sorption-enhanced methanol synthesis: dynamic modeling and optimization

Journal of the Taiwan Institute of Chemical Engineers xxx (2013) xxx–xxx

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JTICE-799; No. of Pages 11

Sorption-enhanced methanol synthesis: Dynamic modeling andoptimization

Z. Dehghani, M. Bayat, M.R. Rahimpour *

Department of Chemical Engineering, School of Chemical and Petroleum Engineering, Shiraz University, Shiraz 71345, Iran

A R T I C L E I N F O

Article history:

Received 1 July 2013

Received in revised form 27 November 2013

Accepted 1 December 2013

Available online xxx

Keywords:

Dynamic simulation

Methanol synthesis

Adsorption

Optimization

Catalyst deactivation

Zeolite 4A

A B S T R A C T

Owing to the global energy concerns in today’s world, alternative fuels such as methanol have become an

increasingly attractive option to meet the growing power demand. This work considers a dynamic

mathematical model of a gas-flowing solids-fixed bed reactor (GFSFBR) with in situ water adsorption for

methanol synthesis in the face of long term catalyst deactivation. Contact of gas and fine solid particles

inside packed bed results in the selective adsorption of water from the methanol synthesis that leads to

higher methanol production compared to the conventional methanol reactor (CMR). Moreover, a

theoretical investigation has been performed in order to evaluate the optimal operating conditions and

maximize the methanol production in a GFSFBR using differential evolution (DE) algorithm as a robust

method. Dynamic optimization result has shown that under optimum values of inlet temperature of gas

phase, inlet temperature of flowing solid phase, and inlet temperature of shell side the highest methanol

production can be achieved during the operating period.

� 2013 Published by Elsevier B.V. on behalf of Taiwan Institute of Chemical Engineers.

Contents lists available at ScienceDirect

Journal of the Taiwan Institute of Chemical Engineers

jou r nal h o mep age: w ww.els evier . co m/lo c ate / j t i c e

1. Introduction

Development of the alternative clean energy sources such asalcohols and ethers has received a great deal of attention, as aresult of increasing rate of the world oil consumption, pollutantsemission from diesel engines, and global warming. These alterna-tive fuels and fuel additives are less polluting and have goodburning characteristics.

1.1. Methanol

Methanol, also called methyl alcohol or wood alcohol, is amultipurpose base chemical that has a simple molecular structure.It can be made from many plentiful energy resources, predomi-nantly natural gas. Thermodynamic equilibrium limitations andcatalyst deactivation are parameters that affect the rate ofmethanol production in an industrial reactor [1]. This alcoholand its derivatives are important in numerous industrial processesand useful in production of fuels, pesticides, and drugs [2]. Hence,there have been a lot of studies conducted to improve theefficiency of the industrial methanol synthesis reactor [3–6].

Hydrogenation of CO, hydrogenation of CO2, and reversedwater–gas shift (WGS) reaction due to the presence of water thatmakes the reaction of CO with H2O happen and converts CO to CO2

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

E-mail address: [email protected] (M.R. Rahimpour).

Please cite this article in press as: Dehghani Z, et al. Sorption-enhanTaiwan Inst Chem Eng (2013), http://dx.doi.org/10.1016/j.jtice.2013

1876-1070/$ – see front matter � 2013 Published by Elsevier B.V. on behalf of Taiwan

http://dx.doi.org/10.1016/j.jtice.2013.12.001

[7], are the three overall reactions involved in the methanolsynthesis process (see Table 1).

(r1)–(r3) are not independent consequently, (r2) is a linearcombination of the others. In this study, the kinetic rateexpressions have been selected from Graaf et al. [8].

1.2. Gas-flowing solids-fixed bed reactor (GFSFBR)

Using the idea of sorption-enhanced reaction in a gas-flowingsolids-fixed bed reactor (GFSFBR) is a practical solution to by-passthe thermodynamic limitation of several processes. In thesesystems, flowing solids, as the additional phase with the selectiveadsorption capability, are introduced to the reaction zone in orderto shift the equilibrium toward more products formation. Gasphase along with these fine adsorbent particles is flowing throughthe packed bed of catalyst in a co-current or counter-currentoperation. Two phase or three phase system can be considered inthis type of equipment [9].

In the case of methanol synthesis, a novel idea is proposed in thecurrent study based on the sorption-enhanced reaction processconsidering zeolite 4A as the water adsorbent. Zeolite 4A is a solidparticle with the composition of Na12(Si12Al12O48)�27H2O and highwater adsorption affinity which makes it favorable for waterremoval or separation [10]. In situ water removal in a gas-flowingsolids-fixed bed methanol synthesis reactor contributes to thedisplacement of water gas-shift equilibrium which increases CO2

conversion into methanol through a sorption-enhanced reactionprocess [11].

ced methanol synthesis: Dynamic modeling and optimization. J.12.001

Institute of Chemical Engineers.


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Table 1Reactions involved in methanol synthesis.

Hydrogenation

of CO (r1):

CO þ 2H2$ CH3OH DH298 ¼ �90:55 kJ=mol

Hydrogenation

of CO2 (r2):

CO2 þ 3H2$ CH3OH þ H2O DH298 ¼ �49:43 kJ=mol

Reversed WGS

reaction (r3):

CO2 þ H2$ CO þ H2O DH298 ¼ þ41:12 kJ=mol

Z. Dehghani et al. / Journal of the Taiwan Institute of Chemical Engineers xxx (2013) xxx–xxx2

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Low pressure drop, low axial dispersion of flowing phases, highmass and heat transfer rates, and application of regenerableadsorbents are the favorable characteristics of GFSFBR. A dominantproblem involved in the conventional sorption-enhanced reactionprocess is the discontinuous operation of the reactor. Since theeffects of separation are lost at the equilibrium state of theadsorbent, it is essential to perform a cyclic regeneration of solidsduring the whole process [11]. In order to overcome thispredicament, a continuous regeneration of zeolite 4A is carriedout in GFSFBR based on desorption of water vapor. In most cases,dehydration of zeolites is carried out under vacuum or by a flow ofcarrier gas, with a simultaneous rise in temperature to 300–400 8C[12]. Zeolite 4A crystal has a relatively good thermal stability andthe change of its structure accompanied by the decrease in itswater capacity takes place only at temperatures higher than1073 K [10].

1.3. Dynamic simulation

Dynamic modeling of processes has gained much moreattention to describe a wide range of applications including:start-up and shut-down investigations, system identification,safety, control, optimization, transient behavior, and operabilitystudies. In operability studies, due to the application of morepowerful numerical strategies in the solution of dynamic modelscompared to the steady-state ones, the realistic description of thetransient states obtained through dynamic simulation are moretrustworthy than the steady-state solution. As a result, it is moresecure and reliable to study the optimization and control ofmethanol synthesis reactor by a dynamic simulator [13,14].

1.4. Optimization

Dynamic optimization has its particular jargon to addressspecific features of the problem. Most of the optimizationproblems in the process industry can be broken down into non-linear, non-convex, and constrained optimization problems [15].The important plant parameters which are chosen for optimizationare equipment size, recycle flows, and operating conditions such asconcentration, temperature and pressure. An optimum design isbased on the best or the most favorable conditions. Almost always,these optimum conditions can eventually be reduced to aconsideration of profits or costs. Consequently, an optimumeconomic design could be achieved based on conditions givingthe highest profit per unit of production or the lowest cost per unitof time. When one design variable is changed, it is frequently foundthat some costs rise and the others reduce. Under thesecircumstances, the total cost can be achieved with minimumamount at one value of the specific design variable, and this valuewould be considered as an optimum.

Common optimization techniques have limited applications.The main difficulty in using these techniques is the feasibility ofidentifying the local optimum instead of global one owing to theirsensitivity to initial guess. Considering this fact, it is essential todevelop more useful optimization techniques based on naturalphenomena (evolutionary computation), including: simulatedannealing (SA) [16], evolution strategies (ESs) [17], genetic


algorithms (GAs) [18,19] and differential evolution (DE) algorithm[20].

1.5. Literature review

The concept of contacting gas and fine flowing solid particleswithin a packed bed was proposed about sixty years ago [21].Kuczynski et al. [22] investigated an experimental study ofmethanol synthesis in a counter-current gas–solid–solid trickleflow reactor and considered amorphous LA-25 low-aluminacracking as methanol adsorbent. The obtained result indicated ahigher conversion of the reactants for the situation of removingproduct from the reactor. In 1988, Westerterp et al. [23] comparedthe intensified process with the conventional methanol synthesisin a highly optimized Lurgi process. They reported a considerableenergy saving in the synthesis loop as a result of reduction in therecirculation rate and pressure drop inside the reactor. A steady-state mathematical model for ammonia synthesis with in situadsorption in a co-current gas-flowing solids-fixed bed reactor wasdeveloped by Nickacevic et al. [24]. Modeling result showed thatthe conversion stays higher than those in the conventional reactoreven if the reactor performs at much lower temperatures andpressures. In order to evaluate the performance of sorption-enhanced dimethyl ether (DME) synthesis reactor, Iliuta et al. [11]recommended an isothermal, unsteady-state model of the process.The yields of methanol and DME as well as DME selectivity werefavored and a reduced fraction of unconverted methanol wasobserved under H2O removal conditions. On the other hand, therehave been a lot of studies on the optimization of methanolsynthesis in the literature. A novel radial-flow spherical-bedmethanol synthesis reactor was optimized by Rahimpour et al. [25]using DE algorithm to maximize the overall methanol production.Parvasi et al. [15] simulated and optimized methanol synthesisloop with membrane reactor. Dynamic optimization of tempera-tures was implemented for improving the overall methanolproduction using DE method. Networks (NTWs) of four catalyticreactors with periodically switched inlet and outlet sections forreversible exothermic reactions of methanol synthesis werestudied by Mancusi et al. [26,27] and Altimari and Mancusi [28].They analyzed the effects of various switching strategies on theNTW stability and performance. Recently, Bayat et al. [29]proposed a steady-state mathematical model of a gas-flowingsolids-fixed bed reactor (GFSFBR) for methanol synthesis and amulti-objective optimization of GFSFBR operating conditions withthe purpose of maximizing methanol production rate andselectivity using NSGA-II algorithm. They also proposed amultifunctional reactor (MR) for simultaneous production ofhydrogen and methanol with the application of GFSFBR in theexothermic side of this novel configuration. Then, they performedan optimization of MR using DE algorithm, in order to maximizeboth hydrogen mole fraction and methanol yield [30].

1.6. Objective

The presence of flowing adsorbents inside the methanolsynthesis packed bed reactor results in the significant changesin transport characteristics of GFSFBR along with a more complexflow pattern and solving procedure. Besides, it is functionally moredemanding to apply a GFSFBR with continuous adsorbentregeneration than a conventional reactor [31]. Dynamic modelingof a gas-flowing solids-fixed bed methanol synthesis reactorconsidering the simultaneous effects of water vapor adsorptionand catalyst deactivation as well as optimization of GFSFBRoperating conditions using DE algorithm is the goal of the presentstudy. A critical examination of the literature reveals that there isno information available regarding the use of GFSFBR with in situ



Z. Dehghani et al. / Journal of the Taiwan Institute of Chemical Engineers xxx (2013) xxx–xxx 3

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water adsorption and taking into account the catalyst deactivationfor methanol synthesis.

2. Process description

The conventional methanol reactor (CMR) is a vertical heatexchanger type reactor with the catalysts packed in the tubes(boiling water surrounds these vertical pipes). Methanol synthesisreactions take place over commercial CuO/ZnO/Al2O3 catalysts.Boiling water receives the heat from the exothermic reactionswhich leads to steam generation.

Fig. 1 illustrates a schematic diagram of gas-flowing solids-fixedbed methanol synthesis reactor. In the gas-flowing solids-fixed bedmethanol synthesis reactor, an additional flowing phase (the

Fig. 1. Schematic diagram of GFS


adsorbent particles) is introduced to the gas phase for water vaporadsorption. Methanol synthesis occurs in the tube side over theconventional catalyst via a sorption-enhanced reaction process.The flowing adsorbents are regenerated after each reaction processby means of a solids regenerator and as a result, fresh particles arecontinuously fed into the inlet of GFSFBR. The technical design dataof catalyst pellet, flowing solid, and the reactor specifications arelisted in Table 2. The methanol reactor feed inlet conditions arealso tabulated in Table 3 [32].

3. Mathematical modeling

We postulated an unsteady-state one-dimensional heteroge-neous mathematical model of methanol synthesis in GFSFBR to

FBR for methanol synthesis.



Table 2Specifications of catalyst, flowing solid, and reactor.

Parameters Value

Catalyst particle densitya, rs 1770 (kg/m3)

Catalyst diametera, ds 5.47 � 10�3 (m)

Specific heat of the catalyst at constant pressurea, Cps 5.0 (kJ/mol)

Specific surface area of catalyst pelleta, as 626.98 (m2/m3)

Number of tubesa 2962

Tube lengtha, L 7.022 (m)

Tube diameter, D 38 (mm)

Adsorbent particle densityb, r0s 1245 (kg/m3)

Void fraction of catalytic bed a, e 0.39 (m3/m3)

Diameter of flowing solids, d0s 300–1300 (mm)

Specific heat of adsorptionc, DHads 64 (kJ/mol)

Mass flux of flowing solids, S 1 � 10�4–0.1 (kg/m2 s)

a Obtained from Rezaie et al. [32].b Obtained from Iliuta et al. [11].c Obtained from Zhu et al. [10].

Table 3Methanol reactor feed inlet conditions [32].

Feed conditions Value

Composition (mol%)

CH3OH 0.50

CO2 9.40

CO 4.60

H2O 0.04

H2 65.90

N2 9.30

CH4 10.26

Total molar flow rate per tube (mol/s) 0.64

Inlet temperature (K) 503

Pressure (bar) 76.98


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analyze the concept of H2O adsorption and catalyst deactivation,which includes: mass and energy balances, pressure dropequation, solids hold up relations, auxiliary correlations, anddeactivation model. The major assumptions of the model are: (a)constant bed void fraction in radial directions, (b) negligible heatloss, (c) significantly lower axial diffusion of mass and heatcompared to the gas bulk movement, and negligible axialdispersion in the fluid phase as a result of L/dp > 30, (d) co-currentdown-flow of the gas and flowing solid particles, and (e) no radialheat and mass diffusion in catalyst pellet.

The mole and energy balance equations were achieved inaccordance with the assumptions (a)–(e) and the differentialelement along the axial direction of the reactor. These balancesconsist of convection, transport to the solid phase, adsorption, andreaction. Table 4 reports the mass balance, energy balance, and

Table 4Mass balance, energy balance, and boundary conditions for catalyst and gas phases.

Mass and energy balance equations for the bulk gas phase

e � ct �@yi

@t¼ � 1

Ac

dFi

dzþ as � ct � kgiðyis � yiÞ � g � k0g � a0s � r0s qe � qð Þ i ¼ 1; 2; 3; . . . ; N

e � ct � C pg �@Tg

@t¼ � 1

AcC pg

@ðFt � TgÞ@z

þ as � h f � ðTs � TgÞ þ pDi

Ac� UshellðTshell � TgÞ � h0f � a

Mass and energy balance equations for the catalyst pellets

es � ct �dyis

dt¼ as � ct � kgiðyi � yisÞ þ rs � h � ria i ¼ 1; 2; 3; . . . ; N

rB � C ps �dTs

dt¼ as � h f � ðTg � TsÞ þ h � rs � a

Xn

j¼1

r j � ð�DH f ;iÞ

Boundary conditions : yi ¼ yi0; Tg ¼ Tg0; q ¼ 0 at z ¼ 0

Initial conditions : yi ¼ yssi ; yis ¼ yss

is ; Tg ¼ Tssg ; Ts ¼ Tss

s ; a ¼ 1 at t ¼ 0


boundary conditions for gas and catalyst phases. In Eq. (1), g isequal to 1 for H2O component and zero for the other components.Also, h (the ratio between the observed reaction rate and the realreaction rate) presented in Eqs. (3) and (4) is obtained from thecalculations of a dusty gas model [8].

As a consequence of continuous reduction in total molar flowrate along the industrial fixed-bed methanol synthesis reactor,consideration of constant total molar flow rate diminishes theaccuracy of prediction of the reactor outlet mole fractions.Accordingly, in the current study, the total molar flow rate isassumed to vary along the reaction pathway. Moreover, themolecular weights, heat capacities, viscosity, density, and otherproperties are considered to vary for the mathematical modeling.

3.1. Material balance

Concentration of H2O in the flowing adsorbents is enhancingalong GFSFBR. The material balance for a differential volume of theflowing solids can be formulated as follows:

u0sdq

dz¼ k0ga0sðqe � qÞ (7)

where k0g is determined based on the well-known Ranz–Marshallcorrelation for the gas-flowing solids mass transport [33].

A three-parameter isotherm equation named as Unilanequation is regularly utilized to correlate the adsorption equilibri-um data of several solids, such as activated carbon and zeolite [34].In order to describe the adsorption/desorption isotherm of H2O onzeolite 4A particles, the developed Unilan equation by Zhu et al.[10] was employed in this study:

qe ¼qm

2sln

1 þ esKPH2O

1 þ e�sKPH2O

� �(8)

The parameters K and s are changing in the dependence oftemperature, with the parameter K taking the usual van’t Hoffequation for the adsorption affinity that can be written as [10]:

K ¼ K0expEads

RT0

T0

T� 1

� �� (9)

and the following functional form of the temperature dependencepresented for parameter s:

s ¼ s0T0

T(10)

Table 5 gives the Unilan model parameters.

ð1Þ

0s Tg � T 0s� �

ð2Þ

ð3Þ

ð4Þ

ð5Þ

ð6Þ



Table 5Adsorption/desorption isotherm of water on zeolite 4A particles-Unilan model

parameters [10].

Unilan model equations and parameters Value

Saturation capacity, qm 15.81 � 10�3 kmol/kg

Adsorption affinity at reference temperature, K0 4.722 kPa�1

Average energy of adsorption, Eads 56.23 kJ/mol

Reference temperature, T0 340.6 K

Parameter, s0 4.67


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3.2. Energy balance

The term for the heat released owing to the adsorption (DHads)and the term for the heat transferred between the gas and theflowing solids phases compose the energy balance of the flowingsolids phase:

u0sr0sC p0s

dT 0sdz¼ �DHadsSa0s qe � qð Þ þ h0f a0s Tg � T 0s

� �(11)

3.3. Pressure drop

The two main contributions of the overall pressure drop inGFSFBR are: (a) resistance of the packed bed (modified Ergunequation) and (b) the drag due to co-current flow as well ascomplicated interactions between the adsorbents and gas [24].

d p

dz¼ � 150

Resþ 1:75

� �u2

grg

deq

1 � e0ð Þe03

� 3

4

Cdbdrgu2r

d0se0(12)

3.4. Solids holdup

The sum of dynamic and static holdups is generally identified asthe flowing solids holdup, b. Dynamic holdup (bd) corresponds tothe fraction of flowing solids that is suspended in the voidsbetween the packing elements. Once the inlets for the gas andflowing particles are closed, these fine adsorbents will flow out.The dynamic holdup has been evaluated using empirical correla-

Table 6Physical properties, mass and heat transfer correlations.

Parameter Equ

Component heat capacity C p

Mixture heat capacity C p

Viscositym ¼

Mass transfer coefficient between gas and packing elements kgi

Res

Sci

Dim

Di j

Overall heat transfer coefficient 1

Ush

Heat transfer coefficient between gas phase and reactor wall

C p

Heat capacity of flowing solidsC p

Drag coefficientCd


tions [24]:

bd ¼ 9:67 � Re0s1:123 � Ar�0:486 � S2

r0s � rg � u2g

!0:453

� deq

Di

� ��0:647

� e�0:404 � 1 � eð Þ0:726 (13)

Static holdup (bs) corresponds to the fraction of fine particlesresting on the packing elements. After shutting down the solidsand gas inlets, the mass of solids that remains in the bed representsthe static holdup. The following empirical correlation is providedfor the calculation of static holdup [24]:

bs ¼ 0:0295 � b0:214d � deq

Di

� ��1:82

� f�2:69 � e�0:31 1 � eð Þ1:61 (14)

3.5. Auxiliary correlations

In order to complete the simulation of the GFSFBR, auxiliarycorrelations should also be added to the model. Owing to thetransfer phenomena effects in the heterogeneous model, heat andmass transfer along with the overall heat transfer coefficientbetween three phases have to be considered. On the other hand,estimation of physical properties is another important issue incalculations. The correlations used for physical properties as wellas mass and heat transfer coefficients are summarized in Table 6[35–41].

3.6. Deactivation model

Catalyst deactivation is one of the most challenging issues incatalytic reactors and the three major factors affecting catalyticactivity are sintering, poisoning, and wearing. Catalyst deactiva-tion model for the commercial methanol synthesis catalyst isadopted from Hanken [42]:

� da

dt¼ �kdexp

�Ed

R

1

T� 1

TR

� �� a5 (15)

ation Reference

gi ¼ a þ bT þ cT2 þ dT3

g ¼X

yiC pgi

C1TC2

1 þ ðC3=TÞ þ ðC4=T2Þ[35]

¼ 1:17Re�0:42s Sc�0:67

i ug � 103 [36]

¼dequgrg

ð1 � eÞm

¼ m

rgDim � 10�4

¼ 1 � yiPi¼ jyi=Di j

[37]

¼1:43 � 10�7T3=2 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

1=Mi þ 1=M j

pffiffiffi2p

Pðv1=3ci þ v1=3

c j Þ2

[38]

ell¼ 1

hiþ AilnðDo=DiÞ

2pLKwþ Ai

Ao

1

ho

hi

grgm

C pgm

K

� �2=3

¼ 0:458

ergugds

m

� ��0:407 [39]

0s ¼

0:2 þ 0:0119ðT � 273Þ þ 4:2W

1 þ W

[40]

¼ 24

Re0s1 þ 0:173Re0s0:6567� �

þ 0:413

1 þ 16; 300Re0s�1:09

[41]



Fig. 2. Elemental volume of GFSFBR.

0 20 0 40 0 600 800 10 00 120 0200

220

240

260

280

300

320

340

360

380

400

Time (da y)

Met

hano

l pro

duct

ion

rate

(ton

/day

)

Plant da taSimulation

Fig. 3. Calculated results of production rate and observed plant data [43].

Table 7Parameters used in the optimization of GFSFBR for methanol synthesis.

Objective functions Decision variables

max OF ¼ �ðMethanol Production RateÞ þ 107XN

i¼1

G2i

400 < Tg< 543

G = max (0, T � 543) 400 < T 0s < 543

400 < Tshell< 543


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where TR, Ed and kd are the reference temperature, activationenergy and deactivation constant of the catalyst, respectively. Thenumerical values of TR is 513 K, Ed is 91,270 J/mol, and kd is0.00439 h�1.

4. Numerical solution

In order to solve the set of algebraic, ordinary differential, andpartial differential equations, a two-step procedure comprising asteady-state stage followed by a dynamic stage is used. Identifica-tion of the steady-state condition as the initial condition of thedynamic simulation is performed by setting the whole time-derivatives equal to zero and considering the activity equal to one.The solving procedure is clarified below.

After rewriting the model equations at steady-state condition, aset of differential algebraic equations (DAEs) is achieved. Here,backward finite difference approximation is applied to solve theseequations and a non-linear algebraic set of equations is obtained.Subsequently, the reactor is divided into 100 separate sections. Thediscretized ordinary differential equations via backward finitedifference for node k are as follows (see Fig. 2):

in

z

L¼ 0 ! k ¼ 0

z

L¼ 1 ! k ¼ 101

Dz

L¼ 1

100

8>>>><>>>>:

(16)

The mass and energy balance equations for the bulk gas phase:

� 1

Ac

ðFiÞk � ðFiÞk�1

Dzþ as � ct kgi

� �kyisð Þk � yið Þk

� g k0g

ka0s � r0s qe � qð Þk

¼ 0 (17)

� 1

AcC pg

ððFtTgÞk � ðFtTgÞk�1ÞDz

þ as � h f Tsð Þk � Tg

� �k

þ pDi

AcUshellð Þk Tshellð Þk � Tg

� �k

� h0f a0s Tg

� �k � T 0s� �k

¼ 0 (18)

The mass and energy balance equations for the catalyst pellets:

as � ct kgi

� �kyið Þk � yisð Þk

þ rs � h rið Þk ¼ 0 (19)

as � h f Tg

� �k � Tsð Þk

þ h � rs �Xn

j¼1

r j

� �k � ð�DH f ;iÞk ¼ 0 (20)


The Gauss–Newton method in MATLAB programming envi-ronment is employed to solve the non-linear algebraic equations ineach section. This procedure should be repeated for the entirenodes along GFSFBR and the achieved results of node k areassumed as inlet conditions for the next node (k+1). At the end, theconcentration of components and temperature can be plottedversus length.

For the dynamical solution of the set of rigid model equationsbased on steady-state results as the initial conditions, equationshave been discretized respect to axial coordinate. ModifiedRosenbrock formula of the second order has been applied to thediscretized equations in every node of the reactor length tointegrate the set of equations with respect to the time usingMATLAB ode23s solver that can simulate complex dynamicalsystems. Besides, 1200 days of operation have been considered asthe process duration.

4.1. Model validation

The model of methanol synthesis was validated against CMR fora particular case of constant coolant temperature under the designconditions. Methanol production rate is the most importantcharacteristic parameter in the methanol synthesis reactor. Itwas observed that the model performed satisfactorily well underindustrial conditions and an acceptable agreement was obtainedbetween the observed plant data and simulation data. Thecalculated results of production rate and the correspondingobserved plant data are depicted in Fig. 3 [43].

5. Results and discussions

A parametric analysis is executed to address the essentialparameters, such as the temperature of the reactor, catalystactivity, water mole fraction, and methanol production rateprofiles along the GFSFBR.



0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

1

2

3

4

5

6

7

8

9

Axial reactor length

Con

cent

ratio

n (m

ol/k

g)First day

Equilibrium co ncentration of adsorbed waterConcentration of water adsorbe d in flowing so lids

qe

q

Fig. 4. Concentration of water on zeolite 4A versus GFSFBR length at first day of

operation.

0 1 2 3 4 5 6 70

0.01

0.02

0.03

0.04

0.05

0.06

0.07


Met

hano

l mol

frac

tion

First day

CMRGFSFB R

Fig. 5. Comparison of methanol mole fraction along CMR and GFSFBR at first day of

operation.


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Dynamic optimization of gas-flowing solids-fixed bed metha-nol synthesis reactor is investigated in the current research, usingDE algorithm and MATLAB programming environment. Because ofthe extensive use of methanol as a feedstock for production ofnumerous polymers, maximization of methanol production rate(OF) is selected as the objective function (see Table 7). Further-more, since the catalyst deactivation occurs at the temperaturehigher than 543 K, this temperature is considered as a constraintfor the catalytic bed temperature along GFSFBR.

A penalty function method which involves penalizing theobjective function in proportion to the extent of constraintviolation (i.e., the penalty function takes a finite value when aconstraint is violated and a value of zero when constraint issatisfied) is also applied using 107 as the penalty parameter toautomatically omit the undesirable results. This parameterdepends on the order of magnitude of the decision variables andcan vary from problem to problem.

As presented in Table 7, inlet temperature of gas phase, inlettemperature of flowing solids phase, and inlet temperature of shellside are chosen as the decision variables.

A brief description of the DE method is given in Appendix A.

5.1. Simulation results

5.1.1. Results of steady-state simulation

Fig. 4 reveals the concentration of H2O on zeolite 4A (q) as afunction of axial reactor length at first day of operation. In theentrance region of GFSFBR, the partial pressure of H2O increaseswhich contributes to an enhancement in the rate of adsorption.Concentration of H2O on zeolite 4A will continue to increase untilthe water production is stopped and the adsorption of H2O reachesthe equilibrium. This occurs in the middle of the reactor.Consequently, an almost constant rate of adsorption can beobserved from the middle to the end of the reactor. Theequilibrium concentration of H2O on zeolite 4A (qe) is also shownin this figure. As can be seen in this figure, qe is higher than q alongGFSFBR, as a result of the fact that more water adsorption can beobtained in the equilibrium state in comparison with the non-equilibrium one.

Fig. 5 illustrates the comparison of methanol mole fractionalong CMR and GFSFBR at first day of operation. The difference


between CMR and GFSFBR performance is attributed to thepositive effect of utilizing adsorbent in the GFSFBR, since wateradsorption increases the reaction rate and methanol productionrate considerably. As a consequence, methanol mole fraction inGFSFBR is 14.664% higher than that in CMR.

5.1.2. Results of dynamic simulation

Simulations with position dependent catalytic activity profileshave been carried out to study the effects of deactivation andapplication of water adsorbents on the methanol production rateby using simulation results and showing the reasons for betterperformance of GFSFBR in comparison with CMR. Temperature ofthe reactor, activity and methanol mole fraction profiles along CMRand GFSFBR at 100th day and 1200th day of operation arepresented in Fig. 6. Application of water adsorbents increases thereaction rate and allows more heat of reaction to be releasedwithin the reactor. The heat released during adsorption is alsoadded the heat of reaction. Thus, higher gas phase temperatureprofile in GFSFBR in comparison with CMR will be the outcome ofthese changes (see Fig. 6a and d).

On the other hand, the local variation of temperature results inthe local change of activity along the reactor which affects thecatalytic activity of the bed. Therefore, higher temperature profilealong GFSFBR leads to a higher rate of catalyst deactivation and thisreactor has a lower activity profile in comparison with CMR, asshown in Fig. 6b and e.

Introduction of flowing adsorbents to GFSFBR causes asignificant enhancement in the reaction rate. Hence, highermethanol mole fraction can be observed in the GFSFBR incomparison with CMR, as perceived by Fig. 6c and f. Besides,GFSFBR operates at a higher temperature than CMR which leads toa higher improvement in the reaction rate.

Comparison of gas phase temperature profiles (Fig. 6a and d),activity profiles (Fig. 6b and e), and methanol mole fraction profiles(Fig. 6c and f) at 100th and 1200th days of operation indicateslower gas phase temperature, activity, and methanol mole fractionfor both GFSFBR and CMR at 1200th day. Reduction of catalystactivity (via sintering) during the operation decreases the reactionrate which is the main reason for the decline of gas phasetemperature and methanol mole fraction.

Fig. 7a and b demonstrates GFSFBR temperature and catalystactivity profile versus length and time, respectively. As shown inFig. 7a, as a consequence of fresh catalyst application andenhancement in the conversion at first days of operation, the



0 1 2 3 4 5 6 7500

505

510

515

520

525

530


Tem

pera

tre o

f rea

ctor

(K)

100th day

CMRGFSFBR

0 1 2 3 4 5 6 70.87

0.88

0.89

0.9

0.91

0.92

0.93

0.94

0.95


Act

ivity

100th day

CMRGFSFBR

0 1 2 3 4 5 6 70

0.01

0.02

0.03

0.04

0.05

0.06

0.07


Met

hano

l mol

frac

tion

100th day

CMRGFSFB R

0 1 2 3 4 5 6 7500

505

510

515

520

525

530


Tem

pera

tre o

f rea

ctor

(K)

1200 th day

CMRGFSFBR

0 1 2 3 4 5 6 70.54

0.56

0.58

0.6

0.62

0.64

0.66

0.68

0.7


Act

ivity

1200 th day

CMRGFSFBR

0 1 2 3 4 5 6 70

0.01

0.02

0.03

0.04

0.05

0.06

0.07


Met

hano

l mol

frac

tion

1200th day

CMRGFSFBR

a b

c d

e f

Fig. 6. Comparison of (a) and (d) methanol mole fractions, (b) and (e) temperature profiles, and (c) and (f) activity profiles between GFSFBR and CMR at 100th and 1200th days

of operation.

0200

400600

8001000

1200

0

2

4

6

8500

505

510

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530

535

Time (day)


Tem

pera

tre o

f rea

ctor

(K)

0

500

1000

1500

0

2

4

6

80.5

0.6

0.7

0.8

0.9

1

Time (day)


Act

ivity

a b

Fig. 7. The profiles of GFSFBR (a) temperature and (b) catalyst activity versus length and time.


G Model


Please cite this article in press as: Dehghani Z, et al. Sorption-enhanced methanol synthesis: Dynamic modeling and optimization. JTaiwan Inst Chem Eng (2013), http://dx.doi.org/10.1016/j.jtice.2013.12.001


0200

400600

800100 0

1200

0

2

4

6

80

0.005

0.01

0.015

0.02

Time (day)


H2O

mol

frac

tion

Fig. 8. The profile of H2O mole fraction versus GFSFBR length and time.

0200

400600

800100 0

1200

0

2

4

6

80

0.01

0.02

0.03

0.04

0.05

0.06

0.07

Time (day)


Met

hano

l mol

frac

tion

Fig. 9. The profile of methanol mole fraction versus GFSFBR length and time.

0 200 400 600 80 0 100 0 12 00240

260

280

300

320

340

360

Time (day)

Met

hano

l pro

duct

ion

rate

(ton

/day

)

CMRGFSFBR

Fig. 10. Comparison of methanol production rate profiles between GFSFBR and CMR

versus time.

0 200 400 600 80 0 100 0 12 00518

519

520

521

522

523

524

525

526

Time (day)

Tem

pera

ture

of s

hell

side

Fig. 11. Dynamic optimal temperature profile of GFSFBR shell side.

0 200 400 600 80 0 100 0 12 00310

320

330

340

350

360

370

Time (day)

Met

hano

l pro

duct

ion

rate

(ton

/day

)

GFSFBROGFSFBR

Fig. 12. Optimal methanol production rate of GFSFBR.


G Model


temperature of the reacting gas mixture is higher. The rate ofreaction heat and accordingly, temperature decreases duringfurther operation as the catalyst is deactivated. A continuousreduction of catalyst activity in the course of time can be seen inFig. 7b. During the operation time, the catalyst deactivation occursprincipally due to thermal sintering which is the loss of catalystactive surface area as a result of crystallite growth of either supportmaterial or active phase.

Water mole fraction versus GFSFBR length and time is plotted inFig. 8. Owing to application of fresh catalyst, higher methanolproduction is observed at first days operation which is accompa-nied by higher water production inside the reactor. The catalystsare being more deactivated over time, thus, methanol productionand water mole fraction are diminishing in the course of time. Thelowest water mole fraction profile is observed at 1200th day ofoperation.

Fig. 9 shows profile of methanol mole fraction along GFSFBRversus time. This profile is similar to the steady-state simulationwhere methanol mole fraction increases along GFSFBR, althoughthe rate of conversion declines as time goes on. Catalystdeactivation is the main reason for reduction in methanol molefraction and because of fresh catalyst application at first days ofoperation, higher methanol production can be achieved.

Fig. 10 presents comparison of methanol production rate forCMR and GFSFBR during 1200 days of operation. The simulationresult of this figure reveals that methanol production rate inGFSFBR is significantly higher than that in CMR and highermethanol production rate can be obtained in GFSFBR. As it was

Please cite this article in press as: Dehghani Z, et al. Sorption-enhanced methanol synthesis: Dynamic modeling and optimization. JTaiwan Inst Chem Eng (2013), http://dx.doi.org/10.1016/j.jtice.2013.12.001



G Model


previously mentioned, application of water adsorbents in GFSFBRenhances the reaction rate and contributes to a better performanceof the reactor which improves methanol production rate. In bothtypes of reactors, the rate of production declines in the course oftime and catalyst deactivation is the major reason for reduction inmethanol production rate.

5.2. Optimization results

In the situation of reversible exothermic reactions, choosing arelatively low inlet temperature permits higher conversion,however this should be balanced by the slower rate of reactionresulting in the need for a great amount of catalyst. Hence, thethree selected inlet temperatures of the reactor can be adjusted (atoptimal temperatures) to maximize the methanol production rate.Thus, according to the deactivation rate, dynamic optimal inlettemperatures are achieved over catalyst lifetime. Fig. 11 depictsthe optimal inlet temperature profile of shell side through catalystlifetime for GFSFBR. The optimization result shows that theoptimal inlet temperature of gas phase solids phase have theconstant value of 542.99 K during the operation time.

Fig. 12 compares the methanol production rate during 1200days of operation for GFSFBR and optimized GFSFBR (OGFSFBR).Optimization shows that the highest methanol productioncorresponds to OGFSFBR.

6. Conclusion

A dynamic mathematical description has been given to evaluatethe potential of a three phase system with in situ water adsorptionfor methanol synthesis in a gas-flowing solids-fixed bed reactor(GFSFBR). Zeolite 4A is considered as H2O adsorbent owing to itshigh water adsorption capacity. The aim of utilizing wateradsorbents is to increase the methanol productivity. The dynamicsimulation result indicates that methanol production would behigher in GFSFBR under H2O removal condition and with continuesadsorbent regeneration in comparison with conventional metha-nol reactor (CMR). Moreover, a continuous decline of catalystactivity (via sintering) is observed in the course of time which is themajor reason for the reduction in the temperature and methanolproduction of both GFSFBR and CMR during 1200 days ofoperation. Afterwards, dynamic optimization of GFSFBR wasimplemented using DE algorithm which is a powerful optimizationmethod. The obtained dynamic optimization result gives theoptimum values of inlet temperature of gas phase, inlet tempera-ture of flowing solids phase, and inlet temperature of shell sideunder which the highest methanol production can be obtained.

Appendix A. DE optimization algorithm

DE is an effective and simple optimization method, which is

noticeably fast and strong in numerical optimization and more likely

to find a function’s true global optimum [44]. According to the kind of

optimization problem, different strategies and different values of

number of population (NP), DE-step size (F), and crossover probability

constant (CPR) should be identified. Variation can be occur between

these strategies regarding the vector to be perturbed, number of

difference vectors considered for perturbation and the type of

crossover used. In this investigation, the proper value chosen for NP is

100, the range of DE step size is 0.5–1.0, and crossover probability

constant is within the range of 0.0–1.0. Usually, CPR should be as large

as possible [45]. Babu and Angira [44] and Babu and Munawar [45]

investigated on more details of DE basic version, its strategies, and

selecting the operating parameters.


Appendix B. Nomenclature

List of symbols

Ac cross section area of each tube (m2)

Ai inner area of each tube (m2)

Ao outside are of each tube (m2)

Ar Archimedes number for flowing solid particles

ð¼ d3prgðr p � rgÞg=m2Þ

a activity of catalyst

as specific surface area of catalyst pellet (m2/m3)

a0s specific surface area of flowing solid (m2/m3)

Cd drag coefficient

C pg specific heat of the gas at constant pressure (J/mol K)

Cps specific heat of the catalyst at constant pressure (J/

mol K)

C p0s specific heat of the flowing solid at constant pressure

(J/mol K)

ct total concentration (mol/m3)

Di tube inside diameter (m)

Dij binary diffusion coefficient of component i in j (m2/s)

Dim diffusion coefficient of component i in the mixture (m2/

s)

Do tube outside diameter (m)

deq equivalent diameter of packing particles,

ð¼ 6ð1 � eÞ=ðas þ ð4=DÞÞÞ (m)

ds catalyst diameter (m)

d0s flowing solid diameter (m)

Eads average energy of adsorption (kJ/mol)

Fi molar flow of species i (mol/s)

Ft total molar flow per tube (mol/s)

G mass flux of gas (kg/m2 s)

DHads specific heat of adsorption (J/mol)

DHf,i enthalpy of formation of component i (J/mol)

DH298 enthalpy of reaction at 298 K (J/mol)

hf gas-catalyst heat transfer coefficient (W/m2 K)

h0f gas–solid heat transfer coefficient (W/m2 K)

hi heat transfer coefficient between fluid phase and

reactor wall (W/m2 K)

ho heat transfer coefficient between coolant stream and

reactor wall (W/m2 K)

K conductivity of fluid phase S (W m/K)

K adsorption equilibrium constant (kPa�1)

K0 adsorption affinity at reference temperature T0 (kPa�1)

kgi gas-catalyst mass transfer coefficient for component i

(m/s)

k0g gas–solid mass transfer coefficient (m/s)

L length of reactor (m)

Mi molecular weight of component i (g/mol)

N number of components used in the model (N = 7)

P total pressure (bar)

q concentration of water adsorbed in flowing solids

(mol/kg)

qe equilibrium concentration of adsorbed water (mol/kg)

qm saturation capacity (kmol/kg)

R universal gas constant (J/mol K)

Res Reynolds number of packing elements

Re0s Reynolds number of flowing solids

ri reaction rate of component i (mol/kg s)

S mass flux of flowing solids (kg/m2 s)

s parameter to characterize the heterogeneity of system




G Model


Tg bulk gas phase temperature (K)

Ts temperature of catalyst phase (K)

T 0s temperature of flowing solids (K)

Tshell temperature of coolant stream (K)

Ushell overall heat transfer coefficient between coolant and

process streams (W/m2 K)

Ug real gas velocity, ð¼ G=rge0Þ (m/s)

ug superficial gas velocity (m/s)

ur relative velocity for co-current flow of gas and flowing

solids ð¼ Ug � u0sÞ ðm=sÞu0s real flowing solids velocity, ð¼ S=r0sbÞ (m/s)

yi mole fraction of component i in the fluid phase (mol/

mol)

yis mole fraction of component i in the catalyst phase

(mol/mol)

z axial reactor coordinate (m)

Greek letters

b flowing solids holdup ¼ bd þ bsð Þbd dynamic flowing solids holdup

bs static flowing solids holdup

e void fraction of catalytic bed (m3/m3)

es void fraction of catalyst

e’ void fraction corrected due to presence of the flowing

solids ¼ e � bð Þ (m3/m3)

f sphericity of packed bed element

h effectiveness factor

m dynamic viscosity (Pa s)

rB catalytic bed density (kg/m3)

rg gas density (kg/m3)

rS catalyst density (kg/m3)

r’S flowing solid density (kg/m3)

Superscript

ss initial condition (i.e., steady-state condition)

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