8/3/2019 Heating Values of Fuel http://slidepdf.com/reader/full/heating-values-of-fuel 1/19 Steam: its Generation and Use Table of ContentsPrevious Chapter [Pg 173]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. Moist Fuel Dry Fuel C 83.95 84.45 H 4.23 4.25 O 3.02 3.04 N 1.27 1.28 S .91 .91 Ash 6.03 6.07 ––––––––––– 100.00 Moisture .59 .59 –––––––––––
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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 havingalmost 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
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.
TABLE 37
WEIGHT AND CALORIFIC VALUE OF VARIOUS GASES
AT 32 DEGREES FAHRENHEIT AND ATMOSPHERIC PRESSURE
WITH THEORETICAL AMOUNT OF AIR REQUIRED FOR COMBUSTION
(C2H6) = 3.55, marsh gas (CH4) = 72.15 and hydrogen = 21.95. All but the oxygen and thecarbon dioxide are combustibles, and the heat per cubic foot will be,
From CO = 0.0095 × 347 = 3.30
C2H4 = 0.0066 × 1675 = 11.05
C2H6 = 0.0355 × 1862 = 66.10
CH4 = 0.7215 × 1050 = 757.58
H = 0.2195 × 349 = 76.61–––––––––––
B. t. u. per cubic foot = 914.64
[Pg 176]
The net air required for combustion of one cubic foot of the gas will be,
CO = 0.0095 × 2.39 = 0.02
C2H4 = 0.0066 × 14.33 = 0.09
C2H6 = 0.0355 × 16.74 = 0.59
CH4 = 0.7215 × 9.57 = 6.90
H = 0.2195 × 2.41 = 0.53–––––––
Total net air per cubic foot = 8.13
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 degreescentigrade, 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.
Va.Fire Creek Rush Run 22.87 71.56 83.71 4.64 3.67 1.70 .71 5.57 2.14
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 andthe 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
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 whichhave 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 brokenand 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 handledwrench 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 [Pg 186]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. Anothermethod 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 thesame 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 inall 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.
FIG. 25. GRAPHIC METHOD OF RECORDING BOMB C ALORIMETER RESULTS
After the bomb is placed in the calorimeter, and before the coal is ignited, readings of thetemperature 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 [Pg 187]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 methodsuggested. 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 betweenthe initial and final rates; the rate of radiation at a point three-quarters of the distance
between B andC 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:
C = N( R +
R' - R––––––––––
T' - T( T" - T ))
(19)
Where C = correction in degree centigrade,
N = number of intervals over which correction is made,
R = initial radiation in degrees per interval,
R' = final radiation in degrees per interval,
T = average temperature for period through which initial radiation is computed,
T" = average temperature over period of combustion[39],
T' = average temperature over period through which final radiation is computed.[39]
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
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 minutebefore 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,
C =2R + 2R'–––––––––––––––
2+ ( N - 2 ) R', or R + (N - 1)R' ( 20)
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
C =MR + MR'–––––––––––––––––
2+ ( N - M ) R' =
M––––
2R + ( N -
M––––
2) R' ( 21)
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 resultswithin .003 degrees Fahrenheit for the limits within which its application holds [Pg
189]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 calorimetertogether 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, or22.3 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 thecorrected 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.
Table of Contents Next Chapter
FOOTNOTES
[36]See page 161.
[37]U. S. Geological Survey.
[38]See “Steam Boiler Economy”, page 47, First Edition.
[39]To agree with Pfaundler’s formula the end ordinates should be given half values in determining T", i. e., T" =((Temp. at B + Temp. at C) ÷ 2 + Temp. all other ordinates) ÷ N