Formulas for calculating the calorific value of coal and coal chars: Development, tests, and uses

Formulas for calculating the calorific value of coal and coal chars: Development, tests, and uses

Fuel Processing Technology, 7 (1983) 11--22 11 Elsevier Scientific Publishing Company, Amsterdam -- Printed in The Netherlands FORMULAS FOR CALCULA...

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Fuel Processing Technology, 7 (1983) 11--22


Elsevier Scientific Publishing Company, Amsterdam -- Printed in The Netherlands



Institute of Gas Technology, 3424 South State Street, Chicago, Illinois 60616 (U.S.A.) (Received June 16th, 1980; accepted May 17th, 1982)

ABSTRACT A new formula for calculating the calorific value of coal from its ultimate analysis has been obtained by regression analysis of a data bank consisting of data on 775 samples of U.S. coals of all ranks. It yielded zero average difference between observed and calculated values and a standard deviation of 129 Btu/lb (300 kJ/kg). Neither average difference nor standard deviation varied much with rank of the coal. The Dulong, Mott-Spooner, Boie, and Grummel--Davies formulae were also tested with the data but gave substantially poorer results. The new formula has been substantiated with data from other laboratories and with data on chars. The distribution of variance, attributable to variability of mineral matter, variability of coal organic matter not related to rank, and variance of laboratory determinations was estimated. Use of the formula to monitor performance of a laboratory is illustrated, as is modification to obtain maximum precision in heat balance calculations on a coal conversion process.


The gross calorific value, also called gross or upper heating value, of coal is routinely determined by bomb calorimetry according to one of the two ASTM Methods [1, 2]. (The misnomer "heat c o n t e n t " has recently appeared in the literature as a s y n o n y m for calorific value or heating value. Instead, "heat c o n t e n t " is a thermodynamics term equivalent to enthalpy [3] .) Because water produced from hydrogen in the coal by combustion is condensed, the measurement yields the gross rather than the net calorific value. The gross calorific value is of great importance for heat balance calculations in the conversion of coal to other useful forms of fuel, as well as in its direct use in combustion. The significance of the correlation of calorific value with composition in ordinary fuel usage is shown by the development, as early as 1940, of some 9 different formulae for calculating calorific value from the ultimate analysis, and of 11 formulae for calculating it from the proximate analysis [4]. At least four additional ultimate analysis formulae have been proposed in recent years [ 5--8]. The correlation is perhaps of even greater importance for the rationalization and modeling of conversion processes now being developed.

12 Our own work on this problem was carried out for a project on preparation of a "Coal Conversion Systems Technical Data Book", supported by the U.S. Department of Energy and its predecessors. TEST OF FORMULAS A data bank (including experimental gross calorific values, ultimate analyses, forms of sulfur, and rank) was established, from sample data published by the Coal Research Section of Pennsylvania State University [9] and 681 samples analyzed by the Bureau of Mines [10--13]. The Penn State samples were channel samples from whole seams [14]. The data bank covers all ranks and a wide range of coal fields of the United States. The calorific values ranged from 7900 Btu/lb (18,375 kJ/kg) for a lignite to 15,320 Btu/lb (35,635 kJ/kg) for a medium volatile bituminous coal. Four formulas were selected for testing. They are as follows: Dulong [4]


Q = 145.44 (C) + 620.28 (H) + 40.5 (S) -- 77.54 (O) Boie [15] Q = 151.2 (C) + 499.77 (H) + 45.0 (S) -- 47.7 (O) + 27.0 (N)


Grummel--Davies [4, 16]


I654.3 (H) + 424.62 ] [(C)/3 + (H) -- (O)/8 + (S)/8] (100 -- (A))


Mott--Spooner [4, 17] Q = 144.54 (C) + 610.2 (H) + 40.5 (S) -- 62.46 (O) Q = 144.54 (C) + 610.2 (H) + 40.5 (S) (O) > 15

[ 65.88

(o) < 15%


30.96 (O)

1 (o) (100 -- (A)) J (4b)

In the formulas above, Q is the calculated gross calorific value in Btu/lb on the dry basis and (C), (H), (S), (O), (N), and (A) are the respective contents of carbon, hydrogen, sulfur, oxygen, nitrogen, and ash in weight percent, also on the dry basis. For a fair test of the formulas on samples representing commercial coal we set aside samples with more than 30% ash, leaving a total of 775 out of the original 802 samples. Those remaining consisted of 40 anthracite, 406 bituminous, 180 sub-bituminous, and 149 lignite samples. With a given formula, subtraction of the calculated calorific value from the observed experimental value yields a residual for each sample. Statistics of the residuals were calculated for each rank of coal and also with all ranks pooled, as follows:




(Qi observed -- Qi calculated)

I ~[RMS)2


(Qi observed -- Qi calculated)

R o o t Mean Square (RM8) = Standard Deviation =



(Mean)2]n/( n



1) I ~





where n is the number of samples of a given rank or the total of all ranks, as the case may be. The mean of the residuals is the bias of the calculated values, and these two designations are used interchangeably in this paper. Results from the four formulas are presented in Table 1; the means (column 3) and standard deviations (column 5) give the best description of the sets of residuals; the latter also indicate the results that would be expected if the formulas were modified by a correction term for each rank of coal. We also calculated the standard deviations (column 6) t h a t are obtained if each formula is modified by addition of a single correction term, namely the allranks bias obtained from our data bank. In addition to calculation with the formulas per se, we also calculated calorific values by use of Given and Yarzab's modified Parr equation for mineral matter content, and their corrections to obtain carbon, hydrogen, sulfur, and oxygen on a mineral-matter-free basis [18]. This calculation requires values for pyritic sulfur t h a t were n o t available for some of the samples. Results obtained with the modified Mott--Spooner equations on 646 samples on which pyritic sulfur contents were available are also shown in Table 1; results from other formulas were also improved slightly, but the Mott--Spooner equation gave the best results. Details of this calculation and additional results are reported elsewhere [19]. DEVELOPMENT OF THE DATA BOOK FORMULA The data bank was also subjected to a least squares regression analysis. Carbon, hydrogen, sulfur, ash, and oxygen terms were significant; nitrogen and cross and square terms were not. To reduce to a minimum the required number of determinations, we adopted an oxygen-plus-nitrogen term instead of an oxygen term. The resulting equation, which we refer to here as the Data Book Equation, is as follows: Q = 146.58 (C) + 568.78 (H) + 29.4 (S) -- 6.58 (A) -- 51.53 (O + N)


When 100 -- (C + H + S + A) is substituted for ( 0 + N), an equivalent form is obtained: Q = 198.11 (C) + 620.31 (H) + 80.93 (S) + 44.95 (A) -- 5153


14 TABLE 1 Test o f f o r m u l a s for calculation o f calorific value







Statistics of residuals (Btu/Ib)** No. of samples


Root mean square

Standard deviation With rank Withall-ranks mean mean

40 406 180 149 775

--123 --138 128 175 - - 15

155 221 212 254 223

97 173 170 185 --

144 212 222 265 222

40 406 180 149 775

--400 --248 --207 --298 --256

412 279 249 329 291

100 129 138 138 --

175 129 146 144 139

40 406 180 149 775

80 --128 47 40 - - 44

132 208 167 171 189

106 164 161 167 --

163 184 185 186 183

40 406 180 149 775

- - 56 --134 - - 31 - - 85 - - 96

106 197 151 169 178

91 144 149 147 --

99 149 162 147 150


- - 42




40 406 180 149 775

- - 14 10 13 - - 45 0

93 124 140 137 --

92 123 139 129 --


Dulong Anthracite Bituminous Sub-bituminous Lignite All R a n k s

Boie Anthracite Bituminous Sub-bituminous Lignite All R a n k s

Grummel--Davies Anthracite Bituminous Sub-bituminous Lignite All R a n k s

Mot t--Spooner Anthracite Bituminous Sub-bituminous Lignite All R a n k s

Mo t t--Spoo ner modified Parr basis All r a n k s

N ew formula Anthracite Bituminous Sub-bituminous Lignite All ranks

*Average o b s e r v e d value - - average calculated value = bias o f t h e calculated values. * * 1 B t u / l b = 2.326 kJ/kg.

Results from this new formula

a r e a l s o s h o w n i n T a b l e 1. T h e b i a s f o r d i f -

ferent ranks of coal ranges only from --45 Btu/lb

(105 kJ/kg) on lignite to

13 Btu/lb (30 kJ/kg) on sub-bituminous coal and does not show a trend with r a n k . T h e s t a n d a r d d e v i a t i o n ( o r s t a n d a r d e r r o r o f e s t i m a t e ) is s i g n i f i c a n t l y


less than those of the other unmodified formulas, even after improving these by a bias correction. (Note that eqn. (7) must be modified for use here according to the appropriate loss of degress of freedom caused by evaluation of the coefficients of eqn. (8a)). The new formula has a b o u t the same accuracy as the Mott--Spooner with modified Parr corrections, b u t the latter is more complicated and requires pyritic sulfur determination. The effect of ash content on the accuracy and precision of the formula was investigated, with the results shown in Table 2. For this test, the formula was also applied to the 27 high-ash samples that had been set aside. It is evident that the bias does not show a trend with ash content b u t that the standard deviation does increase with ash content. The increase of the standard deviation with ash content can be attributed to the effects of differing contributions of the mineral matter to determined carbon and hydrogen contents, and differing heats of dehydration and reaction of the mineral matter. A c o m p u t e r analysis of the data in which it was assumed that the variance is linear with ash content indicated that the variance increases by (21.7 Btu/lb) 2 ((50.5 kJ/kg) 2) per percent of ash, and that the standard deviation on ash-free samples is 106 Btu/lb (247 kJ/kg). TABLE 2 E f f e c t o f ash c o n t e n t o n t h e c a l c u l a t i o n o f calorific value with the n e w f o r m u l a Ash c o n t e n t

Number of samples

wt % 0--I0 10--20 20--30 > 30

394 320 61 27


Standard deviation



6 --15 26 20

113 144 141 211

• 1 Btu/lb = 2.326 kJ/kg.

The contribution of pyritic sulfur to the variance was also investigated. A regression analysis was performed in which a term for pyritic sulfur, added to the existing formula, was evaluated. No decrease in standard deviation of the 646 samples having pyritic sulfur values, or of those having 1% or more of pyritic sulfur, was observed when the pyritic sulfur term was added. It is of interest to determine h o w much of the remaining variance, (106 Btu/lb) 2 ((247 kJ/kg)2), can be attributed to the laboratory determinations. The expected variance attributed to these can be estimated according to Var (det) = Var Q + 198.112 Var (C) + 620.312 Var (H)

+ 80.932 Var S + 44.952 Var (A) where V a t Q, V a t (C), etc., are variances of the respective determinations.



Some precision data, reported in the Appendix, have become available from the HYGAS ® program at IGT and can be used for the estimation. When applied in eqn. (9), the standard deviations of the repeatability determinations (after bias corrections) from Table A-1 (in the Appendix) yield the value 64 Btu/lb (151 kJ/kg) as the expected standard deviation of the calculation residuals. This represents 77% of the variance (73 Btu/lb) 2 ((170 kJ/kg)2), found for a large set of HYGAS data discussed later in this paper. However, it represents only 25% of the total variance, (129 Btu/lb) 2 ((300 kJ/kg)2), of the original data set, or 36% of the variance estimated for mineral-matterfree coal. As a source of the remaining variance of the latter, it is possible but unlikely that the repeatability of the data bank determinations is significantly worse than that of IGT determinations. The absence of a trend in bias with rank of the coals (Table 1) indicates that the source of the unaccounted-for variance is not related to rank. The most likely source is the effect of the maceral composition of the coal. TEST AND USES

Data for testing of the new formula were solicited from outside laboratories. Results from three laboratories presented in Table 3 show good precision, but the large bias values suggest the presence of systematic error, or, more likely, t h a t coals from a single mine or region exhibit a characteristic bias. TABLE 3 Tests of new calorific value formula at other laboratories Laboratory


Kind of coal

Bituminous Illinois Basin Sub-bituminous

No. of samples

42 78 40


Standard deviation



--97 68 --50

129 113 90

*1 Btu/lb = 2.326 kJ/kg.

Results from a fourth laboratory illustrate an important use of the formula. The experimental data were obtained over a period of several years and were furnished to us in the sequence in which they were obtained by the laboratory. We eliminated a few samples having more than 35% ash or less than 3% oxygen, because the latter are likely to be chars. On the remaining data, the root mean squares of the residuals obtained from consecutive sets of 50 samples are shown in Fig. 1. On the first 650 samples the mean residual was 32 Btu/lb (74 kJ/kg) and the standard deviation was 136 Btu/lb {316 kJ/kg), in good agreement with our results on the original data bank. On subsequent

17 5OO

z 400



!iii iiiii!i i ¸!

$ w 200

i~ ~i~iliii!

iiiiiiii!i!i ~i~i~i'i) I!!I











.i 800

i 9OO



Fig. 1. Variability of the difference between observed and calculated calorific value in a laboratory.

samples the results indicate a substantial deterioration in laboratory precision. Thus, a control chart of this kind can serve as a monitor of laboratory performance. Also, the difference between observed and calculated heating values on an individual sample can be used by the laboratory supervisor as a criterion of acceptability of the heating value and carbon--hydrogen determinations. The difference is less sensitiveto errors of the sulfur and ash values. Another important use of a heating value formula is in analysis and modeling of coal conversion processes. Data on heating value and composition of samples of coal and char obtained at IGT under the H Y G A S pilot plant program were analyzed for this purpose. In the H Y G A S process, non-agglomerating coals are dried but are not otherwise pretreated. Bituminous coals are pretreated at temperatures of 750 ° to 800°F (400--425°C) to destroy their agglomerating properties. The resulting product is referred to here as "pre-treated coal" rather than "char". Samples referred to as "chars" are from later intermediate gasificationstages or are spent (residue) char. Ash in the spent char from the runs on bituminous coal averaged 36%, but ranged up to about 85%. To augment the data from runs on sub-bituminous and lignite coals, we have added some samples taken from streams that contain feed coal in addition to char, such as the dust collected by a cyclone in the reactor product gas stream. Results are presented in Table 4, together with those obtained on the original data bank. The most important criterion for use of a heating value formula in heat balance calculations (for example, in a computer model) of a coal conversion process is the bias or average difference between observed and calculated values, because it shows h o w closely the formula represents the average properties of the coal. O n the 294 samples of raw (untreated) bituminous coals, the calculated values are, on the average, 18 Btu/Ib (42 kJ/kg) less

18 TABLE 4 Test on HYGAS routine samples of the new formula for calculation of calorific value No. of samples

Bias Standard deviation (Btu/lb) a (Btu/lb) a

294 572

18 157

71 76

105 106 570 781

58 2 28 28

79 106 92 94

49 80 66

--47 15 15

51 57 53

80 44

34 12

77 77

40 406 180 149 775

--14 10 13 --45 0

93 124 140 137 129

H Y G A S Data B a n k B i t u m i n o u s coal b

Raw Pre-treated coal Chars First stage hydrogasification Second stage hydrogasification Spent char All char S u b - b i t u m i n o u s coal c

Coal Chars Mixtures of coal and char Lignite d

Chars Mixtures of coal and char Original Data Bank

Anthacite Bituminous coal Sub-bituminous coal Lignite All samples

a l Btu/lb = 2.326 kJ/kg. b F r o m Illinois No. 6 seam. About 5% of the raw coal samples and 17% of the others were from runs on high-volatile B bituminous coal from Saline County, with the remainder from runs on high-volatile C bituminous coal from Christian County. CFrom the Rosebud Seam, Rosebud County, Montana. d F r o m the Savage Mine, Richland County, Montana.

than the observed values. This differs by only 8 Btu/lb (18.6 kJ/kg) from the value f o u n d on the 406 samples of bituminous coal in the original data bank. The standard error shown for these coal samples is substantially less than was f o u n d on the bituminous coals of the original data bank. The difference may be a result of the limited range of source of the HYGAS samples: all were from the Illinois No. 6 seam and 95% were from a single mine; the ash c o n t e n t averaged 10.7%. On pre-treated bituminous coal the calculated values are, on the average, 157 Btu/lb (365 kJ/kg} lower than the observed values. For better results, a bias correction can be applied or a formula can be obtained by regression analysis of the pre-treated coal data. The difference in bias between the parent and pre-treated coals, 139 Btu/lb (323 kJ/kg), can be attributed to a difference in structure (bonding); the formula has already taken into account

19 differences in elemental composition. Such differences in structure include effects of incorporation of oxygen in a different form from that ordinarily present. In other processes the difference in bias may be greater or less, depending on processing conditions such as temperature and presence or absence of oxygen; in the HYGAS process the difference is reduced to about 40 Btu/lb (93 kJ/kg) at the stage where the temperature reaches a b o u t 1200°F (650°C). The calculated values on all chars from bituminous coals are, on the average, only 28 Btu/lb (65 kJ/kg) less than the observed values; the difference is of a b o u t the same order for chars from sub-bituminous coal and lignite. A more accurate formula could be obtained for the chars from the bituminous coal, b u t the Data Book formula should be adequate for most practical purposes; the accuracy should be judged according to unit weight of coal feed rather than unit weight of char. CONCLUSIONS A new five-term formula for calculating the calorific value of coal from its carbon, hydrogen, sulfur, and ash contents was obtained by regression analysis of data on 775 samples of U.S. coals of all ranks, most of which were analyzed by the U.S. Bureau of Mines. The standard error of estimate of the new formula was 129 Btu/lb (300 kJ/kg), compared with apparent standard errors (root mean squares of differences) ranging from 178 to 229 Btu/lb (414--533 kJ/kg) obtained on the same set of data from the Dulong, Boie, Grummel--Davies, and Mott--Spooner formulas. The bias (average difference of calculated from observed values) of the new formula varied with rank but did not exhibit a trend with rank. The data indicate that there is little hope of obtaining a more accurate formula based on ultimate analysis only. The variance of the results with the new formula was analyzed and the a m o u n t contributed by various sources was estimated. Approximately 32% can be attributed to the effects of the variability of the mineral matter. The variance contributed by variance of the experimental determinations, including that of the calorific value, was estimated from repeatability data obtained in IGT laboratories; if the repeatability of determinations in the laboratories performing the analyses on the 775 samples of our data bank is the same as that at IGT, then the variance from this source accounts for an additional 26%. The remainder, 42%, is attributed to variability of the organic matter unrelated to rank, such as maceral composition. Because the results showed no trend in bias with rank of coal, little if any variance can be attributed to rank-related properties of the coal. Application of the formula to bituminous coal oxidatively pre-treated at 750 ° to 800°F (398°--427°C) to destroy agglomerating properties yields a bias indicating that its heat of formation is higher than expected from elemental and ash contents by a b o u t 140 Btu/lb (325 kJ/kg}; this is attributed to difference in structure (bonding). The formula gives satisfactory results


on higher temperature HYGAS chars, and, with application of a bias correction, on pre-treated coal. The formula is advantageous for use in heat balance calculations on conversion processes and for monitoring test data on coal and char. ACKNOWLEDGEMENT

The work reported here was conducted as part of a project, sponsored by the U.S. Department of Energy, on preparation of a Coal Conversion Systems Technical Data Book. Use of data obtained under the HYGAS program is gratefully acknowledged.

REFERENCES 1 ASTM D 2015, 1981. Gross Calorific Value of Solid Fuel by the Adiabatic Bomb Calorimeter. 1981 Annual Book of ASTM Standards, Part 26, American Society for Testing and Materials, Philadelphia. 2 ASTM D 3286, 1981. Gross Calorific Value of Solid Fuel by the Isothermal-Jacket Bomb Calorimeter. 1981 Annual Book of ASTM Standards, Part 26, American Society for Testing and Materials, Philadelphia. 3 Rossini, F.D., 1950. Chemical Thermodynamics: 46. John Wiley, New York. 4 Selvig, W.A. and Gibson, F.H., 1945. Calorific Value of Coal. In: H.H. Lowry (Editor), Chemistry of Coal Utilization, John Wiley, New York, Vol. 1, p. 139. 5 Subramanian, T.K., 1977. How to calculate Btu values of coal. Coal Age, 82: 153-158. 6 Lloyd, W.G. and Francis, H.E., 1979. Personal communication. 7 Lloyd, W.G. and Davenport, D.A., 1980. Applying thermodynamics to fossil fuels. Journal of Chemical Education, 57 : 56--60. 8 Neavel, R.C., Hippo, E.J., Smith, S.E. and Miller, R.N., 1980. Prepr. Pap. Am. Chem. Soc., Div. Fuel Chem., 25(3): 246--257. 9 Spackman, W. et al., 1976. Evaluation and Development of Special Purposes Coals, Final Report ERDA No. FE-0930-2, NTIS, Springfield, Virginia. 10 Swanson, V.E. et al., 1976. Collection, Chemical Analysis, and Evaluation of Coal Samples in 1975. U.S. Department of the Interior, Geological Survey, Open File Report 76-468, Washington, D.C. 11 Gilmour, E.H. and Dahl, G.G., Jr., 1967. Montana Coal Analyses. Montana Bureau of Mines and Geology, Special Publication 43, Butte, Montana. 12 Glass, G.B., 1975. Analyses and Measured Sections of 54 Wyoming Coal Samples (collected in 1974). Geological Survey of Wyoming Report of Investigation No. 11, Laramie, Wyoming. 13 Sondreal, E.A., Kube, W.R. and Elder, J.L., 1968. Analysis of the Northern Great Plains Province lignites and their ash. U.S. Bureau of Mines Report of Investigation No. 7158, Washington, D.C. 14 Institute of Gas Technology, 1978. Coal Conversion Systems Technical Data Book. U.S. Department of Energy No. HCP/T2286-01, Superintendent of Documents, Washington, D.C. 15 Boie, W., 1953. Fuel technology calculations. Energietechnik, 3: 309--316. 16 Grummel, E.S. and Davies, I.A., 1933. A new method of calculating the calorific value of a fuel from its ultimate analysis. Fuel, 12." 199--203. 17 Mott, R.A. and Spooner, C.E., 1940. The calorific value of carbon in coal. Fuel, 19: 226--231,242--251.

21 18 Given, P. and Yarzab, R.F., 1975. Problems and Solutions in the Use of Coal Analyses. Technical Report No. 1, ERDA No. FE-0390-1, NTIS, Springfield, Virginia. 19 Institute of Gas Technology, 1978. Preparation of a Coal Conversion Systems Technical Data Book. ERDA No. FE-2286-32, NTIS, Springfield, Virginia. 20 ASTM D 2013, 1981. Preparing Coal Samples for Analysis. 1981 Annual Book of ASTM Standards, Part 26, American Society for Testing and Materials, Philadelphia. APPENDIX

Repeatability of Experimental Determinations at IGT Sources o f variance t hat apply t o the problem were considered. The calorific value and th e analytical determinations (carbon, hydrogen, sulfur, and ash) are all run on an analysis sample of coal t hat has been ground finer than No. 60 sieve size [ 2 0 ] . Thus, the variance f r om sampling of the coarse sample s u b mitted to the l a b o r a t o r y is n o t of concern. If the moisture c o n t e n t does n o t change during all o f t he sample withdrawals for the various determinations, no variance is c o n t r i b u t e d by the moisture determination; however, if several days elapse between heating value and c a r b o n - - h y d r o g e n determinations, a c o n t r i b u t i o n f r om this source is likely, either from a change in moisture or f r o m the variance of its redetermination. Variance can also be cont r ib u ted by day-to-day Variations in e q u i p m e n t and operator; thus re-determination on the same day would n o t serve the purpose. Instead, our procedure consisted of re-submitting f r om time to time a n u m b e r of analysis samples o f coal (in the same 4 oz (113 gm) bottles as originally sampled from) for re-determination of moisture, heating value, carbon, hydrogen, sulfur, and ash. Each r e p o r t e d value for carbon, hydrogen, ash, and calorific value is the average o f t w o determinations run at the same time; for sulfur only one TABLE A-1 Summary of IGT repeatability data

Calorific Value

No. of duplicates

Average value





(wt %) 0.037 0.25 0.028 0.051 --0.011 0.084

(Btu/Ib)c Carbon Hydrogen Sulfur

41 41 55

64.07 4.52 4.39

Ash, SO3-free



Standard deviation (o)b

Before bias After bias correction correction




27 0.24 0.051 0.086


aOriginal minus duplicate. bof reported values, each the average of two determinations run at the same time, except single determinations for sulfur. Cl Btu = 2.326 kJ/kg.

22 determination is made. Completion of the duplicate analysis ranged from 9 to 46 days after completion of the original analysis. Slight average changes in values from the original analysis to the duplicate, such as an average decrease in calorific value of 13 Btu/lb (30 kJ/kg), occurred; t h e s t a n d a r d deviations were calculated both with and without correction for this effect. The duplicate differences from this program were examined for outliers. Three sulfur, one ash, and one calorific value, all with differences between duplicates greater than 3.8 X 2 ~ o, were discarded. In addition, a calorific value with a duplicate difference of 2.8 X 2 ~ a, and also having a difference between observed and calculated values of 3.5 a, was discarded. The analysis of the remaining data is presented in Table A-1.