The heating value of a fuel may be determined either by a calculation from a chemical analysis or by burning a sample in a calorimeter.

In the former method the calculation should be based on an ultimate analysis, which reduces the fuel to its elementary constituents of carbon, hydrogen, oxygen, nitrogen, sulphur, ash and moisture, to secure a reasonable degree of accuracy. A proximate analysis, which determines only the percentage of moisture, fixed carbon, volatile matter and ash, without determining the ultimate composition of the volatile matter, cannot be used for computing the heat of combustion with the same degree of accuracy as an ultimate analysis, but estimates may be based on the ultimate analysis that are fairly correct.

An ultimate analysis requires the services of a competent chemist, and the methods to be employed in such a determination will be found in any standard book on engineering chemistry. An ultimate analysis, while resolving the fuel into its elementary constituents, does not reveal how these may have been combined in the fuel. The manner of their combination undoubtedly has a direct effect upon their calorific value, as fuels having almost identical ultimate analyses show a difference in heating value when tested in a calorimeter. Such a difference, however, is slight, and very close approximations may be computed from the ultimate analysis.

Ultimate analyses are given on both a moist and a dry fuel basis. Inasmuch as the latter is the basis generally accepted for the comparison of data, it would appear that it is the best basis on which to report such an analysis. When an analysis is given on a moist fuel basis it may be readily converted to a dry basis by dividing the percentages of the various constituents by one minus the percentage of moisture, reporting the moisture content separately.

Calculations from an Ultimate Analysis—The first formula for the calculation of heating values from the composition of a fuel as determined from an ultimate analysis is due to Dulong, and this formula, slightly modified, is the most commonly used to-day. Other formulae have been proposed, some of which are more accurate for certain specific classes of fuel, but all have their basis in Dulong’s formula, the accepted modified form of which is:

Heat units in B. t. u. per pound of dry fuel =

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where C, H, O and S are the proportionate parts by weight of carbon, hydrogen, oxygen and sulphur.

Assume a coal of the composition given. Substituting in this formula (18),

Heating value per pound of dry coal

This coal, by a calorimetric test, showed 14,843 B. t. u., and from a comparison the degree of accuracy of the formula will be noted.

The investigation of Lord and Haas in this country, Mabler in France, and Bunte in Germany, all show that Dulong’s formula gives results nearly identical with those obtained from calorimetric tests and may be safely applied to all solid fuels except cannel coal, lignite, turf and wood, provided the ultimate analysis is correct. This practically limits its use to coal. The limiting features are the presence of hydrogen and carbon united in the form of hydrocarbons. Such hydrocarbons are present in coals in small quantities, but they have positive and negative heats of combination, and in coals these appear to offset each other, certainly sufficiently to apply the formula to such fuels.

High and Low Heat Value of Fuels—In any fuel containing hydrogen the calorific value as found by the calorimeter is higher than that obtainable under most working conditions in boiler practice by an amount equal to the latent heat of the volatilization of water. This heat would reappear when the vapor was condensed, though in ordinary practice the vapor passes away uncondensed. This fact gives rise to a distinction in heat values into the so-called “higher” and “lower” calorific values. The higher value, i. e., the one determined by the calorimeter, is the only scientific unit, is the value which should be used in boiler testing work, and is the one recommended by the American Society of Mechanical Engineers.

There is no absolute measure of the lower heat of combustion, and in view of the wide difference in opinion among physicists as to the deductions to be made from the higher or absolute unit in this determination, the lower value must be considered an artificial unit. The lower value entails the use of an ultimate analysis and involves assumptions that would make the employment of such a unit impracticable for commercial work. The use of the low value may also lead to error and is in no way to be recommended for boiler practice.

An example of its illogical use may be shown by the consideration of a boiler operated in connection with a special economizer where the vapor produced by hydrogen is partially condensed by the economizer. If the low value were used in computing the boiler efficiency, it is obvious that the total efficiency of the combined boiler and economizer must be in error through crediting the combination with the heat imparted in condensing the vapor and not charging such heat to the heat value of the coal.

Heating Value of Gaseous Fuels—The method of computing calorific values from an ultimate analysis is particularly adapted to solid fuels, with the exceptions already noted. The heating value of gaseous fuels may be calculated by Dulong’s formula provided another term is added to provide for any carbon monoxide present. Such a method, however, involves the separating of the constituent gases into their elementary gases, which is oftentimes difficult and liable to simple arithmetical error. As the combustible portion of gaseous fuels is ordinarily composed of hydrogen, carbon [Pg 175] monoxide and certain hydrocarbons, a determination of the calorific value is much more readily obtained by a separation into their constituent gases and a computation of the calorific value from a table of such values of the constituents. Table 37 gives the calorific value of the more common combustible gases, together with the theoretical amount of air required for their combustion.

In applying this table, as gas analyses may be reported either by weight or volume, there is given in Table 33[36] a method of changing from volumetric analysis to analysis by weight.

Examples:

1st. Assume a blast furnace gas, the analysis of which in percentages by weight is, oxygen = 2.7, carbon monoxide = 19.5, carbon dioxide = 18.7, nitrogen = 59.1. Here the only combustible gas is the carbon monoxide, and the heat value will be,

The net volume of air required to burn one pound of this gas will be,

2nd. Assume a natural gas, the analysis of which in percentages by volume is oxygen = 0.40, carbon monoxide = 0.95, carbon dioxide = 0.34, olefiant gas (C₂H₄) = 0.66, ethane (C₂H₆) = 3.55, marsh gas (CH₄) = 72.15 and hydrogen = 21.95. All but the oxygen and the carbon dioxide are combustibles, and the heat per cubic foot will be,

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The net air required for combustion of one cubic foot of the gas will be,

Proximate Analysis—The proximate analysis of a fuel gives its proportions by weight of fixed carbon, volatile combustible matter, moisture and ash. A method of making such an analysis which has been found to give eminently satisfactory results is described below.

From the coal sample obtained on the boiler trial, an average sample of approximately 40 grams is broken up and weighed. A good means of reducing such a sample is passing it through an ordinary coffee mill. This sample should be placed in a double-walled air bath, which should be kept at an approximately constant temperature of 105 degrees centigrade, the sample being weighed at intervals until a minimum is reached. The percentage of moisture can be calculated from the loss in such a drying.

For the determination of the remainder of the analysis, and the heating value of the fuel, a portion of this dried sample should be thoroughly pulverized, and if it is to be kept, should be placed in an air-tight receptacle. One gram of the pulverized sample should be weighed into a porcelain crucible equipped with a well fitting lid. This crucible should be supported on a platinum triangle and heated for seven minutes over the full flame of a Bunsen burner. At the end of such time the sample should be placed in a desiccator containing calcium chloride, and when cooled should be weighed. From the loss the percentage of volatile combustible matter may be readily calculated.

The same sample from which the volatile matter has been driven should be used in the determination of the percentage of ash. This percentage is obtained by burning the fixed carbon over a Bunsen burner or in a muffle furnace. The burning should be kept up until a constant weight is secured, and it may be assisted by stirring with a platinum rod. The weight of the residue determines the percentage of ash, and the percentage of fixed carbon is easily calculated from the loss during the determination of ash after the volatile matter has been driven off.

Proximate analyses may be made and reported on a moist or dry basis. The dry basis is that ordinarily accepted, and this is the basis adopted throughout this book. The method of converting from a moist to a dry basis is the same as described in the case of an ultimate analysis. A proximate analysis is easily made, gives information as to the general characteristics of a fuel and of its relative heating value.

Table 38 gives the proximate analysis and calorific value of a number of representative coals found in the United States.
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Steam: its Generation and Use

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