Modeling of Gas Turbine Combustors—A Convenient Reaction Rate Equation

1972 ◽  
Vol 94 (3) ◽  
pp. 173-180 ◽  
Author(s):  
D. Kretschmer ◽  
J. Odgers
Keyword(s):  
Rate Equation ◽  
Reaction Rate ◽  
Reaction Order ◽  
Bimolecular Reaction ◽  
Rate Equations ◽  
Combustion System ◽  
Wide Range ◽  
Simple Mass ◽  
Rich Mixtures ◽  
Reaction Rate Equation

In order to model a practical combustion system successfully, it is necessary to develop one or more reaction rate equations which will describe performance over a wide range of conditions. The equations should be kept as simple as possible and commensurate with the accuracy needed. In this paper a bimolecular reaction is assumed, based upon a simple mass balance. Temperatures derived from the latter are related to measured practical ones such that, if required, an evaluation of the partly burned product composition can be made. A convenient reaction rate equation is given which describes a wide range of blow-out data for spherical reactors at weak mixture conditions. NVP2φ={1.29×1010(m+1)[5(1−yε)]φ[φ−yε]φe−C/(Ti+εΔT)}/{0.082062φyε[5(m+1)+φ+yε]2φ[Ti+εΔT]2φ−0.5} Analysis of the components used in the above equation (especially the variation of activation energy) clearly shows its empirical nature but does not detract from its engineering value. Rich mixtures are considered also, but lack of data precludes a reliable analysis. One of the major results obtained is the variation of the reaction order (n) with equivalence ratio (φ): weak mixtures, n = 2φ; rich mixtures, n = 2/φ. Some support for this variation has been noticed in published literature of other workers.

The kinetics of the decarboxylation of β-resorcylic acid in catechol

1976 ◽  
Vol 29 (2) ◽  
pp. 443 ◽  
Author(s):  
MA Haleem ◽  
MA Hakeem
Keyword(s):  
Rate Equation ◽  
Kinetic Data ◽  
Reaction Rate ◽  
Complex Mechanism ◽  
First Order ◽  
Absolute Reaction Rate ◽  
First Time ◽  
Kinetics Of ◽  
Absolute Reaction ◽  
Reaction Rate Equation

Kinetic data are reported for the decarboxylation of β-resorcylic acid in resorcinol and catechol for the first time. The reaction is first order. The observation supports the view that the decomposition proceeds through an intermediate complex mechanism. The parameters of the absolute reaction rate equation are calculated.

scholarly journals Modified Rate Law for Bimolecular Reactions: Applicable to Surface as well as Non-surface Reactions

2021 ◽  
Vol 37 (6) ◽  
pp. 1429-1433
Author(s):  
Gami Girishkumar Bhagavanbhai ◽  
Rawesh Kumar
Keyword(s):  
Reaction Rate ◽  
Surface Reaction ◽  
Catalyst Surface ◽  
Chemical Species ◽  
Bimolecular Reaction ◽  
Rate Equations ◽  
Bimolecular Reactions ◽  
Rate Law ◽  
Langmuir Adsorption ◽  
Adsorption Desorption

The rate equations in kinematics are expressed through basic laws under surface reaction as well as non-surface reaction. Rate law is center theme of non-surface reaction whereas Langmuir adsorption isotherms are basis of surface reaction rate expressions. A modified rate equation for bimolecular reaction is presented which considers both catalyst surface affairs as well as fraction of successful collision of different reactant for cracking and forming bonds. The modified rate law for bimolecular reaction for surface as well as non-surface reaction is stated as “Rate of a reaction is directly proportional to concentration as well as catalyst surface affair of each reactant” as r = k ΩA[A] ΩB[B] where catalyst surface affair of ith species is defined as Ωi = Ki/(1+Ki[i] + Kj[j] + …). Here, Ki is the equilibrium constant of “i” species for adsorption-desorption processes over catalyst. i, j,… indicates the different adsorbed chemical species at uniform catalyst sites and the same [i], [j], … indicates the concentration of different adsorbed chemical species at uniform catalyst sites.

Modeling of {311} Defects

1999 ◽  
Vol 568 ◽  
Author(s):  
G. Hobler ◽  
C.S. Rafferty
Keyword(s):  
Experimental Data ◽  
Rate Constant ◽  
Strain Energy ◽  
Reaction Rate ◽  
Reaction Rate Constant ◽  
Rate Equations ◽  
The Core ◽  
Core Energy ◽  
Wide Range ◽  
Improved Model

ABSTRACTAn improved model of {311} defect evolution is developed based on the rate equations approach. A new expression for the reaction rate constant is presented that is based on the assumption that interstitials may react with the {311} defects along their whole surface. The energetics of {311} defects is treated by calculating the strain energy within the framework of the theory of dislocations in isotropic continua. Using the core energy of the atoms in the defects as the only fit parameter, we explain a wide range of experimental data. Furthermore, we apply the model to investigate closure assumptions used in moments models and propose a new two-moments model that uses the rate equations solver as a pre-processor.

The Kinetic Study on Phosphorous Acid Reducing Adamsite

2012 ◽  
Vol 550-553 ◽  
pp. 2699-2703
Author(s):  
Xin Wang ◽  
Zhong Lin Cai ◽  
Shan Mao Li ◽  
Ji Zhang Wang ◽  
Wei Li ◽  
...  
Keyword(s):  
Reaction Mechanism ◽  
Kinetic Study ◽  
Rate Equation ◽  
Theoretical Basis ◽  
Reaction Rate ◽  
Phosphorous Acid ◽  
Reduction Reaction ◽  
Kinetic Process ◽  
Reaction Rate Equation

The kinetic process of the reduction reaction between phosphorous acid and adamsite has been studied to determine the reaction rate equation and to deduce the reaction mechanism, providing the theoretical basis for destroying adamsite by phosphorous acid.

The reactivity of p-nitrophenyl esters with surfactants in apolar solvents. V. p-Nitrophenyl acetate in benzene solutions of butane-1,4-diamine bis(dodecanoate)

1983 ◽  
Vol 36 (5) ◽  
pp. 895 ◽  
Author(s):  
CJ O'Conner ◽  
TD Lomax
Keyword(s):  
Rate Equation ◽  
Reaction Rate ◽  
Water Environment ◽  
Water Concentration ◽  
Bimolecular Reaction ◽  
Micellar Catalysis ◽  
Similar Reaction ◽  
Arrhenius Parameters

The rate of decomposition of p-nitrophenyl acetate in benzene in the presence of butane-1,4-diamine bis(dodecanoate) (budb) has been measured at temperatures between 333 and 353 K. The data fit a rate equation which consists of a term arising from micellar catalysis and a term arising from a bimolecular reaction between the ester and the components of budb. Arrhenius parameters have been estimated for the two reaction modes and compared with newly extended data for the similar reaction with dodecylammonium propionate (dap). 13C n.m.r. analysis of the products from there action of p-nitrophenyl propionate in the presence of dap has revealed that the amide is formed by an aminolysis reaction. The decrease in reaction rate observed with increasing water concentration is interpreted in terms of a biphasic water environment.

scholarly journals Time Fractional Fisher–KPP and Fitzhugh–Nagumo Equations

Entropy ◽  
2020 ◽  
Vol 22 (9) ◽  
pp. 1035
Author(s):  
Christopher N. Angstmann ◽  
Bruce I. Henry
Keyword(s):  
Diffusion Equation ◽  
Reaction Kinetics ◽  
Rate Equation ◽  
Reaction Rate ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equations ◽  
Mass Action ◽  
Diffusion Equations ◽  
Mixed Systems ◽  
Reaction Rate Equation

A standard reaction–diffusion equation consists of two additive terms, a diffusion term and a reaction rate term. The latter term is obtained directly from a reaction rate equation which is itself derived from known reaction kinetics, together with modelling assumptions such as the law of mass action for well-mixed systems. In formulating a reaction–subdiffusion equation, it is not sufficient to know the reaction rate equation. It is also necessary to know details of the reaction kinetics, even in well-mixed systems where reactions are not diffusion limited. This is because, at a fundamental level, birth and death processes need to be dealt with differently in subdiffusive environments. While there has been some discussion of this in the published literature, few examples have been provided, and there are still very many papers being published with Caputo fractional time derivatives simply replacing first order time derivatives in reaction–diffusion equations. In this paper, we formulate clear examples of reaction–subdiffusion systems, based on; equal birth and death rate dynamics, Fisher–Kolmogorov, Petrovsky and Piskunov (Fisher–KPP) equation dynamics, and Fitzhugh–Nagumo equation dynamics. These examples illustrate how to incorporate considerations of reaction kinetics into fractional reaction–diffusion equations. We also show how the dynamics of a system with birth rates and death rates cancelling, in an otherwise subdiffusive environment, are governed by a mass-conserving tempered time fractional diffusion equation that is subdiffusive for short times but standard diffusion for long times.

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