scholarly journals Nonlinear and Linear Equation of Gas Diffusion in Coal—Theory and Applications

2021 ◽  
Vol 11 (11) ◽  
pp. 5130
Author(s):  
Marek Gawor ◽  
Norbert Skoczylas ◽  
Anna Pajdak ◽  
Mateusz Kudasik
Keyword(s):  
Exact Solution ◽  
Analytical Solution ◽  
Least Squares Method ◽  
Gas Diffusion ◽  
Diffusion Equations ◽  
Hard Coal ◽  
Sorption Experiment ◽  
Actual Measurement ◽  
Linear Solution ◽  
Kinetics Of

The authors derived the analytical solution to diffusion equations. The solution requires linearization of diffusion equations, as well as developing the obtained expression into a series. In particular, the result of the first procedure is highly deviated from the exact solution. The authors conducted a sorption experiment and then, in relation to the registered kinetics of the diffusion of CO2 inside hard coal grains, approximated the linear solution and the numerical nonlinear solution by means of the least squares method. As confirmed by the lower value of the sum of deviation squares, it can be clearly demonstrated that the nonlinear equation represents the actual measurement more accurately.

Kinetics of nonisothermal dehydration of unirradiated and γ-ray irradiated neodymium (III) acetate hydrate

2019 ◽  
Vol 107 (2) ◽  
pp. 165-178
Author(s):  
Noura Mossaed Saleh ◽  
Ghada Adel Mahmoud ◽  
AbdelRahman AbdelMonem Dahy ◽  
Soliman Abdel-Fadeel Soliman ◽  
Refaat Mohamed Mahfouz
Keyword(s):  
Absorbed Dose ◽  
Isoconversional Methods ◽  
Gas Diffusion ◽  
Conversion Degree ◽  
Monoclinic System ◽  
Air Atmosphere ◽  
Dehydration Reactions ◽  
Γ Ray ◽  
Acetate Hydrate ◽  
Kinetics Of

Abstract Kinetics of dehydration of unirradiated and γ-ray irradiated neodymium (III) acetate hydrate with 103 kGy total γ-ray dose absorbed in air atmosphere were studied by isoconversional nonisothermal method. The dehydration proceeds in two steps with the elimination of 0.8 and 0.4 mol of H2O, respectively. This result indicates that the investigated neodymium (III) acetate hydrate contains 1.2 mol of crystalline water in its structure. The dehydration reactions are best described by nucleation (A2 model) and gas diffusion (D4 model) for unirradiated and γ-ray irradiated samples, respectively. Analysis of the kinetic data using linear and nonlinear isoconversional methods showed that the apparent activation energy, Ea (kJ/mol) is dependent on the conversion degree, α, of the dehydration process. The Ea−α plots for both unirradiated and γ-ray irradiated neodymium (III) acetate hydrate showed that the dehydration is a complex process and contains multistep reactions. The results showed that γ-ray irradiation has a significant effect on the kinetics and thermodynamic parameters of the dehydration reaction. Powder X-ray diffraction showed that neodymium (III) acetate hydrate has a monoclinic system (SG P2/m) and no phase transformation was detected by γ-ray irradiation up to 103 kGy absorbed dose. The system maintains the same crystal structure before and after dehydration.

scholarly journals Two-dimensional numerical modeling of chemical transport–transformation in fluvial rivers: formulation of equations and physical interpretation

2009 ◽  
Vol 11 (2) ◽  
pp. 106-118 ◽  
Author(s):  
Sui Liang Huang
Keyword(s):  
Sediment Transport ◽  
Chemical Transport ◽  
Transformation Model ◽  
Diffusion Equations ◽  
Desorption Kinetics ◽  
Two Dimensional ◽  
Transformation Equation ◽  
Governing Equations ◽  
Convection Diffusion ◽  
Kinetics Of

Based on previous work on the transport–transformation model of heavy metal pollutants in fluvial rivers, this paper presents the formulation of a two-dimensional model to describe chemical transport–transformation in fluvial rivers by considering basic principles of environmental chemistry, hydraulics and mechanics of sediment transport and recent developments along with three very simplified test cases. The model consists of water flow governing equations, sediment transport governing equations, transport–transformation equation of chemicals and convection–diffusion equations of sorption–desorption kinetics of particulate chemical concentrations on suspended load, bed load and bed sediment. The chemical transport–transformation equation is basically a mass balance equation. It demonstrates how sediment transport affects transport–transformation of chemicals in fluvial rivers. The convection–diffusion equations of sorption–desorption kinetics of chemicals, being an extension of batch reactor experimental results, take both physical transport, i.e. convection and diffusion, and chemical reactions, i.e. sorption–desorption into account. The effects of sediment transport on chemical transport–transformation were clarified through three simple examples. Specifically, the transport–transformation of chemicals in a steady, uniform and equilibrium sediment-laden flow was calculated by applying this model, and results were shown to be rational. Both theoretical analysis and numerical simulation indicated that the transport–transformation of chemicals in sediment-laden flows with a clay-enriched riverbed possesses not only the generality of common tracer pollutants, but also characteristics of transport–transformation induced by sediment motion. Future work will be conducted to present the validation/application of the model with available data.

scholarly journals Exact Solution to the Extended Zwanzig Model for Quasi-Sigmoidal Chemically Induced Denaturation Profiles: Specific Heat and Configurational Entropy

2014 ◽  
Vol 2014 ◽  
pp. 1-11
Author(s):  
G. E. Aguilar-Pineda ◽  
L. Olivares-Quiroz
Keyword(s):  
Exact Solution ◽  
Analytical Solution ◽  
Specific Heat ◽  
Configurational Entropy ◽  
Naturally Occurring ◽  
Thermodynamic Potentials ◽  
Chemically Induced ◽  
Denaturation Profile ◽  
Average Internal Energy ◽  
Proteins And Peptides

Temperature and chemically induced denaturation comprise two of the most characteristic mechanisms to achieve the passage from the native state N to any of the unstructured states Dj in the denatured ensemble in proteins and peptides. In this work we present a full analytical solution for the configurational partition function 𝒵qs of a homopolymer chain poly-X in the extended Zwanzig model (EZM) for a quasisigmoidal denaturation profile. This solution is built up from an EZM exact solution in the case where the fraction α of native contacts follows exact linear dependence on denaturant’s concentration ζ; thus an analytical solution for 𝒵L in the case of an exact linear denaturation profile is also provided. A recently established connection between the number ν of potential nonnative conformations per residue and temperature-independent helical propensity ω complements the model in order to identify specific proteinogenic poly-X chains, where X represents any of the twenty naturally occurring aminoacid residues. From 𝒵qs, equilibrium thermodynamic potentials like entropy 𝒮 and average internal energy 〈E〉 and thermodynamic susceptibilities like specific heat C𝓋 are calculated for poly-valine (poly-V) and poly-alanine (poly-A) chains. The influence of the rate at which native contacts denature as function of ζ on thermodynamic stability is also discussed.

scholarly journals Gasification Kinetics of Bituminous Coal Char in the Mixture of CO2, H2O, CO, and H2

Energies ◽  
2019 ◽  
Vol 12 (3) ◽  
pp. 496 ◽  
Author(s):  
Junwei Chen ◽  
Weibin Chen ◽  
Yang Jiao ◽  
Xidong Wang
Keyword(s):  
Bituminous Coal ◽  
Gas Diffusion ◽  
Coal Char ◽  
Conversion Degree ◽  
Diffusion Control ◽  
Diffusion Resistance ◽  
Gasification Process ◽  
Control Step ◽  
Kinetics Of ◽  
Gasification Temperature

The gasification kinetics of bituminous coal char was investigated in a mixture of CO2, H2O, CO, H2, and N2 under isothermal conditions. In addition, the impacts of gasification temperature, gasification time, and gas composition on the gasification process were analyzed. As the experimental results suggest, there is a significant increase of the carbon conversion degree of bituminous coal char not just when gasification temperature and time increase, but also when H2 and CO concentration decreases. The kinetics of bituminous coal char in the gasification process was successfully modeled as a shrinking unreacted core. It is concluded that the gasification of bituminous coal char is controlled by an internal chemical reaction in the early stage and diffusion in the later stage. The activation energies of bituminous coal char gasification for different stages were studied. Moreover, it is proposed for the first time, to our knowledge, that the diffusion-control step is significantly shortened with the decrease of the CO2/H2O ratio. As scanning-electron-microscopy results suggest, bituminous coal char gasified in CO2/H2O = 1/3 atmosphere has numerous inner pores (0–5 m). Therefore, in the process of gasification, the inner pores provide a gas channel that reduces the gas diffusion resistance and thus shortens the diffusion-control step. These results can serve as a reference for industrialized application of the technology of coal gasification direct reduced iron.

An analytical solution of multi-dimensional space fractional diffusion equations with variable coefficients

2020 ◽  
pp. 2150006
Author(s):  
Pratibha Verma ◽  
Manoj Kumar
Keyword(s):  
Analytical Solution ◽  
Diffusion Coefficients ◽  
High Efficiency ◽  
Dimensional Space ◽  
Adomian Decomposition Method ◽  
Fractional Diffusion ◽  
Variable Coefficients ◽  
Diffusion Equations ◽  
Fractional Diffusion Equations ◽  
Adomian Decomposition

In this paper, we have considered the multi-dimensional space fractional diffusion equations with variable coefficients. The fractional operators (derivative/integral) are used based on the Caputo definition. This study provides an analytical approach to determine the analytical solution of the considered problems with the help of the two-step Adomian decomposition method (TSADM). Moreover, new results have been obtained for the existence and uniqueness of a solution by using the Banach contraction principle and a fixed point theorem. We have extended the dimension of the space fractional diffusion equations with variable coefficients into multi-dimensions. Finally, the generalized problems with two different types of the forcing term have been included demonstrating the applicability and high efficiency of the TSADM in comparison to other existing numerical methods. The diffusion coefficients do not require to satisfy any certain conditions/restrictions for using the TSADM. There are no restrictions imposed on the problems for diffusion coefficients, and a similar procedures of the TSADM has followed to the obtained analytical solution for the multi-dimensional space fractional diffusion equations with variable coefficients.

Anticoagulation Kinetics Following Bolus Heparin Injections

1979 ◽  
Author(s):  
L F. Mockros ◽  
S.D. Hirson ◽  
L. Zuckerman ◽  
J.A. Caprini ◽  
W.P. Robinson ◽  
...  
Keyword(s):  
Least Squares Method ◽  
Test Methods ◽  
Assay Method ◽  
Heparin Dose ◽  
Intravenous Heparin ◽  
Using Data ◽  
Kinetics Of ◽  
Dose Dependent ◽  
Low Dosage ◽  
Clot Time

Anticoagulation (AC) levels were monitored simultaneously in dogs by 3 whole blood (WB) and 2 plasma CP) clotting assays. Three levels of heparin (50,100 and 200 U/kg were tested in 26 experiments by Intravenous injection. Blood was sampled at 10 and 30 min then repeated every 30 min for 4 hours. The WB clotting tests provided more sensitivity with respect to the kinetics of neutralization of the heparin than did the P assays. The levels of AC determined by each assay method was fit to exponential curves using a computerized iterative least squares method. The points were weighted inversely with the variance and the censored data was used by fitting the known values to a gamma distribution and deriving the average and SEN of the series. The coagulation curves were dependent upon the heparin dose and test methods. Extrapolated levels of initial AC demonstrate from 3 to 67 fold increases in relative clotting times for 50 and 200 U/kg dosages respectively, depending on the assay method. The AC half lives (T½) with the three WB assays varied from 15 to 41 min for the low dosage and 24 to 34 min and 27 to 30 min for 100 and 200 U/kg dosages respectively. The shortness of these T½ is a consequence-of using data acquired at 10 to 30 tnin post injection. Reanalysis of our data using sampling periods >60 min significantly prolonged the derived T½. Finally there was a marked post heparin shortening (less than pre-heparin values) of the WB assays at 2-4 hours. The values appeared to be dose dependent, as the shortest values occurred In those animals receiving the highest heparin dose. Therefore, intravenous heparin can be associated with high Initial AC followed within 2-4 hours by a quicker than normal clot time.

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