mathematical modelling and simulation of bubbling fluidised bed gasifiers

Ž .Powder Technology 120 2001 105–112www.elsevier.comrlocaterpowtec

Mathematical modelling and simulation of bubbling fluidisedbed gasifiers

Stefan Hamel), Wolfgang KrummLehrstuhl fur Energie-und UmweltÕerfahrenstechnik, Institut fur Energietechnik, UniÕersitat Siegen, Paul-Bonatz-Str. 9-11, D-57068 Siegen, Germany¨ ¨

Abstract

A mathematical model for simulation of gasification processes of solid fuels in atmospheric or pressurised bubbling fluidised bedsincorporating bed and freeboard hydrodynamics, fuel drying and devolatilization, and chemical reaction kinetics is presented. The modelhas been used to simulate four bubbling fluidised bed gasifiers, described in literature, of different scales from atmospheric laboratoryscale up to pressurised commercial scale, processing brown coal, peat and sawdust. The gasifiers have been operated within a wide rangeof parameters using air, airrsteam or oxygenrsteam as gasification agent, operating with or without recirculation of fines at operatingpressures up to 2.5 MPa. The simulation results for overall carbon conversion, temperature and concentrations of gaseous species agreesufficiently well with published experimental data. q 2001 Elsevier Science B.V. All rights reserved.

Keywords: Gasification; Pressurised fluidised bed; Biomass; Coal

1. Introduction

The traditional approach necessary to establish commer-cial plant technology is based on comprehensive experi-mental investigations, progressing from a laboratory scaletest unit to a pilot scale plant, before building a full-scalecommercial demonstration plant. For process optimisation,an extensive investigation of the plant behaviour depend-ing on various operating parameters is required for eachscale up step. To support this optimisation procedure,mathematical models are helpful to reduce the temporaland financial efforts. Pre-condition is a reliable simulationtool, which includes the mathematical formulation of allimportant chemical and physical processes by describingtheir dependency on operating parameters and their inter-dependencies.

As an extension of former works that have been carriedout in the field of bubbling and circulating fluidised bedcombustion at the Institute of Energy Technology of theUniversity of Siegen, a comprehensive model for pres-surised bubbling fluidised bed gasification reactors is pre-sented. The model includes bed and freeboard hydrody-namics, kinetic models for drying and devolatilization, andfor chemical reactions. The comparison between experi-

) Corresponding author. Tel.: q49-271-740-2107, q49-271-740-2634;fax: q49-271-740-2636.

Ž .E-mail address: [email protected] S. Hamel .

mental results of an atmospheric laboratory scale gasifierw xprocessing peat 1 , of a small pilot scale pressurised

w xgasifier using brown coal, peat and sawdust 2 , of aŽ .High-Temperature Winkler HTW pressurised gasification

w xplant 3 and an HTW commercial scale demonstrationw xplant processing brown coal 4,5 with simulation results

are used to discuss the quality of the presented mathemati-cal model.

2. Model description

The presented model is the result of an advanced devel-opment based on the works on atmospheric bubbling flu-

w xidised beds for coal combustion 6 , sewage sludge com-w xbustion 7 , and on works on atmospheric and pressurised

w xcirculating fluidised bed plants 8,9 . The development ofthe model, the applied formulas and the mathematical

w xsolution procedure have been reported in detail 10 .Therefore, the sources of the applied submodels are refer-enced and only a short description of the main features isgiven here.

2.1. Cell model

The gasifiers and other required components, as forexample, the cyclone and connection pipes, are dividedinto a number of in-series arranged discrete balance seg-ments, so-called cells. According to the two-phase theory,

0032-5910r01r$ - see front matter q 2001 Elsevier Science B.V. All rights reserved.Ž .PII: S0032-5910 01 00356-4

( )S. Hamel, W. KrummrPowder Technology 120 2001 105–112106

each cell is subdivided into a solid-free bubble phase andan emulsion phase. The schematic presentation of thesubdivision of the gasifier into cells and the gas, solid andenergy flows in each cell is shown in Fig. 1. The massflow balances for the bubble and the emulsion phase areseparately solved. The energy balance is formulated foreach cell. The energy transfer caused by feed and carry outof solid and gas flow, by energy conversion throughchemical reactions and through wall heat transfer surfacesis taken into consideration. To design this simulation pro-gram highly flexible, each cell is theoretically providedwith gas, solid and energy flows from neighbour cells aswell as with inputs for gas and solid feed from outside,solid recirculation from distant cells, as for example, fromthe cyclone cells, as well as outlets for solid dischargeflow. In practice, solid discharge or gasification agentsupply has not to be considered in every cell, but thismodel structure enables one to project any geometricreactor configurations.

The fluid dynamic model for the bubbling fluidised bedallows to estimate the average volume of the bubble phase,which is used for a proportional separation of the cellvolume in a bubble and an emulsion phase. Due to theassumption that the bubble is simplified, supposed to besolid-free, only homogeneous chemical reactions have tobe considered inside the bubble phase. Homogeneous andheterogeneous chemical reactions have to be regarded inthe emulsion phase consisting of gas and solid. Besides theinert bed material, an open number of solids can behandled with this simulation program. The balance equa-tions have to be formulated for each solid type like coke orlimestone. Each of the considered active solids is allocatedto heterogeneous conversion reactions. This strategy en-ables to take into account different kinetic parameters ofvarious cokes in case of co-gasification. Each regardedsolid type in this simulation is represented by a definitenumber of discrete particle diameters.

2.2. Fluid dynamic model

The calculated values from the fluid dynamical model,e.g. upward and downward gas and solid flows, the poros-ity, the residence times of gas and solid inside the reactor,and the gas exchange between bubble and emulsion phase,are important boundary conditions for other submodels,e.g. for heat transfer, drying and pyrolysis, and reactionrates.

The fluid flow inside classic gasrsolid fluidised beds isdecisively determined by the formation and the movementof the bubbles. Ascending bubbles cause a vertical mixingof solid particles, the average voidage depends on size andrise velocity of the bubbles. The calculation of the bedhydrodynamics depending on the bed height above thedistributor is based on the model for atmospheric bubbling

w xfluidised beds proposed by Hilligardt 11 improved byw xWein 12 . The influence of increased system pressure on

the bubble size and velocity is taken into account follow-w xing the approach of Heinbockel 9 to expand the Hilligardt

w xmodel 11 by keeping the atmospheric state unchangedand using the bubble parameters, which have been deter-

w xmined by experiments 13 . These values qualitativelyrepresent the bubble parameters up to a pressure of 1.6MPa.

w xThe experimental results of Olowson and Almstedt 13w xand the observations of Hoffmann and Yates 14 and

w xRowe et al. 15 indicate that the average bubble size isgrowing with increasing pressure passes a maximum be-fore a decrease of the bubble size with increasing pressurecan be observed.

Bursting bubbles at the fluidised bed surface eject inertsolid particles as well as active particles from the fluidisedbed into the freeboard. The elutriation of fine char particlesleads to inefficient carbon conversion of fluidised bedgasification. A mathematical model based on a probability

w xapproach for bubble behaviour near the bed surface 16,17

Fig. 1. Schematic diagram of the applied cell model.

( )S. Hamel, W. KrummrPowder Technology 120 2001 105–112 107

is applied to predict the mass flux from the fluidised bedinto the freeboard. The entrained mass consists of activeand inert particles due to the calculated mass fractionsinside the fluidised bed. The gas flow in the freeboardabove the fluidised bed surface is described using theso-called ghost bubble approach according to Pemberton

w x w xand Davidson 18 and Hamdullahpur and Mackay 19 ,w xwhich was also applied successfully by others 20–22 .

The determination of the solid movement and residencetime as well as the solid concentration profile in thefreeboard is based on the trajectory calculation for differ-ent particle classes. The equation for the particle motionconsidering the active forces inertial, buoyancy, weightand drag force for a single particle is solved for the inertand active particles, which are furthermore superposedwith a particle size distribution different for inert andactive material, an initial particle starting velocity distribu-tion and a particle shape distribution. The particle startingvelocity is assumed by a Gaussian distribution according

w xto an approach from Levy et al. 23 . The deviation of thespherical particle shape, which is usually assumed, istaking into account by using a method proposed by Haider

w xand Levenspiel 24 for calculating the drag coefficientdepending on the particle sphericity. Based on the trajec-tory calculation for different particle classes, the solidconcentration profile in the freeboard and the elutriation ofthe active and inert particles is determined.

2.3. Drying and deÕolatilization

Fuel drying and devolatilization and combustion orgasification of the volatile and solid pyrolysis residualsusually occur in the mentioned sequence. But certainly, atemporal superposed proceeding is possible; for example,the devolatilization of large fuel particles starts at the outersurface although the drying process of the wet core is stilllasting. Knowledge of the kinetics of drying and de-volatilization in combination with the fluid dynamics

is important for a better interpretation of variations inoperation behaviour using moist fuel. Under certain cir-cumstances, reactor behaviour, i.e. temperature profile, isdecisively affected by the vertical location of water evapo-ration and volatile release. Therefore, it is necessary toconsider the fuel feed location, the fuel particle size distri-bution, the fuel moisture content and kinetic parameters ofdrying and devolatilization in combination with the fluiddynamics to calculate the water and volatile release as afunction of reactor height.

To calculate simultaneous fuel drying and devolatiliza-tion of fuel particles, the model proposed by Agarwal et al.w x25 is applied. Assuming that drying takes place at aboundary moving from the outer surface to the centre ofthe particle, an unsteady-state heat conduction equation inspherical coordinates with a convective boundary condi-tion is solved analytically. The determined temperatureprofile in the dried shell is used in a numerical integrationover the volume of particle to calculate the volatile releaseusing a non-isothermal fuel decomposition kinetic. Theamount of volatile matter released is calculated using thedistributed activation energy model of Anthony and

w xHoward 26 . The coupled drying and devolatilizationw xmodel of Agarwal et al. 25 was successfully applied by

w xDersch 8 , modelling a circulating fluidised bed combus-tor firing wet brown coal.

The yields of char, gas and tar from the pyrolysis ofbrown coal are estimated according to experimental resultsfrom literature obtained in a pressurised fluidised bed

w xoperating at pressures up to 2.5 MPa 27 . The sum of thetars released during pyrolysis is simplified represented bytwo-model components. The model components are twodifferent higher hydrocarbons, which are composed in thatway to obtain the molar HrC ratio according to theexperimental determined molar HrC ratio of the pyrolysistar of brown coal.

The products from the fluidised bed pyrolysis of peat isw xestimated due to the results reported in Ref. 28 . In the

Table 1Considered chemical reactions

No. Chemical reaction DH ReferenceR

1 2 2w xR1 Cq O ™ 2y COq y1 CO y393.5 -DH -y110.5 kinetic parameters: Hobbs et al. 29 ;2 2 Rž / ž /F F F w xin kJrmol C mechanism factor F : Field et al. 30c c c c

w xR2 CqH O™COqH q131.4 kJrmol C Hobbs et al. 292 2w xR3 Cq2 H ™CH y74.9 kJrmol C Hobbs et al. 292 4

w xR4 CqCO ™2CO q172.5 kJrmol C Weeda 312w xR5 COq1r2 O ™CO y283 kJrmol CO bubble: Hottel et al. 32 ; emulsion:2 2w xHayhurst and Tucker 33

w xR6 H q1r2 O ™H O y241.9 kJrmol H Jensen et al. 342 2 2 2w xR7 CH q3r2 O ™COq2 H O y519,4 kJrmol CH Jensen et al. 344 2 2 4

w xR8 COqH O™H qCO y41.1 kJrmol CO Chen et al. 352 2 2w xR9 CH qH O™COq3 H q206.3 kJrmol CH Chen et al. 354 2 2 4

w xR10 TarqO ™COqH DH -0 Siminski ref. in Smoot and Smith 362 2 Rw xR11 TarqH O™COqH qCH DH )0 bubble: Serio et al. 37 ; emulsion:2 2 4 R

w xCorella et al. 38


case of sawdust, several literature sources and own experi-mental results are used to estimate the product yields. Adetailed description of the evaluation of the available

w xliterature data is given in Ref. 10 .

2.4. Chemical reaction kinetics

The products of fuel drying and pyrolysis water, char,gases and tar are reacting with the gasification agent andamong each other. The chemical reactions assumed to takeplace in the fluidised bed gasifier are listed in Table 1.

Besides the heterogeneous gasification reactions no.Ž . Ž .R2–R4 Table 1 , the char combustion reaction no. R1 is

considered because the simulated HTW gasification reac-tors are operated in autothermal mode. The required heat

Ž .for driving the endothermic carbon–steam R2 and theŽ .carbon–carbon dioxide R4 reactions is provided by the

exothermic combustion of char and volatiles with air oroxygen. Furthermore, homogeneous oxidation of carbon

Ž . Ž . Ž .monoxide R5 , hydrogen R6 and methane R7 is in-Ž .cluded. Water–gas shift reaction R8 and methanation

Table 2Main operating parameters of the different simulated gasifiers

HTW pressurised HTW demonstration Pressurised fluidised bed gasifier according tow x w x w xgasification plant 39 plant 39 Kurkela and Stahlberg 2

Reactor height 14.5 3.7 mFreeboard B 0.6 2.75 0.25 mSimulation no. LU O2 BE KU1 KU2 KU3 KU4 KU5 KU6 KU7 KU8 –

aFuel RB RB RB RB RB RB RB FP FP FP FP –Pressure 2.5 2.5 1.0 0.5 0.5 0.5 0.7 0.5 0.5 0.5 0.5 MPaFuel feed 3377 6859 25,769 46.9 41.4 41.4 49.0 68.8 65.5 61.6 63.7 kgrh

b b b 3Primary air feed airrH O O rH O O rH O 51.8 51.6 51.4 62.2 43.8 60.7 53.3 48.1 N m rh2 2 2 2 23Secondary air feed 30.1 37.5 46.5 42.8 49.5 21.9 31.9 46.9 N m rh

Steam feed 6.8 9.0 6.8 11.3 – 15.5 5.4 – kgrhcER 0.337 0.268 0.238 0.33 0.40 0.44 0.41 0.31 0.29 0.32 0.37 –

Recirculation of fines yes yes yes no yes yes yes no no no no –

Fuel propertiesW 16.9 15.8 12.4 11.8 11.7 11.9 11.8 16.1 14.8 15.9 18.5 wt.%Ž .A dry 11.41 8.31 12.1 4.3 4.3 wt.%Ž .VM daf 53.42 52.7 53.38 53.0 68.4 wt.%

Ž .C dry 61.5 62.9 61.1 63.8 54.5 wt.%Ž .H dry 4.1 4.03 4.4 4.6 5.6 wt.%Ž .O dry 21.8 23.3 20.7 26.2 33.6 wt.%Ž .N dry 0.68 0.88 0.7 0.8 1.8 wt.%Ž .S dry 0.51 0.58 1.0 0.3 0.25 wt.%

Pressurised fluidised bed gasifier according Fluidised bed gasifier accordingw x w xto Kurkela and Stahlberg 2 to Leppalahti and Kurkela 1¨

Reactor height 3.7 3.65 mFreeboard B 0.25 0.158 mSimulation no. KU9 K10 K11 K12 K13 K14 K15 LPA LPB LPC LPD LPE –

aFuel FP FP FP FP FP SD SD FP FP FP FP FP –Pressure 0.7 1.0 0.5 0.4 0.5 0.4 0.4 0.1 0.1 0.1 0.1 0.1 MPaFuel feed 76.3 62.5 45.0 26.5 50.2 42.8 40.0 11.2 10.3 11.7 10.7 9.8 kgrh

3Primary air feed 62.7 65.2 51.4 38.9 47.0 39.1 37.6 12.5 10.4 12.5 12.9 13.0 N m rh3Secondary air feed 35.7 34.0 27.7 10.4 41.6 11.6 22.3 – 1.1 3.5 – – N m rh

Steam feed 18.7 27.0 6.5 7.9 7.6 2.9 12.8 – – – – – kgrhcER 0.30 0.29 0.40 0.43 0.41 0.28 0.39 0.26 0.25 0.32 0.26 0.29 –

Recirculation of fines no no yes yes yes no no no no no yes yes –

Fuel propertiesW 16.2 15.5 15.7 16.0 16.1 11.3 5.9 15.2 10.7 15.2 8.4 8.4 wt.%Ž .A dry 4.3 0.2 5.2 wt.%Ž .VM daf 68.4 83 68.4 wt.%

Ž .C dry 54.5 50.2 54.3 wt.%Ž .H dry 5.6 6.1 5.7 wt.%Ž .O dry 33.6 43.4 33.1 wt.%Ž .N dry 1.8 0.1 1.5 wt.%Ž .S dry 0.25 0 0.2 wt.%

aRBs rhenish brown coal; FPs finnish peat; SDssawdust.b The gasification agent is fed at up to 10 different locations into the reactor.c ERsequivalent O -ratio.2


Fig. 2. Comparison of the different scale up levels of the simulated fluidised bed gasifiers including the preferred cell structure.

Ž .R9 are calculated by a kinetic expression proposed byw xChen et al. 35 . They determined experimentally the ki-

netic rate parameters taking into account the catalyticinfluence of coal ash in a fluidised bed reactor. Theconversion of tars are estimated applying kinetic rate

Ž .expressions for oxidation R10 and decomposition in theŽ .presence of steam R11 .

3. Description of the simulated reactors

The laboratory scale pressurised fluidised bed gasifierw xwas used by Kurkela and Stahlberg 2 to study the gasifi-

cation of low grade fuels, peat and waste wood at operat-ing pressures from 0.4 up to 1.0 MPa. A detailed des-cription of the reactor, the operating parameters and the

w xexperimental results are reported in Ref. 2 . Experimentalresults of the gasification of peat in the atmospheric labo-ratory scale gasifier are described by Leppalahti and Kur-¨

w xkela 1 . The data necessary for simulation of this twogasifiers are taken from the literature sources mentionedabove.

The original measurement data of the HTW pressurisedgasification plant and of the HTW commercial scaledemonstration plant are provided by the company Rhein-braun and its engineering partner Krupp-Uhde. The HTW

ŽFig. 3. Calculated results in comparison with experimental data of airrsteam gasification of the HTW pressurised gasification reactor simulation no. ALUB.according to Table 2 .


pressurised gasification plant was designed to operate at asystem pressure of 2.5 MPa and a maximum throughput of6.5 tons brown coalrh. Plant operation with airrsteam asgasification agent was possible as well as operation with

w xoxygenrsteam 3 .In Rheinbraun’s commercial scale, HTW demonstration

plant gas for methanol synthesis was produced from Rhen-ish brown coal continuously from 1986 to 1997. The plantworked at an operating pressure of 1.0 MPa with a maxi-mum throughput of 30 tons brown coalrh. With the aim toproduce synthesis, gas oxygen and steam are feed as

w xgasification agents 4,5 . The main operating parametersand fuel properties for the different gasifiers are listed inTable 2. The four gasifiers are displayed schematically inFig. 2 including the preferred cell structure required by thesimulation program.

4. Simulation results

The simulation results of temperature and gas concen-trations depending on the reactor height are displayed

Ž .exemplary for run number ALUB see Table 2 in Fig. 3 forthe HTW pressurised gasification reactor. To represent thecomplete calculated results, the cells of the connection

Ž .pipe between cyclone and reactor see Fig. 2 and thecyclone cells itself are appended vertical at the top of the

Ž .reactor cells see left sketch in Fig. 3 .Comparisons of the average freeboard temperature, the

overall carbon conversion and the molar fractions of CO,H , H O and CH in product gas are shown in Fig. 4a–f.2 2 4

w xFor the two laboratory scale gasifiers 1,2 , only one datapoint for the freeboard temperature is published. There-fore, in Fig. 4a, the average value of the calculated free-

Fig. 4. Comparison of the predicted average freeboard temperature, the overall carbon conversion and the CO, H , H O and CH concentrations with2 2 4

measured data.


board temperature profile is compared with the publishedtemperature. After adjusting the overall heat loss of thereactors according to the published overall energy balance

w xfor the laboratory scale gasifiers 2 , the deviations ofcalculated steady-state temperature and measurements arewithin an error range of "10%. The individual calculatedtemperature profiles suitably correspond with the HTW

w xgasifier measurements 39 . The calculations of the overallŽ .carbon conversion Fig. 4b and the concentration of H O2

Ž .Fig. 4f are also within a deviation of "10%. TheŽ . Ž .calculated CO Fig. 4c and CH Fig. 4d concentrations4

are slightly overestimated especially for the data points ofpeat gasification while the prediction of the concentration

Ž .of H Fig. 4e is again within a "10% range. The results2

indicate that some correlations used in the model have tobe improved.

In lack of individual kinetic parameters for the combus-tion and gasification reactions of the different fuel chars atthe moment, a set of kinetic parameters is used for thedifferent fuel chars as referenced in Table 1. The results ofthe carbon conversion especially in the cases of peatgasification indicates that a better agreement could beexpected by integrating individual kinetics into the pro-gram.

The final gas composition is decisively affected by theŽ .water–gas shift reaction WGSR and their kinetics, partic-

ularly in case of secondary gasification agent supply. Thecatalytic influence of the bed material and the fuel ashinfluence on the kinetics of the WGSR are taken intoaccount by the applied model. However, the parameters

w xare validated using one special coal ash 35 . Kineticparameters valid for different bed materials or fuel ashesare not available. Thus, an extrapolation of the currentkinetic model is necessary.

Regarding the wide range of operation parameters andrecalling that the introduction of plant specific parametershad been avoided in order not to limit the validity andflexibility of the model the calculated results are verysatisfying.

5. Conclusion

w xA previously developed mathematical model 10 forbubbling fluidised bed gasifiers is used to simulate fourgasifiers of various scales. A wide range of operation

Žmodes is tested using air, airrsteam or O rsteam ERs2.0.23–0.44 , processing brown coal, peat and sawdust,

operating either with or without recirculation of fines,operating with or without secondary gasification agentsupply at pressures up to 2.5 MPa. Simulation results ofthe present model agree sufficiently well with the experi-mental data represented by overall carbon conversion,freeboard temperature and the concentrations of individualgas species.

Acknowledgements

The authors gratefully acknowledge the financial sup-port from the Ministry of School, Science and Research of

Ž .Nordrhein-Westfalen Project-No. IV A 4- 9021.1 andŽfrom the German Research Foundation DFG-Project No.

.KR 892r9-1 .

References

w x Ž .1 J. Leppalahti, E. Kurkela, Fuel 70 1991 491–497.¨w x Ž .2 E. Kurkela, P. Stahlberg, Fuel Process, Technol. 31 1992 .w x Ž .3 W. Adlhoch, J. Keller, P.K. Herbert, VGB Kraftwerkstech. 72 4

Ž .1992 .w x4 R. Wischnewski, A. Mittelstadt, W. Renzenbrink, C. Lutge, R.¨ ¨

Ž .Abraham, DGMK Tagungsber. 9802 1998 143–150, ISBN 3-931850-40-4.

w x5 H-P. Schiffer, A. Mittelstadt, R. Wischnewski, C. Lutge, J. Klein,¨ ¨Ž .VDI-Ber. 1387 1998 .

w x6 K.J. Burkle, PhD Thesis, University of Siegen, 1991.¨w x Ž7 M. Wirsum, PhD Thesis, University of Siegen VDI Verlag,

.Dusseldorf , 1998.¨w x8 J. Dersch, PhD Thesis, University of Siegen, 1994.w x9 I. Heinbockel, PhD Thesis, University of Siegen, Germany, 1995.w x Ž10 S. Hamel, F.N. Fett, W. Krumm, Final Report of the MWF Secre-

.tary of Science and Research of Nordrhein-Westfalen, GermanyProject-No. IV A4-9021.1, 1999.

w x11 K. Hilligardt, PhD Thesis, TU Hamburg-Harburg, Germany, 1986.w x12 J.W. Wein, PhD Thesis, TU Hamburg-Harburg, Germany, 1992.w x Ž . Ž .13 P.A. Olowson, A.E. Almstedt, Chem. Eng. Sci. 45 7 1990 1733.w x Ž .14 A.C. Hoffmann, J.G. Yates, Chem. Eng. Commun. 41 1986 133–

149.w x15 P.N. Rowe, P.U. Foscolo, A.C. Hoffmann, J.G. Yates, in: D. Kunii,

Ž .R. Toei Eds. , X-Ray Observation of Gas Fluidized Beds underPressure. Fluidization Tokyo, United Engineering Trustees, 1984,pp. 53–60.

w x16 C.L. Briens, M.A. Bergougnou, A.T. Baron, Powder Technol. 54Ž .1988 183.

w x17 T. Baron, C.L. Briens, P. Galtier, M.A. Bergougnou, Powder Tech-Ž .nol. 63 1990 149–156.

w x Ž .18 S.T. Pemberton, J.F. Davidson, Chem. Eng. Sci. 39. Jg. 1984 , H.5, S. 829–840.

w x Ž .19 F. Hamdullahpur, G.D.M. MacKay, AIChE J. 32. Jg. 1986 , H. 12,S. 2047–2055.

w x20 M. Sciazko, J. Raczek, J. Brandrowski, Chem. Eng. Process. 24. Jg.Ž .1988 , S. 49–55.

w x Ž .21 A.S. Fung, F. Hamdullahpur, Powder Technol. 74. Jg. 1993 , S.121–133.

w x Ž .22 K.-G. Berkelmann, U. Renz, Powder Technol. 68. Jg. 1991 , S.271–280.

w x Ž .23 E.K. Levy, H.S. Caram, J.C. Dille, S. Edelstein, AIChE J. 29 3Ž .1983 383–388.

w x Ž .24 A. Haider, O. Levenspiel, Powder Technol. 58 1989 63–70.w x Ž .25 P.K. Agarwal, W.E. Genetti, Y.Y. Lee, Chem. Eng. Sci. 41 9

Ž .1986 .w x Ž . Ž .26 D.B. Anthony, J.B. Howard, AIChE J. 22 4 1976 625–656.w x27 R. Hegermann, PhD Thesis, University of Karlsruhe, Germany,

1990.w x Ž .28 V. Arpiainen, M. Lappi, J. Anal. Appl. Pyrolysis 1989 355–374.w x Ž . Ž .29 M.L. Hobbs, P.T. Radulovic, L.D. Smoot, AIChE J. 38 5 1992

681–702.w x30 M.A. Field, D.W. Gill, P.G.W. Hawksley, B.B. Morgan, Combus-

tion of Pulverized Coal. Cheney & Sons, Banbury, England, 1967.w x31 M. Weeda, PhD Thesis, University of Amsterdam, Netherlands,

1995.


w x32 H.C. Hottel, G.C. Williams, N.M. Nerheim, D.R. Schneider, Proc.of 10th Symposium on Combustion. The Combustion Institute,1965, pp. 111–121.

w x Ž .33 A.N. Hayhurst, R.F. Tucker, Combust. Flame 79 1990 175–189.w x34 A. Jensen, J.E. Johnsson, J. Andries, K. Laughlin, G. Read, M.

Ž . Ž .Mayer, Fuel 74 11 1995 1555–1569.w x35 W.J. Chen, F.R. Sheu, R.L. Savage, Fuel Process. Technol. 16

Ž .1987 279–288.

w x36 L.D. Smoot, P.J. Smith, Coal Comb. and Gasification. Plenum, NewYork, 1985.

w x37 M.A. Serio, W.A. Peters, J.B. Howard, Ind. Eng. Chem. Res 26Ž .1987 1831–1838.

w x38 J. Corella, M.P. Aznar, J. Delgado, E. Aldea, Ind. Eng. Chem. ResŽ .30 1991 .

w x39 S. Hamel, W. Krumm, R. Abraham, A. Mittelstadt, G. Karkowski,¨Proc. of 4th Int. Symp. on Coal Combustion, Beijing, 1999.

mathematical modelling and simulation of bubbling fluidised bed gasifiers

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