General equations for the reaction kinetics of solids

1976 ◽  
Vol 29 (1) ◽  
pp. 27
Author(s):  
JH Taplin
Keyword(s):  
Experimental Data ◽  
Boundary Condition ◽  
Reaction Kinetics ◽  
Theoretical Basis ◽  
Reaction Equation ◽  
Kinetics Of

The index-of-reaction equation (i.r.e.): dF/dtZ = kZ(l - βF)m is compared with a generalized Prout-Tompkins equation (g.P.T.e.): dF/dt = kn(l - βF)y With the boundary condition F = 0, t = 0 the equations are equivalent for z = 2 or m = 0 or β ≤ 1 and the i.r.e, is closely approximated by the g.P.T.e. for other values of the parameters by use of the following approximation ∫(1- F)-m dF ≈ AF(1-BF)5 The parameter s is a function of m. Both A and B are close to unity for 1/3 < m < 3. The i.r.e. is recommended as being more useful than the g.P.T.e. because the i.r.e. has a better theoretical basis and because it is more readily integrated and fitted to experimental data.

scholarly journals Mechanism of reaction of silica and carbon for producing silicon carbide

2019 ◽  
Vol 45 ◽  
pp. 146867831989141
Author(s):  
Bahador Abolpour ◽  
Rahim Shamsoddini
Keyword(s):  
Experimental Data ◽  
Silicon Carbide ◽  
Reaction Kinetics ◽  
Direct Effect ◽  
Solid Reaction ◽  
Carbon Reduction ◽  
Temperature Range ◽  
Carbon Particles ◽  
Mechanism Of Reaction ◽  
Kinetics Of

The reaction kinetics of carbon reduction of silica were investigated using thermodynamic concepts and by fitting to relevant models the experimental data obtained for this reduction using a thermogravimetric unit in the temperature range of 1566 to 1933 K. The results show that the only way to produce SiC in this reduction is the reaction of Si, SiO, or SiO2 at the surface or by diffusion of SiO inside the carbon particles while CO and CO2 have no direct effect on the process. The controlling step of this reduction at temperatures lower than 1750 K is the chemical gas–solid or solid–solid reaction at the surface of the carbon particles, while at higher temperatures, the rate of SiO diffusing inside the carbon particles controls the rate of this reduction.

scholarly journals Hydrothermal Carbonization Kinetics of Lignocellulosic Agro-Wastes: Experimental Data and Modeling

Energies ◽  
2019 ◽  
Vol 12 (3) ◽  
pp. 516 ◽  
Author(s):  
Michela Lucian ◽  
Maurizio Volpe ◽  
Luca Fiori
Keyword(s):  
Experimental Data ◽  
Reaction Kinetics ◽  
Reaction Pathway ◽  
Hydrothermal Carbonization ◽  
Kinetics Model ◽  
Transient Phase ◽  
Lumped Model ◽  
Gaseous Products ◽  
Best Fitting ◽  
Kinetics Of

Olive trimmings (OT) were used as feedstock for an in-depth experimental study on the reaction kinetics controlling hydrothermal carbonization (HTC). OT were hydrothermally carbonized for a residence time τ of up to 8 h at temperatures between 180 and 250 °C to systematically investigate the chemical and energy properties changes of hydrochars during HTC. Additional experiments at 120 and 150 °C at τ = 0 h were carried out to analyze the heat-up transient phase required to reach the HTC set-point temperature. Furthermore, an original HTC reaction kinetics model was developed. The HTC reaction pathway was described through a lumped model, in which biomass is converted into solid (distinguished between primary and secondary char), liquid, and gaseous products. The kinetics model, written in MATLABTM, was used in best fitting routines with HTC experimental data obtained using OT and two other agro-wastes previously tested: grape marc and Opuntia Ficus Indica. The HTC kinetics model effectively predicts carbon distribution among HTC products versus time with the thermal transient phase included; it represents an effective tool for R&D in the HTC field. Importantly, both modeling and experimental data suggest that already during the heat-up phase, biomass greatly carbonizes, in particular at the highest temperature tested of 250 °C.

scholarly journals Anionic Polymerization of ε-Caprolactam under the Influence of Water: 2. Kinetic Model

2020 ◽  
Vol 4 (1) ◽  
pp. 8 ◽  
Author(s):  
Rainer Wendel ◽  
Philipp Rosenberg ◽  
Michael Wilhelm ◽  
Frank Henning
Keyword(s):  
Experimental Data ◽  
Kinetic Model ◽  
Reaction Kinetics ◽  
Water Content ◽  
Anionic Polymerization ◽  
Polyamide 6 ◽  
External Influences ◽  
Influence Of Water ◽  
Kinetics Of

The reaction kinetics of anionic polymerization for the production of anionic polyamide 6 (aPA6) are widely understood. It is also known that this reaction is very sensitive to external influences such as water. This paper analyzes and quantifies the influence of water on the reaction of ε-caprolactam to anionic polyamide 6. A kinetic model is developed in which the reactive molecules of the activator and catalyst are defined as variables and the concentrations of activator and catalyst as well as water content are considered. A model for the calculation of the reaction kinetics is established and validated with experimental data. The developed model can be used to predict the influence and compensation of water by addition of surplus activator and catalyst during the polymerization of ε-caprolactam.

Study on the Optimal Fermentation Time and Kinetics of Bioflocculant Produced by Bacterium F2

2010 ◽  
Vol 113-116 ◽  
pp. 2379-2384 ◽  
Author(s):  
Jie Xing ◽  
Ji Xian Yang ◽  
Fang Ma ◽  
Li Wei ◽  
Ke Xin Liu
Keyword(s):  
Experimental Data ◽  
Theoretical Basis ◽  
Kaolin Clay ◽  
Clay Suspension ◽  
Fermentation Time ◽  
Flocculating Activity ◽  
Flocculating Rate ◽  
Kinetics Of

We isolated flocculants-producing bacteria F2 from soil. It shows high and stable flocculating activity for Kaolin clay suspension. In order to increase yield of flocculants, we need determine the optimal obtained time. We measured the changes of several parameters using shaking flask experiment, including flocculating- rate, the content of polysaccharide, protein and glucose. It’s showed that the optimal obtained time of bio-flocculants is 21 h. And we built the model about the production of bio-flocculants. Through the comparison of experimental data and the corresponding calculated values from the models, we found that the data joint well and the model can provide theoretical basis for Industrialization of bio-flocculants.

Kinetic and Thermodynamic Aspects of the Bainite Reaction in a Silicon Steel

1983 ◽  
Vol 21 ◽  
Author(s):  
G. Papadimitriou ◽  
J.M.R. Genin
Keyword(s):  
Experimental Data ◽  
Silicon Carbide ◽  
Reaction Kinetics ◽  
Silicon Content ◽  
Silicon Steel ◽  
Tentative Model ◽  
Secondary Stage ◽  
Two Stages ◽  
Kinetics Of ◽  
And Diffusion

ABSTRACTThe bainite reaction in an Fe - 3.85 wt pct Si - 0.9 wt pct C steel is studied by several experimental techniques in the range of 250–450°C.The high silicon content prevents the formation of cementite, so that the reaction is separated to two clearly distinct stages. In the primary stage ferrite forms alone, except at temperatures lower than 310°C where some carbides precipitate in it, and austenite becomes enriched in carbon. In the secondary stage occurring only above 400°C, the enriched austenite decomposes to ferrite and an unknown silicon carbide.The microstructure, the enrichment of the austenite and the overall reaction kinetics of the two stages are studied and are found to be consistent with a displacive mechanism of the bainite reaction.A tentative model, accounting for the competition of shear and diffusion, is proposed in order to fit our experimental data.

scholarly journals Comparison of diffusion models for description of osmotic dehydration of radish slices dipped in brine

2015 ◽  
Vol 35 (5) ◽  
pp. 894-904
Author(s):  
Wilton P. da Silva ◽  
Cleide M. D. P. da S. E Silva ◽  
Josivanda P. Gomes
Keyword(s):  
Experimental Data ◽  
Boundary Condition ◽  
Low Temperature ◽  
Osmotic Dehydration ◽  
Two Dimensional ◽  
Dimensional Model ◽  
The Third ◽  
Two Dimensional Model ◽  
Mass Transfers ◽  
Kinetics Of

ABSTRACT This paper aims at describing the osmotic dehydration of radish cut into cylindrical pieces, using one- and two-dimensional analytical solutions of diffusion equation with boundary conditions of the first and third kind. These solutions were coupled with an optimizer to determine the process parameters, using experimental data. Three models were proposed to describe the osmotic dehydration of radish slices in brine at low temperature. The two-dimensional model with boundary condition of the third kind well described the kinetics of mass transfers, and it enabled prediction of moisture and solid distributions at any given time.

Kinetics of the carbon monoxide conversion with steam at elevated pressures

1979 ◽  
Vol 44 (3) ◽  
pp. 652-659 ◽  
Author(s):  
Pavel Fott ◽  
Jan Vosolsobě ◽  
Vladimír Glaser
Keyword(s):  
Experimental Data ◽  
Carbon Dioxide ◽  
Carbon Monoxide ◽  
Reaction Kinetics ◽  
Gaseous Phase ◽  
Reaction Rate ◽  
Surface Reaction ◽  
Elevated Pressures ◽  
Limiting Step ◽  
Kinetics Of

The kinetics of the carbon monoxide conversion with steam on a Czechoslovak FeCr catalyst was investigated. The experimental data were obtained on a gradient-free differential reactor with recirculating gaseous phase at temperatures of 633 and 693 K and pressures from the range 0.1-0.9 MPa. The evaluation of experimental data showed that the reaction rate increases with increasing pressure according to a downward convex and that it also increases with increasing content of carbon monoxide in the gas and with decreasing content of carbon dioxide. The reaction kinetics was described by an equation derived from the Langmuir-Hinshelwood concept for the case when the limiting step of the reaction is a surface reaction.

A fuzzy neural network approach for modeling the growth kinetics of FeB and Fe2B layers during the boronizing process

2018 ◽  
Vol 106 (6) ◽  
pp. 603 ◽  
Author(s):  
Bendaoud Mebarek ◽  
Mourad Keddam
Keyword(s):  
Neural Network ◽  
Experimental Data ◽  
Fuzzy Neural Network ◽  
Treatment Time ◽  
Calculation Model ◽  
Average Error ◽  
Network Approach ◽  
Neural Network Approach ◽  
Fuzzy Neural ◽  
Kinetics Of

In this paper, we develop a boronizing process simulation model based on fuzzy neural network (FNN) approach for estimating the thickness of the FeB and Fe2B layers. The model represents a synthesis of two artificial intelligence techniques; the fuzzy logic and the neural network. Characteristics of the fuzzy neural network approach for the modelling of boronizing process are presented in this study. In order to validate the results of our calculation model, we have used the learning base of experimental data of the powder-pack boronizing of Fe-15Cr alloy in the temperature range from 800 to 1050 °C and for a treatment time ranging from 0.5 to 12 h. The obtained results show that it is possible to estimate the influence of different process parameters. Comparing the results obtained by the artificial neural network to experimental data, the average error generated from the fuzzy neural network was 3% for the FeB layer and 3.5% for the Fe2B layer. The results obtained from the fuzzy neural network approach are in agreement with the experimental data. Finally, the utilization of fuzzy neural network approach is well adapted for the boronizing kinetics of Fe-15Cr alloy.

Impact Of Synthesis Route on the Water Oxidation Kinetics of Hematite Photoanodes

2020 ◽  
Author(s):  
Camilo A. Mesa ◽  
Ludmilla Steier ◽  
Benjamin Moss ◽  
Laia Francàs ◽  
James E. Thorne ◽  
...  
Keyword(s):  
Oxygen Vacancy ◽  
Reaction Kinetics ◽  
Water Oxidation ◽  
Oxidation Kinetics ◽  
Oxidation Reaction ◽  
Charge Accumulation ◽  
Optical Signals ◽  
Current Voltage ◽  
Voltage Performance ◽  
Kinetics Of

<p><i>Operando</i> spectroelectrochemical analysis is used to determine the water oxidation reaction kinetics for hematite photoanodes prepared using four different synthetic procedures. Whilst these photoanodes exhibit very different current / voltage performance, their underlying water oxidation kinetics are found to be almost invariant. Lower photoanode performance was found to correlate with the observation of optical signals indicative of charge accumulation in mid-gap oxygen vacancy states, indicating these states do not contribute directly to water oxidation.</p>

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