Combustion and Flame 156 (2009) 1503–1513

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Combustion and Flame

journal homepage: www.elsevier .com/locate /combustflame

A model for the oxidative pyrolysis of wood

Chris Lautenberger *, Carlos Fernandez-PelloDepartment of Mechanical Engineering, University of California, Berkeley, Berkeley, CA 94720, USA

a r t i c l e i n f o

Article history:Received 26 January 2008Received in revised form 8 April 2009Accepted 8 April 2009Available online 20 May 2009

Keywords:WoodPyrolysisOxidative pyrolysisCharringChar oxidation

0010-2180/$ - see front matter � 2009 Published bydoi:10.1016/j.combustflame.2009.04.001

* Corresponding author. Fax: +1 510 642 1850.E-mail address: clauten@me.berkeley.edu (C. Laute

a b s t r a c t

A generalized pyrolysis model (Gpyro) is applied to simulate the oxidative pyrolysis of white pine slabsirradiated under nonflaming conditions. Conservation equations for gaseous and solid mass, energy, spe-cies, and gaseous momentum (Darcy’s law approximation) inside the decomposing solid are solved tocalculate profiles of temperature, mass fractions, and pressure inside the decomposing wood. The con-densed phase consists of four species, and the gas that fills the voids inside the decomposing solid con-sists of seven species. Four heterogeneous (gas/solid) reactions and two homogeneous (gas/gas) reactionsare included. Diffusion of oxygen from the ambient into the decomposing solid and its effect on localreactions occurring therein is explicitly modeled. A genetic algorithm is used to extract the requiredmaterial properties from experimental data at 25 kW/m2 and 40 kW/m2 irradiance and ambient oxygenconcentrations of 0%, 10.5% and 21% by volume. Optimized model calculations for mass loss rate, surfacetemperature, and in-depth temperatures reproduce well the experimental data, including the experimen-tally observed increase in temperature and mass loss rate with increasing oxygen concentration.

� 2009 Published by Elsevier Inc. on behalf of The Combustion Institute.

1. Introduction

During a compartment fire, combustible solids may be exposedto oxygen concentrations ranging from the ambient value (nor-mally 21%) to near zero when a surface is covered by a diffusionflame. The presence or absence of oxygen can affect solid materials’decomposition kinetics and thermodynamics to different degrees.For example, the thermal stability of polymethylmethacrylate(PMMA) is relatively insensitive to oxygen [1] when comparedwith polypropylene (PP) and polyethylene (PE) which both showa marked decrease in thermal stability as oxygen concentrationis increased [2]. During wood pyrolysis in an inert environment,the volatile formation process is endothermic [3], but in oxidativeenvironments such as air, oxidative reactions occurring near thesurface are exothermic and can lead to visible glowing.

The effect of oxygen concentration on decomposition rates inthermogravimetric experiments has been widely investigated,and models for oxygen-sensitive decomposition have been devel-oped [4,5]. However, there are negligible gradients of temperatureand species concentrations in thermogravimetric experiments, andthe oxygen concentration that the degrading sample ‘‘feels” isapproximated as the ambient value. Consequently, zero-dimen-sional models based on transient ordinary differential equationscan be applied.

In comparison, significant gradients of temperature and speciesare usually present during the pyrolysis of a solid fuel slab (for

Elsevier Inc. on behalf of The Com

nberger).

example, in a Cone Calorimeter experiment). Near the exposed sur-face, oxygen concentrations may approach ambient values; how-ever, there may be little or no oxygen present in-depth. Due tothese spatial variations in temperature and species concentrations,which can only be simulated by solving partial differential equa-tions, modeling oxidative pyrolysis of a solid fuel slab is more com-plex than simulating a zero-dimensional thermogravimetricexperiment.

Despite the potentially significant effect of oxidative pyrolysison a material’s overall reaction to fire, modeling the effect of oxy-gen concentration on the decomposition of a thermally stimulatedsolid fuel slab has been infrequently explored. Reaction kineticsand thermodynamics of polymer oxidative pyrolysis have been di-rectly related to the free-stream oxygen concentration [6,7].

Although many models have been presented for the pyrolysis ofwood slabs, rarely are exothermic oxidative reactions explicitlyconsidered. Shen et al. [8] modeled the pyrolysis of several differ-ent species of wet wood using three parallel reactions. Althoughthey simulated Cone Calorimeter experiments conducted in air,all three reactions were modeled as endothermic, so oxidativepyrolysis was not explicitly considered. Oxidative pyrolysis ofwood has been simulated by including the effect of exothermicreactions in the exposed face boundary condition [9,10], but oxida-tive reactions do not necessarily occur only immediately at the ex-posed surface.

This paper presents a comprehensive model for the oxidativepyrolysis of a wood slab. A novel feature is that conservation equa-tions are solved for each gaseous species inside the decomposingwood. Rather than relating reaction kinetics and thermodynamics

bustion Institute.

Nomenclature

LettersA condensed phase species A (reactant)b exponent in Eq. (15)B condensed phase species B (product)c specific heat capacityE activation energyh enthalpyhc convective heat transfer coefficient_j00 diffusive mass fluxk thermal conductivityK number of heterogeneous reactions or permeability‘ index of homogeneous gas phase reactionL number of homogeneous gas phase reactions_m00 mass flux

M molecular weight or number of condensed phase spe-cies

N number of gaseous speciesn exponent (reaction order, O2 sensitivity, property tem-

perature dependence)p exponent in Eq. (15)P pressureq exponent in Eq. (15)_q00 heat flux_Q 000 heat generation per unit volumeR universal gas constantt timeT temperatureX volume fractiony yieldY mass fractionz distanceZ pre-exponential factor

Greek symbolsc radiative conductivity parameterd thickness or Kronecker deltae emissivity

j radiative absorption coefficientm viscosity (l/q) or reaction stoichiometry coefficient (Eq.

(8))q bulk density in a vacuumw porosity_x000 reaction rate

Subscripts0 initial1 ambientR see Eq. (9)ash ashchar charcop char oxidation productsd destructiondw dry woode externalf formationg gaseousH2O water vapori condensed phase species ij gaseous species jk reaction index‘ homogeneous reaction indexop oxidative pyrolysateO2 oxygenr radiative or references solids–g solid to gassol solidtp thermal pyrolysatev volatilesvol volatilesww wet wood

Superscripts� at time t

1504 C. Lautenberger, C. Fernandez-Pello / Combustion and Flame 156 (2009) 1503–1513

to the free-stream oxygen concentration, they are related to the lo-cal oxygen concentration inside the pore space of the decomposingwood. This is made possible by estimating the diffusion rate of oxy-gen from the ambient into the pores of a decomposing wood slabwhere it may participate in oxidative pyrolysis. Both heteroge-neous (gas/solid) and homogeneous (gas/gas) reactions inside thedecomposing solid are considered. The model’s predictive capabil-ities are assessed by comparing its calculations to experimentaldata for the oxidative pyrolysis of white pine [11,12].

2. Formulation of generalized charring pyrolysis model

The modeling presented in this paper is a specific application ofGpyro, an open-source generalized pyrolysis model developed bythe authors [13–15]. Although this model is described in detailelsewhere [13–15], the main equations are presented here forcompleteness.

2.1. Governing equations

A slab of thermally decomposing wood is modeled as consistingof a condensed phase (wood, char, and ash) coupled to a gas phase(oxygen, nitrogen, water vapor, pyrolysate, etc.). The gas phaseoutside of the decomposing wood slab (the exterior ambient) is

not modeled, so any discussion of the gas phase refers to the gasesinside the pores or voids that form in decomposing wood. The fol-lowing assumptions are invoked:

� One-dimensional behavior.� Each condensed phase species has well-defined properties: bulk

density, specific heat capacity, effective thermal conductivity,emissivity, permeability, porosity ðwi ¼ 1� qi=qs0;iÞ.

� Thermal conductivity and specific heat capacity of each con-densed phase species vary as kðTÞ ¼ k0ðT=TrÞnk andcðTÞ ¼ c0ðT=TrÞnc where Tr is a reference temperature, k0 and c0

are the values of k and c at Tr, and the exponents nk and nc spec-ify whether k and c (respectively) increase or decrease withtemperature.

� Radiation heat transfer across pores is accounted for by adding acontribution to the effective thermal conductivity that increasesas T3, i.e. kr,i = cirT3.

� Averaged properties appearing in the conservation equations(denoted by overbars) are calculated by appropriate mass or vol-ume weightings.

� All gaseous species have equal diffusion coefficients and specificheat capacities (independent of temperature).

� Darcian pressure-driven flow through porous media (Stokesflow).

C. Lautenberger, C. Fernandez-Pello / Combustion and Flame 156 (2009) 1503–1513 1505

� Unit Schmidt number (m = D).� Gas phase and condensed phase are in thermal equilibrium.� No shrinkage or swelling (volume change) occurs.

The conservation equations that result from these assumptionsare given as Eqs. (1)–(7):

Condensed phase mass conservation:

@�q@t¼ � _x000fg ð1Þ

Condensed phase species conservation:

@ �qYið Þ@t

¼ _x000fi � _x000di ð2Þ

Gas phase mass conservation:

@ qg�w

� �@t

þ @_m00

@z¼ _x000fg ð3Þ

Gas phase species conservation:

@ qg�wYj

� �@t

þ@ _m00Yj� �@z

¼ �@_j00j@zþ _x000fj � _x000dj ð4Þ

Condensed phase energy conservation:

@ð�q�hÞ@t

¼ � @_q00

@z� _Q 000s—g þ

XK

k¼1

_Q 000s;k þXM

i¼1

_x000fi � _x000di

� �hi ð5Þ

Gas phase energy conservation:

Tg ¼ T ðthermal equilibriumÞ ð6Þ

Gas phase momentum conservation (assumes Darcian flow):

@

@tP �MRTg

�w

� �¼ @

@z

�Km@P@z

� �þ _x000fg ð7Þ

In Eq. (4), the diffusive mass flux is calculated from Fick’s law as_j00j ¼ ��wqgD @Yj

@z , and in Eq. (5) the conductive heat flux is calculatedfrom Fourier’s law as _q00 ¼ ��k @T

@z. Note that Yi is the mass of con-densed phase species i divided by the total mass of all condensedphase species, and Yj is the mass of gaseous species j divided bythe mass of all gaseous species. Similarly, _x000fi is the formation rateof condensed phase species i, and _x000di is the destruction rate of con-densed phase species i. The analogous gas phase quantities are _x000fjand _x000dj. The temperature-dependent diffusion coefficient D in Eq.(4) is obtained from Chapman–Enskog theory [16]. Eq. (3) is notexplicitly solved, but it is used to form Eq. (7) after substitutingthe ideal gas law ðqg ¼ P �M

RTgÞ and Darcy’s law ð _m00 ¼ � �K

m@P@zÞ.

2.2. Reactions and source terms

There are K heterogeneous (solid/gas) reactions, and individualcondensed phase reactions are indicated by the index k. Heteroge-neous reaction k converts condensed phase species Ak to con-densed phase species Bk plus gases:

1 kg Ak þXN

j¼1

m0j;k kg gas j! mB;k kg Bk þXN

j¼1

m00j;k kg gas j ð8aÞ

mB;k ¼qBk

qAk

ð8bÞ

m0j;k ¼ �ð1� mB;kÞminðys;j;k; 0Þ ð8cÞm00j;k ¼ ð1� mB;kÞmaxðys;j;k;0Þ ð8dÞ

Here, ys,j,k is a user-specified N by K ‘‘species yield matrix” thatestablishes the values of m0j;k and m00j;k. Its entries are positive for the

formation of gaseous species and negative for the consumption ofgaseous species.

The destruction rate of condensed phase species Ak by reaction kis calculated as:

_x000dAk¼

�qYAk

�qYAk

� �R

!nk

�qYAk

� �RZk exp � Ek

RT

� �ðfor nO2 ;k ¼ 0Þ ð9aÞ

_x000dAk¼

�qYAk

�qYAk

� �R

!nk

�qYAk

� �R 1þ YO2

� �nO2 ;k � 1h i

Zk

� exp � Ek

RT

� �ðfor nO2 ;k–0Þ ð9bÞ

�qYið ÞR � �qYið Þjt¼0 þZ t

0

_x000fi sð Þds ð9cÞ

In Eq. (9), the parameter nO2 ;k controls a reaction’s oxygen sensitiv-ity, and the oxygen mass fraction ðYO2 Þ is the local value inside thedecomposing solid determined by solution of Eq. (4).

Combining Eqs. (8) and (9), it can be seen that the volumetricformation rate of condensed phase species Bk by reaction k is:

_x000fBk¼ mB;k _x000dAk

¼qBk

qAk

_x000dAkð10Þ

Similarly, the formation rate of all gases due to consumption of con-densed phase species Ak by reaction k is:

_x000fgk¼ 1� mB;k

� �_x000dAk¼ 1�

qBk

qAk

!_x000dAk

ð11Þ

It also follows from Eqs. (8) and (9) that the formation and destruc-tion rates of gaseous species j by reaction k are:

_x000fj;k ¼ m00j;k _x000dAk¼ _x000fg;k max ys;j;k;0

� �ð12aÞ

_x000dj;k ¼ m0j;k _x000dAk¼ � _x000fg;k min ys;j;k; 0

� �ð12bÞ

The volumetric rate of heat release or absorption to the solidphase due to reaction k is calculated as:

_Q 000s;k ¼ � _x000fBkDHsol;k � _x000fgk

DHvol;k ð13Þ

where DHsol,k and DHvol,k are the heats of reaction associatedrespectively with the formation of condensed phase species andgas phase species by reaction k.

Homogeneous gas phase reactions inside the pores of thedecomposing wood are also considered. Just as there are K con-densed phase reactions and individual condensed phase reactionsare indicated by the index k, there are L homogeneous gas phasereactions and individual reactions are indicated by the index ‘.Each homogeneous gas phase reaction ‘ converts two gas phasereactants (A‘ and B‘) to gaseous products.

The stoichiometry of homogeneous gas phase reactions is ex-pressed on a mass basis:

1 kg A‘ � yg;B‘ ;‘ kg B‘ !XN

j¼1

max yg;j;‘;0� �

kg gas j ð14Þ

In Eq. (14), yg,j,‘ is the user-specified N by L ‘‘homogeneous gaseousspecies yield matrix”, analogous to the gaseous species yield matrix(ys,j,k) discussed earlier with reference to heterogeneous reactions.The physical meaning of the entries in yg,j,‘ is the mass of gaseousspecies j produced by reaction ‘ (for positive entries) or consumedby reaction ‘ (for negative entries) per unit mass of gaseous speciesA‘ consumed. Eq. (14) has been written assuming that yg;A‘ ;‘ ¼ �1,i.e. the reaction is normalized to 1 kg of gaseous species A‘.

The reaction rate of the ‘th homogeneous gas phase reaction isthe destruction rate of gas phase species A‘:

0

3

6

9

12

0 100 200 300 400 500 600

Time (s)

Mas

s lo

ss r

ate

(g/m

2 -s)

0% oxygen

21% oxygen

10.5% oxygen

(a)

0

100

200

300

400

500

600

700

0 100 200 300 400 500 600

Time (s)

Surf

ace

tem

pera

ture

(ºC

)

0% oxygen

21% oxygen

10.5% oxygen

(b)

Fig. 1. Experimentally observed [12] effect of oxygen concentration on the surfacetemperature and mass loss rate of white pine irradiated at 40 kW/m2. (a) Mass lossrate; (b) Temperature

1506 C. Lautenberger, C. Fernandez-Pello / Combustion and Flame 156 (2009) 1503–1513

_x000dA‘¼ ½A‘�p‘ ½B‘�q‘Tb‘Z‘�w exp � E‘

RTg

� �ð15Þ

In Eq. (15), [A] denotes the molar gas phase concentration of gas-eous species A:

A½ � ¼qgYA

MAð16Þ

The creation or destruction of gaseous species j by homogeneousgaseous reaction ‘ is calculated from the homogeneous gaseous spe-cies yield matrix (yg,j,‘) as:

_x000g;j;‘ ¼ _x000dA‘yg;j;‘ ð17Þ

The volumetric rate of heat release to the gas phase by homoge-neous gaseous reaction ‘ is:

_Q 000g;‘ ¼ � _x000dA‘DH‘ ð18Þ

where DH‘ is the heat of reaction associated with homogeneous gasphase reaction ‘.

Since multiple reactions (both heterogeneous and homoge-neous) occur, the source terms appearing in the governing equa-tions must be determined by summing over all reactions. Thetotal formation rate of all gases from the condensed phase is:

_x000fg ¼XK

k¼1

_x000fgkð19Þ

Similarly, the total formation/destruction rates of condensed phasespecies i and gas phase species j are obtained as:

_x000di ¼XK

k¼1

di;Ak_x000dAk

where di;Ak¼

1 if i ¼ Ak

0 if i–Ak

�ð20aÞ

_x000fi ¼XK

k¼1

di;Bk_x000fBk

where di;Bk¼

1 if i ¼ Bk

0 if i–Bk

�ð20bÞ

_x000dj ¼XK

k¼1

_x000dj;k �XL

‘¼1

min _x000g;j;‘; 0� �

ð21aÞ

_x000fj ¼XK

k¼1

_x000fj;k þXL

‘¼1

max _x000g;j;‘;0� �

ð21bÞ

The source term _Q 000s—g appearing in the condensed phase energyconservation equation is the volumetric rate of heat transfer fromthe condensed phase to the gas phase:

_Q 000s—g ¼ _m00cpg@T@z�XL

‘¼1

_Q 000g;‘ ð22Þ

Due to the assumption of thermal equilibrium between the gaseousand the condensed phases (Eq. (6)), any heat release due to homo-geneous gas phase reactions (Eq. (18)) is added to the condensedphase energy conservation equation via _Q 000s—g . In a ‘‘two tempera-ture” model where thermal equilibrium between the condensedphase and the gas phase is not assumed, the heat release due tohomogeneous gas phase reactions (right most term in Eq. (22))would be added to the source term appearing in the conservationof gas phase energy equation.

2.3. Solution methodology

When discretized, the above equations yield a system of cou-pled algebraic equations that are solved numerically. The recom-mendations of Patankar [17] are followed closely. Due to thenonlinearity introduced by the source terms and temperature-dependent thermophysical properties, a fully-implicit formulationis adopted for solution of all equations. The condensed phase

energy conservation equation, gas phase species conservationequation, and gas phase momentum conservation equation aresolved using a computationally efficient tridiagonal matrix algo-rithm (TDMA). The condensed phase mass and condensed phasespecies conservation equations are solved with a customized fullyimplicit solver that uses relaxation to prevent divergence. Sourceterms are split into positive and negative components to ensurephysically realistic results and prevent negative mass fractions ordensities from occurring [17]. Newton iteration is used to extractthe temperature from the weighted enthalpy and the condensedphase species mass fractions. Additional details are given in Ref.[15]. Initial and boundary conditions are presented in Section 3.2.

3. Simulating white pine oxidative pyrolysis

In this section, the charring pyrolysis model presented above ingeneral form is applied to simulate the oxidative pyrolysis of whitepine slabs irradiated under nonflaming conditions. Model calcula-tions are compared with the experimental data of Ohlemiller et al.[11,12] who studied the effects of ambient oxygen concentrationon the nonflaming gasification of irradiated white pine slabs. Inthe experiments, white pine cubes 3.8 cm on edge (initial densityof 380 kg/m3 and moisture content of 5% by mass) were irradiatedat 25 kW/m2 and 40 kW/m2 in oxygen concentrations of 0%, 10.5%,and 21% (normal air) by volume.

Fig. 1 illustrates some of the key measurements that make thisset of experiments particularly interesting from a modeling per-spective. Fig. 1a shows that in the 40 kW/m2 experiments, the massloss rate measured in air is approximately double that measured in

C. Lautenberger, C. Fernandez-Pello / Combustion and Flame 156 (2009) 1503–1513 1507

nitrogen. The effect of oxidative exothermic reactions is also evi-dent in Fig. 1b, where it can be seen that the surface temperatureof the sample tested in air was approximately 150 �C greater thanthat of the sample tested in nitrogen. In addition to the mass lossrate and surface temperature measurements shown in Fig. 1, in-depth thermocouple temperature measurements are also reported[12].

3.1. Modeling approach

The model described in Section 2 is presented in general form,meaning that it could potentially be used to simulate many differ-ent charring materials or experimental configurations. What differ-entiates one material or experiment from another is the material’sthermophysical properties and reaction mechanism (sometimescalled material properties) as well as the initial and boundary con-ditions that describe the experimental conditions. Postulating a ba-sic modeling approach (number of species to track, reactionmechanism, physics to include in the simulation) and then deter-mining the required model input parameters is one of the mostchallenging aspects of pyrolysis modeling. In this work, geneticalgorithm optimization [18,19] is used to extract the required in-put parameters from the experimental data at 25 kW/m2 and40 kW/m2 irradiance.

In the modeling approach applied here, white pine is simulatedas consisting of four condensed phase species, numbered as fol-lows: (1) wet wood, (2) dry wood, (3) char, and (4) ash. The bulkdensity of each species is constant, but thermal conductivitiesand specific heat capacities are temperature dependent. Each spe-cies has a different surface emissivity to account for blackening ofthe wood as it chars. All condensed phase species are opaque (nodiathermancy) and radiation heat transfer across pores is ac-counted for in the char and ash species (which have high porosi-ties). Permeability of all species is held fixed at 10�10 m2 becausescoping simulations indicated that permeability had a negligibleeffect on the calculated mass loss rate and temperature profiles(the experimental measurements against which the model calcula-tions are judged).

In addition to the four condensed phase species, seven gaseousspecies are tracked: (1) thermal pyrolysate, (2) nitrogen, (3) watervapor, (4) oxygen, (5) oxidative pyrolysate, (6) char oxidation prod-ucts, and (7) pyrolysate oxidation products. It is assumed that allspecies have identical specific heat capacities (1100 J/kg K) andequal mass diffusivities. As mentioned earlier, unit Schmidt num-ber (m = D) and thermal equilibrium between the condensed andgaseous phases are assumed.

Four condensed phase (heterogeneous) reactions are consid-ered. Reaction 1 converts wet wood to dry wood and water vapor.Reaction 2 is the anaerobic conversion of dry wood to char plusthermal pyrolysate. Reaction 3 also converts dry wood to char,but consumes oxygen in the process to produce oxidative pyroly-sate. Finally, reaction 4 converts char to ash, consuming oxygenin the process, and produces char oxidation products. This reactionmechanism is summarized as:

wet wood! mdwdry woodþ mH2OH2O ð23:1Þdry wood! mcharcharþ mtpthermal pyrolysate ð23:2Þdry woodþ mO2dwO2 ! mcharcharþ mopoxidative pyrolysate ð23:3Þcharþ mO2charO2 ! mashashþ mcopchar oxidation products ð23:4Þ

The first (drying) reaction is modeled after Atreya [20]. Per Eq. (8),the m coefficients in Eq. (23) are related to bulk density ratiosand the heterogeneous gaseous species yield matrix discussed ear-lier, e.g. mdw = qdw/qww and mop = (1 � qchar/qww)ys,5,3.

Two homogeneous (gas/gas) reactions are also considered. Theyare oxidation of thermal pyrolysate to form pyrolysate oxidation

products, and oxidation of oxidative pyrolysate to form pyrolysateoxidation products:

thermal pyrolysate�yg;4;1O2!yg;7;1 pyrolysate oxidation products

ð24:1Þoxidative pyrolysate�yg;4;2O2!yg;7;2 pyrolysate oxidation products

ð24:2Þ

In Eq. (24), yg,j,‘ is the homogeneous gaseous species yield matrixdiscussed earlier.

The reaction mechanism in Eqs. (23) and (24) differs from theconventional modeling approach wherein char oxidation is viewedas a heterogeneous process occurring at (or near) the surface of adecomposing solid [9,10]. In the present work, oxidative exother-mic reactions, including both heterogeneous reactions (Eqs.(23.3) and (23.4)) and homogeneous gas/gas reactions (Eqs.(24.1) and (24.2)), are permitted to occur in-depth.

Considerable simplifications are inherent in the reaction mech-anisms embodied in Eqs. (23) and (24). Gaseous ‘‘virtual” or ‘‘sur-rogate” species are used to represent complex gas mixtures. Forexample, a single gaseous species called ‘‘char oxidation products”is used to represent the gases that form via heterogeneous charoxidation (Eq. (23.4)). In reality, these gases may include a mixtureof CO, CO2, H2O, unburned hydrocarbons, etc., but since very littleis known about the actual composition of these gases, they aretracked in the model by a single surrogate species. Another approx-imation stems from the simultaneous formation of ‘‘char” by thethermal pyrolysis of dry wood (Eq. (23.2)) and the oxidation ofdry wood (Eq. (23.3)). In reality, the chemical composition of charformed by thermal pyrolysis of wood is not expected to be thesame as that formed by oxidation of the wood. However, the com-plexity of the above mechanism is increased significantly if a sec-ond char species (such as oxidative char) is added.

Similarly, thermal pyrolysate (which forms in the absence ofoxygen from the pyrolysis of dry wood) and oxidative pyrolysate(which forms by the oxidation of dry wood) are chemically distinctmixtures of species that are tracked by a single surrogate species.Thus, it is expected that their combustion products would be dif-ferent. However, it can be seen from Eqs. (24.1) and (24.2) thatthe oxidation of both species produces pyrolysate oxidation prod-ucts. Again, this approximation is invoked to reduce the number ofspecies that must be tracked.

3.2. Initial and boundary conditions representing experimentalconfiguration

Initial and boundary conditions are specified to simulate theexperiments described in Ref. [12]. The initial temperature, pres-sure, gaseous species mass fractions, and condensed phase speciesare initially uniform throughout the thickness of the solid:

ð�qDzÞ�jt¼0 ¼ �q0Dz0 ¼XM

i¼1

ðXi0qi0ÞDz0 ð25Þ

�qYiDzð Þ�jt¼0 ¼ �q0Yi0Dz0 ¼XM

i¼1

ðXi0qi0ÞYi0Dz0 ð26Þ

Y�jt¼0¼ Yj0 ð27Þ

T�jt¼0 ¼ T0 ) �h�t¼0 ¼

XM

i¼1

Yi0hi0ðT0Þð Þ ð28Þ

P�jt¼0 ¼ P1 ð29ÞIn Eqs. (25) and (26), Xi0 (and Yi0) are 1.0 for wet wood and 0.0 for allother condensed phase species. T0 in Eq. (28) is 300 K. The initialgaseous mass fractions (Eq. (27)) are 1.0 for thermal pyrolysateand 0.0 for all other gaseous species. The ambient pressure (Eq.(29)) is 101,300 Pa.

Table 1Condensed phase parameters for white pine simulations.

i Name k0 (W/m K) nk (–) q0 (kg/m3) nq (–) c0 (J/kg K) nc (–) e (–) j (m�1) c (m) K (m2) qs0 (kg/m3)

1 wet wood 0.186 0.185 380 0 1764 0.406 0.757 1 0 1 � 10�10 3902 dry wood 0.176 0.594 360 0 1664 0.660 0.759 1 0 1 � 10�10 3903 char 0.065 0.435 73.0 0 1219 0.283 0.957 1 3.3 � 10�3 1 � 10�10 3904 ash 0.058 0.353 5.7 0 1244 0.315 0.955 1 6.4 � 10�3 1 � 10�10 390

Table 2Reaction parameters for white pine simulations.

k From To v (–) DHsol (J/kg) DHvol (J/kg) Z (s�1) E (kJ/mol) n (–) nO2 (–)

1 wet wood dry wood 1 0 2.41 � 106 4.29 � 103 43.8 0.99 02 dry wood char 1 0 5.33 � 105 3.29 � 109 135.0 4.78 03 dry wood char 1 0 �9.94 � 105 6.00 � 109 124.2 4.99 1.164 char ash 1 0 �3.77 � 107 9.79 � 1013 192.4 1.86 1.04

Table 3Gaseous yields for white pine simulations. Only nonzero yields are shown.

j k

1 2 3 4

1 (thermal pyrolysate) 12 (nitrogen)3 (water vapor) 14 (oxygen) �0.1 �2.05 (oxidative pyrolysate) 1.16 (char oxidation products) 3.07 (pyrolysate oxidation products)

1508 C. Lautenberger, C. Fernandez-Pello / Combustion and Flame 156 (2009) 1503–1513

No boundary conditions are needed for the condensed phasespecies or mass conservation equations because the condensedphase species and mass conservation equations in each cell reduceto first order transient ordinary differential equations with sourceterms attributed to species formation and destruction, i.e. there areno convective or diffusive terms in Eqs. (1) and (2).

The boundary conditions on the condensed phase energy equa-tion are:

��k@T@z

z¼0¼ �e _q00e � hcðTjz¼0 � T1Þ � �er T4

z¼0� T4

1

� �ð30aÞ

� �k@T@z

z¼d

¼ hcd Tjz¼d � T1� �

ð30bÞ

In Eq. (30), _q00e is the externally-applied radiative heat flux in theexperiment being simulated, hcd is 10 W/m2 K, T1 is 300 K, and hc

is the front-face convective heat transfer coefficient. The effect ofblowing on the latter is estimated with a Couette approximation[21]:

hc ¼_m000cpg

exp _m000cpg=hc;nb

� �� 1

ð30cÞ

Here, hc,nb (the front face heat transfer coefficient with no blowing)is 10 W/m2 K, _m000 is the calculated mass flux of gases at the exposedsurface (z = 0), and cpg is 1100 J/kg K.

The boundary conditions on the pressure evolution equation aresuch that the pressure at the front face is set to the ambient value.

Table 4Homogeneous gaseous reaction parameters for white pine simulations.

l Reactant 1 Reactant 2 p (–) q (–)

1 thermal pyrolysate oxygen 1.0 1.02 oxidative pyrolysate oxygen 1.0 1.0

The pressure gradient at the back face is set to give a zero mass flux(impermeable approximation) per Darcy’s law:

Pjz¼0 ¼ P1 ð31aÞ@P@z

z¼d

¼ 0 ð31bÞ

Eq. (4) (gas phase species conservation) requires two boundary con-ditions for each gaseous species j. The back face (z = d) is assumedimpermeable so there is no flow of volatiles across the back face:

@Yj

@z

z¼d

¼ 0 ð32aÞ

The diffusive mass flux of gaseous species into or out of the decom-posing solid at the front face is approximated as:

��wqgD@Yj

@z

z¼0� hc

cpgY1j � Yj

z¼0

� �ð32bÞ

where Y1j is the ambient mass fraction of gaseous species j.

3.3. Simulation of nitrogen experiments

Even with the approximations noted in Section 3.1, almost 50model input parameters (kinetics coefficients, thermophysicalproperties, etc.) must be determined. Consequently, model inputparameters are estimated from the experimental data in two sep-arate steps. First, genetic algorithm optimization [18,19] is used inconjunction with the experimental data obtained under nitrogen toestimate values of input parameters that do not involve oxygen(oxidative reactions and species formed by oxidative reactionsare not considered). Next, these parameters are held constantwhile the remaining parameters are determined by genetic algo-rithm optimization from the experimental data obtained in oxida-tive atmospheres. The model input parameters determined bygenetic algorithm optimization (used in all calculations reportedin this paper) are listed in Tables 1–5.

In the first stage of the model input parameter estimation pro-cess, only heterogeneous reactions that do not involve oxygen (Eqs.(23.1) and (23.2)) affect the calculations. Ash is not formed in thesimulations since it is produced only through an oxidative reaction

b (–) Z(kg m2/(mole2s)) E (kJ/mol) DH (J/kg)

0.0 2.01 � 109 162.7 �1.88 � 107

0.0 2.09 � 109 161.3 �1.73 � 107

Table 5Homogeneous gaseous yields for white pine simulations. Only nonzero yields areshown.

j l

1 2

1 (thermal pyrolysate) �1.02 (nitrogen)3 (water vapor)4 (oxygen) �1.6 �1.55 (oxidative pyrolysate) �1.06 (char oxidation products)7 (pyrolysate oxidation products) 2.6 2.5

0

2

4

6

8

10

0 120 240 360 480 600

Time (s)

Mas

s lo

ss r

ate

(g/m

2 -s)

Exp.Pred.

Fig. 3. Comparison of modeled mass loss rate and experimental data for pyrolysisof white pine at 25 kW/m2 irradiance in nitrogen.

C. Lautenberger, C. Fernandez-Pello / Combustion and Flame 156 (2009) 1503–1513 1509

(Eq. (23.4)). Similarly, the homogeneous gas phase reactions bothconsume oxygen, so they do not occur in the nitrogen simulations.Any model input parameters associated with these reactions (orthe species they produce) have no effect on the nitrogen simula-tions and can be excluded from the first step of the property esti-mation process.

Fig. 2 compares the measured and calculated temperatures andmass loss rate under nitrogen at 40 kW/m2. The calculated surfacetemperature is slightly higher than the experimental data, but thecalculated temperatures at depths of 5 mm and 10 mm match theexperimental data well. The mass loss rate is also well predicted,except that the peak mass loss rate is slightly under-predictedand occurs 30 s earlier than in the experiment.

Fig. 3 compares the measured and modeled mass loss rate at25 kW/m2 irradiance under nitrogen. It can be seen that the shapes

0

100

200

300

400

500

600

700

0 120 240 360 480 600

Time (s)

Tem

pera

ture

(°C

)

Exp. - 0 mmPred. - 0 mmExp. - 5 mmPred. - 5 mmExp. - 10 mmPred. - 10 mm

10 mm

0 mm

5 mm

(a)

0

3

6

9

12

Time (s)

Mas

s lo

ss r

ate

(g/m

2 -s)

Exp.Pred.

(b)

0 120 240 360 480 600

Fig. 2. Comparison of model calculations using optimized input parameters andexperimental data for pyrolysis of white pine at 40 kW/m2 irradiance in nitrogen.(a) Temperature; (b) mass loss rate.

of the curves are qualitatively similar, but the calculated peak massloss rate is overpredicted and occurs approximately 2 min earlierin the model than in the experiment. Discrepancies between themodel calculations and the experimental data at this lower heatflux level may be attributed to the simplified reaction mechanismand decomposition kinetics used here. At lower heat flux levels,temperatures are lower and decomposition kinetics play a moresignificant role than at higher heat flux levels where mass loss

0

100

200

300

400

500

600

700

0 120 240 360 480 600

Time (s)

Tem

pera

ture

(°C

)

Exp. - 0 mmPred. - 0 mmExp. - 5 mmPred. - 5 mmExp. - 10 mmPred. - 10 mm

10 mm

0 mm

5 mm

(a)

0

100

200

300

400

500

600

700

0 120 240 360 480 600

Time (s)

Tem

pera

ture

(°C

)

Exp. - 0 mmPred. - 0 mmExp. - 5 mmPred. - 5 mmExp. - 10 mmPred. - 10 mm

10 mm

0 mm

5 mm

(b)

Fig. 4. Comparison of experimentally measured [12] and modeled temperatures atseveral depths below the surface of white pine irradiated at 40 kW/m2 in oxidativeatmospheres. (a) 10.5% O2 atmosphere; (b) 21% O2 atmosphere.

0

3

6

9

12

0 120 240 360 480 600

Time (s)

Mas

s lo

ss r

ate

(g/m

2 -s)

Exp.Pred.

(a)

0

3

6

9

12

0 120 240 360 480 600

Time (s)

Mas

s lo

ss r

ate

(g/m

2 -s)

Exp.Pred.

(b)

Fig. 5. Comparison of experimentally measured [12] and modeled mass loss rate ofwhite pine at 40 kW/m2 irradiance in oxidative atmospheres. (a) 10.5% O2

atmosphere; (b) 21% O2 atmosphere.

0

2

4

6

8

10

0 120 240 360 480 600

Time (s)

Mas

s lo

ss r

ate

(g/m

2 -s)

Exp.Pred.

(a)

1510 C. Lautenberger, C. Fernandez-Pello / Combustion and Flame 156 (2009) 1503–1513

rates are controlled primarily by a heat balance. Thus, slight inac-curacies in the decomposition kinetics may lead to larger discrep-ancies between the model calculations and experimental data atlower heat flux levels.

3.4. Simulation of oxidative experiments

The second stage of the property estimation process involvesoxidative atmospheres (10.5% O2 and 21% O2 by volume). Model in-

0

100

200

300

400

500

600

0 120 240 360 480 600

Time (s)

Tem

pera

ture

(°C

)

0 mm - Exp.

0 mm - Model

5 mm - Exp.

5 mm - Model

10 mm - Exp.

10 mm - Model

15 mm - Exp.15 mm - Model

Fig. 6. Comparison of experimentally measured [12] and modeled temperatures atseveral depths below the surface of white pine irradiated at 25 kW/m2 in 10.5% O2

atmosphere.

put parameters determined from the nitrogen experiments areheld constant, and genetic algorithm optimization is used to ex-tract additional parameters from the oxidative experimental data.

A comparison of the experimental measurements [12] and theoptimized model calculations in oxidative environments at40 kW/m2 irradiance is given in Figs. 4 and 5. Fig. 4 compares themodeled temperatures with experimental data at oxygen concen-trations of 10.5% and 21%. The increase in temperature with ambi-ent oxygen concentration is captured because the combinedexothermicity of the heterogeneous and homogeneous reactionscauses the temperature to increase as the ambient oxygen concen-tration is increased.

Fig. 5 compares the calculated mass loss rate with analogousexperimental data (40 kW/m2 irradiance, 10.5% and 21% O2). Qual-itatively, the calculated shape of the mass loss rate curve is similarto the experimental data. Quantitatively, calculated mass loss ratesare under-predicted after the initial peak. This may be due to anunder-prediction of the char oxidation rate, or perhaps the onsetof another reaction that is not included in the simplified reactionmechanism (Eq. (23)).

Figs. 6 and 7 compare model calculations and experimental data[12] under oxidative conditions at 25 kW/m2 irradiance. It can beseen from Fig. 6 that the temperature calculated at four differentlocations in the decomposing pine slab is usually within 50 �Cof the experimental data for the duration of the experiment. Whenone considers the uncertainty in the experimental measurements,this is considered a good fit.

0

2

4

6

8

10

0 120 240 360 480 600

Time (s)

Mas

s lo

ss r

ate

(g/m

2 -s)

Exp.Pred.

(b)

Fig. 7. Comparison of experimentally measured [12] and modeled mass loss rate ofwhite pine at 25 kW/m2 irradiance in oxidative atmospheres. (a) 10.5% O2

atmosphere; (b) 21% O2 atmosphere.

0.00

0.10

0.20

0.30

0.40

0 100 200 300 400

Temperature (°C)

The

rmal

con

duct

ivit

y (W

/m-K

)

Dry wood - present workDry wood - literature (generic)Dry wood - literature (white pine)Wet wood - present workWet wood - literature (generic)

(a)

0.2

0.4

0.6

0.8

1.0

The

rmal

con

duct

ivit

y (W

/m-K

) Char - present work

Char - literature (generic)

Char - literature (white pine)

(b)

C. Lautenberger, C. Fernandez-Pello / Combustion and Flame 156 (2009) 1503–1513 1511

A comparison of the measured and modeled mass loss rates(25 kW/m2, 10.5% O2, and 21% O2) is shown in Fig. 7. The generalshapes of the curves are well represented by the model, but thereare some quantitative differences. Again, when one considers theexperimental uncertainty and the complexity of the problem, thisis considered a good fit.

3.5. Comparison of optimized thermal properties with literature data

In the present study, temperature-dependent specific heatcapacities and thermal conductivities are used for each condensedphase species. Figs. 8 and 9 compare the optimized thermalproperties determined by genetic algorithm optimization in thepresent work with the data of Yang et al. [22] as well as thermalproperty correlations for generic wood compiled in Ref. [13]. InFigs. 8 and 9, generic wood property correlations reported in Ref.[13] are denoted ‘‘literature (generic)” and values used by Yanget al. [22] to simulate the pyrolysis of white pine are denoted ‘‘lit-erature (white pine)”.

In Fig. 8a, the specific heat capacity of wet wood and dry woodare compared with the available literature data. It can be seen thatthe specific heat capacity of dry wood as determined by the geneticalgorithm falls between the available literature data. The specificheat capacity of wet wood used in these calculations is close tothe literature data. Fig. 8b shows the specific heat capacity of charas optimized by the genetic algorithm falls between the availableliterature data.

Fig. 9 gives similar plots for thermal conductivity. It can be seenfrom Fig. 9a that the thermal conductivity of both wet wood and

0

1000

2000

3000

4000

5000

0 100 200 300 400

Temperature (°C)

Spec

ific

hea

t ca

paci

ty (

J/kg

-K) Dry wood - present work

Dry wood - literature (generic)

Dry wood - literature (white pine)

Wet wood - present work

Wet wood (literature)

(a)

0

500

1000

1500

2000

2500

3000

3500

0 100 200 300 400 500 600

Temperature (°C)

Spec

ific

hea

t ca

paci

ty (

J/kg

-K)

Char - present workChar - literature (generic)Char - literature (white pine)

(b)

Fig. 8. Comparison of temperature-dependent specific heat capacity determined bygenetic algorithm optimization with literature data. (a) Virgin wood; (b) Char.

0.00 100 200 300 400 500 600

Temperature (°C)

Fig. 9. Comparison of temperature-dependent thermal conductivity determined bygenetic algorithm optimization with literature data. (a) Virgin wood; (b) Char.

dry wood optimized by the genetic algorithm is approximately afactor of two higher than the generic wood literature data, butmatches the white pine literature data within 20%. Interestingly,Fig. 9a shows the opposite trend for wood char. That is, the thermalconductivity optimized by the genetic algorithm matches the gen-eric wood literature data, but is only 20–50% that of the white pineliterature data.

4. Discussion

The simulations described above include both heterogeneousand homogeneous oxidative reactions, but char oxidation is con-ventionally viewed as a heterogeneous process. Consequently, itis not clear whether the homogeneous reactions included in thepresent simulations are realistic. The effect of these homogeneousreactions on the simulation results was assessed by running calcu-lations with only heterogeneous reactions, only homogeneousreactions, both types of reactions, and neither type of reaction.The results are shown in Fig. 10. Comparing the surface tempera-ture in Fig. 10a for the case where both types of reactions occurwith the case where only heterogeneous reactions occur, it canbe seen that the homogeneous reactions start to have an effect asthe surface temperature approaches 600 �C.

In order to determine whether it is feasible that homogeneousgas phase reactions could start to have an appreciable effect attemperatures near 600 �C, the characteristic time scale of homoge-neous gas phase combustion reactions must be compared with thegas phase residence time in the hot char layer. If these time scalesare of the same order of magnitude, it is conceivable that

0

100

200

300

400

500

600

700

0 100 200 300 400 500 600

Time (s)

Surf

ace

tem

pera

ture

(°C

)

neither

both

homogeneous only

heterogeneous only

(a)

0

3

6

9

12

0 100 200 300 400 500 600

Time (s)

Mas

s lo

ss r

ate

(g/m

2 -s)

neither

both

homogeneous only

heterogeneous only

(b)

Fig. 10. Calculated effect of heterogeneous and homogeneous reactions on oxida-tive pyrolysis of white pine at 40 kW/m2 irradiance and 21% O2. Text in figuresindicates reactions included in simulations. (a) Surface temperature; (b) mass lossrate.

0

100

200

300

400

500

600

700

0 100 200 300 400 500 600

Time (s)

Surf

ace

tem

pera

ture

(°C

)

blowing

no blowing(a)

0

3

6

9

12

15

18

Time (s)

Mas

s lo

ss r

ate

(g/m

2 -s)

blowing

no blowing

(b)

0 100 200 300 400 500 600

Fig. 11. Calculated effect of blowing on white pine oxidative pyrolysis at 40 kW/m2

irradiance and 21% O2. (a) Surface temperature; (b) mass loss rate.

1512 C. Lautenberger, C. Fernandez-Pello / Combustion and Flame 156 (2009) 1503–1513

homogeneous gas phase combustion reactions could occur as com-bustible volatiles generated in-depth flow through the hot charlayer and react with oxygen that is diffusing inward from the ambi-ent. The order of magnitude of the volatiles’ velocity near the sur-face is 10 mm/s. Consequently, the residence time in the charlayer, assuming it has a thickness of 5 mm, is approximately0.5 s. Although low-temperature gas phase combustion chemistryis not well understood, experimental data [23] suggests the spon-taneous ignition delay time of a lean propane/air premixture at670 �C (the lowest temperature at which data were reported) isapproximately 0.2 s. Thus, at temperatures above 600 �C, the gasphase combustion time scale could approach the residence timein a heated char layer. Consequently, it seems plausible that in oxi-dative environments, homogenous gas phase reactions could occurinside the pores or voids of a thermally stimulated solid and con-tribute to the overall heat release. However, no firm conclusionscan yet be drawn, and future work in this area is encouraged tohelp unravel the physical mechanism of oxidative pyrolysis, in par-ticular whether or not homogeneous gas phase reactions occur.

The present simulations include a simple Couette model forblowing (see Eq. (30c)) that, while probably better than notaccounting for blowing at all, may not accurately represent oxygendiffusion through the natural convection boundary layer in theexperiments. The calculated surface temperature and mass lossrate for the 21% O2 case are shown in Fig. 11 with and withoutblowing. It can be seen that the surface temperature is higherwhen blowing is disabled due to greater diffusion of oxygen tothe surface. Blowing also has an appreciable effect on the calcu-

lated peak mass loss rate. Boonmee and Quintiere [9] used the clas-sical stagnant layer model (sometimes called the Stefan problem)to account for the effect of blowing through a Spalding mass trans-fer number (B number).

5. Concluding remarks

A model for the oxidative pyrolysis of wood is presented anddemonstrated by simulating the nonflaming gasification of whitepine slabs irradiated at 25 kW/m2 and 40 kW/m2 in atmosphereshaving 0% O2, 10.5% O2, and 21% O2 by volume (balance nitrogen).Diffusion of gaseous oxygen from the ambient into the porous charlayer and its effect on oxidative reactions occurring within thedecomposing solid is explicitly modeled. Both heterogeneous(gas/solid) and homogeneous (gas/gas) oxidative reactions are con-sidered. A novel feature of the model is that it includes the capabil-ity to automatically adjust to changes in environmental conditions(in particular, reduction in the oxygen concentration that a surfacefeels due to blowing, immersion in an oxygen-vitiated upper layer,or the presence of a nearby diffusion flame). Model calculations arecompared to experimental oxidative pyrolysis data [12] for massloss rate, surface temperature, and in-depth temperature with gen-erally good agreement.

Due to the relatively large number of species and reactions in-cluded in the modeling approach (four condensed phase species,seven gas phase species, four heterogeneous reactions, and twohomogeneous reactions) almost 50 model input parameters (ther-mal properties, reaction coefficients, etc.) must be determined. Ge-netic algorithm optimization [18,19] is used to estimate therequired input parameters from available experimental data. Tem-

C. Lautenberger, C. Fernandez-Pello / Combustion and Flame 156 (2009) 1503–1513 1513

perature-dependent specific heat capacities and thermal conduc-tivity estimated by genetic algorithm optimization are comparedto literature data (generic wood properties [13] and propertiesfrom an earlier pyrolysis modeling study of white pine [22]). Itwas found that the specific heat capacity for wet wood, dry wood,and char falls between literature values for generic wood and spe-cific data for white pine. However, the optimized values of thermalconductivity for wet wood and dry wood are slightly higher thananalogous literature data. The thermal conductivity of char is closeto one literature value, but it is considerably lower than anotherliterature value. Although no firm conclusions can be drawn, theauthors believe that the optimized model input parameters deter-mined by genetic algorithm can be treated as material properties,meaning that they should be independent of environmental condi-tions (applied heat flux, oxygen concentration, etc.).

Acknowledgments

This work was supported by the National Science Foundationunder Grant 0730556 and the NASA Graduate Student ResearcherProgram under Grant NNC-04HA08H.

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