POROUS CARBON PARTICLE COMBUSTION IN AIR

Transcription

1 MCS 7 Chia Laguna, Cagliari, Sardinia, taly, 11-15, 11 POOUS CABON PATCLE COMBUSTON N A V. M. Gremyahkin grema@ipmnet.ru nstitute for Problems in Mehanis, AS, Mosow, ussia Abstrat Theoretial investigation of porous arbon partile ombustion in air is presented. The diffusivekineti model onsidering heat and mass transfer both inside the porous partile and over partile surfae as well as kineti equations of both heterogeneous and homogeneous reations is investigated. t is shown the homogeneous reation may be onsidered as diffusive-limited reation for rather large sie of the partile. Two regimes of the arbon partile ombustion are observed: (1) high-rate regime for large internal surfae of the partile and () low-rate regime for the partile with lower internal surfae. The temperature of the partile is dereased with rate of the partile ombustion inreasing in high-rate regime beause inside the partile the endothermi reation of arbon with arbon dioxide is ourred. n low-rate regime the temperature of the partile is inreased with rate of the partile ombustion inreasing beause the reation of arbon with oxygen takes plae inside the partile. The dependene of the rate of the partile ombustion on the value of internal surfae is determined. The distributions of the onentrations and flows of reatants on radial oordinate as well as rates of the reations are determined both inside the porous partile and outside the partile.. ntrodution n the theory of porous arbon partile ombustion and gasifiation next positions have to be taken into aount [1]: the intensity of the ombustion proess is depended as on kinetis of the hemial reations so on mass and heat transfer of reatants and reations produts () burning out of arbon partile takes plae on the internal surfae inside the partile and at the partile external surfae (3) the produts of the arbon partile interation with oxygen are both arbon monoxide and arbon dioxide. The absene of the kinetis equations of the heterogeneous reations of arbon with gaseous reatants is a main hindrane for theory of arbon partile ombustion and gasifiation development. The diffusive-kineti model for porous arbon partile ombustion in pure oxygen has been onsidered [, 3]. Two regimes of the arbon partile ombustion are existed: (1) low-rate and high-rate regimes. The heterogeneous reations of arbon with oxygen are ourred in both lowrate and high rate regimes of the partile ombustion in pure oxygen. The differene between the regimes of the partile ombustion was onneted with formation of arbon dioxide in low-rate regime and onsumption of arbon dioxide inside the porous partile in high-rate regime. t is interesting to onsider the ombustion of the arbon partile in environment with lower onentration of oxygen, for example, in air beause oxygen may be supplied totally in homogeneous reation over partile surfae and that does not reah the partile surfae. Besides suh kind of arbon partile ombustion is more impotent for pratie.

2 Diffusive-kineti model of porous arbon partile ombustion The diffusive-kineti model onsiders porous arbon partile having radius a what is burning out in air in a furnae with wall temperaturet w. The model onsiders the equations of diffusion and heat transfer what are written in form of elements (arbon and oxygen) and full enthalpy onservation. m Ws div = (1) n div = () div( h + ) = swh δ ( r a) (3) h 4 4 Here =1, and 3 orrespond to CO. CO and O, = σ ( T Tw ) is heat losses by radiation, m and n are numbers of arbon and oxygen atoms in moleular of substane onsidering. The rate of arbon onsumption inside the partile equals to sum of the rates of heterogeneous reations of arbon with reatants and that is proportional to the value of the internal surfae of the porous partile. f mass flow of gas through unit surfae is denoted U = ε ρ u than the mass flows of substanes and heat may written in form = U ε ρ Dgrad, = UT [ ελ + ( i ε ) λ gradt (4) h g ] λ and Here g λ are oeffiients of heat ondutivity in gas and in solid arbon. The equation of gas disontinuity is div U = s (5) The equation for pressure alteration inside the porous partile is determined by Dary law k ε u = gradp (6) Besides the diffusive equation for arbon dioxide inluding kineti equations for hemial reations have to be onsidered Here and oxygen orrespondingly and div = ( o + ε ) (7) 3 g 1 o are the rates of heterogeneous reations of arbon with arbon dioxide and with g is the rate of homogeneous reation.

3 Boundary onditions for equations (1)-(7) are dp r =, U =, =, =, = (8) h dr r =, =, T = T w, P = P (9) Equations (1)-(3) may be integrated over radial oordinate. Exluding the summary rate of arbon onsumption from equations (1) and (5) and integrating the equations with boundary onditions (8) the next orrelations between flows of different substanes are reeived m U = (1) n = (11) a h + = Uh ( r a) h r θ (1) The left side of the equation (1) inludes the summary flow of full enthalpy in gas and the flow of heat inside the solid arbon. f heat effets of the reations are high and porosity of the partile is rather high as well the heat flow in solid arbon will be negligible in omparison with flow of full enthalpy in gas. The equations (1)-(1) may be integrated over radial oordinate one more with boundary onditions (9) if it is assumed the riteria Lewis equals to unit. n the result of integrating in aount of = + ) next equations may be reeived in r > a : ( in m η 1 1 = e ) + n η = e m ( (13) n ( h T ) e η + = [ ( + T w ) + ] U U η η r < a : ( h + T ) = e [ ( + T ) + (1 e ) ] (16) w U (14) (15)

4 Here U η = dr r ε ρ D The equation (6) may be integrated on radial oordinate also if it s assumed the value not altered inside the partile p / ρ is r < a r > a η η P = P + ; κ P = P (18) Here κ = kρ / ρd p is parameter determining gas penetration of porous partile and alteration of pressure inside the partile and η = η if r = a. η au / D = ρ is dimensionless rate of the partile ombustion. egimes of the porous arbon partile ombustion in air The equations (13)-(16) are valid both in gas phase over partile surfae and inside the porous partile. Consequently these equations are valid at the partile surfae as well. The solution of the equations (13)-(16) at the partile surfae has a sense if onentrations of all substanes at the partile surfae are positive values. This ondition determines a domain where the solutions of the equations are existed. Suh domain is shown in fig.1 for ase of arbon partile ombustion in air in a furnae with wall temperature T w =.15 K. The domain is restrited by urves a, b and where onentrations ofco. CO and O equal to ero orrespondingly. The point A where the rate of the partile ombustion reahes maximum value orresponds to diffusive-limited rate of the partile ombustion η =.159. Besides urves 1 and are shown in the fig.1 where the flow of arbon dioxide equals to ero and ondition of homogeneous reation equilibrium is fulfilled orrespondingly. The rate of the homogeneous reation CO + O = CO is determinate by the equation [4] g [ CO ] 1.5 o.5 = exp( 1493/ T )[ CO][ O ] [ H O] d = (19) dt where onentrations are determined in units mol/liter The dependene of the rate of the homogeneous reation on onentration of steam is rather week. However, the presene of steam is need for this reation aring out. n the following alulations the dependene of the rate of homogeneous reation on onentration of steam is not taken into aount.

5 Figure 1 The domain where the solutions of the equation are existed. 1 flow of arbon dioxide equals to ero, equilibrium of homogeneous reation.. t may be assumed the homogeneous reation is arried out in diffusive-limited regime for rather high temperature what is realied in proess of arbon partile ombustion. The diffusivelimited regime is realied if the rate of the homogeneous reation determining by the equation (19) is higher the rate of the reation d determining by the diffusive flows of reatants. The diffusive-limited rate of the homogeneous reation is determined from the equation 1 ξ dj 1 = dξ W d () Here J1 = ε ρ D1 / a and W1 = ε ρ Dd / a are dimensionless flow of arbon dioxide and diffusive-limited rate of the homogeneous reation. f the homogeneous reation is arried out in diffusive-limited regime the onentrations of reatants will equal to equilibrium onentrations. So the ondition of the homogeneous reation equilibrium is written in form 1/ 3 ke 3 = (1) Here k e is onstant of the reation CO +.5O = CO equilibrium determined from [5]. From the ondition that diffusive-limited rate is lower the kineti rate of the homogeneous reation next orrelation may be reeived a ( ρ D / ) 1/ d g ()

6 Figure shows the dependene the minimum radius of arbon partile when orrelation () is fulfilled on radial oordinate over partile surfae. The alulations have been fullfielded for ase of the rate of the partile ombustion η =. 14 and for furnae temperature T w = 15 K. So it may be onsidered the equilibrium of the homogeneous reation is valid for radius of arbon partile more 1 k. f the assumption about equilibrium of homogeneous reation is valid the real dependene of the partile ombustion rate on the partile surfae temperature is determined by urve in the fig.1. n this ase two regimes of the arbon partile ombustion in air may be onsidered: (1) low-rate regime where temperature of the partile is inreased with rate of the partile ombustion inreasing and () high-rate regime where the temperature of the partile is dereased with the rate of the partile ombustion inreasing. Figure. The dependene of minimum radius of the partile on radial oordinates when the homogeneous reation is arried out in diffusive-limited regime. Figure 3 shows the dependene of the flows of substanes to the partile surfae on the rate of the partile ombustion in air for furnae temperature T w = 15 K and for sie of the partile 4 orresponding parameter A = a/ ρ D= 1 what is orrespond to a 11 m. n the high-rate regime oxygen is supplied in the homogeneous reation over partile surfae pratially totally and that does not reah surfae of the partile. The onsumption of arbon determining the rate of the partile ombustion is ourred by mean of endothermi reation of arbon with arbon dioxide beause the temperature of the partile is dereased with rate of the partile ombustion inreasing.

7 ,8,6 Flows to the Partile Surfae - fs,4,, -, -, ,6,,,4,6,8,1,1,14 Dimensionless ate of the Partile Combustion - η Figure 3. Dependene of the substanes flows to the partile surfae on the rate of the partile ombustion in air: 1 - CO, - CO, and 3 - O. n the low-rate regime of the partile ombustion oxygen reahes the partile surfae and the reation of oxygen with arbon is ourred inside the porous partile. The produt of the partile ombustion in low-rate regime is arbon dioxide (see fig.3). The homogeneous reation over partile surfae in low-rate regime is pratially absent. Figure 3 shows the high-rate regime of the arbon partile ombustion in air is ourred if the rate of the partile ombustion η >.1 but low-rate regime is realied if η <.6. At the middle rates of the partile ombustion (.6< η <.1) is arried out transition regime. n this regime the flow of oxygen to the partile is dereased but flow of arbon dioxide is altered the diretion with rate of partile ombustion inreasing. Proesses inside the porous arbon partile The rate of porous arbon partile ombustion is depended on summary rates of heterogeneous reations what is proportional to internal surfae of porous arbon partile. The rate of porous arbon partile ombustion has to be determined from the onsideration of proesses inside the porous partile. t may be done if kineti equations for heterogeneous reations of arbon with oxygen and with arbon dioxide are known. The kineti equation of the reation of arbon with arbon dioxide to unit of the internal surfae my be onsidered as known [6] 76 exp( 35 / ) = T ρ (3) 3 3

8 The dependene of the rate of porous arbon partile ombustion on partile temperature for ase of the partile ombustion in oxygen is presented in [7].This dependene for low rate of the partile ombustion and for the partile temperature near to furnae temperature may be written in form.3 1 exp( 57 / ) o = T ρ 1 1 (4) Using the equations for the rates of heterogeneous reations (3)-(4) the equation of disontinuity (5) may written in form 1 ξ dβ = ( Φo + Φ ) S dξ dη β = dξ ξ (5) (6) Φ = A are the dimensionless rates of the reations of arbon with Here Φ o = o A and oxygen and with arbon dioxide orrespondingly, S = sa / ε and funtion β = ξ d η / dξ determines the rate of gaseous flow of the reations produts. The internal surfae of the arbon partile may be altered [8] with arbon partile burning out. However here it will be assumed the internal surfae of the partile is onstant and that is not depended on radial oordinate. The equations (13)-(15) together with ondition of the homogeneous reation equilibrium (1) may be solved and onentrations and temperature are determined as a funtionη. So the rates of the reations Φ and Φ o are the funtion of η also. n this ase the equations (5)-(6) may be integrated with boundary onditions ξ =, β = ; ξ = 1, η = η, β = β = η / ε (7) Here ε is porosity at the partile surfae. So the distributions of funtion β and η as well as onentrations and temperature on radial oordinate ξ inside the porous partile are determined. The additional boundary ondition. (7) gives the possibility to determine the parameter S orresponding to the rate of the partile ombustion η.the dependene of the parameter S on the rate of the partile ombustion is shown in fig. 4. n the high-rate regime the rate of the partile ombustion is inreased with parameter S inreasing. But in the low-rate regime the value of the parameter S is not inreased with the rate of the partile ombustion inreasing monotony. So, two rates of the partile ombustion are realied for the same value of the parameter S. The dereasing of the parameter S with η inreasing is onneted with sharp inreasing of the partile temperature in low-rate regime. Beause the rate of the partile ombustion η is inreased with the partile temperature inreasing stronger then that is inreased with parameter S inreasing. t may be assumed the

9 realiation of different regimes of the partile ombustion for the same internal surfae of the partile is onneted with proess of the partile ignition. f the arbon partile is ignited by mean of high temperature of environment gas the high-rate regime of the partile ombustion is realied but if the partile is ignited by means of radiation when the temperature of the partile is higher the environment gas the low-rate regime of the partile ombustion will be realied. Figure 4. Dependene of parameter S on the dimensionless rate of the partile ombustion for different furnae temperature : 1 - T w =13 K, - 15 K, 3 17 K. Conlusion The theoretial diffusive-kineti model is onsidered for porous arbon partile ombustion in air. The investigations show: - two regimes of the arbon partile ombustion in air are realied in dependent on the value of the internal surfae of the partile: (1) low-rate regime and () high-rate regime, - in the high-rate regime the endothermi heterogeneous reation of arbon with arbon dioxide is ourred therefore the temperature of the partile is dereased with the rate of the partile ombustion inreasing, - in the low-rate regime the heterogeneous reation of arbon with oxygen is ourred, - the homogeneous reation of arbon monoxide with oxygen is arried out in diffusivelimited, equilibrium regime for the arbon partile rather large sie, - the dependene of the arbon partile ombustion rate on the value of the internal surfae of the porous partile is determined, - the distributions of reatants onentrations and flows as well as rates of heterogeneous and homogeneous reations on radial oordinate inside the porous partile are determined as well.

10 Nomenlature a radius of the partile C heat apaity of gaseous substanes to kmoll с heat apaity of gaseous substanes to kg D diffusivity fluxes of substanes h flux of heat H enthalpies of substanes formation from elements to kmoll h enthalpies of substanes formation from elements to kg h enthalpy of solid arbon k gas penetration of porous partile m numbers of atoms of arbon in moleular of substane n numbers of atoms of oxygen in moleular of substane g rate of homogeneous reation rate of the reation of arbon with arbon dioxide rate of arbon onsumption in heterogeneous reations o1 rate of arbon onsumption in the reation o rate of arbon onsumption in the reation P pressure in units of atmosphere r radial oordinate s internal surfae of the partile T temperature T w temperature of furnae T temperature of the partile surfae U mass flux of gas u veloity of gas mass frations C + O = CO + H C + O = CO

11 mass frations in environment mass frations at the partile surfae Greek symbols λ heat transfer oeffiient in gas visosity of gas moleular mass of gaseous substanes moleular mass of arbon ε porosity of the partile density of gas ρ σ Stephan-Boltsman onstant ndexes : 1 CO CO 3 O eferenes [1]. Chukhanov Z. F., Some Problems of Fuels and Power Energy, AS USS. 1961, P.35 (in ussian). []. Gremyahkin V.M., Fortsh D., Shnell U., Hein K..G., A model of the ombustion of a porous arbon partile in oxygen, Combust. & Flame, 13; ( ) [3] Gremyahkin V. M., To kinetis of heterogeneous reations of arbon with oxygen in the porous arbon partile ombustion in oxygen, Combustion, Explosion and Shok Waves, 4(3): P. 11- (6). [4] Lavrov N. V., oenfeld A.., Khaustovih G. P., Proesses of Fuel Combustion and Defense of Environment, :Metallurgy, 1981.V. 13, - P. 161.(in ussian) [5] Thermodynami Properties of ndividual Substanes, ef. Book (Glushko V. P. Ed.) Nauka, [6] Lee S., Angus J.C., Edwards.V., Gardrer N.C. Nonatalyti oal har gasifiation, AChE Journal. 3:, P.583 (1981) [7] Levendis Y.A., Flagan.C., Gavalas G.., Oxidation kinetis of monodisperse spherial arbonaeous partiles of variable properties, Combust. & Flame, 76: P. 1 (1989) [8]. Aarna, E. M. Suuberg.. Changes in reative surfae area and porosity during har oxidation, 7-th Symposium (nternational) on Combustion, 1998, P /