Direct dimethyl ether (DME) synthesis through a thermally coupled heat exchanger reactor

ro

, Miraz

Available online 12 November 2010

Keywords:Direct DME synthesisCoupling exothermic and endothermic

alte) seE fr

thermic and exothermic reactions in heat exchanger reactors. Consequently, in this study, a double inte-

no serious problem for the storage, transportation and usage ofDME due to its higher boiling point compared with the LPG. Thus,DME could replace LPG and be considered as an alternative fuel todecrease the dependency on petroleum [410].

DME is traditionally produced through dehydration of methanolwhich is synthesized from syngas. This process is called two-stepor indirect method of DME production. Indirect method is carriedout in an adiabatic packed bed reactor using acidic porous

taneously, the cost of methanol purication could be eliminated[10,12].

A lot of work on modelling and simulation of direct and indirectsynthesis of DME in different reactor congurations have been con-ducted as well as experimental studies. Nasehi et al. [13] modelledand simulated indirect synthesis of DME in an adiabatic xed bedreactor and investigated the effects of changes in inlet conditionson the reactor operation. An experimental study and simulationof an adiabatic xed bed reactor for dehydration of methanolto DME was performed by Raoof et al. [14]. Their results

Corresponding author. Tel.: +98 711 2303071; fax: +98 711 6287294.

Applied Energy 88 (2011) 12111223

Contents lists availab

lseE-mail address: [email protected] (M.R. Rahimpour).Synthesis of new liquid fuels from coal or natural gas has beenunder much attention in many countries in recent years. Amongthese alternatives, dimethyl ether appears to have the largestpotential impact on society and is one of the superior candidatesfor high-quality diesel fuel in near future [13]. Combustion ofDME does not produce pollutants such as hydrocarbons, carbonmonoxide, nitrogen oxides, and particulates. Also, DME has a suit-able cetane number about 5560. The physical properties of DMEare similar to liqueed petroleum gas (LPG). Moreover, there exists

mercial methanol synthesis catalyst and methanol dehydrationcatalyst [10,11]. Compared to the indirect process via methanolsynthesis, the direct method is more economical because of the fol-lowing two reasons:

The limitations associated with thermodynamic equilibrium ofCO conversion to methanol could be exceeded by the synergyeffect of hybrid catalyst for methanol synthesis and methanoldehydration.

Because methanol and DME are produced in one reactor simul-reactionCyclohexane dehydrogenationAuto-thermal reactor

1. Introduction

1.1. Dimethyl ether (DME)0306-2619/$ - see front matter 2010 Elsevier Ltd. Adoi:10.1016/j.apenergy.2010.10.023grated reactor for DME synthesis (by direct synthesis from syngas) and hydrogen production (by thecyclohexane dehydrogenation) is modelled based on the heat exchanger reactors concept and asteady-state heterogeneous one-dimensional mathematical model is developed. The correspondingresults are compared with the available data for a pipe-shell xed bed reactor for direct DME synthesiswhich is operating at the same feed conditions. In this novel conguration, DME production increasesabout 600 Ton/year. Also, the effects of some operational parameters such as feed ow rates and the inlettemperatures of exothermic and endothermic sections on reactor behaviour are investigated. The perfor-mance of the reactor needs to be proven experimentally and tested over a range of parameters underpractical operating conditions.

2010 Elsevier Ltd. All rights reserved.

catalysts. Moreover, DME can be produced directly from syngasin a single-step (direct method). Hybrid catalysts are used for thisaim. Hybrid catalysts are made by pressing the powders of com-2010Accepted 12 October 2010

the indirect process via methanol synthesis. Multifunctional auto-thermal reactors are novel concepts inprocess intensication. A promising eld of applications for these concepts could be the coupling of endo-Direct dimethyl ether (DME) synthesis thexchanger reactor

R. Vakili, E. Pourazadi, P. Setoodeh, R. EslamloueyanDepartment of Chemical Engineering, School of Chemical and Petroleum Engineering, Sh

a r t i c l e i n f o

Article history:Received 12 July 2010Received in revised form 24 September

a b s t r a c t

Compared to some of thefuels, dimethyl ether (DMEThe direct synthesis of DM

Applied

journal homepage: www.ell rights reserved.ugh a thermally coupled heat

.R. Rahimpour University, Shiraz 71345, Iran

rnative fuel candidates such as methane, methanol and FischerTropschems to be a superior candidate for high-quality diesel fuel in near future.om syngas would be more economical and benecial in comparison with

le at ScienceDirect

Energy

vier .com/locate /apenergy

nergNomenclature

av specic surface area of catalyst pellet (m2 m3)AC cross section area of each tube (m2)Ai inside area of inner tube (m2)Ao outside area of inner tube (m2)c total concentration (mol m3)Cp specic heat of the gas at constant pressure (J mol1)dp particle diameter (m)Di tube inside diameter (m)Dij binary diffusion coefcient of component i in j (m2 s1)Dim diffusion coefcient of component i in the mixture

(m2 s1)Do tube outside diameter (m)fi partial fugacity of component i (bar)F total molar ow rate (mol s1)G mass velocity (kg m2 s1)hf gassolid heat transfer coefcient (W m2 K1)hi heat transfer coefcient between uid phase and reac-

tor wall in exothermic side (Wm2 K1)ho heat transfer coefcient between uid phase and reac-

tor wall in endothermic side (Wm2 K1)DHf,i enthalpy of formation of component i (J mol1)ki reaction rate constantskg mass transfer coefcient for component i (m s1)K conductivity of uid phase (Wm1 K1)KB adsorption equilibrium constant for benzene (Pa1)K equilibrium constant of reaction i in DME synthesisKi adsorption equilibrium constant for component i in

1212 R. Vakili et al. / Applied Edemonstrated that using pure methanol as the feed of the processcontributes to much slower catalyst deactivation. Song et al. [15]studied direct process for DME production from syngas in apilot-scale xed bed reactor. They applied one-dimensional heter-ogeneous model to their reactor and found good agreement be-tween their model-based simulation and experimental results.Liu et al. [16] modelled and designed a three-phase bubble columnreactor for direct synthesis of DME from syngas considering theinuence of inert carrier back mixing on transfer and the inuenceof catalyst grain sedimentation on reaction. Slurry reactors are ableto provide an efcient heat management because of a liquid phaseexistence but there would be a very high mass transfer resistancein this kind of reactors [17,18]. Lu et al. [19] simulated a uidizedbed reactor for DME synthesis from syngas by using plug owmodel. The experimental results showed considerable differencesin CO conversion and DME productivity in comparison to xedbed and slurry reactors. Omata et al. [20] studied DME productionfrom syngas in a temperature gradient reactor to overcome boththe equilibrium limitations at high temperatures and low catalystactivity related to low temperatures. Then, they optimized theoperating conditions of the reactor for higher CO conversion bycombining genetic algorithms and articial neural networks. Themathematical model of the pipe-shell xed bed reactor was builtbased on the global kinetics of the direct synthesis of DME fromsyngas on hybrid catalyst by Hu et al. [21]. Furthermore, the opti-mum structure and optimum operating conditions of the pipe-shell xed bed reactor were specied in their study. Farsi et al.[22] modelled a shell and tube xed bed reactor for indirect DMEproduction. Also, the DME production in the isothermal reactor ismaximized by adjusting the optimal temperature distributionalong the reactor using genetic algorithm.

DME synthesis reactionKp equilibrium constant for dehydrogenation reaction (Pa3)Kpi equilibrium constant based on partial pressure for com-

ponent i in methanol synthesis reactionKw thermal conductivity of reactor wall (Wm1 K1)L reactor length (m)Mi molecular weight of component i (g mol1)N number of components (N = 8 for methanol synthesis

reaction, N = 4 for dehydrogenation reaction)P total pressure (for exothermic side: bar; for endother-

mic side: Pa)Pi partial pressure of component i (Pa)rCO rate of reaction for hydrogenation of CO (mol kg1 s1)rCO2 rate of reaction for hydrogenation of CO2 (mol kg

1 s1)rDME rate of reaction for dehydration of metha-

nol(mol kg1 s1)rC rate of reaction for dehydrogenation of cyclohexane

(mol m3 s1)ri reaction rate of component i (for exothermic reaction:

mol kg1 s1; for endothermic reaction: mol m3 s1)R universal gas constant (J mol1 K1)Rp particle radius (m)Re Reynolds numberSci Schmidt number of component iT temperature (K)u supercial velocity of uid phase (m s1)ug linear velocity of uid phase (m s1)U overall heat transfer coefcient between exothermic

and endothermic sides (Wm2 K1)vi atomic diffusion volumesyi mole fraction of component i (mol mol1)

y 88 (2011) 121112231.2. Coupling

Process intensication (PI) is currently one of the most signi-cant trends in chemical engineering and process technology. Ithas been paid much attention in the research world [23]. It is re-lated to strategies for reduction of emissions as well as consump-tion of energy and materials. Innovations in catalytic reactortechnologies, which somehow could be the heart of chemical pro-cesses, are often the preferred starting point. In this way multi-functional auto-thermal reactor is a novel concept in processintensication. At present, coupling of endothermic and exother-mic reactions would be a promising eld of using multifunctionalauto-thermal reactors. In this type of reactors, an exothermic reac-tion is considered as the heat producing source to drive the endo-thermic reaction(s) [24,25]. In recent years, auto-thermal reactorshave been regarded to an important topic of so many articles inthe literature. In addition, an extension of their applications forcoupling of endothermic and exothermic reactions has been at-tempted. Bhat and Sadhukhan [26] reviewed the process intensi-cation for methane steam reforming by coupling and using themembrane separation technologies to overcome mass transfer,heat transfer and thermodynamic equilibrium associated limita-tions. Hunter and McGuire [27] were among the rst ones whosuggested and did the experimental coupling of endothermic andexothermic reactions by means of indirect heat transfer. They con-sidered heat exchangers in which catalytic combustion or anotherhighly exothermic reaction was utilized (or applied) as a heatsource for preparation of the necessary heat for an endothermicreaction. Altimari and Bildea [28] discussed about design and con-trol of plant wide systems including coupling of exothermic andendothermic reactions (a rst-order reaction for endothermic side

z axial reactor coordinate (m)

and a second order for exothermic one) at steady-state condition.Annaland and Nijssen [29] studied a new reactor concept for highlyendothermic, heterogeneously catalyzed gas phase reactions, athigh temperature with rapidity and reversible catalyst deactiva-tion to provide necessary heat for endothermic side. Patel andSunol [30] developed a distributed mathematical model for a ther-mally coupled membrane reactor in order to couple the methanesteam reforming with the exothermic methane combustion. Kiril-lov et al. [31] studied a mathematical model and applied a numer-ical method to analyze the operation of coupled methane steamreforming by fuel oxidation. They used a two dimensional mathe-matical models to describe the processes in exothermic and endo-thermic compartments of the reformer. Glockler et al. [32]presented a short-cut theory to design and analyze an optimalsystem for coupling exothermic and endothermic reactions in anadiabatic xed-bed reactor with reverse ow mode. Elnashaieet al. [33] considered a specic system which contains simulta-neous catalytic dehydrogenation of ethyl benzene and hydrogena-tion of benzene coupled through hydrogen selective membranes.Also, rigorous models were developed and used to explore thebasic characteristics of a number of congurations for a numberof catalysts and membranes. Abo-Ghander et al. [34] investigatedco-current and counter-current operation modes for the aboveconguration and compared the simulation results with achievedcorresponding results from an industrial adiabatic xed bed reac-tor at the same feed conditions. Khademi et al. [35] considered

tional and capital costs due to utilizing of multifunctional auto-thermal reactors, it seems direct synthesis of DME in a multifunc-tional heat exchanger reactor to be a proper route especially fromthe view point of economic considerations. Thus, we decided toinvestigate mathematically the direct synthesis of DME and thedehydrogenation of cyclohexane to benzene simultaneously in anauto-thermal heat exchanger reactor. Due to the complexity ofthe process stem from the interaction between exothermic andendothermic reactions in heat exchanger reactors, a suitable math-ematical model is required to make an appropriate initial sense ofwhat could be achieved in coupled reactors. Besides, this suitablemathematical model will then be used for the optimization ofthe process conditions and reactor control. The experimental datafor practical operating conditions can be utilized in conjunctionwith the mathematical model in order to develop and modify themodel as a future work for new plant setups and revamps of pro-cess improvements. The corresponding results of our coupled reac-tor simulation are compared with the results of a pipe-shell xedbed reactor which has been proposed by Hu et al. [21].

2. Process description

2.1. Conventional direct DME synthesis reactor (CDR)

Direct synthesis of DME has been proposed in a pipe-shell xed

R. Vakili et al. / Applied Energy 88 (2011) 12111223 1213co-current mode of a membrane heat exchanger reactor congura-tion with three sides in which methanol synthesis and dehydroge-nation of cyclohexane to benzene took place in the exothermic andendothermic sides respectively and hydrogen which was producedin the endothermic side permeated from surface membrane to thethird side. Farsi et al. [36] simulated the methanol dehydration todimethyl ether (indirect DME synthesis) with cyclohexane dehy-drogenation in an integrated reactor which formed of two xedbeds as a heat exchanger reactor.

Considering great advantages of direct synthesis of DME fromsyngas through indirect method and also large savings in opera-

Steam Reforming

Syngas

Natural GasFig. 1. Schematic diagram of a pipe-shell xed bedbed reactor by Hu et al. [21]. Fig. 1 demonstrates a schematic fordirect synthesis of DME from syngas. In this reactor, hybrid cata-lysts placed in the pipes. Also, the syngas and boiling water enteredin the pipe and shell side, respectively. The heat of DME synthesisreactions is transferred to the boiling water from the pipe wall. Therelated catalyst specications and operational conditions are gath-ered in Table 1.

2.2. DME coupled reactor

A conceptual schematic for the co-current mode of a two-sideheat exchanger reactor conguration is shown in Fig. 2. In this

Distillation Unit-1

Steam Drum

Steam

Fresh Water

DMEreactor for DME synthesis directly from syngas.

novel coupled reactor, the rst side is the exothermic side whereDME synthesis takes place on the hybrid catalyst. The second sideis an endothermic side which is used as a coolant medium, insteadof boiling water, where hydrogenation of cyclohexane to benzenetakes place on Pt/Al2O3 catalyst. Heat is transferred continuouslyfrom the exothermic side to the endothermic one and drive the

3. Reaction scheme and kinetics

3.1. Dimethyl ether synthesis

DME synthesis from syngas is an exothermic equilibrium reac-tion. In the current work, a hybrid catalyst (mass ratio 1:1) of com-mercial methanol synthesis (CuO/ZnO/Al2O3) and methanoldehydration (c-Al2O3) is utilized. The synthesis of methanol fromCO as well as CO2 and dehydration of methanol in the system is re-garded as the independent reactions.

CO 2H2 $ CH3OH DH298K 90:55 kJ=mol 1

CO2 3H2 $ CH3OHH2O DH298K 49:43 kJ=mol 2

2CH3OH$ CH3OCH3 H2O DH298K 21:003 kJ=mol 3

The rates expressions have been selected from Nie et al. [39]and are represented as follow:

rCO k1fCOf 2H2 1 b1

1 KCOfCO KCO2 fCO2 KH2 fH2 34

rCO2 k2fCO2 f

3H21 b2

1 KCOfCO KCO2 fCO2 KH2 fH2 45

rDME k3fCH3OH1 b31 KCH3OHfCH3OHp 2 6

Table 1Operational conditions and properties of catalyst for conventional DME reactor [21].

Parameter Value Unit

Feed composition (mole fraction)CO 0.1716 CO2 0.0409 DME 0.0018 CH3OH 0.003 H2O 0.0002 H2 0.4325 N2 0.316 CH4 0.044 Inlet temperature 493 KInlet pressure 50 barNumber of pipes 4177 Diameter of pipes /38 2 mmVolumetric ow rate of raw gas 2.04 105 Nm3 h1Length of reactor 5.8 mTemperature of boiling water 513 KThermal conductivity of wall 48 W m1 K1

Typical properties of catalystParticle diameter /5 5 mmDensity of catalyst bed 1200 kg/m3

Porosity 0.455

1214 R. Vakili et al. / Applied Energy 88 (2011) 12111223endothermic reaction properly in order that hydrogen productionoccurs. The associated operational conditions for endothermic sideare reported in Table 2.

ReformerNatural GasCyclohexaneArgon Endothermic Side

Exothermic SideSyngas

Heat Transfer

DME

HydrogenBenzene

Fig. 2. Schematic diagram for the co-current modProductSeparation Unit-1 DME

BenzeneP-48b1 fCH3OH

Kf1fCOf 2H27

Syngas

Cyclohexane TankCyclohexane Feed Line

Separation Unit-2

Hydrogen

Argon Tanke of a heat exchanger reactor conguration.

b2 fCH3OHfH2OKf2fCO f 3

8

Table 2Operational conditions and properties of catalyst for benzene synthesis process.

Parameter Value Unit

Feed composition (mole fraction)C6H12 0.3 C6H6 0.0 H2 0.0 Ar 0.7 Total molar ow rate 0.15 mol s1

Inlet temperature 493 KInlet pressurea 1.013 105 PaShell inner diameter 0.08 mBed void fraction 0.39 Particle diameterb 3.55 103 m

a Obtained from Kusakabe et al. [37].b Obtained from Markatos et al. [38].

R. Vakili et al. / Applied Energ2 H2

b3 fDMEfH2OKf3f 2CH3OH

9

where fi and K are the fugacity of component i and equilibriumconstant of reaction i, respectively [40,41]. The reaction rate con-stants are tabulated in Table 3.

3.2. Dehydrogenation of cyclohexane

Hydrogen would be a cost-effective fuel which can be producedin large scale in near future. One method for hydrogen productionis the use of alternative fuels which are easily transformed tohydrogen and can be stored in liquid form [42]. One of these men-tioned fuels is cyclohexane. The reaction scheme for dehydrogena-tion of cyclohexane to benzene is represented as follows:

C6H12 $ C6H6 3H2 DH298K 206:2 kJ=mol 10The following equation is used for cyclohexane dehydrogena-

tion rate, rC [43]:

rC kKPPC=P3H2 PB1 KBKPPC=P3H2

11

where k, KB, and KP are the reaction rate constant, the adsorptionequilibrium constant for benzene, and the reaction equilibrium con-

Table 3dP 150l 1 e2 Q 1:75q 1 e Q

2

16

Reaction rate constants for DME synthesis.

k = A exp (B/RT) A B

k1 1.828 103 43,723k2 0.4195 102 30,253k3 1.939 102 24,984KCO 8.252 104 30,275KH2 2.1 103 31,846KH2 0.1035 11,139KCH3OH 1.726 104 60,126

Table 4The reaction rate constant, the adsorption equilibrium constant, and the reactionequilibrium constant for dehydrogenation of cyclohexane reaction.

k = A exp (B/T) A B (K)

k 0.221 mol m3 Pa1 s1 4270KB 2.03 1010 Pa1 6270Kp 4.89 1035 Pa3 3190dz /2s d2p

e3 Ac /sdp e3 A2cThe following mass and energy balances are written for theuid phase:

1AC

dFi;jdz

avjcjkgi;j ysi;j ygi;j

0 14

Cgpj

AC

dFjTgj dz

av jhf Tsj Tgj

pDjAC

U Tg2 Tg1 0 15

where Fi,j and Tgj are the uid-phase ith-component molar ow rate

and temperature in jth side of the reactor, respectively. In Eq. (15),the positive sign for the third term is related to the exothermic sideand the negative sign is used for the endothermic one.

4.3. Ergun equation

The pressure drop through the catalytic beds is calculated basedon the Ergun equation [45]. The related equation for tubular reac-tors is:stant, respectively, which are clubbed into Table 4 Pi is the partialpressure in Pa.

4. Mathematical model

The mathematical model for simulation of the novel coupledreactor with co-current ow regime has been developed basedon the following assumptions:

The gas mixture is considered as an ideal gas in both catalyticreactor sides.

One-dimensional heterogeneous model is considered for bothreactor sides.

The reactor is simulated in the steady-state condition. The radial diffusion in the catalyst particles is neglected in eachside.

Bed porosity in both axial and radial directions is constant. Heat loss to surrounding is neglected.

4.1. Solid phase

The mass and energy balance equations for solid phase are rep-resented as follow:

avcjkgi;jygi;j ysi;j gri;jqb 0 12

avhf Tgj Tsj qbXNi1

gri;jDHf ;i 0 13

where ysi;j and Tsj are the solid-phase ith-component mole fraction

and temperature in jth side of reactor, respectively. gk,j is effective-ness factor of kth reaction in jth side of the reactor which isobtained from a dusty gas model calculations [44]. Detailed infor-mation about such a dusty gas model is given in Appendix A.

4.2. Fluid phase

y 88 (2011) 12111223 1215where dP is the pressure gradient, Q is the volumetric ow rate, dp isthe particle diameter, /s is the sphericity (for spherical particles isunity), and l and q are the uid viscosity and density, respectively.

should be added to the modelling section. These auxiliary correla-

nergtions which estimate physical properties as well as the mass andheat transfer coefcients are summarized in Table 5. The heattransfer coefcient between gas phase and the reactor wall isapplicable for heat transfer between gas phase and solid catalystphase.

5. Numerical solution4.4. Boundary conditions

At the entrance of the reactor, the inlet temperature, pressureand molar ow rate of the reactant gas (in the both sides) areknown. Therefore, the following boundary conditions are appliedto the differential equations system:

z 0; Fi;j Fi0;j Tgj Tg0j Pgj Pg0j 17

4.5. Auxiliary correlations

To complete the simulation procedure, auxiliary correlations

Table 5Physical properties and mass and heat transfer correlations.

Parameter Equation Ref.

Component heat capacity Cp = a + bT + cT2 + dT3

Gas density q PRTAverage molecular weight MWave

PMWi yi

Viscosity of reaction mixtures l C1TC21C3T

C4T2

[46]

Mixture thermal conductivity [47]Mass transfer coefcient between

gas and solid phaseskgi 1:17Re0:42Sc0:67i ug 103 [48]

Re 2RpuglSci lqDim104Dim 1yiP

ijyiDij

[49]

Dij 107T3=2

1=Mi1=Mj

p

P v3=2civ3=2

cj

[50]Overall heat transfer coefcient 1

U 1hi Ai lnDo=Di

2pLKw AiAo

1ho

Heat transfer coefcient betweengas phase and reactor wall

hCpql

CplK

2=3 0:458eB

qudpl

0:407 [51]

1216 R. Vakili et al. / Applied EMATLAB software is used to solve the ordinary differentialequations in axial direction. The related set of ODEs are convertedto nonlinear algebraic equations by using backward nite differ-ence method. The reactor length is divided to 100 separate sectionsand nonlinear algebraic equations are solved for both reactor sidesin each section, simultaneously.

6. Results and discussion

In this section, various observed behaviours for co-current owin a thermally coupled reactor (TCR) are discussed. The effects ofoperational and design parameters variations on the exothermicand endothermic mole fractions, carbon monoxide and cyclohex-ane conversions and temperature proles during the process areinvestigated. Two denitions are introduced as follows to examinethe carbon monoxide and cyclohexane conversions through thereactor length:

XCO FCO;in FCO;outFCO;in 18

XC6H12 FC6H12 ;in FC6H12 ;out

FC6H12 ;in196.1. Base case

In order to establish a reference point for the coupled reactor, sothat the inuence of various parameters can be evaluated, calcula-tions are rst carried out for a base case. The operating condi-tions used for both sides of this mentioned case have been givenin Tables 1 and 2 previously.

6.1.1. Molar behaviour(a) Exothermic side:Fig. 3af shows components mole fraction changes in exother-

mic side of coupled reactor in CDR proposed by Hu et al. [21].Fig. 3a illustrates the mole fraction of DME in the exothermic sideof TCR and CDR versus the dimensionless reactor length. It is obvi-ous that the DME mole fraction is enhanced by about 0.8% in TCRcompared with the CDR which leads to a higher production rateof 600 Ton/year. Fig. 3bf presents similar results for the othercomponents in the exothermic section of the TCR. Among DMEsynthesis reactions (Eqs. (4)-(6)), the reversible reaction represent-ing the hydrogenation of carbon dioxide occurs in backward direc-tion which leads to carbon dioxide production as demonstrated inFig. 3c. Also, outlet water content from the TCR is higher than thatof the CDR (see Fig. 3e) which is related to higher DME (in Eq. (6))and lower carbon dioxide production (in Eq. (5)) in the TCR.Although the proles of mole fractions along the TCR and CDRare not the same under steady-state conditions, there are not con-siderable differences between the outlet values from the TCR andCDR. The TCR and CDR simulation results related to the study ofHu et al. [21] are summarized in Table 6. As it is illustrated, themaximum relative error obtained is about 3.8% which is feasibleand acceptable.

(b) Endothermic side:Fig. 3g reveals simultaneously the plots of cyclohexane, ben-

zene and hydrogen mole fractions in the endothermic side of theTCR as functions of the reactor dimensionless length. The cyclohex-ane conversion reaches to 64% with a total hydrogen productionrate of 860 kmol/h.

(c) Total molar ow rate:In recent studies on the coupled reactors [35,52,53], a constant

molar ow rate during the modelling has been considered, whichreduces the accuracy in prediction of reactor outlet mole fractions.In the CDR the total molar ow rate decreases along the reactorlength continuously. Therefore, in this work total molar ow rateis considered to be variable along the reactor length. The total mo-lar ow rates (for both sides of TCR) are depicted in Fig. 4. As it isillustrated, the variations of the molar ow rates are obtained 17%and 36% for exothermic and endothermic sides, respectively. Themolecular weights, heat capacities, viscosity, density and the otherproperties are considered to be variable during the mathematicalmodelling.

6.1.2. Thermal behaviourFig. 5 illustrates the axial temperature proles for CDR and TCR

in both the exothermic and endothermic sides, respectively. Fig. 5ashows the temperature proles in the exothermic side of both theTCR and CDR. As it can be understood, the maximum temperaturein the TCR is about 4K lower and the temperature prole is im-proved in comparison with the ones of the CDR. This lower temper-ature permits a higher DME conversion. Along the exothermic side,temperature increases smoothly and a hot spot develops Becauseof the amount of the generated heat (in exothermic side) is higherthan the amount of the consumed one in endothermic side. Therates of the exothermic reactions are reduced by temperature in-

y 88 (2011) 12111223crease at the end of the reactor due to the equilibrium limitations.Thus, the consumed heat in endothermic side will be higher thanthe generated one in exothermic side and consequently the

0 0.2 0.4 0.6 0.8 10

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

0.045

0.05

Dimensionless Length

DM

E m

ole

fract

ion

0.95 0.98 10.046

0.048

0.05

Coupled reactorHu et al. [21]

0 0.2 0.4 0.6 0.8 10.08

0.09

0.1

0.11

0.12

0.13

0.14

0.15

0.16

0.17

0.18


CO

mol

e fra

ctio

n


0 0.2 0.4 0.6 0.8 10.04

0.045

0.05

0.055

0.06

0.065

0.07

0.075

0.08


CO

2 m

ole

fract

ion


c

a

b

0 0.2 0.4 0.6 0.8 12

3

4

5

6

7

8

9

10

11x 10-3


Met

hano

l mol

e fra

ctio

n


d

e

f

0 0.2 0.4 0.6 0.8 10

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04


H 2O

mol

e fra

ctio

nCoupled reactorHu et al. [21]

0 0.2 0.4 0.6 0.8 10.32

0.34

0.36

0.38

0.4

0.42

0.44


H2

mol

e fra

ctio

n


0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.05

0.1

0.15

0.2

0.25

0.3

0.35


Mol

e fra

ctio

n

C6H12C6H6H2

g

Fig. 3. Comparison of: (a) DME, (b) CO, (c) CO2, (d) methanol, (e) H2O and (f) H2 mole fraction along the reactor length between exothermic sides of TCR and CDR, (g) molefraction of cyclohexane, benzene, and hydrogen in the endothermic side along the reactor length.

R. Vakili et al. / Applied Energy 88 (2011) 12111223 1217

0.55ic 0.2 mi

0 0.2 0.4 0.6 0.8 1485


Fig. 5. Variation of temperature for CDR and TCR in: (a) exothermic side, (b)

nergtemperature decreases to 511 K (see Fig. 5a). The temperature of

0 0.2 0.4 0.6 0.8 10.4

0.45

0.5

Mol

ar fl

ow ra

te o

f exo

ther

m

0 0.2 0.4 0.6 0.8 10.14

0.16

0.18

Mol

ar fl

ow ra

te o

f end

othe

r

dimensionless length

mol

/s

mol

/s

Fig. 4. Changes of molar ow rate of exothermic and endothermic stream along thereactor length.Table 6Comparison between steady state simulation results and Hu et al. [21].

Components Hu et al. [21] Simulation results Relative error (%)

Output composition (mole fraction)CO 0.0877 0.089 1.5CO2 0.0671 0.064 3.7DME 0.0491 0.0495 0.8CH3OH 0.0106 0.0103 2.8H2O 0.0338 0.0351 3.8H2 0.033 0.0333 0.9Temperature (K) 516.60 510.70 1.1

0.6

stre

am,

0.22

c st

ream

,

1218 R. Vakili et al. / Applied Ethe endothermic side in the TCR is always lower than that of theexothermic side in order to make a driving force for heat transferfrom the solid wall. At the reactor entrance, the transferred heatfrom the solid wall is lower than the consumed heat by the endo-thermic side, which is due to low temperature difference. There-fore, temperature begins to decrease and a cold spot forms asdemonstrated in Fig. 5b. Afterward, the endothermic temperaturestarts to increase in order to increase the exothermic temperatureand the heat transfer from the exothermic side to the endothermicsection. Considering that the consumed heat in endothermic side ishigher than the generated in exothermic side the temperature de-creases to 501 K at the end part of the shell side (endothermicsection).

6.2. Inuence of inlet temperature of endothermic stream

Fig. 6a and b depict the inuence of various inlet temperature ofendothermic stream on the temperature proles in the exothermicand endothermic sides along the TCR. By decreasing the inlet tem-perature of endothermic side, the temperature driving force be-tween the shell and tube sides increases. Besides, the rate ofdehydrogenation decreases. Consequently, the endothermic tem-perature starts to increase and the cold spot is vanished as it isillustrated in Fig. 6a. Higher inlet temperatures create a biggermaximum for the exothermic section (see Fig. 6b). The carbonmonoxide and cyclohexane conversions decrease signicantlyfrom 48% to 39.5% and 64% to 54%, respectively for a 13 C deple-tion the inlet temperature of the endothermic side.

6.3. Inuence of molar ow rate of endothermic stream

Fig. 7a and b examines the inuence of the molar ow rates inendothermic stream on the temperature proles in the exothermic0 0.2 0.4 0.6 0.8 1490

495

500

505

510

515

520

525

530

535


Tem

pera

ture

,K

coupled reactorHu et al. [21]

490

495

500

505

510

515

Tem

pera

ture

,K

b

a

y 88 (2011) 12111223and endothermic sides. With increasing the ow rate of endother-mic stream, axial temperature variations become lower due tohigher transferred heat through the solid wall (Fig. 7a). The tem-perature of the endothermic side is always lower than that of theexothermic one in order to make a temperature driving force.Therefore, the temperature of endothermic side changes pursuantto the exothermic one (Fig. 7b). Fig. 7c illustrates how the carbonmonoxide and cyclohexane conversions vary when the ow rateof endothermic stream increases from 0.1 to 0.24 mol s1. Carbonmonoxide and cyclohexane conversion decrease from 53.3% to40.2% and from 89% to 39.5% respectively. Decreasing of carbonmonoxide is due to lower axial temperature prole (see Fig. 7a)and consequently lower reaction rates. Decreasing of cyclohexaneconversion is an obvious consequence of the fact that the amountof catalyst on endothermic side is not enough for these higher owrates.

6.4. Inuence of molar ow rate of exothermic stream

In this section, the reactor thermal behaviour and performanceare studied for different exothermic stream molar ow rates. Byincreasing the ow rate of exothermic stream lower degree of reac-tion is taken owing to lower residence time. Hence, the tempera-ture of exothermic side decreases. Consequently, hot spot whichis due to the equality of generated and consumed heats is ap-proached to end of reactor length as it can be seen in Fig. 8a. Inthe entrance of the reactor, the consumed heat (for endothermicside) is higher than the transferred one, therefore the system startsto cool down and thus a minimum in temperature is observed forthe endothermic side. By further increasing the exothermic owrate, this minimum becomes bigger which is due to lower heat

endothermic side along the reactor length.

4800 c inlet tem 0 0.2 0.4 0.6 0.8 1

510


Tem

495

500

505

510

515

520

Tem

pera

ture

,K

F=0.15

F=0.2

F=0.1

F=0.12

b

nergEndotherm

iDimensionless length

510

520

530

rmic

tem

pera

ture

, K

b485490

4950.5

1480

485

490

495

500

505

510

515

perature, K

End

othe

rmic

tem

pera

ture

, K

a

R. Vakili et al. / Applied Etransfer from the solid wall to the endothermic side (compareFig. 8b and c). Finally, outlet temperature in endothermic side be-comes higher due to increase of the transferred heat from the exo-thermic reaction side. The effect of increasing of the exothermicstream ow rate on the reactor performance is showed in Fig. 8d.Carbon monoxide conversion decreases from 58.8% to 24.5% whenmolar ow rate increases from 0.2 to 1 mol s1 which is mainly dueto lower residence time for feed to react on the catalyst surface.Also, cyclohexane conversion is maximized at molar owrate = 0.65 mol s1 and then it is reduced which can be denedby Fig. 8e.

6.5. Simultaneous effects of inlet temperature and molar ow rate ofendothermic stream on the reactor performance

For better understanding of reactor performance, we investi-gated simultaneous effects of variations in the inlet temperatureand the molar ow rate of endothermic stream on the carbon mon-oxide and cyclohexane conversions. In this work, inlet temperatureand molar ow rate change from 480 to 493 K and 0.1 to.24 mol s1. All other parameters are kept at their base case values.Maximum carbon monoxide conversion is equal to 53.3% when theinlet temperature and the molar ow rate are 493 K and 0.1 mols1, respectively. By increasing the molar ow rate to 0.24 mol s1

and decreasing the inlet temperature to 480 K, carbon monoxideconversion is reduced to 24.3% as demonstrated in Fig. 9a. Thiscan be considered for cyclohexane conversion, similarly. Maximumand minimum cyclohexane conversions are 89% and 27%, respec-

Endotherm

ic inlet tem

perature, K

480485

490495

00.20.40.6

0.81490

500

Dimensionless length

Exo

the

Fig. 6. Inuence of inlet temperature of endothermic stream on the temperatureproles in: (a) endothermic side and (b) exothermic side along the reactor lengthfor TCR.490

500

F=0.2520

530

540

550

pera

ture

,K

F=0.15

F=0.12

F=0.1

a

y 88 (2011) 12111223 1219tively. Fig. 9b reveals the simultaneous effects of endothermic mo-lar ow rate and inlet temperature on the hydrogen yield(cyclohexane conversion).

6.6. Sensitivity analysis on the reaction rates

Fig. 10a and b illustrates the effect of inlet temperature of theexothermic and endothermic sides on the main components(cyclohexane and DME) in the endothermic and exothermic sec-tions, respectively. By increasing the inlet temperature of the exo-thermic side the related reaction rate increases. Consequently,more heat is transferred from the solid wall to the endothermicside and this contributes to more hydrogen production from thedehydrogenation reaction (see Fig. 10a). At higher inlet tempera-ture of the endothermic side, the heat transfer from the exothermic

0 0.2 0.4 0.6 0.8 1485

490


0.1 0.12 0.14 0.16 0.18 0.2 0.22 0.240.4

0.42

0.44

0.46

0.48

0.5

0.52

0.54

CO

con

vers

ion

0.1 0.12 0.14 0.16 0.18 0.2 0.220.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Cyc

lohe

xane

con

vers

ion

Molar flow rate of endothermic stream, mol/s

c

Fig. 7. Inuence of molar ow rate of endothermic stream on: (a) axial temperatureprole in exothermic side, (b) axial temperature prole in endothermic side,(c) carbon monoxide and cyclohexane conversion.

F=0.55

nerg480

490

500

510

Tem

pera

ture

, K F=1

F=1.5F=0.9520

530

F=0.3 F=0.7

a c

1220 R. Vakili et al. / Applied Eside decreases owing to the lower temperature difference betweenexothermic and endothermic compartments. Consequently, moreDME is produced. The underneath area below the Fig. 10b showsthe DME production rates for various endothermic inlet tempera-ture. These areas are 105.67, 94.93 and 76.71 (mol s1) for inlettemperatures of 493, 480 and 470 K, respectively.

7. Conclusion

Direct DME synthesis was coupled with dehydrogenation ofcyclohexane to benzene by means of indirect heat transfer. Thereactor considered in this study is composed of two separated sidesfor exothermic and endothermic reactions. In this work, a steady-

0 0.2 0.4 0.6 0.8 1470


F=1

0 0.2 0.4 0.6 0.8 1475

480

485

490

495

500

505

510

515


Tem

pera

ture

,K

F=0.3

F=0.3

F=0.4

F=0.55

F=0.7

0 0.2 0.410

15

20

25

30

35

40

45

50

55

60

Dimensoinless

Con

sum

ed h

eat ,

W

d

e

b

Fig. 8. Inuence of molar ow rate of endothermic stream on: (a) axial temperaturetransferred heat from solid wall to endothermic side, (d) carbon monoxide and cyclohexa10

20

30

40

50

60

Tran

sfer

red

heat

, W

F=0.3

F=0.55F=0.4

F=0.7

y 88 (2011) 12111223state heterogeneous one-dimensional model for the mentionedreactor has been developed. This new conguration representssome important improvement in comparison to conventionalDME synthesis reactor (CDR) such as: reduction in reactor size;lowering outlet temperature of product stream; production ofhydrogen and benzene as additional valuable products by about15,000 and 196,000 Ton/year respectively and achievable auto-thermal conditions within the reactors. About 600 Ton/year DMEwas enhanced by the new proposed coupled conguration. More-over, hot spot temperature was lowered in about 4 K. The effectsof inlet temperature and the endothermic stream molar ow rateon the axial temperature prole of exothermic and endothermicsides as well as carbon monoxide and cyclohexane conversionswere examined. Higher ow rate of endothermic stream results

F=0.55

0 0.2 0.4 0.6 0.8 10


0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10.2

0.3

0.4

0.5

0.6

0.7

CO

con

vers

ion

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10.4

0.45

0.5

0.55

0.6

0.65

Cyc

lohe

xane

con

vers

ion

Molar flow rare of exothermic stream, mol/s

0.6 0.8 1 length

F=0.65

prole in exothermic side, (b) axial temperature prole in endothermic side, (c)ne conversion and (e) consumed heat in endothermic side along the reactor length.

0.2

1

1.5

2R

ate

o

nerg0.1 0.12 0.14 0.16 0.180.2 0.22 0.24480

485490

495

Molar flow rate of endothermic stream, mol/s

Inlet temperature ,K

0.1 0.12 0.14 0.160.18 0.2 0.22 0.24480

485

490

4950.2

0.4

0.6

0.8

1

Molar folw rate of endothermic stream, mol/s

Inlet temperature ,K

Cyc

lohe

xane

con

vers

ionb

Fig. 9. Simultaneous effect of inlet temperature and molar ow rate of endothermic0.25

0.3

0.35

0.4

0.450.5

0.55C

O c

onve

rsio

na

R. Vakili et al. / Applied Ein lower carbon monoxide conversion. These are because of lowertemperature prole in exothermic side and also lower cyclohexaneconversion due to the fact that the amount of catalyst in the endo-thermic side is not enough for these higher ow rates. The inu-ence of exothermic stream molar ow rate on reactor thermalbehaviour and performance was also studied. By increasing themolar ow rate of exothermic side, hot spot temperature is ap-proached to the end of the reactor length and carbon monoxideconversion decreased due to residence time depletion. Whenmolarow rate was 0.65 mol s1, cyclohexane conversion was maxi-mized and then decreased due to decrease of consumed heat inthe endothermic side. Rigorous mathematical models are excellenttools for exploration of the basic characteristics of such novel con-gurations and are able to provide a good initial sense about whatwould be achieved in the coupled reactors. Such an exploration cancontribute to considerable savings in money and time during theexpensive stage of pilot plant development. The continuous devel-opment of the model in conjunction with the pilot plant optimalutilization can also lead to considerable benets on the road to-wards the successful commercialization of such efcient novelcongurations and would be considered as a future work.

Appendix A. Dusty gas model

When reactants diffuse into the pores to react and form prod-ucts, bulk, Knudsen and surface diffusions may take place simulta-neously, depending on the size of the pores, the molecules involvedin the diffusing stream, the operating conditions and the geometryof the pores [54]. In the dusty gas model which is based on StefanMaxwell equations, both diffusional and convective mass transportterms are considered, and this includes the description of pressuredrop over the catalyst particle resulting from the stoichiometry of

stream on: (a) carbon monoxide conversion, (b) cyclohexane conversion.0 0.2 0.4 0.6 0.8 10.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8


Rat

e of

cyc

lohe

xane

deh

ydro

gena

tion,

3 s

)

T01=470K

T01=480KT01=493K

2.5

3

3.5

4

4.5

5x 10-3

f met

hano

l deh

ydra

tion.

ca

ts)

T02

=470KT

02=480K

T02

=493K

a

b

mol

/(kg

mol

/(m

y 88 (2011) 12111223 1221reaction and accompanying convective transport of molecules [55].The results of sensitivity analysis show that at low pressures (up to10 bar), Knudsen diffusion is the most important diffusing term,while at high pressures (100 bar) bulk diffusion predominates[44]. In this model, it is assumed that pore walls consist of giantmolecules (dust) which are uniformly distributed in the space.These dust molecules are considered to be dummy, or pseudo spe-cies in the mixture [56].

The dusty gas ux relations can be offered as follows, with asmall change in the notation as to avoid conicting with othernotations used in the model [57]:

NiDEffi

XNij

yjNi yiNjDEffij

! P

RTdyidr yiRT

1 B0PlDEffi

!dPdr

A:1

In the above equation, B0 is permeability of catalyst pellet, DEffi is

effective Knudsen diffusion coefcient and DEffij is effective binarydiffusion coefcient which are presented by Eqs. (A.2) and (A.3) be-low, respectively [58,59]:

DEffi aPess23

8RTpMi

1=2A:2

DEffij essDij A:3

where ap is the mean pore radius.The dusty gas ux relations (Eqs. (A.1)-(A.3)) contain three

parameters: the mean pore radius, a, the ratio of porosity and tor-tuosity factors, es/s and the permeability parameter, B0. Using

0 0.2 0.4 0.6 0.8 1Dimensionless length

Fig. 10. Inuence of: (a) exothermic inlet temperature on the rate of cyclohexanedehydrogenation and (b) endothermic inlet temperature on the rate of methanoldehydration.

B0 aP A:4

nerg8

The reader should note that the ux relations (Eq. (A.1)) couldbe rewritten for distinct components to form a set of ordinary dif-ferential equations, yielding expressions for dyi/dr [45]. Knowingthe fact that summation of all components equals to 1 (i.e.,PN

1yi 1), N 1 ordinary differential equations should be writtenfor the ux relations.

To complete the mathematical modelling of dusty gas model,the material balances and the stoichiometric relations have to beadded in order to be able to describe the multi component reac-tiondiffusion problem. Since we have used the detailed Graafkinetics for the system of methanol synthesis process, which isbased on three-independent reactions [44], and cyclohexane dehy-drogenation reaction, four material balances are needed to beadded to ux relations. For a spherical and isothermal particle, thisyields [57]:

dXkdr

r2rkk 1;2;3;4 A:5

dyidr

1r2

X3k1

XkX5j1

vkjFij

!; i 1;2; . . . ;N 1 A:6

Fii RTP1

DEffiX5

j1;ji

yiDEffij

yiDEffi

1 B0PlDEffi

!1w

!A:7

Fij RTPyiDEffi

yiDEffj

1 B0PlDEffi

!1w

!A:8

w 1 B0PlXNi1

yiDEffi

A:9

where Fii, Fij, w and Xk are auxiliary parameters and v is the stoichi-ometric coefcient.

The pressure drop in radial coordinate is given by:

dPdr 1

r2RTw

XNi1

1

DEffi

Xk

v ikXk

!A:10

The boundary conditions for the set of ordinary differentialequations are given by:

Xk 0 at r 0 A:11

yi ysi at r RP A:12

P Ps at r RP A:13The effectiveness factor for reaction k is given by:

gk R Rp0 rkdrRprsk

A:14

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R. Vakili et al. / Applied Energy 88 (2011) 12111223 1223

Direct dimethyl ether (DME) synthesis through a thermally coupled heat exchanger reactorIntroductionDimethyl ether (DME)Coupling

Process descriptionConventional direct DME synthesis reactor (CDR)DME coupled reactor

Reaction scheme and kineticsDimethyl ether synthesisDehydrogenation of cyclohexane

Mathematical modelSolid phaseFluid phaseErgun equationBoundary conditionsAuxiliary correlations

Numerical solutionResults and discussionBase caseMolar behaviourThermal behaviour

Influence of inlet temperature of endothermic streamInfluence of molar flow rate of endothermic streamInfluence of molar flow rate of exothermic streamSimultaneous effects of inlet temperature and molar flow rate of endothermic stream on the reactor performanceSensitivity analysis on the reaction rates

ConclusionDusty gas modelReferences

Documents

Direct dimethyl ether (DME) synthesis through a thermally coupled heat exchanger reactor