Mathematical model for prediction of pyrolysis and ignition of wood under external heat flux

PROGRESS IN NATURAL SCIENCEVol. 12 ,No.11 , November 2002Mathematical model for prediction of pyrolysis andignition of wood under external heat flux*CHEN Xiaojun', YANG Lizhong ,JI Jingwei and DENG Zhihua( State Key Laboratory of Fire Science , University of Science and Technology of China , Hefei 230026 , China)Received April 20 , 2002 ; revised June 21 , 2002Abstract The pyrolysis and ignition of combustible materials is an important aspect of the processes taking place in an unw antedfire. A prediction model presented in this paper is to study pyrolysis and ignition time of w ood under external heat flux. The solution of themodel provides the temperature at each point of the solid and the local solid conversion. And the time to ignition of the wood is predictedwith the solution of surface temperature. In general ,a good agreement bet w een experimental and theoretical results is obtained.Keywords: pyrolysis , time to ignition , wood , model.The adequate prediction of fire risk is becomingface temperature has been included157]. Liu etinereasingly important in minimizing the loss causedal.!81 studied the thermal decomposition of biomassby fire. Real scale experiments are usually expensive ,under both atmosphere and nitrogen using thermo-so the use of mathematical models is particularly ap-gravimetry( heating rate 10 k/ min , flow rate 60 mL/propriate. In most cases the model is improved bymin ). They found two peaks of mass loss rate and thecomparing the result from the model with small scalefirst is around 300 C , and Reina' 5 91 ex periment alsoexperimental data. The combustion of combustiblegot the same result. U nder these conditions ，thematerials results in fire and its progress , and therapid pyrolysis of hemicellulose and cellulose producemathematical model requires more understanding ofplentiful combustible products. In this paper , we alsocombustion properties of combustible materials inuse the concept of critical surface temperature to pre-building fires , especially ignition property , time todict the time to pilot ignition with the solution of theignition, mass loss rate and heat release rate. As amathematic model. The predicted time is comparedcommonly used material ，the pyrolysis and combus-with the obtained experimental data in a conetion behavior of wood is interesting in many ways. .calorimeter.Numerous theoretical studies have been carriedut1~4].There are many factors influencing the pyrolysisand combust process of w ood , including the intrinsicOne of the most important processes in fire is thephysical and chemical properties of wood，like speciesignition phenomenon. In the study of risk to struc-of wood , initial density and chemical composition.tures and people , the time to ignition of a combustible .The other factors are combustion environment such asmaterial is one of the most w idely used parameters. Itexternal heat flux , restriction of geometry ，flow rateis used in many cases such as fire detection and sup-of air , and grain orientation of wood. In general ,pression at early stage ，and evacuation etc. A veryheat flux is the key factor. The py rolysis process andimportant conclusion from the point of view of firetime to ignition is obviously different under differentprotection and modeling was drawn by Martir 31 ,heat flux. The model presented in this paper can pre-w ho studied diffusion controlled ignition of cellulosedict the process of w ood pyrolysis and time to ignitionunder conditions of intense radiative heating ，andofwo中国煤化工odel provides the tem-stated that' The persistence of ignition depends onlyperatiC N M H Glid and the local solidupon the continued flow of flammable，volatile prod-conversion." 1 WO princrpa efects are explored inucts , not on any unique composition of the mixture"here : the effect of initial sample density and ex ternalIn many early works an ignition criterion-critical sur-heat flux.* Supportyt h出ational Natural Science Foundation of China( Grant Nos. 59936140 and 50006012 )** To whomd coropadence should be addressed. E-mail : xjchen @ ustc. edu. cnProgress in Natural Science Vol.12 No.11 20028751 Brief description of the mathematical modeltail.In early works3,10] we presented a modified2.1 Effect of initial sample densitymodel of py rolysis for charring materials in fire. TheSuuberg et al.t12] studied the pure pyrolysis ki-computational fluid dynamics ( CFD ) model mainlynetics of wood. In their experiment wood slab madeincludes one py rolysis rate equation and two conserva-of pure wood cellulosic powder was used. The effecttion equations.of density mentioned here is that the properties ofThe py rolysis rate equation isw ood samples are similar but their densities are differ-dp,=-A(( P3-ρc)". (- E( 1)ent. A typical example is compositive wood slabs.dtexp(RTThese materials are commonly used in furniture andbuilding decoration. Figs. 1 and 2 show the fractionthe mass conservation equation isaMg1.01000kg t m'xa(2).----750kgIm'600kg1 m'and the energy conservation equation is0.8----400kg1m3aT_旦aTHeat fux 30 kW 1 m2]psCps =我hisx)+ MgCpg xf 0.6h.0。hoPw ]+ 0ll0+hg+Pw-Pe0。~Pw-Pc(3)0.44The boundary condition isaT|。= q"-h( T,- To)-ed( T。- r),”0一600一1200.1800 24000 3000ax x=0Heating time (S)(4)Fig. 1. Effect of initial density on mass loss rate. Mass remains asand the initial condition isa function of time.T= To，ρ=po，Mg=0( t=0).. (5)500With the above equations the parameterp x it ), M[(x ,t )and T( x ,t )can be predicted.40The solution of the model provides the temperature at400 kg1 m'，300----- 600 kg1 m}ach point of the solid and the local solid conversion....... 750 kg/ m'00kg1m2 Results and discussionHeat fux 30kW 1m2Pyrolysis of large cellulosic samples is different100from pyrolysis of small samples due to transport( heat广一600120001800 2400- 3000and mass ) limitations. During the pyrolysis of largeHeating time (s)samples there is a temperature profile present ，and aFig.2. Efect of initial density on surface temperature. Surfacetemperature as a function of time.sample is never isothermal. The existence of a tem-perature profile means that the heating rate of differ-remaining mass and surface temperature as a functionent parts of a sample is different. That fact can have aof time for four samples w ith different densities andsignificant impact on pyrolysis kinetics and on differ-with heat flux of 30kW/m2. It can be seen from Fig.ent pyrolysis routes. According to Ref. [ 11 ] trans-1 that the earlier pyrolysis starts , the lower the sam-port limitations play a significant role in overall beple density is. Because the lower density samples be-havior of the material. In a fire , transport limitationshave中国煤化工their surface tempera-often determine the course of the event.tureYHCNMHGresults in an earlieronsetur Pyuulyono. 1 现oulsouutemperature as a func-In general ,heat flux is the key factor that deter-tion of time curve always shows an inflection point atmines the py rolysis process and time to ignition. Andaround the py rolysis onset temperature. The reasonaccording to the Arrhenius reaction rate equation ,for this is that as cellulose decomposes , the materialtemperature plays ,a significant role. So the tempera-properties ( surface emissivity and thermal conductivi-ture with' tihe8气ach point of solid is analyzed in de-876Progress in Natural Science Vol.12 No.11 2002ty) will change , and a reaction endotherm occurs .500From the onset of pyrolysis the surface temperature一+ Experimentalremains to increase continuously and this results in-◆- Model400the temperature gradient ，and mass loss rate remains, 60 kW/m2constant until the surface temperature reaches maxi-e 300mum. And as the process continues，the temperature40 kW/m?名200gradient cannot remain and the mass loss rate decreas-es. All of these results are in agreement with the ex-perimental results of Suuberg' s.20 kW/m20.2 0.40.60.8 102.2 Effect of heat fluxDimensionless distance from surfaceFig.3. Comparison of predicted and experimental temperatureAs is anticipated the higher the heat flux , theprofiles( 691kg/m3 ,1= 200s).earlier pyrolysis starts and finishes. In general , heattransport limitation influences the process. Lee et→+ Experimentelal.! 13] performed one-dimensional radiative heating-毋- Model(83.7 kW/m2 and 38 kW/m2 ) experiments on bulk400[60 kW/m2wood samples ( 620 kg/m3 ). Different behavior was00seen that the pyrolysis wave was thinner and mass40 kW/m2、loss rate was fast when the heat flux was high. I200case of low heat flux , the pyrolysis wave w as muchthicker，which means the heating rate of different100parts of a sample is different. This is very importantand useful for fire models .00.264Fig.4. Comparison of predicted and experimental temperatureFigs.3 and 4 show the comparison of predictedprofiles( 458 kg/m' ,t= 200s). .and ex perimental temperature profiles of two differentdensities of wood( Ref.[ 12 ], density 691 kg/ m3 and50kW/m2458kg/m3 , t = 200s ) under different heat flux. It-40kWm23can be seen that the higher the heat flux , the steeper日500. 30 kW/m2the temperature gradient( aT/ax ). This is reason--20 kW/m2able , since the thermal conductivity is the same fosamples with the same density and the only differenceis the heat flux for conduction. Because of heat trans-Density (600 kg/m3)port limitation ，the heat accumulates near the surfaceand the surface temperature increases continuously.60012001800广 2400广 3000Surface temperature as a function of heating time isHeating time (8)presented in Fig. 5. It can be seen that temperatureFig.5. Effect of heat flux on surface temperature. Surface tem-increases faster under high heat flux and final temper-perature as a function of time.ature is higher. The higher temperature gradientmakes heat transfer into inside quicker and this re-sults in high mass loss rate. The fraction of remaining0.8一20 kW/m?mass as a function of heating time is presented in Fig.--- .30 kW/m?6. It can be seen that the sample begins py rolysis-- 50 kW/m2soon after the effect of heat flux. And the mass loss中国煤化IDensity (600kgtm>)rate remains constant for a long time. Even after along time heating ，the temperature of sample risesIYHCNMHGslowly , and the rate of decomposition is slower w henthe heat flux is low( < 20kW/m2 ). This is because600 120018002400 3000there is not enough heat available for conduction intoHeating time (S)the sample intsrior. Both Lee and Subberg' s experi-Fig. 6. Efect of heat flux on mass loss rate. Mass remains as amental studes drew the same conclusion .function of time.Progress in Natural Science Vol.12 No.11 20028772.3 Prediction of time to ignition3 ConclusionWe should note here that the ignition time .Transport limitations play a significant role inmentioned here is pilot ignition time. We predict theoverall pyrolysis and combustion properties of largetime to ignition also using the concept of critical sur-ize wood material. The major factor that influencesace temperature with the solution of mathematicthe mass loss rate and time to ignition of wood is ex-model ( surface temperature as a function of time ).ternal heat flux and initial sample density , especiallyWhen the surface temperature reaches the critical sur-external heat flux. The higher heat flux results inface temperature we consider that ignition occurs.higher temperature and deeper temperature gradient ,and thus the pyrolysis wave is thinner. The lowerM easurement of surface temperature at ignitiondensity wood is a better heat insulator which resultsduring cone calorimeter tests for several ply w oods andin earlier onset of pyrolysis and the surface tempera-particle board was performed by Jadwiga14]. In hiture increases more quickly.study temperature was measured by both thermocou-ples( Al-CrAl0.2 mm in diameter ) and a Chino radi-The concept of critical surface temperature is ap-ation pyrometer. He suggested that ignition tempera-propriate in predicting the time to pilot ignition. Ifture of wood is around 572 K~ 593 K. Liut 81 studiedthe ignition temperature is properly determined , andthe thermal decomposition of biomass thermo-the surface temperature as a function of heating timegravimetry and found that the first peak mass lossis determined with theoretical or numerical solution ,rate is around 300 9C. According to Jadwiga' s andthe time to ignition can be predicted accurately.Liu s studies，we suggest that the pilot ignition tem-perature is about 290 C ~ 310 C for most wood.ReferencesThree critical ignition surface temperatures( 290 C,1 Di Blasi, C. Modeling and simulation of combustion process of300 C and 310 C ) were used to predict the time tocharring and non-charring solid fuels. Prog. Energy Combust.ignition of wood under different heat flux. TableISci. ,1993 ,19 :71.shows the experimentally obtained pilot time to igni-2 Chen,Y. et al. Material pyrolysis properies , Part I : an integralmodel for one-dimensional transient pyrolysis of charing and non-tion of priceless wood( 100 mmX 100 mmx 23 mm ,charring materials. Combust Sci. Technol.，1993 , 88 : 309.density about 900 kg/ m3 ) in a cone calorimeter( ISO3 Kung ,H. C. A mathematical model of w ood pyrolysis. Combustion5660/ASTM E1354 ，Model CONE2A ). And theand Flame , 1972 ,18 :185.comparison of predicted and experimental time to ig-4 Jia,F. et al. Numerical simulation of mass loss process in py roliz-ing char materials. Fire and Materials , 1999 ,23 :71nition of wood under different heat flux is presented5 Martin, S. Diffusion-controlled ignition of cellulosic materials byin Fig.7 , which shows a good agreement bet ween ex-intense radiant energy. Tenth International Symposium on Com-perimental and predicted results.bustion , Cambridge ,UK , 1965 ,877.6 Jassens, M. L. In : Heat Release in Fires( ed. Babrauskas , V. ),Table 1. Experimental obtained pilot time to ignition of priceless woodLondon and New York : Elsevier Applied Science , 1992.Heat flux( kW/m2 )304(507 Michael J s. Predicting the ignition and burming rate of wood inthe cone calorimeter using an integral model. NIST GCR 99-775，Time to ignitior( s)1699443134798 Liu,N. A. et al. New mass loss kinetic model for thermal decom-position of biomass. Chinese Sci. Bull. ,2001 , 4610):876.9 Reina ,J.et al. Kinetic study of the py rolysis waste wood. Indus-18001 Experimmentaltrial & Engineering Chemistry Research , 1998 ,37 :1267 .●T=290 c含1500▲T=300 C0 Yang,L.Z. et al. A modified model of pyrolysis for charring ma-看1200▼Tg=310 °Cterials in fire. Chinese Sci. Bul. ( in Chinese), 2001 ,46( 23 ):2019e 900-11 Milosavljevie ,1. et al. Effects of transport limitations on pyrolysisof ellulosics. ACS Div. Fuel Chem. Prepr. ,1992 ,37(4 ):204.600-12 s中国煤化工haring materils in simulated00; , 1994.YHCNMHGorwoodinfresbylersimw.o 20lation. Sixteenth ( Int ) Symposium on Combustion ，Mas-Healffux (kW 1m)sachusetts, USA , 1976 , 1459.Fig. 7. Comparison of predicted and experimental time to ignition14 Jadwiga , F. Surface temperature at ignition of w ooden based slabs.of wood under dfferent heat flux.Fire Safety Joumal , 1996 ,27 :249.