Characterization of Coal and Biomass Conversion Behaviors in Advanced Energy Systems

Transcription

1 Characterization of Coal and Biomass Conversion Behaviors in Advanced Energy Systems Investigators Reginald E. Mitchell, Associate Professor, Mechanical Engineering; Paul A. Campbell and Liqiang Ma, Graduate Researchers Abstract Currently, energy from coal accounts for about 23% of the energy consumed in the United States and it is projected that coal use will increase over the next few decades. Because of the low efficiencies and high pollutant emission characteristics of present-day schemes for converting the energy in coal to useful energy, advanced energy conversion schemes having high efficiencies and near-zero pollutant emissions with carbon dioxide capture are being investigated. Technologies that utilize biomass in concert with coal are also being investigated as means of reducing the release of fossil-carbon to the atmosphere. The objective of this research project was to develop and validate models that accurately describe the behaviors of coal and biomass char particles in the types of environments likely to be established in advanced coal-based energy conversion systems. The models will allow the development of robust combustor and gasifier codes that can be used to evaluate alternative power-plant design options and strategies. Such comprehensive codes will enable the development of efficient, non-polluting coal-fired and biomass-fired power plants. The combustion and gasification of coal and biomass are complex processes involving various physical and chemical subprocesses, which include gas transport across boundary layers surrounding particles, gas transport through pores inside particles, reactions that occur on carbonaceous surfaces, and surface area evolution that occurs during char conversion. At high temperatures, these subprocesses occur simultaneously. Our research activities devoted towards providing validated combustion and gasification models that account for these subprocesses are summarized in this report. An extensive study was undertaken to characterize char reactivity to oxygen. A variety of carbonaceous materials were employed in the study including coal-derived chars, biomass-derived chars and synthetic chars. Oxy-reactivity tests were performed under kinetics-limited conditions in a pressurized thermogravimetric analyzer (PTGA) equipped with real-time diagnostics to permit the measurement of the concentrations of CO, CO2 and O2 along with mass loss during the course of an experiment. The PTGA system was also employed in performing gas adsorption tests, the results of which were used to determine the specific surface areas of chars. A detailed char oxidation model was developed based on the results of the oxyreactivity and surface area evolution tests. The kinetic and pore structure parameters were adjusted to reproduce the results of the oxy-reactivity and CO2-adsorption experiments. The model was used to investigate the effects of surface oxide complexes and their distributions on char reactivity as well as to investigate the impact of surface area evolution on the char conversion process. It was demonstrated that the use of a single, effective activation energy to reflect the distribution in the energies of adsorbed

2 oxide complexes can yield misleading results. It was also demonstrated that account must be made for the dynamic changes that occur in specific surface area if the concentrations of adsorbed surface species are not to be under-predicted. Based on the detailed heterogeneous reaction mechanism, a reduced mechanism, simple enough to be used in robust coal-fired combustor codes, was developed that accurately describes the key reaction pathways during char oxidation at high temperatures and elevated pressures. An extensive study was also undertaken to characterize the mode of char-particle burning. Under pulverized coal combustion conditions, char particles burn with reductions in both diameter and apparent density due to the O 2 concentration gradients established inside burning particles at high temperatures. A direct numerical simulation of a single burning char particle was developed and used to characterize the variations in particle size and apparent density that occur during high-temperature oxidation. The results of these calculations were used to establish a relationship between the effectiveness factor and the Thiele modulus, which was employed in the development of a reactivity-based mode-of-burning model. The mode-of-burning model allows for variations in particle size and apparent density during burnoff that depend on the instantaneous state of the char particle. It was demonstrated that the model accurately predicts the burning behaviors of char particles burning in the type of environments established in real combustors and furnaces. In many proposed advanced coal conversion technologies, the char conversion process occurs at elevated pressures. Consequently, in our research activities, a study having the objective of ensuring that the models developed were adequate for highpressure applications was undertaken. The separate effects of total pressure, oxygen mole fraction and oxygen partial pressure on char reactivity as particles burn were examined using the char particle oxidation model. The calculated results compared favorably with results of experiments performed in our pressurized flow reactor. In high-pressure studies, it has been observed that the physical structures of char particles produced during devolatilization of bituminous coals can differ, and can be characterized as being cenospherical, mixed and dense. The fraction of cenospherical particles increases with increasing pressure. To more accurately predict char combustion behavior at elevated pressures, models for the different char structures were developed and integrated into the char combustion model. Calculated mass loss and apparent density profiles agreed with profiles measured in experiments performed at elevated pressures in our flow reactor. The calculated particle temperatures were consistent with the measurements of particle temperatures at comparable burning conditions in other studies. The model adequately predicted the behaviors of char particles burning under conditions of high temperature and high pressure. In order to accurately predict char conversion rates during gasification, it is necessary to accurately characterize the rate of the reaction between carbon and carbon dioxide. Published models for the C-CO 2 reaction do not predict char conversion rates accurately in the high-pressure, high-co containing environments that can be established in advanced gasifiers. Towards eliminating this deficiency in our predictive capability, a carbon-carbon dioxide reaction mechanism was developed and validated employing data obtained in previously published investigations as well as data obtained in experiments undertaken during this project. The reaction mechanism developed was evaluated using

3 gasification rates determined from experiments performed with coals, biomass and synthetic chars under different gasification conditions. It was demonstrated that the mechanism developed provides accurate predictions of char reactivity to CO 2 over a wide range of temperatures, pressures, and gas compositions. Introduction The goal of this project was to develop models that predict accurately coal and biomass gasification and combustion behaviors in the types of environments likely to be established in advanced energy systems. This required acquiring the information needed to understand and characterize the fundamental chemical and physical processes that govern coal and biomass conversion at high temperatures and pressures. The models that were developed can be used to determine operating conditions that optimize efficiency during the char conversion process and to examine design strategies for integrating combined cycles for the production of synthesis gas, hydrogen and electric power with minimum impact on the environment. Background The coal-fired power plant will continue to be the workhorse of America s electric power sector for the next 50 years. Improvements in burner designs, refractory materials and high-temperature heat exchangers in combination with hybrid schemes that combine coal combustion and coal gasification have the potential for the development of highly efficient, environmentally clean, power-generating technologies. The increased efficiencies yield lower emissions of greenhouse gases, carbon dioxide emissions being the most critical to reduce. Higher efficiencies also mean that less fuel is used to generate the rated power, resulting in improved system economics. Biomass is a renewable fuel, and is considered to be CO 2 -neutral with respect to the greenhouse gas balance if the use of fossil fuels in harvesting and transporting the biomass is not considered. By increasing the fraction of renewable energy in the energy supply, the extent that carbon dioxide emissions will adversely impact the environment can be diminished. Co-firing biomass with coal in traditional coal-fired boilers and furnaces or using biomass-derived gas as a reburn fuel in coal-fired systems represent two options for combined renewable and fossil energy utilization. Configurations that employ both biomass and coal in integrated gasification combined gas and steam power cycles and hybrid technologies that produce synthesis gas for fuel cells as well as produce electric power in combined gas and steam power cycles offer additional options. Coal and biomass contain significant quantities of hydrogen, and several schemes have been advanced for the efficient and economical production of hydrogen from coal and biomass. With CO 2 capture and sequestration, partial coal or biomass oxidation is a promising technology for the production of electric power and hydrogen that uses integrated gasification combined-cycle technology with little adverse environmental impact. The design of efficient coal/biomass co-utilization energy systems with integrated thermal management to minimize waste heat requires an understanding of the processes that control the physical transformations that coal and biomass particles undergo when exposed to hot environments and the chemical reactions responsible for conversion of the solid material to gaseous species and ash. The goal of this research project was to

4 provide the needed understanding. Our efforts resulted in fundamentals-based submodels for particle mass loss, size, apparent density, and specific surface area evolution during conversion of coal and biomass materials to gas-phase species during gasification and combustion processes. Discussion of Significant Results This final report summarizes the results of our research activities. First we summarize the results of our efforts to characterize the chemical reaction pathways that are important in describing the reactivities of coal and biomass chars to oxygen. Next, the results of our efforts to characterize the mode of burning during high-temperature oxidation are described. This is followed by a summary of the results of our efforts to account for the variations in particle structures that occur when coals are devolatilized at high pressures. The results of our investigation of the effects of pressure on char reactivity to oxygen are then summarized. Finally summarized are the results of our activities associated with characterizing coal and biomass char gasification reactivities to carbon dioxide. I. Characterization of Coal and Biomass Char Reactivity to Oxygen A critical aspect of the overall char oxidation process is the heterogeneous chemical interactions occurring at the char surface. These interactions are functions of the physical surface of the char and the heterogeneous reactions that occur. While surface species are often viewed as having singular and specific kinetic properties, it is understood that surface complexes have no single nature. Instead they are characterized by a distribution of chemical properties due to the local microscopic irregularities typical of char surfaces. During oxidation, besides the microscopic surface interactions that occur yielding species distributions, macroscopic surface area changes due to evolution of the pore structure of the char also occur. Such changes impact the char conversion rate. During the course of char conversion, the total surface area of very microscopic chars must first increase as internal pore volume increases. Pore walls will then merge and coalesce resulting in a decrease in surface area, eventually leading to a total elimination of the surface at full conversion. While previous research efforts acknowledged this surface area behavior during char oxidation, the microscopic chemical behaviors were modeled as occurring independently of the global surface behaviors. In our efforts, attention was given to quantifying the effects of surface oxide population distributions and surface area evolution on the overall carbon-oxygen reaction rate. In the sections that follow, results that demonstrate the impact of the distributions of surface oxides and surface area evolution on char conversion behavior are presented. Experimental Approach and Data Analysis In the experiments designed to provide data needed to validate the heterogeneous reaction mechanism developed, a synthetic char containing no mineral matter was employed. The use of synthetic char allows the study of char oxidation without the complications of unknown chemical composition and unknown porosity inherent in real coals and biomass and without the possible catalytic effects of ash. The procedure employed for making synthetic chars with controlled porosity involved the polymerization of furfuryl alcohol, using p-toluenesulfonic acid as a catalyst [1,2].

5 Carbon black and lycopodium plant spores were used as pore formers, yielding chars having porosities in the range 15% to 36%. Char particles were sieved and classified to obtain particles in the μm size range for testing. A scanning electron micrograph (SEM) of synthetic char particles used in some of the tests is shown in the left panel of Fig. 1. For comparison, also shown are SEMs of bituminous coal particles and almond shell (biomass) particles that were also examined during the course of this project. 200 μm (a) (b) (c) Figure 1: Scanning electron micrographs of (a) synthetic char particles (25% porosity), (b) Lower Kittanning (bituminous) coal particles, and (c) almond shell particles. In our experimental activities, char samples were subjected to temperatureprogrammed desorption (TPD) and oxy-reactivity tests in order to characterize the chemical pathways that control the char conversion rate and product distribution. These tests were performed in our pressurized thermogravimetric analyzer (PTGA) under wellcontrolled conditions. The PTGA microbalance reading and the O 2, CO, and CO 2 concentrations in the PTGA exhaust gas were monitored continuously throughout the char conversion process. At various extents of conversion during an oxidation test, char samples were subjected to gas adsorption tests in order to determine BET specific surface areas [3]. Carbon dioxide was used as the adsorption gas, and adsorption tests were carried out at 296 K and 10 atm. For a char oxidation process, the char at the onset of oxidation was taken to be the carbonaceous material remaining after initially heat-treating the sample in nitrogen to remove any oxides already adsorbed. The oxide-free chars were subjected to the CO 2 -BET procedure to determine the surface area of the char at the onset of oxidation. Oxidation tests were interrupted at selected extents of mass loss so that in situ gas adsorption tests could be performed. An in situ gas adsorption test was also performed immediately after the post-oxidation TPD test and cool-down. Thus, the specific surface area as a function of conversion was determined for a single char sample. The recorded PTGA thermograms and the composition profiles of the PTGA exhaust gases were analyzed in conjunction with the surface area measurements to determine ashfree conversion rates, O 2 adsorption rates, CO and CO 2 desorption/production rates, and overall surface-oxide concentrations, as functions of time and conversion. The instantaneous mass of the char was determined by integrating the measured CO and CO 2

6 molar production rate profiles, where the molar production rates were determined from the flow rate of the PTGA exhaust gas and the measured mole fractions of CO and CO 2 in the exhaust. The char conversion rate was determined from its mass loss rate. The instantaneous net rate at which oxygen accumulated on the surface was calculated from the difference between the mass loss rate based on the PTGA microbalance reading and the mass loss rate of the carbonaceous material, as determined from the CO and CO 2 measurements. An oxygen balance yielded the net rate of chemisorption of oxygen molecules on the carbonaceous surface of the char. The measured surface areas were correlated using the model developed by Bhatia and Perlmutter [4] to permit the determination of surface area at all extents of char conversion. The results of one of several sets of experimental data are shown as symbols in Fig. 2. The error bars in the figure reflect the uncertainty associated with the experimental procedures, data reduction scheme, surface area measurements, and the extent of CO conversion in the gas phase downstream of the PTGA balance pan. Figure 2: Comparison of model results with experimental results of the char oxidation process in the PTGA. Shown are (a) the CO 2 concentration in PTGA exhaust gases, (b) the CO concentration in PTGA exhaust gases, and (c) the oxide loading on the char sample.

7 Numerical Approach In an effort to determine the reaction rate parameters of the char, a mathematical model of the oxidation process was developed. Any loss in char mass during oxidation is accounted for in carbon-containing desorption products, specifically CO and CO 2. Consequently, dm C = S tot ˆM C ( ˆRS,CO + ˆR S,CO2 ), (1) dt where the CO and CO 2 molar production rates depend on the reaction mechanism and S tot is the total char surface area (S tot = m C S gc ), calculated employing the Bhatia-Perlmutter model for the specific surface area of the char: 1 ϕ ln( 1 x C ). (2) S gc = S gc,0 Here, ϕ is a structural parameter that increases with increasing microporosity of the char, and is determined by fitting the measured surface area data. Similarly, for the total mass, dm tot dt = S tot all gas species ˆM j ˆRS, j. (3) Since x C is related to m C,0 according to m C = m C,0 (1-x C ), Eq. (1) can be expressed in terms of conversion rate: dx C dt = S tot ˆM C m C,0 ( ˆRS,CO + ˆR S,CO2 ) (4) Assuming that all surface species, except for free carbon sites (-C) can be accounted for by applying the law of mass action to the individual reactions of the mechanism, the total moles of species j on the char surface changes according to dn j dt = S tot ˆRS, j. (5) When N j = [X j ] S tot is substituted into Eq. (5) and the result is expanded, it can be shown that dθ j + θ j ds tot = η j S, j, (6) dt S tot dt []ˆR ξ where θ j is the fraction of carbon sites occupied by adsorbed species j, η j is the number of carbon sites that one molecule of species j occupies, and [ξ] is the total surface concentration of all carbon sites, whether free or occupied. The rate of change in the total surface area is evaluated by differentiating the product m C S gc, employing Eq. (2). A species mass balance on the control volume about the PTGA balance pan yields the following expression for the rate of change in the gas-phase species mole fractions as a result of char oxidation dy dt j = N& N in gas ( y y ) j, in j 1 + N gas S tot Rˆ S, j y j all gas species j S tot Rˆ S, j. (7)

8 In the above expression, y j,in and y j are the mole fractions of species j in the inflowing gases and in the gas phase, respectively; and &N in and &N out are the total molar flow rates of gases entering and exiting the control volume, respectively. For a given heterogeneous reaction mechanism, the rates of reactions for species j can be expressed in terms of temperature-dependent rate coefficients and species concentrations permitting the integration of Eqs. (6) and (7) to predict the adsorbed species site fractions and gas-phase species mole fractions as a function of time when the char is exposed to the hot oxidizing environment established in the reaction chamber of the PTGA. The initial char conditions and the flow rates of the gases supplied to the PTGA must be specified. Distributed Desorption Energies Since temperature programmed desorption experiments have shown that different oxide complexes on a char can exhibit a wide distribution of desorption energies [5-9], the model developed allows for distributions in activation energy of the adsorbed oxygen complexes. Previous research has shown that the probability of a newly-formed oxide complex having a specific activation energy of desorption is approximately similar to a Gaussian [5,7-9], however in this work, a distribution similar to the range between the minima of a symmetric 4 th -order polynomial was used for it more accurately accounts for the low-energy populations than does the Gaussian distribution. The distribution, ψ(e des ), is not too dissimilar from a Gaussian between its minima, and is expressed in the following form: ( ) 2 ( E E min ) 2. (8) ( ) 5 ψ( E)= ψ 0 E E max E max E min The parameters ψ 0, E min, and E max are determined from fits to the TPD data. In the model, the full range of desorption energies is discretized into L equally spaced subranges. The portion of complexes populating the l th subrange has a desorption energy of E des,l, and the span of each subrange is ΔE des. The gross formation rate of the l th subpopulation of -C(O) by the i th reaction is ( ) d -C O l = ν i, j ˆRR, j Ψ( E des,l ), (9) dt l formation where Ψ(E des,l ) is the integral of ψ(e des ) over the energy range of the l th subpopulation, i.e. the fraction of -C(O) formed within the l th subpopulation. Viewing desorption as a unimolecular process, the desorption rate of the l th -C(O) subspecies is ( ) d -C O l dt ldesorption = -C( O) Φ ( E des,l)k des ( E des,l )= -C( O) l k des ( E des,l ), (10) where Φ(E des,l ) is the fractional contribution of the l th subpopulation. By solving Eqs. (9) and (10), the model keeps account of the populations of the l th -C(O) subspecies. Similar capabilities were extended to model CO 2 desorption from dioxide complexes, -C 2 (O 2 ).

9 The Heterogeneous Reaction Mechanism Based on an analysis of the oxy-reactivity and TPD results, and in consideration of the contributions of other researchers, the heterogeneous reaction mechanism shown in Table I was determined to be descriptive of the heterogeneous char oxidation process. In the reactions presented, free carbon sites, -C, are included to show mass conservation. For every carbon gasified, an underlying bulk carbon -C- is brought to the surface. The complex -C(O m ) represents migrating chemisorbed oxides. Multiple forward arrows for reaction progress represent reactions that proceed according to the distributive nature of a reactant species. Table I: Detailed heterogeneous reaction mechanism for char reactivity to O 2. -C-( O 2 ) + -C + -C- -C-( O 2 ) + -C + -C- ( ) + -C( O) + -C- -C- O 2 -C-( O 2 ) + -C 2 ( O 2 ) + -C- phy, f phy, b -C + O 2 -C-(O 2) chm0 m (R1) (R2) -C-(O 2 ) + -C -C(O ) + -C(O ) chm1 CO + -C( O m )+ -C (R3) chm3b -C-( O 2 ) + -C( O) + -C- -C O m chm2 CO 2 + -C + -C chm3a CO + -C O m CO + -C O m -C( O m ) ( ) + -C O -C O m ( ) + -C 2 O 2 ( ) ( ) -C O ( ) -C 2 O 2 chm4a m (R4) ( ) + -C( O m ) (R5a) ( ) + -C O m CO 2 + -C O m mig1 -C O ( ) mig2a ( )+ -C O m ( ) (R5b) ( ) + -C (R6) ( ) (R7) ( ) (R8a) -C 2 O 2 mig2b -C 2 O 2 mig3a -C O m mig3b -C( O) + -C- -C O m des1 ( ) + -C( O) (R8b) ( ) (R9a) ( ) + -C O CO + -C ( ) (R9b) (R10) -C 2 ( O 2 ) + -C- des2 CO 2 + -C + -C (R11) The char oxidation mechanism comprises fourteen distinct reactions. In some reactions, one of the reactants may be a single-oxygen oxide site, -O, that may be associated with either a monoxide -C(O) or a dioxide -C 2 (O 2 ) complex. If the energetics of these reactions were considered to be independent of the oxide association, these almost-duplicate reactions are designated a and b. When duplicates are considered, the mechanism reduces to eleven reactions. In terms of the 11-step form of the mechanism, physisorption is defined by one reversible reaction, (R1); chemisorption consists of five reactions, three with free-site reactants, (R2) to (R4), and two with stable-

10 oxide-site reactants, (R5) and (R6); migration has three reactions, (R7) to (R9); and desorption is defined by reactions (R10) and (R11). The kinetic parameters determined for a 25% porosity synthetic char are shown in Table II. Comparisons of the results of the PTGA oxy-reactivity experiments with the results of the numerical model, based on the suggested mechanism and parameters, were shown as the solid lines in Fig. 2. Agreement is deemed to be quite good. The heterogeneous reaction mechanism adequately describes the key reaction pathways in char oxidation. Table II: Kinetic parameters determined for a synthetic char. Reaction A c b E o (kj/mol) ω a (kj/mol) (R1) a a Notes Reverse of (R1) (R2) (R3) (R4) (R5) b (R6) b (R7) Reverse of (R9) (R8) b Reverse of (R9) (R9) b (R10) , E = E min, E max (R11) , E = E min, E max Assuming Arrhenius-type dependency: k = A T b exp(-e/rt). a E = E o (1-(1-θ) a )ω/a; ω = surface energy constant; For a = 1, traditional Elovich applies. b The specified A assumes -C(O) is reactant. If -C 2 (O 2 ), A is twice the value specified. c Units in (s -1, m 3 mol -1, m 2 mol -1 ) Elovich-type formulations are employed to account for free-site population distributions and to empirically reproduce the observed trends of decreasing chemisorptivity with increasing surface coverage. The Elovich-type model here is not confined to the traditional relationship, which assumes a linear dependence between surface coverage and activation energy. While allowing for this possibility, this study suggests that as surface coverage increases, the activation energy of adsorption may approximately asymptote to the mode-average activation energy of the free-sites. As the most chemisorptive sites are occupied during initial oxide buildup, the remaining sites tend to differ less from one another, leading to a more constant activation energy at higher surface coverages (See footnote a in Table II). This non-traditional Elovichtype effect was not observed for reactions (R2) and (R3), but was for reaction (R4). This

11 suggests that CO 2 formation favors the most chemisorptive free-sites, dominating the chemisorption process until the inhibitory effects of stable oxides on these sites restrains the process. During the course of char conversion, some of the chars studied exhibited a second increase in gasification rates at times beyond the early-peak. This second source of char reactivity coincides with a buildup of stable surface oxides, suggesting that the presence of oxides enhances the chemisorption process. Migration and Desorption The results of the TPD experiments supported the inclusion of reactions (R7) through (R11). TPD profiles beginning at the lowest test temperature (673 K) yielded results most consistent with the full ψ(e des ) spectrum for CO and CO 2 desorption. The gas evolution rates of CO and CO 2 for this experiment are shown in Fig. 3. Results of numerical models approximating the TPD experiment are also shown. Probability distributions were assumed for both -C(O) and -C 2 (O 2 ). The model surface, assumed to initially have distributions according to ψ(e des1 ) and ψ(e des2 ), respectively, is subjected to a simulated TPD process. Without migration, simulated gas evolution rates resemble a Gaussian shape similar to that observed by other researchers in their TPD tests [6-9]. However a bimodal CO 2 evolution profile and slightly rightskewed CO evolution profile were experimentally observed. While similar bimodal profiles were observed by Skokova [10], such bimodal profiles are conspicuously absent from the other TPD studies. However, in these other efforts, CO 2 is evolved in insignificant quantities compared to CO. Skokova [10] demonstrated the significance of migration during char oxidation and its effect of increasing overall CO 2 formation. Building on this foundation, the current results demonstrate that migration is not only responsible for increased total CO 2 production, but for the bimodal nature of the CO 2 evolution profiles as well. Figure 3: Comparison of TPD experimental results versus model results, and the effect of neglecting migration. The second peak is a consequence of the rates of reactions (R9a) and (R9b) approaching the desorption rates as temperature increases. As temperature increases,

12 stable oxides are excited to form mobile oxides via these reactions. The mobile oxides subsequently migrate and cluster with stable oxides (via reactions (R8a) and (R8b)) to form dioxide complexes. These dioxide complexes have a relatively low activation energy for CO 2 desorption, resulting in an almost immediate decomposition of the newly formed -C 2 (O 2 ) species, thereby enhancing CO 2 production above 1073 K. The rightskewed nature of CO production is due to the concurrent depletion of -C(O) complexes. Impacts of Distributed Desorption Energies and Dynamic Surface Area The effect of using finite numbers of subpopulations to approximate site distributions for oxide desorption energies is illustrated in Fig. 4. In the cases shown, identical initial conditions were used in the model, while the number of subpopulations approximating the -C(O) desorption distribution was varied. (R3) (R5) (R10) Figure 4: Model results demonstrating how (a) 1-site, (b) 2-site, (c) 4-site, and (d) 10-site approximations to the -C(O) desorption distribution affects the evolution of CO during the oxidation process. Comparison of the cases shown in Fig. 4 reveals that as L increases, the observed oxidation behavior converges toward that of the true behavior (best represented by the L = 10 case, which yields results essentially the same as those for L > 10). Furthermore,

13 it was not until four or more sites were used that oxidation behaviors even resembled the full distribution. Also, as L decreases, the model approximation fails to accurately acknowledge the relative contributions of different reactions to overall production of CO that is observed. An exercise demonstrating the effects of utilizing the dynamic versus the quasi-steady surface assumption is illustrated in Fig. 5, in which surface oxide coverage and surface area evolution is shown for a char initially having little microporosity (a macroscopic char) and a char having significant microporosity (a microscopic char). In the dynamic case, as surface area decreases (as it does at high conversions), oxide complexes are forced to populate less overall surface area, causing an increase in surface-oxide concentrations. The converse is also true. As surface area increases (as it does during the early periods of char conversion for microporous chars having large values of ϕ), oxide complexes have more overall area to populate, causing a reduction in surface-oxide concentrations. Consequently, since pore structure changes are inevitable during char conversion, the chemical processes on the char surface never reach a steady-state condition. This invalidates the quasi-steady, adsorbed-oxygen concentration approximation made by many investigators. In the results shown in Fig. 5, when the impact of surface area change on adsorbed species concentrations is neglected, steadystate conditions are reached by about 10% and 30% conversion, respectively, for the microporous and macroporous chars. As illustrated, adsorbed oxygen complexes never reach a steady-state in the dynamic surface area case. (a) ϕ 2 (b) ϕ Figure 5: Model results comparing the effects of the dynamic versus quasisteady surface models on the surface coverage of oxide complexes during oxidation in 6 kpa O 2 at 773 K. In case (a), the initial char is macroporous, with ϕ = 2.0. In case (b), the initial char is microporous, i.e. ϕ. These results support the utilization of the dynamic surface assumption as an improvement upon the quasi-steady surface assumption. This impact might be especially critical in modeling chars that initially have poor pore development and in modeling near-burnout conditions when surface areas tend to decrease dramatically.

14 A Reduced Heterogeneous Reaction Mechanism The heterogeneous oxidation mechanism described above is too complex to be used in combustion models developed to describe oxidation under Zone II oxidation conditions in which the overall particle burning rate is limited by the combined effects of chemical reaction and pore diffusion. Therefore, a reduced mechanism was developed and tested for its ability to describe observed reactivities to oxygen. By assuming quasi steady-state concentrations for physisorbed oxygen and migratory adsorbed oxygen atoms, the six-step reaction mechanism presented in Table III can be derived. Table III: Reduced heterogeneous reaction mechanism for char reactivity to O 2. Kinetic parameters are for a 25% porosity synthetic char. a 2 C f + O 2 C(O) + CO (R1a) 2 C f + O 2 C 2 (O 2 ) (R1b) C b + C f + C(O) + O 2 CO 2 + C(O) + C f C b + C f + C(O) + O 2 CO + 2C(O) C b + C(O) CO + C f C b + C 2 (O 2 ) CO 2 + 2C f (R2) (R3) (R4) (R5) A i a E i (kj/mol) σ i (kj/mol) 3.87e e e e e e k exp( ˆ i = Ai Ei RT ), units of A i in mol, m 2 -surface/m 3 -fluid, s; k i,eff = k i E f E, E i,σ i 0 ( ) ( ) In the mechanism, C f represents a free carbon site, one available for oxygen adsorption, and C(O) and C 2 (O 2 ) represent adsorbed oxygen atoms, one oxygen atom per carbon site. Bulk carbon atoms, C b, are assumed to have unity activity. The rates of Reactions (4) and (5) were modeled using a distributed activation energy approach in order to account for the variations in the strengths of adsorbed oxygen atoms. The rate parameters shown in the table were determined using data obtained with a 25% porosity synthetic char. In this particular case, when determining the reaction rate coefficients for the desorption reactions, the temperature programmed desorption data were fit to Gaussian distributions. Using the rate parameters shown in Table III, CO and CO 2 release rates and mass loss rates during TPD experiments and during oxidation tests are adequately characterized. Comparisons between predicted and measured reactivities as a functions of conversion for synthetic chars burning in selected environments are shown in Fig. 6 for burning under Zone I conditions in which the overall particle burning rates are limited solely by chemical kinetic effects. Agreement is deemed to be good. Both temperature and pressure effects on char reactivity are adequately characterized using the reduced reaction mechanism to account for the rate-limiting chemical reaction pathways. The Bhatia- Perlmutter surface area model was also used in the calculations to account for the specific surface area and its evolution as carbon is gasified under Zone I burning conditions. The agreement depicted in Fig. 6 is typical of that observed for tests at other conditions.

15 4 Char reactivity, 10-6 gc/(m 2.s) atm, 6% O K 773 K 723 K x c, conversion 25% porosity synthetic char 36% porosity synthetic char Figure 6: Measured and calculated intrinsic reactivities for synthetic chars burning under kinetic-controlled conditions, i.e., in Zone I. Agreement between measured and calculated reactivities was also found to be adequate for chars produced from real coals. Typical comparisons are shown in Fig. 7; data were obtained with the char of Lower Kittanning coal, a bituminous coal from Pennsylvania. The char was extracted from the entrained flow reactor, just after devolatilization under high temperature-high heating rate conditions and hence, is typical of chars produced in real pulverized-coal combustors. The kinetic parameters, determined by fitting the thermogravimetric data obtained in oxidation tests, are shown in Table IV. The agreement observed supports the use of the reduced mechanism to describe coal-char mass loss rates under conditions in which the overall burning rate is controlled by chemical kinetic effects. 6 6 mol-% O2, 1 atm Reactivity, g/(m 2.s) x K 873 K Conversion, x c Figure 7: Comparison of measured and calculated char reactivities to oxygen during kinetics-limited burning. The calculations were made using the mechanism and parameters shown in Table IV. The char was derived from Lower Kittanning coal.

16 Table IV: Reduced heterogeneous reaction mechanism for char reactivity to O 2. Rate parameters are for the char produced from Lower Kittanning coal. a 2 C f + O 2 C(O) + CO (R1a) 2 C f + O 2 C 2 (O 2 ) (R1b) C b + C f + C(O) + O 2 CO 2 + C(O) + C f C b + C f + C(O) + O 2 CO + 2C(O) C b + C(O) CO + C f C b + C 2 (O 2 ) CO 2 + 2C f (R2) (R3) (R4) (R5) A i a E i (kj/mol) σ i (kj/mol) 2.32e e e e e e k exp( ˆ i = Ai Ei RT ), units of A i in mol, m 2 -surface/m 3 -fluid, s; k i,eff = k i E f E, E i,σ i 0 ( ) ( ) The Specific Surface Area The determination of char reactivity from the thermogravimetric data obtained during oxidation tests requires that account is made for variations in the specific surface area of the char. From Eq. (1) above, the rate of mass loss, specific surface area, and char reactivity are related as follow: 1 dm C = S gc R ic, (11) m C dt where R ic is the intrinsic chemical reactivity of the char on a mass basis, calculable from the CO and CO 2 molar release rates described by the reaction mechanism. In our efforts, the specific surface areas of the chars examined are measured, and the data are used to determine the structural parameter ϕ in the Bhatia-Perlmutter model (see Eq. (2)). This model accounts for the opposing effects of pore growth and pore coalescence during char conversion under Zone I burning conditions. The structural parameter increases with increasing microporosity. For macroporous carbons, the value of ϕ is small (less than 2), and the surface area per unit particle volume progressively decreases with char conversion. For microporous carbons, ϕ is greater than 2; it can be quite large. For such particles, the surface area per unit volume initially increases as surface area due to pore growth outweighs surface area loss due to pore wall collapse. Eventually pore wall collapse dominates and char-particle surface area begins to decrease with conversion. A maximum in surface area occurs near 35% conversion for microporous carbons. Surface area measurements were made in the PTGA at room temperature and a pressure of 10 atm using CO 2 as the adsorption gas. The approach due to Brunauer, Emmett, and Teller [3] was used in the analysis of the adsorption data to yield specific surface areas. During selected oxidation tests, in situ surface area measurements were made throughout the course of oxidation by abruptly interrupting the test at a selected extent of conversion by switching to a nitrogen environment and cooling to 298 K, obtaining CO 2 adsorption data at 10 atm and 298 K, and reheating to the oxidation test temperature in a nitrogen environment before restarting the oxygen flow and continuing the oxidation test. Results of a typical test are shown in Fig. 8; the least squares fit to the data yielded a structural parameter of ϕ =7 for this particular char.

17 S gc = S gc,0 ϕ = 7 1 ϕ ln( 1 x C ) Figure 8. Specific surface area evolution in the Zone I burning regime. The line was calculated using the Bhatia-Perlmutter model (Eq. (2)) with ϕ = 7. Based on the analysis of the results of our investigations of the heterogeneous reaction mechanism, the following conclusions can be drawn: The migration of chemisorbed oxide complexes on char surfaces influences the distribution of desorption energies, especially at temperatures above 1000 K. For adsorbed surface species that have activation energy-based distributions, a 4- site approximation, at minimum, is needed to capture the behavior of the full distribution. Using fewer sites to represent the distribution is likely to lead to results that misrepresent the true behavior of the adsorbed oxygen complexes. Failure to dynamically link surface area evolution to changes in surface species concentration can lead to significant errors in modeling the char conversion process. These errors are significant with microporous chars, especially at high extents of conversion. II. Characterization of the Mode of Burning for Char Particles at High Temperatures Several studies have shown that during the combustion of coal particles in conditions typical of those existing in industrial, pulverized coal-fired boilers and furnaces, char particles burn at rates limited by the combined effects of chemical reaction and pore diffusion. This burning regime is referred to as Zone II. Due to the oxygen concentration gradients established inside particles and the associated distribution of rates of mass loss due to chemical reaction, particle diameters, apparent densities, and specific surface areas decrease with mass loss when burning is in the Zone II burning regime. The char conversion model that we have developed accounts for these variations in the physical structure of the char during the mass loss process. Theoretical Development In the theoretical approach taken, a spherical char particle initially of size D p0, apparent density ρ C0, and specific surface area S gc0, is divided into K concentric annular volume elements, V k, each of which contains a portion of the initial total mass of the particle (m C0,k = ρ C0 V k ) that burns at a rate governed by the local conditions (see Fig. 9).

18 From Eq. (1), the rate that the mass of the carbonaceous particle material in each volume element is oxidized to CO and CO 2 is governed by the equation 1 m C.k dm C,k dt = R ic,k S gc,k. (12) D p V k r r k r k+1 ( ) Figure 9: Concentric annular volume elements: V k = 4π r k+1 r k The intrinsic chemical reactivity of the particle material depends upon the local oxygen concentration, which is governed by the following equation: C O2 t 1 r 2 r r2 D eff C O2 r = ˆR io2 ρ C S gc. (13) Here, D eff is the effective overall oxygen pore diffusion coefficient. When evaluating D eff in each volume element, account is made for the combined effects of bulk and Knudsen diffusion of oxygen through pores. The Knudsen diffusion coefficient depends on the mean pore size in the volume element, which is determined from the local volume-tototal surface area ratio, taking into account surface roughness and the local porosity. Simultaneous integration of the set of differential equations represented by Eq. (12) (an equation for each volume element) and the finite difference form of Eq. (13) permits the determination of the state of the char particle at various times after the onset of oxidation. The conversion, apparent density and specific surface area of the carbonaceous material in each volume element k are determined from the relations x C,k = 1 m C,k /m C0,k, ρ C,k = m C,k /V k, and S gc,k = S gc0,k (1-ϕln(1-x C,k )) 0.5, respectively. The mass, apparent density and specific surface area of the char particle at any instant are calculated using the relations m C = m C,k, ρ C = m C V k, and S gc = S gc,k m C,k k k k ( ) m C. (14a,b,c)

19 Particle Temperature In order to permit the evaluation of temperature-dependent parameters, the particle temperature needs to be followed as the particle burns. For the small particles of interest, the thermal conductivity of the char particle is assumed to be sufficiently large to maintain a uniform particle temperature. Consequently, despite the distribution of the oxidation rate inside the particle owing to the distribution in the oxygen concentration profile, each particle is assumed to be isothermal. The temperature of the char particle depends on its size and is calculated from an energy balance, wherein the rate of energy generation due to char oxidation is balanced by the rates of energy loss by conduction, convection, and radiation. The following energy balance relates gas and particle temperatures when the approach of Frank- Kamenetskii [11] is taken in accounting for the effects of Stefan flow in the boundary layer surrounding a particle: qδh = Nu λ g D p κ ( 1 e T κ p T g )+ εσ T 4 4 p T w ( ), where κ = γ c p,gd p ν O2 q ˆM C λ g Nu (15a,b) In this equation, q denotes the overall particle burning rate per unit external surface area and ΔH is the effective heat release due to carbon oxidation to CO and CO 2. The values of ΔH, ν O2, γ, and κ depend upon the products of the heterogeneous carbon oxidation reaction, as determined via the reaction mechanism. For specified gas temperature, Eq. (15) yields the temperature of a particle of given size and overall burning rate, and is solved simultaneously with Eqs. (12) - (14). Overall Particle Burning Rate and the Effectiveness Factor The oxygen conservation equation provides the link between the oxygen concentration (or partial pressure) in the gas phase surrounding the particle and that at the outer surface of the particle. Equating the flux of oxygen to the outer surface of the particle to the overall consumption rate of oxygen inside the particle yields the following set of relations for the overall particle burning rate per unit external surface area: q = k d P γ ln 1 γ P s P 1 γ P g P = 1 + ηd pρ C S gc 6 R ic,ex, where k d = ˆM C D O2 Sh ˆRT m D p ν O2 (16a,b) In deriving the above expressions, account was made for the effect of Stefan flow in determining the flux of oxygen to the external particle surface when homogeneous reaction in the boundary layer surrounding the particle was assumed to be negligible. The effectiveness factor η, which accounts for the oxygen reactivity distribution inside the particle, is calculated from the oxygen consumption rate in each of the volume elements into which the particle is divided, as follows: ˆR io2,kρ C,k S gc,k V k k η = = ˆR io2,maxρ C,k S gc,k V k k ˆR io2,kρ C,k S gc,k V k. (17) ρ C,k S gc,k V k k ˆR io2,ex The effectiveness factor is calculated as the particle burns, using the instantaneous values of the oxygen concentration and adsorbed O-atom site fractions in volume element k to k

20 evaluate the oxygen reactivity. The maximum reactivity of oxygen is assumed to exist at the particle s external surface, where the oxygen concentration is highest. Since the char reactivity is evaluated at the external surface of the particle in Eq. (16a), these equations provide a means of determining both the overall particle burning rate and the oxygen concentration (or partial pressure) at the outer surface of the particle. Calculated Size and Apparent Density Variations with Mass Loss In the results presented below, the kinetic parameters shown in Table III were employed, which were determined for a 25% porosity synthetic char having an apparent density of ρ C0 = 1.0 g/cm 3, specific surface area of S gc0 = 247 m 2 /g, and a surface area structural parameter of ϕ = 3.0. The char was heat-treated in a laminar flow reactor at 1650 K in 6 mol-% oxygen for 47 ms before being tested in our PTGA for oxidation rate data. The char production procedure and methods for determining specific surface areas from gas adsorption data and for extracting kinetic parameters from mass loss and surface area data are described elsewhere [12,13]. In the calculations, the initial char particle radius (D p0 = 100 μm) was divided into 103 increments, distributed such that the initial mass in each of the 103 volume elements into which the overall particle volume was partitioned, was nearly the same. The nonuniform radial grid was used in the finite difference representation of Eq. (13). The resulting system of 412 ordinary differential equations were integrated simultaneously for the mass, oxygen concentration, and adsorbed oxygen atom site fractions in each volume element for specified integration times up through 99% overall char conversion. Shown as symbols in Fig. 10 are calculated size, apparent density and specific surface area profiles as functions of conversion for burning at 873 K throughout the course of oxidation. At this low temperature, the data exemplify Zone I burning: diffusion is fast compared to chemical reaction rendering a relatively uniform oxygen concentration inside the particle. The time required for the particle to reach 90% conversion (τ 90% ) is the same as the characteristic chemical time to reach 90% conversion, τ chem,90%, the time required to reach 90% conversion in the absence of mass transfer limitations. D p /D p0, ρ p /ρ p0, S gp /S gp T gas = 873 K P O2 = 0.06 atm T part, avg = 873 K τ chem, 90% = 3510 s τ 90% = 3510 s surface area (ψ = 3) diameter apparent density x c, conversion Figure 10: Calculated size, apparent density and specific surface area profiles during oxidation under Zone I conditions.

21 The solid and dashed lines in the Fig. 10 were calculated using the power-law mode of burning model with α = 1, for constant diameter burning. The power-law mode of burning model is commonly used to predict apparent density and size variations with mass loss, and is represented by the following relations [14-16]: ( ) α and DD p = ( m C m c0 ) β (18a,b) ρ C ρ C 0 = m C m c0 The parameter α lies between zero and one, and for spherical particles, α + 3β = 1. This is an empirical expression having no fundamental basis. It is valid under Zone I burning conditions when apparent density varies proportionally with mass loss and particle size remains unchanged (α = 1) and also under Zone III burning conditions with particles burn as shrinking spheres at constant density (α = 0). For 0 < α < 1, the model predicts that both apparent density and diameter decrease with mass loss, as is the case in Zone II, however with a fixed value of α, size and apparent density variations early in mass loss are the same as they are in the late stages of burning, an unrealistic scenario. As particles burn, pore diffusion resistances lessen as closed-off pores open and pores merge and coalesce. Whereas in the early stages of burning mass loss is confined primarily to the outer periphery of particles in Zone II, in the late stages, mass loss occurs throughout particle volumes. Thus, the functional relationships between extent of mass loss and particle size and apparent density are expected to change as burning progresses. The line through the specific surface area data in Fig. 10 was calculated using Eq. (2), with ϕ = 3.0. For this Zone I burning regime case, conversion in each volume element was the same; the surface area in each volume element evolved in a similar manner. Shown as symbols in Fig. 11 are calculated size, apparent density and specific surface area profiles as functions of conversion for burning under conditions that render burning in Zone II during the course of oxidation. In each of the environments, at very early times when the adsorbed oxygen atom concentrations are low, modest amounts of oxygen penetrate the particle, reaching the particle s center. At the onset of char oxidation, there is internal burning at both low and high temperatures. D p /D p0, ρ p /ρ p0, S gp /S gp T gas = 1150 K P O2 = 0.06 atm T part, avg = 1158 K diameter apparent density τ chem, 90% = 2.42 s τ 90% = 10.8 s surface area x c, conversion Weak Zone II burning D p /D p0, ρ p /ρ p0, S gp /S gp T gas = 1600 K P O2 = 0.06 atm T part, avg = 1645 K τ chem, 90% = s surface area diameter τ 90% = 0.37s x c, conversion apparent density Strong Zone II burning Figure 11: Calculated size, apparent density and specific surface area profiles during oxidation under Zone II conditions at moderate (left) and high temperatures (right).

22 At moderate gas temperatures (T gas ~ 1150 K, left panel), there is significant internal burning up until about 35% conversion. Up to this point, burning is close to the Zone I burning regime boundary, as evidenced by the nearly constant diameter burning. The surface area, however, does not show the increase indicative of oxidation in the Zone I burning regime. Once the oxygen that penetrated the particle at early times is consumed, the particle burns primarily at its periphery until about 80% conversion, at which point the particle burns with significant decreases in both size and apparent density. The solid and dashed lines in the top panel of Fig. 11 were calculated using the power-law mode of burning sub-model with α = 0.16, which provides adequate characterization of size and apparent density changes with mass loss at conversions greater than 80%. A higher value of α would yield better agreement at earlier extents of conversion but significantly worse agreement at later extents of conversion. No constant value of α yields good agreement over the entire conversion range, demonstrating an inadequacy of the power-law model for the mode of burning in the moderate gas temperature regime. At higher temperatures (T gas = 1600 K, right panel), after the consumption of the oxygen that penetrated the particle at early times, burning is confined to the particle periphery. After a slight decrease in apparent density at the onset of oxidation, the apparent density remains nearly constant up to about 90% mass loss. The solid and dashed lines in the bottom panel of Fig. 11 were calculated using the power-law mode of burning model with α = 0.03, which provides adequate characterization of size and apparent density changes with mass loss over most of the conversion range, except near the onset of oxidation when internal burning is somewhat important. Note the significant increases in burning times due to mass transport limitations when burning under Zone II conditions. At T gas = 1150 K (weak Zone II conditions), τ 90% is about 4.5τ chem,90% and at 1600 K (strong Zone II conditions), τ 90% is about 176τ chem,90%. The burning times calculated under strong Zone II conditions are consistent with the burning times observed experimentally under high-temperature oxidizing conditions. When the overall particle conversion and apparent density are used in Eq. (2), no value of ϕ yields the type variations in surface area with conversion shown in Fig. 11. However, assuming that only reductions in apparent density lead to changes in specific surface area, the model of Bhatia and Perlmutter [4] can be modified for Zone II burning by replacing the quantity (1-x C ) in Eq. (2) by the quantity ρ C /ρ C0. Under Zone I burning conditions where constant diameter burning is exhibited, ρ C /ρ C0 equals (1-x C ), rendering no change in predictions for Zone I applications. Thus, for both Zone I and Zone II burning: S gc = S gc 0 1 ϕ ln( ρ C ρ C 0 ), (19) where ρ C is the overall apparent density of the particle at conversion x C. The solid lines through the surface area data in Fig. 11 were plotted using this expression for the specific surface area of the particle employing the value of ϕ determined for Zone I burning. Agreement is adequate, the model yielding a slight over-prediction of specific surface area with conversion. Equation (19) is also adequate for Zone III burning, when there is relatively little internal burning. For such cases ρ C ρ C0, and the specific surface area remains relatively constant at its initial value.

23 Of particular interest is the prediction of the particle s effectiveness factor during conversion under conditions when the burning rate is limited by the combined effects of pore diffusion and the intrinsic chemical reactivity of the particle material. For burning in selected gaseous environments, effectiveness factors as a function of conversion were calculated using the predicted oxygen reactivities, apparent densities and specific surface areas for each volume element k in Eq. (17). Results are shown as symbols in Fig. 12, where the effectiveness factor is given as a function of the Thiele modulus, φ, a measure of the relative importance of chemical reaction and mass diffusion inside a burning particle [17]. The Thiele modulus is defined as ( ) ( C D O2,ex eff ), (20) φ = ( D p 2) R ρ S io2,ex C gc where C O2,ex is the oxygen concentration and R io2,ex is the oxygen reactivity, both evaluated at the outer surface of the particle. For small values of φ, oxygen diffuses to the particle center before being appreciably consumed, and the particle burns in the Zone I burning regime. For large values of φ, oxygen does not diffuse deeply into the particle interior before being consumed, and the particle burns in the Zone II or III burning regime, depending upon the particle temperature. Note that under weak Zone II burning conditions (the 1150 and 1200 K, 6 mol-% O 2 environments in Fig. 12), the effectiveness factor can exceed unity, a consequence of the reactivity being higher on internal surfaces than on the external surface of the particle. Although the gas-phase oxygen concentration is greatest at the outer surface of the particle, the adsorbed oxygen atom concentration is not. The maximum reactivity occurs several microns inside the periphery of the particle and hence, η > 1. This happens only during weak Zone II burning, and only at late extents of conversion. Figure 12: Effectiveness factor versus Thiele modulus. The φ η relation predicted by the model is described adequately using the following expression, which is based on the results of Thiele for first-order irreversible reaction in a sphere:

24 η = φ m tanhφ m, where φ = φ (m + 1) / 2 (21a,b) m φ m Metha and Aris [18] used this modified Thiele modulus approach to account for reaction orders other than unity (m = 1) when using the above relationship to determine η. Here however, we do not associate m with an indication of reaction order with respect to the oxygen concentration for as noted in the Fig. 12, values for m between zero and two fit the φ η relationship reasonably well, with the best-fit value being greater than one, an unsupported value for carbon oxidation. Using Eqs. (21a,b) to determine η instead of using Eq. (17) yields results quite similar to those shown in Fig. 11 with any choice of m between 0.5 and 1.5. The simulations indicate that at gas temperatures less than about 900 K, oxygen completely penetrates pulverized-coal char particles, and the particles burn under Zone I conditions. As temperature is increased (T g in the range 900 to 1200 K), weak Zone II burning is encountered, wherein particles burns at nearly constant size up to 30% to 50% conversion before both size and apparent density decrease with mass loss. At higher gas temperatures (T g > 1200 K), the strong Zone II burning regime is encountered in which particles burn with decreases in size and apparent density from almost the onset of char oxidation. Even at high temperatures, oxygen significantly penetrates the particle at very early times due to the low levels of adsorbed oxygen, rendering low heterogeneous reaction rates. As the adsorbed oxygen level builds up, gas-phase oxygen inside the particle is consumed, confining reaction essentially to the periphery of the particle. Based on the results of the numerical calculations, the following conclusions are put forth: The manner in which particle size and apparent density decrease during mass loss under Zone II burning conditions does not vary in the manner characterized by the power-law mode of burning relations. Equation (19) can be used to determine surface area evolution from the variations in apparent density with char conversion under all burning regimes. Equations (21a,b) can be used to determine the effectiveness factor from the instantaneous values of the Thiele modulus when the 6-step reaction mechanism is used to describe char reactivity to oxygen. Mode-of-Burning Model To overcome the limitations of the power-law mode of burning model, a model for the mode of particle burning based on the instantaneous value of the effectiveness factor was developed. The model considers the separate effects of internal and external burning and uses the effectiveness factor to determine their relative contributions to the char particle s overall mass loss rate. In our approach, the intrinsic reactivity of the char is based on the reduced 6-step reaction mechanism, and account is made for Knudsen diffusion in pores that grow in size with conversion as well as for the variations in specific surface area that occur during oxidation. In activities to validate the model, synthetic chars with controlled porosities were produced and burned in a laboratory-scale entrained flow reactor. Char samples,

25 extracted from the reactor at selected residence times, were characterized for extent of mass loss, particle size distribution, apparent density, specific surface area, and chemical reactivity. The data were used to evaluate model parameters, and then the model was used to calculate variations in particle diameter and apparent density with mass loss for particles exposed to environments similar to the ones used in the high-temperature experiments. The model is shown to characterize accurately the variations in char particle size and apparent density during combustion in conditions typical of pulverized coal-fired boilers and furnaces. Derivation of the mode of burning model for spherical char particles follows the lead of Essenhigh [15,19] and starts with the following relationship between particle mass, apparent density and diameter for the ash-free particle: m c = ρ c πd p 3 /6. Differentiating with respect to time and dividing through by the particle external surface area yields the following expression for q, the overall particle burning rate per unit external surface area: q 1 dm C 2 π D p dt = ρ C 2 dd p dt + D p 6 dρ C dt ( R + R ic,ex ic,in). (22) The first term in the parenthesis on the right-hand-side of this equation defines R ic,ex and the second term, R ic,in, for external and internal burning rates per unit external surface area, respectively. Dividing R ic,in by R ic,ex yields dρ c dd p = 3ρ c D p R ic,in R ic,ex = 3ρ c ( ) in. (23) ( ) ex D p dm c dt dm c dt The internal burning rate is related to the maximum possible internal burning rate by the effectiveness factor: R ic,in = η (R ic,in ) max. The maximum possible internal burning rate occurs when the particle temperature and oxygen concentration throughout the particle are the same as that existing at the particle's external surface. Under such conditions, the internal burning rate per unit internal surface area is the same as the external burning rate per unit external surface area. Thus, for the maximum possible mass loss rate, maximum mass loss rate ( on internal surfaces ) total internal ( surface area ) ( ) in,max dm c dt = ( π /6)D 3 p ρ c S gc mass loss rate on ( external surface ) total external ( surface area ) ( dm c dt) ex (24) 2 π D p Employing the definition of the effectiveness factor, Eqs. (23) and (24) can be combined to yield the following expression for the change in particle apparent density with respect to a change in diameter: dρ C = ηρ C dd p 2 2 S gc. (25) Before this equation can be integrated, the effectiveness factor must be expressed in terms of apparent density and size. Taking the limit of Eq. (21a) as φ approaches infinity yields

26 η = 3 = 3 1/2 2 φ m φ m + 1. (26) This limiting form accurately describe the η φ relation given by Eq. (21a) for values of the Thiele modulus greater than 10. For φ = 10, η ~ 0.25, a value found to be indicative of weak Zone II burning. In our approach, we use this limiting relation to describe the η φ relation during burning in the Zone II burning regime. Using Eqs. (20) and (26) in Eq. (25), writing the porosity in terms of the true and apparent densities (θ = 1-ρ C /ρ t ), and integrating, assuming isothermal conditions, yields the following expression for the mode of burning: ( ) ( ) = D p ρ C ρ t ρ C 0 ρ C 0 ρ t ρ C D p0 ζ, where ζ = 3D p ρ C S gc 2φ m θ. (27a,b) Equations (27a,b) describe how apparent density varies with diameter during oxidation of a porous carbon particle initially at ρ c0 and D p0. It shows that during oxidation, ρ c and D p at any time depend on the reaction rate, which varies with char conversion. Since for spherical particles, m c /m c0 = (ρ c /ρ c0 )(D p /D p0 ) 3, the following relation is obtained for m c /m c0 : ( ) ( ) m C = ρ ρ C C ρ t ρ C 0 m C 0 ρ C 0 ρ C 0 ρ t ρ C 3/ζ. (28) This equation gives variations in apparent density with the fractional remaining mass. Eqs. (27a,b) and (28) represent the mode-of-burning model for carbon particles when account is made for the intrinsic chemical reactivity of the carbonaceous particle material, Knudsen diffusion inside pores, pore growth, and surface roughness. For a given extent of conversion of a spherical char particle, ρ C can be determined from Eq. (28), and then D p can be determined from Eqs. (27a,b). Impact of Ash The mass of the char particle (m p ) at any time equals the mass of the ash plus the mass of the combustible material that has not yet been burned. Assuming that no ash leaves the particle during the combustion process, the apparent density of the ashcontaining char particle (ρ p ) is given by 1 = X a ( + 1 X a) X = a0 ( + m p m p0 ) X a0, (29) ρ p ρ a ρ C ( m p m p0 )ρ a ( m p m p0 )ρ C where ρ C is determined from Eq. (28). It is assumed that the ash is finely distributed throughout the char-particle volume, either being embedded within the carbonaceous matrix or clinging to the insides of pore walls, thereby not contributing to the overall size of the char particle. Similarly, the specific surface area of the particle is assumed to be composed of the specific surface area of the ash and that of the carbonaceous material, on a mass-weighted basis:

27 S gp = X a S ga + ( 1 X a )S gc. (30) The specific surface area of the ash is taken to be 5 ±5 m 2 /g, the average of the values measured in our laboratory for several samples of coal ash. Mode-of-Burning Model Validation The mode-of-burning model was validated by comparing predictions with data obtained in combustion tests performed in well-controlled environments employing synthetic chars as well as chars produced from a coal and biomass. Synthetic chars having porosities of 16%, 25%, and 36% were produced for this study. The chars were pulverized and sieved to yield particles in the μm size range. Chars of Lower Kittanning coal (a low-volatile bituminous coal from Pennsylvania) and almond shells (biomass from California) were produced by injecting pulverized samples ( μm size range) of the raw materials into an entrained flow reactor and extracting partially reacted chars at selected residence times. When collecting the coal chars, gas flow rates to the reactor were adjusted to provide an environment containing 12 mol-% oxygen at nominally 1650 K and when collecting the biomass chars, gas flow rates were adjusted to provide an environment containing 8 mol-% oxygen at nominally 1243 K. In these flow reactor environments, the char particles burned under Zone II conditions. The synthetic chars were also heat-treated in the entrained flow reactor. During heat treatment, the environment established in the reactor contained 6 mol-% oxygen at nominally 1650 K. When collecting char samples for investigation, measured amounts of material were injected into the flow reactor and partially reacted samples were extracted at selected residence times, ranging from 17 to 117 ms. The collected samples were weighed in order to determine the extents of conversion at the residence times selected. Each sample was analyzed to determine particle size distributions, apparent densities, specific surface areas, and reactivities to oxygen. Analysis of the measured size distributions on a differential numbers basis indicated the presence of a relatively large number of particles having diameters less than 20 μm in each of the char samples extracted from the flow reactor, suggesting the occurrence of fragmentation. The weight-averaged cumulative size distributions, however, indicated that little of the mass resided in particles this small. The intrinsic chemical reactivities of the partially reacted chars were determined from char conversion rate and specific surface area data obtained in tests in the PTGA. Oxidation tests were performed at selected oxygen levels, at atmospheric pressure, and at temperatures below 873 K, temperatures low enough to ensure that mass loss rates were controlled solely by the intrinsic chemical reactivity of the carbonaceous material and not limited by any mass transport effects. Comparisons between Calculations and Experimental Data Measured values of D p /D p0 and ρ C /ρ C0 for the partially reacted synthetic chars extracted from the flow reactor are plotted against conversion (determined from the measured values of m C /m C0 ) in Fig. 13. The solid lines in the figures were calculated using the mode-of-burning relations given by Eqs. (27a,b) and (28).

28 1.0 16% porosity % porosity ρ C /ρ C0 0.6 D p /D p x c, conversion x c, conversion % porosity % porosity ρ C /ρ C0 0.6 D p /D p x c, conversion x c, conversion % porosity % porosity ρ C /ρ C0 0.6 D p /D p x c, conversion x c, conversion Figure 13: Measured and calculated mode-of-burning profiles for the synthetic chars. The solid lines were calculated using the mode-of-burning relations given by Eqs. (27a,b) and (28) with ζ evaluated using measured data in Eq. (27b).

29 When determining values for the Thiele modulus for use in Eq. (27b), the intrinsic reactivities of the synthetic chars at the temperatures and oxygen levels in the flow reactor were evaluated using the reaction mechanism and rate parameters determined for each material. Particle temperatures at the times particles were extracted from the entrained flow reactor were calculated using Eqs. (15a,b) and the oxygen partial pressures at the outer surfaces of the particles were calculated via Eqs. (16a,b). The agreement between measurements and calculations for the synthetic chars is deemed to be quite good. It supports the validity of the mode-of-burning model for the synthetic chars. Measurements and calculations made with ash-containing Lower Kittanning coal particles and almond shell biomass particles are shown in Fig. 14. The calculations were made using measured data to determine ζ in the mode-of-burning relation. The apparent densities, size distributions, specific surface areas, and intrinsic reactivities were measured in previous work [12]. The density of ash was taken to be 2000 kg/m 3 when determining the apparent density of the ash-containing particles via Eq. (29) Lower Kittanning Coal 5% ash 10% ash 20% ash Lower Kittanning Coal ρ p /ρ p D/D m p /m p m p /m p0 ρ p /ρ p Almond Shell 20% ash 30% ash 40% ash D/D Almond Shell m p /m p m p /m p0 Figure 14: Measured and calculated mode-of-burning profiles for the Lower Kittanning coal and almond shell biomass char particles. The solid lines were calculated based on the mode-of-burning relations given by Eqs. (27a,b) and (28) with ζ evaluated using measured data in Eq. (27b), and ash content considered.

30 As observed, the Lower Kittanning coal char particles burn with relatively little change in apparent density until late in burnoff, when the apparent density increases approaching that of the ash in the particle. In contrast, the apparent densities of the almond shell char particles increased quite early in burnoff, approaching that of the ash as the carbonaceous material is burned away. Such behavior is typical of high ash-content particles. The almond shell char particles extracted from the flow reactor at the earliest resident time (17 ms) contained over 50% ash. The calculated apparent density of the carbonaceous particle material decreased with mass loss during Zone II burning for both the Lower Kittanning and almond shell char particles. The agreement depicted in Fig. 14 indicates that the mode-of-burning model accurately characterizes the behaviors of the ash-containing chars of coals and biomass materials while burning in high-temperature, oxidizing environments. Based on the results of this investigation into the mode of char-particle burning, the following conclusions have been reached: The mode-of-burning model, represented by Eqs. (27a,b) and (28), accurately describes the variations in particle diameter and apparent density with mass loss during char oxidation in the Zone I, Zone II and Zone III burning regimes. Equations (29) and (30) can be used to determine the apparent density and specific surface area of the ash-containing char particle at any extent of conversion after accounting for variations in the apparent density and specific surface area of the ash-free, carbonaceous portion of the char. III. Accounting for Differences in the Structures of Char Particles Some coals exhibit thermoplastic behavior when heated, and during combustion, small particles of these coals melt to form a highly viscous liquid before resolidifying, forming char particles. Bituminous coals having carbon content in the range of 81-92% exhibit maximum fluidity, and these coals experience significant change in pore structure during devolatilization rendering char particles having porosities that differ significantly from the porosities of the parent coal particles. Anthracites, subbituminous coals and lignites exhibit limited or negligible thermoplastic behavior. The pore structures of the char particles formed subsequent to devolatilization of these carbonaceous materials have the same character as the pore structures of the parent coal particles. The decomposition of coal particles generates gases, char and metaplast within the coal particles. When the coal develops fluidity, viscous flow closes off pores, and the open pore structure disappears. The transport of volatiles inside the particle occurs by formation and expansion of bubbles and by diffusion of volatiles dissolved in the coal melt. This results in the growth of bubbles inside the particles leading to swelling of the particles. Depletion of the metaplast due to diffusion, decomposition, and polymerization causes the coal to resolidify, resulting in a char. Char structure plays an important role in influencing gas diffusion during combustion and hence, has an influence on char conversion rates. For char particle oxidation at high temperatures, pore diffusion is one of the rate-controlling processes, and the diffusion rate of reactant and product gases within the particle is strongly influenced by the pore size distribution and porosity. The structure of a char particle also has a significant

31 impact on char fragmentation and ash formation. Fragmentation can shift the particle size distribution to smaller sizes, which reduces the char burnout time. The physical structure of the char particle after devolatilization is influenced significantly by the pressure. It was found that chars produced at elevated pressures had thinner walls and more spherical structures [20]. For the particles with thinner walls, the reactant gases are easier to transport through the porous particle, and the particles are more likely to fragment. Chars produced at high pressure have higher macro-porosity, and the internal surface area is lower than chars produced at atmospheric pressure [21]. Several classification methods for char particles of different physical structures have been proposed. For the purpose of modeling char combustion, Benfall et al. [20] summarized different char structures and classified them into three groups: cenoshperical, mixed and dense. This classification was adopted in our approach. Char-Particle Structure Characterization Coal combustion experiments were conducted in a pressurized flow reactor facility, created by enclosing our entrained flow reactor in a high-pressure chamber. Samples of pulverized Lower Kittanning coal particles were injected along the centerline of the flow reactor and partially reacted char particles were extracted at different residence times for examination. Scanning electron microscopic (SEM) images of samples of particles collected just subsequent to devolatilization in an environment containing 12 mol-% oxygen at a total pressure of 2 atm are shown in Fig. 15. (a) cenospherical char particle (b) mixed type char particle (c) dense char particle (d) Ash particles embedded in char Figure 15: SEMs of different kinds of char particles collected at a residence time of 47 ms during the combustion of Lower Kittanning coal in 12 mol-% O 2 at a nominal gas temperature of 1600 K and a total pressures of 2 atm.

32 The cenospherical char particles (Fig. 15(a)) have non-uniformly distributed voids with a large central void (of the size of the particle) surrounded by a very thin shell (< 10 μm), and hence have porosities higher than 70%. The mixed type char particles (Fig. 15(b)) also have high porosities compared to dense chars, but with voids rather uniformly distributed within the particle, and the sizes of the voids are much smaller than that of the particle. The large voids in the particles can facilitate the transport of the reactant gas. With no large voids within the particle or openings at the external surface, the dense char particles (Fig. 15(c)) have the lowest porosities and highest char density. Some ash particles are also observed in the sample (Fig. 15(d)); the ash particles are spherical due to the melt and re-solidification of the minerals under high temperature conditions. The criteria for classifying the char particles into three groups are summarized in Table V. Key parameters are the particle porosity, wall thickness, void size distribution, and shape factor. These properties were determined by cross-sectional image analysis of scanning electron micrographs (SEMs) of the collected char samples. For easy analysis, the gray-scale images were first transformed into blackand-white binary images. Table V. Classification criteria of char particle structure. Typical schematic of particles cross-section Group I (Cenospherical char) Group II (Mixed char) Group III (Dense char) Porosity Highly porous particles with porosities > 70% Porous particles with variable porosities between 40-60% Dense non-porous particles with porosities < 40% Wall thickness Very thin wall (with thickness <10 μm) Medium thick wall (with thickness >10 μm) Thick wall (with thickness > 10 μm) Void size distribution 0 D p 0 D p 0 D p Existence of void about the same size as particle diameter Voids are smaller than particle diameter but larger than 5 μm Almost no voids larger than 5 μm Shape factor Round particles with shape factor > 0.85 Moderately round particles with shape factor > 0.8 Irregular particles with shape factors < 0.7

33 For a cenospherical char particle in Group I, there is a large central void of size comparable to the particle size inside the particle with non-uniform smaller pores inside the thin wall of the cenosphere. Thus, the porosity of a cenospherical particle is greater than 70%. The macropores within the thin wall open up to the particle surface; the reactant gas outside the particle can readily diffuse into the particle s interior. The thickness of the wall may vary at different locations in the particle, but the average thickness is generally smaller than 10 μm. For a dense char particle in Group III, there is almost no large void inside the particle, and the carbonaceous material is almost uniformly distributed in the particle. Pore sizes range from micro-scale to macro-scale. The porosities of Group III char particles are generally small, less than 40%, and the wall thickness is about the same scale as the particle size. For char particles in Group II, a number of voids of different sizes are distributed throughout the particle material, but the voids are not as large as the central void in Group I particles. The scanning electron micrographs (SEMs) of the partially reacted chars of Lower Kittanning coal extracted from the flow reactor 47 ms after injection at total pressures of 1 and 2 atm are shown in Fig. 16. When the total pressure increases, the volume fractions of Group I and Group II char particles increase while that of Group III chars decreases. For the example of this case, when the pressure increases from 1 atm to 2 atm, the volume of lowest density Group I particle increases from about 10% to 30%, and the rather low density Group II particle also increases. However, there is a significant decrease in the dense char particle volume. The large number of Group III chars, especially small particles (< 20 μm), is mainly due to fragmentation of char particles from all three groups of chars. From the images, based on the classification criteria of char particles in Table VI, at a mass loss of 30% (with respect to raw coal) in 2 atm, approximately 30% to 40% of the char particles, by volume, have cenospherical structures, 20% to 30% of the particles are dense chars with no large void, and the remaining 30% to 50% of the char particles are mixed type char particles. 1 atm total pressure 2 atm total pressure Figure 16: Scanning electron microscopic images of char samples collected during the combustion of Lower Kittanning coal in 12 mol-% O 2 at a nominal gas temperature of 1600 K and total pressures of 1 and 2 atm.