Energy Fuels 2010, 24, 945–953 Published on Web 12/23/2009
: DOI:10.1021/ef901110k
Approach To Predict Emission of Sulfur Dioxide during Switchgrass Combustion Employing the Discrete Particle Method (DPM) Bernhard Peters* and Joanna Smuza-Ostaszewska 6, rue Coudenhove-Kalergi, L-1359 Luxembourg, Luxembourg Received September 30, 2009. Revised Manuscript Received November 24, 2009
The demand for a net reduction of carbon dioxide and restrictions on energy efficiency make thermal conversion of biomass a very attractive alternative for energy production. However, emissions of sulfur dioxide are a major environmental concern and may lead to an increased corrosion rate of boilers in the absence of sulfatation reactions. Therefore, the objective of the present study is to evaluate the kinetics of formation of sulfur dioxide during switchgrass combustion. Experimental data that record the combustion process and the emission formation versus time, carried out by the National Renewable Energy Institute in Golden, CO, were used to evaluate the kinetic data. The combustion of switchgrass is described sufficiently accurate by the discrete particle method (DPM). It predicts all major processes, such as heating-up, pyrolysis, and combustion of switchgrass by solving the differential conservation equations for mass and energy. The formation reactions of sulfur dioxide are approximated by an Arrhenius-like expression, including a pre-exponential factor and an activation energy. Thus, the solution of the DPM was compared to measurements, and the kinetic parameters were subsequently corrected by the least-squares method until the deviation between measurements and predictions was minimized. The kinetic data determined yielded good agreement between experimental data and predictions.
sulfur dioxide (SO2) and was released below 500 C during combustion of annual biomass. Moreover, samples rich in potassium and calcium but low in silicon showed only a slight increase of sulfur release to the gas phase with a further increase of the combustion temperature. However, the release of sulfur increased abruptly above 700-800 C for biomass with a high silicon content. Further investigations by Knudsen et al.10,11 on wheat straw and beech wood showed that SO2 captured by secondary reactions during char burnout was retained in the bottom ash. This process was most effective at about 600 C, where approximately 85% of released SO2 was retained. Van Lith et al.3 found that sulfur was released through evaporation of sulfates or as SO2 for woody biomass. A maximum release rate close to 100% was observed at ∼1150 C. They described potential reaction paths, and their chemical analysis included scanning electron microscopy and predictions for the equilibrium state. Wiinikka et al.4 investigated the formation of high-temperature aerosols during fixed-bed combustion dependent upon the ash composition of the fuel. It was observed that particles of alkali sulfates (K2SO4 and Na2SO4) and chlorides (KCl and NaCl) were formed from the inorganic vapor during cooling of the flue gas. The initial alkali concentration and the alkali/silicon ratio, (K þ Na)/Si, influenced the amount of vaporized aerosols. Their total concentration in the gas phase was correlated to the amount of alkali sulfates and chlorides volatilized from the fuel bed. To increase retention of sulfur in the bottom ash, Lang et al.5 added a sulfur-binding calcium sorbent to annual biomass. The complex and temperature-dependent interactions between the adsorbent and the components of the fuel, such as sulfur, potassium, and silicon, affected the retention of sulfur to a large amount. They suggested that, at temperatures of ∼800 C, reactions between silicon and sulfates of potassium
Introduction A continuous effort to reduce the net emission of carbon dioxide (CO2) makes renewable fuels, such as biomass, an attractive alternative for energy production. However, conditions for both combustion and operation of plants impose further challenges1 because the composition of biomass differs considerably from coal. The combustion of biomass results in a significant formation of acidic pollutants, high mass loading of aerosols in the flue gas, and agglomeration of these aerosols on heat-transfer surfaces.1-9 Among these pollutants are sulfur components that contribute significantly to the above-mentioned risks.4,5,10,11 Observations presented by Knudsen et al.2 allowed for the determination that 30-55% sulfur was transformed into *To whom correspondence should be addressed. E-mail: bernhard.
[email protected]. (1) Sciazko, M.; Zuwala, J.; Pronobis, M.; Winnicka, G. Problemy Zwiazane ze Wspolpalaniem Biomasy w Kotlach Energetycznych; Instytut Chemicznej Przer obki Wegla: Zabrze, Poland, 2007 (in Polish). (2) Knudsen, J. N.; Jensen, P. A.; Dam-Johansen, K. Energy Fuels 2004, 18, 1385–1399. (3) van Lith, S. C.; Alonso-Ramirez, V.; Jensen, P. A.; Frandsen, E. J.; Glarborg, P. Energy Fuels 2006, 20, 964–978. € (4) Wiinikka, H.; Gebart, R.; Boman, C.; Bostrom, D.; Ohman, M. Fuel 2007, 86, 181–193. (5) Lang, T.; Jensen, P. A.; Knudsen, J. N. Energy Fuels 2006, 20, 796–806. (6) Dayton, D. C.; French, R. J.; Milne, T. A. Energy Fuels 1995, 9, 855–865. (7) Misra, M. K.; Ragland, K.; Baker, A. J. Biomass Bioenergy 1993, 4, 103–116. (8) Aho, M.; Silvennoinen, J. Fuel 2004, 83, 1299–1305. (9) Michelsen, H. P.; Frandsen, E.; Dam-Johansen, K.; Larsen, O. H. Fuel Process. Technol. 1998, 54, 95–108. (10) Knudsen, J. N.; Jensen, P. A.; Lin, W.; Frandsen, F. J.; Dam-Johansen, K. Energy Fuels 2004, 18, 810–819. (11) Knudsen, J. N.; Jensen, P. A.; Lin, W.; Dam-Johansen, K. Energy Fuels 2005, 19, 606–617. r 2009 American Chemical Society
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Energy Fuels 2010, 24, 945–953
: DOI:10.1021/ef901110k
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Figure 1. Simplified scheme of sulfur transformations under reduction/oxidizing conditions (bold species indicate major products).
and calcium according to CaSO4 ðsÞ þ SiO2 ðsÞ f CaO 3 SiO2 ðsÞ þ SO3 ðgÞ
ð1Þ
2KClðsÞ þ SO2 ðgÞ þ O2 T K2 SO4 ðsÞ þ Cl2 ðgÞ
ð2Þ
sulfates to alkali sulfites, which may be oxidized by oxygen to sulfur dioxide. Alkali sulfates are reduced to sulfur dioxide in an oxidizing environment in the presence of either aluminum silicates (T > 800 C) or water vapor (T > 1000 C). Furthermore, sulfates may evaporate from biomass with low contents of silicates at temperatures higher than 1000 C.2,4,5,12 Although sulfur causes emission problems, it is accompanied by a positive side-effect because of the following reactions:1,9,13,14 2KClðsÞ þ SO2 ðgÞ þ 1=2O2 þ H2 O f K2 SO4 ðsÞ þ 2HClðgÞ
contribute to an increased release of sulfur oxides instead of retaining sulfur as sulfates. At temperatures between 800 and 1100 C, sulfation reactions became dominant but were limited by the low fraction of sulfur that remained in a char after the initial devolatilization phase. Their results showed that ∼25-35% of sulfur dioxide could be retained in the ash at 1100 C, when calcium sorbents were added. Lang et al.5 also suggested that an optimum desulfurization effectiveness would be obtained, if the atomic ratio (Ca þ1/2K)total/Sitotal called the SRI factor by them would be greater than 2 or even closer to 4. On the basis of the above-mentioned review of the literature,2,3,5,12 Figure 1 for transformation of sulfur during thermal treatment of biomass was derived. Sulfur appears in biomass as both organic-bound sulfur (organic S) and inorganic salts (inorganic S) that follow different reaction paths. Organically Bound Sulfur. During devolatilization and temperatures below ∼500 C, organic sulfur follows three reaction paths that yield gaseous sulfur, hydrogen sulfide, or sulfur dioxide. These products may undergo further reactions during which sulfur attaches to the char matrix for temperatures above ∼600 C. Furthermore, hydrogen sulfide may form alkali sulfides that in conjunction with char-bound sulfur constitute the major products during pyrolysis and gasification of biomass. In the presence of oxygen, char-bound sulfur is converted to sulfur dioxide,2,4,5,12 which may form sulfates in the presence of alkali metals. Inorganically Bound Sulfur. Alkali salts of sulfur stemming also from the decomposition of organically bound sulfur usually undergoe different reactions at elevated temperatures above ∼600 C after the devolatilization phase. At a temperature higher than ∼600 C, carbon monoxide reduces
ð3Þ or in the absence of water vapor K2 SO4 ðsÞ þ SiO2 ðsÞ f K2 O 3 SiO2 ðsÞ þ SO3 ðgÞ
ð4Þ
As an advantage, hydrogen chloride and chlorine formed by reactions 3 and 2, respectively, do not condensate on boiler surfaces contrary to alkali chlorides.9,15 However, a protective effect of these reactions occurs for a fuel molar ratio S/Cl not smaller than 2.0 and under oxidizing conditions.1 Comprehensive discussions of sulfation of chlorides in boiler deposits may be found in the following articles.1,9,13,15 Co-firing of different biomass fuels or coal usually does not lead to reduced sulfur emissions because inherently existing potassium chloride has a higher reactivity with aluminum silicates than sulfur compounds.8,12,15 Therefore, chlorides are reduced by co-firing straw with coals having high levels of Si and Al instead of high sulfur content coals or the addition of significant amounts of SO2. Zheng et al.12 suggested that known molar ratios of K/Si, K/(S þ Si), S/Cl, and Ca/Si could be used to predict co-combustion products of potassium chloride and sulfate, respectively. Their results of potassium chloride and sulfate concentrations in the fly ash showed reasonable agreement with full-scale plant data presented in the literature. (13) Nielsen, H. P.; Frandsen, F. J.; Dam-Johansen, K.; Baxter, L. L. Prog. Energy Combust. Sci. 2000, 26, 283–298. (14) Matsuda, H.; Ozawaw, S.; Naruse, K.; Ito, K.; Kojima, Y; Yanase, T. Chem. Eng. Sci. 2005, 60, 545–552. (15) Aho, M.; Ferrer, E. Fuel 2005, 84, 201–212.
(12) Zheng, Y.; Jensen, P. A.; Sander, B.; Junker, H. Fuel 2007, 86, 1008–1020.
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Figure 3. Concentration of sulfur dioxide cSO2 released during combustion of ∼40 mg of switchgrass in an atmosphere of 20% O2 in He and a furnace temperature of 1100 C.
Figure 2. Measured temperature profile during switchgrass combustion.
According to the best knowledge of authors, data presented in the literature never includes kinetic parameters of chemical reactions during biomass combustion forming SO2 emissions. Dayton et al.6 measured the evolution of emission of components during combustion of switchgrass. From these results, kinetic data were derived to predict emission formation by the discrete particle method (DPM).
Table 1. Proximate Analysis for Switchgrass wt % dry basis 16.22 79.19 4.59 0.11
where the integral represents the total number of moles ntot released. Applying the above-mentioned relationships, the measured intensity was converted to a concentration profile shown in Figure 3. Experimental data in Figure 3 suggest that the first peak of emitted sulfur dioxide occurs during pyrolysis, while the following period of emissions takes place during combustion of the charred material. As mentioned in the previous section, sulfur dioxide is primarily formed from sulfur bound to char and the potassium sulfate according to the following conversion reactions: S þ O2 f SO2 ð7Þ
Evaluation of Chemical Kinetics Analysis of Experimental Data. At first, experimental data were analyzed and processed. It includes the time-dependent release of SO2 and the properties of the switchgrass sample. Then, the DPM was employed to describe both the combustion of switchgrass and the release of sulfur dioxide. The results obtained were compared to experimental data, and the kinetic parameters were corrected to minimize the deviation. Analysis of Sulfur Dioxide Release. The emission of SO2 at different ambient conditions during the combustion of switchgrass was investigated and reported by Dayton et al.6 They combusted ∼40 mg of ground switchgrass placed in a boat in an electric clamshell furnace preheated up to ∼1100 C. A total gas flow rate of 4.4 L/min with an oxygen concentration of 5, 10, or 20% flowed through the reactor, which amounts to a residence time of ∼0.1 s. Figure 2 depicts the gas temperature in the vicinity of the switchgrass sample. It was measured by a type-K thermocouple surrounded by a 0.5 mm diameter inconel sheath. Sample gases were extracted from the reactor and subsequently analyzed by molecular beam/mass spectrometry (MBMS). This yielded a complete mass spectrum of the combustion gas every 1.0-1.5 s. For a detailed description of the experimental setup, the reader is referred to the paper by Dayton et al.6 The ion intensity measured by the MBMS was converted into a concentration profile for SO2. Because the intensity I is proportional to the concentration ci (I ∼ ci), the instantaneous intensity can be written as _ i ð5Þ I ¼ γQc
K2 SO4 ðsÞ þ SiO2 f K2 O 3 SiO2 ðsÞ þ SO2 þ 1=2O2
ð8Þ
The former corresponds to a reaction that takes place at low temperature up to 500 C, whereas the latter is predominantly restricted to higher temperatures above 800 C. This temperature dependence becomes apparent in Figure 3, in which sulfur dioxide is formed during two different periods that correspond to different temperature regions according to Figure 2. Thus, the respective areas of the profile represent the fraction of sulfur dioxide formed by the reactions 7 and 8, respectively. Evaluation of the areas gives a ratio of 74:26 for sulfur dioxide formed by both reactions. The analysis of switchgrass6 is shown in Table 1. The density of chopped switchgrass amounts to F ∼ 108 kg/m3.16 Properties of the Packed Bed of Switchgrass. Approximately 40 mg of ground and loosely packed switchgrass was placed inside the furnace, which resembles a packed bed of switchgrass particles. To represent all individual particle processes by a single particle, gradients concerning both temperature and reaction within the packed bed have to vanish, which is comparable to a well-stirred reactor model.17 Therefore, Damk€ ohler
with γ and Q_ being the constant of proportionality and the volumetric flow rate, respectively. The volumetric flow rate was constant; thus, an integration of eq 5 between the times t1 and t2 yields the amount of species i released: Z t2 Z t2 Idt ¼ γQ_ ci dt ¼ ntot ð6Þ t1
proximate fixed carbon volatile ash S
(16) McLaughlin, S.; Bouton, J.; Bransby, D.; Conger, B.; Ocumpaugh, W.; Parrish, D.; Talia-ferro, C.; Vogel, K.; Wullschleger, S. In Perspectives on New Crops and New Uses; Janick, J., Ed.; ASHS Press: Alexandria, VA, 1999; Chapter Developing Switchgrass as a Bioenergy Crop, pp 282-299. (17) Peters, B. Combust. Flame 1998, 116, 297–301.
t1
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gaseous and solid species Yi describe particle conversion X l DðFcp TÞ 1 D n DT ð11Þ ω_ k Hk ¼ n r λeff þ Dt r Dr Dr k ¼1
numbers for the ratio of the reaction and heat generation time to a convective transport time were assessed. The Damk€ ohler numbers employed are Da1 ¼
_ ωL vF0
_ ωQL Da2 ¼ vFcp T
ð9Þ ð10Þ
where ω· , L, v, Q, F, cp, and T denote a representative reaction rate, length scale, gas velocity, heat source because of conversion, density, specific heat capacity, and temperature, respectively. The reaction rate ω· was assessed by the mass of switchgrass over the conversion time of 20 s, whereby the length scale was assumed to be the order of 10-2 m. The gas velocity was evaluated with ∼0.4 m/s derived from the flow rate applied. The remaining material properties were taken as those of switchgrass, so that both Damk€ ohler numbers were estimated as 10-2 and 10-5, respectively. Hence, these values indicate homogeneous conditions throughout the packed bed with vanishing gradients similar to a well-stirred reactor.17 Therefore, the behavior of a single particle represents the overall behavior of the packed bed, and thus, predictions of a single particle describe the process with sufficient accuracy. Although in the current application, a simple lumped parameter model for thermally thin particles would suffice, the approach chosen treats both thermally thin and thick particles. This is reasoned by the fact that technical applications in general deal with thermally thick particles and that such an approach covers both reacting and shrinking core behavior simultaneously. DPM. To predict the process of switchgrass combustion, including heat up, pyrolysis, combustion, and emission formation, the DPM was employed. Contrary to the continuum mechanics approach, the DPM considers a packed bed of solid fuel as composed of discrete particles with individual shapes and sizes. The conversion processes are described by transient and one-dimensional conservation equations for mass and energy with sufficient accuracy. Chapman18 states that, in general, elaborate models are required to gain a deeper insight into the complexity of solid fuel conversion,19-21 as employed in the current study. The one-dimensional approach is supported by Man and Byeong,22 whereas the transient character is emphasized by Lee et al.23,24 These requirements are met by the DPM and, therefore, offer a high degree of flexibility and detailed information. With the following assumptions: (i) one-dimensional and transient behavior, (ii) intrinsic rate modeling, (iii) particle geometry represented by slab, cylinder, or sphere, and (iv) thermal equilibrium between gaseous, liquid, and solid phases inside the particle, the differential conservation equations for energy,
X l DYi, gas 1 D n DYi, gas ¼ n þ ω_ k, i, gas r Di Dt Dr r Dr k ¼1
ð12Þ
l X DYi, solid ¼ ω_ k, i, solid Dt k ¼1
ð13Þ
where n defines the geometry of a slab (n = 0), cylinder (n = 1), or sphere (n = 2). The locally varying conductivity λeff is evaluated as25 λeff ¼ εP λg þ ηλswitchgrass þ ð1 - ηÞλc þ λrad
ð14Þ
which takes into account heat transfer by conduction in the gas, solid, char, and radiation in the pore. The source term on the right-hand side represents heat release or consumption because of chemical reactions. The conservation equations for the gas and solid phase represent the time and spatially varying mass fractions of species Yi, including a reaction source term and diffusive transport for gas species. An effective diffusion coefficient Di,eff = DiεP/τ, with εP and τ being porosity and tortuosity, is employed to describe the diffusive transport.26,27 Reactions 7 and 8, employed to describe the formation of sulfur dioxide for which the reaction rate terms, are approximated by an Arrhenius expression of the following form: dcSO2 ¼ k1 e-Ea, 1 =RT cS cO2 dt
ð15Þ
dcSO2 ¼ k2 e-Ea, 2 =RT cK2 SO4 cSiO2 dt
ð16Þ
where ki, Ea,i, and T stand for the reaction rate coefficients, activation energies, and the local temperature of switchgrass, respectively. Thus, the parameters ki and Ea,i are determined by a least-squares approach, so that the error between the predicted and measured profile is minimized. Initial and Boundary Conditions. Switchgrass was ground to a þ20/-80 mesh, which yields a mean particle diameter of d = 5.0 10-5 m. Within the reactor, the sample is heated by a radiative flux, which evaluates with a temperature Trad=1373 K to q00rad= 2.0 105 W/m2. Because of the shielding effect of the boat for the sample, only half of the radiation flux reaches the switchgrass. It is cooled additionally by a convective flux of the incoming helium-oxygen mixture, of which the temperature in the vicinity of the sample was measured and is displayed in Figure 2. According to Kaume,28 the Nusselt number Nu for heat transfer evaluates as Nu ¼ fNum, sphere
(18) Chapman, P. CFD enhances waste combustion design and modification. Combustion Canada ’96, Ottawa, Ontario, Canada, June 5-7, 1996. (19) Specht, E. Kinetik der Abbaureaktionen; Habilitationsschrift: TU Clausthal-Zellerfeld, Germany, 1993. (20) Laurendeau, N. M. Prog. Energy Combust. Sci. 1978, 4, 221. (21) In Chemistry of Coal Utilization; Elliott, M. A., Ed.; Wiley: New York, 1981; Chapter Fundamentals of Coal Combustion, Supplementary Vol. 2. (22) Ha, M. Y.; Choi, B. R. Combust. Flame 1994, 97, 1–16. (23) Lee, J. C.; Yetter, R. A.; Dryer, F. L. Combust. Flame 1995, 101, 387–398. (24) Lee, J. C.; Yetter, R. A.; Dryer, F. L. Combust. Flame 1996, 105, 591–599. (25) G., M. Ph.D. Thesis, Norwegian University of Science and Technology (NTNU), Trondheim, Norway, 1996. (26) Pai, S.-I. Two-Phase Flows; Vieweg Tracts in Pure and Applied Physics: Braunschweig, Germany, 1977.
ð17Þ
for a loosely packed switchgrass sample with f and Num,sphere being an empirical correlation f = 1.0 þ 1.5(1.0 - ε) and the mean Nusselt number for a spherical geometry, respectively. Under laminar conditions prevailing during experiments, the latter is defined by Num, sphere ¼ 2:0 þ 0:664Re1=2 Pr1=3
ð18Þ
where Re and Pr denote the Reynolds and Prandlt numbers (Pr ∼ 0.6829), respectively. Similarly, a mass transfer is described by (27) Dullien, F. A. L. Porous Media Fluid Transport and Pore Structure; Academic Press: San Diego, CA, 1979. (28) Kaume, M. Transports Organge in der Verfahrenstechnik; Springer: New York, 2003. (29) Hanel, D. Molekulare Gasdynamik; Springer: New York, 2004.
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Figure 4. Viscosity of the helium-oxygen mixture.
Figure 5. Conversion of organic sulfur and potassium sulfate during combustion of switchgrass.
a Sherwood number Shm,sphere30 Shm, sphere ¼ 2:0 þ 0:664Re1=2 Sc1=3
data, and the kinetic parameters were subsequently corrected by a least-squares method, so that the deviation between measurements and predictions was minimized, as shown in Figure 5. A comparison between measured data and predictions shows good agreement for both the distribution and the period needed to form sulfur dioxide. The values for the activation energy and pre-exponential factor describing the reaction rate are listed in eqs 22 and 23.
ð19Þ
where Sc is the Schmidt number. The viscosity of the heliumoxygen mixture was evaluated by data given by Kaye et al.31 and is shown versus the temperature for the relevant range in Figure 4. Summarizing the previous section, the following boundary conditions for mass and heat transfer of a particle are applied: DT : -λeff ¼ RðTR - T¥ Þ þ qrad ð20Þ Dr R -Di, eff
Dci ¼ βi ðci, R - ci, ¥ Þ Dr R
ð21Þ
where T¥, ci,¥, R, and β denote the ambient gas temperature, the concentration of species i, and heat- and mass-transfer coefficients, respectively. Additionally, a radiative heat flux q_ rad emanating from reactor walls is taken into account. For a detailed description of the DPM, the reader is referred to refs 32 and 33. Evaluation of Kinetic Parameters. The solution for heat up, pyrolysis, and combustion of a switchgrass particle was obtained by the DPM. Pyrolysis was modeled by an approach by Miller and Belan34 for organic matter, while combustion of charred material was represented by the model by Kulasekaran et al.35 It includes an intrinsic rate mechanism, that approximates the combustion process with sufficient accuracy.32 The kinetics of the sulfur-dioxide-emission-forming reactions 7 and 8 are described by an Arrhenius equation, which includes an activation energy Ea,i and a pre-exponential factor ki. For a given set of kinetic parameters and in conjunction with mass and heat transfer because of convection and radiation, the spatial and time-dependent temperature and species distribution within the particle was obtained by the DPM. The profiles of sulfur dioxide were compared to experimental
dcSO2 ¼ 7:29 105 e-59500:0=RT cS cO2 dt
ð22Þ
dcSO2 ¼ 1:21 105 e-130000:0=RT cK2 SO4 cSiO2 dt
ð23Þ
The switchgrass sample was ground to a sufficiently small size, so that intraparticle gradients vanished. Therefore, the kinetic equation does not include any transport properties. This is confirmed by the predictions of the temperature field in a particle in Figure 6 that shows negligible gradients, and therefore, the conversion process occurs within the kinetic regime. The corresponding surface temperature of the switchgrass particle is shown in Figure 7. The experimental data correspond to the ambient temperature measured in the vicinity of the sample. During the first stage of the process, a rapid increase of the temperature on the switchgrass surface appears as an effect of the radiative heat flux. The heat transfer because of convection is described with the empirical relationship of eq 17, assuming that the gas temperature contributes to the convective flux between the particle and the gas. Thus, as seen in Figure 7, the temperature profiles of the surface and the gas are compatible, however, with a shift varying between ∼300 and ∼400 K during the conversion process. Error Estimation. The accuracy of the predicted results, in particular, the kinetic parameters, such as pre-exponential factors and activation energies, are addressed in the following section. Because of a lack of radiative material properties of the interior part of the reactor, the sensitivity of the radiative flux on the kinetic parameters was investigated. A given reactor temperature of TR ∼ 1372 K would evaluate to a maximum specific radiative heat flux of q_ 00 ∼ 100 000 W/m2, including the shielding effect of the boat by a factor of 0.5. However, radiative material properties reduce the above-mentioned flux, so that half of the values were taken as a lower bound. The rate of formation was predicted under these conditions, and its results are shown in Figure 8.
(30) Schonbucher, A. Thermische Verfahrenstechnik; Springer: New York, 2002. (31) Kaye, G. W. C.; Laby, T. H. Handbook of Physics; Springer: New York, 2002. (32) Peters, B. Thermal Conversion of Solid Fuels; WIT Press: Southampton, U.K., 2003. (33) Peters, B.; Raupenstrauch, H. In Combustion Handbook; Winter, R., Lackner, M., Agarwal, A. K., Eds.; Wiley: New York, 2010; Chapter Modelling Moving and Fixed Bed Combustion, in press. (34) Miller, R.; Bellan, J. Combust. Sci. Technol. 1997, 126, 97–137. (35) Kulasekaran, S.; Linjewile, T. M.; Agarwal, P. K.; Biggs, M. J. Fuel 1998, 77 (14), 1549–1560.
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Figure 6. Spatial and temporal distribution of the temperature of a switchgrass particle during combustion.
Figure 7. Temperature of a switchgrass particle during combustion and the gas temperature measured in its vicinity.
Figure 8. Influence of heat transfer on the evaporation of sulfur dioxide release.
It leads to the following expressions of the reaction rates: dcSO2 : ¼ 1:21 106 e -69997:0=RT cS cO2 for q00 ∼100000 W=m2 dt dcSO2 : ¼ 1:11 105 e -119925:0=RT cK2 SO4 cSiO2 for q00 ∼100000 W=m2 dt dcSO2 : ¼ 3:83 105 e -48903:0=RT cS cO2 for q00 ∼50000 W=m2 dt dcSO2 : ¼ 5:52 105 e -161132:0=RT cK2 SO4 cSiO2 for q00 ∼50000 W=m2 dt Although the radiative heat transfer varies by a factor of ∼2, the standard error evaluated by ffiffiffiffiffiffiffiffiffiffiffiffiffiffi rP Δy2 SE ¼ ð24Þ n
Figure 9. Decrease of organic sulfur and potassium sulfate (dimensionless) in a cylindrical and spherical particle during combustion of switchgrass.
amounts to 9 and 14% for the upper and lower bounding curves in Figure 8, respectively. Therefore, the kinetic parameters between the upper and lower bounding curves are assumed to best fit the kinetics of sulfur dioxide formation.
Results and Discussion Because the results of the previous section refer to almost pulverized switchgrass samples, the studies within the 950
Energy Fuels 2010, 24, 945–953
: DOI:10.1021/ef901110k
Peters and Smuza-Ostaszewska
following section address predictions of emissions of raw material as harvested and delivered for combustion. Influence of Blade Geometry. Thus, further investigations into sulfur dioxide formation concern particle shape and
size. The cylindrical geometry describes blades of grass more properly than the spherical one. Thus, the conservation equations for mass and energy are solved in a cylindrical system. To examine the impact of geometry on the solution, the radius is kept constant, for which the results are presented in Figure 9. A faster sulfur dioxide formation is predicted for a cylindrical geometry with the formation periods shortened by ∼6 and ∼10 s for organic sulfur and potassium sulfate, respectively. Because the surface/volume ratio of a cylinder is bigger than that of a sphere, a cylinder offers a larger surface for heat transfer. It generates a higher heating rate, as depicted in Figure 10, and thus, increases the formation rate of sulfur dioxide. Influence of the Blade Size. To account for the different sizes of switchgrass, the radius was varied between r1 = 1 mm and r2 = 5 mm, which is assumed to cover the range of harvested switchgrass. The impact on the formation time under furnace-relevant heat-transfer rates of q_ 00 = 20.0 kW/ m2 is presented in Figure 11. The result in Figure 11 indicates that the period of complete formation increases by ∼40%, while the size of the switchgrass blades increases by Δr = 4 mm. In comparison to thermally thin particles, as depicted in Figure 6, larger particles experience significant spatial gradients. Hence, larger blades undergo a much more prolonged combustion period, and thus, higher temperatures evolve inside a blade, as shown in Figure 12. Once, the blade has reached ignition conditions, it enters a period of steady-state combustion with temperatures of ∼2150 K, as compared to temperatures of ∼1700 K for the ground sample. Toward the end of the combustion period at a time of ∼35 s, the remaining ash of the switchgrass undergoes heat transfer only, resulting in decreasing temperatures. Although the spatial temperature is rather uniform during the combustion period, the distribution of oxygen experiences large gradients versus the radius of the switchgrass blades, as shown in Figures 13 and 14. In particular, Figure 14 depicts the strong gradients of oxygen between the surface and half of the radius inside the blade over an enlarged period during combustion, thus indicating that the reaction process is limited by the transport of
Figure 10. Temperature of a cylindrical and spherical switchgrass particle during combustion.
Figure 11. Time of formation of sulfur dioxide depending upon the radius for a cylindrical shape.
Figure 12. Temperature profile for a cylindrical switchgrass blade of 5 mm in radius.
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Energy Fuels 2010, 24, 945–953
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Figure 13. Oxygen profile for a cylindrical switchgrass blade of 5 mm in radius.
Figure 14. Enlarged oxygen profile for a cylindrical switchgrass blade of 5 mm in radius.
available oxygen. Contrary to lumped parameter models, the DPM resolves spatial gradients and is therefore equally wellapplicable to reacting and shrinking core modes of combustion that a particle most likely undergoes during a transition. Correlation between the Formation of Sulfur Dioxide and the Depletion of the Organic Matrix. Undoubtedly, the formation of any kind of emission is strongly coupled to the overall conversion of organic material. During thermal conversion of switchgrass, its organic matrix is first converted to charred material during pyrolysis. Because a part of available sulfur is bound to the organic matrix, the depletion of organically bound sulfur is correlated to the conversion of the organic matrix, as shown in Figure 15. The prediction illustrates that ∼80% of organically bound sulfur reacts during the period of pyrolysis. Similarly, inorganically bound sulfur reacts mainly during the conversion period of charred material. Predicted results in Figure 15 suggest that the start and end of depletion of
Figure 15. Correlation between emission formation and depletion of the organic matrix.
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Peters and Smuza-Ostaszewska
potassium sulfate correlate very well with the combustion period of charred material.
DPM. This method represents a transient and one-dimensional approach for solving the differential conservation equations of mass and energy. Thus, in conjunction with initial and boundary conditions and a given set of kinetic parameters, the sulfur dioxide emission was predicted. Good agreement between measurements and predictions was achieved. An error analysis showed that an upper standard error of 14% was not exceeded. In a further study, a similar approach will be employed to predict emission of chlorides. Thus, the release of sulfur dioxide and chlorides to the gas phase from biomass particles is described by applying the DPM to packed-bed combustion. Representing the gas phase by a computational fluid dynamics (CFD) approach, including appropriate gas-phase reactions for sulfur dioxide and chlorides, allows for the assessment of corrosion of boilers.
Summary The formation of sulfur dioxide during combustion of a switchgrass was investigated and compared to experimental data presented by Dayton et al.6 The formation of sulfur dioxide was modeled by two reactions, namely, an oxidation of sulfur bound in an organic matrix and a reaction between potassium sulfate and silicon dioxide. The Arrhenius-like approach was employed to describe the kinetics of the reactions. Kinetic parameters, i.e., an activation energy and a pre-exponential factor, were determined by a least-squares method, so that the deviation between the measured and predicted profiles was minimized. A simulation of the conversion of the switchgrass, including heating up, pyrolysis, and combustion, was modeled by the
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