The Influence of Reaction Interface Extension in the Combustion of Gaseous Fuel Constituents
Authors: Wohlenberg W. J. 
Published: December 2022

Abstract
A burning mixture is in general composed of zones, called concentration zones, differentiated with respect to their surroundings by differences in concentrations of the several kinds of molecules present in the mixture. Some of these zones are rich in fuel molecules and others in oxygen molecules. This results in diffusion of oxygen and fuel molecules each from its own concentration zone toward a concentration zone of the other. At the interzone between the two, fuel and oxygen molecules collide with each other in such numbers per unit volume that vigorous combustion ensues, provided that the temperature is well above the ignition point.
The essential geometrical characteristics of this system to which the energy release rate per unit volume of the mixture is proportional for a given set of conditions otherwise, is the extent of the interzone per unit volume of the mixture. It is shown that the extent factor, in this sense, of the interzone is the area of an imaginary interface within the interzone per unit volume of the mixture.
The foregoing proportionality between extent of reaction interface and reaction rate per unit of volume applies whenever the concentration zones are large compared to molecular dimensions and this proportionality holds under these conditions independently of the mechanism of the processes by which the fuel and oxygen molecules approach the interface for a given set of conditions such as pressure, temperature, and composition. The concept of reaction interface extension thus appears to be of a fundamental nature with respect to reaction rate and combustion progress.
It is shown that inclusion of the co-ordinate reaction interface extension has an influence on the magnitude of the pressure and temperature effects on the reaction rate for compressible mixtures. This follows because the extension of interface in a unit of volume depends, among other things, on the density of the mixture. It is found also that a large part of the macroscopic effects of turbulence on the reaction rate may be accounted for by the increase in reaction interface extension which results because of turbulence. A large part of the effect of eddy diffusion on the reaction rate is thus accounted for in the present analysis by the increase in reaction interface extension which results because of turbulence.
The paper contains the reaction-rate and combustion-progress equations which result when reaction interface extension is included as one of the co-ordinates on which the rate of the reaction per unit volume of the mixture depends. One set of these equations is based on the frequency of effective collisions between fuel and oxygen molecules per unit area of reaction interface. The reaction rate per unit volume of the mixture is the product of the foregoing, times the interface extension per unit volume of the mixture. The combustion-progress equation results by integration of the rate equation over an interval of combustion progress.
The foregoing equations are applied to a mixture containing natural gas as the fuel and with varying air-fuel ratios. The results are shown in both tabular and graphical form.
The equations permit also establishment of the order of magnitude of the maximum possible mean energy release rates over a given combustion progress. These maxima should occur when the molecular distribution in the mixture is uniform. It is shown that with natural gas as the fuel, when burned with 1.2 times theoretical air to within 99 per cent of completion, at one atmosphere furnace pressure, this average maximum over this combustion progress is of the order of 2 × 106 Btu per hour per cu ft of furnace volume.