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 oxy-reactivity 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

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 O2 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 high-pressure 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-CO2 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

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 CO2 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 CO2-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 CO2 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

provide the needed understanding. Our efforts resulted in fundamentals-based sub-models 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].

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 75 – 125 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 temperature-programmed 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 well-controlled conditions. The PTGA microbalance reading and the O2, CO, and CO2 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 CO2-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 ash-free conversion rates, O2 adsorption rates, CO and CO2 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 CO2

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 CO2 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 CO2 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 CO2 concentration in PTGA exhaust gases, (b) the CO concentration in PTGA exhaust gases, and (c) the oxide loading on the char sample.

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 CO2. Consequently,

dmC

dt= −Stot M̂C R̂S,CO + R̂S,CO2( ), (1)

where the CO and CO2 molar production rates depend on the reaction mechanism and Stot is the total char surface area (Stot = mCSgc), calculated employing the Bhatia-Perlmutter model for the specific surface area of the char:

SgC = SgC ,0 1 − ϕ ln 1 − xC( ) . (2) 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,

dmtot

dt= −Stot M̂ j

all gasspecies

∑ R̂S, j . (3)

Since xC is related to mC,0 according to mC = mC,0(1-xC), Eq. (1) can be expressed in terms of conversion rate:

dxC

dt= −

Stot M̂C

mC ,0R̂S,CO + R̂S,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= Stot R̂S, j . (5)

When Nj = [Xj] Stot is substituted into Eq. (5) and the result is expanded, it can be shown that

dθ j

dt+

θ j

Stot

dStot

dt=

η j

ξ[ ]R̂S, j , (6)

where θj is the fraction of carbon sites occupied by adsorbed species j, ηj 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 mCSgC, 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

( )⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛∑−+−=

j speciesgas all

,,,ˆˆ1

jStotjjStotgas

jinjgas

inj RSyRSN

yyNN

dtdy &

. (7)

In the above expression, yj,in and yj are the mole fractions of species j in the inflowing gases and in the gas phase, respectively; and and are the total molar flow rates of gases entering and exiting the control volume, respectively.

&Nin&Nout

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 4th-order polynomial was used for it more accurately accounts for the low-energy populations than does the Gaussian distribution. The distribution, ψ(Edes), is not too dissimilar from a Gaussian between its minima, and is expressed in the following form:

ψ E( )=ψ0 E − Emax( )2 E − Emin( )2

Emax − Emin( )5 . (8)

The parameters ψ0, Emin, and Emax 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 lth subrange has a desorption energy of Edes,l, and the span of each subrange is ΔEdes. The gross formation rate of the lth subpopulation of -C(O) by the ith reaction is

d -C O( )⎡⎣ ⎤⎦l

dt

⎛

⎝⎜

⎞

⎠⎟

lformation

= ν i, j R̂R, jΨ Edes,l( ), (9)

where Ψ(Edes,l) is the integral of ψ(Edes) over the energy range of the lth subpopulation, i.e. the fraction of -C(O) formed within the lth subpopulation. Viewing desorption as a unimolecular process, the desorption rate of the lth -C(O) subspecies is

d -C O( )⎡⎣ ⎤⎦l

dt

⎛

⎝⎜

⎞

⎠⎟

ldesorption

= − -C O( )⎡⎣ ⎤⎦Φ Edes,l( )kdes Edes,l( )= − -C O( )⎡⎣ ⎤⎦lkdes Edes,l( ), (10)

where Φ(Edes,l) is the fractional contribution of the lth subpopulation. By solving Eqs. (9) and (10), the model keeps account of the populations of the lth-C(O) subspecies. Similar capabilities were extended to model CO2 desorption from dioxide complexes, -C2(O2).

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(Om) 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 O2.

,

2 ,-C + O -C-(O )phy f

phy b⎯⎯⎯→←⎯⎯⎯ 2

(R1) (R2) )-C(O)-C(OC-)-C-(O mm0chm

2 +⎯⎯ →⎯+

-C- O2( ) + -C + -C- chm1⎯ →⎯⎯ CO + -C Om( )+ -C (R3)

(R4)

-C- O2( ) + -C + -C- chm2⎯ →⎯⎯ CO2 + -C + -C

-C- O2( ) + -C O( ) + -C- chm3a⎯ →⎯⎯ CO + -C Om( ) + -C Om( ) (R5a)

-C- O2( ) + -C2 O2( ) + -C- chm3b⎯ →⎯⎯ CO + -C Om( ) + -C Om( )+ -C Om( ) (R5b)

-C- O2( ) + -C O( ) + -C- chm4a⎯ →⎯⎯ CO2 + -C Om( ) + -C (R6)

-C Om( ) mig1⎯ →⎯⎯ -C O( ) (R7)

-C Om( ) + -C O( ) mig2a⎯ →⎯⎯ -C2 O2( ) (R8a)

-C Om( ) + -C2 O2( ) mig2b⎯ →⎯⎯ -C2 O2( ) + -C O( ) (R8b)

-C O( ) mig3a⎯ →⎯⎯ -C Om( ) (R9a)

-C2 O2( ) mig3b⎯ →⎯⎯ -C Om( ) + -C O( ) (R9b)

(R10)

(R11)

-C O( ) + -C- des1

⎯ →⎯⎯ →⎯⎯⎯ →⎯⎯⎯ CO + -C

-C2 O2( ) + -C- des2

⎯ →⎯⎯ →⎯⎯⎯ →⎯⎯⎯ CO2 + -C + -C

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 -C2(O2) 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-

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 Ac b Eo (kJ/mol)

ωa (kJ/mol)

aa Notes

(R1) 2.40 × 105 0.5 0 - - -

1.15 × 1014 - 50 - - Reverse of (R1)

(R2) 8.73 × 1012 - 137 60 1 - (R3) 1.00 × 1021 - 310 150 1 -

(R4) 2.61 × 1014 - 154 150 10 -

(R5)b 3.94 × 1017 - 206 - - -

(R6)b 1.98 × 1017 - 195 - - -

(R7) 1.00 × 1017 - 23 - - Reverse of (R9)

(R8)b 8.95 × 1011 - 18 - - Reverse of (R9)

(R9)b 3.98 × 1005 - 200 - - -

(R10) 1.00 × 1013 - 150, 480 - - E = Emin, Emax

(R11) 1.00 × 1013 - 114, 365 - - E = Emin, Emax

Assuming Arrhenius-type dependency: k = A Tb exp(-E/ℜT). a E = Eo (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 -C2(O2), A is twice the value specified. c Units in (s-1, m3·mol-1, m2·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 Elovich-type effect was not observed for reactions (R2) and (R3), but was for reaction (R4). This

suggests that CO2 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(Edes) spectrum for CO and CO2 desorption. The gas evolution rates of CO and CO2 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 -C2(O2). The model surface, assumed to initially have distributions according to ψ(Edes1) and ψ(Edes2), 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 CO2 evolution profile and slightly right-skewed 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, CO2 is evolved in insignificant quantities compared to CO. Skokova [10] demonstrated the significance of migration during char oxidation and its effect of increasing overall CO2 formation. Building on this foundation, the current results demonstrate that migration is not only responsible for increased total CO2 production, but for the bimodal nature of the CO2 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,

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 CO2 desorption, resulting in an almost immediate decomposition of the newly formed -C2(O2) species, thereby enhancing CO2 production above 1073 K. The right-skewed 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,

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, steady-state 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.

(b) ϕ → ∞

(a) ϕ → 2

Figure 5: Model results comparing the effects of the dynamic versus quasi-steady surface models on the surface coverage of oxide complexes during oxidation in 6 kPa O2 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.

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 O2. Kinetic parameters are for a 25% porosity synthetic char.

2 Cf + O2 → C(O) + CO (R1a) 2 Cf + O2 → C2(O2) (R1b) Cb + Cf + C(O) + O2 → CO2 + C(O) + Cf (R2) Cb + Cf + C(O) + O2 → CO + 2C(O) (R3) Cb + C(O) → CO + Cf (R4) Cb + C2(O2) → CO2 + 2Cf (R5)

Aia Ei (kJ/mol) σi (kJ/mol)

3.87e04 60 0 1.95e03 55 0 1.18e09 120 0 3.74e16 250 0 1.00e13 320 26 1.00e13 280 453

a )ˆexp( TREAk iii = , units of Ai in mol, m2-surface/m3-fluid, s; ki,eff = ki E( )0

∞∫ f E, Ei ,σ i( )

In the mechanism, Cf represents a free carbon site, one available for oxygen adsorption, and C(O) and C2(O2) represent adsorbed oxygen atoms, one oxygen atom per carbon site. Bulk carbon atoms, Cb, 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 CO2 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.

0.0 0.2 0.4 0.6 0.8 1.00

1

2

3

4

823 K

773 K

723 K

Cha

r rea

ctiv

ity, 1

0-6 g

C/(

m2 .s

)

xc, conversion

8 atm, 6% O2

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.

0.0 0.2 0.4 0.6 0.80

1

2

3

4

5

6

773 K

Rea

ctiv

ity, g

/(m2 .s

) x 1

06

Conversion, xc

873 K

6 mol-% O2, 1 atm

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.

Table IV: Reduced heterogeneous reaction mechanism for char reactivity to O2. Rate parameters are for the char produced from Lower Kittanning coal. 2 Cf + O2 → C(O) + CO (R1a) 2 Cf + O2 → C2(O2) (R1b) Cb + Cf + C(O) + O2 → CO2 + C(O) + Cf (R2) Cb + Cf + C(O) + O2 → CO + 2C(O) (R3) Cb + C(O) → CO + Cf (R4) Cb + C2(O2) → CO2 + 2Cf (R5)

Aia Ei (kJ/mol) σi (kJ/mol)

2.32e05 60 0 8.47e02 32 0 3.01e08 106 0 1.90e16 237 0 1.00e13 273 25 1.00e13 218 45

a )ˆexp( TREAk iii = , units of Ai in mol, m2-surface/m3-fluid, s; ki,eff = ki E( )0

∞∫ f E, Ei ,σ i( )

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:

1mC

dmC

dt= SgC RiC , (11)

where RiC is the intrinsic chemical reactivity of the char on a mass basis, calculable from the CO and CO2 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 CO2 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 CO2 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.

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.

SgC = SgC,0 1− ϕ ln 1 − xC( )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 Dp0,

apparent density ρC0, and specific surface area SgC0, is divided into K concentric annular volume elements, Vk, each of which contains a portion of the initial total mass of the particle (mC0,k = ρC0Vk) that burns at a rate governed by the local conditions (see Fig. 9).

From Eq. (1), the rate that the mass of the carbonaceous particle material in each volume element is oxidized to CO and CO2 is governed by the equation

1mC .k

dmC ,k

dt= RiC ,k SgC ,k . (12)

Dp

Vk

rk rk+1

r

Figure 9: Concentric annular volume elements: Vk = 4π rk+13 − rk

3( ) 3 .

The intrinsic chemical reactivity of the particle material depends upon the local oxygen concentration, which is governed by the following equation:

∂CO2

∂t−

1r2

∂∂r

r2Deff∂CO2

∂r⎛⎝⎜

⎞⎠⎟

= − R̂iO2ρCSgC . (13)

Here, Deff is the effective overall oxygen pore diffusion coefficient. When evaluating Deff 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-to-total 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 xC,k = 1 – mC,k/mC0,k, ρC,k = mC,k/Vk, and SgC,k = SgC0,k(1-ϕln(1-xC,k))0.5, respectively. The mass, apparent density and specific surface area of the char particle at any instant are calculated using the relations

mC = mC ,k

k∑ ,

ρC = mC Vk

k∑ , and SgC = SgC ,kmC ,k( )

k∑ mC . (14a,b,c)

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 λg

Dp

κ1− eκ Tp − Tg( )+ εσ Tp

4 − Tw4( ) , where κ =

γ cp,gDpνO2q

M̂CλgNu (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 CO2. The values of ΔH, νO2, 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 =kdPγ

ln1 − γ Ps P1 − γ Pg P

⎛

⎝⎜

⎞

⎠⎟ = 1 +

ηDpρCSgC

6⎛⎝⎜

⎞⎠⎟

RiC ,ex , where kd =M̂C DO2

ShR̂TmDpνO2

(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:

η =R̂iO2 ,kρC ,kSgC ,kVk

k∑

R̂iO2 ,maxρC ,kSgC ,kVkk∑

=R̂iO2 ,kρC ,kSgC ,kVk

k∑

R̂iO2 ,ex ρC ,kSgC,kVkk∑

. (17)

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

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 ρC0 = 1.0 g/cm3, specific surface area of SgC0 = 247 m2/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 (Dp0 = 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 non-uniform 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 (τ90%) is the same as the characteristic chemical time to reach 90% conversion, τchem,90%, the time required to reach 90% conversion in the absence of mass transfer limitations.

0.0 0.2 0.4 0.6 0.8 1.00

1

2

3

4

apparent density

diameter

Dp/D

p0, ρ

p/ρp0

, Sgp

/Sgp

0

xc, conversion

Tgas = 873 KPO2 = 0.06 atmTpart, avg = 873 Kτchem, 90% = 3510 sτ90% = 3510 s

surface area (ψ = 3)

Figure 10: Calculated size, apparent density and specific surface area profiles during oxidation under Zone I conditions.

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]:

ρC ρC 0 = mC mc0( )α and D Dp = mC mc0( )β (18a,b) 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.

0.0 0.2 0.4 0.6 0.8 1.00.0

0.5

1.0

1.5

2.0

Dp/D

p0, ρ

p/ρp0

, Sgp

/Sgp

0

xc, conversion

apparent density

diameter

surface area

Tgas = 1150 KPO2 = 0.06 atmTpart, avg = 1158 K

τchem, 90% = 2.42 sτ90% = 10.8 s

0.0 0.2 0.4 0.6 0.8 1.0

0.0

0.2

0.4

0.6

0.8

1.0

1.2

Dp/D

p0, ρ

p/ρp0

, Sgp

/Sgp

0

xc, conversion

Tgas = 1600 KPO2 = 0.06 atmTpart, avg = 1645 Kτchem, 90% = 0.0021 sτ90% = 0.37s

surface area

diameter

apparent density

Weak Zone II burning 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).

At moderate gas temperatures (Tgas ~ 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 (Tgas = 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 Tgas = 1150 K (weak Zone II conditions), τ90% is about 4.5τchem,90% and at 1600 K (strong Zone II conditions), τ90% is about 176τchem,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-xC) in Eq. (2) by the quantity ρC /ρC0. Under Zone I burning conditions where constant diameter burning is exhibited, ρC /ρC0 equals (1-xC), rendering no change in predictions for Zone I applications. Thus, for both Zone I and Zone II burning:

SgC = SgC 0 1 − ϕ ln ρC ρC 0( ) , (19)

where ρC is the overall apparent density of the particle at conversion xC. 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 ρC ≈ ρC0, and the specific surface area remains relatively constant at its initial value.

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

φ = Dp 2( ) RiO2 ,exρCSgC( ) CO2 ,ex Deff( ) , (20)

where CO2,ex is the oxygen concentration and RiO2,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-% O2 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:

η =

3φm

1tanhφm

−1

φm

⎛

⎝⎜⎞

⎠⎟ , where φm = φ (m + 1) / 2 (21a,b)

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 (Tg 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 (Tg > 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,

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: mc = ρcπDp

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

π Dp2

dmC

dt= −

ρC

2dDp

dt+

Dp

6dρC

dt⎛⎝⎜

⎞⎠⎟

≡ − RiC ,ex + RiC ,in( ). (22)

The first term in the parenthesis on the right-hand-side of this equation defines Ric,ex and the second term, Ric,in, for external and internal burning rates per unit external surface area, respectively. Dividing Ric,in by Ric,ex yields

dρc

dDp=

3ρc

Dp

Ric,in

Ric,ex=

3ρc

Dp

dmc dt( )in

dmc dt( )ex

. (23)

The internal burning rate is related to the maximum possible internal burning rate by the effectiveness factor: Ric,in = η (Ric,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( ) ≡

dmc dt( )in,max

π / 6( )Dp3ρcSgc

=

mass loss rate on external surface( )total external surface area( ) ≡

dmc dt( )ex

π Dp2 (24)

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:

dρC

dDp

=ηρC

2 SgC

2 . (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

η =3

φm

=3φ

2m + 1

⎛⎝⎜

⎞⎠⎟

1/2

. (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-ρC /ρt), and integrating, assuming isothermal conditions, yields the following expression for the mode of burning:

ρC ρt − ρC 0( )ρC 0 ρt − ρC( ) =

Dp

Dp0

⎛

⎝⎜

⎞

⎠⎟

ζ

, where ζ =3DpρCSgC

2φmθ. (27a,b)

Equations (27a,b) describe how apparent density varies with diameter during oxidation of a porous carbon particle initially at ρc0 and Dp0. It shows that during oxidation, ρc and Dp at any time depend on the reaction rate, which varies with char conversion. Since for spherical particles, mc/mc0 = (ρc/ρc0)(Dp/Dp0)3, the following relation is obtained for mc/mc0:

mC

mC 0

=ρC

ρC 0

ρC ρt − ρC 0( )ρC 0 ρt − ρC( )

⎡

⎣⎢

⎤

⎦⎥

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, ρC can be determined from Eq. (28), and then Dp can be determined from Eqs. (27a,b).

Impact of Ash The mass of the char particle (mp) 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 ash-containing char particle (ρp) is given by

1ρp

=Xa

ρa

+1− Xa( )

ρC

=Xa0

mp mp0( )ρa

+mp mp0( )− Xa0

mp mp0( )ρC

, (29)

where ρC 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:

Sgp = XaSga + 1 − Xa( )SgC . (30)

The specific surface area of the ash is taken to be 5 ±5 m2/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 75 - 106 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 (75 - 106 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 Dp/Dp0 and ρC/ρC0 for the partially reacted synthetic chars

extracted from the flow reactor are plotted against conversion (determined from the measured values of mC/mC0) in Fig. 13. The solid lines in the figures were calculated using the mode-of-burning relations given by Eqs. (27a,b) and (28).

0.0 0.2 0.4 0.6 0.80.2

0.4

0.6

0.8

1.0

ρ C /ρ

C0

xc, conversion

16% porosity

0.0 0.2 0.4 0.6 0.8

0.2

0.4

0.6

0.8

1.0

Dp/D

p0

xc, conversion

16% porosity

0.0 0.2 0.4 0.6 0.80.2

0.4

0.6

0.8

1.0

ρ C /ρ

C0

xc, conversion

25% porosity

0.0 0.2 0.4 0.6 0.8

0.2

0.4

0.6

0.8

1.0

Dp/D

p0

xc, conversion

25% porosity

0.0 0.2 0.4 0.6 0.80.2

0.4

0.6

0.8

1.0

ρ C /ρ

C0

xc, conversion

36% porosity

0.0 0.2 0.4 0.6 0.8

0.2

0.4

0.6

0.8

1.0

Dp/D

p0

xc, conversion

36% porosity

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).

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/m3 when determining the apparent density of the ash-containing particles via Eq. (29).

1.0 0.8 0.6 0.4 0.2 0.00.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

5% ash 10% ash 20% ash

ρ p/ρp0

mp/mp0

Lower Kittanning Coal

1.0 0.8 0.6 0.4 0.2 0.00.0

0.2

0.4

0.6

0.8

1.0

D/D

0

mp/mp0

Lower Kittanning Coal

1.0 0.8 0.6 0.4 0.2

1.0

1.2

1.4

1.6

1.8

2.0 20% ash 30% ash 40% ash

ρ p/ρp0

mp/mp0

Almond Shell

1.0 0.8 0.6 0.4 0.2 0.00.0

0.2

0.4

0.6

0.8

1.0

D/D

0

mp/mp0

Almond Shell

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.

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

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-% O2 at a nominal gas temperature of 1600 K and a total pressures of 2 atm.

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 black-and-white binary images.

Table V. Classification criteria of char particle structure.

Group I (Cenospherical char)

Group II (Mixed char)

Group III (Dense char)

Typical schematic of particles’ cross-section

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)

Dp0

Void size distribution

Existence of void about the same size as particle diameter

Dp0

Voids are smaller than particle diameter but larger than 5 μm

Dp0

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

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-% O2 at a nominal gas temperature of 1600 K and total pressures of 1 and 2 atm.

Particle Population Balance Model A particle population balance [22] is used to describe the changes in the particle size

and density distributions with time as a result of char oxidation. The size distribution of char particles at any time is described by I discrete size classes or size bins. Size bin i is characterized by its upper and lower cutoffs, xi and xi+1, respectively. Thus, size bin i consists of particles as large as xi and as small as xi+1. Size bin 1 contains the largest-size particles in the distribution (particle diameter in the range x1 to x2) and bin I, the smallest-size particles (diameters in the range xI to 0). The size distribution within any particular size bin is assumed to be uniform, consequently, of the total number of particles in bin i at any time, the fraction that have diameters between x and xi+1 is (x - xi+1)/(xi - xi+1), where x is between xi and xi+1. The upper and lower cutoffs of each size interval vary by a constant factor γ, defined as γ = xi /xi+1. This treatment yields uniformly spaced size intervals in the log domain and is effective in resolving size distributions in the small-size range in which particle number densities can be large.

There is a distribution of apparent densities in each size bin, which at any time is described by K discrete density bins. The upper cutoff of the k-th density bin is ρk -1 and the lower cutoff is ρk. Thus, density bin k consists of particles having apparent densities as high as ρk -1 and as low as ρk. The highest-density bin (density bin 1), consists of particles having apparent densities of ρ1 and higher. The apparent density distribution within a density bin is assumed to be uniform, consequently, of the number of particles in density bin k at any time, the fraction that have apparent densities between ρ and ρk is (ρ - ρ k)/( ρ k -1 - ρ k), where ρk -1 is between and ρk.

In this model, it is assumed that the ash contained in the char particles is uniformly distributed within the carbonaceous material, and has no impact on the char reaction kinetics and the oxygen diffusion process. This assumption allowed the calculations to be performed based on the ash-free particle properties. During the char oxidation process, if the size and apparent density of an ash-free particle is reduced to zero, an ash particle is formed. Thus, by setting the lower limits of the K-1 density bins and the I-1 size bins to zero, density-bin K for each size bin and size-bin I for each density bin will consist of ash particles. The schematic divisions of the size bins and density bins are demonstrated in Fig. 17.

i, k+1 i+1, ki, ki-1, k

i, k-1

LL aarr gg

ee pp aa

rr ttii cc

ll eess

low-density particles

high-density particles

SS mm

aa llll

pp aarr tt

ii ccll ee

ss

density bins

size bins

ash

part

icle

s

Figure 17: Schematic of the density and size bins in the particle population balance model.

In our application of the particle population balance model, for particles in each size bin and density bin, the particles are further categorized into three groups of char structures (Group I, II and III), as described above. In order to see more clearly the changes in size and density distributions as a result of char oxidation at elevated pressure and to assess the impact of variations in density with particle size on overall mass loss

rates, fragmentation was not allowed in this study. When fragmentation is neglected, the change in the number of particles in each structure group and in density class k of size bin i as a result of combustion is described by the following differential equation:

IIIor II, I, Groupin particles 21 21

, 1111

===

+−+−= −−−−

n ;K,...,,k;I,...,,i

NDNDNCNCdt

dN nk,i

nk,i

nk,i

nk,i

nk,i

nk,i

nk,i

nk,i

nk,i

(31)

where Ci,k

n =dDp dt( )

n xi+1

xi − xi+1

and Di,kn =

dρC dt( )n ρk

ρk −1 − ρk

. (32a,b)

Here, the superscript n = I, II or III represents the particles in Group I, II and III, respectively. Ni,k is the number of particles in size bin i within density bin k, (i.e., in bin (i, k)). The parameters Ci,k is the fraction of particles in bin (i, k) at time t that burns out of the bin per unit time because of a decrease in diameter. These particles enter bin (i+1, k). The rate that particles leave the bin depends on the value of dD/dt at the lower limit of the size bin. The parameters Di,k is the fraction of particles in bin (i, k) at time t that burns out of the bin per unit time because of a decrease in apparent density. These particles enter bin (i, k+1). The rate that particles leave the bin depends on the value of dρ/dt at the lower limit of the density bin. Values of Ci,k and Di,k depend on the values of dD/dt and dρ/dt, respectively, at the lower size and density limits of bin (i, k) and are evaluated differently for three groups of char particles. The first two terms in Eq. (31) represent the rates at which particles leave and enter the bin as a result of changes in size due to burning and the last two terms represent the rates at which particles leave and enter the bin as a result of changes in density due to burning. For specified initial size and apparent density distributions (i.e., for specified Ni,k,0), Eq. (31) is integrated to yield the numbers of particles in each bin (i, k) after burning for some time t. Values for Ni,k at time t and Ni,k,0 are used to evaluate m/m0 at this time. The extent of conversion at time t is calculated accordingly: xC = 1 – m/m0. It is assumed that particles in each char-structure group stay within the same group during oxidation, a reasonable assumption in the light of no fragmentation.

The temperatures of particles in each size-density bin and each class structure were calculated via Eqs. (15a,b). Also in the particle population balance model, the specific surface areas of all particles are assumed to vary during oxidation in the same manner. The variation in specific surface area at time t is calculated using Eq. (2).

Regression rates for dense char particles Dense char particles have rather uniform structures without large voids inside their

outer surfaces. Such particles were the focus of Section II above, and the relations already presented apply. The relations can be combined to yield the following expression for the overall particle burning rate per unit external surface area, q:

q = 1+

ηρCSgc Dp

6

⎛

⎝⎜

⎞

⎠⎟ RiC ,ex . (33)

The rate of change in the diameter of the char particle is given by

dDp

dt= −

2qρC

⎛

⎝⎜⎞

⎠⎟1+

ηρCSgc Dp

6⎛

⎝⎜

⎞

⎠⎟ , (34)

and the rate of change in the apparent density of the char particle is

dρC

dt= − ηρCSgcq( ) 1+

ηρCSgc D6

⎛

⎝⎜

⎞

⎠⎟ . (35)

Equations (34) and (35) are used in Eq. (32a,b) to calculate the parameters, and in the particle population balance model.

Ci,kIII Di,k

III

Regression rates for cenospherical char particles The geometry of a cenospherical char particle can be simplified as a concentric

annular shell with external diameter of Dpo and wall thickness of δ, as shown in Fig. 18. The overall particle burning rate per unit external area for the cenospherical particle consists of the burning rate on the external surface and the burning rate on the internal surface including the interior void surface and the internal surface within the carbonaceous material. Since the wall is very thin for cenospherical particles, the interior void surface area and the internal surface area within the carbonaceous material are comparable, and hence the burning rate on both kinds of internal surface has to be taken into account.

δ δ

Dpi

Dpo

Figure 18: Schematic of a cenospherical char particle, indicating its physical characteristics.

Using the same method as described for dense, uniform porosity char particles, the internal burning rate is related to the maximum possible internal burning rate by Ric,in = ηI (Ric,in)max, where ηΙ is the effectiveness factor for cenospherical particles. Based on the definition of effectiveness factor, the effectiveness factor of cenospherical particles can be calculated by

( ) ( ) ( )( )33,

2/

2/,

2

2/

2/,

2

2/

2/,

2

2/2/ˆ

)(ˆ3

)(ˆ4

)(ˆ4

2

2

2

2

δπ

πη

−−

∫=

∫

∫=

popoexOi

D

DOi

D

DpOi

D

DOi

IDDR

drrRr

drRRr

drrRrpo

pi

po

pi

po

pi . (36)

The numerator is the actual oxygen consumption rate inside the particle, which depends on the local reactivity, and the denominator is the maximum possible reactivity, which would be realized if the reactivity throughout the particle were the same as that at the outer surface of the particle where the oxygen concentration is maximum. Due to the central void inside the particle, the effectiveness factor of cenospherical particles, ηΙ, is different from that of a spherical particle with uniform porosity, η.

For specified values of particle size and void volume, the differential equation governing oxygen transport through the wall of the cenospherical particle was solved numerically along with support equations. Effectiveness factors were determined using the resulting oxygen concentration profiles to calculate oxygen reactivity profiles for use in Eq. (36). The ηI as a function of Thiele modulus were correlated with the effectiveness factor of a spherical uniform, low-density particle of the same diameter and Thiele modulus by:

, where . (37a,b) ηI = η 1−θv( )n

n =

389.25η3 − 103.69η2 + 12.10η + 0.21, for η ≤ 0.10.13η2 + 2.16η + 0.55, for η > 0.1

⎧⎨⎪

⎩⎪

Here, θv is the porosity of the central void in the particle, i.e., θv = Vv /Vp, where Vv is the volume of the void and Vp is the volume of the particle.

The overall burning rate per unit external surface area of the cenospherical particle is given by:

q = Rex + Rvoid + Rsh = Rex 1+

Rvoid

Rex

+Rsh

Rex

⎛

⎝⎜⎞

⎠⎟= Rex 1+ α I svoid +

ηI ρCSgc Dpo

6

⎛

⎝⎜

⎞

⎠⎟ . (38)

where Rvoid, Rsh and Rex are the burning rates per unit external surface area at respectively, the interior void surface, the internal surface within the shell, and the external surface. The parameter αI is the ratio of reaction rates at the interior void surface and external surface, and is assumed to be equal to the ratio [O2]in/[O2]ex, a reasonable assumption for thin-walled cenospherical particles and the parameter svoid is the ratio of the interior to external surface area. The external burning rate can be characterized by the reduction rate of the external particle diameter Dp0, and the internal burning rate can be characterized by both the burning of carbonaceous material within the shell and the increase in internal void diameter Dpi due to burning at the interior surface. It can be shown that the surface regression rate for a cenospherical particle is:

dDpo

dt= −

2sshqρC

⎛

⎝⎜⎞

⎠⎟1+

ηI ρCSgc Dpo

6+ α I svoid

⎛

⎝⎜

⎞

⎠⎟ , (39)

where ssh is the ratio of the shell volume to the total particle volume. The rate of change in apparent density is

dρC

dt= − q ηI ρCSgc +

6α I svoid

Dpo

⎛

⎝⎜

⎞

⎠⎟ 1+

ηI ρCSgc Dpo

6+ α I svoid

⎛

⎝⎜

⎞

⎠⎟ , (40)

Equations (39) and (40) are used in Eq. (32) to calculate the parameters in the particle population balance model for cenospherical particles. These equations reduce to Eqs. (34) and (35) when δ = Dpo/2, (i.e., when svoid = 0 and ssh = 1, the situation for uniform-porosity particles). The internal surface regression rate is given by

dDpi

dt= −

2sshqρC

⎛

⎝⎜⎞

⎠⎟1+

ηI ρCSgc Dposvoid

6− α I svoid

⎛

⎝⎜

⎞

⎠⎟ . (41)

Regression rates for mixed-type char particles For a mixed type char particle, it is assumed that all voids are about the same size and

are distributed uniformly inside the particle, as shown in Fig. 19. Since the wall is medium thick and the carbonaceous material is quite abundant, the interior void surface area is much smaller than the surface area within the carbonaceous material, and can be neglected in the calculation of overall particle burning rate. By further assuming that the oxygen concentration inside a void is uniform, the oxygen concentration inside the void is about the same as that at the interface of volumes V1 and V2 in Fig. 19. The burning rate inside the volume V2 is based on the oxygen diffused from the void or from the interface of V1 and V2, which can be approximated as the case in the cenospherical particle at the right of Fig. 19.

V1 V2 V1 V2

Figure 19: A mixed type char particle is approximated as a cenospherical particle having the same volume of carbonaceous material.

When oxidation occurring at the interior surface of the void is neglected, the overall burning rate per unit external surface, external surface regression rate, and density reduction rate take similar forms as Eqs. (33), (34), and (35), except replacing the spherical particle effectiveness factor η with ηII. For Group II char particles, the effectiveness factor, ηII, can be approximated in the same manner as Group I char particles:

ηII = η 1−θv( )n (42)

where θv is determined from the characteristics of the mixed particle and n is given by Eq. (37b).

Samples of Lower Kittanning coal, a bituminous coal from Pennsylvania, were screened to obtained particle sizes between 75 and 106 μm. The particles were injected along the centerline of the high pressure, entrained laminar flow reactor when the flow rates of the reactor feed gases were adjusted to provide environments containing 6 and 12 mol-% oxygen at nominally 1600 K. Chars were extracted from the reactor at residence times ranging from 47 to 117 ms, spanning mass conversions from 35% to 66% on an ash-free basis. Results of tests to characterize the partially reacted chars extracted from the flow reactor are shown in Table VI. As described in previous work [12,16,22], fractional mass remaining values (m/m0) were determined from measured ash contents, a tap density technique was used to determine apparent densities, a Coulter multisizer was used to measure particle size distributions, and CO2 adsorption measurements were used to determine BET surface areas. The onset of char oxidation in the 2-atm environment was assumed to occur near a residence time of 47 ms, the same as that observed in the atmospheric pressure tests.

Table VI. Properties of partially reacted chars of Lower Kittanning coal burning in 12 mol-% oxygen at nominally 1600 K and 2 atm.

Residence time (ms) m/m0

xC(daf)

Ash content

ρ (g/cm3)

ρC(g/cm3)

Dp,ave

(μm) Sgp

(m2/g) SgC

(m2/g)47 70% 35% 14.7% 0.79 0.72 42 135 158 72 45% 62% 23.0% 0.62 0.51 27 181 233 95 43% 65% 24.3% 0.61 0.50 22 259 340 117 41% 66% 25.2% 0.53 0.43 29 261 347

The properties measured for the 47-ms char were used as initial values when

integrating the governing equations in the particle population balance model. In the calculations, 27 size bins and 9 density bins were used, with the ninth density bin for the ash particles. Of course the numbers of particles of each char-structure type in each size-density class for the 47-ms char were not known. Consequently, the numbers of Group I, II, and III particles in each size-density bin were assumed, based on the measured size distribution and the SEM image analysis results for the 47-ms char. Particles larger than 106 μm were deemed to result from swelling during devolatilization and were distributed into low-density bins. Group I particles were considered to be more likely to distribute into larger size bins and Group III particles into the smaller size bins. Also, because of the nature of the char structure, Group I particles were considered to more likely distribute into lower density bins and Group III particles were considered to more likely reside in the higher density bins.

Comparisons between the measured and calculated mass remaining and apparent density profiles for the Lower Kittanning coal char particles burning in the flow reactor in an environment containing 12 mol-% oxygen at about 1600 K and 2 atm are shown in Fig. 20. Under these conditions, the overall burning rates of particles were limited by the combined effects of chemical reaction and oxygen pore diffusion. The overall burning behaviors of the ensemble of particles were calculated by taking the mass fraction-weighted average of corresponding properties of the three structural groups. The reaction mechanism and kinetic parameters presented in Table IV used in the calculations. In the

figure, the oxidation time is the time since char formation, hence data for the 47-ms char is plotted at time zero. The measured ash content of the 47-ms char was 14.7%. Lines calculated for 5% and 25% ash are also shown to reflect the variations in ash-content of particles. The apparent densities of the particles decrease with burning for a certain period of time, and then start to increase due to the loss of carbonaceous material and relative increase in ash content (the apparent density of the ash was taken to be 2 g/cm3). For high initial ash content, such as 25% ash, the particle apparent density starts to increase at earlier times. The agreement exhibited is deemed to be quite good, and serves to validate the combustion model.

0 50 100 150 200 2500.0

0.2

0.4

0.6

0.8

1.0 15% ash 25% ash 5% ash

Frac

tiona

l Mas

s R

emai

ning

- m

p/mp0

Oxidation time, ms

2 atm, 12 mol-% O2

0 50 100 150 200 250

0.0

0.2

0.4

0.6

0.8

1.0 15% ash 25% ash 5% ash

App

aren

t Den

sity

- ρ p /

ρ p0

Oxidation time, ms 0 50 100 150 200 250

1300

1400

1500

1600

1700

1800

1900

Tem

pera

ture

, K

Oxidation time, ms

gas temperature particle temperature

(a) (b) (c)

Figure 20: Comparisons between measured and calculated (a) mass remaining and (b) apparent density profiles for Lower Kittanning coal char particles burning in 12 mol-% O2. (c) Calculated average particle temperature and measured gas temperature.

The calculated average particle temperature profile is shown in Fig. 20c. The particle

temperature increases first from its initial value due to the heat release from rapid char oxidation at 1650 K, and then decreases as gas temperatures fall below 1600 K and char oxidation rates decrease. The values of particle temperature are consistent with values measured under similar combustion conditions [16,23], where the average particle temperatures were 100 to 200 K higher than the local gas temperatures.

The calculated mass loss and apparent density profiles calculated for Group I, II and III char particles are presented in Fig. 21. As expected, the residence times required to reach a specified extent of conversion is significantly shorter for cenospherical char particles than for dense char particles. As noted in Fig. 21(a), in the 12 mol-% O2 environment only about 15 ms was needed for the cenospherical char particles to reach 50% burnoff whereas almost 60 ms was needed for the dense char particles to reach this extent of conversion. The predicted results are in qualitative agreement with other experimental observations [24]. The high burning rates for cenospherical char particles are attributed to their physical structure. Such particles have very little mass and have high internal and external surfaces areas, a consequence of swelling during devolatilization. Due to the thin shell and voids, cenospherical char particles are exposed to relatively higher average oxygen concentrations inside the particle than dense char particles, which is manifest through higher burning rates and effectiveness factors for cenospheres.

0 50 100 150 200 2500.0

0.2

0.4

0.6

0.8

1.0

Frac

tiona

l Mas

s R

emai

ning

- m

p/mp0

Oxidation time, ms

Data Group I Group II Group III

0 50 100 150 200 250

0.0

0.2

0.4

0.6

0.8

1.0

App

aren

t Den

sity

- ρ p /ρ

p0

Oxidation time, ms

Data Group I Group II Group III

Figure 21: Predicted mass loss (left) and apparent density (right) profiles for Group I, II and III char particles burning in 12 mol-% oxygen.

The variations in apparent density with time for the three types of char particles are shown in Fig. 21(b). All particles have decreasing apparent densities initially, but the apparent density of Group I particles (cenospheres) starts to increase after about 100 ms when the ash begins to become important in influencing particle properties.

As shown in Fig. 22, the Group I char particles have the highest particle temperatures, about 300 K higher than the gas temperature at the 72 ms residence time. The temperatures of Group III char particles are very close to the gas temperature. It is also noted that the Group I particles exhibit the widest temperature distribution. This is due to the increased significance of internal burning for cenospheric type char particles relative to the internal burning that occurs in dense, Group III char particles. The burning particles have diverse oxygen concentrations inside the particles, and hence, the internal burning rates are more diverse than external burning. This diversity in the internal burning results in the observed particle temperature distributions.

1400 1500 1600 1700 1800 1900 20000.0

0.2

0.4

0.6

0.8

1.0

Frac

tion

of P

artic

les

Particle Temperature, K

Group I particles72 msTgas = 1615 K

1400 1500 1600 1700 1800 1900 2000

0.0

0.2

0.4

0.6

0.8

1.0Group II particles72 msTgas = 1615 K

Frac

tion

of P

artic

les

Particle Temperature, K 1400 1500 1600 1700 1800 1900 2000

0.0

0.2

0.4

0.6

0.8

1.0Group III particles72 msTgas = 1615 K

Frac

tion

of P

artic

les

Particle Temperature, K (a) (b) (c)

Figure 22: Distribution of particle temperature for (a) Group I, (b) Group II and (c) Group III chars at a residence time of 72 ms in 12 mol-% oxygen.

The initial and calculated particle size and density distributions of the three types of chars at residence time of 72 ms (25 ms after the onset of char oxidation) are presented in Fig. 23. Initially, Group I char particles are mainly distributed in density bins in the range of 0.1ρ0 to 0.5ρ0, and in size bins larger than 90 μm. Group II char particles reside in density bins in the range of 0.5ρ0 to 0.9ρ0, and in the medium size bins. Group III

chars have densities higher than 0.9ρ0, and sizes smaller than 50 μm. The calculations indicate that as burning progressed, both the apparent density and particle size distributions become broader.

47 ms 72 ms

0 16 27 43 71 115 1880

10

20

30

40

50

60

Num

ber o

f Par

ticle

s

Particle diameter, μm

apparent density bins B: 1.1 < ρ/ρ0 < 1.2 C: 0.9 < ρ/ρ0 < 1.1 D: 0.7 < ρ/ρ0 < 0.9 E: 0.5 < ρ/ρ0 < 0.7 F: 0.3 < ρ/ρ0 < 0.5 G: 0.1 < ρ/ρ0 < 0.3 H: 0.001 < ρ/ρ0 < 0.1 I: ash particles

47 ms, Group I

0 16 27 43 71 115 188

0

10

20

30

40

50

60

Num

ber o

f Par

ticle

sParticle diameter, μm

apparent density bins B: 1.1 < ρ/ρ0 < 1.2 C: 0.9 < ρ/ρ0 < 1.1 D: 0.7 < ρ/ρ0 < 0.9 E: 0.5 < ρ/ρ0 < 0.7 F: 0.3 < ρ/ρ0 < 0.5 G: 0.1 < ρ/ρ0 < 0.3 H: 0.001 < ρ/ρ0 < 0.1 I: ash particles

72 ms, Group I

0 16 27 43 71 115 1880

50

100

150

200

250

Num

ber o

f Par

ticle

s

Particle diameter, μm

B C D E F G H I

47 ms, Group II

0 16 27 43 71 115 188

0

50

100

150

200

250apparent density bins 72 ms, Group II

Num

ber o

f Par

ticle

s

Particle diameter, μm

B C D E F G H I

0 16 27 43 71 115 1880

10

20

30

40

50

60

70

80

90

Num

ber o

f Par

ticle

s, x

103

Particle diameter, μm

apparent density bins A: 1.2 < ρ/ρ0

B: 1.1 < ρ/ρ0 < 1.2 C: 0.9 < ρ/ρ0 < 1.1 D: 0.7 < ρ/ρ0 < 0.9 E: 0.5 < ρ/ρ0 < 0.7 F: 0.3 < ρ/ρ0 < 0.5 G: 0.1 < ρ/ρ0 < 0.3 H: 0.001 < ρ/ρ0 < 0.1 I: ash particles

47 ms, Group III

0 16 27 43 71 115 1880

10

20

30

40

50

60

70

80

90

Num

ber o

f Par

ticle

s, x

103

Particle diameter, μm

apparent density bins A: 1.2 < ρ/ρ0

B: 1.1 < ρ/ρ0 < 1.2 C: 0.9 < ρ/ρ0 < 1.1 D: 0.7 < ρ/ρ0 < 0.9 E: 0.5 < ρ/ρ0 < 0.7 F: 0.3 < ρ/ρ0 < 0.5 G: 0.1 < ρ/ρ0 < 0.3 I: ash particles

72 ms, Group III

(a)

(b)

(c)

Figure 23: Calculated particle number, size and density distribution of (a) Group I, (b) Group II and (c) Group III chars after 72 ms of burning in 12 mol-% O2 at nominally 1600 K.

After 25 ms of burning, some smaller-size and lower-density bins were filled by particles having all three types of char structures. Group I char particles reside in the density bins between 0.001ρ0 and 0.5ρ0, and in the size bins about the same as those at the onset of oxidation. Group II particles are distributed in the density bins from 0.001ρ0 to 0.9ρ0, and in some smaller size bins compared to those in the 47-ms char. Group III particles have apparent densities as low as 0.5ρ0, and the particle size distribution shifts to smaller sizes. It is observed that char particles in Groups I and II experience more broadening in apparent densities than particles in Group III, which implies that there are significant variations in internal burning for Groups I and II char particles. This observation is consistent with the result that Groups I and II char particles burn faster than Group III char particles. This result is due to the fact that for particles of comparable sizes burning within the Zone II burning regime (burning rates limited by the combined effects of pore diffusion and chemical reaction), the particles having the lower densities exhibit faster reductions in both diameter and apparent density.

The measured and predicted particle size distributions of chars derived from combustion at different residence times are shown in Fig. 24. The measurements indicate a significant number of small particles (< 20 μm), a feature that the predictions did not capture. This is attributed to the neglect of fragmentation in the model; incorporation of fragmentation would produce more small fragments, similar to the actual measurements. For the initial raw coal sample, most particles were within the 75 - 106 μm size range. The increase in particle size compared to the raw coal sample is due to swelling during devolatilization, which increases with pressure.

0 100 2000.0

0.2

0.4

0.6

0.8

1.0

Data Prediction

Cum

ulat

ive

%-V

olum

e

72 ms

0 100 200

95 ms

Particle Diameter, μm0 100 200

117 ms

Figure 24: Comparison of experimental measurements (symbols) and model predictions (dashed lines) of particle size distributions of char collected after 72, 95 and 117 ms exposure to 12 mol-% O2 at nominally 1600 K.

Based on the results of this investigation into the impact of char structure on the characteristics of burning char particles, the following conclusions have been reached:

• A range of particle structures, from high-density uniform low-porosity particles to low-density high-porosity cenospherical particles, can be produced during the devolatilization of pulverized coals at high pressures.

• The fraction of low-density, high-porosity chars increases with increasing pressure rendering a broader variation in char-particle type with pressure.

• The relations put forth in this study to characterize the overall burning rates per unit external surface area, the surface regression rates and the density reduction rates of Group I, II and III char particles are sufficient to capture the behaviors of particles burning under conditions in which burning rates are limited by the combined effects of chemical reaction and pore diffusion.

• A large number of small fragments (< 20 μm) are generated during char oxidation. Accounting for fragmentation during char oxidation would yield better predictions of the evolution of particle size distribution.

IV. Characterization of the Impact of Pressure on Char Reactivity Pressurized gasification and combustion of fossil fuels have the advantages of

increased conversion efficiency, decreased pollutant emissions, and reduced reactor furnace size. Characterizing the impact of pressure on char conversion was one of the goals of this project. To this end, experiments were undertaken to increase the data available on the conversion rates of coal chars at elevated pressures. We used the data, supplemented with calculations, to characterize the separate effects of total pressure and oxygen mole fraction on char reactivity in the type environments likely to be established in advanced energy systems. Pressure influences both chemical reaction rates and the rate of oxygen transport to the particle’s outer surface and through the particle’s pores. Consequently, understanding the impact of pressure on char conversion rates requires understanding the impact of pressure on both chemistry and mass transport.

The impact of pressure on char conversion rates depends upon the particle temperature. At relatively low temperatures when chemical reaction rates are slow compared to mass transport rates (Tp < ~900 K), oxygen completely penetrates the particle and the particle burns in the Zone I burning regime in which char conversion rates are controlled by the rates of chemical reactions. In this regime, pressure impacts reaction rates only to the extent that it impacts the partial pressure of oxygen (PO2 = yO2P). Thus, for fixed oxygen mole fraction, if pressure is increased the partial pressure of oxygen is increased, increasing chemical reaction rates, and the time for complete char conversion decreases. At sufficiently high particle temperatures when reaction rates are fast compared to mass transport rates (Tp > ~ 1800 K), oxygen is consumed at the particle periphery, and the particle burns in the Zone III burning regime in which char conversion rates are controlled by the rate that oxygen diffuses to the outer surface of the particle. Bulk diffusion coefficients are inversely proportional to pressure, thus at high temperatures, for fixed oxygen mole fraction if pressure is increased, oxygen transport rates decrease and the time for complete conversion of the char increases.

In the Zone II burning regime (~900 K < Tp < ~1800 K), the combined effects of chemical reaction and mass transport control char conversion rates. Both Knudsen and bulk diffusion can control the rate that oxygen diffuses through the particle, depending upon the pore size. In small pores, Knudsen diffusion dominates, and oxygen transport is

independent of pressure. As conversion progresses and pores merge and coalesce becoming larger, bulk diffusion inside particles becomes ever more rate-controlling, and oxygen transport rates decrease as pressure is increased.

In our experimental activities, the reactivities for a synthetic char burning in the Zone I regime at different total pressures and constant oxygen partial pressure were determined from thermogravmetric data obtained in the PTGA. Data were obtained at different gas temperatures. Analysis of the data indicated that at a given temperature, char reactivity is determined solely by the oxygen partial pressure (PO2 = yO2P), independent of the individual values of total pressure P and oxygen mole fraction yO2 when burning is chemical kinetically controlled. The reaction mechanism presented in Table III yielded calculations that accurately described the experimental results, further supporting the validity of the mechanism at elevated pressures.

Calculations indicated that for fixed oxygen mole fraction and gas temperature, particle temperatures remain relatively constant as pressure is increased for Zone I burning. Calculations also indicated that the instantaneous apparent reaction order, n, a measure of the sensitivity of the char reactivity to the oxygen partial pressure, was a function of T, P and yO2, and is not constant over the whole range of oxygen partial pressures, as suggested in many studies. Calculations indicated that at a given temperature, the value of n increases with oxygen partial pressure. When comparing the values of n at a fixed oxygen partial pressure for different temperatures within the Zone I regime, the rate of reactivity increase with respect to oxygen partial pressure was found to be lower at higher temperature, i.e., n T2( )PO2

,P< n T1( )PO2

,P if T . 2 > T1

Calculations also indicated that under Zone II burning conditions, such as at 1600 K, the value of n is not a constant over the whole range of oxygen partial pressures studied, and is pressure dependent. Although there is an almost constant value of n for low values of the oxygen partial pressure at the particle surface PO2,s, n tends to decrease with increase in PO2,s. This trend differs from that observed under Zone I burning conditions, in which n increases with increasing oxygen partial pressure. It is clear that the decrease in the value of n is due to pore diffusion limitations.

At high temperatures (Tgas = 1600 K), the burning is restricted to the periphery of the particle (strong Zone II). Under strong Zone II burning conditions, both the reactivity and average particle temperature decrease with total pressure. In the strong Zone II burning regime, the reactivity is controlled by both chemistry and pore diffusion during the whole conversion of the material, even at atmospheric pressure. With elevated pressures, the molecular diffusivity decreases, rendering the impact of diffusion limitation on reactivity more significant. When the pore diffusion rate has decreased to a certain extent, external bulk diffusion will become the controlling factor on reactivity, and burning enters the Zone III burning regime.

At moderate gas temperatures (Tgas = 1140 K), there is significant internal burning at nearly constant diameter up to certain extents of conversions (weak Zone II). Under weak Zone II burning conditions, the reactivity also decreases with total pressure but at a slower rate than the transport rate. The overall effect is that as pressure increases, the chemical rate controlling steps become less important, and diffusion control becomes more significant.

Since over a range of total pressure the molecular diffusivity is inversely proportional to total pressure and Knudsen diffusivity is independent of total pressure, pore diffusion limitation becomes more significant at elevated pressures. However, in Zone II burning with fixed oxygen partial pressure, the reactivity is lower at higher total pressure. With fixed temperature and oxygen partial pressure, the burning regime could change from Zone I to Zone II as the total pressure increases.

At constant gas composition, the total effect of increasing total pressure is to increase the reactivity, with a trade-off between higher chemical reaction rates due to a higher oxygen concentration and a proportionately lower diffusion coefficient. This effect is weak (in weak Zone II) or negligible (in strong Zone II) at pressures above 10 atm. At fixed oxygen partial pressure, the transition temperature from Zone I to Zone II is lower at higher total pressure.

V. Characterization of Char Reactivity to Carbon Dioxide Technologies based on gasification rather than combustion provide alternative means

of using coal and biomass for generating electricity as well as for providing synthesis gas that can be used to produce transportation fuels and hydrogen. Integrated gasification combined cycle (IGCC) systems generate electricity at efficiencies in a range comparable to that for current PC plants, but are expected to achieve higher efficiencies as gas turbine technology develops. Also, while an IGCC power plant without CO2 capture is currently more costly than a pulverized fuel power plant, an IGCC plant is often less costly if CO2 capture is added to pulverized fuel-based power plants [25].

The reaction between carbon and carbon dioxide is very important in modeling the gasification process, in predicting the synthesis gas production, and in designing the gasifiers. The classical Ergun [26] mechanism for the C-CO2 reaction has been found to be adequate for near atmospheric pressure environments. Although modifications have been made to account for elevated pressures and for the retarding affects of modest amounts of carbon monoxide, no model exists that accurately predicts char reactivity to carbon dioxide in high-pressure, high-carbon monoxide gasification environments. Consequently, a study was undertaken to correct this deficiency in our predictive capability. Based on previously published work and the results of reactivity tests performed in our laboratory, a reaction mechanism that accurately describes char reactivity to CO2 was developed, and its performance was evaluated.

Char-CO2 Reaction Mechanism In light of the results of the earlier work by Ergun [26], Blackwood and Ingeme [27],

and Tsai [28], and work performed during this project, the reaction mechanism presented in Table VII was developed to describe the key reaction pathways during the conversion of carbon to gaseous species in CO2-containing environments. Reaction (R.1) is a reversible CO2 dissociative adsorption reaction. A free carbon site Cf is attacked by a CO2 molecule, forming a CO gas-phase molecule and oxygenated carbon site, i.e. C(O) surface oxide. In Reaction (R.2), the surface oxide escapes from the bondage of neighboring atoms, exposing a new free carbon site. Reaction (R.3) represents the rate-limiting step of the overall interaction between CO2 and a chemisorbed oxygen atom. Reaction (R.4) is the reversible CO adsorption on active sites, forming surface complexes. Reaction (R.5) represents CO2 formation as a result of gas-phase CO

interacting with adsorbed CO. Reactions (R.4) and (R.5) are possible pathways by which adsorbed CO affects the gasification process.

Table VII. Reduced heterogeneous reaction mechanism for char reactivity to CO2

(R.1) CO2 + Cf k1f

k1b

⎯ →⎯← ⎯⎯ CO + C(O)

(R.2) Cb + C(O) k2⎯ →⎯ CO + Cf

(R.3) Cb + CO2 + C(O) k3⎯ →⎯ 2CO + C(O)

(R.4) Cf + CO k4f

k4r

⎯ →⎯← ⎯⎯ C(CO)

(R.5) CO + C(CO) k5⎯ →⎯ CO2 + 2Cf

Mechanism validation: low pressure and low CO concentration regime

To verify the applicability of the mechanism to gasification at low pressures, the experimental gasification rate data from Koenig et al. [29] were used. These data are reactivities for a coconut char obtained at ambient pressure and temperatures from 1053 to 1094 K with a CO partial pressure of 10 kPa. A least squares procedure was used to determine rate coefficients that yielded calculated profiles that agreed with the data. The optimized values are shown in Table VIII. The uncertainties for the rate coefficients were determined based on the reported reactivity data with about 15% errors. It is noted that there are significant variations of k4f and k5, with which the calculated reactivities are within the range of errors. This means that the reactivity is not sensitive to Reactions (R.4f) and (R.5). Also note that the temperature range was too narrow to permit the determination of activation energies.

Table VIII. Values for rate coefficients determined for data of Koenig, et al. [29] T

(K) k1f × 106

m3/mol·s k1r× 105

m3/mol·s k2× 106

1/s k3× 106

m3/mol·s k4f× 104

m3/mol·sk4r× 102

1/s k5× 105

m3/mol·s1053 3.08 1.0 ± 0.44 0.02 ± 0.55 ± 0.2 0.47 ± 0.03 1.0 ± 3.0 1.0 0.2 ± 1.0 3.0 ±1073 13.0 8.0 ± 1.92 1.5 ± 2.25 ± 1.0 0.79 ± 0.2 1.5 ± 4.0 2.0 0.5 ± 2.3 6.0 ±1078 3.78 1.0 ± 5.15 0.1 ± 29.9 ± 20 1.16 ± 0.6 1.5 ± 4.0 2.0 0.2 ± 2.3 6.0 ±1094 15.6 4.0 ± 2.25 2.0 ± 3.85 ± 2.5 1.56 ± 0.3 2.0 ± 8.0 4.0 1.0 ± 2.5 5.0 ±

In Fig. 25, the lines are the calculated reactivities using the rate coefficients obtained

above. The calculated reactivities using these rate coefficients are in good agreement with the experimental values, supporting the reaction mechanism presented in Table VII.

In order to test the ability of the model to predict the reactivity trend observed with CO concentration varied, the char reactivities at various CO concentrations were also calculated using the rate coefficients shown in Table VIII. The calculated reactivities are compared with the experimental data of Koenig et al. [29] in Fig. 26. It is observed that the mechanism developed can capture accurately the CO retarding effect on char gasification reactivities. The agreement between the experimental data and the calculated reactivity is good up to the CO concentration of 3 mol/m3.

2 4 6 8 100.0

0.5

1.0

1.5

2.0

2.5

Rea

ctiv

ity, g

/(m2 .s

)x10

8

[CO2], mol/m3

pCO = 10 kPa 1053 K 1073 K 1078 K 1094 K

Figure 25: Comparison of measured (symbols) and calculations (lines) reactivity vs. CO2 concentration with pCO = 10 kPa at a total pressure of 101.3 kPa (data from Koenig et al., [29]).

0 1 2 3 40

1

2

3

4

Rea

ctiv

ity, g

/(m2 .s

)x10

8

[CO], mol/m3

pCO2 = 50 kPa

Figure 26: Prediction of average char reactivity at various CO concentrations with pCO2 = 50 kPa and T = 1078 K (data from Koenig et al., [29]).

Mechanism validation: high pressure and low CO concentration regime Generally, industrial gasifiers operate under high-pressure conditions. In order to

verify if the reaction mechanism developed could be applied to describe the gasification rate at elevated pressures, the high-pressure experimental data from Blackwood and Ingeme [27] were used. These gasification rate data were obtained at conditions of different total pressures (P up to ~ 40 atm), temperatures (T = 1063 - 1143 K), and CO2 and CO partial pressures (pCO2 = 1 - 36 atm, pCO = 0.5 - 1 atm). For these experimental data, the gasification rates were evaluated as the net rate of CO formation.

The optimal rate coefficients for the reactions in the mechanism were determined using a search scheme, and are listed in Table IX. The uncertainties for the reaction rate coefficients were determined based on the reported reactivity data with about 15% errors, and are also listed in the table. It is noted that there are wide ranges of k4f and k5 that can be tolerated without compromising the goodness of fit of the model to the reported data. Because of the low concentrations of gas-phase and adsorbed CO, the contributions of the reaction rates of (R.4) and (R.5) to the overall reaction rate are small. The sensitivities of reaction rate to k4f, k4r and k5 are low, and there is a range of values of these parameters that could be used to fit the experimental data.

Table IX. Values for rate coefficients determined for the data of Blackwood and Ingeme [27].

T (K) k1f× 10-5 k1r× 10-7 k2× 10-7 k3× 10-5 k4f k4r× 10-2 k5

0.70 ± 0.1 4.87 ± 2.0 5.02 ± 2.5 1.70 1.6 ±1063 2.10 ± 0.3 1.12 ± 0.7 1.05 ± 0.8

1103 9.64 ± 1.1 9.24 ± 1.0 6.26 ± 1.0 4.93 ± 0.8 20.2 ± 10 5.45 ± 3.7 19.9 18 ±

1143 28.2 8.5 9.68 0.2 9.71± ± ± 0.8 9.80 ± 2.0 28.8 15 2.76 ±± 1.5 24.8 12 ±

Units of mo m g at t f ·g

partial pressures of CO and CO partial pressures of 0.5 and 1 atm were calculated, and plo

ki in m5/g· l·min and 2/min·g to ive gasific ion ra es o unit mol-CO/min .

Using the kinetic parameters shown in the table, the gasification rates at various 2

tted against the experimental data in Fig. 27. The calculations (represented by thelines) based on these parameters agree quite well with the experimental data.

0 10 20 30 400

1

2

3

4

5

6

7

1063 K

1103 K

RC

O, m

ol/(g

.min

)x10

4

pCO2, atm

1143 K

Figure 27: Prediction of gasification rate with CO2 partial pressure p at fixed p = 0.5 atm (solid symbol) and 1 atm (open symbol)

Under hig f generated CO gas when there is no CO in the inlet gas flow was evaluated. The gasification rates calculated using the

CO2 CO(Data from Blackwood and Ingeme [27]).

h-pressure conditions, the retarding effect o

par

ed

ower

ameters determined above are plotted together with the experimental data from Blackwood and Ingeme [27] in Fig. 28. The solid line was calculated by taking into account the retarding effect of CO generated in the reaction and the dashed line wascalculated by assuming no CO adsorption. The comparison of these calculations showthat the retarding effect of generated gas-phase CO is small because of the low concentration of CO. The incurred error due to neglecting CO adsorption is small at the given conditions. It is also noticed that the retarding effect of CO is smaller at lpressures.

0 10 20 30 400.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

Data Calculation with CO adsorption Calculation without CO adsorption

RC

O, m

ol/(g

.min

)x10

4

pCO2, atm Figure 28: Gasification rates as a function of CO2 partial pressure when no CO gas in inlet gas (open symbol) (Data from Blackwood

Mechanism validation: high pressure and high CO concentration regime

In real gasifier environments, there can be significant amounts of CO in the gas concentration

nee ents

test the ia a

be char reactivity to

CO

and Ingeme [27]).

phase. The performance of the mechanism under conditions with high COds to be investigated. The gasification of the char of Illinois #6 coal in environm

containing high levels of CO was investigated by Tsai [28], who considered the affect of high CO concentrations on the intrinsic reactivity of carbon to CO2 at atmospheric and elevated pressures. Experimental mass loss data and reaction rates for a range of temperatures (1200 and 1273 K), pressures (1.41 to 25 atm), and gas compositions (different CO2/CO and CO2/N2 mixtures) were obtained. These data were used to mechanism presented in Table VII. The optimal kinetic parameters were obtained vleast squares procedure, and are shown in Table X. The uncertainties in activation energies were calculated based on the uncertainties of the rate coefficients at each temperature, and are largely due to the narrow temperature range.

Comparisons between calculations and the Tsai data are shown in Fig. 29. Theagreement suggests that the reaction mechanism put forth to descri

2 is an adequate model for describing char reactivities at 1200 and 1273 K, total pressures up to 25 atm, and at CO partial pressures as high as 18 atm.

Table X. Values for reaction rate coefficients for data of Tsai [28]

Ε (kJ/mol) T = 1200 K T = 1273 K × ×k1f (m /mol·s) 4.51(3 ± 1.0) 10-5 3.17( ± 1.5) 10-4 E1f = 339 ± 128

k1r (m /mol·s) 3 1.14( 0.4)± × ×10-3 2.57( ± 0.5) 10-3 E1r = 199 98 ±

k2 (1/s) 3.92( 1.0)± × ×10-4 3.07( ± 1.0) 10-3 E2 = 358 ± 04

k3 (m

13/mol·s) 2.98( 0.3)± × ×10-7 4.17( ± 0.4) 10-7 E3 = 58 34 ±

k4f (m /mol·s) 3 2.33( 0.7)± × ×10-7 5.55( ± 2.1) 10-7 E = 151 123±4f

k4r (1/s) 1.31( 0.5)± × 1.8)×10 1 4.59(-1 ± 10 1

k5 (m

-1 E4r = 218 142 ±3/mol·s) 2.91( 1.2)± × ×110-7 1.74( ± 0.4) 0-6 E5 = 311 117 ±

0 5 10 15 20 250

1

2

3

4

5

6

Ri,C

, g/(m

2 .s) x

107

pCO2, atm

CO2/CO mixture

0 5 10 15 20 250

1

2

3

4

Ri,C

, g/(m

2 .s) x

106

pCO2, atm

CO2/CO mixture: 0.141 MPa 1 MPa 2.5 MPa

T = 1273 K

CO2/N2 mixture

P = 25 atmP

0.141 MPa 1 MPa 2.5 MPa

T = 1200 K

CO2/N2 mixture

P = 25 atm0 atmP=

.41

atm

p CO = 0

Data from Tsai [1998]

= 10

P =

1

P = 1

1

atm

.41

atm

p CO = 0

Data from Tsai [1998]

Figure 29. Comparison of experimental gasification rates at 1200 K (left) and 1273 K (right) in different gas compositions with calculated rates using the model developed.

E

To characterize the effects of temperature, pressure, and gas composition on char %-porosity synthetic char

wer res

2perature. In the figure, the

sym

;

ffect of Gasification Conditions on Char Reactivity to CO2

reactivity to carbon dioxide, a series of experiments with a 16e conducted in our laboratory. The gasification conditions cover a range of pressu

(from 1 to 20 atm) and gas compositions (CO2/N2 mixtures with yCO2 = 50% to 100%) inisothermal environments (1173 and 1273 K). The gasification tests were performed in our pressurized thermogravimetric analyzer.

The effect of gasification temperature on char reactivity to CO is shown in Fig. 30. The reactivities are observed to increase with increasing tem

bols represent the reactivity data obtained from experiments and the lines are the reactivities calculated using the reaction mechanism developed. Account was made for variations in specific surface area during the char conversion process using the Bhatia-Perlmutter (see Eq. (2)) surface area model. Gasification reactions are sufficiently slow that carbon dioxide completely penetrates small particles at the temperatures employedparticles gasify under Zone I conditions. The predictions followed the measured reactivity profiles quite well, supporting the validity of the mechanism.

0.0 0.2 0.4 0.6 0.80.0

0.5

1.0

1.5

2.0

2.5

3.0

0.0 0.2 0.4 0.6 0.80.0

0.5

1.0

1.5

2.0

2.5

3.0

1173 K

1223 K

Rea

ctiv

ity, R

i,C, g

/(m2 .s

) x 1

0

Conversion, xC

1273 K

6 P = 1 atm, yCO2 = 50%

Rea

ctiv

ity, R

i,C, g

/(m2 .s

) x 1

0

Conversion, xC

1173 K

1223 K

1273 K

CO2

Figure 30: The variation of reactivities with conversion at different gasification temperatures. Symbols are experimental data and lines are calculations based on the reaction mechanism presented in Table VII.

re As shown in Fig. 1, when the gasification temperature (T = 1223 K) and CO mole fraction (y = 50%)

wer from

6 P = 20 atm, y = 50%

In real gasification processes, the effect of total pressure on char gasification activity at constant temperature and gas composition is of concern.

3 2 CO2e held constant, the reactivity increased when the total pressure was increased

1 to 20 atm. The increase of total pressure with fixed gas composition will increase the CO2 partial pressure (and hence, CO2 concentration) in the reaction gas, and the reactivityincreases with CO2 concentration.

0.0 0.2 0.4 0.6 0.80.0

0.5

1.0

1.5

2.0

2.5

3.0

Rea

ctiv

ity, R

i,C, g

/(m2 .s

) x 1

0

Conversion, xC

CO2

20 atm

1 atm

4 atm

10 atm

Figure 31: The variation of reactivities with conversion at different total pressures. Symbols are experimental data, and lines are calculations based on the reaction mechanism

It is noted th ng total pressure. The pe . As shown in the figure, at ambient pressure the peak reactivity occurs at about ~2% conversion, but

6 T = 1273 K, y = 50%

.

at the peak reactivities shift to higher conversions with increasiak also becomes more prominent as pressure is increased

whe

of

stant gasification temperature and pressure increases the reac

n the pressure is elevated to 20 atm, the peak reactivity occurs at around 15% conversion.

Char reactivities at a temperature of 1273 K and pressure of 4 atm are shown in Fig.32 for CO2 mole fractions of 50%, 75% and 100%. It is observed that the increaseCO2 mole fraction at con

tivity, similar to the effect of total pressure on reactivity. This is due to the increasedCO2 concentration when increasing yCO2 at constant pressure.

0.0 0.2 0.4 0.6 0.80.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5T = 1273 K, P = 4 atm

Rea

ctiv

ity, R

i,C, g

/(m2 .s

) x

Conversion, xC

106

yCO2 = 50% yCO2 = 75% yCO2 = 100%

Figure 32: The variation of reactivities with conversion at different CO2 mole fractions. Symbols are experimental data, and lines are calculations based on the reaction mechanism.

Based on th dioxide, e following co

ith pressure and the sensitivity to k4r decreases.

ConEx

chara ments at high nd pressures. Models were developed and model parameters were

det ata

e results of our investigation of the reactivities of chars to carbonnclusions have been reached: th

• The reaction mechanism put forth to characterize char reactivity to CO2 can predict accurately the gasification rates at low and high pressures under conditions of low-CO or high-CO concentrations.

• The reaction Cb + CO2 + C(O) → 2 CO + C(O) is the key reaction that compensates for the underestimation of gasification rates by the Ergun mechanism at high pressures.

• Reactions R.4 and R.5 are responsible for the observed lower gasification rates at high CO concentrations at high pressure. The sensitivity of reactivity to k5 increases w

clusions periments were undertaken in order to provide the information needed to

cterize the behaviors of char particles in reactive gas environtemperatures a

ermined based on the experimental data obtained in this work as well as the d

obtained by other researchers. Conclusions of our extensive investigations are summarized below.

Characterization of Char Reactivity to Oxygen Oxygen physisorption and chemisorption and surface oxide surface migration and

for the chemical pathways associated wit

le

in both size and apparent er-law relations (Eqs (18a,b) do not accurately

des w

l yields

es

e generated during the devolatilization of ospheric char particles to high-

den

nd

es ,

he analysis of the impact of pressure on overall char-ure has a dual effect on

chag e

desorption must be considered when accountingh describing char reactivity to oxygen. Allowance must be made for the distribution

of desorption energies of the adsorbed surface complexes. The heterogeneous reactionmechanism presented in Table I accurately describes the reactivity of a variety of chars burning under chemical kinetics-controlled conditions (under Zone I conditions). The reduced mechanism presented in Table III faithfully reproduces the trends predicted using the full mechanism. Account must be made for surface area evolution in order todetermine accurate kinetic parameters employing measured mass loss data. The Thiemodulus approach effectively accounts for the oxygen concentration distribution inside particles burning at high temperatures (under Zone II or III conditions). Equation (21) accurately characterizes the Thiele modulus-effectiveness factor relation when the reactivity is described by the full and reduced mechanisms.

Characterization of the Mode of Burning At high temperatures, char particles burn with decreases

density and the commonly employed powcribe the variations over the burnout times of the particles. The mode-of-burning la

developed and validated during the course of this project (Eqs. (27a,b) and (28)) eliminates the shortcomings of the power-law model by associating size and apparent density variations with the instantaneous value of the Thiele modulus. The modevariations in the size and apparent density of uniform porosity char particles burning under Zone II conditions that agree with measurements obtained with several synthetic chars, a bituminous coal char and a biomass char. The model is applicable to all regim(Zones I, II, and III) in which particles burn.

Accounting for Differences in Char-Particle Structure A variety of char particle morphologies ar

bituminous coals, from low-density, high-porosity, censity, low-porosity dense, irregularly shaped char particles. The morphological

variations increase with increasing devolatilization pressure. These particles burn at different rates, consequently for accurate prediction of char-particle burnout times atemperatures, account must be made for the different particle structures. The models developed for cenospherical char particles (Eqs. (15a,b), (37) - (41)), mixed char particl(Eqs. (15a,b), (33) - (35) with η = ηII, Eq. (42)), and dense char particles (Eqs. (15a,b)(21a,b), (33) - (35)) yield calculated size, apparent density, and temperature profiles that agree with measurements for an ensemble of char particles having different structures burning under Zone II conditions.

Characterization of the Impact of Pressure on Char Reactivity The models developed permit t

particle burning rates. Under Zone II burning conditions, pressr burning behavior, impacting both chemical kinetics and mass transport rates. For

fixed oxygen partial pressure, increasing total pressure decreases the char overall burninrate due to the lower diffusion coefficient at higher pressure. For fixed total pressure, th

reactivity increases with increasing oxygen partial pressure. For constant gas composition, the overall effect of increasing total pressure is to increase the reactivity, with a trade-off between higher chemical reaction rate due to higher oxygen concentration and a proportionately lower diffusion coefficient.

At fixed oxygen partial pressure and gas temperature, the burning regimefrom Zone I to Zone II when the total pressure increases. At fixe

can change d total pressure and

oxy

influence of ces of adsorbed CO on carbon

surf n

mproved g the coal and biomass char oxidation and gasification processes. With this

und

Ph.D. theses were completed during this project: Campbell, “Investigation into the Roles of Surface Oxide Complexes and their

hanism,” Ph.D. Thesis,

2. niversity, June 2006.

1.

submitted to Combustion &

3. d Fuels,” being submitted to Energy & Fuels in April 2007.

07. Tab

Ai species i (mol/m , mol/m )

gen partial pressure, the burning regime can change from Zone I to Zone II when the gas temperature increases. Zone II burning is favored at high pressure.

Characterization of Char Reactivity to Carbon Dioxide In order to predict accurately the impact of elevated pressures and the

high CO-levels on char gasification rates, the consequenaces must be taken into account. The reaction mechanism presented in Table VII ca

describe the reactivity of carbon to CO2 at low and high pressures under conditions of both low-CO and high-CO concentrations. The reaction between gas-phase CO and adsorbed CO is important under high pressure and high CO concentration conditions. Accurate determination of gasification kinetic parameters employing mass loss data requires that account is made for variations in the total surface area during char conversion.

The results of this research effort have contributed in significant ways to an iunderstandin

erstanding, we have developed models that accurately describe char combustion and gasification behavior in the types of environments established in current combustors and gasifiers as well as in the types of environments expected in advanced combustors and gasifiers. With these models, it is possible to investigate different design options and strategies of converting the chemical energy in coals and biomass materials to useful sensible energy.

Publications The following1. Paul A.

Distributions in the Carbon-Oxygen Heterogeneous Reaction MecMechanical Engineering Department, Stanford University, August 2005. Liqiang Ma, “Combustion and Gasification of Chars in Oxygen and Carbon Dioxide at Elevated Pressures,” Ph.D. Thesis, Mechanical Engineering Department, Stanford U

The following journal articles have been prepared for publication: Mitchell, R. E., Ma, L. and Kim, B. J. “On the Burning Behaviors of Pulverized Coal Chars,” accepted for publication in Combustion & Flame in February 2007.

2. Campbell, P. A., Mitchell, R. E., and Ma, L. “Impact of Distributed Surface-Oxides and their Migration on the Heterogeneous Carbon-Oxygen Mechanism,” beingFlame in April 2007. Ma, Liqiang and Mitchell, Reginald E. “A Model for the Mode of Burning during Combustion of the Chars of Pulverize

4. Ma, Liqiang and Mitchell, R. E. “Modeling Char Oxidation Behavior under Zone II Burning Conditions at Elevated Pressures,” being submitted to Combustion & Flame in April 20

le of Nomenclature pre-exponential factor in Arrhenius form for reaction Ri

Ci concentration of 3 2

Ci,k parameter in population balance model (see Eq. (45))

/s) l (see Eq. (45))

nospherical particle (m)

g the lth subrange, kJ/mol on R

ction Ri e distribution of desorption energies

(21b))

ol) mt t) mC ) us char sample, kg

, global reaction order for O2 concentration

cp,g gas specific heat of the gas (J/mol·K) Deff effective overall oxygen pore diffusion coefficient (m2

Di,k parameter in population balance mode DO2 oxygen bulk diffusion coefficient into gas mixture (m2/s) Dp particle diameter (m) Dpi internal diameter of cenospherical particle (m) Dpo external diameter of ce E activation energy; desorption energy, kJ/mol Edes,l desorption energy of adsorbed species populatin Ei activation energy in Arrhenius form for reacti i kd oxygen mass transfer coefficient (s/m) ki reaction rate coefficient for reaction Ri ki,eff effective reaction rate coefficient for rea L number of distinct sites considered in th m mass; parameter in modified Thiele modulus (see Eq. mC mass of carbonaceous particle material (g) mp mass of the particle (g) M̂ C atomic mass of carbon, (g/mol)

M̂ molecular mass of species i (g/mi ot( instantaneous total mass, kg (t instantaneous mass of the carbonaceo

n parameter defined in Eq. (37) &N molar flow rate, mol/s Nj total moles of species j, mol N ize bin i and density bin k

ambient gas (atm)

particle (atm) te per unit external surface area (g/m2·s)

rk e area (g/m2·s)

aterial (g/m2·s) ce of the particle (g/m2·s)

rface area of char, mol/s·m2

void

perature (K) re in the boundary layer surrounding the particle (K)

ent k (m ) the particle

i Nu Nusselt number (taken as 2)

,k number of particles in s

P total pressure (atm) Pg oxygen partial pressure in the Pi partial pressure species i Ps oxygen partial pressure at the outer surface of the q overall particle burning raℜ, R̂ universal gas constant, J/mol·K r, radius, radius of volume element k (m) R reactivity per unit external surfac RiC intrinsic reactivity of the carbonaceous m RiC intrinsic reactivity evaluated at the external surfa,e

R̂iO molar reactivity of oxygen (mol-O /mx

2 2

2

3·s)

molar reaction rate of reaction i per unit suR̂R,i

molar production rate of species j per unit surface area of char, mol/s·mR̂S, j

s ratio of surface area at interior and external surfaces for a cenospherical particle s ratio of shell volume to total particle volume for a cenospherical particlesh SgC specific char surface area, m2/g Stot total char surface area, m2

Sh Sherwood number (taken as 2) t time, s T temperature, K Tg ambient gas tem Tm mean temperatu Tp particle temperature (K) Tw wall temperature (K)

3 Vk volume of annular volume elem Xa mass fraction of ash in

xC conversion of the carbonaceous material xi lower cutoff size for size bin i yi mole fraction of gas species i [j] surface concentration of species j, mol/m2

(taken to be 1.072x10-4 mol/m2)

k

change in volume upon reaction per mole of oxygen consumed

le (taken as 0.85) sic reactivity-based model

nductivity (W/m·K) per mole carbon gasified

reactant in the ith reaction

particle, apparent density of the char (g/cm3)

energy distribution (kJ/mol)

des) odulus

Φ n energies

[ξ] total surface concentration of all carbon sites

G ee α, β burning mode parameters in power-law relations

r

γ δ particle wall thickness (m) ΔH effective heat of reaction (J/gC) ε emissivity of the char partic ζ burning mode parameter in intrin η particle effectiveness factor ηj number of carbon sites that one molecule of species j occupies θ particle porosity θj fraction of carbon sites occupied by species j θv void porosity κ parameter defined via Eq. (15b) λg gas thermal co νO2 number of moles oxygen reacted νi,j reaction coefficient for species j as a ρ apparent density (g/cm3) ρ k lower cutoff density for density bin k (g/cm3) ρ C apparent density of ash-free ρ t true density of carbon (g/cm3) σ Stefan-Boltzmann constant (W/m2·K4) σ i standard deviation in activationφ Thiele modulus φ(E true distribution of oxygen complexes on the char surface φm modified Thiele m

(Edes,l) fractional contribution of the lth subpopulation of desorptioϕ pore structure parameter ψ(E ) distribution function of desorbed species des

(EΨ gy range of the lth subpopulation

perties of ash C s material

ticle external surface II article

roperty of inlet stream

l for cenospherical particle id tral void in cenospherical particle

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cri

a proc, properties of carbonaceouex property at the parI, II, I property for Group I, II and III char pin property at the particle internal surface, pk properties at volume element k p properties of char particles sh property within the particle shelvo property related with the cen

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CR

t eginald E. Mitch