1. Background

Pulverised solid fuels such as [GLOSS]coal[/GLOSS] or [GLOSS]petroleum coke[/GLOSS] are widely used today in various types of boilers and furnaces. The modelling of the associated combustion processes is of interest both for particle burnout times, and for understanding and predicting the formation of gas phase pollutants.

If one focuses on a single particle, the combustion process can be described in the following simplified way. On heating, the particle undergoes a thermal degradation called [GLOSS]devolatilisation[/GLOSS]. During this phase, the fuel particle will release [GLOSS]volatile matter[/GLOSS], and a solid carbonaceous residue – called [GLOSS]char[/GLOSS] – is left.  On the one hand the volatile matter will oxidise, releasing part of the total energy of combustion. On the other hand, the char residue will oxidise, producing the remainder of the energy. This part of the combustion process is particularly interesting since char oxidation releases 40% to 98% of the total energy amount.

It is particularly important to know if the char particle will ignite or not.  Quantitative criteria to determine particle ignition were described in two linked Combustion Files CFs 257 and 258. Downloadable from this page is an Microsoft [GLOSS]Excel[/GLOSS] spreadsheet. This is a calculator for the computation of the heat released by combustion and of the heat exchanged with the surroundings versus the particle temperature. It determines the equilibrium particle temperature.

2. Use of the spreadsheet-calculator for single particle ignition calculations

The spreadsheet uses a macro to perform an iterative solution to the equations it uses, and plots a graph of the results. The relative positions and crossings of the two lines on the graph directly indicate the ignition condition of the particle as described in CF257.

 When activating the spreadsheet, the user must enable Macros in order to achieve full functionality. The Spreadsheet will also require the user to have installed and activated the Excel ‘Solver’ Add-in.

See CFs 257 and 258 for a detailed explanation of the equations and method used in this spreadsheet, and also for a more detailed background.

The variables generally have no boundary limits, except for what is sensibly unrealistic/physically impossible.

The spreadsheet itself contains the instructions as to its use. The ‘Start Macro’ button must be used – some values are calculated without it, but not all. Click on a different cell to the input cell you have modified – the data shall not change properly if you do not.

Interpreting the graph of the spreadsheet: remember that particle ignition occurs when the two curves cross well above ambient temperatures, and when the heat released curve (Q_comb, purple) is above the heat loss curve (Q_loss, blue dotted) at  particle temperatures below the intercept (i.e. to the left of the intercept).

Users of this combustion file should note:

• This workbook can be downloaded by the reader and saved to a local hard disk.
• To achieve this click on the ‘xls‘ icon on the left hand side of the banner above. The file will be retrieved from the server, and with up-to-date versions of the browser, will appear in a separate window, from which it may be saved to the user’s hard disk.
• The data in this worksheet is not protected – when the reader modifies any of the non-input data (i.e. what is not in green text), at this point the accuracy and integrity of the data becomes the responsibility of the reader.

3. Short example – finding the particle diameter of ignition for a set temperature

With all inputs held constant as in the spreadsheet, except for the particle diameter, the minimum and maximum particle diameters achieving ignition can be found. The inputs held constant (as default in the spreadsheet) are:

Temperature of the furnace wall                           1000 ^oC

Temperature of the surrounding gas                       1000 ^oC

Molar fraction of O₂ in the gas                            0.21

Particle density                                                  840 kg/m³

Density of the solid fraction                                1550 kg/m³

Particle surface emissivity                                   0.9

Frequency factor for the char oxidation                 30000 kg.s^-1.m^-2.atm^-1

Activation energy for the char oxidation reaction    179 400 J.mol^-1.K^-1

Specific surface area of the char                           50000 m²/kg

By varying the particle diameter between 50 microns and 400 microns (and pushing the “Start Macro” button each time), it can be seen, looking at the graph, that ignition begins to occur at around 200 microns. Ignition becomes highly stable after around 350 microns.

Sources

Sylvain Salvador

Acknowledgements

The author would like to thank Brian Stanmore for his scientific support, and the IFRF staff for their kind and efficient help in writing this program and the related Combustion Files. Thanks to Jean-Michel Commandré for his help in developing the “automatic” software.