Dynamic optimal design of an industrial ethylene oxide (EO) reactor via differential evolution algorithm

Journal of Natural Gas Science and Engineering 12 (2013) 56e64

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Dynamic optimal design of an industrial ethylene oxide (EO) reactor via differential evolution algorithm M. Bayat a, M. Hamidi a, Z. Dehghani a, M.R. Rahimpour a, b, * a b

Department of Chemical Engineering, School of chemical and Petroleum Engineering, Shiraz University, Shiraz 71345, Iran Department of Chemical Engineering and Materials Science, University of California, Davis, 1 Shields Avenue, Davis, California 95616, United States

a r t i c l e i n f o

a b s t r a c t

Article history: Received 17 December 2012 Received in revised form 24 January 2013 Accepted 28 January 2013 Available online

In this study, the operating conditions of an industrial fixed-bed ethylene oxide reactor are optimized via differential evolution (DE) algorithm to boost the ethylene oxide yield with taking into account the catalyst deactivation. A mathematical heterogenous model of the reactor has been used in order to evaluate the optimal operating conditions, both at steady state and dynamic conditions. Two different cases have been investigated in this regard. In the first case, optimum inlet molar flow rate, inlet pressure of the reaction side and temperatures of shell and tube sides have been obtained within their practical ranges. In the second case, a stepwise approach has been followed in order to determine the optimal temperature profiles for saturated water and gas in three steps during operation. The objective of each optimization case study is to maximize the ethylene oxide production rate. The effect of optimal operating conditions on the reactor performance has been compared with corresponding industrial conditions over a period of three operating years. 1.726% and 4.22% yield enhancement of ethylene oxide production can be achieved by application of first and second optimization case studies, respectively. Ó 2013 Elsevier B.V. All rights reserved.

Keywords: Ethylene oxide reactor Dynamic optimization Differential evolution method Long-term catalyst deactivation

1. Introduction 1.1. Ethylene Ethylene is widely used in chemical industry, and its worldwide production (over 109 million ton in 2006) exceeds that of any other organic compound. It is mostly used to produce three chemical compounds: ethylene oxide, ethylene dichloride, and ethylbenzene, and a variety of kinds of polyethylene. Moreover, it is an ideal base material for many other petrochemicals, as it is readily available at high purity, low cost, high purity and usually reacts with other lowcost components, such as oxygen and water (Tarafder et al., 2005). Currently, ethylene is produced in the petrochemical industry by thermal cracking of alkanes such as ethane, propane, butane, naphtha and gas oil (Grace Chan et al., 1998; Keyvanloo et al., 2012; Lee and Aitani, 1990). The choice of feedstock is an important economic issue as it influences other costs as well. In this process, feedstocks are heated to 700e900
C. This process converts large hydrocarbons into smaller ones and introduces unsaturation. The

reactor effluent is quickly quenched to avoid further reaction, then compressed, and finally sent to a separation unit for the recovery of ethylene and other products such as methane, ethane, propane, propylene, butylenes, and pyrolysis gasoline (Tarafder et al., 2005). 1.2. Ethylene oxide Ethylene oxide is an important industrial chemical used as an intermediate in the production of glycols and other plastics (Serafin et al., 1998). EO is produced by selective oxidation of ethylene over the supported silver catalyst in a fixed bed multi-tubular reactor with operating temperatures from 180
C to 240
C and pressure of 2.1 MPa (Zhu, 1992; Baratti et al., 1994; Moudgalya and Goyal, 1998; Bingchen et al., 1999; Zhou and Yuan, 2005; Arsenijevic et al., 2006). Ethylene oxide is commercially produced by a direct gas phase oxidation of ethylene over silver catalysts with adequate activity and selectivity in Fixed-Bed Reactor (FBR) (Stoukides and Pavlou, 1986). The general reaction schemes for oxidation of ethylene to EO are expressed as: Ag

* Corresponding author. Department of Chemical Engineering, School of chemical and Petroleum Engineering, Shiraz University, Shiraz 71345, Iran. Tel.: þ98 711 2303071; fax: þ98 711 6287294. E-mail addresses: [email protected], [email protected] (M.R. Rahimpour). 1875-5100/$ e see front matter Ó 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.jngse.2013.01.004

C2 H4 þ 0:5O2 ! C2 H4 O Ag

DH298 ¼ 105:39

C2 H4 þ 3O2 ! 2CO2 þ 2H2 O

kj mol

DH298 ¼ 1321:73

(1) kj mol

(2)

M. Bayat et al. / Journal of Natural Gas Science and Engineering 12 (2013) 56e64

The principal stage in EO process is ethylene oxidation reaction (reaction 1) which undergoes a rapid oxidation reaction (reaction 2). The mechanism of these reactions has been studied and reported by Van Santen and Kuipers (1987). Boskovic et al. (2004) investigated the catalyst deactivation through an accelerated approach upon ethylene epoxidation process in a Berty reactor. 1.3. Dynamic simulation From a theoretical point of view, in the field of modeling and simulation of catalytic fixed-bed reactors under typical operating conditions, two different policies have been implemented: (1) Conventional steady state simulation and (2) Dynamic (transient) simulation. The extreme complexity of the processes involved in ethylene oxide production, justifies the computer simulations of such processes to get further understanding of system without the need to perform expensive and time-consuming experiments. The dynamic simulation of ethylene oxide processes has a wide range of applications including: the start-up and shut-down investigations, system identification, safety, control, optimization, transient behavior, and operability studies. In operability studies, it is more favorable to use dynamic simulation rather than steady-state simulation, since a realistic description of transient states of the reactor can be obtained by using dynamic simulation. It is due to the fact that the numerical solution strategies used in dynamic models are more powerful than the solution of a typical steady-state model. Therefore, it allows for safe and reliable studies of control and optimization of the reactor (Vasco de Toledo et al., 2001; Setinc and Levecb, 2001). Due to great importance of EO in industry and its large scale of production, process optimization of ethylene epoxidation is undoubtedly another important research topic. However, papers contributed to this topic are very scarce. 1.4. Optimization The same as the world of modeling, dynamic optimization has its own jargon to address specific characteristics of the problem. Most optimization problems in process industry can be broken down into non-linear, non-convex, and constrained optimization problems (Parvasi et al., 2009). Typical important parameters which are selected to be optimized for plant optimization are equipment size, recycle flows and operating conditions such as concentration, temperature and pressure. An optimum design is based on the best or most desired conditions. In most cases, these optimum conditions can ultimately be reduced to a consideration of profits or costs. Therefore, an optimum economic design could be achieved based on conditions giving the maximum profit per unit of production or the least cost per unit of time. When one design variable is changed, it is often found that some costs increase and others decrease. Under these conditions, the total cost can be achieved with minimum amount at one value of the particular design variable, and this value would be considered as an optimum. Recently, a number of search algorithm methods such as evolutionary programming (EP) (Fogel et al., 1966), genetic algorithms (GAs) (Huang et al., 2008) evolution strategies (ES) (Rechenberg, 1973), and particle swarm optimization (PSO) (Kennedy and Eberhart, 1995) have been developed to cope with optimization problems.

constraints. It is a population based algorithm like genetic algorithm using the same operators: crossover, mutation, and selection. The main difference between these two methods is that genetic algorithm depends on crossover while DE relies on mutation operation and it makes DE method a better technique. This main operation is founded on the differences of randomly sampled pairs of solutions in the population. Three most significant advantages of this algorithm are as follows; finding the true global minimum regardless of the initial parameter values, fast convergence, and using a few control parameters. Being simple, easy to use, fast, very easily adaptable for integer and discrete optimization, quite effective in non-linear constraint optimization including penalty functions and useful for optimizing multimodal search spaces are the other important features of DE (Farsi et al., 2010). 1.6. Literature review Many authors and researchers have been investigated this reaction in various cases. In recent years, they attempt to modify this process with possible assumptions. Hwang and Smith (2004a,b) presented results of ethylene oxide reactor simulation with the purpose of finding an optimal operating temperature for this reactor under steady-state conditions ignoring catalyst deactivation. Zhou and Yuan (2005) optimized an industrial ethylene epoxidation process with considering feed composition, feeding rate and operating pressure as variable parameters using a onedimensional homogenous model in steady-state conditions. In the work of Cornelio (2006) a dynamic heterogenous model of an industrial EO reactor was developed and afterwards simplified into a pseudo-homogenous model. Lahiri and Khalfe (2009) used an integrating support vector regression and genetic algorithm method in order to model and optimize an industrial ethylene oxide reactor. Aryana et al. (2009) modeled and optimized an industrial ethylene oxide oil coolant reactor without taking into account the mass balance on catalyst for species. Recently, the artificial neural network has been applied by Rahimpour et al. (2011) for modeling and simulation of an industrial ethylene oxide (EO) reactor. 1.7. Objective In this theoretical study, the production of ethylene oxide in an industrial fixed bed reactor has been maximized. Optimization tasks have been investigated by a novel optimization tool, differential evolution. Two different cases will be discussed in this regard. In the first case, an optimization program has been developed to obtain more ethylene oxide production through optimum inlet pressure, inlet molar flow rate, temperatures of feed and cooling saturated water. In the second case, the optimal temperature profile at three periods of operation has been considered to reach maximum ethylene oxide production rate. The objective function in this optimization procedure is maximizing ethylene oxide production throughout 1100 days of the catalyst life. 2. Reaction kinetics The kinetics of ethylene oxidation has been widely studied by many researchers (Stegelmann et al., 2004; Zhou and Yuan, 2005; Borman and Westerterp, 1995; Gianpiero and Tronconi, 2001). In the current work, the corresponding rate expressions have been selected from Gu et al. (2003) and are represented as follows:

1.5. Differential evolution (DE) method DE, a new evolutionary algorithm, is a stochastic optimization method which minimizes an objective function with considering

57

rEO


8358:5 3=4 PET $PO2 exp 10:30  T ¼ ð1 þ Dn Þ

(3)

58

M. Bayat et al. / Journal of Natural Gas Science and Engineering 12 (2013) 56e64

rCO2


9835:2 PET $PO2 exp 12:54  T ¼ ð1 þ Dn Þ

(4)

rEO and rCO2 are the reaction rates of ethylene oxide and carbon dioxide, while PET and PO2 are the pressure of ethylene and oxygen, respectively. Dn is calculated as follows:


9812:8  21:68 $PCO2 Dn ¼ 1 ¼ exp T 
16129:2 1=2  34:58 $PCO2 $PH2 O þ exp T

(5)

Table 1 Ethylene oxide reactor feed inlet condition (Rahimpour et al., 2011). Parameter

Value

Feed composition (mole fraction) C2H4 O2 C2H4O H2O CO2 N2 CH4 Total molar flow rate (mol s1) Inlet pressure (bar) Inlet temperature (K) Coolant water temperature (K)

0.25 0.08 0.0001 0.0025 0.07 0.1271 0.4703 0.89 21.7 463 503

3. Process description A schematic diagram showing a conventional ethylene oxide reactor is provided in Fig. 1. A conventional ethylene oxide reactor is basically a vertical shell and tube heat exchanger. The catalyst is packed in vertical tubes and surrounded by water, which through boiling removes the heat. The exothermic ethylene oxide reactions are carried out over silver catalyst and the heat of reactions is transferred to the boiling water and subsequently steam is produced. The specifications of the reactor, feed composition and catalyst are tabulated in Tables 1 and 2.

According to above assumptions and the differential element along the axial direction inside the reactor, the mass and energy balance equations were obtained. The balances typically account for convection, transport to the catalyst and reaction. The mass and energy balances, boundary conditions and initial conditions for gas and solid phases are summarized in Table 3. In Equations (3) and (4), h is catalyst effectiveness factor and is obtained from a dusty gas model calculation (Rezaie et al., 2005). The detail of the dusty gas model is available in literature (Rezaie et al., 2005).

4. Mathematical model

4.1. Pressure drop

The mathematical model for simulation of an industrial fixedbed ethylene oxide reactor has been developed based on the following assumptions:

The Ergun equation is used to give the pressure drop along the reactor:

ð1  3 Þug r ð1  3 Þ2 mug dP ¼ 150 þ 1:75 dz 3 3 d2 3 3 dp p 2

 One-dimensional heterogenous model (reactions take place over the catalyst particles)  Plug flow pattern is considered in each side  Axial diffusion of heat and mass are neglected compared with the convection  No radial heat and mass diffusion in catalyst pellet  Bed porosity value in axial and radial directions is constant  Gas mixtures considered to be ideal  Heat loss is negligible

Steam Drum Saturated water

Ethylene Oxygen

(12)

where the pressure drop is in Pascal. 4.2. Auxiliary correlations In order to complete the simulation procedure, auxiliary correlations should be added to the modeling section. The correlations used for heat and mass transfer between gas and solid phases, physical properties of chemical species and overall heat transfer coefficient between two sides are listed in Table 4. The heat transfer coefficient between gas phase and reactor wall is applicable for heat transfer between gas phase and solid catalyst phase. In recent reactor studies, a constant total molar flow rate has been considered during modeling. This assumption reduces the accuracy of prediction for reactor outlet mole fractions. In the industrial fixed-bed ethylene oxide reactor, a continuous decrease of total molar flow rate exists along the reactor length. Therefore, in this study, the total molar flow rate is considered to be variable along the reaction pathway. Moreover, the molecular weights, heat capacities, viscosity, density and other properties are assumed to be variable for mathematical modeling.

Table 2 Catalyst and reactor specifications.

Reaction side (Fixed-bed)

Ethylene oxide Fig. 1. Schematic diagram of an industrial fixed bed ethylene oxide reactor (CR).

Quantity

Value

Particle diameter (m) Heat capacity (kJ kg1 K1) Specific surface area (m2 m3) Bed void fraction Number of tubes Length of reactor (m)

7.74  103 1.0 387.59 0.5 5523 8.7

M. Bayat et al. / Journal of Natural Gas Science and Engineering 12 (2013) 56e64 Table 3 Mass and energy balances, boundary and initial conditions for solid and fluid phases in tube side of CR.

vyi vFi ¼  þ av $ct $kgi ðyis  yi Þ vt Ac $vz

i ¼ 1; 2; 3; :::; N

(6)

5. Numerical solution

pDi vT 1 vðFt :TÞ ¼  Cpg þ av $hf $ðTs  TÞ þ $Ushell ðTshell  TÞ vt Ac vz Ac

3 B $Ct $Cpg $

(7)

Mass and energy balance equations for the catalyst pellets

3 s $Ct $

dyis ¼ kgi $av $ct $ðyi  yis Þ þ rB $h$a$ri dt

(14)

On the a-Al2O3 support, silver crystallites have sizes of about a few hundred nanometers and act as bulk silver (Kestenbaum et al., 2002).

Mass and energy balance equations for the bulk gas phase

3 B $Ct $

59


 E kd ¼ kd0 $exp RT

i ¼ 1; 2; 3; :::; N

n   X dTs ¼ av $hf $ðT  Ts Þ þ h$rB $a$ rj $ DHf ;i dt j¼1

rB $Cps $

Boundary conditions : yi ¼ yi0 ; T ¼ T0 at z ¼ 0

(8)

5.1. Steady state identification (9)

(10)

ss ss Initial conditions : yi ¼ yss i ; yis ¼ yis ; T ¼ Tss ; Ts ¼ Ts ; a ¼ 1 at t ¼ 0

(11)

4.3. Catalyst deactivation Catalyst deactivation is one of the most challenging issues in catalytic reactors. The three main factors affecting catalytic activity are sintering, poisoning and wearing, while sintering is the principal reason of Ag catalyst deactivation (Hoflund and Minahan, 1996; Montrasi et al., 1983). This process reduces the catalyst active sites. Reduction of catalyst active sites is usually expressed by the generalized power law expression as follows (Bartholomew, 2001):

da ¼ kd ða  aN Þ2  dt

The governing equations of model form a system comprising algebraic, ordinary differential and partial differential equations. A two-stage approach consisting of a steady-state simulation followed by a dynamic simulation is the solution procedure of these equations.

(13)

where kd is the sintering rate constant and is a function of temperature:

Identification of the steady-state condition of the ethylene oxide reactor with taking into account catalyst deactivation, in principle, is a matter of determining the concentration and temperature profile along the reactor axis at time zero. This is done by setting all timederivative of the fresh catalyst. In this way, the initial temperature and concentration can be specified for the dynamic simulation. After rewriting the model equations under steady state condition, a set of differential algebraic equations (DAEs) is obtained. Backward finite difference approximation is utilized to solve these equations and a non-linear algebraic set of equations is achieved. Then, the reactor is divided into 100 separate sections and the GausseNewton method in MATLAB programming environment is employed to solve the non-linear algebraic equations in each section. The result of the steady state simulation is used as initial conditions for time-integration of dynamic model. 5.2. Solution of dynamic model To solve the set of stiff model equations dynamically, equations have been discretized respect to axial coordinate. Modified Rosenbrock formula of order 2 has been used to integrate the set of equations with respect to time. The process duration has been considered to be 1100 days of operation. 5.3. Model validation In order to verify the accuracy of the model, simulation results are compared with the historical process data during 1100

Table 4 Physical properties, mass and heat transfer correlations. Parameter

Equation

Component heat capacity Mixture heat capacity

Cp ¼ a þ bT þ cT2 þ dT3 PN Cp;m ¼ i ¼ 1 yi  Cpi

Viscosity

C1 T C2 C C 1 þ 3 þ 42 T T 0:42 0:67 kgi ¼ 1:17Re Sci ug  103 2Rp ug Re ¼

Mass transfer coefficient between gas and solid phases

m ¼

Reference

Perry et al. (1997)

Cussler (1984)

m

Sci ¼

m rDim  104

1y Dim ¼ P y i i i ¼ j Dij

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1:43  107 T 3=2 1=Mi þ 1=Mj Dij ¼ pffiffiffi 1=3 1=3 2Pðvci þ vcj Þ2 Overall heat transfer coefficient Heat transfer coefficient between gas phase and reactor wall

1 1 Ai lnðDo =Di Þ Ai 1 ¼ þ þ U hi 2pLKw Ao ho

0:407 2=3 m C h 0:458 rudp p ¼ m Cp rm K 3B

Wilke (1949)

Reid et al. (1977)

Smith (1980)

60

M. Bayat et al. / Journal of Natural Gas Science and Engineering 12 (2013) 56e64

operating days under the design specifications (Rahimpour et al., 2011). The most significant characteristic parameter in this reactor is the production rate of ethylene oxide. The calculated results of production rate and the corresponding observed data of the plant are presented in Table 5. The plant data employed for evaluation is taken from a typical Petrochemical Complex in Iran. It is noticed that, the model performed satisfactorily well under industrial conditions and there was an acceptable agreement between observed plant data and simulation data. 6. Optimization and results Differential evolution method is applied for ethylene oxide production process to determine the optimal operating conditions. The main target of this survey is maximizing the ethylene oxide production during 1100 operating days. For tubular and exothermic reactors, temperature is an important parameter that changes during reactor length and time and has a direct effect on catalyst activity. Optimization of reactor is studied in two cases. The first case is to determine optimal temperature profile along the ethylene oxide reactor to achieve utmost amount of product through the optimization of inlet molar flow rate, inlet pressure and the temperatures of feed gas and cooling saturated water while the second one is an investigation to reach optimal temperature utilizing three-stage temperature profiles for cooling water and feed gas, as a realistic approach. 6.1. First case of optimization In this case, four parameters consist of inlet pressure of reaction side, inlet feed gas temperature, inlet cooling saturated water temperature and inlet molar flow rate should be optimized. All constraints used for optimization are as follows:

453 < Tf < 513 460 < Tshell < 520 18 < Pinlet < 22 0:7 < Finlet < 1 513 K is considered as the constraint for the temperature of catalytic bed along the reactor due to the catalyst deactivation at higher temperatures. A penalty function method is employed to automatically eliminate the unacceptable results. In this study, 107 is considered Table 5 Comparison between predicted ethylene oxide production rates by heterogenous model with plant data (Rahimpour et al., 2011). Time (Day)

Plant (t/day)

Heterogenous model Predicted (t/day)

Deviation%

0 100 200 300 400 500 600 700 800 900 1000 1100

370.00 370.60 372.10 369.12 368.50 361.69 360.58 347.61 354.74 352.39 345.43 347.20

370.23 366.61 363.10 359.67 356.37 353.143 350.00 346.94 343.96 341.06 338.23 335.47

0.0627 1.086 2.477 2.621 3.403 2.420 3.022 0.192 3.133 3.322 2.128 3.495

as the penalty parameter, however, this value depends on order of magnitude of the variables in the problem. The objective function that should be minimized is:

OF ¼ ðProduct rate of EOÞ þ 107

N X i¼1

G2i

(15)

where

G ¼ maxð0; T  513Þ The optimization results (using differential evolution method and MATLAB programming) are summarized in Table 6. In this table, Tshell and TF are the temperatures of cooling water and feed gas, respectively. Optimization results of this table are used to simulate the industrial fixed bed ethylene oxide reactor and the results of this simulation are shown in several figures. Fig. 2 shows the ethylene oxide mole fraction and temperature profiles for conventional reactor (CR) and optimized conventional reactor (OCR) at 1st day (fresh catalyst) and 1100th day of operation. As it can be seen in Fig. 2(a), at the first day, the ethylene oxide mole fraction in OCR is higher than CR. According to Fig. 2(b), the temperature in the OCR is higher mainly owing to higher inlet temperature of saturated water. Fig. 2(c) and (d) (1100th day), show that OCR provides better results in ethylene oxide mole fraction and temperature profile along the reactor. Fig. 3 compares the ethylene oxide production rate during 1100 days of operation for CR and OCR. The average ethylene oxide production rate of OCR is 1.73% more than conventional EO reactor for first optimization case. 6.2. Second case of optimization Optimal temperature profiles give us some beneficial information about reactor operating condition. The results show that it is possible to enhance the production rate utilizing an appropriate temperature strategy in the reactor. The catalyst activity decreases sharply in the first few operating days and in the rest of the operating time the activity lands slowly. Because of catalyst deactivation, in each time, the optimal temperature of bed should be considered. On the other hand, the bed temperature can be controlled by the coolant. For this purpose, in this section, optimization trends are performed by changing coolant temperature at 300th and 800th days of operation. Similar to previous section, maximizing of the main product, ethylene oxide is the objective function. In this optimization method, 6 parameters consist of three parameters for inlet gas temperature and three parameters for cooling water temperature are determined. Inlet pressure and inlet molar flow rate are considered the same as the first optimization case and the formulation of optimization problem is the overall ethylene oxide production in all periods of time. The result of optimal temperature profile at 3 periods of time is illustrated in Fig. 4. Fig. 5(a)e(c) shows 3D plots of temperature, ethylene oxide mole fraction and total molar flow rate as a function of the reactor length and time in the optimal conditions. Fig. 5(a), demonstrates bed temperature with sudden rises in 300th and 800th days of operation due to increasing of cooling gas temperature along the reactor in each three times. Fig. 5(b) depicts 3D plot for ethylene Table 6 The optimized parameters for first case. Tshell (K)

TF (K)

Inlet pressure (bar)

Inlet molar flow rate (mole/s)

503.52

499.3

22

0.9

M. Bayat et al. / Journal of Natural Gas Science and Engineering 12 (2013) 56e64

a

b

Fresh catalyst

0.025

61

Fresh catalyst

520

CR OCR

CR OCR 510

Temperature (K)

Ethylene oxide mole fraction

0.02

0.015

0.01

0.005

0 0

500

490

480

470

460 0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

0

1

0.1

0.2

0.3

Dimensionless length

c

d

1100th day

0.025

0.4

0.5

0.6

0.7

0.8

0.9

1

Dimensionless length

1100th day

520

CR OCR

CR OCR 510

Temperature (K)

Ethylene oxide mole fraction

0.02

0.015

0.01

500

490

480

0.005 470

0 0

0.1

0.2

0.3

0.4 0.5 0.6 0.7 Dimensionless length

0.8

0.9

1

460 0

0.1

0.2

0.3

0.4 0.5 0.6 0.7 Dimensionless length

0.8

0.9

1

Fig. 2. Comparison of (a) ethylene oxide mole fraction, (b) temperature profiles at 1st day and (c) ethylene oxide mole fraction, (d) temperature profiles at 1100th day for CR and OCR.

oxide mole fraction. As it is illustrated in Fig. 5(c), the variations of molar flow rates are about 0.4919%, 0.4929% and 0.4857% for 3 periods of time, respectively. Fig. 6(a) presents the comparison of ethylene oxide production in OCR and CR during 3 years. Production rate of the optimized

conventional ethylene oxide reactor increases about 4.22% compared to that of the conventional ethylene oxide reactor. The difference between ethylene oxide production in the first case and the second case of optimization increases with time. In fact, selection of 3 different temperatures makes sudden increases

380

515

CR OCR

375

TFeed

370 365

505

Temperture (K)

EO production rate (ton/day)

TShell

510

360 355 350

500

495

345 340 490

335 330

0

100

200

300

400

500

600

700

800

900

1000

1100

Time (day) Fig. 3. Comparison of EO production rate for optimized and non-optimized conventional ethylene oxide reactors.

485

0

100

200

300

400

500

600

700

800

900

1000

1100

Time (day) Fig. 4. Temperatures of coolant and feed as a function of time for second case of optimization.

M. Bayat et al. / Journal of Natural Gas Science and Engineering 12 (2013) 56e64

in the production rate at the 300th and 800th operating days. Fig. 6(b) shows 2.54% further yield for production rate of the second optimization compared with the first optimization. Sometimes, the production rate in the first optimized reactor is higher than the other and vice versa, but in general, the overall production rate of the second case is higher than that of the first case. Fig. 7 compares overall ethylene oxide production for two cases of optimization with non-optimized reactor during 1100 days. As it can be seen, there is a considerable increase in the amount of ethylene oxide production in the second case of OCR.

a

380 375 370

EO production rate (ton/day)

62

365 360 355 350 345 340

CR 2nd optimization case

335 330

0

100

200

300

400

500

600

700

800

900

1000

1100

700

800

900

1000 1100

Time (day)

b

380

EO production rate (ton/day)

375

370

365

360

355

350

345

340

1st optimization case 2nd optimization case 0

100

200

300

400

500

600

Time (day) Fig. 6. (a) Comparison of ethylene oxide production rate in CR and the second case of optimization, (b) Comparison of ethylene oxide production rate in two cases of optimization.

4.1

x 10

4

4.05

EO production

4

3.95

3.9

3.85

3.8

Fig. 5. 3D profile of (a) temperature of reactor bed, (b) ethylene oxide mole fraction and (c) total molar flow rate for second optimization.

CR

1st case

2nd case

Fig. 7. Comparison of overall ethylene oxide production during 1100 operating days.

M. Bayat et al. / Journal of Natural Gas Science and Engineering 12 (2013) 56e64

7. Conclusion

yi

In this study, the dynamic optimization of an industrial fixedbed ethylene oxide reactor was investigated. A mathematical heterogenous model was used in this regard and the optimal temperature for an EO reactor was obtained utilizing differential evolution (DE) method as a simple and robust optimization technique which gives good solution for this constrained nonlinear problem. Overall EO production during 1100 days of catalyst life was considered as the optimization criterion that should be maximized. The optimization consists of two cases: In the first case, 4 variables were tuned which they were feed gas temperature, inlet pressure and molar flow rate in the reaction side and cooling water temperature. In the latter case, based on the results arisen from the first case, optimization was followed by another task that optimal behaviors of cooling water and feed gas temperature were obtain. This novel design leads us to optimal operation strategy which results in 1.726% and 4.22% yield enhancement of ethylene oxide production by application of first and second optimization case studies, respectively.

yis

Nomenclature Ac Ai Ao a av cPg cPs ct Di Dij Dim Do dp Ed Ft fi DHf,i DH298 hf hi ho K Kd kgi L Mi N P R Rp T Ts Tshell t Ushell U ug

cross section area of each tube (m2) inner area of each tube (m2) outside are of each tube (m2) activity of catalyst specific surface area of catalyst pellet (m2 m3) specific heat of the gas at constant pressure (J mol1) specific heat of the solid at constant pressure (J mol1) total concentration (mol m3) tube inside diameter (m) binary diffusion coefficient of component i in j (m2 s1) diffusion coefficient of component i in the mixture (m2 s1) tube outside diameter (m) particle diameter (m) activation energy used in the deactivation model (J mol1) total molar flow per tube (mole s1) partial fugacity of component i (bar) enthalpy of formation of component i (J mol1) enthalpy of reaction at 298 K (J mol1) gasesolid heat transfer coefficient (W m2 K1) heat transfer coefficient between fluid phase and reactor wall (W m2 K1) heat transfer coefficient between coolant stream and reactor wall (W m2 K1) conductivity of fluid phase S (W m K1) deactivation model parameter constant (s1) mass transfer coefficient for component i (m s1) length of reactor (m) molecular weight of component i (g mol1) number of components used in the model (N ¼ 7) total pressure (bar) universal gas constant (J mol1 K1) particle radius (m) bulk gas phase temperature (K) temperature of solid phase (K) temperature of coolant stream (K) time (s) overall heat transfer coefficient between coolant and process streams (W m2 K1) superficial velocity of fluid phase (m s1) linear velocity of fluid phase (m s1)

z

63

mole fraction of component i in the fluid phase (mol mol1) mole fraction of component i in the solid phase (mol mol1) axial reactor coordinate (m)

Greek letters void fraction of catalytic bed (m3 m3) rB density of catalytic bed (kg m3) rg density of fluid phase (kg m3) rS density of solid phase (kg m3)

3B

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