAVEN were used to account for the unpredictable behavior of electricity markets. An autoregressive moving average (ARMA) model was used to analyze price signals from the Pennsylvania-New Jersey-Maryland (PJM) market and were applied to the HERON analysis in order to optimize a system with the best economics. Transient modeling evaluation was then performed using Modelica models within the HYBRID repository, which was developed at INL for the Department of Energy Integrated Energy Systems program for the characterization of dynamic integrated system behavior and feedback. This includes evaluation of the TES-coupled A-LWR systems’ impact on physical and thermal system response during imposed system demands. Additional TES-coupled reactor types, coupling approaches, markets, and TES technologies will be evaluated in future work.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2023

Synthetic Electricity Market Data Generation and HERON Use Case Setup of Advanced Nuclear Reactors Coupled with Thermal Energy Storage Systems

This study evaluates and optimizes advanced nuclear reactors coupled with thermal energy storage (TES) systems in an Integrated Energy System (IES) architecture to enable advanced nuclear power plants (A NPP) to participate in multi-commodity markets, thus enhancing their economic competitiveness. Nuclear-TES coupling scenarios studied herein are designed attenuate the nuclear heat dynamics and defer energy delivery to a later time, enabling the nuclear reactor to continue operating at or near steady-state design conditions as usual while also enabling flexible generation. Three A-NPPs, namely, an advanced light-water reactor (A LWR), a high temperature gas-cooled reactor (HTGR) and a liquid-metal fast reactor (LMFR) were selected as the initial use cases for demonstrating the technoeconomic of thermally balanced energy storage coupling design for thermal power extraction. Each of the reactor technologies were evaluated in two different electricity markets. Stochastic optimization approach was adopted which included the evaluation of price signals from the Pennsylvania-New Jersey-Maryland (PJM) market, and Electric Reliability Council of Texas (ERCOT), using an autoregressive moving average (ARMA) model. Risk Analysis Virtual Environment (RAVEN) tool and its dispatch optimization plugin, the Holistic Energy Resource Optimization Network (HERON), were used to perform dispatch and capacity optimization, using the price data provided by the ARMA models. The results from the Nuclear-TES use cases will be used to design and characterize dynamic integrated system behavior and feedback.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2026

Phase change material-to-refrigerant heat exchangers: Experimental validation and uneven melting analysis

Thermal energy storage (TES) using phase change materials (PCMs) enables load shifting and reduces mismatches between the building's thermal demand and the heat pump (HP) system's thermal capacity. While most TES studies have focused on single-phase heat transfer fluids, PCM-to-refrigerant heat exchangers (PRHX), in which the refrigerant undergoes liquid-vapor phase change, remain largely underexplored. Here, to address this gap, this study systematically investigates a shell-and-tube PRHX operating as the condenser in an HP through experiments and simulations. A two-dimensional enthalpy-based finite-volume PRHX model was developed and validated against experimental data, including refrigerant and PCM temperature profiles, PRHX capacity, and system-level performance. Results show three characteristic stages: Stage I, the condenser temperature rapidly increases with PCM in the solid state absorbing sensible heat; Stage II, stable operation during PCM phase change; and Stage III, performance decline once part of the PCM becomes fully melted. Heat transfer analysis revealed that uneven PCM melting along the condenser length was driven primarily by variations in the refrigerant-side heat transfer coefficient, rather than local approach temperature differences. Further study demonstrated that minimizing refrigerant outlet subcooling led to more uniform PCM melting and extended Stages I and II by up to 89%. This paper provides a validated PRHX model, clarifies the mechanisms of uneven PCM melting, and highlights subcooling control as an effective strategy to improve TES performance in HP systems without requiring secondary loops.

Graphite matrix↗
DOE OSTI2023

Model data for numerical evaluation of photosensitive tracers as a strategy for separating surface and subsurface transient storage in streams

This model-data archive pertains to a study aimed at the numerical evaluation of the photosensitive tracers as a potential strategy for separating the effects of surface and hyporheic storage zones (SSZs and HSZs, respectively). Separating effects of SSZ and HSZ are important for accurately representing stream function as HSZs and SSZs expose solutes to significantly different biogeochemical conditions. We perform numerical experiments using a multiscale reactive transport model for stream corridors implemented in ATS code, which allows for representing multiple storage zones with their respective travel time distributions and biogeochemistry. For each of the numerical experiment, we provide in this model-data archive python wrapper to drive ATS (forward_model.py), synthetic observation (synthetic_btc.py, BTC_observed.csv), forward model files including ATS input (multiscale_transport.tpl), PFLOTRAN inputs (reactions_channel.tpl, reactions_hz.tpl, reactions_sz.tpl), MCMC (mcmc_run.py), predictive uncertainty (pred_uncert.py, BTCs_simulated_day.csv, BTCs_simulated_night.csv), MCMC outputs (tracer_test_GR.npy, tracer_test_logps.npy, tracer_test_parameters.npy) and Jupyter notebook for post-processing and visualization (post-processing.ipynb). For the denitrification application, ATS input file (denitrification_multisubgrid.tpl), PFLOTRAN input files (denitrification_channel.in, denitrification_hz.in), predictive uncertainty (pred_uncert_denitrification.py, BTCs_simulated_DO.csv, BTCs_simulated_DOC.csv, BTCs_simulated_Nitrate.csv).

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

Delivery of Dynamic Thermal Energy Storage Models and Advanced Reactor Concept Models to the HYBRID Repository

This publication details newly created energy storage and reactor models developed within the HYBRID modeling repository as part of the Department of Energy Office of Nuclear Energy (DOE-NE) Integrated Energy Systems (IES) program, led by Idaho National Laboratory (INL). Model development to-date includes creation of dynamic systems-level models of a pebble bed high temperature gas reactor (HTGR), sodium fast reactor (SFR), compressed air energy storage (CAES), liquid air energy storage (LAES) and Modelica standard library based two-tank sensible heat storage (SHS) in the IES-based HYBRID repository. Models are developed using the latest publicly available data and incorporate the possibility of control strategy inclusion for use with the existing IES modeling, analysis, and optimization toolset. Simulations showcase the abilities of each technology to flexibly operate in ways consistent with IES operation expectations. When these models are available, they can be utilized within different integrated energy park concepts to understand optimal system operation, control, and dispatching. Moreover, given the generic nature of the models, industrial partner technologies can be quickly added to the repository using the existing models as a basis. Additional dynamic models for thermal energy storage concepts can be developed and added to the HYBRID repository as needed. Also detailed in this report are future development goals for the HYBRID repository including adding suites of steady-state models, economic costing information, and reduced-order models. By adding these models in addition to the physical transient models currently existing within HYBRID, HYBRID will be a fully integrable tool for FORCE users.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2023

Numerical evaluation of photosensitive tracers as a strategy for separating surface and subsurface transient storage in streams

For this work, we numerically evaluated photosensitive tracers as a potential strategy for separating the effects of surface and hyporheic storage zones (SSZs and HSZs, respectively) on stream corridor transport. Correctly separating HSZ and SSZ effects is critical to estimating the hydro-biogeochemical function of a stream because HSZs and SSZs expose solutes to significantly different biogeochemical conditions, like sunlight exposure, microbial processes, and oxygen availability. Our numerical experiments used a multiscale river-corridor transport model implemented in the ATS code, which accommodates multiple storage zones with distinct travel time distributions and biogeochemical reactions. For parameter inferences, we used Bayesian inverse modeling. We found that breakthrough curves for photo-decaying tracers from day and night injection can delineate surface and hyporheic transient storage contributions, but only when interpreted jointly through a two-storage zone model. Numerical experiments that used only daytime injection or interpreted breakthrough curves with a single storage zone model yielded good fit to breakthrough curves, but parameter estimates were biased and controlling processes misattributed, examples of good model fits for the wrong reasons. Using those biased parameter estimates in reactive transport simulations resulted in significantly different projections of denitrification, which underscores the potential for stream function to be mischaracterized if tracer tests are interpreted through an inappropriately simplified model for transient storage. More generally, this study highlights the role of modeling in evaluating the experimental design and identifying the potential of system mischaracterization and its implications.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Operating Characteristics of Metal Hydride-Based Solar Energy Storage Systems

Thermochemical energy storage systems, based on a high-temperature metal hydride coupled with a low-temperature metal hydride, represent a valid option to store thermal energy for concentrating solar power plant applications. The operating characteristics are investigated for a tandem hydride bed energy storage system, using a transient lumped parameter model developed to identify the technical performance of the proposed system. The results show that, without operational control, the system undergoes a thermal ratcheting process, causing the metal hydride concentrations to accumulate hydrogen in the high-temperature bed over time, and deplete hydrogen in the low temperature. This unbalanced system is compared with a ’thermally balanced’ system, where the thermal ratcheting is mitigated by thermally balancing the overall system. The analysis indicates that thermally balanced systems stabilize after the first few cycles and remain so for long-term operation, demonstrating their potential for practical thermal energy storage system applications.

25 ENERGY STORAGE↗
DOE OSTI2024

Semi–Analytical Modeling of Transient Stream Drawdown and Depletion in Response to Aquifer Pumping

Analytical and semi–analytical models for stream depletion with transient stream stage drawdown induced by groundwater pumping are developed to address a deficiency in existing models, namely, the use of a fixed stream stage condition at the stream–aquifer interface. Here field data are presented to demonstrate that stream stage drawdown does indeed occur in response to groundwater pumping near aquifer–connected streams. A model that predicts stream depletion with transient stream drawdown is developed based on stream channel mass conservation and finite stream channel storage. The resulting models are shown to reduce to existing fixed–stage models in the limit as stream channel storage becomes infinitely large, and to the confined aquifer flow with a no–flow boundary at the streambed in the limit as stream storage becomes vanishingly small. The model is applied to field measurements of aquifer and stream drawdown, giving estimates of aquifer hydraulic parameters, streambed conductance, and a measure of stream channel storage. The results of the modeling and data analysis presented herein have implications for sustainable groundwater management.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

SAM Two-Phase Flow Model Development and Applications for Operational Transients in Advanced Reactors

As advanced nuclear technologies continue to develop, the need for the flexible operation and generation of these advanced reactors becomes necessary to maximize economic potential. As large-scale experiments are not always feasible, modeling and simulations of advanced reactors play a crucial role in design optimization and analysis. The SAM (System Analysis Module) code developed at Argonne National Laboratory is a state-of-the-art system-level thermal-hydraulic code aimed at simulating advanced reactor systems. Recent code developments have implemented two-phase flow modeling using the homogeneous equilibrium model, and a new steam generator component has been developed to utilize the two-phase flow implementation. In addition to verification tests, a load-following simulation was performed to model a realistic load-following transient in a proposed integrated system consisting of a conceptual advanced reactor known as the Advanced Burner Test Reactor (ABTR) and thermal energy storage (TES) tanks. The integrated system model uses two large TES tanks designed for sodium and a model helical coil steam generator to simulate the operational load-following transient. The flow rates of the feedwater and secondary loops are regulated to meet a prescribed steam generator load consistent with the electricity demand over a 24-h period. In conclusion, the results found the ABTR system was able to maintain stable reactor conditions and primary- and secondary-side characteristics over the course of the load-following transient.

Advanced Burner Test Reactor (ABTR)↗
DOE OSTI2021

Modelled land use and land cover change emissions – a spatio-temporal comparison of different approaches

Abstract. Quantifying the net carbon flux from land use and land cover changes (fLULCC) is critical for understanding the global carbon cycle and, hence, to support climate change mitigation. However, large-scale fLULCC is not directly measurable and has to be inferred from models instead, such as semi-empirical bookkeeping models and process-based dynamic global vegetation models (DGVMs). By definition, fLULCC estimates are not directly comparable between these two different model types. As an important example, DGVM-based fLULCC in the annual global carbon budgets is estimated under transient environmental forcing and includes the so-called loss of additional sink capacity (LASC). The LASC results from the impact of environmental changes on land carbon storage potential of managed land compared to potential vegetation and accumulates over time, which is not captured in bookkeeping models. The fLULCC from transient DGVM simulations, thus, strongly depends on the timing of land use and land cover changes mainly because LASC accumulation is cut off at the end of the simulated period. To estimate the LASC, the fLULCC from pre-industrial DGVM simulations, which is independent of changing environmental conditions, can be used. Additionally, DGVMs using constant present-day environmental forcing enable an approximation of bookkeeping estimates. Here, we analyse these three DGVM-derived fLULCC estimations (under transient, pre-industrial, and present-day forcing) for 12 models within 18 regions and quantify their differences as well as climate- and CO2-induced components and compare them to bookkeeping estimates. Averaged across the models, we find a global fLULCC (under transient conditions) of 2.0±0.6 PgC yr−1 for 2009–2018, of which ∼40 % are attributable to the LASC (0.8±0.3 PgC yr−1). From 1850 onward, the fLULCC accumulated to 189±56 PgC with 40±15 PgC from the LASC. Around 1960, the accumulating nature of the LASC causes global transient fLULCC estimates to exceed estimates under present-day conditions, despite generally increased carbon stocks in the latter. Regional hotspots of high cumulative and annual LASC values are found in the USA, China, Brazil, equatorial Africa, and Southeast Asia, mainly due to deforestation for cropland. Distinct negative LASC estimates in Europe (early reforestation) and from 2000 onward in the Ukraine (recultivation of post-Soviet abandoned agricultural land), indicate that fLULCC estimates in these regions are lower in transient DGVM compared to bookkeeping approaches. Our study unravels the strong dependence of fLULCC estimates on the time a certain land use and land cover change event happened to occur and on the chosen time period for the forcing of environmental conditions in the underlying simulations. We argue for an approach that provides an accounting of the fLULCC that is more robust against these choices, for example by estimating a mean DGVM ensemble fLULCC and LASC for a defined reference period and homogeneous environmental changes (CO2 only).

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

TRANSIENT THERMAL MODELING OF THE HIGH BURNUP DEMONSTRATION RESEARCH PROJECT CASK USING STAR-CCM+ AND COBRA-SFS

The Department of Energy in collaboration with the Electric Power Research Institute is in the process of conducting the High Burnup Demonstration Project. Where the objective is to characterize the performance of high-burnup fuel in long term storage. As part of this demonstration, a TN-32B dry storage cask was instrumented and loaded with spent nuclear fuel at North Anna Nuclear Generating Station in November 2017. The project cask provides a unique opportunity to gain information on spent fuel and cask performance from an in-service operational system. The cask was instrumented with thermocouples inside of the fuel assemblies, then loaded and dried using normal procedures. After the drying process a thermal soak period where the cask was left indoors was used to obtain steady temperatures for model comparison along with surface temperatures. This paper details thermal modeling validation work that was done to model both the steady state and transient cases. Two modeling tools were used to predict temperatures in the cask. The general purpose CFD and heat transfer code STAR-CCM+ was used with both a detailed pin-by-pin model was used along with a more efficient k-effective simplification. The other code is COBRA-SFS, a purpose-built detailed thermal modeling tool developed and maintained at PNNL. Results from all the modeling tools were compared blind to the test data. Each model utilized general design information and compared reasonably well to the blind steady state data using convection and surface temperature boundary conditions. Post-test adjustments were later made to better reflect the “as built” conditions of the cask. Based on lessons learned from the steady state analysis the vacuum drying process was modeled in both codes. Utilizing the measured loading conditions the transient models were able to compare very well with the measured data. Overall the project showed an ability to model spent fuel storage conditions very well and future work is planned to generalize the methodology used for vacuum drying.

Thermal Analysis, Spent Fuel, Dry Storage↗
DOE OSTI2025

Modeling Co2 Flow Through Faulted/Fractured Reservoirs Using Tedfm in Corner-Point Grids

Interest in underground CO2 storage has increased significantly over the last decade, driven by growing concern about global warming and rising levels of greenhouse gases in the atmosphere. Given that CO2 accounts for 80% of these greenhouse gases, carbon capture, utilization, and storage (CCUS) is considered one of the most direct approaches to achieving the net-zero carbon target. Although CO2 storage in deep saline aquifers and depleted gas reservoirs has been studied extensively, most studies use commercial simulators that model faults/fractures by simply modifying the transmissibility in the direction perpendicular to the fault surfaces. This work shows that this simplistic approach ignores the accelerated flow in the directions parallel to the fault plane, leading to significantly higher leakage along the fault surface. To accurately model CO2 flow in faulted reservoirs, we present the first transient embedded discrete-fracture model for corner-point grids (tEDFM-CPG). By comparing the tEDFM-CPG results with high-resolution reference solutions, we show that this approach is accurate and efficient at predicting CO2 flow in faulted/fractured reservoirs. In conclusion, this work presents the use of mixed reality (MR) to efficiently observe CO2 gas migration in the interior of these corner-point grid systems.

02 PETROLEUM↗
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↗