scholarly journals Clayton Copula as an Alternative Perspective of Multi-Reaction Model

2018 ◽  
Vol 22 (1) ◽  
pp. 83-106 ◽  
Author(s):  
Alok Dhaundiyal ◽  
Suraj B. Singh ◽  
Muammel M. Hanon ◽  
Norbert Schrempf
Keyword(s):  
Activation Energy ◽  
Distribution Function ◽  
Numerical Solutions ◽  
Analytical Data ◽  
Initial Distribution ◽  
Reaction Model ◽  
Bivariate Distribution ◽  
Clayton Copula ◽  
Scale Parameters ◽  
Temperature Ramp

Abstract This study proposes to assess the effect of some relevant parameters of biomass pyrolysis on the numerical solutions of nthorder distributed activation energy model (DAEM) or multi reaction model (MRM). The two-step process mechanisms of pyrolysis is described by replacing the initial distribution function of f (E) with the Clayton copula. The upper limit (E∞) of ‘dE’ integral, activation energy (A), heating rate (m), and the shape and scale parameters of bivariate distribution function. Temperature ramp rate is assumed to vary linearly with time. Thermo-analytical data is obtained with the help of thermogravimetric (TG) analysis. Asymptotic technique is adopted to approximate double exponential and bivariate distribution function f (E1, E2), where E1and E2are the activation energies for bivariate scheme.

scholarly journals A Modified Model for Kinetic Analysis of Petroleum Coke

2019 ◽  
Vol 2019 ◽  
pp. 1-8
Author(s):  
Iman Eslami Afrooz ◽  
Dennis Ling Chuan Ching
Keyword(s):  
Activation Energy ◽  
Distribution Function ◽  
Normal Distribution ◽  
Heating Rate ◽  
Reaction Model ◽  
Normal Distribution Function ◽  
Gravimetric Analysis ◽  
Heating Rates ◽  
Shrinking Core ◽  
Volume Reaction

In this study, a nonisothermal kinetics analysis of petcoke was performed at heating rates of 10, 15, and 20°C/min using thermal gravimetric analysis (TGA). The behaviour of petcoke at different gasification stages (dewatering, volatilization, char burning, and burnout) was studied. The effect of heating rate on the activation energy of petcoke gasification was also investigated. The activation energy of petcoke was estimated using different kinetic models that include volume reaction model (VRM), shrinking core model (SCM), random pore model (RPM), Coats and Redfern model (CRM), and normal distribution function (NDF). The NDF model was modified in this study. It was found that the experimental data were best fitted with the modified normal distribution function (MNDF) and SCM. The results also showed that activation energy decreases as heating rate increases, leading to reduction in gasification completion time.

scholarly journals Approximations to the Non-Isothermal Distributed Activation Energy Model for Biomass Pyrolysis Using the Rayleigh Distribution

2017 ◽  
Vol 20 (3) ◽  
pp. 78-84 ◽  
Author(s):  
Alok Dhaundiyal ◽  
Suraj B. Singh
Keyword(s):  
Activation Energy ◽  
Numerical Solutions ◽  
Frequency Factor ◽  
Rayleigh Distribution ◽  
Energy Model ◽  
Biomass Pyrolysis ◽  
Distributed Activation Energy Model ◽  
Scale Parameters ◽  
Thermoanalytical Data

AbstractThis paper deals with the influence of some parameters relevant to biomass pyrolysis on the numerical solutions of the nonisothermalnthorder distributed activation energy model using the Rayleigh distribution. Investigated parameters are the integral upper limit, the frequency factor, the heating rate, the reaction order and the scale parameters of the Rayleigh distribution. The influence of these parameters has been considered for the determination of the kinetic parameters of the non-isothermalnthorder Rayleigh distribution from the experimentally derived thermoanalytical data of biomass pyrolysis.

Gas Cell Infrared and Attenuated Total Reflection Infrared Spectroscopic Studies for Organic–Inorganic Interactions in Adsorption of Fulvic Acid on the Goethite Surface Generating Carbon Dioxide

2021 ◽  
pp. 000370282199121
Author(s):  
Yuki Nakaya ◽  
Satoru Nakashima ◽  
Takahiro Otsuka
Keyword(s):  
Carbon Dioxide ◽  
Activation Energy ◽  
Fulvic Acid ◽  
Spectroscopic Studies ◽  
Reaction Model ◽  
Total Reflection ◽  
Attenuated Total Reflection ◽  
Gas Cell ◽  
Rate Determining Step ◽  
Ir Spectroscopic

The generation of carbon dioxide (CO2) from Nordic fulvic acid (FA) solution in the presence of goethite (α-FeOOH) was observed in FA–goethite interaction experiments at 25–80 ℃. CO2 generation processes observed by gas cell infrared (IR) spectroscopy indicated two steps: the zeroth order slower CO2 generation from FA solution commonly occurring in the heating experiments of the FA in the presence and absence of goethite (activation energy: 16–19 kJ mol–1), and the first order faster CO2 generation from FA solution with goethite (activation energy: 14 kJ mol–1). This CO2 generation from FA is possibly related to redox reactions between FA and goethite. In situ attenuated total reflection infrared (ATR-IR) spectroscopic measurements indicated rapid increases with time in IR bands due to COOH and COO– of FA on the goethite surface. These are considered to be due to adsorption of FA on the goethite surface possibly driven by electrostatic attraction between the positively charged goethite surface and negatively charged deprotonated carboxylates (COO–) in FA. Changes in concentration of the FA adsorbed on the goethite surface were well reproduced by the second order reaction model giving an activation energy around 13 kJ mol–1. This process was faster than the CO2 generation and was not its rate-determining step. The CO2 generation from FA solution with goethite is faster than the experimental thermal decoloration of stable structures of Nordic FA in our previous report possibly due to partial degradations of redox-sensitive labile structures in FA.

scholarly journals Gas-phase detonation propagation in mixture composition gradients

2012 ◽  
Vol 370 (1960) ◽  
pp. 567-596 ◽  
Author(s):  
D. A. Kessler ◽  
V. N. Gamezo ◽  
E. S. Oran
Keyword(s):  
Activation Energy ◽  
Reaction Model ◽  
Single Step ◽  
Mixture Composition ◽  
Composition Gradient ◽  
Detonation Properties ◽  
High Activation ◽  
Zone Structure ◽  
Detonation Cell ◽  
High Activation Energy

The propagation of detonations through several fuel–air mixtures with spatially varying fuel concentrations is examined numerically. The detonations propagate through two-dimensional channels, inside of which the gradient of mixture composition is oriented normal to the direction of propagation. The simulations are performed using a two-component, single-step reaction model calibrated so that one-dimensional detonation properties of model low- and high-activation-energy mixtures are similar to those observed in a typical hydrocarbon–air mixture. In the low-activation-energy mixture, the reaction zone structure is complex, consisting of curved fuel-lean and fuel-rich detonations near the line of stoichiometry that transition to decoupled shocks and turbulent deflagrations near the channel walls where the mixture is extremely fuel-lean or fuel-rich. Reactants that are not consumed by the leading detonation combine downstream and burn in a diffusion flame. Detonation cells produced by the unstable reaction front vary in size across the channel, growing larger away from the line of stoichiometry. As the size of the channel decreases relative to the size of a detonation cell, the effect of the mixture composition gradient is lessened and cells of similar sizes form. In the high-activation-energy mixture, detonations propagate more slowly as the magnitude of the mixture composition gradient is increased and can be quenched in a large enough gradient.

scholarly journals Analytical solution of integro-differential equations describing the process of intense boiling of a superheated liquid

2021 ◽  
Author(s):  
Irina Alexandrova ◽  
Alexander Ivanov ◽  
Dmitri Alexandrov
Keyword(s):  
Distribution Function ◽  
Analytical Solution ◽  
Approximate Analytical Solution ◽  
Initial Distribution ◽  
Size Distribution Function ◽  
Superheated Liquid ◽  
Balance Equations ◽  
The Laplace Transform ◽  
And Shifts ◽  
Initial Distribution Function

In this article, an approximate analytical solution of an integro-differential system of equations is constructed, which describes the process of intense boiling of a superheated liquid. The kinetic and balance equations for the bubble-size distribution function and liquid temperature are solved analytically using the Laplace transform and saddle-point methods with allowance for an arbitrary dependence of the bubble growth rate on temperature. The rate of bubble appearance therewith is considered in accordance with the Dering-Volmer and Frenkel-Zeldovich-Kagan nucleation theories. It is shown that the initial distribution function decreases with increasing the dimensionless size of bubbles and shifts to their greater values with time.

Thermal Degradation of Complexes Derived from Cu (II) Groundnut (Arachis hypogaea) and Sesame (Sesamum indicum) Soaps

2018 ◽  
Vol 0 (0) ◽  
Author(s):  
Anju Joram ◽  
Rashmi Sharma ◽  
Arun kumar Sharma
Keyword(s):  
Activation Energy ◽  
Fatty Acid ◽  
Thermal Degradation ◽  
Arachis Hypogaea ◽  
Edible Oils ◽  
Analytical Data ◽  
Spectroscopic Technique ◽  
Sesamum Indicum ◽  
Energy Of Activation ◽  
Significant Information

Abstract The complexes have been synthesized from Cu (II) soaps of groundnut (Arachis hypogaea) and sesame (Sesamum indicum) oils, with ligand containing nitrogen and sulfur atoms like 2-amino-6-methyl benzothiazole. The complexes were greenish brown in color. In order to study TGA, first characterized them by elemental analysis, and spectroscopic technique such as IR, NMR and ESR. From the analytical data, the stoichiometry’s of the complexes have been observed to be 1:1 (metal:ligand). These complexes have been thermally analyzed using TGA techniques to determine their energy of activation. These complexes show three step thermal degradation corresponding to fatty acid components of the edible oils and each complex has three decomposition steps in the range of 439–738 K. Various equations like Coats–Redfern (CR), Horowitz–Metzger (HM) and Broido equations (BE) were applied to evaluate the energy of activation. The values of energy of activation are observed to be in the following order for both copper groundnut benzothiazole (CGB) and copper sesame benzothiazole (CSeB) complexes: CGB > CSeB. CGB is observed to be more stable than CSeB due to its higher activation energy. The above studies would provide significant information regarding the applications of synthesized agrochemicals and their safe removal through parameters obtained in degradation curves and its relation with energy.

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