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At least 217 records · Page 12

Development of Steady-State and Dynamic Mass and Energy Constrained Neural Networks for Distributed Chemical Systems Using Noisy Transient Data

The paper presents the development of algorithms for mass and energy constrained neural network models that can exactly conserve the overall mass and energy of distributed chemical process systems, even though the noisy transient data used for optimal model training violate the same. In contrast to approximately satisfying mass and energy balance constraints of a system by soft penalization of objective function, algorithms have been developed for solving equality-constrained nonlinear optimization problems, thus providing the guarantee of exactly satisfying the system mass and energy conservation laws. For developing dynamic mass-energy constrained network models for distributed systems, hybrid series and parallel dynamic-static neural networks have been leveraged. The developed algorithms for solving both the training and forward problems are validated using both steady-state and dynamic data in the presence of various noise characteristics. The developed data-driven algorithms are flexible to exactly satisfy mass and energy balance constraints for dynamic chemical processes if the system holdup information is available. The proposed network structures and algorithms are applied to the development of data-driven lumped and distributed models of an adiabatic superheater/reheater system, a nonisothermal continuous stirred tank reactor, as well as an electrically heated plug-flow reactor system where one form of energy gets transformed to another. It has been observed that the mass-energy constrained neural networks yield a root mean squared error of <1% with respect to the system truth for the case studies evaluated in this work.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Multistage Surface-Heated Vacuum Membrane Distillation Process Enables High Water Recovery and Excellent Heat Utilization: A Modeling Study

Surface-heated membrane distillation (MD) enhances the energy efficiency of desalination by mitigating temperature polarization (TP). However, systematic investigations of larger scale, multistage, surface-heated MD system with high water recovery and heat recycling are limited. Here, we explore the design and performance of a multistage surface-heated vacuum MD (SHVMD) with heat recovery through a comprehensive finite difference model. In this process, the latent heat of condensation is recovered through an internal heat exchanger (HX) using the retentate from one stage as the condensing fluid for the next stage and an external HX using the feed as the condensing fluid. Model results show that surface heating enhances the performance compared to conventional vacuum MD (VMD). Specifically, in a six-stage SHVMD process, 54.44% water recovery and a gained output ratio (GOR) of 3.28 are achieved with a surface heat density of 2000 W m –2 , whereas a similar six-stage VMD process only reaches 18.19% water recovery and a GOR of 2.15. Mass and energy balances suggest that by mitigating TP, surface heating increases the latent heat trapped in vapor. The internal and external HXs capture and reuse the additional heat, which enhances the GOR values. We show for SHVMD that the hybrid internal/external heat recovery design can have GOR value 1.44 times higher than that of systems with only internal or external heat recovery. Furthermore, by only increasing six stages to eight stages, a GOR value as high as 4.35 is achieved. The results further show that surface heating can reduce the energy consumption of MD for brine concentration. As a result, the multistage SHVMD technology exhibits a promising potential for the management of brine from industrial plants.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Analysis of AP1000 Small-Break Loss-of-Coolant Accident Using Reactor Transient Simulator

The Westinghouse Electric Company’s Advanced Passive Reactor (AP1000) is characterized by the incorporation of passive safety systems (PSSs) designed to ensure core cooling during transient events. The assessment of PSSs requires evaluation of their performance through a combination of experiments and simulations employing various thermal-hydraulic codes. In addition, detailed evaluation of PSSs for a specific reactor system transient analysis such as loss-of-coolant-accident analysis supports understanding representative integral effects test facility development and the further evolution model development and assessment process. Developing a reactor system code is a complex and time-consuming process that requires significant engineering expertise and effort. It can take several months to even years to complete in the early stages of reactor system design and analysis. However, this process can be expedited through the use of transient simulator models for similar reactor systems, which can be used for lesson learning and training purposes. This study uses the Personal Computer Transient Analyzer (PCTRAN) code. The main advantage of PCTRAN is its ease of use and ability to run faster than real time. This study presents the results obtained for a small-break loss-of-coolant accident (SBLOCA) for two breaks using the full version (licensed) of PCTRAN. The purpose of this investigation is to evaluate the overall system behavior during the postulated SBLOCA event as well as assess the capability of the PCTRAN code to reproduce the system response during transient events. The obtained results were compared with the Westinghouse NOTRUMP system code. The PCTRAN code proved to be reliable in predicting the qualitative behavior of the system in both transient cases. As for the system response, it was found that it is contingent on the activation time of the PSSs. The differences in reactor coolant system pressure between the two codes were attributed to the critical flow model and simplification of mass and energy balance. Despite PCTRAN’s limitations, it can still provide a reasonable prediction of various reactor parameters such as pressure, mass flow rate, and void fraction during a SBLOCA scenario. It is worth noting that PCTRAN currently employs a bulk approach similar to that of the Modular Accident Analysis Program (MAAP) and MELCOR codes. However, the upcoming version of PCTRAN will include an artificial intelligence–based detection and accident prevention system, as well as different models for different reactor components. Consequently, PCTRAN has the potential to be upgraded to match the system thermal-hydraulic codes of the U.S. Nuclear Regulatory Commission and become more widely used in cybersecurity to safeguard nuclear power plants from cyberattacks.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Numerical predictions of cryogenic hydrogen vertical jets

Here, a comparison of Computational Fluid Dynamics (CFD) predictions with measurements is presented for cryo-compressed hydrogen vertical jets. The stagnation conditions of the experiments are characteristic of unintended leaks from pipe systems that connect cryogenic hydrogen storage tanks and could be encountered at a fuel cell refueling station. Jets with pressure up to 5 bar and temperatures just above the saturation liquid temperature were examined. Comparisons are made to the centerline mass fraction and temperature decay rates, the radial profiles of mass fraction and the contours of volume fraction. Two notional nozzle approaches are tested to model the under-expanded jet that was formed in the tests with pressures above 2 bar. In both approaches the mass and momentum balance from the throat to the notional nozzle are solved, while the temperature at the notional nozzle was assumed equal to the nozzle temperature in the first approach and was calculated by an energy balance in the second approach. The two approaches gave identical results. Satisfactory agreement with the measurements was found in terms of centerline mass fraction and temperature. However, for test with 3 and 4 bar release the concentration was overpredicted. Furthermore, a wider radial spread was observed in the predictions possibly revealing higher degree of diffusion using the k-ε turbulence model. An integral model for cryogenic jets was also developed and provided good results. Finally, a test simulation was performed with an ambient temperature jet and compared to the cold jet showing that warm jets decay faster than cold jets.

08 HYDROGEN↗

Effect of water droplet growth dynamics on electrode current in fuel-cell catalyst layers

Fuel cells are a promising next-generation energy-conversion technology designed to replace internal combustion engines in transportation applications. However, much work remains to optimize them. Operation at high humidities causes liquid water droplet formation on Pt catalyst particles during oxygen reduction, potentially impeding reactant arrival to the reactive electrode. In this work, four different cases of water droplet growth in fuel-cell catalyst layers are considered: pinned or advancing droplets on a bare Pt surface, advancing droplets on a Nafion film, and water-layer growth in carbon nanopores. Transient drop growth is captured with a combination of mass, species mass, and momentum balances, and the subsequent limiting current is determined via oxygen diffusion and Tafel kinetics. Further, water droplets are found not to be mass-transfer limiting due to the relatively large liquid-gas area compared to the Pt nanoparticle. Mass-transfer-limited behavior is calculated in carbon nanopores.

25 ENERGY STORAGE↗

Code Benchmark of Depressurized Conduction Cooldown Transient in the High Temperature Test Facility

This paper presents results from modeling of a depressurized conduction cooldown (DCC) transient at the High Temperature Test Facility (HTTF) as part of the OECD-NEA Thermal Hydraulics Code Validation Benchmark for High-Temperature Gas-Cooled Reactors using HTTF Data . This paper briefly describes the benchmark and the models being used. It then presents a comparison of steady state and transient results based on the Problem 2 Exercise 1A and 1B definitions. We compare block and helium temperature distributions, mass flow distribution, and energy balance in steady state. All models show comparable mass flow distributions and energy balances. The temperatures within the core and outer regions are comparable in all models too, but inner reflector temperatures can vary significantly. Despite that, we find that the models are in good agreement for the full-power steady state. In the DCC, we look at block temperature at the core midplane and RCCS water exit temperature. The INL and ANL models are found to be in excellent agreement with one another on block temperature over time, while the agreement when the KAERI and NRG models are added into consideration is good. Differences in the transient heat removal from the RCCS cause the differences in block temperature over time in these models. The CNL models show similar trends to the INL, ANL, KAERI, and NRG models, but the temperatures are high because the volumes used in calculating the average temperature include the heater rods in the CNL models only. The HUN-REN model shows results that suggest significantly lower heat removal in the RCCS which merit further investigation.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Magnesium production by molten salt electrolysis with liquid tin cathode and multiple effect distillation

Low-cost clean primary production of magnesium metal is important for its use in many applications, from light-weight structural components to energy technologies. This work describes new experiments and cost and emissions analysis for a magnesium metal production process. The process combines molten salt electrolysis of MgO using MgF₂-CaF₂ electrolyte and a reactive liquid tin cathode, with gravity-driven multiple effect thermal system (G-METS) distillation to separate out the magnesium product, and re-use of the tin. Electrolysis experiments with carbon anodes showed current yield above 90%, while a yttria-stabilized zirconia solid oxide membrane (SOM) anode experiment showed 84% current yield. G-METS distillation is an important component of the envisioned process. It can potentially lower costs and energy use considerably compared with conventional magnesium distillation. Techno-economic analysis including detailed mass and energy balances shows that this electrolyte composition could lower costs by utilizing CaO, which is the primary impurity in MgO, as the Hall-Héroult process uses the sodium impurity in alumina. Analysis options include: raw material types (magnesite rock vs. brine or seawater), drying and calcining using electricity vs. natural gas, and carbon vs. SOM anode type. Using SOM inert anodes results in a cost premium around 10%–15%, mostly due to higher electrical energy usage resulting from membrane resistance, and reduces GHG emissions by approximately 1 kg CO₂/kg Mg product. Capital and operating cost estimates, and cradle to gate greenhouse gas (GHG) emissions analysis under several raw material and process technology scenarios, show comparable costs and emissions to those of aluminum production.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Finite Element Analysis and Techno-economic Modeling of Solar Silicon Molten Salt Electrolysis

A new process is presented for low-cost one-step production of pure solid silicon from natural quartzite by molten salt electrolysis. At a process temperature of 1100°C, a techno-economic model including detailed mass and energy balances estimates energy consumption below 15 kWh/kg, with operating cost of $\$1.74$/kg and capital cost around $\$10,500$ per t/a (tonne annually) of production capacity for a 160,000 t/a plant. Use of an inert solid oxide membrane anode results in a pure oxygen by-product and no direct emissions. As a result, finite element analysis estimates the current density distribution and total current to inform the design of slab-shaped solid silicon cathodes.

14 SOLAR ENERGY↗

Machine learning for surrogate process models of bioproduction pathways

Technoeconomic analysis and life-cycle assessment are critical to guiding and prioritizing bench-scale experiments and to evaluating economic and environmental performance of biofuel or biochemical production processes at scale. Traditionally, commercial process simulation tools have been used to develop detailed models for these purposes. However, developing and running such models can be costly and computationally intensive, which limits the degree to which they can be shared and reproduced in the broader research community. This study evaluates the potential of an automated machine learning approach to develop surrogate models based on conventional process simulation models. The analysis focuses on several high-value biofuels and bioproducts for which pathways of production from biomass feedstocks have been well-established. The results demonstrate that surrogate models can be an accurate and effective tool for approximating the cost, mass and energy balance outputs of more complex process simulations at a fraction of the computational expense.

09 BIOMASS FUELS↗

Expanding the horizon of bio-naphtha beyond gasoline blend: property characterization and conversion opportunity assessment through technoeconomic and life-cycle analyses

Bio-naphtha, a common by-product of biorefineries, is expected to experience substantial growth in supply due to increasing demands for renewable diesel and synthetic aviation fuel (SAF). However, demand for bio-naphtha itself as a gasoline blendstock is limited because of the electrification of light-duty vehicles. This work investigated valorization opportunities for bio-naphtha from catalytic fast pyrolysis, hydrothermal liquefaction, Fischer–Tropsch synthesis, and hydrotreated esters and fatty acids pathways. These opportunities include producing polymer-grade olefin via steam cracking, SAF via steam cracking followed by olefin oligomerization, and renewable aromatics benzene, toluene, and xylene (BTX) and hydrogen via catalytic reforming. Process models were developed in Aspen Plus V14 and Aspen HYSYS V14 to calculate the mass and energy balances for each conversion step. Technoeconomic assessment and life-cycle analysis were conducted to evaluate the minimum fuel/product selling price, conversion cost, and life-cycle CO2 equivalent (CO2e) emission reduction. Technoeconomic assessment results suggest a minimum fuel/product selling price as low as $1.9/kg of olefins, $6.30/gal of gasoline-equivalent SAF, and $1.2/kg of BTX without any incentives. For all pathways, these prices are dominated by bio-naphtha feedstock costs, which account for at least 76% of the total cost. Compared with petroleum baselines, bio-naphtha-derived SAF, olefins, and BTX can achieve significant CO2e emission reductions from the use of renewable carbon resources. The results of life-cycle analysis and subsequent technoeconomic assessment, incorporating carbon credits, indicate the economic viability of using bio-naphtha for polymer-grade olefin and BTX production, with product costs comparable to market prices.

Xu, Shuang↗

A simple and practical process modeling methodology for pressure swing adsorption

Although many dynamic models exist for the design and simulation of pressure swing adsorption (PSA) processes, these models involve the solution of a complex system of coupled partial differential equations. Process engineers need a simple, practical, and yet robust short-cut model that helps decide whether to implement a PSA system in a process flowsheet. This work presents a “virtual” moving bed modeling methodology that considers only mass and energy balances and adsorption isotherms to describe the cyclic steady state behavior of PSA systems. Similar to tray efficiencies in distillation calculations, adsorption efficiencies are further introduced to account for system “non-ideality.” Finally, a lab-scale air separation system is used to illustrate the application of this modeling methodology.

42 ENGINEERING↗

A fast and accurate modeling approach for water and steam thermodynamics with practical applications in district heating system simulation

In U.S. district heating (DH) systems, steam is the most common heat transport medium. Industry demand for new advanced modeling capabilities of complete steam DH systems is increasing; however, the existing models for water/steam thermodynamics are too slow for large system simulations because of computationally expensive algebraic loops that require the solution to nonlinear systems of equations. For practical applications, this work presents a novel split-medium approach that implements numerically efficient liquid water models alongside various water/steam models, breaking costly algebraic loops by decoupling mass and energy balance equations. New component models for steam DH systems are also presented. We implemented the models in the equation based Modelica language and evaluated accuracy and computing speed across multiple scales: from fundamental thermodynamic properties to complete districts featuring 10 to 200 buildings. Compared to district models with the IF97 water/steam model and equipment models from the Modelica Standard Library, the new implementation improves the scaling rate for large districts from cubic to quadratic with negligible compromise to accuracy. Additionally, for an annual simulation with 180 buildings, this translates to a computing time reduction from 33 to 1-1.5 h. These results are critically important for industry practitioners to simulate steam DH systems at large scales.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

A gradient-based deep neural network model for simulating multiphase flow in porous media

We report simulation of multiphase flow in porous media is crucial for the effective management of subsurface energy and environment-related activities. The numerical simulators used for modeling such processes rely on spatial and temporal discretization of the governing mass and energy balance partial-differential equations (PDEs) into algebraic systems via finite-difference/volume/element methods. These simulators usually require dedicated software development and maintenance, and suffer low efficiency from a runtime and memory standpoint for problems with multi-scale heterogeneity, coupled-physics processes or fluids with complex phase behavior. Therefore, developing cost-effective, data-driven models can become a practical choice, and in this work, we choose deep learning approaches as they can handle high dimensional data and accurately predict state variables with strong nonlinearity. In this paper, we describe a gradient-based deep neural network (GDNN) constrained by the physics related to multiphase flow in porous media. We tackle the nonlinearity of flow in porous media induced by rock heterogeneity, fluid properties, and fluid-rock interactions by decomposing the nonlinear PDEs into a dictionary of elementary differential operators. We use a combination of operators to handle rock spatial heterogeneity and fluid flow by advection. Since the augmented differential operators are inherently related to the physics of fluid flow, we treat them as first principles prior knowledge to regularize the GDNN training. We use the example of pressure management at geologic CO 2 storage sites, where CO 2 is injected in saline aquifers and brine is produced, and apply GDNN to construct a predictive model that is trained with physics-based simulation data and emulates the physics process. We demonstrate that GDNN can effectively predict the nonlinear patterns of subsurface responses, including the temporal and spatial evolution of the pressure and saturation plumes. We also successfully extend the GDNN to convolutional neural network (CNN), namely gradient-based CNN (GCNN), and validate its capability to improve the prediction accuracy. GDNN has great potential to tackle challenging problems that are governed by highly nonlinear physics and enable the development of data-driven models with higher fidelity.

42 ENGINEERING↗

A pilot-process for calcium hydroxide production from iron slag by low-temperature precipitation

The production of Ca(OH) 2 via thermal decomposition of limestone is an energy intensive process resulting in significant CO 2 emissions. However, if produced in a manner that obviates the need for the thermal decomposition of limestone, Ca(OH) 2 could be a “CO 2 -negative” material. Herein, we design and demonstrate the operation of a continuous, low-temperature (< 100 °C), aqueous-phase pilot-process to produce Ca(OH) 2 using calcium extracted from alkaline industrial wastes. The three-step process encompasses unit operations including: (i) calcium leaching from basic oxygen furnace BOF slag, (ii) leachate concentration by reverse osmosis (RO), and (iii) Ca(OH) 2 precipitation by temperature swing. Here this process presents several advantages compared to the traditional route. First, it advances the recycling of waste from the steel industry. Second, it operates significantly below the temperature used in conventional lime production (900 °C) as it bypasses limestone calcination, responsible for ~65% of the CO 2 emissions from the current process. Thus, the new process has a lower CO 2 footprint and enables the use of industrial waste heat. The mass and energy balances were quantified to reveal that increasing the calcium concentration of the feed solution and the precipitation temperature, decrease the energy demands of the RO step, thereby reducing the process’s overall CO 2 footprint. The pilot system operated continuously and achieved a production rate of nearly 1 kg per day of Ca(OH) 2 with a purity greater than 95 wt%. The average particle size of the precipitates depended on the residence time in the precipitation reactor, demonstrating an ability to produce size-controlled particulates. Importantly, the process achieved full water recirculation/reutilization level indicative of a low-consumable water demand. The outcomes offer new insights and understanding relevant to developing and upscaling low-CO 2 processes for cement, lime, and portlandite.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Modeling and Optimization of a Rotating Packed Bed Contactor with a Tetraamine-Appended Metal−Organic Framework for CO 2 Capture

A potential contactor technology for sorbent-based CO 2 capture is the rotating packed bed that contains separate sections for continuous adsorption and desorption. A heat exchanger can be embedded to remove heat in the adsorption section and add heat in the desorption section. In this work, we develop a two-dimensional (2D) model of a rotating packed bed for use in CO 2 capture applications. Mass and energy balances for the model are developed based on a Ljungström-type air preheater, which accounts for the counter-current axial flow of gas phases in separate sections of the bed and the rotation of a solid sorbent, which cycles between adsorption and desorption sections. The sorbent used for this analysis is the tetraamine-appended metal−organic framework Mg 2 (dobpdc)(3−4− 3), chosen for its stability and affinity for CO 2 at low partial pressures, such as those from a natural gas power plant source. An optimization problem is solved that considers the trade-off between maximizing the productivity of the bed and minimizing energy consumption. Maximum productivity and minimum energy are found to be 8.53 kg/h/m 3 and 3.84 MJ/kg, respectively, when these objectives are optimized independently. It is observed that the flue gas pressure and bed rotational speed are the desired operating variables to vary for model-based design of experiments to reduce uncertainty in parameter estimation, as these two variables yielded the most information content based on the Fisher information matrix.

20 FOSSIL-FUELED POWER PLANTS↗

Recovering Rare Earth Elements from Coal Mine Drainage Using Industrial Byproducts: Environmental and Economic Consequences

Coal mine drainage (CMD) impairs tens of thousands of kilometers of U.S. waterways each year, in part with the leaching of low concentrations of rare earth elements (REEs). REEs are essential for modern technologies, yet economically viable natural deposits are geospatially limited, thus engendering geopolitical concerns, and their mining is energy intense and environmentally destructive. This work summarizes laboratory-scale experimentalresults of a trap-extract-precipitate (TEP) process and uses the mass and energy balances to estimate the economic costs and environmental impacts of the TEP. The TEP process uses the alkalinity and filtering capacity of stabilized flue gas desulfurization (sFGD) material or water treatment plant (WTP) sludge to remediate CMD waters and extract REEs. Passive treatment systems that use WTP sludge are cheaper than those that use sFGD material ($\$$89,300/year or $\$$86/gT-REE vs. $\$$89,800/year or $\$$278/gT-REE) and have improved environmental performance across all indicators from two different impact assessment methods. These differences are largely attributable to the larger neutralizing capacity of WTP sludge in the treatment application.

01 COAL, LIGNITE, AND PEAT↗

Medium-Scale Methanol Pool Fire Model Validation

In this work, medium scale (30 cm diameter) methanol pool fires were simulated using the latest fire modeling suite implemented in Sierra/Fuego, a low Mach number multiphysics reacting flow code. The sensitivity of model outputs to various model parameters was studied with the objective of providing model validation. This work also assesses model performance relative to other recently published large eddy simulations (LES) of the same validation case. Two pool surface boundary conditions were simulated. The first was a prescribed fuel mass flux and the second used an algorithm to predict mass flux based on a mass and energy balance at the fuel surface. Gray gas radiation model parameters (absorption coefficients and gas radiation sources) were varied to assess radiant heat losses to the surroundings and pool surface. The radiation model was calibrated by comparing the simulated radiant fraction of the plume to experimental data. The effects of mesh resolution were also quantified starting with a grid resolution representative of engineering type fire calculations and then uniformly refining that mesh in the plume region. Simulation data were compared to experimental data collected at the University of Waterloo and the National Institute of Standards and Technology (NIST). Validation data included plume temperature, radial and axial velocities, velocity temperature turbulent correlations, velocity velocity turbulent correlations, radiant and convective heat fluxes to the pool surface, and plume radiant fraction. Additional analyses were performed in the pool boundary layer to assess simulated flame anchoring and the effect on convective heat fluxes. This work assesses the capability of the latest Fuego physics and chemistry model suite and provides additional insight into pool fire modeling for nonluminous, non-sooting flames.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Hydrologic windows into the crystalline basement and their controls on groundwater flow patterns across the Paradox Basin, western USA

Conceptual models of sedimentary basin groundwater flow systems typically assume that the crystalline basement acts as an impermeable boundary and can be neglected. In this study, we use hydrologic models constrained by isotopic and geochemical datasets to argue that the La Sal Mountains, Utah, USA, act as a hydrologic window into the Paradox Basin’s lower aquifer system and underlying crystalline basement. We conducted a sensitivity study in which we varied crystalline basement/laccolith permeability as well as fault zone connectivity along a cross-sectional transect from the La Sal Mountains to Lisbon Valley. When the crystalline basement/laccolith units are set at relatively permeable levels (10–14 m 2 ), simulated tracers that include total dissolved solids, oxygen isotopic composition of pore fluids (δ 18 O), and groundwater residence times are in closest agreement with field measurements. Model results indicate that pore fluids in the basal aquifer system underlying the Paradox Formation confining unit are a mixture of relatively young meteoric fluids and older Paradox Formation brines. The presence of faults did not significantly modify fluid exchange between the upper and lower aquifer systems. This was due, in part, to underpressuring within the Paradox Formation. Our study concludes that the Paradox Basin represents a regional recharge area for the Colorado Plateau, with groundwater discharge occurring along the Colorado River within the Grand Canyon some 375 km away to the southwest. This is only possible with a permeable crystalline basement. Our findings help explain the genesis of Mississippi Valley-type ore deposits of the US Midcontinent, where the presence of a permeable basement may be useful in addressing issues related to solute mass and energy balance.

54 ENVIRONMENTAL SCIENCES↗