Pressurized Pulverized Fuel Combustion in ... - ACS Publications

been studied by several researchers.3-6 The combustion rate is usually ..... global formula of Shah et al.41 The measurements were made in atmospheric...
0 downloads 0 Views 681KB Size

Energy & Fuels 1996, 10, 121-133


Pressurized Pulverized Fuel Combustion in Different Concentrations of Oxygen and Carbon Dioxide Jaakko J. Saastamoinen,* Martti J. Aho, and Jouni P. Ha¨ma¨la¨inen VTT Energy, P.O. Box 1603, 40101 Jyva¨ skyla¨ , Finland

Rolf Hernberg and Timo Joutsenoja Department of Physics, Tampere University of Technology, Tampere, Finland Received June 12, 1995X

Theoretical and experimental studies showed that increasing gas pressure at constant gas composition most strongly increases the combustion rate of less reactive coals, which are difficult to burn completely in atmospheric pulverized fuel boilers. The effect of pressure increase is greatest near 0.1 MPa and less at higher pressures. The limit at which increase in pressure has an effect varies from coal to coal, depending on the particle size. With less reactive coals and small particles, the effect can be seen at pressures greater than 1 MPa. The relative effect of pressure increases when the gas oxygen content is low, improving the burnout in furnaces. The effect of pressure is small for large particles and reactive fuels. At high pressures the rates of homogeneous and heterogeneous reactions increase raising the maximum particle temperature; the higher temperature may increase the extent of devolatilization and further decrease the total combustion time. Combustion rate and the temperature of burning coal particles were measured in experiments with a pressurized entrained flow reactor under the following conditions: gas temperature 1073-1473 K, pressure 0.2-0.8 MPa, oxygen partial pressure 0.025-0.1 MPa, and partial pressure of CO2 0.05-0.2 MPa. Measured and calculated results showed increased carbon dioxide concentration in the combustion environment to have an insignificant effect on the combustion rate in the studied temperature region, but it lowered the particle temperature to some extent, suggesting that the gasification reaction CO2-C takes place as well. Calculations indicated that in pressurized combustion the rate of gasification reaction is greater at higher temperatures.

Introduction Future combustion systems may be based on combustion at high pressures with a large concentration of CO2 in the combustion environment. The major aim in the development of pressurized combustion is to increase the efficiency of electricity production by using combined power cycle processes. Pressurized combustion would also allow reduction in the size of the pulverized fuel furnace. With a combined power cycle the proportion of electrical energy obtained from fuel can be increased from an average of 38% to about 50%. Thus, pressurized combustion processes would effectively cause less pollution and CO2 emissions, since less fuel is required for the same electrical energy production. Pressurized combustion of pulverized wood has also been studied with the aim of developing small scale electricity production based on gas turbines. In future oxygen-enriched combustion systems, instead of air, pure oxygen could be introduced to the furnace. The combustion temperature could be regulated to a lower level by mixing oxygen with recirculated flue gases consisting mainly of carbon dioxide and steam. Higher combustion temperatures might be applied as well, since then thermal NO formation would be weaker due to the small N2 content in the gases. The X

Abstract published in Advance ACS Abstracts, December 15, 1995.


oxygen enrichment also reduces the amounts of flue gas to be cleaned. The flue gas CO2 content becomes also high in some industrial processes, where the high temperatures that are required are obtained by oxygen enrichment in addition to the preheating of combustion gases. In the possible removal of carbon dioxide from flue gases to reduce CO2 emissions,1,2 it would be desirable to increase the CO2 content of the flue gases to improve the efficiency of the recovery. The effect of pressure on the combustion rate of millimeter-size particles in fluidized bed conditions has been studied by several researchers.3-6 The combustion rate is usually unaffected by the pressure, but increasing rate with pressure has sometimes been found.3 Also, the behavior of pulverized coal particles under pressure (1) Audus, H. Greenhouse Gas Releases from Fossil Fuel Power Stations. IEAGHG/SR1, No 65, 1993, IEA Greenhouse Gas R&D Programme, Cheltenham, U.K. (2) Kikkinides, E. S.; Yang, R. T. Ind. Eng. Chem. Res. 1993, 32, 2714. (3) Turnbull, E.; Kossakowski, E. R.; Davidson, J. F.; Hopes, R. B.; Blackshaw, H. W.; Goodyear, P. T. Y. Chem. Eng. Res. Des. 1984, 62, 223. (4) Shiao, S.-Y.; Warchol, J. J.; Botros, P. E. In 11th International Conference on Fluidized Bed Combustion; Anthony, E. J., Ed.; The American Society of Mechanical Engineers: New York, 1991; p 1183. (5) Wallman, P. H.; Carlsson, R. C. J. In 11th International Conference on Fluidized Bed Combustion; Anthony, E. J., Ed.; The American Society of Mechanical Engineers: New York, 1991; p 1517. (6) Miccio, M.; Nastri, V.; Poletto, M. In 11th International Conference on Fluidized Bed Combustion; Anthony, E. J., Ed.; The American Society of Mechanical Engineers: New York, 1991; p 1233.

© 1996 American Chemical Society


Energy & Fuels, Vol. 10, No. 1, 1996

has been studied.7,8 In experiments with small pulverized coal particles, Monson et al.7 found that increasing oxygen pressure at constant total pressure results in substantial increase in particle temperature, whereas increasing the total pressure at constant oxygen pressure leads to substantial decrease in particle temperature. Mu¨hlen and Schulte,8 in turn, showed that the pressure does not significantly affect the combustion rate of Westerholt high-volatile bituminous coal at 1143 K and pressures 0.1-1.5 MPa when the particle size is relatively large (315-500 µm). The effect of pressure is greater for less reactive anthracite (100-125 µm). The effect of pressure on the ignition temperature of solids has also been studied.9,10 Shulte et al.9 found experimentally that the heterogeneous ignition temperature decreases with increasing pressure. The influence of pressure on the pyrolysis of coal particles at high heating rates also has been investigated much.11-25 The general trend, from which also deviations occur, is that a decrease in heating rate or an increase in the pressure decreases the total yield of volatiles in inert atmosphere. Unlike the behavior of most fuels, we found pressure significantly to increase the rate of pyrolysis of one pulverized peat in an entrained-flow reactor. Reuther and Jenkins26 discuss the role of CO2 in rapid pyrolysis. They measured devolatilization of a lignite in mixtures of N2, He, and CO2 at two pressure levels and found that the weight loss increased in the early stage of pyrolysis when He was replaced by CO2. They concluded that this was due to interaction of CO2 with the devolatilizing sample and not due to gasification or heat transfer effects. The swelling that occurs during devolatilization is great especially in the combustion of black liquor, which may swell 30 or more times in volume. Swelling is advantageous, since the combustion rate increases for a larger char residue with smaller density and greater porosity. The influence of initial particle density on the char reactivity has recently been discussed by Essenhigh.27 Some studies have been made on the effect of pressure on the swelling of coal particles. At heating (7) Monson, C. R.; Germane, G. J.; Blackham, A. U.; Smoot, L. D. Combust. Flame 1995, 100, 669. (8) Mu¨hlen, H.-J.; Schulte, A. Proc. Int. Conf. Coal Sci. Tokyo 1989, 1, 269. (9) Schulte, A.; Mu¨hlen, H.-J.; van Heek, K. H. Proc. Int. Conf. Coal Sci. 1987; 789. (10) Wen, L.; Xing-Zhong, S.; Jin-Sheng, G. Fuel Sci. Technol. Int. 1993, 11, 1441. (11) Anthony, D. B.; Howard, J. B.; Hottel, H. C.; Meisner, H. P. 15th Symposium (International) on Combustion, [Proceedings]; The Combustion Institute: Pittsburgh, PA, 1975; p 1303. (12) Wagner, R.; Wanzl, W.; van Heek, K. H. Fuel 1985, 64, 571. (13) Tamhankar, S. S.; Sears, J. T.; Wen, C.-Y. Fuel 1984, 63, 1231. (14) Suuberg, E. M.; Unger, P. E.; Lilly, W. D. Fuel 1985, 64, 956. (15) Lee, C. W.; Jenkins, R. G.; Schobert H. H. Energy Fuels 1991, 5, 547. (16) Lee, C. W.; Scaroni, A. W.; Jenkins, R. G. Fuel 1991, 70, 957. (17) Griffin, T. P.; Howard, J. B.; Peter, W. A. Fuel 1994, 73, 591. (18) Fatemi, M.; Scaroni, A. W.; Lee, C. W.; Jenkins, R. G. Prepr. Pap.sAm. Chem. Soc., Div. Fuel Chem. 1987, 32 (3), 117. (19) Phuoc, T. X.; Durbetaki, P. Int. J. Heat Mass Transfer 1987, 30, 2331. (20) Takeuchi, M.; Berkowitz, N. Fuel 1989, 68, 1311. (21) Gibbins, J.; Kandiyoti, R. Energy Fuels 1989, 3, 671. (22) Canel, M.; Wanzl, W. Fuel 1994, 73, 139. (23) Cai, H.-Y.; Gu¨ell, A. J; Dugwell, D. R.; Kandiyoti, R. Fuel 1993, 72, 321. (24) Serio, M. A.; Solomon, P. R.; Heninger, S. G. Prepr. Pap.sAm. Chem. Soc., Div. Fuel Chem. 1986, 31 (3), 210. (25) Gilot, P.; Stanmore, B. R. Energy Fuels 1995, 9, 126. (26) Reuther, R. B.; Jenkins, R. G. Prepr. Pap.sAm. Chem. Soc., Div. Fuel Chem. 1989, 34 (4), 1124. (27) Essenhigh, R. H. Combust. Flame 1994, 99, 269.

Saastamoinen et al.

rates of 50 and 400 K/s Schulte et al.8 found that increase of pressure clearly decreased the swelling. At high heating rates Lee et al.15,16 found that the maximum swelling of a bituminous coal was reached at a specific pressure of 0.8 MPa. The rate of gasification with CO2 is small compared to the rate of combustion with O2. Modeling of the combustion of single char particles is reviewed by Sotirchos et al.,28 who consider also simultaneous combustion and gasification. Simultaneous combustion (C/O2) and gasification (C/CO2) has been studied by Mitchell and Madsen,29 Makino and Law,30 Makino,31 Shadman and Cavendish,32 and Wang et al.33 The overall burning rates of char particles (115 µm) were unaffected by the carbon dioxide when the oxygen content was 3 and 6 vol % and the gas temperature varied between 1344 and 1507 K in the combustion experiments carried out by Mitchell and Madsen,29 at two concentration levels of CO2 (2.1 and 8 vol %). Oscillations of particle temperature, with periods from 10 to 100 s, were found in experiments carried out by Kurylko and Essenhigh.34 These oscillations were considered to be caused by the changing location and intensity of the homogeneous oxidation of CO to CO2, but, in part, could also have been due to the internal endothermic CO2 gasification producing CO.34 In our paper, especially the combined effects of pressure and CO2 concentration on combustion rate and particle temperature are studied. Experimental Techniques The experiments (except one at 0.1 MPa) were performed in an electrically heated pressurized entrained flow reactor, where the conditions can be controlled with high precision. The structure of the device has been described earlier.35 The fuels used were Polish bituminous coal and Niederberg anthracite from Germany dried, milled, and sieved to a particle size fraction of 140-180 µm. The Polish coal contained 31.9% volatiles and 9.0% ash (analyzed by DIN norm). It had the following elemental composition (wt % mf): 74.5 C, 4.3 H, 1.5 N, 0.63 S, and 9 O (by difference). The anthracite contained 8.5% volatiles and 5.0% ash and it had the following elemental composition (wt % mf): 86.3 C, 3.0 H, 1.7 N, 0.9 S, and 3 O (by difference). Experimental parameters were varied separately inside the following ranges: pressure (p) 0.2-0.8 MPa, gas temperature (Tg) 1073-1473 K, oxygen partial pressure (pO2) 0.025-0.10 MPa, and the partial pressure of carbon dioxide (pCO2) 0.050.2 MPa. Table 1 shows range of the experimental parameters and Table 2 the experimental plan and gas concentrations. Oxygen concentrations varied between 3.1 and 50 vol % and the concentrations of CO2 between 6.3 and 80 vol %. The flow of pulverized coal was adjusted to consume 1.0 vol % O2 from (28) Sotirchos, S. V.; Srinivas, B.; Amundsen, N. L. Rev. Chem. Eng. 1984, 2, 175. (29) Mitchell, R. E; Madsen, O. H. Twenty-First Symposium (International) on Combustion, [Proceedings]; The Combustion Institute: Pittsburgh, PA, 1986; p 173. (30) Makino, A.; Law, C. K. Twenty-First Symposium (International) on Combustion, [Proceedings]; The Combustion Institute: Pittsburgh, PA, 1986; p 183. (31) Makino, A. Combust. Flame 1992, 90, 143. (32) Shadman, F.; Cavendish, J. C. Can. J. Chem. Eng. 1980, 58, 470. (33) Wang, C. S.; Berry, G. F.; Chang, K. C. Combust. Flame 1988, 72, 301. (34) Kurylko, L.; Essenhigh, R. H. 14th Symposium (International) on Combustion, [Proceedings]; The Combustion Institute: Pittsburgh, PA, 1975; p 1375. (35) Aho, M.; Paakkinen, K.; Pirkonen, P.; Kilpinen, P.; Hupa, M. Combust. Flame 1995, 102, 387.

Pressurized Pulverized Fuel Combustion

Energy & Fuels, Vol. 10, No. 1, 1996 123

Table 1. Experimental Parameters and Their Variations levels

variable Tg (K)a p (MPa) pO2 (MPa) pCO2 (MPa)

1073 0.2 0.025 0.05

1173 0.4 0.050 0.10

1273 0.6 0.075 0.15

1373 0.8 0.100 0.20

a For Polish coal; for anthracite temperatures were 100 K higher.

Table 2. Experimental Plan and Gas Composition gas compositionb X1 X2 X3 X4 expt Ta (K) p (MPa) pO2 (MPa) pCO2 (MPa) 1 2 3 4 5 6 7 8 9 10 11 12 13 14

1073 1073 1173 1373 1373 1273 1273 1373 1173 1073 1173 1173 1073 1273

0.8 0.8 0.8 0.8 0.6 0.6 0.6 0.4 0.4 0.4 0.2 0.2 0.2 0.25

0.050 0.075 0.025 0.025 0.075 0.100 0.100 0.050 0.050 0.075 0.100 0.050 0.025 0.025

0.05 0.2 0.15 0.05 0.2 0.15 0.10 0.05 0.10 0.10 0.05 0.10 0.15 0.20

O2 (%)

CO2 (%)

6.3 9.4 3.1 3.1 12.5 16.7 16.7 12.5 12.5 18.8 50.0 25.0 12.5 10.0

6.3 25.0 18.8 6.3 33.3 25.0 16.7 12.5 25.0 25.0 25.0 50.0 75.0 80.0

Figure 1. Measured effect of pressure on the combustion time and particle temperature of Polish coal (particle diameter 140180 µm), when pO2/p ) 0.1 and Tg ) 1175 K.

a For Polish coal; for anthracite temperatures were 100 K higher. b The rest is N2.

the reaction gas. The gas velocity in the reaction tube, where combustion occurs, was 2-3 m/s depending on the type of experiment. In each experiment, the time needed to 90% burnout of the organic mass (tb) was measured by taking several solid samples after various residence times. The combustion degree was evaluated by ash tracing technique. Because of the small amounts of sampled residues, the ash contents were analyzed by thermogravimetry. This was an accurate method: results were close to the values of the ash analysis made by DIN norm.36 The temperatures (Tp) of individual particles were measured by two-color pyrometry using wavelength bands 610-720 and 1059-1069 nm. The used wavelengths were chosen so that emission bands of combustion gases and absorption of media do not affect the temperature measurement. This was confirmed by measuring the emission spectrum from 600 to 1100 nm by using a prism monochromator and a silicon photodiode array in a separate test. Measurement of Tp was performed from two observation ports. The higher temperature was selected for further consideration. Usually, Tp remained nearly constant during combustion. The residence time from fuel feeding to the temperature measurement point varied between 60 and 500 ms depending on the requirements of the experiment. The accuracy is estimated to be better than (20 K for a single 100 µm particle in the range 1273-1473 K and better than (50 K in the range 1473-2773 K.37 Experimental data were treated with multivariable partial least-squares (PLS) method38 to find regression equations between Tp and the experimental variables.

Results and Discussion Experimental Results. The measured effect of pressure on the time needed for 90% burnout and on (36) Saastamoinen, J.; Aho, M.; Linna, V. Fuel 1993, 72, 599. (37) Aho, M.; Hernberg, R.; Ha¨yrinen, V.; Joutsenoja, T. Submitted for publication in Energy Fuels. (38) Box, G. E.; Hunter, W. G.; Hunter, J. S. Statistics for Experiments. An Introduction to Design Data Analysis and Model Building; Wiley: New York, 1978.

Figure 2. Predicted versus measured values of 90% burnout time. The regression coefficient is 0.973.

Tp, when Tg ) 1173 K, pO2/p ) 0.1, pCO2/p ) 0 for Polish coal is shown in Figure 1. Every point represents an invidual measurement in this figure. Increase of pressure increases Tp and decreases tb. The following regression equation was found for 90% burnout time of the Polish coal from the set of 14 experiments (Table 2):

tb ) 1276 - 0.405Tg - 125p - 7330pO2 1037pCO2 - 0.000152Tg2 + 416p2 + 26500pO22 + 4650pCO22 (1) where units of time and pressure are ms and MPa, respectively. Root mean square error of prediction (RMSEP) is 40 ms. The predicted versus the measured values are presented in Figure 2. Curves can be calculated with eq 1 by using either constant partial pressures or constant volume (and mass) fractions. If experiments are performed in the traditional way by raising pressure and keeping the oxygen concentration constant, only the latter option can be calculated. Our approach enabled us to find effects of both partial pressure (pO2 and pCO2) and concentrations (pO2/p and pCO2/p) on tb. The curves calculated with these equations revealed clear the trends. Figure 3a shows the effects of pressure on tb separately from the other variables at four levels of gas temperature. Increase of total pressure, while oxygen partial pressure was kept constant and oxygen concentration decreased, increased the burnout time. The effect became stronger as pressure


Energy & Fuels, Vol. 10, No. 1, 1996



Saastamoinen et al.

increased. No effect of pCO2 on tb was found: the differences in the curves were below the RMSEP values (Figure 3c). Figure 3d shows the combined effect of pressure and oxygen partial pressure on tb at four gas temperatures (pO2/p is constant, 0.1 S O2 ) 10%). Increase of pressure in the range 0.2-0.6 MPa decreased the burnout time. The relative decrease was stronger at high temperatures. For example, an increase of pressure from 0.2 to 0.6 MPa at 1350 K decreased the burnoff time to one-half. Pressure and pO2 had reverse effects on the combustion rate. The effect of pO2 dominated at pressures between 0.2 and 0.5 MPa, whereas the reverse effects compensated each other in the pressure range of 0.6-0.8 MPa. For the anthracite the regression equations for the 90% burnout time and particle temperature (K) are the following:

tb ) 1229 - 1.191Tg + 1277p2 + 32.164/pO2 1173pCO2 (2) Tp ) 533 + 0.518Tg + 97.19/p + 7814pO2 - 940pCO2



Figure 3. Effects of experimental parameters on the time needed for 90% burnoff of Polish coal (particle diameter 140180 µm) calculated with eq 1. Separate effect of pressure at four temperature levels, pO2 ) 0.05 MPa, pCO2 ) 0.10 MPa (a). Separate effect of P at four levels of oxygen partial pressure Tg ) 1250 K, pCO2 ) 0.10 MPa (b). Separate effect of p at three levels of pCO2, Tg ) 1250 K, pO2 ) 0.05 MPa (c). Combined effect of p and pO2. pCO2 ) 0.10 MPa (d).

increased. Figure 3b shows the separate effect of pressure on tb with four levels of pO2. Increase of pO2 decreased burnout times, but the effect weakened as pO2

RMSEP is 80 ms for tb and 43 K for Tp. The trends for anthracite are similar as for Polish coal, but the pressure effects were somewhat greater and the tb values much greater at pO2 < 0.06 MPa (Figure 4). However, also anthracite burns fast at pO2 > 0.05 MPa when p is low ( 0.3 MPa. The results suggest that an increase of pCO2 from 0.05 to 0.1 MPa slightly lowers Tp. The differences between the curves for pCO2 0.05, 0.1, and 0.15 MPa were 43 K, which were close to the RMSEP value (45 K) (Figure 5c). Additional measurements were carried out with smaller 100-125 µm particles at 1143 K. As can be seen (Figure 6) increasing the pressure greatly increases the combustion rate near 0.1 MPa. The change in the combustion rate is significant when pressure is increased from 0.1 to 0.3 MPa, but the change is no longer so great when the pressure is increased from 0.3 to 1.3 MPa (see also Figure 3d). The 90% burnout times are 360 and 420 ms for the two particle sizes 100-125 µm (from Figure 6) and 140-180 µm (calculated with eq 1), respectively, under conditions Tg ) 1143 K, pO2 ) 0.02 MPa, and p ) 0.3 MPa. Heat and Mass Transfer. The gas heat conductivity is insensitive to pressure, when p < 2 MPa.39 The property that effectively determines the rate of diffusion of oxygen is the product of diffusivity and gas density, which remains constant at low and moderate pressures up to about 2 MPa, since the density is proportional to (39) Perry, R. H.; Green, D. Perry’s Chemical Engineers’ Handbook, 6th ed.; McGraw-Hill Book Co.: Tokyo, 1984.

Pressurized Pulverized Fuel Combustion

Energy & Fuels, Vol. 10, No. 1, 1996 125









Figure 4. Effects of experimental parameters on the time needed for 90% burnoff of anthracite (particle diameter 140180 µm) calculated with eq 2. Separate effect of pressure at four temperature levels, pO2 ) 0.05 MPa, pCO2 ) 0.10 MPa (a). Separate effect of P at four levels of oxygen partial pressure Tg ) 1250 K, pCO2 ) 0.10 MPa (b). Separate effect of p at three levels of pCO2, Tg ) 1250 K, pO2 ) 0.05 MPa (c). Combined effect of p and pO2. pCO2 ) 0.10 MPa (d).

the pressure and the binary diffusion coefficients of gases vary inversely with pressure.39 At very high pressures this product is no longer constant, but decreases with increasing pressure. Prandtl and Schmidt numbers are more or less constant at pressures lower than 1 MPa.

Figure 5. Effects of experimental parameters on particle temperature of anthracite calculated with eq 2. Separate effect of pressure at three temperature levels. pO2 ) 0.05 MPa, pCO2 ) 0.10 MPa (a). Separate effect of p at four levels of oxygen partial pressure Tg ) 1250 K, pCO2 ) 0.10 MPa (b). Separate effect of P at three levels of pCO2, Tg ) 1250 K, pO2 ) 0.05 MPa (c). Combined effect of p and pO2. pCO2 ) 0.10 MPa (d).

Thus heat and mass transfer coefficients are insensitive to pressure up to 2 MPa when the particles are small (Reynolds number Re of the particle is small). Increase in the pressure increases the heat and mass transfer between large particles (Re is large) and gas if the relative velocity between the particle and the gas remains constant. Nusselt and Sherwood numbers depend on Re. At pressures lower than 1 MPa the


Energy & Fuels, Vol. 10, No. 1, 1996

Saastamoinen et al.

Figure 6. Measured effect of pressure on combustion of Polish bituminous coal particles at 1143 K and oxygen volume fraction (6-7% O2).

viscosity of gas is quite insensitive to increase in pressure, but at very high pressure the effect of pressure becomes important.39 However, the slip velocity is usually smaller in pressurized systems than in atmospheric systems. The Reynolds number Re ) wdF/η is proportional to wF, which is constant at moderate pressures, if the slip velocities encountered in pressurized systems are w ∼ 1/F. The particle drag coefficient is inversely propertional to Re for small spherical particles, but the effective product in the equation of motion that determines the particle velocity is ηCDRe, which remains constant for small particles and increases for large particles with increasing pressure. The combustion rate of large char particles, when diffusion is controlling the combustion, is usually not affected by the pressure to any great extent. However, pressure affects the combustion rate of large particles at high slip velocities if the slip velocity at different pressures is kept constant. When the particles are small or the temperature is low, the combustion becomes controlled by the chemical kinetics. Initial Heating Stage of a Particle. The calculated effect of pressure on initial heating of a particle is insignificant if the commonly used value Nu ) 2 for the Nusselt number for small particles is applied. The value Nu ) 2 is based on the assumption of a steady state temperature distribution around a particle and applies well in a gaseous environment with low density. When the pressure is increased, the effect of heat storage in the gas around the particle becomes more influential at the initial heating stage. The effect of pressure on the initial heating rate can be examined by studying the transient heat transfer around a particle. It is assumed that the particle is suddenly introduced into a quiescent hot gaseous environment. The energy equation for the gas around the particle is



∂Tg 1 ∂ ∂Tg ) 2 ρgcg λgr2 ∂t ∂r r ∂r


Since the particle is small, the particle temperature is assumed to be uniform. The boundary condition for the heat exchange between the gas and the particle surface is

σ(Tw4 - Tp4) + λg

( ) ∂Tg ∂r

dTp 1 ) ρpcpR r)R 3 dt


If constant gas properties are assumed and radiation is neglected, the analytical solution of eqs 3 and 4 with the initial conditions Tp(t)0) ) Tp0 and Tg(t)0,r) ) Tg∞ can be found by using the Laplace transform. The

Figure 7. Effect of pressure on a 100 µm particle heating at 1273 K.

solution for the transient particle temperature is

θp )

Tp - Tg∞ 1 ) R[w(z)] I[w(z)] Tp0 - Tg∞ [4γ/3 - 1]1/2

where 2

w(z) ) e-z erfc(-iz), i ) x-1, and z ) (1/2γ)[(12γ - 9)Fog]1/2 + i(3/2γ)xFog (5) The function erfc(x) is the complementary error function and Fog ) λgt/FgcgR2. The real (R) and imaginary (I) parts of the function w(z) have been tabulated.40 The transient gas temperature distribution around the particle is

θg )

Tg - Tg∞ ) Tp0 - Tg∞ 1 1 -(x-1)2/4Fog e R[w(z)] I[w(z)] (6) x [4γ/3 - 1]1/2






1 3 x-1 [(12γ - 9)Fog]1/2 + i + xFog 2γ 2xFog 2γ


and the transient Nusselt number becomes

Nu ) -

( )

1 ∂θg θp ∂x




2/xπFog 2 + (7) γ R[w(z)] - I[w(z)]/[4γ/3 - 1]1/2

The pressure has an effect on the gas density, Fg ∼ p, on which the dimensionless time Fog and parameter γ are dependent. Density depends on the temperature, and in a more accurate treatment the coupling between the heat, mass and momentum transfer around the particle should be accounted for by numerical calculations. An example of a calculation for an inert 100 µm particle with density 1200 kg/m3 is shown in Figure 7. Constant gas properties of air at 1 bar and 773 K have been used in the illustration, and the gas density is related to pressure p by Fg ) pM/RuT. When pressure is 0.1 MPa, the assumption of the steady state Nusselt number Nu ) 2 gives practically the same heating (40) Abramowitz, M.; Stegun, I. Handbook of Mathematical Functions, Dover Publications, Inc.: New York, 1970.

Pressurized Pulverized Fuel Combustion

Figure 8. Transient gas temperature distributions around a heated 100 µm particle (a) at 0.1 MPa and (b) at 2 MPa.

profile as the transient case. The maximum temperature difference between the two cases is then about 10 K. At 2 MPa the difference is greater and corresponds to about 45 K at maximum, and the particle is heated about 3 ms faster to 873 K. At both pressures the maximum difference occurs at the initial stage at 11 ms. The contribution of radiation to the particle heat-up is neglected in this analysis. The temperature difference 45 K has some significance since the rate of pyrolysis considerably depends on particle temperature. The pyrolysis may start earlier under greater pressure due to higher particle temperature. Note that we assumed that the particle was introduced to the hot environment quickly with no pressurized cooler carrier gas around it. If the particle is first surrounded by pressurized cooler carrier gas, the heatup of this gas requires time and energy, and the particle initial heating rate is lowered. The developments of the gas temperature distributions in the vicinity of the particle at 0.1 and 2 MPa are shown in Figure 8. It is clearly seen that the temperatures around the particle are essentially transient. In the case of moist fuels the evaporation of moisture is delayed, because increase in pressure increases the boiling temperature of water. Thus, raising the pressure from 0.1 to 2 MPa increases the boiling temperature of water from 373 to 486 K. The heat of vaporization drops with increasing pressure. Gas Phase Reactions. The particle combustion rate is also affected by the gas phase reactions. During pyrolysis, combustion of volatiles in the vicinity of the particle has an effect on the particle temperature and on the availability of oxygen at the particle surface. Particle temperature affects the extent of pyrolysis, the contributions of faster homogeneous combustion and slower heterogeneous combustion, and the reactivity of the resulting char. Pressure affects the kinetics of these gas phase reactions. The rate of volatiles combustion is directly proportional to pressure according to the experimentally based global formula of Shah et al.41 The measurements were made in atmospheric conditions. Owing to the higher

Energy & Fuels, Vol. 10, No. 1, 1996 127

reaction rate, the higher pressure reduces the distance of volatile flame from the particle and increases the temperature of the flame. As a result, the heat transfer from the flame to particle, and the devolatilization rate and extent, are increased. The pressure also affects the rate of gas phase reactions (combustion of CO to CO2) in the boundary layer in the char combustion stage. According to the model calculations of Mitchell et al.42 for atmospheric conditions and small particles ( dcr1 ) fDShDacr1/kc, where, for example, Dacr1 ) 10. Correspondingly, in the regime of the control of chemical kinetics, d < dcr2 ) DShDacr2/kc, where Dacr2 ) 0.1. The diameters dcr1 and dcr2 can be understood as the definitions of the sizes of “large” and “small” particles. The particle temperature is assumed to be uniform and it is calculated by the equation

dTs 1 ρpcR ) 3 dt

∑m˘ ′′c,i∆Hi + h(T∞ - Ts) + σ(Tr4 - Ts4)


where h ) λNu/2R. The Nusselt and Sherwood numbers are calculated by the Ranz-Marshall equation

Nu ) 2 + 0.6Pr1/3Re1/2, Sh ) 2 + 0.6Sc1/3Re1/2 (20) The great effect of pressure close to 0.1 MPa on combustion rate and particle temperature is clearly seen in Figure 9 for char A (Fc ) 800 kg/m3, 2R0 ) 170 µm), which is initially cool and is suddenly introduced into a hot environment. At higher pressures the combustion is changed more toward diffusion control, and the further increase in the pressure has little effect. The

Pressurized Pulverized Fuel Combustion

Figure 10. Calculated effect of pressure on the combustion of char B, gas oxygen content pO2/p ) 0.10, T∞ ) Tr ) 1273 K, particle diameter 170 µm. Temperature scale is normalized so that 0 corresponds to 273 K and 1 to 1763 K.

Figure 11. Calculated effect of CO2 content of atmosphere on combustion of char A (diameter 170 µm) at pressure p ) 1.0 MPa, gas oxygen content pO2/p ) 0.10, T∞ ) Tr ) 1273 K. Temperature scale is normalized so that 0 corresponds to 273 K and 1 to 1717 K.

increase of pressure increases the relative combustion rate of the less reactive char A more than that of the reactive char B (Figure 10). The effect of pressure is not great for the more reactive char B (170 µm) and nor for char A with larger size 300 µm. In both these cases the combustion rate is controlled to a greater extent by diffusion. It should be noted that the apparent Arrhenius parameters that are based on particle external area and used in these calculations have been measured at atmospheric conditions and their validity at higher pressures is questionable. Monson et al.7 recently found pressure dependency for the apparent Arrhenius parameters. The increase in the intrinsic char reactivity at elevated pressures makes the penetration depth of the reaction zone in the particle thinner and the combustion process behaves more as a particle combusting with shrinking a radius (Thiele modulus increases), if the intrinsic reaction order is greater than zero. However, the increase in the pressure decreases the access of oxygen to the particle surface due to intensified gas phase reactions, which could be one reason for the pressure dependency of the apparent Arrhenius parameters. The effect of carbon dioxide content of the atmosphere is shown in Figure 11 for char A (170 µm). The carbon dioxide content has no effect on the combustion rate, but there is some effect on the particle temperature, which decreases when more CO2 is present. The reduced particle temperature does not suppress the combustion rate because the particle mass loss due to C-CO2 gasification reaction compensates the reduction

Energy & Fuels, Vol. 10, No. 1, 1996 131

Figure 12. Calculated effect of CO2 content of atmosphere on combustion of char A (diameter 170 µm) in pressure p ) 1.0 MPa, gas oxygen content pO2/p ) 0.2, T∞ ) Tr ) 1273 K. Temperature scale is normalized so that 0 corresponds to 273 K and 1 to 2289 K.

Figure 13. Calculated effect of CO2 content of atmosphere on combustion of char A (diameter 170 µm) in pressure p ) 1.0 MPa, gas oxygen content pO2/p ) 0.02, T∞ ) Tr ) 1873 K. Temperature scale is normalized so that 0 corresponds to 273 K and 1 to 1963 K.

in the C-O2 oxidation reaction rate. The effect of carbon dioxide on the particle temperature becomes greater when the pressure, gas temperature, and the gas oxygen and gas carbon dioxide contents are high. The pressure and gas oxygen content are high in the example presented in Figure 12, which increases the particle temperature. The addition of carbon dioxide in turn markedly decreases the particle temperature; the difference between the curves pCO2/p ) 0 and 0.5 is 400 K at time 200 ms. The conversion rate increases with increasing carbon dioxide content, when gas temperature is high and oxygen content low (Figure 13). With high carbon dioxide content the particle temperature is about 100 K lower than the gas temperature, and with no carbon dioxide in the atmosphere about 8090 K higher. The measured 90% burnoff times are compared to calculations with this simplified model (assuming the pyrolysis occur fast compared to char combustion) for Polish coal. The following values were used in calculations: coal density 1000 kg/m3,  ) 0.9, and d0 ) 150 µm (for particles 140-180 µm, slip velocity 0.12 m/s) except in two cases d0 ) 110 µm (smaller particles 100125 µm, slip velocity 0.06 m/s). The Arrhenius parameters of char A were used for the C-CO2 reaction. The Arrhenius parameters E ) 85 kJ/mol, A ) 0.015 k gm-2 s-1 atm-1, and n ) 1 were used for the C-O2 reaction. These values of E and A were chosen simply by matching the five calculated and measured tb values presented in Figure 1 (and denoted by 4 in Figure 14). It is seen that the simple model can predict the combustion


Energy & Fuels, Vol. 10, No. 1, 1996

Saastamoinen et al.

can be calculated from the equation tc ) tref/G(tc/τ) iteratively. In the pore model of Bathia and Perlmutter64 the internal surface changes during the conversion are calculated by f(X) ) (1 - X)[1 - Ψ ln(1 - X)]1/2, where Ψ is a structural parameter. Then F(X) ) 2[1 Ψ ln(1 - X)]1/2/Ψ - 2/Ψ and

G(u) )

Figure 14. Comparison of measured and calculated 90% burn-off times. (9)