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Ind. Eng. Chem. Res. 2009, 48, 4796–4809
Wood Fast Pyrolysis: Comparison of Lagrangian and Eulerian Modeling Approaches with Experimental Measurements Olivier Authier,*,† Monique Ferrer,† Guillain Mauviel,† Az-Eddine Khalfi,‡ and Jacques Le´de´† LSGC, ENSIC, CNRS-Nancy UniVersite´, 1 rue GrandVille, BP 20451, 54001 Nancy cedex, France, and Fluid Mechanics, Energy and EnVironment Department, EDF R&D Chatou, 6 quai Watier, BP 49, 78401 Chatou cedex, France
The aim of the present paper is to validate Lagrangian and Eulerian modeling approaches of biomass fast pyrolysis from comparison with experimental measurements. Wood samples are submitted during measured times to a controlled and concentrated radiation delivered by an image furnace. The heat flux densities are close to those encountered when wood is surrounded by hot bed particles in a dual fluidized bed (DFB) gasifier. In the image furnace, the sample is placed inside a transparent quartz reactor fed by a cold carrier gas. The volatile matter (condensable vapors and gases) released by the solid is quenched inside the reactor. It is hence possible to selectively study primary pyrolysis phenomena occurring at the solid level. All the pyrolysis products (char, vapors, and gases) are recovered, and their masses are measured as a function of the flash time allowing the assessment of mass balances. The yield of vapors does not significantly depend on the available heat flux density, unlike the gases and char yields. The experimental results are compared to data derived from two different modeling approaches. Their basic assumptions are discussed from characteristic time values which reveal the controlling phenomena. Mass transfer limitations are neglected in comparison with heat transfer and chemical phenomena. The first type of pyrolysis model relies on an original Lagrangian approach where mathematical equations of heat and mass balances are written with the assumptions that wood and char form two distinct layers. In the second one, a classical Eulerian approach is considered: equations are directly written at the whole particle level. The results of the two models as well as the experimental data (sample mass losses and product yields) are in quite good agreement. 1. Introduction Among the possible biomass conversion technologies, gasification represents an interesting and cost-effective route where biomass is transformed into a syngas at high temperatures in the presence of an oxidizing agent. The gasifiers may be divided into three main groups: entrained flow, fluidized bed (bubbling/ circulating), and fixed bed.1 A high-quality gas can be produced by using a dual fluidized bed (DFB) system with steam as the gasification agent.2,3 The process (Figure 1) includes two reactors in series with circulation of the hot fluidizing particles (catalysts): a gasification reactor (gasifier) inside which virgin biomass is fed, and a combustion reactor (riser). Combustion of residual char and of additional fuels inside the riser provides the energy required for the endothermic reactions occurring in the gasifier.4 A good understanding of the chemical and physical phenomena involved in the biomass degradation inside the gasifier is required for the development, optimization, and scale-up of the process. Typically, biomass samples enter the fluidized bed inside which they undergo heating and physicochemical transformations which depend on the intensity of heat transfer efficiencies (hot particle collisions, convection, and radiation). After drying,5 the biomass temperature increase induces pyrolysis with char formation (carbon-rich residue) and release of volatile matter, resulting in up to 80% biomass weight loss.6 Volatile matter is composed of gases (low molecular mass products: H2, CO, CO2, C1-C3) and vapors (products that are * To whom correspondence should be addressed. Tel.: +33 (0)3 83 17 52 82. Fax: +33 (0)3 83 32 29 75. E-mail:
[email protected]. † CNRS-Nancy Universite´. ‡ EDF R&D Chatou.
liquids at room temperature). The structure and composition of the char, which undergoes subsequent gasification reactions, depend on biomass properties and process operating conditions. At the same time, primary volatile products undergo secondary cracking/reforming reactions. Their release may also cause the fragmentation of the pyrolyzing biomass particles because of inner pressure increase during pyrolysis.7 In addition, particle attrition due to the mechanical influence of bed particles may occur, resulting in the separation of small char fragments.8 Analysis of all these phenomena is made complicated by the fact that they all occur simultaneously inside the reactor. It is then difficult to study them separately. Unfortunately, mathematical modeling for reliable scale-up of the gasifier requires the knowledge of all these involved steps. That is why the main involved elementary phenomena such as chemical reactions and transfer phenomena should be decoupled and studied independently of each other. There are few available models in the literature taking into account drying, pyrolysis, gasification, and homogeneous and heterogeneous reactions in competition with heat and mass transfers inside a biomass fluidized bed gasifier.9,10 In several cases,thepyrolysisprocessisalsoassumedtobeinstantaneous9,11-13
Figure 1. Schematic representation of a dual fluidized bed process.2
10.1021/ie801854c CCC: $40.75 2009 American Chemical Society Published on Web 04/14/2009
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Figure 2. Image furnace: qualitative scheme of the experimental setup used for studying the primary steps of biomass fast pyrolysis. Table 1. Sample Ultimate Analysis (wt %)a sample
C (wt %)
H (wt %)
O (wt %)
Ash (wt %)
oak char (φ1) char (φ2)
49.1 90.2 82.6
5.8 1.7 2.5
44.2 3.7 11.1
0.3 0.4 1.7
a The values given for char are obtained after total wood conversion and for two values of the available heat flux density (φ1 ) 0.8 MW · m-2, φ2 ) 0.3 MW · m-2). Values are known with absolute accuracies close to (0.5%.
as soon as the biomass particles enter the bed, i.e., before mixing with bed material. However, the validity of such an assumption depends on the particle size and is only valid for thin particles.14 Under high heat transfer efficiency conditions, the pyrolysis time cannot be neglected for particles a few millimeters in size, resulting in internal temperature gradients.15-17 Moreover, kinetics of fast primary pyrolysis should be determined, so far as possible, under thermal conditions similar to those encountered in a fluidized bed. Unfortunately only a few reliable works made under such conditions have been published. For example, the models are often written on the basis of experiments performed in thermogravimetric devices18,19 which are not representative of fast pyrolysis. The aim of the present paper is to validate Lagrangian and Eulerian modeling approaches of biomass fast pyrolysis under thermal conditions close to those prevailing in a DFB. For that purpose, experiments are performed with an image furnace delivering a concentrated radiation under clean conditions of heat flux densities which can be controlled inside large domains.16,20 Experimental data (rate of sample mass loss; gases, vapors, and char masses as a function of the flash time) are then compared to the results of the models. Two approaches (i.e., Lagrangian and Eulerian) are considered for pyrolysis modeling of a biomass particle. The Lagrangian reference considers a wood/char interface moving through space and time inside the particle, whereas the Eulerian reference considers changes as they occur at a fixed point. In the Eulerian approach, classical with regard to other pyrolysis models from the literature, equations are directly written on the whole particle. In the original Lagrangian approach representative of experimental observations of the present work, mass and heat balances are written in the assumptions that wood and char form two distinct layers. These models, written on the basis of the controlling phenomena determined from the calculation of characteristic times, are hence representative of biomass fast pyrolysis under specific conditions.
Table 2. Typical Examples of Mass Balances and Gas Compositions for Two Values of the Available Heat Flux Density (φ1 ) 0.8 MW · m-2, φ2 ) 0.3 MW · m-2)a flux
flash time (s)
φ1
3.33
φ2
13.25
flux
φ1 φ2 a
mass and mass and mass and mass mass yield (wt %) yield (wt %) yield (wt %) balance loss of gases of vapors of char (wt %) 12.9 25 7.1 12
29.3 57 36.1 61
6.0 12 11.8 20
45.1
94
47.6
93
flash time (s)
molar fractions (in %) of gas species (excluding N2) H2
CO
CO2
CH4
C2H6
C2H4
C2H2
C3H8
3.33 13.25
17.3 6.0
52.6 57.5
13.4 18.3
9.0 12.0
0.6 0.7
5.4 4.4
1.0 0.3
0.7 0.8
All masses are in 10-6 kg.
2. Experimental Section 2.1. Heat Transfer in Fast Pyrolysis. The literature often reports experimental data related to pyrolysis performed as a function of a reference temperature and/or heating rate. Unfortunately, these parameters are difficult to define. They can correspond to those of the heat source or of the sensor, and not necessarily to those of biomass itself.20 That is why available heat flux density at the particle level has been suggested as a more reliable criterion to characterize the pyrolysis thermal operating conditions.21 In a fluidized bed, heat is transferred to biomass by three possible mechanisms: gas convection, radiation, and contact with the material bed particles. The heat transfer coefficients depend on a great number of physical properties (particles and gas) and of reactor characteristics. They may vary along the bed height. Nevertheless, global heat transfer coefficients in a fluidized bed commonly range from 200 to 800 W · m-2 · K-1.22-24 Moreover, due to efficient mixing and intensive heat transfer between particles, the material temperature can be considered as practically uniform in the whole fluidized bed volume. Assuming a material bed temperature of about 1120 K,4 the available heat flux density at the biomass particle surface during pyrolysis can be considered as ranging from about 0.2 to 0.8 MW · m-2. 2.2. Image Furnace: Source of Controlled Heat Flux Density. Experiments are performed in an image furnace (Figure 2) already used to study the elementary processes of biomass fast pyrolysis.6,16,20,21,25-30 The principle of the image furnace has been already described in details in the works of Boutin et
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Figure 3. Variations of mass losses, and gases, vapors, and char masses as a function of the flash time for two values of the available heat flux density (φ1 ) 0.8 MW · m-2, φ2 ) 0.3 MW · m-2).
Figure 4. Molar fractions (in %) of pyrolysis gases (a, CO, CO2, H2; b, hydrocarbons) as a function of the flash time for two values of the available heat flux density (φ1 ) 0.8 MW · m-2, φ2 ) 0.3 MW · m-2).
al.20,25,26 Hence, the experimental setup and procedure are only briefly described. Wood samples are submitted to the flux of a controlled and concentrated radiation chosen in order to be representative of fast pyrolysis. The radiation is delivered by a 5 kW high pressure xenon arc lamp (Osram XBO 5000 W/H CL OFR) placed at the first focus (F1) of a first elliptical mirror. In its original configuration,21,25,26 the sample was placed at the first focus (F2) of a second elliptical mirror; both mirrors have the same second focus (F3). In the present study, the sample is simply placed at the focus F3. The available heat flux densities can be varied and controlled by using specific metallic grids intercepting the radiation issued from the first mirror. It is measured through
the use of a specific device relying on temperature measurements.25 The experimental results reported in this study have been obtained under two values of flux densities: 0.8 MW · m-2 (φ1) and 0.3 MW · m-2 (φ2). The flash times are controlled through a moving pendulum20 intercepting the light beams and placed downstream of the grid. Sensors fixed on the pendulum are connected to a computer in order to determine the value of the flash time which can be varied from 1 to 20 s (accuracy of about 0.01 s). 2.3. Pyrolysis Reactor and Product Recoveries. The wood sample which absorbs radiation is placed inside a cylindrical transparent quartz reactor (inside diameter, 30 × 10-3 m; height,
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50 × 10 m) fed by two flows of N2 (overall flow rate, 3.7 × 10-5 STP m3 · s-1). The injector nozzles are set up on both sample sides and at its bottom vicinity, in order to prevent vapor deposition on the reactor walls. The reactor position is adjusted with a three-axis translation device, and its precise alignment at the focus F3 is obtained with two laser beams. In usual pyrolysis reactors, the condensable vapor yields may depend on their residence time in the hot zone because of secondary cracking reactions. Studying primary pyrolysis occurring at the solid level requires fast cooling of the vapors. This is another advantage of the image furnace where the condensable vapors and gases released from the surface of the biomass sample are quenched inside the reactor by mixing with the cold nonabsorbing carrier gas (N2). The gas mixture temperature in the reactor is hence close to room temperature, while only biomass is heated by absorption of the concentrated radiation. After leaving the reactor under atmospheric pressure, condensable vapors are trapped by a quartz fiber filter (Whatman GF/A) and two cartridges (diameter, 1 × 10-2 m; length, 20 × 10-2 m) packed respectively with zeolite particles (Siliporite G5 pellet 1.6 × 10-3 m) and glass wool. All the permanent gases are then recovered in a sampling bag through a solenoid valve. The sampling time is adjusted according to the flash time and the residence time of the gases between the reactor and the bag. The carrier gas bypasses the bag before and after each experiment. 2.4. Sample Preparations and Measurements. The experiments are performed with oak samples cut out from the longitudinal plane of a wooden board. The samples are cylinders (radius, 5 × 10-3 m; thickness, 3 × 10-3 m; mass, ∼125 × 10-6 kg) prepared with a lathe. Before pyrolysis, the samples are dried for 1 day in an oven at 378 K. A new one is prepared for each experiment. The mass loss of the sample is determined by weighing it before and after the flash time. The mass increases of the reactor, the filter, and the cartridges give the mass of condensable vapors (including water), whereas the mass of gases is calculated from their composition, the mass flow rate of inert gas, and the sampling time. The composition of the gaseous products (i.e., CO, CO2, H2, CH4, C2H6, C2H4, C2H2, C3H8) which are highly diluted in the carrier gas is determined by gas chromatography, with a Varian CP-3800 using FID (CP-Poraplot U type capillary column with silica packing, 27.5 × 0.63.10-3 m) and TCD (carbosphere column, 2 × 2.10-3 m) detectors, and a Varian 3900 using a TCD detector. The mass of char accumulated on the sample surface is simply determined by scraping the sample after the flash time. All the weighed masses are obtained with an accuracy of about 10-7 kg. The solids ultimate analysis (C, H, O, and ash mass fractions) is carried out at the “Service Central d’Analyse” of CNRS (Solaize, France). The related methods are given in Le´de´ et al.31 The char ultimate analysis is performed after complete wood conversion, once for each heat flux density (Table 1). Sample mass losses and masses of all the pyrolysis products are studied as a function of the flash time. The yields of pyrolysis products are calculated by comparing the masses of each product with respect to the reacted biomass (mass loss + mass of char). It is hence possible to determine mass balances by summing the yields of pyrolysis products. 2.5. Experimental Results and Discussion. Typical examples of mass balances are reported in Table 2. Mass balance closures range from about 90% to 95%. Results obtained for both available heat flux densities are given in Figures 3 and 4. In a first approximation, all the masses increase linearly with
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Table 3. Average Values of Pyrolysis Products Yields (wt %) Obtained for Two Values of the Available Heat Flux Density (φ1 ) 0.8 MW · m-2, φ2 ) 0.3 MW · m-2)a flux
gases (wt %)
vapors (wt %)
char (wt %)
φ1 φ2
21 ( 7 8(4
62 ( 5 61 ( 6
11 ( 2 22 ( 9
a Because of linear tendencies (Figure 3), the average value for each product is obtained by dividing the sum of the yields at different flash times by the number of experiments; standard deviation is then calculated.
Figure 5. Simplified kinetics pathway representing the primary steps of biomass pyrolysis according to Shafizadeh and Chin.39 Table 4. Reaction Kinetic Rate Constants (Associated with the Simplified Kinetics Pathway Reported in Figure 5) Used in the Models According to Chan et al.47 kinetic parameter (s-1)
activation energy (J · mol-1)
preexponential factor (s-1)
kG kV kC
140 000 133 000 121 000
1.3 × 108 2.0 × 108 1.08 × 107
the flash time once pyrolysis has begun. The shrinking or swelling of the char layer that slightly modifies the accurate sample surface adjustment at the focus F3 does not seem to induce a deviation from the linearity. This linear tendency especially for the mass loss is also mentioned in the case of the main wood components of fast pyrolysis performed under a higher available radiant flux density (7.4 MW · m-2), for cellulose26 and lignins.27 For the heat flux density φ1 (0.8 MW · m-2), Figure 3 shows that the formation of all products begins for a flash time, calculated from linear regression, of approximately 0.7 s. This period corresponds to the preheating of the biomass until the pyrolysis temperature is reached at the surface. Let us define the specific rate of mass loss as the ratio of the slope of the mass loss straight line calculated from linear regression with respect to the value of the sample cross section submitted to the radiant flux. For φ1, a specific mass loss rate of about 0.163 kg · m-2 · s-1 can be calculated. For the lower heat flux density (φ2), the mass loss begins after a heating period of about 3.2 s and the related specific rate of mass loss is 0.055 kg · m-2 · s-1. The specific mass loss rate clearly increases with the available heat flux density, whereas the pyrolysis starting time decreases. The specific mass loss rates are also lower than those obtained under higher available radiant flux (7.4 MW · m-2) for cellulose samples26 (1.190 kg · m-2 · s-1; radius, 2.5 × 10-3 m) and Organocell lignin samples27 (0.395 kg · m-2 · s-1; radius, 5 × 10-3 m). For the heat flux density φ1, it is not possible to distinguish significant differences between the starting times for each pyrolysis products, showing that gas and vapor release, and char formation occur at the same time. This observation is also mentioned for lignin,27 whereas, in the case of cellulose,26 a transient period with the formation of a layer of intermediate liquid compound (ILC) is observed. For the heat flux density φ2, gas formation seems to occur shortly after the beginning of the mass loss and char formation but the experimental accuracy is not sufficient to confirm this tendency.
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Table 5. Physicochemical Parameters of Wood and Char Chosen for the Models parameter
wood
r (m) L (m) F (kg · m-3) Cp (J · kg-1 · K-1) λ (W · m-1 · K-1) R Kf (m2) parameter -1
Df (m · s ) µf (Pa · s) Pf (Pa) hcg (W · m-2 · K-1) T∞ (K) ∆Hj (J · kg-1) 2
reference
-3
5 × 10 3 × 10-3 540 -436.3 + 5.6856T 0.35 0.63 ∼10-14
char
reference
5 × 10 3 × 10-3 170 420 + 2.09T - (6.85 × 10-4)T2 0.10 0.06 ∼10-12
measured 59 36 measured 50
-3
measured measured measured measured 60 measured 50 value
reference
-6
typical value at 500 K56 typical value at 500 K56 volatile matter over pressure may be higher56 gas flow parallel to a vertical plate61 -
∼10 ∼10-5 ∼105 20 293 418 × 103
Figure 4 shows that the fractions of CO, CO2, and CH4, slightly vary with the flash time once the pyrolysis has begun. In each case, the most abundant gaseous product is CO. The molar fraction of H2 is quite low at the beginning of pyrolysis and then increases. The light hydrocarbon mole fractions contain mainly CH4 and C2H4 with minor fractions of C2H2, C2H6, and C3H8. The gas composition obtained in the present study is also close to that obtained by Le Dirach et al.6 for oak samples submitted to a higher heat flux density. The noticeable variability of the amount of hydrogen is generally explained by secondary thermal cracking reactions.32-34 However, several authors have rather suggested that hydrogen formation may result from reactions occurring inside the reacting sample at the level of ILC21,27,35 formed at the beginning of biomass pyrolysis. The average product yields and their standard deviations are reported in Table 3. The yields of vapors do not significantly depend on the heat flux density, contrary to the yields of gases and char that respectively increase and decrease with the heat flux density (see also Table 2). Regarding the evolution of wood pyrolysis products as a function of the heat flux density, Gronli and Melaaen36 report that the char and vapor final yields experimentally decrease while the gas yield increases when the heat flux density increases from 0.080 to 0.130 MW · m-2. In their experiments performed using a xenon arc lamp as a radiant heat source,36 such a phenomenon could result from a higher temperature in the char layer for higher heat flux densities that favor secondary reactions. Indeed, Gronli and Melaaen36 studied the pyrolysis of thick samples (length, 30 × 10-3 m) in comparison to ours (length, 3 × 10-3 m) that greatly increases the intraparticle resistance to mass transfer and vapors cracking by contact with a thick char layer. Experiments of Di Blasi et al.37 performed in a furnace with tubular quartz infrared lamps also showed that product distribution during pyrolysis depends on heating conditions. For lower applied heat flux densities in the range 0.040-0.080 MW · m-2, the same trends as those of the present work are obtained for several wood species (length, 40 × 10-3 m); vapor yield is also nearly constant whereas the final yields of char and gases respectively decrease and increase as the heat flux density increases. It is interesting to notice that the increase of gas yield does not seem to result from gas phase cracking reactions since the vapor yield is quite constant. The pyrolysis product distribution could be explained by intraparticular secondary reactions, which could be of less importance in the case of thin biomass samples. The results of the solids ultimate analysis are reported in Table 1. The oak ultimate analysis is quite similar to typical wood ultimate analysis.38 For char samples, the carbon and oxygen fractions respectively increase and decrease with the heat flux
47
Table 6. Characteristic Times and Dimensionless Numbers of the Main Processes Involved during Fast Pyrolysis of Wood characteristic times (s) thc tdm tcm tht
tp
wood
char
23.4 9.0×10-2 4.6 8.6 1.6 2.9×10-2
21.8 9.0
9.0×10-4 1.2 0.7 2.3 1.0 -
Tref (K)
φi (MW · m-2)
600 600 1800 600 1800 800 1000
dimensionless number
orders of magnitude
Pe Le Bi Th
∼102-104 ∼10-5-10-3 ∼1-10 ∼1 -103
0.8 0.8 0.3 0.3
density. By contrast, the absolute hydrogen amount in the char does not vary significantly. The difference of ultimate analysis between both char samples may be due to the differences of temperatures reached by the char. 3. Theoretical Section The purpose of this section is to compare two different models representing the pyrolysis of a wood sample submitted to a given heat flux density. The choice of the simplified kinetic model used, as well as the main assumptions (relying on the values of several characteristic times) are first discussed. Then, the results of both models are compared and discussed with regard to those reported in the Experimental Section. 3.1. Kinetic Scheme of Biomass Pyrolysis. Because kinetic models based on a one-step global reaction are not valid to predict the variations of pyrolysis product distribution, several authors use a kinetic scheme relying on three parallel reactions as represented in Figure 5. However, such a kinetic scheme is undoubtedly a simplification and is not representative of the true chemical behavior of wood pyrolysis that includes a great number of reactions of depolymerization, dehydratation, decarboxylation, etc. The first comprehensive models have been developed for pure cellulose which is the major component of wood and because its properties are well-known. It has been, for example, clearly shown that cellulose pyrolysis gives primary rise to an ILC.20,40 More recently, Luo et al.41 proposed a comprehensive pathway taking into account ILC. Lignin, another component of wood, is also known to pass through a liquid phase.27,42 In addition, the fusionlike phenomenon of wood first identified by Le´de´ et al.43,44 results from the fact that
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internal mass transfer by diffusion:
internal mass transfer by convection: tht )
external heat transfer:
tdm )
L Df
tcm )
L2µf PfKf
FCpL h
pyrolysis time for a three parallel reactions scheme: 1 1 tp ) ) kP kG + kV + kC
Figure 6. Schematic representation of a sample submitted at one side to a uniform radiant flux: “layers” Lagrangian model (LM) and “global” Eulerian model (GM).
wood passes through a liquid phase at a rather constant temperature during fast pyrolysis. Le´de´ et al.40 have shown that ILC resulting from wood primary decomposition cannot be ignored in conditions of fast pyrolysis. However, it is difficult to use the standard Broido-Shafizadeh type model45 because the relative fractions of char and gas may vary according to the experimental conditions. For the sake of simplification, the three competitive reactions scheme is however chosen in the present paper because it can simply account for different product selectivities according to the experimental conditions. Unfortunately, there is no consensus concerning the kinetics parameters to be used for each of these three parallel reactions, despite the numerous works reported in the literature.46-49 The predictions of the various kinetic data sets deeply differ6,50 certainly because of the multiplicity of wood types used, experimental techniques, operating conditions, inaccurate models, and poor knowledge of physical parameters. In the present study, the kinetic parameters of Chan et al.47 (Table 4) are used for the modeling because they have already proved to be appropriate under pyrolysis conditions controlled by heat transfer.36,50 3.2. Characteristic Times Analysis. According to experimental conditions and to wood and char physicochemical properties, pyrolysis can be controlled by chemical reactions, heat transfer, and/or mass transfer. If the rate-controlling phenomena are not identified, mathematical models should take into account complex couplings between conservation of mass, momentum, and energy in the solid matrix.5,36,51,52 The estimation of characteristic times is a useful tool for defining the controlling steps and thus solving simplified models. However, such an analysis is only qualitative because many parameters vary during pyrolysis (solid properties such as thermal conductivity, heat capacity, density, porosity, permeability, diffusivity). Furthermore, the choices of reference temperatures may be arbitrary. The characteristic time analysis for biomass thermal reactions has been already used by several authors.14,47,53-57 The main characteristics times associated with pyrolysis are listed as follows: internal heat transfer by conduction:
thc )
FCpL2 λ
(1)
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2
(2)
(3) (4)
(5)
The characteristic length L is the ratio of the sample volume to the surface exposed to external heating. For a cylinder in our case, it is simply equal to the particle thickness. For the calculation of the pyrolysis time, the reference temperature is chosen as the local temperature of the pyrolysis zone, which is the small volume inside which reactions occur. The choice of a relevant temperature is critical for the calculation accuracy. Yet, few experimental studies have been devoted to determine its appropriate value during fast pyrolysis.44,58 Its value is representative of the reacting biomass temperature that varies inside relatively narrow limits (∼800-1000 K from the model predictions, see section 3.6.2). The chemical rate constants are supposed to obey Arrhenius-type laws:
( RTE )
k ) A exp -
(6)
For the external heat transfer time calculation, the reference temperature value is the temperature at the surface (virgin biomass at the beginning and then char) exposed to the incident radiation (∼600-1800 K from the model prediction, see section 3.6.2). By applying blackbody laws, the available heat flux density is related to the temperature of the xenon arc lamp delivering the radiation and to the Stefan-Boltzmann constant, as follows: φi)σTi4
(7)
The heat source temperature is calculated from eq 7:
()
φi 1⁄4 (8) σ In the case of the image furnace, the external radiant heat transfer coefficient is then equal to Ti ∼
h ) σ(Ti + Tref)(Ti2 + Tref2)
(9)
The parameters used for the calculation of characteristic times are given in Tables 4 and 5 (see section 3.5 for details about the values of the physicochemical parameters). The results are summarized in Table 6. In order to examine the relative importance of the main physicochemical phenomena occurring during wood pyrolysis, let us consider the following dimensionless numbers relying on the characteristic times and whose orders of magnitude are given in Table 6: Peclet number:
Pe )
PfKf tdm ) Dfµf tcm
(10)
Pe is much greater than 1, showing that volatile species transfer by diffusion is slower than by convection. As a consequence, a model taking into consideration volatile release could disregard diffusion in the gas mixture phase comparative to convective mass transfer. The mass transfer importance
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Table 7. Balance Equations of the LM mass balance
heat balance
Layer (I) shrinking velocity:
temperature:
∂uB )∂x
λB ∂2T 1 ∂T 1 dλB ∂T ∂T ) + uB + 2 ∂t FBCp,B ∂x FBCp,B dT ∂x ∂x Cp,B
∑k
j
j
uB(x,t)0) ) 0 uB(x)0,t) ) 0
(
)
∑ k ∆H j
j
j
T(x,t)0) ) T0
product masses:
dmB ) uB(x)LB)FBS dt mB(t)0) ) mB,0
dmj ) F BS dt
∫
LB
0
kj(x) dx
mj(t)0) ) 0 length:
LB )
mB FBS
Layer (I′) length:
temperature:
mC LC ) FCS
λC ∂2T ∂T 1 dλC ∂T ) + ∂t FCCp,C ∂x2 FCCp,C dT ∂x
2
( )
(if LC > 10-6 m)
Interface (I′′) -
(λ ∂T∂x ) B
x)LB-
(
) λC
∂T ∂x
)
x)LB+
(if LC > 10-6 m)
Side (II) -
(λ ∂T∂x )
) -σεB(T4 - T∞4) - hcg(T - T∞) (if LB > 10-6 m)
(λ ∂T∂x )
) -σεC(T4 - T∞4) - hcg(T - T∞) (if LB < 10-6 m)
B
C
x)0
x)0
Side (III) -
(λ ∂T∂x ) B
x)LB
) (1 - RB)φ - σεB(T4 - T∞4) - hcg(T -
(λ ∂T∂x ) C
comparative to heat transfer is then determined by the Lewis number value. Lewis number:
Le )
tcm µfλ ) PfKfFCp thc
(11)
Le is much less than 1, showing that the pyrolysis model should mainly focus on internal heat transfer rather than mass
x)LB+LC
T∞) (if LC < 10-6 m) ) (1 - RC)φ - σεC(T4 - T∞4) - hcg(T T∞) (if LC > 10-6 m)
transfer. The volatile release from the particle can be assumed as an instantaneous process. Internal pressure increase during pyrolysis5 also induces the formation of larger pores in the char layer, making mass transfer easier. Biot number:
Bi )
hL thc ) λ tht
(12)
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Table 8. Balance Equations of the GM mass balance
heat balance
Volume (I′′′) product masses:
∂mB )∂t
temperature:
∑ k F S dx
∂T ) ∂t
j B
j
S dx
∑m C
k p,k
(
λ
∂2T dλ ∂T 2 + ∂x2 dT ∂x
( )
∑ k F ∆H j B
j
j
)
k
mB(t)0) ) mB,0
T(x,t)0) ) T0
∂mj ) kjFBS dx ∂t
parameters:
mj(t)0) ) 0
S ) πr2
length:
λ)
∑λ η
k k
k
∂L 1 ) ∂t S
∑ F1 k
k
∂mk ∂t
ηk )
mk
∑m
k
k
ε)
∑η ε
k k
k
Side (II) -
(λ ∂T∂x )
) -σε(T4 - T∞4) - hcg(T - T∞)
(λ ∂T∂x )
) (1 - R)φ - σε(T4 - T∞4) - hcg(T - T∞)
x)0
Side (III) x)L
Bi is greater than 1: internal heat transfer by conduction is controlling. Because of intraparticle thermal gradients, the temperature distribution in the whole particle volume is not uniform. Thiele number:
Th )
FCpL2kp thc ) λ tp
(13)
Th is greater than 1, showing that the internal heat transfer proceeds slower than the pyrolysis reaction. Consequently, pyrolysis occurs inside a thin zone which moves from the surface of the sample through the particle.53 In summary, for a thin pellet submitted to a high heat flux density, the times of intrinsic pyrolysis and of volatile mass transfer within the pores are significantly smaller than the time scale of heat transfer inside the solid matrix and internal heat transfer is rate-controlling. 3.3. Model Assumptions. In order to facilitate the implementation of the pyrolysis model into a global gasifier model, some of the following assumptions are made according to the above-mentioned elements. The main assumptions and characteristics are as follows: (a) The model is one-dimensional. (b) Volatiles leave instantaneously the sample, and gaseous transport phenomena through the porous char matrix are neglected.
(c) Heat is transferred by conduction inside the solid assumed to behave as a homogeneous medium. (d) The simultaneous absorption of heat flux density (provided by the xenon arc lamp), radiative losses, and convective carrier gas cooling are considered on the heated side. Convective and radiative losses are considered on the opposite nonexposed side. (e) The available heat flux density is uniform on the exposed surface. (f) The specific heat capacity is assumed to be a function of the local temperature, whereas wood and char densities are constant and independent of the temperature. (g) Wood and char are gray bodies whose surfaces’ spectral properties do not depend on wavelengths and temperature. As for cellulose, their transmittance is neglected.62 Spectral reflectivity and emissivity are connected by 1-R)ε
(14)
(h) Despite the uncertainties revealed by the literature on pyrolysis heats (negligible, endothermic, or exothermic), their values may be of importance in thermal effects modeling, causing an impact on temperature profiles.42 Other results have been reported about the minor effect of heat pyrolysis.55 The heat of pyrolysis is considered endothermic, and the same is considered for the three primary reactions.47
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Figure 7. Comparison of experimental and theoretical (LM and GM) variations of mass losses as a function of the flash time for two values of the available heat flux density (φ1 ) 0.8 MW · m-2, φ2 ) 0.3 MW · m-2). Table 9. Values of the Criterion J (LM and GM) Obtained for Two Values of the Available Heat Flux Density (φ1 ) 0.8 MW · m-2, φ2 ) 0.3 MW · m-2) and Calculated by eq 15 φ1 (n ) 16)
mass loss gas mass vapor mass char mass
φ2 (n ) 11)
LM
GM
LM
GM
0.06 0.27 0.18 0.89
0.05 0.19 0.10 0.42
0.03 2.26 0.06 0.07
0.11 1.36 0.14 0.14
(i) The volume of the sample decreases (structural change by solid shrinkage) according to the release of volatiles and gases and to both wood and char densities. Note that, for a use in a fluidized bed, some adaptations will have to be made in the pyrolysis model assumptions, for extension to nonconstant heat flux and to larger diameter particles (e.g., two-dimensional model). 3.4. Basic Balance Equations. Two approaches are considered for the pyrolysis models of a single biomass particle. The first one relies on an original Lagrangian approach (LM, “layers” model) where mathematical equations of mass and heat balances are written in the assumptions that wood and char form two distinct layers. Thus, the char layer is separated from the virgin wood by an interface that propagates through the sample. In the second one, a classical and global Eulerian approach (GM, “global” model) is considered: mass and heat equations are written on the whole particle. At any time, a partially pyrolyzed element in the particle is considered as a mixture of both char and wood. A schematized representation of both approaches is given in Figure 6. 3.4.1. Balance Equations of the “Layers” Model (LM). The LM relies on concepts similar to those developed in previous papers6,26,30,53 and on experimental observations made on wood samples having partially reacted in fast pyrolysis conditions, showing the presence of a distinct layer of char surmounting the unreacted biomass. The particle is simply divided into two zones (I) and (I′) (Figure 6) corresponding respectively to the wood and char layers. The model can also be compared with the unreacted-core-shrinking approximation used for wood degradation modeling.63 The mass and energy conservation equations for both layers are reported in Table 7. The boundary conditions are written on the surface receiving the incident radiation (III), on the other nonexposed side (II), and at the interface between wood and char (I′′). The transition between wood and char layer is arbitrarily chosen as corresponding to a small assigned char thickness equal to 10-6 m.26
3.4.2. Balance Equations of the “Global” Model (GM). Such an approach has been already carried out with the simplifying assumption of an instantaneous outflow of volatiles out of the solid and internal heat transfer limitation.54,64-66 The mass and energy conservation equations are written on the whole particle (I′′′) (Figure 6) and are given in Table 8. The boundary conditions are written on the surface receiving the incident radiation (III) and on the other nonexposed side (II). The sample physical properties are calculated by linear interpolation of the properties of wood and char. 3.5. Values of the Parameters Used in the Models. The values of the parameters required for solving the models are reported in Tables 4 and 5. Some values of the physical constants of wood and char used in the models have been measured. The apparent density of char is determined with a pycnometer with capillary cap (volume 25 × 10-6 m3). The samples are previously covered by a thin layer of varnish in order to make easier their contact with water and to avoid water penetration. The heat capacity is measured with a differential scanning calorimeter (Pyris 1 DSC PerkinElmer). Linear relationships are obtained as a function of temperature between 293 and 373 K. However, because the measurement of heat capacity at higher temperatures is difficult, a correlation from the literature has been retained for char.59 The reflectivities of wood and char have been measured by hemispherical directional reflection with a spectrophotometer (Cary 500) and integrating sphere, at ambient temperature and for wavelengths between 0.35 × 10-6 and 2.5 × 10-6 m. The values of the thermal conductivities established at ambient temperature are obtained from the literature.36,60 3.6. Modeling Results. Both models have been solved in the case of two available heat flux densities (φ1 and φ2) and compared to the experimental results. The systems of differential equations are solved by the method of lines67 with the DDASSL solver. For both heat flux densities, the simulation time is chosen as the highest experimental flash time. 3.6.1. Comparison with the Experimental Results and Discussion. Let us define a criterion to quantify the difference between model predictions and experimental results. Experimental and theoretical masses (i.e., mass loss, gas, vapor, and char masses) may be compared according to Jl )
(
E M n ml,z (tz) - ml,z (tz) 1 E n z)1 m (t )
∑
l,z z
)
2 E for ml,z (tz) > 0
(15)
Ind. Eng. Chem. Res., Vol. 48, No. 10, 2009
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Figure 8. Comparison of experimental and theoretical (LM and GM) variations of pyrolysis product masses (a, gases; b, vapors; c, char) as a function of the flash time for two values of the available heat flux density (φ1 ) 0.8 MW · m-2, φ2 ) 0.3 MW · m-2).
Figure 7 shows that the time evolution of the mass loss and the starting time of pyrolysis are quite well represented by the two models and for both available heat flux densities. For the highest value (φ1), differences appear for times above about 4 s. In the case of the lower heat flux density (φ2), the mass loss predicted by the GM is higher than by the LM for flash times above about 10 s. It may be noticed that the value of criterion J is hence higher for GM than for LM (Table 9). The distribution of pyrolysis products is given in Figure 8. Both models are in agreement with experiments for the vapors (Figure 8b and Table 9). Gas masses (Figure 8a) are overestimated by both models in the case of the lower heat flux density (φ2). On the other hand, they are underestimated for the higher one (φ1). In both cases, the value of the criterion J is higher
Table 10. Average Values (LM, GM, and Experimental) of Pyrolysis Product Yields (wt %) Obtained for Two Values of the Available Heat Flux Density (φ1 ) 0.8 MW · m-2, φ2 ) 0.3 MW · m-2) flux
approach
gases (wt %)
vapors (wt %)
char (wt %)
φ1
LM GM experimental LM GM experimental
16 ( 1 17 ( 1 21 ( 7 15 ( 1 15 ( 1 8(4
65 ( 1 65 ( 1 62 ( 5 64 ( 1 65 ( 1 61 ( 6
19 ( 2 18 ( 3 11 ( 2 21 ( 1 20 ( 1 22 ( 9
φ2
(Table 9) than its value for vapors. The char mass (Figure 8c) is significantly overestimated for the higher heat flux (φ1) (Table 9). The starting times of the phenomena are always quite well estimated for each product. The average yields of pyrolysis
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Figure 9. Theoretical (LM and GM) variations, as a function of the flash time, of the sample length and pyrolysis zone thickness (a) and temperatures (b, c) for two values of the heat flux density. A, φ1 ) 0.8 MW · m-2; A.1, exposed side; A.2, nonexposed side; A.3, wood-char interface (LM) and pyrolyzing zone (GM). B, φ2 ) 0.3 MW · m-2; B.1, exposed side; B.2, nonexposed side; B.3, wood-char interface (LM) and pyrolyzing zone (GM)
products obtained from the models are given in Table 10. They do not significantly depend on the heat flux density, contrary to the experimental values for gases and char. Because the masses of pyrolysis products are dependent on the choice of the kinetic rate constants (activation energies and preexponential factors), another approach would have been to fit these chemical parameters on the basis of the observed variations of the product distribution thanks to an optimization procedure. The validity of such fittings implies perfect mass balances and an accurate knowledge of the physicochemical properties of wood and char. This is not the case for most of them and particularly their variations as a function of the temperature.
For the sake of simplification, our models rely on a kinetic scheme and related constants taken from Chan et al.47 As mentioned by these authors, the kinetic parameters for the formation of volatile matter (gases and vapors) are issued from experimental data obtained by Hajaligol et al.68 for the pyrolysis of cellulose, in an electric heated grid reactor and under temperatures where secondary cracking reactions could not be avoided. In addition, the kinetic parameters for char formation have been determined from a model validation of wood pyrolysis.47 Next, our kinetic scheme does not take into account the formation of ILC mainly because of the uncertainties about the values of its physicochemical constants. In spite of these approximations, the agreement between our experimental data
Ind. Eng. Chem. Res., Vol. 48, No. 10, 2009
and model predictions is quite satisfactory. It can also be noticed that, in the case of the biomass fast pyrolsis performed in a fluidized bed, Kersten et al.50 reports a good agreement between experimental vapor yields and a model prediction relying on Chan et al. kinetic constant values.47 3.6.2. Variations of Sample Length and Temperatures. The variations of the length and temperatures of samples as predicted by both models are reported in Figure 9. Shrinkage of the sample is observed for both models (Figure 9a). In the case of GM, let us quantitatively define the pyrolyzing zone as the region where the wood conversion (i.e., the ratio, inside an elementary volume, of the mass of reacted biomass to the initial biomass mass) is in the range 0.1-0.9. As mentioned in calculation of the Thiele number in the characteristic time analysis, the reaction occurs in a thin reaction zone that propagates through the solid as the reaction proceeds. For the higher heat flux (φ1), the pyrolyzing zone thickness varies from about 100 × 10-6 to 225 × 10-6 m. For the lower heat flux (φ2), it is significantly larger and varies from about 180 × 10-6 to 750 × 10-6 m (Figure 9a). Therefore the model predicts that the pyrolysis zone thickness decreases with the increase of the external heat supply. In the case of φ2 and above about 16 s, the thickness of the pyrolyzing zone suddenly decreases when its back temperature reaches the nonexposed side temperature (Figure 9b,c). The sample thicknesses are also similar for both models from the beginning to the end of pyrolysis. The experimental measurement of the particle temperature is difficult. Indeed, a thermocouple located in the vicinity of the focus of the image furnace cannot accurately give the true temperature of the solid surface because of possible incident radiation absorption. Pyrometric measurement is also made difficult. The measurement could only be performed in a specific range of wavelengths and could be largely disturbed by the vigorous release of volatile matter from the surface. It is hence difficult to confirm the following model previsions. Predicted time evolutions of temperatures at different positions in the solid are given in Figures 9b and 9c. The results show that the temperature of the exposed side increases due to absorption of the heat flux (Figure 9b). When the surface temperature becomes high enough, pyrolysis begins at the solid surface. A sharp increase of the temperature is observed when the char layer is formed in the LM because char has a higher absorptivity than wood. The transition time is longer for the GM because global optical properties are calculated in this case from the mass fraction and optical properties of both wood and char. It is noticed that the starting times of this sharp temperature increase and of product formation are similar (Figures 7, 8, and 9b). The temperatures of the nonexposed side also show good agreement for both models. The temperatures of the wood-char interface (LM) and inside the pyrolyzing zone (GM) are deduced from the modeling (Figure 9c). For the GM and after an induction period due to biomass preheating, the temperatures slightly decrease during pyrolyis from 1180 to 780 K (stabilization phase between about 780 and 900 K) for the higher heat flux density (φ1), and from 1000 to 760 K (stabilization phase between about 760 and 900 K) for the lower one (φ2). Pyrolysis temperatures are in good agreement for both approaches. These variations of temperatures, despite an intensive heat supply, may be explained by the competition and equilibrium between the heat demand for pyrolysis and the heat density absorbed by the sample, in agreement with the fusion-like behavior of wood pyrolysis.44 Similar trends are clearly obtained by both approaches of the pyrolysis models. LM and GM suitably predict the behavior of
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biomass submitted to high heat flux densities with few discrepancies between both theoretical approaches. Differences between experimental measurements and models may result from uncertainties of physicochemical properties and kinetic parameters. 4. Concluding Remarks Theoretical and experimental studies of biomass fast pyrolysis made under controlled heat flux densities similar to those encountered in a fluidized bed have been compared. The experiments performed in an image furnace have shown that, under our operating conditions, the yields of vapors do not significantly depend on the value of the heat flux density, in the range 0.3-0.8 MW · m-2. However, the gas and char yields as well as their compositions clearly depend on these thermal conditions. The calculations of characteristic times have pointed out that mass transfer limitations could be neglected comparative to competitive heat transfer and chemical reactions. On this basis, two theoretical approaches have been considered for modeling: Eulerian and Lagrangian approaches. The original Lagrangian approach relies on experimental observations under fast pyrolysis conditions showing the presence of two layers in the partially reacted sample (i.e., the unreacted biomass surmounted by a distinct layer of char). The Eulerian approach is classical with regard to other pyrolysis models from the literature. Both approaches give similar results for predicting mass evolutions and are in quite good agreement with the experimental results. Consequently, they are both valid to model the pyrolysis of a biomass particle under thermal conditions close to those prevailing in a DFB. The agreement between theoretical predictions and measurements is very satisfying considering the future use of the pyrolysis model in a comprehensive gasifier model. Acknowledgment This research has been performed thanks to EDF R&D financial support. The authors are also grateful to J.-P. Corriou (LSGC, ENSIC, CNRS-Nancy Universite´) for his relevant advice in the use of the DDASSL solver employed for the resolution of the differential equations systems, M. Bouroukba (LTMP, ENSIC, CNRS-Nancy Universite´) for his help in the heat capacity measurements, and B. Monod (LEMTA, ENSEM, CNRS-Nancy Universite´) for the reflectivity measurements. Note Added after ASAP Publication: The version of this paper that was published on the Web April 14, 2009 had an error in Table 8. The corrected version of this paper was reposted to the Web April 17, 2009. Nomenclature A ) preexponential factor (s-1) Cp ) heat capacity (J · kg-1 · K-1) D ) diffusivity (m2 · s-1) E ) activation energy (J · mol-1) h ) heat transfer coefficient (W · m-2 · K-1) ∆H ) reaction heat (J · kg-1) J ) criterion used to quantify the difference between models and experiments k ) kinetic rate constant (s-1) K ) permeability (m2) L ) thickness, characteristic length (m) m ) mass (kg) n ) experiment number
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P ) pressure (Pa) r ) radius of sample cross section (m) R ) gas constant, 8.314 J · mol-1 · K-1 S ) surface (m2) t ) time (s) T ) temperature (K) u ) shrinking velocity (m · s-1) x ) axis (m) Greek Symbols R ) reflectivity ε ) emissivity η ) solid fraction φ ) available flux density (W · m-2) λ ) thermal conductivity (W · m-1 · K-1) µ ) viscosity (Pa · s) F ) mass density (kg · m-3) σ ) Stefan-Boltzmann constant, 5.67 × 10-8 W · m-2 · K-4 Subscripts ∞ ) ambient 0 ) initial B ) biomass C ) char cg ) cooling gas cm ) internal mass transfer by convection dm ) internal mass transfer by diffusion f ) volatile matter (gases and vapors) G ) gases hc ) internal heat conduction ht ) external heat transfer i ) heat source j ) gases, vapors, char k ) biomass, char l ) mass loss, gases, vapors, char P ) pyrolysis ref ) reference V ) vapors Superscripts E ) experimental M ) model Dimensionless Numbers Bi ) Biot number Le ) Lewis number Pe ) Peclet number Th ) Thiele number
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ReceiVed for reView December 03, 2008 ReVised manuscript receiVed February 19, 2009 Accepted March 13, 2009 IE801854C
