Fuel 89 (2010) 1156–1168

Contents lists available at ScienceDirect

Fuel

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

Effects of particle shape and size on devolatilization of biomass particle

Hong Lu, Elvin Ip, Justin Scott, Paul Foster, Mark Vickers, Larry L. Baxter *

Chemical Engineering Department, Brigham Yong University, 350 CB, Provo, UT 84602, United States

a r t i c l e i n f o

Article history:Received 5 January 2008Received in revised form 3 October 2008Accepted 7 October 2008Available online 7 November 2008

Keywords:BiomassPyrolysisReactivityShapeSize

0016-2361/$ - see front matter � 2008 Elsevier Ltd. Adoi:10.1016/j.fuel.2008.10.023

* Corresponding author. Tel.: +1 801 422 8616; faxE-mail addresses: larry_baxter@byu.edu, luhonglew

a b s t r a c t

Experimental and theoretical investigations indicate particle shape and size influence biomass particledynamics, including drying, heating rate, and reaction rate. Experimental samples include disc/flake-like,cylindrical/cylinder-like, and equant (nearly spherical) shapes of wood particles with similar particlemasses and volumes but different surface areas. Small samples (320 lm) passed through a laboratoryentrained-flow reactor in a nitrogen atmosphere and a maximum reactor wall temperature of 1600 K.Large samples were suspended in the center of a single-particle reactor. Experimental data indicate thatequant particles react more slowly than the other shapes, with the difference becoming more significantas particle mass or aspect ratio increases and reaching a factor of two or more for particles with sizes over10 mm. A one-dimensional, time-dependent particle model simulates the rapid pyrolysis process of par-ticles with different shapes. The model characterizes particles in three basic shapes (sphere, cylinder, andflat plate). With the particle geometric information (particle aspect ratio, volume, and surface area)included, this model simulates the devolatilization process of biomass particles of any shape. Model sim-ulations of the three shapes show satisfactory agreement with the experimental data. Model predictionsshow that both particle shape and size affect the product yield distribution. Near-spherical particles exhi-bit lower volatile and higher tar yields relative to aspherical particles with the same mass under similarconditions. Volatile yields decrease with increasing particle size for particles of all shapes. Assumingspherical or isothermal conditions for biomass particles leads to large errors at most biomass particlesizes of practical interest.

� 2008 Elsevier Ltd. All rights reserved.

1. Introduction

At least two compelling forces drive global interest in renew-able energy supplies: (1) increasing concern about environmentalimpacts associated with fossil fuels and nuclear energy; and (2)increasing anxiety regarding the security and longevity of fossilfuel resources. One potential strategy that addresses both concernsis the supplementing traditional, dominantly fossil, fuels withrenewable biomass fuels, since biomass fuels come from indige-nous sources and can be essentially CO2-neutral if derived fromsustainable cultivation practices. Thermal conversion (combustionand gasification) represents the most common commercial utiliza-tion of biomass. Black liquor (which is usually presumably roundbefore it is heated up and starts to swell during drying and devol-atilization, and observed to be aspherical in most cases during/after swelling) and hog fuel used at pulp and paper mills representby far the largest contributions to non-hydro renewable energy inthe US and many other countries. Both current and future technol-ogies employed in the pulp and paper industry benefit from more

ll rights reserved.

: +1 801 422 0151.@hotmail.com (L.L. Baxter).

accurate understanding of the processes occurring in the conver-sion systems. This investigation focuses on issues common to mostconversion systems – particle conversion characteristics.

Biomass particles commonly have more irregular shapes andmuch larger sizes than pulverized coal or other entrained-flow,low-grade fuels, with typical aspect ratios between 2 and 15. Lar-ger particle sizes establish the potential for large internal temper-ature and composition gradients that complicate combustionmodels. At present, particle models used in computational fluiddynamics (CFD) codes and elsewhere generally assume spherical,isothermal biomass particles [1,2]. Furthermore, various particleshapes result in different particle exterior surface area-to-volumeratios, which are essential to heat and mass transfer and further af-fect the devolatilization and oxidation rates. Spheres represent anextreme case with lowest surface area-to-volume ratios of anyshape and therefore are especially inappropriate for modeling bio-mass particles (though very common).

Simplified models were developed to simulate wood particledrying, pyrolysis, and combustion process [3–5]. Peters and Bruch[4] modeled the drying and pyrolysis of wood particles and com-pared with experimental data. They also applied the model to apacked bed and satisfactory results were obtained. Thunmanet al. [3] divided the wood particle into four layers: moist wood,

Nomenclature

Ai pre-exponential factor, s�1

AR aspect ratio, length/diameter for cylinder; diameter/thickness for plate

Cp heat capacity, J kg�1 K�1

dpore pore diameter, mDeff effective diffusivity, m2 s�1

DAB molecular diffusivity, m2 s�1

DK Knudson diffusivity, m2 s�1

Ei activation energy, J mol�1

hf heat transfer coefficient, W m�1 K�1

H enthalpy, J kg�1

k thermal conductivity, W m�1 K�1

g permeability, m2

Ki rate constant, s�1

M molecular weight, kg kmol�1

MW gas average molecular weight, kg kmol�1

n shape factorNu Nusselt numberP pressure, PaPr Prandtl numberr radius coordinate, mRe Reynolds numberRg universal gas constant, J mol-1 K�1

Rp particle radius, mRSA surface area ratiot time, sSA surface area, m2

Si source termT temperature, Ku gas velocity, m s�1

Y mass fraction

Greek symbolse porosityl viscosity, Pasq density, kg m�3

r Boltzman constant, W m�2 K�4

x emissivity�DH heat of reaction, J kg�1

Subscripts0 initial value or reference stateB biomass1, . . ., 5 reaction #C charcon conductivityg gas phaseG light gasI inert gasM moisturerad radiationV water vaporT tarw wall

H. Lu et al. / Fuel 89 (2010) 1156–1168 1157

dry wood, char residue, and ash. A shape factor, which is the area ofthe control surface at particle radius, was used to describe differentshapes. Saastamoinen [5] similarly included three zones in thewood particle during drying and pyrolysis: char, dry biomass,and wet biomass. This model can also simulate particles with threeshapes: sphere, cylinder, and plate. No experimental data andmodeling results for non-spherical particles were reported in thesepapers even their models are capable of simulating non-sphericalparticles.

Other particle shapes have also been considered. Jalan andSrivastava [6] studied pyrolysis of a single cylindrical biomassparticle, and particle size and heating rate effects were investi-gated. In Horbaj’s model [7] and Liliddahl’s model [8], a particlegeometric factor was introduced to account for the particle shape,which can deal with a prism (or slab), a cylinder (or rod), and asphere.

In 2000, Janse and Westerhout [9] simulated the flash pyrolysisof a single wood particle. To investigate the influence of particleshape, simulations have been carried out with spherical, cylindricaland flat particle shapes [9]. Results show that spherical particlesreact most quickly compared to other particle shapes if the charac-teristic size is taken as the minimum particle dimension. The high-er surface area-to-volume ratio of spherical particles on this basisexplains this observation; flat particles react most slowly. At smallparticle diameters (typically less than 200 lm), the rate of reactionbecomes dominant and the different particle shapes exhibit nearlyequal conversion times. Flat particles seem to yield less gas andmore char. This research also showed that an increase in particlediameter (or conversion time) caused no change in bio-oil yield,a slight decrease in gas yield and slight increase in char yield. Thismight be due to the low reactor temperature (surface temperature823 K) they used to simulate this process.

A substantial experimental and modeling literature for biomassparticle pyrolysis processes exists, with varying kinetic mecha-

nisms and related parameters. A one-step global model, which isdescribed by one global reaction suffices for relatively simpleapplications [10–14]. The drawback of the one-step model is thatit cannot predict the variation of total mass or individual productyield distributions with temperature and heating conditions. Typ-ical wood applications use one- or two-stage multiple reactionmodels [15–19]. Two-step models include a primary stage, duringwhich wood thermally decomposes to produce light gases, tars,and chars, and a secondary stage, during which tars undergo addi-tional cracking to produce gases. Much more sophisticated devola-tilization models exist [20,21], including some under developmentby this research group [22], and these will be incorporated into thisanalysis in the future, but the present simple models are adequateto illustrate the impacts of shape and size on particle conversionand to develop accurate models of the process.

Intra-particle heat and mass transfer effects must be accountedfor to accurately predict the devolatilization rate of millimeter-sized particles and consequently heat release in conversion equip-ment [23]. Biomass particle models usually include mass, energy,and momentum transport equations [6,8,9,24–34]. Few of theseparticle models simulate aspherical shapes but several are suitablefor incorporation into CFD codes. The paucity of experimental datasuitable for validating these model predictions compromises thepotential contributions of such models to engineering or scientificinvestigations.

This investigation summarizes experimental drying, heating,and conversion rates for wood particles (sawdust) of three shapesin an entrained-flow reactor and large poplar particles in a single-particle reactor, together with a model that satisfactorily predictsthese data. The particle model simulates devolatilization of bio-mass particle of any shape. The model demonstrates overall im-pacts of aspherical shapes and large size on particle dynamicsunder practically relevant conditions, including a wider range ofconditions than is available from experimental data.

Tray 1 Tray 2 Tray 3 Tray 4 Air Inlet

Air distributor

Sample Feeding System

Fig. 2. Tunnel separator schematic diagram.

1158 H. Lu et al. / Fuel 89 (2010) 1156–1168

2. Experimental

2.1. Fuel sample preparation

Spherical, cylindrical, and flat/flake wood particles with similarvolumes/masses but different shapes form the basis of this investi-gation. Samples are classified into two groups: hardwood sawdustparticles (6300 lm) and poplar dowel particles (P2 mm), basedon size range. Particle images are shown in Fig. 1. The first threeimages are for hardwood sawdust particles with flake-like, cylin-der-like, and near-spherical shapes. The last image is for poplarparticles with different shapes and sizes.

Sieves and aerodynamic classifiers separate the small sawdustparticles into groups with similar characteristics. Four steps wereinvolved in the sample preparation procedures:

� Step 1. Separation with sieve shaker: This step preliminarily sep-arates the sample by size. A series of standard sieves were put ina sieve shaker in order from 25 to 80 mesh, with the 80 meshsieve at the bottom of the stack. The top sieve is filled with saw-dust particles and the sieve shaker operates for 40–45 mins.Samples left in each sieve are collected in sample bags,respectively.

� Step 2. Aerodynamic classification: A tunnel separator was builtto aerodynamically classify sawdust samples by shape and den-sity, as shown in Fig. 2. Compressed air is introduced from theair inlet at the bottom of the air distribution pipe. Sawdust par-ticles are fed from the top of the tunnel. Drag forces and gravitydetermine the trajectory of each particle. Less dense and fuzzyparticles end up in tray four or out the end of the tunnel. Traystwo and three are normally mixed together and used to getflakes and cylinders, while tray one is used to primarily get cubi-cal/spherical particles. Samples collected in these four trays mayhave to run through the tunnel separator more than once.

� Step 3. Shape separation by sieve: In this step, samples collectedwith the tunnel separator in tray one, tray two, and tray threeare separated into near-spherical, flake-like, and cylinder-likeparticles. While shaking the sieve with samples in, particles withsmaller aspect ratios fall through the sieve before the largerones. Based on the residence time difference, particles with dif-ferent shapes and aspect ratios can be separated. Usually near-spherical particles pass through the sieve most quickly, followedby flake-like and cylinder-like particles. Samples with differentresidence time are collected separately.

� Step 4. Further shape separation by friction plate: A two-foot-long board with 600 grit sand paper along the length of it refinesthe particle shape separation so that more uniform particleswith specific shape and size can be obtained. The board is heldat about 30� angle and 1 or 2 g of sample are poured at thetop. Sawdust samples proceed to fall the length of the board,with only the most cubical/spherical particles making it all theway to the bottom. The sand paper has the effect of increasingthe frictional resistance to the sawdust particles. Those withthe smallest surface area-to-volume ratio travel the furthestalong the length of the board.

(a) flake-like particle (b) cylinder-like particle

Fig. 1. Photographs of sawdust particles a

Parts or all of these procedures sometimes must be repeated toimprove separation.

Large particles were prepared from untreated poplar dowel. Abench saw was used to cut the poplar dowel to various shapesand sizes.

2.2. Fuel particle surface area and volume

It is difficult to directly measure the external surface area andvolume of small particles with irregular shape. This paper hasdeveloped a 3-Dimensional particle shape reconstruction algo-rithm to measure and calculate sawdust particle surface area andvolume based on three images taken from orthogonal directions.The algorithm includes three major steps: image acquisition andprocessing, image contour alignment, and surface generation.

The algorithm developed in this project uses three images of aparticle or object taken from three orthogonal directions withknown orientation, as illustrated in Fig. 3. The direction of the Zcoordinate in this system is opposite from a regular coordinate(this is a left-hand rather than a right-hand xyz diagram) for oper-ation convenience, but this is immaterial to this method and themathematical reconstruction. If any camera is set with the specificviewpoint and orientation shown in Fig. 3, the image taken withthe camera can be rotated or flipped to meet the orientationrequirements.

Three images taken for a short, near-spherical sawdust particle(�160 lm) are named XY, XZ, and ZY, respectively, as shown inFig. 4. First, the edge contour in each image of the particle is de-tected using a color threshold which identifies those pixels thatlie in the boundary between the background and the particle im-age, illustrated in Fig. 4 by blue traces. If the three images have dif-ferent scales due to camera setup difference, they must be rescaledbased on one known image.

(c) near-spherical particle (d) poplar samples

nd poplar particles of different shape.

Fig. 3. Camera setup orientation for imaging acquisition from three orthogonaldirections.

MaxxY

MaxXy

MinxY

MinXy

X

Y

MaxxZ

MaxXz

MinxZ

MinXz

X

Z

MaxzY

MaxZy

MinzY

MinZy

Z

Y

Fig. 5. Image alignment procedure.

Fig. 6. Sawdust particle skeleton after image contour alignment.

H. Lu et al. / Fuel 89 (2010) 1156–1168 1159

On the edge contour trace in each 2-D image, four extremepoints exist that have either minimal or maximum horizontal/ver-tical coordinates. A simple example is used to illustrate the imagealignment using six common points. As shown in Fig. 5, the fourextreme points in the XZ image are marked as MinX, MaxX, MinZ,and MaxZ. A total of twelve extreme points appear in these threeimage contours. As a result, the space coordinates of six commonpoints can be determined for a particle. Strictly speaking, thesepoints will only be common in the limit of infinite focal lengths,but in this application focal lengths are long compared to particlesize and this is a minor issue.

For example, for the MinXy point in the XY image, its first twocoordinates X and Y can be determined from the XY image. Assum-ing a convex particle surface, this point must correspond to theMinXz in image XZ. The third coordinate of this point must corre-spond to the point MinXz in the XZ image. Similarly, complete coor-dinates of another five points can be determined. With these sixpoints, an approximate skeleton of the object is obtained, as shownin the right upper corner in Fig. 5. Only two coordinates (XY, or XZ,or ZY) for those points on the lines between any two adjacent ex-treme points are known, so the cubic spline interpolation algo-rithm approximates the third coordinate.

A skeleton for the sawdust particle including eight surface seg-ments (octants) results, as illustrated in Fig. 6.

The exact locations of the points on the remaining particle sur-face lie between known bounds but cannot be precisely deter-mined from this algorithm. In no case can the algorithm detect3D concave features such as pits. However, the fixed or knownpoints along the skeleton provide a means for estimating theremaining particle surface. An interpolation method called inversedistance weighting (IDW) generates surface point coordinates.IDW can be used both for curve fitting and surface fitting. A simple

Fig. 4. Three images of a sawdust particle t

IDW weighting factor is xðdÞ ¼ 1=dp, where xðdÞ is the weightingfactor applied to a known value, d is the distance from the knownvalue to the unknown value, and p is a user-selected power factor.Here weight decreases as distance increases from the knownpoints. Greater values of p assign greater influence to values closestto the interpolated point. The most common value of p is 2.

A general form of interpolating a value using IDW is given in Eq(1).

Z ¼

Pi

Zid�piP

id�p

i

; ð1Þ

where Z is the value of the interpolated point, Zi is a known value,di ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffix2

i þ y2i

qis the distance from the known point i to the un-

known point.

aken from three orthogonal directions.

Fig. 7. Reconstructed 3-D shape of a sawdust particle.

Table 1Sawdust sample properties.

Sample shape Flake-like Cylinder-like Equant

Volume (�10�11 m3) 1.697 1.682 1.794Equivalent diameter (mm) 0.32 0.32 0.325Surface area (�10�7m2) 4.91 4.79 3.438Aspect ratio 4.0 (width/thickness) 6.0 1.65

Note: Average errors for surface area and volume measurements are ±5.1% and±6.2%, respectively.

Table 2Poplar sample I properties.

Sample shape Disc Cylinder Equant

Aspect ratio 8.0 (diameter/thickness)

8.0 (length/diameter)

1.0 (height/diameter)

Diameter (mm) 12.7, 19, 25.4 3.2, 4.8, 9.5 6.4, 9.5, 12.7

Table 3Poplar sample II properties.

Sample shape Disc Cylinder Equant

Aspect ratio 5.0 (diameter/thickness)

5.0 (length/diameter)

1.0 (height/diameter)

Diameter (mm) 3.2–25.4 3.2–11 3.2–15.9

1160 H. Lu et al. / Fuel 89 (2010) 1156–1168

The alignment of the three traces divides the soon-to-be surfaceinto eight areas, called octants. The inverse distance weighting(IDW) interpolation method applies to each octant separately,using the trace points that define the octant boundaries. The algo-rithm produces the same results along any boundary or at anyfixed point independent of the direction from which it is ap-proached, ensuring smooth transitions from one octant to the next.The interpolation only determines the Z value for a surface point inthe XY plane, and the XY image is used as an outline that is filledwith a 2-D grid of points. These points are assigned a Z value inthe IDW interpolation. This makes the XY image a backbone inthe algorithm in that it has more influence in the final shape ofthe object 3-D model than the other two images. This is not inher-ent in the algorithm. In principle, similar interpolations could beapplied to each of the other planar images generating additionalsurface points. However, this has thus far proven both unnecessaryand too time consuming in this project.

Two variables are used to adjust the reconstructed shape. Inaddition to the power factor, p, in the original IDW method, theXY influence coefficient provides some flexibility. This variable isnot in the original IDW algorithm, but the effect of increasing thisvalue is that the XY image’s trace will have a greater influence ofthe Z value of interpolated points. It was discovered that the IDWinterpolation algorithm worked well at generating a sphericalshape, but not so well with a cubic shape. By manipulating thepower factor p and XY influence coefficient, a cube-like shapereconstruction can be improved.

A reconstructed 3-D shape of the sawdust particle appears inFig. 7, with surface points interpolated by the modified IDW meth-od. This image is more readily appreciated on a computer screenwhere it can be rotated and examined from various angles thanin this projection.

Once the particle surface is generated, its surface area and vol-ume can be calculated using the coordinates of all points on thesurface.

Another example for a cylindrical particle shape reconstructionappears in Fig. 8. The first three images are taken by a black/whitecamera from orthogonal directions, and the last one is the com-puter generated 3D particle model.

Fig. 8. Shape reconstruction of

To examine the accuracy of this algorithm for a randomlyshaped particle with respect of volume and surface area, twopieces of randomly chosen rocks were used since it is difficult todirectly measure small sawdust particle. The volumes of the tworocks were measured with containers filled with water and thesurface areas were measured with paper wrapped around the rocksurface. Results show that the average volume calculation error is±5.1% and the average surface area calculation error is ±6.2%. Thesawdust particle volume was verified by measuring over 2000 par-ticles and the known particle density (650 kg/m3).

Sawdust particle sample properties appear in Table 1.As for large poplar dowel particles, two groups of samples have

been prepared. Poplar sample I includes particles with similar vol-ume and mass but different shapes and they are limited to threesizes; poplar sample II also includes three shapes but they arenot limited to similar volume and mass, which gives broader sizeoptions. Since all poplar samples have regular shapes (disc, shortcylinder, and long cylinder), both surface areas and volumes ofpoplar particles were calculated based on the particle diameterand length. Particle dimensions for poplar samples are tabulatedin Table 2 and Table 3. Standard deviation of poplar particle diam-eter and length measurement is 5%.

The details of the aerodynamic separation, particle reconstruc-tion algorithm, and other preparation and characterization tech-niques unique to this investigation appear in [35]. All sampleswere dried at 90 �C for 2 h before feeding.

a cylindrical wood particle.

H. Lu et al. / Fuel 89 (2010) 1156–1168 1161

2.3. Experimental setup and procedure

Devolatilization experiments used both an entrained-flow reac-tor and a single-particle reactor. Sawdust particle pyrolysis datawere collected on the entrained-flow reactor and the single-parti-cle reactor focused on large particles (poplar dowel particles). Bothreactors operate at atmospheric pressure.

2.4. Entrained flow reactor

As shown in Fig. 9, the entrained-flow reactor includes a feedingsection, reactor body, collection section, and separation section. Arecrystallized SiC tube of 60 mm OD and 50 mm ID lines the reac-tor main body. The height of the tube is 0.7 m.

The feeding section consists of a syringe feeder and a water-cooled feeding probe, which can obtain a feeding rate as low as1.0 g/h. An electrically heated preheater heats the secondary gasup to 500 �C before it enters the reactor. Kanthal super heatingelements heat the reactor body, providing a maximum reactorwall temperature of 1650 K. The reactor also provides up to0.5 s residence time, and the residence time can be changed byadjusting the relative distance between the feeding probe andcollection probe. A nitrogen-quench probe with cooling waterjacket collects the particles at the reactor exit. The flow rate ra-tio of the quench nitrogen and the secondary gas is about 7–10,providing relatively rapid quenching. Char primarily collects inthe first cyclone separator, which has a 25 lm cut point. Thesecond cyclone collects much of the condensed tar with a5 lm cut point. Finally, the very fine particles collect on the fil-ter. The pore size of the filter is 1 lm.

F

G

H

I

E

D

outer jacket cooling water

inner jacket cooling water

quench

cooling water incool

ing

wat

er o

ut

A - entrain flow reactor B - preheater C - syF - 1st cyclone separator G - 2nd cyclone separator H - fi

Fig. 9. Entrained flow react

2.5. Single-particle reactor

The entrained-flow reactor residence time and operating condi-tions do not lend themselves to experiments on large (>3 mm) par-ticles. Fig. 10 schematically illustrates a second experimentalreactor designed and built for single-particle combustion investi-gations on this large particle reactor. The reactor body is built byKastolite refractory with an ID of 0.15 mm and a height of 0.5 m.Blanket insulates the outer surface. Six view ports were openedthrough the reactor wall, with one horizontal port opened for ther-mocouple and sample access and the other five being closed byoptical window. Four heating elements heat both the reactor andparticle from the bottom of the reactor. Nitrogen is heated to700 �C in the preheater before it enters the reactor from the bottomof the reactor and exits from the top opening of the reactor.

Single biomass particles (both poplar sample I and II) of variousshapes (equant, disc, and cylinder) and diameters (3–12 mm) sus-pended on type-K thermocouples provide simultaneous internaltemperature and mass loss data. A wireless data logger, from PACEScientific (Model XR440), records internal temperature data from athermocouple at 20 Hz. The data logger, thermocouple, and bio-mass particle rest on a balance (Model SCIENTECH SA310IW). Asmall hole about the size of the thermocouple wire (�0.2 mm)through the center the particle provides access for the bead at theparticle center. The balance records mass loss data at a resolutionof 0.1 mg and an accuracy of ±0.2 mg. An experiment begins bymoving the balance, data logger, thermocouple, and biomass sam-ple toward the reactor until the sample reaches the center, throughone of the horizontal ports. The data logger and the balance beginrecording data simultaneously, synchronized within 0.1 s.

A

B

C

cooling water out

nitrogen

nitrogen

primary gas

secondary gas

ringe feeder D - feeding probe E - collection probe lter I - vacuum

or schematic diagram.

View Port*

*: View ports are in three orthogonal directions

Biomass Particle

Preheater

CCD Camera

Thermocouple

Mass Balance

Data Logger

N2 Air

Gas Out

Heating Elements

Temperature Controller

Fig. 10. Schematic diagram of the single-particle reactor.

1162 H. Lu et al. / Fuel 89 (2010) 1156–1168

This single-particle reactor provides time-resolved, simulta-neous mass loss, surface and internal temperatures, size, and shapedata during pyrolysis and combustion processes.

All experiments reported here from both reactors involve nitro-gen environments and include temperature and reactivity results.

2.6. Description of the mathematical model

As biomass particles flow through the entrained-flow reactoror are suspended in the single-particle reactor, they experienceboth radiative and convective heat transfer. These experimentsexcluded oxygen to allow focus on convective and radiative heat-ing and devolatilization without the complications of heats ofreaction and oxidative mass loss. The devolatilization process in-volves heating of raw biomass or organic materials in the absenceof oxidizer, thermal degradation of the biomass components,mass transport of the devolatilization products in the particleby means of advection and diffusion, and convection of the gasproducts at the surface of the particle. The two-stage wood pyro-lysis kinetics model [28], shown in Fig. 11, predicts the productyields and distribution variations with temperature and heatingrate that are significantly influenced by particle shape and size.In this kinetic model, biomass cracks to light gas, tar, and charwhen heated up. Tar also experiences secondary cracking intolight gas and char. Except simple one- or two-step global kineticmodels, there are more advanced models, such as CPD [22,36],FG-DVC [37], and FLASHCHAIN [38]. The two-step kinetic model

Wood

Light Gas

Tar

Char

K1

K3

K5

K2

K4Note:

K1 – K5 are the rate constants for reaction 1-5 respectively

Fig. 11. Reaction scheme for thermal decomposition of biomass.

was used since it is commonly used and this paper tends to focuson particle shape and size effects on pyrolysis rate. The experi-ments reported here use dry particles to maximize the particlesize that can react in the residence time limited entrained flowreactor. Drying of this nature removes all of the free moistureand bound water.

Assumptions included in the mathematical model described be-low include:

� Particles can be described by a one-dimensional, time-depen-dent computational domain.

� Local thermal equilibrium exists between the solid and gasphase in the particle, so temperatures and their gradients arethe same for the solid and gas.

� Gases behave as ideal gases, including both relationshipsbetween pressure, temperature, and specific volume and depen-dence of heat capacity on temperature only.

� Particle aspect ratios and shapes do not change during devolatil-ization – a simplifying assumption for this case but not requiredby the model in general.

� Heat and mass transfer at particle boundaries increase relativeto that of the respective shape by the ratio of the particle surfacearea to that of the volume-equivalent specific shape.

In the particle model, the particle shapes are represented by aparameter n. A spherical particle is described by n = 2, cylinder par-ticle n = 1, and flat plate particle n = 0. Biomass particles initiallycontain inert gas that is distinguished from nitrogen in the model.There are totally seven species included in the model: biomass,char, moisture, light gas, tar, water vapor, and inert gas. The trans-port equations for species mass, momentum, and total energy, withtheir initial and boundary conditions appear as Eqs. (2)–(24)below.

The biomass temporal mass balance contains three consump-tion terms, one each for the reactions to light gas, tar, and char,where all terms in this expression and most terms in the followingexpressions are functions of both time and position. These depen-dencies are not explicitly shown to avoid clutter. Most terms aredefined by context in this discussion and all appear, with units,in the nomenclature section

H. Lu et al. / Fuel 89 (2010) 1156–1168 1163

oqB

ot¼ �ðK1 þ K2 þ K3ÞqB ð2Þ

where q is density, subscript B is biomass, and t is time.Similarly, the char temporal mass balance contains two source

terms, one from the conversion of biomass to char and one forthe char yield from the secondary reactions of tar.

oqC

ot¼ K3qB þ eK5qT ð3Þ

where subscript C is biomass, e is particle porosity, and T is tar.The conservation equations for all gas-phase components (light

gas, tar, and inert gas) include temporal and spatial gradients andsource terms as follows:

o

otðeqgYiÞ þ

1rn

o

orðrneqgYiuÞ ¼

1rn

o

orðrneDeff ;iqg

oYi

orÞ þ Si ð4Þ

where Y is mass fraction of any component in the gas phase, u is gasconvection velocity in particle, and Deff is the effective gas diffusiv-ity, r is radius, and S is source term; subscript i is any gas compo-nent (T for tar, G for light gas, and I for inert gas) and g the gasphase. Source terms are defined asST ¼ K2qB � eK4qT � eK5qT ; SG ¼ K1qB þ eK4qT ;

SI ¼ 0ð5Þ

The total gas-phase continuity equation includes the sum ofthese species and has the form

o

oteqg þ

1rn

o

orðrneqguÞ ¼ Sg ð6Þ

where

Sg ¼ K1qB þ K2qB � eK5qT ð7Þ

The gas-phase velocity in the particle obeys a Darcy-law-typeexpression

u ¼ � gl

oPor

ð8Þ

where g is the solid permeability, l is gas viscosity, and gaspressure

P ¼qgRgT

MWð9Þ

where MW is the mean molecular weight, Rg is the gas constant, T istemperature, and the permeability g is expressed as a mass-weighted function of the individual solid-phase permeabilities

g ¼ qB

qB;0gB þ 1� qB

qB;0

!gC ð10Þ

where, subscript 0 means the initial state. Arrhenius expressionsdescribe the temperature dependence of the kinetic rate coefficientsfor reactions (1)–(5) as illustrated in Fig. 11

Ki ¼ Ai exp � Ei

RT

� �ð11Þ

The energy conservation equation appears as

o

otqBHB þ qCHC

� �þ eqg YGHG þ YIHI þ YT HT

� �h iþ 1

rn

o

orrneqgu YGHG þ YT HT þ YIHI

� �h i¼ 1

rn

o

orrnkeff

oTor

� �þ 1

rn

o

orrnqge Deff ;T

oYT

orHT

��

þ Deff ;GoYG

orHG þ Deff ;I

oYI

orHI

��ð12Þ

where, H is the enthalpy, keff is the effective particle thermal con-ductivity, and

Hi ¼ H0i;f þ

Z T

T0

CpidT ð13Þ

where Cp is heat capacity and subscript i represents each of thethree gas-phase components as before. implicitly include the heatof reaction of all reactions involved in the pyrolysis process.

This form of the energy equation relates to standard theoreticalanalyses [39] for multi-component systems. In Eq. (12), the firstterm represents energy accumulation; the second term representsenergy convection; the third term (first term after the equalitysign) accounts for conductive heat transfer, and the last term ac-counts for energy associated with diffusion of species in the gasphase and the liquid phase. The last term generally contributesonly negligibly to the overall balance and is commonly justifiablyignored. No heats of reaction appear in the expression since the en-ergy balances total enthalpy (both phases) and is not written interms of temperature or separate particle and gas phases. Heatsof reaction only become apparent when separately modeling theparticle and gas phases or using temperature instead of enthalpy.

The effective diffusivity of gas species in the particle can be cal-culated by the parallel pore [40] model, as shown in Eq. (14)Deff ¼ De=s;1=D ¼ 1=DAB þ 1=Dk ð14Þwhere, s is the particle pore tortuosity factor, DAB and DK are molec-ular diffusivity and Knudsen diffusivity. The effective particle ther-mal conductivity includes conductive and radiative componentswith some theoretical basis [41,42] and with empirical verificationfor wood [9]

keff ¼ kcond þ krad ð15Þwhere the particle structure is assumed to be close to the upper lim-it for thermal conductivity, that is, is assumed to have high connec-tivity in the direction of conduction

kcond ¼ ekgas þ ð1� eÞ qB

qB;0kB þ 1� qB

qB;0

!kC

" #ð16Þ

and where radiation contributes approximately to the third powerof the temperature

krad ¼erT3dpore

xð17Þ

where, r is Boltzman constant, dpore is pore diameter, x isemissivity.

Initial conditions include experimental conditions for a non-reacting particle. That is, at t = 0,

Pðt ¼ 0; rÞ ¼ Patm

Tðt ¼ 0; rÞ ¼ 300K ðtypicallyÞuðt ¼ 0; rÞ ¼ 0YIðt ¼ 0; rÞ ¼ 1YTðt ¼ 0; rÞ ¼ YV ðt ¼ 0; rÞ ¼ YGðt ¼ 0; rÞ ¼ 0

ð18Þ

Boundary conditions at the particle center reflect symmetry,that is, at r = 0

oPor

t;r¼0 ¼ 0) uðt; r ¼ 0Þ ¼ 0

oTor

t;r¼0 ¼ 0

oYIor

t;r¼0 ¼ 0

ð19Þ

Boundary conditions at the particle outer surface are defined byexternal conditions of pressure, heat and mass flux, and

pðt; r ¼ rpÞ ¼ patm;

oYiðj;kÞ

or

r¼rp

¼ hmhmRSAðYiðj;kÞ;1 � Yiðj;kÞ;SÞ

keffoTor

r¼rp

¼ hT hT RSAðTf � TÞ þ RSAxrðT4w � T4Þ

ð20Þ

Table 4Kinetic parameters of wood pyrolysis process.

Reaction no. Frequencyfactor (s�1)

Activationenergy(kJ/mol)

Reference Heat ofreaction(kJ/kg)

Reference

1 Hardwood sawdust 1.52 � 107 139.2 [16] �418 [24]Poplar dowel particle 1.11 � 1011 177 [46]

2 Hardwood sawdust 5.85 � 106 119 [16] �418 [24]Poplar dowel particle 9.28 � 109 149 [46]

3 Hardwood sawdust 2.98 � 103 73.1 [16] �418 [24]Poplar dowel particle 3.05 � 107 125 [46]

4 4.28 � 106 107.5 [47] 42 [48]5 1.0 � 105 107.5 [49] 42 [48]

Table 5Physical properties of biomass particles.

Variable Value Reference

Sawdust density qB 650 kg/m3

Poplar density 580 kg/m3

Porosity e 0.4Emissivity x 0.9Permeability g gB = 1 Darcy [31]

gC = 100 Darcy [31]Thermal conductivity k kgas = 0.026 W/m K [52]

kB = 0.11 W/m K [53]kC = 0.071 W/m K [53]

Pore size dpore 3.2 � 10�6 m [9]Molecular weight M MT = 145 kg/kmol [9]

MG = 31 kg/kmol [9]MI = 28 kg/kmolMV = 18 kg/kmol

Viscosity l lgas = 3�10�5 Pa.s [52]Diffusivity DAB DAB = 1.0 � 10�5 m2/s for allHeat capacity Cp (J/kg K) Cpa ¼

1000Rg

7:72

� �g 380

T

�þ 2g 1800

T

�� [51]

Cpc1000Rg

11:3

� �g 380

T

�þ 2g 1800

T

�� [51]

Where, gðxÞ ¼ x2ex

ðex�1Þ2

CpT = �100 + 4.4 � T�0.00157 � T2 [31]CpG = 770 + 0.629 � T�0.000191 � T2 [31]CpI = 950 + 0.188 � T [31]

1164 H. Lu et al. / Fuel 89 (2010) 1156–1168

where hm and hT represent mass and thermal blowing factors,respectively [39], hm and hT are mass and heat transfer coefficients,Tf and Tw are bulk gas and wall temperatures, respectively, RSA rep-resents the exterior surface area ratio, which is the surface area ofthe particle divided by the characteristic surface area as follows

RSA ¼ SA=ð4pR2PÞ

RSA ¼ SA=ð4pR2PARÞ

RSA ¼ SA=ð4R2PAR2Þ

ð21Þ

for spheres, cylinders, and flat plates, respectively, where SA is thesurface area, AR is aspect ratio, Rp is particle radius.

Each shape employs heat transfer coefficients developed forthat particular shape. Correlations suitable for random particle ori-entation during flight appear in the literature for some particles.Where such a model is not available, the average particle dimen-sion forms the characteristic length. For near-spherical particles,Masliyah’s prolate spheroid model [43] provides a suitable correla-tion, as indicated in Eq. (22)

Nu ¼ 1:05þ 0:6Re0:65Pr0:33 ð22Þ

Cylinders at low Reynolds numbers adopt the correlation ofKurdyumov [44] (see Eq. (23)).

Nu ¼WoðReÞPr0:33 þW1ðReÞ;

where

W0 ¼

0:46271exp 1:01633ðlog10ðReÞÞþ0:5121ðlog10ðReÞÞ2� �

;

10�26 Re6 3:14;

0:597ðRe= lnð1=ReÞÞ1=3;

Re< 10�2;

8>>>>>>>>>><>>>>>>>>>>:

W1 ¼0:10666exp

0:41285ðlog10 ReÞþ0:43847ðlog10 ReÞ2

þ0:1915ðlog10 ReÞ3þ0:01802ðlog10 ReÞ4

�0:005225ðlog10 ReÞ5

0BBBBB@

1CCCCCA

0:0917; Re< 10�2

8>>>>>>>>><>>>>>>>>>:

ð23Þ

The heat transfer coefficient of flat plates uses Pohlhausen’sexpression [45], appears as Eq. (24).

Nu ¼ 0:644Re0:5Pr0:33 ð24Þ

The kinetic parameters for wood pyrolysis found in literaturesvary over a wide range. They are usually measured at low to mod-erate temperature (usually <900 K). No high-temperature kineticdata for the two-stage scheme have been reported. Font et al.[16] presented kinetic data for the three primary reactions thatare found to be comparable to what Nunn et al. [10] reported forthe single reaction kinetic data for hardwood in the high-tempera-ture range (573–1373 K). Font et al.’s results are used in this modelwithout modification. The pre-exponential factors, activation en-ergy, and heat of reactions of all the reactions used in this modelappear in Table 4. For reaction 1–3, there are two sets of kineticparameters used. One set is for hardwood sawdust particle andthe other is for poplar dowel particles, as indicated in Table 4.

The physical properties of the biomass particles significantly af-fect the heat and mass transfer process [30,50]. In this work, tem-perature-dependent heat capacity correlations describe all species.The heat capacity of biomass and char adopt the model suggested

by Merrick [51]. Gronli et al. [31] suggested a correlation for tarheat capacity, which is based on some typical pyrolysis tar compo-nents (closely related to benzene). All physical properties appear inTable 5 and none is tailored to these data sets.

A fourth-order Runge–Kutta algorithm solves the mass conver-sion equations of biomass, char, and moisture. The control volume(finite volume) [54] method is applied to solve the gas speciesmass conservation equations and energy conservation equations.A power-law scheme and the SIMPLE algorithm accelerate the con-vergence of the solution procedure.

3. Results and discussion

Wood particle pyrolysis data (mass loss vs. residence time)were collected on both the entrained flow reactor-sawdustsamples and the single-particle reactor-large poplar dowel parti-cles, and compared with model predictions.

3.1. Effects of particle shape on mass loss rate and temperature historyfor small particles

The wall and gas temperatures in the entrained flow reactormeasured by type B thermocouples during sawdust pyrolysisexperiments appear in Fig. 12.

As illustrated in Table 1, the sawdust samples used in thisexperiment have similar particle volumes and mass but differentshapes and surface areas. Based on these average temperature pro-

H. Lu et al. / Fuel 89 (2010) 1156–1168 1165

files of reactor and gas, the mathematical model simulates the dev-olatilization process of the sawdust particle with the specificshapes described in the sample preparation section.

Fig. 13 illustrates the mass loss history of the three samples. Allthree samples (near-spherical, flake-like, and cylinder-like) havevery close volume and mass but different surface areas and shapes.

0.0 0.1 0.2 0.3 0.40

400

800

1200

1600

2000

2400

Tem

pera

ture

, K

Distance from Entrance, m

Wall Gas at center

Fig. 12. Reactor wall temperature and gas temperature at center.

0.0 0.1 0.2 0.3 0.4 0.50.0

0.2

0.4

0.6

0.8

1.0

Mas

s Lo

ss, d

af

Residence Time, s

exp. model flake-like cylinder-like near-spherical

Fig. 13. Mass loss histories of sawdust particles with different shapes and similarmass and volume during pyrolysis in entrained flow reactor. Tw = 1625 K,Tg = 1310 K, dpeq = 0.32 mm, ARflake-like = 4, ARnear-sphere = 1.65, ARcylinder-like = 6.

0.0 0.1 0.2 0.3 0.4 0.5200

400

600

800

1000

1200

1400

1600

Sur

face

Tem

pera

ture

, K

Residence Time, s

Flake-like Cylinder-like Near-spherical

(a) particle surface temperature

Fig. 14. Predicted particle temperature history of sawdust samples with different shapesTg = 1310 K, dpeq = 0.32 mm, ARflake-like = 4, ARnear-sphere = 1.65, ARcylinder-like = 6.

See Table 1 for detail sample properties. Symbols in Fig. 13 areexperimental data and lines are model predictions. Each experi-mental data point was repeated three times and average experi-mental error is 8.5%. Both the experimental data and modelpredictions show that the near-spherical particle loses mass mostslowly compared with the other two shapes, while the flake-likeparticle devolatilizes slightly faster than cylinder-like particle.For each of the three samples, the slope of the model predictionis found to be steeper than that of the experimental data. This pos-sibly arises from the imperfect size and/or shape distribution of thesample, even though the samples are considered to be very uni-form after the delicate sample preparation procedure. These varia-tions in shape and size tend to smooth the observed curve of massloss vs. time as the small particles react faster than the largerparticles.

The data and the model agree quantitatively that near-sphericalparticles react more slowly than do less symmetrical particles. Themass losses differ by as much as a factor of two during most of theparticle histories based on both the predictions and the measure-ments. These data indicate that even at these relatively small sizes,asphericity plays a significant role in overall conversion rate.

The predicted surface and center temperatures for the threesamples appear in Fig. 14. As expected, the near-spherical particleheats more slowly than the other two shapes.

3.2. Effects of particle shape on mass loss rate for large particles

The effect of particle shape on conversion time and product dis-tribution should be more apparent for large particles than smallparticles. Large particles that sustain substantial internal tempera-ture and composition gradients transfer heat and mass at rates thatscale with surface area. Spheres have the lowest surface area-to-volume ratio of all shapes and should therefore transfer heat andmass at slower rates than aspherical particles of the same vol-ume/mass. By contrast, particles with little or no internal temper-ature and compositions gradients transfer mass and heat at ratesproportional to total particle volume. These typically smallparticles are less sensitive to shape than are larger particles ofthe same material in the same environment. These data and theanalyses quantify these theoretical trends and indicate that parti-cles as small as 0.3 mm equivalent diameter experience significantdifferences in conversion rate based on shape. This renders spherespoor choices for many if not most biomass fuels. This concept issimilar to but not identical with using a Biot number to determinewhen internal temperature (and composition) gradients are signif-icant. The Biot number determines when internal temperature

0.0 0.1 0.2 0.3 0.4 0.5200

400

600

800

1000

1200

1400

1600

Cen

ter

Tem

pera

ture

, K

Residence Time, s

FLake-like Cylinder-like Near-spherical

(b) particle center temperature

and similar mass and volume during pyrolysis in entrained flow reactor. Tw = 1625 K,

1166 H. Lu et al. / Fuel 89 (2010) 1156–1168

(and composition) gradients can be ignored (Bi < 0.1) but does notin itself help determine how to treat the impacts of shape on suchgradients when they should not be ignored.

The above figures include available data from the entrainedflow reactor, but the data do not range over sufficient size to pro-vide convincing experimental verification of the model predictions(because of reactor limitations). Investigations in the single-parti-cle reactor resolve this data gap. Specifically, the effects of particleshape on conversion time for large size particles appear (experi-mentally and theoretically) next with data collected in the sin-gle-particle reactor.

The mass loss rate differences between the near-spherical andaspherical particles increases with increasing size. Mass loss dataduring pyrolysis were collected in the single-particle reactor forthree samples (near-sphere, cylinder, and plate), which have thesame mass and volume. As illustrated in Fig. 15 for particles withan equivalent diameter of 9.5 mm and different shapes, the near-spherical particle pyrolyzes most slowly compared with the othertwo aspherical particles, consistent with model predictions. Thesolid star, square, and circle are experimental data for plate, cylin-der, and near-sphere, respectively; the long-dash line, short-dashline, and the solid line are model predictions for plate, cylinder,and sphere, respectively.

Relative to the objective of this investigation, the data and themodel agree quantitatively and definitively demonstrate thatnear-spherical particles react more slowly than do less symmet-rical particles of the same mass. The mass losses differ by asmuch as a factor of two during most of the particle historiesbased on both the predictions and the measurements. Small sizesawdust pyrolysis data indicate that at these sizes, which aresmall relative to commercial uses of biomass, asphericity playsa significant role in overall conversion. The effects of asphericityincrease with increasing size and increasing aspect ratio, as dis-cussed below.

3.3. Effects of particle shape and size on particle conversion times

In general, the conversion time of near-spherical particles canbe twice that of aspherical particles with aspect ratios of 5 for par-ticle sizes larger than 10 mm, as illustrated in Fig. 16. Here conver-sion time is defined as the residence time of the particle in thereactor once it is placed in the reactor till the particle mass stopschanging. Both experimental data and model predictions are pre-

0 5 10 15 20 25 30 35 400.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Mas

s Lo

ss, 1

-m/m

0

Residence Time, s

Exp. ModelPlateCylinderNear-sphere

Fig. 15. Mass loss profiles of large poplar particles with different shape and samemass during pyrolysis in nitrogen, dpeq. = 9.5 mm, ARcylinder = 8.0, ARplate = 8.0,ARnear-sphere = 1.0, Tw = 1273 K, Tg = 1050 K.

sented in Fig. 16, where the solid dots are conversion time ratioof near-spherical particle over plate (both have the same massand volume at a specific equivalent diameter) as function of equiv-alent particle diameter, with square symbol for cylinder over plate;the dash line and solid line are model predictions, respectively.Equivalent diameter is the diameter of a sphere with the same vol-ume/mass as the aspherical particle.

The conversion time ratio becomes greater, up to 2.5 when theaspect ratio of aspherical particles increases to 8.0, as illustrated inFig. 17. Commercially significant biomass particles commonly haveaspect ratios as large as 12. Less difference exists between the twoaspherical shapes since they have about the same surface area tovolume ratio.

The above illustrations show that particle asphericity and sizeplay important roles in particle conversion. A spherical assumptionwould lead to substantial error in predicting combustion behaviorsof biomass particles of commercial size and shape.

To understand what relation exists between the ratio of particlesurface area over volume and conversion time ratio, the authorscompared the conversion time ratio (experimental data) of differ-ent shape particles with surface area ratio. Fig. 18 shows the sur-face area ratios of aspherical particles to spherical particles withthe same volume, plotted as a function of aspect ratio. Both cylin-ders and plates have higher surface area-to-mass ratios thanspheres, and the difference increases with increasing aspect ratio(the surface area ratio does not change with equivalent particlesize). Basically the surface area ratios of plate-like particle overspherical particle are about 1.6 and 2.0 at aspect ratios of 5 and8, respectively for equivalent particles (same mass and volumeparticles). The pyrolysis conversion time ratios of spherical particleover plate-like particle for particles larger than 12 mm are about 2and 2.5, respectively as shown in Figs. 16 and 17. It is not a linearrelation between surface area ratio and conversion time ratio, andthe authors believe particle shape effects on boundary heat andmass transfer also contribute to the conversion rate. For particlesless than 12 mm, it’s even more difficult to obtain a simple corre-lation between surface area ratio and conversion rate ratio.

3.4. Effects of particle shape and size on particle volatile yields

Model predictions also show that the near-spherical particlesproduce slightly lower volatiles yields relative to the other shapes.Volatile yields are taken as the mass loss fraction until the particlemass stops changing. A combination of different particle tempera-

0 2 4 6 8 10 12 14 16 181.0

1.2

1.4

1.6

1.8

2.0

2.2Exp. Model

Near-sphere/PlateCylinder/Plate

Con

vers

ion

Tim

e R

atio

Equivalent Diameter dp,eq.

, mm

Fig. 16. Effects of particle shape and size on conversion time during pyrolysis innitrogen (non-spherical particle AR = 5.0), Tw = 1273 K, Tg = 1050 K.

0 2 4 6 8 10 12 14 16 18 20

1.2

1.5

1.8

2.1

2.4

2.7

3.0

3.3

Con

vers

ion

Tim

e R

atio

Equivalent Diamter dp,eq., mm

Exp. ModelNear-sphere/PlateCylinder/Plate

Fig. 17. Effects of particle shape and size on conversion time during pyrolysis innitrogen (non-spherical particle AR = 8.0), Tw = 1273 K, Tg = 1050 K.

0 2 4 6 8 10

1.2

1.4

1.6

1.8

2.0

2.2

Surfa

ce A

rea

Rat

io

Aspect Ratio

Cylinder/SphereDisc Plate/Sphere

Fig. 18. Surface area ratios of aspherical particles to spherical particles with thesame volume, plotted as a function of aspect ratio.

0.0 0.8 1.6 2.4 3.2 4.0

0.80

0.84

0.88

0.92

0.96

Fig. 19. Predicted volatile yields comparison of various particle shape and size.Tw = 1625 K, Tg = 1310 K, ARflake-like = 4, ARnear-sphere = 1.65, ARcylinder-like = 6.

0.0 0.1 0.2 0.40.3 0.50.0

0.2

0.4

0.6

0.8

1.0

center surface

Residence Time

Biom

ass

Mas

s Fr

actio

n

0.00

0.02

0.04

0.06

0.08

center surface

Char M

ass Fraction

Fig. 20. Composition of the near-spherical particle as functions of timedp,eq. = 0.32 mm, A = 1.65, Tw = 1625 K, Tg = 1310 K.

H. Lu et al. / Fuel 89 (2010) 1156–1168 1167

ture histories due to the particle shape and longer average pathlengths for tars to travel in spherical particles compared to theaspherical counterparts causes these differences. The flake-likeand cylinder-like particles have larger surface areas and smallerthicknesses, which result in higher heating rates and faster heatand mass transfer to the particle. The effects of particle shapeand size on volatile yields appear in Fig. 19, where the volatile yieldof all particles decreases with increasing particle size. Model pre-dictions show that the near-spherical particles yield slightly lowervolatiles relative to the other shapes. Both different particle tem-perature histories due to the particle shape and longer averagepath lengths for tars to travel in spherical particles compared totheir aspherical counterparts lead to this result. Both flake-likeand cylinder-like particles behavior similarly. The difference be-tween the near-spherical and other shapes increases with increas-ing size.

3.5. Solid composition change during pyrolysis

The predicted composition gradients inside the dry, near-spher-ical particle (dpeq = 0.32 mm) appear in Fig. 20. Both the biomassdensity and the char density changes at the particle center and sur-face appear as functions of residence time in the figure.

4. Conclusion

Both hardwood sawdust particle and poplar dowel particlepyrolysis data data were collected in an entrained-flow reactorand a single-particle reactor, respectively for particles with flake-like, cylinder-like, and near-spherical shapes. Particle volumesand surface areas of irregular particles were measured with a par-ticle shape reconstruction algorithm developed in this investiga-tion. An one-dimensional, time-dependent single particlepyrolysis model was developed and simulate particles with differ-ent shape and size. Model simulations of the three shapes showsatisfactory agreement with the experimental data. Both experi-mental and theoretical investigations indicate the impact particleshape and size have on overall particle reactivity. Experiments con-ducted on biomass particles at relevant temperatures and a varietyof well-characterized shapes indicate that particle shape impactsoverall reaction rates relative to those of spheres with the samemass/volume by factors of two or more at relatively small sizes.Theoretical models developed and validated against the data indi-cate that the impact of shape increases with increasing size and ismuch greater at sizes relevant biomass utilization in practical con-ditions. Spherical mathematical approximations for fuels thateither originate in or form aspherical shapes during thermal treat-ment (combustion, gasification, or similar processes) poorly repre-sent combustion behavior when particle size exceeds 200–300 lm.This includes a large fraction of the particles in both biomass andblack liquor combustion. Additionally, experimental data and

1168 H. Lu et al. / Fuel 89 (2010) 1156–1168

model predictions indicate that the pyrolysis process is a heattransfer dominant process instead of kinetics dominant processsince both shape and size influence the conversion time dramati-cally, especially for large particles.

Acknowledgements

This investigation was supported in part by US Department ofEnergy (DOE)/EE Office of Industrial Technologies. Thanks are gi-ven to Drs. Thomas Fletcher, Søren K�r, and Dr. Dale Tree for help-ful discussions. Kelly Echoes, Brian Spears, and Russ Johnsoncontributed to this project.

References

[1] Gera D, Mathur M, Freeman M, O’Dowd W. Moisture and char reactivitymodeling in pulverized coal combustors. Combust Sci Tech 2001;172:35–69.

[2] Fletcher DF, Haynes BS, Christo FC, Joseph SD. A CFD based combustion modelof an entrained flow biomass gasifier. Appl Math Model 2000;24(3):165–82.

[3] Thunman H, Leckner B, Niklasson F, Johnsson F. Combustion of wood particles -a particle model for Eulerian calculations. Combust Flame 2002;129(1–2):30–46.

[4] Peters B, Bruch C. Drying and pyrolysis of wood particles: experiments andsimulation. J Anal Appl Pyrol 2003;70(2):233–50.

[5] Saastamoinen J. Simplified model for calculation of devolatilization in fluidizedbeds. Fuel 2006;85(17–18):2388–95.

[6] Jalan RK, Srivastava VK. Studies on pyrolysis of a single biomass cylindricalpellet kinetic and heat transfer effects. Energ Convers Manage1999;40(5):467–94.

[7] Horbaj P. Model of the kinetics of biomass pyrolysis. Drev Vysk1997;42(4):15–23.

[8] Liliedahl T, Sjostrom K. Heat transfer controlled pyrolysis kinetics of a biomassslab, rod or sphere. Biomass Bioenerg 1998;15(6):503–9.

[9] Janse AMC, Westerhout RWJ, Prins W. Modelling of flash pyrolysis of a singlewood particle. Chem Eng Process 2000;39:239–52.

[10] Nunn TR, Howard JB, Longwell JP, Peters WA. Product compositions andkinetics in the rapid pyrolysis of sweet gum hardwood. Ind Eng Chem, ProcessDesign Develop 1985;24(3):836–44.

[11] Varhegyi G, Antal MJJ, Szekely T, Szabo P. Kinetics of the thermaldecomposition of cellulose, hemicellulose, and sugar cane bagasse. EnergFuel 1989;3(3):329–35.

[12] Antal MJJ, Gabor V. Cellulose pyrolysis kinetics: the current state ofknowledge. Ind Eng Chem Res 1995;34:703–17.

[13] Antal MJJ, Varhegyi G, Jakab E. Cellulose pyrolysis kinetics: revisited. Ind EngChem Res 1998;37(4):1267–75.

[14] Guo J, LA C. Kinetic study of pyrolysis of extracted oil palm fiber: isothermaland non-isothermal conditions. J Therm Anal Calorimetry 2000;59:763–74.

[15] Di Blasi C. Comparison of semi-global mechanisms for primary pyrolysis oflignocellulosic fuels. J Anal Appl Pyrol 1998;47:43–64.

[16] Font F, Marcilla A, Verdu E, Devesa J. Kinetics of the pyrolysis of almond shellsand almond shells impregnated with CoCl2 in a fluidized bed reactor and in apyroprobe 100. Ind Eng Chem Res 1990;29:1846–55.

[17] Thurner F, Mann U. Kinetic investigation of wood pyrolysis. Ind Eng Chem Res1981;20(3):482–8.

[18] Brown AL, Dayton DC, Daily JW. A study of cellulose pyrolysis chemistry andglobal kinetics at high heating rates. Energ Fuel 2001;15(5):1286–94.

[19] Babu BV, Chaurasia AS. Modeling, simulation and estimation of optimumparameters in pyrolysis of biomass. Energ Convers Manage2003;44(13):2135–58.

[20] Niksa S, Kerstein AR, Fletcher TH. Predicting devolatilization at typical coalcombustion conditions with the distributed-energy chain model. CombustFlame 1987;69(2):221–8.

[21] Solomon PR, Fletcher TH, Pugmire RJ. Progress in coal pyrolysis. Fuel1993;72(5):587–97.

[22] Fletcher TH, Pond HR, Webster J, Wooters J, Baxer LL. In: Prediction of tar andlight gas during pyrolysis of black liquor and biomass, 3rd Annual jointmeeting of the US sections of the Combustion Institute, Chicago, IL, 2003.

[23] Bharadwaj A, Baxter LL, Robinson AL. Effects of intraparticle heat and masstransfer on biomass devolatilization: experimental results and modelpredictions. Energ Fuel 2004;18(4):1021–31.

[24] Chan W-CR, Kelbon M, Krieger BB. Modeling and experimental verification ofphysical and chemical processes during pyrolysis of a large biomass particle.Fuel 1985;64(11):1505–13.

[25] Shen MS, Lui AP, Shadle LJ, Zhang GQ, Morris GJ. Kinetic studies of rapid oilshale pyrolysis. 2. Rapid pyrolysis of oil shales in a laminar-flow entrainedreactor. Fuel 1991;70(11):1277–84.

[26] Di Blasi C. Numerical simulation of cellulose pyrolysis. Biomass Bioenerg1994;7(1–6):87–98.

[27] Di Blasi C. Kinetic and heat transfer control in the slow and flash pyrolysis ofsolids. Ind Eng Chem Res 1996;35(1):37–46.

[28] Di Blasi C. Heat, momentum and mass transport through a shrinking biomassparticle exposed to thermal radiation. Chem Eng Sci 1996;51(7):1121–32.

[29] Miller RS, Bellan J. A generalized biomass pyrolysis model based onsuperimposed cellulose, hemicellulose and lignin kinetics. Combust SciTechnol 1997;126:97–137.

[30] Di Blasi C. Influences of physical properties on biomass devolatilizationcharacteristics. Fuel 1997;76:957–64.

[31] Gronli MG, Melaaen MC. Mathematical model for wood pyrolysis –comparison of experimental measurements with model predictions. EnergFuel 2000;14(4):791–800.

[32] Brown AL, Dayton DC, Nimlos MR, Daily JW. Design and characterization of anentrained flow reactor for the study of biomass pyrolysis chemistry at highheating rates. Energ Fuel 2001;15(5):1276–85.

[33] Hagge MJ, Bryden KM. Modeling the impact of shrinking on the pyrolysis ofdry biomass. Chem Eng Sci 2002;57:2811–23.

[34] De Diego LF, Garcia-Labiano F, Abad A, Gayan P, Adanez J. Modeling of thedevolatilization of nonspherical wet pine wood particles in fluidized beds. IndEng Chem Res 2002;41(15):3642–50.

[35] Lu H. Experimental and modeling investigations of biomass particlecombustion. Provo, Utah: Brigham Young University; 2006.

[36] Fletcher TH, Kertein AR, Pugmire RJ, Grant DM. Chemical percolation model fordevolatilization. 3 Direct used of 13C NMR data to predict effects of coal type.Energ Fuel 1992;6(4):414–31.

[37] Chen YG, Charpenay S, Jensen A, Wojtowicz MA. In: Modeling of biomasspyrolysis kinetics, 27th Symposium (International) on combustion/TheCombustion Institute, 1998. p. 1327–1334.

[38] Niksa S. In: Predicting the rapid devolatilization of diverse forms of biomasswith bio-FLASHCHAIN, 28th International Symposium on Combustion/Thecombustion institute, Edinburgh, United Kingdom, 2000. p. 2727–33.

[39] Bird RB, Stewart WE, LE N, Transport phenomena. 2nd ed. New York/Chichester/Weinheim/Brisbane/Singapore/Toronto: John Wiley and Sons,Inc.; 2002.

[40] Wheeler A, Advances in catalysis, vol. III. New York: Academic Press; 1951. p.250.

[41] Robinson AL, Buckley SG, Baxter LL. Thermal conductivity of ash deposits 1:measurement technique. Energ Fuel 2001;15:66–74.

[42] Robinson AL, Buckley SG, Yang NYC, Baxter LL. Thermal conductivity of ashdeposits 2: effects of sintering. Energ Fuel 2001;15:75–84.

[43] Masliyah JH, Epstein N. Numerical solution of heat and mass transfer fromspheroids in steady axisymmetric flow. Prog. Heat Mass Transfer1972;6:613–32.

[44] Kurdyumov VN, Fernandez E. Heat transfer from a circular cylinder at lowReynolds numbers. Journal of Heat Transfer, Trans ASME 1998;120(1):72–5.

[45] Pohlhausen E. Der WÄRMEAUSTAUSCH zwischen festen Körpern undFlüssigkeiten mit kleiner Reibung und kleiner Wärmeleitung. Z Angew MathMech 1921;1:115–21.

[46] Wagenaar BM, Prins W, Van Swaaij WPM. Flash pyrolysis kinetics of pinewood. Fuel Process Technol 1993;36:291.

[47] Liden CK, Berruti F, Scott DS. A kinetic model for the production of liquids fromthe flash pyrolysis of biomass. Chem Eng Commun 1988;65:207–21.

[48] Koufopanos CA, Papayannakos N, Maschio G, Lucchesi A. Modelling of thepyrolysis of biomass particles. Studies on kinetics, thermal and heat transfereffects. Can J Chem Eng 1991;69(4):907–15.

[49] Di Blasi C. Analysis of convection and secondary reaction effects within poroussolid fuels undergoing pyrolysis. Combust Sci Technol 1993;90:315–40.

[50] Raveendran K, Ganesh A, Khilart KC. Influence of mineral matter on biomasspyrolysis characteristics. Fuel 1995;74(12):1812–22.

[51] Merrick D. Mathematical models of the thermal decomposition of coal – 2.Specific heats and heats of reaction. Fuel 1983;62(5):540–6.

[52] Kansa EJ, Perlee HE, Chaiken RF. Mathematical model of wood pyrolysisincluding internal forced convection. Combust Flame 1977;29(3):311–24.

[53] Lee CK, Chaiken RF, Singer JM. Charring pyrolysis of wood in fires by lasersimulation. Symp (Int) on combust, 16th, MIT, Aug 15–20, 1976. p. 1459–70.

[54] Patankar SV. Numerical Heat Transfer and Fluid Flow. Taylor and Francis;1980.