daesung song, wonjuncho, dal keun park, and en sup yoon · 2007. 9. 20. · 816 daesung song,...

Introduction1)

Dimethyl ether (DME), the simplest ether is considered

as a substitute fuel that could potentially replace petro-

leum-based fuels [1]. Its physical properties are similar to

those of liquefied petroleum gas (LPG). So it can exploit

the existing land-based and ocean-based LPG infra-

structures with minor modification. DME with its cetane

number of 55 to 60 is also considered as a substitute for

diesel fuel (cetane number 55) [2-5]. Compared with die-

sel fuel, combustion of DME produces much less pollu-

tants such as hydrocarbons, carbon monoxide, nitrogen

oxides and particulates in CIDI engine tests [5-9]. DME

has been traditionally produced by dehydration of meth-

anol, which is produced from syngas, products of natural

gas reforming. This traditional process is thus called

two-step method of DME preparation. However, DME

can be prepared directly from syngas (single-step)

[10-12]. Single-step method needs only one reactor for

†To whom all correspondence should be addressed.

(e-mail: [email protected])

DME synthesis, instead of two for two-step process. It

can also alleviate thermodynamic limitation of methanol

synthesis by converting it as produced into DME, there-

by potentially enhancing overall conversion of syngas to

DME. We can choose from several types of reactor for

DME synthesis. Fluidized bed reactor is proposed as an

ideal reactor for the highly exothermic DME synthesis

[13]. But development of fluidised bed reactor for DME

synthesis is still in the early stage of development, and

feasibility of it is not established yet. Investigators have

studied two different reactor types for the commercialisa-

tion of DME synthesis: bubbling slurry reactor [14] and

fixed bed reactor. In a slurry reactor fine catalyst par-

ticles are suspended in a solvent and feed gas enters as

bubbles from below. Control of reactor temperature is

manageable due to large heat capacity of the solvent that

is cooled by heat exchange tubes in the reactor. But re-

actants should be transferred from gas bubbles to liquid

phase solvent and then to catalyst particles for the syn-

thesis reaction. Low diffusivity in the liquid phase can

slow down overall reaction rate. Loss of fine catalyst par-

ticles from the reactor could be also a problem. Much

Daesung Song, Wonjun Cho , Dal Keun Park, and En Sup Yoon†

School of Chemical and Biological Engineering, Seoul National University, Seoul 151-744, Korea

*LNG Technology Research Center, KOGAS, Incheon 406-110, Korea

Received March 14, 2007; Accepted June 4, 2007

Abstract:Dimethyl Ether (DME, CH3OCH3) is the simplest ether and considered as one of the leading candidates

for the substitute of petroleum-based fuels. In this work, we analyzed one-step DME synthesis in a shell and rube

type fixed bed reactor and carried out simulation with a one-dimensional, steady state model of heterogeneous

catalyst bed with consideration of the heat and mass transfer between catalyst pellet and reactants gas and effec-

tiveness factor of catalysts together with reactor cooling through reactor tube wall. We compared behaviours of

the reactor using two different arrangements of catalysts, mixture of catalyst pellets and hybrid catalyst. The ef-

fects of several parameters including feed temperature, GHSV (Gas Hourly Space Velocity), H2 to CO ratio in

the feed gas, reactor pressure and ratio of methanol synthesis catalyst to methanol dehydration catalyst were

investigated. Results of the simulation indicate that hybrid catalyst is better than mixture of pellets in terms of

CO conversion, DME yield and DME productivity due to proximity of active sites of two different catalysts.

Keywords: dimethyl ether, fixed bed reactor, simulation

Daesung Song, Wonjun Cho, Dal Keun Park, and En Sup Yoon816

Table 1. Reaction Mechanism, Reaction Kinetics, Kinetic Parameters and Equilibrium Constant

Reaction mechanismCO2 + 3H2 CH3OH + H2O (1a)CO + H2O CO2 + H2 (1b)2CH3OH CH3OCH3 + H2O (1c)

Reaction kinetics

Kinetic parameters

parameter = A(i)exp(B(i))/RT)

A (i) B (i) parameter

k1 1.65 36696 4846.93

k2 3610 0 3610

k3 0.37 17197 15.61

k4 7.14 × 10-11 124119 38.34

k5 1.09 × 1010 -94765 12.07

Kch3oh 0.00079 70500 3633.13

k6 3.7 × 1010 -105000 4.417

KH20 0.084 41100 643.376

Equilibrium constant

empiricism would be needed for the scale-up of the

process.

In a fixed bed reactor the main difficulty would be the

prevention of the occurrence of hot spot as the reactions

in DME synthesis are severely exothermic. Catalysts can

be irreversibly deactivated once exposed to above 330oC. One simple way of limiting temperature rise is con-

trolling conversion, but this is not desirable economi-

cally. Therefore it necessitates understanding and pre-

dicting the behaviour of reactor at various conditions for

the design and scale-up of the DME synthesis process.

But it is not feasible to gather all the data experimentally,

and numerical simulation will be very valuable in the

process development. In this study we developed a math-

ematical model to simulate a pilot-plant scale, shell and

tube type DME reactor. In this work, we analyzed one-

step DME synthesis, and carried out simulation of a pilot

scale, fixed bed reactor with a one-dimensional heteroge-

neous reactor model under steady state condition with

consideration of the heat and mass transfer between cata-

lyst pellet and reactants gas and effectiveness factor of

catalysts together with reactor cooling through reactor

wall. We compared and analyzed the behaviour of the re-

actor using two different arrangements of catalysts, mix-

ture of catalyst pellets (a commercial methanol synthesis

catalyst, CuO/ZnO/Al2O3 and a methanol dehydration

catalyst, γ-alumina) and hybrid catalyst. By mixture of

catalyst pellets we envision pellets of methanol synthesis

and those of dehydration are uniformly mixed and put in-

to reactor tubes. Hybrid catalyst is, by our definition, cat-

alyst pellets prepared from mixture of fine powdered cat-

alysts aforementioned. Thus active sites for methanol

synthesis and those for dehydration of methanol are in-

ter-mixed within a catalyst pellet in the case of hybrid

catalyst. Intuition tells us that hybrid scheme would be

more effective than mixture of pellets due to proximity

of active sites of two different catalysts. In the specific

case of DME synthesis, however, we need a systematic

analysis in order to evaluate how the type of the catalyst

arrangement influences the behaviour of a reactor and

control the reaction heat from the highly exothermic

DME synthesis. We also investigated the effects of vari-

Comparison of the Performance of a Fixed Bed Reactor in the Two Cases, Mixture of Catalyst Pellets and a Hybrid Catalyst, for Dimetyl Ether Synthesis 817

Table 2. Heat and Mass Transport Property Correlations on the Surface of the Catalyst

The conventional expressions for the heat transfer coefficient

The heat transferred between the surface of the catalyst and the reaction fluid

ous variables on the performance of the reactor.

Development of the ReactorModel

Reactormodel assumptions

For modeling the reactor the following assumptions are

made: (1) a one-dimensional heterogeneous model, (2)

negligible radial temperature gradient and axial dis-

persion in the reactor tube, (3) radial temperature gra-

dient in catalyst pellets are insignificant because the con-

ductivity of the catalyst pellets are sufficiently high as to

discount any temperature difference between core and

surface, and (4) the dynamics of catalyst deactivation are

ignored due to a large time constant.

Reaction Kinetics

The preparation of DME from syngas can be repre-

sented by three catalytic reactions, as shown in Table 1

[15].

Reaction (1a) corresponds to the synthesis of methanol

from carbon dioxide and hydrogen. Reaction (1b) is the

water gas shift reaction. These two reactions are cata-

lyzed by the methanol synthesis catalyst (CuO/ZnO/

Al2O3). Reaction (1c) is the methanol dehydration re-

action, i.e. the DME synthesis reaction catalyzed by an

acidic catalyst (γ-alumina). Combinations of these three

reactions can explain the other schemes of preparation of

DME from syngas. We also use the reaction rate equa-

tions in Table 1 [16,17]. These three reactions are all

exothermic. Therefore, the handling of the reaction heat

is very important for the control of the reactions. The val-

ues of the kinetic parameters in the kinetic expressions

are summarized in Table 1. The equilibrium constant of

each reaction in Table 1 is taken from the literature

[18,19].

Heat and Mass Transfer on the Surface of the Catalyst

Due to the highly exothermic nature of the reactions,

the temperature of the catalyst pellets can differ from that

of the bulk stream of the reactants. Likewise, there could

be a difference in the concentration of the reactants be-

tween the bulk and catalyst pellets surface. The heat and

mass transport rate correlations on the surface of the cat-

alyst are summarized in Table 2.

Therefore, we investigated the heat and mass transfer on

the surface of the catalyst pellets. We employed conven-

tional expressions (4) for the heat transfer coefficient

[20-22]. The temperature of the catalyst particles should

satisfy the energy balance between the heat transfer and

heat of reaction: at steady state, the reaction heat should

be equal to the heat transferred between the surface of

the catalyst and the reaction fluid (5).

Effectiveness Factor

The intrinsic reaction rate can differ from the global re-

action rate, because of pore diffusion in the catalyst pel-

lets when their diameter is of the order of several milli-

meters. The effectiveness factor correlations are summar-

ized in Table 3.

We assume that the temperature of each catalyst pellet

is uniform and equal to the temperature on its surface and

consider only the mass balance within it. For spherical

catalyst pellets the concentration of the reactants and

products can be obtained by solving the partial different

equations given in Table 3 [23]. The effective diffusivity

of the gases through the porous catalyst pellets was esti-

mated from the molecular diffusivity, porosity and tor-

tuosity of the pores using equation (7). The solutions of

these equations provide the concentration profiles of the

gas species in the catalyst pellets together with the global

reaction rates.

Heat TransferBetween Tubes and Shell

The heat generated from the chemical reactions in the

catalyst is transferred to the gases flowing through the re-

actor tubes, and then to the cooling medium on the shell

side of the reactor. The heat transport property correla-

tions are summarized in Table 4.

Equation (8) holds for the whole reactor, as well as for

any given section of it. It calculates the temperature rise

of the reactants by subtracting the heat transferred to the

coolant from the heat generated by the chemical reacti-

ons. In order to estimate the heat transfer coefficient (9a),


Table 3. Effectiveness Factor Correlations

Steady state mass balances in the catalyst

Boundary conditions

Effective diffusivity

Table 4. Heat Transport Property Correlations

Overall heat balance

Overall heat transfer coefficient

Shell side heat transfer coefficient

Tube side heat transfer coefficient

U, we need to know both the shell side and tube side heat

transfer coefficients. The common method of calculating

the heat transfer coefficient can be employed for the esti-

mation of the shell side heat transfer coefficient (9b), as

heat transferring liquid or boiling water is used as the

cooling medium in the shell [24]. However, the presence

of the catalyst pellets makes the estimation of the heat

transfer coefficient on the tube side much more com-

plicated. Although several correlations are available in

the literature, their reliability should be experimentally

verified. As we do not have experimental values for the

tube side heat transfer coefficient, we selected the corre-


Table 5. Properties of the Catalyst and Pilot-plant Scale Reactor

Catalyst

Density (kg/m3) 1783.5

Porosity (%) 45.53

Pore tortuosity 1.69

Mass (kg) 7.85

Pellet diameter (m) 0.006

Reactor

Tube diameter (m) 0.03

Length (m) 1.6

Tube number 7

lation (10) for the estimation of the tube side heat trans-

fer coefficient [20].

Simulation of the Reactor

Equation (11) is used to calculate the mass flowrate pro-

file in the tube of the reactor [25,26].

(11)

In order to solve the above ODE, the axial length of the

reactor tube is divided into 1000 sections. First, the re-

action rates are calculated with the use of the correlations

listed in the reaction kinetics section. For this calculation,

the heat and mass transfer on the surface of the catalyst

described in the Heat and Mass Transfer on the surface

of the catalyst section and the effectiveness factor de-

scribed in the Effectiveness factor section are incorpo-

rated in order to reflect their effects on the reaction rates.

Then, the correlations of the Heat transfer between tubes

and shell section are used for the calculation of the re-

actor temperature in each section. Iterative procedures

for determining the temperature and reaction rates in

each section are necessary, as the temperature and re-

action rates are inter-dependent. After determining the

temperature in the section of the tube, the mass balance

in each section is calculated using Equation (11) and then

the simulation is allowed to proceed to the next step.

We used the following correlations to evaluate the re-

actor performance, such as the CO conversion, DME

Yield and DME productivity:

COconversion =COin -COout

× 100COin (12a)

DMEyield =DMEout ×2

× 100COin - COout (12b)

DMEproductivity =DMEout

mass of catalyst (12c)

Figure 1. Reaction rate of CO2 hydrogenation and water gas

shift in methanol synthesis catalyst.

Results and Discussion

Using the simulator we developed, behavior of a pi-

lot-scale DME reactor was studied. Base condition of the

reactor for simulation is as follows: GHSV 2000 hr-1,

feed temperature 240oC, reactor pressure 50 bar, H2 : CO

ratio 2:1, inlet temperature of cooling water 210oC. We

compared reactor performance in two cases of mixture of

pellets and hybrid catalyst as we changed values of pa-

rameters such as feed temperature, GHSV (Gas Hourly

Space Velocity), H2:CO ratio in the feed gas, reactor

pressure and ratio of methanol synthesis catalyst to meth-

anol dehydration catalyst affecting the behaviour of the

reactor. The properties of the catalyst and the information

concerning the pilot-plant scale reactor are shown in

Table 5.

Reaction Rates Analysis in the Catalyst Pellet and Ef-

fectiveness Factor Analysis Along the Length of Reac-

tor

The simulator evaluates effectiveness factor of the cata-

lyst pellet by solving mass balance equations for pore

diffusion and chemical reactions within the catalyst

pellet. Figures 1 and 2 show profiles of reaction rates

within catalyst pellets for the case of mixture of pellets.

In this case catalyst pellets for the synthesis of methanol

from syngas (CuO/ZnO/Al2O3, 6 mm pellets for reaction

1 and 2) and catalyst pellets for the synthesis of DME by

dehydration of methanol (γ-alumina, 7.7 mm pellets for

reaction 3) are present as a mixture inside the reactor

tubes. We used reaction conditions at entrance zone of

the reactor and can observe strong influence of pore dif-

fusion on reaction rate. Reaction rate of water gas shift

decreased in core part of a catalyst pellet due to strong

effect of diffusion, i.e., paucity of available reactants.


Figure 2. Reaction rate of methanol dehydration in methanol

dehydration catalyst.

Figure 3. Reaction rate of CO2 hydrogenation, water gas shift

and methanol dehydration in hybrid catalyst.

But, reaction rates of methanol synthesis showed max-

imum value in the region about 2 mm from the catalyst

surface. It was caused by CO2 increase from water gas

shift reaction. Note that methanol dehydration occurs on-

ly on the methanol dehydration catalyst in the case of

mixture of pellets. Thus, Figure 2 shows effects of pore

diffusion on reaction rate.

However, quite a different picture emerges in the case

of hybrid catalyst (Figure 3). Here all three reactions oc-

cur in the same catalyst pellet. Although reaction rate of

water gas shift reaction decreases toward the center of

the catalyst pellet as a result of pore diffusion effects, re-

action rates of methanol synthesis and methanol dehy-

dration in the core region of the catalyst pellets are high-

er than those of near pellet surface. As the reactions (1),

(a)

(b)

Figure 4. Effectiveness factor vs. Reactor location in the case

of (a) mixture of pellets and (b) hybrid catalyst.

(2), and (3) involved in the synthesis of methanol and

DME are interrelated in a complex way including pore

diffusion, their rates within the catalyst pellet reflect in-

ter-play of mass transfer and chemical reactions as well

as variations of species concentration within the catalyst.

As two cases have different reaction profiles in catalyst

pellet, we evaluated effectiveness factor for three re-

actions along the reactor axial distance from the reactor

entrance.

Figure 4 shows that lines of effectiveness factor of

methanol synthesis reaction and water gas shift reaction

are similar but that of DME synthesis reaction shows a

clearly different picture. DME is scarcely produced in the

core part of the catalyst due to pore diffusion effects in

the case of mixed pellets, but all reactions were active

showing little effects of pore diffusion in the case of hy-

brid catalyst. Therefore effectiveness factor for DME

synthesis reaction is well over 100 % in the entrance

zone of the reactor since DME is produced lively inner

catalyst, that for methanol synthesis above 100 % in the


(a) (b)

Figure 5. Flow rate and temperature profile in the fixed bed reactor for DME synthesis (in the case of mixture of pellets: 80 % meth-

anol synthesis catalyst, 20 % methanol dehydration catalyst).

(a) (b)

Figure 6. Flow rate and temperature profile of the reactor filled by hybrid catalyst (methanol synthesis catalyst component 80 %).

entrance zone of the reactor and that for methanol syn-

thesis increases to around 100 % as that of water gas

shift reaction increases to around 150 %. Besides effec-

tiveness factor for DME synthesis reaction in the hybrid

catalyst is always above 50 % after the entrance zone of

the reactor, whereas that for DME synthesis reaction in

the mixed catalyst is around 25 % (Figure 4).

Comparison of Flow Rate and Temperature Profile

Figure 5 shows reactor behaviour for the case of mix-

ture of pellets. It shows the temperature of reactant

stream rises rapidly (240 to 303oC) and then falls slowly

as it moves down through reactor tube. It means chem-

ical reactions in the entrance region of the reactor are

very fast due to high concentration of reactants. In the

case of mixture of catalyst pellets CO conversion is 27.1

% and DME productivity is 51.8 kg/D.

Reactor performance for hybrid catalyst is shown in

Figure 6. In this case, hybrid catalyst consists of meth-

anol synthesis component and methanol dehydration

component whose ratio is 8:2. Maximum temperature in

the reactor is 343oC, higher than that of mixture of cata-

lyst pellets, 303oC (Figure 5). In this case, CO con-

version is 40.2 %, DME productivity is 313.8 kg/D,

higher than that of mixture of pellets. In hybrid catalyst

active sites for methanol synthesis and methanol dehy-

dration coexist thereby realizing synergy effects of their

proximity.


(a) (b)

Figure 7. Effects of feed temperature on the reactor performance in the case of (a) mixture of pellets and (b) hybrid catalyst.

(a) (b)

Figure 8. Effects of GHSV on the reactor performance in the case of (a) mixture of pellets and (b) hybrid catalyst.

In the case of mixture of pellets it seems that the dis-

tance between catalysts is too large to realize synergy

effects. As we notice in Figures 5 and 6, maintaining uni-

form temperature along the reactor length is not a trivial

problem due to highly exothermic nature of the reactions

involved in DME synthesis even with shell and tube type

reactor design.

Effects of feed temperature

The effect of feed temperature within the range of 230

300∼oC in case of mixture of pellets is shown in Figure

7 (a). This shows that the higher the feed temperature,

the better DME productivity could be obtained due to the

thermal effect on the kinetics. But CO conversion is

around 27 %. And DME productivity is highest at feed

temperature of 300oC. Figure 7(b) shows that of the hy-

brid catalyst. DME yield and DME productivity is almost

same within the range of 240 300∼oC. Since reactions

are accelerated rapidly by high temperature and synergy

effects in catalyst in the entrance region of the reactor,

the temperature becomes higher. But overall performance

of the reaction is similar since water gas shift reaction

and methanol synthesis reaction are slow over 320oC.

Effects of GHSV (Gas Hourly Space Velocity)

The effect of GHSV within the range of 800 4800 in∼


(a) (b)

Figure 9. Effects of H2:CO ratio in the feed gas on the reactor performance in the case of (a) mixture of pellets and (b) hybrid

catalyst.

case of mixture of pellets is shown in Figure 8(a). At low

value of GHSV residence time in the reactor is large, so

CO conversion and DME yield are high. But feed rate is

small with low GHSV, and productivity can be small as

well (See Figure 8(a)). On the other hand, at high value

of GHSV residence time is small, so conversion and

yield are low. Therefore, there is an optimum value of

GHSV for the maximum DME productivity. Figure 8(a)

shows DME productivity is largest when GHSV is 1600

within the GHSV range of 800 4800. The effect of∼

GHSV within the range of 800 4800 in case of hybrid∼

pellets is shown in Figure 9(b). It has similar pattern with

the case of mixed pellets but the decreased degree is

small within the range of 1600 4800 due to synergy ef∼ -

fect of hybrid catalyst although residence time is short.

Figure 9(b) shows DME productivity is largest when

GHSV is 2800 within the GHSV range of 800 4800.∼

Effects of Feed Composition (H2 : CO ratio)

The ratio of H2 : CO in syngas varies depending on the

feed stock to reforming and post-treatment of syngas. We

studied the effects of H2 : CO ratio in the feed gas on the

reactor performance by varying its value within the range

1 3.0. When the ratio is low, CO∼ 2 hydrogenation de-

creased. This causes to produce not enough water for wa-

ter gas shift reaction, thereby decreasing reaction rate of

the latter. CO conversion increases with the H2 : CO

ratio. But due to excess water, methanol dehydration de-

creases at higher

H2 : CO ratio. The overall result is that DME pro-

ductivity is about the same for the H2 : CO ratio of 1.5∼

2.3 (Figure 9(a)). Figure 9(b) shows analogous pattern in

the case of hybrid catalyst but the decreased degree is

small within the region 1 1.3. The reason is that meth∼ -

anol dehydration reaction is increased by synergy effect

of hybrid catalyst from the entrance region of the reactor

and this makes enough water which accelerates water gas

shift reaction. Thereby all reactions are accelerated. On

the other hand, methanol synthesis reaction is accelerated

within the region 2 3 and this makes too much water∼

which causes to decrease methanol dehydration. The

overall result is that DME productivity is about the same

for the H2 : CO ratio of 1.3 to 2.0 (Figure 9(b)).

Effects of Reactor Pressure

Figure 10(a), (b) shows the effects of reactor pressure.

As gas volume decreases with the synthesis of DME

from syngas, higher pressure favours the reaction.

Therefore DME synthesis is practised at high pressures.

Within the range 40 100 bar DME productivity was∼

best at 100 bar. We just see the difference of the per-

formance by synergy effect by hybrid catalyst.

Effect of the Ratio of Methanol Synthesis Catalyst to

Methanol Dehydration Catalyst

The effects of the ratio of methanol synthesis catalyst to

methanol dehydration catalyst are shown in Figure 11(a).

Note that the mixture of two different catalyst pellets is

used and the ratio can be varied at will. With too little

methanol synthesis catalyst methanol synthesis catalyst

DME production capability (i.e., methanol dehydration)

cannot be fully utilized due to limited supply of metha-

nol. On the other hand reaction rate of methanol dehy-

dration will not be sufficient to process methanol in the


(a) (b)

Figure 10. Effects of reactor pressure on the reactor performance in the case of (a) mixture of pellets and (b) hybrid catalyst.

(a) (b)

Figure 11. Effects of methanol synthesis catalyst to methanol dehydration catalyst ratio on the reactor performance in the case of (a)

mixture of pellets and (b) hybrid catalyst.

case of too little dehydration catalyst in the reactor.

Figure 11(a) shows that DME productivity is best when

the reactor filled with 50 % methanol synthesis catalyst

and 50 % methanol dehydration catalyst. Figure 11(b)

shows the effects of composition of hybrid catalyst on

the reactor performance. Comparing this with Figure

11(a), we can notice that hybrid catalyst is much better

than mixture of pellets with regards to the reactor perfor-

mance. Optimum ratio of catalyst components in this

case is also 50 : 50. The variation within the range of ra-

tio 0.3 0.4 and 0.6 0.8 is small since methanol dehy∼ ∼ -

dration is accelerated by hybrid catalyst from the en-

trance region of the reactor and it makes enough water

which cause to accelerate water gas shift reaction.

Thereby methanol synthesis reaction is accelerated again.

Conclusion

In this work we developed a simulator of a shell and

tube type pilot-scale fixed bed reactor for single-step

DME synthesis from syngas, applying the one-dimen-

sional heterogeneous model under steady state. We ex-

amined behaviour of the reactor at various conditions for


the case of mixture of pellets and hybrid catalyst. We

found that complex reactions coupled with pore diffusion

within the catalyst pellet affects can show unusual values

of effectiveness factor. Employing hybrid catalyst yield-

ed higher productivity compared with using mixture of

catalyst pellets. But, we have to take extra care about re-

action heat and more careful cooling of reactor is needed

as more reaction heat is released near reactor entrance.

When we compared with mixed pellets with regards to

effects of parameters such as feed temperature, GHSV

(Gas Hourly Space Velocity) H2/CO ratio, feed pressure

and the ratio of methanol synthesis catalyst pellets, syn-

ergy effects of hybrid catalyst contributed to change the

performance of the reactor more smoothly.

Acknowledgments

Support of KOGAS (Korea Gas Corporation) and BK21

(Brain Korea21) for this study is gratefully acknow-

ledged.

Nomenclature

AP : Surface area of the catalyst, m2

At : External surface area of the tubes, m2

CAo.i : Concentration of component i in reactants

fluid, kmol/m3

Co,i : Concentration of component i on the cata-

lyst surface, kmol/m3

Cpg, Cpfluid : Specific heat of fluid, cal/mol K⋅

Cps, Cpw : Specific heat of particles at the surface

and of cooling water, cal/mol K⋅

dHr,ΔHr : Heat of reaction, kJ/mol

dp : Particle diameter, m

DAB : Binary diffusivity of gas, cm2/s

Deff,i : Effective diffusivity of component i with-

in a catalyst pellet, m2/h

Di, Do : Tube inside and outside diameter, m

DL : Equivalent diameter of a tube, m

Fi : the molar flow rate of species i, kmol/h

gcat1, gcat2 : Mass of the MeOH synthesis catalyst and

the MeOH dehydration catalyst, g

hdi, hdo : Fouling resistance of a tube side and a

shell side at heat transfer, kJ/h m2K

hi, ho : Film coefficient at a tube inside and out-

side, J/m2

h⋅ ⋅oC

hp : Film coefficient at heat transfer on a cata-

lyst pellet, J/m2

h⋅ ⋅oC

hpacket : Film coefficient in a packet, J/m2

h⋅ ⋅oC

hr : heat transfer coefficient for a radiation,

J/m2

h⋅ ⋅oC

keo, k

oew : effective thermal conductivity at the fixed

bed and the wall region, J/m h⋅ ⋅oC

kg : Fluid thermal conductivity, J/m h⋅ ⋅oC

ki : Reaction rate constants

km, ks : Heat conductivity of a wall and a particle,

J/m h⋅ ⋅oC

Ki, Keqm,j : Adsorption constant and Equilibrium con-

stant of reaction j

L : the height of the bed, m

mf : Mole flow rate of the fluid in the tube, g-

mol/h

nc, nr : Number of components and reactions

Nnu : Nusselt number

Npr : Prandtl number

NResph : Particle Reynolds number

Δp : The pressure drop, bar

Pi : Partial pressure of components i

r : Radial distance in the catalyst, m

ri : Reaction rate of i reactions, mol/gcat h⋅

rMS : Reaction rate of the methanol synthesis re-

action, mol/gcat h⋅

rRWGS : Reaction rate of the reverse water gas shift

reaction, mol/gcat h⋅

rWGS : Reaction rate of the water gas shift re-

action, mol/gcat h⋅

rMD : Reaction rate of the methanol dehydration

reaction, mol/gcat h⋅

rj : reaction rate of the j th reaction, mol/gcat h⋅

R : Gas constant, 8.314 J/mol K⋅

RP : Particle radius, m

Tf : Fluid Temperature, K

To, Tp : Temperature of cooling water and cata-

lyst, K

TΔ f : Temperature difference of fluid, K

uo : Volumetric average fluid velocity, m/s

Uo : Overall heat transfer coefficient, J/m2

h⋅

⋅

oC

xw : thickness of a wall, m

Greek letters

ε : The void space of the bed.

εmf,εw : The void fraction at the minimum fluidiz-

ing bed and at the wall layer

øw : Ratio of effective thickness of gas film

around a contact point to particle diameter

for contact between particle and surface

øb : Ratio of effective thickness of gas film

around a contact point to particle diameter

for contact between adjacent particles

ηj : Effectiveness factor of j reaction

ηMS : Effectiveness factor of the methanol syn-

thesis reaction

ηWGS : Effectiveness factor of the water gas shift

reaction

ηMD : Effectiveness factor of the methanol dehy-


dration reaction

μ,μa : Dynamic viscosity and absolute viscosity,

kg/m h⋅

ρ,ρg : Fluid density, kg/m3

ρb : Bulk density of the bed, kg/m3

ρp,ρp1,ρp2 : Particle density of hybrid catalyst, MeOH

synthesis catalyst and MeOH dehydration

catalyst, g/m3

ρw : Cooling water density, kg/m3

ν : Fluid line velocity, m/s

νw : Cooling water line velocity, m/s

τt : Residence time, h

γi,j : Stoichiometric coefficient of the i th com-

ponent in the j th reaction

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