Single particle studies of pulverized coal oxy-combustion

Modeling and experimental studies of the oxy-combustion behavior of pulverized coal chars are detailed in this work. During oxy-combustion, nitrogen is separated from oxygen before the introduction of oxygen, recycled flue-gas, and fuel into a coal boiler. The nearly pure CO2 effluent (after condensation of H2O) can be captured through condensation, and then utilized or stored, preventing the climate changing impacts of this greenhouse gas. Although oxy-combustion has been considered and studied for over a decade, there are still misunderstood aspects of the science th a t this research aims to clarify through modeling and experimental studies. First, a detailed model of a single char particle is presented. The detailed model is employed to assess the impact of CO2 and steam gasification reactions on the oxy-combustion of coal chars. The detailed model indicates th a t gasification reactions reduce the predicted char particle temperature significantly. Lower temperatures reduce the radiant emission and rate of char oxidation, but the char carbon consumption rate actually increases by approximately 1 0%, since the gasification reactions are consuming carbon (in addition to the oxygen). Gasification reactions account for about 20% of the carbon consumption in low oxygen conditions, and about 30% of the carbon consumption under oxygen enriched conditions. Secondly, typical pulverized coal char combustion modeling assumptions are described and two simplified models are compared to the detailed model. The single-film model, wherein gas-phase reactions are ignored yields accurate results, with particle temperature predictions accurate to within 270 K, and carbon consumption rate predictions accurate to within 16%. Finally, an entrained flow reactor (EFR) was used to make measurements of singleparticle temperatures under a wide range of conditions for three coal chars. The environments ranged from 24-60% O2, 10-14% H2O, with N2 or CO2 serving as the diluent. Collected chars were also analyzed for burnout and surface area. Kinetic parameters were found for the simplified model to fit the experimental data, for each of the coal chars, over the wide range of environments studied. The model described herein and these kinetic parameters can be used in more complex CFD codes to accurately predict the oxy-combustion behavior of coal chars.

SINGLE PARTICLE STUDIES OF PULVERIZED COAL OXY-COMBUSTION by E than S. Hecht A dissertation submitted to the faculty of The University of Utah in partial fulfillment of the requirements for the degree of Doctor of Philosophy Department of Chemical Engineering The University of Utah May 2013 Copyright © Ethan S. Hecht 2013 All Rights Reserved The Unive r si t y of Utah Gradua te School STATEMENT OF DISSERTATION APPROVAL The dissertation of Ethan S. Hecht has been approved by the following supervisory committee members: JoAnn S. Lighty Chair Jan 4, 2013 Date Approved Christopher R. Shaddix Member Jan 4, 2013 Date Approved Jost O. Wendt Member Jan 4, 2013 Date Approved Philip J. Smith Member Jan 4, 2013 Date Approved James C. Sutherland Member Jan 4, 2013 Date Approved and by JoAnn S. Lighty the Department of Chemical Engineering Chair of and by Donna M. White, Interim Dean of The Graduate School. ABSTRACT Modeling and experimental studies of the oxy-combustion behavior of pulverized coal chars are detailed in this work. During oxy-combustion, nitrogen is separated from oxygen before the introduction of oxygen, recycled flue-gas, and fuel into a coal boiler. The nearly pure CO2 effluent (after condensation of H2O) can be captured through condensation, and then utilized or stored, preventing the climate changing impacts of this greenhouse gas. Although oxy-combustion has been considered and studied for over a decade, there are still misunderstood aspects of the science th a t this research aims to clarify through modeling and experimental studies. First, a detailed model of a single char particle is presented. The detailed model is em­ployed to assess the impact of CO2 and steam gasification reactions on the oxy-combustion of coal chars. The detailed model indicates th a t gasification reactions reduce the predicted char particle temperature significantly. Lower temperatures reduce the radiant emission and rate of char oxidation, but the char carbon consumption rate actually increases by approximately 1 0%, since the gasification reactions are consuming carbon (in addition to the oxygen). Gasification reactions account for about 20% of the carbon consumption in low oxygen conditions, and about 30% of the carbon consumption under oxygen enriched conditions. Secondly, typical pulverized coal char combustion modeling assumptions are described and two simplified models are compared to the detailed model. The single-film model, wherein gas-phase reactions are ignored yields accurate results, with particle temperature predictions accurate to within 270 K, and carbon consumption rate predictions accurate to within 16%. Finally, an entrained flow reactor (EFR) was used to make measurements of single­particle temperatures under a wide range of conditions for three coal chars. The envi­ronments ranged from 24-60% O2, 10-14% H2O, with N2 or CO2 serving as the diluent. Collected chars were also analyzed for burnout and surface area. Kinetic parameters were found for the simplified model to fit the experimental data, for each of the coal chars, over the wide range of environments studied. The model described herein and these kinetic parameters can be used in more complex CFD codes to accurately predict the oxy-combustion behavior of coal chars. iv CONTENTS A B S T R A C T .................................................................................................................................... iii L IS T O F F IG U R E S .................................................................................................................... vii L IS T O F T A B L E S ......................................................................................................................... xi A C K N O W L E D G E M E N T S ...................................................................................................... xii 1......IN T R O D U C T IO N ............................................................................................................... 1 2. M O D E L D E S C R IP T IO N ................................................................................................. 7 2.1 SKIPPY Model Description .......................................................................................... 7 2 .1 .1 Governing E q u a tio n s............................................................................................... 7 2.1.2 Discretization and Boundary Conditions ........................................................ 9 2.1.3 Solution P ro c e d u r e ................................................................................................. 11 3. E F F E C T O F C O 2 A N D S T E A M G A S IF IC A T IO N R E A C T IO N S ON T H E O X Y -C O M B U S T IO N O F PU L V E R IZ E D CO AL C H A R ................. 13 3.1 Abstract .............................................................................................................................. 13 3.2 Introduction ....................................................................................................................... 14 3.3 Gasification Rates at 1 a tm ............................................................................................ 15 3.4 Model Description ............................................................................................................. 17 3.5 Results .................................................................................................................................. 21 3.5.1 Effect of Gasification Rate Coefficients on Particle Temperature and Species Profiles 21 3.5.2 Effect of Gasification Rate Coefficients on Char Consumption Rate . . . 25 3.5.3 Gas Temperature and Particle Size Effects ..................................................... 27 3.5.4 Gasification Reactions in Oxy- vs. Air-fired Combustion Environments 31 3.5.5 Implications for Char Combustion Modeling and Interpretation of Ex­perimental Measurements 34 3.6 Conclusions........................................................................................................................ 35 4. AN ALY SIS O F T H E E R R O R S A S SO C IA T ED W IT H T Y P IC A L P U L ­V E R IZ E D COAL C H A R C O M B U S T IO N M O D E L IN G A S SU M P T IO N S F O R O X Y -FU E L C O M B U S T IO N 36 4.1 Abstract .............................................................................................................................. 36 4.2 Nomenclature .................................................................................................................... 37 4.3 Introduction ....................................................................................................................... 38 4.4 Description of Models ...................................................................................................... 39 4.4.1 Single-film Model ................................................................................................... 41 4.4.2 Double-film Model ................................................................................................. 42 4.4.3 Heterogeneous Reactions....................................................................................... 43 4.4.4 Solution P ro c e d u r e ................................................................................................. 44 4.5 Results and D is c u ss io n ................................................................................................... 45 4.6 Modeling Imp lic a tio n s...................................................................................................... 59 4.7 Conclusions........................................................................................................................ 63 5. E X P E R IM E N T A L D E S C R IP T IO N ......................................................................... 65 6 . E X P E R IM E N T A L M E A S U R EM E N T S A N D A N A LY S IS O F COAL C H A R S R E A C T IN G IN O X Y -C O M B U S T IO N E N V IR O N M E N T S . . 70 6.1 Introduction ....................................................................................................................... 70 6.2 Methods .............................................................................................................................. 72 6.3 Results and Discussion ................................................................................................... 76 6.3.1 Experimentally Measured Temperatures.......................................................... 76 6.3.2 Experimentally Measured Surface Area and B u rn o u t.................................. 81 6.3.3 Kinetic F i t s ............................................................................................................... 87 6.3.4 Parametric A n a ly ses............................................................................................... 92 6.4 Conclusions ......................................................................................................................... 96 7. C O N C L U S IO N S .................................................................................................................... 99 R E F E R E N C E S .............................................................................................................................. 103 vi LIST OF FIGURES 1.1 Van Krevelen diagram for biomass through anthracite coal. Labels are either the mine name, country of origin, or composition for biomass............................... 2 1.2 Ratio of CO2 to N2 properties at 2000 K ...................................................................... 5 3.1 Predicted and measured [56] char particle temperatures for a particle reacting in a 1690K, 14% H2O, O2, balance N2 environment while varying the presumed surface area and activation energy of the steam and CO2 gasification reactions. Units of activation energy are k J/m o l............................................................................. 20 3.2 Temperature and species profiles as functions of normalized distance from the center of a 100 ^m diameter char particle burning in 1 2% O2 in CO2 at 1690 K. r / r p = 1 corresponds to the surface of the particle. The panels on the left represent a dry-recycle oxy-combustion environment, with 14% H2O in the bulk gas, whereas the panels on the right represent a wet-recycle oxy-combustion environment, with 25% H2O in the bulk gas. Different line colors represent different assumed rate coefficients for the CO2 gasification reaction, whereas different line styles represent different assumed rate coefficients for gasification by H2O, as shown in the legend. The thick black line represents the best-guesses of CO2 and H2O gasification rate coefficients. For gasification by CO2, the best-guess pre-exponential value (corresponding to a normalized rate coefficient of 1) is 3.6 x 1015 mol/cm2 ■ s and for gasification by H2O, the best-guess pre-exponential is 4.4 x 1014 mol/cm2 ■ s................................................... 22 3.3 Temperature and species profiles as a function of normalized distance from the center of a char particle burning in 36% O2 in CO2 at 1690 K. Right/left panel conventions and line styles and colors are the same as for Fig. 3.2............ 24 3.4 Contour plots showing the total carbon consumption rates as the CO2 and H2O gasification rate coefficients are varied. The gasification rate coefficients have been normalized using the same best-guess pre-exponentials as for Figs. 3.2 and 3.3. Carbon consumption rates have been normalized by the rate at the best-guess gasification rates (normalized rate of 1). Absolute carbon consumption rates at the best-guess gasification rate coefficients are shown on the plots............................................................................................................................. 26 3.5 Relative contributions to carbon consumption by reactions with oxygen, car­bon dioxide, and steam. Size of circle is proportional to overall carbon con­sumption rate, and percentages of contributions are shown on the chart. Open circles show particle surface temperature and relative carbon consumption rate without gasification reactions (only oxidation), and filled circles include gasification reactions at our best-guess rate coefficients............................................ 28 3.6 Particle temperature and carbon consumption rate as a function of gas tem­perature and particle size for dry-recycle oxy-fuel combustion in 1 2% and 36% O2. Solid lines are simulations using the best-guess gasification rates, dashed lines are simulations without gasification reactions. When varying gas temperature, a particle diameter of 1 0 0 ^m is used, and when varying particle diameter a gas temperature of 1690 K is used............................................................. 29 3.7 Temperature and species profiles as a function of normalized distance from the center of a 100 ^m char particle burning in an air-fired environment (N2 diluent) at 1690 K. Left panel are results for 12% O2 in the bulk gas, and the right panel are results for 36% O2 in the bulk gas (note the separate axes). Solid lines include oxidation and gasification reactions using the best-guess rate coefficients while dashed lines only include oxidation reactions..................... 32 4.1 Comparison temperatures and mole-fractions of gas phase species in the par­ticle and in the boundary layer for the 1 0 0 ^m particle characterized by Table 4.2. Results are for the single-film, double-film, and SKIPPY models. Thick, solid gray line is SKIPPY with all chemistries; thin, solid blue line is SKIPPY without gas-phase chemistry. The diluent gas on the following page is CO2 and on the second following page is N2. Both plots have 14 vol-% H2O and 24% O2 in the bulk gas. N2 diluent includes 4% CO2 in the bulk gas. . . . 47 4.1 Continued................................................................................................................................ 49 4.2 Particle temperatures (top) and carbon fluxes at the particle surface (bottom) predicted by the different models for the 1 0 0 ^m particle characterized by Table 4.2. Frames on the left are for the CO2 diluent and frames on the right are for the N2 diluent. In the bottom frames, the bars leading up to the d a ta points with the same line style show the portion of carbon consumption attrib u ted to the gasifiying species shown in the legend (O2, CO2, or H2O). . . 51 4.3 Particle temperatures and carbon consumption rates for the models as a function of particle size. Bulk oxygen concentration increases from top to bottom, as listed in the top of each frame. CO2 diluent results are in the left frames, and N2 diluent results in the right. Line colors and styles match those in Fig. 4.2. ............................................................................................................................ 54 4.4 Temperatures and carbon consumption rates as a function of specific surface area. The three sets of frames to the left are for a CO2 diluent, and the three frames to the right for the N2 diluent for different sizes of particles, as labeled at the top. The oxygen concentration in the bulk gas increases from top to bottom, as listed in each frame. Line colors and styles match those in Fig. 4.2. 57 4.5 Top frames show the pre-exponential factors required by the apparent kinetic model required to match the temperatures and carbon consumption rates (for each of the three reactants) predicted by the intrinsic single-film model for a 100 ^m char particle. Middle and bottom frames are the temperature and carbon consumption rates for the apparent and intrinsic models, where the pre-exponential factors for the apparent kinetic model are 3900, 210, 3100, 1200 m /s for Rxns. 4.1-4.4, respectively. CO2 diluent results are in the left frames, and N2 diluent results in the right. Line colors and styles match those in Fig. 4.2, or are shown in the legends.......................................................................... 61 viii 5.1 Optically accessible laminar entrained flow reactor. Particles are fed into the center of a flat-flame Hencken burner and react as they travel upwards in a quartz chimney. A laser scatters off individual particles when they are in the focus plane of the optics, triggering the d a ta acquisition system, which measures the particle emission at two wavelengths as the image travels across a coded ap e rtu re .................................................................................................................... 6 6 5.2 Brunauer-Emmett-Teller (BET) and Dubinin-Radushkevich (DR) isotherms. BET isotherms are labeled by the number of adsorbed layers................................ 68 6.1 Gas temperature measurements in the different environments. There is hys­teresis in some of the d a ta as the thermocouple approached the burner and then moved away.................................................................................................................... 77 6.2 Digital photos of 90-106 ^m Utah Skyline char combustion in different envi­ronments. Capital letter A denotes a diluent (balance) gas of CO2 and capital B denotes a N2 diluent. Lowercase letters denote: a) 24% O2, 14% H2O b) 36% O2, 10% H2O c) 36% O2 , 14% H2O, d) 60% O2 , 10% H2O, e) 60% O2 , 14% H2O, f) b) 60% O2, 16% H2O. The bright blue at the bottom of the picture is the Hencken burner and the particles are flowing and reacting upwards in the pictures. The top of the picture is about 18 in above the burner, and the limit of the quartz chimney................................................................................................. 78 6.3 Utah Skyline char temperatures. Legend describes fed particle size, diluent gas (balance other th an O2 and H2O), and O2 and H2O vol-%. Circles are mean temperatures, and shaded region in the background are the normalized number density of particles within 20 K bins, showing the spread of the data. 79 6.4 Char temperatures as a function of fed char diameter. Closed circles with long dashes have CO2 as a diluent while open circles and short dashes have N2 as a diluent. Colors are different steam concentrations, and the oxygen concentration varies with the vertical frames, as shown on the graph.................. 80 6.5 Complete set of burnout da ta as a function of residence time in the reactor. Faint dashed lines in the background are the gas temperatures for the different environments. Symbol types and sizes are related to fed char size, and colors are related to steam concentration. N2 diluent has open symbols, and CO2 are filled, as detailed in the legend. Error bars are the standard deviation, and are only shown on da ta where experiments were repeated............................... 82 6 .6 Measured surface areas as a function of residence time in the reactor (left), and corresponding fixed carbon and measured particle temperatures (right), with mean temperatures shown by the symbols, and histograms of the measured particles in 20 K increments shown by the light shading in the background. . 85 6.7 SEM images of the starting chars (top) and partially reacted chars (bottom). . 86 6 .8 Reaction rate coefficients using the fit kinetic parameters shown in Table 6.2. The left-hand frames show the rate coefficients grouped by reaction, and the right-hand frames displays the rate coefficients grouped by char........................... 88 6.9 Simulated and experimentally measured char temperatures as a function of fed char diameter. Simulations using the kinetics given in Table 6 .2 are shown by the lines, while the da ta of Fig. 6.4 are plotted as the symbols for comparison. Symbol styles and colors are the same as Fig. 6.4....................................................... 89 ix 6.10 Reaction rate coefficients using the computer optimized kinetic parameters shown in Table 6.2 for the Black Thunder char, and the manually adjusted rate parameters shown in Table 6.3 for the bituminous chars................................. 91 6.11 Simulated and experimentally measured char temperatures as a function of fed char diameter. Black Thunder char kinetics are given in Table 6.2, while bituminous char kinetics (both Utah Skyline and Illinois # 6 ) are given in Table 6.3. Simulations are shown by the lines, while the d a ta of Fig. 6.4 are plotted as the symbols for comparison. Symbol styles and colors are the same as Fig. 6.4................................................................................................................................ 92 6.12 Temperature and burnout characteristics of the three chars used in this study. Symbols/density plots are experimental data, and lines are simulations. The fed size and environment were held constant at the conditions shown above the plot. BT is Black Thunder, US is Utah Skyline, and I6 is Illinois # 6 .......... 93 6.13 Temperature and burnout characteristics of two chars used while holding all but the oxygen concentration constant. Symbols/density plots are experimen­tal data, and lines are simulations. .............................................................................. 94 6.14 Temperature and burnout characteristics of two chars used while holding all but the fed particle size constant. Symbols/density plots are experimental data, and lines are simulations. ..................................................................................... 94 6.15 Temperature and burnout characteristics while holding all but the diluent con­stant. Symbols/density plots are experimental data, and lines are simulations. ................................................................................................................................................... 95 6.16 Temperature and burnout characteristics while holding all but the bulk steam concentration constant. Symbols/density plots are experimental data, and lines are simulations. ........................................................................................................ 96 x LIST OF TABLES 3.1 Ratio of Steam Gasification to Oxidation at 800 ° C ................................................ 17 3.2 Heterogeneous reaction m e ch an ism ................................................................................ 18 3.3 Properties for the base-case simulations, which are the same as the sub-bituminous char studied by Geier et al. [56] and as assumed in the simulations by Hecht et al. [17]................................................................................................................ 19 3.4 Effectiveness factors for each reactant under dry-recycle oxy-fuel combustion conditions................................................................................................................................ 30 3.5 Decrease in surface temperature and increase in char conversion rate if gasifi­cation reactions are included in the model. Percentages are calculated based off the values considering only oxidation reactions..................................................... 33 4.1 Heterogeneous reaction mechanism. The density of surface carbon sites is 1.7 x 10- 5 molCs/m 3 ............................................................................................................. 40 4.2 Properties for the base-case simulations, which are the same as the sub-bituminous char studied by Geier et al. [56] and as assumed in the simulations by Hecht et al. [17, 28]......................................................................................................... 46 6.1 Proximate and Ultimate analyses for the three project coals ............................... 73 6.2 Best fit kinetic parameters for the three project chars. Units of A are m/s, and units of E are k J /m o l.................................................................................................. 87 6.3 Manually adjusted kinetic parameters for the bituminous chars. Units of A are m/s, and units of E are k J /m o l................................................................................. 90 ACKNOWLEDGEMENTS There are many people and organizations to whom I am grateful for their support. I would first like to thank my advisor, Prof. JoAnn Lighty, and Dr. Chris Shaddix, for realizing what a perfect candidate I was for this project, and seeing the potential for such a synergistic relationship between myself, the University of Utah, and Sandia National Labs. My time and tuition was funded through the Sandia National Laboratories Doctoral Studies program, and additional funding was provided by both the National Energy Technology Laboratory's Power Systems Advanced Research Program, managed by Dr. Robert Romanosky, through Sandia, and the University of Utah, Institute for Clean and Secure Energy Clean Coal program, as Award Number DE-NT0005015, managed by David Lang. In addition to recommending and suggesting my work on this project, I also appre­ciate the guidance and scientific insights provided by Prof. JoAnn Lighty and Dr. Chris Shaddix, as well as my other committee members, Prof. Jost Wendt, Prof. Phil Smith, and Prof. James Sutherland. I am grateful to Stephanie ‘Skipper' Coates and Cristina Jaramillo for performing many of the TGA experiments th a t I would not have had time to run on my own. Dana Overacker did a great job of keeping the labs at the U in order and supplies stocked. Finally, I would like to thank my wife, Jennifer, for her emotional support and encour­agement to pursue a Ph.D., even though it meant we had to spend time apart. CHAPTER 1 INTRODUCTION Coal is a heterogeneous rock of vegetable origin th a t contains large amounts of carbon (65-95%), some hydrogen, oxygen, sulfur, and nitrogen, along with mineral m atter th at remains as ash postcombustion. A contiguous layer of coal, or seam, will have a fairly uniform composition and the combustion kinetics can be characterized with limited error. Coals from different seams, however, can range widely in composition and combustion characteristics. Coals are classified by rank, which is an indication of reactivity. If one plots the atomic hydrogen to carbon ratio as a function of the atomic oxygen to carbon ratio on a Van Krevelen diagram, different groupings appear. A Van Krevelen diagram is shown in Fig. 1.1, with more ordered carbons, or higher rank coals on the bottom left of the chart, and less ordered carbons with larger amounts of oxygen and hydrogen towards the upper right corner of the chart. The highest rank coals are classified as anthracite, then bituminous, sub-bituminous and the lowest rank, lignite. As shown on the chart, biomass is of comparable rank to lignite coal. High rank coals contain and release the most energy during combustion, but are also more difficult to ignite and burn to completion. On Stones by Theophrastus provides written evidence of lignite coal combustion by the Greeks as early as 200 BC [1]. Electric power generation from coal combustion on a commercial scale began with a plant built by Thomas Edison in 1882 [2]. Today, coal is still an abundant resource with 860 billion tons of proved recoverable reserves in the world in 2008, around 27% of which is in the United States [3]. In 2009, coal was responsible for about 27% of the world energy supply, almost 41% of the global electricity supply, but was also responsible for 43% of the world CO2 emissions [4]. With the abundance and current usage of coal, it is likely to be an important part of energy generation for many years to come. Over the past few decades, climate change concerns have prompted the development of regulations and technologies to reduce carbon dioxide emissions. 2 i i i i i i r • Biomass O Lignite • Sub-bituminous O Bituminous • Anthracite Eucalyptus--^ North Antelope^ Black Thunder-^ l Com S to v er^ Illinois ...- Utah Skyline-^ ^^Highvale 8 7 South Afi 6 Spanish"^ 3____ i___ i__ i__i__i_i-L 3 4 5 6 7 8 9 2 J______ I_____I____I___I__ I__l-t 3 4 5 6 7 8 9 0.1 1 O/C (atomic) F ig u re 1.1. Van Krevelen diagram for biomass through anthracite coal. Labels are either the mine name, country of origin, or composition for biomass. Coal combustion, accounting for such a large share of CO2 emissions, will require cost-an d /o r storage as the regulations become more stringent. There are several strategies th at allow CO2 to be captured from coal combustion. The first is precombustion CO2 capture. In the integrated gasification combined cycle (IGCC) system, the fuel is first gasified to syngas and then the water gas shift reaction converts the fuel to H2 , capturing the CO2 along the way. The H2 is then used as the fuel for a gas turbine. postcombustion capture is also possible. The second strategy for coal combustion while capturing CO2 is amine stripping, which can be used to condense dilute CO2 after conventional combustion. The third approach is oxy-combustion with flue-gas recirculation, where oxygen is separated from the air before combustion and then mixed with a portion of the flue-gas (primarily consisting of CO2 and steam) before injection into a coal boiler. Flue-gas recirculation is required to moderate the combustion temperature and prevent excessive furnace slagging. This method generates a highly-concentrated CO2 effluent th a t can be readily compressed and utilized or stored. Some research has found this to be a more efficient strategy than conventional combustion with tail-end CO2 capture by amine stripping [5, 6 ]. While IGCC has the potential for slightly higher efficiencies and lower capital costs th an newly-built oxy-combustion facilities with carbon capture, this technology is not available for retrofit on the extensive infrastructure th a t exists for conventional pulverized coal combustion. In effective technology to capture this combustion product and make it available for utilization 3 a recent review, Chen et al. [6 ] summarize studies on capital cost and generating efficiencies of different strategies of coal combustion with carbon capture. They find th a t oxy-fuel combustion is slightly more efficient th an postcombustion capture and has a much lower capital cost as a retrofit technology. Pressurized oxy-combustion is estimated to offer even higher efficiencies th an atmospheric pressure combustion [6 , 7], but would be limited to newly built coal boilers. In addition to the greater efficiency of oxy-combustion th an conventional combustion with amine stripping, Chen et al. [6] also report th a t lower NOx emissions are attrib u ted to less thermal and prompt NOx formation. Reduced NOx is attrib u ted to the reduced partial pressure of N2, the effect of CO2 as a getter for radicals, and the reburning of NO as the flue-gas is recycled. Unfortunately, higher concentrations of SOx are also observed, due to lower volumes of total emissions, with the same volume of SOx as would be present in traditional combustion. Increased SOx could cause corrosion in the furnace. Increased CO emissions as compared to conventional combustion are also possible, due to CO2 dissociation. In this work, the combustion characteristics of pulverized coal particles are considered, with a characteristic dimension less than 2 0 0 ^m. At the beginning of the combustion process, a coal particle is rapidly heated and moisture and loosely bound volatile components are released. These gas phase volatiles combust rapidly, producing bright emissions from the soot generated [8 ]. The heating rate and oxygen concentration, in addition to coal rank and composition affect both the amount of volatile matter released and the resulting char pore structure [9]. As the oxygen concentration increases (for a given diluent), the size of the soot cloud, the ignition delay, and the volatile combustion time decrease [8 ]. This work is not concerned with the kinetics or mechanisms of devolatilization. The focus of this work is on the processes th a t occur after devolatilization, when the resulting porous carbon and ash, or char, particles continue to burn. Char combustion kinetics are much slower th an gas phase combustion, and the burn-out characteristics are important in coal fired boiler design, so a high-quality ash th a t is a commodity rather th an waste stream is generated [10]. Pulverized coal char combustion is not necessarily only limited by kinetics, but can also have mass-transfer limitations, both in the gas-phase and within the porous particle, making d a ta analysis and modeling more complex. Coal combustion literature describes three different zones: Zone I is combustion when there are no mass-transfer limitations, with reactions occurring throughout the pores of the particle; Zone II is combustion when there are both mass-transfer and kinetic limitations; and Zone III is combustion where mass-transfer in the boundary layer limits the reaction rates, and 4 the combustion only occurs on the surface of the particle. Pulverized coal combustion typically occurs under Zone II conditions, requiring a description of boundary-layer mass-transfer, heterogeneous kinetics, and mass-transfer within the pores of the particle. Because pulverized coal particles are small, the slip velocity between the gas and particle is also small. The gas layer can be thought of as being stagnant with respect to the particles, and therefore one-dimensional, assuming th a t the particles are spherically symmetrical. The kinetics of coal chars reacting with oxygen have been studied extensively [9, 11-13], b ut the reactions of chars with CO2 and H2O are often neglected due to high activation energies and low concentrations of reactants (in the bulk gas). During oxy-combustion with flue-gas recycle, there are much higher concentrations of CO2 in the bulk gas, and the potential for much higher concentrations of H2O, depending on the extent to which the flue-gas is dried before recycle. Furthermore, different oxygen feed strategies during oxy-combustion may be necessary to achieve flame stability and since pure oxygen must be available for the oxy-combustion process, there is the potential to have higher concentrations of oxygen, either in the primary and secondary streams, or as oxygen lances in various locations in the coal burner. Exothermic oxidation reactions in regions with high oxygen concentrations will cause high coal char temperatures, overcoming high activation energies. Therefore, there is a much greater potential for gasification reactions to have an impact on coal combustion kinetics under oxy-fired conditions. There has been some speculation th at the gasification reactions may enhance the char burning rate in oxy-fuel combustion [14-16]. In a previous study, our group at Sandia found th a t the overall consumption rate of a char particle reacting at a temperature near the gas temperature (i.e. at low O2 concentration in the surrounding gas) is slightly increased by the CO2 gasification reaction, but when the particle is reacting at a temperature considerably higher th an the ambient gas temperature (i.e. an O2-enriched environment), the CO2 gasification reaction decreases the overall carbon removal rate, again by a small amount [17]. Under air-fired conditions, nearly 80% of the gas is N2. Replacing N2 with CO2 and increased levels of steam under oxy-combustion conditions affects the gas-phase properties, as shown in Fig. 1.2. A reduction in burning rate of char particles is attrib u ted to the lower rate of oxygen diffusion through CO2 in the particle boundary layer [18-20]. Ignition delay and volatile combustion times are also found to increase slightly when CO2 replaces N2 [8 , 20-22]. Flame stability problems are also reported due to the lower adiabatic flame temperature, flame propagation speed [23], and delayed ignition in CO2. In addition, both CO2 and H2O are radiantly active gas species, altering heat transfer between the particles 5 Molar Heat Capacity Molecular Weight ^ Density,--------- Thermal Conductivity Viscosity 0 2 Diffusivity ]_ 3 /vvC^nI s co2/n 2 Q H20/N2 at 2000 K 0.0 0.5 1.0 1.5 2.0 F ig u re 1.2. Ratio of CO2 to N2 properties at 2000 K. and the boiler surfaces. Differences in density and viscosity between CO2 and N2 could also affect the coal delivery, which is conventionally carried by preheated air [6 ]. Differences on the combustion temperatures and burnout profiles in the presence of CO2 (and to a lesser extent H2O) rather than N2 are discussed in the literature. Dhaneswar and Pisupati [24] report th a t for a given residence time, the presence of CO2 as a diluent, rather th an N2, leads to a higher conversion for low rank coals, but a lower conversion for high rank coals. This is a ttributed to the higher reactivities and combustion temperatures of low ranked coals. Hu et al. [25] find th a t the presence of CO2 rather th an N2 leads to a higher conversion, but the presence of both H2O and CO2 rather th an N2 leads to a lower conversion. Brix et al. [26] find th a t under pure kinetic control, the burnout time in both CO2 and N2 diluents are roughly equal, but when mass transfer provides resistance, conversion occurs faster in the N2 diluent. Although modern computers have large memory capacities and fast processor speeds at low cost, it is still not possible to include full chemistry, resolve boundary-layer and intraparticle gas transport for millions of char particles in a flow field the size of a pulverized coal boiler. The range of length scales is too vast. Simplifications must be made in tracking particles and in domain discretization. The state-of-the-art large eddy simulation (LES) code ARCHES developed at the University of Utah uses a direct quadrature method of moments (DQMOM) [27] formulation to implement a population balance on reacting char particles. Mass-transfer coefficients and Arrhenius laws describing apparent char kinetics are used to calculate reaction times and temperatures. The aim of this work is to improve kinetic fits and the physical description currently provided by the single particle submodel 6 for char combustion to more accurately predict temperature and burnout profiles. The improved physical description of the combustion process will still require simplifications to allow efficient implementation in an LES code, such as eliminating the need to resolve the microscopic length scales in the boundary layer and within a particle, and reducing the chemistry complexity. The research objective is to provide a validated single-particle combustion submodel for the ARCHES LES code. This submodel will need to include enough physics to describe the combustion of coal char in oxy- and air-fired environments, but make enough simplifications so th a t the LES performance is not limited. The work will be divided into three parts. First, detailed modeling of single particles with and without the CO2 and H2O gasification reactions will highlight the impact of gasification reactions on the oxy-combustion of coal. Secondly, simplified models for single-particle combustion will be proposed and compared to the detailed model. This will elucidate the errors ascribed to the modeling simplifications, and allow for error estimation on the simplified models. Finally, a wide range of experiments designed to elucidate the significance of the gasification reactions and evaluate kinetic parameters will be presented. This work will focus on determining the kinetics of oxidation and gasification reactions. A validated submodel for single-particles will have broad appeal in the coal combustion community. It will be directly applicable to the ARCHES LES code, and will help alleviate shortcomings in in current experimental d a ta analysis techniques. In the review by Chen et al. [6 ], fundamental research needs include the determining the oxy-combustion characteristics of different coal types, and the development of models for subprocesses designed specifically for oxy-combustion (as opposed to air combustion), which are directly addressed in this research. Results from this study will also help advance coal combustion science and improve the understanding of the coal combustion process. CHAPTER 2 MODEL DESCRIPTION 2.1 SKIPPY Model Description SKIPPY (Surface Kinetics in Porous Particles) is a code th a t describes a steady-state spherical, reacting porous particle and its reacting boundary layer. The spherical domain is assumed to be one-dimensional in the radial direction. The equations solved by SKIPPY are similar to those in the PREMIX code [29], but the code allows for additional hetero­geneous reactions. The code also employs different boundary conditions th an PREMIX and appropriately describes the gas transport in the pores of the particle. Homogeneous and heterogeneous reaction rates are calculated by subroutines from the CHEMKIN II [30] and SURFACE CHEMKIN [31] packages, respectively. Specific heat capacities and specific enthalpies are also computed with CHEMKIN II subroutines [30]; the TRANSPORT [32] package is used to calculate diffusion coefficients and thermal conductivities. 2.1.1 Governing Equations Unlike a premixed flame, heterogeneous reactions can add mass to the gas phase, so conservation of mass requires dm Kg ^ T = ^ s k Wk O A (2.1) k=l where r is the radial spatial coordinate [m]; m = puA, the mass flow rate [kg/s]; p, the gas density [kg/m3]; u, the mass-averaged velocity [m/s]; Sk, the molar rate of production per unit area by surface reactions of the kth species [mol/m2 -s] (with K g gas-phase species); Wk, Reprinted with permission from Ref. [28]. Coauthors: Christopher R. Shaddix, Manfred Geier, Alejandro Molina, and Brian S. Haynes. 8 the molar weight of the kth species [kg/mol]; or , the specific surface area for heterogeneous reactions [m2/m 3]; and A = 4 n r2, the area normal to the direction of the flow [m2]. The perfect gas equation is used to calculate the gas density, PP = PRWT . ((2.)2) wherep is the pressure [Pa]; R, the universal gas constant [J/mol-K]; T , the temperature [K]; and W , the mean molecular weight [kg/mol]. Heterogeneous reactions do not occur outside the particle; from a modeling point of view, one way of writing this is th a t the area available for surface reactions, or = 0 for r > rp (where rp is the radius of the particle [m]). This reduces the continuity equation to dm/d r = 0 for r > rp. Outside the particle (r > rp), chemical reactions cause only small spatial variations in the mass-averaged velocity th a t are, for th a t reason, neglected in the momentum balance. Within the porous particle, Darcy's Law (or the Hagen-Poiseuille equation, corrected for the nonlinear flow path) is used to describe the flow. The momentum equation is thus given by dp m 8 ^ t 3 ) dr PA rp,ore 0 where ^ is the mixture averaged viscosity [Pa-s]; 0, the porosity, or void fraction; t , the tortuosity; and rpore, the average pore radius [m]. Outside the porous particle (r > rp), the tortuosity is zero, reducing the momentum balance to dp/dr = 0 . Changes in the gas-phase mass fractions, Yk, are caused by convection, diffusion, hetero­geneous reactions (for r < rp), and homogeneous reactions. The equation of species mass conservation is 1 d A d r (m + PVk A)Yk = Sk Wk Or + uJk Wk 0, for k = 1 ,..., Kg, (2.4) where Vk is the diffusion velocity of the kth species [m/s], and ojk is the molar rate of production per unit volume by gas-phase reactions of the kth species [mol/m3 -s]. Note th at this equation is valid throughout the entire spatial domain as outside the porous particle (r > rp), or equals 0 and the void fraction, 0 equals 1 . A multicomponent description of diffusion is used by SKIPPY to calculate the diffusion velocities. The Fickian diffusion coefficients are required, calculated by inverting the [^] matrix where & = DiKg + £ DYikk q x i Pn = ^ ~ - i=k for i , j = 1,..., Kg - 1 (2.5) Yi 9 where x i is the mole fraction of species i and Dij is the binary diffusion coefficient between species i and species j , [m2/s]. Within the pores of the particle (r < rp), the Fickian diffusion coefficients, [D] = [ ^ ] - 1 are corrected for the nonlinear p ath of pore diffusion by the ratio of the void fraction to tortuosity: Dij,r<rp = Dj<fi/r. The diffusion velocity of each species can then be calculated (in the entire domain) as K - 1 V = - W E Di k ^ , for k = 1 , ..., K - 1 (2 .6 ) i= 1 Kg-1 VKg = - j Vk. (2.7) k=1 A thermal energy balance (neglecting gas radiation) yields 1 d , 1 d ( , . d T \ ^ j , , A d r (m + P k A)Yk hk + A d r ( -A *A^ ) = E Sk h k Wk ^ r , (2.8) k= 1 k=Kf where h k is the specific enthalpy of the kth species [J/kg]; At = A0 + Ap(1 - 0), the total thermal conductivity [W/m-K]; A, the mixture-averaged gas thermal conductivity [W/m-K]; Ap, the thermal conductivity of the solid particle [W/m-K]; K f , the first surface species; and K , the last bulk species. Note th a t the source term on the right-hand side of the equation contains only the surface and bulk species. The enthalpy flow term on the left-hand side of the equation accounts for gas-phase and heterogeneous reactions of the gaseous species; the additional source term on the right-hand side of the equation accounts for the release of energy as solid species are converted to gas, and bulk species to surface species. As the code produces a steady-state solution, the net-production rate of surface species must be zero, i.e. s k = 0, for k = K f ,...,K S , (2.9) where K ls is the last surface species. 2.1.2 Discretization and Boundary Conditions A finite volume approach is taken to represent and solve the system of coupled differential equations th a t describe the reacting particle and boundary layer. This results in a system of algebraic equations th a t are solved using the hybrid damped Newton's method and 10 time-marching scheme described in the next section. As an example, conservation of mass (Eq. 2.1) is written as Tfj+l - Tfj- 1 Kg ^ S k , j Wk k=l rj + rj+ i 2 (2 .1 0 ) where the subscript j is a reference to a discrete point. At the particle surface, radiation to the surroundings must be included in the energy balance. The discretized energy balance at the particle surface (Eq. 2.8), with the additional radiation term included, is Kg K ^ ( m + pVk A)Ykhk - j 4n jp rjp-i + rP 'Y ^ r n + pVkA)Ykhk I . k=l / jP- i jp rjp+l - rP + At,jp-i4n rp+ ^ jp+ l \ Tjp Tjp-i J rP - rjp-i + ea4nrl (Tfp - TW) = Y sk,jph k,jpWkA r k=Kf (2 .1 1 ) where e is the emissivity of the reacting particle; a, the Stefan-Boltzmann constant [W/m2 -K4] Tw is the temperature of the wall, or surface to which the particle is radiating [K]; the index j p marks the location where r = rp; and the surface area available for reaction is given by 4n A rxn - ar "3" rrp3 -- r jp -i + rP 2 + (1 - ^ )4 n r2. (2 .1 2 ) At a large radius, the temperature, pressure, and species mass fractions are specified as those of the bulk gas, and there are no gradients in mass flow. Care must be taken by the user to define a radius th a t is large enough th a t gradients in all of the dependent variables at the infinite boundary are sufficiently small to ensure th a t the boundary layer is not constrained by the extent of the domain. In general, a domain radius 100 times the particle radius is sufficient for the simulation of reacting pulverized coal particles. Alternatively, if one wants to constrain the size of the boundary layer, for example to reflect the imposition of turbulent mixing of the surrounding flow, then the chemical composition of the bounding flow needs to be carefully chosen to reflect the influence of combustion intermediates (such as CO and NO) th a t are being produced by heterogeneous reactions and diffusing through the boundary layer. Equations 2.4 and 2.8 are second-order equations (the second derivative in the species balance is tied into the diffusion velocity calculation), and additional constraints for this boundary-value problem must be specified. At r - 0 , symmetry dictates th a t gradients in the dependent variables vanish, and there is zero mass flow at this location. 3 3 2 3 11 2.1.3 Solution Procedure The solution is found using the two-point boundary-value solver, TWOPNT, described by Grcar [33], which is a hybrid damped Newton's method and time-marching scheme. TWOPNT uses Newton's algorithm to attempt convergence of the steady-state problem. If Newton's method begins to stray from the bounds of the problem (e.g. mass fractions outside the bounds 0 < Yk < 1, or negative temperatures), a time-marching scheme is executed to a ttempt to bring the solution back into the domain (the final solution is not affected by this time-marching scheme-it is only an approach to aid the numerical solution procedure). This requires unsteady forms of the governing equations. For example, the unsteady form of Eq. 2.4 is dYk 1 d P~dt + A dr (rh + pVkA)Yk = 4 WkUr + Wk0 for k = 1,..., Kg, (2.13) with the time differential approximated as Y n+1 - Y n p f r K p'n+l k j h k,j • (2*14) where the superscript n indicates the time level and h is the time step [s], specified by the user. All other terms are discretized in the spatial coordinate as discussed previously and evaluated at time n + 1. The backward Euler method is used to solve these coupled equations, and the solution marches forward in time a number of steps specified by the user. Further details regarding this solution procedure are provided by Kee et al. [29]. Convergence is defined when the Newton correction step, A $ , satisfies the following relation: |A $ | < max(A, R $ ). (2.15) In this equation, $ is the solution vector, [m i, T \ ,p \, Y ^ i,..., YKg , i , ..., rhj ,Tj ,p j , Y i j ,..., YKg ,j, ...,mj ,T j ,p j , Yi)j ,..., YKg, j ], (with point 1 located where r = 0 and point J at the "right" boundary, or largest domain radius); A and R are the absolute and relative tolerances specified by the user. The TWOPNT solver also includes a provision for mesh refinement, and d a ta points are added when one of three criterion are met: 1 . the magnitude of a component's change exceeds some fraction (5) of the component's global change: | $n,j - $ n ,j- i| > 5 (m ax $ n - min $ n ) , (2.16) 12 2 . the magnitude of change in a derivative exceeds a fraction (7 ) of the global change: >Y, , (2.17) $n,j + 1- $ n,j $n,j-$n,j-1 rj + 1- r j rj - r j - 1 ma^l # " j + 1 *"j rj+i- r j y) - min V( # "rjj++ 11 - r*j"j 3. the magnitude of change in a component exceeds a fraction (a) of the magnitude of th a t component: \^n,j ^ n ,j - 1 \ > a \^ n ,j1 . (2.18) At the edge of the particle (r = rp), there are physical reasons for a discontinuity in the slope of the dependent variables. The refinement criteria given by Eq. 2.17 is ignored when j = jP to prevent continual mesh refinement at this point. CHAPTER 3 EFFECT OF CO2 AND STEAM GASIFICATION REACTIONS ON THE OXY-COMBUSTION OF PULVERIZED COAL CHAR 3.1 Abstract For oxy-combustion with flue gas recirculation, elevated levels of CO2 and steam affect the heat capacity of the gas, radiant transport, and other gas transport properties. A topic of widespread speculation has concerned the effect of gasification reactions of coal char on the char burning rate. To asses the impact of these reactions on the oxy-fuel combustion of pulverized coal char, we computed the char consumption characteristics for a range of CO2 and H2O reaction rate coefficients for a 100 ^m coal char particle reacting in environments of varying O2, H2O, and CO2 concentrations using the kinetics code SKIPPY (Surface Kinetics in Porous Particles). Results indicate th a t gasification reactions reduce the char particle temperature significantly (because of the reaction endothermicity) and thereby reduce the rate of char oxidation and the radiant emission from burning char particles. However, the overall effect of the combined steam and CO2 gasification reactions is to increase the carbon consumption rate by approximately 1 0% in typical oxy-fuel combustion environments. The gasification reactions have a greater influence on char combustion in oxygen-enriched environments, due to the higher char combustion temperature under these conditions. In addition, the gasification reactions have increasing influence as the gas temperature increases (for a given O2 concentration) and as the particle size increases. Reprinted with permission from Ref. [28]. Coauthors: Christopher R. Shaddix, Manfred Geier, Alejandro Molina, and Brian S. Haynes. 14 Gasification reactions account for roughly 20% of the carbon consumption in low oxygen conditions, and for about 30% under oxygen-enriched conditions. An increase in the carbon consumption rate and a decrease in particle temperature are also evident under conventional air-blown combustion conditions when the gasification reactions are included in the model. 3.2 Introduction Coal combustion accounts for over 40% of the global electricity supply [34] and is likely to continue to be used for stationary power generation well into the future. As the international community considers enacting carbon dioxide emissions regulations, the development of cost-effective technologies to capture CO2 is becoming increasingly important, particularly for the coal combustion processes (which also accounts for over 40% of the worldwide energy-related CO2 emissions [35]). One promising method for carbon capture while producing electricity is oxy-combustion of coal [5]. In this approach, oxygen is separated from air before combustion and then mixed with a portion of the flue gas (primarily consisting of CO2 and steam) before injection into a coal boiler. Flue gas recirculation is required to moderate the combustion temperature and prevent excessive furnace slagging. The flue gas from this process is rich in CO2 and can be readily compressed and transported for utilization or storage once the moisture has been removed. With flue gas recirculation, the CO2 levels in the furnace gases are much higher in oxy-fuel combustion (reaching 60-70 vol-%) than in conventional, air-fired combustion. In principle, flue gas recycling may occur before or after moisture removal, but commercial applications of oxy-fuel combustion will most likely utilize at least some wet flue gas recycling [36], leading to water vapor levels of up to 25-35 vol-% in postflame furnace gases. In order to implement this technology efficiently, the coal combustion characteristics in these environments, which are different th an conventional air-fired environments, must be understood. Various aspects of the coal combustion process have been found to be different in oxy-combustion environments, which can be partially attrib u ted to the differences in the gas-phase properties (e.g. heat capacity and radiant characteristics) between an oxy-combustion environment and an air-fired environment. For instance, the rate of coal volatile consumption is reduced and coal ignition is delayed in environments containing high concentrations of CO2, for a given furnace temperature and oxygen concentration [8 , 2 0 - 2 2 ]. The burning rate of char particles is reduced due to the lower rate of oxygen diffusion through CO2 in the particle boundary layer [18-20]. In addition to these well-established 15 effects, there has been speculation th a t the gasification reactions may enhance the char burning rate in oxy-fuel combustion [14-16]. While long considered too slow to compete with the oxidation reactions under air-fired combustion conditions, the gasification reactions may contribute to the overall consumption of the char because of the higher concentrations of CO2 and H2O in an oxy-fired boiler. By directly reacting with the solid carbon, one might expect the gasification reactions to increase the consumption of the char. However, the gasification reactions are strongly endothermic, requiring 172 kJ per mole of solid carbon when the reaction occurs with CO2 and 131 k J/m o lc for reaction with steam. Therefore, the occurrence of these reactions lowers the char particle temperature, which in tu rn reduces the rate of oxidation. We previously studied the consequences of including the gasification reaction of CO2 with solid carbon [17]. We found th a t the overall consumption rate of a char particle reacting at a temperature near the gas temperature (i.e. at low O2 concentration in the surrounding gas) is slightly increased by the CO2 gasification reaction. Alternatively, when the particle is reacting at a temperature considerably higher th an the ambient gas temperature (i.e. in an O2-enriched environment), the CO2 gasification reaction decreases the overall carbon removal rate, though by a small amount [17]. In either case, the CO2 gasification reaction was shown to substantially reduce the char particle combustion temperature. In the work reported here, the combined effects of both CO2 and steam gasification reactions on the overall char consumption characteristics are evaluated. 3.3 Gasification Rates at 1 atm The gasification rates of different carbonaceous materials with CO2 or steam as gasifying agents have been studied extensively, primarily at low and intermediate temperatures, using thermogravimetric analyzers (TGAs) [37-39]. Although the actual mechanism of these two reactions and the types of carbon sites the reactants can access is still the subject of some debate, the gasification processes under atmospheric pressure are generally assumed to follow the global reaction scheme [37, 40-42]: CO2 + Cs C(O)s + CO (3.1) k1 ,r H2O + Cs C(O)s + H2 (3.2) k2,r C(O)s + Cb CO + Cs (3.3) 16 where the subscript s denotes a surface species th a t is available to react heterogeneously, Cb is bulk carbon below the reacting mono-layer, and k is the reaction rate coefficient in the direction specified by the arrow. Assuming a first-order concentration dependence, the overall rate of CO2 gasification (described by reactions 3.1 and 3.3, in mol/m2 -s) follows a Langmuir-Hinshelwood kinetic expression, according to Eq. 3.4 [37, 40, 41]: r -------k k l' pCO C ------- , (3.4) 1 + - g f pCO2 + -kf-PCO where [Ct] refers to the total concentration of surface active sites and p is the partial pressure. Eq. 3.5 is a similar expression th a t describes the rate of steam gasification [37, 40, 42]: r -------k 2' ' pH2 k2 - ° [Ck-2] -r------ . (3.5) 1 + ^ pH2O + ^ pH2 The kinetic rate coefficients for reactions 3.1-3.3 are likely well-represented by an Ar­rhenius law, but the associated parameters are not well-established. It is widely recognized th a t the overall activation energies for the char gasification reactions are substantially greater th an the ~ 160 kJ/mol activation energy for reaction of coal chars with O2 [9]. Laurendeau [37] reviewed the major studies of atmospheric pressure char gasification before 1978 and concluded th a t the effective activation energy was between 230-270 kJ/mol for gasification by CO2 and between 190-270 kJ/mol for gasification by H2O. The overall kinetic rate of char gasification (or oxidation) is highly dependent on the char source and thermal history, as emphasized by Radovic et al. [43], and as explicitly recognized via the proportionality of overall rate to active site concentration, as expressed in Eqs. 3.4 and 3.5. Because of this, the best option for estimating the gasification rate coefficient when char oxidation is also important is to use rate coefficients of CO2 and steam gasification relative to the rate coefficient for oxidation, for a given char. Then, when using a given kinetic expression to describe the char oxidation process, appropriate expressions for the CO2 and steam gasification rate coefficients can be readily derived. Note, however, th at this approach necessarily ignores the further subtlety represented by possible differences in the intrinsic reaction order of the overall gasification and oxidation rates. In light of the uncertainties in the kinetics parameters, this omission will only have a minor effect on the conclusions presented in this study. Several studies in the literature have determined the relative kinetic rate coefficients of gasification by CO2 and H2O to oxidation by O2, primarily at 800 °C [40, 44-49]. From these measurements, one can reasonably bound the rate coefficient of the CO2 gasification reaction relative to th a t of oxidation as falling between 1 .0 - 2 0 x 1 0 - 5 , at 800 °C, with a best-guess 17 of 6.2 x 10- 5 , as summarized in ref. [17]. For steam gasification, several measurements of rate coefficients relative to oxidation have been reported, as shown in Table 3.1. From these measurements, one can reasonably bound the relative rate coefficient of steam gasification of coal chars to be from 1.0-10 x 10- 4 at 800 °C (the Harris and Smith petcoke and Mann et al. results appear to be outliers). Liu et al. [50] recently compared the steam gasification rate of three different coal chars relative to gasification in CO2. For all of the coal chars, the steam rate exceeded the CO2 rate by a factor of 2-3 over the temperature range of 1400-1800 K. This agrees in magnitude with the rate coefficients shown in Table 3.1 relative to the rate coefficients for gasification by CO2 . On this basis, our best-guess relative rate coefficient of steam gasification is 2.0 x 10- 4 at 800 °C, a value th a t is about three times higher than our best-guess relative rate coefficient of CO2 gasification. 3.4 Model Description Char particle simulations were performed using SKIPPY (Surface Kinetics in Porous Particles), a computer program developed at the University of Sydney. The details of this FORTRAN program are included in 2.1. Briefly, SKIPPY solves the steady-state mass, species, and energy conservation equations for a reacting porous particle and its reacting boundary layer. From this solution, SKIPPY predicts species concentrations and temperatures within the pores of the char, at the outer surface of the char, and within the boundary layer surrounding the char. Both heterogeneous (gas-solid) and gas-phase chemical reactions are considered. The model assumes: • a single, spherical particle in an unconstrained and unperturbed boundary-layer • steady-state • a 1-dimensional (radial) domain T a b le 3.1. Ratio of Steam Gasification to Oxidation at 800 °C____________________ Source Carbon Type Relative Rate Coefficient Degroot and Richards, 1989 [46] cellulose char 1.1 x 1 0 - 3 Harris and Smith, 1991 [47] pet coke 2 .2 x 1 0 - 6 lignite 2 .0 x 1 0 - 4 Roberts and Harris, 2000 [48] hv bituminous 2.3 x 10- 4 semi-anthracite 1.3 x 10- 4 Mann et al., 2004 [49] lignite char 4.5 x 10- 7 18 • gases are radiantly inactive over this spatial scale • homogeneous and heterogeneous reactions proceed according to the law of mass action, the formalism is described by Kee et al. [51] GRI-MECH 3.0 [52] was used to describe the gas-phase reaction kinetics, while the het­erogeneous char reaction kinetics were described using the mechanism specified in Table 3.2. This surface mechanism is the same as th a t applied previously by Molina et al. [53, 54] with the addition of two steps describing the char gasification reactions with CO2 and steam. Oxidation and gasification reactions are treated as adsorption-limited, with arbitrarily fast desorption reaction rates th a t guarantee insignificant accumulation of oxygen complexes on the surface of the char. While it is understood th a t the gasification reactions should be written as multistep pro­cesses with reverse reaction contributions from H2 and CO reacting with the oxygen-bound surface sites, our lack of knowledge of the relevant intrinsic reaction rates makes it necessary to use overall gasification steps with rate coefficients based on best estimates of activation energy and relative rate coefficients. This simplification is at least partly justified under the conditions investigated here because any H2 th a t is produced from steam gasification reacts rapidly with oxygen and oxidizing radicals in the high-temperature boundary layers, and the reverse reaction of CO with surface oxides has a low activation energy and becomes increasingly unimportant at high temperatures [55]. Base-case simulations considered a single sub-bituminous coal char particle, with the properties shown in Table 3.3. The effects of the gasification reactions as a function of the gasification rate coefficients and gas environment were explored in this study. These effects were considered for a single particle, eliminating other variabilities, such as variations in the oxidation kinetics, or char properties th a t change during burnout, such as the particle T a b le 3.2. Heterogeneous reaction mechanism Reaction A (mol/cm2 ■ s) E (kJ/mol) Cb + Cs + O2 ^ CO + C(O)s C(O)s + Cb ^ CO + Cs Cs + O2 ^ C(O2)s C(O2)s + Cb ^ CO2 + Cs Cs + CO2 ^ CO + C(O)s Cs + H2O ^ H2 + C(O)s 3.3 x 1015 167.4 1 .0 x 1 0 8 0 . 9.5 x 1013 142.3 1 .0 x 1 0 8 0 . variable 251.0 variable 2 2 2 .0 19 T a b le 3.3. Properties for the base-case simulations, which are the same as the sub-bitu­minous char studied by Geier et al. [56] and as assumed in the simulations by Hecht et al. [17]. _____________________________________ diameter 10 0 ^m bulk density 500 k g /m 3 thermal conductivity 1.33 W /m ■ K (inert) ash content 3% tortuosity 5 void fraction 0.4 gas temperature 1690 K wall temperature 500 K emissivity 0 .8 porosity, diameter, and ash content. The small amount of ash th a t was modeled here was assumed to be inert, ignoring any potential catalytic effects. The specific active surface area is also required to model this system. There is disagree­ment in the literature on how the pore structure is related to the surface area for hetero­geneous oxidation and gasification reactions, as discussed by Molina and Mondragon [57], but there is widespread evidence th a t little of the micropore surface area (which dominates traditional measures of total char surface area) is accessed during high-temperature char oxidation and gasification [58-61]. In our previous simulations of char combustion, the active surface area was varied as a function of bulk gas oxygen concentration to get reasonable agreement of the predictions with the trends in measured char particle temperatures as a function of bulk gas oxygen content [17]. While a somewhat reduced surface area (or surface active site density) might arise from devolatilizing coal particles in the higher temperature volatiles flames produced in an elevated O2 environment, the magnitude of the surface area variation (from 8 m2/g at 1 2% O2 down to 0.225 m2/g at 36% O2) th a t was required to match the model predictions with the experimental d a ta strained belief. Without conclusive experimental evidence of how the devolatilization condition affects the active surface area, in the current study, we sought agreement with experimentally mea­sured char particle temperatures while keeping the assumed surface area density constant. The relative rate coefficients were fixed at our best-guess values at 800 °C (6 .2 x 10- 5 for gasification by CO2 and 2.0x10- 4 for gasification by H2O, each relative to the oxidation rate, as described previously). Then the activation energies were adjusted within the literature bounds (230-270 kJ/mol for gasification by CO2 and 190-270 kJ/mol for gasification by H2O [37]) until predicted temperatures matched experimentally measured temperatures under the constraint of constant specific surface area. 20 The predicted char particle temperatures are shown in Fig. 3.1 for char reacting in N2 diluent environments as a function of the presumed active surface area. The gasification reactions tend to cool the char particles as the active surface area increases. When both gasification reactions are included in the reaction mechanism, good agreement between the model and experiment can be achieved at a fixed surface area at all three of the oxygen concentrations studied with kinetic parameters in the range of values reported in the literature. We find an active surface area of 10 m2/g with activation energies of 222 kJ/mol for steam gasification and 251 kJ/mol for gasification by CO2 to give the best agreement between the model predictions and mean measured char particle temperatures [56]. This magnitude of surface area approximately corresponds to the sum of macropore and mesopore surface area as measured by mercury porisiometry for high heating rate chars investigated experimentally [62] and therefore is physically reasonable. 2600 2500 2400 2300 ^ 2200 & 2100 2000 1900 1800 1700 F ig u re 3.1. Predicted and measured [56] char particle temperatures for a particle reacting in a 1690K, 14% H2O, O2, balance N2 environment while varying the presumed surface area and activation energy of the steam and CO2 gasification reactions. Units of activation energy are kJ/mol. 1 1 1 1 1 1 1 11 1 1 1 1 1 1 1 1 - ^ ........................... i i i i i i f , " " " ' ......... ■O' *"* 36% 0 2 24% 0 2 12% 0 2 Measured T . Ea> H20 222, Ea> C02 2j 1 . .......................-Trm- ....... Ea,H2o 251,E^C02 251 ■.......No H20 rxns, E^ C02 - 251 = = = Ea, h 2o = 251»No c °2 ___i___i__i i i i i 11_____ i___i__i i i i i i _____ i___i__i i i i 2 3 4 5 6 7 2 3 4 5 6 7 2 3 4 5 6 7 1 10 2 Active Surface Area (m /g) 21 To determine the effects of the gasification reactions over a wide range of possible rate coefficients, the activation energies were held fixed and the pre-exponentials, A, for the char gasification steps were varied in separate simulations. For gasification by CO2 , the pre-exponential value was varied from 0 (i.e. no gasification by CO2) up to a value of 1.8 x 1016 mol/cm2 ■ s. For gasification by H2O, the pre-exponential value was varied from 0 (i.e. no gasification by H2O) up to a value of 2 .2 x 1015 mol/cm2 ■ s. At 800 °C, these maximum pre-exponentials yield relative rate coefficients th a t are 2 x 1 0 - 4 and 1 x 1 0 - 3 (for CO2 and steam, respectively) times the oxidation rate coefficient at this temperature. These correspond to the highest relative rate coefficients found in the literature by Goetz et al. [44] (for CO2 gasification) and Degroot and Richards [46] (for gasification by H2O). The wide ranges of gasification rate coefficients evaluated here were chosen both on account of the uncertainties in the actual gasification rate coefficients and to more clearly evaluate the trends in the char particle response as a function of the gasification rate coefficients. Simulations were conducted for gas environments characteristic of dry-recycle oxy-fuel combustion, with a moisture level of 14 vol-%, and wet-recycle oxy-fuel combustion, wherein only the primary oxidizer is dried, with a furnace moisture content of 25 vol-%. The balance of the furnace gas was assumed to be composed of O2 and CO2. Oxygen levels ranging from 12 vol-% to 36 vol-% were considered, spanning the range from conventional combustion to strongly oxygen-enhanced combustion (in boilers char combustion generally occurs at substantially lower oxygen contents th an exist in the boiler inlets). The effects of gas temperature and particle size were also evaluated, and environments with a N2 diluent (characteristic of a conventional air-fired boiler) were simulated. 3.5 Results 3.5.1 Effect o f Gasification Rate Coefficients on Particle Temperature and Species Profiles The computed radial profiles of temperature and gas species for a 100 ^m diameter char particle reacting in 12% O2 in an oxy-fuel environment at 1690 K are shown in Fig. 3.2. The profiles sta rt near the particle center and extend into the boundary layer to 100 times the particle radius. As shown in the top frame of Fig. 3.2, the rate coefficient of gasification by CO2 affects the char temperature much more th an the rate coefficient of gasification by H2O. This is due to the combined effect of a higher concentration of CO2 than steam in the surrounding gas, and the greater endothermicity of the CO2 gasification reaction. At 22 1900 _i85° ^ 1 8 0 0 H 1750 1700 0.04 0.03 X 0.02 0.01 0 .0 0 0.1 10 _ l 100 r/r„ r/r„ F ig u re 3.2. Temperature and species profiles as functions of normalized distance from the center of a 100 ^m diameter char particle burning in 1 2% O2 in CO2 at 1690 K. r / r p = 1 corresponds to the surface of the particle. The panels on the left represent a dry-recycle oxy-combustion environment, with 14% H2O in the bulk gas, whereas the panels on the right represent a wet-recycle oxy-combustion environment, with 25% H2O in the bulk gas. Different line colors represent different assumed rate coefficients for the CO2 gasification reaction, whereas different line styles represent different assumed rate coefficients for gasification by H2O, as shown in the legend. The thick black line represents the best-guesses of CO2 and H2O gasification rate coefficients. For gasification by CO2, the best-guess pre-exponential value (corresponding to a normalized rate coefficient of 1) is 3.6 x 1015 mol/cm2 ■ s and for gasification by H2O, the best-guess pre-exponential is 4.4 x 1014 mol/cm2 ■ s. 23 our best-guess rate coefficient for gasification by H2O, ignoring CO2 gasification causes the particle temperature to be 60-70 K (depending on the H2O concentration in the bulk gas) higher th an the result when using our best-guess rate coefficient for gasification by CO2 . Similarly, using a CO2 gasification rate coefficient th a t is five times the best-guess rate coefficient results in a particle temperature th a t is lower by 70-80 K th an the result using the best-guess CO2 gasification rate coefficient. When fixing the CO2 gasification reaction to its best-guess rate coefficient, ignoring H2O gasification only causes an error of 7-14 K, and using a H2O gasification rate coefficient th a t is five times the best-guess rate coefficient yields a particle temperature th a t is 18-30 K lower th an the temperature prediction th at includes the gasification reactions proceeding at the best-guess rates. The species profiles in the lower frames of Fig. 3.2 show th a t under the modeled condition (with 1 2% O2 in the bulk gas), the 100 ^m char particle is burning near the diffusion limit, with a low concentration of O2 ( « 4%) at the particle surface. The gasification reactions have little influence on the O2 diffusion to the particle (and therefore barely affect the char oxidation rate). In contrast, the CO and CO2 concentrations within the char particle are strongly influenced by the CO2 gasification reaction, as this reaction converts solid carbon and CO2 into CO. Also, as expected, the concentrations of H2O and H2 within the char particle are strongly dependent on the steam gasification reaction rate coefficient. The CO2 gasification reaction also affects the H2 concentration within the char particle. When the CO2 gasification reaction is ignored, a high particle temperature causes the steam gasification reaction to proceed at a relatively fast rate, generating significant H2, and as the CO2 gasification rate coefficient is increased, the particle temperature, steam gasification rate, and amount of H2 generated by the steam gasification reaction all decrease. To determine the influence of the gasification reactions during oxygen-enriched com­bustion, simulations were performed for the same char particle reacting in 24% and 36% O2. Similar trends as those seen in the 1 2% O2 environment were evident in both of these oxygen-enriched cases. Profiles from the simulations with 36% O2 are shown here (in Fig. 3.3), as these show the strongest effects from the gasification reactions. As shown in Fig. 3.3, at a fixed steam gasification rate, predicted particle temperatures are up to 270 K higher th an when the CO2 gasification reaction proceeds using our best-guess rate coefficient. At five times the best-guess rate, the temperature is 140 K lower th an the best-guess prediction. At this bulk O2 level, the char particle temperature is over 2100 K, despite the occurrence of the endothermic gasification reactions. At this high temperature (which causes fast gasification rates), the CO2 gasification reaction completely consumes 24 2600 ^ 2 4 0 0 &2200 H 2000 1800 r/r„ r/r„ F ig u re 3.3. Temperature and species profiles as a function of normalized distance from the center of a char particle burning in 36% O2 in CO2 at 1690 K. Right/left panel conventions and line styles and colors are the same as for Fig. 3.2. 25 the CO2 within the particle when the presumed gasification rate coefficient is at least half of the best-guess value. Similarly, steam is nearly completely consumed within the char particle when the rate coefficient for gasification by steam is at least half of its best-guess value. This is in contrast to the results for combustion in 12% bulk O2 (shown in Fig. 3.2), where steam and CO2 are only partially consumed within the char particle, for even the highest gasification rates considered. Similar to the 1 2% O2 case, the oxidation of the 1 0 0 ^m particle is proceeding near the diffusion limit, such th a t the gasification reactions have little impact on the O2 diffusion profile through the boundary layer. 3.5.2 Effect o f Gasification Rate Coefficients on Char Consumption Rate Figure 3.4 presents contour plots of the char carbon consumption rates for a 100 ^m diameter char particle burning in oxy-fuel combustion environments as functions of the H2O and CO2 gasification rate coefficients. For both the dry- and wet-recycle cases, the carbon consumption rate is strongly dependent on the CO2 gasification rate coefficient, whereas the steam gasification rate coefficient only has a significant influence for a relative rate coefficient greater than one (the contours are nearly vertical for the bottom half of each plot). For the wet-recycle cases, the contours have a greater dependence on the H2O gasification rate coefficient because the higher steam concentration increases the steam gasification rate. The steam gasification rate coefficient (relative to the CO2 gasification rate coefficient) has less influence on carbon consumption as the oxygen concentration increases, for both the dry- and wet-recycle cases. Because the activation energy of the CO2 gasification reaction is higher th an th a t of the steam gasification reaction, at high oxygen concentrations (resulting in high particle temperatures), the CO2 gasification rate will increase faster than the steam gasification rate. Thus, at higher oxygen concentrations, the steam gasification reaction becomes relatively less important. The contour plots in Fig. 3.4 show a carbon consumption rate variation of about 1 0% over the range of relative rate coefficients considered in this study. For a given oxygen concentration, an increase in the H2O concentration causes the net carbon consumption to increase slightly, as shown by the carbon consumption rates listed in Fig. 3.4. Although the carbon consumption rate does not appear to be as strongly tied to the steam gasification rate coefficient as the CO2 rate coefficient, the steam gasification reaction does consume carbon. In these simulations, as in boilers, an increase in steam concentration 12% On 24% On 36% On o o X 0.1 0.1 0.92 0.96 1.00 0.1 k c o / k c o 2, best Figure 3.4. Contour plots showing the total carbon consumption rates as the CO2 and H2O gasification rate coefficients are varied. The gasification rate coefficients have been normalized using the same best-guess pre-exponentials as for Figs. 3 .2 and 3.3. Carbon consumption rates have been normalized by the rate at the best-guess gasification rates (normalized rate of 1 ). Absolute carbon consumption rates at the best-guess gasification rate coefficients are shown on the plots. Otoi 27 requires a decrease in CO2 concentration, convolving the effect of concentration variations. The relative contributions of oxidation, CO2 gasification, and steam gasification to carbon consumption are shown in Fig. 3.5. With 12% oxygen in the bulk gas (which yields relatively low reaction temperatures), gasification reactions (with CO2 and H2O) are responsible for about 2 0% of the carbon consumption. At 36% O2 in the bulk gas, these gasification reactions account for about 31% of the overall carbon consumption. Inspection of the right panel as compared to the left shows th a t exchanging some (0.11 atm) of the CO2 for H2O causes the relative carbon consumption due to steam to nearly double while only slightly decreasing the relative consumption from CO2 , and results in a net increase in the relative carbon consumption from gasification reactions. The relative consumption from oxygen also decreases slightly while the surface temperature increases by a few degrees as the steam concentration increases. Figure 3.5 highlights the complex interplay between the heterogeneous reactions oc­curring during the oxy-combustion of pulverized coal. If gasification reactions are not considered, nearly 400 kJ/molC is released by the oxidation reaction, leading to predictions of high particle temperatures shown by the open circles in Fig. 3.5. When the endothermic gasification reactions are included, the enthalpy released by the heterogeneous reactions drops significantly, resulting in considerably lower predicted particle temperatures. The enthalpy released can be calculated by summing the product of the reaction rate and its heat release for the oxidation and gasification reactions. At 1 2% O2 in the bulk gas, around 280 kJ/molC are released by the reactions, and at 36% O2 , only about 220 kJ/molC. The rate of carbon oxidation by O2 is slower at lower temperature, but the additional carbon consumption from the CO2 and H2O gasification reactions slightly increases the predicted carbon consumption rate. Boundary layer reactions, for example, O2 reacting with the CO and H2 produced from the gasification reactions, feed energy back to the particle, adding additional complexity to an energy balance. 3.5.3 Gas Temperature and Particle Size Effects Figure 3.6 summarizes the results of a series of simulations in which the ambient gas temperature and the char particle diameter were varied over a wide range. The left panel of Fig. 3.6 shows the carbon consumption rate and particle temperature for a 100 ^m char particle burning in 1 2% and 36% O2 dry-recycle oxy-fuel combustion environments as a function of the bulk gas temperature. Both the particle temperature and the carbon con- 2600 - 2400 - 2200 - 2000 - 1800 - Figure 3.5. Relative contributions to carbon consumption by reactions with oxygen, carbon dioxide, and steam. Size of circle is proportional to overall carbon consumption rate, and percentages of contributions are shown on the chart. Open circles show particle surface temperature and relative carbon consumption rate without gasification reactions (only oxidation), and filled circles include gasification reactions at our best-guess rate coefficients. OO 29 Jo £o Sh 60 40 20 0 - - 36% 0 2 - 12% 07 ■ 1 1 1 1 1500 1600 1700 1800 1900 Gas Temperature (K) Char Particle Diameter (^m) F ig u re 3.6. Particle temperature and carbon consumption rate as a function of gas temperature and particle size for dry-recycle oxy-fuel combustion in 1 2% and 36% O2. Solid lines are simulations using the best-guess gasification rates, dashed lines are simulations without gasification reactions. When varying gas temperature, a particle diameter of 100 ^m is used, and when varying particle diameter a gas temperature of 1690 K is used. 30 sumption rate increase as the gas temperature increases, due to the reaction rates increasing at higher temperatures. Simulations th a t ignore the gasification reactions (dashed lines) clearly predict higher temperatures and lower carbon consumption rates th an simulations th a t include the gasification reactions. This is not an intuitive result, once again showing the trade-offs between endothermic gasification reactions lowering the reaction temperatures and rates, and the additional carbon consumption caused by the gasification reactions. As the gas temperature increases, the effect of the gasification reactions on particle temperature and consumption rate increases, as would be expected based on the high activation energies of these reactions. The right panel of Fig. 3.6 shows the carbon consumption rate and particle temperature as a function of the char particle size during combustion in a 1690 K environment. Larger particles burn at lower temperature and at lower surface-specific rates than smaller particles because larger particles have greater radiative losses and less reactant penetration. As a measure of reactant penetration, effectiveness factors, which are the ratio of the carbon consumption rate by a species to the theoretical carbon consumption rate by th a t species if not slowed by pore diffusion, were calculated. As shown in Table 3.4 , oxygen penetrates much less than either CO2 or H2O and there is less reactant penetration under the high oxygen conditions. From a practical perspective, reactant penetration not only affects the consumption of carbon and the local heat release, but also the local concentration of CO2, which can influence the extent of ash vaporization during char combustion [63]. At all sizes considered, gasification reactions decrease the particle temperature while increasing the carbon consumption rate. During combustion in 36% O2, the considerable effect of gasification reactions on the char particle temperature is nearly independent of particle size. During combustion in 12% O2, the effect of the gasification reactions on char temperature is quite small for 50 ^m particles, and then increases slightly to a temperature difference th a t is once again nearly independent of particle size for particles larger than T a b le 3.4. Effectiveness factors for each reactant under dry-recycle oxy-fuel combustion conditions. __________________________________________ 12% O2 36% O2 50 ^m 150 ^m 50 ^m 150 ^m O2 0.24 0 .1 1 0.09 0.05 CO2 0.99 0.83 0.55 0.37 H2O 1 .0 0.90 0.82 0.53 31 80 ^m. Reactant penetration and radiant and conductive heat losses all affect the particle temperature, and this complex balance causes the local maximum temperature around 80 ^m, when gasification reactions are not included in the simulations. This local maximum temperature in the 1 2% O2 condition shifts to smaller particles (below 50 ^m) when the gasification reactions are included in the simulations. 3.5.4 Gasification Reactions in Oxy- vs. Air-fired Combustion Environments Because of the increased concentrations of CO2 and (most likely) H2O in an oxy-fuel combustion environment, it is natural to consider the potential influence of gasification reactions for this application. However, during conventional, air-fired char combustion, gasification reactions may also contribute to the consumption of solid carbon. Locally, or throughout the reactor, there may be high steam concentrations from residual moisture in the coal and from volatile combustion. Also, high CO2 and H2O concentrations may be generated within the boundary layer of char particles when CO and H2 are fully oxidized to CO2 and H2O. To investigate the potential role of these reactions under such conditions, simulations were conducted using the same base conditions as for the oxy-fuel simulations, but with N2 replacing CO2 as the bulk diluent gas. A small concentration of CO2 (4 vol-%) was assumed to remain in the bulk gas, as well as 14 vol-% H2O, which would be characteristic of an air-fired boiler, and is consistent with our previous study [17]. Temperature and species profiles for a 100 ^m char particle reacting in an air-fired envi­ronment are presented in Fig 3.7. As with the oxy-fuel simulations, particle temperatures are higher if gasification reactions are excluded from the calculations, as shown in the top frame. This effect is more pronounced at higher oxygen concentrations (and higher particle temperatures), shown in the right frames of the figure. Char oxidation and boundary layer reactions in fact produce substantial CO2 near the particle. If gasification reactions are included in the simulations, the CO2 is at least partly consumed and converted to CO within the particle. However, CO is oxidized in the boundary layer, producing a higher concentration of CO2 near the particle than either in the bulk gas, or within the particle. Similarly, H2O from the bulk gas is at least partly consumed within the particle. The H2O gasification reaction produces one mole of CO and one mole of H2 from one mole of H2O, enhancing the molar flux of CO coming from the particle (adding to the flux from the CO2 gasification and oxidation reactions). The H2 generated heterogeneously is oxidized back 32 h? 0.008 |- 0.004 I- 0 .0 0 0 0.1 10 100 0.1 10 2800 - 2600 - 2400 - 2200 - 2000 1800 - 1 0 .0 0 - 0.025 - 0.020 - 0.015 - 0.010 - 0.005 0 .0 0 0 100 r/r„ r/r„ F ig u re 3.7. Temperature and species profiles as a function of normalized distance from the center of a 100 ^m char particle burning in an air-fired environment (N2 diluent) at 1690 K. Left panel are results for 12% O2 in the bulk gas, and the right panel are results for 36% O2 in the bulk gas (note the separate axes). Solid lines include oxidation and gasification reactions using the best-guess rate coefficients while dashed lines only include oxidation reactions. 33 to steam in the boundary layer, with no net generation of H2O. Table 3.5 gives the calculated decrease in particle temperature and increase in the char consumption rate for equivalent N2 diluent and CO2 diluent reaction conditions when including the best-guess steam and CO2 gasification rate coefficients. As is apparent, the gasification reactions do play a role in the prediction of both temperature and char consumption rates during air-fired combustion. As the ambient oxygen concentration increases, the char particles burn at a higher temperature, increasing the rates of the gasification reactions and the conversion of gasification products (CO to CO2 and H2 to H2O) in the particle boundary layer, leading to a greater influence of the gasification reactions. The gasification reactions have a greater influence on char consumption for oxy-fuel combustion conditions, as expected, but for char combustion in elevated oxygen levels, regardless of the diluent gas composition, the gasifications have a significant impact. With the activation energies used in this study, and our best-guess relative rate coefficients at 800 °C, the gasification rate coefficients scale to about 1% of the oxidation rate coefficient at 2000 K. Although the oxidation rate coefficient is appreciably higher th an the gasification rate coefficients, the gasification reactions are significant due to the local concentrations of CO2 and H2O and their greater penetration into the particle. A higher concentration of steam slightly decreases the influence of the gasification reactions on the particle temperature, but increases the carbon consumption rate, which can be seen by comparing the dry- to wet-recycle cases in Table 3.5. This behavior is due to the higher activation energy and endothermicity of the CO2 gasification reaction than the H2O gasification reaction, as discussed earlier with respect to Figs. 3.4 and 3.5. T a b le 3.5. Decrease in surface temperature and increase in char conversion rate if gasification reactions are included in the model. Percentages are calculated based off the values considering only oxidation reactions. 12% O2 24% O2 36% O2 T [K] rc mol (%) T [K] rc mol (%) T [K] rc mol (%) N2 diluent 37 0.3 (3.4) 144 1.2 (5.9) 246 2.5 (7.6) dry oxy-fuel 84 0 .6 (8 .8 ) 235 1 .8 (1 0 .1 ) 356 3.4 (11.4) wet oxy-fuel 79 0.7 (9.5) 225 2.0 (10.7) 347 3.7 (11.9) m2s m2s m2s 34 3.5.5 Implications for Char Combustion Modeling and Interpretation o f Experimental Measurements Using a fine radial mesh on each particle and detailed kinetics to determine the tem­perature and species profiles in a coal fired boiler would require immense computing re­sources. To reduce computational complexity, CFD codes typically consider char particles as source/sink terms to the gas-phase model and employ global kinetics in a heterogeneous char combustion submodel. CFD calculations of conventional, air-fired boilers, and even several recent oxy-combustion submodels have considered oxygen as the only molecule reacting with the solid carbon [6 ]. As shown in this study, neglecting reactions with CO2 and H2O causes a higher predicted particle temperature, often significantly higher than those from simulations th a t include gasification reactions, and a lower carbon consumption rate. This can lead to erroneous predictions of of burnout times and heat release profiles in oxy-combustion simulations. Since the gasification reactions can also influence the perceived global kinetics under air-fired conditions, the oxidation kinetics currently used in CFD codes will likely need to be reevaluated when including these reactions. In general, the relevance of gasification reactions hampers derivation of accurate high-temperature oxidation kinetic d a ta because the oxidation combustion products (CO2 and H2O) are themselves reactants and are present in high concentration locally near the reaction sites. Conversion of char nitrogen to NOx (and NOx precursors) is highly dependent on temperature [53]. Modeling efforts to predict these pathways must be sensitive to the effect of the gasification reactions on char combustion temperatures. Reactions of coal char with CO2 and H2O might also influence the way in which char-N (and char-S) is released from the particle, potentially adding complexity to the prediction of NOx (and SOx) formation. The steam gasification reaction is important when considering the extent to which the flue-gas must be dried before recycle. We have shown th a t with a higher steam concentration, the steam gasification reaction causes the char combustion temperature to decrease and the carbon consumption rate to increase. These effects must be accounted for when designing an oxy-combustion system. This study has demonstrated th a t char gasification reactions influence the char tempera­ture and carbon consumption during both oxy- and conventional combustion of coal, and we have demonstrated the influence over a wide range of potential gasification rate coefficients. Accurate high-temperature, atmospheric pressure gasification rate d a ta are still needed for more quantitative treatment of these reactions and improved CFD coal combustion models. 35 3.6 Conclusions Using rate parameters for char gasification by steam and CO2 established from literature data, the char combustion of a 1 0 0 ^m diameter high-volatile bituminous coal particle was modeled for candidate dry-recycle and wet-recycle oxy-fuel combustion environments with various oxygen levels using the Surface Kinetics in Porous Particles (SKIPPY) code. The simulations revealed th a t char gasification by both steam and CO2 reduce the char combus­tion temperature, with the CO2 gasification reaction having the predominant influence. The gasification reactions were found to have greater influence for char combustion in elevated oxygen environments, where the char combustion temperature is higher. The gasification reactions augment the char carbon consumption rate, but only by about 10%. Simulations were also conducted over a range of gas temperatures and particle sizes. In general, the gasification reactions have increasing influence as the gas temperature increases (for a given O2 concentration) and as the particle size increases. Simulations of traditional N2 diluent combustion reveal th a t gasification reactions can influence char combustion in these environ­ments, as well. Based on our existing (albeit limited) knowledge of char gasification rates, it appears th a t it is important to include these reactions when interpreting experimental measurements of char combustion or when simulating char combustion, especially in oxy-fuel combustion environments. CHAPTER 4 ANALYSIS OF THE ERRORS ASSOCIATED WITH TYPICAL PULVERIZED COAL CHAR COMBUSTION MODELING ASSUMPTIONS FOR OXY-FUEL COMBUSTION 4.1 Abstract In CFD models of pulverized coal combustion, which often have complex, turbulent flows with millions of coal particles reacting, the char combustion submodel needs to be computationally efficient. There are several common assumptions th a t are made in char combustion models th a t allow for a compact, computationally efficient model. In this work, oft used single- and double-film simplified models are described, and the temperature and carbon combustion rates predicted from these models are compared against a more accurate continuous-film model. Both the single- and double-film models include a description of the heterogeneous reactions of carbon with O2, CO2, and H2O, along with a Thiele-based description of reactant penetration. As compared to the continuous-film model, the double­film model predicts higher temperatures and carbon consumption rates, while the single­film model gives more accurate results. A single-film model is therefore preferred to a double-film model for a simplified, yet fairly accurate description of char combustion. For particles from 65-135 ^m, in O2 concentrations ranging from 12-60 vol-%, with either CO2 or N2 as a diluent, particle temperatures from the single-film model are expected to be accurate within 270 K, and carbon consumption rate predictions should be within 16%, with greater accuracies for a CO2 diluent and at lower bulk oxygen concentrations. A In Press Combustion and Flame, available at h ttp ://d x .d o i.o rg /1 0 .1 0 1 6 /j.c om b u s tflam e .2 0 1 3 .0 2 . 015. Coauthors: Christopher R. Shaddix, JoAnn S. Lighty 37 single-film model th a t accounts for reactant penetration and both oxidation and gasification reactions is suggested as a computationally efficient submodel for coal char combustion th at is reasonably accurate over a wide range of gas environments. 4.2 Nomenclature A 0 pre-exponential factor for rate coefficient [molc /s-m2 ■ (molgas/m 3)] c molar concentration [mol/m3] cp heat capacity [J/mol-K] D diffusivity [m2/s] E a activation energy [J/mol] e emissivity of the particle 0 porosity (or void fraction) h molar enthalpy [J/mol] n effectiveness factor k reaction rate coefficient [molc /s-m2 ■ (molgas/m 3)] k heat transfer Peclet number Km mass transfer Peclet number A gas thermal conductivity [W/m-K] Mt Thiele modulus N moles [mol] n gas number of gas phase species P Pressure [Pa] Q heat [J] R universal gas constant [J/mol-K] r radius [m] a Stefan-Boltzmann constant [W/m2 -K4] ar specific surface area for heterogeneous reactions [m2/m 3] t tortuosity T temperature [K] x mole fraction Subscripts 1 between the particle and flame sheet 2 between the flame sheet and 38 app apparent C carbon from the particle eff effective f at the flame sheet outside the boundary layer in the bulk gas reaction number p surface of the particle i species i ref reference t total of all gas species w wall (to which the particle is radiating) Superscripts ' flow rate [s-1 ] " mean value " per unit area [m-2 ] 4.3 Introduction Char combustion is a complex process th a t involves gaseous transport, homogeneous gas-phase chemistry, heterogeneous gas-solid chemistry, and porous media transport through tortuous geometries. Equations to mathematically describe these phenomena exist, but using spatially resolved detailed models for a large number of particles reacting in complex, often turbulent flow conditions would require computational power of an immense scale. Assumptions and simplifications are regularly made and often necessary to model char combustion [64-67]. Two common char combustion submodels used in CFD simulations are one developed by Baum and Street [6 8 ], and a model first proposed by Smith [9]. In both of these models, oxygen is the only species th a t reacts with the char, while recent work has suggested th a t gasification reactions of char with CO2 and H2O can have an impact on combustion temperatures and burning rates [17, 28, 56, 69]. The Baum and Street model is based on apparent kinetics, wherein oxygen diffusion and kinetic resistances govern the burning rate, but oxygen does not penetrate into the pores of the char. Smith's model includes reactant penetration, based on the Thiele modulus, and the combustion rate is dependent 39 on intrinsic kinetics and the pressure of oxygen at the particle surface. In both of these models, homogeneous chemistry in the boundary layer is neglected. Globally, the reactions of carbon with combustion gases are 2 C + O2 ^ 2CO (4.1) C + O2 ^ CO2 (4.2) C + CO2 ^ 2 CO (4.3) C + H2O ^ C O + H 2 (4.4) There is a multitude of literature documenting experiments to measure the kinetics of these reactions, including those specifically aimed at determining the relative production of CO and CO2 during oxidation [70, 71] and those aimed at determining the relative rates of gasification (Rxns. 4.3 and 4.4) to oxidation [40, 44-49]. Regardless of the specific rates, carbon preferentially oxidizes to CO at high temperature, and there is a potential for H2 to be present in the boundary layer. Oxidation of CO and H2 in the boundary layer can alter the energy balance and the species available for reaction at the particle surface. In this work, we seek to quantify uncertainties th a t arise from typical pulverized coal char combustion modeling assumptions. Some of the modeling assumptions examined in this analysis include the effects of homogeneous chemistry, the description of the heterogeneous chemical reactions, and intraparticle diffusion and reaction. Bounds on errors in char par­ticle temperature and carbon consumption rate are determined, to aid in the interpretation of CFD model results th a t make these assumptions and guide the development of char combustion submodels. In particular, assessments of the uncertainty in CFD predictions of coal boiler performance (e.g. heat transfer, LOI, and pollutant formation) rely on such an evaluation of the uncertainties in the char combustion model. 4.4 Description of Models In this work, several models of varying complexity are compared to each other. Across all models, the following is assumed: • a single, spherical particle in an unconstrained and unperturbed boundary-layer • steady-state • a 1-dimensional (radial) domain 40 • gases are radiantly inactive over this spatial scale The most detailed and physically accurate model used in this work is the Surface Kinetics in Porous Particles code (SKIPPY), as described elsewhere [28]. SKIPPY solves the steady-state mass, species, and energy conservation equations for a reacting porous particle and its reacting boundary layer. From this solution, SKIPPY predicts species concentrations and temperatures within the pores of the char, at the outer surface of the char, and within the boundary layer surrounding the char. Both heterogeneous (gas-solid) and gas-phase chemical reactions are considered. In the work presented here, GRI-MECH 3.0 [52] was used to describe the gas-phase reaction kinetics, while the heterogeneous char reaction kinetics were described using the mechanism specified in Table 4.1. This mechanism is the same as th a t used in our previous work [28]. Oxidation and gasification reactions are treated as adsorption-limited, with arbitrarily fast desorption reaction rates th a t guarantee insignificant accumulation of oxygen complexes on the surface of the char. Recent work has suggested a 5-step mechanism to describe carbon oxidation rather th an this 4-step oxidation mechanism to capture both the pressure and temperature dependence of the CO2/CO ratio [72]. Since the 4-step surface mechanism captures the more important temperature dependence (but not the pressure dependence) of the CO2/CO ratio, it should be accurate under the atmospheric pressure conditions considered in this analysis. The rate coefficients chosen for the oxidation and gasification reactions are based on the analysis conducted in our previous work [17, 28]. Two simplified models are compared to SKIPPY in this work. The first is a single-film model, which assumes there are no reactions in the boundary layer. The second model considered is a double-film model, which is closely related to the Moving Flame Front model described by Zhang et al. [73-76], except our model accounts for Stefan flow. The double-film model assumes th a t there is an infinitely-thin flame-sheet at a point in the T a b le 4.1. Heterogeneous reaction mechanism. The density of surface carbon sites is 1.7 x 10- 5 molCs/m 3. Reaction A (mol/cm2 -s) E a (kJ/mol) Cb + Cs + O2 ^ CO + C(O)s Cs + O2 ^ C(O2)s Cs + CO2 ^ CO + C(O)s Cs + H2O ^ H2 + C(O)s C(O)s + Cb ^ CO + Cs C(O2)s + Cb ^ CO2 + Cs 3.3 x 1015 167.4 9.5 x 1013 142.3 3.6 x 1015 251.0 4.4 x 1014 2 2 2 .0 1 .0 x 10 8 0 . 1 .0 x 10 8 0 . 41 boundary layer th a t converts CO to CO2 and H2 to H2O. At all other points in the boundary layer, the gases are unreactive. In contrast to a classical double-film model, the oxygen is not necessarily completely consumed in the boundary layer, and O2, CO2, and H2O each react and consume the solid carbon. In the unreactive region(s) of the boundary layer, the total and species molar flow rates are constant. Assuming th a t the assumptions associated with Fick's law hold, and th a t we can decouple the species continuity equations by assuming an effective diffusivity, species continuity reduces to dx ■ Ni - XiNt - 4 n r2ctDi;eff- T . (4.5) The steady flow of heat in the boundary layer can be described by a similar equation "sas . -T Q - ^ 2 Nihi - 4 n r2A- , (4.6) i=1 The enthalpy is related to temperature through the heat capacity, cp - (d h /d T )p where the subscript p denotes th a t the differential occurs at constant pressure. Assuming th a t the gas layer is at constant pressure and the heat capacity is not a function of temperature, we can integrate this equation using a reference point to find hi = hi, ref + cp,i(T - Tref), (4.7) where the heat capacity of species i is evaluated at a mean temperature between T and Tref. Equations 4.5 and 4.6 (after substitution of Eq. 4.7) can be integrated, leading to algebraic expressions describing species continuity and energy flow in unreactive section(s) of the boundary layer. 4.4.1 Single-film Model In the single-film model, the entire boundary layer is unreactive, and integration of Eq. 4.5 from the radius of the particle to to (the edge of the boundary layer), results in the expression N'' ( N " \ XiP - ^ + X i^ - N Z ) e-Km,i, (4.8) i ,P N 'p \ i ' ~ N? p ) , ( ) where uc ■ ctDi, eff rPN ' p Km,i - , (4.9) 42 is a version of the mass transfer Peclet number (the Peclet number characterizes the ratio of convective to diffusive transport). The heat flow in the boundary layer must be balanced by the energy released from reactions in the particle, and radiation losses from the particle. The enthalpy advection term (the summation in Eq. 4.6) already accounts for the enthalpy change of the gases during heterogeneous reactions, but does not account for the enthalpy released as the solid carbon is converted to gas phase species [51]. After integration of Eq. 4.6, using the particle surface as the reference point in Eq. 4.7, a thermal energy balance is written as where, A N C,phC,p - (TP - TW) - hi,P + ~ i= 1 K - A * N i,PCP,'‘ i=1 eK - 1 (Tp - T ^ ) (4.10) (4.11) is a version of the heat transfer Peclet number. K p rp 4.4.2 Double-film Model In the double-film model, it is assumed th a t an infinitely thin flame sheet exists some­where in the boundary layer. There are two unreactive gas layers, with the unreactive layer between the particle and the flame sheet denoted as region 1 , and the unreactive layer between the flame and the bulk gas (at r - to) denoted as region 2. In region 2, all of the CO and H2 th a t were generated at the particle are assumed to have been oxidized to CO2 and H2O in the flame sheet. Therefore, the only species fluxes in region 2 are oxygen towards the particle, and CO2 from the particle, which must be equal (on a molar basis, because of the conservation of oxygen), requiring N t,2 - 0 . Armed with this knowledge, integration of Eq. 4.5 in the two regions yields N 11 ( N 11 \ X'i-P - ^ + Xi,f - N P i e -Km,J (1- r , / r , ), (4.12) Nt,p,1 V Nt,p, 1 ) N 11 r f Xi,f - %i,(x + ^ , (4.13) where Km,i,1 is the same as Km,i (Eq. 4.9), except the total molar flux is NV"p 1 rather than t,p 43 Integrating Eq. 4.6 in regions 1 and 2 yields (4.14) (4.15) In these equations, k 1 is given by Eq. 4.11, where A = T1 and cP;i are evaluated at the mean temperature in region 1, assumed to be (Tp + T f )/2 . Similarly, k2 is also described by Eq. 4.11, where A = A2 and Am are evaluated at the mean temperature in region 2. The heat transfer by the gas in region 1 must once again be balanced by the surface reactions and radiation; assuming th a t the particle radiation to the surroundings is not affected by the presence of the flame, The gas heat transfer in region 1 must also be balanced by the gas heat transfer in region 2 , or While there is no explicit term to describe heat release by the flame in this equation, the enthalpy advection terms properly account for chemical reactions. In the double-film model, the flame can be arbitrarily placed, or as suggested by Zhang et al. [73], placed to maximize the overall consumption rate of solid carbon (NC). 4.4.3 Heterogeneous Reactions Within the char particle, reactions 4.1-4.4 are considered, and it is assumed th a t these reactions follow the law of mass action kinetics where each rate coefficient follows an Arrhenius expression, The particle is porous, and the analysis by Thiele [77] is followed, to account for reactant penetration into the pores. Assumptions include first order, irreversible reactions th a t are proportional to the concentration of one reacting species; a uniform particle temperature; pores are connected and can be described by a constant (average) ratio of perimeter to flow area; there is no net mass flow (Stefan flow is neglected in the pores); and, other (4.17) (4.18) 44 reactions/reactants do not affect the rates. The diffusivity of the reactants in the pores is corrected by the ratio of the void fraction to tortuosity. The overall reaction rate coefficient for oxygen is found by adding the reaction rate coefficients of reactions 4.1 and 4.2, then for each of the reactive gases, i = O2, CO2, H2O, the Thiele modulus is calculated as M x , = . (4 .1 9 ) Y T eff An effectiveness factor for each of the three reactive gases is then found as n* M x , ^ tanh(Mx,i) Mx,*) ( ) For each of the four reactions, the molar flux of the reactant i due to reaction j at the particle surface is calculated as j = - n k ( ^ ) ( ) . (4 .2 1 ) LP / Finally, the flux of carbon and each gas species can be calculated NC,p = (2NNp;O2,rxn 4.1 + O2,rxn 4.2 + qq2 ,rxn 4.3 + A ^O ,™ 4.4) (4.22) NO2,p = Np,o 2,rxn 4.1 + Njp,O2,rxn 4.2 (4.23) NCO2,p = ^p,CO2,rxn 4.3 - ^O ^ rx n 4.2 (4.24) ^CO^p = - 2Np,O2,rxn 4.1 - 2Np,CO2,rxn 4.3 - Np,H2O,rxn 4.4 (4.25) NH2O,p = Np,H2O,rxn 4.4 (4.26) NH2,p = -N P/H2O,rxn 4.4 (4.27) Note th a t for the double-film model, these are the species fluxes in region 1, and the species fluxes in region 2 are r 2 NO 2,/,2 = - i f NC,p,1 (4.28) rf r2 n Co2 ,/,2 = 4 NC;p;1 (4.29) r f 4.4.4 Solution Procedure The fluxes described by Eqs. 4.22-4.27 are dependent on the mole fractions of O2, CO2, and H2O at the particle surface as well as the particle temperature. To solve for the mole fractions at the particle surface (Eq. 4.8 for the single-film model or Eq. 4.12 for the 45 double-film model) or the particle temperature (Eq. 4.10 for the single-film model or Eq. 4.16 for the double-film model), the species and carbon fluxes must be known. A damped-Newton method is used to simultaneously solve these equations. Initially, predictions are made for mole fractions and temperature at the particle surface (and the flame, in the case of the double-film model). From this, the species fluxes and properties are calculated, and the mole fractions and temperatures at the particle surface (and the flame, in the case of the double-film model) are recalculated. Newton's method is used to calculate a correction step on the mole fractions and temperatures. Damping on the correction step occurs when the corrected solution is outside the bounds (the mole fractions are constrained to lie between 0 and 1, and the particle temperature must be less th an 6000 K). The solution is considered converged when the normalized error in mole fractions and temperatures are below a given tolerance. The double-film model requires an additional solver to determine the radius of the flame. A Nelder-Mead simplex algorithm, as implemented in SciPy [78], is used to find the radius of the flame where the carbon consumption rate is maximized. 4.5 Results and Discussion To compare the models, the reaction mechanism specified in Table 4.1 was implemented in both the single-film and double-film models described previously. Because Surface CHEMKIN [31] is used by SKIPPY to determine reaction rates, the pre-exponential factors, A, were multiplied by the density of carbon sites (given in the caption of Table 4.1) to determine the pre-exponential factor, A0, for use in the simplified models. The same char parameters shown in Table 4.2 were also used in each of the models. Typical profiles of the temperature and mole fractions within the particle and in the boundary layer are shown in Fig. 4.1, for combustion with 24 vol-% O2 in the bulk gas, 14% H2O, and either CO2 as a diluent gas (to model oxy-combustion conditions), or N2 as a diluent (with 4% CO2 in the bulk gas, which is closer to air-fired combustion conditions). In the figure, SKIPPY results are referred to as the continuous-film model, where reactions occur throughout the boundary layer (and within the pores of the particle). Results labeled ‘no homogeneous chemistry' are also SKIPPY results, where gas-phase chemistry has been turned off. This result reduces SKIPPY to a single-film model (and neglects any homogeneous chemistry in the particle pores). The agreement between the SKIPPY results without homogeneous chemistry and the single-film model confirms th a t SKIPPY is reduced 46 T a b le 4.2. Properties for the base-case simulations, which are the same as the sub-bitu­minous char studied by Geier et al. [56] and as assumed in the simulations by Hecht et al. [17, 28]. ______________________________________ diameter 10 0 ^m bulk density 560 kg/m 3 thermal conductivity 1.33 W /m ■ K (inert) ash content 3% tortuosity 5 void fraction 0.4 specific surface area 1 x 10 4 m2/kg gas temperature 1690 K wall temperature 500 K emissivity 0 .8 47 Figure 4.1. Comparison temperatures and mole-fractions of gas phase species in the particle and in the boundary layer for the 100 ^m particle characterized by Table 4.2. Results are for the single-film, double-film, and SKIPPY models. Thick, solid gray line is SKIPPY with all chemistries; thin, solid blue line is SKIPPY without gas-phase chemistry. The diluent gas on the following page is CO2 and on the second following page is N2. Both plots have 14 vol-% H2O and 24% O2 in the bulk gas. N2 diluent includes 4% CO2 in the bulk gas. 48 CO2 diluent 3400 3200 3000 ^ 2800 « 2600 ^ 2400 2200 2000 1800 1600 0.25 0 .2 0 - (M 0.1 5 0 s 0 .1 0 0 .0 5 - 0. 00 0.9 0. 8 0 .7 2 0. 6 0 0.5 0 0 .4 0 .3 - 0.2 - 0.1 0. 0 1.0 0 2 tq 8 0. 8 T----1---1-I I I I I 0 0 .6 0 8 0 .4 0.2 - 0. 0 0. 08 0. 07 0. 06 0. 05 0. 04 0. 03 0. 02 0. 01 0. 00 0 .1 6 0 .1 4 0.12 0 .1 0 0. 08 0. 06 0. 04 0. 02 single-film no homogeneous chemistry double-film, r j = 4rp double-film continuous-film 0. 00 0. 1 1.0 10.0 1 00 .0 r / r P 49 2 8 0 0 2 6 0 0 2 4 0 0 2 2 0 0 2 0 0 0 1 8 0 0 1 6 0 0 0 .5 5 2 a 0 .5 0 8 0. 45 N 2 d ilu en t ----i-i i i i i 0 .4 0 0 .2 5 0 .2 0 cs 0 .1 5 0 a 0 .1 0 0 .0 5 0 .0 0 0 .2 5 0 .2 0 0 .1 5 0 .1 0 0 .0 5 0 .0 0 0 .6 0 .5 0 . 4 00 0 .3 H 0 .2 00 8 0 .1 0 .0 0 .0 8 0 . 0 7 0 .0 6 2 0 .0 5 i; 0.04 H 0 .0 3 0 .0 2 0 .0 1 0 .0 0 0 .1 6 0 . 1 4 0 .1 2 0 0 .1 0 ^ 0 .0 8 H 0 .0 6 0 . 0 4 0 .0 2 0 .0 0 0 .1 1 .0 1 0 .0 1 0 0 .0 r /r P Figure 4.1. Continued. 50 to a single-film model when the homogeneous chemistry is turned off. Small differences in temperatures and mole fractions are due to the simplifications made in the single-film model. One simplification is that an effective diffusivity rather than a multicomponent diffusion description allowed the species diffusion equations to be decoupled. Secondly, diffusivity and other transport properties are evaluated at a mean temperature, which may not be representative of the entire boundary layer temperature. Finally, the Thiele description for reactant penetration is only valid for one species reacting in a cylindrical pore, whereas in these simulations, three species are reacting with the solid carbon, and CO2 is both a product and a reactant. Nonetheless, under these conditions, the two models agree well. The double-film and continuous-film models also show some similar trends. Reactions in the boundary layer release heat. For the continuous-film model, the temperature still decays away from the particle surface, but is higher than the single-film model temperatures throughout the boundary layer. Meanwhile, the double-film model has a temperature peak at the flame-front. Boundary layer reactions increase the concentration of CO2 and decrease the concentration of O2 available to react at the particle surface. These reactions also drive the concentrations of H2 and CO to zero at a point closer to the particle surface than the single-film models. Char combustion models must accurately predict carbon consumption rates, in addition to char particle temperatures, so that the burnout of the char can be predicted. Figure 4.2 shows the particle temperatures and carbon consumption rates for the same 100 ^m particle as a function of bulk oxygen concentration. Both the particle temperatures and carbon consumption rates increase as the oxygen concentration increases. The temperatures and carbon consumption rates predicted by the continuous-film model (which is the most phys­ically accurate) are most closely matched by the single-film model over the entire range of conditions studied here. The SKIPPY model without homogeneous chemistry agrees well with the full SKIPPY model at low oxygen concentrations, but both the temperature and carbon consumption rates begin to diverge at the higher oxygen concentrations. The two double-film model results shown in Figs. 4.1 and 4.2 are the same model with two placements of the flame sheet. One result is where the flame sheet is somewhat arbitrarily placed at 4rp, and the other, labeled simply ‘double-film', follows the suggestion of Zhang et al. [73] in placing the flame sheet in the position that maximizes the carbon consumption rate. When CO2 is the diluent, this approach causes the flame sheet to be located where it would in a classical double-film model, at the point where the O2 is completely consumed in the boundary layer, and CO2 and H2O are the only species consuming the carbon. When N2 51 CO 2 diluent N2 diluent x O 2 ,0 0 ( v ° l -% ) x O 2 ,0 0 ( v ° l -% ) Figure 4.2. Particle temperatures (top) and carbon fluxes at the particle surface (bottom) predicted by the different models for the 100 ^m particle characterized by Table 4.2. Frames on the left are for the CO2 diluent and frames on the right are for the N2 diluent. In the bottom frames, the bars leading up to the data points with the same line style show the portion of carbon consumption attributed to the gasifiying species shown in the legend (O2, CO2, or H2O). 52 is the diluent, the maximum carbon consumption rate occurs when the flame sheet is further from the particle, and O2 is not completely consumed in the boundary layer. Regardless of where the flame sheet is placed in the boundary layer, the particle temperatures and total carbon consumption rates predicted by the double-film model are significantly higher than those predicted by the continuous-film model. Maximizing the carbon consumption rate in the double-film model causes even higher particle temperatures and carbon consumption rates than when the radius of the flame is four times the radius of the particle. The flame sheet, wherein CO and H2 are oxidized, transfers significant heat to the particle. Although the mole fraction of O2 at the particle surface decreases and the mole fractions of H2O and CO2 increase, causing the gasification reaction rates to increase and the oxidation reaction rate to decrease, the endothermic gasification reactions do not consume enough heat to reduce the particle temperature back to where it would be without the flame sheet in the boundary layer. Moving the flame sheet further out in the boundary layer causes the predicted particle temperatures to decrease until eventually, the predictions between the single and double-film models are identical. A careful inspection of the lower panels of Fig. 4.2 elucidates the species responsible for the carbon consumption. With the exception of the double-film model, the majority of carbon consumption is due to O2, followed by CO2, and then H2O across the range of oxygen concentrations in the bulk gas. CO2 is responsible for the majority of the carbon consumption for the double-film model, when CO2 is the diluent, and a large fraction for the N2 diluent. The fraction of consumption by CO2 is also larger for the continuous-film and double-film model where f - 4rp, than for either version of the single-film models. Boundary-layer reactions, when accounted for, generate significant quantities of CO2 as CO is oxidized. Consequently, the flux of CO2 to the particle, and the mole fraction of CO2 at the particle surface, increases, while the O2 flux and concentration at the particle decreases, due to O2 utilization in the boundary layer. The net effect is a greater proportion of carbon consumption attributed to CO2, but a similar overall carbon consumption rate prediction as when boundary layer reactions are neglected. Since the gasification reactions are endothermic, one might expect the particle tem­perature to be lower when boundary layer reactions are active and a larger portion of carbon consumption is due to CO2 gasification. In fact, the heat released by the CO and H2 oxidation in the boundary layer feeds back to the particle and the temperatures predicted by the double-film model are higher than those predicted by the single-film model. When the heat release in the boundary layer is spread out over a larger distance, as 53 in the continuous-film model, the temperatures predicted are slightly higher than those predicted by the single-film models at low oxygen concentrations, but lower at high bulk O2 concentrations, highlighting the complexities in these models. As another parametric study, Fig. 4.3 shows the temperatures and carbon consumption rates as a function of particle size for three bulk oxygen concentrations. The double-film model with a maximized carbon consumption rate has been omitted from this plot, due to the large deviations from the continuous-film model. Smaller particles burn at higher temperatures, and have a higher flux of carbon (although it should be noted that the flux is normalized to the external surface area of the particle, 4nrp, and the flow rate of carbon (mol/s) actually increases as the diameter increases). Although there are endother-mic gasification reactions along with the exothermic oxidation reactions, the net result of heterogeneous chemistry is exothermic. Smaller particles have larger effectiveness factors, and subsequently higher reaction rates. This causes the larger carbon consumption rate and higher temperatures for smaller particles. A comparison of the particle temperatures in N2 and CO2 diluent environments shows consistently higher temperatures for all particle sizes and for all models in N2 environments, because of the reduced contribution of the endothermic CO2 gasification reaction and the higher diffusivity of oxygen through nitrogen as compared to CO2 [6]. Across the range of sizes (60-135 ^m) and bulk oxygen concentrations (24-60%), of the two simplified models, the single-film model predicts both carbon consumption rates and particle temperatures that are more similar to continuous-film model predictions. There is also very little difference between the single-film model and SKIPPY model without ho­mogeneous chemistry, confirming that the simplifications regarding the effectiveness factor and gas diffusion are reasonable. The errors between the single-film models and the full SKIPPY model are larger with nitrogen as a diluent as compared to CO2 and as the bulk O2 concentration increases, but the differences between the models are not a strong function of particle size. The largest error in temperature between the single-film model and the continuous-film model is 270 K for a 60 ^m particle with 60% O2 in the bulk gas and N2 as the diluent. The largest relative error in carbon consumption rate between the single-film and continuous-film models is 15.3% for a 135 ^m particle with 36% O2 in the bulk gas and N2 as the diluent. A base surface area of 10 m2/g was used for all of the previous simulat