Incorporating differential evolution (DE) optimization strategy to boost hydrogen and DME production rate through a membrane assisted single-step DME heat exchanger reactor

Journal of Natural Gas Science and Engineering 9 (2012) 28e38

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Incorporating differential evolution (DE) optimization strategy to boost hydrogen and DME production rate through a membrane assisted single-step DME heat exchanger reactor R. Vakili, M.R. Rahimpour*, R. Eslamloueyan 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

a b s t r a c t

Article history: Received 15 April 2012 Received in revised form 11 May 2012 Accepted 16 May 2012 Available online 26 June 2012

The present contribution aims to enhance dimethyl ether (DME) production rate as well as hydrogen as clean-burning fuels and versatile applications. In this regard, a thermally coupled membrane configuration (TCMDR), which is able to produce hydrogen and DME simultaneously, is proposed. Here, direct DME synthesis from syngas and cyclohexane dehydrogenation reaction are coupled and occur in the exothermic and endothermic compartments, respectively. The dehydrogenated product (hydrogen) is pushed through the wall of the third partition, which is a Pd/Ag membrane composite, in order to overcome the equilibrium constraints of dehydrogenation reaction. Moreover, the optimal operating conditions are sought by aid of differential evolution (DE) algorithm as a powerful optimization technique. During the optimization step, the sum of carbon monoxide and cyclohexane conversions along with the hydrogen mole fraction in the permeation side is considered as the objective function. Finally, the TCMDR behavior is examined based on the achievements during the optimization procedure and a one-dimensional steady-state heterogeneous model. The results show considerable DME enhancement in the TCMDR by 10.3% and 11.4% compared with the conventional direct DME synthesis reactor (CDR) and thermally coupled DME reactor (TCDR) arrangements and at the same time the amount of endothermic raw material drops about 120.3 kmol/h. Ó 2012 Elsevier B.V. All rights reserved.

Keywords: Thermally coupled heat exchanger reactor Pd/Ag membrane Direct dimethyl ether (DME) synthesis Hydrogen production Differential evolution optimization approach

1. Introduction

1.1. Direct DME synthesis

Energy is an indispensable element in our everyday life and most of the energy we use nowadays comes from fossil fuels. Natural gas is one of the major fossil energy sources and main options for the use of natural gas are power generation and conversion to petrochemicals like ammonia, dimethyl ether (DME) and methanol. Since, air pollution is one of the most serious environmental challenges all over the world converting natural gas to clean burning fuels like DME can be a helpful way to decline greenhouse-gas (GHG) emissions (Economides and Wood, 2009; Abbas and Wan Daud, 2010). The introduction section is divided into some subsections in order to give crucial orientations on various aspects of the present work. The first section provides an economical overview of direct DME production rather its customary approach as well as a short summary about hydrogen as a green fuel. Secondly, the concept of process integration and its alternatives are discussed.

With ever growing concerns on environmental pollution, energy security, and future oil supplies, the global community is seeking non-petroleum based alternative fuels, along with more advanced energy technologies to increase the efficiency of energy use. The most promising alternative fuel will be the fuel that has the greatest impact on society. The major impact areas include well-towheel greenhouse gas emissions, non-petroleum feed stocks, wellto-wheel efficiencies, fuel versatility, infrastructure, availability, economics, and safety. Compared to some of the other leading alternative fuel candidates (i.e., methane, methanol, ethanol, and FischereTropsch fuels), dimethyl ether appears to have the largest potential impact on society. Thus, it is one of the superior fuel candidates for the next generation and should be considered to eliminate the dependency on petroleum (Semelsberger et al., 2006; Omata et al., 2002). Therefore, several studies have been done in recent years concerning to increase and improve the productivity of DME process (Liu et al., 2011; Khaleel, 2010; Jin et al., 2007; Wang et al., 2009; Sai-Prasad et al., 2008). Broadly speaking, DME is conventionally produced by a two stage process. In the first step,

* Corresponding author. Tel.: þ98 711 2303071; fax: þ98 711 6287294. E-mail address: [email protected] (M.R. Rahimpour). 1875-5100/$ e see front matter Ó 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.jngse.2012.05.006

R. Vakili et al. / Journal of Natural Gas Science and Engineering 9 (2012) 28e38

syngas undergoes methanol synthesis followed by a dehydrogenation plant to DME production. This is known as the indirect method of DME synthesis. Recently, a new technique called direct DME synthesis, was proposed and gained much more attention due to its economical superiority over the indirect method (Nie et al., 2005). In this new process, the methanol production and dehydration step occur simultaneously on the hybrid (bi-functional) catalysts in one bed and consequently the methanol purification unit can be ignored. Undoubtedly, the direct method has higher economic feasibility in comparison with the conventional illustration (indirect method) since the production costs of the single-step process are 20% lower compared with the two-step one. Indeed, the initial investment will be smaller (Fukunaga et al., 2008; Tan et al., 2005). Hydrogen offers the best energy-to-weight ratio of any fuel. It is not only an ideal energy carrier for the future mainly due to its high conversion efficiency, recyclability and nonpolluting nature but also a fundamental raw material and feedstock in petroleum, chemical engineering, chemical fertilizer and metallurgical industries (Adris et al., 1997). Although hydrogen is often referred as an clean energy that its combustion produces only water, the production of hydrogen from hydrocarbons by means of current processes yields CO2, a greenhouse gas (Wang et al., 2008; Kariya et al., 2003; Yolcular and Olgun, 2008). One of the environmentally friendly methods to produce hydrogen without CO2-emission is cyclohexane dehydrogenation (Biniwale et al., 2005). 1.2. Process intensification Process intensification is a concept that was introduced in the late 1970’s in the chemical industry for the purpose of reducing environmental emissions, energy and materials consumptions. In practice, it is the established convention within the industry and it relates to reduction of at least 3e4 fold in magnitude. As far as chemical reactors form the heart of any chemical processes, innovations in catalytic reactors are often the preferred starting point. Over the last two decades, innovative multifunctional heat exchanger and membrane reactors have been developed to intensify chemical processes by synergistically combining chemical reaction with heat and mass transport in a single vessel (Harmsen, 2010; Van der Bruggen et al., 2004; Stankiewicz and Moulijn, 2004). 1.2.1. Thermally coupled reactor (heat exchanger reactor) Multifunctional reactors integrate, in one vessel, one or more transport processes and a reaction system and are increasingly used in industries as process intensification tools. A multifunctional reactor can be used for coupling exothermic and endothermic reactions. The exothermic reaction is utilized as the energy source to drive the endothermic one. The coupled reactors are divided into three various configurations.

UOP (Dautzenberg and Mukherjee, 2001) and BP (Ramaswamy, 2006) for styrene and syngas productions respectively by coupling with combustion reactions. 1.2.2. Membrane reactor The potential of membranes for gas separation has been known for more than 30 years (Baker, 2002). During this time, significant development in membrane science has been come to stage from academic and industrial viewpoints (Bottino et al., 2002; Criscuoli et al., 2001; Brunetti et al., 2007) and studies are still in progress. Two groups of polymeric and inorganic membranes are discussed, but the major investigations have been concentrated on the inorganic membrane reactors thanks to their excellent thermal stability at high reaction temperature (Choi et al., 2000). It is commonly accepted that using membrane technology in the conventional plants drives toward greater economic and environmental efficiency (Sousa et al., 2001). Membrane reactors offer the possibility to combine reaction and product separation in a single operation. Therefore, the interest in such a configuration resides in their capability to control the reaction zone confinement and their selectivity. The membrane provides a selective removal of one or more products simultaneously with the reaction, so that the reaction equilibrium is continually shifted to increase the product formation (Basile et al., 2001). There are a multitude of units and various hydrogenation and dehydrogenation reactions which need to reach optimal productivity. One apparent opportunity that would seem to match well with the current feature of membrane is the dehydrogenation of cyclohexane to benzene (Yang and Chou, 2008). Here, membrane can be used effectively to increase hydrogen production and benzene selectivity. 1.3. Objectives Since DME and hydrogen are optimum large-scale fuels in the near future, even minuscule improvements in their production processes, which would be tantamount to higher production capacities, are economically favorable. Considering this, a multifunctional auto-thermal fixed-bed reactor for recuperative coupling of single-step DME synthesis from syngas and cyclohexane dehydrogenation reaction was proposed by Vakili et al. (2011). Now, in a continuous effort we probe the effect of incorporating membrane concept into this configuration. Furthermore, differential evolution (DE) strategy is exploited to identify the most favorable operating conditions which enhance the desired production rates (hydrogen and DME production rates). Generally,

Fresh water

Syngas

 Direct coupling (directly coupled adiabatic reactor).  Regenerative coupling (reverse-flow reactor).  Recuperative coupling (co and counter-current heat exchanger reactors). The latter configuration offers several advantages over the other ones. First, the products of the endothermic reaction always separate from the exothermic side. In addition, here the reactors have more flexibility for their operational parameters in both sides separately and can adjusted independently without affecting the other streams (Ramaswamy, 2006). The researches were carried out by Hunter and McGuire (1980), Van Sint Annaland and Nijssen (2002), Elnashaie et al. (2000) and Altimari and Bildea (2009) are appreciable in this regard. Among all of these laboratories scale experiments, two commercial scale configurations also installed by

29

Natural Gas

Steam drum

Reforming unit

Distillation unit Fig. 1. A schematic diagram of CDR.

Pure DME

30

R. Vakili et al. / Journal of Natural Gas Science and Engineering 9 (2012) 28e38

Table 1 Operating conditions and catalyst characteristics for conventional DME reactor (Hu et al., 2008). Parameter

Value

Unit

Feed composition (mole fraction) CO CO2 DME CH3OH H2O H2 N2 CH4 Inlet temperature Inlet pressure Number of pipes Diameter of pipes Volumetric flow rate of raw gas Length of reactor Temperature of boiling water Thermal conductivity of wall

0.1716 0.0409 0.0018 0.003 0.0002 0.4325 0.316 0.044 493 50 4177 f38  2 2.04  105 5.8 513 48

e e e e e e e e K bar e mm Nm3 h1 m K W m1 K1

Typical properties of catalyst Particle diameter Density of catalyst bed Porosity

5 1200 0.455

mm kg/m3 e

Table 2 The operating conditions for endothermic and permeation sides of TCDR and TCMDR. Parameter

Value

Endothermic side Feed composition (mole fraction) C6H12 C6H6 H2 Ar Total molar flow rate (mol s1) Inlet pressurea (Pa) Inlet temperature (K) Particle diameterb (m) Bed void fraction

0.2 0.0 0.0 0.8 0.12 1.013  105 493.0 3.55  103 0.39

Permeation side Feed composition (mole fraction) Ar H2 Total molar flow rate (mol s1) Inlet pressure (bar)

1.0 0.0 1.0 0.1

a b

Obtained from Jeong et al. (2004). Obtained from Koukou et al. (1997).

2. Process description

to others. A schematic diagram of CDR suggested by Hu et al. (2008) for one-step DME synthesis is shown in Fig. 1. Here, the DME synthesis occurs in tube compartments over bi-functional catalyst packs where methanol production and dehydration occur concurrently. The boiling water in the shell side absorbs the heat of reactions and produces water vapor. The characteristics and operating conditions of this configuration are presented in Table 1.

2.1. Conventional direct DME synthesis reactor (CDR)

2.2. Thermally coupled DME reactor (TCDR)

Due to more available information on the design and manufacturing of fixed-bed reactors in industrial scales, the direct DME production is generally proposed in these reactors compared

In TCDR (Vakili et al., 2011), the direct DME synthesis takes place in the tube side and a catalytic dehydrogenation reaction (endothermic reaction) is supposed for the shell side instead of using

the main objective of this work is optimization of a thermally coupled membrane reactor for more hydrogen and DME production.

CO,CO2,DME,CH3OH,H2O,H2 ,N2,CH4

C6H12,H2

CO,CO2,DME,CH3OH, H2O,H2,N2,CH4

C6H12,H2

Permeation side

Endothermic side (Cyclohexane dehydrogenation)

Exothermic side (Direct DME synthesis)

Fig. 2. A schematic diagram of TCDR.

INSULATED WALL

Pd-Ag MEMBRANE LAYER

H2 PERMEATION

SOLID WALL

HEAT TRANSFER

SOLID WALL

H2 PERMEATION

Pd-Ag MEMBRANE LAYER

INSULATED WALL

INSULATED WALL

SOLID WALL

HEAT TRANSFER

SOLID WALL

INSULATED WALL

Ar

Exothermic side (Direct DME synthesis)

Endothermic side (Cyclohexane dehydrogenation) Fig. 3. A schematic diagram of TCMDR.

R. Vakili et al. / Journal of Natural Gas Science and Engineering 9 (2012) 28e38

31

k ¼ AexpðB=RTÞ

A

B(K)

the permeation of hydrogen shifts the thermodynamic equilibrium of endothermic reaction and sequentially increases the cyclohexane conversion. The specifications of the permeation side were provided in Table 2.

kðmol m3 pa1 s1 Þ KB ðpa1 Þ KP ðpa3 Þ

0.221 2.03  1010 4.89  1035

4270 6270 3190

3. Reactions scheme and kinetics expressions

Table 3 Reaction rate constant, the adsorption equilibrium constant, and the reaction equilibrium constant for cyclohexane dehydrogenation.

3.1. Direct DME synthesis (exothermic side) boiling water. The generated heat in the tube side is continuously transferred to the endothermic side (shell compartment) and drives the dehydrogenation reaction. As a result, DME and hydrogen are produced in a recuperative reactor by achieving autothermal condition. A conceptual schematic for TCDR in co-current mode is provided in Fig. 2. The corresponding operating conditions are clubbed into Table 2. It worth to mention that, the operating conditions of conventional process including the catalyst load, inlet molar flow rate, inlet temperature of reacting materials and etc. are considered as the basic principles for the design of TCDR and achieving the endothermic side characteristics.

DME synthesis from syngas is consists of three exothermic reversible reactions. In this study, a bi-functional catalyst has been used which is made of the commercial catalysts of methanol synthesis (CuO/ZnO/Al2O3) and methanol dehydration (g-Al2O3) with a mass ratio 1:1. The following reactions are considered as independent reactions in the direct synthesis of DME from syngas.

CO þ 2H2 4CH3 OH

DH298K ¼ 90:55 kJ=mol

(1)

CO2 þ 3H2 4CH3 OH þ H2 O

DH298K ¼ 49:43 kJ=mol

(2)

2CH3 OH4CH3 OCH3 þ H2 O DH298K ¼ 21:003 kJ=mol 2.3. Thermally coupled membrane DME reactor (TCMDR) Innovations in catalytic reactor technologies, which somehow could be the heart of chemical processes, are often the preferred starting point to revamp and improve the operability. Hence, a membrane feature of thermally coupled DME reactor is suggested here (see Fig. 3). Basically, the operation of TCMDR which is composed of three concentric tube reactors is similar to that of TCDR except with minor changes. As can be seen from Fig. 3, the DME synthesis and cyclohexane dehydrogenation take place in the inner and the middle compartments, respectively. In this novel configuration, the wall of endothermic side is coated by a PdeAg membrane to extract hydrogen from endothermic side into the third side (permeation side). According to Lechatelier’s principle,

The reaction rate expressions which have been selected from Nie and Fang (2004) together with reaction constants have been reported in our previous work (Vakili et al., 2011). 3.2. Dehydrogenation of cyclohexane (endothermic side) Today, hydrogen carriers such as cyclohaxane are considered for hydrogen storage and transmission because of main advantages from the following points of view (Itoh et al., 2003; Jain et al., 2010):  Higher hydrogen content (e.g., 7.1 wt.% of cyclohexane) which is very attractive compared with metal hydrides (at most 3 wt.%).

Table 4 Mass and energy balance equations, pressure drop equation and corresponding boundary conditions. Definition

Equation

Exothermic and endothermic sides Mass and energy balances for solid phase


 av cj kgi;j ygi;j  ysi;j þ hj ri;j rb ¼ 0

(6)

N

 X hj ri;j DHf ;i ¼ 0 av hf Tjg  Tjs þ rb

(7)

Mass and energy balances for fluid phase

i1


 pDj 1 dFi;j þ avj cj kgi;j ysi;j  ygi;j  b J ¼ 0  AC dz AC H2 
g
 Cpgj d Fj Tj  g  g pDj pDj g g g  T  T1  b T  T3 ¼ 0 U U  þ avj hf Tjs  Tj AC AC 12 2 AC 23 2 dz

(8)

(9)

Pressure drop equation

dP 150m ð1  3 Þ2 Q 1:75r ð1  3 Þ Q 2 ¼ 2 þ fs dp dz Ac 33 33 A2c fs d2p

(10)

Boundary conditions

g g ; Pjg ¼ P0j z ¼ 00Fi;j ¼ Fi0;j ; Tjg ¼ T0j

(11)

Permeation side Mass and energy balances

dFi;j  þ 4pDj JH2 ¼ 0 dz 
ZT2 d Fj Tjg  g g g g CpH2 dT þ pDj U23 T2  T3 ¼ 0 þ pDj JH2 Cpj dz

(12)

(13)

T3

Boundary conditions

(3)

g z ¼ 00Fi;3 ¼ Fi0;3 ; T3g ¼ T0;3

(14)

32

R. Vakili et al. / Journal of Natural Gas Science and Engineering 9 (2012) 28e38

 More convenient for storage and transportation due to high boiling point (bp ¼ 80.7  C)  The dehydrogenated products, benzene and toluene, can be reversibly hydrogenated and reused and those are all liquids at ordinary temperatures.  Its essentially zero CO2 impact, giving a positive environmental contribution and also solves the troubles and problems in hydrogen storage conditions and medium preparation.

Table 6 Comparison between simulation results and Hu’s model. Parameters

The dehydrogenation of cyclohexane to benzene reaction is represented as follow:

C6 H12 4C6 H6 þ 3H2

DH298K ¼ þ206:2 kJ=mol

(4)

The following equation is used for cyclohexane dehydrogenation rate, rC (Itoh, 1987):


 3 P k KP PC =PH B 2
 rC ¼ 3 1 þ KB KP PC =PH 2

(5)

where k, KB, Pi, and KP are the reaction rate constant, the adsorption equilibrium constant for benzene, the partial pressure in Pa, and the reaction equilibrium constant, respectively, which are clubbed into Table 3. Pt/Al2O3 pellets are utilized for this reaction.

4. Mathematical modeling 4.1. Governing equations The following assumptions are considered for modeling of the proposed TCDR and TCMDR:  One-dimensional heterogeneous model is considered for both endothermic and exothermic sides.  The reactors are simulated under the steady-state condition.  Axial diffusion of heat and mass are neglected compared with the convection and bulk movement.  The radial diffusion in the catalyst particles is neglected in each side.  Packed beds have symmetry in both axial and radial directions (bed porosity is constant).  The gas mixture is considered as an ideal gas in both catalytic reactor sides.

Hu et al. (2008) Simulation result Relative error (%)

Output components (mole fraction) DME 0.0491 CO 0.0877 CO2 0.0671 Outlet temperature (K) 516.6

0.05 0.0903 0.064 519.5

1.8 2.8 4.8 0.56

 Heat loss to surrounding is neglected (insulated walls). In order to obtain the mass and energy balance equations, a differential fragment is selected along the axial direction inside the reactor. After writing steady state balances, the equations are divided by the length of the differential element, which is then approached zero. This work leads to a set of ordinary differential equations (ODEs). These governing equations as well as the related boundary conditions are summarized in Table 4. The pressure drop in fixed-bed reactor is calculated based on Ergun’s equation as is presented by Eq. (10) (Fogler, 1992). In Eq. (9), positive and negative signs are used for the exothermic and endothermic sides, respectively. Moreover, b is equal to zero for exothermic side and is one for endothermic side. In the mass balance equation of the permeation side, 4 is equal to 1 for hydrogen and zero for Argon. Auxiliary correlations related to heat transfer and physical properties should be added to solve the set of differential equations (see Table 5). The composite membranes in this study are made of a 6 mM thin layer of palladiumesilver alloy. The membrane is deposited as a continuous layer on the outer surface of a thermo stable support. The flux of hydrogen permeating through the outer Pd/Ag membrane is assumed to follow Sievert’s law. The accuracy of this model increases with temperature. According to the latest studies, reasonable results achieve when P20:5  P30:5 is below 600 Pa1/2. Sievert’s law is expressed by:

JH2

  EH ;p Q0 Exp  2
qffiffiffiffiffiffiffiffiffiffiffi qffiffiffiffiffiffiffiffiffiffiffi RT PH2 ;2  PH2 ;3 ¼

dH2

where PH2 and dH2 are hydrogen partial pressure in Pa and the membrane thickness, respectively. The pre-exponential factor Q0 is taken to be 6:33  107 molm1 s1 Pa0:5 and the activation energy EH2 ;p is 15.7 kJmol1 (Chen, 2004; Shu et al., 1994).

Table 5 Auxiliary correlations. Parameter

Equation

Component heat capacity Mixture heat capacity Viscosity of reaction mixtures Mixture thermal conductivity Mass transfer coefficient between gas and solid phases

Cp ¼ a þ bT þ cT 2 þ dT 2 Based on local compositions Based on local compositions ug  103 kgi ¼ 1:17Re0:42 Sc0:67 i 2Rp ug Re ¼ Sci ¼

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1:43  107 T 3=2 1=Mi þ 1=Mj Dij ¼ pffiffiffi 1=3 1=3 2Pðvci þ vcj Þ2

Heat transfer coefficient between gas phase and reactor wall

Ref.

Lindsay and Bromley (1950) Cussler (1984)

m m rDim  104

1y Dim ¼ P y i i i ¼ j Dij

Overall heat transfer coefficient

(15)

1 1 Ai lnðDo =Di Þ Ai 1 ¼ þ þ U hi 2pLKw Ao ho   0:407 2=3 Cp m h 0:458 rudp ¼ m Cp rm K 3B

Wilke (1949)

Reid et al. (1997)

Smith (1980)

R. Vakili et al. / Journal of Natural Gas Science and Engineering 9 (2012) 28e38 Table 7 Optimization results of TCMDR, the applied strategy and parameters in DE algorithm.

33

1500

1000

Parameter

Value

The optimization results Initial molar flow rate of exothermic side (mol/s) Initial molar flow rate of endothermic side (mol/s) Exothermic inlet temperature (K) Endothermic inlet temperature (K) Inlet temperature of sweep gas (K)

0.594 0.112 513.4 513.4 454.0

Strategy and parameters Strategy Number of population (NP) Scaling factor (F) Crossover constant (CR)

DE/best/1/bin 50 0.8 0.8

Heat (W/m)

500

0

-500 Generated heat in the exothermic side Transferred heat from solid wall Consumed heat in the endothermic side Transferred heat from membrane surface Net transferred heat to the endothermic side

-1000

4.2. Numerical solution -1500

In order to solve the set of differential equations, the related ODEs are converted to non-linear algebraic equations by backward finite difference method. The inlet operating conditions of three sides are obvious. Hence, the GausseeNewton method in MATLAB programming environment is used to solve this initial value problem (IVP). The reactor length is divided to 100 sections (no grid dependency is observed) and the solution for one node is used as the initial conditions of the next one.

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Dimensionless length Fig. 5. Variations of generated, consumed and transferred heat in OTCMDR.

i h ObjFun ¼ XCO þ Xcyc þ 10yH2;3

(16)

5. Optimization

0:05 < F0;exo < 1:5 mol=s

(17)

5.1. Objective function & decision variables

0:05 < F0;endo < 1:5 mol=s

(18)

The present study seeks to identify the optimum design of the proposed configuration and maximizing DME and benzene productions as well as hydrogen recovery in TCMDR. Therefore, the sum of carbon monoxide and cyclohexane conversions and the hydrogen mole fraction in the permeation side is considered as objective function:

493 < T0;exo < 533 K

(19)

423 < T0;endo < 523 K

(20)

298 < T0;3 < 533 K

(21)

4.3. Model validation

a

b

535 530

Endothermic temperature (K)

525

Temperature (K)

520

520

510

500

500

480

490

460

CDR TCDR OTCMDR

520 515 510 505 500 495

TCDR OTCMDR

490 0

0.1

0.2

0.3

0.4

0.5

0.6

Dimensionless Length

0.7

0.8

0.9

1

480

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Dimensionless length

Fig. 4. Temperature profiles of (a) exothermic side, (b) endothermic and permeation sides in CDR, TCDR and OTCDMR versus reactor dimensionless length.

440

Temperature of permeation side (K)

In order to check the validity of the mathematical model and reaction rates under the simplified assumptions, the proposed CDR by Hu et al. (2008) is modeled and the achieved results are compared against our numerical predictions. The successful achievements regarding this step are depicted in Table 6.

The hydrogen mole fraction in above equation has been multiplied by ten to assimilate the order of magnitudes. Since, typical optimization parameters are equipment size, recycle flows and operating conditions like temperature, pressure and concentration; five decision variables are manipulated during the optimization process. These variables are the inlet molar flow rates and inlet temperatures of the exothermic and endothermic sides as well as the inlet temperature of the permeation side. The variation ranges of these variables are:

34

R. Vakili et al. / Journal of Natural Gas Science and Engineering 9 (2012) 28e38

a

b

415

0.06

390 375 360 345 330

0.04 0.03 0.052 0.048 0.046

0.01

300

0.96

0.98

1

0 CDR

TCDR

0

OTCMDR

0.1

0.2

0.3

CDR TCDR OTCMDR

0.4

0.5

0.6

0.7

CO2 mole fraction

0.15 0.14 0.13 0.12 0.11

0.9

1

CDR TCDR OTCMDR

0.07

0.16

0.8

Dimensionless Length

d 0.075

0.18 0.17

CO mole fraction

0.05

0.02

315

c

CDR TCDR OTCMDR

0.05

DME mole fraction

DME production (ton day-1)

405

0.065 0.06 0.055 0.05

0.1 0.045 0.09 0.04

0.08 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0

0.1

0.2

0.3

Dimensionless Length

e

-3

11

x 10

f

0.6

0.7

0.8

0.9

1

0.42

9 8

H2 mole fraction

0.0108 0.0106

7

0.0104

6

0.0102 0.9

0.95

1

5

0.4

0.34 0.335

0.38 0.33 0.325

0.36

0.96

0.98

1

4 CDR TCDR OTCMDR

0.34 3 2

0.32 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0

0.1

0.2

Dimensionless Length

g

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Dimensionless Length

0.04 CDR TCDR OTCMDR

0.035 0.03

H2O mole fraction

Methanol mole fraction

0.5

0.44

CDR TCDR OTCMDR

10

0.4

Dimensionless Length

0.025

0.038 0.036

0.02

0.034

0.015

0.032 0.9

0.95

1

0.01 0.005 0 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Dimensionless Length Fig. 6. (a) DME production, mole fraction of (b) DME, (c) CO, (d) CO2, (e) Methanol, (f) H2 and (g) H2O in various reactor.

1

R. Vakili et al. / Journal of Natural Gas Science and Engineering 9 (2012) 28e38

35

5.2. Constraints

6.1. Thermal behavior

The temperature of exothermic side should be higher than the endothermic temperature to have an appropriate heat transfer driving force. From another perspective, higher temperatures endanger the catalyst longevity and aggravate the probability of rapid catalyst deactivation due to sintering. Therefore, the maximum temperatures of the reaction sides are set to be lower than 533 and 523 in both sides, respectively (Nie and Fang, 2004; Itoh, 1987). The following constraints are applied to control this optimization problem:

Fig. 4(a) illustrates the temperature profile of the exothermic side in CDR, TCDR and OTCDMR as a function of reactor dimensionless length. The trend of the temperature profile variations in the exothermic reactions is crucial in the reaction progress. Since, at the reactor entrance the reaction kinetic is predominant, temperature surge (high temperature) is in favor of reaction rate and conversion enhancement. By the time, the thermodynamic equilibrium will prevail and the temperature profile declines to augment production yield. Based on the above descriptions, the OTCMDR reminds the most favorable temperature history along the reactor length since it provides the highest temperature at the reactor inlet and reduces it to the minimum amount at the outlet (Fig. 4(a)). The temperature profiles along the endothermic and permeation sides of TCDR and OTCMDR are compared in Fig. 4(b). Fig. 5 justifies the corresponding thermal behavior of OTCMDR. As can be seen, at the reactor entrance, the generated heat in the exothermic side precedes the transferred heat from solid wall which triggers to a hot spot. As the temperature goes up, the exothermic reaction reaches to its equilibrium and the generated heat of exothermic side decreases compared with the transferred heat. As a result, the temperature reduces gradually. On the contrary, the absolute heat which is transferred to the endothermic side (i.e. transferred heat from the exothermic and permeation sides) is less compared with the consumed heat by the endothermic reaction. As a result a deep is created in its temperature profile (Fig. 4(b)). Afterward, the temperature amplifies up to dimensionless length ¼ 0.45 and diminishes further.

Texo >Tendo

(22)

max Texo  533

(23)

max  523 Tendo

(24)

out out  FDME;CDR FDME

(25)

FCout  FCout 6 H6 6 H6 ;TCDR

(26)

The last two terms (Eqs. (25) and (26)) confirm DME and benzene enhancements in the optimized thermally coupled membrane DME reactor (OTCMDR) compared with other configurations. The above constraints are considered in the optimization procedure using penalty function. The penalty function method eliminates the unacceptable results. This method involves penalizing the objective function in proportion to the extent of constraint violation (i.e., the penalty function takes a finite value when a constraint violates and a value of zero when constraint is satisfied) (Edgar et al., 2001). In this study, the penalty parameter is 108 however it may change from problem to problem. The ultimate objective function for minimization is as follows:

Result ¼ ObjFun þ 108

3 X

G2i

(27)

i¼1

where:

G1 ¼ maxf0; ðTendo  Texo Þg

(28)

 max 

 533 G2 ¼ max 0; Texo

(29)

 max 

 523 G3 ¼ max 0; Tendo

(30)

o n
out out G4 ¼ max 0; FDME;CDR  FDME

(31)

o n
 FCout G5 ¼ max 0; FCout 6 H6 ;TCDR 6 H6

(32)

More details about DE algorithm, its strategies and also adaptation of operating parameters have been presented in previous works (Babu and Munawar, 2007; Babu and Angira, 2006).

6.2. Molar behavior Generally, flow augmentation leads to residence time reduction and eventually lower extent of reaction. Surprisingly, the optimization procedure enables us to increases the exothermic feed molar flow rate of OTCMDR up to 8% compared with CDR and TCDR while the final DME mole fraction in the outlet stream remains constant. The DME production capacity boosts up to 38.6 ton/day (10.3%) and 42 ton/day (11.4%) compared with the CDR and TCDR, respectively. Fig. 6(a) and (b) proves these facts. Fig. 6(c)e(g) examines the molar behavior of exothermic elements. Table 8 evaluates the total value of exothermic and endothermic reaction rates in the TCDR and OTCMDR. As can be noticed, both exothermic and endothermic reaction rates are higher in the OTCMDR. This can be explained by the fact that the suggested configuration under the optimized conditions provides a superior temperature profile. In OTCMDR the initial molar flow rate of endothermic side declines about 120.3 kmol/h compared to the TCDR which offers a higher residence time. Implementing lower cyclohexane feed flow rate plus integration of membrane concept to the reactor (to overcome the equilibrium constraints and prevail the hydrogen production rate) recover the cyclohexane conversion and benzene mole fraction about 8.3% and 58% (Fig. 7(a) and (b)). Generally, the endothermic section of OTCMDR operates with the least feed flow

6. Results and discussion Table 7 lists the obtained results from optimization of TCMDR, the applied strategy and the employed parameters. The optimized thermally coupled membrane reactor (OTCMDR) is simulated based on the optimum identified values and the performance of this optimized configuration is compared with CDR and TCDR one’s.

Table 8 Values of reaction rates in TCDR and OTCMDR. Reaction rate (mol/s) R1 R2 R3 R4

(CO hydrogenation) (CO2 hydrogenation) (methanol dehydration) (cyclohexane dehydrogenation)

TCDR

OTCMDR

252.74 29.58 104.13 95

280.68 31.11 116.54 96.35

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R. Vakili et al. / Journal of Natural Gas Science and Engineering 9 (2012) 28e38

rate and highest cyclohexane conversion while benzene production does not change in comparison with TCDR. These facts recognize that utilizing OTCMDR is beneficial and has more economical feasibility due to higher production rates. Fig. 7(c) depicts hydrogen

0.9

Cyclohexane conversion

FH2 ;3 FC6 H12 ;in

(33)

7. Conclusion

0.7 0.6 0.5 0.4 0.3 0.2 TCDR OTCMDR

0.1 0 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Dimensionless length 0.18

b

0.16 0.14

Benzene mole fraction

Hydrogen recovery ¼

a

0.8

0.12 0.1

In our theoretical investigation the effect of membrane concept into a thermally coupled heat exchanger reactor is examined for hydrogen and direct DME production. Besides, the best configuration with the optimal geometric and operating variables is followed in order to improve the reactor performance. Even minor improvements in production efficiency may result in significant profit increase, energy conservation and environmental protection, especially for such large-scale units. The simulation results show that the temperature profile of exothermic side in OTCMDR improves in comparison with other configurations. The DME production increases about 10.3% and 11.4% relative to CDR and TCDR. Besides, cyclohexane conversion raises about 8.3% compared with that of TCDR while the endothermic feed flow rate decreases 120.3 kmol/h. Therefore, utilizing OTCMDR not only enhances the net profit of plant owing to more DME production also reduces operational costs owing to reduction in endothermic feed flow rate. As far as, this is a relatively new concept in Chemical engineering and Reactor design, immediate needs for theoretical studies are tangible. Mathematical modeling in conjunction with the optimization strategy helps policy makers to identify promising technologies as well as the advantages and disadvantages of such a configuration. In addition, it can contribute to considerable savings in money and time during the expensive stage of pilot plant development. However, the lab scale experiment along with the optimal investigation is considered as the subsequent step in the road toward successful commercialization of this configuration.

0.08

Notations 0.06 0.04 TCDR OTCMDR

0.02 0 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Dimensionless length 0.06

3

0.05

2.5

0.04

2

0.03

1.5

0.02

1

0.01

0.5

0

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Hydrogen recovery

c

H2 mole fraction

recovery and hydrogen mole fraction in the permeation side of OTCMDR. Hydrogen recovery is defined as:

0 1

Dimensionless length Fig. 7. (a) Cyclohexane conversion and (b) benzene mole fraction in the endothermic side, (c) hydrogen recovery and hydrogen mole fraction in the permeation sides.

av AC Ai Ao C Cp CpH2 dp Di Dij Dim Do fi F G hf hi ho

DHf,i JH2 ki kg K

specific surface area of catalyst pellet (m2 m3) cross section area of each tube (m2) inside area of inner tube (m2) outside area of inner tube (m2) total concentration (mol m3) specific heat of the gas at constant pressure (J mol1) specific heat of hydrogen at constant pressure (J mol1) particle diameter (m) 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) partial fugacity of component i (bar) total molar flow rate (mol s1) mass velocity (kg m2 s1) gasesolid heat transfer coefficient (W m2 K1) heat transfer coefficient between fluid phase and reactor wall in exothermic side (W m2 K1) heat transfer coefficient between fluid phase and reactor wall in endothermic side (W m2 K1) enthalpy of formation of component i (J mol1) hydrogen permeation flux (mol m2 s1) reaction rate constants mass transfer coefficient for component i (m s1) conductivity of fluid phase (W m1 K1)

R. Vakili et al. / Journal of Natural Gas Science and Engineering 9 (2012) 28e38

KB Kfi Ki Kp Kpi Kw L Mi N

P Pi rCO rCO2 rDME rC R Rp Re Sci T Tj,max ug U vi yi Z

h 3B 3

rb rs m 4s

adsorption equilibrium constant for benzene (Pa1) equilibrium constant of reaction i in DME synthesis adsorption equilibrium constant for component i in DME synthesis reaction equilibrium constant for dehydrogenation reaction (Pa3) equilibrium constant based on partial pressure for component i in methanol synthesis reaction thermal conductivity of reactor wall (W m1 K1) reactor length (m) molecular weight of component i (g mol1) number of components (N ¼ 8 for DME synthesis reaction, N ¼ 4 for cyclohexane dehydrogenation reaction, N ¼ 2 for third side) total pressure (for exothermic side: bar; for endothermic side: Pa) partial pressure of component i (Pa) rate of reaction for hydrogenation of CO (mol kg1 s1) rate of reaction for hydrogenation of CO2 (mol kg1 s1) rate of reaction for dehydration of methanol (mol kg1 s1) rate of reaction for dehydrogenation of cyclohexane (mol m3 s1) universal gas constant (J mol1 K1) particle radius (m) Reynolds number Schmidt number of component i temperature (K) maximum temperature in jth side linear velocity of fluid phase (m s1) overall heat transfer coefficient between exothermic and endothermic sides (W m2 K1) atomic diffusion volumes mole fraction of component i (mol mol1) axial reactor coordinate (m) catalyst effectiveness factor void fraction of catalytic bed catalyst void fraction density of catalytic bed (kg m3) density of catalyst (kg m3) viscosity of fluid phase (kg m1 s1) sphericity factor

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