PROBLEMS UNDERLYING THE NUMERICAL INTEGRATION OF THE CHEMICAL AND VIBRATIONAL RATE EQUATIONS IN A NEAR-EQUILIBRIUM FLOW

1963 ◽  
Author(s):  
George Emanuel
Keyword(s):  
Numerical Integration ◽  
Rate Equations ◽  
Equilibrium Flow

scholarly journals Combining simulation to nonlinear fitting for the determination of rate constants of elementary reactions by using Excel spreadsheets

2012 ◽  
Vol 8 (4) ◽  
Author(s):  
Ammar M. Tighezza ◽  
Daifallah M. Aldhayan ◽  
Nouir A. Aldawsari
Keyword(s):  
Experimental Data ◽  
Numerical Integration ◽  
Chemical Kinetics ◽  
Chemical Reactions ◽  
Rate Constants ◽  
Model Equation ◽  
Rate Equations ◽  
Unknown Parameters ◽  
Elementary Reactions ◽  
Nonlinear Fitting

A common problem in chemistry is to determine parameters (constants) in an equation used to represent experimental data. Examples are fitting a set of data to a model equation (straight line or curve) to obtain unknown parameters. In chemical kinetics, a set of data is usually a number of concentrations versus time, but the model equation is not well defined! Instead of a well defined model equation we have a set of coupled ODE’s (ordinary differential equations) which represent rate equations for reactants and products. The analytical integration of these ODE’s is rarely possible. The numerical integration is the alternative. In this work are combined the simulation of chemical reactions, by using numerical integration, and nonlinear regression (curve fitting) by using “Solver add-in” of Microsoft Excel to find rate constants of elementary reactions from experimental data. This method is illustrated on three complex mechanisms. The simulation of chemical reactions in Excel spreadsheets is illustrated with/without VBA programming. The automation (automatic obtaining of rate equations from mechanism: no need of chemical kinetics knowledge from the end user!) of mechanism simulation is demonstrated on many example.

scholarly journals Analysis of progress curves by simulations generated by numerical integration

1989 ◽  
Vol 258 (2) ◽  
pp. 381-387 ◽  
Author(s):  
C T Zimmerle ◽  
C Frieden
Keyword(s):  
Computer Program ◽  
Numerical Integration ◽  
Rate Constants ◽  
Weighted Least Squares ◽  
Rate Equations ◽  
Kinetic Rate ◽  
Fitting Procedure ◽  
Progress Curve ◽  
Kinetic Rate Constants ◽  
Simulated Test

A highly flexible computer program written in FORTRAN is presented which fits computer-generated simulations to experimental progress-curve data by an iterative non-linear weighted least-squares procedure. This fitting procedure allows kinetic rate constants to be determined from the experimental progress curves. Although the numerical integration of the rate equations by a previously described method [Barshop, Wrenn & Frieden (1983) Anal. Biochem. 130, 134-145] is used here to generate predicted curves, any routine capable of the integration of a set of differential equations can be used. The fitting program described is designed to be widely applicable, easy to learn and convenient to use. The use, behaviour and power of the program is explored by using simulated test data.

Rate of Reaction of OH with HCN Between 298 and 563 K

1979 ◽  
Vol 32 (12) ◽  
pp. 2571 ◽  
Author(s):  
LF Phillips
Keyword(s):  
Numerical Integration ◽  
Rate Constant ◽  
Flow System ◽  
Rate Equations ◽  
Side Reactions ◽  
Resonance Fluorescence ◽  
Discharge Flow ◽  
Temperature Range ◽  
Rate Of Reaction ◽  
Estimated Error

Hyroxyl resonance fluorescence was used to study the reaction of OH with HCN in a discharge-flow system. The effect of side reactions involving OH was assessed by numerical integration of the rate equations for the system. The rate constant for the reaction: OH + HCN → products as measured at pressures above 10 Torr and under conditions where side reactions were believed to be unimportant, is given by the expression: k = 1.60 ° 10-11 T-1exp(-1.86 × 103/T) cm3 molecule -1 s-1 with an estimated error of � 20% over the temperature range from 298 to 563 K.

Energy transfer through a dissociated diatomic gas in Couette flow

1958 ◽  
Vol 4 (5) ◽  
pp. 441-465 ◽  
Author(s):  
John F. Clarke
Keyword(s):  
Energy Transfer ◽  
Gas Phase ◽  
Couette Flow ◽  
Chemical Reaction ◽  
Chemical Equilibrium ◽  
Reaction Rate ◽  
Surface Reaction ◽  
Rate Equations ◽  
Equilibrium Flow ◽  
Diatomic Gas

The transfer of energy through a dissociated diatomic gas in Couette flow is considered, taking oxygen as a numerical example. The two extremes of chemical equilibrium flow and chemically frozen flow are dealt with in detail, and it is shown that the surface reaction rate is of prime importance in the latter case. The chemical rate equations in the gas phase are used to estimate the probable chemical state of the gas mixture, this being deduced from the ratio of a characteristic chemical reaction time to a characteristic time for atom diffusion across the layer. The influence of the surface reaction appears to spread outwards through the flow from the wall as gas-phase chemical reaction times decrease. For practical values of the surface reaction rate on a metallic wall, the energy transfer rate may be significantly lower in chemically frozen flow than in chemical equilibrium flow under otherwise similar circumstances.Similar phenomena to those discussed will arise in the more complicated case of boundary layer flows, so that a treatment of the simpler type of shear layer represented by Couette flow may be of some value in assessing the relative importance of the various parameters.

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