ABSTRACT Bharvirkar, Ranjit. Quantification of Variability and Uncertainty in Emission Factors and Emissions Inventories. (Under the guidance of Dr. H. Christopher Frey.) The purpose of this research is to demonstrate a methodology for quantifying the variability and uncertainty in emission factors and emission inventories. Emission inventories are used for various policy-making purposes, such as characterization of temporal emission trends, emissions budgeting for regulatory and compliance purposes, and the prediction of ambient pollutant concentration using air quality models. Failure to account for variability and uncertainty in emission inventories may lead to erroneous conclusions regarding source apportionment, compliance with emission standards, emission trends, and the impact of emissions on air quality. Variability is the heterogeneity of values of a quantity with respect to time, space, or across a population while uncertainty arises due to lack of knowledge about the true value of a quantity. The sources of variability and uncertainty are distinct and hence variability and uncertainty affect policymaking in different ways. For example, variability in emissions arises from differences in operating conditions among different power plants. Uncertainty arises due to measurement errors, systematic errors, and random sampling errors. It is possible to reduce uncertainty by taking more accurate and precise measurements (i.e. reducing measurement error) or by taking a larger number of measurements (i.e. random sampling error). However, it is not possible to reduce variability. Therefore, in this research variability and uncertainty are treated separately. A methodology for simultaneous characterization of variability and uncertainty in emission and activity factors and their propagation through an emission inventory model is described. Variability was characterized using probability distributions developed on the basis of data analysis. The uncertainty due to random sampling error was characterized
using parametric bootstrap simulation. A methodology for the quantification of variability and uncertainty in censored data sets containing below detection limit values was developed. This methodology is demonstrated for three case studies. In Case Study 1, the variability and uncertainty in the activity and emission factors for NO x emissions from selected coal-fired power plant systems was quantified based on data obtained from the U.S. Environmental Protection Agency. An illustrative partial probabilistic NO x emission inventory was developed for the state of North Carolina. In Case Study 2, the variability and uncertainty in the total short-term average emissions and in annual emissions of nine hazardous air pollutants (HAP) from a power plant was quantified by propagating the probability distributions for coal concentrations, boiler partitioning factors, and fabric filter partitioning factors through an emissions model. In Case Study 3, the effect of various levels of censoring on the variability and uncertainty in CO and HC emission factor data sets for diesel transit buses was studied. The main findings regarding the methodology demonstrated in this research include: (1) uncertainty due to random sampling error is substantial and in many cases was found to be of the same order of magnitude as the variability in the data set; and (2) the methodology developed for quantifying the variability and uncertainty in censored data sets is reasonably robust and accurate. The main insights obtained from the application of the methodology include: (1) the uncertainty in the total NO x emissions from selected power plants in North Carolina is ± 25 percent around the nominal value; (2) the uncertainty in the short-term average emissions of all HAPs from a power plant is substantially high in the upper percentiles (e.g., the width of the 95 percent confidence interval on the 95th percentile is 385 lb) than in the lower percentiles (e.g., the width of the 95 percent confidence interval on the median value is 60 lb) ; (3) the range of uncertainty in the annual average emissions is much wider than the
range of variability in annual average emissions from one year to another; and (4) the uncertainty in the median value of censored CO and HC emission factor data sets increases as the level of censoring increases.
BIOGRAPHY 11th May, 1975 Born to Meera and Ramesh Bharvirkar in Pune. 1981-84 Primary school education at Shri Shivaji Preparatory Military School, Pune. 1984-90 Secondary school education at Jnana Prabodhini Prashala, Pune. Graduated with first rank in school. 1990-92 Attended junior college at Fergusson to study Science and Mathematics. 1993-97 Attended under-graduate college at Indian Institute of Technology, Bombay, Mumbai to study Civil Engineering. 1997-99 Attended graduate school at North Carolina State University to study Environmental Engineering and simultaneously worked as a research assistant with Dr. H. Christopher Frey. ii
ACKNOWLEDGMENTS Family: Parents and sister, for their constant encouragement and support. Advisor: Dr. H. Christopher Frey, Ph.D., for his invaluable guidance. Friends in India.: Aditya, Charu, Abhay, Raghu, Shantanu, Bhide, Vineet, Atul, Aditya-Kiran, Kunal, Omkar, Bhaskar, Ankur, Dhananjay, Bob, Inchie, Kassy, Saand, Vora, and Saurabh. Friends in U.S.: Parra, Muggy, Hayat, Karle, Sujay, Govinda, Sachin, Raghu, Sheldon, Timex, Kishan, Atul, Vandita, and Badrish, for making my stay in Raleigh memorable. Colleagues: Alper, Junyu, Maysa, Amita, Matt, Sudeep, and Ken, for those stimulating discussions andalso for making the work environment so pleasant. Sponsors: Office of Air Quality Planning and Standards, U.S. Environmental Protection Agency and STAR Grants Program, National Center for Environmental Reseacrh and Quality Assurance Special thanks: Steve Bromberg and Rhonda Thompson, for their help in otaining the data and information required for this project iii
TABLE OF CONTENTS BIOGRAPHY... II ACKNOWLEDGMENTS... III LIST OF FIGURES... VIII LIST OF TABLES...XXXIII INTRODUCTION...1 1.1 Motivation...1 1.2 Objectives...4 1.3 Current Approaches to Evaluating the Quality of Emission Inventories...8 1.3.1 Qualitative Methods...8 1.3.2 Semi-Quantitative Methods...9 1.3.3 Quantitative Methods... 10 1.4 Expected Benefits of this Thesis... 13 1.5 Overview of this Report... 14 2.0 METHODOLOGY... 17 2.1 General Approach... 19 2.2 Visualizing Data Using Empirical Distributions and Scatter Plots... 20 2.3 Theoretical Basis for Selecting Parametric Probability Distribution Models... 24 2.4 Fitting Two-Parameter Probability Distribution Model to Data Sets... 25 2.5 Fitting Probability Distribution Models to Censored Data Sets... 28 2.6 Fitting Probability Distribution Models to Data with a Minimum Threshold: Three- Parameter Distributions... 39 2.7 Evaluation of Goodness of Fit of a Probability Distribution Model... 41 2.8 Bootstrap Simulation and Application to Characterization of Variability and Uncertainty Using Parametric Distributions... 42 2.9 Two-Dimensional Simulation of Uncertain Frequency Distributions... 46 3.0 EXAMPLE CASE STUDY 1: PROBABILISTIC NO X EMISSION INVENTORY. 58 3.1 Compilation and Evaluation of Database... 58 3.2 Statistical Analysis... 62 3.2.1 Dependencies Among Activity and Emission Factors... 63 3.2.2 Intra-Unit Variability Over Time... 64 3.2.3 Evaluation of ÒSeasonalÓ Variation... 73 3.2.4 Effect of Temporal Averaging on Variability... 77 3.3 Fitting, Evaluation, and Selection of Probability Distribution Models for Activity Data Sets... 79 3.4 Evaluation of Both Variability and Uncertainty in Distributions Fitted to Emission and Activity Factor Data Sets... 84 3.5 Effect of Spatial Averaging (or Population Size) Over Uncertainty... 86 3.6 Development of an Illustrative Probabilistic Emission Inventory... 97 4.0 EXAMPLE CASE STUDY 2: HAZARDOUS AIR POLLUTANT EMISSIONS...102 4.1 Compilation of Database...103 4.2 Development of Probability Distribution Models...105 4.2.1 Pollutant Concentrations in Coal...105 iv
4.2.2 Boiler Partitioning Factor Data Sets...110 4.2.3 Fabric Filter Partitioning Factor Data Sets...113 4.3 Quantification of Uncertainty in the Frequency Distribution for Model Inputs..115 4.4 Estimating Variability and Uncertainty in a Model Output...123 4.5 Discussion...130 5.0 EXAMPLE CASE STUDY 3: CHARACTERIZING VARIABILITY AND UNCERTAINTY IN CENSORED EMISSION DATA SETS FROM DIESEL TRANSIT BUSES...132 5.1 Possible Detection Limits for RSD Measurements of Selected Transit Buses...133 5.2 Description of Data Set...137 5.3 Distribution Models for Representing Variability in Emission Factor Data...138 5.4 Effect of Censoring on Uncertainty in Frequency Distributions...144 5.5 Effect of Censoring on Uncertainty in Median of Frequency Distribution...149 5.6 Effect of Censoring on Uncertainty in Mean...152 5.7 Discussion...156 6.0 CONCLUSIONS...157 6.1 Methodology...158 6.2 Insights from Case Studies...160 6.2.1 Case Study 1: NO x Emissions from Electric Utilities...160 6.2.2 Case Study 2: HAPs Emissions from Electric Utilities...161 6.2.3 Case Study 3: CO and HC Emissions from Transit Buses...163 6.3 Recommendations for Future Work...164 7.0 REFERENCES...167 APPENDIX A: RESULTS OF TESTING METHODOLOGY FOR CENSORED DATA SETS...176 A.1 Gamma Distribution...176 A.2 Lognormal Distribution...184 A.3 Weibull Distribution...192 APPENDIX B: CASE STUDY 1: NO X EMISSIONS FROM ELECTRIC UTILITIES..200 B.1 Results for Dry Bottom Wall-Fired Boilers with No NO x Controls...200 B.1.1 Correlations...200 B.1.2 Intra-unit Variability Over Time: Mean Versus Standard Deviation...202 B.1.3 Intra-unit Variability Over Time: Plot for Coefficient of Variation...204 B.1.4 Intra-unit Variability Over Time: Comparison of CDFs of High/Low/Medium CV Units...206 B.1.5 Evaluation of ÒSeasonalÓ Variation...208 B.1.6 Effect of Temporal Averaging on Variability...210 B.1.7 Probability Distribution Models Fitted to Six-Month Average Activity and Emission Factor Data...212 B.1.8 Evaluation of Variability and Uncertainty in Distributions Fitted to Activity and Emission Factor Data...214 B.1.9 Effect of Spatial Averaging on Uncertainty...216 B.2 Results for Dry Bottom Wall-Fired Boilers with Low NO x Burners and Overfire Air...222 B.2.1 Correlations...222 B.2.2 Intra-unit Variability Over Time: Mean Versus Standard Deviation...224 B.2.3 Intra-unit Variability Over Time: Plot for Coefficient of Variation...226 v
B.2.4 Intra-unit Variability Over Time: Comparison of CDFs of High/Low/Medium CV Units...228 B.2.5 Evaluation of ÒSeasonalÓ Variation...230 B.2.6 Effect of Temporal Averaging on Variability...232 B.2.7 Probability Distribution Models Fitted to Six-Month Average Activity and Emission Factor Data...234 B.2.8 Evaluation of Variability and Uncertainty in Distributions Fitted to Activity and Emission Factor Data...236 B.2.9 Effect of Spatial Averaging on Uncertainty...238 B.3 Results for Tangential Fired Boilers with No NO x Controls...242 B.3.1 Correlations...242 B.2.2 Intra-unit Variability Over Time: Mean Versus Standard Deviation...244 B.3.3 Intra-unit Variability Over Time: Plot for Coefficient of Variation...246 B.3.4 Intra-unit Variability Over Time: Comparison of CDFs of High/Low/Medium CV Units...248 B.3.5 Evaluation of ÒSeasonalÓ Variation...250 B.3.6 Effect of Temporal Averaging on Variability...252 B.3.7 Probability Distribution Models Fitted to Six-Month Average Activity and Emission Factor Data...254 B.3.8 Evaluation of Variability and Uncertainty in Distributions Fitted to Activity and Emission Factor Data...256 B.3.9 Effect of Spatial Averaging on Uncertainty...258 APPENDIX C: CASE STUDY 2: HAZARDOUS AIR POLLUTANT EMISSIONS...264 C.1 Development of Probability Distribution Models for Coal Concentration Data Sets264 C.2 Development of Probability Distribution Models for Boiler Partitioning Factor Data Sets...266 C.3 Development of Probability Distribution Models for Fabric Filter Partitioning Factor Data Sets...269 C.4 Two-Dimensional Plots Illustrating Uncertainty in Frequency Distribution for Model Inputs...273 C.5 Two-Dimensional Plots Illustrating Uncertainty and Variability in Model Outputs279 C.6 Cumulative Distribution Functions Illustrating Year-to-Year Uncertainty in Model Outputs...281 APPENDIX D: CASE STUDY 3: CO AND HC EMISSIONS FROM TRANSIT BUSES283 D.1 CO Emission Factor Data Set for ÒAll RDU BusesÓ...284 D.1.1 Comparsion of Fitted Distributions with Empirical Distribution...284 D.1.2 Results of Two-Dimensional Simulations...285 D.1.3 Effect of Censoring on Uncertainty in Mean...288 D.2 HC Emission Factor Data Set for ÒAll RDU BusesÓ...289 D.2.1 Comparsion of Fitted Distributions with Empirical Distribution...289 D.2.2 Results of Two-Dimensional Simulations...290 D.2.3 Effect of Censoring on Uncertainty in Mean...294 D.3 HC Emission Factor Data Set for ÒRDU Bus No. 3Ó...295 D.3.1 Comparsion of Fitted Distributions with Empirical Distribution...295 D.3.2 Results of Two-Dimensional Simulations...296 D.3.3 Effect of Censoring on Uncertainty in Mean...300 D.4 CO Emission Factor Data Set for ÒRDU Bus No. 4Ó...301 D.4.1 Comparsion of Fitted Distributions with Empirical Distribution...301 D.4.2 Results of Two-Dimensional Simulations...302 D.4.3 Effect of Censoring on Uncertainty in Mean...305 D.5 HC Emission Factor Data Set for ÒRDU Bus No. 4Ó...306 vi
D.5.1 Comparsion of Fitted Distributions with Empirical Distribution...306 D.5.2 Results of Two-Dimensional Simulations...307 D.5.3 Effect of Censoring on Uncertainty in Mean...311 D.6 CO Emission Factor Data Set for ÒRDU Bus No. 7Ó...312 D.6.1 Comparsion of Fitted Distributions with Empirical Distribution...312 D.6.2 Results of Two-Dimensional Simulations...313 D.6.3 Effect of Censoring on Uncertainty in Mean...316 D.7 HC Emission Factor Data Set for ÒRDU Bus No. 7Ó...317 D.7.1 Comparsion of Fitted Distributions with Empirical Distribution...317 D.7.2 Results of Two-Dimensional Simulations...318 D.7.3 Effect of Censoring on Uncertainty in Mean...322 D.8 CO Emission Factor Data Set for ÒAll TTA BusesÓ...323 D.8.1 Comparsion of Fitted Distributions with Empirical Distribution...323 D.8.2 Results of Two-Dimensional Simulations...324 D.8.3 Effect of Censoring on Uncertainty in Mean...327 D.9 HC Emission Factor Data Set for ÒAll TTA BusesÓ...328 D.9.1 Comparsion of Fitted Distributions with Empirical Distribution...328 D.9.2 Results of Two-Dimensional Simulations...329 D.9.3 Effect of Censoring on Uncertainty in Mean...333 vii
LIST OF FIGURES Figure 2-1. Flow Diagram Illustrating the Propagation of Variability in Emission Inventory Inputs to Obtain a Point Estimate of Total Emissions.... 18 Figure 2-2. Flow Diagram Illustrating the Propagation of Variability and Uncertainty in Emission Inventory Inputs to Quantify the Uncertainty in the Estimate of Total Emissions... 19 Figure 2-3. Empirical Distribution Function for Capacity Factor of a Tangential Fired Boiler Using Low NO X Coal and Overfire Air Option 1... 23 Figure 2-4. Scatter Plot for Six Month Average NO X Emission Factor versus Six Month Average Capacity Factor for Tangential Fired Boiler Using Low NO X Coal and Overfire Air Option 1... 23 Figure 2-5. Comparison of Cumulative Distribution Functions for each set of Estimated Parameters with the Empirical Distribution Function for a Data Set Containing 10 Data Points, Generated from a Beta Distribution... 37 Figure 2-6. Comparison of Cumulative Distribution Functions for each set of Estimated Parameters with the Empirical Distribution Function for a Data Set Containing 20 Data Points, Generated from a Beta Distribution... 37 Figure 2-7. Comparison of Cumulative Distribution Functions for each set of Estimated Parameters with the Empirical Distribution Function for a Data Set Containing 30 Data Points, Generated from a Beta Distribution... 37 Figure 2-8. Comparison of Cumulative Distribution Functions for each set of Estimated Parameters with the Empirical Distribution Function for a Data Set Containing 40 Data Points, Generated from a Beta Distribution... 38 Figure 2-9. Comparison of Cumulative Distribution Functions for each set of Estimated Parameters with the Empirical Distribution Function for a Data Set Containing 50 Data Points, Generated from a Beta Distribution... 38 Figure 2-10. Simplified Flow Diagram for Bootstrap Simulation and Two-Dimensional Simulation of Uncertainty and Variability. (Key: B = Number of Bootstrap Replications, q = Sample Size Used for Uncertainty, p = Sample Size Used of Variability.) (Frey and Rhodes, 1998)... 47 Figure 2-11. Comparison of Fitted Distribution for Variability in Six-Month Average Emission Factor, with Bootstrap Confidence Intervals, to Data for Dry Bottom Wall-fired Boilers with Low NO X Burners and Overfire Air.... 48 Figure 2-12. Two-Dimensional Plot Indicating the Effect of Censoring on Bootstrap Confidence Intervals for a Data Set Containing 10 Data Points. (Key: (A) 0 % Censoring; (B) 20 % Censoring; (C) 40 % Censoring; (D) 60 % Censoring)... 52 Figure 2-13. Two-Dimensional Plot Indicating the Effect of Censoring on Bootstrap Confidence Intervals for a Data Set Containing 20 Data Points. (Key: (A) 0 % Censoring; (B) 25 % Censoring; (C) 50 % Censoring; (D) 75 % Censoring)... 53 Figure 2-14. Two-Dimensional Plot Indicating the Effect of Censoring on Bootstrap Confidence Intervals for a Data Set Containing 30 Data Points. (Key: (A) 0 % Censoring; (B) 27 % Censoring; (C) 53 % Censoring; (D) 80 % Censoring)... 54 Figure 2-15. Two-Dimensional Plot Indicating the Effect of Censoring on Bootstrap Confidence Intervals for a Data Set Containing 40 Data Points. (Key: (A) 0 % Censoring; (B) 25 % Censoring; (C) 50 % Censoring; (D) 75 % Censoring)... 55 Figure 2-16. Two-Dimensional Plot Indicating the Effect of Censoring on Bootstrap Confidence Intervals for a Data Set Containing 50 Data Points. (Key: (A) 0 viii
% Censoring; (B) 40 % Censoring; (C) 60 % Censoring; (D) 80 % Censoring)... 56 Figure 3-1. Scatter Plot for 3-Month Average Heat Rate versus 3-Month Average Capacity Factor for Tangential-Fired Boilers Using Low NO x Burners and Overfire Air Option 1.... 65 Figure 3-2. Scatter Plot for 3-Month Average NO X Emissions on Input Basis versus 3- Month Average Capacity Factor for Tangential-Fired Boilers Using Low NO x Burners and Overfire Air Option 1.... 65 Figure 3-3. Scatter Plot for 3-Month Average NO X Emissions on Output Basis versus 3- Month Average Capacity Factor for Tangential-Fired Boilers Using Low NO x Burners and Overfire Air Option 1.... 65 Figure 3-4. Scatter Plot for 3-Month Average NO X Emissions on Input Basis versus 3- Month Average Heat Rate for Tangential-Fired Boilers Using Low NO x Burners and Overfire Air Option 1.... 66 Figure 3-5. Scatter Plot for 3-Month Average NO X Emissions on Output Basis versus 3- Month Average Heat Rate for Tangential-Fired Boilers Using Low NO x Burners and Overfire Air Option 1.... 66 Figure 3-6. Mean and Standard Deviation of 3-Month Average Heat Rates for Six Quarters for Tangential-Fired Boiler Using Low NO x Burners and Overfire Air Option 1... 67 Figure 3-7. Mean and Standard Deviation of 3-Month Average Capacity Factors for Six Quarters for Tangential-Fired Boiler Using Low NO x Burners and Overfire Air Option 1.... 67 Figure 3-8. Mean and Standard Deviation of 3-Month Average NO X Emission Factor on Fuel Input Basis for Six Quarters for Tangential-Fired Boiler Using Low NO x Burners and Overfire Air Option 1.... 68 Figure 3-9. Mean and Standard Deviation of 3-Month Average NO X Emission Factor on Electricity Output Basis for Six Quarters for Tangential-Fired Boiler Using Low NO x Burners and Overfire Air Option 1.... 68 Figure 3-10. Variability in the Coefficient of Variation for 3-Month Average Heat Rate of Tangential-Fired Boilers Using Low NO x Burners and Overfire Air Option 1.... 69 Figure 3-11. Variability in the Coefficient of Variation for 3-Month Average Capacity Factor of Tangential-Fired Boilers Using Low NO x Burners and Overfire Air Option 1.... 70 Figure 3-12. Variability in the Coefficient of Variation for 3-Month Average NO X Emission Factor on Fuel Input Basis of Tangential-Fired Boilers Using Low NO x Burners and Overfire Air Option 1.... 70 Figure 3-13. Variability in the Coefficient of Variation for 3-Month Average NO x Emission Factor on Electricity Output Basis of Tangential-Fired Boilers using Low NO x Burners and Overfire Air Option 1.... 70 Figure 3-14. Comparison of Variability in 3-Month Average Heat Rates for Three Units Having a Low, Intermediate, and High Coefficient of Variation of Tangential-Fired Boilers using Low NO x Burners and Overfire Air Option 1.... 72 Figure 3-15. Comparison of Variability in 3-Month Average Capacity Factors for Three Units Having a Low, Intermediate, and High Coefficient of Variation of Tangential-Fired Boilers using Low NO x Burners and Overfire Air Option 1.... 72 Figure 3-16. Comparison of Variability in 3-Month Average NO X Emissions on Fuel Input Basis for Three Units Having a Low, Intermediate, and High Coefficient of Variation of Tangential-Fired Boilers using Low NO x Burners and Overfire Air Option 1.... 73 ix
Figure 3-17. Comparison of Variability in 3-Month Average NO X Emissions on Electricity Output Basis for Three Units Having a Low, Intermediate, and High Coefficient of Variation of Tangential-Fired Boilers using Low NO x Burners and Overfire Air Option 1.... 73 Figure 3-18. Comparison of Confidence Intervals for 3-Month Average Heat Rate and Standard Deviation in Heat Rate, between each of the Four Quarters of 1997, for Tangential-Fired Boilers Using Low NO x Burners and Overfire Air Option 1.... 76 Figure 3-19. Comparison of Confidence Intervals for 3-Month Average Capacity Factor and Standard Deviation in Capacity Factor, between each of the Four Quarters of 1997, for Tangential-Fired Boilers Using Low NO x Burners and Overfire Air Option 1... 76 Figure 3-20. Comparison of Confidence Intervals for 3-Month Average NO X Emissions on Fuel Input Basis and Standard Deviation in NO X Emissions on Fuel Input Basis, between each of the Four Quarters of 1997, for Tangential-Fired Boilers Using Low NO x Burners and Overfire Air Option 1... 76 Figure 3-21. Comparison of Confidence Intervals for 3-Month Average NO X Emissions on Electricity Output Basis and Standard Deviation in NO X Emissions on Electricity Output Basis, between each of the Four Quarters of 1997, for Tangential-Fired Boilers Using Low NOx Burners and Overfire Air Option 1.... 77 Figure 3-22. Comparison of 3-month and 6-month Variability in Heat Rate for Tangentialfired Boiler Using Low NO x Burners and Overfire Air Option 1. (Number of Data Points: 3-month = 156, 6-month = 26)... 79 Figure 3-23. Comparison of 3-month and 6-month Variability in Capacity Factor for Tangential-fired Boiler Using Low NO x Burners and Overfire Air Option 1. (Number of Data Points: 3-month = 156, 6-month = 26)... 80 Figure 3-24. Comparison of 3-month and 6-month Variability in NO X Emissions on Fuel Input Basis for Tangential-fired Boiler Using Low NO x Burners and Overfire Air Option 1. (Number of Data Points: 3-month = 156, 6-month = 26)... 80 Figure 3-25. Comparison of 3-month and 6-month Variability in NO X Emissions on Electricity Output Basis for Tangential-fired Boiler Using Low NO x Burners and Overfire Air Option 1. (Number of Data Points: 3-month = 156, 6- month = 26)... 80 Figure 3-26. Six Month Average Heat Rate (Btu/kWh) Data for Tangential-Fired Boiler Using Low NO x Burners and Overfire Air Option 1, Fitted to 3-Parameter Lognormal Distribution.... 81 Figure 3-27. Six Month Average Capacity Factor Data for Tangential-Fired Boiler Using Low NO x Burners and Overfire Air Option 1, Fitted to 2-Parameter Beta Distribution... 81 Figure 3-28. Six Month Average NO X Emission Factor (g /GJ) on Fuel Input Basis Data for Tangential-Fired Boiler Using Low NO x Burners and Overfire Air Option 1, Fitted to 2-Parameter Gamma Distribution.... 82 Figure 3-29. Six Month Average NO X Emission Factor (g/gj) on Electricity Output Basis Data for Tangential-Fired Boiler Using Low NO x Burners and Overfire Air Option 1, Fitted to 2-Parameter Gamma Distribution.... 82 Figure 3-30. Evaluation of the Adequacy of the Fitted Distribution for Representing the Six-Month Average Heat Rate for Tangential Fired Boilers Using Low NOx Burners and Overfire Air Option 1.... 86 Figure 3-31. Evaluation of the Adequacy of the Fitted Distribution for Representing the Six-Month Average Capacity Factor for Tangential Fired Boilers Using Low NO x Burners and Overfire Air Option 1.... 87 x
Figure 3-32. Evaluation of the Adequacy of the Fitted Distribution for Representing the Six-Month Average NO x Emissions on Fuel Input Basis for Tangential Fired Boilers Using Low NO x Burners and Overfire Air Option 1... 87 Figure 3-33. Evaluation of the Adequacy of the Fitted Distribution for Representing the Six-Month Average NO x Emissions on Electricity Output Basis for Tangential Fired Boilers Using Low NO x Burners and Overfire Air Option 1.... 87 Figure 3-34. Two-Dimensional Plots Showing Effect of Spatial Averaging on Uncertainty in the Frequency Distribution of Six-Month Average Heat Rate for Tangential-Fired Boilers Using Low NO x Burners and Overfire Air Option 1. (Key: (A) Number of Units = 5; (B) Number of Units = 10; (C) Number of Units = 20)... 89 Figure 3-35. Two-Dimensional Plots Showing Effect of Spatial Averaging on Uncertainty in the Frequency Distribution of Six-Month Average Capacity Factor for Tangential-Fired Boilers Using Low NO x Burners and Overfire Air Option 1. (Key: (A) Number of Units = 5; (B) Number of Units = 10; (C) Number of Units = 20)... 91 Figure 3-36. Two-Dimensional Plots Showing Effect of Spatial Averaging on Uncertainty in the Frequency Distribution of Six-Month Average NO x Emissions on Fuel Input Basis for Tangential-Fired Boilers Using Low NO x Burners and Overfire Air Option 1. (Key: (A) Number of Units = 5; (B) Number of Units = 10; (C) Number of Units = 20)... 92 Figure 3-37. Two-Dimensional Plots Showing Effect of Spatial Averaging on Uncertainty in the Frequency Distribution of Six-Month Average NO x Emissions on Electricity Output Basis for Tangential-Fired Boilers Using Low NO x Burners and Overfire Air Option 1. (Key: (A) Number of Units = 5; (B) Number of Units = 10; (C) Number of Units = 20)... 93 Figure 3-38. Uncertainty in Mean of Six-Month Average Heat Rate for Tangential-Fired Boiler Using Low NO x Burners and Overfire Air Option 1.... 95 Figure 3-39. Uncertainty in Mean of Six-Month Average Capacity Factor for Tangential- Fired Boilers Using Low NO x Burners and Overfire Air Option 1... 95 Figure 3-40. Uncertainty in Mean of Six-Month Average NO X Emission Factor on Fuel Input Basis for Tangential-Fired Boiler Using Low NO x Burners and Overfire Air Option 1... 96 Figure 3-41. Uncertainty in Mean of Six-Month Average NO X Emission Factor on Electricity Output Basis for Tangential-Fired Boiler Using Low NO x Burners and Overfire Air Option 1.... 96 Figure 3-42. Uncertainty and Point Estimates for Partial Utility NO X Emission Inventory for the State of North Carolina. (Based on Six Month Average Data)...100 Figure 3-43. Uncertainty Estimates for Utility NO X Emissions for Selected Technologies for North Carolina (Based on Six Month Average Data). Key: DB = Dry Bottom Wall-Fired Boiler; T = Tangential-fired; U = Uncontrolled; C = Controlled (e.g., Low NO x Burners)...101 Figure 4-1. Simplified Schematic of a Coal-Fired Power Plant...104 Figure 4-2. Three-Day Average Arsenic Concentration in Coal fitted to a Gamma Distribution...108 Figure 4-3. Three-Day Average Cobalt Concentration in Coal fitted to a Gamma Distribution...108 Figure 4-4. Three-Day Average Nickel Concentration in Coal fitted to a Gamma Distribution...111 Figure 4-5. Three-Day Average Boiler Partitioning Factor for Arsenic fitted to a Beta Distribution...112 Figure 4-6. Three-Day Average Fabric Filter Partitioning Factor for Arsenic fitted to a Beta Distribution...114 xi
Figure 4-7. Two-Dimensional Plot Showing Uncertainty in the Frequency Distribution of Three-Day Average Arsenic Concentration in Coal. (Note: X-axis is Logarithmic)...116 Figure 4-8. Two-Dimensional Plot Showing Uncertainty in the Frequency Distribution of Three-Day Average Boiler Partitioning Factor for Arsenic....117 Figure 4-9. Two-Dimensional Plot Showing Uncertainty in the Frequency Distribution of Three-Day Average Fabric Filter Partitioning Factor for Arsenic...117 Figure 4-10. Two-Dimensional Plot Showing Uncertainty in the Frequency Distribution of Three-Day Average Cobalt Concentration in Coal. (Note: X-axis is Logarithmic)...118 Figure 4-11. Two-Dimensional Plot Showing Uncertainty in the Frequency Distribution of Three-Day Average Boiler Partitioning Factor for Cobalt....118 Figure 4-12. Two-Dimensional Plot Showing Uncertainty in the Frequency Distribution of Three-Day Average Fabric Filter Partitioning Factor for Cobalt....119 Figure 4-13. Algorithm for Simulating Non-Detects in Bootstrap Samples Generated from a Multiply-Censored Parent Population...120 Figure 4-14 Two-Dimensional Plot Showing Uncertainty in the Frequency Distribution of Three-Day Average Nickel Concentration in Coal...122 Figure 4-15. Two-Dimensional Plot Showing Uncertainty in the Frequency Distribution of Three-Day Average Boiler Partitioning Factor for Nickel....123 Figure 4-16. Two-Dimensional Plot Showing Uncertainty in the Frequency Distribution of Three-Day Average Fabric Filter Partitioning Factor for Nickel....123 Figure 4-17. Flow Diagram Illustrating the Propagation of Two-Dimensional (2-D) and One-Dimensional (1-D) Inputs through Model to Obtain Two-Dimensional Output (Note: nu is the uncertainty dimension and nv is the variability dimension)...126 Figure 4-18. Two-Dimensional Plot Illustrating the Uncertainty and Variability in the Total Arsenic Emissions for a Three-Day Averaging Period...127 Figure 4-19. Two-Dimensional Plot Illustrating the Uncertainty and Variability in the Total Cobalt Emissions for a Three-Day Averaging Period....127 Figure 4-20. Two-Dimensional Plot Illustrating the Uncertainty and Variability in the Total Nickel Emissions for a Three-Day Averaging Period....127 Figure 4-21. Two-Dimensional Plot Illustrating the Uncertainty and Variability in the Total HAPs Emissions for a Three-Day Averaging Period...128 Figure 4-22. Cumulative Distribution Functions Illustrating the Year-to-Year Uncertainty in the Average Annual Arsenic Emissions...129 Figure 4-23. Cumulative Distribution Functions Illustrating the Year-to-Year Uncertainty in the Average Annual Cobalt Emissions....129 Figure 4-24. Cumulative Distribution Functions Illustrating the Year-to-Year Uncertainty in the Average Annual Nickel Emissions....129 Figure 4-25. Cumulative Distribution Functions Illustrating the Year-to-Year Uncertainty in the Average Annual Total HAPs Emissions...130 Figure 5-1. Comparison of Empirical Distribution and the Gamma Distributions Fitted to the CO Emission Factor Data Set for Bus No. 3, censored at g/mile, 5.0 g/mile, and 1 g/mile....140 Figure 5-2. Comparison of Empirical Distribution and the Weibull Distributions Fitted to the CO Emission Factor Data Set for Bus No. 3, censored at g/mile, 5.0 g/mile, and 1 g/mile....143 Figure 5-3. Comparison of Empirical Distribution and the Lognormal Distributions Fitted to the CO Emission Factor Data Set for Bus No. 3, censored at g/mile, 5.0 g/mile, and 1 g/mile...143 Figure 5-4. Comparison of Empirical Distribution Function with Bootstrap Confidence Intervals for Carbon Monoxide Emissions from New Bus No. 3, Fitted to Gamma Distribution (DL = g/mile)...145 xii
Figure 5-5. Comparison of Empirical Distribution Function with Bootstrap Confidence Intervals for Carbon Monoxide Emissions from New Bus No. 3, Fitted to Weibull Distribution (DL = g/mile)...145 Figure 5-6. Comparison of Empirical Distribution Function with Bootstrap Confidence Intervals for Carbon Monoxide Emissions from New Bus No. 3, Fitted to Lognormal Distribution (DL = g/mile)...145 Figure 5-7. Comparison of Empirical Distribution Function with Bootstrap Confidence Intervals for Carbon Monoxide Emissions from New Bus No. 3, Fitted to Gamma Distribution (DL = 5.0 g/mile)...146 Figure 5-8. Comparison of Empirical Distribution Function with Bootstrap Confidence Intervals for Carbon Monoxide Emissions from New Bus No. 3, Fitted to Weibull Distribution (DL = 5.0 g/mile)...146 Figure 5-9. Comparison of Empirical Distribution Function with Bootstrap Confidence Intervals for Carbon Monoxide Emissions from New Bus No. 3, Fitted to Lognormal Distribution (DL = 5.0 g/mile)...146 Figure 5-10. Comparison of Empirical Distribution Function with Bootstrap Confidence Intervals for Carbon Monoxide Emissions from New Bus No. 3, Fitted to Gamma Distribution (DL = 1 g/mile)...148 Figure 5-11. Comparison of Empirical Distribution Function with Bootstrap Confidence Intervals for Carbon Monoxide Emissions from New Bus No. 3, Fitted to Weibull Distribution (DL = 1 g/mile)...148 Figure 5-12. Comparison of Empirical Distribution Function with Bootstrap Confidence Intervals for Carbon Monoxide Emissions from New Bus No. 3, Fitted to Lognormal Distribution (DL = 1 g/mile)...148 Figure 5-13. Effect of Censoring on Uncertainty in Mean CO Emissions (g/mile) from New Bus No. 3, when Fitted to Gamma Distribution...155 Figure 5-14. Effect of Censoring on Uncertainty in Mean CO Emissions (g/mile) from New Bus No. 3, when Fitted to Weibull Distribution...155 Figure 5-15. Effect of Censoring on Uncertainty in Mean CO Emissions (g/mile) from New Bus No. 3, when Fitted to Lognormal Distribution...155 Figure A-1. Comparison of Cumulative Distribution Functions for each set of Estimated Parameters with the Empirical Distribution Function for a Data Set Containing 10 Data Points, Generated from a Gamma Distribution...176 Figure A-2. Comparison of Cumulative Distribution Functions for each set of Estimated Parameters with the Empirical Distribution Function for a Data Set Containing 20 Data Points, Generated from a Gamma Distribution...177 Figure A-3. Comparison of Cumulative Distribution Functions for each set of Estimated Parameters with the Empirical Distribution Function for a Data Set Containing 30 Data Points, Generated from a Gamma Distribution...177 Figure A-4. Comparison of Cumulative Distribution Functions for each set of Estimated Parameters with the Empirical Distribution Function for a Data Set Containing 40 Data Points, Generated from a Gamma Distribution...177 Figure A-5. Comparison of Cumulative Distribution Functions for each set of Estimated Parameters with the Empirical Distribution Function for a Data Set Containing 50 Data Points, Generated from a Gamma Distribution...178 Figure A-6. Two-Dimensional Plot Indicating the Effect of Censoring on Bootstrap Confidence Intervals for a Data Set Containing 10 Data Points. (Key: (A) 0 % Censoring; (B) 20 % Censoring; (C) 40 % Censoring; (D) 60 % Censoring)...179 Figure A-7. Two-Dimensional Plot Indicating the Effect of Censoring on Bootstrap Confidence Intervals for a Data Set Containing 20 Data Points. (Key: (A) 0 % Censoring; (B) 25 % Censoring; (C) 50 % Censoring; (D) 75 % Censoring)...180 xiii
Figure A-8. Two-Dimensional Plot Indicating the Effect of Censoring on Bootstrap Confidence Intervals for a Data Set Containing 30 Data Points. (Key: (A) 0 % Censoring; (B) 27 % Censoring; (C) 53 % Censoring; (D) 60 % Censoring)...181 Figure A-9. Two-Dimensional Plot Indicating the Effect of Censoring on Bootstrap Confidence Intervals for a Data Set Containing 40 Data Points. (Key: (A) 0 % Censoring; (B) 25 % Censoring; (C) 50 % Censoring; (D) 75 % Censoring)...182 Figure A-10. Two-Dimensional Plot Indicating the Effect of Censoring on Bootstrap Confidence Intervals for a Data Set Containing 50 Data Points. (Key: (A) 0 % Censoring; (B) 40 % Censoring; (C) 60 % Censoring; (D) 80 % Censoring)...183 Figure A-11. Comparison of Cumulative Distribution Functions for each set of Estimated Parameters with the Empirical Distribution Function for a Data Set Containing 10 Data Points, Generated from a Lognormal Distribution...184 Figure A-12. Comparison of Cumulative Distribution Functions for each set of Estimated Parameters with the Empirical Distribution Function for a Data Set Containing 20 Data Points, Generated from a Lognormal Distribution...185 Figure A-13. Comparison of Cumulative Distribution Functions for each set of Estimated Parameters with the Empirical Distribution Function for a Data Set Containing 30 Data Points, Generated from a Lognormal Distribution...185 Figure A-14. Comparison of Cumulative Distribution Functions for each set of Estimated Parameters with the Empirical Distribution Function for a Data Set Containing 40 Data Points, Generated from a Lognormal Distribution...185 Figure A-15. Comparison of Cumulative Distribution Functions for each set of Estimated Parameters with the Empirical Distribution Function for a Data Set Containing 50 Data Points, Generated from a Lognormal Distribution...186 Figure A-16. Two-Dimensional Plot Indicating the Effect of Censoring on Bootstrap Confidence Intervals for a Data Set Containing 10 Data Points. (Key: (A) 0 % Censoring; (B) 20 % Censoring; (C) 40 % Censoring; (D) 60 % Censoring)...187 Figure A-17. Two-Dimensional Plot Indicating the Effect of Censoring on Bootstrap Confidence Intervals for a Data Set Containing 20 Data Points. (Key: (A) 0 % Censoring; (B) 25 % Censoring; (C) 50 % Censoring; (D) 75 % Censoring)...188 Figure A-18. Two-Dimensional Plot Indicating the Effect of Censoring on Bootstrap Confidence Intervals for a Data Set Containing 30 Data Points. (Key: (A) 0 % Censoring; (B) 27 % Censoring; (C) 53 % Censoring; (D) 60 % Censoring)...189 Figure A-19. Two-Dimensional Plot Indicating the Effect of Censoring on Bootstrap Confidence Intervals for a Data Set Containing 40 Data Points. (Key: (A) 0 % Censoring; (B) 25 % Censoring; (C) 50 % Censoring; (D) 75 % Censoring)...190 Figure A-20. Two-Dimensional Plot Indicating the Effect of Censoring on Bootstrap Confidence Intervals for a Data Set Containing 50 Data Points. (Key: (A) 0 % Censoring; (B) 40 % Censoring; (C) 60 % Censoring; (D) 80 % Censoring)...191 Figure A-21. Comparison of Cumulative Distribution Functions for each set of Estimated Parameters with the Empirical Distribution Function for a Data Set Containing 10 Data Points, Generated from a Weibull Distribution...192 Figure A-22. Comparison of Cumulative Distribution Functions for each set of Estimated Parameters with the Empirical Distribution Function for a Data Set Containing 20 Data Points, Generated from a Weibull Distribution...193 xiv
Figure A-23. Comparison of Cumulative Distribution Functions for each set of Estimated Parameters with the Empirical Distribution Function for a Data Set Containing 30 Data Points, Generated from a Weibull Distribution...193 Figure A-24. Comparison of Cumulative Distribution Functions for each set of Estimated Parameters with the Empirical Distribution Function for a Data Set Containing 40 Data Points, Generated from a Weibull Distribution...193 Figure A-25. Comparison of Cumulative Distribution Functions for each set of Estimated Parameters with the Empirical Distribution Function for a Data Set Containing 50 Data Points, Generated from a Weibull Distribution...194 Figure A-26. Two-Dimensional Plot Indicating the Effect of Censoring on Bootstrap Confidence Intervals for a Data Set Containing 10 Data Points. (Key: (A) 0 % Censoring; (B) 20 % Censoring; (C) 40 % Censoring; (D) 60 % Censoring)...195 Figure A-27. Two-Dimensional Plot Indicating the Effect of Censoring on Bootstrap Confidence Intervals for a Data Set Containing 20 Data Points. (Key: (A) 0 % Censoring; (B) 25 % Censoring; (C) 50 % Censoring)....196 Figure A-28. Two-Dimensional Plot Indicating the Effect of Censoring on Bootstrap Confidence Intervals for a Data Set Containing 30 Data Points. (Key: (A) 0 % Censoring; (B) 27 % Censoring; (C) 53 % Censoring)....197 Figure A-29. Two-Dimensional Plot Indicating the Effect of Censoring on Bootstrap Confidence Intervals for a Data Set Containing 40 Data Points. (Key: (A) 0 % Censoring; (B) 25 % Censoring; (C) 50 % Censoring)....198 Figure A-30. Two-Dimensional Plot Indicating the Effect of Censoring on Bootstrap Confidence Intervals for a Data Set Containing 50 Data Points. (Key: (A) 0 % Censoring; (B) 40 % Censoring; (C) 60 % Censoring)....199 Figure B-1. Scatter Plot for 3-Month Average Heat Rate versus 3-Month Average Capacity Factor for Dry Bottom Wall-Fired Boilers with no NOx Controls....200 Figure B-2. Scatter Plot for 3-Month Average NO X Emissions on Input Basis versus 3- Month Average Capacity Factor for Dry Bottom Wall-Fired Boilers with no NOx Controls....200 Figure B-3. Scatter Plot for 3-Month Average NO X Emissions on Output Basis versus 3- Month Average Capacity Factor for Dry Bottom Wall-Fired Boilers with no NOx Controls....201 Figure B-4. Scatter Plot for 3-Month Average NO X Emissions on Input Basis versus 3- Month Average Heat Rate for Dry Bottom Wall-Fired Boilers with no NOx Controls...201 Figure B-5. Scatter Plot for 3-Month Average NO X Emissions on Output Basis versus 3- Month Average Heat Rate for Dry Bottom Wall-Fired Boilers with no NOx Controls...201 Figure B-6. Mean and Standard Deviation of 3-Month Average Capacity Factors for Six Quarters for Dry Bottom Wall-Fired Boilers with no NOx Controls...202 Figure B-7. Mean and Standard Deviation of 3-Month Average Heat Rates for Six Quarters for Dry Bottom Wall-Fired Boilers with no NOx Controls...202 Figure B-8. Mean and Standard Deviation of 3-Month Average NO X Emission Factor on Fuel Input Basis for Six Quarters for Dry Bottom Wall-Fired Boilers with no NOx Controls....202 Figure B-9. Mean and Standard Deviation of 3-Month Average NO X Emission Factor on Electricity Output Basis for Six Quarters for Dry Bottom Wall-Fired Boilers with no NOx Controls....203 Figure B-10. Variability in the Coefficient of Variation for 3-Month Average Capacity Factor of Dry Bottom Wall-Fired Boilers with no NOx Controls....204 Figure B-11. Variability in the Coefficient of Variation for 3-Month Average Heat Rate of Dry Bottom Wall-Fired Boilers with no NOx Controls...204 xv
Figure B-12. Variability in the Coefficient of Variation for 3-Month Average NO X Emission Factor on Fuel Input Basis of Dry Bottom Wall-Fired Boilers with no NOx Controls....204 Figure B-13. Variability in the Coefficient of Variation for 3-Month Average NO X Emission Factor on Electricity Output Basis of Dry Bottom Wall-Fired Boilers with no NOx Controls....205 Figure B-14. Comparison of Variability in 3-Month Average Heat Rates for Three Units Having a Low, Intermediate, and High Coefficient of Variation of Dry Bottom Wall-Fired Boilers with no NOx Controls....206 Figure B-15. Comparison of Variability in 3-Month Average Capacity Factors for Three Units Having a Low, Intermediate, and High Coefficient of Variation of Dry Bottom Wall-Fired Boilers with no NOx Controls...206 Figure B-16. Comparison of Variability in 3-Month Average NO X Emissions on Fuel Input Basis for Three Units Having a Low, Intermediate, and High Coefficient of Variation of Dry Bottom Wall-Fired Boilers with no NOx Controls...206 Figure B-17. Comparison of Variability in 3-Month Average NO X Emissions on Electricity Output Basis for Three Units Having a Low, Intermediate, and High Coefficient of Variation of Dry Bottom Wall-Fired Boilers with no NOx Controls...207 Figure B-18. Comparison of Confidence Intervals for 3-Month Average Capacity Factor and Standard Deviation in Capacity Factor, between each of the Four Quarters of 1997, for Dry Bottom Wall-Fired Boilers with no NOx Controls...208 Figure B-19. Comparison of Confidence Intervals for 3-Month Average Heat Rate and Standard Deviation in Heat Rate, between each of the Four Quarters of 1997, for Dry Bottom Wall-Fired Boilers with no NOx Controls...208 Figure B-20. Comparison of Confidence Intervals for 3-Month Average NO X Emissions on Fuel Input Basis and Standard Deviation in NO X Emissions on Fuel Input Basis, between each of the Four Quarters of 1997, for Dry Bottom Wall- Fired Boilers with no NOx Controls....209 Figure B-21. Comparison of Confidence Intervals for 3-Month Average NO X Emissions on Electricity Output Basis and Standard Deviation in NO X Emissions on Electricity Output Basis, between each of the Four Quarters of 1997, for Dry Bottom Wall-Fired Boilers with no NOx Controls...209 Figure B-22. Comparison of 3-month and 6-month Variability in Heat Rate for Dry Bottom Wall-Fired Boilers with no NOx Controls. (Number of Data Points: 3- month = 156, 6-month = 26)...210 Figure B-23. Comparison of 3-month and 6-month Variability in Capacity Factor for Dry Bottom Wall-Fired Boilers with no NOx Controls. (Number of Data Points: 3-month = 156, 6-month = 26)...210 Figure B-24. Comparison of 3-month and 6-month Variability in NO X Emissions on Fuel Input Basis for Dry Bottom Wall-Fired Boilers with no NOx Controls. (Number of Data Points: 3-month = 156, 6-month = 26)...210 Figure B-25. Comparison of 3-month and 6-month Variability in NO X Emissions on Electricity Output Basis for Dry Bottom Wall-Fired Boilers with no NOx Controls. (Number of Data Points: 3-month = 156, 6-month = 26)...211 Figure B-26. Three Month Average Heat Rate (Btu/kWh) Data for Dry Bottom Wall-Fired Boilers with no NOx Controls, Fitted to 3-Parameter Lognormal Distribution...212 Figure B-27. Three Month Average Capacity Factor Data for Dry Bottom Wall-Fired Boilers with no NOx Controls, Fitted to 2-Parameter Beta Distribution.. 212 xvi
Figure B-28. Three Month Average NO X Emission Factor (g /GJ) on Fuel Input Basis Data for Dry Bottom Wall-Fired Boilers with no NOx Controls, Fitted to 2- Parameter Gamma Distribution....212 Figure B-29. Three Month Average NO X Emission Factor (g/gj) on Electricity Output Basis Data for Dry Bottom Wall-Fired Boilers with no NOx Controls, Fitted to 2-Parameter Gamma Distribution...213 Figure B-30. Evaluation of the Adequacy of the Fitted Distribution for Representing the Six-Month Average Heat Rate for Dry Bottom Wall-Fired Boilers with no NOx Controls....214 Figure B-31. Evaluation of the Adequacy of the Fitted Distribution for Representing the Six-Month Average Capacity Factor for Dry Bottom Wall-Fired Boilers with no NOx Controls....214 Figure B-32. Evaluation of the Adequacy of the Fitted Distribution for Representing the Six-Month Average NO x Emissions on Fuel Input Basis for Dry Bottom Wall-Fired Boilers with no NOx Controls...214 Figure B-33. Evaluation of the Adequacy of the Fitted Distribution for Representing the Six-Month Average NO x Emissions on Electricity Output Basis for Dry Bottom Wall-Fired Boilers with no NOx Controls....215 Figure B-34. Two-Dimensional Plots Showing Effect of Spatial Averaging on Uncertainty in the Frequency Distribution of Six-Month Average Heat Rate for Dry Bottom Wall-Fired Boilers with no NOx Controls. (Key: (A) Number of Units = 5; (B) Number of Units = 10; (C) Number of Units = 20)...216 Figure B-35. Two-Dimensional Plots Showing Effect of Spatial Averaging on Uncertainty in the Frequency Distribution of Six-Month Average Capacity Factor for Dry Bottom Wall-Fired Boilers with no NOx Controls. (Key: (A) Number of Units = 5; (B) Number of Units = 10; (C) Number of Units = 20)...217 Figure B-36. Two-Dimensional Plots Showing Effect of Spatial Averaging on Uncertainty in the Frequency Distribution of Six-Month Average NO x Emissions on Fuel Input Basis for Dry Bottom Wall-Fired Boilers with no NOx Controls. (Key: (A) Number of Units = 5; (B) Number of Units = 10; (C) Number of Units = 20)...218 Figure B-37. Two-Dimensional Plots Showing Effect of Spatial Averaging on Uncertainty in the Frequency Distribution of Six-Month Average NO x Emissions on Electricity Output Basis for Dry Bottom Wall-Fired Boilers with no NOx Controls. (Key: (A) Number of Units = 5; (B) Number of Units = 10; (C) Number of Units = 20)...219 Figure B-38. Uncertainty in Mean of Six-Month Average Heat Rate for Dry Bottom Wall- Fired Boilers with no NOx Controls....220 Figure B-39. Uncertainty in Mean of Six-Month Average Capacity Factor for Dry Bottom Wall-Fired Boilers with no NOx Controls...220 Figure B-40. Uncertainty in Mean of Six-Month Average NO X Emission Factor on Fuel Input Basis for Dry Bottom Wall-Fired Boilers with no NOx Controls.. 220 Figure B-41. Uncertainty in Mean of Six-Month Average NO X Emission Factor on Electricity Output Basis for Dry Bottom Wall-Fired Boilers with no NOx Controls...221 Figure B-42. Scatter Plot for 3-Month Average Heat Rate versus 3-Month Average Capacity Factor for Dry Bottom Wall-Fired Boilers with Low NOx Burners and Overfire Air...222 Figure B-43. Scatter Plot for 3-Month Average NO X Emissions on Input Basis versus 3- Month Average Capacity Factor for Dry Bottom Wall-Fired Boilers with Low NOx Burners and Overfire Air...222 Figure B-44. Scatter Plot for 3-Month Average NO X Emissions on Output Basis versus 3- Month Average Capacity Factor for Dry Bottom Wall-Fired Boilers with Low NOx Burners and Overfire Air...223 xvii
Figure B-45. Scatter Plot for 3-Month Average NO X Emissions on Input Basis versus 3- Month Average Heat Rate for Dry Bottom Wall-Fired Boilers with Low NOx Burners and Overfire Air...223 Figure B-46. Scatter Plot for 3-Month Average NO X Emissions on Output Basis versus 3- Month Average Heat Rate for Dry Bottom Wall-Fired Boilers with Low NOx Burners and Overfire Air...223 Figure B-47. Mean and Standard Deviation of 3-Month Average Capacity Factors for Six Quarters for Dry Bottom Wall-Fired Boilers with Low NOx Burners and Overfire Air...224 Figure B-48. Mean and Standard Deviation of 3-Month Average Heat Rates for Six Quarters for Dry Bottom Wall-Fired Boilers with Low NOx Burners and Overfire Air...224 Figure B-49. Mean and Standard Deviation of 3-Month Average NO X Emission Factor on Fuel Input Basis for Six Quarters for Dry Bottom Wall-Fired Boilers with Low NOx Burners and Overfire Air...224 Figure B-50. Mean and Standard Deviation of 3-Month Average NO X Emission Factor on Electricity Output Basis for Six Quarters for Dry Bottom Wall-Fired Boilers with Low NOx Burners and Overfire Air...225 Figure B-51. Variability in the Coefficient of Variation for 3-Month Average Capacity Factor of Dry Bottom Wall-Fired Boilers with Low NOx Burners and Overfire Air...226 Figure B-52. Variability in the Coefficient of Variation for 3-Month Average Heat Rate of Dry Bottom Wall-Fired Boilers with Low NOx Burners and Overfire Air.226 Figure B-53. Variability in the Coefficient of Variation for 3-Month Average NO X Emission Factor on Fuel Input Basis of Dry Bottom Wall-Fired Boilers with Low NOx Burners and Overfire Air...226 Figure B-54. Variability in the Coefficient of Variation for 3-Month Average NO X Emission Factor on Electricity Output Basis of Dry Bottom Wall-Fired Boilers with Low NOx Burners and Overfire Air....227 Figure B-55. Comparison of Variability in 3-Month Average Heat Rates for Three Units Having a Low, Intermediate, and High Coefficient of Variation of Dry Bottom Wall-Fired Boilers with Low NOx Burners and Overfire Air....228 Figure B-56. Comparison of Variability in 3-Month Average Capacity Factors for Three Units Having a Low, Intermediate, and High Coefficient of Variation of Dry Bottom Wall-Fired Boilers with Low NOx Burners and Overfire Air.228 Figure B-57. Comparison of Variability in 3-Month Average NO X Emissions on Fuel Input Basis for Three Units Having a Low, Intermediate, and High Coefficient of Variation of Dry Bottom Wall-Fired Boilers with Low NOx Burners and Overfire Air....228 Figure B-58. Comparison of Variability in 3-Month Average NO X Emissions on Electricity Output Basis for Three Units Having a Low, Intermediate, and High Coefficient of Variation of Dry Bottom Wall-Fired Boilers with Low NOx Burners and Overfire Air....229 Figure B-59. Comparison of Confidence Intervals for 3-Month Average Capacity Factor and Standard Deviation in Capacity Factor, between each of the Four Quarters of 1997, for Dry Bottom Wall-Fired Boilers with Low NOx Burners and Overfire Air....230 Figure B-60. Comparison of Confidence Intervals for 3-Month Average Heat Rate and Standard Deviation in Heat Rate, between each of the Four Quarters of 1997, for Dry Bottom Wall-Fired Boilers with Low NOx Burners and Overfire Air...230 Figure B-61. Comparison of Confidence Intervals for 3-Month Average NO X Emissions on Fuel Input Basis and Standard Deviation in NO X Emissions on Fuel Input xviii