Mfi

MS

a

ARRAA

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Chemical Engineering and Processing 50 (2011) 85–94

Contents lists available at ScienceDirect

Chemical Engineering and Processing:Process Intensification

journa l homepage: www.e lsev ier .com/ locate /cep

odeling, simulation and control of dimethyl ether synthesis in an industrialxed-bed reactor

. Farsi, R. Eslamloueyan ∗, A. Jahanmirichool of Chemical and Petroleum Engineering, Shiraz University, Mollasadra Avenue, Shiraz, Fars 713481154, Iran

r t i c l e i n f o

rticle history:eceived 26 December 2009eceived in revised form 2 September 2010ccepted 29 November 2010vailable online 4 December 2010

eywords:

a b s t r a c t

Dimethyl ether (DME) as a clean fuel has attracted the interest of many researchers from both industrialcommunities and academia. The commercially proven process for large scale production of dimethylether consists of catalytic dehydration of methanol in an adiabatic fixed-bed reactor. In this study, theindustrial reactor of DME synthesis with the accompanying feed preheater has been simulated and con-trolled in dynamic conditions. The proposed model, consisting of a set of algebraic and partial differentialequations, is based on a heterogeneous one-dimensional unsteady state formulation. To verify the pro-

ixed-bed reactoreterogeneous modelME reactor control

posed model, the simulation results have been compared to available data from an industrial reactorat steady state conditions. A good agreement has been found between the simulation and plant data. Asensitivity analysis has been carried out to evaluate the influence of different possible disturbances onthe process. Also, the controllability of the process has been investigated through dynamic simulationof the process under a conventional feedback PID controller. The responses of the system to disturbanceand setpoint changes have shown that the control structure can maintain the process at the desired

priate

conditions with an appro

. Introduction

Dimethyl ether as a basic chemical product is mainly consumedn industries as a solvent and propellant in various aerosol products1]. The similarity of some physical properties of DME, liquefiedetroleum gases and diesel fuel has presented DME as a clean fuelhat can be used in diesel engines, power generation, and otherurposes such as a substitute for LNG [2]. It can be produced fromvariety of feed-stock such as natural gas, crude oil, residual oil,

oal, waste products and bio-mass [3]. Although the commerciallyroven technology for DME production is through dehydration ofure methanol in an adiabatic fixed-bed reactor, many researchersre working on the direct conversion of syngas to DME over a dualeterogeneous catalyst [4].

DME can be produced in packed bed or slurry reactors. Althoughlurry reactors have the advantage of better heat removal capa-ility by coil or jacket and good productivity and good interface

ontacting due to small solids particle size, they suffer from signif-cant mass transfer resistance due to the use of inert liquid phasesuch as waxy liquid [5]. At present, DME is commercially producedhrough methanol dehydration using acidic porous catalysts in adi-

∗ Corresponding author. Tel.: +98 711 2303071; fax: +98 711 6287294.E-mail addresses: eslamlo@shirazu.ac.ir, reslamlou@gmail.com

R. Eslamloueyan).

255-2701/$ – see front matter © 2010 Elsevier B.V. All rights reserved.oi:10.1016/j.cep.2010.11.013

dynamic behavior.© 2010 Elsevier B.V. All rights reserved.

abatic packed bed reactors [6]. Due to simplicity and lower costs,adiabatic fixed bed reactors can be the first choice for catalytic pro-cesses having low or intermediate heat of reactions [7]. However, incase of highly endothermic or exothermic reactions, the problemsof reaction extinguishing or catalyst sintering may happen [8]. Thefluidized bed reactors have been suggested by some researchersas a perfect reactor for DME synthesis [9,10]. Fluidized bed reac-tors showed the better heat removal characteristics due to freelymoving catalyst particles in the bed. However, collision betweencatalyst particles and the reactor wall causes loss of catalyst.

Simulation of packed bed reactors is not an easy task, since sys-tems of nonlinear partial differential equations have to be solvedalong with nonlinear algebraic relationships [11]. Modeling andsimulation of fixed-bed reactors have been done for many indus-trial and pilot scales reactors. For instance, Shahrokhi et al. modeledand simulated the dynamic behavior of a fixed bed reactor formethanol production from syngas and proposed an optimizer tomaximization of the production rate [12]. Jahanmiri and Eslam-loueyan modeled and simulated the isothermal fixed-bed reactorfor methanol production in industrial scale [13]. They calculated theoptimal temperature profile of the shell side to maximize methanol

production.

Fixed-bed DME synthesis reactors have been investigatedthrough a number of research studies. Lee et al. modeled and ana-lyzed DME production from syngas in a fixed-bed reactor at steadystate condition [14]. Nasehi et al. simulated an industrial adiabatic

86 M. Farsi et al. / Chemical Engineering and Processing 50 (2011) 85–94

Table 1The reaction kinetics and equilibrium constants.

Parameter k = A(i)expB(i)/RT

A(i) B(i)

fiaosratbla�Tt

dfiddpatc[iosm

fds

2

o

2

k

r

w

l

k

Kewu

Table 2Equipment and catalyst parameters.

Parameter Value

ReactorCatalyst density (kg m−3) 2050Catalyst void fraction 0.2Specific surface area of catalyst pellet 673Catalyst diameter (m) 0.3175 × 10−2

Ratio of void fraction to tortuosity of catalyst particle 0.066Reactor Length (m) 8Reactor diameter (m) 4Bed void fraction 0.5Catalyst density (kg m−3) 2010Density of bed (kg m−3) 1005

Heat exchangerTube side diameter (m) 1.905 × 10−2

Tube thickness (m) 2.11 × 10−3

ber = 0.0125)

Biot number is a dimensionless number defined in conduction heattransfer, and gives a simple index of the ratio of the heat transfer

k0 3.7 exp10 −1,05,000KH2O 0.84 exp−1 41,100KCH3OH 7.9 exp−4 7050

xed-bed reactor for DME production from methanol dehydrationt steady state condition, and showed that the difference betweenne and two dimensional models is negligible [15]. Omata et al.tudied DME production from syngas in a temperature gradienteactor for overcoming both the equilibrium limit of the reactiont high temperature and low activity of the catalyst at low tempera-ure [16]. Then, they optimized the reactor for higher CO conversiony a combination of genetic algorithm and neural networks. Fazlol-

ahnejad et al. investigated methanol dehydration in a bench scalediabatic packed reactor [17]. The reactor was packed with 1.5 mm-Al2O3 pellets as catalyst and operated at atmospheric pressure.hey investigated the effects of weight hourly space velocity andemperature on methanol conversion.

Although many research studies have been carried out on theynamic simulation and control of fixed bed reactors, we could notnd any work in this field for DME synthesis from methanol dehy-ration. Fixed-bed catalytic reactors are often difficult to controlue to nonlinearity, process dead time and positive feedback of feedreheating by the reactor effluent stream [18]. Jorgensen presentedgood review for dynamic modeling and control of fixed bed reac-

ors [19]. Aguilar et al. developed a robust PID control law in order toontrol the outlet temperature of a fluid catalytic cracking reactor20]. The controller is synthesized using an input–output lineariz-ng control law coupled to a proportional-derivative reduced orderbserver to infer on-line the unknown heat of reaction. This controltrategy was robust against model uncertainties, noisy temperatureeasurements and set point changes.In this paper, we develop an unsteady heterogeneous model

or dynamic simulation of an industrial DME synthesis reactor andesign a conventional feedback control system to maintain the inlettream temperature at the desired value.

. Reaction kinetics

The reaction equation of DME synthesis from dehydrogenationf methanol is as the following.

CH3OH � CH3OCH3 + H2O, �H298 = −23.4 (kJ/mol) (1)

In this work, the rate expressions have been selected from theinetic model proposed by Bercic et al. [21].

=k · K2

CH3OH((CCH3OH − (CC2H6OCH2O)/Keq))

(1 + 2(KCH3OHCCH3OH).5 + KH2OCH2O)4

(2)

here,

n (Keq) = 086 log T + 3138T

+ 1.33 × 10−3 T − 1.23

× 10−5 T2 + 3.5 × 10−10 T (3)

= A(i) expB(i)/RT (4)

Ci is the molar concentration of component i in mol/m3. k1,CH3OH and KH2O are the reaction rate constant and the adsorptionquilibrium constant for methanol and water vapor, respectively,hich are tabulated in Table 1. Commercially, �-Al2O3 catalyst issed in methanol dehydration reaction. Also, the characteristics of

Shell diameter (m) 0.615Overall heat transfer coefficient (W m−1 K−1) 325Heat exchanger length (m) 4.57

the catalyst pellet and the reactor design specifications are sum-marized in Table 2.

3. Process description

DME production loop consists of an adiabatic packed bed reactoras well as a shell and tube heat exchanger as depicted in Fig. 1.The inlet feed to the reactor is preheated in the heat exchangerthrough heat transfer to the outlet products from the reactor. Thereactor product is transferred to DME purification unit, and DME isseparated from water and methanol. Also, the unreacted methanolis recycled to the reactor.

The developed model of this process includes modeling equa-tions for both the reactor and the feed preheater.

3.1. Reactor model

In this study, a one dimensional heterogeneous model has beenconsidered for steady state simulation of the process. The basicstructure of the model is composed of heat and mass conservationequations coupled with thermodynamic and kinetic relations aswell as auxiliary correlations for prediction of physical properties.In the dynamic modeling of the reactor the following assumptionshave been considered.

- No heat loss to the surrounding from the reactor wall- Plug flow pattern and negligible concentration and temperature

variations in radial direction- Uniform temperature within each catalyst pellet (Biot num-

Fig. 1. Process flow diagram of DME production.

M. Farsi et al. / Chemical Engineering a

Table 3Feed specification of the industrial DME reactor.

Parameter Value

T (◦C) 260P (bar) 18.2Mass flow rate (kg/s) 50.81Mass fraction (%)

Methanol 94%

rsttaitr(mbtrbto

e

ε

�

(

(

[

−

gt

B

I

3

uhd

Water 1%DME 5%

esistances inside and at the surface of a body. For the Biot numbersmaller than 0.1, the heat conduction inside the body is much fasterhan the heat convection away from the surface, and the tempera-ure gradient is negligible inside of the body. To justify the first twossumptions, it should be notified the industrial reactor consideredn this study have insulation that causes the heat loss from the reac-or wall to the environment negligible in comparison to the heatelease in the reactor, and also because of high Reynold’s numberabout 10,000), the assumption of plug flow is reasonable. Further-

ore, Nasehi et al. simulated the reactor at steady state conditiony using a two-dimensional heterogeneous model with considera-ion of the heat loss from the insulation to environment [22]. Theesults of this simulation showed that the temperature differenceetween the reactor center and the reactor wall is at most 4 ◦C. So,he heat loss has a negligible influence on the simulation results inne-dimensional plug flow model.

The mass and energy balances for the gas and solid phase arexpressed by the following equations:

Gas phase:

∂Ci

∂t= −us

∂Ci

∂z− kgiav(Ci − Cs

is) (5)

gcpgε∂T

∂t= −us�gcp

∂T

∂z+ hfav(Ts

s − T) (6)

Solid phase:

1 − ε)∂Cis

∂t= −kgiav(Ci − Cs

is) + �i�Bsri (7)

1 − ε)�Bscps∂Ts

∂t= −hf av(Ts

s − T) − �i�Bs(−�H)ri (8)

The pressure drop in the bed is calculated by Ergun equation23]:

dp

l= 150

(1 − ε)2� · uc

d2ε3+ 1.75

(1 − ε)� · u2c

d · ε3(9)

The initial and boundary conditions for these equations areiven below. Also, the feed specification of the industrial DME reac-or is reported in Table 3.

oundary conditions : C∣∣Z=0

= C0, T∣∣Z=0

= T0, P∣∣Z=0

= P0

nitial conditions : Ci

∣∣Z,t=0

= Cssi , T

∣∣Z,t=0

= Tssi

.2. Heat exchanger model

There are no phase changes in the heat exchanger and thisnit is small in compare with the reactor unit. The shell and tube

eat exchanger used for preheating feed stream is modeled at theynamic condition by the following equations:

dThot

dt= −ug

dThot

dz− Di�

� · Ahot · CpU(Thot − Tcold) (10)

nd Processing 50 (2011) 85–94 87

dTcold

dt= −ug

dTcold

dz+ Do�

� · Acold · CpU(Thot − Tcold) (11)

The overall heat transfer coefficient in the heat exchanger iscalculated from

1U

= 1hi

+ Ai ln(Do/Di)2�LKw

+ Ai

Ao

1ho

(12)

In Eq. (12), the heat transfer coefficient in the shell side (ho) andthe tube side (hi) are calculated using the following equations [24]:

hoDo

kf= 0.33(Re)0.6

(Cp�

k

)1/3

(13)

hiDi

k= 0.023(Re)0.8

(Cp�

k

)1/3( �

�w

)0.14(14)

3.3. Auxiliary equation

Auxiliary equations are used for prediction of the model param-eters. In these equations �i is the effectiveness factor which isdefined as actual reaction rate per particle to theoretical reactionrate based on the external pellet surface concentration, which isobtained from dusty gas model calculations [25]. It can be calcu-lated from the following equation:

�i =∫

ri dVp

Vp. ri

∣∣surface

(15)

In the heterogeneous model the physical properties of chemi-cal species and overall mass and heat transfer coefficients betweencatalyst solid phase and gas phase must be estimated. The over-all mass transfer coefficient between solid and gas phase has beenobtained from the correlation proposed by Cussler [26].

kgi = 103(1.17Re−0.42Sci−0.67ug) (16)

In Eq. (16), the Sc is calculated for components along the reac-tor. Mass transfer diffusion coefficient for each component in themixture has been estimated by:

Dim = 1 − yi∑(yi/Dij)

(17)

Binary mass diffusion coefficient has been determined by thefollowing equation [20]:

Dij =10−7T3/2

√(1/Mi) + (1/Mj)

P(3/2ci

+ 3/2cj

)2

(18)

The overall heat transfer coefficient between solid and gas phase(hf) has been predicted from [27]:

hf

Cp��

(Cp�

K

)2/3

= 0.458εB

(�udp

�

)−0.407

(19)

The overall heat capacity in Eq. (19) depends on the temperatureand composition, and is calculated using Eqs. (20) and (21):

Cp(i) = a + bT + cT2 + dT3 (20)

Cp =∑

yiCp(i) (21)

Table 4 presents the values of a, b, c and d in Eq. (20).

4. Numerical solution

To solve the set of nonlinear partial differential equations (PDE)obtained from dynamic modeling, the reactor length is divided intoequal discrete intervals, and by using finite difference method thePDEs are converted into a set of ordinary differential equations

88 M. Farsi et al. / Chemical Engineering and Processing 50 (2011) 85–94

Table 4Parameters of heat capacity coloration.

a b c × 10−5 d × 10−9

(R

dgscodetm

5

msefmDibtPt

6

6

twad

Table 5Comparison of the steady state simulation results of the reactor with plant data.

Simulationresult

Plant data Absoluteerror

DME exit mole flow rate (kmol/h) 2457 2506 1.95%MeOH exit mole flow rate (kmol/h) 940.6 937.7 0.31%Outlet temperature (K) 652.2 644 1.27%

0 1 2 3 4 5 6 7 80

1000

2000

3000

4000

5000

6000

Mol

e Fl

ow (k

mol

hr-1

)

DMEMEOHWater

DME 0.18 17.02 5.23 1.92CH3OH 21.15 0.07 2.59 0.29H2O 32.24 0.002 1.06 3.6

ODE) in time domain. The set of equations are solved by 4th orderunge–Kutta [28].

Before carrying out dynamic simulation, the stationary con-ition of the system should be obtained through solving theoverning steady-state equations. The aim of performing steadytate simulation of the DME reactor is to determine the con-entration and temperature profiles along the reactor at normalperation. These steady state profiles are used as the initial con-itions of the unsteady state PDEs. After rearranging the modelingquations for the steady state condition, a set of ordinary differen-ial equation is obtained. This set of equations was solved by the

ethod of 4th order Runge–Kutta.

. Control structure

The main objective of the control system of DME reactor is toaintain the operating condition at the optimum designed state in

pite of probable disturbances. Since DME is produced through anxothermic reaction in a fixed bed adiabatic reactor, the control ofeed temperature is crucial for keeping the conversion at its maxi-

um level. The proposed control structure for a typical industrialME reactor is shown in Fig. 2. The reactor feed stream is preheated

n a shell and tube heat exchanger with the hot reactor effluent. Aypass stream around this heat exchanger is manipulated to controlhe reactor feed temperature. In this study, a conventional feedbackID algorithm carries out the load rejection and set-point trackingasks.

. Results and discussion

.1. Steady state simulation

In this section, steady state simulation results of DME reac-or have been presented. Assuming an adiabatic tubular reactorith plug flow pattern, the reactor has been simulated based onone dimensional heterogeneous model. Modeling validation is

one through comparing the simulation results with the industrial

Fig. 2. Schematic of the

Length (m)

Fig. 3. The profiles of mole flow rates of DME, Methanol and water along the reactor.

reactor data provided by Petrochemical Research and technologyCompany which is a subsidiary of National Iranian PetrochemicalCompany. Table 5 indicates the absolute errors of the steady-statesimulation results in comparison to available data of the industrialreactor. This table shows that the proposed model has been able topredict the exit concentrations and temperature very well.

Fig. 3 illustrates the molar flow rate of DME, methanol and wateralong the reactor length at steady state condition.

The mole fraction of DME along the reactor in solid and gas phase

predicted by the heterogeneous model has been compared in Fig. 4.Near the end of the reactor, where the reaction equilibrium is pre-vailed, the difference between gas and solid phase concentrationsis vanished.

control structure.

M. Farsi et al. / Chemical Engineering and Processing 50 (2011) 85–94 89

0 1 2 3 4 5 6 7 80.05

0.14

0.23

0.32

0.41

0.5M

ole

Frac

tion

Gas PhaseSolid Phase

oar

catrtcai

6

tpt

Table 6Calculated average mass transfer and effective diffusion coefficients in the reactor.

DDME-mixture (m s−1) 0.1737 × 10−6

DMeOH-mixture (m s−1) 0.1745 × 10−6

Dwater-mixture (m s−1) 0.2685 × 10−6

kDME (m2 s−1) 0.0036kMeOH (m2 s−1) 0.0036kwater (m2 s−1) 0.005

010

2030

4050

02

46

8520

560

600

640

680

Time (sec)Length (m)Te

mpe

ratu

re (K

)

Length (m)

Fig. 4. DME mole fraction in solid and gas phase.

Also, the predicted temperature profile along the reactorbtained from the simulation is shown in Fig. 5. The temperaturepproaches to equilibrium temperature due to heat generation byeaction, and remains constant.

The calculated average heat transfer coefficient between gas andatalyst phase (hf) in Eq. (19) is about 1170 W m−2 K−1. Also, theverage estimated viscosity and molar heat capacity of the reac-ion mixture are about 1.6 × 10−7 kg m−1 s−1 and 69.5 W mol−1 K−1,espectively. The effective diffusion coefficients of components inhe mixture and mass transfer coefficients for components arealculated along the reactor. The average effective diffusion andverage mass transfer coefficients of DME, MeOH and water vaporn the mixture are presented in Table 6.

.2. Open loop dynamic simulation

The open loop behavior of the reactor has been considered inwo levels. In the first level the behavior of the reactor without itsreheater has been studied. The second level investigates both ofhe reactor and the related preheater as a heat integrated process.

0 1 2 3 4 5 6 7 8520

555

590

625

660

Length (m)

Tem

pera

ture

(K)

Fig. 5. Predicted temperature profile along the reactor.

Fig. 6. Dynamic temperature profile along the reactor for 10 ◦C step change in theinlet stream to the reactor.

To investigate the influence of disturbances on the dynamicbehavior of DME reactor, the feed temperature, pressure and com-position have been considered as the main probable effective loadsof the system.

Figs. 6 and 7 indicate the step response of the system to 10 ◦Cincrease in the feed temperature. In Fig. 6, dynamic variation ofthe temperature along the reactor length has been illustrated ina three-dimensional diagram. Fig. 7 represents time variations ofDME concentration along the reactor bed.

As shown in Fig. 8, the response of the outlet temperature ofthe reactor for this disturbance has a time delay about 15 s, and itreaches to the new steady state point in 50 s.

010

2030

4050

02

46

80

0.1

0.2

0.3

0.4

0.5

Time (sec)Length (m)

DM

E m

ole

frac

tion

Fig. 7. Dynamic DME mole fraction profile along the reactor for 10 ◦C step changein the inlet stream to the reactor.

90 M. Farsi et al. / Chemical Engineering and Processing 50 (2011) 85–94

0 10 20 30 40 50651

653

655

657

659

661Te

mpe

ratu

re(K

)

Fi

cFt

c

adnc

ar

ootDAtt

Fv

010

2030

4050

02

46

80

0.1

0.2

0.3

0.4

0.5

Time (sec)Length (m)

DM

E m

olef

ract

ion

Fig. 10. Dynamic DME mole fraction profile for 0.05 step change in the methanoland water vapor mole fractions of the inlet stream.

0 10 20 30 40 50647.5

648.5

649.5

650.5

651.5

652.5

Time (sec)

Tem

pera

ture

(K)

Time (sec)

ig. 8. The outlet temperature profile from the reactor to 10 ◦C step change in thenlet temperature.

The feed composition effect was studied by applying 0.05 stephanges in the mole fractions of both methanol and water vapor.igs. 9 and 10 represent dynamic responses of the reactor tempera-ure and DME mole fraction profiles along the reactor, respectively.

The response of the reactor outlet temperature to the stephange in composition is shown in Fig. 11.

Applying 2 bar step change in the reactor inlet pressure gener-tes the outlet temperature response shown in Fig. 12. As can beeduced from this figure, the change in inlet pressure has no sig-ificant effect on the temperature and consequently the productomposition of the reactor effluent.

The above mentioned results indicate that the feed temperaturend composition are the major process disturbances that should beejected by the designed control system.

In order to have a more realistic influence of inlet temperaturen the reactor dynamic response, we have also studied the responsef the reactor effluent temperature to a step change in the fresh feed

emperature to the preheater. The reactor output temperature andME mole fraction have been respectively shown in Figs. 13 and 14.ccording to these figures, increasing of the inlet feed temperature

o the heat exchanger will cause an increase in the reactor feedemperature and consequently reactor outlet temperature. Due to

010

2030

4050

02

46

8520

560

600

640

680

Time (sec)Length (m)

Tem

pera

ture

(K)

ig. 9. Dynamic temperature profile for 0.05 step change in the methanol and waterapor mole fractions of the inlet stream.

Fig. 11. The outlet temperature profile for 0.05 step change in the feed mole fraction.

0 10 20 30 40 50652.2

652.25

652.3

652.35

652.4

652.45

Time (sec)

Tem

pera

ture

(K)

Fig. 12. The outlet temperature profile for 2 step change in the feed pressure.

M. Farsi et al. / Chemical Engineering and Processing 50 (2011) 85–94 91

0 5 10 15 20650

690

730

770

810

850

Time (min)

Tem

pera

ture

(K)

Fp

tcrt

6

tstaTsutpuap

Fp

0 5 10 15 20 25 30 35651

652

653

654

655

656

657

Time (min)

Tem

pera

ture

(K)

ig. 13. The outlet temperature profile for 10 ◦C step change in the fresh feed tem-erature to preheater.

emperature increase, conversion in the reactor decreases and thisause a new equilibrium point for the process. But, variation of theector outlet temperature is lesser than the variation of the inletemperature.

.3. Closed loop process simulation

Although packed bed reactors are distributed parameter sys-ems, the output variables are usually measured at the process exittreams. In order to control the inlet feed temperature to the reac-or, a feedback control loop as shown in Fig. 2 is designed based onconventional Proportional–Integral–Derivative (PID) controllers.he PID control algorithm is usually used for the industrial controlystems. In this study, the PID controller has been tuned throughsing Closed Loop Ziegler–Nichols method. This algorithm is one of

he most common methods for tuning PID controllers. The gain ofroportional controller is increased (from zero) until it reaches theltimate gain, at which the output of the control loop oscillates withconstant amplitude. The parameters of the controller, i.e. the pro-ortional gain, reset time, and derivative value, are derived from the

0 5 10 15 200.402

0.412

0.422

0.432

0.442

Time (sec)

DM

E m

olef

ract

ion

ig. 14. The outlet DME concentration for 10 ◦C step change in the fresh feed tem-erature to preheater.

Fig. 15. Outlet temperature response for rejection of the disturbance by the closedloop control system.

ultimate gain and the sustained period of oscillation [29]. This typeof tuning creates a quarter wave decay ratio which is acceptablefor most systems. According to this procedure, the controller gain,reset time and derivative constant estimated in this work are 9.6,0.56 min and 0.14 min, respectively. To compare Ziegler–Nichols’tuning method to other tuning rules, we have tuned the reactorcontroller loop by using Luyben’s method [30]. This method havesmaller decay ratio, but it has slower response than Ziegler–Nichols’method. According to Luyben method, the controller gain, integralconstant and derivative constant are 7.5, 2.45 min and 0.18 min,respectively. Both methods were examined through their applica-tion to the set point tracking of the reactor controller. Accordingto this investigation, Ziegler–Nichols’ method led to better con-trol responses, so in this study the Ziegler–Nichols’ tuning rulesare applied.

In this section, the dynamic closed-loop behavior of the process

consisting of the reactor and preheater in response to predefineddisturbances and set point variation are presented and analyzed.

0 5 10 15 20 25 30 350.4378

0.438

0.4382

0.4384

0.4386

0.4388

0.439

Time (min)

DM

E m

olef

ract

ion

Fig. 16. Outlet DME concentration response for rejection of the disturbance by theclosed loop control system.

92 M. Farsi et al. / Chemical Engineering and Processing 50 (2011) 85–94

0 5 10 15 20 25 30 350

50

100

150

200

250

300

Mol

e flo

w (m

ol s

ec-1

)

6

attrcalTs

d

6

hpooabmdc

ris

TC

TD

0 10 20 30 40652

656

660

664

668

Time (min)

Tem

pera

ture

(K) Set point

Fig. 18. The variation of the outlet temperature for set point tracking.

0 10 20 30 400.4355

0.4364

0.4373

0.4382

0.439

Time (min)

DM

E m

olef

ract

ion

Fig. 19. The variation of the outlet DME mole fraction for set point tracking.

400

Time (min)

Fig. 17. Manipulated variable variations in case of load rejection.

.3.1. Load rejectionTo observe the performance of the proposed control structure

nd applied PID controller for the system, 15 ◦C step change in theemperature of the fresh feed to the preheater has been introducedo the process as the most influential disturbance. The closed loopesponse of the process has been presented in Figs. 15 and 16. Asan be seen from these figures, the load is completely rejected afterbout 7 min using a PID controller. The variation of the manipu-ated variable, i.e. bypass flow rate, has been represented in Fig. 17.he manipulated variable response has no sever oscillation and isimilar to the behavior of an appropriate control system.

The dynamic characteristics of the control loop response foristurbance rejection are presented in Table 7.

.3.2. Setpoint trackingThe setpoint tracking capability of the propose control system

as been investigated by applying 10 ◦C step changes in the set-oint of the reactor inlet temperature. Figs. 18 and 19 indicate theutlet temperature and DME mole fraction from the reactor. Theutlet temperature approaches to the new setpoint with accept-ble speed and oscillations. In Fig. 20, the molar flow rate of theypass stream has been represented. This figure indicates that theanipulated variable response for the servo problem has suitable

ynamic behavior and can be implemented easily by an ordinaryontrol valve.

Table 8 presents the dynamic characteristics of the control loopesponse for the set point tracking. Table 8 shows that character-stics response of controller is acceptable and proper in industrialcale.

able 7haracteristics of the control loop response for disturbance rejection.

Time (min)

Rise time 4Peak time 9.7Settling time 17.3

able 8ynamic properties of the closed loop response for setpoint tracking.

Overshoot 42%Rise time (min) 3.8Settling time (min) 19.8

0 10 20 30 400

80

160

240

320

Time (min)

Mol

e fo

lw (m

ol s

ec-1

)

Fig. 20. Variation of the bypass stream flow rate for set point tracking.

M. Farsi et al. / Chemical Engineering a

0 7 14 21 28 35652

656

660

664

668Te

mpe

ratu

re(K

)

activity:1.0activity: 0.7activity: 0.5

F

icwtrosachc

7

tcrciittthdldtocclnidleoarc

Time (min)

ig. 21. Setpoint tracking response for different values of catalyst deactivation.

As mentioned in the modeling section, the catalyst deactivations not included in the model because of lack of deactivation rateorrelation in open literature. However, it should be noted that theorst condition for examining the capability of the control sys-

em structure would be for the case of fresh catalyst in which theeaction rate is at the highest level. Therefore, since the objectivef this work is to examine the controllability characteristics of theuggested control structure, very slow catalyst deactivation cannotffect the control system structure. To illustrate the influence of theatalyst deactivation on the control system response, the processas been simulated for three levels of catalyst deactivation, and theontroller responses are illustrated in Fig. 21.

. Conclusion

In this study, an industrial DME synthesis reactor from dehydra-ion of methanol has been simulated in steady and unsteady stateonditions. The reactor mathematical formulation is based on aigorous one-dimensional heterogeneous model. Also, a feed-backontrol system has been designed and tuned to control the reactornlet temperature. The comparison of the simulation results and thendustrial data show that the proposed model can predict the reac-or outlet temperature and concentrations with relative errors lesshan 2%. Some important disturbances such as fresh feed tempera-ure, inlet reactor temperature, inlet pressure and feed compositionave been applied to the process for investigating its open loopynamic behavior. Since the deactivation rate equation of the cata-

yst used in this study is not available in open literature, the catalysteactivation, which usually occurs very slowly in industrial reac-ors, has not been included in the modeling. In fact, the objectivef this article is the investigation of controllability of the proposedontrol system structure for DME reactor, and because the reactorontrol system responds very faster (about 30 min) than the cata-yst deactivation time (about 2 years), the catalyst deactivation haso significant influence on the objective of this research. Anyway,

f experimental data or mathematical correlation for predicting theeactivation of DME indirect synthesis catalyst becomes available

ater, inclusion of the catalyst deactivation rate will be an inter-

sting subject for future work. The dynamic characteristics of thepen loop system have been used to design a PID controller fordjusting the preheater bypass flow rate in order to maintain theeactor inlet temperature at its setpoint. The suggested feedbacklosed loop system has shown a good performance for the cases of

nd Processing 50 (2011) 85–94 93

disturbance rejection and setpoint tracking so that it can controlthe reactor in a time period of 20–30 min.

Appendix A. Nomenclature

av specific surface area of catalyst pellet (m2 m−3)Acold cross section area of cold side in heat exchanger (m2)Ahot cross section area of hot side in heat exchanger (m2)Ci molar concentration of component i (mol m−3)Cp specific heat of the gas at constant pressure (J mol−1)dp catalyst diameter (m)Di tube inside diameter of heat exchanger (m)Do tube outside diameter of heat exchanger (m)Dij binary diffusion coefficient of component i in j (m2 s−1)Dim diffusion coefficient of component i in the mixture

(m2 s−1)F total molar flow rate (mol s−1)hf gas–solid heat transfer coefficient in reactor (W m−2 K−1)hi tube side heat transfer coefficient in heat exchanger

(W m−2 K−1)ho shell side heat transfer coefficient in heat exchanger

(W m−2 K−1)k rate constant of dehydrogenation reaction

(mol m−3 Pa−1 s−1)kg mass transfer coefficient for component i (m s−1)Keq reaction equilibrium constant for methanol dehydration

reaction (mol m−3)Ki adsorption equilibrium constant for component i

(m3 mol−1)L reactor length (m)M molecular weight (g mol−1)P total pressure (Bar)r rate of reaction for DME synthesis (mol kg−1 s−1)R tube diameter in heat exchanger (m)Re Reynolds numberSci Schmidt number of component iT temperature (K)u superficial velocity of fluid phase (m s−1)ug linear velocity of fluid phase (m s−1)U overall heat transfer coefficient (W m−2 K−1)V volume (m3)vci critical volume of component i (cm3 mol−1)yi mole fraction of component i (mol mol−1)z axial reactor coordinate (m)

Greek letters� viscosity of fluid phase (kg m−1 s−1)� density of fluid phase (kg m−3) tortuosity of catalystε void fraction

Superscriptsg in bulk gas phases at surface catalysto inlet conditionsi chemical species

References

[1] T.A. Semelsberger, R.L. Borup, H.L. Greene, Dimethyl ether (DME) as an alter-

native fuel, Journal of Power Sources 156 (2) (2006) 497–511.

[2] V.V. Galvita, G.L. Semin, V.D. Belyaev, T.M. Yurieva, V.A. Sobyanin, Productionof hydrogen from dimethyl ether, Applied Catalyst 216 (1–2) (2001) 85–90.

[3] C. Arcoumanis, C. Bae, R. Crookes, E. Kinoshita, The potential of dimethyl ether(DME) as an alternative fuel for compression-ignition engines: a review, Fuel87 (2008) 1014–1030.

9 ring a

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[[

4 M. Farsi et al. / Chemical Enginee

[4] L. Makarand, R. Gogate, C.J. Kulika, A novel single-step dimethyl ether (DME)synthesis in a three-phase slurry reactor from co-rich syngas Sunggyu, Chem-ical Engineering Science 47 (13–14) (1992) 3769–3776.

[5] J.W. Guo, Y.Q. Niu, B.J. Zhang, Macro kinetics study on DME synthesis fromsyngas in slurry reactor, Natural Gas Chemical Industry 25 (2000) 4–7.

[6] W.Z. Lu, L.H. Teng, W.D. Xiao, Simulation and experiment study of Dimethlyether synthesis from syngas in a fluidized-bed reactor, Chemical EngineeringScience 59 (2004) 5455–5464.

[7] G.F. Froment, K.B. Bischoff, Chemical Reactor Analysis and Design, 2nd edn.,John Wiley & Sons, New York, 1990.

[8] H.S. Fogler, Elements of Chemical Reaction Engineering, 2nd edn., Prentice-Hall,1992.

[9] Y.C. Ray, T.S. Jiang, C.Y. Wen, Particle attrition phenomena in a fluidized bed,Powder Technology 49 (3) (1987) 193–206.

10] Y. Petukhov, H. Kalman, A new apparatus for particle impact tests, Particle andParticle Systems Characterization 20 (4) (2003) 267–275.

11] D.R. Parisi, M.A. Laborde, Modeling steady-state heterogeneous gas–solid reac-tor using feed forward neural networks, Computer and Chemical Engineering25 (9–10) (2001) 1241–1250.

12] M. Shahrokhi, G.R. Baghmisheh, Modeling, simulation and control of a methanolsynthesis fixed-bed reactor, Computer and Chemical Engineering 60 (15)(2005) 4275–4286.

13] A. Jahanmiri, R. Eslamlueyan, Optimal temperature profile in methanol synthe-sis reactor, Chemical Engineering Communications 189 (6) (2002) 713–741.

14] S.B. Lee, W. Cho, D.K. Park, E.S. Yoon, Simulation of fixed bed reactor for dimethylether synthesis, Korean Journal of Chemical Engineering 23 (4) (2006) 522–530.

15] S.M. Nasehi, R. Eslamlueyan, A. Jahanmiri, Simulation of DME reactor frommethanol, in: Proceedings of the 11th Chemical Engineering Conference, 2006.

16] K. Omata, T. Ozaki, T. Umegaki, Y. Watanabe, N. Nukui, M. Yamada, Optimizationof the temperature profile of a temperature gradient reactor for DME synthesisusing a simple genetic algorithm assisted by a neural network: high-qualitytransportation fuels, Energy & Fuels 17 (4) (2003) 836–841.

17] M. Fazlollahnejad, M. Taghizadeh, A. Eliassi, G. Bakeri, Experimental studyand modeling of an adiabatic fixed-bed reactor for methanol dehydration

[

[

nd Processing 50 (2011) 85–94

to dimethyl ether, Chinese Journal of Chemical Engineering 17 (4) (2009)630–634.

18] E.M. Assaf, R.C. Giordano, C.A.O. Nascimento, Thermal runaway of ethyleneoxidation reactors: prevision through neural network, Chemical EngineeringScience 51 (11) (1996) 3107–3112.

19] S.B. Jorgensen, Fixed bed reactor dynamics and control: a review, in: Proceed-ings of the IFAC Control of a Distillation Columns and Chemical Reactors, Oxford,1986, pp. 11–24.

20] R. Aguilara, A. Poznyakb, R. Martınez-Guerrab, R. Maya-Yescasc, Temperaturecontrol in catalytic cracking reactors via a robust PID controller, Journal ofProcess Control 12 (6) (2002) 695–705.

21] G. Bercic, J. Levec, Intrinsic and global reaction rate of methanol dehydrationover Al2O3 pellets, Industrial and Engineering Chemistry Research 31 (1992)1035–1040.

22] M. Nasehi, R. Eslamloueyan, A. Jahanmiri, Simulation of DME synthesis reac-tor from methanol, in: 11th National Iranian Chemical Engineering Congress,Tehran, Iran, 2006.

23] J.F. Richardson, J.H. Harker, J.R. Backhurst, Chemical Engineering, vol. 2, 5thedn., Butterworth–Heinemann, 1999.

24] A.P. Colburn, A method of correlating forced convection heat transfer data anda comparison with fluid friction, Transaction on AIChE 29 (1933) 174–210.

25] G.H. Graaf, H. Choltens, E.J. Tamhuis, A.A.C.M. Beenackers, Intra-particle dif-fusion limitations in low-pressure methanol synthesis, Chemical EngineeringScience 45 (4) (1990) 773–783.

26] E.L. Cussler, Diffusion Mass Transfer in Fluid Systems, Cambridge UniversityPress, United Kingdom, 1984.

27] J.M. Smith, Chemical Engineering Kinetics, McGraw Hill, New York, 1980.28] J.R. Dormand, P.J. Prince, A family of embedded Runge–Kutta formulae, Journal

of Computational and Applied Mathematics 6 (1980) 19–26.29] J.B. Ziegler, N.B. Nichols, Optimum settings for automatic controllers, ASME

Transactions 64 (1942) 759–768.30] W.L. Luyben, Design of proportional integral and derivative controllers for inte-

grating dead-time processes, Industrial and Engineering Chemistry Research 35(1996) 3480.