THE DETERMINATION OF HEATING VALUES OF FUELS

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THE DETERMINATION OF HEATING VALUES OF FUELS

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 =

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 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,

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.

Table 39 gives for comparison the ultimate and proximate analyses of certain of the coals with which tests were made in the coal testing plant of the United States Geological Survey at the Louisiana Purchase Exposition at St. Louis.

The heating value of a fuel cannot be directly computed from a proximate analysis, due to the fact that the volatile content varies widely in different fuels in composition and in heating value.

Some methods have been advanced for estimating the calorific value of coals from the proximate analysis. William Kent[38] deducted from Mahler’s tests of European coals the approximate heating value dependent upon the content of fixed carbon in the combustible. The relation as deduced by Kent between the heat and value per pound of combustible and the per cent of fixed carbon referred to combustible is represented graphically by Fig. 23.

Goutal gives another method of determining the heat value from a proximate analysis, in which the carbon is given a fixed value and the heating value of the volatile matter is considered as a function of its percentage referred to combustible. Goutal’s method checks closely with Kent’s determinations.

All the formulae, however, for computing the calorific value of coals from a proximate analysis are ordinarily limited to certain classes of fuels. Mr. Kent, for instance, states that his deductions are correct within a close limit for fuels containing more than 60 per cent of fixed carbon in the combustible, while for those containing a lower percentage, the error may be as great as 4 per cent, either high or low.

While the use of such computations will serve where approximate results only are required, that they are approximate should be thoroughly understood.

Calorimetry—An ultimate or a proximate analysis of a fuel is useful in determining its general characteristics, and as described on page 183, may be used in the calculation of the approximate heating value. Where the efficiency of a boiler is to be computed, however, this heating value should in all instances be determined accurately by means of a fuel calorimeter.

In such an apparatus the fuel is completely burned and the heat generated by such combustion is absorbed by water, the amount of heat being calculated from the elevation in the temperature of the water. A calorimeter which has been accepted as the best for such work is one in which the fuel is burned in a steel bomb filled with compressed oxygen. The function of the oxygen, which is ordinarily under a pressure of about 25 atmospheres, is to cause the rapid and complete combustion of the fuel sample. The fuel is ignited by means of an electric current, allowance being made for the heat produced by such current, and by the burning of the fuse wire.

A calorimeter of this type which will be found to give satisfactory results is that of M. Pierre Mahler, illustrated in Fig. 24 and consisting of the following parts:

A water jacket A, which maintains constant conditions outside of the calorimeter proper, and thus makes possible a more accurate computation of radiation losses.

The porcelain lined steel bomb B, in which the combustion of the fuel takes place in compressed oxygen.

The platinum pan C, for holding the fuel.

The calorimeter proper D, surrounding the bomb and containing a definite weighed amount of water.

An electrode E, connecting with the fuse wire F, for igniting the fuel placed in the pan C.

A support G, for a water agitator.

A thermometer I, for temperature determination of the water in the calorimeter. The thermometer is best supported by a stand independent of the calorimeter, so that it may not be moved by tremors in the parts of the calorimeter, which would render the making of readings difficult. To obtain accuracy of readings, they should be made through a telescope or eyeglass.

A spring and screw device for revolving the agitator.

A lever L, by the movement of which the agitator is revolved.

A pressure gauge M, for noting the amount of oxygen admitted to the bomb. Between 20 and 25 atmospheres are ordinarily employed.

An oxygen tank O.

A battery or batteries P, the current from which heats the fuse wire used to ignite the fuel.

This or a similar calorimeter is used in the determination of the heat of combustion of solid or liquid fuels. Whatever the fuel to be tested, too much importance cannot be given to the securing of an average sample. Where coal is to be tested, tests should be made from a portion of the dried and pulverized laboratory sample, the methods of obtaining which have been described. In considering the methods of calorimeter determination, the remarks applied to coal are equally applicable to any solid fuel, and such changes in methods as are necessary for liquid fuels will be self-evident from the same description.

Approximately one gram of the pulverized dried coal sample should be placed directly in the pan of the calorimeter. There is some danger in the using of a pulverized sample from the fact that some of it may be blown out of the pan when oxygen is admitted. This may be at least partially overcome by forming about two grams into a briquette by the use of a cylinder equipped with a plunger and a screw press. Such a briquette should be broken and approximately one gram used. If a pulverized sample is used, care should be taken to admit oxygen slowly to prevent blowing the coal out of the pan. The weight of the sample is limited to approximately one gram since the calorimeter is proportioned for the combustion of about this weight when under an oxygen pressure of about 25 atmospheres.

A piece of fine iron wire is connected to the lower end of the plunger to form a fuse for igniting the sample. The weight of iron wire used is determined, and if after combustion a portion has not been burned, the weight of such portion is determined. In placing the sample in the pan, and in adjusting the fuse, the top of the calorimeter is removed. It is then replaced and carefully screwed into place on the bomb by means of a long handled wrench furnished for the purpose.

The bomb is then placed in the calorimeter, which has been filled with a definite amount of water. This weight is the “water equivalent” of the apparatus, i. e., the weight of water, the temperature of which would be increased one degree for an equivalent increase in the temperature of the combined apparatus. It may be determined by calculation from the weights and specific heats of the various parts of the apparatus. Such a determination is liable to error, however, as the weight of the bomb lining can only be approximated, and a considerable portion of the apparatus is not submerged. Another method of making such a determination is by the adding of definite weights of warm water to definite amounts of cooler water in the calorimeter and taking an average of a number of experiments. The best method for the making of such a determination is probably the burning of a definite amount of resublimed naphthaline whose heat of combustion is known.

The temperature of the water in the water jacket of the calorimeter should be approximately that of the surrounding atmosphere. The temperature of the weighed amount of water in the calorimeter is made by some experimenters slightly greater than that of the surrounding air in order that the initial correction for radiation will be in the same direction as the final correction. Other experimenters start from a temperature the same or slightly lower than the temperature of the room, on the basis that the temperature after combustion will be slightly higher than the room temperature and the radiation correction be either a minimum or entirely eliminated.

While no experiments have been made to show conclusively which of these methods is the better, the latter is generally used.

After the bomb has been placed in the calorimeter, it is filled with oxygen from a tank until the pressure reaches from 20 to 25 atmospheres. The lower pressure will be sufficient in all but exceptional cases. Connection is then made to a current from the dry batteries in series so arranged as to allow completion of the circuit with a switch. The current from a lighting system should not be used for ignition, as there is danger from sparking in burning the fuse, which may effect the results. The apparatus is then ready for the test.

Unquestionably the best method of taking data is by the use of co-ordinate paper and a plotting of the data with temperatures and time intervals as ordinates and abscissae. Such a graphic representation is shown in Fig. 25.

After the bomb is placed in the calorimeter, and before the coal is ignited, readings of the temperature of the water should be taken at one minute intervals for a period long enough to insure a constant rate of change, and in this way determine the initial radiation. The coal is then ignited by completing the circuit, the temperature at the instant the circuit is closed being considered the temperature at the beginning of the combustion. After ignition the readings should be taken at one-half minute intervals, though because of the rapidity of the mercury’s rise approximate readings only may be possible for at least a minute after the firing, such readings, however, being sufficiently accurate for this period. The one-half minute readings should be taken after ignition for five minutes, and for, say, five minutes longer at minute intervals to determine accurately the final rate of radiation.

Fig. 25 shows the results of such readings, plotted in accordance with the method suggested. It now remains to compute the results from this plotted data.

The radiation correction is first applied. Probably the most accurate manner of making such correction is by the use of Pfaundler’s method, which is a modification of that of Regnault. This assumes that in starting with an initial rate of radiation, as represented by the inclination of the line AB, Fig. 25, and ending with a final radiation represented by the inclination of the line CD, Fig. 25, that the rate of radiation for the intermediate temperatures between the points B and C are proportional to the initial and final rates. That is, the rate of radiation at a point midway between B and C will be the mean between the initial and final rates; the rate of radiation at a point three-quarters of the distance between B and C would be the rate at B plus three-quarters of the difference in rates at B and C, etc. This method differs from Regnault’s in that the radiation was assumed by Regnault to be in each case proportional to the difference in temperatures between the water of the calorimeter and the surrounding air plus a constant found for each experiment. Pfaundler’s method is more simple than that of Regnault, and the results by the two methods are in practical agreement.

Expressed as a formula, Pfaundler’s method is, though not in form given by him:

The application of this formula to Fig. 25 is as follows:

As already stated, the temperature at the beginning of combustion is the reading just before the current is turned on, or B in Fig. 25. The point C or the temperature at which combustion is presumably completed, should be taken at a point which falls well within the established final rate of radiation, and not at the maximum temperature that the thermometer indicates in the test, unless it lies on the straight line determining the final radiation. This is due to the fact that in certain instances local conditions will cause the thermometer to read higher than it should during the time that the bomb is transmitting heat to the water rapidly, and at other times the maximum temperature might be lower than that which would be indicated were readings to be taken at intervals of less than one-half minute, i. e., the point of maximum temperature will fall below the line determined by the final rate of radiation. With this understanding AB, Fig. 25, represents the time of initial radiation, BC the time of combustion, and CD the time of final radiation. Therefore to apply Pfaundler’s correction, formula (19), to the data as represented by Fig. 25.

Pfaundler’s formula while simple is rather long. Mr. E. H. Peabody has devised a simpler formula with which, under proper conditions, the variation from correction as found by Pfaundler’s method is negligible.

It was noted throughout an extended series of calorimeter tests that the maximum temperature was reached by the thermometer slightly over one minute after the time of firing. If this period between the time of firing and the maximum temperature reported was exactly one minute, the radiation through this period would equal the radiation per one-half minute before firing plus the radiation per one-half minute after the maximum temperature is reached; or, the radiation through the one minute interval would be the average of the radiation per minute before firing and the radiation per minute after the maximum. A plotted chart of temperatures would take the form of a curve of three straight lines (B, C', D) in Fig. 25. Under such conditions, using the notation as in formula (19) the correction would become,

This formula may be generalized for conditions where the maximum temperature is reached after a period of more than one minute as follows:

Let M = the number of intervals between the time of firing and the maximum temperature. Then the radiation through this period will be an average of the radiation for M intervals before firing and for M intervals after the maximum is recorded, or

In the case of Mr. Peabody’s deductions M was found to be approximately 2 and formula (21) becomes directly, C = R + (N - 1)R' or formula (20).

The corrections to be made, as secured by the use of this formula, are very close to those secured by Pfaundler’s method, where the point of maximum temperature is not more than five intervals later than the point of firing. Where a longer period than this is indicated in the chart of plotted temperatures, the approximate formula should not be used. As the period between firing and the maximum temperature is increased, the plotted results are further and further away from the theoretical straight line curve. Where this period is not over five intervals, or two and a half minutes, an approximation of the straight line curve may be plotted by eye, and ordinarily the radiation correction to be applied may be determined very closely from such an approximated curve.

Peabody’s approximate formula has been found from a number of tests to give results within .003 degrees Fahrenheit for the limits within which its application holds good as described. The value of M, which is not necessarily a whole number, should be determined for each test, though in all probability such a value is a constant for any individual calorimeter which is properly operated.

The correction for radiation as found on page 188 is in all instances to be added to the range of temperature between the firing point and the point chosen from which the final radiation is calculated. This corrected range multiplied by the water equivalent of the calorimeter gives the heat of combustion in calories of the coal burned in the calorimeter together with that evolved by the burning of the fuse wire. The heat evolved by the burning of the fuse wire is found from the determination of the actual weight of wire burned and the heat of combustion of one milligram of the wire (1.7 calories), i. e., multiply the weight of wire used by 1.7, the result being in gram calories or the heat required to raise one gram of water one degree centigrade.

Other small corrections to be made are those for the formation of nitric acid and for the combustion of sulphur to sulphuric acid instead of sulphur dioxide, due to the more complete combustion in the presence of oxygen than would be possible in the atmosphere.

To make these corrections the bomb of the calorimeter is carefully washed out with water after each test and the amount of acid determined from titrating this water with a standard solution of ammonia or of caustic soda, all of the acid being assumed to be nitric acid. Each cubic centimeter of the ammonia titrating solution used is equivalent to a correction of 2.65 calories.

As part of acidity is due to the formation of sulphuric acid, a further correction is necessary. In burning sulphuric acid the heat evolved per gram of sulphur is 2230 calories in excess of the heat which would be evolved if the sulphur burned to sulphur dioxide, or 22.3 calories for each per cent of sulphur in the coal. One cubic centimeter of the ammonia solution is equivalent to 0.00286 grams of sulphur as sulphuric acid, or to 0.286 × 22.3 = 6.38 calories. It is evident therefore that after multiplying the number of cubic centimeters used in titrating by the heat factor for nitric acid (2.65) a further correction of 6.38 - 2.65 = 3.73 is necessary for each cubic centimeter used in titrating sulphuric instead of nitric acid. This correction will be 3.73⁄0.297 = 13 units for each 0.01 gram of sulphur in the coal.

The total correction therefore for the aqueous nitric and sulphuric acid is found by multiplying the ammonia by 2.65 and adding 13 calories for each 0.01 gram of sulphur in the coal. This total correction is to be deducted from the heat value as found from the corrected range and the amount equivalent to the calorimeter.

After each test the pan in which the coal has been burned must be carefully examined to make sure that all of the sample has undergone complete combustion. The presence of black specks ordinarily indicates unburned coal, and often will be found where the coal contains bone or slate. Where such specks are found the tests should be repeated. In testing any fuel where it is found difficult to completely consume a sample, a weighed amount of naphthaline may be added, the total weight of fuel and naphthaline being approximately one gram. The naphthaline has a known heat of combustion, samples for this purpose being obtainable from the United States Bureau of Standards, and from the combined heat of combustion of the fuel and naphthaline that of the former may be readily computed.

The heat evolved in burning of a definite weight of standard naphthaline may also be used as a means of calibrating the calorimeter as a whole.

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