COMBUSTION AND GASIFICATION OF CHARS IN OXYGEN AND CARBON DIOXIDE AT ELEVATED PRESSURE

Transcription

1 COMBUSTION AND GASIFICATION OF CHARS IN OXYGEN AND CARBON DIOXIDE AT ELEVATED PRESSURE A DISSERTATION SUBMITTED TO THE DEPARTMENT OF MECHANICAL ENGINEERING AND THE COMMITTEE ON GRADUATE STUDIES OF STANFORD UNIVERSITY IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY Liqiang Ma August 2006

2 Copyright by Liqiang Ma 2006 All Rights Reserved ii

3 I certify that I have read this dissertation and that, in my opinion, it is fully adequate in scope and quality as dissertation for the degree of Doctor of Philosophy. (Reginald E. Mitchell) Principal Advisor I certify that I have read this dissertation and that, in my opinion, it is fully adequate in scope and quality as dissertation for the degree of Doctor of Philosophy. (Craig T. Bowman) I certify that I have read this dissertation and that, in my opinion, it is fully adequate in scope and quality as dissertation for the degree of Doctor of Philosophy. (David M. Golden) Approved for the University Committee on Graduate Studies. iii

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5 Abstract Coal has been an important energy resource for more than 100 years, and it will continue to be an important energy resource in the 21 st century. Currently, the energy from coal accounts for 23% of the energy consumed in the United States and about 70% in China. However, the traditional schemes for utilization of coal have been criticized for their low efficiency and high pollution characteristics compared to oil and natural gas. Some clean coal technologies, such as Integrated Gasification Combined Cycle (IGCC) and Pressurized Fluidized Bed Combustion (PFBC) have been identified as viable technologies to address these problems. Fundamental understanding of the physical and chemical processes involved in these advanced coal conversion technologies is necessary to achieve higher efficiency and smaller impact on the environment. Char combustion and gasification are complicated technologies, involving several chemical and physical processes. These processes include the transport of reactive gases across the boundary layer surrounding the char particle, the transport of gases through the porous structure of the char particle, and the chemical reactions on the carbon surfaces within the char particle. In order to gain an understanding of these processes and their effects on the char conversion process, extensive experimental efforts were made to characterize the reactivity of chars of a variety of carbonaceous materials. The experiments, conducted in a Pressurized Thermogravimetric Analyzer (PTGA) and in a High Pressure Flow Reactor (HPFR), cover a wide range of temperatures ( K), pressures (1-20 atm), and gas compositions (different mixtures of O 2 /N 2 and CO 2 /N 2 ). Under pulverized coal combustion conditions, char particles burn with reductions in both diameter and apparent density due to the O 2 concentration gradients established inside burning particles at high temperatures. The power-law mode of burning model is used by many to relate particle apparent density, diameter and mass loss during char oxidation. However, this model pre-supposes that the relationship between particle diameter and apparent density is fixed even as rate-limiting steps change during the course of burning. A single char particle conversion model that eliminates this shortcoming was developed in this study and used to calculate variations in particle size and apparent density when burning at high temperatures. The results of these calculations were used to establish a relationship between the v

6 effectiveness factor and the Thiele modulus, which was employed in the development of the intrinsic reactivity-based mode-of-particle-burning model. The relations allow for variations in particle size and apparent density during conversion that dep on the instantaneous state of the char particle. In the model, a 6-step reaction mechanism was used to describe the char reactivity. It was demonstrated that the mode of particle burning model can predict the burning behaviors of coal and biomass char particles undergoing oxidation in the type of environments in real burners and furnaces. In advanced coal conversion technologies such as IGCC and PFBC, the char conversion process occurs at elevated pressures. The separate effects of total pressure, oxygen mole fraction and oxygen partial pressure on the char reactivity as particles burn were examined using the single char particle conversion model developed. At low temperature, where chemistry controls the reaction rate, the reactivity was found to be depent solely on the oxygen partial pressure for fixed temperature. The calculated results at high temperatures indicated that the reactivity decreases with increasing total pressure at constant oxygen partial pressure. At fixed total pressure, the reactivity increases with increasing oxygen mole fraction. These predicted trs were confirmed by the results of experiments performed in the high pressure flow reactor. The model also explained the observations of high and low global reaction orders at high temperatures from various other studies. It was found in other studies that the physical structures of the char particles after devolatilization are different and can be characterized as being cenospherical, mixed and dense. For some coals (primarily bituminous coals), cenospherical char particle formation increases with increasing pressure. To more accurately characterize char combustion under elevated pressures, a char structure model was integrated with the char combustion model previously developed to capture the different burning behaviors of char particles with different structures. Calculations of the mass loss and apparent density agreed with the experimental values measured from the experiments at elevated pressure. The calculated particle temperatures were consistent with the measurements of particle temperature at comparable burning conditions in other studies. The model adequately predicted the behaviors of char particles burning under conditions of high temperature and elevated pressure. In characterizing char conversion during gasification, it is necessary to investigate the reaction between carbon and carbon dioxide for better predictions of char reactivity. A carbon-carbon dioxide reaction mechanism was developed based on previous investigations vi

7 and current work. The reaction mechanism developed was evaluated using gasification rates determined from experiments under different gasification conditions. It was demonstrated that the mechanism developed can provide accurate predictions of char reactivity over a wide range of temperatures, pressures, and gas compositions, which the previous models were not capable of doing. vii

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9 Acknowledgement I would like to thank my advisor, Professor Mitchell, for the enthusiastic support for making it possible for me to conduct this work, and for encouraging my creative tencies in the research. I wish to thank my reading committee, Professor Bowman and Professor Golden, for devoting time to this thesis and for assistance throughout my Ph.D. studies. My thanks also go to my colleagues in the Heterogeneous Combustion Laboratory: Paul Campbell, Lars Sørum, Illka Saarenpää, Andrew Lee and Bumjick Kim. Thank you all for your cooperation, technical assistance and helpful discussion. I also want to gratefully acknowledge my fris at Stanford: Xin Zhou, Shuhuai Yao, Yue Liang, Xiaojun Yu and Jian Luo, for the help and friship during our study together. I want to thank my wife Hongrui. She has encouraged me and helped me with her love, patience and understanding throughout my study. Thanks are also due to my family for their encouragement and prayers. Last but definitely not least, I want to express my highest praise to my Lord, Jesus Christ. Although I just knew Him for only about half a year, I felt that He has always accompanied me and helped me during my thesis work. May the Lord be pleased with my work and the glory is His. ix

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11 Table of Contents Abstract Acknowledgement Table of Contents List of Tables List of Figures Nomenclature v ix xi xv xvii xxvii Chapter 1. Introduction Background Motivation and objectives Organization of the thesis Chapter 2. Experimental Facilities High pressure flow reactor (HPFR) Laminar flow reactor Particle feeding and collection systems Pressure vessels Flow reactor temperature measurement Characterization of flow reactor Pressurized thermogravimetric analyzer (PTGA) Reactor chamber Furnace chamber Microbalance chamber Control panel Data acquisition Coulter multisizer Chapter 3. Test Materials, Experimental Methods and Data Analyses Test materials Synthetic chars xi

12 3.1.2 Other materials Experimental methods and data analyses Extent of mass loss Particle size distribution Apparent density measurements Specific surface area measurements Char reactivity measurements Heterogeneous reaction mechanism Temperature-programmed desorption (TPD) test.. 38 Chapter 4. Burning Behaviors of Pulverized Coal and Biomass Chars Introduction Power-law relations Single char particle conversion model Effective diffusion coefficient Particle temperature Heterogeneous chemical reaction mechanism Effectiveness factor Model calculation results Model parameters Model simulation in Zone I burning regime Model simulation in Zone II burning regime Mode-of-particle-burning model development Model formulation Impact of ash Model implementation Test materials Results and discussion Summary Chapter 5. Modeling of Char Oxidation at Elevated Pressure Introduction Char combustion model.. 81 xii

13 5.1.2 Effects of pressure on char oxidation rates Calculated results from single char particle conversion model Effective diffusion coefficient Model parameters Effects of total pressure and oxygen partial pressure under chemistry-controlled conditions Effects of total pressure and oxygen partial pressure under Zone II burning conditions Char structure model Formation of char structure Char structure model Particle population balance model Burning rate for dense char Burning rate for cenospherical char Burning rate for mixed-type char Results from char combustion model Summary Chapter 6. Gasification of Chars in CO 2 at Elevated Pressure Gasification mechanisms Ergun s gasification mechanism Blackwood s gasification mechanism Proposed gasification mechanism Model evaluation Low pressure and low CO concentration High pressure and low CO concentration High pressure and high CO concentration Brute force sensitivity analysis Summary Chapter 7. Summary, Conclusions and Future Work Model of particle burning behaviors xiii

14 7.2 High pressure combustion kinetics Impacts of char structure Carbon-carbon dioxide gasification mechanism Contribution of this work Suggestions for future work Appix A High Pressure Flow Reactor Characterization A.1 Flow rate settings for different experiment conditions A.2 Flow calculation for gases A.3 Flow reactor temperature profiles Appix B Uncertainty Analysis B.1 Uncertainty in measurements B.2 Uncertainty in parameter estimates B.2.1 Confidence interval of parameter estimates B.2.2 Graphical method for uncertainty estimation Appix C Program Source Codes C.1 Source code for the single char particle conversion model C.2 Source code for inversion of activation energy distribution from TPD C.3 Source code for the char combustion model C.4 Source code for the carbon-carbon dioxide gasification model Bibliography. 245 xiv

15 List of Tables Chapter 3 Table 3.1 Ultimate analyses of materials tested Chapter 4 Table 4.1 Reaction rate parameters for a 25% porosity char Chapter 5 Table 5.1 General trs of the effect of oxygen partial pressure with increased total pressure on the combustion rate of char particle Table 5.2 Classification criteria of char particle structure Table 5.3 Properties of partially reacted chars of Lower Kittanning coal at total pressure of 2 atm Table 5.4 Kinetic parameters for the char of Lower Kittanning coal at residence time of 47 ms Table 5.5 Summary of formulations for the burning behaviors of Group I, II and III char particles Chapter 6 Table 6.1 Values for reaction rate coefficients determined for data of Koenig Table 6.2 Values for rate coefficients determined for the data of Blackwood and Ingeme Table 6.3 Values for reaction rate coefficients for data of Tsai Appix A Table A.1 Flow rate settings for fuel and oxidizing gases for different experiment conditions Table A.2 Formulas for calculating the gas flow through metering valves Appix B Table B.1 Summary of the uncertainty analysis for the CO desorption rate. 186 xv

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17 List of Figures Chapter 1 Figure 1.1 Schematic flowchart of an advanced coal gasification-based system... 3 Figure 1.2 Schematic flowchart of an advanced PFBC combined system... 4 Chapter 2 Figure 2.1 Schematic diagram of the high pressure flow reactor systems and flow control system.. 9 Figure 2.2 Photograph of coal particles injected along the centerline of the laminar flow reactor. A flat diffusion flamelet burner is situated at the reactor inlet.. 10 Figure 2.3 Diagram of the sampling probe tip Figure 2.4 Configuration of the flow reactor and pressure vessels Figure 2.5 Schematic diagram of the pressurized thermogravimetric analyzer. 15 Chapter 3 Figure 3.1 Figure 3.2 Figure 3.3 Figure 3.4 Figure 3.5 Scanning electron micrographs of synthetic chars produced for testing. 21 Scanning electron micrographs of (left) raw Lower Kittanning coal particles and (right) raw almond shell particles 22 The cumulative and differential particle size distributions measured for the 16%-porosity char shown on both a number-basis and a volume-basis.. 24 Measured tap-density data for the 16%-porosity char and four of its partially reacted chars extracted from the laminar flow reactor at successive residence times CO 2 adsorption data. The weight of CO 2 adsorbed by a partiallyreacted sample of the 16%-porosity synthetic char for selected gasphase CO 2 /N 2 mixtures is recorded. The plateaus indicate complete CO 2 adsorption for each gas-phase mixture xvii

18 Figure 3.6 A typical BET plot. A measure of gas adsorption for selected partial pressures of CO 2 relative to the CO 2 saturation pressure at room temperature Figure 3.7 In situ surface areas measurements are used to determine the specific surface area structural parameter ψ. The lines were calculated using Equations (3.5) and (3.7), with the indicated values for ψ Figure 3.8 A typical thermogram and temperature profile measured in the PTGA. Particles are in an inert (100% N 2 ) environment up to 3100 s, at which time, they are exposed to an oxidizing environment. The thermogram shown is for a partially reacted sample of the 16%- porosity synthetic char exposed to 6 mol-% O 2 at 873 K Figure 3.9 Conversion rate as a function of conversion for the partially reacted sample of a 16%-porosity char exposed to 6 mol-% oxygen at 873 K. The char was extracted from the laminar flow reactor 47 ms after injection of the unreacted material into an environment containing 6 mol-% O 2 at nominally 1650 K Figure 3.10 Intrinsic reactivity of the partially reacted char of the 16%-porosity synthetic char that was extracted from the flow reactor 47 ms after injection into 6 mol-% O 2 at ~1650 K. Reactivity measurements were in 6 mol-% O 2 at 873 K 34 Figure 3.11 Conversion rates determined in isothermal and transient reactivity tests in 6 mol-% oxygen in the PTGA. The char particles were extracted from the laminar flow reactor at the 47-ms residence time in 6 mol-% oxygen at ~1650 K. The 16%-porosity synthetic char was used in the tests.. 34 Figure 3.12 Ratio of reactivities at different temperatures for the 16%-porosity synthetic char particles burning in 6 mol-% oxygen in the PTGA Figure 3.13 Some possible adsorbed oxygen atoms on carbon surface Figure 3.14 CO and CO 2 evolution during TPD tests on petroleum pitch and cellulose -derived chars Figure 3.15 CO and CO 2 generation rates in TPD as a function of (a) time and (b) temperature xviii

19 Figure 3.16 Figure 3.17 Figure 3.18 Figure 3.19 Plot of left-hand-side of Equation (3.22) as a function of inverse temperature in TPD Inversion of desorption activation energy distribution from the TPD CO desorption rate by assuming A 4 = /s.. 45 Effect of pre-exponential factor A 4 on the desorption activation energy distribution determined from the TPD CO desorption rate Least-square fittings of the CO and CO 2 desorption rate using Gaussian distribution approximation by assuming A = /s Chapter 4 Figure 4.1 Measured and calculated mode-of-burning profiles for the 16% synthetic char. The lines are calculated assuming power-law relations with the indicated values for α and β Figure 4.2 Measured and calculated mode-of-burning profiles for the 25% synthetic char. The lines are calculated assuming power-law relations with the indicated values for α and β Figure 4.3 Measured and calculated mode-of-burning profiles for the 36% synthetic char. The lines are calculated assuming power-law relations with the indicated values for α and β Figure 4.4 Concentric annular volume elements Figure 4.5 Calculated size, apparent density and specific surface area profiles during oxidation under Zone I conditions Figure 4.6 Calculated size, apparent density and specific surface area profiles during oxidation under Zone II conditions. (top) moderate temperature (bottom) high temperature Figure 4.7 Evolution of O 2 concentration profiles established inside a char particle (D p0 = 100 μm) burning under strong zone II conditions (T gas = 1600 K, y O2 = 6%), with surface oxygen partial pressure and particle diameter for corresponding conversions shown at the right. 67 Figure 4.8 Calculated particle temperature as a function of conversion at different oxidation conditions Figure 4.9 Effectiveness factor versus Thiele modulus xix

20 Figure 4.10 Figure 4.11 Figure 4.12 Figure 4.13 Mass remaining, apparent density and particle diameter profiles during oxidation of the 25% porosity char exposed to 6 mol-% oxygen at nominally 1650 K Measured and calculated mode-of-burning profiles for the synthetic chars. The solid lines are calculated based on the mode-of-burning relations given by Equations (4.40) and (4.42) with ζ evaluated using measured data Measured and calculated mode-of-burning profiles for the Lower Kittanning coal and almond shell biomass chars. The solid lines are calculated based on the mode-of-burning relations given by Equations (4.40) and (4.42) with ζ evaluated using measured data and ash content considered Comparison of the performance of power-law relations and the intrinsic reactivity based mode-of-burning model under Zone II conditions.. 79 Chapter 5 Figure 5.1 Figure 5.2 Figure 5.3 Figure 5.4 Figure 5.5 General trs of CO-to-CO 2 ratio as a function of inverse temperature 84 Calculated bulk and Knudsen diffusion coefficients as a function of temperature and pressure for different pore radius by assuming a porosity of 50%: (a) r p = 0.01 μm, (b) r p = 0.1 μm, and (c) r p = 1 μm.. 90 Different diffusion control regions and the relationships between temperature, pressure and mean pore radius calculated using (a) D 10D and DK, eff 10D (b) O D 2 O 100D and 2 K, eff DK, eff 100D as O2 O2 K, eff the controlling criteria by assuming a porosity of 50% Variation of intrinsic reactivities of 25%-porosity synthetic char with oxygen partial pressures at temperatures of (a) 873 K, (b) 1140 K and (c) 1600 K under purely chemistry-controlled conditions Effect of total pressures (2, 4 and 8 atm) on reaction rate at constant oxygen partial pressure (P O2 = 0.24 atm) for a 16%-porosity synthetic char. 94 xx

21 Figure 5.6 Reactivity as a function of conversion with constant oxygen partial pressure at different total pressures (1, 5, 10 and 20 atm) and temperature of 873 K for 25%-porosity synthetic char Figure 5.7 Reactivity and particle temperature with increasing total pressure and constant oxygen mole fraction at gas temperatures of 873 K for 25%- porosity synthetic char Figure 5.8 Calculated variations of (a) reactivities and (b) particle temperatures with respect to oxygen partial pressure at particle surface at gas temperature of 1600 K for 25%-porosity synthetic char.. 96 Figure 5.9 The depence of reactivity and particle temperature on total pressure with constant oxygen partial pressure (0.06 atm) at different gas temperatures (873, 1140 and 1600 K) for 25%-porosity synthetic char. 98 Figure 5.10 Reactivity as a function of conversion with constant oxygen partial pressure at different total pressures (1, 5, 10 and 20 atm) and gas temperatures of (a) 1140 K and (b) 1600 K for 25%-porosity synthetic char. 99 Figure 5.11 Transition from Zone I to Zone II burning with increasing total pressure and fixed gas temperature and oxygen partial pressure for 25%-porosity synthetic char. 99 Figure 5.12 Reactivity and particle temperature with increasing total pressure and constant oxygen mole fraction at gas temperatures of (a) 1140 K and (b) 1600 K for 25%-porosity char. 100 Figure 5.13 Change of burning zone with gas temperature at different total pressures: (a) 2 atm, (b) 10 atm and (c) 20 atm for 25%-porosity char. 101 Figure 5.14 The simplified mechanism of the evolution of a char s structure. 105 Figure 5.15 Scanning electron microscopic images of different kinds of particles collected from combustion of Lower Kittanning coal at nominal gas temperature of 1650 K, 12 mol-% O 2, total pressures of 2 atm and residence time of 47 ms: (a) Group I cenospherical char; (b) Group II mixed type char; (c) Group III dense char; and (d) ash particle embedded in char particles 106 xxi

22 Figure 5.16 Black-and-white binary images of (a) cenospherical, (b) mixed type and (c) dense char particle for analysis of porosity, wall thickness and void size. 108 Figure 5.17 Scanning electron microscopic images of char samples collected from combustion of Lower Kittanning coal at nominal gas temperature of 1650 K, 12 mol-% O 2, and total pressures of (a) 1 atm and (b) 2 atm Figure 5.18 Schematics of the density and size bins in the particle population balance model Figure 5.19 Schematics of a cenospherical char particle and its physical characteristics. 116 Figure 5.20 Comparison of effectiveness factor of Group I particles as a function of center void porosity from approximate theoretical calculation (Equation (5.18)) and empirical approximation (Equation (5.20)) Figure 5.21 A mixed type char particle can be approximated as a cenospherical particle with the same volume of carbonaceous material. 120 Figure 5.22 Fitting of calculated reactivities with measurements under TGA conditions. Symbols represent the measured data, and lines represent the calculation using the mechanism with parameters shown in Table Figure 5.23 Comparison between (a) measured and calculated mass remaining profiles, (b) apparent density for Lower Kittanning particles burning in 12 mol-% oxygen at nominally 1650 K. Calculated average particle temperature is compared with the gas temperature in (c). 124 Figure 5.24 Predicted mass loss profiles (a) and apparent density (b) for Group I, II and III char particles Figure 5.25 Distribution of particle temperature for (a) Group I, (b) Group II and (c) Group III chars at residence time of 72 ms Figure 5.26 The initial particle number, size and density distributions of (a) Group I, (b) Group II and (c) Group III chars (t = 47 ms). 129 Figure 5.27 Calculated particle number, size and density distribution of (a) Group I, (b) Group II and (c) Group III chars at 72 ms of burning in 12 mol- % O 2 at nominally 1650 K xxii

23 Figure 5.28 Figure 5.29 Figure 5.30 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-% O 2 at nominally 1650 K Comparison of mass loss profiles from experiments at oxygen mole fraction and total pressures of 1, 2 and 4 atm Comparison of mass loss profiles from experiments at constant oxygen partial pressure and total pressures of 1, 2 and 4 atm Chapter 6 Figure 6.1 Evolution rates of CO and CO 2 with time after a step change of 10% 13 CO 2 in Ar to pure Ar Figure 6.2 Figure 6.3 Figure 6.4 Figure 6.5 Figure 6.6 Figure 6.7 Figure 6.8 Figure 6.9 Comparison of experimental reactivity (symbols) and calculations (lines) vs. CO 2 concentration with p CO = 10 kpa at pressure of kpa Prediction of average char reactivity at various CO concentrations with p CO2 = 50 kpa and T = 1078 K Calculated surface complexes site fractions and reactivity as a function conversion for given condition: T = 1073 K, p CO = 10 kpa Relationship between p CO2 /R CO and mean partial pressure of CO at the fixed pressure of CO Prediction of gasification rate with CO 2 partial pressure p CO2 at fixed p CO = 0.5 atm (solid symbol) and 1 atm (open symbol) Gasification rates as a function of CO 2 partial pressure when no CO gas in inlet gas (open symbol) The variation of reactivities with conversion at different gasification temperatures. Symbols are experimental data, and lines are calculations based on the reaction mechanism The variation of reactivities with conversion at different total pressures. Symbols are experimental data, and lines are calculations based on the reaction mechanism xxiii

24 Figure 6.10 The variation of reactivities with conversion at different CO 2 mole fractions. Symbols are experimental data, and lines are calculations based on the reaction mechanism Figure 6.11 Fit kinetic parameters k i at different temperatures Figure 6.12 Calculated (a) surface oxide coverage fraction and CO concentration vs. conversion; (b) variations of reaction rates vs. conversion, at given gasification conditions (P = 1 atm) Figure 6.13 Calculated (a) surface oxide coverage fraction and CO concentration vs. conversion; (b) variations of reaction rates vs. conversion, at given gasification conditions (P = 20 atm) Figure 6.14 Comparison of calculated reactivities based on actual θ O and steadystate θ O,ss Figure 6.15 Linear curve fitting for experimental gasification rates in CO 2 /N 2 environment at 1200 K and 1273 K with Equation (6.31). s and i are values for slope and intercept, respectively Figure 6.16 Comparison of experimental gasification rates (symbols) at (a) 1200 K and (b) 1273 K in different gas compositions with calculated rates (lines) using the model developed Figure 6.17 Sensitivity analyses of reaction rate parameters at different pressures and CO mole fractions at a temperature of 1200 K Appix A Figure A.1 Calibration of the CH 4 mass flow controller Figure A.2 Calibration of the H 2 mass flow controller Figure A.3 Calibration of the air mass flow controller Figure A.4 Calibration of the N 2 mass flow controller Figure A.5 Values of flow coefficients at different turns open for S series metering value Figure A.6 Values of flow coefficients at different turns open for M series metering value Figure A.7 Correlation of flow rate with number of turns of S series metering valve for sample feeding entrainment N xxiv

25 Figure A.8 Correlation of flow rate with number of turns of M series metering valve for probe quenching gas Figure A.9 Axial temperature profiles above the burner surface. The measurements at 2 atm corresponds to higher inlet gas velocity; measurements at 4 atm corresponds to lower inlet gas velocity Figure A.10 Comparison of measured and simulated axial temperature profiles above the burner surface. Measurements are represented in symbols, and simulations are represented in lines Figure A.11 Calculated axial gas velocity at the centerline for different distances from the burner Figure A.12 Axial temperature profiles above the burner surface with residence times in the flow reactor Appix B Figure B.1 Figure B.2 Demonstration of the graphical method for the determination of uncertainty in reaction rate coefficients Demonstration of the graphical method for the determination of uncertainty in the activation energy Appix C Figure C.1 The structure of the program for the single char particle conversion model. 192 xxv

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27 Nomenclature A parameters defined in Equation (3.15) A i pre-exponential factor in Arrhenius form for reaction R i A m molecular cross sectional area of the adsorbent molecule (C 2 ) C i concentration of species i (mol/m 3, mol/m 2 ) C i,k (i,k) c p,g D eff D i,k D K D K,eff D O2/N2 D p D pi D po parameter in population balance model concerning surface regression rate for bin gas specific heat of the gas (J/mol K) effective overall oxygen pore diffusion coefficient (m 2 /s) parameter in population balance model concerning density reduction rate for bin (i,k) Knudsen diffusion coefficient (m 2 /s) effective oxygen Knudsen diffusion coefficient (m 2 /s) oxygen bulk diffusion coefficient into gas mixture (m 2 /s) particle diameter (m) internal particle diameter (m) external particle diameter (m) E i i k B k d activation energy in Arrhenius form for reaction R i intercept of line with vertical axis Boltzmann constant (J/K) oxygen mass transfer coefficient (s/m) k i k i,eff reaction rate coefficient for reaction R i effective reaction rate coefficient for reaction R i with distributed activation energies K O2 constants defined in Equation (4.36) m mass; parameter in modified Thiele modulus m C m p mass of carbonaceous particle material (g) mass of the particle (g) M ˆ i molecular weight of species i (g/mol) M R molar CO to CO 2 heterogeneous product ratio n global reaction order to oxygen concentration; fitting parameter in Equation (5.21) N AV Avogadro s number (mol -1 ) N i,k number of particles in size bin i and density bin k xxvii

28 Nu Nusselt number (taken as 2) P total pressure (atm) P 0 saturation pressure of CO 2 (atm) P g oxygen partial pressure in the ambient gas (atm) P s oxygen partial pressure at the outer surface of the particle (atm) q overall particle burning rate per unit external surface area (g/m 2 s) rf surface roughness factor r, r k radius, radius of volume element k (m) r p mean pore radius (m) ˆR gas constant (J/mol K) R C specific char reactivity (1/s) R ic intrinsic reactivity of the carbonaceous material (g/m 2 s) intrinsic reactivity evaluated at the external surface of the particle (g/m 2 s) R ic,ex R molar reactivity of oxygen (mol-o ˆiO2 2 /m 3 s) S carbon site density (#-sites/m 2 ) S gc specific surface area of particle (m 2 /gc) S g,tot total surface area of particle (m 2 /gc) Sh Sherwood number (taken as 2) S i i t T T b T g T m T p T w T sensitivity slope of line time (s) temperature (K) measured bead temperature (K) ambient gas temperature (K) mean temperature in the boundary layer surrounding the particle (K) particle temperature (K) wall temperature (K) surrounding temperature (K) V g pore volume per gram v total volume of CO 2 adsorbed (cm 3 ) v m monolayer adsorption volume (cm 3 /gc) V k volume of annular volume element k (m 3 ) sample weight on PTGA microbalance (g) W c xxviii

29 X a x i x C y i mass fraction of ash in the particle lower cutoff size for size bin i conversion of the carbonaceous material mole fraction of gas species i Greek Symbols α, β burning mode parameters in power-law relations δ particle wall thickness (m) ΔH effective heat of reaction (J/gC) ε emissivity of the char particle (taken as 0.85) ε b emissivity of the thermocouple bead (taken as 0.3) φ Thiele modulus φ m γ η modified Thiele modulus change in volume upon reaction per mole of oxygen consumed particle effectiveness factor κ parameter defined via Equation (4.18) λ, λ g gas thermal conductivity (W/m K) ν O2 θ θ f θ θ Ο θ Ο Ο θ v number of moles oxygen reacted per mole carbon gasified particle porosity fraction of free sites available for oxygen adsorption particle porosity adsorbed O atom site fraction adsorbed O-O atoms site fraction void porosity ρ apparent density (g/cm 3 ) ρ k lower cutoff density for density bin k (g/cm 3 ) ρ pc apparent density of ash-free particle (g/cm 3 ) ρ t true density of carbon (g/cm 3 ) σ Stefan-Boltzmann constant (W/m 2 K 4 ) σ i standard deviation in activation energy distribution (kj/mol) τ particle tortuosity factor (taken as 3) ψ surface area structural parameter xxix

30 ζ burning mode parameter in intrinsic reactivity-based model Subscripts 0 initial particle properties a properties of ash ave average property b property of thermocouple bead c properties of carbonaceous material ex property at the particle external surface I, II, III property for Group I, II and III char particle in property at the particle internal surface iso isothermal k properties at volume element k p properties of char particles sh property within the particle shell for cenospherical particle ss quasi steady-state value trans transient void property related with the central void in cenospherical particle xxx

31 Chapter 1 Introduction Coal, as an important energy resource, has been extensively studied over the past century. In this chapter, the current status of coal and biomass utilization is introduced, and some promising advanced coal and biomass conversion technologies are discussed. Motivation for the work is also presented, along with specific objectives. The organization of the thesis is discussed at the of this chapter. 1.1 Background Coal has been the dominant energy resource for more than a century, and currently in the 21 st century, it is still the second most important energy resource, accounting for 23% of the energy consumed in US and about 70% in China. At the current rate of consumption, coal can sustain the growth of energy demand for over 200 years. Although the reserves of coal are large compared to oil and natural gas, the utilization of coal has been restricted because of the traditional methods of coal conversion, such as combustion, which result in some complications in conversion efficiency and impacts on the environment. In a conventional coal-fired power plant, coal combustion in the boiler and furnace converts chemical energy in coal to heat, which is used to generate high temperature and high pressure steam to drive the steam turbine. It is known that coal combustion makes a net contribution to atmospheric CO 2. Traditional methods of coal conversion have higher associated CO 2 emissions per unit of useful energy produced than oil or gas conversion technologies. It has been claimed that the net release of greenhouse gas, CO 2, results in global warming. Currently, there is intensive research on the capture, sequestration and storage of CO 2. High temperature conversion of coal causes the emissions of nitrogen and sulfur in the coal as NO x and SO x, which are responsible for acid rain and smog problems. Coal combustion also contributes to particulate emissions in the atmosphere and toxic particulate disposal, and poses other environmental challenges due to trace species in the fuel. As a renewable energy resource, biomass has gained more and more attention around the world due to its environmental benignancy and abundance. Annually, around 220 billion dry tons of new biomass is produced, which is approximately 10 times as much energy as the world consumes from all energy resources [Hall et al., 1993]. The biomass conversion will 1

32 Chapter 1 make no net contribution to atmospheric CO 2 if the average growth rate is the same as the consumption rate, because the carbon released in biomass conversion, would be photosynthesized by new biomass growth. However, the global exploitation of biomass is unevenly distributed around the world. Biomass energy contributes only about 3% to the primary energy consumption for developed countries, and about 35% for developing countries. This exploitation is unsustainable with destroying forests followed by soil erosion, ecosystem imbalance, and climate issues. Biomass is widely dispersed and the energy content is low compared to other fossil fuels. Due to the low cost and high reserves of coal, research is directed to explore the emerging scientific and social issues in coal conversion and to develop more efficient and clean coal utilization technologies. Current fuel processing and exhaust scrubber technologies have made traditional coal combustion cleaner than ever. Combined cycle power generation system has been popular and recognized as a high efficiency and low emission technology. It has been shown that Integrated Gasification Combined Cycle (IGCC) and Pressurized Fluidized Bed Combustion (PFBC) are the most viable alternatives for the clean utilization of coal [Kristiansen, 1996; Takematsu and Maude, 1991]. The combined cycle systems could have thermal efficiency of 43%, compared to about 35% for traditional coal combustion systems. With the advances made in refractory materials, burner designs, high-temperature heat exchangers and combined cycle systems, coal-based power plants have the potential to be energy efficient, environmentally benign suppliers of chemicals, transportation fuels, and hydrogen as well as electricity. Some advanced hybrid technologies have been proposed, as exemplified in Figure 1.1. Coal, biomass and other solid fuels are gasified in a gasifier, and the generated syngas is purified in the gas cleanup system. The clean syngas can then be separated and used to generate electricity through combustion in gas turbines or through fuel cells. The syngas can also be used as raw material for chemicals. The gas turbine is integrated with a steam turbine by a heat recovery boiler to generate more electricity. In terms of environmental advantages, this system can recover more than 99.9% of sulfur, compared to 90% in current scrubbers in coal combustion systems. NO x and particulate emissions are also reduced in this kind of system [Lamarre, 1994]. Integrated Gasification Combined Cycle technology for coal is being tested but is still capital intensive and does not fully address the inherent CO 2 emissions. Technologies that use coal efficiently while avoiding or capturing CO 2 might allow use of coal in a low greenhouse gas future. CO 2 separation and storage technologies could leverage the vast amounts of 2

33 Introduction energy stored in coal reserves without increasing atmospheric concentrations, while coalbased hydrogen production might allow another pathway for coal energy to be cleanly distributed to the point of use. GASIFICATION-BASED SYSTEM CONCEPTS Gas Steam Cleanup/ Gasifier Component Separation Syngas CO/H2 Fuels Chemicals Coal Biomass Petroleum Coke/Residue Waste Feedstock Gaseous Constituent Particulates Solids Marketable Solid Byproducts Sulfur/ Sulfuric Acid Air Oxygen ASU Air Steam H2 Fuel Cell Combustion Turbine Exhaust H2 Exhaust Heat Recovery Steam Generator Transportation Fuels Combined Cycle Water Electric Power CO2 Stack Steam Turbine Electric Power Figure 1.1. Schematic flowchart of an advanced coal gasification-based system [Courtesy of the National Energy Technology Laboratory (NETL), USA]. The advanced PFBC combined system is a power generation system that combines a steam turbine supplied by steam from the pressurized fluidized bed boiler, and a gas turbine using the high-pressure and high-temperature exhaust gas from the boiler and a partial gasifier (Figure 1.2). Compared with those systems using only a steam turbine, the thermal efficiency is considerably improved. PFBC has the ability to burn low-quality fuels and, therefore, has fuel flexibility. The demonstrated PFBC technology has more than 90% SO 2 removal, with calcium-to-sulfur (Ca/S) molar ratio of 1.5 to 3.0, NO x emissions of 100 to 200 ppm through low temperature combustion. NO x emissions can be reduced further with the utilization of selective noncatalytic or SCR reduction technologies. The PFBC technology has the potential to achieve higher plant efficiency (up to 45%), with demonstrated 43% efficiency in a combined cycle arrangement. Also, this technology has lower capital costs than IGCC or pulverizedcoal with wet scrubbers. 3

34 Chapter 1 Figure 1.2. Schematic flowchart of an advanced PFBC combined system [Courtesy of the New Energy and Industrial Technology Development Organization (NEDO), Japan]. 1.2 Motivation and objectives Since coal is formed from sedimentary plant matter, it is mainly carbonaceous material bonded with other elements such as hydrogen, oxygen, nitrogen, sulfur. The older the coal, the less the fraction of these other elements in the coal. Biomass, on the other hand, can be treated as very young coal. When coal is exposed to high temperature environments such as that of combustion and gasification processes, the bonded hydrocarbons are released as light hydrocarbon gases and liquid tars. This is the devolatilization process, after which chars with porous structures are left. Subsequent oxidation of the char is much slower than devolatilization. Therefore, char oxidation is the most important process from the point view of enhancing conversion efficiency. An energy efficient design of a coal gasifier or burner should take advantage of all the carbon in the char. Due to the long conversion time of char compared to oil and natural gas, the residence times in the reactors have to be long enough to ensure complete conversion of char. Consequently, char conversion times determine the size of the reactor required. Coal and biomass conversion processes involve physical and chemical interactions between gases and solids, such as mass and heat transport between gases and solids, within the solids, and heterogeneous gas-solid chemical reactions. Understanding of the fundamental 4

35 Introduction reaction kinetics and heat and mass transport behaviors are important to accurately characterize the burning behaviors of carbonaceous materials. This fundamental understanding is also important in the design of reactors such as gasifiers and burners. In early times when the detailed information on the interactions between gas and solid was very limited, the modeling and design of combustion and gasification processes relied mainly on some empirical relations. However, with the advancement in knowledge of the conversion processes and regulations on the reactor performance, it is more and more necessary to develop models based on fundamental principles of chemistry and physics. Generally, the oxidation of char consists of the following processes: (1) the diffusion of the reactant gas through the external boundary layer of the particles, (2) the diffusion of reactant gas through the porous structure of char particles, (3) the adsorption of reactant gas molecules onto the char surface, (4) the chemical reactions on the char surface, (5) the desorption of product gases from the char surface, (6) the diffusion of the desorbed product gases through the porous structure of char particles and away from the particle. To fully understand the conversion of char, not only does the burning rate have to be known, but also the burning mode must be taken into account. Actually, to accurately calculate the burning rate of the char, both internal burning and external burning have to be characterized. Due to the existence of oxygen concentration gradients within the char particles, the internal and external burning are obviously different. The internal burning rate is expected to be slower than the external burning rate. The external burning is responsible for the reduction in particle size, and the internal burning contributes to the decrease in particle apparent density. Deping on the relative rates of step (1), (2) and chemical reactions (step (3) and (4)), different levels of internal and external burning are identified and categorized as three burning regimes. The burning behavior of char is also highly depent upon the structure of the char. The structure of the char significantly affects the active surface area for gas-solid reaction and the availability of reactant gas within the particles. Therefore, the effects of char structure on char burning behaviors cannot be ignored. The porous structure of the char can mainly be attributed to the release of gases and liquid tars during devolatilization. The void space and linkage between aromatic clusters can also form some small pores. These different pores are randomly connected, forming a network of pores in the particles through which the reactant and product gases diffuse within the particles. The chemical reactions occur on the walls of these pores. 5

36 Chapter 1 The efficiency of a combined cycle system relies on the performance of the gasifier. In order to optimize the gasification process, an understanding of the gasification kinetics is needed to distinguish the effects of gasification kinetics from those of heat transfer and mass transport on the configuration of the gasifier. A plausible reaction mechanism for char gasification that works in a wide range of reaction conditions is necessary to develop gasification models to predict the gasification process and then determine the optimal operating conditions for highest system efficiency. Industrial gasification processes cover a wide range of temperatures, pressures and gas compositions. The gasifier in an IGCC system generally operates at pressures between 1-30 atm and temperatures from 973 to 1773 K. CO 2 and H 2 O are the reactant gases in gasification, and CO and H 2 are the product gases that can inhibit the gasification rate by reacting with adsorbed oxygen or occupying free carbon sites for oxygen. PFBC operates at pressures higher than atmospheric pressure (5-20 atm) and temperatures from 1073 to 1173 K. Operating at higher pressure can increase the coal throughput, reduce the pollutant emissions and increase the reaction intensity [Harris and Patterson, 1995]. The effects of pressure on reaction rates can be investigated from three aspects: the effect of total pressure with a fixed partial pressure of reactant gas, the effect of total pressure with a fixed mole fraction of a certain reactant gas, and the effect of partial pressure of a certain reactant gas at a fixed total pressure. Fundamental understanding of the effect of operating pressure on reactions is essential to the development of pressurized coal conversion technologies. The overall objective of this thesis work is to gain the understanding needed to develop models that predict accurately coal and biomass conversion behavior in environments likely to be established in advanced combustion and gasification systems. Specific objectives are the following: 1. Under pulverized coal combustion conditions, char particles burn with reductions in both diameter and apparent density. The specific surface areas of chars also vary during mass loss. The objective is to develop the capability to predict accurately the chemical and physical characteristics of char particles undergoing mass loss at both low and high temperatures. Efforts are directed towards developing and validating models for char reactivity, mode of particle burning, and specific surface area evolution that dep upon the instantaneous state of the char. 6

37 Introduction 2. The objective of studying char oxidation at elevated pressure is to increase the data available on the conversion rates of coal chars at elevated pressures. The data are used to characterize the separate effects of total pressure, oxygen mole fraction and oxygen partial pressure on char reactivity, instantaneous apparent reaction order, particle temperature and pore diffusion limitation under Zone I and Zone II burning conditions. Models are developed to characterize the different char structures and their corresponding combustion behaviors and reactivity. 3. Commercial coal gasifiers are operated at elevated pressures and relatively high levels of CO are present. An understanding of the fundamental physical and chemical processes during the gasification of the char is required. The goal of this study is to develop and validate a C-CO 2 reaction mechanism that can accurately describe the carbon conversion rates observed in environments of high pressure and high CO concentration. 1.3 Organization of the thesis In Chapter 2, three different experimental facilities used in this work are described: a high pressure flow reactor (HPFR), a pressurized thermogravimetric analyzer (PTGA), and a Coulter multisizer. Synthetic chars with three different porosities were used in the experiments. The procedures for making these chars are described in Chapter 3. A series of experiments for characterizing char reactivity were conducted. These experiments include: particle size distribution, tap-density technique for apparent density, CO 2 -BET adsorption tests for surface area determination, char reactivity measurements in the PTGA, and temperatureprogrammed desorption (TPD) tests. These experimental methods are described in Chapter 3. The methods for data analyses are discussed as well. In Chapter 4, the widely used but empirically based power-law relations for char oxidation are investigated. To accurately characterize the burning behaviors of char, a single char particle conversion model is developed. Burning behaviors in the Zone I and Zone II burning regimes are calculated. Using the results obtained, a model for the mode of particle burning based on intrinsic reactivity is developed. The experimental data for synthetic chars, coal and biomass chars collected from the flow reactor were used to validate the model. In Chapter 5, using the single char particle conversion model, the separate effects of total pressure, oxygen mole fraction, and oxygen partial pressure on char reactivity, instantaneous apparent reaction 7

38 Chapter 1 order, particle temperature and pore diffusion limitation in different burning regimes are calculated. A char combustion model using a particle population balance model, accounting for different types of char structures, is developed and implemented for Lower Kittanning coal chars produced from high pressure flow reactor experiments. In Chapter 6, different kinds of C-CO 2 gasification mechanisms are reviewed. In light of the experimental results from isotope tracing, TPD, and transient kinetic tests, together with Ergun s [1959] and Blackwood and Ingeme s [1960] mechanisms, a new reaction mechanism is proposed. This reaction mechanism is then evaluated under the following different gasification conditions: a. low total pressure and low CO partial pressure; b. high total pressure and low CO partial pressure ; c. high total pressure and high CO partial pressure ; The commonly used steady state assumption for concentrations of surface complex is tested under some given gasification conditions. The error incurred due to this assumption is analyzed. In Chapter 7, the thesis work is summarized and future work is suggested. Appix A is used to present the calibration tests conducted on the high pressure flow reactor. The method of uncertainty analysis used in this work is explained in Appix B. The source codes for the models and some data processing methods are attached in Appix C. 8

39 Chapter 2 Experimental Facilities A series of experiments were designed to measure some key quantities that lead to evaluation of the critical parameters in the char-particle combustion and mode of burning models. These experiments include measuring specific surface areas, apparent densities, particle size distributions, and reactivities of char samples at various extents of conversion. A high pressure flow reactor, a thermogravimetric analyzer, and a Coulter multisizer were employed to enable such measurements for information on char-particle burning rates and physical properties during oxidation and gasification. 2.1 High pressure flow reactor (HPFR) Feeding Flow Control Feeder Chamber CH 4 H 2 Air N 2 /O 2 N 2 Flow Reactor Flow Control H 2 O Cooling H 2 O Flow Control N 2 Flow Reactor Chamber Pressurization Flow Control N 2 Quenching Flow Control Sampling probe Sampling Probe System Figure 2.1. Schematic diagram of the high pressure flow reactor systems and flow control system. To conduct the studies of char oxidation at elevated pressures, a high pressure flow reactor (HPFR) facility was built. This facility is shown in a schematic diagram in Figure 2.1. The 9

40 Chapter 2 HPFR consists of a flow reactor, pressure vessels, feeding and sampling system. The control panel regulates the gas and water flows into and out of the flow reactor. The systems will be discussed in detail in the following sections. The temperature and velocity profiles in the flow reactor are also characterized Laminar flow reactor onset of heating onset of char oxidation t=0 onset of devolitilization Partially reacted char samples. Figure 2.2. Photo of coal particles injected along the centerline of the laminar flow reactor. A flat diffusion flamelet burner is situated at the reactor inlet (Inverted from photo of Mitchell [2003]). An entrained laminar flow reactor system, designed to simulate environments typical of pulverized coal combustors, was used to produce chars at high heating rates and temperatures to obtain char samples at various extents of conversion in high-temperature, oxidizing environments (Figure 2.2). The laminar flow reactor is fed by an array of diffusion flamelets fueled by CH 4 -H 2 -O 2 -N 2 mixtures that can be adjusted to provide homogeneous post-flame environments in the temperature range 1100 K to 1800 K. Oxygen concentrations can be adjusted from trace amounts to approximately 30 mol-%. Pulverized coal or biomass particles are injected at the top of the reactor, along the centerline, at loadings that do not appreciably affect the post-flame temperature or oxygen concentration. Before injecting particles, the burner and the reactor wall are allowed to warm up for about 45 minutes to reach quasi steadystate thermal conditions. Deping upon flow rates, particle residence times up to 250 ms 10

41 Experimental Facilities can be accomplished in the 5x5-cm square quartz-walled flow reactor. Particle heating rates are from 10 4 to 10 5 K/s in the flow reactor, thus, the chars extracted from the reactor for examination are similar to those produced in practical pulverized coal-fired boilers and furnaces Particle feeding and collection systems The particle feeding system is operated based on a cylinder-piston type arrangement. The particles are loaded into a syringe and are forced through the syringe using a plunger attached to a stepping motor. The feeding rate can be changed by controlling the speed of the stepping motor. When particles are injected along the reactor centerline, they are entrained into the flow of post flame gases, and burn in the high-temperature oxidizing environment. The nominal feeding rate for particles is set to about 1 g/hr. With this low feeding rate, the gas environment is not significantly impacted by the burning of the particles; hence, the burning conditions among the particles are uniform. Also, particles remain near the centerline of the reactor for easy capture by the sampling probe. Hot gas in reactor H 2O N 2 Cooling water in Cooling water out Flue gas with particles Figure 2.3. Diagram of the sampling probe tip The high pressure flow reactor is equipped with a particle collection system consisting of an isokinetic, nitrogen-quench solids sampling probe designed to quench reactions and to capture all particles at selected distances below the reactor inlet (Figure 2.3). The probe is made of stainless steel with a water-cooled jacket at the outer surface to protect the probe from overheating. The cooling water flow rate is adjusted so that the probe is cooled sufficiently to 11

42 Chapter 2 ensure water condensation on the external surface of the probe. In order to quench the reaction sufficiently, the flow rate of quenching gas (nitrogen) is adjusted to assure that the temperature of the gas right after mixing is below 600 o C. The cooling rate is estimated to be about 10 6 K/s [Campbell, 2005]. The isokinetic condition is obtained by regulating the quenching gas and the exhaust gas flow rates so that the gas velocity entering the probe is about the same as the velocity of gas at that point in the reactor when the probe is absent. The char particles flowing through the probe are collected on a filter paper placed in the flow path. Due to the low temperature in the probe, the char particles do not experience oxidation as they pass through the probe, and the particles collected on the filter paper are essentially representative of the char at the location of the probe tip Pressure vessels For pressurized combustion experiments, the laminar flow reactor is enclosed by a pressure vessel (Figure 2.4). The pressure inside the vessel is controlled by a back-pressure regulator placed downstream in the exhaust line. The reactor pressure vessel is made of a seamless steel tube with outside diameter of 50.8 cm, wall thickness of 1.27 cm, and length of 127 cm. There are 4 quartz viewing windows installed in the vessel wall at a height of 50.8 cm above the bottom of the vessel. The vessel is sealed from the environment by O-rings. The pressure vessel can sustain total pressures up to 50 atm and temperatures up to 90 o C. A Series-M BiSlide assembly is used within the reactor pressure vessel to support and move the flow reactor up and down. The maximum travel distance of the reactor is about 28 cm, which is the maximum distance between the probe tip and the burner surface. There are six ports in the side of vessel wall and six ports at the bottom of the vessel (diameter of 1.27 cm) for gas tubing and electrical wiring. A 5-cm port is located in the center of the vessel bottom for the sampling probe. The vessel pressure is monitored with a pressure gauge. Over-pressurization is prevented by placing a burst disc in parallel with the exhaust line. All exhaust lines up to the backpressure regulating valve are water cooled. The flow reactor can move up and down inside the vessel, and the sample collecting probe is positioned at the bottom of the vessel, along with the reactor centerline. Residence times of the particles are varied by moving the reactor. A particle feeding system is positioned inside another pressure vessel, the feeder pressure vessel (Figure 2.4). The feeder pressure vessel is made by welding a tube with diameter of 12

43 Experimental Facilities 30.5 cm and wall thickness of 0.95 cm together with a dome. The closure cap can be screwed onto the vessel, and O-ring sealing is applied. A 1.27 cm port and a 2.54 cm port are used to connect the feeding tube to the flow reactor and for gas tubing and electrical wiring. The pressure in the feeding pressure vessel and the pressure in the flow reactor pressure vessel are maintained about equal through the central feeding tube at the burner. Feeder Pressure Vessel Burner Flow Reactor Vessel Flow Reactor Movable Stage View Window Figure 2.4. Configuration of the flow reactor and pressure vessels Flow reactor temperature measurements Temperature measurements in the flow reactor were made using a type R platinumplatinum 13% rhodium thermocouple having a bead diameter of inch. Since the measurements are generally made for temperatures above 1200 K, there is significant radiative loss from the thermocouple bead, resulting in a lower measured temperature than the actual gas temperature. To determine the actual gas temperature, account is made for the radiative loss. Since the conduction losses from the bead are negligible compared to the radiative 13

44 Chapter 2 losses, the actual gas temperature can be estimated from the following equation [Fristrom and Westenberg, 1965]: b b g b b Nu λg 4 4 ( ) ε d σ T = T + T T (2.1) where T g is the gas temperature, T b is the measured bead temperature, T is the wall temperature in the surroundings, taken as 500 K, ε b is the bead emissivity, taken as 0.3 [Mitchell et al., 1984], d b is the bead diameter, σ is the Stefan-Boltzmann constant, Nu is the Nusselt number of the bead, taken as 2, and λ g is the thermal conductivity of the gas. Typically, at a temperature of about 1600 K, the magnitude of the radiation correction is about 50 K Characterization of flow reactor Before the combustion experiments are performed on the high pressure flow reactor, the flow reactor has to be characterized in terms of temperature and velocity profiles. 1. The flow control valves and the mass flow controllers have to be calibrated. 2. The axial flow reactor temperature profiles have to be measured. The temperature distribution along the centerline of the flow reactor as a function of distance away from the burner surface are determined from these measurements. 3. The axial velocity profiles in the flow reactor have to be estimated. Based on the experimental conditions and temperature measurements, a CFD code (FEMLAB) is used to simulate the both temperature profiles and velocity profiles. Axial centerline velocity profiles are used to estimate the residence times in the reactor. A detailed description of these characterization experiments can be found in Appix A. 2.2 Pressurized themogravimetric analyzer (PTGA) The pressurized thermogravimetric analyzer (PTGA) is designed to accurately monitor sample weight change when exposed to a desired gas mixture in a temperature-controlled environment. A schematic diagram of the PTGA is shown in Figure 2.5. The PTGA systems consist of furnace chamber, reaction chamber, microbalance chamber, control panel and data acquisition system. The PTGA can measure weight changes of material over a wide dynamic 14

45 Experimental Facilities temperature range (300 to 1373 K) at a wide range of pressures (10-5 torr to 100 atm) in controlled environments [Campbell, 2005]. Microbalance Chamber Balance Control Purge Gas In - He Gas Out Furnace Gas In - N 2 Data Acquisition Sample Pan Reaction Chamber Reaction Gas In Furnace Chamber Furnace Gas Out Thermocouple Temperature Control Figure 2.5. Schematic diagram of the pressurized thermogravimetric analyzer Reaction chamber The reaction chamber is where the gas-solid reactions occur. The reaction chamber is made of a cylindrical quartz tube with an internal diameter of 3.8 cm. Samples are placed on a sample pan that hangs in the middle of the reaction chamber. The sample pan is attached to one arm of the microbalance by a nichrome wire Furnace chamber The furnace chamber is an electrically heated enclosure around the reaction chamber, and the furnace gas flows inside the furnace chamber and around the reaction chamber. Generally, the furnace gas is nitrogen. In oxidation or gasification experiments, the furnace gas helps maintain the reaction chamber temperature in accordance with the desired setting and cools 15

46 Chapter 2 the reaction chamber wall, preventing overheating. The furnace gas also helps balance the pressure inside and outside of the reaction chamber Microbalance chamber The sample weight is monitored by a Thermo digital recording microbalance with an accuracy of 1 μg over a scale up to 10 g. The microbalance is enclosed by a pressure chamber, which is purged by helium gas during all the experiments. The microbalance chamber is connected to the reaction chamber, and the mixture of reaction and purge gas exhausts at the same port to the ambient Control panel The control panel is configured to control all the gas flows into and out of the PTGA system. The main source gases used in PTGA include the reaction gas, the furnace gas and the purge gas. The reaction gas is either nitrogen, oxygen, CO 2 or mixtures of these gases. The furnace gas is typically nitrogen; the purge gas is helium. The flow rates of these gases are controlled by mass flow controllers. The exhaust is open to the ambient for atmospheric pressure experiments, and for pressurized experiments, the exhaust flow is restricted by a back-pressure regulator to control the pressure in the chambers Data acquisition system The data acquisition system interfaces with the temperature controller and the microbalance controller, collecting the real-time data from the controllers and sing the user commands to the controllers. The temperature, sample weight, chamber pressure and gas flow rates are acquired and recorded at intervals of 5 seconds for the duration of each experiment. The temperature measurement is made by inserting a K-type thermocouple in the reaction chamber. The thermocouple bead is about 5 mm below the bottom of the sample pan. Due to the proximity of the thermocouple and the sample, the gas and sample temperatures are nearly the same. A sensor panel is configured to analyze the gases leaving the PTGA reaction chamber, and the concentrations of O 2, CO 2 and CO can be measured and recorded. According to Campbell [2005], during the transport of gases from the sample pan to the sensors, the extent of gas phase reactions is small. Therefore, the gas concentrations measured by the sensors are representative of the gas concentrations produced after gas-solid reactions at the sample pan. 16

47 Experimental Facilities 2.3 Coulter multisizer Particle size distributions are measured using a Coulter multisizer, which uses an electroresistive method to determine particle size and the size distribution. Generally, the measurements are made for over 20,000 particles in each run. The equipment has a reservoir that is filled with 1% wt/vol NaCl electrolyte solution. An orifice tube is submerged in the electrolyte solution. The orifice tube and the reservoir are connected only through an orifice with diameter larger than the maximum particle size expected. One electrode is inserted in the electrolyte solution reservoir, but out of the orifice tube, and the other electrode is inserted within the orifice tube. The sample particles are dispersed in the electrolyte solution, and when a particle passes through the orifice, the electric conductance varies deping upon the size of the particle. Therefore, the particle size and number can be determined based on the changes of the electric signals. 17

48 18

49 Chapter 3 Test Materials, Experimental Methods and Data Analyses In order to investigate the burning behaviors of pulverized coal and biomass chars and validate the combustion models developed, several different materials (three kinds of synthetic chars, one coal and one biomass) were studied. The methods for producing synthetic chars are presented in this chapter. The experimental methods to characterize the properties of these materials are introduced. The approaches used in this study to interpret and analyze the data are also developed and discussed. 3.1 Test materials Synthetic chars Synthetic chars with carefully controlled properties were used in oxidation tests to provide data free of the uncertainties associated with coal and biomass heterogeneity. For example, real coals contain many minerals whose oxides can potentially catalyze reactions controlling the overall char conversion rate. Particle-to-particle variations in mineral matter content t to scatter observed reactivities, rering data interpretation difficult. Synthetic chars are free of mineral matter, thereby eliminating uncertainties associated with possible catalysis. Real coals also have pores that are irregularly shaped, have varying cross-sections, and are randomly oriented. The various unknown degrees of anisotropy and inhomogeneity of the pore structure increase data scatter as well. Synthetic chars can be produced with controlled porosities thereby minimizing uncertainties associated with the availability of internal particle surfaces. It has been shown that the synthetic chars can facilitate the study of char burning phase of coal combustion. This kind of synthetic carbonaceous material has similar combustion characteristics as coal char [Senior and Flagan, 1984]. The procedure for making the synthetic chars was developed by Senior [1984]. Furfuryl alcohol is polymerized with p-toluenesulfonic acid in a water bath maintained at a temperature of o C, forming a monomer. After the monomer is kept in the bath for 10 minutes, it becomes a thick liquid polymer. The furfuryl alcohol polymer is thinned with acetone so that pore-formers and inorganic inclusions can be mixed into the polymer. The polymer is cured 19

50 Chapter 3 in bulk in an inert environment at 125 o C for 6 hours, and then at 200 o C for 10 hours. After the polymer is completely cured, it is carbonized at 550 o C for 1 hour. The glassy carbon produced is a low surface area, low porosity material. In order to increase the surface area and microporosity, nominally 20 nm carbon black particles are added just after the initial polymerization, using acetone to thin the mixture. Carbon black increases the porosity by causing the carbonized furfuryl alcohol matrix to crack around the locations of the carbon black inclusions [Schmitt et al., 1976; Levis and Flagan, 1989]. A microporous structure is established within the carbonaceous material with the largest pores about 0.05 μm in diameter. Pore-formers, mixed into the liquid polymer prior to carbonization, are used to control the macroporosity of the char. The pore-former agent employed in this study was the spore of the lycopodium plant with a tight size distribution. Akan-Etuk and Niksa [1991] found that the addition of lycopodium plant spores produced macropores of a uniform size of nominally 20 μm. Overall char porosity is controlled by monitoring the spore-to-polymer weight ratio. The resulting char is then pulverized to a size range between μm. Shown in Figure 3.1 are scanning electron micrographs of three synthetic chars produced for use in this study, chars having porosities of 16%, 25%, and 36%. The 16%-porosity char was produced with only carbon black and hence, has only a microporous structure with the largest pores being about 0.05 μm in diameter. The 25%- and 36%-porosity chars were produced using both carbon black and lycopodium spores and hence, have bimodal pore structures: a micropore structure with all pores less than 0.05 μm in diameter and a macropore structure with all pores near 20 μm in diameter. The same amount of carbon black was used when producing each of the chars, thus the microporous structures of the chars are deemed to be comparable Other materials Lower Kittanning coal, a low-volatile bituminous coal from Pennsylvania having an ashcontent of 10.3%, was also studied. The Lower Kittanning coal was ground and screened by a combination of wet and dry sieving to yield a distribution of particles having sizes of μm and μm. Almond shells, a high ash-content biomass, were also studied. The raw almond shell particles were screened to eliminate sizes greater than 1 millimeter. The SEM 20

51 Test Materials, Experimental Methods and Data Analyses images of the Lower Kittanning coal and almond shell biomass are shown in Figure 3.2. Shown in the Table 3.1 are the ultimate analyses of the synthetic char, Lower Kittanning bituminous coal and almond shell biomass that were examined. 16%-porosity char 25%-porosity char 36%-porosity char Figure 3.1. Scanning electron micrographs of synthetic chars produced for testing. 21

52 Chapter μm Figure 3.2. Scanning electron micrographs of (left) raw Lower Kittanning coal particles and (right) raw almond shell particles. Element Table 3.1. Ultimate analyses of materials tested Synthetic char Lower Kittanning coal Almond shell biomass Carbon Hydrogen Nitrogen Sulfur Ash Oxygen < Cl - <0.01 < Experimental methods and data analyses A series of experiments were conducted in the flow reactor and PTGA to characterize the properties of the materials tested, such as the apparent density, particle size distribution, surface area and char reactivity Extent of mass loss Extents of mass loss were determined for each char sample extracted from the laminar flow reactor. For the ash-free synthetic chars, m c /m c0 = m p /m p0 ; values were determined from the weights of material fed to the flow reactor (m p0 ) and the weights of char collected (m p ). For the coal and biomass chars, the weight fraction of ash in each extracted sample (X a ) was 22

53 Test Materials, Experimental Methods and Data Analyses determined by completely burning an aliquot of the sample in an oxidation test in the PTGA to obtain the weight of the ash in the aliquot. The weight fraction of ash in each aliquot was calculated (X a = (weight of ash in aliquot)/(initial weight of aliquot)). The unreacted material was treated similarly to obtain X a,0. Assuming that all the ash in a given coal or biomass particle remains in the particle during devolatilization and oxidation in the flow reactor, the fractional mass remaining at the time of extraction from the laminar flow reactor is calculated, as follows: m p m po = X a,0. (3.1) X a Particle size distribution The particle size distributions of the feed materials and of solid samples extracted from the flow reactor were measured using a Coulter Multisizer, an instrument that uses an electroresistive method for measuring the size distribution of susped particles [Mitchell and Akanetuk, 1996]. Approximately more than 20,000 particles were monitored for each sample, and the sizes were distributed into 256 channels of the Multisizer, spanning the 6.0 to 185 μm size range. This yielded the numbers of particles in 0.71-μm size intervals starting from about 6 μm. Presented in Figure 3.3 are the particle size distributions measured for the 16%-porosity char used in the oxidation tests. The distributions are shown on both a number-basis and a volume-basis, the volume-basis emphasizing the more massive particles. The cumulative distributions are shown in the panel on the top and the differential distributions are shown on the bottom. For the char extracted from the flow reactor at a residence time of 47 ms, the number-averaged particle diameter is about 56.6 μm, and about 20% of the particles have diameters below 20 μm. The volume-averaged (or mass-averaged) particle diameter is μm. Note that very little of the total amount of mass that has to be burned is contained in particles having diameters less than 20 μm. For this reason, volume-averaged diameters are used in our approach to validate the mode of burning model. They are representative of where most of the mass resides. 23

54 Chapter 3 % Cumulative number % Number per μm D pn 0 ms, ms, ms, ms, ms, Particle diameter, μm D pn 0 ms, ms, ms, ms, ms, 41.6 % Cumulative mass % Mass per μm D pm 0 ms, ms, ms, ms, ms, Particle diameter, μm D pm 0 ms, ms, ms, ms, ms, Particle diameter, μm Particle diameter, μm Figure 3.3. The cumulative and differential particle size distributions measured for the 16%- porosity char shown on both a number-basis and a volume-basis Apparent density measurements The apparent densities of the chars were determined employing a tap density procedure in which the weights and volumes occupied by char samples introduced into a graduated tube are measured [Mitchell et al., 1992]. The outside of the tube is tapped until the particles are wellsettled before the volume is recorded. Data are obtained for different amounts of char added to the tube, and then plotted, weight versus volume occupied. The slope of the line plotted is the bulk density of the material in the tube. Assuming that the packing factors for the raw material and its partially reacted char are the same (a good assumption for particles of nominally the same size), the ratio of the slopes of the lines for the char and parent material equals the ratio of the apparent density of the char to that of the parent material, ρ p /ρ p0. Based on data obtained with a variety of coal chars, a packing factor of 0.42 has been found to be adequate to describe the packing of particles in the size range 5 to 200 μm. 24

55 Test Materials, Experimental Methods and Data Analyses Tap-density measurements obtained with the 16%-porosity synthetic char and four of its partially reacted chars that were extracted from the laminar flow reactor at successive residence times are shown in Figure 3.4. The uncertainty in sample mass measurement by table balance is ± 10 μg, and the uncertainty in volume measurement is ± 10 μl. Therefore, the uncertainty in the tap density measurement is less than ± 1%. It is also noted that the R- squared values for the linear fitting of mass-volume data are very close to unity. The slopes of the lines decrease with time, indicating that during oxidation in the hot gaseous environment, the apparent density of the carbonaceous particle material progressively decreased with mass loss. Mass (g) time (ms) ρ a (g/cm 3 ) R-squared values t = 0, ρ a = t = 47, ρ a = t = 72, ρ a = t = 95, ρ a = t = 117, ρ a = %-porosity Volume (μl) Figure 3.4. Measured tap-density data for the 16%-porosity char and four of its partially reacted chars extracted from the laminar flow reactor at successive residence times Specific surface area measurements The specific surface areas of the feed materials and partially reacted char samples were measured via gas adsorption techniques using carbon dioxide as the adsorption gas at 298 K [Anderson et al., 1965; Walker and Kini, 1965; Walker and Patel, 1970]. The adsorption data were analyzed using the approach of Brunauer, Emmett, and Teller [1938] for (BET) surface areas. Surface areas were calculated assuming that micropore volume is approximately equal to the BET monolayer capacity [Mahajan and Walker, 1978]. A value of 25.3 nm 2 was used for the surface area of the CO 2 molecule. The CO 2 adsorption measurements were made in the PTGA at a total pressure of 10 atm at room temperature. Making the adsorption measurements at an elevated pressure increases the 25

56 Chapter 3 dynamic range for gas adsorption. The analytical procedure and method for making buoyancy corrections to the weight measurements were formalized by Tsai [1998]. The sample for testing is placed in the balance pan of the PTGA, and the PTGA chamber is pressurized with helium to 10 atm. Nitrogen is then allowed to flow into the reactor at a fixed flow rate, displacing the helium. After the sample weight stabilizes in the nitrogen environment, a mixture of CO 2 in N 2 is admitted into the reactor, maintaining the total flow rate at the fixed value. When the CO 2 comes into contact with the sample in the balance pan, an equilibrium amount of CO 2 is adsorbed onto the sample over a period of time. The amount adsorbed deps on the partial pressure of CO 2 in the mixture and the saturation pressure of the CO 2 at the temperature in the chamber. After the sample weight stabilizes, the CO 2 /N 2 mixture is changed. An equilibrium amount of CO 2 is adsorbed consistent with the new CO 2 partial pressure in the chamber. Adsorption data obtained with a partially-reacted sample of the 16%-porosity synthetic char that was extracted from the flow reactor 47 ms after synthetic char injection are shown in Figure 3.5. Each step change in weight recorded by the PTGA balance corresponds to a step change in the CO 2 partial pressure. Buoyancy corrections are made in order to ensure accurate measures of the weight of CO 2 adsorbed in the high-pressure environments so as to permit accurate determination of the specific surface area. Figure 3.5. CO 2 adsorption data. The weight of CO 2 adsorbed by a partially reacted sample of the 16%-porosity synthetic char for selected gas-phase CO 2 /N 2 mixtures is recorded. The plateaus indicate complete CO 2 adsorption for each gas-phase mixture. 26

57 Test Materials, Experimental Methods and Data Analyses Specific surface areas were determined from the adsorption data using the Brunauer- Emmett-Teller (BET) analysis, assuming multi-layer adsorption of CO 2. Shown in Figure 3.6 is the characteristic BET plot, which gives the adsorption quantity P/[v(P 0 P)] as a function of P/P 0, P 1 1 = + c P v P P v c v c P, (3.2) ( ) 0 m m 0 where P is the CO 2 partial pressure, P 0 the saturation pressure of CO 2 at the adsorption temperature, and v is the total volume of CO 2 adsorbed, determined from the weight gain measurements. The uncertainty in the reported data is ± 6% as represented by the error bars in the figure, which can be estimated using the method presented in Appix B. The straight line observed can be described by the intercept i and the slope s: 1 i = vc m and c 1 s = vc. m (3.3)(3.3a,b) The linearity supports multi-layer adsorption of CO 2 on the carbonaceous material. From the slope and intercept of this line, the monolayer adsorption volume v m (cm 3 /gc), is determined, from which the specific surface area (m 2 /g) of the sample is calculated [Tsai, 1998]: S g v N A m AV m 20 = (1 10 ). (3.4) where A m (C 2 ) is the molecular cross sectional area of the adsorbent molecule P/(V(P o -P)) = 6.837E P/P o R-squared value = P/(V(P o -P)) (g/cm 3 ) P/P o Figure 3.6. A typical BET plot. A measure of gas adsorption for selected partial pressures of CO 2 relative to the CO 2 saturation pressure at room temperature. 27

58 Chapter 3 During selected oxidation tests, in situ surface area measurements were made. Before the start of heating in an oxidation test, the nitrogen in the reaction chamber is displaced by CO 2, and the pressure is raised to 10 atm. Carbon dioxide adsorption measurements are made, as described above. The pressure is then lowered to atmospheric, and the CO 2 is displaced by nitrogen. The oxidation test is initiated, as described. At selected extents of conversion, the PTGA heating element is turned off and the temperature in the reaction chamber is allowed to decrease to room temperature, quenching the char oxidation process. The oxygen/nitrogen reactive mixture is displaced by nitrogen, and the pressure is raised to 10 atm. Again, carbon dioxide adsorption measurements are made using different CO 2 /N 2 mixtures. Afterwards, the pressure is lowered to 1 atm, the CO 2 is displaced by nitrogen, the sample is re-heated to the reaction temperature, the nitrogen is displaced by the reactive gas mixture, and char oxidation is continued until the next time the heating element is turned off and another CO 2 adsorption measurement is made. An in situ surface area measurement is made at complete burnoff. This gives the surface area of the ash (S ga ), in the sample being tested. Our results support a nominal value of 5 ± 7 m 2 /g (taking non-negative values) for the specific surface areas of all ashes examined in this study. The in situ surface area measurements yield the char-particle total specific surface area (S gp ) as a function of char conversion, from which the specific surface area of the carbonaceous material (S gc ) as a function of char conversion is calculated, assuming that the particle s total specific surface area is distributed between the ash and carbonaceous components on a mass-weighted basis: ( 1 ) S = X S + X S. (3.5) gp a ga a gc Here, X a is the mass fraction of the ash in the char particle. The reaction surface area per unit of particle volume of coal-derived and biomass-derived chars attains a maximum during burning under Zone I conditions due to the opposing effects of pore growth and pore overlap as mass is lost. The surface area initially increases due to micropore reactions and then it decreases due to pore wall destruction and merging. The rate of decrease deps upon the competition between area formation and area destruction. Bhatia and Perlmutter [1980] developed a pore evolution model that accounts for these effects, and found that the following relation adequately reflects the volumetric surface area evolution of the carbonaceous particle material during conversion: 28

59 Test Materials, Experimental Methods and Data Analyses ( ) ψ ( ) Sv = Sv,0 1 xc 1 ln 1 xc. (3.6) Here, x c is conversion of the carbonaceous material (i.e., char-particle conversion on an ashfree basis) and ψ is a structural parameter ( ( ) 2 = 4πL 1 θ / S ), in which L v,0 is the v,0 0 v,0 equivalent length of overlapping pores per unit volume of char, θ 0 is the initial char porosity, and S v,0 is initial volumetric surface area. The volumetric surface area, S v, can be related to specific surface area per unit mass S g by S v = ρ c S gc. Under Zone I burning conditions, the burning occurs uniformly throughout the particle, and mass loss is directly proportional to density change, i.e., (1-x c ) = ρ c /ρ c0. Thus, Equation (3.6) can be transformed to specific surface area evolution with conversion in the Zone I burning regime: ( ) Sgc = Sgc0 1 ψ ln 1 xc (3.7) The structural parameter ψ can be determined from fits to measured specific surface areas. The uncertainty in structural parameter fitting is shown in the figure with an interval for confidence level of 95%. The method of this uncertainty analysis is discussed in Appix B. This is demonstrated in Figure 3.7, which shows in situ measurements of specific surface area of a partially-reacted sample of a synthetic char undergoing oxidation under Zone I conditions. The different indepent measurements exhibit a certain extent of scatter, with an estimated uncertainty of about ± 18%. This uncertainty in the surface area measurements is represented by the error bars in the figure. As carbon is gasified, by 40% conversion the specific surface area of the char is noted to increase by more than a factor of 2, and by 97% conversion the specific surface area of the char increase by a factor of about 7. A value for ψ of 7 fits the data, in the least squares sense. 29

60 Chapter 3 8 ψ = S gc /S gc, Conversion, x C Figure 3.7. In situ surface areas measurements are used to determine the specific surface area structural parameter ψ. The lines were calculated using Equations (3.5) and (3.7), with the indicated values for ψ Char reactivity measurements The intrinsic chemical reactivities of chars extracted from the flow reactor at successive residence times were measured via gravimetry using the PTGA. Since the partially reacted chars were extracted while burning under Zone II conditions, the measured reactivities reflect the consequences of carbon deactivation experienced by the char particles up to the time of extraction. Since the char particles experienced higher temperatures in the flow reactor than they experienced in the gravimetry tests, no carbon deactivation is expected to occur during the oxidation tests in the PTGA. The measured reactivity is expected to accurately reflect the reactivity of the char at the time of extraction from the flow reactor. Weight loss measurements were made under both isothermal and transient conditions in the PTGA, at atmospheric pressure. In the isothermal tests, the char was heated at a rate of 25 K/min to the desired reaction temperature, and then weight loss was monitored at constant temperature until the combustible material was completely burned. In the transient tests, temperature was varied in a prescribed manner (usually a ramped temperature profile) during the course of char oxidation. Such transient tests provide more accurate determination of activation energies of the rate controlling reactions than do the steady-state tests alone. Accurate assessment of chemical reaction effects requires that mass transport limitations are minimized during weight loss measurements in the PTGA. Using a char sample produced 30

61 Test Materials, Experimental Methods and Data Analyses from a bituminous coal, tests at various temperatures and with different sample sizes indicated that 873 K was the highest temperature at which there were negligible mass transport effects during char oxidation of 100-μm diameter particles in the PTGA. At higher temperatures, the overall mass loss rates were found to dep on the amount of material placed in the balance pan of the PTGA, indicative of mass transfer limitations. With a char sample produced from almond shells that had an intrinsic reactivity about 1000 times higher than that of the coal char, tests indicated that mass transport limitations become significant at temperatures near 700 K. Accordingly, only reactivity tests performed at temperatures below 873 K were used to extract kinetic parameters with coal and synthetic chars and only reactivity tests performed at temperatures below 700 K were used to extract kinetic parameters with biomass chars. A typical thermogram (measured weight loss profile) and temperature profile for an isothermal test at 873 K, employing a heating ramp of 25 K/min, are shown in Figure 3.8. A partially reacted sample of the 16%-porosity synthetic char was used in this test. In the test, the char particles were purged in an inert environment at ambient temperature and pressure for 5 minutes, and then heated at an average rate of 25 K/min to 873 K. The particles were then held at this temperature in the inert environment for 30 minutes, after which time, the particles were exposed to 6 mol-% O 2 at the 873 K isotherm until complete burnout. The purge in the inert environment served to drive off any adsorbed oxygen complexes from particle surfaces prior to testing. Figure 3.8. A typical thermogram and temperature profile measured in the PTGA. Particles are in an inert (100% N 2 ) environment up to 3100 s, at which time, they are exposed to an oxidizing environment. The thermogram shown is for a partially reacted sample of the 16%- porosity synthetic char exposed to 6 mol-% O 2 at 873 K. 31

62 Chapter 3 The thermograms were analyzed to determine the ash content of the material and to determine the char reactivity in the test conditions. The specific char reactivity at any time t after the onset of char oxidation was calculated using the following equation, which allows for the combined effects of chemical reaction and changes in surface area that occur during oxidation: 1 dw 1 dx R = = R S c c c i, c gc Wc dt (1 xc) dt. (3.8) Here, Rc is the specific char reactivity, the char reactivity per unit mass of char; Wc is the char weight at time t; x c is char conversion, ash-free; and R ic, is the intrinsic char reactivity per unit of char surface area. Rc, as a function of conversion, is determined from the instantaneous differentials of the weight loss curves. Specific surface area as a function of conversion permits the determination of R ic, as a function of conversion. Shown in Figure 3.9 is a plot of the conversion rate (dx c /dt) as a function of conversion for the 16%-porosity char particles exposed to 6 mol-% oxygen at 873 K. Note that the char exhibits an initial increase in conversion rate followed by a decrease in the rate. This is due to the combined effects of variations in surface area and intrinsic chemical reactivity during char oxidation. The surface area initially increases as closed-off pores are opened, and then decreases as pores merge and coalesce whereas the intrinsic reactivity initially increases as the adsorbed oxygen atom concentration builds up to its quasi-steady-state level. Figure 3.9. Conversion rate as a function of conversion for the partially reacted sample of a 16%-porosity char exposed to 6 mol-% oxygen at 873 K. The char was extracted from the laminar flow reactor 47 ms after injection of the unreacted material into an environment containing 6 mol-% O 2 at nominally 1650 K. 32

63 Test Materials, Experimental Methods and Data Analyses An expression for char reaction rate (R i,c ) was determined by combining Equations (3.7) and (3.8) to yield: R ic, Rc dxc / dt = =. (3.9) S S 1 x 1 ψ ln(1 x ) ( ) gc gc0 c c Quantities on the right-hand-side of this equation are measured, permitting evaluation of Ric, as a function of conversion. As an example, presented in Figure 3.10 is the intrinsic reactivity profile determined for the partially reacted char of the 16%-porosity synthetic char exposed to 6 mol-% O 2 at 873 K. The intrinsic char reactivity is noted to increase rapidly to a peak value at about 30% conversion and then to decrease to about 55% of the peak rate. Such a reactivity profile is a consequence of adsorbed oxygen atoms (initially none being on the carbonaceous surface) building up to quasi steady-state levels during the early stages of reaction. Note that at such low reaction temperatures, the char does not reach a quasi-steady burning rate until quite late in burnoff, after over 80% of the carbonaceous material has been gasified. The characteristics of the reactivity profile dep mostly on the variation of the concentration of adsorbed oxygen atoms. As derived later from the reaction mechanism, the reactivity is a certain function of (1-θ O -θ O-O )θ O, where θ and θ are surface carbon site coverage fraction by C(O) and C 2 (O 2 ). Since the concentration of C 2 (O 2 ) is generally orders of magnitude lower than that of C(O), the reactivity profile is depent on (1 - θ O )θ O, which is a quadratic function. If the C(O) coverage fraction, θ O, increases to more than 0.5 over the range of conversion, the reactivity profile will have a peak. However, if θ O is below 0.5 over the whole range of conversion, no peak will be observed in the reactivity profile, but the reactivity will increase monotonically or maintain almost the same value over certain conversions, deping on the relative importance of different reactions. An average reactivity for oxidation in an environment of specified temperature, pressure, and composition is defined as follows: O O O R ic 1 R ( x ) dx 0 = 1 dx ic c c 0 c. (3.10) Averaging R ic over the entire conversion range removes the depence of the reactivity on conversion and hence, serves to rank the relative reactivities of different carbonaceous materials in selected environments. 33

64 Chapter 3 Char reaction rate, gc/(m 2.s)x %-porosity char x c, conversion Figure Intrinsic reactivity of the partially reacted char of the 16%-porosity synthetic char that was extracted from the flow reactor 47 ms after injection into 6 mol-% O 2 at ~1650 K. Reactivity measurements were in 6 mol-% O 2 at 873 K. Intrinsic char reactivity was also determined from measurements obtained in transient oxidation tests in the PTGA. Shown in Figure 3.11 are char conversion rates determined from the weight loss data obtained in 6 mol-% oxygen when the temperature in the PTGA chamber was increased from 623 K at a rate of 1.5 K/min until complete burnout of the sample placed in the balance pan. Char conversion rates for an isothermal test at 873 K in 6 mol-% oxygen are also shown in the figure. The data were obtained with the partially reacted 16%-porosity synthetic char extracted from the flow reactor at the 47-ms residence time. Figure Conversion rates determined in isothermal and transient reactivity tests in 6 mol- % oxygen in the PTGA. The char particles were extracted from the laminar flow reactor at the 47-ms residence time in 6 mol-% oxygen at ~1650 K. The 16%-porosity synthetic char was used in the tests. 34

65 Test Materials, Experimental Methods and Data Analyses At each extent of conversion, the surface areas of the chars in the two tests are comparable, therefore, the ratio of the conversion rates at each extent of conversion deps only on the ratio of the intrinsic char reactivities at the temperatures at which the reactivities are compared, as shown in Equation (3.11): C iso ( 1 ) ( 1 ) dx R S x C dt R trans = = dx dt R S x R ic, gc C trans i, C, trans ic, gc C iso i, C, iso. (3.11) This ratio deps only on temperature for a fixed oxygen concentration. The plot shown in Figure 3.12 demonstrates that the ratio of reactivities when plotted against inverse temperature yields an Arrhenius-type relation from which an effective (or overall) activation energy for the oxidation rate can be estimated. The lines are the calculated reactivity ratio based on the reaction mechanism. These calculations neglect any mass transport effects. The data show some influence of mass transport effects as temperatures exceed about 900 K. Such data at low temperatures serve to assess the values determined for the activation energies of the reactions in the heterogeneous reaction mechanism. Figure 3.12 Ratio of reactivities at different temperatures for the 16%-porosity synthetic char particles burning in 6 mol-% oxygen in the PTGA Heterogeneous reaction mechanism At the start of this work, the following heterogeneous surface reaction mechanism was used to characterize the char oxidation process: 2 C f + O 2 2 C(O) (R1) C b + C f + C(O) + O 2 CO 2 + C(O) + C f (R2) C b + C f + C(O) + O 2 CO + C(O) + C(O) (R3) 35

66 Chapter 3 C b + C(O) CO + C f (R4) Here, C b is bulk carbon atom. In reaction (R.1), an oxygen molecule is adsorbed onto the carbon surface, and interacts with two nearby free carbon sites, C f, forming two chemisorbed oxygen atoms. Reaction (R.4) is treated as a reaction with no distributed activation energy. Based on the research of Haynes [2001; St and Haynes, 2004] on chemisorption of O 2 on carbon surface, one of the formed C(O) in reaction (R.1) can quickly be desorbed, forming a gas phase CO molecule. In accordance with this observation, the reaction (R.1) of the 4-step reaction mechanism was revised to: 2 C f + O 2 CO + C(O) (R1) The results from temperature-programmed desorption tests show that the oxidized carbon surface can release both CO and CO 2 under N 2 environment. This is evidence that another kind of surface oxide besides C(O) exists, or surface oxide C(O) interacts with nearby C(O), or desorbed CO gas molecule can be re-adsorbed onto the surface and interact with C(O) forming CO 2 gas molecule. Zhuang et al. [1994] attempted to identify the actual chemical structure of the complexes on the carbon surface. By using the TPD technique together with spectroscopic techniques, it was confirmed that CO may be formed primarily from carbonyl and/or ether-type complexes, while CO 2 would be formed primarily from the decomposition of lactone and/or acid anhydride-type complexes, i.e., C b + C(O) CO + C f C 2 (O 2 ) CO 2 + C f. Here, the complex C(O) would be qualitatively interpreted as the concentration of carbonyl and ether-type complexes, while C 2 (O 2 ) denotes the lactone and acid anhydride-type complexes. According to Zhuang et al. s result and Campbell s 11-step detailed reaction mechanism, the following 6-step reaction mechanism was developed to account for CO 2 desorption during TPD and heterogeneity of the surface sites: k1 a 2 f 2 ( ) C + O C O + CO (R.1a) ( ) k1b 2Cf O2 C2 O2 + (R.1b) k2 ( ) ( ) C + C + C O + O CO + C O + C (R.2) b f 2 2 f 36

67 Test Materials, Experimental Methods and Data Analyses b f k3 ( ) ( ) ( ) C + C + C O + O CO+ C O + C O (R.3) b 2 k4 E ( ) C + C O CO+ C (R.4) b k5 ( ) E f C + C O CO + C (R.5) Reactions (R.4) and (R.5) are modeled using a distributed activation energy approach in order to account for the variations in the strengths of adsorbed oxygen atoms. Temperature programmed desorption experiments were used to determined the distributions. Since each C(O) complex occupies one carbon site and each C 2 (O 2 ) complex occupies two adjacent carbon sites, site concentrations and site fractions are related by f S C O = Nav ( ) θ O and C ( O ) = O O 2 N θ av S. where θ and θ are surface carbon site coverage fractions by C(O) and C 2 (O 2 ), O O O respectively, and θ + θ + θ = 1, where θ f is the fraction of free sites. O O O f An expression for the intrinsic reactivity of the char (i.e., the rate of removal of CO and CO 2 from the bulk carbonaceous material) can be derived from the heterogeneous chemical reaction mechanism. The resulting expression is R 2 2 S 2 S k ( 1 θ θ ) [ O ] + k ( 1 θ θ ) θ [ O ] =, (3.12) 1a O O O 2 2 O O O O 2 ˆ Nav Nav ic, MC 2 S S k5, eff S + k3 ( 1 θo θo O) θo[ O2] + k4, eff θo + θo O Nav Nav 2 Nav where k = k ( E) f ( E) de and ( ) ( ) 4, eff k = k E f E de. 5, eff Before the calculation of char reactivity is possible, the surface carbon site coverage fractions θ and θ have to be determined. Based on the mechanism, O O O dn O S 2 S S = k1 a ( 1 θo θo O) [ O2] + k3 ( 1 θo θo O) θo[ O2] k4 θo g, tot av av av S dt N N N O O 2 and 2 ( 1 ) [ ] 2 1 dn S S = k θ θ O k θ S dt N N 1b O O O 2 5 O O g, tot av av, (3.14) (3.13) 37

68 Chapter 3 where N O and N O-O are the total moles of C(O) and C 2 (O 2 ) on the surface, respectively. S g,tot is the total surface area of carbonaceous material. During the char conversion process, the variation of C(O) and C 2 (O 2 ) concentrations deps not only on the chemical reactions, but also on the variation of the total surface area, i.e., ( ) d C O 1 dno 1 ds = C( O) dt S dt S dt gtot, gtot, 1 dno = C( O) AR S dt gtot, ic, g, tot, (3.15) S where the factor, A S S 2 2 g0 ψ g 2 g 2 Sg0. Similarly, for C 2 (O 2 ) concentration, gtot, ( O ) 1 dn d C O O 2 2 = + ( ) S dt dt C2 O2 ARiC,. (3.16) Therefore, the rates of change in surface carbon sites coverage by C(O) and C 2 (O 2 ) are dθ O S ( 1 ) 2 S = k θ θ [ O ] + k ( 1 θ θ ) θ [ O ] k θ θ AR dt N N 1a O O O 2 3 O O O O 2 4 O O i, C av av (3.17) dθ dt S = k θ θ O k θ θ AR O O 2 and 2 ( 1 ) [ ] 1b O O O 2 5 O O O O i, C Nav. (3.18) The reactivity as well as concentrations of adsorbed oxygen atoms can be obtained by solving Equations (3.12), (3.17) and (3.18) simultaneously Temperature-programmed desorption (TPD) test Introduction Because the surface structure of char is very complex and non-uniform, the adsorbed oxygen atoms formed on the surface have a broad spectrum of binding energies (Figure 3.13). Thus, the desorption of these adsorbed oxygen atoms will exhibit a wide range of activation energies. Also, the stability of these surface complexes may also be affected by factors such as local environment, domains of order, etc. This figure illustrates several possible adsorbed oxygen atoms on carbon surface. It was found that the carbonyl-type complexes are more 38

69 Test Materials, Experimental Methods and Data Analyses likely to yield CO, and the lactone and/or acid anhydride-type complexes are more likely to yield CO 2. Figure Some possible adsorbed oxygen atoms on carbon surface [Courtesy of Du, 1990]. The temperature-programmed desorption (TPD) technique has been widely used to investigate the characteristics of surface oxide on carbon surfaces. The product formation rate during TPD can be interpreted in terms of equivalent kinetics for desorption of the parent surface complexes [Carter, 1962; Redhead, 1962]. The TPD spectrum usually consists of some peaks, as seen from Figure The shape of the peak and location of the peak with respect to temperature are related to the desorption process and, hence, the bonding energies of the adsorbed species. For a first order desorption reaction, a higher temperature of the peak corresponds to higher desorption activation energy. 39

70 Chapter 3 Figure CO and CO 2 evolution during TPD tests on petroleum pitch and cellulose - derived chars [Courtesy of Skokova, 1997 and Campbell, 2005]. However, it was observed that one single set of kinetic parameters can not reproduce the full spectrum of TPD [Ma, et al., 1993]. Therefore, it is desirable to have variable kinetic parameters for the desorption model. The kinetic parameters of the desorption process may be depent on the surface overage θ, i.e., A(θ ) and E(θ ). Some studies proposed some techniques for determining these parameters [Redhead, 1962; Taylor and Weiberg, 1978; Love, et al., 1991]: ( θ ) dn v E = na 0 ( θ) θ exp dt RT, (3.19) where θ = n/n 0 and n is the adsorbate quantity. Generally, both A(θ ) and E(θ ) are higher for lower surface overage θ. The kinetic parameters may also vary with the heterogeneity of the carbon surface. A carbon surface may consist of many indepent desorption sites with distributed activation energies, f(e). The product, f(e)δe, represents the amount of desorption sites with activation energy between E and E +ΔE, and the desorption rate is then expressed as 40

71 Test Materials, Experimental Methods and Data Analyses ( E) dn dθ f ( EdE ) dt =. (3.20) 0 dt This expression uses a statistical method to account for the heterogeneity of the surface and variations of A and E. Equation (3.20) is widely used to describe the kinetics of decomposition of carbonaceous materials and surface oxides [Du, et al. 1990; Brown et al., 1990; Calo and Hall, 1990]. This approach is used here. Experimental procedure and analysis A typical temperature-programmed desorption test, performed in the PTGA, is as follows: 1. The char sample was placed in the quartz sample pan in the PTGA and cleaned by heating in N 2 at 1273 K for about 20 minutes. 2. The sample was then cooled to the desired chemisorption temperature (generally 773 K), and the oxidizing gas (21% O 2 and 79% N 2 mixture) was introduced into the reaction chamber. This temperature was maintained for about 30 minutes, before the reaction chamber temperature was lowered to 523 K in the same environment. 3. During this 30-minute period of time, oxygen atoms were chemisorbed onto the carbon surface, forming chemisorbed oxygen atoms with a spectrum of activation energy for desorption. After this treatment, the chamber temperature was increased from initial temperature, T i = 523 K up to final temperature, T f = 1373 K. During the heating up, the chemisorbed oxygen atoms were desorbed from the carbon surface. Chemisorbed oxygen atoms with low activation energies are desorbed at relatively low temperatures, and chemisorbed oxygen atoms with high activation energies are desorbed from the surface at higher temperature. The activation energy distribution, f(e) can be derived from the CO or CO 2 generation rates as a function of temperature. The CO and CO 2 generation rates in the TPD process for 25% synthetic char are plotted as symbols in Figure The area under each desorption curve represents the total amount of CO and CO 2 desorbed. The dashed lines represent the uncertainty of the reported desorption rates, which is discussed in Appix B. Since the desorption reactions of CO and CO 2 are very similar, the following discussion on derivation of activation energy distribution uses CO desorption as an example ( C( O) [1993]. k4 ( E) CO). The derivation process follows the lead of Du [1990] and Ma et al. 41

72 Chapter 3 d[co]/dt, d[co 2 ]/dt, mol/(min.m 2 )x d[co]/dt d[co 2 ]/dt Time, min (a) d[co]/dt, d[co 2 ]/dt, mol/(min.m 2 )x d[co]/dt d[co 2 ]/dt Temperature, K Figure CO and CO 2 generation rates in TPD as a function of (a) time and (b) temperature. (b) When the desorption reaction has one single activation energy, i.e., all surface oxides are desorbed at the same activation energy. Then the activation energy distribution is just a delta function as ( ) δ ( ) f E = E E 4. Under this condition, the CO generation rate can be expressed as: [ ] d CO dt exp E A4 C( O) t RT 4 =, (3.21) where A 4, E 4 are the Arrhenius parameters for the desorption reaction, and [C(O)] t is the surface oxide concentration at any time t. Rearrangement of Equation (3.21) gives [ ]/ C( O) d CO dt E0 log = log A0 t RT. (3.22) It is shown that Equation (3.22) should be a linear function of inverse temperature. The term on the left-hand-side of the above equation is plotted versus inverse temperature in Figure However, a curve with different slopes is observed in the plot, although there is a rather straight portion, suggesting the existence of a range of activation energies. Assuming that the desorption reaction has an activation energy distribution f(e), then f(e)δe is the fraction of total C(O) with an activation energy between E and E +ΔE, and we should have 0 ( ) f E de = 1. (3.23) 42

73 Test Materials, Experimental Methods and Data Analyses Log(d[CO]/dt/[C(O)] t ), 1/s /T, 1/K Figure Plot of left-hand-side of Equation (3.22) as a function of inverse temperature in TPD. Let F t (E) denotes the fraction of surface oxide with an activation energy smaller than E at time t, i.e., t ( ) F E 0 E ( ) Et, E ( ) ( ) 0 C O de Et, 0 C O de Et, = = C( O) de C O total, t, (3.24) C O E is [C(O)] concentration left on carbon surface with an activation energy where ( ) Et, between E and E +ΔE at time t, and The activation energy distribution at time t is ( ) ( ) C O = C O de. (3.25) total, t 0 E, t ( ) df E ft ( E) de Taking the derivative of Equation (3.24) with respect to E yields t =. (3.26) ( ) ( ) ( ) C O = C O f E, (3.27) E, t total, t t and at an initial time t = 0, this expression gives the initial distribution of C(O) with different activation energies, ( ) ( ) ( ) C O = C O f E E,0 total,0 0. (3.28) 43

74 Chapter 3 Here, f 0 (E) is the initial surface oxide desorption activation energy distribution before the start of TPD. The desorption rate of C(O) with an activation energy of E is expressed as follow: [ ] d C( O) d CO dt ( ) ( ) E Et, = = 4 E, t dt k E C O. (3.29) Integration of Equation (3.29) over the spectrum of activation energy E gives the overall CO desorption rate: [ ] d C( O) d CO dt = = k4 ( E) C( O) de 0 Et, dt. (3.30) Integrating Equation (3.29) with respect to time from the initial time 0 to time t yields Combining Equations (3.31) and (3.30) gives ( ) / C( O) ( 4 ) t ( ) ( ) exp ( ) C O = C O k E dt. (3.31) Et, E,0 0 d C O total,0 t = A4exp ( E / RT ) exp A4 exp ( E / RT ) dt f0( E) de dt 0 0. (3.32) Defining the following non-dimensional variables: ε = E / RT and τ = AT 4 α, where α = dt / dt, Equation (3.32) becomes ( ) / ( ) d C O C O e R τ e exp τ e ε e du 1 f ( E) dε dt u u total,0 ε ε ε = 0 ε.(3.33) Following the approach of Vand [1943], for broad, smooth distribution functions (half width of features not less than about 2RT), the double exponential term in Equation (3.33) goes from 1 to 0 over a small range of E (E-2RT, E+2RT) around a characteristic value of E * : τ = ε e ε. Typically, the value of τ is larger than 10 13, and ε * is almost indepent of τ, because dε / dτ τ < 10 * 1 13 where ( ). Therefore, Equation (3.33) can be simplified as ( ) / C( O) d C O dt ( τ ) ( ) R I f E total,0 0, (3.34) u ε ε ε e I0 τ = τ e exp τ e ε e du 1 dε 0 ε u. (3.35) 44

75 Test Materials, Experimental Methods and Data Analyses The activation energy distribution can then be inverted in Equation (3.34), [ ] d CO f ( E ) = R I0 ( τ ). (3.36) dt The application of Equation (3.36) to extract the activation energy distribution from the TPD CO desorption profile is shown in Figure Clearly, the distribution can be approximated as a Gaussian distribution with a mean activation energy, E, and standard deviation, σ. In the calculation, the pre-exponential factor A 4 is treated as a known constant parameter. The effect of A 4 on the derived distribution is presented in Figure It is shown that the shapes of the distributions are about the same, except that the mean activation energy becomes higher and standard deviation gets broader when A 4 is increased. Based on kinetic theory, for unimolecular reactions, a typical frequency factor is on the order of s -1 [Strange and Walker, 1976]. Follow the suggestions of previous authors [Du, 1990], the pre-exponential factors for desorption are taken to be s -1. f (E) x 100%, mol/kj TPD derived A 4 = /s Gaussian Approx. E = kj/mol σ = kj/mol τ 873 K = 10 4 s τ 1600 K = 10-4 s 0.2 τ 873 K = 10-2 s τ 1600 K = 10-8 s E, kj/mol Figure Inversion of desorption activation energy distribution from the TPD CO desorption rate by assuming A 4 = /s. 45

76 Chapter f (E) x 100%, mol/kj A 4 = A 4 = E, kj/mol Figure Effect of pre-exponential factor A 4 on the desorption activation energy distribution determined from the TPD CO desorption rate. Alternatively, the integration of Equation (3.29) can be carried out over a short time interval Δt from time t n to t n+1, ( 4 ) tn+ 1 ( ) ( ) exp ( ) C O = C O k E dt. (3.37) Et, n+ 1 Et, n tn Since the low heating rate of about 25 K/min, over this short time interval Δt = t n+1 - t n, the temperature can be treated as the same, and then reaction rate constant k 4 (E) is a constant over this time interval. Equation (3.37) is integrated to give the expression for the concentration of C(O) at activation energy E and next time step t n+1 : Combining Equations (3.38) and (3.30), ( ) ( ) exp ( )( ) C O = C O k E t t Et, 4 1 n 1 Et, n+ n. (3.38) + n [ ] d CO dt tn+ 1 ( ) ( ) exp ( )( ) 4, 4 n 1 n 0 Et + n = k E C O k E t t de. (3.39) Given A 4 for this reaction, by least-square fitting the CO desorption rate measured from TPD test with Equations (3.28), (3.38) and (3.39), the mean activation energy, E, and its standard deviation, σ, can be determined using an optimization algorithm. The activation energy distribution for CO 2 desorption is obtained in the same manner. The least-square fitting of the CO and CO 2 desorption rate using a Gaussian distribution approximation are shown in Figure The mean activation energies obtained are within the expected range of kj/mol indicated by Haynes (Brown and Haynes, [1992]; Haynes, [2001]). 46

77 Test Materials, Experimental Methods and Data Analyses d[co]/dt, d[co 2 ]/dt, mol/(min.m 2 ) x E = kj/mol σ = 36+3 kj/mol d[co]/dt E = kj/mol σ = 45+7 kj/mol d[co 2 ]/dt Temperature, K Figure Least-square fittings of the CO and CO 2 desorption rate using Gaussian distribution approximation by assuming A = /s. The previous equations for calculating the CO desorption rate is only applicable to TPD process, without adsorption of oxygen onto the carbon surface. In the case of char oxidation, the surface oxides are not only desorbed from the surface, but also chemisorbed onto the surface. The above derivation will not work. However, for char oxidation, it is reasonably assumed that both C(O) desorption and adsorption have similar activation energy distributions. Thus, the desorption activation energy distribution, f(e), will not change with char conversion, i.e., f(e) = f 0 (E), which is not a function of time. This assumption has been verified by Du [1990] that the activation energy distribution was insensitive to carbon conversion, suggesting that the active carbon sites can be regenerated during oxidation. From the above discussion, we can conclude that at any time ( ) ( ) ( ) C O = C O f E. (3.40) E, t total, t The CO desorption rate under oxidation condition is given by: [ ] d CO dt ( ) ( ) ( ) ( ) ( ) Et, totalt, = k E C O de = k E C O f E de ( ) 4 ( ) ( ) total, t 0 C( O), = C O k E f E de k 4, eff total, t (3.41) k = k E f E de. where ( ) ( ) 4, eff

78 48

79 Chapter 4 Burning Behaviors of Pulverized Coal and Biomass Chars Under pulverized coal combustion conditions, char particles burn with reductions in both diameter and apparent density. The specific surface areas of chars also vary during mass loss. In this chapter, after the previous work is reviewed, a single char particle conversion model is developed to predict accurately the chemical and physical characteristics of char particles undergoing mass loss at both low and high temperatures. A mode-of-particle-burning model is also developed to characterize the functional relationships between particle size and apparent density with mass loss as burning proceeds. Experiments in the flow reactor were conducted to validate the model. 4.1 Introduction The overall char combustion process is controlled by the following chemical and transport processes: (1) the transport of oxygen and energy as heat across the external boundary layers surrounding particles; (2) the transport of oxygen and energy as heat through the porous particle structure; and (3) the reaction of oxygen with solid surfaces within the particles. The rates of these processes are controlled by particle size, apparent density, surface area, and porosity as well as by the intrinsic chemical reactivity of the carbonaceous particle material. Pioneered by Walker et al. [1959] and Gray et al. [1976], the existence of three different burning zones or regimes was postulated, in which one or more of the above processes control the reaction rate. Over most of the lifetime of a burning coal or biomass char particle, burning occurs in a regime in which the characteristic rates for pore diffusion and chemical reaction are of similar magnitudes, making both effects important in determining the overall mass loss rate of the particle. This is the so-called Zone II burning regime. During the late stages of burning, particles become smaller and the pores within particles have merged and coalesced to the point that diffusion resistances are minor. A transition to the Zone I burning regime is expected, the regime in which chemical reaction become more significant than pore diffusion in limiting overall mass loss rates. For particles that are identical at the onset of char oxidation, the final particle size, apparent density and specific surface area dep upon the regime in which the particle burns. In the Zone I burning regime, in which oxidation occurs at low temperatures, rering mass 49

80 Chapter 4 loss rates limited by chemical reaction rates, a particle burns more or less uniformly throughout its volume. Its size is relatively unchanged and its apparent density varies directly with mass loss. The specific surface area of the particle can be predicted using the grain and pore models that have been developed for such uniform burning. In the Zone III burning regime in which oxidation occurs at high temperatures, rering mass loss rates limited by the rates of oxygen diffusion to the outer surfaces of particles, a particle burns primarily at its periphery. Its apparent density is relatively unchanged and its diameter varies to the 3rd power with mass loss. The specific surface area of the particle is relatively unchanged in this burning regime, there being relatively little interior burning during mass loss. During the combustion of coal particles in conditions typical of those existing in industrial, pulverized coal-fired boilers and furnaces, char particles burn in the Zone II burning regime, the regime in which the particle burning rates are limited by the combined effects of chemical reaction and pore diffusion. Due to the oxygen concentration gradients established inside particles and the associated distribution of rates of mass loss due to chemical reaction, the particle diameters, apparent densities, and specific surface areas vary with mass loss when burning is in this regime. In the Zone II burning regime, the variations in particle size, apparent density, and specific surface area with mass loss have not been characterized by a model to the extent that these particle properties can be predicted based on the extent of conversion. 4.2 Power law relations Power law relations During combustion in high-temperature environments, char particles burn with variations in both size and apparent density. In order to reflect this phenomenon in char combustion models, power-law relations have been used to correlate particle sizes and apparent densities with overall extents of mass loss [McKenzie et al., 1974; Smith, 1982; Essenhigh, 1988; Mitchell et al., 1992; Hurt and Mitchell, 1992; Hurt et al., 1998]. For example, the following expressions are often used to relate particle apparent density, diameter and mass during oxidation of a carbon particle: ρ ρ m C C = C,0 m C,0 α and D D p m m C = p0 C,0 β. (4.1)(4.1a,b) Here, the subscript 0 denotes initial particle conditions. For spherical particles, α + 3β = 1, and in the approaches taken, the parameters α and β are constants. For α = 0, β = 1/3, 50

81 Burning Behaviors of Pulverized Coal and Biomass Chars particles burn at constant density (in the Zone III burning regime in which external diffusion of oxygen to particles controls mass loss rate) and for α = 1, β = 0, particles burn at constant diameter (in the Zone I burning regime in which intrinsic reactivity controls mass loss rates). For 0 < α < 1, 0 < β < 1/3, particles burn with decreases in both size and apparent density (in the Zone II burning regime). Second effectiveness factor Essenhigh [1988] proposed a second effectiveness factor as: R R int ε = 1+ (4.2) where R int and R ext are the internal and external burning rates per unit external surface area, respectively. This second effectiveness factor is related to the burning mode parameter in power law relations by ε = 1 + α /3β, and hence ext R R int ext α =. (4.3) 3β According to the definition of effectiveness factor, η (the ratio between actual and maximum possible burning rates), Rint ηsint =. (4.4) R S Therefore, the effectiveness factor and the second effectiveness factor are related by ext ext α ηsint 3β = S. (4.5) This expression indicates how the value of α /β changes with different burning regimes or carbon conversions. In the Zone I regime, η = 1, and α /β = 3S int /S ext. Since S int /S ext is generally very large, and thus, α /β is a larger number, as indicated by the power law relations (In Zone I, α = 1, β = 0, and α /β ). In the Zone III regime, η 0, and α /β = 0, which is consistent with the values from power law relations (In Zone III, α = 0, β = 1/3, and α /β 0 ). In the Zone II regime, η is small, and the value of α /β will be down to some finite number, around 2 or 3 reported by Essenhigh [1988]. Essenhigh [1994] exted the above analysis to show that the ratio α /β varies with the initial char density. Compilation of experimental data from literature sources indicated most ext 51

82 Chapter 4 of the values of α /β are in the range of 1-3 regardless of different experimental methods, char types, particle sizes and reaction temperatures. It was concluded that intrinsic reactivity of different chars may be very similar. The differences in reaction rate may be attributed more to differences in the physical access to the particle surface and the interior, rather than determined by the chemical reactivity. The initial char density can be regarded as a measure of the accessibility to the particle interior. Essenhigh correlated the mode of burning parameters in power-law relations to some particle properties by distinguishing the internal and external burning. As burning proceeds, it is expected that η and S int /S ext vary with conversion. Therefore, the value of α/β should also change with conversion. However, he did not delve into the variation of mode of burning relations as burning proceeds. He addressed the constancy of these burning parameters and concluded that there is still much to be resolved about the sensitivity of the ratio α/β to the temperature and burn-off, but that the values are more or less constant during char burnout. In most of the approaches taken, the parameters in the relations are constants, thus the manner in which apparent density and diameter vary with mass loss during the early stages of burning is the same as that during the late stages. The mode of particle burning late in burnoff is the same as that early in burn-off - an unrealistic scenario. As particles burn, pore diffusional 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 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. Measured values of D/D 0 and ρ C /ρ C0 for partially reacted synthetic chars extracted from the flow reactor are plotted against the measured values of conversion in Figure 4.1 to Figure 4.3. The symbols are the values determined from the experimental measurements, with error bars representing the scatter of the data from different measurement replicates. The solid lines in the figures were the best fits using the power law mode of burning relations given by Equation (4.1) with α and β evaluated by least-square fitting the measured data. Note that α + 3β 1, as required for spherical particles. The fits yield (α + 3β) in the range 0.8 to 0.9 for the synthetic chars. This could be a consequence of the actual non-sphericity of the synthetic char particles used in the tests or an indication of an inadequacy in the power-law model. 52

83 Burning Behaviors of Pulverized Coal and Biomass Chars ρ C /ρ C data power-law α = D p /D p data power-law β = x c, conversion x c, conversion Figure 4.1. Measured and calculated mode-of-burning profiles for the 16% synthetic char. The lines are calculated assuming power-law relations with the indicated values for α and β ρ C /ρ C0 0.8 data power-law D p /D p0 0.8 data power-law 0.6 α = β = x c, conversion x c, conversion Figure 4.2. Measured and calculated mode-of-burning profiles for the 25% synthetic char. The lines are calculated assuming power-law relations with the indicated values for α and β ρ C /ρ C0 0.8 data power-law D p /D p0 0.8 data power-law 0.6 α = β = x c, conversion x c, conversion Figure 4.3. Measured and calculated mode-of-burning profiles for the 36% synthetic char. The lines are calculated assuming power-law relations with the indicated values for α and β. 53

84 Chapter 4 To overcome shortcomings associated with the power-law model, a single char particle conversion model is developed and used to examine the variations of particle properties with conversion. Based on the results of the direct numerical simulation, an intrinsic kinetics reactivity-based model for mode of particle burning is developed. The model allows for variations in particle size and apparent density during conversion that dep on the instantaneous state of the char. In this chapter, this mode-of-particle-burning model is described and results of experiments used to validate the model are presented. 4.3 Single char particle conversion model In the theoretical approach taken, a spherical char particle initially of size D p0, apparent density ρ C0, and specific surface area S gc0, is divided into K concentric annular volume elements, V k, each of which contains a portion of the initial total mass of the particle (m C0,k = ρ C0 V k ) that burns at a rate governed by the local conditions (Figure 4.4). The rate that the mass of the carbonaceous particle material in each volume element is oxidized to CO and CO 2 is governed by the equation m 1 Ck, Ck. dm dt = R S, (4.6) ic, k gc, k where the intrinsic chemical reactivity of the particle material deps upon the local oxygen concentration, which is governed by the following equation: CO d C 2 rd 2 = R 2 S t r dr r 1 2 O ˆ 2 eff io ρc gc. (4.7) When evaluating D eff in each volume element, account is made for the combined effects of bulk and Knudsen diffusion of oxygen through pores. The Knudsen diffusion coefficient deps 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, which is calculated from the local apparent density and the true density of carbon. 54

85 Burning Behaviors of Pulverized Coal and Biomass Chars D p V k r r k r k Figure 4.4. Concentric annular volume elements: Vk = π ( rk+ 1 rk ) 4 3 Simultaneous integration of Equations (4.6) and (4.7) yields the state of the particle at various times during its lifetime. The conversion and apparent density in each volume element are determined from the relations x C,k = 1 m C,k m C 0,k and ρ C,k = m C.k V k, (4.8) and the specific surface area of the carbonaceous material in volume element k is calculated using the expression ( ) S = S 1 ψ ln 1 x. (4.9) gc, k gc0, k Ck, This expression for the specific surface area, due to Bhatia and Perlmutter [1980], accounts for the opposing effects of pore growth and pore coalescence during char conversion under Zone I burning conditions. The relative competition between area formation and area destruction is controlled by the value of the structural parameter, ψ. The mass, apparent density and specific surface area of the char particle at any instant are calculated using the relations m C = mc, k, C mc Vk k k ρ =, (4.10)(4.10a,b) and (,, ) S = S m m. (4.11) gc gck Ck C k 55

86 Chapter Effective diffusion coefficient In general, both bulk and Knudsen diffusion may contribute to the mass transport rate of oxygen within the porous structure of a burning char particle. The combined effects of these two diffusion mechanisms can be described by an effective diffusion coefficient, D eff, which can be calculated using the following expression [Satterfields, 1970]: = +. (4.12) D D D eff O2 / N2 K, eff Here, D O2/N2 is the bulk diffusion coefficient of oxygen into the gas mixture and D K,eff is the effective Knudsen diffusion coefficient for oxygen, which characterizes transport through pores having diameters less than the oxygen mean free path. For convenience, the bulk diffusion coefficient is calculated using the following correlation derived from the Chapman- Enskog relations by Mitchell [1980]: D O2 N =, (4.13) / T P and the effective Knudsen diffusion coefficient is calculated using the following expressions: D Keff, =, where D θ K τ D K 2rp 8kBNavT =. (4.14) 3 π Mˆ O2 The expression for the Knudsen diffusion coefficient (D K ) is based on the kinetic theory for Knudsen diffusion of gases in a straight round pore. The porosity (θ ) is introduced so that the gas flux is based on the total cross section of the porous particle, not just on the pore cross section. The tortuosity factor (τ ) is introduced to take into account the tortuous path through which gas must diffuse, the effect of the varying cross section of the individual pores, and the various unknown degrees of anisotropy and inhomogeneity of the pore structure. A value of three is taken for randomly oriented, uniform pores [Satterfield, 1970]. In Equation (4.14), k B, N av, and ˆM denote respectively, the Boltzmann constant, Avogadro s number, and the molecular weight of the diffusing gas, oxygen in the present case. For a porous material with smooth, continuous cylindrical pores, the average pore radius is given as: r p 2V g =, (4.15) S gc 56

87 Burning Behaviors of Pulverized Coal and Biomass Chars where V g is the pore volume per gram. Wheeler [1951] took into account of wall roughness and interconnections of the pores, and derived the following expression for mean pore radius: r p 2V g = rf ( 1 θ ), (4.16) S gc where rf is the roughness factor, taken as 2 for carbon surfaces. However, this expression was derived for non-consuming porous catalysts. The opening of the pores due to chemical consumption of the material was not considered. For burning carbonaceous material, with V g = θ /ρ c, the mean pore radius is approximated by r p 2 rf θ =. (4.17) ρ S c gc Particle temperature Char-particle temperature is calculated from the following energy balance, wherein the rates of energy generation due to char oxidation are balanced by the rates of energy loss by conduction, convection, and radiation. Assuming that particles attain a state of thermal equilibrium with the surrounding gas as they burn, gas and particle temperatures satisfy the following particle energy balance equation: Nu λg κ qδ H = T T + T T D 1 p e κ 4 4 ( p g) εσ ( p w ), where κ γ c Dν q Mˆ λ Nu pg, p O2 =.(4.18)(4.18a,b) C g In this equation, q denotes the overall particle burning rate per unit external surface area. Gas and particle temperatures are given by T g and T p, respectively. Nu is the Nusselt number (taken as 2) and λ g and c p,g are the thermal conductivity and specific heat of the gas. The emissivity of the char particle is ε (taken as 0.85), the temperature of walls to which particles radiate is T w, and the Stefan-Boltzmann constant is σ. Temperature-depent properties in the particle boundary layer are evaluated at the mean of the gas and particle temperatures, T m. ν O2 is the moles of oxygen consumed per mole of carbon gasified, γ is the change in gas volume upon reaction per mole of oxygen consumed, and ΔH is the effective heat release due to carbon oxidation to CO and CO 2, calculable from the heats of reaction of CO and CO 2. 57

88 Chapter 4 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: kp d 1 γ Ps P Mˆ D 2Sh q = ln, where k γ 1 γ Pg P ˆ C O d =. (4.19)(4.19a,b) RTmDνO2 In deriving the above expressions, reaction was assumed not to occur in the boundary layer surrounding the particle, and account was made for the effects of Stefan flow in determining the flux of oxygen to the external particle surface [Frank-Kamenetskii, 1969]. In the above equations, k d is the mass transfer coefficient, and Sh is the Sherwood number (taken as 2). The oxygen partial pressures at the outer surface of the particle and in the ambient gas are denoted by P s and P g, respectively, and P is the total pressure Heterogeneous chemical reaction mechanism The intrinsic chemical reactivities determined from analysis of the PTGA data need to be expressed as functions of temperature and oxygen concentration. In the present approach, the following surface mechanism is used to characterize the intrinsic reactivities: k1 a 2 f 2 ( ) C + O C O + CO (R.1a) ( ) k1b 2Cf O2 C2 O2 + (R.1b) k2 ( ) ( ) C + C + C O + O CO + C O + C (R.2) b f 2 2 f b f k3 ( ) ( ) ( ) C + C + C O + O CO+ C O + C O (R.3) b 2 k4 E ( ) C + C O CO+ C (R.4) b k5 ( ) E f C + C O CO + C (R.5) Here, C f represents a free carbon site, available for oxygen chemisorption, and C(O) and C 2 (O 2 ) represent adsorbed oxygen atoms, one oxygen atom per carbon site. In accord with the type of oxide complexes identified by Zhuang et al. [1994] on carbon surfaces during oxidation, the complex C(O) is representative of carbonyl- and ether-type complexes (the desorption of which leads to CO), and C 2 (O 2 ) is representative of lactone- and acid anhydride-type f 58

89 Burning Behaviors of Pulverized Coal and Biomass Chars complexes (the desorption of which leads to CO 2 ). So that the reactions are balanced, bulk carbon atoms, C b, are shown; they are assumed to have unity activity. Reaction (R.1) (represented by reactions (R.1a) and (R.1b)) is assumed to have two product channels, one leading to the formation of C(O) and the other, to C 2 (O 2 ). Based on the kinetic parameters determined for reactions (R.1a) and (R.1b), the branching ratio (= k 1a /(k 1a +k 1b )) is temperature depent, and can be determined from Arrhenius parameters for reactions (R.1a) and (R.1b). It is assumed that each free carbon atom represents a potential adsorption site, and that desorption of a chemisorbed oxygen atom removes the underlying carbon atom to uncover a further adsorption site. Reactions (R.1a), (R.2), (R.3), and (R.4) are based on the carbon reactivity model developed by Haynes and co-workers [2001; 2004]. Hurt and Calo [2001] have shown that this type of mechanism is capable of describing the trs reported in various studies with respect to reaction order, activation energy, and CO-to-CO 2 product ratio. Under Zone I burning conditions, the mechanism is capable of describing high intrinsic orders of reaction with respect to the oxygen partial pressure and under Zone II burning conditions, the mechanism is capable of describing low intrinsic reaction orders, in accord with experimental observations. Reactions (R.1b) and (R.5) were included to account for the significant quantities of CO 2 observed in temperature-programmed desorption (TPD) tests performed in this study and in the TPD tests of Campbell [2005] and Sokova [1997]. The rates of Reactions (R.4) and (R.5) are modeled using a distributed activation energy approach in order to account for the variations in the strengths of adsorbed oxygen atoms. temperature-programmed desorption experiments were used to determine mean activation energies and standard deviations for use in a Gaussian distribution. With this mechanism, the intrinsic char reactivity in volume element k is given by ( ) R = Mˆ RR + RR + RR + RR + RR (4.20) ic, k C 1a k where RR i.k is the rate for reaction i, evaluated using the rate coefficients and oxygen concentration and adsorbed O-atom site fractions in volume element k. The adsorbed O-atom site fractions in volume element k satisfy the relations dθok, θo dstotal = ( Nav S )( RR1a + RR3 RR4) dt k Stotal dt k (4.21) and 59

90 Chapter 4 dθ θ ds = ( N S)( RR RR ) O O, k O O total 2 av 1b 5 dt k Stotal dt k, (4.22) where θ O and θ O-O are the fractions of the total sites having adsorbed oxygen atoms, and S total is the total surface area of the particle. The first terms on the right-hand-sides represent the changes of adsorbed O-atom concentrations due to heterogeneous reaction, and the second terms on the right-hand-sides represent the changes of adsorbed O-atom concentrations due to the evolution of the total surface area in volume element k. As a consequence of pore growth and coalescence, the evolution of total surface area in volume element k can be expressed as ds total S gc0 ψ S gc = R 2 ic,. (4.23) Stotal dt S gc 2 S k gc0 k Based on the reaction mechanism presented above, the molar CO to CO 2 heterogeneous product ratio is given by M R [ ] [ ] 2 ( ) [ ] ( ) [ ] ( ) θθ [ ] + d CO dt k S N θ O + k S N θθ O + k θ = d CO dt k S N O k 1a av f 2 3 av f O 2 4, eff O 2 2 av f O 2 5, effθo O, (4.24) where k = k ( E) f ( E) de and ( ) ( ) 4, eff k = k E f E de. The function, f(e), is the 5, eff Gaussian distribution for activation energy. The fraction of sites that is available for oxygen adsorption (i.e., free sites) is θ f. Since sites are either free or occupied, θ f +θ O +θ O-O = 1. This product ratio, M R, is noted to dep upon both temperature and the oxygen concentration. Values calculated for M R are used to determine values for ν O2, γ, and ΔH. A least squares procedure was used to determine Arrhenius parameters for the reaction rate coefficients that yield calculated reactivities that agree with measurements. In the approach taken to determine Arrhenius parameters, the activation energies for reactions (R.1), (R.2), and (R.4) were restricted to be in the ranges of values recommed by others [Hurt and Calo, 2001], and the temperature-depences of M R were restricted to be similar to those observed in other studies [Arthur, 1951; Rossberg, 1956; Skokova, 1997] Effectiveness factor The effectiveness factor for a porous carbon particle deps upon the oxygen consumption rate and is defined as follows: 60

91 Burning Behaviors of Pulverized Coal and Biomass Chars actual O consumption rate maximum possible O consumption rate 2 η. (4.25) 2 Due to pore diffusion resistances and chemical reaction, an oxygen concentration gradient exists inside the particle, causing the oxygen consumption rate to vary with particle radius. Equation (4.7) was solved with the reactivity varying with radial position, for specified initial values of particle properties. Based on the calculated instantaneous local oxygen concentration profile, the effectiveness factor at any time was evaluated by integrating the oxygen consumption rates at the various radial positions inside the particle and comparing the total consumption rate with that determined if the oxygen concentration profile were uniform inside the particle: Rˆ ρ S V Rˆ ρ S V k η = Rˆ ρ S V = Rˆ ρ S V k io2, k C, k gc, k k io2, k C, k gc, k k k io2,max C, k gc, k k io2, ex C, k gc, k k k (4.26) The maximum reactivity of oxygen is assumed to exist at the particle s external surface, where the oxygen concentration is highest. The effectiveness factor η was then correlated with the Thiele modulus φ, which is evaluated at the external surface of the particle [Thiele, 1939], Dp φ = 2 R io, ex C gc C 2 O, ex 2 ρ S D eff. (4.27) where ρ C is the apparent density of the carbonaceous material, D eff is the effective diffusion coefficient of oxygen through the porous particle structure, and C O2,ex is the oxygen concentration at the outer surface of the particle. For large values of the Thiele modulus, oxygen does not diffuse deeply into the particle interior before being consumed. In such cases, the particle burns in the Zone II or III burning regime, deping upon the actual oxygen penetration depth. For small values of the Thiele modulus, oxygen diffuses to the particle center before being appreciably consumed. The particle burns in the Zone I burning regime for such cases. Under isothermal conditions, the extent to which diffusion effects inside the char particle are significant is solely determined by the value of the Thiele modulus. 61

92 Chapter Model calculation results Model parameters Equations (4.21) and (4.22) are integrated simultaneously with Equations (4.6) and (4.7). In the results presented in the following section, the kinetic parameters shown in Table 4.1 were employed, which were determined for a 25% porosity synthetic char having an apparent density of ρ C0 = 1.0 g/cm 3, specific surface area of S gc0 = 247 m 2 /g, and a surface area structural parameter of ψ = 3.0. The char was heat-treated in a laminar flow reactor at 1650 K in 6 mol-% oxygen for 47 ms before testing in the PTGA for oxidation data. The char production procedure and method for extracting kinetic parameters from mass loss and surface area data are described in Chapter 3. The char reactivities obtained at different temperatures ( K) in the PTGA environments were used to determine the rate coefficients for each reaction in the mechanism, and the Arrhenius parameters were then calculated by linear regression. The kinetic parameters for desorption reactions (R.4) and (R.5) were determined by inversion of TPD data as described in Chapter 3. The uncertainties in the kinetic parameters obtained are also shown in Table 4.1. Using the rate parameters shown in the Table 4.1, CO and CO 2 release rates and mass loss rates during TPD experiments and during oxidation tests are accurately characterized for burning in the Zone I burning regime. Table 4.1. Reaction rate parameters for a 25% porosity char A i a E i (kj/mol) σ i (kj/mol) 2 C f + O 2 C(O) + CO (R.1a) 3.87( ± 1.75) ± 13 0 C 2 (O 2 ) (R.1b) 1.95( ± 0.88) ± 13 0 C b + C f + C(O) + O 2 CO 2 + C(O) + C f (R.2) 1.18( ± 0.57) ± 24 0 C b + C f + C(O) + O 2 CO + 2C(O) (R.3) 3.74( ± 0.06) ± 3 0 C b + C(O) CO + C f (R.4) ± 5 36 ± 3 C b + C 2 (O 2 ) CO 2 + 2C f (R.5) ± 8 45 ± 7 a units of A i in mol, m 2 -surface/m 3 -fluid, s; exp ( ˆ ) or ( ) (,, σ ) k A E RT k k E f E E de = =. i i i i, eff 0 i i i In the calculations discussed, the initial char particle radius (D p0 = 100 μm) was divided into 103 increments, distributed such that the initial mass in each of the 103 volume elements into which the overall particle volume was partitioned, was nearly the same. The non-uniform radial grid was used in the finite difference representation of Equation (4.7). The resulting 62

93 Burning Behaviors of Pulverized Coal and Biomass Chars system of 412 ordinary differential equations were integrated simultaneously for the mass, oxygen concentration, and adsorbed oxygen atom concentration (site fraction) in each volume element for specified integration times up through 99% overall char conversion. With the grid employed, resolution in the particle radius during the course of burnout was approximately 1 μm Model simulation in Zone I burning regime Shown as symbols in Figure 4.5 are calculated size, apparent density and specific surface area profiles as functions of conversion for burning at a relatively low temperature (873 K) throughout the course of oxidation. The data exemplify Zone I burning: diffusion is fast compared to chemical reaction; the oxygen concentration is relatively uniform inside the particle. The time required for the particle to reach 90% conversion (τ 90%) is the same as the characteristic chemical time to reach 90% conversion, τ chem,90%, the time required to reach 90% conversion in the absence of mass transfer limitations. D p /D p0, ρ p /ρ p0, S gp /S gp T gas = 873 K P O2 = 0.06 atm T part, avg = 873 K τ chem, 90% = 3510 s τ 90% = 3510 s surface area (ψ = 3) diameter apparent density x c, conversion Figure 4.5. Calculated size, apparent density and specific surface area profiles during oxidation under Zone I conditions. The solid and dashed lines in the Figure 4.5 were calculated using the power-law modeof-burning model with α = 1, for constant diameter burning. The line for specific surface area was calculated using Equation (4.9), assuming uniform internal burning with ψ = 3.0. For this case, conversion in each volume element was the same; the surface area in each volume element evolved in a similar manner. 63

94 Chapter Model simulation in Zone II burning regime Shown as symbols in Figure 4.6 are calculated size, apparent density and specific surface area profiles as functions of conversion for burning under conditions that rer 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, moderate amounts of oxygen penetrate the particle, reaching the particle s center. At the onset of char oxidation, there is internal burning at both low and high temperatures. D p /D p0, ρ p /ρ p0, S gp /S gp T gas = 1150 K τ chem, 90% = 2.42 s P O2 = 0.06 atm τ 90% = 10.8 s T part, avg = 1158 K surface area (ψ = 1.8) diameter apparent density x c, conversion D p /D p0, ρ p /ρ p0, S gp /S gp surface area (ψ = 1.2) diameter 0.6 T gas = 1600 K 0.4 P O2 = 0.06 atm T part, avg = 1645 K 0.2 τ chem, 90% = s τ 90% = 0.37s x c, conversion apparent density Figure 4.6. Calculated size, apparent density and specific surface area profiles during oxidation under Zone II conditions. (top) moderate temperature (bottom) high temperature. 64

95 Burning Behaviors of Pulverized Coal and Biomass Chars At moderate gas temperatures (T gas ~ 1150 K), 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 Figure 4.6 were calculated using the power-law mode-of-burning 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. No constant value of α yields good agreement over the entire conversion range. At higher temperatures (T gas = 1600 K), 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 Figure 4.6 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 where internal burning is significant. Note the significant increases in burning times due to mass transport limitations when burning under Zone II conditions. At T gas = 1150 K (weak Zone II conditions), τ 90% is about 4.5τ chem,90% and at 1600 K (strong Zone II conditions), τ 90% is about 176τ chem,90%. When the overall particle conversion are used in Equation (4.9), no value of ψ yields the type variations in surface area with conversion shown in Figure 4.6. However, assuming that only reductions in apparent density lead to changes in specific surface area, the model of Bhatia and Perlmutter [1980] can be modified for Zone II burning by replacing the quantity (1-x c ) in Equation (4.9) by ρ C /ρ C0. Under Zone I burning conditions where constant diameter burning is exhibited, ρ C /ρ C0 equals (1-x c ), rering no change in predictions for Zone I applications. Thus, for both Zone I and Zone II burning: S gc = S gc0 1 ψ ln( ρ C ρ C,0 ). (4.28) 65

96 Chapter 4 where ρ C is the overall apparent density of the particle at conversion x C. The solid lines through the surface area data in Figure 4.6 were plotted employing this expression for the specific surface area of the particle employing different values of ψ from that determined for Zone I burning. Agreement is adequate, the model capturing the surface area evolution characteristics. It is indicated that with higher burning temperature, the structural parameter ψ is smaller compared to the value determined in Zone I burning. Since the structural parameter is experimentally obtained in the PTGA under Zone I burning conditions, this value is more suitable for burning under Zone I conditions. In the Zone II burning, with the internal burning much less, the pore structures are expected to open up slower, resulting in smaller structural parameter ψ. It should be noted that the noise in the predicted apparent density and surface area profiles is a consequence of not having a fine enough grid. With the grid used, the model is restricted to discrete decreases in diameter, on the order of 2 μm (1 μm resolution in radius). With a finer grid, the decreases in diameter with mass loss can be more accurately tracked, yielding smoother variations in apparent density and surface area with mass loss. Plotted in Figure 4.7 are calculated oxygen concentration profiles established inside an initially 100 μm diameter char particle burning under strong Zone II conditions, in 6 mole-% oxygen at 1600 K. At the earliest time shown (at 0.32% conversion), there is a considerable amount of oxygen inside the particle, however there is relatively little mass loss at early times because of the low concentration of adsorbed O-atoms. As time progresses, the adsorbed O- atom concentration increases and simultaneously, the gas-phase oxygen concentration inside the particle decreases as higher reaction rates near the particle periphery prevent the penetration of additional oxygen. By 2.5% conversion, a steep oxygen concentration gradient is established near the outer surface of the particle with relatively little oxygen inside the particle. Burning is significant only in the outer portions of the particle, the reactivity decreasing by about an order of magnitude 3 μm into the particle. By 34% conversion, the mean pore size has increased to the extent that oxygen more readily penetrates the particle, and the oxygen level inside the particle starts to increase, the internal burning becoming more significant. As the pores merge and coalesce further, the level of oxygen inside the particle increases. By about 80% conversion, the O 2 concentration at the particle center is roughly half that at the outer surface, and burning is significant throughout the particle volume. It should be noted that the particle diameter is not the same for each of the profiles shown in the figure 66

97 Burning Behaviors of Pulverized Coal and Biomass Chars for the diameter is decreasing with conversion from nearly the onset of oxidation under these strong Zone II burning conditions. It should also be noted that the O 2 concentration at the outer surface of the particle is not the same at each extent of conversion. The calculations indicate that the particle temperature varies under Zone II burning conditions, increasing from an initial value corresponding to the temperature of a non-reactive sphere in the hot gaseous environment to a value that exceeds the gas temperature. As the particle size decreases during oxidation, radiative heat losses decrease, and the particle temperature increases. The average temperature over the lifetime of the particle is shown in Figure 4.8. The burning times and particle temperatures predicted by the model for Zone II burning conditions are in agreement with the measurements of Mitchell et al., [1992] for the char of a low-volatile bituminous coal burning in 6 mol-% oxygen at nominally 1600 K. x c (%) P s (atm) D p (μm) Figure 4.7. Evolution of O 2 concentration profiles established inside a char particle (D p0 = 100 μm) burning under strong zone II conditions (T gas = 1600 K, y O2 = 6%), with surface oxygen partial pressure and particle diameter for corresponding conversions shown at the right. 67

98 Chapter 4 Figure 4.8. Calculated particle temperature as a function of conversion at different oxidation conditions. The O 2 concentration profiles shown in Figure 4.7 indicate that at the earliest extents of mass loss, the effectiveness factor is relatively high (η > 0.5) for the particle is nearly completely penetrated by oxygen. As burning continues, the effectiveness factor decreases, reaching a minimum value when conversion is about 2.5% in this 6 mol-% O 2, 1600 K environment. The effectiveness factor then begins to increase, approaching unity as the conversion approaches 100%. 1 η, effectiveness factor T gas = 873 K, 6% O T gas = 1150 K, 6% O 2 T gas = 1200 K, 6% O 2 T gas = 1400 K, 6% O T gas = 1600 K, 6% O 2 φ -η equation with m = 0 φ -η equation with m = 1 φ -η equation with m = 2 1E-3 1E φ m, modified Thiele modulus Figure 4.9. Effectiveness factor versus Thiele modulus 68

99 Burning Behaviors of Pulverized Coal and Biomass Chars 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. Results are shown in Figure 4.9, where the effectiveness factor is given as a function of the Thiele modulus, φ. The φ η relation is described adequately using the following expression, η = φ m tanhφ m, (4.29) where φm = φ ( m + 1) / 2. Metha and Aris [1971] used this modified Thiele modulus approach to account for reaction orders other than unity when using the above relationship to determine η, which is based on char reactivity being proportional to the oxygen concentration to the first power (m = 1). Note that under weak Zone II burning conditions (in the 1150 and 1200 K, 6 mol-% O 2 environments), effectiveness factors can exceed unity, a consequence of the adsorbed oxygen atom concentration being higher on internal surfaces than on the surfaces near the particle s periphery. This occurs only during weak Zone II burning, at late extents of conversion (for example, x c > 85%). Using Equation (4.29) in the model to determine η instead of using Equation (4.26) yields results similar to those shown in the figures presented. With the relation, the internal burning can be accounted for in the manner originally put forth by Thiele using the reduced reaction mechanism and not power-law kinetics. φ m 4.5 Mode-of-burning model development Model formulation Derivation of the mode-of-burning model for spherical char particles follows the lead of Essenhigh [1988; 1994] and starts with the following relationship between particle mass, apparent density and diameter for the ash-free particle: m C = ρ C πd 3 p /6. Differentiating with respect to time yields the following expression for the particle's rate of mass loss: 3 3 dm ρπ C Dp dd C p πdp dρc = +. (4.30) dt 2 dt 6 dt The first term on the right-hand-side is the mass loss rate due to burning at the external 69

100 Chapter 4 particle surface and the second term is the mass loss rate due to internal burning. Dividing through by the particle external surface area yields the following expression for q, the overall particle burning rate per unit external surface area: 1 dm C ρ dd C p Dp d ρ C q = 2 + π Dp dt 2 dt 6 dt. (4.31) The first term in the parenthesis on the right-hand-side of this equation defines R ic,ex and the second term, R ic,in, for external and internal burning rates per unit external surface area, respectively, i.e., R 1 dm dd C ρc = D dt = 2 dt ic, ex 2 π p ex p 1 dmc Dp d ρc and Ric, in = 2 π D dt = 6 dt p in.(4.32)(4.32a,b) Dividing these two terms yields 3 R, 3 ( dmc dt ic in ) = =. (4.33) ( ) d ρ ρ ρ dd D R D dm dt C C C in p p ic, ex p C ex Using the concepts put forth by Thiele [1939], the internal burning rate is related to the maximum possible burning rate (R ic,in ) max by the effectiveness factor: R ic,in = η (R ic,in ) max. The maximum possible internal burning rate occurs when the particle temperature and oxygen concentration throughout the particle are the same as that existing at the particle's external surface. Under such conditions, the internal burning rate per unit internal surface area is the same as the external burning rate per unit external surface area. Thus, for the maximum possible mass loss rate, maximum mass loss rate mass loss rate on on internal surfaces ( dmc dt),max external surface dm in C dt = 3 2 total internal ( π /6) D ρ total external CSgC πdp surface area surface area ( ) ex. (4.34) With the definition of the effectiveness factor, combining Equations (4.33) and (4.34), yields the following expression for the change in particle apparent density with respect to a change in diameter: 2 d ρ ηρ C CSgC =. (4.35) dd 2 70

101 Burning Behaviors of Pulverized Coal and Biomass Chars Before this equation can be integrated, the effectiveness factor must be expressed in terms of apparent density and size. From the calculation from the previous section, Mehta and Aris s [1971] correlation between effectiveness factor and modified Thiele modulus is used in the model. The Thiele modulus is evaluated at the external surface of the particle. As the particle burns, the Thiele modulus φ changes in accordance with changes in surface area and other properties of the particle. Assuming that Knudsen diffusion dominates the transport of oxygen through the particle pores, the effective oxygen diffusion coefficient can be expressed in terms of the particle porosity (θ ), temperature (T p ), and mean pore radius (r p ) as follows: D 2r 8k N T r D θ = θ θ K T. (4.36) K p B AV p p eff O ˆ 2 p τ 3τ π M τ O2 Here, K O2 is a constant implicitly defined by the last equality in Equation (4.36). Using Equations (4.17) and (4.36) in Equation (4.27), yields DρcS gc νo R 2 ic, exτ φ = 2 2K ˆ θ O M [ ] 2 C O2 rf T ex p 1/2. (4.37) For large values of φ, the effectiveness factor can be estimated for any order of reaction m using the following relation: η 3 2 = φ m + 1 1/2. (4.38) This limiting form is based on the functional relationship between η and φ for irreversible, first-order reaction in a sphere and uses the results of Mehta and Aris [1971] for evaluating φ for arbitrary reaction order. Large values of φ correspond to little penetration of oxygen inside the particle. Thus, this limiting relationship is deemed to be appropriate for burning in the Zone II burning regime. An analogous relation was used by Essenhigh [1988] in developing his exted resistance model to account for the internal particle burning. Using Equations (4.37) and (4.38) in Equation (4.35), and writing the porosity in terms of the true and apparent densities (θ = 1-ρ C /ρ t ), the following expression for the variation in 71

102 Chapter 4 apparent density with diameter can be derived: [ 2 ] ( + ) 1/2 ˆ 2 O 3 2 C p ex ρc gc dρc 6ρ K rf M T O S C ρ C = 1 =. (4.39) dd D ρ ν R m 1 τ 2φ t O2 ic, ex m This equation can be rearranged and integrated, assuming isothermal conditions, to yield the following expression for the mode of burning when Knudsen diffusion controls oxygen transport through the pores: where ( 0 ) ( ) ρc ρt ρ D C p = ρc0 ρt ρ C D p0 ζ, (4.40) [ 2 ] ( m+ ) K rf Mˆ T O 3D ρ S ζ = 6 = ν O R 2 ic, ex 1 τ 2φmθ 1/2 O2 C p ex p c gc, (4.41) Equations (4.40) and (4.41) describe how apparent density varies with diameter during oxidation of a porous carbon particle initially at ρ c0 and D 0. It shows that during oxidation, ρ c and D at any time dep on the reaction rate, which varies with char conversion. Since for spherical particles, m C /m C0 = (ρ C /ρ C0 )(D p /D p0 ) 3, the following relation is obtained for m c /m c0 : m m ( 0 ) ( ) ρ ρ ρ ρ C C C t C = C0 ρc0 ρc0 ρt ρc 3/ ζ. (4.42) This equation gives variations in apparent density with the fractional remaining mass. Equations (4.40), (4.41) and (4.42) represent the mode-of-burning model for carbon particles when account is made for pore intersections, surface roughness, intrinsic reactivity and Knudsen diffusion inside pores. For a given extent of conversion of a spherical char particle, ρ c can be determined from Equation (4.42), and then D can be determined from Equation (4.40) Impact of Ash The mass of the char particle (m p ) at any time equals the mass of the ash plus the mass of the combustible material that has not yet been burned. Assuming that no ash leaves the 72

103 Burning Behaviors of Pulverized Coal and Biomass Chars particle during the combustion process, the apparent density of the ash-containing char particle (ρ p ) is given by ( 1 X ) ( ) ( ) ( ) 1 Xa a X m 0 p m a p0 Xa0 = + = +, (4.43) ρ ρ ρ m m ρ m m ρ p a C p p0 a p p0 C where ρ c is determined from Equation (4.42). 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 distributed between the specific surface area of the ash and that of the carbonaceous material, on a mass-weighted basis: ( 1 ) S = X S + X S. (4.44) gp a ga a gc The specific surface area of the ash is taken to be 5 m 2 /g, a value measured for several samples of coal ash. The ash-free fractional conversion is calculated from values for X a0 and m p /m p0 (the quantities actually measured) using the expression m m m / m X = 1 x = c p p0 a0 c c0 1 Xa0. (4.45) 4.6 Model implementation Test materials To validate and implement the model, a series of combustion tests using synthetic chars was performed. The use of synthetic char allows the study of char combustion without the complications of unknown chemical composition and unknown porosity inherent in real coals and without the possible catalytic effects of ash. A procedure for making a synthetic char particle with controlled porosity has been presented in Chapter 3. Chars having porosities of 16%, 25%, and 36% were produced. The synthetic chars were pulverized and sieved to yield particles in the μm size range for this study. 73

104 Chapter 4 The synthetic chars were injected into the entrained laminar flow reactor when the gas flow rates were adjusted to provide a test environment containing 6 mol-% oxygen at nominally 1650 K. Chars of coal and biomass were produced by injecting the raw fuels into the flow reactor when gaseous environments containing 12 mol-% oxygen at nominally 1650 K for Lower Kittanning coal and 8 mol-% oxygen at nominally 1243 K for Almond Shell were established inside the reactor. Measured amounts of char were fed to the flow reactor and partially reacted samples were extracted at selected residence times (17 to 117 ms) and weighed. Particle size distributions, apparent densities, specific surface areas, and reactivities were measured for each sample Results and discussion Comparisons between measured and calculated mass remaining, apparent density, and diameter profiles for the 25%-porosity synthetic char particles burning in the flow reactor under Zone II burning conditions are shown in Figure The symbols are the values determined from the experimental measurements, with error bars representing the scatter of the data from different measurement replicates. The solid lines were calculated employing the char combustion model [Mitchell, 2000], using properties measured for the 47-ms char as initial values when integrating the governing equations. The dashed lines before 47 ms were arbitrarily drawn to represent the variations of the particle properties during devolatilization process. The agreement between calculation and measurement is deemed to be good, and is typical of that observed with the other synthetic chars. The model adequately predicts the behaviors of the synthetic char particles burning under Zone II conditions, conditions in which the overall char-particle burning rate is controlled by the combined effects of pore diffusion and the intrinsic chemical reactivity of the carbonaceous particle material. 74

105 Burning Behaviors of Pulverized Coal and Biomass Chars m c /m c Time (ms) Apparent Density - ρ c /ρ c Time (ms) 1.0 Particle diameter - D/D Time (ms) Figure Mass remaining, apparent density and particle diameter profiles during oxidation of the 25% porosity char exposed to 6 mol-% oxygen at nominally 1650 K. 75

106 Chapter 4 Measured values of D p /D p0 and ρ C /ρ C0 for partially reacted chars extracted from the flow reactor are plotted against the measured values of m C /m C0 in Figure The solid lines in the figures were calculated using the mode-of-burning relation given by Equations (4.40) and (4.42) with ζ evaluated using measured data in Equation (4.41). The reactivities 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 flow reactor were calculated from an energy balance: energy loss via conduction and radiation from the particle are balanced by energy generated via chemical reaction. 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 Figure 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 [Campbell et al., 2000]. The density of ash was taken to be 2000 kg/m 3 when determining the apparent density of the ash-containing particles via Equation (4.43). As observed, the char of the Lower Kittanning coal burns with relatively little change in apparent density until late in burnoff, when the particle apparent density increases, approaching that of the ash in the particle. The almond shell char particles were mostly ash after devolatilization; particles extracted from the flow reactor at the earliest resident time (17 ms) contained over 50% ash. Due to the high-ash content of the almond shell biomass, the apparent densities of the almond shell char particles increased quite early during burnoff, approaching that of the ash as the carbonaceous material was burned away. The 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 Figure 4.12 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. 76

107 Burning Behaviors of Pulverized Coal and Biomass Chars % porosity % porosity ρ C /ρ C0 0.6 D p /D p x c, conversion x c, conversion % porosity % porosity ρ C /ρ C0 0.6 D p /D p x c, conversion x c, conversion % porosity % porosity ρ C /ρ C0 0.6 D p /D p x c, conversion x c, conversion Figure Measured and calculated mode-of-burning profiles for the synthetic chars. The solid lines are calculated based on the mode-of-burning relations given by Equations (4.40) and (4.42) with ζ evaluated using measured data. 77

108 Chapter Lower Kittanning Coal 5% ash 10% ash 20% ash Lower Kittanning Coal ρ p /ρ p D/D m p /m p0 m p /m p0 ρ p /ρ p Almond Shell 20% ash 30% ash 40% ash D/D Almond Shell m p /m p m p /m p0 Figure Measured and calculated mode-of-burning profiles for the Lower Kittanning coal and almond shell biomass chars. The solid lines are calculated based on the mode-of-burning relations given by Equations (4.40) and (4.42) with ζ evaluated using measured data and ash content considered. The performance of the intrinsic reactivity based mode-of-burning model is compared with that of the power-law relations in Figure The power-law relations are shown with different values of parameter α. The burning behaviors from the mode-of-burning model were calculated for temperatures of 1150 K and 1600 K, i.e., in the weak and the strong Zone II burning regimes. As shown in this figure, the power-law relations with constant parameters could somewhat describe the changes in the particle apparent density and diameter with mass loss in the strong Zone II burning regime. However, in the weak Zone II burning regime, the calculations from the mode-of-burning model show a transition from near Zone I burning to strong Zone II burning with conversion, and the power-law relations with constant parameters can not accurately describe these changes. 78

109 Burning Behaviors of Pulverized Coal and Biomass Chars 1.0 α = T = 1600 K α = 0.1 T = 1150 K α = 1 T = 1150 K α = 0.5 α = 0 ρ C /ρ C α = 0.5 α = 1 D/D α = 0.1 T = 1600 K 0.2 Dashed lines: power-law relations Solid lines: model calculation m c /m c0 0.2 Dashed lines: power-law relations Solid lines: model calculation m c /m c0 Figure Comparison of the performance of power-law relations and the intrinsic reactivity based mode-of-burning model under Zone II conditions. 4.7 Summary A direct numerical simulation of a burning char particle was used to examine the changes in size, apparent density and surface area as particles burn in the Zone II combustion regime. Predicted results indicate that the power-law mode-of-burning model is not capable of predicting the variations in the sizes and apparent densities of char particles undergoing oxidation in the Zone II burning regime. If the power-law model were to be modified to capture the observed variations, the burning mode parameter α would have to vary during the course of burning. At temperatures less than about 900 K, oxygen completely penetrates char particles having sizes of the order 100 μm and less, and the particles burn under Zone I conditions. As temperature is increased ( K range), 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, 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 level of adsorbed oxygen, rering relatively low heterogeneous reaction rates. As the adsorbed oxygen level builds up, oxygen inside the particle is consumed, confining reaction to the periphery of the particle. A mode-of-burning model that accurately characterizes the variations in the particle diameter and apparent density with mass loss during the char oxidation process is developed 79

110 Chapter 4 and validated. The mode-of-burning model is based on char reactivity and takes into account pore intersections, surface roughness, and Knudsen diffusion inside pores. Like all char oxidation models based on the intrinsic chemical reactivity of the char, the model requires the use of a model to describe the variation in the specific surface area of the char with mass loss. When burning under Zone I burning conditions, the surface area model developed by Bhatia and Perlmutter is quite accurate. By replacing the quantity (1-x c ) in the random pore model by ρ C /ρ C0, it can be used for Zone II burning. Under Zone II burning conditions, adequate variations in specific surface area with mass loss can be achieved by lowering the structural parameter ψ for high temperature, accounting for the difference in pore structure evolutions between Zone I and Zone II. With the new mode-of-particle-burning model, calculated variations in apparent density and size during the oxidation process dep upon the intrinsic chemical reactivity of the char and the instantaneous state of the char particle, a realistic concept. Using the char combustion model developed, it is possible to predict accurately the behaviors of coal and biomass char particles undergoing oxidation at the high temperatures that exist in real boilers and furnaces. 80

111 Chapter 5 Modeling of Char Oxidation at Elevated Pressure The char combustion process has been extensively studied. The approaches taken are reviewed and the shortcomings are discussed in this chapter. The single char particle conversion model developed in Chapter 4 is used here to characterize the separate effects of total pressure, oxygen mole fraction, and oxygen partial pressure on char reactivity in different burning regimes. At elevated pressures, the modeling of coal combustion has to take into account of the oxidation of char particles of different structures. A char combustion model using the particle population balance model and the char structure model is developed and implemented on Lower Kittanning coal chars produced from high pressure flow reactor experiments. 5.1 Introduction Char combustion model Global kinetics In early work, an empirical n th order power-law reaction rate equation was often used to describe kinetics of char oxidation: C + O2 CO / CO2 [Smith, 1982; Hurt and Mitchell, 1992; Monson et al., 1995; Solomon and Fletcher, 1994; Hurt et al., 1998]. E q= ksp = A exp P RT n obs n Os obs 2 Os 2, (5.1) where k s is the apparent rate coefficient; A obs and E obs are the observed Arrhenius parameters; P O2,s is the oxygen partial pressure at the surface; and n is the global reaction order. This simple equation provides a method for estimating char oxidation rates in comprehensive computer models. By measuring the reaction rate at high temperature for coal chars, Mitchell [1995] and Hurt and Mitchell [1992] obtained a global reaction order of 0.5, and observed activation energies between 63.9 and kj/mol. Studies have shown that the reaction order, n, varies between zero and unity, deping on the reaction conditions. In a review by Hurt and Calo [2001], global intrinsic reaction orders from various studies have been compiled. It is shown 81

112 Chapter 5 that at the low temperature Zone I regime, high reaction order was observed (0.6-1) [Du et al., 1990; Sorenson et al., 1996; Lin et al., 2000; Suuberg et al., 1988; Hecker et al., 1992; Ranish and Walker, 1993; Harris and Smith, 1990; Croiset et al., 1996]. In the Zone II regime, some studies showed an intrinsic reaction order of zero [Mathies, 1996; Monson et al., 1995; Mitchell and McLean, 1982; Smith and Tyler, 1974; Hamor et al., 1973; Kurylko and Essenhigh, 1973; Essenhigh, 1996; Young and Smith, 1981], but some other studies showed intrinsic reaction orders of unity [Smith, 1971; Field, 1970]. This inconsistency indicates the inadequacy of a global rate expression for predicting rates over wide ranges of experimental conditions. This power-law rate expression, due to its lack of theoretical basis, has been controversial. It cannot predict the reaction rates over wide ranges of conditions, such as char oxidation at high pressures (Monson et al., 1995; Essenhigh, 1996). The significant pressure depence of observed kinetic parameters is deemed as evidences of the inadequacy of this global reaction rate expression in predicting the reaction rates. By using the Haynes turn over model, Hurt and Haynes [2004] showed that the different levels of surface heterogeneity can explain the high fractional orders in the carbon-oxygen reaction. Therefore, a detailed model of the carbon-oxygen heterogeneous reaction mechanism is necessary. Langmuir-Hinshelwood kinetics Since Langmuir discovered the attachment of oxygen to carbon surfaces, research on the adsorption and desorption mechanism for gas-solid reactions has been extensively conducted. A simple model for the carbon-oxygen reaction involves chemisorption of oxygen on the carbon surface, adsorbed oxygen surface diffusion, the reaction of adsorbed oxygen on the surface, and desorption of product gas from the surface [Langmuir, 1915; Hinshelwood, 1925; Essenhigh, 1981; Essenhigh, 1991; Du et al., 1991]. Langmuir-Hinshelwood kinetics is more meaningful than the global reaction rate Equation (5.1), with the following reactions: ( ) C+ O2 C O (R.1) C( O) CO. (R.2) The corresponding reaction rate equation, by assuming steady state condition for surface complex concentration, [C(O)], is: kk 1 2PO 2 r = kp + k 1 O2 2. (5.2) 82

113 Modeling Char Oxidation at Elevated Pressure However, the predicted reaction order is low at low temperature and high at high temperature, which is opposite to the experimental behavior. Langmuir-Hinshelwood kinetics cannot describe the observed almost constant reaction order over a times of change in oxygen partial pressure [Sawaya et al., 1999; Suuberg et al., 1988]. More detailed reaction mechanism By utilizing isotope-labeling techniques using 18 O 2 and 16 O 2 as reactants, Walker et al. [1967] drew the conclusion that the adsorbed oxygen atoms C(O) were precursors to the formation of both CO and CO 2. After establishing this, Walker proposed the formation of CO 2 from surface complexes as C( O) + C( O) CO2 + C f. Zhuang et al. [1994] combined spectroscopic and temperature-programmed desorption techniques and identified the actual chemical structure of surface oxide complexes formed on the carbon surface during char oxidation, such as lactone, acid anhydride, carbonyl, and ether-type complexes. Zhuang also distinguished the complexes responsible for the production of CO and CO 2. CO desorbs primarily from carbonyl and/or ether-type complexes, while CO 2 desorbs primarily from lactone and/or acid anhydride-type complexes, i.e., ( ) ( ) C O CO C O CO C f. Here the complex C(O) represents the carbonyl and ether-type complexes, while C 2 (O 2 ) denotes the lactone and acid anhydride-type complexes. It is assumed that each oxygen atom occupies one carbon site. In transient kinetic tests, when switching quickly from 18 O 2 to 16 O 2, isotopically mixed carbon dioxide, C 18 O 16 O, is observed as the product gas [Zhuang et al., 1995; Haynes and Newbury, 2000]. This observation supported the following reaction: ( ) 2 / 2 C O + O CO CO. The kinetics of this reaction has been studied by comparing the population of complexes on a surface before and after exposure to isotopically labeled oxygen. Complexes were formed initially on the carbon surface by reaction with 18 O 2, and then switched to 16 O 2. Comparison of TPD spectra from just before and after exposure in 16 O 2 showed that the amount of labeled ( 18 O) complexes decreased. This observation confirmed the occurrence of this reaction. This reaction, together with the two reactions in Langmuir-Hinshelwood kinetics, forms the 83

114 Chapter 5 following 4-step reaction mechanism, which is the basis of the reaction mechanism developed in this work. 2 C f + O 2 2 C(O) (R1) C b + C f + C(O) + O 2 CO 2 + C(O) + C f C b + C f + C(O) + O 2 CO + C(O) + C(O) C b + C(O) CO + C f Studies showed that both CO and CO 2 were primary products of the heterogeneous char oxidation process [Arthur, 1951; Rossberg, 1956; Walker, 1959], although CO 2 may also be formed through homogeneous reactions within the porous network of char. The ratio of carbon monoxide to carbon dioxide (CO-to-CO 2 ratio) during char oxidation has been extensively studied. Walker et al. [1959] and Mitchell [1988] correlated this product ratio to the particle temperature with Arrhenius-type expression, such as CO/CO 2 = A exp(-e/rt p ). Other researchers [Otterbein and Bonnetain, 1968; Phillips, 1970; Tognotti et al., 1990; Du et al., 1991] revised this expression based on the observation of the effect of oxygen partial pressure on the CO-to-CO 2 ratio, and proposed another expression: CO/CO Rossberg [1956] Tognotti [1990] Skokova: Cellulose derived Pitch derived Graphite Lower Kittanning Coal 2 n O2 ( p) (R2) (R3) (R4) CO / CO = A P exp E / RT. (5.3) Almond shell CO/CO 2 (AS) = 24858e /(T/1000) Arthur [1951] CO/CO 2 (LK - 10%) = e /(T/1000) Phillips: 10 m Torr 100 mtorr Otterbein [1968] (LK - 1%) /T - [(1000 K) -1 ] Figure 5.1. General trs of CO-to-CO 2 ratio as a function of inverse temperature [Campbell, et al., 2000]. 84

115 Modeling Char Oxidation at Elevated Pressure The findings of some studies investigating the CO-to-CO 2 ratio are summarized in Figure 5.1. It is clear that all the studies showed increase in CO-to-CO 2 ratio with increasing temperature, and a weak or slight decrease in product ratio with increasing oxygen partial pressure. The work by Campbell et al. [2002] and Skokova [1997] showed an inverse depence of the CO-to-CO 2 ratio on graphiticity, i.e., the CO-to-CO 2 ratio for highlyordered graphite is lower than that of young chars, such as biomass char Effects of pressure on char oxidation rates At elevated pressures, coal combustion can produce chars with very different structures; the diffusion coefficient of reactant gas is different from that at atmospheric pressure; and, the chemical kinetics also changes with pressure or oxygen partial pressure. In order to optimize the coal combustion process and reactor designs, the effects of pressure have to be investigated and characterized. Some researchers have investigated the effect of pressure on the combustion rate of coal char. Joutsenoja et al. [1999] performed pressurized combustion experiments on coal particles ( μm) of different ranks for total pressures of 2-10 atm, temperatures of K, and oxygen mole fractions of 3-30% in a pressurized entrained flow reactor. The time for 90% conversion of the chars was measured. For the least reactive anthracite sample studied, the reaction rate increased the most at increased pressure, whereas pressure had no effect on the combustion of the most reactive lignite sample. Saastamoinen et al. [1996] measured combustion rate and temperature of burning coal particles in a pressurized entrained flow reactor under the following conditions: gas temperature K, pressure 2-8 atm, and oxygen partial pressure atm. The effect of increased pressure was greatest near 1 atm and less at higher pressures. The pressure effect was still obvious at pressures higher than 10 atm for less reactive coals and small particles, but the effect of pressure was small for reactive coals and large particles. In addition, char reactivity was also affected by the swelling behavior during pyrolysis at elevated pressures. The general trs of different effects of total gas pressure and oxygen partial pressure are summarized in Table 5.1. Turnbull et al. [1984] measured burn-out time for mm carbon particles in an airfluidized bed at pressures up to 17 atm and bed temperatures of K. The effect of increased pressure was to increase the combustion rate by increasing the oxygen partial 85

116 Chapter 5 pressure. As pressure increases, the chemical rate controlling steps become less important, and combustion is more diffusion-controlled. Table 5.1. General Trs of the Effect of Oxygen Partial Pressure with Increased Total Pressure on the Combustion Rate of Char Particle [Saastamoinen et al., 1996] Oxygen mole fraction, y O2 Constant Decreased Oxygen partial pressure, P O2 Increased Constant Diffusion control, Da 1 Large particle High temperature Reactive fuel High oxygen content Kinetic control, Da 1 Small particle Low temperature Nonreactive fuel Low oxygen content Weak effect Increasing effect Decreasing effect Weak effect Richard et al. [1994] measured the effects of pressure, oxygen partial pressure, oxygen flow rate, total gas flow rate and temperature on the combustion rates of chars from three different coals in a small fixed bed, linked to a high pressure thermobalance. The experiments were performed at total pressures of 1-21 atm and temperatures of K. It was observed that for all three chars, the combustion rate increased with oxygen partial pressure at constant total pressure. The combustion rate decreased with increasing total pressure from 1-5 atm at constant oxygen partial pressure, and further increase in total pressure had less effect on combustion rate. Monson et al. [1995] performed char oxidation experiments at total pressure of 1, 5, 10, and 15 atm in a drop-tube reactor with temperatures between 1000 and 1500 K and 5-21 mol- % oxygen. The results showed that increasing total pressure from 1 to 5 atm in constant gas composition environment led to a modest increase in reaction rate, while the rate decreased with further increases in pressure from 5 to 15 atm. It was also noted that the apparent reaction rate coefficients in global reaction expression showed significant pressure depence, which implies that the global rate equation is not valid over the range of pressures. Lester et al. [1981] studied the intrinsic reaction rates of bituminous coals over a particle temperature range of K, total pressures of atm, and oxygen mole fractions 86

117 Modeling Char Oxidation at Elevated Pressure of 10-50% in a shock tube. It was found that the surface reaction rates decreased with increasing total pressure from atm. Croiset et al. [1996] performed bituminous coal combustion experiments in a fixed-bed reactor at K for total pressures of 2, 6, and 10 atm. It was observed that the effect of increasing total pressure up to 6 atm was to decrease the reaction rate if the overall n th -order rate equation is expressed in terms of oxygen partial pressure, but this effect was very weak if the overall n th -order rate equation is expressed in terms of oxygen mole fraction. Another effect of increasing total pressure is that the reaction rate changes from chemistry-controlled to diffusion-controlled at a lower temperature. Tidona [1980] used a laser to ignite the coal particles ( μm) in quiescent oxygen at room temperature, and measured the burning time of these particles at three different pressures (1, 1.5, and 2 atm). The burnout times were observed to vary with the square of the initial particle diameter, but did not change with pressures. Essenhigh and Mescher [1996] compiled three sets of experimental data at elevated pressures up to 15 atm, and used a model based on gas-solid rate kinetics and diffusion rate kinetics. The reaction rates from the model prediction agreed reasonably well with the experimental data. It showed indepence of burning rates with pressure for Tidona data [1980], and a minor influence of pressure on reaction rate at higher temperature due to decreasing reaction penetration factor with increasing pressure for Monson et al. data [1995]. Essenhigh and Mescher [1996] also measured the temperatures of coal particles of similar size to Tidona s coal particle during heating up. The ignition temperature is determined as the point of inflection of the T-t curve. No depence of ignition temperature on pressure was observed for the Essenhigh and Mescher data [1996]. It was then concluded that there is minor or no influence of pressure on combustion rates in the temperature range studied ( K). From the studies cited above, some authors showed a relatively small depence of the rates of char oxidation on total pressure whereas others showed a significant impact. In efforts to resolve these controversies, experiments were conducted at elevated pressures in both the PTGA and the high pressure flow reactor. Char combustion models were developed to characterize the separate effects of total pressure and oxygen mole fraction on char reactivity. 87

118 Chapter Calculated results from single char particle combustion model Effective diffusion coefficient In the case of coal combustion in the Zone II burning regime, pore diffusion is a controlling step in determining the char oxidation rate in addition to chemical kinetics. Two major mechanisms for pore diffusion are bulk and Knudsen diffusion. Bulk diffusion occurs when the pores are relatively large or the gas concentration is high, therefore the collisions of gas molecules with pore walls are negligible. On the contrary, Knudsen diffusion occurs when the pore size is small or gas concentration is low, and the molecular collisions within the pores are less significant compared to collisions with pore walls. The effective diffusion coefficient could be controlled by bulk diffusion, Knudsen diffusion or both, deping on the temperature, pressure and mean pore size. Over a wide range of total pressures, the bulk diffusion coefficient is inversely proportional to total pressure, while Knudsen diffusion is indepent of total pressure; therefore, bulk diffusion becomes more important as total pressure increases. With an increase in total pressure at a certain temperature, the Knudsen diffusion rate remains fixed, but the bulk diffusion rate decreases. Knudsen diffusion is also proportional to mean pore radius and, hence, increases with conversion since the mean pore radius enlarges with conversion. As pores enlarge during combustion, the limiting diffusion mechanism changes. Therefore, the relative importance of bulk and Knudsen diffusion is not solely determined by the individual values of pressure and mean pore radius, as shown in Figure 5.2. When the mean pore radius is small, such as 0.01 μm (Figure 5.2 (a)), bulk diffusion is apparently faster than Knudsen diffusion. When the pore radius is increased to 0.1 μm (Figure 5.2 (b)), the bulk diffusion coefficient could be higher or lower than the Knudsen diffusion coefficient, deping on temperature and pressure conditions. Further increase of pore radius to 1 μm results in a lower bulk diffusion coefficient than the Knudsen diffusion coefficient at most of the temperatures and pressures presented (Figure 5.2 (c)). Knudsen diffusion control When D Keff, D O2, the mass transport process is controlled by Knudsen diffusion. For example, when DO 2 100D, K eff, the following expression relating pore radius, particle temperature and pressure is derived: 88

119 Modeling Char Oxidation at Elevated Pressure 1.17 T rp p 6 θ KO (5.4) 2 τ For a char particle with a certain porosity θ and pore tortuosity τ, the mean pore radius and burning conditions such as T and P follow the constraint of Equation (5.4). Bulk diffusion can be neglected in calculating the effective diffusion coefficient, i.e., Deff DK, eff. Bulk diffusion control When D Keff, D O2, the mass transport process is controlled by bulk diffusion. When for example, DKeff, 100D O2, yielding 1.17 T rp p 2 θ KO (5.5) 2 τ Under bulk diffusion limited conditions, the mean pore radius and burning conditions such as T and P have to follow the constraint in Equation (5.5), and the effective diffusion coefficient can be approximated as the bulk diffusion coefficient, i.e., D D. eff O 2 In order to clearly show the effects of combustion conditions on the different mechanisms of pore diffusion, some sample calculations for 50% porosity and different combustion conditions were made and different diffusion control regions were identified and shown in Figure 5.3. In Figure 5.3 (a), example calculations using D 10D and D O2 K, eff, 10D as criteria for separating different diffusion control regions are shown. The calculations using D 100D and D O2 K, eff, 100D are shown in Figure 5.3 (b). In each figure, there are three K eff O2 diffusion controlling regions in terms of pore radius, separated by two planes representing Equations (5.4) and (5.5). The top and bottom parts are the bulk diffusion and Knudsen diffusion control regions, respectively. The middle part is the transition control region, where bulk diffusion and Knudsen diffusion are comparable. The comparison of Figure 5.3 (a) and (b) indicates that more strict criteria (as in Figure 5.3 (b)) give a wider range of pore radii for transition control region. K eff O2 89

120 Chapter 5 (a) (b) Figure 5.2. Calculated bulk and Knudsen diffusion coefficients as a function of temperature and pressure for different pore radius by assuming a porosity of 50%: (a) r p = 0.01 μm, (b) r p = 0.1 μm, and (c) r p = 1 μm. (c) 90

121 Modeling Char Oxidation at Elevated Pressure (a) (b) Figure 5.3. Different diffusion control regions and the relationships between temperature, pressure and mean pore radius calculated using (a) DO 10D and 2 K, eff DK, eff 10D (b) O2 DO 100D and K eff DK, eff 100D as the controlling criteria by assuming a porosity of 50%. O 2, Model parameters The single char particle conversion model developed in Chapter 4 was used to calculate the char reactivity for different total pressures, oxygen partial pressures and oxygen mole fractions. The intrinsic chemical reactivity of the 25% porosity synthetic char was determined from the reaction rate parameters shown in Table 4.1. Other characteristics of this char were also described in Chapter 4, Section

122 Chapter Effects of total pressure and oxygen partial pressure under chemistry-controlled conditions In the Zone I burning regime where the reactivity is controlled by chemistry only, the oxygen partial pressure within the particle is the same as that in the environment, and the reactivity is uniform throughout the particle. The calculated reactivity as a function of oxygen partial pressures is shown as symbols in Figure 5.4. The curves were plotted to show the tr of reactivity variations. These calculations were made using the chemistry model only and, hence, assume no diffusion limitation at any of the temperatures of 873, 1140 or 1600 K. Under kinetics limited burning, the reactivity increases with the oxygen partial pressure at all temperatures studied, i.e. ( RiC, ) ( PO ) ln n > 0 ln 2 T, P (5.6) However, n, (the instantaneous apparent reaction order, which is a function of T, P, and y O2 ), is not a constant over the whole range of oxygen partial pressures studied. Because these calculations are for Zone I burning with only chemistry control, the apparent reaction order, n, is actually the true reaction order. Also, n increases with oxygen partial pressure, as indicated in Figure 5.4. When P O2 increases from 0.1 to 3.2 atm, n increases from 0.82 to 0.97 at low particle temperature (873 K), from 0.45 to 0.95 at medium temperature (1140 K), and from 0.38 to 0.92 at high temperature (1600 K). Therefore, n(p O2,2 ) Tp,P > n(p O2,1 ) Tp,P when P O2,2 > P O2,1. When comparing the value of n at a fixed oxygen partial pressure for different temperatures, it is shown that the rate of reactivity increase with respect to oxygen partial pressure at higher temperature is lower, n(t 2 ) PO2,P < n(t 1 ) PO2,P if T 2 > T 1. For example in Figure 5.4, at a certain oxygen partial pressure, such as P O2 = 0.1 atm, n(873 K) > n(1140 K) > n(1600 K). 92

123 Modeling Char Oxidation at Elevated Pressure -3.0 T p = 873 K atm 5 atm 20 atm Log(R i,c ) n = 0.96 n = 0.97 (a) Log(R i,c ) Log(R i,c ) -5.5 n = T p = 1140 K 1 atm 5 atm 20 atm Log(P O2 ) n = T p = 1600 K 1 atm 5 atm 20 atm Log(P O2 ) n = 0.86 n = 0.95 n = 0.92 (b) (c) 1.0 n = 0.76 n = Log(P O2 ) Figure 5.4. Variation of intrinsic reactivities of 25%-porosity synthetic char with oxygen partial pressures at temperatures of (a) 873 K, (b) 1140 K and (c) 1600 K under purely chemistry-controlled conditions. 93

124 Chapter 5 The reactivities at different total pressures and constant oxygen partial pressure for a 16%- porosity synthetic char were experimentally studied and plotted in Figure 5.5. For an oxygen partial pressure of 0.24 atm and temperatures of 723 and 773 K, the reaction rates are almost the same during the whole range of conversion. This effect of total pressure on reactivity with constant oxygen partial pressure throughout the conversion of the char was also simulated with the model, and the results are shown in Figure 5.6. For an oxygen partial pressure of 0.06 atm, total pressures of 1, 5, 10, and 20 atm, and temperature of 873 K, the reactivities are the same during the whole range of conversion. This implies that at a given temperature in Zone I burning, the reactivity is only determined by oxygen partial pressure (P O2 = y O2 P), indepent of the individual values of total pressure P and oxygen mole fraction y O2. Reaction rate, gc/(m 2.s) x atm, 12% O 2 4 atm, 6% O 2 8 atm, 3% O K, P O2 = 0.24 atm x c, conversion Reaction rate, gc/(m 2.s) x atm, 12% O 2 4 atm, 6% O 2 8 atm, 3% O K, P O2 = 0.24 atm x c, conversion Figure 5.5. Effect of total pressures (2, 4 and 8 atm) on reaction rate at constant oxygen partial pressure (P O2 = 0.24 atm) for a 16%-porosity synthetic char. 94

125 Modeling Char Oxidation at Elevated Pressure Reactivity, g/(m 2.s) x T gas = 873 K, P O2 = 0.06 atm, T p = 873 K 1 atm 5 atm 10 atm 20 atm conversion, x c Figure 5.6. Reactivity as a function of conversion with constant oxygen partial pressure at different total pressures (1, 5, 10 and 20 atm) and gas temperature of 873 K for 25%-porosity synthetic char. Reactivity, g/(m 2.s) x T gas = 873 K, y O2 = 12% Total pressure, atm Figure 5.7. Reactivity and particle temperature with increasing total pressure and constant oxygen mole fraction at gas temperatures of 873 K for 25%-porosity synthetic char. At constant gas temperature and gas composition, the reactivity and particle temperature at different total pressures were calculated using the model, which accounts for both the effects of chemistry and mass transport on overall reactivity. Calculated results are shown in Figure 5.7. For constant gas composition burning in Zone I, the effect of increasing total pressure is to increase the reactivity because the chemical reactions of char oxidation are enhanced by the higher oxygen partial pressure. However, calculated particle temperatures remain about the same at all the pressures investigated. Therefore, by combining the results derived above, it can be concluded that in Zone I burning, the increase in reactivity with increasing oxygen partial pressure and fixed temperature is due to higher oxygen concentration throughout the particle, without any enhancement from particle temperature because the particle temperature remain constant T p, K 95

126 Chapter Effects of total pressure and oxygen partial pressure under Zone II burning conditions In the Zone II burning regime, the effect of increasing oxygen partial pressure at a constant gas temperature and total pressure is shown in Figure 5.8. Although the fact that the gas temperature was constant (T gas = 1600 K), the particle temperature during the burnout increased in response to the increasing oxygen partial pressure. Therefore, the increase in reactivity must be partially attributed to the increased particle temperature T gas = 1600 K -1.0 Log(R i,c ) atm 5 atm 20 atm atm Log(P O2, s ) (a) 5 atm T gas = 1600 K 20 atm T p, K P O2,s, atm (b) Figure 5.8. Calculated variations of (a) reactivities and (b) particle temperatures with respect to oxygen partial pressure at the particle surface at gas temperature of 1600 K for 25%-porosity synthetic char. 96

127 Modeling Char Oxidation at Elevated Pressure The increase in reactivity with increased oxygen partial pressure, n, can be determined from the slope of the curves in Figure 5.8 (a). 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 pressure studied, and is pressure depent. Although there is an almost constant value of n for low values of the surface oxygen partial pressure, P O2,s, n gradually decreases with increase in P O2,s. This tr differs from that observed under Zone I burning conditions, in which n increases with increasing oxygen partial pressure. Considering the facts that the oxygen partial pressure at the particle surface P O2,s is lower than P O2 in the environment at high temperature and that the particle temperatures increase by about K over the range of P O2,s studied, it is implied that the decrease in the value of n is due to pore diffusion limitations. These calculations explain some of the inconsistent values determined for n in the Zone II burning regime; i.e., some authors reported half-order apparent kinetics, implying an intrinsic order of zero, and some studies reported first-order apparent kinetics implying an intrinsic order of unity [Hurt and Calo, 2001]. From Figure 5.8 (a), at low oxygen partial pressure, the slopes of the curves give high apparent reaction order, but at higher oxygen partial pressure, this apparent reaction order decreased to low values. Therefore, at high temperature burning, both high and low apparent reaction orders can be observed, deping on the actual burning conditions. This result is consistent with the recent study by Hurt and Haynes s [2004]. They also showed the global reaction order decreases gradually with increasing oxygen partial pressure. They attributed the high fractional reaction order in carbon-oxygen reaction to the breadth of activation energy distribution of adsorption and desorption. Our model, having taken into account the distributed activation energies, gives similar results. The depence of reactivity and particle temperature on total pressure when oxygen partial pressure remains fixed is presented in Figure 5.9. In the Zone I burning regime, such as at 873 K, the reactivity is indepent of total pressure as long as the oxygen partial pressure is held constant, and the average particle temperature is the same as gas temperature. At low temperature, when burning happens in Zone I, the reactivity is determined solely by chemistry, and diffusion limitation will not come into play, even at elevated pressures. At high temperatures (T gas = 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 bulk diffusion 97

128 Chapter 5 coefficient decreases, rering the impact of diffusion 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. Since bulk diffusion coefficients are inversely proportional to pressure, under Zone III burning conditions, the reactivity is expected to decrease with increase in pressure. Reactivity, g/(m 2.s) x T gas = 1600 K T gas = 1140 K T gas = 873 K P O2 = 0.06 atm T p R i,c Total pressure, atm T p R i,c T p R i,c Figure 5.9. The depence of reactivity and particle temperature on total pressure with constant oxygen partial pressure (0.06 atm) at different gas temperatures (873, 1140 and 1600 K) for 25%-porosity synthetic char. 800 T p, K At moderate gas temperatures (T gas = 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. Weak Zone II is a situation between Zone I and strong Zone II, where the material burns close to the Zone I boundary at early conversions and in Zone II in later conversions. The overall effect is that as pressure increases, the chemical rate controlling steps become less important, and diffusion control becomes more significant. It was previously shown that at given temperature in Zone I burning, the reactivity is only determined by P O2, indepent of the individual values of P and y O2. However, in Zone II burning with fixed oxygen partial pressure and gas temperature (Figure 5.10(a) and (b)), at higher total pressure, both the reactivities and the particle temperatures are lower. At certain temperatures and oxygen partial pressures, the burning could change from Zone I to Zone II as the total pressure increases. As shown in Figure 5.11, at 1100 K and P O2 =

129 Modeling Char Oxidation at Elevated Pressure atm, the burning remains in Zone I below 5 atm, and above 5 atm, the burning starts to change to Zone II. 1.6 T gas = 1140 K, P O2 = 0.06 atm 0.04 T gas = 1600 K, P O2 = 0.06 atm Reactivity, g/(m 2.s) x atm, T p,avg = 1221 K 5 atm, T p,avg = 1123 K 10 atm, T p,avg = 1115 K 20 atm, T p,avg = 1098 K conversion, x c Reactivity, g/(m 2.s) atm, T p,avg = 1624 K atm, T p,avg = 1526 K atm, T p,avg = 1503 K conversion, x c (a) (b) Figure Reactivity as a function of conversion with constant oxygen partial pressure at different total pressures (1, 5, 10 and 20 atm) and gas temperatures of (a) 1140 K and (b) 1600 K for 25%-porosity synthetic char. 3.0 T gas = 1100 K, P O2 = 0.06 atm Reactivity, g/(m 2.s) x Total pressure, atm Figure Transition from Zone I to Zone II burning with increasing total pressure and fixed gas temperature and oxygen partial pressure for 25%-porosity synthetic char. For constant gas composition, the effect of increasing total pressure is to increase the reactivity because the chemical reactions of char oxidation are enhanced by the higher oxygen concentration, as shown in Figure On the other hand, higher total pressure decreases the oxygen diffusion coefficient. Therefore, the overall effect of increasing total pressure is a trade-off between higher chemical reaction rates due to higher oxygen concentrations and proportionately lower diffusion coefficients. In the Zone II burning regime, the effect of 99

130 Chapter 5 pressure below 10 atm clearly is stronger than that above 10 atm. This effect is weak (in weak Zone II) or negligible (in strong Zone II) at pressures above 10 atm. The particle temperatures level off after a certain critical pressure of about 10 atm at T gas = 1140 K, and after a critical pressure of about 4 atm at T gas = 1600 K. Therefore, the critical pressure where the particle temperature starts to level off is lower at higher gas temperatures Reactivity, g/(m 2.s) T p, K (a) T gas = 1140 K, y O2 = 12% Total pressure, atm Reactivity, g/(m 2.s) T gas = 1600 K, y O2 = 12% T p, K (b) Total pressure, atm Figure Reactivity and particle temperature with increasing total pressure and constant oxygen mole fraction at gas temperatures of (a) 1140 K and (b) 1600 K for 25%-porosity char. The reactivity as a function of inverse temperature is presented in Figure It is shown that the slope of reactivity increase with temperatures changes, which designates the transition from Zone I to Zone II burning regime. For total pressures of 2 and 10 atm, the transition temperatures from Zone I to Zone II are about 1160 K and 1110 K, respectively. For total pressure of 20 atm, the slope almost does not change, which implies that at this pressure, burn- 100

131 Modeling Char Oxidation at Elevated Pressure P = 2 atm, P O2 = 0.06 atm T tr = 1160 K Ln(R i,c ) -4-5 (a) /T gas, K -1 P = 10 atm, P O2 = 0.06 atm -3 T tr = 1110 K Ln(R i,c ) -4-5 (b) /T gas, K -1 P = 20 atm, P O2 = 0.06 atm -3 Ln(R i,c ) -4-5 (c) -6 T tr <= 873 K /T gas, K -1 Figure Change of burning zone with gas temperature at different total pressures: (a) 2 atm, (b) 10 atm and (c) 20 atm for 25%-porosity char. 101

132 Chapter 5 ing is always in Zone II within this temperature range, and the transition temperature must be below 873 K. Therefore, the transition temperature from Zone I to Zone II decreases with increasing total pressure, which means that Zone II burning is favorable at elevated pressures, a similar result from the experimental data of Croiset et al. [1996]. 5.3 Char structure model Formation of char structure The combustion of coal consists of a devolatilization process and a heterogeneous oxidation process of the char. While the volatile matter is released during the devolatilization process, the physical structures of the coal char particles may change significantly. Some coals exhibit thermoplastic behavior when heated and these coals melt to form a highly viscous liquid. Usually, the bituminous coals having carbon content in the range of 81-92% exhibit maximum fluidity. These coals experience significant change in pore structure during devolatilization. Anthracites, subbituminous coals and lignites exhibit limited or negligible thermoplastic behavior. These coals more or less retain the pore structure during devolatilization. The decomposition of coal particles generates gases, char and metaplast (thermallyderived plasticizing agent) 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 and swelling of the particles. At even higher temperature or longer time, depletion of metaplast due to diffusion, decomposition, and polymerization causes the coal to resolidify. The resultant char structure plays an important role in determining the char reactivity and gas diffusion during the subsequent combustion. For char oxidation at high temperature, pore diffusion is one of the rate-controlling processes, and the diffusion rate of reactant and product gases within the particle is determined by the pore size distribution and porosity. The structure of a char also has significant impacts on char fragmentation and ash formation. Char fragmentation is another important process during coal combustion, which has a significant impact on ash formation and combustion efficiency. Fragmentation can shift the particle size distribution to smaller sizes, which could reduce the char burnout time. 102

133 Modeling Char Oxidation at Elevated Pressure Some classification methods for char particles of different physical structures have been proposed. Most of these methods have tried to categorize char particles into different morphological structures by image processing. Lightman and Street [1968] and Street et al. [1969] heat treated a wide range of coals in a tube furnace. Four types of char were produced and described as lacy, ballon, C-shaped, and solid. Jones et al. [1985] studied the combustion of concentrates of vitrinite and inertinite macerals. The char morphology, porosity and pore size were studied by optical microscopy and image analysis, and the chars were classified into three types: cenosphere, honeycomb, and unfused char. These types of chars have different structures and burning characteristics. Bailey et al. [1990] outlined a char morphology classification system based on the physical and optical properties, such as particle shape, vesicle volume, pore shape, wall thickness and anisotropy. This char morphology classification is more detailed with 11 types: tenuisphere, crassisphere, tenuinetwork, mesosphere, fragment, inertoid, solid, fusinois, mixed porous, mixed dense, and mineroid. The produced char type and its morphology were correlated with the parent coal petrographic components. Cloke and Lester [1994] classified the char particles by structural parameters such as the particle external dimension, macro-porosity, macro pore size distribution, wall thickness and anisotropy. They classified the particles into 10 groups similar to Bailey et al.[1990], such as tenuisphere, tenuinetwork, tenuifragment, crassisphere, crassinetwork, crassifragment, fusinoid, mixed porous, mixed solid, and solid. Although this detailed classification is very informative on char structures, the complexity prevents its actual utilization in modeling of char combustion. Different studies may give different names for the same kind of char structures. For the purpose of modeling char combustion and simplicity, Benfall et al. [2000] summarized different char structures and classified them into three groups (cenoshperical, mixted and dense). The physical structure of the char particle after devolatilization is significantly influenced by the pressure. It was found that chars produced at elevated pressures had thinner walls and more spherical structures [Benfell et al., 2000]. 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 had higher macro-porosity, and the internal surface area was lower than char produced at atmospheric pressure [Zeng and Fletcher, 2005]. Some studies indicated that high pressure influences char formation because of the increase in resistance of volatiles release and further secondary reactions at elevated pressure 103

134 Chapter 5 [Oh et al., 1989; Sheng and Azevedo, 2000; Yu et al., 2004]. Under high pressure, the metaplast content and fluidity increase, and the gas-phase yields increase due to secondary reactions. This effect leads to increased bubble growth rate, and hence higher swelling ratio of the particle. However, higher pressure also increases the resistance for bubble growth, and hence reduces bubble growth rate and swelling ratio. Consequently, the overall effect of pressure on char structure should be a trade-off between these two effects. Lower Kittanning coal, as a low volatile bituminous coal, is expected to experience the significant pore structure change described previously Char structure model The plastic stage during devolatilization is a key step for the evolution of char particles structures. A simplified model for the evolution of char structure during devolatilization is illustrated in Figure The softened coal particle starts with some pores, and lots of small bubbles grow based on these pores. The bubbles grow by the diffusion of volatile matter into bubbles, which is generated from coal decomposition. When the bubble expands to the particle surface, the bubbles may rupture, and the volatiles inside the bubbles are released from the particle. The particle swelling is directly related to the growth of bubbles inside the particle. Therefore, the physical structure of the particle changes with the release of volatiles. The simplified mechanism of the process for the transport of volatile matter and the evolution of the char structure assumes that the shape of a coal particle is spherical throughout the process; bubbles are spherical and have a uniform spatial distribution throughout the coal melt and a uniform size during the whole plastic stage; chemical and physical properties of the whole particle are uniform; the whole coal particle is heated uniformly, and the true density of coal remains constant during the course of heating. When the particle resolidifies at higher temperature or longer time, the ultimate structure of the char particle is determined and can be categorized into three groups based on the porosity, wall thickness, and void size distribution. The classification and definition of these char groups follow the lead of Bailey et al. [1990] and Benfall et al. [2000]. A char particle is composed of three main components: pores/voids, dense carbonaceous material, and minerals. The pores or voids are produced from degassing and softening during devolatilization, but the dense carbonaceous material contains very few or no voids, indicating this material has not experienced extensive softening and bubbling in the devolatilization process. Deping on 104

135 Modeling Char Oxidation at Elevated Pressure the relative amount of pores/voids and dense carbonaceous material, the char particles can be classified as cenospherical, dense, and mixed chars. If the pores/voids occupy most of the particle volume with little dense material, this particle is defined according to its porous part, as cenospherical if there exists one large central void, or as a mixed char if a number of smaller voids distributed inside the particle. If a particle consists of mainly dense carbonaceous material with very few or no visible pores/voids inside the particle, it is defined as a dense char particle. Any particle that is neither cenospherical nor dense char is defined as mixed char, i.e., with mixed portions of both pores/voids and dense carbonaceous material. Foam structure Dense char Cenospheric char Foam structure Figure The simplified mechanism of the evolution of a char s structure [Courtesy of Yu, et al., 2004]. Coal combustion experiments were conducted in the high pressure flow reactor described in Chapter 2. Partially reacted char particles were extracted from the high pressure flow reactor at different residence times, and scanning electron microscopic images of the collected particles are shown in Figure The cenospherical chars 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% (Figure 5.15 (a)). The mixed type chars 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 (Figure 105

136 Chapter (b)). The large void in the particle can facilitate the transport of the reactant gas. With no large void within the particle or opening at the external surface, the dense chars obviously have the lowest porosities and highest char density (Figure 5.15 (c)). The transport of reactant gas through the dense char particles deps upon the macro- or micro-pores in the particles. Some ash particles are also observed in the sample, and the ash particles are in round shape due to the melt and re-solidification of the minerals under high temperature condition (Figure 5.15 (d)). (a) (b) (c) (d) Figure Scanning electron microscopic images of different kinds of particles collected from combustion of Lower Kittanning coal at nominal gas temperature of 1650 K, 12 mol-% O 2, total pressures of 2 atm and residence time of 47 ms: (a) Group I cenospherical char; (b) Group II mixed type char; (c) Group III dense char; and (d) ash particle embedded in char particles. 106

137 Modeling Char Oxidation at Elevated Pressure The criteria for classifying the char particles into three groups are summarized in Table 5.2. The meaning of these parameters and methods for determining them are explained later in detail. Table 5.2. Classification criteria of char particle structure Group I (Cenospherical char) Group II (Mixed char) Group III (Dense char) Typical schematics 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) Void size distribution 0 D p 0 D p 0 D p Existence of void about the same size as particle diameter Voids are smaller than particle diameter but larger than 5 μm Almost no voids larger than 5 μm Shape factor Round particles with shape factor > 0.85 Moderately round particles with shape factor > 0.8 Irregular particles with shape factors < 0.7 Porosity: Although the pore volume could be obtained using mercury porosimetry, the measurement from this technique includes the volume of both intra-particle and inter-particle pores. In our study, the porosity of a particle is determined by cross-sectional image analysis 107

138 Chapter 5 of microscopic pictures. In order to analyze the internal physical structure of the char particle, the char cross-sectional samples were prepared using epoxy as the binding material in a manner similar to Yu et al. [2003]. The cross-sectional microscopic images obtained are in gray scale. The carbonaceous material and the pores are generally in different shades of gray. For easy analysis of the particle, the gray scale images were first transformed into black-andwhite binary images, and then the carbonaceous material was represented by a white block of irregular shape with scattered black portions as pores within the particle (Figure 5.16). The area of the whole char particle, A part, was measured using an image analysis program [Dove, 2002], which can be representative of the whole particle volume V part. The volume of the pores V pore could be determined by measuring the total area of black objects (pores) A pore inside the white region (carbonaceous material). Thus, the porosity could be calculated by V θ = pore pore. V part It should be noted that the porosity obtained using this image analysis method generally deviates from the true porosity of the particle. The measurement and calculation of porosity is based on the assumption that the particle and the pores are symmetric along the cross section. However, this assumption is generally not true, and in the preparation of the cross-sectional sample, the cut cross section may not be along the equator of a spherical particle. Due to the limited resolution of the images, the pore volume from micropores was not counted during the porosity measurement. However, for the purpose of char particle classification, determining the porosity with this image analysis method is adequate. A A part (a) (b) (c) Figure Black-and-white binary images of (a) cenospherical, (b) mixed type and (c) dense char particle for analysis of porosity, wall thickness and void size. 108

139 Modeling Char Oxidation at Elevated Pressure Wall thicknes: Wall thickness is another measure to classify char particles in three groups, which is also determined by cross-sectional image analysis of microscopic pictures described above. At any location on the particle surface, the wall thickness is determined at corresponding location in terms of pixels within the digital image, and then the wall thickness in micron can be calculated after spatial calibration. The average wall thickness is determined based on the measurement of the thickness at different locations. If more than 75% of the particle outer surface is smaller than 10 μm, the average wall thickness is defined as <10 μm. If more than 75% of the particle outer surface is larger than 10 μm, the average wall thickness is defined as >10 μm. Wall thickness can significantly impact the char particle reaction rate by influencing the reactant gas diffusion into the particle. Shape factor: The shape factor characterizes the closeness of the particle shape to a sphere, 2 which can be computed as: 4 π A / P, where A is the particle cross section area, and P is the perimeter. The result gives a value between 0 and 1. The greater the value, the more spherical the particle. Because the perimeter and area are approximations, it is possible to get roundness values that are above 1. This factor is useful, not as an absolute measure, but rather as a relative one. For Group I and III chars, the particles experienced the extensive softening and plastic stage during devolatilization, the shape of the particles are more spherical than that of Group III dense char particles. Group I: cenospherical char particles 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, and the reactant gas outside the particle can easily diffuse into the interior. The thickness of the wall may vary at different locations in the particle, but the average thickness is generally smaller than 10 μm. This kind of char structure may influence the char conversion process and the char reactivity significantly during char combustion process. Group III: dense char particles 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, with pores of sizes 109

140 Chapter 5 from micro scale to macro scale. The porosities of Group III char particles are generally small, such as below 40%. The wall thickness of the particle is about the same scale as the particle size. The char oxidation model for Group III chars follows the lead of Mitchell in the particlepopulation balance model [Mitchell, 2000]. Group II: mixed char particles 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. This kind of particles originates from the foam structures during devolatilization. In this char structure model, these three groups of char particles are considered separately. The char samples collected from the high pressure flow reactor at different extents of conversions are examined under a scanning electron microscope (SEM). The scanning electron micrographs 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 Figure 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 5.2, at a mass loss of 30% (with respect to raw coal) in 2 atm, approximately 30-40% of the char particles by volume have cenospherical structures, 20-30% of the particle are dense chars with no big void formed from volatile releasing, and the remaining 30-50% of the char particles are classified as mixed type chars. 110

141 Modeling Char Oxidation at Elevated Pressure (a) (b) Figure Scanning electron microscopic images of char samples collected from combustion of Lower Kittanning coal at nominal gas temperature of 1650 K, 12 mol-% O 2, and total pressures of (a) 1 atm and (b) 2 atm. 5.4 Particle population balance model The particle population balance model is used to describe the changes in the particle size and density distributions with time as a result of char oxidation and fragmentation. The 111