EPA-450/3-77-044 November 1977 PRELIMINARY EVALUATION OF SULFUR VARIABILITY IN LOW-SULFUR COALS FROM SELECTED MINES ~ U.S. ENVIRONMENTAL PROTECTION AGENCY Office of Air and Waste Management Office of Air Quality Planning and Standards Research Triangle Park, North Carolina 27711 ------- EPA-450/3-77-044 PRELIMINARY EVALUATION OF SULFUR VARIABILITY IN LOW-SULFUR COALS FROM SELECTED MINES Prepared l>\ PKDCo Km iionmciilal. I in 11499 Chester Koad (Cincinnati, Ohio 45246 Conliact No. hK-OJ Task \<>. U I'.PA Project Officers: (i ------- This report is issued by the Environmental Protection Agency to report technical data of interest to a limited number of readers. Copies are available free of charge to Federal employees, current contractors and grantees, and nonprofit organizations - in limited quantities - from the Library Services Office (MD-35) , Research Triangle Park, North Carolina 27711; or, for a fee, from the National Technical Information Service, 5285 Port Royal Road, Springfield, Virginia 22161. This report was furnished to the Environmental Protection Agency by PEDCo Environmental, Inc. , Cincinnati, Ohio, in fulfillment of Contract No. 68-02-1312, Task 41. The contents of this report are reproduced herein as received from PEDCo Environmental, Inc. The opinions, findings, and conclusions expressed are those of the author and not necessarily those of the Environmental Protection Agency. Mention of company or product names is not to be considered as an endorsement by the Environmental Protection Agency . Publication No. EPA-450/3-77-044 11 ------- ACKNOWLEDGEMENT A study of this complexity cannot be conducted without the cooperation of many companies and individuals. The project was initiated at a meeting with representatives of four companies: Peabody Coal Company, Consolidation Coal, AMAX Coal Company and Island Creek Coal Sales Company, all of whom supplied data. Individuals at Penelec, Duke Power Company, Tennessee Valley Authority, Virginia Electric Power Company, and Carolina Power and Light also provided data that are included in the study. The cooperation of those who supplied data and reviewed the report is greatly appre- ciated. PEDCo also expresses appreciation to David Kirchgessner and Constancio Miranda, EPA Project Officers, for their active interest in the project: arrangement of meetings, participation in the meetings, and review of the report. In particular we appreciate the contribution by Constancio Miranda of Appendix C to the report. We also appreciate the recommendations and timely suggestions of other members of the Energy Strategies Branch: John Fink and Rayburn Morrison. ------- CONTENTS Page SUMMARY vi 1.0 INTRODUCTION 1-1 2.0 VARIABILITY OF SULFUR IN COAL 2-1 2.1 Background 2-1 2.2 Approach 2-6 3.0 DATA BASE 3-1 4.0 DATA ANALYSIS 4-1 5.0 IMPLICATIONS OF STATISTICAL ANALYSIS 5-1 5.1 Background and Introduction 5-1 5.2 Data Analysis 5-3 5.3 Average Sulfur Content Required 5-7 for Compliance 5.4 Examples 5-19 6.0 CONCLUSIONS AND RECOMMENDATIONS 6-1 7.0 REFERENCES 7-1 APPENDIX A - SELECTED DATA SETS A-l APPENDIX B - METHODS OF DATA ANALYSES B-l APPENDIX C - SULFUR VARIABILITY WITH LOT SIZE C-l APPENDIX D - SELECTED REVIEW COMMENTS D-l iv ------- FIGURES No. Page 2-1 Variation in Pyritic and Organic 2-2 Sulfur Contents of Pittsburgh Seam Coal (West Virginia) 2-2 Hypothetical Distribution of Sulfur 2-3 in 30-Ysar Coal Reserve 4-1 Histogram of Weekly Averages for 4-5 Data Set U-l 4-2 Cumulative Frequency Graph of 4-6 Data Set U-l 4-3 Average Weekly Sulfur Content of Coal 4-8 of Data Set U-l Vs. the Number of the Week 5-1 RSD Vs. Averaging Period/Tons of Coal 5-8 (Days/Hours/Tons) 5-2 Determination of Required Average 5-10 Sulfur Content 5-3 Sulfur Content Vs. Heating Value of 5-13 Coal Required to Yield 1.2 Ib SO-/ MM Btu 5-4 Determination of Required Average Sul- 5-14 fur Content Assuming Lognormal Distri- bution 5-5 Required Average Sulfur Content Vs. 5-18 Sulfur Variability A-l Variation in Sulfur Content, Ib SO / A-3 MM Btu, with Time, Data Set C-2 A-2 Variation in Weekly Average Sulfur A-4 Content, Ib S02/MM Btu A-3 Variation in Sulfur Content, Ib SO / A-6 MM Btu, Vs. Time, Data Set C-3 A-4 Minimum and Maximum Values of Sulfur A-9 Content, Ib SOVMM Btu, for Unit Trains Within One Month, Data Set C-5 A-5 Comparison of Core Data and Run- A-39 of-Mine Data ------- FIGURES (continued) No. Page A-6 Frequency Distribution of One Day A-40 Averages of Weight Percent Sulfur in Coal A-7 Frequency Distribution for Data A-41 Set U-18 B-l Scatter Diagram of a Sample of B-14 Data Set U-l B-2 Relationship of Standard Deviation B-17 to Mean Sulfur Content B-3 Frequency Distribution for Data B-18 Set U-l B-4 Application of Quality Control Chart B-26 to Control Sulfur Variability B-5 Moving Average and Moving Range B-29 Quality Control Charts C-l Hypothetical Example Illustrating C-3 Lot Size Variability C-2 Statistics for Normal Distribution C-4 C-3 Data Set C-2: RSD Vs. Lot Size Tons ' C-8 C-4 Data Set C-2: Variability Effect C-9 on the Mean SO- C-5 RSD of SO vs. Lot Size for Mines 1160, C-10 4186 and 8150 C-6 RSD of SO vs. Lot Size for Mines 4830 C-ll and 5717 C-7 RSD of SO2 vs. Lot Size for NGS Data C-12 C-8 Unit Train and Monthly Variation of C-15 SO-/106 Btu for Data Set C-2 vi ------- TABLES No. Page 2-1 Pertinent Factors in Studying 2-5 Sulfur Variability 3-1 Summary of Data Sources 3-2 4-1 Summary of Sulfur Variability Data 4-2 4-2 Comparison of Average and RSD of 4-3 Sulfur content of Run-of-Mine Coal and Corresponding Core Drilling Samples 4-3 Frequency Tabulation of Weekly 4-4 Weighted Average of Sulfur (Dry Basis) for Data Set U-l 5-1 Expected Values of the Relative Stan- 5-9 dard Deviation of Weight Percent Sulfur Vs. Number of Composite Samples Per Indicated Averaging Period/Tons 5-2 Summary of Compliance Computations 5-17 A-l Minimum, Maximum and Average Sulfur A-43 Weight Percent for Each Data Set B-l Analysis of Variance B-4 B-2 Analysis of Variance for Data Set U-l B-4 B-3 Estimation of Means and Standard B-6 Deviations (Components of Variation) of Sulfur Content B-4 Estimation of Means and Standard B-7 Deviations (Components of Variation) of Sulfur Content (Coals with Less Than 1 Percent Sulfur) B-5 Expected Values and Limiting Values for B-8 Absolute and Relative Standard Devia- tion for Each Component of Variance B-6 Cross-Tabulation of Sulfur and Btu B-13 Contents B-7 Data and Computation of Control Chart B-28 Limits for Moving Average Charts for Sulfur Content C-l Analysis of Data Set C-2 C-7 ------- SUMMARY Data on the variability of sulfur content and heating value of coal were obtained from several coal and utility companies. These data were analyzed to estimate the mean, standard deviation, and the frequency distribution of weight percent sulfur (dry basis) and the impact of this variability on the average sulfur content required for compliance with an emission regulation. Analysis of composite samples of coal from unit trains indicates that the values of weight percent sulfur are skewed to the rightthat is, they tail off slowly at the higher sulfur levels. This finding suggests the use of a skewed distribution such as the logarithmic normal or the inverted gamma distribution in empirical approximations of the frequency distribution of the weight percent sulfur. The data on heating values (Btu/lb) do not appear to be skewed. The ratio of sulfur dioxide emitted per million Btu (Ib SO?/MM Btu) is also skewed because of the dominating influence of the variation of sulfur content. This report indicates that the relative standard deviation (RSD, the ratio of the standard deviation to the mean expressed as a percent) for sulfur content expressed as Ib S02/MM Btu is 1.02 to 1.05 times the RSD for weight percent sulfur. The statistical correlation between sulfur content and heating value was found to be relatively low but sig- nificant in a few cases, and insignificantly different from zero for almost all of the data sets used in this study. In order to assess the implications of sulfur vari- ability in coal for compliance with emission regulations such as those specified in State Implementation Plans (SIP) and New Source Performance Standards (NSPS), the relative standard deviation of weight percent sulfur was estimated viii ------- as a function of the amount of coal sampled and the number of composite samples for the specified averaging period, e.g. 1 week, 1 month.. These RSD's were then used to estimate the average sulfur .content required to yield 95 and 99 percent compliance with the NSPS emission limitation of 1.2 Ib S02/MM Btu. Detailed computations are given for two sizes of power plants, 500 MW and 25 MW* (250 MM Btu/hour, the smallest plant covered by the IJSPS). Based on averaging periods of 1 month (3 hours), the required averages of weight percent sulfur to achieve 95 percent compliance are estimated to be 0.65 and 0.60 (0.52 and 0.49) for the 500-MW and 25-MW plant, respectively. As the percent of compliance increases, the average sulfur content required for compliance decreases and rapidly approaches sulfur levels at which the availability of uncleaned coal that would allow the user to comply with the NSPS would approach zero. A methodology is provided whereby an analyst may substi- tute values of sulfur content variability expressed as an RSD into a computation or use a graph to estimate the average sulfur content, in Ib SO^/MM Btu or weight percent, that is required for compliance with NSPS. Several hypothetical examples are given to illustrate application of the data and methodology. If an analyst cannot obtain data specific to a coal supply, he may use typical or nominal values given in this report. These values may be adjusted upward or down- ward if the variation would be expected to be greater or less than that presented in the summary tables and graphs of this report. Assumes 10,000 Btu/kWh heat rate ------- PRELIMINARY EVALUATION OF SULFUR VARIABILITY IN LOW-SULFUR COALS FROM SELECTED MINES 1.0 INTRODUCTION The primary objectives of this report are (1) to summarize results of a study on sulfur variability in coals and (2) to determine the effect of this variability on com- pliance with Federal emission regulations. Data were ob- tained from coal companies, utility companies, EPA files, and earlier reports. The data do not permit a study of sulfur variability for coals from all mines or seams within a district or region, because the data do not represent a random sample of coals from a geographical area. A back- ground discussion concerning variability of sulfur content is given in Section 2, sources of the data used in this study are reported in Section 3, summary results are pre- sented in Section 4, and implications of the results with respect to compliance with emission regulations are dis- cussed in Section 5. Because the volume of data used in the study is too large to include in the report, selected data summaries are given in Appendix A. These data were analyzed by standard statistical methods, described in Appendix B. A possible application of a quality control technique is described in Appendix B.4. Appendix C presents an analysis of the variability of sulfur content as a function of the tonnage of coal sampled. Appendix D gives some comments of reviewers with respect to practical applications of the methods presented herein. 1-1 ------- One of the primary objectives of this study is to assess the effect of the variability of sulfur content of coals on compliance with the Federal New Source Performance Standard (NSPS) limiting the emissions of sulfur dioxide from coal-fired steam-generating units. The pertinent portion of this standard follows: The provisions of this subpart are applicable to each fossil fuel-fired steam generating unit of more than 63 million kcal per hour heat input (250 million Btu per hour), which is the affected facility. Any change to an existing fossil fuel-fired steam gener- ating unit to accomodate the use of combustible mate- rials, other than fossil fuel as defined in this sub- part, shall not bring that unit under the applicability of this subpart. On and after the date on which the performance test required to be conducted by Part 60.8 of the Federal Register is completed, no owner or operator subject to the provisions of this subpart shall cause to be discharged into the atmosphere from any affected facility any gases which contain sulfur dioxide in excess of 2.2 g per million cal heat input (1.2 Ib per million Btu) derived from solid fossil fuel.* The essence of this report consists of the methodology presented in Section 5 and use of the tables and graphs of that section in analysis of the effect of sulfur variability on compliance with emission regulations. Several examples are given to demonstrate application of the results. The user is in no way restricted to the data given in this report. To the extent possible, the user should obtain data on variability of sulfur content of specific coal supplies under consideration; the user can then apply the appropriate methodology in Section 5. The scope of this study does not include determination of how the emission regulations will affect the sale and utilization of coals; the attempt here is to provide the information needed for such a determination. Code of Federal Regulations 40, Protection of the Environment, Parts 60, §60.40 and 60.43 (a) (2), (July 1, 1975, page 743.) 1-2 ------- 2.0 VARIABILITY OF SULFUR IN COAL 2.1 BACKGROUND The sulfur content of coal occurs as the mineral pyrite, as organically sound sulfur, and in trace amounts as sulfate sulfur. The ratio of organically bound sulfur to inorganic sulfur varies widely from coal seam to coal seam, from mine to mine operating in the same seam and to a lesser extent within the same mining complex. An example of the seam variability is shown in the data displayed in Figure 2-1 for Pittsburgh seam (West Virginia) coal. The range of organic sulfur is between 1.0 and 2.92 percent by weight, with a mean and standard deviation of 1.62 and 0.52 percent, respectively. The pyritic sulfur content of these same coals ranges from 0.87 to 4.69 per- cent, with a mean and standard deviation of 2.07 and 0.95 percent, respectively. In midwestern coals, the organic sulfur content is higher on the average than in eastern coals; however, the organic sulfur occurs in a relatively narrow range of con- centrations as compared with the pyritic sulfur in these coals. In most western coals the pyritic sulfur content is extremely low, and therefore little or no reduction in the total sulfur content is achieved by present economical cleaning processes; although in some cases the reduction in sulfur content of western coals would be sufficient to upgrade the coal to NSPS. In a specific coal reserve, the distribution of total sulfur may occur as shown hypothetically in Figure 2-2, which identifies iso-sulfur contours. The range of sulfur content shown is from 1 to 5 percent. If this reserve were mined by surface or strip mining, the variability of sulfur content from month to month or year to year would 2-1 ------- I to a ORGANIC SULFUR o PYRITIC SULFUR 2.0 2.5 3.0 3.5 PERCENT SULFUR BY HEIGHT Figure 2-1. Variation in pyritic and organic sulfur contents of Pittsburgh seam coal (West Virginia). ------- Figure 2-2. Hypothetical distribution of percent sulfur in 30-year coal reserve. 2-3 ------- be significant, since a single large stripping machine is usually operated along a designated path. In deep mining, however, a number of mining machines operate in different sections of the reserve, generally advancing at a constant rate. Variability of sulfur content of the mined product on a daily basis would be higher than the variability of the average sulfur content on a monthly or annual basis. The daily variability would reflect the in-seam variability, the number of machines operating, the type of deep mining and the relative productivity of these machines. Study of sulfur content of coals requires consideration of a number of variables such as those summarized in Table 2-1. Many of these factors are interrelated. For example, the measured differences in sulfur content can reflect not only differences in the coal in the mine or differences in the mining method, but also differences in the methods of sampling, averaging, and measurement. Variability of sulfur content can be determined on the basis of (1) individual samples, e.g., one composite sample taken from each unit train (60 to 100 cars or 6,000 to 10,000 tons) by the Standard ASTM Method and/or (2) weighted averages of these individual samples, corresponding to weekly or monthly averages of coal as received at a utility plant. The four coal companies providing coal data for this study use this ASTM method. The data on sulfur variability can then be used in determining the required average sulfur content of the coal for the user to comply with a given regulation. ?-- ------- Table 2-1 PERTINENT FACTORS IN STUDYING SULFUR VARIABILITY 1. Type of coal Organic and inorganic sulfur content. Distribution of sulfur in coal (coarse pyrite or finely disseminated throughout the coal). The form in which the sulfur occurs is significant when the coal is washed. 2. Stage of sampling Core drilling (or channel samples after operation), Run-of-mine production. After preparation, cleaning. As received at utility plant/consumer. As burned. 3. Coal blending and processing 4. Mining plan (selective) 5. Mining technique Number and location of machines, type of mining 6. Location of coal Seam. Mine. Region or district. 7. Averaging times/tonnages Daily. Weekly. Monthly. Other. 8. Sampling procedure Amount of coal sampled. How the sample is formed as a composite of a large amount of coal. Sample variation. 9. Analytical method 10. Cleaning technique 2-5 ------- Variability in sulfur content and heating value of coals could be associated with each of the factors listed in Table 2-1. A detailed analysis would not be practical, however, in view of the large number of factors and their interdependence. Even though some of this information is available in the records of operating mines and steam plants, the cost of assembling and analyzing the data would be prohibitive. 2.2 APPROACH The approach used in this study was to obtain data on sulfur contents and heating values of coal from several sources and to analyze these data by standard statistical techniques to obtain the following summary information: 1. Averages of sulfur content (weight percent sul- fur) , heating value (Btu/lb), and sulfur emissions (Ib SOp/MM Btu) over different averaging times (per unit train, weekly, monthly, etc.). 2. Standard deviations of weight percent sulfur, Btu/lb, and Ib S02/MM Btu. a. Among individual samples from unit trains. b. Within and among weekly averages. c. Within and among monthly averages. 3. Frequency distribution of weight percent sulfur, Btu/lb, and Ib SO2/MM Btu a. Histograms of data. b. Cumulative frequency distribution. Depending upon the particular data set, one or more of these analyses was conducted for each summary statistic. No attempt was made to obtain random samples of coals from different mines and seams in a given region or district, even though this approach was considered early in the study. 2-6 ------- Because data sources do not coincide with a region or district, inferences cannot be made with respect to the overall variability of all coals in a sampled region. The results are nonetheless useful in assessing the impact of variability of sulfur content on compliance with emission regulations. It would be desirable to know the long-term variability of sulfur content because compliance with emission control regulations is required for the life of the plant. None of the data, however, extend over a long enough period to permit estimation of long-term variability. No attempt was made to isolate the variation in measured sulfur content that is due to the analytical measurement. With respect to coals containing less than 2 weight percent sulfur, one study indicates that the analytical reproduci- bility (the differences between two or more determinations carried out by different laboratories on representative samples taken from the same bulk sample) should be within 0.10 percent in absolute terms. For example, if the mean sulfur content were 0.70 weight percent, the values measured by different laboratories should fall within an interval of 0.65 to 0.75 weight percent. Reference 4 and Appendix B.I.3 provide further details of the analytical method and its precision. 2-7 ------- 3.0 DATA BASE The data base is comprised of 35 data sets. Table 3-1 lists the data sets with comments on each; the sets aro numbered serially with a prefix U or C to denote utility or coal company as the source. All of the sets represent coals mined in recent years (1974, 1975 and 1976), and the sulfur measurements reflect either core samples or composite samples from unit trains. A composite sample may represent 1,000 to 20,000 tons of coal. Of the 35 data sets, 13 were supplied by coal companies in voluntary support of this study; 8 (U-14 thru U-21) were taken from a published report on the Navajo Generating Station; and 1 (U-22) was extracted from Federal Power Commission reports (FPC Form 423) of utility coal purchases. U-22 deals with coal purchased from coal districts 3, 7, and 8, for which the mean emission level of all purchases by a specific plant was less than 1.2 Ib S02/MM Btu (the NSPS limit). A statistical summary of all data sets is given in Section 4, Table 4-1. More detailed statistical summaries are given in Appendix A. 3-1 ------- Table 3-1. SUMMARY OF DATA SOURCES Source of data Comments Coal companies Appalachian coals Data Set C-l Data Set C-2 Data Set C-3 Other coals Data Set C-4 Northern W VA, deep mines, 1972-76. Two- mine operation, crushed to 2 inches, Bradford breaker, shipped to one plant. Raw coal, as loaded, seven continuous and one long wall miners. 702 samples each representing an average of about 12,000 tons of coal. Kentucky, deep mine, 1975. Coal was cleaned at the mine using a jig washer in which the total raw coal stream was cleaned. This is a relatively simple cleaning operation in an older cleaning plant. Sampling of coal was done at the utility plant, 115 samples, each repre- senting about 5600 tons. Kentucky, deep mine, 1975. Coal was cleaned in a modern cleaning plant. The +l/4-inch coal was cleaned in a heavy media vessel, the -1/4-inch coal on a deister table. Filter cake -28M was re- jected. 157 samples, each representing about 2500 tons, shipped to one plant. Montana, 1975-76. Two-seam operation with blending of each seam or possible loading of each seam separately. This depends entirely upon the mining 3-2 ------- Table 3-1. (continued) Source of data Comments Data Set C-5 Data Set C-6 Data Set C-7 Data Set C-8 Data Set C-9 Data Set C-10 Data Set C-ll operation and geological factors. Raw coal shipments, no cleaning. 370 samples, each representing about 10,000 tons, shipped to one plant. Arizona, 1974-1976. Multiple seam operation with all or part of the seams loaded simultaneously. Raw coal ship- ments with the as-mined coal passing through a Bradford breaker to remove large rock. No further cleaning. 316 samples, each representing about 3000 tons, shipped to one plant. Montana, Core data for one seam of data set C-4, raw coal, 72 cores. Montana, Core data for other seam of data set C-4, raw coal, 110 cores. SE Ohio, Deep mine, 1973-76. One mine operation crushed to 4 inches, no picking, shipped to one plant. ASTM sampling and analysis as loaded. Raw coal, 8 con- tinuous miners, 272 samples, each repre- senting about 10,000 tons. Western PA, Upper Freeport Seam. data, raw coal. Core Central Utah Coal Reserve, I & J Seams. Core data, bottom bench, raw coal. Central Utah Coal Reserve, I & J Seams. Core data, top bench, raw coal. (continued) 3-3 ------- Table 3-1. (continued) Source of data Comments Data Set C-12 Data Set C-13 Utility companies: Appalachian coals Data Set U-l Data Set U-2 Data Set U-3 Data Set U-4 Data Set U-5 SE Ohio, Seams 8 and 9. Raw, strip mining coal, 3 large shovels. ASTM sampling and analysis as loaded. (559 samples, each representing about 10,000 tons.) Wyoming. Core data, raw coal. 140 cores, raw coal. As received at one plant, coal as-burned, 103 weekly averages, 721 samples each representing about 5700 tons of coal. 1973-1975. Eastern KY, 1972-1975. Raw coal, as received at one plant. Sampling and analysis at plant, ASTM procedure. 312 samples each representing about 11,000 tons. Eastern Kentucky, 1972-1975. Raw coal, same coal as above, sampling as burned. 103 samples, each representing about 40,000 tons. Eastern Kentucky, 1974-1976. Raw coal, as received at one plant. Modified ASTM sampling at plant. 162 samples each representing about 12,000 tons. Eastern Kentucky, 1974-1976. Raw coal, as received at one plant. Modified ASTM sampling at plant. 250 samples each representing about 13,000 tons. (continued) 3-4 ------- Table 3-1. (continued] Source of data Comments Data Set U-6 Data Set U-7 Data Set U-8 Data Set U-9 Data Set U-10 Data Sets U-ll, and U-13 Other Coals Data Set U-14 Data Set U-15 West Virginia, District 7, 1975-1976. As received at one plant. 90 samples each representing about 2500 tons. West Virginia, District 7, 1974. As received at one plant. 120 samples, each representing about 1800 tons. West Virginia, District 7, 1974. As received at one plant. 61 samples, each representing about 1000 tons. West Virginia, District 7, 1974. As received at one plant. 74 samples, each representing about 1500 tons. West Virginia, 1975. As received from one supplier for one plant. Hand sampled in part, ASTM for almost all samples. 50 samples each representing about 20 cars on the average. Pennsylvania coal, 1975. Run-of-mine coal, U-12 receives sizing operation in a Bradford breaker which reduces the coal to 1 1/4-inch maximum while removing some shale in the process. Magnetic pulley removes any tramp iron in the raw coal stream. All three data sets - single mine operation. Raw coal. About 250 samples each representing about 4000 to 12000 tons. Arizona, Core data. 82 core samples, raw coal. Arizona, Core data. 83 core samples, raw coal. (continued) 3-5 ------- Source of data Comments Data Set U-16 Data Set U-17 Data Set U-18 Data Set U-19 Data Set U-20 Data Set U-21 Data Set U-22 Arizona, Core data. 395 core samples, raw coal. Arizona, Core data. 132 core samples, raw coal. Arizona, As received data corresponding to U-14. 770 samples. Arizona, As received data corresponding to U-15. 113 samples. Arizona, As received data corresponding to U-16. 768 samples. Arizona, As received data. 1766 samples. Districts 3, 7, and 8 purchases by utilities during 1974 and 1975. FPC form 423 data. 63 samples, each representing all purchases for which the mean Ib S02/MM Btu for one plant was less than 1.2. Data sets U-14 through U-21 are described in greater detail in reference 1. 3-6 ------- 4.0 DATA ANALYSIS The methods of data analysis are described in Appendix B, except for some standard methods that are given in c f: *j statistical texts. ' ' The data sets are presented in Appendix A, with results of pertinent analyses. This section summarizes the results of the analyses. Table 4-1 summarizes sulfur variability data by data set. The arithmetic mean (or average) and the standard deviation of the measurements of sulfur content are given in columns 2 and 3. The relative standard deviation* (RSD) is the ratio of the standard deviation to the mean, expressed as a percentage, and is given in column 4. For example, for Data Set C-5, the mean is 0.42, the standard deviation is 0.048, and the RSD is 11.5 percent. There is a preference for using the RSD's when the standard deviation depends on the average concentration. Comparison of the RSD's for the core data with those of the run-of-mine data indicates clearly that the core data show larger variations by factors ranging from 1^ to 4, as illustrated in Table 4-2. This is an expected result; the core sample repre- sents a very small amount of coal relative to a composite sample from a unit train of several thousand tons. Similar analyses were performed with respect to heating value or Btu content. It is readily apparent that the RSD of Btu content is much smaller, 2 to 5 percent, than that for sulfur content which is 5 to 25 percent. *The RSD is also referred to as the coefficient of variation, 4-1 ------- I ro Data set C-l C-2 C-3 C-4 C-5 C-6 C-7 C-8 C-9 C-10 C-ll C-12 C-13 U-l U-2 U-3 U-4 U-5 U-6 U-7 U-8 U-9 U-10 U-ll U-12 U-13 U-14 U-15 U-16 U-17 U-18 U-19 U-20 U-21 0-22 Weight percent sulfur Average 2.30 0.60 0.81 1.38 0.42 Standard deviation 0.224 0.030 0.088 0.253 0.049 2.14 0.705 1.50 2.60 1.G3 0.58 0. 88 3.42 0.58 0.74 0.88 0.82 1.04 0.93 0.79 0.80 0.84 0.81 1.74 3. 10 2.25 2.15 0.49 0.53 0.68 0.66 0.37 0.46 0.60 0.55 0.405 0.130 0.780 0.247 0.535 1). 344 0.090 0.129 0.103 0.160 0.180 0.170 0.150 0.170 0.220 0.160 0.59 0.366 0.157 0.152 0.195 0.164 0.180 0.180 0.035 0.055 0.092 0.086 RSDa of variation, % 8.0 5.0 10.9 18.3 11.7 33.0 27.0 5.0 47.8 42.6 60.7 10.1 15.5 17.4 11.7 19.5 17.3 18.3 19.0 21.3 26.2 19.8 33.9 11.8 7.0 7.1 39.8 30.9 26.5 27.3 9.5 12.0 15.3 15.6 Btu/lb Average 13,050 Standard deviation 224 RSD of variation, % 1.7 12,310 161 ! 1.3 12,250 276 ' 2.3 11,540 263 2.3 12,150 , 197 1.6 11,540 i 291 2.5 11,480 283 2.5 12,480 708 5.7 14,190 142 1.0 13,170 332 2.5 12, 700 291 . 2.3 12,000 160 , 1.3 11,970 191 1.6 12,500 250 2.0 12,000 250 2.1 11,000 210 1.9 12,000 11,900 11,800 12,300 12,200 12,000 12,070 11,030 11,770 11,480 280 , 2.3 280 ', 2.4 400 3.4 488 4.0 636 5.2 665 5. 5 382 \ 3.2 332 ! 3.0 251 267 2.1 2. 3 Ib SO2/MM Btu Average 4. 21 0.93 1.26& 2. 34 0.65b 3.52b 2.48b 4.08 2.25 0.88 1. 39 5.69 0.95 1.16 1. 39b 1.42b 1.73 1.55 1. 34 1.29 1.37 1 . 35 2.83 5. 34b 3.36b 3.56b 1.03C Standard deviation 0. 34 0.07 0. 14 0.43 0.08 1.20 0.67 0. 30 1.08 0.38 0.86 0.59 0.15 0.21 0.17 0.28 0.23 0.18 0.27 0.28 0. 34 0. 27 0.96 0.65 0.25 0.27 0.16 RSD of variation, % 8.1 7.1 11.1 Core data 18.4 i 33.1 27.1 7.6 47.8 42.7 60. 7 10.4 15.6 17.5 11.9 19.6 16.2 11.6 20.1 21.7 26.7 20.0 34.1 12.2 7.4 7.6 15.8 yes yes yes yes yes yes yes yes yes yes RSD (relative standard deviation) is the ratio of the standard deviation to the average, multiplied by 100 to yield the standard deviation as a percent of the average. Estimated from weight percent sulfur and Btu/lb data, not by direct computation. Positive square root of pooled variance estimates, coals purchased in Districts 3, 7, and 8, for which the mean or average sulfur content is less than 1.2 Ib SO2/MM Btu. ------- Analysis of sulfur content in Ib S02/MM Btu was performed by two methods: 1. Using Ib S02 computed by multiplying weight per- cent by 1.90 (Ib SC>2 emitted per Ib sulfur in coal), dividing by the Btu content, and expressing the results in Ib S02/MM Btu. 2. By direct use of results from analysis of weight percent sulfur and Btu/lb. In case 2, the RSD of Ib S02/MM Btu is given by the ap- proximation, square root of the sum of squares of the RDS's of weight percent sulfur and Btu content. See Appendix B.I.5 for the explanation of this method. Also in case 2, the average Ib SC^/MM Btu is given by the quotient of the corresponding average of weight percent sulfur x 1.90 by average Btu/lb x 10~ . Table 4-2. COMPARISON OF AVERAGE AND RSD OF SULFUR CONTENT OF RUN-OF-MINE COAL AND CORRESPONDING CORE DRILLING SAMPLES Run-of-mine data Data set C-4 U-18 U-19 U-20 x 1.38 0.37 0.46 0.60 RSD, % 18.3 9.5 12.0 15.3 Core drilling data Data set /C-6 \C-7 U-14 U-15 U-16 x 2.14 1.50 0.49 0.53 0.68 RSD, % 33 27 39.8 30.9 26.5 Standard frequency tabulations were made of almost all the data sets with low sulfur content, less than or equal to 1 percent. The tabulation for Data Set U-l is given in Table 4-3. A histogram and a cumulative frequency distribution are given for these same data in Figures 4-1 and 4-2, respectively. The cumulative frequency is plotted on logarithmic normal probability paper because the data 4-3 ------- Table 4-3. FREQUENCY TABULATION OF WEEKLY WEIGHTED AVERAGE OF SULFUR (DRY BASIS) FOR DATA SET U-l3 Weighted average, % 0.62 - 0.64 - 0.66 - 0.68 - 0.70 - 0.72 - 0.74 - 0.76 - 0.78 - 0.80 - 0.82 - 0.84 - 0.86 - 0.38 - 0.90 - 0.92 - 0.94 - 0.96 - 0.98 - 0.63 0.65 0.67 0.69 0.71 0.73 0.75 0.77 0.79 0.81 0.83 0.85 0.87 0.89 0.91 0.93 0.95 0.97 0.99 Frequency 1 6 5 14 21 13 6 11 8 3 2 4 1 4 0 1 1 1 1 x = 0.742 s = 0.0732 Each weekly weighted average is a weighted average of the seven daily measurements of weight percent sulfur for a composite sample from an average of about 5700 tons of coal, 4-4 ------- 0.575 0.655 0.735 0.815 0.895 0.975 WEIGHT PERCENT SULFUR Figure 4-1. Histogram of weekly averages for data set U-l, 4-5 ------- 2.0 ex: UJ 1.0 0.90 0.80 0.70 0.60 0.50 I I 12 5 10 20 30 40 50 60 70 80 90 95 98 99 PERCENT OF AVERAGES AT OR BELOW CORRESPONDING ORDINATE Figure 4-2. Cumulative frequency graph of data set U-l ------- are skewed toward the high values. This skewing is obvious upon examination of the histogram in Figure 4-1, which shows tail-off of the data at the higher values of weight percent sulfur. Reference 1 discusses this point in considerable detail and suggests the inverted gamma fre- quency distribution. The lognormal is another good empir- ical approximation, which is more convenient than the inverted gamma and gives results that are identical for all practical purposes. Rational explanations for the logarithmic normal distribution are given in statistical literature. One other graphical analysis that is useful in inter- preting the variability of sulfur content in coal is a time series plot of the sulfur measurements by unit train and by weekly average, as shown in Figure 4-3 for Data Set U-l. This plot allows comparison of short-term variation (week-to-week) and a 4-week moving average. The definite tendency is for the values of successive weeks to be closer than those that are more separated in time (that is, a greater correlation among the weight percent sulfur values with a short time lag). No sophisticated time series analyses were conducted because the time increments between unit train samples are not typically the same within data sets. Data set U-l is unique in this respect in that there is one data value for each day. Several analyses were made of the correlation between the sulfur and Btu contents of the coal; these were done by a combination of cross-tabulation and computation of the correlation coefficient. Results are given in Appen- dix A (cross-tabulations) and Appendix B (for Data Set U-l) . 4-7 ------- 1.00 4 WEEK MOVING AVERAGE MEAN VALUE * 0.742 0.60 25 30 MUMKR OF WEEK Figure 4-3. Average weekly sulfur content of coal of data set U-l vs. the number of the week. ------- 5.0 IMPLICATIONS OF STATISTICAL ANALYSIS 5.1 BACKGROUND AND INTRODUCTION The purpose of this section is to provide a methodology for estimating the impact of the variability of sulfur as a function of the tons (e.g., per 3 hours) and/or the number of composite samples analyzed and averaged (per week, month, etc.) on determination of compliance with SIP or NSPS emission regulations. Since the impact will be similar for both types of regulations, only NSPS compliance is considered here. (An example is given for a regulation other than NSPS.) THE NSPS 1.2 Ib SO-/MM Btu, is stated as a maximum value never to be exceeded. A legal interpretation of the NSPS would require that at no instant of time would the value 1.2 be exceeded. An interpretation of the NSPS based on a continuous monitoring procedure is that the maximum 3-hour average should not exceed 1.2 Ib SO-/MM Btu. A typical plant of 500 MW capacity will burn about 600 tons of coal in three hours. The smallest plant covered by the NSPS, 25 MW, will burn about 33 tons of coal in 3 hours. Although no data sets in this study contain samples that represent an amount of coal as small as either 600 or 33 tons, data set C-12 and other selected data sets provide statistical evidence of a trend toward smaller RSD's as the quantity (tons) of coal sampled increases. (See Appendix C for a detailed discussion of this relationship.) This tendency is consistent with that 5-1 ------- expected from the standpoint of a physical explanation of the sampling process (see ASTM procedure ). The .avail- able data are extrapolated to yield a reasonable estimate of the RSD as a function of quantity of coal sampled in order to estimate the impact of the variability in sulfur content on compliance with NSPS. It will be more difficult for a small plant to comply with the NSPS, on the assump- tion that the coal burned during each 3-hour period will vary more in sulfur content than will that burned at a typical 500-MW plant. This problem is discussed further in Section 5.2. If the interpretation of NSPS involved a longer period, such as 1 week or 1 month, and if several composite samples were analyzed and the results averaged for the longer period of compliance, then the impacts on compliance with NSPS can be estimated by use of the data and methods presented in this section. Compliance in this case would be determined by averaging, for example, all the composite analyses of sulfur content for the specified period, say 1 month. If this average is less than some specified value, such as 1.2 Ib S02/MM Btu, one would infer that the coal would provide compliance. In this case, the variability of the average depends on (1) the amount of coal represented by each composite sample and (2) the number of composite samples averaged during the specified period. The results will vary less as either the tonnage and/or the number of samples increases. The smaller plants are expected to receive smaller quantities per sample as well as fewer samples per month, and hence, the averages for a specified period of 1 month will vary more than those of a larger plant. A methodology is presented wherby an analyst or 5-2 ------- company may use estimates of the RSD based on computations with available data or perhaps by computer simulation models to yield a measure of the likelihood of compliance with NSPS or other emission regulations. As an illustration of the determination of the impact of sulfur variability on compliance with the NSPS, consider the following example. A typical 500-MW plant uses 600 tons of coal per 3 hours, 4800 tons per day, and receives coal four times per week (four unit trains), averaging 8400 tons each delivery. Thus 16 composite samples are analyzed for Ib S02/MM Btu averaged for 1 month. If this monthly average is used as a basis for compliance, what is the expected frequency with which the average exceeds 1.2 Ib SC>2/MM Btu? What is the average required sulfur content (weight percent) that will enable compliance with the regulation assuming that variability is (1) as estimated in this study and (2) as estimated from data available to the company? Although NSPS does not legally permit a single value to exceed a standard, in practice it is necessary to admit noncompliance for some minimal number or percentage of cases (averaging periods). The percentage of noncompliance can be maintained at a small value that will provide a reasonable trade-off between availability of coals (costs) and average emission levels. Several hypothetical examples are posed at the end of this section to illustrate use of the methodology. 5.2 DATA ANALYSIS Analyses were performed on the data to (1) relate the variability of sulfur content to the amount (tonnage) of the coal from which the composite sample was taken and/or the number of composite samples used in obtaining the 5-3 ------- average, (2) estimate the form of the frequency distribution of the individual analyses of composite samples from unit trains, and (3) estimate the impact of sulfur-content varia- bility on the determination of compliance with emission regulations. Appendix B.I.2 presents a brief description of the statistical methods and a summary of the means and the estimates of the standard deviations of the several sources of variation corresponding to the number of composite samples analyzed and averaged during one week, month, etc. All of these analyses were performed using the data in their ori- ginal scale, that is, with no transformations. Logarithmic transformations are often used to stabilize the variance if the standard deviation in the original scale varies directly as the mean (see Figure B-2). In several analyses essen- tially the same result was obtained with and without the transformation. It can be readily established that the standard deviation of In x is approximately equal to the RSD of x. Thus the use of RSD's results in a stabilization of the variance in situations where the logarithmic transfor- mations are indicated. The RSD's are also more useful for making comparisons in the study of the variability of sulfur in coal. At the bottom of Table B-5 are given the weighted average or pooled standard deviations and the average relative standard deviations. These are typical values that might occur for a particular application. The coals repre- sented in this table have had different degrees of preparation and cleaning and have been mined by different techniques. If one knows that the mining and processing techniques of a given operation will provide a coal of less (or greater) variation in sulfur content than the average, then the lower (or upper) limits in Table B-6 might be used, as 5-4 ------- described in Appendix B.I.3. NOTE; It is emphasized that the values are based on a collection of coal data made available by selected companies. Each company using the approach presented herein is urged to use its own data in estimating the variability of sulfur content for specified averaging times or tonnages. As stated earlier, the data for estimating sulfur variability are based on analyses of composite samples from unit trains in quantities ranging from about 1,000 tons to 20,000 tons; none of the data extended to the range of 33 tons or 600 tons, as required to estimate the impact of variability on compliance in a 3-hour averaging time for either a small plant or an average plant. Thus, an attempt is made to extrapolate the available data to smaller amounts of coal (in tons) by use of specific data sets as a basis for obtaining a relationship between the relative standard deviation and the amount of coal sampled. For the region of extrapolation, this relationship is assumed to be linear in the logarithm of the amount of coal sampled in tons, i.e., the RSD is given by RSD = a + b log,0T (Equation 5-1) where RSD = relative standard deviation of weight percent sulfur, T = tons of coal sampled, log,QT = log of T, base 10 (common logarithms), and a,b = constants to be determined by the data. Data set C-12, gives the following results for the relative standard deviation as a function of the amount of coal sampled. 5-5 ------- Weight percent sulfur Amount of coal sampled, tons 2,000 10,000 Minimum 1.76 2.54 Maximum 5.04 4.34 Mean, X 3-. 42 3.42 Standard deviation, 0.4251 0.3436 RSD = s s/X 0.1243 0.1005 Using these data and equation 5-1, one obtains 0.1005 = a + b log1Q10,000 0.1243 = a + b Iog1()2,000, and hence, upon solving for a and b, a = 0.237 b 0.0341, and RSD = 0.289 - 0.0341 log1()T. For this particular coal (Data Set C-12) the RSD is slightly smaller than the average for all of the coal data analyzed; hence, the value of RSD was adjusted by increasing the constant term, a, from 0.237 to 0.289. Thus the final equation for RSD , i.e., the predicted RSD, is RSD = 0.289 - 0.0341 log1QT. (Equation 5-2) Because this equation is based on a small amount of data, it is desirable to extrapolate the result to the extreme, comparable to a core sample representing, say, 50 pounds of coal. For T = 50/2000 = 0.0250, RSD = 0.289 - 0.0341(log 0.025) = 0.344, which is consistent with the core sample data. That is, in Table 4-1 the RSD's for core sample data (indicated by a yes in the last column) range from 26 to 48 percent and one value is at 61 percent. Thus, the 34 percent value is a reasonable extrapolation of the results. 5-6 ------- These results are given in Table 5-1 above the dashed line for a 25-MW plant (33 tons of coal burned in 3 hours) and below the dashed line for a 500-MW plant (600 tons of coal burned in 3 hours, 4800 tons per day, 4 unit trains per week, 16 sample results averaged per month). Figure 5-1 also shows the impacts on the RSD of the weight percent sulfur of the amount of coal represented by a composite sample and/or the number of sample results averaged during the specified averaging period. The extrapolation to 33 tons for the 25-MW plant is shown by a dashed line. At the extreme right-hand portion of the curve it is desired that the RSD tend to zero as the averaging time approaches the life of the typical mine, say 20 years. The RSD for the left-hand portion of the curve approaches that of core samples. Hence, the two ends of the curve in Figure 5-1 are reasonably well determined, as are some of the central portions, particularly for the amount of coal represented by one unit train and for averages of results of 16 composite samples per month. 5.3 AVERAGE SULFUR CONTENT REQUIRED FOR COMPLIANCE Computation of the average sulfur content required for compliance with the 1.2 Ib SO /MM Btu regulation is based on appropriate assumptions concerning the frequency distribution of the data. The computations assume a typical 500-MW plant or 25-MW plant, as indicated. 5.3.1 Averaging Period of One Month, Assuming Normality, 500-MW Plant Let m be the mean required sulfur content, then for 16 samples per month, RSD = 0.069 for weight percent sulfur, Table 5-1. It is assumed that the RSD for Ib S02/MM Btu = 1.05 x RSD for weight percent sulfur. See Appendix B.I.5 5-7 ------- I 00 » in 0.24 0.20 0.16 0.12 0.08 0.04 48 33 TONS (3 HOURS FOR -THE 25 MM PLANT) 480 TONS OF COAL 4800 48,000 480,000 4.8 x 10" 600 TONS (3 HOURS FOR 500 MM PLANT) Q*V REGION OF EXTRAPOLATION -4800 TONS (1 DAY FOR 500 MM PLANT) -8400 (1 UNIT TRAIN FOR 500 MH PLANT) AVERAGING PERIOD 3 HOURS 1 DAY 7 (500 MM) AVERAGING PERIOD/TONS OF COAL (DAYS/HOURS/TONS) 30 90 180 360 Figure 5-1. RSD versus averaging period/tons of coal (days/hours/tons) ------- Table 5-1. EXPECTED VALUES OF THE RELATIVE STANDARD DEVIATION3 OF WEIGHT PERCENT SULFUR VS. NUMBER OF COMPOSITE SAMPLES PER INDICATED AVERAGING PERIOD/TONS . (Based on data for coals with 1.0 percent sulfur or less) Averaging period/ (tons) 3 hours/ 33 tons, 25 MW plant 3 hours/ 600 tons, 500 MW plant Among unit trains (composite samples of 8400 tons, 500 MW plant) Weekly averages n= 2C Monthly averages 11.7% Quarterly averages 6.8% Semiannual averages 4.8% Annual averages 3.4% Expected variation 23.7% 19.4% 15.5% w=l w=2 w = 15.5% 14.2% 12 n = 4 n=8 n = 9.3% 7.8% 6. 5.4% 4.5% 4. 3.8% 3.2% 2. 2.7% 2.3% 2. (RSD) 4 w = .3% 11 16 n = 9% 6. 0% 3. 8% 2. 0% 1. 7 .4% 28 5% 8% 7% 9% The relative standard deviation can be used for a wide range of levels of sulfur content. For example, if the coal is 1 weight percent sulfur, the values in the table also serve as the absolute standard deviation; if, however, the coal is 1.5 percent sulfur, the values should be multiplied by 1.5 to yield the absolute standard deviation. The data in this study cover the range up to 1.5 percent, and these percentages seem to be appropriate over this range. See Figure B-2. w is the number of unit trains (composite samples averaged) per week. Q n is the number of unit trains (composite samples averaged) per month. 5-9 ------- for a discussion of this relationship between the RSD's. Hence, the RSD for Ib SO?/MM Btu for averages of composite samples from 16 unit trains, is given by 0.069(1.05) = 0.0725. Figure 5-2 illustrates the determination of the value m, in that for 95 percent compliance the distance between m and 1.2 must be equal to 1.645 a where a is the absolute standard deviation of Ib S02/MM Btu and is 0.0725 m, i.e., the product of the RSD by the mean value, m. The value 1.645 is obtained from a table for areas under a standard g normal curve, corresponding to the 95th percentile. Figure 5-2. Determination of required average sulfur content Hence, u 1.2 - m 0.0725m = 1.645 (Equation 5-3) or m = 1.072. 5-10 ------- The weight percent sulfur for a coal with heating value of 11,500 Btu/lb is given by 0.727 x (1.072/1.2) = 0.65. The value is then adjusted by the ratio 1.072/1.2. Similarly the calculation of m for 99 percent compliance is made by using 2.326 in place of 1.645. Values of m for different amounts of coal sampled/numbers of samples averaged are obtained by multiplying the RSD given in Table 5-1 by 1.05 and substituting it for the 0.0725 in equation 5-3. 5.3.2 Averaging Period of One Month, Assuming Lognormal Distribution, Small Plant In this case, the number of composite samples averaged per month will be smaller than that for the 500-MW plant. For example, if 33 tons are required per 3 hours, 264 tons per day, or 7920 tons per month, it is possible that the entire month's supply would be obtained at one time. For the purpose of illustration, assume that four shipments of about 2000 tons each are received in one month and that the average sulfur content of four composite samples is used to determine compliance with the emission regulation. From Figure 5-1, the expected RSD of weight percent sulfur for samples of 2000 tons is about 18.2 percent. On the assumption that four composite samples are averaged each month, from Table 5-1 we read that RSD is 9.3 percent. However, this is based on samples from a larger tonnage of coal, 8400 tons rather than the 2000 in this example. Hence, assuming the same percentage reduction in the RSD is given for 4 composite samples from the 2000 ton lot as for the 8400 ton lots, an estimate of the RSD is the product of 18.2 by (9.3/15.5) or about 10.9 percent. The RSD of Ib S02/MM Btu is estimated to be 11.5 percent (= 10.9 x 1.05). This value is then used along with the lognormal distribution to obtain an estimate of the required mean sulfur content. 5-11 ------- The normality assumption is not good for averages of a small number of measurements, say less than 5; hence, the lognormal distribution was assumed for this example. The lognormal distribution is skewed toward the larger values as shown in Figure 5-4, upper sketch. The lower distribution is that of the transformed variable, Y = InX, which should be approximately normally distributed. As stated earlier, the lognormal distribution provides a very good empirical fit to several of the data sets, and because of its mathematical convenience, the impact of sulfur con- tent is first determined by use of this distribution. The value of 0.115, is determined as follows: If Y = InX, and the standard deviation of X is (1.05) x 10.9% or 0.115, where m is the mean of X, m1 the mean of Y, then the standard deviation of Y is approximately, 0{Y} = i 0{X} = RSD{X). That is, the estimated standard deviation of InX is essentially equal to the RSD of X. Hence, the transformation Y = InX is a variance stabilizing one, provided the RSD's are approxi- mately the same for all levels of sulfur content. Calcu- lations using the RSD of the sulfur content are essentially equivalent to those using the standard deviation of the logarithm of sulfur content. From Figure 5-3, the sulfur content required for 95 percent compliance with 11,500 Btu/lb heating value would be 0.727 x (0.993/1.2) = 0.60 weight percent sulfur. The multiplication by 0.993/1.2 provides for the adjustment from 1.2 to 0.993 as the required average. 5-12 ------- 13,000 12,000 o » z CO 11,000 10,000 I I 0.60 0.70 0.80 WEIGHT PERCENT SULFUK Figure 5-3. Sulfur content versus heating value of coal required to yield 1.2 Ib S02/MM Btu (1.90 Ib S02/lb S assumed) 5-13 ------- NODE MEDIAN 1.2 0.182 Y « InX Figure 5-4. Determination of required average sulfur content assuming lognormal distribution Referring to Figure 5-4, lower sketch, the following approximate relationship applies, where m1 is the mean of the lognormal distribution, 0.182 = In 1.2. 0.182 - m1 , ,At. u = 0.115 = 1'645 m1 = -0.0072 m ~ em' = 0.993 Ib Btu. 5-14 ------- 5.3.3 Three-Hour Average, Lognormal Distribution , 500-MW Plant Now consider the implication of the expected variation in 3-hour averages for the 500-MW plant with respect to compliance with the NSPS. In this case the graph of Figure 5-1 provides an estimate of the RSD of the weight percent sulfur to equal to 19.4 percent, or 19.4 * 1.05 or 20.4 percent for Ib SO^/MM Btu. Using the same procedure as in earlier computations _ 0.182 - m' U 04 m1 = -0.1536 m - em = 0.858 Ib S02/MM Btu. Using Figure 5-3, the weight percent sulfur assuming 11,500 Btu/lb, must average 0.727 (0.858/1.2) = 0.52 weight percent sulfur. This computation is also performed in Appendix B.3 assuming the inverted gamma distribution; the result is 0.875 compared with the 0.858 obtained using the lognormal distri- bution. This same close relationship was found for a large number of cases computed with both lognormal and inverted gama distributions. 5.3.4 Three Hour Average, Lognormal Distribution, Small Plant For this case, the RSD as read from Figure 5-1 for 33 tons is about 23.7 percent, or about 24.9 percent for Ib SO2/MM Btu. Hence, the estimated mean for 95 percent com- pliance is estimated to be about 0.80. In terms of sulfur content, this transforms to 0.727 x (0.80/1.2) = 0.49 average weight percent sulfur. 5-1! ------- The results of these four analyses are tabulated in Table 5-2 for convenience of subsequent discussion. Table 5-2 shows clearly that the mean weight percent sulfur required for compliance with the NSPS decreases as the averaging period changes from 1 month to 3 hours and also as the plant size decreases. As the percentage of compliance increases, the mean will decrease still further and will rapidly approach a value for which the availability of raw coal for compliance with NSPS tends to be very limited. Figure 5-5 provides a general procedure for determining the average sulfur content of a coal (Ib S02/MM Btu) required to achieve compliance with the NSPS of 1.2 Ib S02/MM Btu for 90, 95, and 99 percent of the averages of individual unit train samples for specified RSD's. Results are given for assumptions of both normal and lognormal distribution of sulfur content (Ib S02/MM Btu). For example, if a company has determined that the monthly averages vary by approxi- mately 7 percent of the mean (RSD = 7%), then for 95 percent compliance, the required mean sulfur content would be about 1.08 (1.07) Ib S02/MM Btu assuming normal (lognormal) dis- tribution. If one does not have information from which to derive the sulfur variability in terms of the RSD, then Figure 5-1 may be used to obtain an estimated value. These values would be multiplied by 1.05 to estimate the RSD of Ib S02/MM Btu in terms of that for weight percent sulfur. The RSD's read from Figure 5-1 would be applicable to coals with sulfur content up to 3 percent, the limit of data used in this study. It is expected, however, that the RSD's also would apply to higher sulfur levels. 5-16 ------- Table 5-2. SUMMARY OF COMPLIANCE COMPUTATIONS (95 AND 99% COMPLIANCE WITH EMISSION RATE OF 1.2 Ib SO /MM Btu) Averaging period 1 month 3 hours Information Number of composite samples per month Tonnage of coal represented by each sample RSD (Ib S02/MM Btu) Assumed heating value Required mean (Ib SO2/MM Btu) for 95% compliance Required mean (weight percent sulfur) for 95% com. Required mean (Ib SO?/ MM Btu) for 99% compliance Required mean (weight percent sulfur) for 99% com. Tonnage of coal represented by each sample RSD (Ib S02/MM Btu) Assumed heating value Required mean (Ib SO2/ MM Btu) for 95% compliance Required mean (weight percent sulfur) for 95% com Required mean (Ib S02/ MM Btu) for 99% compliance Required mean (weight percent sulfur) for 99% com 500-MW plant 16 8,400 7.25% 11,500 1.072 0.65 1.014 0.61 600 20.4 11,500 0.86 0.52 0.75 0.45 25-MW plant 4 2,000 11.5% 11,500 0.993 0.60 0.918 0.56 33 24.9 11,500 0.80 0.49 0.67 0.41 5-17 ------- ASSUMING NORMAL DISTRIBUTION ASSUMING LOG NOftMAL DISTRIBUTION 0 5 10 15 20 25 SULFUR VARIABILITY EXPRESSED AS RELATIVE STANDARD DEVIATION (*) Figure 5-5. Required average sulfur content vs. sulfur variability. 5-18 ------- 5.4 EXAMPLES The essence of this report is application of the tables and graphs of this section, together with necessary back- ground information as described in other sections, to real problems of compliance with NSPS or other emission limita- tions. As an aid in understanding the application of these graphs and tables, several examples are given to represent some typical problems. Example 1 A coal is assumed to vary in a manner consistent with the data in Figure 5-1, having an average weight percent sulfur equal to 0.70. Assume that four unit trains are received each week, i.e., Table 5-1 under w=4. What is the expected range of variation of sulfur content (weight percent) of 95 percent of the weekly averages (2a limits)? Monthly averages? Quarterly averages? Weekly (7 days) averages: 0.70 + 2(0.123) (0.70) = 0.70 + 0.17, Monthly (30 days) averages: 0.70 + 2(0.069)(0.70) = 0.70 + 0.10, Quarterly (90 days) averages: 0.70 + 2 (0.04) (0.70) = 0.70 + 0.056. Example 2 Only two unit trains are received per week (eight per month), and the limits of variation specified in Example 1 are required. In this case one must refer to Table 5-1, third column. The results are as follows: Weekly averages: 0.70 + 2(0.142)0.70 = 0.70 + 0.199, Monthly averages: 0.70 + 2(0.078)0.70 = 0.70 + 0.109, Quarterly averages: 0.70 + 2(0.045)0.70 = 0.70 + 0.063. 5-19 ------- Example 3 Data are available from which it has been determined that monthly averages vary by 10 percent of the mean (RSD = 10%) about an average sulfur content of 0.70 weight percent and that the heating values vary by 2 percent about an average of 12,000 Btu/lb. Would this coal enable the plant to meet the NSPS regulation for 95 percent of the monthly averages? The average and standard deviation of Ib S02/MM Btu is given by the very good approximation, - 0.70 x 1.90 ,n4 _ , n, x 12,000 x 10 ~ 1'11' s -x /tO. 10)2 + (0.02)2 = 1.11(0.102) = 0.113. Using Figure 5-5, for RSD of 10.2 percent and 95 percent compliance, the required average must not exceed 1.03 (1.01) Ib SO2/MM Btu assuming normal (lognormal) distribution. Because x = 1.11 is larger than 1.03^ the relative frequency of compliance will not be 95 percent. The expected fre- quency of compliance can be estimated, assuming normality, by use of the standard normal variable, u, - l-2 - * _ 1.2 - l.ll _ 0 a u - -- - --- -- -- 0.80, Q and a table of normal probabilities to obtain 0.788, or compliance about 79 percent of the time. Example 4 It has been determined that the variability of sulfur content (weight percent) of a unit train sample has an RSD equal to 15 percent. The average sulfur content required for compliance 95 percent of the time is about 0.96 (0.94) Ib SO-/ MM Btu, as read from Figure 5-5 for the assumption 5-20 ------- of normal (lognormal) distribution. Note that Figure 5-5 can be used in many applications. Example 5 A state agency has decided that the monthly averages of sulfur content must provide compliance with the NSPS reg- ulation 99 percent of the time. Assume that a plant receives four unit trains each week, or sixteen per month. What is the average sulfur content required for compliance with the regulation 1.2 Ib S02/MM Btu? It is assumed that Table 5-1 is applicable, that is, the RSD of weight percent sulfur is 0.069 and the RSD for Ib S02/MM Btu is given by 0.069 (1.05) = 0.0725. From Figure 5-5, the 30-day average for 99 percent compliance and assuming normal distribution is read as 1.025 Ib SO_/MM Btu. From Figure 5-3, for heating value of 11,500 Btu/lb, we read 0.727 percent sulfur to yield 1.2 Ib or 0.727 (1.025/1.2) = 0.62 as the required average weight percent sulfur. Figure 5-3 was derived on the assumption that 1.9 pounds of SO_ is emitted per pound of sulfur. Example 6 Same as in Example 5, except that weekly averages are used and 95 percent compliance is acceptable. Using Table 5-1, the RSD for weekly averages (four unit trains) is 12.3 percent; from the 95 percent curve on Figure 5.5 (lognormal distribution), the required average sulfur content should be 0.98 Ib S02/MM Btu. From Figure 5-3, the average sulfur content in weight percent sulfur is determined by reading the value corresponding to 11,500 (i.e., 0.727) and multi- plying by 0.98/1.2 to obtain 0.59 weight percent sulfur. Example 7 An SIP requires compliance 95 percent of the time on emission standard of 2.0 Ib SO_/MM Btu, based on monthly 5-21 ------- averages of 16 unit trains. Assume that the RSD values in Table 5-1 are applicable. From the table, we read the RSD value 6.9 percent. For compliance 95 percent of the time, the standard normal variable u = (2.0 - m)/0.069(1.05)m must equal 1.645 (2.326 for 99 percent compliance). The 1.05 multiplier is used to account for the higher variability of Ib SO2/MM Btu relative to the variability of percent sulfur. Solving the equation, 2.0 - m _ . ..At. 0.0725m - 1'645' we obtain m = 1.787 Ib S02/MM Btu. From Figure 5-3, the required average weight percent sulfur is obtained for an assumed heating value of 12,500 Btu/lb: 0.790 x (1.787/1.2) =1.18 percent. 5-22 ------- 6.0 CONCLUSIONS AND RECOMMENDATIONS CONCLUSIONS 1. The distribution of weight percent sulfur for com- posite samples from unit trains is skewed to the right (has a long tail of large values). This is particularly im- portant when decisions are based on only one or two composite samples from unit trains. 2. The logarithmic normal distribution is used to approximate the skewed distribution. This is a good empir- ical approximation and is convenient for making predictions concerning compliance. The inverted gamma distribution has also been proposed as an empirical fit to the skewed fre- quency distribution. Differences in estimates made using these two distributions are very small. 3. The distribution of Btu content of coals is rea- sonably symmetrical and is approximated rather well using the normal distribution. 4. The distribution of Ib SO_/MM Btu is skewed because of the dominating effect of the distribution of weight percent sulfur. 5. The variation of weight percent sulfur from com- posite samples (unit trains) is approximately 15 percent of the mean sulfur content, with almost all of the values between 10 and 25 percent of the mean. The lower percent- ages result from coal cleaning and/or from mining techniques, such as the number of machines in operation. The higher values would occur with no cleaning or with a mining tech- nique that does not tend to mix or "blend" the coals within 6-1 ------- the mining area. Greater variation also results from mixing coals from two seams with different sulfur content, par- ticularly when the proportions of the two coals also vary. NOTE: It is emphasized that the values provided in this report are not necessarily representative of a specific coal, mining or processing technique. The values are based on a collection of coal data made available by selected companies. Each company using the approach presented herein is urged to use its own data in estimating the variability of sulfur content for specified averaging times or tonnages. 6. The RSD of Btu content is smaller than that of sulfur content; that is, the RSD of Btu content is about 2 to 5 percent of the mean Btu content compared to the RSD of sulfur content that is 10 to 25 percent of the mean sulfur content. 7. The RSD of Ib S02/MM Btu is about 1.02 to 1.05 times the RSD for weight percent sulfur because of the dominating effect of the variation of sulfur. This is not true for the absolute standard deviation (see Appendix B.I.5). Through- out this report a conservative estimate of the RSD of Ib S02/MM Btu is 1.05 * RSD of weight percent sulfur. 8. The sulfur contents of samples from consecutive unit trains will differ by much less than the sulfur contents of samples from trains far apart in time; that is, there is a statistical dependence in the time series of data. Hence, the statistical analysis includes a subdivision of the variation into two components (1) that among unit trains within a week (or month) and (2) that among weekly (or monthly) averages. For a few data sets the year-to-year component can be estimated. These values are then used to determine the impact of averaging period/amount of coal sampled (week, month, quarter; 33 T, 600 T, etc.). 6-2 ------- 9. The average sulfur content required for compliance with the 1.2 Ib S02/MM Btu standard must decrease as the amount of coal in tons and/or the averaging period decreases and as the percentage of compliance time (95%, 99%, etc.) increases. Theoretically, if 100 percent compliance is required, then the average sulfur content approaches zero. 10. The RSD of sulfur content of coal from core drillings is greater by a factor of 1-1/2 to 4 than the variability of sulfur content among unit trains. This indicates the impact of small-increment samples on sulfur variability, since the core sample is a composite sample from a very small amount of coal, approximately 50 pounds. 11. Although sulfur variability is expected to decrease as the stage at which the sample is taken proceeds from core drilling -> run-of-mine coal -» as-cleaned coal -* as-received at plant -> as-burned, the reduction is difficult to detect beyond the first stage core drillings to run-of-mine coal. The reduction of variability in the latter stages should be relatively small; considerable data would be required to verify an expected reduction, if any. 12. Given an estimate of the RSD of sulfur content (weight percent), Figure 5-5 provides a straightforward means of determining the sulfur content in Ib SO2/MM Btu required for compliance with the regulation of 1.2 Ib SO2/MM Btu. 13. A quality control chart is suggested as one means of monitoring the sulfur content of coal to detect signifi- cant trends or changes in either the average or variation of sulfur content over time. Section B.4 of Appendix B discusses this approach, proposing either a standard chart for averages or one for moving averages. 6-3 ------- 14. The correlation of Btu content and sulfur content is relatively low and in almost all cases is insignificantly different from zero. RECOMMENDATIONS 1. As further coal cleaning data become available, it would be desirable to assess the variability of sulfur content before and after cleaning. 2. Additional long-term data (over several years) must be analyzed to determine long-term contractual implications. Recall from Section 2 that for strip mining operations with one machine the long-term variations are expected to be large. Not enough data have been obtained to assess this potential impact with the low-sulfur coals. 3. A computer program incorporating the types of anal- yses proposed in this report would have long-term utility. Furthermore, it would enable the analysis of some of the remaining data available to EPA. 4. Further consideration should be given to impact of sulfur variability, meteorological conditions, and other factors on the environmental SO2 concentrations. 5. A study of the cost impacts of schemes for reducing the average and/or standard deviation of sulfur content would be helpful. 6. Additional data relating the variability of sulfur content to the stages of sampling (core drillings, channel samples, run-of-mine, after cleaning, and as received at the plant) would yield estimates of the expected average re- duction (if any) at each stage. In this report the analysis is limited to a comparison of the core drillings and as- received data. 6-4 ------- 7. An ideal program for further study would be based on composite samples from smaller amounts of coal than the tonnages of unit trains, e.g., 50, 250, 1000, 5000, and 10,000 tons. At least 15 to 25 samples at each level would be needed. Analysis of these data would provide a basis for validating or adjusting the extrapolated region of the curve in Figure 5-1. 8. A study of the correlation between the RSD of data collected by a continuous stack monitor and the RSD of the as-burned coal would enhance the understanding of the poten- tial change in variability at this stage. 6-5 ------- 7.0 REFERENCES 1. Navajo Generating Station Sulfur Dioxide Field Monitoring Program, Volume I. Air Monitoring Center, Rockwell International, Meteorological Research, Inc., Systems Applications, Inc. September 1975. 2. Sulfur Reduction Potential of U.S. Coals: A Re- vised Report of Investigation, EPA-600/2-76-091, Bureau of Mines Rl 8118, April 1976. 3. Standard Methods for Collection of a Gross Sample of Coal. American Society for Testing and Materials, Designation: D 2234-72. 4. Standard Methods of Test for Total Sulfur in the Analysis of Coal and Coke. American Society of Testing Materials, Part 26. Designation: D 3177- 73, pp. 674-677. 5. Dixon, Wilfrid J. and Frank J. Massey, Jr. In- troduction to Statistical Analysis. New York, McGraw-Hill Book Co., 1951. 370 p. 6. Hald, A. Statistical Theory with Engineering Applications. New York, John Wiley and Sons, Inc., 1952. 783 p. 7. Anderson, R.L. and T.A. Bancroft. Statistical Theory in Research - I. Basic Statistical Theory, II. Analysis of Experimental Models by Least Squares. New York, McGraw-Hill Book Co., 1952. 399 p. 8. Hald, A. Statistical Tables and Formulas, John Wiley and Sons, Inc., New York, 1952. 9. Bauer, Edward L. A Statistical Manual for Chemists. New York. Academic Press. 1971. 193 p. 10. Grant, E. I. and R. S. Leavenworth. Statistical Quality Control, McGraw-Hill Book Co., New York, 1972. 7-1 ------- APPENDIX A SELECTED DATA SETS Paqe DATA SET C-l A-l DATA SET C-2 A-2 DATA SET C-3 A-5 DATA SET C-5 A-7 DATA SET C-10 A-10 DATA SET C-ll A-10 DATA SET C-12 A-ll DATA SET C-13 A-12 DATA SET U-l A-13 DATA SET U-2 A-18 DATA SET U-3 A-19 DATA SET U-4 A-20 DATA SET U-5 A-23 DATA SET U-6 A-25 DATA SET U-7 A-28 DATA SET U-8 A-31 DATA SET U-9 A-34 DATA SET U-ll A-37 DATA SETS U-14 to a-21 A-38 DATA SET U-22 A-42 ------- Data Set C-l Variability of Sulfur Content versus Amount of Coal Sampled Weight percent sulfur 2.1 - 2.2 2.2 - 2.3 2.3 - 2.4 2.4 - 2.5 2.5 - 2.6 2.6 - 2.7 2.7 - 2.8 2.8 - 2.9 2.9 - 3.0 3.0 - 3.1 3.1 - 3.2 3.2 - 3.3 3.3 - 3.4 3.4 - 3.5 3.5 - 3.6 3.6 - 3.7 Total Mean Standard deviation RSD Amount of coal sampled (1000 tons) < 8 0 2 4 4 3 4 9 5 10 5 1 3 0 1 0 1 52 2.801 0.301 0.107 8-12 2 2 12 29 36 48 67 66 68 52 24 4 1 1 0 1 413 2.803 0.226 0.081 12 - 16 0 0 1 3 3 12 11 9 7 6 0 1 1 0 0 0 54 2.788 0.199 0.072 16 - 20 0 0 1 6 15 35 39 41 24 5 9 3 4 0 0 1 183 2.805 0.200 0.072 Total 2 4 18 42 57 99 126 121 109 68 34 11 6 2 0 3 702 2.802 0.224 0.080 A-l ------- DATA SET C-2 CROSS-TABULATION OF SULFUR AND BTU CONTENT BtU < 12,000 12,000-12,100 12,100-12,200 12,200-12,300 12,300-12,400 12,400-12,500 12,500-12,600 12,600-12,700 12,700-12,800 Subtotals Weight Percent Sulfur 0.54- 0.55 2 1 0 2 0 0 1 0 0 6 0.56- 0.57 1 1 1 2 3 1 0 0 0 9 0.58- 0.59 0 1 1 4 9 1 0 0 0 15 0.60- 0.61 0 3 7 5 9 8 4 1 0 37 0.62- 0.63 0 0 7 9 5 3 3 0 1 28 0.64- 0.65 0 0 4 2 3 1 4 0 0 14 0.66- 0.67 0 0 0 1 2 0 0 0 0 3 0.68- 0.69 0 0 0 1 0 0 0 0 0 1 0.70- 0.71 0 0 1 0 0 0 0 0 1 2 Subtota 3 6 21 26 30 14 12 1 2 115 Weight Percent Sulfur x = 0.61 weight percent sulfur s = 0.03 weight percent sulfur Btu x = 12,310 Btu s = 158 Btu ANALYSIS OF VARIANCE OF SULFUR CONTENT Source of Variation Sum pf Squares Degrees of Freedom Mean Square Among months 0.03 11 0.0027 Within months 0.07 103 0.0007 Estimated Standard Deviation (within months) = (0.0007)15 = 0.026 Estimated Standard Deviation (among months) - '0.0027 - 0.0007 = 0.015 ------- 3> I GO 1.10 1.05 1.00 0.95 DATA SET C-2 UNIT TRAIN AND MONTHLY AVERAGES FOR SULFUR CONTENT. LB S02/MM BTU EACH UNIT TRAIN REPRESENTS ABOUT _ 5600 TONS OF COAL 0.90 0.85 0.80 WT $ SULFUR MONTHLY AVERAGE (NONOVERLAPPING) 10 20 30 40 50 60 70 80 SERIAL NUMBER OF UNIT TRAIN/COMPOSITE SAMPLE 90 100 110 120 Figure A--1. Variation in sulfur content, Ib SO /MM Btu with time, Data Set C-2. ------- I .t*. 1.10 1.05 1.00 « 0.95 CM a > _« 0.90 0.85 0.80 - DATA SET C-2 MEEKLY AVERAGES FOR SULFUR CONTENT, LI ay** ITU T i i UT X SULFUR BTU/LB 0.605 x " 12.310 0.03 s 161 LB S02/m BTU x - 0.93 S 0.066 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 4i SERIAL NUMBER OF MEEK Figure A-2. Variation in weekly average sulfur content, Ib SO /MM Btu. ------- DATA SET C-3 CROSS-TABULATION OF SULFUR AND BTU CONTENT Btu < 11,700 11,700-11,800 11,800-11,900 11,900-12,000 12,000-12,100 12,100-12,200 12,200-12,300 12,300-12,400 12,400-12,500 12,500-12,600 12,600-12,700 12,700-12,800 12,800-12,900 12,900-13,000 13,000-13,100 13,100-13,200 Subtotals Weight Percent Sulfur 0.54- 0.57 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 2 0.58- 0.61 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.62- 0.65 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 2 0.66- 0.69 3 0 1 2 1 1 1 0 1 0 0 0 0 0 0 0 10 0.70- 0.73 0 4 2 3 3 1 2 5 1 1 1 0 0 0 0 0 23 0.74- 0.77 0 1 1 5 4 2 2 4 1 0.78- 0.81 2 1 1 2 8 4 6 - 6 0 1 2 4 0 0 0 0 0 24 0 1 0 0 0 0 38 0. 82- 0.85 0 0 0 1 2 5 5 4 6 4 2 0 0 0 0 0 29 0.86- 0.89 0 0 0 0 2 2 2 3 3 3 2 1 0 0 1 0 19 0.90- 0.93 0 0 0 0 1 0 0 0 1 0 1 1 1 0 0 0 5 0.94- 0.97 0 0 0 0 0 0 0 0.98- 1.01 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 I 0 0 1 0 1 >1.02 0 0 0 0 0 0 0 0 0 1 2 0 0 0 0 0 3 Sub 1 Weight Percent Sulfur x = 0.807 weight percent sulfur s = 0.088 weight percent sulfur Btu x = 12,250 Btu s = 276 Btu ANALYSIS OF VARIANCE OF SULFUR CONTENT Source of Variation Sum of Squares Degrees of Freedom Mean Square Among months 0.201 11 0.0182 Within months 0.841 146 0.0057 Estimated Standard Deviation (within months) = ,(0.0057)^ = 0.0V76 '0.0182 - 0.0057^ Estimated Standard Deviation (among months) = 13 = 0\ 031 ------- 1.70- DATA SET C-3 WT. X SULFUR UNIT TRAIN AND MONTHLY AVERAGES FOR SULFUR CONTENT, LB S02/MM BTU EACH UNIT TRAIN REPRESENTS ABOUT 5600 TONS OF COAL X - 0.802 X - 12,260 S - 0.088 S Z7« Lft S6,/m BTU X - 1.24 S - 0.121 MONTHLY AVERAGE 10 40 50 60 70 80 NUMBER OF UNIT TRAIN/COMPOSITE SAMPLE 110 120 Figure A-3. Variation in sulfur content, Ib SO-/MM Btu, vs. time, Data Set C-3 ------- DATA SET C-5 CROSS-TABULATION OF SULFUR AND Btu VALUES Btu 11,000-11,200 11,200-12,400 11,400-11,600 11,600-11,800 11,800-12,000 12,000-12,200 12,200-12,400 12,400-12,600 12,600-12,800 12,800-13,000 Total Weight Percent Sulfur £0.33 0 0 0 0 0 0 5 1 0 0 6 0.34- 0.38 0 0 0 1 1 18 42 10 0 0 72 0.38- 0.42 0 0 0 0 11 37 27 2 0 0 77 0.42- 0.46 0 1 1 6 12 55 30 4 0 1 110 0.46- 0.50 0 0 0 2 9 6 10 0 0 0 27 0.50- 0.54 0 0 1 2 5 5 2 0 0 0 15 ^0.55 0 0 0 0 7 2 0 0 0 0 9 Total 0 1 2 11 45 123 116 17 0 1 316 Sulfur Mean, x = 0. 42 Standard Deviation, s = 0.0491 Btu Mean, x = 12,149 Standard Deviation, s = 197 A-7 ------- DATA SET C-5 MEAN AND STANDARD DEVIATION (WEIGHT PERCENT) (Based on a Sample of 10 Values Per Month) Month January February March April May June July August September October November December Mean Year 1974 0.43 0.38 0.37 0.36 0.39 0.35 0.37 0.38 0.36 0.38 0.38 0.47 1975 0.37 - 0.39 0.42 0.40 0.42 0.40 0.39 0.40 0.42 0.42 0.40 1976 0.48 0.38 0.43 0.37 - - - - - - - ~ Standard Deviation Year 1974 0.05 0.05 0.02 0.02 0.04 0.03 0.03 0.04 0.04 0.03 0.05 0.10 1975 0.03 - 0.02 0.05 0.04 0.05 0.05 0.02 0.04 0.04 0.04 0.04 1976 0.03 0.03 0.03 0.04 - - - - - - - ~ A-8 ------- 0.90 0.80 0.70 |