Available online at www.sciencedirect.comJOURMULOFScienceDirectNATURALGASCHEMISTRYEL SEVIERJournal of Natural Gas Chemistry 21(2012)148-157www.elsevier.com/locate/jingcMathematical modeling of a slurry reactor forDME direct synthesis from syngasSadegh Papari，Mohammad Kazemeini*，Moslem FattahiDepartment of Chemical and Petroleum Engineering, Sharif University of Technology, Azadi Avenue, P. O. Box 11365-9465, Tehran, lranl Manuscript reeived July 25, 2011; revised August 23, 2011 ]Abstractsis of dimethyl ether (DME) from syngas. This large- scale reactor is modeled using mass and energy balances, catalyst sedimentation andsingle-bubble as well as two-bubbles class flow hydrodynamics. A comparison between the two hydrodynamic models through pilot plantexperimental data from the literature shows that heterogeneous two-bubbles flow model is in better agreement with the experimental data thanhomogeneous single-bubble gas flow model. Also, by investigating the heterogeneous gas flow and axial dispersion model for small bubblesas well as the large bubbles and slurry (i.e. including paraffins and the catalyst) phase, the temperature profile along the reactor is obtained. Acomparison between isothermal and non-isothermal reactors reveals no obvious performance difference between them. The optimum values ofreactor diameter and height were obtained at 7 m and 50 m, respectively. The effects of operating variables on the axial catalyst distribution,DME productivity and CO conversion are also investigated in this research.Key wordsmodeling; large scale slurry bubble column; optimization; dimethyl ether synthesis; single-bubble class; two bubbles class; isotherm andnon-isotherm1. IntroductionWater gas -shiftCO+H2O←- +CO2+H2△H= -41.1 kJ/mol (3)As the simplest ether, DME may be easily liquefied andbecomes a good substitute for fossil fuels which are harmfulCarbon dioxide hydrogenationto environment, because DME doesn't cause pollution such assolid particulates or toxic gases. DME is utilized as LPG sub-CO2 +3H2←+ CH3OH+H2O NH = - 50.1 kJ/molstitute, transportation fuel, propellant, chemical feedstock and4)fuel cells feed [1]. There are usually two common techniquesSyngas to DME conversion is better conducted in a slurryused to synthesize DME. In the first method, methanol is con-bubble column reactor due to several reasons, including i)verted into DME which is called indirect DME synthesis orsimple reactor construction, i) uniform reactor temperaturedouble-stage process. In the other method, it is synthesizedduring reaction for a highly exothermic reaction, ii) conve-from direct syngas conversion through a bifunctional catalystnient adding and removing of the catalyst convenient and iv)which is called single-stage method. The main advantage ofeasily controlled reactor temperature to avoid sintering of thethe single over double stage process is the lower cost of it. Thecatalyst.reactions of a single-stage process for producing DME mightIn recent decades, numerous studies concerning flowbe divided into the following steps:regime and computational fluid dynamics (CFD) investiga-Methanol synthesistions [2-6], gas hold-up and bubble characteristics [7- 10],volumetric mass transfer coefficient [1I,12] and heat trans-CO+2H2←→ CH3OH QH = - -90.85 kJ/mol (1)fer coefficient measurements [13,14] have been performed inMethanol dehydrationbubble column reactors.Up to now, no commercial scale syngas to dimethyl ether2CH3OH←+ CH3OCH3 +H2O AH = -23.4 kJ/molplant has beer中國煤化Iand undergone pro-2)duction) [15],:mportant to utilize●Corresponding author. Tel: +98-21-66165425; Fax: +98-21-66022853; E-mail: kazemini@shMYHCNMH GCopyrightO2012, Dalian Instiute ofChemical Physics,hinese Academy of Sciences. All rights reserved.doi:10.1016/S1003-9953(1 1)60347-2150Sadegh Papari et al/ Journal of Natural Gas Chemistry Vol. 21 No.2 20123. Mathematical modellingCsLarge bubbles are presented by the fllowing equaion:(1-εc)EsS + [(1- ec)Up - UsL]Cs+(14)8C,B]_ 8(ULBC;LB)_UsLCwve = 08zELBELBθz」(68TpsLUsLT-(1 - ec)psLEsL- = (psLUsLT)o (15)kal8(C; -C;L) = ELB8Cj,LBThe boundary conditions at the outlet of the slurry bubblewhile the small bubbles are presented by:column reactor include:aC;uB = 0(16)8esB EsB8CjisB]_ 8(UsBCjisB)_Oz(7)8C.sB = o(17)8Cj,sBhasB(C; -C;L)=εsB n8CjsL = o(18)and the slury phase is determined through:δzaCs=o(19)8C,sL]_ 8(UsLCj,sL) +元[(0-- sc)EsS0z 」二2+(20)hqauB(Cj - Cg,sL)+ kas(C; - Ci,sL)+(8)and the initial conditions are taken to be:CjLB= Cj,0(21)(1-eo)藝Mmv,r.= (1-eo)0GsLoCj,sB = Cj,0(22)in addition, the particle mass balance is given by: .CjL =Cj(23)Cs=Cave.(24):[(1-E)Es0Cs Iz()z ]T = Tool(25)(9)a-f(1 - ec)Up-UsL]Cs}= (1-εc)aCsThe empirical correlations utilized for the gas hold-up,Ftvolumetric mass transfer coefficient, superficial gas velocityof small bubbles, hindered sedimentation velocity of particles,while the energy balance is provided through:dispersion coffcient of small and large bubbles, as well asfor liquid for predictions of DME production and CO conver-sion in large-scale slurry bubble column reactor are summa-8z ]rized in Table 1.The inlet feed composition were set to YH2 =0.65,UHea(T - Too)+(1-εc), OHDME,i"DME,iyco = 0.32 and YCO2 = 0.03. Temperature of the cooling pipeswas taken to be 503 K. Other slurry bubble column reactorrparameters are provided in Table 2.= (1-ec)At(10)4. Kineticswhere, j =H2, CO, CO2, H2O, CH3OH, CH3OCH3.The boundary conditions at the inlet of the slurry bubbleIn the present study, the chemical kinetics of methanolcolumn reactor are Danckwertz's types, i.e:synthesis, water gas shift and DME synthesis as independentreactions were all taken from the Guo et al. [32]. CommercialULBCG;LaB -ELBELB2= ULBC,o(11)Cu-based methanol synthesis catalyst C301 and dehydrationcatalyst gamma alumina ware nsed [371_ In other words, reac-tion rate of me中國煤化工n the current model8C;sBUspC;sB - esB EsBixsB= UsBCj.o(12)is given by:YHCNMHGki PlL954 P9:9174UsLC;sL-(1-eo)EsLOG.s =0(13)”= (1+ KcoP2o0+ KP02195).2(26).Jourmal of Natural Gas Chemistry Vol. 21 No. 22012151Table 1. Gas hold-up, volumetric mass transter cofflclent, superIcial gas velocity, hindered sedimentation veloctty,dispersion coefficient and overall heat transfer cofficientDescripionEquationsReferences_0.7EsSmall bubble gas bold-up[22]∞=唱(崗) (蹈)0._ 1 (U_- UsB).8Large bubbl gas bhold-upELB=0[2]Total gas boldupεo = euB+esB(1-euB)昭= 1.3kg/m3 and 曜= 0.27。)。.sVolumetric mass transfer cofficient of large bubbles(Aqa)uB.j = 0.5Eu8(D2)[23]Volumetric mass transfer cofficient of small bubbles(qa)sB,j = 1.0esB(D)Det= 2x 10 9m2/sSuperficial gas velocity of small bubblesUsB=VS (1+ ve , v醋= 0.095 mlsSuperficial gas velocity of large bubblesUB = Uc -UsB! 9cD哈(∞o-p) )Hindered sedimentation velocity of particles (m/s)2)。(-ome)[24]Dispersion coffcient of liquid (m2/s)E = 0.35D}33(gUO).33[25]Dispersion coffcicnt of small bubbles (m21s)EsB= E[26]Dispersion cofciet of large bubbls (m2/s)Es=s.64x10~3(0)"”[27]Overall heat transfer coefficientUteu = 17104445(us4. x 10) 0.060(Px 10 60.176[28]Table 2. Slurry phase propertiesCatalyst propertiesLiquid phase properties [29]Slury phase properties [30,31]Density (kg/m3)1987171 x.1616-.5.m)9PSL =EsPs+(1-es)PLViscosity (Pas)m(un) = -3.0912+ 1.7038x一uSL = u(1 +4.5ea)Heat capacity (kgK))9932927Cp,sL = w2Cp,s +(1 - wz)Cp.LWhile the reaction rate of methanol dehydration is taken to be:Table 3. Arrhenius constant and activation energy ofthe global kinetic modelk2P09402Parametersko (mmol(ea-b)Eo (J/mol)(27)2.034x 10814061r2= (1+ KMP1799+ KwP243).44768023533Analysis of online gas chromatography showed that wa-66.63- 1588.2Kor17551ter content in exit stream was very low [33,34]. Thus, it was a .Kw1.225x10-2- -45601foreseen conclusion that water gas shift reaction was at equi-KM2.3362x 10-3- 39572librium. Hence, the H2O partial pressure can be obtained fromthe following equation:Pco2Pr2_(28)5. Gas solubil中國煤化工PoKp,wGsIYH.CNMH Chano, water andwhere, k; = koexp (得),ho (Arrhenius constant) and Eodimethyl ether in the liquid phase are obtained using Henry's(activation energy) are all listed in Table 3.law [35,36]:.152Sadegh Papari et al./ Joural of Natural Gas Chemistry VoL. 21 No. 22012with ARD of 6.8% and 4.5%, respectively. Thus, the two-H =axexppr29)bubble class model was utilized in this paper to investigate theP RTeffect of operating parameters.Values for constants a and b for each component are listedin Table 4.Hj is used for prediction of P' value as fllow: .( StartPj=H;xCj(30)Table 4. Parameters for Henry's constantInput: syngas flow rate, T, P, composition,Componentsa (bar-Lmol)b (J/mol)78.1922854Carbon monoxide109.87939.7Set initial and boundary conditionsCarbon dioxide429.52- 8969.7Methanol8190.6- 30410/ater7936.7- 37421Compute the values of CLB. CsBr C, ULBDimethyl ether2765.46. Results and discussion是|CSB.sew = wCsB.old+ (1-w)CsB.xtw|CLnew = wCLod+(1-w)CLnowIn general, the semi-batch and continuous modes are twoULB.ncw = wULB.old+ (1-w)XULB.nowtypes of valid operation for slury reactors. In this study,the semi-batch mode was simulated. All partial non-linear呂|equations were solved through the partial subtitution finiteEror= .new value - old value|difference method using MATLAB software 2010a. The fol-old valuelowed flow chart in this research for the purpose at hand isshown in Figure 2. The value of“w" was adjusted to achievestable convergence which in this program was chosen to beNoAll errors< 10-50.5. Figure 3 ilustrated the parity plot of CO conversion andDME STY (i.e. DME production rate per catalyst weight) forcomparison between the two models of hydrodynamics (i.e.estwo-bubble class and single-bubble class) with experimentaldata [37]. The catalyst with the size of 10-microns order wasutilized, which is a mixed catalyst containing CuO, ZnO andco conversion, DME productivityAl2O3 [37]. It may be seen from the figure that a good agree-ment between the two-bubble class models and experimentaldata is observed and the average relative deviations (ARD)Print resultsof this model were lower than the other model. The two-bubble class model predicted CO conversion and DME STYFigure 2. The flow chart of the simulation in this researchofA合s營12Fs分0下A411toF0ETwo-bubble classSingle-bubble class上●Two-bubble class20Experimental data by Yagi etal. [37]中國煤化工eal.[3)])Exprimental Co conversion (mol%)MHCNM HG13 14Expnmentar LME sIr (moV(kg*b))Figure 3. Validation of single and two bbles axial dispersion models with pilot plant experimental data: T=260°C, P=5.0MPa, e, =0.3, L=22 m,Dg=2.3m.Journal of Natural Gas Chemisty VolL. 21 No. 22012153Figure 4 depicted the effect of superficial gas velocity onwards a perfectly mixed model. In addition, Figure 4 demon-the axial catalyst concentration distribution. It is clear fromstrated the effect of the aspect (i.e. height to diameter) ratiothis figure that the enhancement of the superficial gas velocityon the axial catalyst concentration distribution. The results re-led to lowering of the slope of the catalyst concentration ver-vealed that the increase of the reactor diameter or decrease ofsus the reactor height, which can be attributed to the increasethe reactor height resulted in more slurry recirculation and lessof the slurry recirculation. Consequently, by rising up the re-sedimentation of catalyst. Hence, the slurry phase in the bub-circulation slurry phase, the behavior considered tended to-ble column might be considered as a perfectly mixed reactor.27030- + Ua=0.19 .+ HID=3十U=0.3028一HID=10260250 F245 t0.0.81.0Dimensionless heightFlgure 4. Axial catalyst concentraion profile vs. dimensionless beight for dfferenot superficial gas velocity and height over diameter ratioOn the other hand, the dense phase temperature of themore heat generation. Furthermore, it demonstrated that thebubble column reactor was controlled by the tube heat ex-variation of temperature along the reactor at higher operatingchangers. The temperature profiles along the reactor attemperatures was smaller than at lower operating temperature.different operating temperatures are ilustrated in Figure 5.It might be a foregone conclusion that at fixed cooling wa-As indicated, the axial temperature profiles from bottom toter and high slurry temperatures the driving force for heat re-top of the slurry reactor changed very little related to that ofmoval is higher than the state at which the reactor operatedhe parafin liquid having a high heat capacity as well as de-at lower temperatures. Therefore, the heat lost was highersirable heat carrying characteristic. Therefore, direct DMEand the slurry temperature became uniform. DME molesynthesis by syngas and carbon dioxide in the slurry reactorflow production and CO consumption in isothermal and non-might be considered as an isothermal reactor. Also, it mayisothermal slurry reactors are illustrated and compared withbe concluded from this figure that the hot region for this sys-experimental results available in the open literature in Fig-tem is situated at height of about 7.5- 10 m above bottom ofure 6. It can be concluded that there is no obvious differenceslurry reactor due to the catalyst grain sedimentation and highbetween the isothermal and non isothermal reactors.syngas partial pressure which led to the increase of methanolThe axial distribution of DME production per catalystsynthesis and methanol dehydrogenation rate thus causingweight is shown in Figure 7. Initially, the DME productionrate along the column height increased to achieve a maximum3500n 20003000藁150002500 E0.6 t2000 E4-150010002Ft 500000 E中國煤化工ooL232402506070AYHCNMH G031.0Slurry temperature (C)Figure 5. Axial slury temperature profiles: cooling water tempera-Fligure 6. A cooperation between non-isotherm and isoherm stury reactorsture = 503 K.154Sadegh Papari et al./ Joural of Natural Gias Chemistry Vol. 21 No.2 2012value, then started to decline. Higher syngas partial pressureindicated in this figure, Co conversion and DME productiv-at the inlet of the slurry reactor resulted in higher methanolity increased initially and achieved maxima at 270 °C, thensynthesis rate which led to an increase of methanol dehydra-started to decline. This trend was confirmed by other datation rate. Also, as mentioned above, the slurry temperature inavailable in the open literature [17]. The ascending functionthis section of the reactor hit a maximum value which can beof temperature for CO conversion and DME productivity inattributed to the high methanol synthesis and methanol dehy-the range of 240- -270 °C might be interpreted as that the ris-drogenation rate. .ing temperature improved the syngas solubility in paraffin liq-uid, hence its volumetric mass transfer coefficient enhanced[36] which accelerated methanol synthesis and its dehydra-tion rates. Descending function of temperature after 270°C16 Ewas rationalized due to the occurrence of methanol synthesisand dehydration at high exothermic reactions. Thus, 270 °C4卡twas determined as the optimum temperature for single-stageDME synthesis. In addition, Figure 9 represented the effect ofpressure on Co conversion and DME productivity. The effectof column height on pressure was neglected in the dispersion1 10model because the operating pressure was considerably higherthan the slury height in the reactor. The increase of pres-8Fsure from 4 to 6 MPa resulted in the increase of CO conver-sion from 62% to 86% and DME productivity from 3214 to0.20.6.84257 td at constant temperature of 260 °。C. The water gasDimensionless heightshift and methanol dehydration have the same number of totalFigure 7. DME production rate per catalyst weight along the bubble columnmoles on both sides of the reaction. However, the methanolThe effects of height over diameter ratio (HID) on CO75n 16conversion and DME productivity operating at constant su-perficial gas velocity UG = 0.2 m/s, catalyst concentrationCs = 30 wt.% and pressure of 5 MPa are ilustrated in Fig-of50 aure 8 at constant reactor volume. As shown in this figure, COconversion and DME productivity increased with enhancedH/D ratio. When this ratio increased to 7, enhanced residence1155time caused a rise in co conversion and DME productivity aswell. However, any further increase in H/D ratio raised the8 60I 150catalyst grain sedimentation and did not have any significanteffect on CO conversion or DME production. Thus, the H/Dratio equal to 7 was chosen as an optimum value for the DME55 LJ14:production reactor. This reactor height and diameter were thusdetermined to be 50 m and 7 m, respectively.HICO conversion and DME productivity versus averageFigure 8. CO conversion and DME productivity vs. height over diametertemperature at different pressures are shown in Figure 9. Asratio: T= 260 °C, P= 5.0 MPa, E。= 0.3, Uc= 0.2 m/s104500-P=60bar間)+ P=60 bar(b◆P=50bar-◆P=50 bar-▲P=40bar7035008603000中國煤化工。240Temperature (C)280TYHCNMHGFigure9. co conversion and DME produtivity Vs. average slurry temperature for dfferenet pressures: Dg =7m, L= 50 m, E, =0.3, UG =0.2 m/s.Joural of Natural Gas Chemistry Vol. 21 No. 22012155synthesis is a stoichiometrical contracting reaction, hence thethan 0.2 m/s, DME productivity was an ascending functionincreased pressure accelerated the rate of this reaction. Thus,of velocity for all catalyst concentrations. Nonetheless, afterit might be considered that the methanol synthesis is the limit-0.2 m/s, DME productivity at lower catalyst concentrationsing step of the overall reaction [33]. Moreover, the rising pres-(lower than 40 wt.%) declined, and at higher catalyst con-sure led to a decrease in the bubble size as well as an increasecentrations (i.e. higher than 40 wt.%) it enhanced. There-in the mass transfer area which in turn caused an increase infore, considering the decrease in Co conversion and DMEthe volumetric mass transfer coefficient. Hence, mass trans-productivity, the optimum value of superficial gas velocityfer between the two phases of slurry and syngas increased atwas chosen to be 0.2 m/s. Furthermore, investigation of cat-higher pressures [36]. It should be noted, however, that oper-alyst concentration on CO conversion and DME productiv-ating at higher pressures results in high costs. Therefore, 50ity in Figure 10 indicated the positive effect of catalyst con-bar might be an accepted value.centration on the aforementioned conversion and production.CO conversion and DME productivity versus superficialHowever, according to the empirical correlation of volumet-gas velocity at different catalyst concentrations (mass frac-ric mass transfer coefficient utilized, further increase of thetion of catalyst in the gas free slurry) are ilustrated in Fig-catalyst concentration led to a decrease in the mass trans-ure 10. As clearly seen from this figure, the increased su-fer coefficient in the slurry phase. Besides, rising in theperficial gas velocity decreased CO conversion due to a low-heat generation of reactions made the reaction temperatureered contact time (i.e. mean residence time) between thecontrol difficult under such conditions. In other words, theslurry and syngas phases, however, DME production demon-enhancement of the slurry concentration had its limiting valuestrated a different behavior. At the superficial velocity loweras well.30 r7000+P=60bar6000rP=50barP= 40 bar5000s,=0.420001s=0.2100 t0.150.200.250.300.35Uo (m/)Ua (m/s)Figure 10. co conversion and DME productvity vs. superficial gas velocity for dfferent catalyst concentratio: DR =7 m, L= 50 m, T= 260°C, P= 5.0 MPa7. Conclusionslyst concentration enhance the reactor performance. Nonethe-less, they have their limits as well before hitting their respec-In this paper, a large-scale slurry bubble column reactortive inflection points. Ultimately, the optimum value for thefor direct synthesis of dimethyI ether from syngas and carbonsuperficial gas velocity is chosen to be 0.2 m/s. It is remindeddioxide is mathematically modelled. The results of this simu-that the developed model in this research is also applicable forlation indicate that for 3800 tUd at temperature of 260 °C, pres-design of other large-scale slurry bubble column reactors.sure of 5 MPa and catalyst concentration of 30 wt.%, the op-timum reactor diameter and height requirements are 7 m andNomenclatures50 m; respectively. Also, the investigation of axial temper-ature profiles and a comparison between the isothermal andHenry constant (barL/mol)non-isothermal reactor behaviors reveal that the slurry bubbleHenry Constant (/mol)column reactor might be considered isothermal without incor-Cj,LB Molar concentation ofj component in large bubble phaseporating many errors into the simulation. In addition, the re-(mol/m' )sults of axial catalyst dispersion indicate that with increasingsuperficial gas velocity and decreasing reactor aspect ratio, theCj,sB Molar中國煤化工n smal bubble phaseslury phase might be considered as a perfectly mixed reactor.(mo/mCHCNMHGCo conversion and DME productivity are demonstrated to riseCzLMolar cwuccuuauul UI s wmpuiun in liquid phasewith increasing temperature up to 270°C. After 270 °C, due(mo/m3)to highly exothermic nature of reactions involved, these valuesCs Catalyst concentration or catalyst density (kg/m3).156Sadegh Papari et al./Jourmal of Natural Gas Chemisty Vol. 21 No. 22012C;Equilibrium molar concentration in liquid (molm3)EG Total gas hold-upCp,sCatalyst particle heat capacity (/kg:K)B Large bubles gas hold-upCp,LLiquid paraffin heat capacity (J/kg:K)Es Solid concentrationpG Gas phase density (kg/m3)Cp,sLSlurry phase heat capacity (Jkg.K)PsL Slurry phase density (kg/m3)DrReactor diameter (m)0j,i Reaction coefficientDjDiffusion coefficient (m2/s)4sL Slury viscosity (Pas)ELBLarge bubble dispersion coficient (m2/s)EsbSmall bubble dispersion coefficient (m2/s)Slurry phase dispersion coefficient (m2/s)References9Acceleration gravity constant (m2/s)(kra)LB Volumetric mass transfer coefficient for[1] Keshavarz A R, Rezaei M, Yaripour F J Nat Gas Chem, 2011,20(3): 334large bubble (1/s)[2] Deglean s, Dudukovic M, Pan Y.AIChEJ, 2001, 47(9): 1913(k:ra)sB Volumetric mass transfer coeffcient for[3] Ruzicka M C, Zahradnik J, Drahos J, Thomas N H. 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