1. Combustion of solid fuels
Combustion of solid fuels is constituted by the following steps:
Drying and heating of the solid fuel particles up to the temperature at which begins the release of volatiles
Volatilization of solid fuel particles and ignition; during the release of volatiles, each solid particle originates a residual char particle
Oxidation of the volatile matter (homogeneous reactions) and char (heterogeneous reactions)
There is no well defined sequence for the previous steps, e.g., the heating of the particle may occur simultaneously with the volatilization and oxidation of the volatiles, and oxidation of the char.
The drying and heating of the particles are endothermic processes controlled by heat and mass transfer, and depend on the temperature and particle size. The amount of heat depends on the moisture present in the particles, their size and properties, e.g., mass diffusivity, specific heat and thermal conductivity.
Solid fuel combustion
Combustion

2. Combustion of solid fuels
Drying starts when the temperature of the particles reaches about 105 ºC, i.e., when moisture vaporizes and is released.
The drying and heating of the particles cause physical changes, e.g., the phase change of the moisture present in the particle may originate cracks sufficient to break the particle in case the vapour is not released fast enough.
Volatilization (release of volatile matter) in the coal begins for temperatures in the range 350ºC – 400ºC. The amount and nature of volatiles depend, e.g., on the heating rate, final temperature, residence time, particle size. The volatiles consist mainly of H2O, CO2, CO, H2, light hydrocarbons (mainly CH4) and tars.
For sufficiently large coal particles, combustion begins with the ignition of the volatiles. There is experimental evidence that below a critical particle diameter, heterogeneous combustion of the particles may begin before or in parallel with the release and combustion of volatiles.
Solid fuel combustion
Combustion

3. Combustion of solid fuels
The char is produced after the volatile matter has been driven from the coal particle and burned, and is constituted mainly by carbon and ashes, with small amounts of hydrogen, oxygen, nitrogen and sulphur.
The char is often approximately spherical, particularly for small particles, and may exhibit cracks and pores, as a result of the release of volatiles, and may be larger than the original particle.
Char groups
Group I
Group II
Group III
2D schematical representation
Porosity (%)
> 70
Variable, 40-70
< 40
Average wall thickness (mm)
< 5
> 5
Shape
Spherical
Sub-spherical
Angular
Coal char morphological classification
Solid fuel combustion
Combustion

4. Combustion of solid fuels
The oxidation of the char is controlled by temperature dependent phenomena, and three different temperature zones may be identified for coal char:
Zone I – Zone of relatively low temperatures where combustion is chemically controlled. The reaction rate is low, and most oxidizer molecules diffuse across the porous structure without reacting. The concentration of oxygen in the pores is similar to that in the vicinity of the particles.
Zone II – The reaction between the carbon and the oxidizer becomes faster with the increase of temperature, being controlled not only be chemical kinetics, but also by diffusion of the oxygen in the porous structure.
Zone III – At high temperature, the reaction at the surface of the particle becomes very fast, and all the oxygen is consumed there, so that the reaction rate is controlled by diffusion of oxygen molecule in the vicinity of the particle to its surface.
Solid fuel combustion
Combustion

5. Combustion of solid fuels
Solid fuel combustion
Combustion

6. Heterogeneous reactions
Heterogeneous reactions involve chemical species in different phyical states, e.g., gas-solid reactions. The overall process os gas-solid reactions may be subdivided as follows:
Transport of the reactant molecules to the surface by convection and/or diffusion.
Adsorption of the reactant molecule on the surface.
Elementary reaction steps involving various combinations of adsorbed molecules, the surface itself, and gas-phase molecules.
Desorption of product molecules from the surface.
Transport of the reactant molecules away from the surface by convection and/or diffusion.
If a reactant molecule A is weakly adsorbed, then
If the reactant molecule A is strongly adsorbed, then
If the reactant molecule A is weakly adsorbed, while the product molecule B is strongly adsorbed, then
Solid fuel combustion
Combustion

7. Combustion of a carbon particle
Combustion of a carbon particle illustrates the combustion of solid fuels.
At the surface of the carbon particle the following reactions may occur, depending mainly on the temperature of the surface:
C + O2  CO2
2C + O2  2CO
C + CO2  2CO
C + H2O  CO + H2
The main product formed at the surface is CO, which diffuses away from the surface through the boundary layer where it combines with the inward-diffusing O2, according to the following global homogeneous reaction:
CO + ½ O2  CO2
The surface of the char particle is porous, and there is diffusion across the surface during the oxidation process.
Solid fuel combustion
Combustion

8. Combustion of a carbon particle
Simplified theoretical models for the combustion of a carbon particle are based on the previous global reactions, and generally assume that the surface is impervious to diffusion.
These models may be classified as one-film, two-film or continuous-film models, depending on the simplifying assumptions about chemical kinetics on the surface and on the gaseous phase.
In the one-film models there is no flame in the gaseous phase, and the maximum temperature occurs at the carbon surface.
In the two-film models the flame front lies at a certain distance from the surface, where the CO produced at the surface reacts with incoming O2 to form CO2.
In the continuous film models the flame region is distributed within the boundary layer, rather than occurring in a sheet.
Solid fuel combustion
Combustion

9. Combustion of a carbon particle
One-film model
Simplifying assumptions
The burning process is quasi-steady
The spherical carbon particle burns in a quiescent, infinite ambient medium that contains only oxygen and an inert gas, such as nitrogen. There are no interactions with other particles, and the effects of convection are ignored.
At the particle surface, the reaction C + O2  CO2 prevails. In general, this assumption is not particularly good since carbon monoxide is the preferred product at combustion temperatures, but eliminates the problem of how and where the CO oxidizes.
The gas phase consists only of O2, CO2 and inert gas. The O2 diffuses inward, reacts with the surface to form CO2, which then diffuses outward.
The thermophysical properties of the gaseous phase, lg, cp,g and rDM , are constant, and the Lewis number is equal to one.
The carbon particle is impervious to gas-phase species.
The particle is at uniform temperature and radiates as a grey body to the surroundings, while the medium is transparent to radiation.
Solid fuel combustion
Combustion

10. Combustion of a carbon particle
One-film model
The main objective of the model is to determine the mass burning rate of the carbon, , and the surface temperature, Ts. Intermediate values of interest are the mass fractions of O2 and CO2 at the carbon surface.
Solid fuel combustion
Combustion

11. Combustion of a carbon particle
One-film model
Mass balance at the surface of the particle
Mass balance at an arbitrary radial position
The CO2 and O2 flow rates can be related to the stoichiometry associated with the reaction at the surface:
1 kg C + s kg O2  (s +1) kg CO2
Conservation equation for the mass fraction of oxygen:
with yO2(rs)=yO2,s and yO2(∞)=yO2,∞
Solid fuel combustion
Combustion

12. Combustion of a carbon particle
One-film model
This yields, after some algebra,
To find yO2,s we assume that the heterogeneous reaction C + O2  CO2 is first order with respect to O2 and the reaction rate RC [kg m-2 s-1] is given by
with the reaction rate constant given by
The relation between the burning rate and the reaction rate of carbon at the surface is given by
Solid fuel combustion
Combustion

13. Combustion of a carbon particle
One-film model
The molar concentration of oxygen may be converted to mass fraction as follows:
Combining the previous equations yields
where the kinetics parameter Kkin depends on the pressure, surface temperature and particle radius.
Solving the previous equation for yO2,s and substituting into the equation for the burning rate yields a non-linear equation that may be solved to find Alternatively, we may use an electrical circuit analog as follows:
Solid fuel combustion
Combustion

14. Combustion of a carbon particle
One-film model
The expression for derived from the conservation equation for the mass fraction of oxygen may be manipulated to yield
with
Expanding the logarithm in a Taylor series and truncating the series by retaining only the linear term yields the following approximation
Note that yO2,s appears in Rdiff, so that the relation between DyO2 and remains non-linear.
Since the burning rate derived from chemical kinetics must be the same as that derived from mass transfer considerations alone, a two-resistor series circuit results.
Taking the potentials to be O2 mass fractions, the carbon flows from a low potential to a high potential, i.e., in a direction opposite to that of O2.
Solid fuel combustion
Combustion

15. Combustion of a carbon particle
One-film model
The burning rate of the carbon particle may be determined from the electrical analogue as follows:
with
An iterative procedure is still needed to determine the solution, because Rdiff includes the unknown yO2,s.
Solid fuel combustion
Combustion

16. Combustion of a carbon particle
One-film model
The value of one of the resistances may be dominant, depending primarily on the particle temperature and size. In fact,
If Rkin/Rdiff << 1, the combustion rate is controlled by diffusion. Therefore, the mass fraction of oxygen at the surface of the particle is close to zero. This happens when kC, rs, p and/or Ts are high (note that even though Ts appears in the denominator of the equation above, its influence on kc is dominant).
If Rkin / Rdiff >> 1, the combustion rate is controlled by kinetics, so that the concentration of oxygen at the surface of the particle is very close to that far away from the particle. This occurs when kC, rs, p orTs are low.
Solid fuel combustion
Combustion

17. Combustion of a carbon particle
One-film model
Energy balance at the surface
qs-i – heat transfer rate by conduction from the surface to the fluid (qs-i = 0) under steady state conditions.
qs-f - convective heat transfer rate from the surface to the fluid.
The equation above may be expressed as follows:
Solid fuel combustion
Combustion

18. Combustion of a carbon particle
One-film model
The temperature derivative at the surface may be obtained from the conservation equation for energy. This equation is identical to that derived for the droplet evaporation model, which yields
Inserting into the previous equation yields
with Z = cp,g / (4p lg)
This equation contains two unknowns: and Ts. To fully solve the carbon burning problem, simultaneous solution of this equation and of the equation for is needed. If both kinetics and diffusion play a role, the equation relating to yO2,s is also required.
Solid fuel combustion
Combustion

19. Combustion of a carbon particle
Two-film model
The two-film model describes more realistically the chemical and physical processes involved in carbon combustion. In particular, the carbon oxidizes to CO rather CO2.
Solid fuel combustion
Combustion

20. Combustion of a carbon particle
Two-film model
The mass flow rates of the various species ca be related by simple mass balances at the particle surface and at the flame front.
(at the surface)
(at the flame front)
yielding
We further known that
1 kg C + ss kg CO2  2 (ss +1) kg CO
1 kg C + sf kg O2  (sf +1) kg CO2
with
Solid fuel combustion
Combustion

21. Combustion of a carbon particle
Two-film model
The mass flow rates of the various species can be related to the burning rate of carbon as follows:
The conservation equation for the mass fraction of CO2 in the inner zone is similar to that for that for the mass fraction of O2 in the one-film model. Hence,
Similarly, at the flame surface,
with yCO2(rs)=yCO2,s and yCO2(rf)=yCO2,f
with yCO2(rf)=yCO2,f and yCO2(∞)=0
Solid fuel combustion
Combustion

22. Combustion of a carbon particle
Two-film model
The conservation equation for the mass fraction of N2 may be expressed as
Integration of the previous equations gives:
with yN2(rf)=yN2,f and yN2(∞)= yN2,∞
Solid fuel combustion
Combustion

23. Combustion of a carbon particle
Two-film model
The previous equations along with the following one for overall mass conservation contain five unknowns:
The remaining equation is obtained from chemical kinetics. The reaction C + CO2  2CO is first-order in CO2 concentration, and thus the rate is expressed in a form identical to that developed for the one-film model:
or more compactly as
Solid fuel combustion
Combustion

24. Combustion of a carbon particle
Two-film model
The first four equations may be manipulated to eliminate all variables except
leading to
with
This equation together with the fifth one (equation for of the last slide) may be solved iteratively to find (and yCO2,s).
If the combustion is controlled by diffusion, then and the burning rate can be directly evaluated from the equation above.
Solid fuel combustion
Combustion

25. Combustion of a carbon particle
Particle burning time
To obtain the surface temperature it is necessary to write and solve energy balances at the surface and at the flame sheet, as formerly done for the one- film model.
For diffusion-controlled burning, the burning time may be determined similarly to the droplet burning time. The diameter of the carbon particle can be expressed as a function of time according to the D2 law:
with the burning rate constant given by
Setting D=0 gives the particle burning time:
Solid fuel combustion
Combustion

26. Combustion of a carbon particle
Particle burning time
In the one-film model the transfer number is B ≡ Bo,m, while in the two-film model is , respectively, for diffusion- controlled combustion.
In order to incorporate in the model the effects of a convective flow over a burning carbon particle, the film theory of the previous chapter can be applied.
For diffusion-controlled conditions with convection, the mass burning rates are augmented by the factor Sh/2. For unity Lewis number, Sh=Nu, and thus
The Nusselt number may be evaluated with reasonable accuracy using the correlation given in the previous chapter.
Solid fuel combustion
Combustion