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Results for “Kinetic Modelling”

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 163 records · Page 9
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Development of a kinetic model to describe six types of symbiotic interactions in a formate utilizing microalgae-bacteria cultivation system

This study investigated an algae/formate-utilizing-bacteria system that has been developed for carbon capture. This photomixotrophic consortium consumed formate to support bacterial growth so that the resulting respiration CO 2 could be simultaneously used by algae to avoid CO 2 gas-lipid mass transfer limitation. To understand biomass growth and population interactions in this unique system, a kinetic model has been developed to describe algae and bacteria multiplication, formate and nitrogen utilizations, CO 2 mass transfer, O 2 generation and consumption, lighting condition and shading effect. The simulation indicated that this ecosystem could form six types of interactions (mutualism, commensalism, parasitism, neutralism, amensalism, and competition) depending on the light intensity and nutrient availability. Furthermore, the simulation of both batch culture and chemostat, along with parameter sensitivity tests and experimental observations, offered insights into optimal applications of algae-bacteria consortium based photobiorefinery.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2025

VERITAS : A density-functional theory-based multiband kinetic model for understanding x-ray spectroscopy of dense plasmas

X-ray spectroscopy has long been a powerful diagnostic tool for hot, dilute plasmas, providing insights into plasma conditions by measuring line shifts and broadenings of atomic transitions. The technique critically depends on the accuracy of atomic physics models used to interpret spectroscopic measurements for inferring plasma properties such as free-electron density and temperature. Over the past decades, the atomic and plasma physics communities have developed robust atomic physics models to account for various processes in hot, dilute classical plasmas. While these models have been successful in that regime, their applicability becomes uncertain when interpreting x-ray spectroscopy experiments of above-solid-density plasmas. Given that finite-temperature density-functional theory (DFT) offers a more accurate description of dense plasma environments, we present the development of a DFT-based multi-band kinetic model, VERITAS, designed to improve the interpretation of x-ray spectroscopic measurements in high-density plasmas produced by laser-driven spherical implosions. This work details the VERITAS model and its application to both time-integrated and time-resolved x-ray spectra from implosion experiments on OMEGA. The advantages and limitations of the VERITAS model will also be discussed, along with potential directions for advancing x-ray spectroscopy of dense and superdense plasmas.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

Kinetics Modeling for Design of Continuous Enzymatic Hydrolysis

Enzymatic hydrolysis of cellulose to monomeric sugars continues to be a limiting step in cost-effectively producing sugar and fermentation-based biofuels from biomass. In particular, the high cost of enzymes coupled with the long time-scale of reaction pose challenges to economic viability. Performing enzymatic hydrolysis in a continuous mode with enzyme recycle may provide a path towards substantially reduced costs for sugar production, but design and analysis are complicated by a lack of suitable kinetics models. Computationally attainable models, such as fractal-based models, require knowledge of the reaction-history of the biomass, and are thus only suitable for describing the batch reactions from which they are derived. Fundamental models, while potentially more generalizable, are often too computationally intensive to use in process or reactor modeling. In this work, a phenomenological rate model is proposed based on a two-phase substrate representation. Good agreement is seen between batch and continuous enzymatic hydrolysis (CEH) experiment data, which validates the model and enables us to solve for reactor design parameters, such as CEH reactor size and stream flow rates, based on process variables like yield. This model is integrated with techno-economic analysis software to explore economic sensitivities. Important design optimizations and tradeoffs are identified and quantified, including the relative cost imposed by rate slowdown from sugar inhibition versus the cost to remove and concentrate sugars at a lower concentration. It also identifies, high-leverage avenues for further exploration, such as increasing the maximum feasible solids concentration, and sustaining high membrane flux and reliability.

09 BIOMASS FUELS↗
DOE OSTI2023

Insights into the thermal history of carbon fibers using Raman spectroscopy and a novel kinetic model

Carbon fibers and carbon fiber composites are applied in high-performance applications, but a key consideration for application is their relative sensitivity to oxidative environments. To enable in-situ characterization of carbon fibers exposed to oxidative conditions, the Raman spectral response of T700 carbon fibers that have been exposed to a variety of dwell temperatures is reported herein with dwell times reaching up to 1 month. Here, we evaluate the spectra holistically by using integrated absolute difference analysis. By combining this analysis with straightforward kinetic models, we connect the total Raman spectral response to the temperature-time curve that could yield such a shift in spectral parameters. Our work connects the Raman spectral response of carbon fibers to their thermal history and can easily be extended to other graphitic materials, such as nuclear graphite.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Autoignition Delay Time Measurements and Chemical Kinetic Modeling of Hydrogen/Ammonia/Natural Gas Mixtures

Abstract In recent years, hydrogen-carrying compounds have accrued interest as an alternative to traditional fossil fuels due to their function as zero-emission fuels. As such, there is interest in investigating hydrogen-carrying compounds to improve understanding of the fuels’ characteristics for use in high-pressure systems. In the current study, the oxidation of ammonia/natural gas/hydrogen mixtures was carried out to study CO formation profiles as well as the ignition delay times behind reflected shock waves in order to refine chemical kinetic models. Experiments were carried out in the University of Central Florida’s shock tube facility by utilizing chemiluminescence to obtain OH* emission and laser absorption spectroscopy to obtain CO profiles. Experimental results were then compared with the GRI 3.0 mechanism, as well as the proprietary UCF 2022 mechanism utilizing CHEMKIN-Pro software. In general, both models were able to capture the trend in autoignition delay times and CO time histories for natural gas and ammonia mixtures. However, for ammonia-hydrogen mixtures, GRI 3.0 failed to predict ignition delay times whereas the UCF 2022 mechanism was able to capture the IDTs within the uncertainty limits of the experiments. A sensitivity analysis was conducted for different mixtures to understand the important reactions at the experimental conditions. Finally, a reaction pathway analysis was carried out to understand important ammonia decomposition pathways in the presence of hydrogen and natural gas.

Baker, Jessica B.↗
DOE OSTI2022

Experimental Ignition Delay Time Measurements and Chemical Kinetics Modeling of Hydrogen/Ammonia/Natural Gas Fuels

In recent years, hydrogen-carrying compounds have accrued interest as an alternative to traditional fossil fuels due to their function as zero-emission fuels. As such, there is interest in investigating hydrogen-carrying compounds to improve understanding of the fuels' characteristics for use in high pressure systems. In the current study, the oxidation of ammonia/natural gas/hydrogen mixtures was carried out to study carbon monoxide (CO) formation profiles as well as the ignition delay times (IDTs) behind reflected shock waves in order to refine chemical kinetic models. Experiments were carried out in the University of Central Florida's shock tube facility by utilizing chemiluminescence to obtain OH* emission and laser absorption spectroscopy to obtain CO profiles over a temperature range between 1200 K and 1800 K with an average pressure of 2.2 atm. Experimental mixtures included both neat and combination natural gas/hydrogen with ammonia addition, with all mixtures except one having an equivalence ratio of 1. Results were then compared with the GRI 3.0 mechanism, as well as the newly developed UCF 2022 mechanism utilizing chemkin-pro software. In general, both models were able to capture the trend in auto-ignition delay times and CO time histories for natural gas and ammonia mixtures. However, for ammonia–hydrogen mixtures, GRI 3.0 failed to predict ignition delay times, whereas the UCF 2022 mechanism was able to capture the IDTs within the uncertainty limits of the experiments. A sensitivity analysis was conducted for different mixtures to understand the important reactions at the experimental conditions. Lastly, a reaction pathway analysis was carried out to understand important ammonia decomposition pathways in the presence of hydrogen and natural gas.

33 ADVANCED PROPULSION SYSTEMS↗
DOE OSTI2020

Shock‐tube spectroscopic water measurements and detailed kinetics modeling of 1‐pentene and 3‐methyl‐1‐butene

Abstract To understand the effects of the chemical structure of two C 5 alkene isomers on their combustion properties, and to highlight the major chemical reactions occurring during their high‐temperature oxidation, water time histories were measured behind reflected shock waves for the oxidation of 1‐pentene (C 5 H 10 ‐1) and 3‐methyl‐1‐butene (3M1B) in 99.5% Ar. The experiments were carried out at three different equivalence ratios ( φ = 0.5, 1.0, and 2.0) at pressures and temperatures ranging from 1.29 to 1.47 atm and 1 331 to 1 877 K, respectively. The H 2 O quantification extends the database for 1‐pentene and provides new insights for 3M1B. These unique results were used to validate and to develop a new detailed kinetics model. Numerical predictions are presented, and the new model was able to capture the results with suitable accuracy, with 3M1B being notably more reactive than C 5 H 10 ‐1. Sensitivity and rate‐of‐production analyses were performed to help explain the results. Under the present conditions, the reactivity is rapidly initiated by molecular dissociation of a fraction of the pentene isomers. The initiation phase then induces H‐atom abstraction by active radicals (H, OH, O, HO 2 , and CH 3 ) to first produce alkenyl C 5 H 9 radicals (or an alkyl radical and an alkenyl radical by breaking a C─C bond) and subsequent, smaller fragments. The difference in terms of reactivity between the isomers is essentially due to the fact that 3M1B has one particularly weak tertiary allylic C─H bond, which allows for fast H‐atom abstraction compared with 1‐pentene.

Grégoire, Claire M.↗
DOE OSTI2021

Severity factor kinetic model as a strategic parameter of hydrothermal processing (steam explosion and liquid hot water) for biomass fractionation under biorefinery concept

Hydrothermal processes are an attractive clean technology and cost-effective engineering platform for bio-refineries based in the conversion of biomass to biofuels and high-value bioproducts under the basis of sustainability and circular bioeconomy. The deep and detailed knowledge of the structural changes by the severity of biomasses hydrothermal fractionation is scientifically and technological needed in order to improve processes effectiveness, reactors designs, and industrial application of the multi-scale target compounds obtained by stream explosion and liquid hot water systems. The concept of the severity factor [log 10 (R 0 )] established > 30 years ago, continue to be a useful index that can provide a simple description of the relationship between the operational conditions for biomass fractionation in second generation of biorefineries. Furthermore, this review develops a deep explanation of the hydrothermal severity factor based in lignocellulosic biomass fractionation with emphasis in research advances, pretreatment operations and the applications of severity factor kinetic model.

09 BIOMASS FUELS↗
DOE OSTI2021

Kinetic Monte Carlo Tool for Kinetic Modeling of Linear Step-Growth Polymerization: Insight into Recycling of Polyurethanes

A kinetic Monte Carlo model of polyurethane polymerization which explicitly tracks the polymer sequences is developed and shared. Here this model is benchmarked against theoretical and experimental polyurethane data and used to investigate the effect on oligomer distributions of unequal reactivity of the first and second isocyanate to react. The reverse reactions using thermodynamic consistency are then added to the framework, and analogous to the addition polymerization concept of ceiling temperature, equilibrium chain length distributions at various temperatures are calculated. For a mixture of three monomers AA, BB, and CC, where BB and CC do not react with one another, are present in stoichiometric proportions, and have different enthalpies of reaction with AA, an odd-even effect emerges. Odd length chains are more likely than even length chains for temperatures at which BB and CC have significantly different equilibrium conversions. The concept of ceiling temperature that is typically cited for addition polymers is extended here to provide a measure of conditions under which depolymerization for recycling is favored.

condensation polymerization↗
DOE OSTI2017

Reaction Kinetic Model of Dilute Acid-Catalyzed Hemicellulose Hydrolysis of Corn Stover under High-Solid Conditions

High solid conditions are desirable in pretreatment of lignocellulosic biomass. An advanced dilute-acid pretreatment reactor has been developed at National Renewable Energy Laboratory (NREL). It is a continuous auger-driven reactor that can be operated with high-solid charge at high temperature and with short residence time resulting high productivity and high sugar concentration. Here, we investigated the kinetics of the reactions associated with dilute-acid pretreatment of corn stover, covering the reaction conditions of the NREL reactor operation: 155-185 C, 1-2 wt% sulfuric acid concentration, and 1:2 solid to liquid ratio. The experimental data were fitted to a first-order biphasic model which assumes that xylan is comprised of two different fragments: fast and slow reacting fractions. Due to the high solid loading condition, significant amount of xylose oligomers was observed during the pretreatment. We also included the oligomers as an intermediate entity in the kinetic model. The effect of acid concentration was incorporated into the pre-exponential factor of Arrhenius equation. The kinetic model with bestfit kinetic parameters has shown good agreement with experimental data. The kinetic parameter values of the proposed model were noticeably different from those previously reported. The activation energies of xylan hydrolysis are lower and the acid exponents are higher than the average of literature values. The proposed model can serve as a useful tool for design and operation of pretreatment system pertaining to corn stover.

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

Kinetic model describing self-limiting CO 2 diffusion in supported amine adsorbents

A reaction–diffusion shrinking core model describing the decay in diffusivity of supported amine sorbents upon CO 2 sorption under both simulated direct air capture and point source capture conditions is described. The decay in CO 2 diffusivity is associated with crosslinking in the aminopolymer samples and general pore blockage in the amino-silane derived samples, which occurs as CO 2 is adsorbed. The model is used to extract four kinetic parameters that govern the CO 2 uptake kinetics and working capacity: an apparent reaction rate constant, an initial effective diffusivity, and two dimensionless decay parameters. Ideally, an initially reaction limited system would allow for direct determination of the intrinsic reaction rate constant; however, sorption experiments suggest mass transfer resistances related to gas mixing, external boundary layers and intraparticle diffusion are present. Reaction rate constants are determined and agree well with theoretical values predicted with the Eyring equation parameterized using density functional theory energies from literature sources. The kinetic performance is expressed as the average effective diffusivity as a function of average conversion, which can be correlated to the dispersion of sorption sites on the support and the morphology of the active sorbent phase. Four supports are impregnated or grafted with amines, SBA-15, single-walled zeolite nanotubes (ZNT), Syloid SiO 2 , and γ-Al 2 O 3 . Due to its pore structure, γ-Al 2 O 3 supported amines can be modeled at the μm scale or at the nm scale, where the shell balance is on the μm-sized macroporous particle aggregate or on the nm-sized amine film on the surface of the Al 2 O 3 nanoparticles, which comprise the spherical particle aggregates. Faster diffusion rates are maintained under 400 ppm rather than 10% CO 2 due to a slower reaction rate giving a slower decay in diffusivity. In conclusion, this work provides a first principles kinetic analysis of CO 2 sorption where previous models are semi-empirical and use arbitrary kinetic parameters.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2018

Kinetic Modelling and Experimental Studies for the Effects of Fe 2+ Ions on Xylan Hydrolysis with Dilute-Acid Pretreatment and Subsequent Enzymatic Hydrolysis

High-temperature (150-170 degrees C) pretreatment of lignocellulosic biomass with mineral acids is well established for xylan breakdown. Fe 2+ is known to be a cocatalyst of this process although kinetics of its action remains unknown. The present work addresses the effect of ferrous ion concentration on sugar yield and degradation product formation from corn stover for the entire two-step treatment, including the subsequent enzymatic cellulose hydrolysis. The feedstock was impregnated with 0.5% acid and 0.75 mM iron cocatalyst, which was found to be optimal in preliminary experiments. The detailed kinetic data of acid pretreatment, with and without iron, was satisfactorily modelled with a four-step linear sequence of first-order irreversible reactions accounting for the formation of xylooligomers, xylose and furfural as intermediates to provide the values of Arrhenius activation energy. Based on this kinetic modelling, Fe 2+ turned out to accelerate all four reactions, with a significant alteration of the last two steps, that is, xylose degradation. Consistent with this model, the greatest xylan conversion occurred at the highest severity tested under 170 ⁰C/30 min with 0.75 mM Fe 2+ , with a total of 8% xylan remaining in the pretreated solids, whereas the operational conditions leading to the highest xylose monomer yield, 63%, were milder, 150 degrees C with 0.75 mM Fe 2+ for 20 min. Furthermore, the subsequent enzymatic hydrolysis with the prior addition of 0.75 mM of iron(II) increased the glucose production to 56.3% from 46.3% in the control (iron-free acid). The detailed analysis indicated that conducting the process at lower temperatures yet long residence times benefits the yield of sugars. The above kinetic modelling results of Fe 2+ accelerating all four reactions are in line with our previous mechanistic research showing that the pretreatment likely targets multiple chemistries in plant cell wall polymer networks, including those represented by the C-O-C and C-H bonds in cellulose, resulting in enhanced sugar solubilization and digestibility.

09 BIOMASS FUELS↗
DOE OSTI2018

(Invited) Kinetic Models for the Degradation Mechanisms of PGM-Free ORR Catalysts

Platinum group metal-free (PGM-free) catalysts, based on earth-abundant elements such as carbon, nitrogen, and transition metals, have shown promising oxygen reduction reaction (ORR) activity in fuel cells. Intensive research activities have focused on the improvement of activity and understanding of active sites in PGM-free catalysts. However, the durability of PGM-free catalysts in fuel cell cathode under realistic operating conditions has been addressed to a much lesser degree than the initial ORR activity, with only qualitative degradation mechanisms proposed to account for the generally fast activity loss in the fuel cell. Herein, we introduce to PGM-free ORR electrocatalysis a quantitative logistic decay model, based on a two-step autocatalytic degradation mechanism to portray catalyst degradation behavior. This model describes well the current-time data measured in the kinetic range of the fuel cell (fuel cell cathode) operation. Here, the results further suggest that the formation of deactivation species during the ORR is responsible for the loss of catalytic active sites and ensuing cell performance loss.

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

Kinetic Model for Moisture-Controlled CO 2 Sorption

The understanding of the sorption/desorption kinetics is essential for practical applications of moisture-controlled CO 2 sorption. We introduce an analytic model of the kinetics of moisture-controlled CO 2 sorption and its interpretation in two limiting cases. In one case, chemical reaction kinetics on pore surfaces dominates, in the other case, diffusive transport through the sorbent defines the kinetics. Here, we show that reaction kinetics, which is dominant in the first case, can be expressed as a linear combination of 1st and 2nd order kinetics in agreement with the static isotherm equation derived and validated in a previous paper. The interior transport kinetics can be described by non-linear diffusion equations. By combining all carbon species into a single equation, we can eliminate — in certain limits — the source terms associated with chemical reactions. In this case, the governing equation is ∂θ/∂t = –∇ · (–D eff ∇ θ ). For a sorbent in a form of a flat sheet or a membrane, one can maintain the same functional form of a diffusion equation by introducing a generalized effective diffusivity D M that combines contributions from both surface chemical reaction kinetics and interior diffusive transport kinetics. Experimental data of transient CO 2 flux in a preconditioned commercial anion exchange membrane fit well to the 1st order model as long as very dry states are avoided, validating the theory. The observed DM for a preconditioned commercial anion exchange membrane ranges from 6.6× 10 -14 to 7.1× 10 -14 m 2 s -1 at 35°C. These small values compared to typical ionic diffusivities imply a very slow kinetics, which will be the largest issue that needs to be addressed for practical application. The collected transient CO 2 flux data are used to predict the magnitude of a continuous CO 2 pumping flux in an active membrane that transports CO 2 against a CO 2 concentration gradient. The pumped CO 2 flux is supported by water flux due to a water concentration gradient.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Thermodynamic and Kinetic Modeling of Co-utilization of Glucose and Xylose for 2,3-BDO Production by Zymomonas mobilis

Prior engineering of the ethanologen Zymomonas mobilis has enabled it to metabolize xylose and to produce 2,3-butanediol (2,3-BDO) as a dominant fermentation product. When co-fermenting with xylose, glucose is preferentially utilized, even though xylose metabolism generates ATP more efficiently during 2,3-BDO production on a BDO-mol basis. To gain a deeper understanding of Z. mobilis metabolism, we first estimated the kinetic parameters of the glucose facilitator protein of Z. mobilis by fitting a kinetic uptake model, which shows that the maximum transport capacity of glucose is seven times higher than that of xylose, and glucose is six times more affinitive to the transporter than xylose. With these estimated kinetic parameters, we further compared the thermodynamic driving force and enzyme protein cost of glucose and xylose metabolism. It is found that, although 20% more ATP can be yielded stoichiometrically during xylose utilization, glucose metabolism is thermodynamically more favorable with 6% greater cumulative Gibbs free energy change, more economical with 37% less enzyme cost required at the initial stage and sustains the advantage of the thermodynamic driving force and protein cost through the fermentation process until glucose is exhausted. Glucose-6-phosphate dehydrogenase (g6pdh), glyceraldehyde-3-phosphate dehydrogenase (gapdh) and phosphoglycerate mutase (pgm) are identified as thermodynamic bottlenecks in glucose utilization pathway, as well as two more enzymes of xylose isomerase and ribulose-5-phosphate epimerase in xylose metabolism. Acetolactate synthase is found as potential engineering target for optimized protein cost supporting unit metabolic flux. Pathway analysis was then extended to the core stoichiometric matrix of Z. mobilis metabolism. Growth was simulated by dynamic flux balance analysis and the model was validated showing good agreement with experimental data. Dynamic FBA simulations suggest that a high agitation is preferable to increase 2,3-BDO productivity while a moderate agitation will benefit the 2,3-BDO titer. Taken together, this work provides thermodynamic and kinetic insights of Z. mobilis metabolism on dual substrates, and guidance of bioengineering efforts to increase hydrocarbon fuel production.

23-butanediol↗
DOE OSTI2022

Elucidating the temperature dependence of TRIP in Q&P steels using synchrotron X-Ray diffraction, constituent phase properties, and strain-based kinetics models

Understanding the deformation-induced martensitic transformation (DIMT) is critical for interpreting the structure-property relationships that govern the performance of transformation-induced plasticity (TRIP) assisted steels. However, modern TRIP-assisted steels often exhibit DIMT kinetics that are not easily captured by existing empirical models based on bulk tensile strain. We address this challenge by combined bulk uniaxial tensile tests and in-situ high energy synchrotron X-ray diffraction, which resolved the phase volume fractions, stress-strain response, and microstructure evolution of each constituent phase. A modification of the Olson-Cohen model is implemented, which describes the martensitic transformation kinetics as a function of the estimated partitioned strain in austenite, rather than the bulk tensile strain. This DIMT kinetic model is used as a framework to clarify the root cause of an insufficiently understood toughness trough reported for TRIP-assisted steels during deformation at elevated temperatures. Here, the importance of the temperature-dependent toughness is discussed, based on the opportunity to modify deformation processes to tailor the DIMT kinetics and mechanical properties during forming and in service.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Global kinetic modeling of NH 3 -SCR with two sites of NH 3 storage on Cu-SSZ-13

A comprehensive selective catalytic reduction (SCR) model is developed to detail the global kinetic reactions in the catalyst which is involved in two type of sites for high- and low-temperature NH 3 adsorption/desorption, as well as a low temperature H 2 O storage. The model accounts for the formation of ammonium nitrate in fast SCR and the decomposition formation of ammonium nitrate in the absence of NO, and addresses N 2 O relative to NO and NO 2 reactions with NH 3 . The model has been validated against commercial Cu-SSZ-13 measurements of NH 3 inventory, NH 3 oxidation, NO oxidation, standard SCR, fast SCR and NO 2 SCR at both comprehensive steady-state and transient conditions. In addition, the application of the SCR model for emissions control over a transient drive cycle at cold start was demonstrated based on diesel oxidation catalyst (DOC) and SCR aftertreatment system for a passenger car. In conclusion, the results show that the SCR model can provide the detailed emissions estimations for steady-state and transient conditions, can assist with understanding the impact of the SCR reaction mechanism, and can assist with the design and optimization of SCR catalysts to develop innovative technologies for co-optimization of engine fuel economy and emissions control technologies.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2019

Kinetic Modeling of the Silicothermic Reduction of Manganese Oxide from Slag

A model was developed to describe the mixed rate control kinetics in systems with MnO-SiO{sub 2}-CaO-Al{sub 2}O{sub 3} slags and Fe-Si metal droplets. During the reaction of Fe-Si droplets and slag, Mn{sup 2+} transport was found to be part of controlling the system but could not sufficiently describe all initial conditions (chiefly, changes to initial silicon content). The current model describes the kinetics of the stated system and offers answers to the question of rate control; the model has been fitted to nine datasets of varying initial conditions including initial [Si], initial (MnO), initial droplet size, and reaction temperature. The fitted mass transfer coefficients for metal and slag were 2.3 × 10{sup −4} and 6.7 × 10{sup −4} m/s, respectively; these values are constant across the nine datasets. Previous claims about the efficiency of silicon usage in reducing manganese have been modified; it appears that the formation of silica is favored throughout the reaction, but that the formation of a silicon monoxide gas layer on the metal surface dramatically impacts the rate of reaction. As a measure of overall fit of the model, the average of the root-mean-square errors for all datasets is 14 pct. Mass transport in slag is twice as influential on rate control as the metal phase. The simultaneous transport of both Mn{sup 2+} and silicate dimers controls mass transport in the slag. Both [Si] and [Mn] can control from the metal side but are dependent on the initial conditions.

36 MATERIALS SCIENCE↗