Diffusion controlled, combustion

The rate of solid waste combustion is controlled by diffusion, rather than by reaction kinetics. In general, the time required for combustion of a single particle of waste (1) can be expressed as ... 

The vapor cloud of evaporated droplets bums like a diffusion flame in the turbulent state rather than as individual droplets. In the core of the spray, where droplets are evaporating, a rich mixture exists and soot formation occurs. Surrounding this core is a rich mixture zone where CO production is high and a flame front exists. Air entrainment completes the combustion, oxidizing CO to CO2 and burning the soot. Soot bumup releases radiant energy and controls flame emissivity. The relatively slow rate of soot burning compared with the rate of oxidation of CO and unbumed hydrocarbons leads to smoke formation. This model of a diffusion-controlled primary flame zone makes it possible to relate fuel chemistry to the behavior of fuels in combustors (7). 

Diffusion flames can best be described as the combustion state controlled by mixing phenomena—that is, the diffusion of fuel into oxidizer, or vice versa—until some flammable mixture ratio is reached. According to the flow state of the individual diffusing species, the situation may be either laminar or turbulent. It will be shown later that gaseous diffusion flames exist, that liquid burning proceeds by a diffusion mechanism, and that the combustion of solids and some solid propellants falls in this category as well. 

If Da = 1 is defined as the transition between diffusionally controlled and kinetically controlled regimes, an inverse relationship is observed between the particle diameter and the system pressure and temperature for a fixed Da. Thus, for a system to be kinetically controlled, combustion temperatures need to be low (or the particle size has to be very small, so that the diffusive time scales are short relative to the kinetic time scale). Often for small particle diameters, the particle loses so much heat, so rapidly, that extinction occurs. Thus, the particle temperature is nearly the same as the gas temperature and to maintain a steady-state burning rate in the kinetically controlled regime, the ambient temperatures need to be high enough to sustain reaction. The above equation also shows that large particles at high pressure likely experience diffusion-controlled combustion, and small particles at low pressures often lead to kinetically controlled combustion. 

The extent to which a given reactant, such as oxygen, is able to utilize this additional surface area depends on the difficulty in diffusing through the particle to reach the pore surfaces and on the overall balance between diffusion control of the burning rate and kinetic control. To broadly characterize these competing effects, three zones of combustion of porous particles have been identified, as shown in Fig. 9.21. In Zone I the combustion rate is fully controlled by the surface reaction rate (kinetically controlled), because the diffusion... 

Weisz, P. B., and Goodwin, R. D. (1963). Combustion of carbonaceous deposits within porous catalyst particles. I. Diffusion controlled kinetics. J. Catal. 2, 397. 

When authors illustrate the subject of thermochemical conversion of solid fuels in the literature, the conversion zone in a packed bed is divided into different process zones (drying zone, pyrolysis zone, char combustion zone, and char gasification zone), one for each thermochemical conversion process. The spatial order of this process zones is herein referred to as the bed process structure or conversion process structure. The conversion process structure is a function of conversion concept. Even more important, the bed process structure can only exist in the diffusion controlled conversion regime when the conversion zone has a significant thickness. 

This example shows that the equilibrium approach in general may work reasonably well for major species in combustion systems, provided that the overall process is diffusion controlled. Even under these conditions the equilibrium approach may fail, however, in predicting concentrations of minor components such as pollutants. 

Rastogi and Bisht (Ref 3a) made combustion studies on hybrid propints consisting of o-s m-and p-toluidine nitTates with aniline-formaldehyde polymer as solid fuels, and red fuming nitric acid as oxidizer. They found that the results fitted a burning rate equation of the type, = a (G)v, where a and v are constants and G is the mass velocity. The authors conclude that the heterogeneous combustion reaction is diffusion controlled, and its rate is dependent on particle size... 

Under reaction-controlled conditions, the total rate of catalytic oxidation is governed by the rate of surface reaction and is independent of the gas transfer rate from the gas phase to the catalyst surface, so that the CTL intensity is also independent of the flow velocity of sample gas around the sensor. Under diffusion-controlled conditions, the rate of catalytic oxidation is independent of the catalytic activity, but depends on the transfer rate of combustible gas in the gas phase, so that the CTL intensity depends on the flow rate of the gas... 

The process of particle combustion depends on the physical and chemical nature of the solid as it heats and burns. Coal is a complex material of volatile and nonvolatile components which becomes increasingly porous during volatilization of low-boiling constituents in burning. The crucial practical questions for boiler design concern whether pulverized fuel combustion is controlled by oxidizer diffusion or by chemical kinetics. 

For combustion reactions Levenspiel (4) gives the constant temperature integration for reaction and gas or ash diffusion controlled cases. The integration of the pyrolysis kinetics will be demonstrated in the following section. 

Both diffusional flame calculations and detailed spatial mapping indicate that the nondispersed injection mode produces a vapor cloud that is characterized by diffusionally controlled combustion and bulk heating while subjecting the droplets to near isothermal conditions. The soot produced in this cloud is strongly influenced by bulk diffusion limitations and as such represents a bulk soot formation extreme. It was found that fuel changes had little effect on the overall soot yield due to this diffusion control. Lower gas temperatures and richer conditions were found to favor soot formation under bulk sooting conditions, probably due to a decrease in the oxidation rate of the soot. 

Under conditions of high current density and low phenol concentration, the complete combustion to C02 was obtained. In this case, due to the high local concentration of OH radicals, the anodic oxidation was a fast reaction under diffusion control, so that the instantaneous current efficiency decreased during the electrolysis as phenol was oxidised. 

No strong differences were observed when multicomponent mixtures of phenols (phenol, benzyl alcohol, 1-phenyl-ethanol and m-cresol) were treated (Morao et al. 2004) the experimental results were interpreted well by assuming that all the components in the mixture were degraded in the same time and that the combustion of the compounds to C02 occurred at the anode surface by means of hydroxyl radicals electrogenerated. The instantaneous current efficiency was unity, until the reaction became diffusion controlled. 

The burning reaction is a relatively slow process, depending upon how finely divided the fuel is, that is, the intimacy of contact between the fuel and the oxygen in the air. Because burning is diffusion-controlled, the more intimately the fuel and oxygen are mixed, the faster they can react. Obviously, the smaller the particles of fuel, the faster the combustion can occur. 

The spectroscopic study of radicals is a vexing business. The most common approach is to isolate these unstable species in a matrix at low temperatures. But if one is interested in atmospheric radicals (such as OCIO or ClOO) or combustion species (CH3 for example), one has to deal with gas-phase radicals. Direct observation of gas-phase radicals is quite difficult they are not stable, commercially available samples. Since radicals are reactive intermediates, they are destroyed by each other at nearly diffusion controlled rates [/]. As a result, one typically has only small concentrations of radicals (roughly 1012 cm-3) to work with. 

Another approach involves the analysis of equations corresponding to the discrete steps of combustion. The ignition parameters are calculated from the coupling condition of the steps by computerized numerical, or approximate analytical methods. In Ref. where the heterogeneous ignition of a condensed system was analyzed, a sharp transition from activation to diffusion control was assumed as ignition criterion ... 

Modem Aspects of Diffusion-Controlled Reactions Low-temperature Combustion and Autoignition Photokinetics Theoretical Fundamentals and Applications Applications of Kinetic Modelling Kinetics of Homogeneous Multistep Reactions Unimolecular Kinetics, Part 1. The Reaction Step Kinetics of Multistep Reactions, 2nd Edition... 

As is seen in Section B.4, if the reaction rate at the surface and the gas pressure are high enough, then the burning rate is controlled by the rate of diffusion in the gas. The occurrence of this diffusion-controlled regime is well established for carbon combustion [31], [37]-[39]. The following analysis will be restricted to this limit, which ceases to apply if the dimensions of the carbon materials become too small [39], [40], [41]. 

The theory discussed here applies mainly to kinetic-controlled reactions. However, combustion synthesis reactions involve many processes, including diffusion control, phase transitions, and multistage reactions, which result in a complex heat release function, Z4> (r/,7). An analysis of the system of combustion equations for various types of heat sources was compared with experimental data, which led to the conclusion that in general, the combustion wave velocity can be represented as follows (Merzhanov, 1990a) ... 

The second model (Fig. 20c) assumes that upon melting of reactant A, a layer of initial product forms on the solid reactant surface. The reaction proceeds by diffusion of reactant B through this layer, whose thickness is assumed to remain constant during the reaction (Aleksandrov et al., 1987 Aleksandrov and Korchagin, 1988). The final product crystallizes (C) in the volume of the melt after saturation. Based on this model, Kanury (1992) has developed a kinetic expression for the diffusion-controlled rate. Using this rate equation, an analytical expression for the combustion wave velocity has been reported (Cao and Varma, 1994)... 

For the case where both reactants melt in the preheating zone and the liquid product forms in the reaction zone, a simple combustion model using the reaction cell geometry presented in Fig. 20d was developed by Okolovich et al. (1977). After both reactants melt, their interdiffusion and the formation of a liquid product occur simultaneously. Numerical and analytical solutions were obtained for both kinetic- and diffusion-controlled reactions. In the kinetic-limiting case, for a stoichiometric mixture of reactants (A and B), the propagation velocity does not depend on the initial reactant particle sizes. For dififiision-controlled reactions, the velocity can be written as... 

The microstructural models described here represent theoretical milestones in gasless combustion. Using similar approaches, other models have also been developed. For example, Makino and Law (1994) used the solid-liquid model (Fig. 20c) to determine the combustion velocity as a function of stoichiometry, degree of dilution, and initial particle size. Calculations for a variety of systems compared favorably with experimental data. In addition, an analytical solution was developed for diffusion-controlled reactions, which accounted for changes in X, p, and Cp within the combustion wave, and led to the conclusion that U< Ud(Lak-shmikantha and Sekhar, 1993). 

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