Energy Fuels 2010, 24, 4820–4832 Published on Web 08/24/2010
: DOI:10.1021/ef100394y
Transient Three-Dimensional Mathematical Model and Experimental Investigation of a Wet Devolatilizing Wood in a Hot Fluidized Bed D. Ruben Sudhakar* and Ajit Kumar Kolar Heat Transfer and Thermal Power Laboratory, Department of Mechanical Engineering, Indian Institute of Technology Madras, Chennai 600 036, Tamil Nadu, India Received March 30, 2010. Revised Manuscript Received July 15, 2010
Devolatilization of a single wet wood particle in a hot atmospheric fluidized bed is studied through a mathematical model and experiments. A typical tropical woody biomass, “Casuarina Equisetifolia”, is used in the study. A three-dimensional (3D) transient model with detailed consideration of (i) fuel anisotropy, (ii) fuel moisture, (iii) shrinkage during drying and devolatilization, (iv) heat generation, and (v) variable properties with a suitable reaction scheme is developed to determine the devolatilization time (τd) and char yield (Yc) of cubic/cuboidal wood particles at various initial fuel moisture contents and bed temperatures. Experiments are conducted for 10, 15, 20, and 25 mm cube-shaped wood particles at bed temperatures of 1023, 1123, and 1223 K. The model predictions agree well with the measured data (present experiments and those reported in the literature) within (10% for the devolatilization time and (11% for the char yield, supporting the validity of the overall structure of the model. A sensitivity analysis is carried out using the 3D model to identify the important parameters influencing the devolatilization time and char yield and the level of confidence (degree of uncertainty) in using them as model inputs. The important parameters considered include the initial wood particle density, thermal conductivity, external surface heat-transfer coefficient, and various kinetic schemes available in the literature. Invariably, the relative influence of the parameters on the devolatilization time and char yield is found to be predominant in larger particle sizes. The initial particle density of wood has the strongest influence on the devolatilization time, followed by the thermal conductivity and specific heat capacity. The devolatilization time increases considerably with an increase in the initial wood density and decreases moderately with an increase in the thermal conductivity of wood, while the char yield remains negligibly influenced by the initial density and thermal conductivity of wood. The devolatilization time decreases considerably when the external surface heat-transfer coefficient is varied from 100 to 500 W m-2 K-1, beyond which the influence is negligible. The prediction of the devolatilization time and char yield is found to be very sensitive to the reaction kinetic parameters (rather than the wood properties), and hence due care must be taken in adopting the right kinetic parameters available in the literature to model.
A detailed literature review of experimental and modeling work on devolatilization of wood in fluidized beds is given by Sreekanth et al.2 Several disparate experimental studies on determination of the devolatilization time and char yield for various shapes of wood in FBC are found in the literature. The empirical design methods and the several correlations available in the literature in abundance are valid only at certain operating conditions and do not give any clear fundamental understanding of the devolatilization and char yield phenomena. Hence, to establish a better reactor design technique, an efficient and accurate fundamental model incorporating all of the physics involved and operating conditions as they exist during the devolatilization process is of great necessity. There are several models available in the literature for devolatilization. Basically, these models can be classified on the following basis: (i) Number of dimensions: As reported in Sreekanth et al.,2 there are many one-dimensional (1D) models and few two-dimensional (2D) models for the pyrolysis of wet wood. Nevertheless, these 1D and 2D models cannot precisely represent the boundary conditions for the
1. Introduction With the sudden spate of awareness on the environmental degradation and climate change due to the use of fossil fuels, the importance of biomass in terms of international energy policy and strategy is on the upsurge. Bioenergy caters roughly 35% of energy demand in developing countries, with the world total at about 13% of energy demand.1 The majority of biomass energy is supplied by wood and wood wastes, accounting for about 64% of the total.1 Fluidized-bed combustion (FBC) has been recognized as a suitable technology for the effective handling of biomass especially with high moisture content for the generation of thermal energy and electricity. Devolatilization is one of the important thermophysical phenomena during FBC/gasification of solid fuels, especially for biomass with high volatile content. Wood, on an average, consists of 70-80% volatiles, contributing to about 25% of the total combustion time and around 75% of the total heat release during the combustion of a single fuel particle in FBC. *To whom correspondence should be addressed. E-mail: rubensudhakar@ gmail.com. (1) Demirbas, M. F.; Balat, M.; Balat, H. Energy Conversion and Management 2009, 50, 1746–1760. r 2010 American Chemical Society
(2) Sreekanth, M.; Ruben Sudhakar, D.; Prasad, B. V. S. S. S.; Kolar, A. K.; Leckner, B. Fuel 2008, 87, 2698–2712.
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heating of a cubical wood particle in FBC. Moreover, with wood being anisotropic, the thermal properties along (longitudinal) and across (transverse) the grain are different, thus necessitating consideration of more than one dimension in accordance with the size and shape of the wood particle, which cannot be taken care of completely by a 1D or 2D model. Hence, a threedimensional (3D) formulation is necessary for modeling of the devolatilization of cube-shaped wood particles. Bonnefoy et al.3 have reported a 3D wood pyrolysis model for a dry isotropic wood under non-FBC conditions. Yuen et al.4 used the kinetic scheme obtained from fitting of the experimental results of Bonnefoy et al.3 in a 3D model under non-FBC conditions. However, this model has not considered the shrinkage and surface regression during the devolatilization process. Also, the model requires knowledge of the final char density a priori. This model has focused on the progress of isotherms and char contours for a particle size of a 10 mm 10 mm 10 mm cube and has not reported any devolatilization time and terminal char yield. (ii) Physical and chemical changes considered: The wood particle goes through various physical changes, namely, heating up, drying, shrinkage and surface regression, release of volatiles, and fragmentation before complete devolatilization. Also, there are numerous chemical reactions taking place within the particle during the above process, which may be endothermic/exothermic, single/multiple steps, and series/parallel. The ideal model in terms of representation of the actual physics of the study and accuracy would be the one that considers all of the above physical changes with a suitable reaction scheme. However, incorporating all of the basic physical phenomena would complicate the model mathematically and thus would be unsuitable for convenient practical prediction purposes. Hence, phenomenon/ parameters of real significance need to be identified and must be appropriately incorporated to give them an ideal level of sophistication and prediction accuracy. Wood being hygroscopic, it absorbs considerable moisture, especially during the rainy season. While the moisture generally ranges from 6 to 12% in sun-dried wood, it can be as high as 50% in the as-received wood. It is widely recognized that the moisture delays the onset of devolatilization and decreases the rate at which the thermal wave propagates inside the wood particle, leading to longer devolatilization times and thus causing a profound effect, as reported by the experiments of de Diego et al.5 Hence, drying becomes important and must essentially be incorporated in the model. According to Pyle and Zaror,6 the assumption of a homogeneous nature could be misleading as far as the behavior of natural materials such as wood is concerned and thus it is important to consider the anisotropy nature of wood in the model. Shrinkage and surface regression, on the one hand, decrease the resistance to thermal conduction within the particle and the volatiles release and, on the
other hand, reduce the surface area available for heat transfer. Woody biomass shrinks volumetrically by almost 50%.7 Therefore, this physical evolution during devolatilization must be included appropriately in the model calculations. The present work aims to develop a 3D devolatilization model in Cartesian coordinates for a wet anisotropic wood in a hot fluidized bed considering (i) the initial moisture content, (ii) shrinkage during drying and devolatilization, (iii) heat generation, (iv) variable properties, and (v) a suitable reaction scheme, comparing and validating the model predictions with the present experiments and those available in the literature. The present model is better than many existing models in that it is more realistic from the physics point of view because it incorporates all of the above-mentioned phenomena, and the results are reliable because the magnitude of shrinkage used in the model is obtained from the same experimental facility as was used to obtain the devolatilization time and char yield. Moreover, it addresses both the concerns of the physics involved and the level of sophistication by incorporating the important processes and neglecting the phenomena happening at the end of devolatilization, e.g., fragmentation. The 3D model developed here is further used to study the sensitivity of the properties/parameters that play an important role, thus leading to the inference on the required level of accuracy of these properties/parameters as inputs into the model. 2. Mathematical Model 2.1. Assumptions. A wet wood of cube/cuboidal shape subjected to hot atmospheric bubbling-fluidized-bed conditions is modeled. The model aims at predicting (i) the transient temperature distribution within the particle, (ii) the density of wood, char, and moisture with time and space, (iii) the devolatilization time, and (iv) the terminal char yield. The model formulation is based on the following assumptions: (i) The wood particle is a 3D wet, porous, anisotropic reacting medium with a well-defined shape (cube/ cuboid) and size, with the void volume initially filled with air and the surface free from cracking. (ii) The fluidizing medium in FBC is considered to be an inert gas not taking part in any reaction at the particle external surface. (iii) The reaction is modeled using a first-order Arrhenius equation, with the three first-order reactions representing the competing thermal degradation of wood into gas, char, and tar. A separate first-order reaction accounting for moisture loss during the drying process is also considered. (iv) The properties of the devolatilizing wood particle vary linearly between the wood and char properties based on the degree of conversion at that spatial location. (v) Convective and radiant heat transfer with a uniform heat transfer coefficient at the wood particle external surface, and heat transfer inside the particle by conduction and radiation. (vi) On the basis of work by Kumar and Kolar,7 the devolatilizing particle is assumed to shrink in both the longitudinal (10%) and transverse (20%) directions, retaining the initial shape of the wood as observed in the experiments conducted in FBC. Fragmentation
(3) Bonnefoy, F.; Gilot, P.; Prado, G. J. Anal. Appl. Pyrolysis 1993, 25, 387–394. (4) Yuen, R. K. K.; Yeoh, G. H.; de Vahl Davis, G.; Leonardi, E. Int. J. Heat Mass Transfer 2007, 50, 4371–4386. (5) de Diego, L. F.; Garcia-Labiano, F.; Abad, A.; Gayan, P.; Adanez, J. Energy Fuels 2003, 17, 285–90. (6) Pyle, D. L.; Zaror, C. A. Chem. Eng. Sci. 1984, 39, 147–158.
(7) Kumar, R. R.; Kolar, A. K. Biomass Bioenergy 2006, 30, 153–165.
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Figure 1. Physical model of a single wood particle devolatilizing in a hot fluidized bed.
mchar is set to 0 at time τ = 0 and 1 at τ = τd (end of pyrolysis). The governing equations and physical parameters used in the present model for wood, char, and moisture are given by eqs 1-16, as shown in Table 1. The reaction scheme considered is shown in Figure 2. As stated in the assumption, no secondary reactions have been considered. The reaction order is taken as 1. The reaction rate is expressed by eqs 6-8 for wood, char, and moisture, respectively. The reaction rate constant used in these expressions is given by the Arrhenius expression (eq 10). The energy changes with time in a single wood particle when exposed to the hot fluidized bed are expressed by the transient energy conservation equation in 3D Cartesian coordinates as given in eq 5. At any spatial location in the wood during devolatilization, the sum of the rate of thermal energy transferred by conduction within a unit volume and the rate of volumetric heat generation will be equal to the rate of storage of thermal energy within that unit volume. The term on the left-hand side of this equation represents the energy accumulation. The first and third terms on the right-hand side represent the heat conduction in the transverse direction (across the grain), and the second term represents the heat conduction in the longitudinal direction (along the grain). The last term represents the heat generation. The heat of reaction during the devolatilization process is considered negative. This means that the thermal energy is consumed because of endothermic reactions. It is worth noting here that the heat of reaction of these endothermic reactions is very small. The shrinkage factors fx and fz are along the transverse directions and fy is in the longitudinal direction. The shrinkage factor depends on the degree of conversion. The thermophysical properties of the devolatilizing wood are assigned an extent-of-reaction and porosity dependence. The effective thermal conductivity includes a radiant thermal conductivity, which accounts for conduction by radiation at higher temperatures. The radiant conductivity is given by eq 13 and the thermophysical data used in the model are given in Table 2.2,7-11
during the devolatilization process is not considered because it is found from the experiments that fragmentation is modest and occurring only at the fag end of the devolatilization process. Hence, fragmentation may not have a significant effect on the devolatilization time and char yield. (vii) The volatile gases and water escape out of the particle instantaneously as they are formed and hence do not undergo any recondensation and secondary reactions. 2.2. Definitions (i) The devolatilization time is defined in the model as the time taken for the density of wood to drop to 1% of its initial value.2 (ii) The char yield is defined as the ratio of the residual mass at the end of the devolatilization process, i.e., the fixed carbon and the mineral matter, to the initial mass of the dry wood particle. 2.3. Physical Model. Figure 1 illustrates a cube-shaped wood particle devolatilizing amidst the hot fluidized-bed environment and the zoomed view of the interaction of the flaming single wood particle with the surrounding environment. The interaction includes heat transfer to the particle surface by convection and radiation and transfer of gases to and from the particle surface and the reactions occurring at the surface, within the particle, and in the surrounding gas phase. 2.4. Mathematical Formulation. The mathematical model is based on general conservation equations for energy and mass. The solid-phase governing-equation set is given in Table 1. Using the model assumptions stated above, the solid-phase governing equation is derived based on the differential governing equations of mass and energy describing drying and pyrolysis within the wood matrix. The wet wood macroscopically consists of solid and moisture. Initially the solid is completely wood and at the end of the pyrolysis process, it is completely char. During pyrolysis, the wood converts in to char as the conversion progresses from the surface toward the center, and hence the solid constitutes char and yet-to-be-converted wood. The mass of solid in a small element inside the particle is defined by msolid ¼ mwood þ mchar
(8) Gr€ onli, M. G.; Melaaen, M. C. Energy Fuels 2000, 14, 791–800. (9) Lee, C. K.; Chaiken, R. F.; Singer, J. M. 16th International Symposium on Combustion; The Combustion Institute: Pittsburgh, 1976; pp 1459-1470.
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Table 1. Summary of Equations Used in the Present Model Mass Conservation Equations F~w ¼ ww Dτ
ð2Þ
F~c ¼ wc Dτ
ð3Þ
F~m ¼ wm Dτ
ð4Þ
conservation of wood
D
conservation of char
D
conservation of moisture
D
Energy Conservation Equations unsteady-state energy DT conservation ð~ Fw Cp, w þ F~c Cp, c þ F~m Cp, m Þ Dτ equation in three dimensions D DT D DT ¼ fx fy fz kx þ fx fy fz ky Dx Dx Dy Dy X 4 D DT kz þ þ fx fy fz ðK F~HÞi ð5Þ Dz Dz i¼1 ww ¼ - ðK2 þ K3 þ K4 Þ~ Fw
ð6Þ
wc ¼ K3 F~w
ð7Þ
rate of moisture loss
wm ¼ - K1 F~w
ð8Þ
heat release rate
K1 F~m H1 þ K2 F~w H2 þ K3 F~w H3 þ K4 F~w H4 ð9Þ
rate of consumption of wood
rate of generation of char
Figure 2. Reaction scheme for the wet wood devolatilization.
The kinetic data used in the base case of the model are taken from Gr€ onli and Melaaen8 and Chan et al.10 and are presented in Table 3 along with other kinetic data12-15 used in the sensitivity analysis (section 4.4). The preexponential factor for drying, as given by Chan et al.,10 has been modified as suggested by Bryden and Hagge16 in order to predict drying at around 100 °C. The heat-transfer coefficient used in this model constitutes the contribution of convection and radiation. The heat-transfer coefficient in the present 3D model ranges from 300 to 650 W m-2 K-1 for the particle shapes/sizes and bed temperatures studied. 2.5. Initial and Boundary Conditions. At τ = 0, T(x,y,z,τ) = T0. Fw ðx, y, z, τÞ ¼ Fw0 ; Fc ðx, y, z, τÞ ¼ 0;
reaction rate (Arrhenius equation)
Ki ¼ Ai expð - Ei =RTÞ
Fm ðx, y, z, τÞ ¼ Fm0
ð17Þ
The heat from the surrounding environment is transferred to the cubical wood surface by convection and radiation. The boundary conditions for the governing energy equation:
ð10Þ
At the planes of symmetry Physical Parameters Used in the Present Model property effective thermal conductivity
thermal conductivity (conduction)
at x ¼ 0,
DT ¼ 0 Dx
ð18Þ
at y ¼ 0,
DT ¼ 0 Dy
ð19Þ
at z ¼ 0,
DT ¼ 0 Dz
ð20Þ
empirical equation/value k ¼ kcond þ krad
kcond ¼ ηkw þ ð1 - ηÞkc
ð11Þ
ð12Þ
At the heated external surfaces thermal conductivity (radiation)
krad ¼
4εg σωdpor T 3 1 - εg
specific heat capacity
Cp, s ¼ ηCp, w þ ð1 - ηÞCp, c ð14Þ
diameter of the pore
dpor ¼ ηdpor, w þ ð1 - ηÞdpor, c ð15Þ
interpolation factor
η ¼ Fw =Fw0
At x = b/2 (for all y and z) DT ¼ hðTbed - Ts, x Þ kx Dx
ð13Þ
ð21Þ
(10) Chan, W. C. R.; Kelbon, M.; Krieger, B. B. Fuel 1985, 64, 1505– 1513. (11) Leckner, B. Heat and Mass Transfer. In Multiphase Flow Handbook; Crowe, C., Ed.; CRC Press: Boca Raton, FL, 2006; Chapter 5.2. (12) Thurner, F.; Mann, U. Ind. Eng. Chem. Process Des. Dev. 1981, 20, 482–488. (13) Di Blasi, C. Combust. Sci. Technol. 1993, 90, 315–340. (14) Font, R.; Marcilla, A.; Verdu, E.; Devesa, J. Ind. Eng. Chem. Res. 1990, 29, 1846–1855. (15) Font, R.; Marcilla, A.; Verd u, E.; Devesa, J. J. Anal. Appl. Pyrolysis 1991, 21, 249–264. (16) Bryden, K. M.; Hagge, M. J. Fuel 2003, 82, 1633–1644.
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Table 2. Thermophysical Data Used in the Present Model Properties Used for the (Base Case) Model Simulations property/parameters
units
values/expression
moisture content of wood dry wood particle density (initial) (Fw,dry) skeletal density biomass specific heat of wood (Cp,w) specific heat of char (Cp,c)
wt % kg m-3 kg m-3 kJ kg-1 K-1 kJ kg-1 K-1
specific heat of char (Cp,m) thermal conductivity of wood in the transverse direction x (kx,w) thermal conductivity of wood in the longitudinal direction y (ky,w) thermal conductivity of wood in the transverse direction z (kz,w) thermal conductivity of char in the transverse direction x (kx,c) thermal conductivity of char in the longitudinal direction y (ky,c) thermal conductivity of char in the transverse direction z (kz,c) pyrolysis kinetics porosity of wood (dpor,w) porosity of char (dpor,c) fluidized-bed heat-transfer coefficient shrinkage factors emissivity (ω) Stephan-Boltzmann constant (σ) universal gas constant (R) initial temperature
kJ kg-1 K-1 W m-1 K-1 W m-1 K-1 W m-1 K-1 W m-1 K-1 W m-1 K-1 W m-1 K-1
6 (measured) 500 (measured) 1400 (Sreekanth et al. [2]) 1.5 þ (1 10-3)T (Gronli and Melaaen. [8]) 0.42 þ (2.09 10-3)T þ 6.85 10-7T2 (Gronli and Melaaen. [8]) 4.182 (Sreekanth et al. [2]) 0.1 (Lee et al. [9]) 0.35 (Gronli and Melaaen. [8]) 0.1 (Lee et al. [9]) 0.05 (Sreekanth et al. [2]) 0.1 (Gronli and Melaaen. [8]) 0.05 (Sreekanth et al. [2]) Chan et al. [10] 5 10-5 (Gronli and Melaaen. [8]) 1 10-4 (Gronli and Melaaen. [8]) Leckner [11] Kumar at al. [7] 0.9 (Gronli and Melaaen. [8]) 5.67 10-8 (Sreekanth et al. [2]) 8.314 (Sreekanth et al. [2]) 300 (measured)
m m W m-2 K-1 W m-2 K-1 J gmol-1 K-1 K
around the reactor to maintain it at the desired temperatures (1023, 1123, and 1223 K). One “K”-type thermocouple, axially located at a height of 70 mm (approximately half of the bed height) from the distributor plate, recorded the bed temperature. Preheated air is supplied to the bed for fluidization, and its flow rate is measured using a calibrated orifice meter. The bed material is round silica sand of mean particle size 375 μm. The static bed height is 130 mm. The fluidization velocity maintained for all of the studies is 5Umf. 3.2. Fuel. The wood samples of cube shape were prepared by cutting the debarked, sun-dried C. equisetifolia wood trunk of mean diameter of 120-150 mm using a band saw. The proximate and ultimate analysis of the wood is given in Table 4. The choice of cube-shaped wood particles is to study the effect of the shape on the devolatilization time and char yield and to facilitate the development of an elegant mathematical modeling of the phenomenon. The cubes were made from the wooden logs such that “along the grain” and “across the grain fibers” lie nearly parallel to the sides of the cube, as shown in Figure 5. 3.3. Procedure. A single cube-shaped C. Equisetifolia wood particle was subjected to devolatilization studies under oxidizing conditions maintained at the desired bed temperature. Preheated air was used as the fluidizing medium. A single wood particle (free from visible surface defects) of known dimension, mass, and moisture content was introduced into the hot fluidized bed using a SS basket. The basket technique is the simplest and most realistic technique among the practical techniques in the open literature. The SS basket was 110 mm in diameter and 200 mm height with an effective mesh opening size of 0.9 mm, allowing the free movement of the bed particles into and out of the basket. The particle was allowed to devolatilize at the specified fluidized-bed conditions, and the same was retrieved from the fluidized bed at several predetermined residence times during devolatilization. As the fuel particle started devolatilization, it was surrounded by a flame of burning volatiles. The reflection of the burning particle was observed in a polished SS mirror located above the hot fluidized-bed vessel. The end of devolatilization was inferred from the flame extinction, an indication of the end of release and burning of all volatiles, a technique known as flame extinction time. The devolatilizing/just devolatilized particles retrieved from the bed were quenched using fine sand at room temperature to stop the devolatilization process abruptly. The time for retrieval and quenching summed to 3 s, which was short compared with the total devolatilization time, and there was not any significant reaction happening before it
At y = a/2 (for all x and z) ky
DT ¼ hðTbed - Ts, y Þ Dy
At z = c/2 (for all x and y) DT ¼ hðTbed - Ts, z Þ kz Dz
ð22Þ
ð23Þ
The heat-transfer coefficient is calculated using Palchanok’s correlation,11 which takes into account the reduction due to floating of the wood particle on the surface of the bed. However, it must be noted that the heat-transfer coefficient given by this correlation does not take into account the fact that the different faces of the cube see different thermal profiles for occasional discrete short durations as the wood particle surfaces on the bed. Here, the heattransfer coefficient constitutes both convective and radiative components.
2.6. Numerical Solution Details. The conservation equations are discretized using a control volume technique. The discretized equations are solved numerically using an explicit finite-differencing scheme. Taking advantage of the cubical shape, only one-eighth of the cube is considered as the computational domain. Figure 3 presents (a) the computational domain with reference to the actual dimension of the wood particle with the grain orientations and (b) the structured grid pattern. On the basis of the grid independency study, the initial dimension of each discretized volume is fixed at 0.25 mm 0.25 mm 0.25 mm. As the wood starts to convert, a new shrunken volume is calculated at every time step and all locations are based on the corresponding extent of conversion. The time step of 0.001 s is used for the computation. 3. Experimental Program To validate the present model, experiments are conducted in a laboratory-scale, hot atmospheric fluidized bed using Casuarina equisetifolia wood. 3.1. Hot Atmospheric Fluidized-Bed Setup. The devolatilization experiments are conducted in a laboratory-scale, hot bubbling fluidized bed, of 130 mm inner diameter and 600 mm height, as shown in Figure 4. The stainless steel (SS) fluidizedbed vessel is electrically heated by silicon carbide rods placed 4824
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E (kJ mol-1)
121.3 106.5 61 73.1
A (s )
1.1 107 7.38 105 2.91 102 2.98 103
150a 420b 420b 420b
Sudhakar and Kolar
H (kJ kg )
150a 420b 420b 420b
E (kJ mol )
133.1 112.7 148 119
A (s )
2.0 108 4.13 106 8.23 108 5.85 106
H (kJ kg )
150a 420b 420b 420b 140.3 88.6 156 139.2
Figure 3. (a) Computational domain of one-eighth of the full cube wood particle (highlighted ABCD-EFGH) used in 3D model. (b) Computational domain showing the structured grid.
-1
E (kJ mol )
-1
iv
H (kJ kg-1)
Energy Fuels 2010, 24, 4820–4832
4. Results and Discussion 4.1. Present Experimental Results. 4.1.1. Devolatilization Time (τd). Figure 6 presents the devolatilization time of the cube-shaped particles obtained from experiments at various bed temperatures of 1023, 1123, and 1223 K as a function of the mass equivalent dimension of the cube-shaped wood particle. The mass equivalent dimension for the cube is expressed as 1=3 m ð24Þ deq ¼ F
1.3 108 1.44 104 6.8 108 1.52 107
where m is the mass of the cube and F is the initial density of the wood particle. As expected, the devolatilization time increases with an increase in the initial wood particle size and decreases with an increase in the bed temperature. For an increase in the particle size from 10 to 25 mm, the devolatilization time increased by about 4.5 times at all bed temperatures studied. The increase in the devolatilization time with the size is due to the longer resistance path to the movement of the volatiles generated within the particle towards the surface. The devolatilization time rose roughly by 31% and 47% with a decrease in the bed temperature from 1223 to 1023 K, for an initial particle size of 10 and 25 mm, respectively. The decrease in the devolatilization time with a rise in the temperature may be due to one or a combination of the following: (i) an increase in the reaction rate at higher temperatures, (ii) an increase in the rate of propagation of the thermal wave from the periphery toward the particle center, and (iii) the development of a large number of cracks due to thermal shock at higher bed temperatures and increased volatile pressure caused by the increased rate of volatiles generated. The increase of the devolatilization time with the initial particle size follows a linear trend until the initial particle size of 20 mm, beyond which there is a sudden increase for the 25 mm particle. The slope of the linear trend decreases with a rise in the bed temperature; i.e., the increase in the devolatilization time per unit increase in the particle size is more at lower temperatures than at higher temperatures. The influence of the bed temperature on the devolatilization time is predominant in the larger particle size than in the smaller one. Also the dispersion in the devolatilization time measurements increases with an increase in the particle size.
E (kJ mol )
88 88 88 88 5.13 1010 5.13 1010 5.13 1010 5.13 1010
Reference 8. b Reference 13.
lodgepole pine oak saw dust almond shells,FBC almond shells, non-FBC Chan et al.10 Thurner and Mann12 Font et al.14 Font et al15
a
biomass ref
-1
i
-1
A (s )
2244 2440 2440 2440
-1
H (kJ kg )
-1
A (s )
ii
-1
-1
-1
reaction number (Figure 2)
Table 3. Kinetic Constants Used in the Present Model
iii
-1
was quenched. The experiment was repeated at least 20 times for the devolatilization time and five times for the char yield. The quenched chars were weighed and preserved in labeled airtight pouches for further analysis.
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Figure 4. Schematic diagram of the hot bubbling-fluidized-bed setup. Table 4. Proximate and Ultimate Analysis of C. equisetifolia content
quantity (%) Proximate Analysis
moisture volatiles fixed carbon ash
6.5 82.6 10.5 0.4 Ultimate Analysis
carbon hydrogen nitrogen oxygen
42.5 6.1 0.16 51.24
Figure 6. Experimentally obtained devolatilization time for cubeshaped wood particles at bed temperatures of 1023, 1123, and 1223 K.
given by the proximate analysis in Table 4, i.e., about 12% on a dry basis. 4.2. Comparison of the Present 3D Model Predictions with the Present Experiments (Cube). It is to be noted that the present 3D model is based on an inert fluidizing medium, whereas the experiments were conducted in air. It is a matter of interest to know if there is an overlap between the devolatilization and char combustion processes. In this context, a standard thermogravimetric analysis experiment was conducted on the candidate wood, and it was found that the devolatilization and char combustion processes were in sequence. This finding is also supported by experiments conducted by de Diego et al.17 in a hot fluidized bed under conditions very similar to those of the present study. Thus, comparison of the present model predictions with our experimental data is quite reasonable. 4.2.1. Devolatilization Time. The devolatilization time predicted by the present 3D model using the properties given in Table 2 is compared with the values obtained from the present experiments for cube-shaped particles of size 10-25 mm at bed temperatures of 1023, 1123, and 1223 K in Figures 8-10. It is found and is presented in Figure 11 that
Figure 5. Preparation of a wood sample showing the grain fiber orientation with reference to the computational domain.
This may be attributed to the increased differences in the wood samples as the particle size increases. 4.1.2. Char Yield. Figure 7 presents the char yield measurements of cube-shaped wood particles at bed temperatures of 1023, 1123, and 1223 K, respectively. Unlike in the devolatilization time of the particles, the char yield follows no specific trend with either the particle size or bed temperature. This lack of variation with smaller bands of dispersion may be due to one or a combination of (i) the difference in the wood samples, especially density, (ii) the entry of fine bed sand particles into the char through cracks, and (iii) the possibility of loss of char fines through the basket. For the particle sizes at the bed temperatures studied, it is found that the char yield lies between 8 and 15%. This roughly corresponds to the sum of the fixed carbon and ash content
(17) de Diego, L. F.; Garcia-Labiano, F.; Abad, A; Gayan, P.; Adanez, J. J. Anal. Appl. Pyrolysis 2002, 65, 173–84.
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Figure 7. Experimentally obtained char yield for cube-shaped wood particles at bed temperatures of 1023, 1123, and 1223 K.
Figure 10. Comparison of the 3D model predictions with the measured devolatilization time for cube-shaped wood particles at a bed temperature of 1223 K.
Figure 8. Comparison of the 3D model predictions with the measured devolatilization time for cube-shaped wood particles at a bed temperature of 1023 K.
Figure 11. Parity plot of the measured (average) and predicted (3D model) devolatilization times of cube-shaped wood particles at bed temperatures of 1023, 1123, and 1223 K.
of 1023, 1123, and 1223 K. The char yield is computed as the ratio of the mass of the char at the end of devolatilization to the initial mass of wood. The deviation of the 3D model predictions from the experimental char yield for all the particle sizes and bed temperatures shows a reasonably good agreement, with the model under/overpredicting the measured mean char yield by (2-11%, as given in Table 5. 4.3. Comparison of the Present Model with Experimental Data from the Literature (Cubes and Cuboids). 4.3.1. Cubes. The 3D model predictions of the devolatilization time and char yield are compared with the data available in the literature for a bubbling fluidized bed.5 The present model is implemented for the particle size, properties, and experimental conditions (bed temperature and moisture) of de Diego et al.,5 as given in Table 6. Figure 13 presents the parity chart (τd/τd0) between de Diego et al.’s experimental data for pine wood (Pinus sylvestris) and the present 3D model predictions for a cube of dimensions 10 10 10 and 15 15 15 mm at bed temperatures of 923 and 1123 K and initial moisture contents of 0, 8, 16, 22, 29, and 47%. It is found that the present 3D model deviates by -13% (except for two points deviating by -16%) from de Diego et al.’s measured devolatilization time. Also, it is found that the agreement is good at lower moisture and sizes and the
Figure 9. Comparison of the 3D model predictions with the measured devolatilization time for cube-shaped wood particles at a bed temperature of 1123 K.
the 3D model predictions at various bed temperatures deviate from the experimental devolatilization time by less than (10%. 4.2.2. Char Yield. Figure 12 compares the char yield predictions of the present 3D model with the measured values from the present experiments at various bed temperatures 4827
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Figure 13. Parity plot of the measured (de Diego et al.5) and predicted (3D model) devolatilization times of cube-shaped wood particles at bed temperatures of 923 and 1123 K.
Figure 12. Comparison of the present 3D model predictions of the char yield with those measured for cube-shaped wood particles at bed temperatures of 1023, 1123, and 1223 K. Table 5. Comparison of the Present 3D Model Predictions of the Char Yield at Bed Temperatures of 1023, 1123, and 1223 K Comparison of the Present 3D Model Predictions of the Char Yield at 1023 K standard no.
size (mm)
experiments
3D model
3D % deviation
1 2 3 4
10 15 20 25
0.10 0.098 0.120 0.140
0.104 0.116 0.123 0.130
-3.30 -18.37 -2.43 þ7.19
Comparison of the Present 3D Model Predictions of the Char Yield at 1123 K standard no.
size (mm)
experiments
3D model
3D % deviation
1 2 3 4
10 15 20 25
0.107 0.107 0.110 0.113
0.101 0.112 0.119 0.125
þ5.35 -4.49 -8.16 -10.69
Figure 14. Comparison of the present 3D model predictions of the devolatilization time with the measured data of de Diego et al.5 for a cuboid-shaped wood particle of 10 16 15 mm at bed temperatures of 923, 1023, 1123, and 1223 K.
Comparison of the Present 3D Model Predictions of the Char Yield at 1223 K standard no.
size (mm)
experiments
3D model
3D % deviation
1 2 3 4
10 15 20 25
0.106 0.113 0.122 0.138
0.098 0.109 0.116 0.122
þ7.74 þ3.98 þ5.31 þ11.56
time by the model may be attributed to the choice of the reaction scheme and kinetic parameters. The inclusion of secondary reactions of tarry volatiles with the present kinetic scheme would improve the model predictions further. Moreover, the kinetic parameters used in the present model are from Chan et al.10 and may not be very appropriate for the case of pine wood used in predicting the measured devolatilization time of de Diego et al.5 4.3.2. Cuboids. The boundary conditions during devolatilization of cuboid wood can be precisely represented only by the 3D model. Hence, the present 3D model is used to predict the devolatilization time of a 10 16 15 mm cuboid particle at different bed temperatures (923, 1023, 1123, and 1223 K, respectively) and initial moisture contenta of 8, 16, 22, 30, and 47%, and the results are presented in Figure 14. The values of the properties used in the model are given in Table 6. It is observed that while the model captures the qualitative trend of the experimental data5 reasonably well, there is a quantitative maximum deviation of 0 to þ11% (overprediction), -3% to þ4%, þ5% to -9%, and -4% to -12% (underprediction) at 923, 1023, 1123, and 1223 K, respectively. The model overpredicts at low temperature and underpredicts at higher temperatures, with the deviation being moderate at either direction in between. This may be
Table 6. Values of Parameters Used in the Present Model To Predict the Experimentally Determined Devolatilization Time and Char Yield Available in the Literature de Diego et al.5 wood used density (kg m-3) % moisture kx,w (W m-1 K-1) Ky,w (W m-1 K-1) kz,w (W m-1 K-1) Kx,c (W m-1 K-1) Ky,c (W m-1 K-1) kz,c (W m-1 K-1) sand size (μm)
pine wood 520 0, 8, 16, 22, 29, 30, and 47 0.14 0.25 0.14 0.11 0.15 0.11 375
deviation increases with an increase in the moisture content and size. This consistent underprediction of the devolatilization 4828
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Figure 15. Influence of the initial density of the cube-shaped wood particle on the devolatilization time at a bed temperature of 1123 K.
Figure 16. Influence of the initial thermal conductivity of the cubeshaped wood particle on the devolatilization time at a bed temperature of 1123 K.
due to the use of a representative density in the model calculations that may differ slightly from sample to sample used in the experiments. In summary, with the wide range of assumptions involved in the model, the predictions of the present 3D model compare well with the experimental data on the devolatilization time available in the open literature for cubes and cuboids. 4.4. Sensitivity Analysis. The present 3D model has been used to identify the most important parameters that cause significant variation in the devolatilization time and char yield and to clarify the relative role of other parameters in the prediction of the model. This study is important because there are different values for a parameter/property available in the literature, with varying degrees of uncertainties that form the input for this model and requiring due care in the selection of the right one if it is found to affect the model predictions considerably. Hence, sensitivity analysis on the devolatilization time and char yield has been carried out with respect to the initial density, initial thermal conductivity, initial specific heat, reaction kinetics (Chan et al.,10 Thurner and Mann,12 Di Blasi,13 and Font et al.,14,15), and the heattransfer coefficient. Parameters were varied by (20% with reference to a base case, except for the heat-transfer coefficient, which took values from 100 to 600 W m-2 K-1. The initial density, thermal conductivity, and specific heat of the wood particle affects the mass loss rate by controlling the rate of propagation of the thermal wave and thus the reaction rate as defined by the thermal diffusivity. However, here the effect of the individual parameters on the devolatilization time and char yield is studied to give it a straightforward interpretation. 4.4.1. Devolatilization Time. The sensitivity of the devolatilization time to the initial density and the thermal conductivity are presented for various particle sizes at a bed temperature of 1123 K in Figures 15 and 16, respectively. The figure compares the effect with the base case simulated at the conditions specified in Table 2. Among the parameters that constitute the thermal diffusivity, the initial density of wood has the strongest influence on the devolatilization time, followed by the thermal conductivity and almost no effect with respect to the specific heat. A (20% change in the initial density and thermal conductivity causes about (2528% and (5-9% changes in the devolatilization time, respectively. It is interesting to note that the effects of all of
Figure 17. Influence of the bed to wood particle heat-transfer coefficient on the devolatilization time of cube-shaped wood particles at a bed temperature of 1123 K.
these parameters are more pronounced in the larger particles. This may be because of the dominance of the heattransfer control over the chemical kinetics with increasing particle size. From this, it is understood that the uncertainties introduced by the use of a mean value of the wood particle density varying from 400 to 1000 kg m-3 may be substantial, and hence it is concluded that consideration of the density rather than the thermal conductivity and specific heat closer to the actual values for a simulation determines the accuracy of the model, especially for larger particle sizes. The heat-transfer coefficient at the surface plays an important role in determining the onset of the devolatilization process and the rate of the reaction within the particle through the thermal wave propagation. Figure 17 presents the effect of the heat-transfer coefficient on the devolatilization time. It can be observed that the improvement in the heat-transfer coefficient from 100 to 300 W m-2 K-1 has a stronger influence on the range of 16% for a 25 mm particle and 40% for a 10 mm particle. Increasing further from 300 to 500 W m-2 K-1 has a mild influence on 4-8%, and beyond 500 W m-2 K-1, there is almost a negligible effect. This may be ascribed to the increase in the conduction resistance due to the rapid buildup of a char layer, which almost acts as an insulator at a higher range of the heat-transfer coefficients, 4829
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Figure 18. Effect of considering various kinetic schemes available in the literature on the devolatilization time of cube-shaped wood particles at a bed temperature of 1123 K.
Figure 19. Influence of the initial density of the cube-shaped wood particle on the char yield at a bed temperature of 1123 K.
thus effecting very little change in the devolatilization time as the heat-transfer coefficient is increased beyond 500 W m-2 K-1. In the present model, for all particle sizes and bed temperatures studied, the heat transfer coefficient given by the Palchanok’s correlation ranges from 300 to 655 W m-2 K-1, thus indicating a noticeable influence on larger particles and little influence on smaller particles. The sensitivity of the devolatilization time for four different kinetic schemes available in the literature is given in Figure 18. In the present study, the kinetic constants proposed by Chan et al.,10 Thurner and Mann,12 and Font et al.14,15 are considered. Chan et al.10 predicts the lowest devolatilization times for all of the particle sizes studied, despite the activation energy being the highest for all of the reactions. This may be because of the strong compensation offered by the preexponential factor, which is higher in the case of Chan et al. than in the cases of refs 12, 14, and 15. This offsets the reduction in the rate due to the higher activation energy. However, it is stated here that more studies on the rate of heating are needed to bring out a decisive cause and effect of the contribution of the individual kinetic constants on the devolatilization time. The Chan et al.10 kinetic scheme is used in the base case, and it is compared with other schemes given in Table 3. Although no absolute decisive inference on the influence of the kinetic parameters can be brought out from this, it is ascertained that a maximum variation of 41% (10 mm) to 47% (25 mm) in the devolatilization time is observed by using the various kinetic constants in the model at a bed temperature of 1123 K. It is interesting to note that the effect of the kinetic constants on the devolatilization time is more pronounced in larger particles compared to the smaller ones. However, it is worth noting that this effect of the kinetic constants on the devolatilization time is not due to the reaction enthalpies because their effect on the devolatilization time is found to be very negligible. It is found that, for a reduction of 20% in the reaction enthalpies, the devolatilization time decreased only by 1.9%. From the above observations, it is concluded that a careful selection of the right kinetic constants is crucial for the successful prediction of the model, especially in the case of larger wood particle sizes. 4.4.2. Char Yield. Figures 19 and 20 give the influence of the initial density and thermal conductivity on the char yield for various particle sizes at a bed temperature of 1123 K. It is
Figure 20. Influence of the initial thermal conductivity of the cubeshaped wood particle on the char yield at a bed temperature of 1123 K.
found from the study that the transport properties have a negligible influence on the char yield. For a (20% change in the initial density used in the base case, the change in the char yield was less than (2%. The thermal conductivity and specific heat also had a very negligible effect of less than a (1% change in the char yield for a change of (20%. The heat-transfer coefficient had a mild influence on the char yield, as observed from Figure 21. For a change of the heat-transfer coefficient from 100 to 300 W m-2 K-1, there was about a 6% decrease in the char yield, indicating that the increase in the rate of heat transfer into the particle marginally reduces the char yield. The effect of the various kinetic schemes available in the literature on the char yield is observed from Figure 22 to be considerable. A maximum variation of 16% (10 mm) to 85% (25 mm) in the char yield is observed in using the various kinetic schemes in the model at a bed temperature of 1123 K. However, it is worth noting that this effect of the kinetic constants on the char yield is not due to the reaction enthalpies because their effect on the char yield is very negligible. It is found that, for a reduction of 20% in the reaction enthalpies, the char yield decreased only by 0.2%. Hence, adopting a suitable reaction kinetic scheme is important for the right prediction of the char yield. 4.4.3. Mass Loss with Time during Devolatilization. Figure 23 presents the mass fraction (instantaneous mass/initial 4830
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Figure 21. Influence of the bed to wood particle heat-transfer coefficient on the char yield of cube-shaped wood particles at a bed temperature of 1123 K. Figure 23. Typical mass of the solid residue at different times during devolatilization of a 10 mm wood particle at a bed temperature of 1123 K using different kinetic models.
Font et al.14 predicts a higher mass loss rate beyond the first quarter of devolatilization, resulting in a lower char yield at the end of devolatilization. On the other hand, Thurner and Mann12 and Font et al.15 predicted a lower mass loss in the last quarter of the devolatilization time, resulting in a higher char yield compared to the base case of Chan et al.10 5. Conclusions 1 The 3D model presented here, the only one of its kind under fluidized-bed conditions, predicts the devolatilization time and char yield for cube-shaped wood particles within deviations of 10% and 11%, respectively, compared to the present experimental data. Moreover, the model successfully predicts the devolatilization time and char yield for cuboid wood particles of various initial moisture contents (0-49%) and bed temperatures (923-1223 K) with a deviation mostly below 13% compared to the experimental data reported in the literature. Further, this is the only 3D model to take into consideration fuel shrinkage during drying and devolatilization. 2 The measured devolatilization time for the cube-shaped wood particles is found to be a strong function of the initial size and bed temperature, while the char yield is almost independent of the initial size and bed temperature, mostly falling in the range of 9-13%. 3 The 3D model predictions show that the devolatilization time and char yield are sensitive to the wood properties. The devolatilization time is found to be most sensitive to the initial density (about (25% for a (20% change in the density) of the wood particle, followed by the thermal conductivity and specific heat. Hence, the values of the above parameters as inputs to the model must be accurate and as realistic as possible. Also, the bed to the fuel-particle heat-transfer coefficient shows a strong influence on the devolatilization time, which reduces to about 33-62% (25-10 mm) for an increase in the heat-transfer coefficient from 100 to 500 W m-2 K-1. 4 The char yield predictions of the 3D model are found to be marginally sensitive to the wood properties. However, a change in the heat-transfer coefficient from
Figure 22. Effect of considering various kinetic schemes available in the literature on the char yield of cube-shaped wood particles at a bed temperature of 1123 K.
mass) of wood as a function of the nondimensional conversion time (instantaneous time/devolatilization time) for a 10 mm wood particle at a bed temperature of 1123 K using different kinetic models. For all of the kinetic models, typically, mass loss is observed to happen in three stages: (i) a rapid or steep mass loss during the first quarter of the devolatilization time, (ii) a gradual mass loss during the second and third quarters of the devolatilization time, and (iii) a slow mass loss during the final quarter of the devolatilization time. In the first stage, the virgin wood surface is exposed to the hot bed, leading to the rapid generation and release of volatiles. In the second stage, as time progresses, because of the considerable growth of the char layer, resistance to heat transfer increases, resulting in the gradual decrease in the mass loss. During the final stage, much of the wood has been converted into char and thus the mass loss rate is very slow. The following can be observed from the figure: while the mass loss is nearly the same for all of the kinetic models in the first stage of mass loss, it is different in the second and third stages of mass loss; i.e., the kinetic models differ in the prediction of the rate of loss of relatively higher molecular weight volatiles compared to moisture and volatiles released during the early stages of devolatilization. When compared to the base case of Chan et al.,10 the case of 4831
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100 to 500 W m K decreased the char yield by 6.5-7.5%. Beyond 500 W m-2 K-1, the heat-transfer coefficient showed almost no influence on both the devolatilization time and char yield. 5 The kinetic parameters used as inputs to the 3D model are the most significantly influencing parameters for the prediction of both the devolatilization time and char yield. The use of various kinetic parameters available in the literature varied the prediction of the devolatilization time by 47% (maximum) and the char yield by 85% (maximum). Hence, the kinetic constant inputs to the model must be as accurate as possible.
s = shrinkage T = temperature (K) · w = rate of generation/loss (kg m-3 s-1) x = dimension in the transverse direction x y = dimension in the longitudinal direction y z = dimension in the transverse direction z Greek Symbols ε = fuel porosity j = property η = interpolation factor F = density (kg m-3) ~ = uncorrected density (kg m-3) = Ffx fy fz F σ = Stephan-Boltzmann constant, 5.670 10-8 W m-2 K-4 τ = time (s) ω = emissivity
Nomenclature A = preexponential factor (s-1) a, b, c = sides of cube/cuboid (m) Cp = specific heat (J kg-1 K-1) E = activation energy (J mol-1) f = shrinkage factor H = heat of reaction (J kg-1) h = heat-transfer coefficient (W m-2 K-1) K = reaction rate (s-1) k = thermal conductivity (W m-1 K-1) l = length (m) R = universal gas constant (8.314 J K-1 mol-1)
Subscripts 0 = initial eq = equivalent c = char cond = conduction i = number of the reaction m = moisture w = wood d = devolatilzation
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