A study to investigate pyrolysis of wood particles of various shapes and sizes

Fire Safety Journal xxx (xxxx) xxx–xxx

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A study to investigate pyrolysis of wood particles of various shapes and sizes ⁎

Yawei Chen, Kumar Aanjaneya, Arvind Atreya

Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI 48109, USA

A R T I C L E I N F O

A BS T RAC T

Keywords: Wildfires Firebrands Pyrolysis Modeling Prolate Oblate

Pyrolysis of centimeter-scale wood particles of various sizes and shapes needs to be understood to determine their burning rate and life. Such particles may be thought of as firebrands, which are a major reason for spotting ignition in wildland and wildland-urban interface fires. The burning lifetime of firebrands controls the maximum distance they can travel to cause spotting. To understand and model this, experiments are done in a vertical tube furnace with wood particles of different sizes and shapes. For computations, two classes of shapes, prolate and oblate ellipsoids, were chosen to represent the arbitrary geometry of such particles. Prolate ellipsoids include shapes ranging from thin needles to spheres, whereas, oblate ellipsoids include shapes ranging from thin disks to spheres. The choice of these smooth shapes, while facilitating expedient computations also enables the coverage of wide ranges of particle shapes and surface area to volume ratios (SVR). Model simulations show satisfactory agreement with relevant literature and experimental data. Particle aspect ratio (ϵ, the ratio of minor and major axes), SVR, and equivalent radius (Re) are used to define the particle geometry. Mass loss and center temperature profiles are presented and discussed. It is shown that with the decreasing of aspect ratio, wood particle decomposes faster and the final char fraction becomes smaller. A power-law based correlation between conversion time (tcon ) and SVR is derived and verified against experiments. Further, it is shown that an increase in the SVR enhances the production of tar and decreases the yield of char while leaving the yield of gas mostly unaffected.

1. Introduction Spotting ignition by lofted firebrands is one of the most significant mechanisms of fire propagation in wildland and wildland-urban interface (WUI) fires. The phenomenon of spotting may be broken down into three consecutive events: (i) generation of various size and shape firebrands by the fire, (ii) transportation of firebrands and (iii) ignition of the fuel present at the landing site [1]. During the last several decades, a substantial amount of research has been done to investigate the behavior of firebrands with particular regards to firebrand trajectory, lifetime, fire transport models, degradation of burning firebrand, etc. [2-5]. Clearly, research on firebrands requires the understanding of a broad range of phenomena. To understand the production of firebrands, the pyrolysis and degradation of trees and shrubs in the main fire need to be investigated. While important, we will not focus on this topic. Firebrands, so generated, typically have irregular shapes and sizes, resulting in various particle surface areas to volume ratios (SVR). SVR is critical for heat and mass transfer rates, which affects the pyrolysis rate and hence the burning rate. This is the main focus of this study because it determines the lifetime of firebrands. This study focuses on the pyrolytic behavior of wood particles of various shapes and sizes.

⁎

Influence of shape and size on pyrolysis of wood particles has been investigated previously. Lu et al. [6] conducted an experimental and theoretical investigation of three types of particles: flake-like, cylinderlike and near-spherical. They concluded that both particle shape and size affect the product yield distribution, particle conversion time and mass loss rate. However, with regards to the variety of shapes studied, this work was limited. Additionally, the two-stage wood pyrolysis model used by the authors fails to predict the peak in center temperature, which is observed in experiments. Di Blasi et al. [7] studied the effects of particle size and density on packed bed pyrolysis of wood. They reported an effect on the conversion time due to variations in heat and mass transfer rates (caused by varying physical properties) but negligible effect on the yield and composition of lumped product classes. In this study, even though different sizes and shapes of particles were used, the effective shape remained unchanged since particles were packed in a cylindrical holder made of stainless steel mesh. Other experimental and theoretical investigations of the effects of particle shapes and sizes on the pyrolysis of biomass particles are limited in the range of particle geometry used [8-10.] One of the most basic issues to be settled is: What should the geometry of the wood particles be for computations that would be

Corresponding author. E-mail address: [email protected] (A. Atreya).

http://dx.doi.org/10.1016/j.firesaf.2017.03.079 Received 15 February 2017; Accepted 15 March 2017 0379-7112/ © 2017 Elsevier Ltd. All rights reserved.

Please cite this article as: Chen, Y., Fire Safety Journal (2017), http://dx.doi.org/10.1016/j.firesaf.2017.03.079

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Tg V Y

Nomenclature Ai B C Cp d e Ei f h ki L2 M P P0 Pt Pg Q R Re S SVR t tcon T Tf

pre-exponential constant (s−1) permeability (m2) specific heat (J/kg/K) specific heat at cons. pres. (J/kg/K) pore size (m ) emissivity activation energy (J/mol/K) focal length (m) heat transfer coefficient (W/m2/K ) reaction rate (s−1) semi-major axis (m) molecular weight (kg/mol) pressure (Pa) ambient pressure (101,300 Pa) tar partial pressure (Pa) gas partial pressure (Pa) heat generation (W/m3) univ. gas constant (8.314 J/mol/K) equivalent radius (m) mass generation (kg/m3/s) surface area to volume ratio (m−1) time (s) pyrolysis conversion time (s) temperature (K) furnace temperature (K)

gas temperature (K) flow velocity (m/s) solid mass fraction

Greek

α, β, η ξ, ϕ, ω ϵ ε ν Δh λ μ ρ σ

spheroidal coordinate spheroidal coordinate aspect ratio porosity degree or extent of pyrolysis heat of pyrolysis(J/kg) thermal conductivity (W/m/K) viscosity (kg/m/s) density (kg/m3) Stefan's constant (5.67 × 10−8W/m2/K )

Subscripts a c, c2 g , g2 is s t v w

virgin solid char char generation reaction gas generation reaction intermediate solid surface tar volatiles initial virgin solid

experiences secondary decomposition into gas and char while the intermediate solid change into char. Major assumptions made in the mathematical model are: (1) Volatiles and solid are in local thermal equilibrium, so temperature and temperature gradients are the same for both. (2) Volume and shape of charring solid remain constant during pyrolysis, i.e., no shrinkage. (3) Volatile gases have ideal gas behavior. (4) Dry biomass particles are used, thus there is no evaporation of water.

representative of different shapes and enable correlating the experimental results? Baum and Atreya [11] developed a quasi-steady burning model in prolate and oblate coordinates to study vaporizing of solids. However, charring solids, which are practically more important, were not examined. Carmo and Lima [12] studied moisture diffusion inside oblate spheroidal solids. These studies conclude that prolate and oblate spheroids can be used to represent wood particles of various shapes and sizes. For aspect ratio (ϵ, the ratio of minor and major axes) equal to unity, both of the aforementioned ellipsoids represent spheres while for the limiting case of (ϵ → 0 ) the former reduces to a thin needle while the latter to a thin disk (see Fig. 3). These smooth shapes are convenient for numerical computation and cover all possible particle shapes and SVR. It must be pointed out that these ellipsoids have smooth surfaces while wood particles found in forests are expected to have sharp and jagged edges. However, these edges are anticipated to be quickly pyrolyzed leaving behind smooth shapes for continued pyrolysis. The biggest advantage offered by these shapes is that only two parameters, namely L2 (semi major axis) and ϵ determine the specific geometry. This results in a considerable simplification of the geometric description of infinitely different shapes having varying degrees of irregularity while accounting for almost all possibilities.

2.1. Prolate and oblate coordinate systems A prolate spheroid results from rotating a two-dimensional ellipse about the symmetry axis on which the foci are located (Fig. 2). The prolate spheroidal coordinates are related to Cartesian coordinates through the following transformations [14].

x = f sinh α sin β cos ω y = f sinh α sin β sin ω z = f cosh α cos β

(1)

Where, f is the focal length, 0 ≤ α ≤ ∞, 0 ≤ β ≤ π , 0 ≤ ω ≤ 2π . Surfaces of constant α form prolate spheroids while those of constant β generate hyperboloids of revolution. An alternative form is defined by:

2. Modeling and experiments

ξ = coshα , η = cosβ , ϕ = ω

Wood pyrolysis involves complex physical and chemical processes such as heating of virgin wood, initiation of primary pyrolysis reactions that release volatiles and form char, mass transport of volatile products by convection and diffusion, condensation of some volatiles in the cooler parts followed by secondary reactions, convection of gas species at the surface of biomass particles, etc. A wood pyrolysis model developed earlier by the authors [13], as schematically shown in Fig. 1, was applied in the present study. The model accounts for the endo/exothermic behavior observed in the experiments and it also predicts the mass loss and temperature profiles very well. In this model, biomass decomposes to gas (non-condensable volatiles), tar (condensable hydrocarbons) and intermediate solid when heated. Tar

Where, 1 ≤ ξ ≤ ∞, − 1 ≤ η ≤ 1, 0 ≤ ϕ ≤ 2π . Then we have

Fig. 1. Reaction scheme for wood pyrolysis.

2

(2)

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2.2. Conservation equations The pyrolysis of virgin wood contains three consumption reactions which convert virgin wood to gas, tar and intermediate solids. Mass balances of wood, intermediate solid and char species are:

∂ρa ∂t

∂ρis ∂t

∂ρc ∂t

f

∂t

(8)

⎡∂ 1 (Vξ (ξ 2 − η2 )(ξ 2 − 1) ) 2 ⎢ f (ξ − η ) ⎣ ∂ξ ⎛ Vϕ(ξ 2 − η2 ) ∂ ∂ ⎜ + (Vη (ξ 2 − η2 )(1 − η2 ) ) + ⎜ ∂η ∂ϕ ⎝ (ξ 2 − 1)(1 − η2 )

→ → + ∇ ·( V ρt ) = St = ktρa − (kc2 + kg2 )ρt → ⎛→ ⎞ + ∇ ·⎜ V ρg ⎟ = Sg = kgρa + kg2ρt ⎠ ⎝

(9)

(10)

Where, ε is the porosity calculated by ε = 1 − ρs / ρw (1 − εw ). Here, ρs and ρw are the total solid and virgin wood densities, εw = 0.4 is the initial wood porosity [13]. Reaction rate is assumed to follow the first-order Arrhenius equation as follow:

elϕ (1 − η2 ) ∂ ∂ + 2 2 ∂ϕ (ξ 2 − η2 ) ∂η f (ξ − 1)(1 − η ) (4)

→→ ∇ ·V =

= Sc = kc ρis + kc2 ρt

∂(ερg )

(3)

Gradient and divergence are given by:

∇ =

(7)

∂t

y = f (ξ 2 − 1)(1 − η2 ) sin ϕ z = fξη

elη (ξ 2 − 1) ∂ + f (ξ 2 − η2 ) ∂ξ

= Sis = kis ρa − kc ρis

∂(ερt )

x = f (ξ 2 − 1)(1 − η2 ) cos ϕ

elξ

(6)

Conservation of each gas phase component can be expressed with terms representing mass change per unit volume, mass flux through control volume boundaries and mass conversion in the volume due to pyrolysis reactions. Only convective mass flux is considered here since the effect of diffusion is very small compared with convection. Mass balances of tar and gas are expressed by

Fig. 2. Characteristics of a prolate spheroid.

⎯→ ⎯

= Sa = − (kt + kg + kis )ρa

⎛ E ⎞ ki = Ai exp⎜ − i ⎟ ⎝ RT ⎠

2

⎞⎤ ⎟⎥ ⎟⎥ ⎠⎦

(11) → The gaseous component flow velocity V is calculated by Darcy's law.

→ B→ V = − ∇P μ

(5)

The wood particle is assumed to be homogeneous and isotropic in this model, thus parameters are symmetric along the z-axis and the last term of Eqs. (4) and (5) can be dropped. Details of oblate spheroid theory can be found in [14] and Supplementary materials (Appendix A). Examples of these solids are shown in Fig. 3. As we can see, two parameters, which are semi-major axis (L2) and aspect ratio (ϵ), determine the specific geometry.

(12)

Where, μ is the viscosity of volatiles. Permeability B is linearly interpolated between char and virgin wood by

B = (1 − ν )Bw + νBc

(13)

L2

Where, ν is the degree of pyrolysis calculated by ν = 1 − (ρa + ρis )/ ρw

L2

Fig. 3. Prolate (left) and oblate ellipsoids (right) for different aspect ratios ϵ varying from 1/9 to 1. As ϵ → 0 , the limiting case of a prolate is a needle while that of an oblate is a disc.

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Pressure is the sum of partial pressure of tar and gas which are assumed to be ideal gases.

P = Pt + Pg,

Pt =

ρt RT Mt

,

Pg =

(ρsolid Csolid + ερv Cv )

ρg RT

+

Mg

(14)

∂ ⎛ εPt ⎞ → ⎛ BPt → ⎞ R ∇ P⎟ + St ⎜ ⎟ = ∇ ·⎜ ∂t ⎝ T ⎠ Mt ⎝ μT ⎠

(20) Effective thermal conductivity λ consists of the conductivity of virgin wood, char, and volatiles as well as the radiative heat transfer through the pores, as depicted below [15]:

(15)

∂ ⎛ εPg ⎞ → ⎛ BPg → ⎞ R ∇ P⎟ + Sg ⎜ ⎟ = ∇ ·⎜ ∂t ⎝ T ⎠ Mg ⎝ μT ⎠

λ = (1 − ν )λ w + νλc + ελ v + 13.5σT 3d / e

(16)

T (ξ, η, 0) = T0, ρa (ξ, η, 0) = ρ0 ,

⎡ ∂ ⎛ BP ∂ ⎛ εPt ⎞ 1 ∂P ⎞ ⎢ ⎜ t (ξ 2 − 1) ⎟ ⎜ ⎟= 2 2 2 ∂t ⎝ T ⎠ ∂ ξ μ T ∂ξ ⎠ ⎝ f (ξ − η ) ⎣

P(ξ, η, 0) = P0 ρis (ξ, η, 0) = 0,

ρc (ξ, η, 0) = 0

(22)

Further, the following symmetry conditions are used,

∂ ⎛ BPt ∂P ⎞⎤ R (1 − η2 ) ⎟⎥ + St ⎜ ∂η ⎝ μT ∂η ⎠⎦ Mt

∂T (ξ, η = 1, t ) = 0, ∂η ∂P(ξ, η = 1, t ) = 0, ∂η

(17)

⎡ ∂ ⎛ BPg ∂ ⎛ εPg ⎞ 1 ∂P ⎞ ⎢ ⎜ (ξ 2 − 1) ⎟ ⎜ ⎟= 2 2 ∂t ⎝ T ⎠ ∂ξ ⎠ f (ξ − η2 ) ⎣ ∂ξ ⎝ μT

∂T (ξ, η = 0, t ) = 0, ∂η ∂P(ξ, η = 0, t ) = 0, ∂η

∂T (ξ = 1, η, t ) =0 ∂ξ ∂P(ξ = 1, η, t ) =0 ∂ξ (23)

∂ ⎛ BPg ∂P ⎞⎤ R (1 − η2 ) ⎟⎥ + Sg ⎜ ∂η ⎝ μT ∂η ⎠⎦ Mg

The pressure at the particle surface is atmospheric. The thermal flux through the boundary is determined by convective and radiative heat transfer.

(18)

P(ξ = ξs, η, t ) = P0

The balance of energy is governed by thermal conduction, gas convection, and the heat generation from pyrolysis reactions. It is assumed that there exists a local thermodynamic equilibrium between gas and solid phase components.

(ρsolid Csolid + ερv Cv )

(21)

Where, σ is the Stefan-Boltzmann constant, e is the emissivity and d is the pore size. Initial conditions at t=0 are:

In prolate coordinate system, the Eqs. (14) and (16) become

+

⎞⎤ B ∂ ⎛ 1 2 ∂T ⎜λ(1 − η ) ⎟⎥ + ρv Cv ∂η ⎝ ∂η ⎠⎦ μ f 2 (ξ 2 − η 2 )

⎡∂ ∂P ∂T ∂T ∂P ∂T ⎤ × ⎢ (ξ 2 − 1) + (1 − η2 ) ⎥+Q ⎣ ∂ξ ∂ξ ∂ξ ∂η ∂η ∂η ⎦

Where, Mt and Mg are molecular weights of tar and gas, R is universal gas constant. Combining Eqs. (9)–(14) gives the partial pressure equations for tar and gas.

+

⎡∂ ⎛ ∂T 1 ∂T ⎞ ⎢ ⎜λ(ξ 2 − 1) ⎟ = 2 2 2 ∂t ∂ξ ⎠ f (ξ − η ) ⎣ ∂ξ ⎝

→ → →→ ∂T + ρv CvV · ∇ T = ∇ ·(λ ∇ T ) + Q ∂t

λ f

ξ 2 − 1 ∂Ts = h(Tg − Ts ) + σε(T f4 − Ts4 ) ξ 2 − η2 ∂ξs

(24)

where, Ts, Tg and Tf are the temperatures of the particle surface, gas and furnace wall respectively. The surface emissivity is calculated by

(19)

⎧ es = ew Ts < 450 K ⎪ ⎪ Ts − 450 ⎨ es = ew + (ec − ew ) 450 ≥ Ts < 550 K 550 − 450 ⎪ ⎪e = e Ts ≥ 550 K ⎩s c

ρsolid Csolid = (ρa + ρis )Cw + ρc Cc , and Where, ρv Cv = ρg Cpg + ρt Cpt Q = − (kt Δht + kgΔhg + kisΔhis )ρa − kcΔhcρis − (kc2Δhc 2 + kg2Δhg2 )ρt . → By replacing V with Eq. (12) and rewriting the energy equation in prolate coordinate system we have

(25)

The chemical kinetic parameters for wood pyrolysis and the physical

Fig. 4. Grid index stencil for control volume method used in this work.

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3.2. Effect of particle shape and size on solid mass fraction and center temperature

properties of wood particles are used from literature [13]. Conservation equations for particles in the oblate coordinate system can be found in Supplementary material (Appendix A).

As mentioned earlier, two types of numerical simulations were performed to document the effect of shape and size on wood pyrolysis. In one set of calculations, the major axis length is kept constant while aspect ratio is varied, whereas in the second one, the equivalent radius is kept constant (i.e., volume) and the major and minor axes are determined according to aspect ratio. A sweep of equivalent radius enables the change in the size of particles and a sweep of aspect ratio gives different shapes, thus allowing us to decouple the effects of shape and size. In the interest of brevity, only the profiles of prolate particles with equivalent radii of 1.0 and 1.5 cm are presented. Solid mass fraction is calculated as Y = m / m 0 , where m is particle mass at a particular instant in the pyrolysis process and m0 is the initial particle weight. Fig. 7(a) and (b) depict the solid mass fraction of prolate particles of equivalent radius 1.0 cm and 1.5 cm respectively, and the aspect ratios change from 1/9 to 1. The mass loss profiles of oblate particles of equivalent radius 1.0 cm and 1.5 cm are shown in Supplementary Fig. D1. In all cases, a mild weight loss rate is observed at the beginning, then the solid mass fraction decreases rapidly and the rate of weight loss remains approximately constant over a long time where the majority of the weight loss occurs, finally the solid mass fraction changes progressively slowly and gradually becomes constant. It can also be observed from Fig. 7(a) and (b) that mass loss profiles vary significantly with aspect ratios when the solid volume is fixed and pyrolysis takes less time to complete for the solids with smaller size. Specifically, decreasing aspect ratio makes wood decompose faster and there is also a smaller final char fraction; while increasing particle size causes wood particles to decompose increasingly slowly and leads to a higher final char fraction. Particles of smaller aspect ratio like needles or disks, or particles of small sizes, enable mass transfer over shorter length scales and higher heating rates which ultimately lead to a quick wood devolatilization. Temperature profiles at the center of prolate and oblate wood particles during pyrolysis are shown in Fig. 8 and Supplementary Fig. D2. The center temperature initially increases almost linearly due to heat transfer via conduction. A plateau then appears in the range of 600–700 K, indicating the occurrence of endothermic reactions of wood decomposing to gas, tar and intermediate solid. Further on, it

2.3. Numerical procedures The computational domain is illustrated in Fig. 4 where the nodal points and lines of constant ξ and η are presented. Finite volume method is applied to solve the energy and gas species conservation equations. Backward Euler method is utilized for time integration to obtain a higher numerical stability. Gauss-Seidel method is used for iterations in each time step. Temperature and pressure equations are coupled with each other, but since they cannot be solved together due to the presence of non-linear terms, they are solved alternately and iterated to obtain consistency between pressure and temperature at each time step. Convection term in the Eq. (20) is discretized by upwind scheme to enhance solution stability.

2.4. Simulation cases The furnace temperature was set at 783 K and gas temperature is 720 K. In order to examine the effects of particle shapes and sizes on the pyrolysis of wood particles, two sets of simulations were performed for both prolate and oblate spheroids. 1. Keeping semi-major axis L2 constant (L2: 0.5 cm, 1.0 cm, 1.5 cm, 2.0 cm) while varying aspect ratio ϵ from 1/9 to 9/9 (with steps of 1/ 9) for each L2. 2. Keeping equivalent radius Re constant (Re: 0.5 cm, 1.0 cm, 1.5 cm, 2.0 cm) while varying aspect ratio ϵ from 1/9 to 9/9 (with steps of 1/ 9) for each Re. Here, equivalent radius (Re) is the radius of a sphere with the same volume or mass as the non-spherical particle. Details of the variation of particle shapes in these two simulations can be found in Supplementary materials (Appendix A).

2.5. Experiments Pyrolysis experiments were carried out under atmospheric pressure in a tube furnace as shown in Fig. 5. The tube (length: 558 mm, ID: 106 mm) is made from mullite and the heating zone is 300 mm long. Argon was used to purge the furnace and carry away pyrolysis vapors. The mass flow rate of argon was controlled by a sonic orifice and set at 0.21 g/s. Particle mass was monitored by the electronic balance and temperature was measured by K-type thermocouples. Experimental apparatus is described in detail in [13]. Maple wood particles of various shapes and sizes were used and their geometrical parameters are listed in Table 1. All the wood particles were dried in an oven at 90 °C for 12 h to remove moisture and subsequently stored in an airtight container. Furnace temperature was set at 783 K (510 °C) and the measured gas temperature near the wood particles was 743 ± 20 K (470 ± 20 °C).

3. Results and discussion 3.1. Verification of the model To validate the numerical methodology used in this work, Fig. 6 demonstrates a comparison between the numerical results obtained in the current study and previous work [13] for wood pyrolysis at 783 K. As can be seen, good agreement was obtained for profiles of solid mass fraction, center temperature, and center pressure.

Fig. 5. Schematic of the experimental apparatus.

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prolate and oblate ellipsoids collapse onto one curve. A power-law based curve fit of the data (excluding the experimental data) yielded the following correlation with a notably good R-squared value (0.9839):

Table 1 Shapes and sizes of maple wood particles. Shape

Nominal dimensions (mm)

Spheres: D Cylinders: D×H Cubes: L Cuboids: L×W×H

10, 15, 20 10×20, 15×20, 20×20 10, 15, 20 10×10×5, 15×10×5, 20×10×10, 20×20×15

tcon = 32019 × SVR−1.244

(26)

When the experimental data is superimposed on this curve, it agrees extraordinarily well with the simulation results. Such a correlation function can serve as an immensely powerful tool since it can be used predict the pyrolysis conversion time of wood particles having arbitrary shapes and sizes. However, it is necessary to mention that such a correlation is a function of the furnace conditions, and both the simulated and the experimental data have been obtained for a furnace temperature of 783 K. If the furnace temperature is changed, a different correlation function is to be expected. In general, it can be stated that a power law based correlation between tcon and SVR can be derived regardless of conditions but the coefficient and the exponential factor are functions of temperature, and possibly pressure. However this statement remains subject to validation in future work.

undergoes a sharp increase and exceeds the furnace temperature because of exothermic reactions. Finally, the temperature stabilizes and a thermal equilibrium is attained within the furnace. It should be stated that for all the cases, the mass fraction remains almost constant when the aforementioned sharp peak in temperature is observed. This leads to the inference that the large heat release does not come from chemical reactions requiring high mass transfer rates. Under such high temperatures regimes, amorphous carbon releases energy by undergoing a transition from a high free energy state to a low free energy state, and this may explain the sharp rise in the center temperature [16]. Temperature profiles shown in Fig. 8(a) and (b) reveal that as we decrease ε of a particle or reduce its size, center temperature peak shifts to the left, indicating higher temperature increase rates. This occurrence is consistent with observations in mass loss profiles and expectations of higher heating rates for smaller particles. For particles of the same Re or volume, reducing aspect ratio means an increase of surface area, allowing more heat to be received from the furnace and ultimately resulting in a higher heating rate, thus the particles will be heated faster and decompose quickly.

3.4. Effect of particle shape and size on conversion time An important parameter characterizing a spheroidal particle is ϵ (aspect ratio), which is defined as the ratio of the minor axis and major axis. Fig. 10 and Supplementary Fig. D3 illustrates the relation between ϵ and conversion time for prolate and oblate particles with Re equal 0.5 cm, 1.0 cm, 1.5 cm, and 2.0 cm. As can be observed from Fig. 10, particle shape and size have a strong influence on the pyrolysis conversion time. For a given ϵ, Fig. 10 shows that with the increase of particle size, the conversion time will increase correspondingly. Besides, the conversion time almost doubles when the ϵ changes from 1/9 to 1 for prolate solids of different Re. Fig. 10 also presents the effect of ϵ on conversion time ratio, which is defined as the ratio between the conversion time of a prolate particle and that of an equivalent sphere (a sphere having Re as its radius). For all Re, conversion time ratio is the lowest for ϵ = 1/9 and monotonically increases to 1 as ϵ increases to 1. This can be explained based on the fact that for lower ϵ, the particle is highly dissimilar as compared to its equivalent sphere and as ϵ increases, the particle becomes progressively similar to its equivalent sphere. The limiting case is ϵ=1 when the particle and its equivalent sphere are exactly the same, thus having exactly the same conversion time which yield a conversion time ratio of 1. It is also interesting to notice that prolate ellipsoid of Re of 0.5 cm has the largest conversion time ratio for each ϵ, but the difference (as compared with particles having different Re) grows increasingly less prominent for higher Re, as we can see from the fact that the prolate solids of 1.5 cm and 2.0 cm equivalent radius share an approximately same profile. The change of conversion time with aspect ratio can also be explained by Fig. 9. While maintaining Re (i.e. the volume) of a wood particle constant, increasing

3.3. Effect of particle surface-to-volume ratio on conversion time Wood conversion takes place as a result of a strong interaction between chemistry and transport phenomena at the levels of the single particle and the reaction environment [17], and how long a particle should be exposed to the external heat flux to accomplish pyrolysis procedure is an important parameter to help understand the burnout time of a firebrand. Here, conversion time (tcon ) is defined as the time interval from the initiation of the pyrolysis to the instant when the mass of the wood particle stops changing. To demonstrate the effect of SVR of a particle on the pyrolysis conversion time, Fig. 9 summarizes the results of all the simulation cases for both prolate and oblate ellipsoids which have Re of 0.5 cm, 1.0 cm, 1.5 cm, 2.0 cm and ϵ ranging from 1/9 to 1. As is unmistakably apparent, the conversion time is significantly affected by SVR and particles with larger SVR have smaller conversion time. This is not hard to understand since larger SVR implies the wood particles will be heated up faster, and thus decompose quicker. A remarkable result is the fact that the conversion times for both

Fig. 6. Comparison of results from the current numerical model (continuous line, ϵ=0.999, L2=1.27 cm) with the results obtained by Park et al. [13] (red circles: simulation, blue diamond: experiment) for pyrolysis of a spherical wood particle of 1.27 cm radius. (a): solid mass fraction; (b): center temperature; (c): ratio of center pressure and ambient pressure. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

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Fig. 7. Mass loss profiles for different prolate particles. (a):Re=1.0 cm; (b):Re=1.5 cm.

Fig. 8. Center temperature profiles for different prolate particles. (a):Re=1.0 cm; (b):Re=1.5 cm.

2

Fig. 9. Effect of surface-to-volume ratio on the conversion time of wood pyrolysis.

Fig. 10. Effect of aspect ratio on the conversion time of prolate wood particles. Re=0.5 cm, 1.0 cm, 1.5 cm and 2.0 cm. Line: conversion time; Dashes: conversion time ratio.

3.5. Effect of particle surface-to-volume ratio on product yield

aspect ratio means the reduction of SVR which reaches the minimum when aspect ratio becomes 1, hence causing slower heating of the particle and longer conversion time. Spherical firebrands have the largest aspect ratio but they are also difficult to loft by fires [3]. In Fig. 10, all the spherical wood particles have the largest conversion time, which indicates that if the spherical firebrands are lofted, they probably will have the longest burnout time and hence are more probable to cause spotting ignition.

Pyrolysis products of wood contain a lot of combustible components, thus a study of the relationship between product constitution and shape/size of particles is highly meaningful. Fig. 11 demonstrates the effect of SVR on the yields of three classes of lumped pyrolysis products, namely char, tar, and gas. As is shown, increasing SVR enhances the production of tar but decreases the yield of char. 7

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yield is also studied, and it is found that increasing SVR enhances the production of tar but decreases the yield of char. On the other hand, the yield of gas remains essentially independent of SVR. Acknowledgments This work was supported by The National Science Foundation (Grant number 1339609, 2013). Appendix A. Supplementary data Supplementary data associated with this article can be found in the online version at http://dx.doi.org/10.1016/j.firesaf.2017.03.079. References Fig. 11. Variation of pyrolysis product yield for different surface-to-volume ratio. Data is obtained from the same modeling cases as Fig. 9.

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However, the yield of gas is not significantly affected. Particle size affects the yield of pyrolysis products by changing the temperature gradients and the residence time of volatile vapors inside the hot wood particles. The discussion in the preceding segment concludes that pyrolysis conversion time decreases with increasing SVR and the correlation can be explained by a power-law based function, thus for particles with higher SVR, decomposition is quicker and the time taken for tar to transport through hot porous solids is shorter and the secondary tar decomposition is weakened consequently, resulting in an increase of tar yield. Slow pyrolysis favors char production, therefore lower SVR leads to more char yield by slowing down the heating rate of wood particles. As shown in Fig. 1, gas production takes place via two routes, i.e. (1) direct decomposition of the virgin wood and (2) secondary decomposition of tar. Increasing SVR causes faster heating of wood particles, thus more gas will be produced by route 1 but less via the secondary tar decomposition (as explained above). These two effects neutralize each other and this can be one of the reasons why the yield of gas is not significantly affected by SVR. 4. Conclusion In this work, pyrolysis of wood particles of various shapes and sizes was studied experimentally and numerically. A two-stage model is employed to explain the complex phenomenon of wood pyrolysis. Prolate and oblate ellipsoids were used to simplify the geometrical description of irregular particles of infinite variation in shapes and sizes. Particle shapes and sizes have an obvious influence on the profiles of solid mass fraction and center temperature. Pyrolysis conversion time is found to be affected by SVR, and increasing SVR makes wood decompose faster and decreases conversion time. Based on the numerical results, a power-law based correlation function between pyrolysis conversion time and SVR is derived and shows satisfactory agreement with the experimental data. This correlation can be utilized to predict pyrolysis conversion time of wood particles of arbitrary geometry. Prolate ellipsoid of Re of 0.5 cm has the largest conversion time ratio for each aspect ratio, but the difference becomes less prominent for particles of larger size. The effect of SVR on product

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