A Fluidized Bed Biomass Combustion Model with Discretized

2346

Energy & Fuels 2007, 21, 2346-2356

A Fluidized Bed Biomass Combustion Model with Discretized Population Balance. 1. Sensitivity Analysis Atif A. Khan,* Wiebren De Jong, Dorian R. Gort, and Hartmut Spliethoff Department of Process & Energy, Section Energy Technology, Faculty 3ME, Delft UniVersity of Technology, Leeghwaterstraat 44, NL-2628 CA, Delft, The Netherlands ReceiVed July 14, 2006. ReVised Manuscript ReceiVed March 22, 2007

A model of a 1 MWth atmospheric bubbling fluidized combustor burning waste wood fuel (feeding) is presented. The model incorporates both the solid and gas phases. The bed is assumed to consist of two phases, of which the emulsion phase takes both gas and solids into account, while the bubble phase consists only of gas. A wide size distribution of biomass feed, representative of the actual boiler feed, has been assumed. The model calculates the gas composition, velocities, and other important hydrodynamic parameters in both the emulsion and bubble phase. A particle size distribution model is included to calculate elutriation losses of fine char particles. This approach is novel in the sense that a population balance for fine particle class is derived, using the well-known mass balance principles, and a coupled discretized population balance equation, valid for the whole particle size range, is presented. The model takes into account devolatilization, fragmentation, and attrition of the solid phase along with gaseous profiles. It includes nine components for which differential equations have been derived and solved to calculate species concentration at any point along the bed height. In total, 20 particle size classes have been considered, 10 of which are considered as feed and the rest as fine classes. The model aims to assess the effect of different parameters on boiler performance and gaseous emissions. A sensitivity analysis of the gaseous emission profiles with respect to different variables and parameters defining different submodels has been carried out. A homogeneous NOx model has been included with individual kinetic parameters for relevant species. It has been found that gas hydrodynamics play a significant role, and the system can be optimized using these parameters.

1. Introduction Due to the increasing demand of energy, higher oil prices, and depleting fossil fuel resources, the need to find alternative energy production systems is greater than ever. Not only that, but also the increasingly stricter environmental emission norms and incentives offered by different governments to promote green energy have made power plants and other small-scale units consider sustainable energy sources, especially biomass. In order to use this vital energy source, existing and future plants and boilers need to be more flexible to cope with the versatile nature of biomass. These circumstances call for better design, simulation optimization, and operation of energy production units. Reliable modeling and the simulation of combustion and gasification processes is thus vital and an important area of research. Such models can help in the prediction of the optimal operating parameters for both commercial and environmental aspects. Fluidized bed combustion (FBC) is a viable technology and certainly one of the best because of its ability to cope with a wide variety of solid fuels and because of its high efficiency. Extensive experimental work has been reported with these nonfossil fuels lately;1-5 however, an understanding of the mechanisms taking place during fluidized bed combustion or * Corresponding author. Tel.: +31 15 2786987. Fax: +31 15 2782460. E-mail: [email protected]. (1) Haykiri-Acma, H. Combustion Characteristics of Different Biomass Materials. Energy ConVers. Manage. 2003, 44, 155-162. (2) Laursen, K.; Grace, J. R. Some Implications of Co-Combustion of Biomass and Coal in a Fluidized Bed Boiler. Fuel Process. Technol. 2002, 76, 77-89.

gasification is still far from complete. A lot of modeling work has also been reported with different interests and approaches.6-15 (3) Annamalaia, K.; Thiena, B.; Sweeten, J. Co-Firing of Coal and Cattle Feedlot Biomass (FB) Fuels. Part II. Performance Results from 30 kWt (100,000 BTU/h) Laboratory Scale Boiler Burner. Fuel 2003, 82, 118393. (4) Suksankraisorn, K.; Patumsawad, S.; Vallikul, P.; Fungtammasan, B.; Accary, A. Co-Combustion of Municipal Solid Waste and Thai Lignite in a Fluidized Bed. Energy ConVers. Manage. 2004, 45, 947-962. (5) Gayan, P.; Adanez, J.; Diego, L. F. d.; Garcı´a-Labiano, F.; Cabanillas, A.; Bahillo, A.; Aho, M.; Veijonen, K. Circulating Fluidised Bed CoCombustion of Coal and Biomass. Fuel 2004, 83, 277-286. (6) Wang, Q.; Luo, Z.; Ni, M.; Cen, K. Particle Population Balance Model for a Circulating Fluidized Bed Boiler. Chem. Eng. J. 2003, 93 (2), 121133. (7) Adanez, J.; Abanades, J. C. Modeling of Lignite Combustion in Atmospheric Fluidized Bed Combustors. 1. Selection of Submodels and Sensitivity Analysis. Ind. Chem. Eng. Res. 1992, 31, 2286-2296. (8) Arena, U.; Camarote, A.; Massimilla, L.; Sicilliano, L.; Basu, P. Carbon Attrition during Combustion of a Char in a Circulating Fluidized Bed. Combust. Sci. Technol. 1990, 7, 383-394. (9) Souza-Santos, M. L. D. Comprehensive Modelling and Simulation of Fluidized Bed Boilers and Gasifiers. Fuel 1989, 68, 1508-1521. (10) Jensen, A.; Johnsson, J. E.; Andries, J.; Laughlin, K.; Read, G.; Mayer, M.; Baumann, H.; Bonn, B. Formation and Reduction of NOx in Pressurized Fluidized Bed Combustion of Coal. Fuel 1995, 76 (11), 15551569. (11) Scala, F.; Salatino, P. Modelling Fluidized Bed Combustion of HighVolatile Solid Fuels. Chem. Eng. Sci. 2002, 57 (7), 1175-1196. (12) Santana, D.; Rodriguez, J. M.; Macias-Machin, A. Modelling Fluidized Bed Elutriation of Fine Particles. Powder Technol. 1999, 106 (1-2), 110-118. (13) Galgano, A.; Salatino, P.; Crescitelli, S.; Scala, F.; Maffettone, P. L. A Model of the Dynamics of a Fluidized Bed Combustor Burning Biomass. Combust. Flame 2005, 140 (4), 371-384. (14) Ngampradit, N.; Piumsomboon, P.; Sajjakulnukit, B. Simulation of a Circulating Fluidized Bed Combustor with Shrinking Core and Emission Models. Sci. Asia 2004, 30, 365-374.

10.1021/ef060322+ CCC: $37.00 © 2007 American Chemical Society Published on Web 06/07/2007

Bubbling Fluidized Bed Combustor Model

Recently, Wang et al.6 presented a two-dimensional particle population model for a circulating fluidized bed boiler taking both size and density into account. Chejne and Hernandez15 developed a one-dimensional steady-state algorithm to simulate the coal gasification process in a bubbling fluidized bed boiler with an instantaneous devolatilization model. Ngampradit et al.14 reported the simulation work carried out in ASPEN PLUS with a shrinking core and emissions model. Moreea-Taha16 presented one- and three-dimensional fluid dynamics models to predict pollutant emissions. Galgano et al.13 presented a fluidized bed combustor model including thermal feedback from the splashing zone. Kuzmanovic and Skala17 developed a coal gasification model with some heterogeneous reactions. Adanez and Abanades7 modeled lignite combustion in an atmospheric fluidized bed combustor and presented a sensitivity analysis of the combustor efficiency. Jensen et al.10 presented a detailed model on the NOx chemistry in a pressurized fluidized bed coal combustor. The model presented by Souza-Santos9 is regarded as a comprehensive one including conservation equations for mass and heat balance and the bubble and emulsion phase, particle size distribution (PSD), and noninstantaneous drying and devolatilization models. He showed how mathematical modeling can be used as powerful engineering design tool by predicting the behavior of a real steady-state unit. Work reported on the fluidized bed combustion of highly volatile fuels/biomass has been limited. The pioneer modeling work dates back to the 1980s when Park et al.,18 and Stubington and Davidson19 proposed a “plume model”. Stubington et al.20,21 suggested a multiple discrete diffusion flame model. Oymak et al.22 modified a continuous fluidized bed model developed for high-quality coals to account for the highly volatile fuels. Irusta et al.23 proposed a three-phase FBC model for lignocellulose waste with an internal devolatilization degree parameter. A modified two-phase plume FBC model for biomass has been proposed by Borodulya et al.,24 Fiorentino et al.,25 Di Benedetto and Salatino,26 Scala et al.,11,27,28 Bruni et al.,29 and Cammarota et al.30 made significant contributions in the modeling of highly (15) Chejne, F.; Hernandez, J. P. Modelling and Simulation of Coal Gasification Process in Fluidised Bed. Fuel 2002, 81 (13), 1687-1702. (16) Moreea-Taha. Modelling and Simulation for Coal Gasification. In IEA Coal Research Report; Putney Hill: London, U.K., 2000. (17) Skala, D.; Kuzmanovic, B. Heterogeneous Gas-Solid Reactions: IV. Equipment. Hem. Ind. 1997, 51 (11), 461-471. (18) Park, D.; Levenspeil, O.; Fitzgerald, T. J. Plume Model for Large Scale Atmospheric Fluidized Bed Combustors. Fuel 1981, 60, 295-306. (19) Stubington, J. F.; Davidson, J. F. Gas-Phase Combustion in Fluidized-Beds. AIChE J. 1981, 27 (1), 59-65. (20) Stubington, J. F.; Chan, S. W.; Clough, S. J. A Model for Volatiles Release into a Bubbling Fluidized-Bed Combustor. AIChE J. 1990, 36 (1), 75-85. (21) Stubington, J. F.; Chan, S. W.; Clough, S. J. The Multiple Discrete Diffusion Flame Model for Fluidized Bed Combustion of Volatiles, 12th International Conference on Fluidized Bed Combustion, San Diego, CA, May 9-13, 1993; ASME: New York, 1993; pp 167-178. (22) Oymak, O.; Selcuk, N.; Onal, I. Testing of a Mathematical-Model for the Combustion of Lignites in an AFBC. Fuel 1993, 72 (2), 261-266. (23) Irusta, R.; Antolin, G.; Velasco, G.; Miguel, D. Modelling of Lignoceullose Waste Combustion in an Atmospheric Bubbling Fluidized Bed Using an Internal DeVolatilization Degree Parameter; Engineering Foundation: New York, 1995; pp 855-862. (24) Borodulya, V. A.; Didalenko, G. I.; Palchonok, L. K.; Stanchitis, L. K. Fluidized Bed Combustion of Solid Organic Wastes and Low-Grades Coals: Research and Modeling, 13th International Conference on Fluidized Bed Combustion, Orlando, FL, May 7-10, 1995; ASME: New York, 1995; pp 935-942. (25) Fiorentino, M.; Marzocchella, A.; Salatino, P. Segregation of Fuel Particles and Volatile Matter During Devolatilization in a Fluidized Bed Reactor. 1. Model Development. Chem. Eng. Sci. 1997, 52 (12), 18931908. (26) Di Benedetto, A.; Salatino, P. Modelling Attrition of Limestone during Calcination and Sulfation in a Fluidized Bed Reactor. Powder Technol. 1998, 95 (2), 119-128.

Energy & Fuels, Vol. 21, No. 4, 2007 2347

volatile fuels. Their work has been mainly focused on the release of volatile matter, segregation, and attrition of fuel and limestone particles. Selcuk et al.31 presented an atmospheric bubbling fluidized model for highly volatile fuel (lignite) with special consideration for volatile release. More recently, Okasha32 presented a two-phase fluidized bed model mainly focused on the burning of volatile matter, heat profile, and combustion efficiency. Nitrogen species, char particle size distribution, elutriation, and attrition effects are not presented in his model. Effects of the parameters such as excess air and bed temperature have also been predicted. Trends are the same as predicted by our model. At higher fluidization velocities, the gaseous emissions (CO) increase due to the decrease in residence time, while an increase in the bed temperature leads to a decrease in gaseous emissions (CO) due to faster combustion kinetics. The work reported here is the development of an atmospheric fluidized bed model to predict the performance of a 1 MWth fluidized bed experimental boiler installed at Delft University of Technology. The steady-state atmospheric bubbling FBC model described here considers two phases, namely, the bubble and emulsion phases. The processes, devolatilization, fragmentation, attrition, and combustion, all have been taken into account. This char PSD calculation approach, presented in this article, is novel in the sense that a population balance for fine particle class is derived, using the well-known mass balance principles, and a coupled discretized population balance equation, valid for the whole particle size range. The model described here was developed to improve the understanding of bubbling fluidized bed boiler operation, to predict the emissions profile over the length of the unit, to calculate the bed inventory, and to estimate char losses. 2. Model Description The main assumptions and the characteristics of the model are as follows: • The model is one-dimensional and steady-state. • The bed consists of an emulsion and a bubble phase. • Gas and solid are the two fluids considered. • The emulsion phase consists of solids and gas. • The bubbles are free of solids.33 • All excess air (u0 - umf) will make bubbles.33 • There is perfect mixing between the solid and gas in the emulsion phase. • Particles are considered as spheres with a sphericity factor. • The bed temperature is taken as a design variable. • The bed is isothermal, and the gas is at the same temperature as the bed. (27) Scala, F.; Cammarota, A.; Chirone, R.; Salatino, P. Comminution of Limestone during Batch Fluidized-Bed Calcination and Sulfation. AIChE J. 1997, 43 (2), 363-373. (28) Scala, F.; Salatino, P.; Chirone, R. Fluidized Bed Combustion of a Biomass Char (Robinia pseudoacacia). Energy Fuels 2000, 14 (4), 781790. (29) Bruni, G.; Solimene, R.; Marzocchella, A.; Salatino, P.; Yates, J. G.; Lettieri, P.; Fiorentino, M. Self-Segregation of High-Volatile Fuel Particles during Devolatilization in a Fluidized Bed Reactor. Powder Technol. 2002, 128 (1), 11-21. (30) Cammarota, A.; Chirone, R.; Salatino, P.; Scala, F.; Urciuolo, M. Attrition Phenomena during Fluidized Bed Combustion of Granulated and Mechanically Dewatered Sewage Sludges. Proc. Combust. Inst. 2005, 30, 3017-3024. (31) Selcuk, N.; Degirmenci, E.; Gogebakan, Y. Modeling of a Bubbling AFBC with Volatiles Release. J. Energy Res. Technol. 2003, 125 (1), 7281. (32) Okasha, F. Modeling Combustion of Straw-Bitumen Pellets in Fluidized Bed. Fuel Process. Technol. [Online] 2006, DOI: 10.1016/ j.funproc.2006.10.012. (33) Davidson, J. F.; Harrison, D. Fluidised Particles; Cambridge University Press: New York, 1963.

2348 Energy & Fuels, Vol. 21, No. 4, 2007

Khan et al. Table 1. Correlations used for Hydrodynamicsa

150(1 - mf) 1.75 Remf2 + Remf ) Ar 3 mf Φs mf3Φs2 Remf )

(1)34,35

umfdpFg dp3Fg(Fs - Fg)g ; Ar ) µg µ2

(2)34,35

g

1 - mf 1 = 14 and 2 3 = 11 3 Φsmf Φs mf

(3)36

db ) dbm - (dbm - db0) e-0.3z/dt

(4)37

db0 ) 0.283(u0 -

(5)38

umf)2

dbm ) 1.633[0.785dt2(u0 - umf)]0.4

(6)38

ub ) u0 - umf + ubr

(7)33,38,39

ub ) 1.6[(u0 - umf) + 1.13db0.5]dt1.35 + ubr

(8)38,40,41

ubr ) 0.711(gdb)0.5

(9)33,38

1 1 1 ) + Kbe Kbc Kce

(10)38

Kbc ) 4.5

() (

)

umf De0.5g0.25 + 5.85 db db5/4

(11)38,41

TDH ) 4.47db0.5

13

uti )

a

[ ()(

Ki* uti ) 0.0001 + 130 exp -10.4 Fgu0 u0

[

0.5

umf u0 - umf

(12)42

)]

(13)43

]

4dp(Fs - Fg)g 3FgCD

0.5

(14)38

CD )

73.69(e-4.0655Φs)Rep 24 [1 + (8.1716 e-4.0655Φs)Rep0.0964+0.5565Φs] + Rep Rep + 5.378 e6.2122Φs

(15)38

Rep )

dputiFg µ

(16)38

All the symbols are explained in the Nomenclature section.

• The plug flow for gas is in both the emulsion and bubble phases. • Empirical relations are used to calculate fluid dynamic parameters (bubble size, velocity, elutriation rate, etc.). • Mass transfer between the gas and solid in the emulsion phase is considered. • Mass transfer between the emulsion and bubble phases in gas is considered. • Devolatilization and drying are considered to occur instantaneously with a uniform release of volatiles in the emulsion phase. • A localized energy balance for the solid particles is included to calculate the particle temperature. • Attrition and elutriation are included for the solid phase. • A discretized population balance including generated fines due to attrition is developed and implemented to calculate the bed inventory and elutriation rate. • Simple kinetic models are used for homogeneous (gas-gas) and heterogeneous (gas-solid) reactions. • The shrinking rate of particles consists of attrition and reaction for fuel particles and reaction for attrited particles. • Differential mass balance equations for all components are included. • The components considered are CH4, CO, CO2, N2, NO, NH3, O2, H2, and H2O.

• Solid types considered include biomass (fuel) and sand (inert material). • Chemical reactions and diffusion are included in the mass balance equations. 2.1. Bed Hydrodynamics. Bed hydrodynamics relations including minimum fluidization velocity, bubble size and velocity, the gas interchange coefficient, transport disengagement height, and elutriation rate are indicated in Table 1. Alternative relations were also considered for hydrodynamics, but the above presented relations were chosen because of their extensive use in the literature and recommendations by a number of authors.10,38,39,44 2.2. Population Balance with Reaction and Attrition. The char particle size distribution was considered to consist of two categories: mother and fine particles. The feed size distribution is taken (34) Couderc, J. P. Fluidization, 2nd ed.; Academic Press: New York, 1985; Chapter 1. (35) Ergun, S. Fluid Flow through Packed Beds. Chem. Eng. Prog. 1952, 48, 89-94. (36) Wen, C. Y.; Yu, Y. H. A Generalized Method for Predicting the Minimum Fluidization Velocity. AIChE J. 1966, 12, 610-612. (37) Mori, S.; Wen, C. Y. Estimation of Bubble Diameter in Gaseous Fluidized Beds. AIChE J. 1975, 21 (1), 109-115. (38) Kunii, D.; Levenspiel, O. Fluidization Engineering, 2nd ed.; Butterworth-Heinemann: Boston, 1991; p 491.



as mother particles, which are subjected to fragmentation upon entering the boiler. The fine particles are generated due to the attrition of the mother particles. Overturf and Kayihan45 derived a discretized population balance for the fluidized bed, that being Pb(Ri) )

F0 P0(Ri) ∆Ri - Wc Ra(Ri+1) Pb(Ri+1) -Wc Ra(Ri) +

WcKi*Ab∆Ri 3Wc Ra(Ri) ∆Ri Wt Ri

WcKfi*Ab∆Rfi 3Wc Ra(Rfi) ∆Rfi Wt Rfi

(18)

where the term Gi represents the intake of fines through the attrition of mother particles. Combining the both balances will give the total particle population balance including fines, rf e ri e rm: Pb(Ri) )

Rfrac ) Rfuelkf-1/3

WcKi*Ab∆Ri 3Wc Ra(Ri) ∆Ri Wt Ri

(19)

where the δ function and generation term are defined as6,46

{

}

δ(Ri) ) 1 for Ri ) Rfi ; Gi ) δ(Ri) ) 0 for Ri * Rfi

Rmax,att3W

∑

c

Pb(Ri) Ra(Ri) ∆Ri Ri

Rmin,att

(20)

The natural grain size distribution of fines, Pfi(Rfi), is given by46 Pfi(Rfi) )

( )( )

1 (ea + eb + 1)! Rfi Rf ea!eb! Rf

ea

1-

Rfi Rf

(22)

eb

(21)

2.3. Solid Fuel Combustion. 2.3.1. Fragmentation. Fuel particles experience a great temperature difference when they are injected into the fluidized bed. The thermal stress together with devolatilization and drying causes the particles to break.39,47-49 Bellgardt et (39) Hannes, J. P. Mathematical Modelling of Circulating Fluidized Bed Combustion. Ph.D. Thesis, Technical University Delft, Delft, The Netherlands, 1996. (40) Werther, J. Bubble Chains in Large Diameter Gas Fluidized Beds. Ger. Chem. Eng. 1977, 1, 166. (41) Geldart, D. Types of Gas Fluidization. Power Technol. 1973, 7, 285-292. (42) Horio, M.; Taki, A.; Hsej, Y.; Muchi, Y. S. Elutriation and Particle Transport through the Freeboard of a Gas-Solid Fluidized Bed. Fluidization; Grace, J. R., Matsen, J. M., Eds.; Engineering Foundation: New York: 1980. (43) Merrick, H. S.; Highley, J. Particle Size Reduction and Elutration in a Fluidized Bed Process. AIChE J. 1974, 62 (137), 366-378. (44) Olowson, P. A.; Almstedt, A. E. Influence of Pressure and Fluidization Velocity on the Bubble Behaviour and Gas Flow Distribution in a Fluidized Bed. Chem. Eng. Sci. 1990, 45 (7), 1733-1741. (45) Overturf, B. W.; Kayihan, F. Computations for Discrete Cut Particle Size Distributions in a Fluidized Bed Reactor. Powder Technol. 1979, 23 (1), 143-147. (46) Ray, Y. C.; Jiang, T. S.; Jiang, T. L. Particle Population Model for a Fluidized Bed with Attrition. Powder Technol. 1987, 52 (1), 35-48. (47) Bellgardt, D.; Hembach, F.; Schoessler, M.; Werther, J. Modeling of Large Scale Atmosheric Fluidized Bed Combustors. International Conference on Fluidized Bed Combustion, Boston, MA, March 5, 1987; Mustonen, J. P., Ed.; ACME: New York, 1987; pp 713-722. (48) Chirone, R.; Camarote, A.; D’Amore, M.; Massimilla, L. Fragmentaton and Attrition in the Fluidized Bed Combustion of Coal. 7th International Conference on Fluidized Bed Combustion, Philadelphia, PA, 1982; Government Institutes: Blue Ridge Summit, PA, 1983; pp 10231029.

Pfrac(Rfuel) ) kf1/3 Pfuel(R)

(23)

The value of kf lies between 1 and 2.47,50 Biomass is more prone to fragmentation due to its highly volatile content, and therefore kf is chosen as 2. 2.3.2. Attrition. There have been several different approaches to model the attrition rate in fluidized beds.46,51-54 One of the most simple models was produced by Merrick and Highley.43 This model uses the superficial gas velocity as the defining factor in the attrition rate. It is a linear relation and simply states that the gas velocity is directly proportional to attrition rate: Ra(Ri) ) -

F0 P0(Ri) ∆Ri - Wc Ra(Ri+1) Pb(Ri+1) - δ(Ri) Gi Pfi(Rfi) -W Ra(Ri) +

Vfuel kf

The radius and probability of fractured particles are given by

-Wc Ra(Rfi+1) Pb(Rfi+1) - Gi Pfi(Rfi) -W Ra(Rfi) +

Vfrac )

(17)

The discrietized population balance for the attrited fine particles can be derived in a similar fashion and is given by Pb(Rfi) )

al.47 proposed that each fuel particle will break into kf particles of small volumes, mathematically formulated as

kattr (u0 - umf)dp 3

(24)

The attrition rate is highly dependent on the types of materials used in the fluidized bed. The attrition rates found in the literature vary greatly, as can be seen in Table 2. The choice was made that the constant from Lin et al.53 would be used for further calculation, as it closely resembles the materials that are present in the modeled bed. Lin et al. performed their experiments in an atmospheric fluidized bed with silica sand as the bed material. The bed material consisted of sizes 125-300 µm with char added of size 0-125 µm. The char used was produced from hardwood, and so the materials correspond nicely with what will be used here. Due to the fact that from the experiments the attrition rate was found to depend exponentially on the superficial velocity, the attrition equation must be changed and rewritten in the following form: Ra(Ri) ) -9.36 × 10-4 exp0.162(u0-umf)(u0 - umf)dp

(25)

One common assumption is that at a certain moment the original particle is so small that it will no longer be subjected to attrition. This is due to the fact that the particle is then so small that, when it gets hit by another particle, it no longer absorbs the impact but just moves along with the impact due to its low inertia. The particle size at which attrition will no longer occur is called the minimal attrition diameter:

{

Ra(Ri) ) -9.36 × 10-4 exp0.162(u0-umf)(u0 - umf)dp dp > dcrit dp e dcrit Ra(Ri) ) 0 (26)

2.4. Mass Balance Equations. The conservation mass balance of the emulsion phase includes the transfer between phases, (49) Stubington, J. F.; Linjewile, T. M. The Effects of Fragmentation on Devolatilization of Large Coal Particles. Fuel 1989, 68, 155-160. (50) Bu¨rkel, K. J. Ein Gesamtmodell fu¨r Klassische Wirbelschichtfeuerungen. Ph.D. Thesis, Siegen University, Germany, 1991. (51) Pis, J. J.; Fuertes, A. B.; Artos, V.; Suarez, A.; Rubiera, F. Attrition of Coal Ash Particles in a Fluidized Bed. Powder Technol. 1991, 66, 4146. (52) Scala, F.; Chirone, R.; Salatino, P. The Influence of Fine Char Particles Burnout on Bed Agglomeration during the Fluidized Bed Combustion of a Biomass Fuel. Fuel Process. Technol. 2003, 84 (1-3), 229-241. (53) Lin, L.; Sears, J. T.; Wen, C. Y. Elutration and Attrition of Char from a Large Fluidized Bed. Powder Technol. 1980, 27, 105-115. (54) Wang, A. L. T. Generation of Fine Chars from Australian Black Coals in Pressurized Fluidized Bed Combustion. Combust. Flame 2002, 129, 192-203.


Khan et al.

Table 2. A Comparison of Attrition Models Available in the Literature

reference

dependency

size of particles (µm)

Merrick and Highley 43 Basu and Subbaro55 Arena et al.8 Lin et al.53

volume surface surface na

0-63 na 880 °C), NO emissions show a little increase with the temperature; this is due to the selective oxidation of NH3 by O2 (R7). In practice, one of the ways to vary the bed temperature while keeping the air-to-fuel ratio constant can be by using an internal heat exchanger.81,82 This will definitely affect the boiler loadings and temperature profile, but it is a useful way to measure temperature effects on the combustion process.

Figure 1. Schematic of the modeled boiler.

3.1.2. Influence of Fluidization Velocity on Gaseous Emissions. Figure 6 depicts the influence of fluidization velocity on gaseous emissions. Increasing the velocity shows a steep increase in CO emissions while the other emissions remain more or less constant. The increase in CO emission is due to the decrease in residence time; therefore, at low boiler loadings, the gases get more time to react in the high-temperature zone. 3.1.3. Influence of Voidage at Minimum Fluidization Velocity mf on Gaseous Emissions. Voidage mf at the minimum fluidization velocity is a very important and fundamental factor in fluidized bed boilers. In practice, this can be varied by using different types and sizes of inert material. It strongly influences the minimum fluidization velocity and consequently the flow regimes in the bed. Figure 7 shows that as mf increases both CO and NO emissions decrease. At low mf values, most of the gas flows in the bubble phase and oxygen required for the combustion of the char and other reactions should be transferred from the bubble to the emulsion phase. Thus, strong reducing and oxidizing conditions exist in the emulsion and bubble phases, respectively. As mf increases, there is more oxygen available for combustion, and thus CO emissions decrease. At mf values between 0.35 and 0.45, there is a transition where the CO emission stays rather constant. This transition phase is due to two competing factors acting simultaneously. On one hand, increasing mf decreases CO emissions in both the emulsion and bubble phases, but on the other hand, this also increases the proportion of the emulsion phase which still has a high percentage of CO, and therefore the two effects cancel out each other. Almost similar is the case with NO emissions. The strong reducing conditions at low mf values cause the production of very high concentrations of NH3 in the emulsion phase, part of (82) de Jong, W.; Khan, A. A.; Spliethoff, H. Biomass Blend Combustion in a 1 MWth Bubbling Fluidized Bed Boiler. Clean Air 2005. 8th Int. Conference on Energy for a Clean Environment, Lisbon, Portugal, 2005.



Figure 2. Simplified algorithm of solution procedure.

Figure 4. Predicted species concentration along the boiler length. Figure 3. Predicted char particle size distribution in bed.

which is then oxidized to NO in the freeboard. Increasing mf shows less reducing and oxidizing conditions in the emulsion and bubble phases, respectively. It should be noted that the NH3 concentrations decrease with increasing mf values, but the total NH3 concentration at the entrance of the freeboard still increases. This is due to the fact that an increasing mf also implies a larger fraction of the emulsion phase, which ultimately results in higher

NH3 concentrations at the entrance of the freeboard. Not only that, but also with increasing mf, the gas interchange coefficient increases (see eqs 1-2, 11), which then causes an increased transfer of gas from one phase to other. Upon further increasing mf values, the conditions in the emulsion and bubble phasse become less reducing and oxidizing, respectively, resulting in a decrease of NH3 concentration in the freeboard, which consequently results in lower NO emissions.


Figure 5. Predicted effect of temperature on gaseous emissions.

Figure 6. Predicted effect of fluidization velocity on gaseous emissions.

Figure 7. Predicted effect of mf on gaseous emissions.

At higher mf values, NH3 is destructed in the bed zone to NO, and it will further react with NH3 and O2 (R8) producing N2 and H2O, resulting in overall lower NO emissions. These are not the only effects contributing to this complex formation and destruction of NH3 and NO. The devolatilization reactions also play their important role as volatilization products, in our devolatilization model, and are uniformly added to the emulsion phase, and all volatile N is converted to NH3. Upon further increasing mf values (>0.455), taking all the effects into account, the total NH3 concentration decreases and thus results in lower conversion into NO in the freeboard. It should also be mentioned that increasing mf also results in an increase in umf and the bed height, which in turn results

Khan et al.

Figure 8. Predicted effect of Kbe on gaseous emissions (Kbe-std ) at conditions given in Table 4).

in high emulsion flows. umf calculated using Ergun’s35 equation was found to be 0.227 m/s for the standard case. Other relations36,83 predict values between 0.17 and 0.32 m/s. Considering Figure 7, it seems that running the system at higher mf values is very beneficial in terms of lower CO and NO emissions, but in practice, higher mf values imply the use of bigger mesh-size sand (or other inert material), which in turn strongly affects the mixing in the bed and also increases the likelihood of segregation of the fuel particles. On the other hand, for a very low mf, the use of a very fine inert material (sand) becomes a must, and running the system at the standard velocity will result in blowing off inert material out of the boiler and consequently will not only affect the mixing efficiency but will also lead to larger elutriation rates of unburned carbon particles. 3.1.4. Influence of Gas Interchange Coefficient on Gaseous Emissions. Equation 11 was used to calculate the gas interchange coefficient. Numerous correlations are available in the literature to predict the value of this parameter, and a choice needs to be made according to the fluidization conditions. Figure 8 shows the effect of gas interchange coefficient variation on gaseous emissions. As the interchange coefficient increases, CO decreases due to the transfer of oxygen from the bubble to the emulsion phase. Due to the severe deficiency of O2 in the emulsion phase, the NH3 concentration (including that due to the devolatilization of biomass) is very high at the entrance of the freeboard. Part of this NH3 later oxidizes to NO, but the overall NO concentration remains low. When Kbe is further increased, there are strong oxidizing conditions everywhere, resulting in high NO and low CO concentrations. With an increasing gas interchange coefficient and the availability of more oxygen, better in-bed combustion is provided and thus low char content in the bed. 3.1.5. Influence of Bubble Diameter and Bubble Velocity on Gaseous Emissions. The effect of the variation of the bubble diameter is shown in Figure 9. The most important effect is that Kbe decreases as the bubble diameter increases. The second effect is the increase in bubble velocity, which in turn results in the high CO emissions (less in-bed combustion). Both effects were well-expected, as bubble diameter is inversely and directly proportional to the gas interchange coefficient and bubble velocity, respectively (see eqs 11 and 8). Figure 10 presents the effect of increasing the bubble velocity and shows the same effect. An additional effect of the variation of bubble velocity (83) Saxena, S. C.; Vogel, G. J. The Measurement of Incipient Fluidization Velocities in a Bed of Coarse Dolomite at Temperature and Pressure. Trans. IChE 1977, 55, 184-189.


Figure 9. Predicted effect of bubble diameter on gaseous emissions.

Figure 10. Predicted effect of bubble velocity on gaseous emissions (ub-std ) at standard conditions as given in Table 4).

is on the bed height. As the bubble velocity decreases, the expanded bed height increases (see eq 41) and, consequently, the in-bed combustion increases, resulting in a decrease of gaseous emissions. When eqs 4-11 are considered, it becomes apparent that umf or mf and u0 are in principle also the controlling parameters for the bubble diameter db, gas interchange coefficient Kbe, and bubble velocity ub. Increasing the difference between the minimum fluidization velocity and superficial gas velocity (u0 - umf) will result in a smaller db and a larger ub and Kbe. Other controlling parameters could be design variables such as bed diameter and air distributor design, which can produce smaller bubbles. 3.1.6. Influence of Fragmentation Factor on Gaseous Emissions and Final Particle Size Distribution. Figure 11 shows the effect of the fragmentation factor on char particle size inventory in the bed. As evident from the figure, with an increasing fragmentation factor, the size distribution curve shifts toward the left and the average particle size reduces. The effect of this shift on the elutriation rate of different particle sizes is depicted in Figure 12. The elutriation rate of smaller particles in the mother particle range increases slightly, but the total elutriation rate, by increasing kf from 1 to 2.8, decreases by 2.5%. This decrease is due to the decrease in the char attrition rate, which is strongly dependent on the particle size (see eq 25); so as the bed particle size decreases, the attrition rate also decreases, resulting in a decrease in the amount of attrited particles and consequently a decrease in the total elutriation rate.


Figure 11. Predicted effect of fragmentation factor on char particle size distribution.

Figure 12. Predicted effect of fragmentation factor on elutriation rate.

4. Conclusions Compared with the usual fluidized bed data available in the literature,81,82 it can be concluded that the model-predicted values follow the same trends. The model is novel in the sense that a discretized population balance including attrition has been applied for the first time. The application of such a balance is at least unknown for the authors. The advantage of such a discretized balance is that it is not only relatively simple but also less sensitive (bed weight and solid flows) in comparison to continuous size distribution models.38,45,84 With respect to the sensitivity analysis, the following conclusions can be drawn: Running the fluidized bed boilers at low velocities increases the residence time and therefore decreases NO, and especially CO emissions and boiler loadings, and increases the system efficiency. The model predicts that increasing the minimum fluidization voidage mf is beneficial in terms of gaseous emissions. The gas interchange coefficient is an important and sensitive parameter in terms of emissions. Measures such as decreasing bubble diameter and increasing bubble velocity can be used to control this parameter. Nomenclature Ab ) area of the bed Ar ) Archimedes number (m2)

(84) Levenspiel, O.; Kunii, D.; Fitzgerald, T. The Processing of Solids of Changing Size in Bubbling Fluidized Beds. Powder Technol. 1968, 2 (2), 87-96.

2356 Energy & Fuels, Vol. 21, No. 4, 2007 Cb,i ) concentration of species i in bubble phase (mol m-3) CD ) drag coefficient Ce,i ) concentration of species i in emulsion phase (mol m-3) db ) bubble diameter (m) dbm ) minimum bubble diameter (m) db0 ) bubble diameter just above the distributor (m) dcrit ) critical particle diameter (m) De ) diffusion coefficient (m2 s-1) dt ) bed diameter (m) dp ) particle diameter (m) ea ) β function parameter eb ) β function parameter exsi ) rate of excess gas production in the emulsion phase (mol m-3 s-1) F0 ) feed rate of char particles (kg s-1) Fb,i ) gas flow rate in bubble phase (mol s-1) Fe,i ) gas flow rate in emulsion phase (mol s-1) Ff,i ) gas flow rate in freeboard (mol s-1) g ) acceleration due to gravity (m s-2) H ) total expanded height of the bed (m) kattr ) attrition constant kreac ) char combustion constant [(mol C)(mol O2 gas/m3)-1(m2 out.surf)-1s-1] Kbc ) gas interchange coefficient between bubble and cloud phase (s-1) Kbe ) gas interchange coefficient between bubble and emulsion phase (s-1) kchar ) total kinetic constant (m s-1) Kce ) gas interchange coefficient between cloud and emulsion phase (s-1) kdiff ) diffusion coefficient to the surface of particle (m s-1) kf ) fragmentation constant Ki* ) elutriation rate (kg m2 s-1) kshrink ) shrink rate due to combustion (m3 mol-1) M ) total number of species MolC ) molecular weight of carbon (kg mol-1) NSIV ) number of size classes P0(Ri) ) feed size distribution frequency Pb(Ri) ) bed size distribution frequency Pfi(Rfi) ) fine particle size distribution frequency Ravg,i ) average shrinkage rate (m s-1) Rchar(Ri) ) reaction rate of char particles (mol m-2 s-1) Ri ) particle radius (m) or represents a particle class Rfi ) fine particle radius (m) Rf ) average fine particle radius (m)

Khan et al. Ri,comb ) rate of heterogeneous reaction (mol m-3 s-1) Ri,n ) rate of homogeneous reaction (mol m-3 s-1) Ri,vol ) production rate of species i by devolatilization (mol m-3 s-1) Ra(Ri) ) shrinking rate due to combustion and attrition (m s-1) Remf ) Reynolds number at minimum fluidization velocity Rep ) Reynolds number using terminal falling velocity of a particle Tp ) particle temperature (K) T∞ ) bulk gas temperature (K) TDH ) transport disengagement height (m) u0 ) superficial gas velocity (m s-1) ub ) bubble velocity (m s-1) ubr ) bubble rise velocity at minimum fluidization conditions (m s-1) umf ) minimum fluidization velocity Vfuel ) volume of the fuel particle (m3) Vfrac ) volume of the fragmented fuel particle (m3) Wc ) char weight in bed (kg) z ) height above the distributor (m) Greek Letters b,avg ) mean bubble fraction b ) local bubble fraction mf ) voidage at minimum fluidization velocity p ) char particle emissivity -∆Hr ) heat of char combustion (J mol-1) ∆Ri ) width between size classes (m) ∆zi ) step in bed height (m) R ) heat transfer coefficient (J mol-1 m-2 s-1) R1,j ) solids volume fraction in emulsion phase µg ) gas viscosity (kg m-1 s-1) σ ) Stefan-Boltzmann constant (J s-1 m-2 K-4) ξC ) carbon fraction in char Φs ) particle sphericity factor Fchar ) char density (kg m-3) Fg ) gas density (kg m-3) Fs ) inert material (sand) density (kg m-3) Acknowledgment. The European Union is acknowledged for funding the research in the framework of NNE5 (Project No.: E52001-00601) via the project “Safe Co-Combustion and Extended Use of Biomass and Biowaste in FB Plants with Accepted Emissions” (contract ENK5-CT2002-00638, FBCOBIOW). EF060322+

A Fluidized Bed Biomass Combustion Model with Discretized

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