Modeling and simulation of simulated countercurrent moving bed chromatographic reactor for oxidative coupling of methane

Chemical Engineering Science 64 (2009) 5143 -- 5152

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Modeling and simulation of simulated countercurrent moving bed chromatographic reactor for oxidative coupling of methane Prodip K. Kundu, Yan Zhang, Ajay K. Ray ∗ Department of Chemical and Biochemical Engineering, University of Western Ontario, London, ON, Canada N6A 5B9

A R T I C L E

I N F O

Article history: Received 10 March 2009 Received in revised form 17 August 2009 Accepted 20 August 2009 Available online 6 September 2009 Keywords: Simulated countercurrent moving bed chromatographic reactor (SCMCR) Oxidative coupling of methane (OCM) Multifunctional reactor Integrated reaction and separation

A B S T R A C T

Oxidative coupling of methane (OCM) is a reaction of industrial importance but per pass equilibrium conversion and product yield in a single reaction column is severely low. The simulated countercurrent moving bed chromatographic reactor (SCMCR) has been reported to significantly improve the methane conversion and C2 -product yield. This paper addresses the mathematical modeling of a five section SCMCR for OCM, which is particularly important for understanding the operation of this SCMCR system. In order to obtain the various process parameters, a realistic and rigorous kinetics was adopted in reactors for OCM and subsequently a kinetic model was developed which can best describe the associated kinetics of OCM in SCMCR. Adsorption isotherm parameters were then derived based on the experimental breakthrough curves acquired using single adsorption column. The proposed mathematical model demonstrated extremely good predictions of the experimental results. Finally, effects of operating parameters, such as switching time, methane/oxygen feed ratio, raffinate flow rate, eluent flow rate, etc., on the behavior of the SCMCR were studied systematically. © 2009 Published by Elsevier Ltd.

1. Introduction Hybrid processes like simulated countercurrent moving bed chromatographic reactor (SCMCR) with integrated separator, have been gaining an increasing amount of attention in recent years in which chemical reaction and separation takes place concurrently. The coupling of two conventional processes into a single apparatus has the potential for making significant improvements in process efficiency and it has been proved that this integrated process can increase process performance substantially, especially for the equilibrium limited reactions (Ray et al., 1990, 1994; Lode et al., 2001). Usually, a SCMCR system consists of a series of interconnected columns packed with catalyst and adsorbent. Feed enters in a particular column for a predetermined length of time, known as switching time and then is shifted to next column. Product streams are also advanced simultaneously. The shifting of the feed and product positions in the direction of the fluid flow thus mimics movement of solids in the opposite direction, simulating the continuous countercurrent flow of fluid and solid phases without the associated problems of actual movement of solids. Studies have been carried out to evaluate the applicability of SCMCR to several categories of reactions, such as esterification

∗ Corresponding author. Tel.: +1 519 661 2111x81279; fax: +1 519 661 3498. E-mail address: [email protected] (A.K. Ray). 0009-2509/$ - see front matter © 2009 Published by Elsevier Ltd. doi:10.1016/j.ces.2009.08.036

(Duennebier et al., 2000; Kawase et al., 1996; Lode et al., 2001; Mazzotti et al., 1996; Migliorini et al., 1999; Yu et al., 2003), etherification (Zhang et al., 2001a), hydrogenation (Ray et al., 1994; Ray and Carr, 1995a, 1995b), isomerization (Hashimoto et al., 1983; Ching and Lu, 1997; Zhang et al., 2004, 2007), oxidative coupling reaction of methane (Bjorklund et al., 2001; Tonkovich and Carr, 1994), reactions involving sugar (Azevedo and Rodrigues, 2001) and so on. Although a reasonable number of experimental and simulation studies on SCMCRs have been reported in the literature, there are very few reported applications of SCMCRs in the chemical industry because of the complexity of the processes and the large amount of kinetic and physical parameters required. A more detailed understanding and criteria for operating SCMCRs are needed before successful applications can be achieved. In this work oxidative coupling of methane (OCM) to ethane and ethylene is investigated in SCMCR. OCM is particularly important because ethylene is precursor to many other reaction products. Methane, the primary constituent in natural gas is present in abundance worldwide could easily be converted to ethane and ethylene through OCM. This has many advantages including the use of large national reserves of natural gas and the environmental advantage of natural gas combustion while decreasing the demand for other fossil fuels as ethylene is currently produced from oil based feed stock (naphtha, NGL, LPG, gas oil and refinery waste gas). But, conversion of methane per pass in a single reaction tube is extremely low; this drives up the expense of a large scale operation. According to

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estimates by MOBIL, a selectivity of 88% towards C2 products at a 35% methane conversion is required for OCM to become viable (Kuo et al., 1989). Again it has been reported that with existing technology, C2 yields (defined as ethane plus ethylene) in excess of 30% would be required for a commercial successful process (Srivastava et al., 1992). Experimental investigation of OCM in SCMCR showed methane conversion of 65%, C2 selectivity of 80% and C2 yield slightly better than 50% can be obtained (Tonkovich et al., 1993; Tonkovich and Carr, 1994). This study aims to provide insights into the operation of the SCMCR for OCM by performing a systematic study on the modeling and simulation of this process. A simplified mathematical model mimicking experimental conditions was developed and solved using numerically tuned kinetic and adsorption parameters. The SCMCR model-predicted results were then verified with that of experimental studies, and finally, sensitivity analysis were performed to investigate the effects of various parameters on the performance of the integrated reactor separator. By doing this, we intend to find the most important design and operating parameters of this process and provide useful guidance in selecting these parameters when they are scaled up to industrial size. 2. Oxidative coupling of methane in a SCMCR system Methane couples in presence of oxygen to form ethane and water. Ethane reacts with oxygen as well to form ethylene and water. The primary side reaction is the complete oxidation of methane to form carbon dioxide. The reaction scheme of OCM is as follows: 2CH4 + 12 O2 → C2 H6 + H2 O

(1)

C2 H6 + 12 O2 → C2 H4 + H2 O

(2)

CH4 + 2O2 → CO2 + 2H2 O

(3)

The oxidative coupling reaction occurs catalytically at elevated temperature (750 ◦ C). The reaction must take place at oxygen lean environment to avoid forming complete oxidation products and the conversion of methane in a single reactor is very low. In order to increase the conversion of methane, a novel SCMCR system was first developed by Tonkovich et al. (1993) for OCM. Fig. 1 demonstrates the experimental arrangement of the SCMCR for OCM. Three incoming fluid streams (feed, carrier gas and eluent) and two outgoing fluid streams (extract and raffinate/carrier gas removed) divide the SCMCR system into five sections (P, Q, R1, R2 and S). Each section contains one high temperature reaction column followed by two low temperature separation columns. Reactors are packed with samarium oxide (Sm2 O3 ) powder as catalyst and separators are packed with activated charcoal as adsorbent. The feed is moved from section to section at a rate faster than the reactant breakthrough time. A primary carrier gas is fed to the system one section behind the feed section. This carrier stream desorbs the reactants adsorbed during the previous cycle and adds them to the new feed. The strongly-sorbed products are desorbed with the aid of an additional carrier gas three sections behind the feed. An isolated purge gas is placed ahead of the feed section to remove all residual material. Details of this SCMCR system can be found elsewhere (Tonkovich and Carr, 1994). 3. Mathematical models 3.1. Reaction kinetics Selection of catalyst is important for OCM because there is a trade-off between high selectivity and activity for most catalysts. Samarium oxide was selected as the catalyst of this SCMCR system in consideration of this trade-off (Keller and Bhasin, 1982; Otsuka

Fig. 1. Schematic diagram of the experimental apparatus of SCMCR for OCM (Tonkovich and Carr, 1994).

and Jinno, 1986). Reaction mechanism and kinetics of OCM over Sm2 O3 has been studied widely by Otsuka and co-workers (Otsuka and Jinno, 1986; Otsuka et al., 1985, 1986). In this study, a similar kinetics model was adopted for the study of OCM using SCMCR as follows:  ri = ki ×

Km × CCH4 1 + Km × CCH4

ai

 ×

Ko × CO2 1 + Ko × CO2

bi (4)

where i refers to both reactants (CH4 and O2 ) and products (C2 H6 , C2 H4 and CO/CO2 ); Km and Ko are the equilibrium constants for the adsorptions of CH4 and O2 on catalyst surface; CCH4 and CO2 are the mole concentration of CH4 and O2 in fluid phase; ki , ai , bi are the kinetic parameters to be determined by fitting the experimental data of OCM over Sm2 O3 reported by Otsuka and Jinno (1986). 3.2. Adsorption isotherm Adsorption isotherm plays an important role during the modeling of SCMCR process. For the OCM reaction, there are up to six components in the system. To precisely describe the adsorption isotherm of such a system is very difficult. Since the concentrations of the components in the system are quite low, it is proposed that a linear adsorption isotherm is accurate enough. qi = Ki Ci

(5)

P.K. Kundu et al. / Chemical Engineering Science 64 (2009) 5143 -- 5152

In this work isotherm parameters were obtained by fitting the experimental breakthrough curves for each component (Tonkovich et al., 1993) to the solution of mathematical model equations of a single adsorption column. Genetic algorithm (Goldberg, 1989; Bhaskar et al., 2000; Kasat and Gupta, 2003; Zhang et al., 2001b, 2006; Rangaiah, 2009) was used as optimization tool to minimize the sum square errors between the experimental and model predicted results. 3.3. Mathematical model for SCMCR A SCMCR unit resembles a fixed bed chromatographic reactor except at the instant of column switching. The dynamic model for a fixed bed chromatographic reactor corresponding to each single column in the SCMCR unit can be developed by adopting an equilibrium dispersive model that also incorporates cyclic port switching. Although equilibrium dispersive model may seem to be too simplified for such a complicated process, the use of more complex models is hindered by two obstacles. First, if full diffusion models (Guiochon et al., 1994) were adopted for both reaction and adsorption for this system, how to solve these models would be a big issue. Second, the full diffusion models contain large numbers of uncertain kinetic parameters; regression to determine the parameters of complex nonlinear models is both difficult and unreliable. Furthermore, for the purpose of gaining insights into the system behavior, it is usually preferable to obtain simpler models that bring out the key features and components of the system. For these reasons, the simplified mathematical models were used in this study. In addition, it is assumed that there is no separation occurring in the reaction column and no reaction taking place in the separation column. Reaction rate constants are set to zero in the separation columns, likewise adsorption equilibrium constants are set to zero in the reaction columns. Thermal effect was not considered in this work for the lack of the relative experimental data. The transient model equations of this SCMCR are summarized in Table 1. Table 1 Transient model equations of the SCMCR for OCM.

The mass balance equations (Eqs. (6) and (7)), initial and boundary conditions as well as kinetic equation (Eq. (4)) and adsorption isotherm (Eq. (5)) completely define the SCMCR system. Mass balance equations can be reduced to a system of ordinary differential equations of initial value problem by method of lines (Schiesser, 1991). In this technique, PDE is first discretized in space using the finite difference method (FDM) to convert the system into a set of several coupled ordinary differential equation (ODE) initial value problems (IVPs), and the system of resultant ODE, which is usually stiff, were solved with DIVPAG subroutine (based on Gear's method) in the IMSL library (Gear, 1971). The concentration profiles are obtained from the solution of the above equations. The first objective of this work is to validate the model predicted results with that of reported experimental data. Subsequently, we will determine whether we can achieve a higher conversion, selectivity and yield for oxidative coupling reaction of methane in SCMCR through systematic optimization. Therefore, the design of the SCMCR configuration and operating conditions to be used therein must be set such that conversion of the limiting reactant CH4 (XCH4 ), yield (YC2 ) and selectivity (SC2 ) of the desired product (C2 H6 and C2 H4 ) are maximized at the product withdrawal port. The above quantities are defined as follows XCH4 =

=

*t



uj *Cij

(N)

+

1 − R

−

R *Z

R



SC2 =

i rij(N) = Di

*Z 2

j = R1 , . . . , R4

(6)

j = S11 , S12 , . . . , S41 , S42

(7)

(1 − )

 ts 0

(N) 2 H6 ,S12

[2CC

(N) 2 H4 ,S12

+ 2CC

(N)

+ CCO

2 /CO,S12

 · CCH4 ,f · ts

( −  +  + )

 ts 0

(N) 2 H6 ,S31

[2CC

(N) 2 H4 ,S31

+ 2CC

]|Z=L dt

(N)

+ CCO

 · CCH4 ,f · ts

2 /CO,S31

|]Z=L dt

(10)

[2 × moles of C2 (C2 H6 + C2 H4 ) collected in extract] [2 × moles of C2 (C2 H6 + C2 H4 ) + moles of C1 (CO2 /CO)] collected in extract  ts

=

(N) 2 H6 ,S31

(N) ]|Z=L 2 H4 ,S31

[2CC

+ 2CC

(N) [2CC H ,S31 0 2 6

(N) 2CC H ,S31 2 4

=  ts

YC2 =

2

* Cij(N)

[(2 × moles of C2 (C2 H6 + C2 H4 ) + CO2 /CO) collected in extract and raffinate] [moles of CH4 fed]

+

Mass balance equation in reactors

*Cij(N)

5145

0

+

dt

(N)

+ CCO

2 /CO,S31

(11)

]|Z=L dt

[2 × moles of C2 (C2 H6 + C2 H4 ) collected in extract] [moles of CH4 fed] ( −  +  + )

 ts 0

(N) 2 H6 ,S31

[2CC

(N) ]|Z=L dt 2 H4 ,S31

+ 2CC

 · CCH4 ,f · ts

(12)

Mass balance equation in separators

*Cij(N) *t

 +

1 − S



S

*q(N) ij *t

uj *Cij

S *Z

4. Results and discussion

2

(N)

+

= Di

* Cij(N) *Z 2

4.1. Adsorption and reaction kinetic parameters

Initial conditions N = 0;

(0)

(0)

Cij = 0;

qij = 0;

(8a)

N ⱖ 1; Ci,j = Ci,j+3 for j = 1 to (Ncol − 3); Ci,j = Ci,j+3−N (N)

(N−1)

(N)

(N−1)

col

for j=(Ncol −2) to Ncol (8b)

Boundary conditions Ci,R |Z=0 = (1 − )Ci,N |Z=L + Ci,f (N)

(N)

1

(N)

col

(N)

Ci,R |Z=0 = Ci,S |Z=L 2

(N)

Ci,R |Z=0 = 3

(N)

12

32

(N)

Ci,R |Z=0 = 4

for raffinate/carrier gas removal point

(1 − ) (N) C |Z=L (1 −  + ) i,S22 (N)

Ci,S |Z=0 = Ci,S |Z=L 31

for feed point

for eluent point

for product take off point

(1 −  − ) (N) Ci,S |Z=L 32 (1 − )

for carrier gas injection point

(9a)

(9b)

(9c)

(9d)

(9e)

In this study, reaction kinetics parameters were obtained in two steps by fitting the literature available experimental data (Otsuka and Jinno, 1986) to the kinetics model (Eq. (4)). In the first step, the values of Km , Ko and kCH4 were determined by fitting the experimental data shown in Fig. 2. Results of these three parameters were listed in Table 2. In the second step, kinetic parameters for the products of C2 H6 , C2 H4 and CO2 /CO were derived by fitting the experimental data illustrated in Fig. 3 using Sigma Plot which is based on Marquardt (1963) method and results are given in Table 3. It can be seen that most of the fitting curves in Fig. 3 are in good agreement with the experimental data. Adsorption isotherm parameters of each component were obtained by fitting the breakthrough curves of CH4 , C2 H6 and C2 H4 in a single adsorption column as shown in Fig. 4. Experimental details on getting these breakthrough curves can be found elsewhere (Tonkovich, 1992). The adsorption equilibrium coefficients (K) as well as the apparent axial dispersion coefficients (D) for species CH4 , C2 H6 and C2 H4 are given in Table 4. It should be stressed that all

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P.K. Kundu et al. / Chemical Engineering Science 64 (2009) 5143 -- 5152

0.008 pO2. RCH4-1 (k Pa. μmol-1.min.m2)

750°C 700°C 0.006

650°C 600°C

0.004

0.002

0.000 0.0

0.5

1.0

1.5 pO2 (k Pa)

2.0

2.5

3.0

pCH4. RCH4-1 (k Pa. μmol-1.min.m2)

0.10

750°C

0.08

700°C 650°C

0.06

600°C 0.04

0.02

0.00 0

10

20

30 pCH (k Pa)

40

50

60

4

Fig. 2. Fitting of experimental data at different temperatures: (a) when CH4 pressure is kept constant; (b) when O2 pressure is kept constant.

The system is found to reach steady state within 100 port switches represented by N in Fig. 5. It can be seen that the concentrations of the C2 H4 , C2 H6 and CO/CO2 within the SCMCR system do increase with time, while the concentration of CH4 decrease significantly. Under the operating conditions used, conversion of CH4 can reach 69.3%, while the selectivity and yield of product can reach 71.0% and 49.0% respectively. This is much higher than the equilibrium conversion of 2–16% (Tonkovich, 1992) in a single column fixed bed reactor at the same operating temperature. The shapes of the concentration profiles of CH4 and CO2 /CO are about the same. This is due to the fact that both of them have low dispersion coefficient (D) and low adsorption desorption coefficient (K), which means they are weakly adsorbed in the adsorption columns and pass through the separation column quickly within the switching period. The shapes of the concentration profiles of the desired products (C2 H6 and C2 H4 ) are also quite similar. Note that in the separators, the concentration profile shows oscillating behavior and the magnitude of the oscillation is decreasing along the flow direction. This is possibly due to the high values of adsorption coefficient (K) of both components. The adsorption of the two components on the activated charcoal is very strong and therefore, they cannot break through within one switching period. The oscillating profile is actually a build-up effect of several switching. The concentration profile of O2 is unique compared to other components. Concentration of oxygen drops significantly in the first reactor. This may be because the design intention is to make the amount of O2 limiting so that methane or its product (C2 H4 and C2 H6 ) cannot be oxidized further and the selectivity remains high. For SCMCR system, effective separation of the products is accomplished by appropriately selecting the switching time and fluid phase velocity such that the more strongly adsorbed component travels with the solid phase while the component with the weaker affinity travels with the fluid phase (especially for section P and S). There is a complex interplay of the various operating parameters of the SCMCR, namely, switching time (tS ), fluid flow rate in each section j(Qj ), fraction of feed (), raffinate collected (), eluent in flow (), carrier gas feed (), reaction temperature (TR ), and methane to oxygen feed ratio (Rf ). All of these operating parameters are very crucial for the design and operation of SCMCR and eventually alters the values of XCH4 , SC2 and YC2 . 4.3. Effects of operating parameters on SCMCR performance

Table 2 Kinetic parameters of CH4 and O2 a TR (◦ C)

Ko (Pa−1 )

Km (Pa−1 )

kCH4 (mmol min−1 m−2 )

kO2 (mmol min−1 m−2 )

600 650 700 750

1118 300 500 600

54 37 102 111

0.994 3.414 6.648 19.21

7.456 2.56 4.987 14.408

a Values of a and b for CH4 and O2 are fixed at 1.0 when fitting Eq. (1) to the experimental data in Fig. 1.

the parameters listed in Table 4 were derived based on the porosity of separation columns (S ) being 0.5, which was predetermined by simulations. Due to the lack of experimental data for the adsorption of CO2 /CO and O2 on activated charcoal (the adsorbent), the adsorption parameters for CO2 /CO and O2 could not be obtained. Hence, in this work, it is assumed that CO/CO2 and O2 have the same K value as CH4 , and have almost the same D value as CH4 also. 4.2. Dynamic behavior of SCMCR system Dynamic behavior of the SCMCR system at different time was illustrated in Fig. 5 with the operating parameters listed in Table 5.

4.3.1. Effect of switching time, ts Switching time (ts ) plays a key role in determining the performance of a SCMCR unit. In Fig. 6, model predicted results are compared with available experimental results at different ts . The figure reveals that the model predictions are in good agreement with the experimental results (Tonkovich and Carr, 1994), except that the model predictions are quite smooth while experimental results are at times slightly erratic due to experimental error. At the reference conditions (Table 4), the conversion is maximum 70.7% at ts of 28 s; experimentally, maximum conversion of 65% was achieved when ts was 27 s. Two major causes lead to the difference between the model prediction and the experimental data. One reason is the simplified mathematical models used in this study. In the mathematical models we neglected the pore diffusion within the catalyst and the adsorbent which may be significant in the real operation of the SCMCR. Secondly, the negligence of the thermal effect on the reaction could also result in the deviations of the model prediction from the experimental data. The effect of ts is quite pronounced. Both conversion and selectivity are a strong function of switching time. An optimal switching time exists which maximizes conversion. When ts is far lower than the breakthrough time, conversion drops. It is expected since there

Rate of production (µmol/min/m2)

1000

60

1400

60

Rate of production (µmol/min/m2)

Rate of production (µmol/min/m2)

600

2500

Rate of production (µmol/min/m2)

Rate of production (µmol/min/m2)

2000

Rate of production (µmol/min/m2)

P.K. Kundu et al. / Chemical Engineering Science 64 (2009) 5143 -- 5152

3500

1800 1600 1400 1200 Model predicted Experimantal data

1000 800 0

10

20 30 40 pCH4 (k Pa)

50

500 400 300 200 0

10

20 30 40 pCH4 (k Pa)

50

800 600 400 200 0 0

10

20 30 40 pCH4 (k Pa)

50

60

5147

2000 1500 1000 500 0.0

0.5

1.0

0 0.0

0.5

1.0

0.5

1.0

1.5 2.0 pO2 (k Pa)

2.5

3.0

1.5 2.0 pO2 (k Pa)

2.5

3.0

2.5

3.0

1200 1000 800 600 400 200

3000 2500 2000 1500 1000 500 0 0.0

1.5 2.0 pO2 (k Pa)

Fig. 3. Fitting of production rate: (a) for C2 H6 when pCH4 is varied keeping pO2 = 0.98 kPa; (b) for C2 H6 when pO2 is varied keeping pCH4 = 18.2 kPa; (c) for C2 H4 when pCH4 is varied keeping pO2 = 0.98 kPa; (d) for C2 H4 when pO2 is varied keeping pCH4 = 18.2 kPa; (e) for CO/CO2 when pCH4 is varied keeping pO2 = 0.98 kPa; (f) for CO/CO2 when pO2 is varied keeping pCH4 = 18.2 kPa.

Table 3 Values of unknown parameters (ki , ai and bi ) of C2 H6 , C2 H4 and C1 (CO, CO2 ). TR (◦ C)

Parameters

O2

CH4

750

a b k (mmol min−1 m−2 ) R2

1 1 14.41 –

1 1 19.21 –

700

a b k (mmol min−1 m−2 ) R2

1 1 4.99 –

650

a b k (mmol min−1 m−2 ) R2

600

a b k (mmol min−1 m−2 ) R2

– Not applicable.

C2 H6

C2 H4

CO/CO2

0.830 0.725 4.15 0.871

0.723 2.002 4.11 0.931

0 2.024 7.3 0.94

1 1 6.65 –

1.180 0.698 1.74 0.980

0.893 1.669 0.45 0.961

0.499 2.405 4.61 0.992

1 1 2.56 –

1 1 3.41 –

0.978 0.814 0.685 0.828

– – – –

0.777 1.768 3.32 0.991

1 1 7.46 –

1 1 0.99 –

1.213 −0.621 0.102 0.906

– – – –

0.843 2.457 1.06 0.992

is not enough time for all of the material, which adsorbed during the previous switching cycle, to desorb from the carrier section. The extra non-desorbed material which remains behind the feed section is lost at the extract port, consequently deteriorates the overall conversion. Again, if ts very close to the breakthrough time, conversion of methane was also found to drop. It is also reasonable since more material is added with the make-up feed than has an opportunity to react. With the increase in the amount of feed, there is an increase in concentration, and therefore, it no longer behaves linearly. The convective velocity of the material increases as a function of concentration which results in a decrease in breakthrough time. The concentrated reactant front moves with a faster convective velocity, which allows significant amount of reactant breaking through the separation column of the feed section, and this material is lost through the raffinate port as well as the extract port. Operating SCMCR at optimal ts is thus crucial in order to overcome reactant loss either through incomplete reactant desorption or early reactant breakthrough. Thus XCH4 is a decreasing function at both ends of the switching time spectrum due to the competing sources of methane losses. The effect of ts on SC2 is also obvious as shown in both Table 6 and Fig. 6(b). As ts decreases, SC2 increases dramatically. The selectivity drops to 65–75% at ts near the original breakthrough time while rising to over 93% at ts far less than the original breakthrough time.

P.K. Kundu et al. / Chemical Engineering Science 64 (2009) 5143 -- 5152

XCH4

0.12

0.08

0.04

Experimental Model predicted

1.5 1.0 0.5

35 Time (s)

40

45

0.0025

XC2H6

0.0020 0.0015 0.0010

Ra

2.0

0.10

N = 50

CH4 O2 C2H4 C2H6 CO/CO2

1.0 0.5

280 300 Time (s)

320

CCH4, CO2, CCO/CO2, mol/m3

260

340

0.0025 0.0020 0.0015

0.00

0.0 Ra

Ex C E Position along columns 0.10 N = 100

CH4 O2 C2H4 C2H6 CO/CO2

1.5 1.0

0.08 0.06 0.04

0.5

0.02

0.0

0.00 F

0.0010

0.06

0.02

2.0 240

0.08

0.04

F

220

XC2H4

E Ex C Position along columns

1.5

0.0005 0.0000

0.06

0.00 F

50

0.08

0.02

0.0

CCH4, CO2, CCO/CO2, mol/m3

30

0.10

0.04

0.00 25

CH4 O2 C2H4 C2H6 CO/CO2

N = 10

CC2H6, CC2H4, mol/m3

CCH4, CO2, CCO/CO2, mol/m3

2.0

CC2H6, CC2H4, mol/m3

0.16

CC2H6, CC2H4, mol/m3

5148

Ra

E

Ex C

Position along columns 0.0005

Fig. 5. Concentration profiles of CH4 , O2 , C2 H6 , C2 H4 and CO/CO2 at different number of switches.

0.0000 160

180

200

220 240 Time (s)

260

280

300 Table 5 Operating parameters for SCMCR system in Fig. 5.

Fig. 4. Experimental data and model predicted breakthrough curve for (a) methane; (b) ethane; (c) ethylene.

Table 4 Adsorption equilibrium coefficient and apparent dispersion coefficient for CH4 , C2 H6 and C2 H4 (S = 0.5). Component

K

D (m2 /s)

CH4 C2 H6 C2 H4

15.85 142.1 118.2

4.0×10−8 6.0×10−8 5.0×10−8

Among the factors that influence SC2 , the decreased contact time for the reactants is the most important one. The reduction of ts increases the solid phase pseudo velocity while decreasing the residence time of reactant in each section. If the rate of complete oxidation reaction is slower than the coupling reaction, then the reduced contact time will favor the formation of C2 products over the side products. If the side reaction to form carbon oxides occurs catalytically on the

SCMCR geometry

Operating parameters

dR = 6.35 mm LR = 508 mm R = 0.4 dS = 6.35 mm LS 1 = 76.2 mma LS 2 = 114.3 mma S = 0.5

TR = 750 ◦ C TS = 100 ◦ C Qp = 1.96×10−6 m3 /s  = 0.153 (1st switch), 0.034 (other switches)  = 1.7  = 0.034  = 0.85 tS = 30 s Rf = 2.47

a LS 1 and LS 2 refer to the lengths of the first and second separation columns in each section of SCMCR.

surface, rather than homogeneously, and if this surface reaction has a longer induction time than the gas phase coupling reaction, then shorter ts (shorter contact times) will preferentially actuate the desired methane coupling reaction over the undesired side reaction. Effect of ts on SCMCR performance can be easily understood by looking through the concentration profiles at different ts demonstrated in Fig. 7. It is noticeable from Fig. 7(a) that when ts is 21 s,

P.K. Kundu et al. / Chemical Engineering Science 64 (2009) 5143 -- 5152

5149

1.0 0.8 XCH4

1 0.6

2 3

0.4

Experimental Simulation

0.2 20

22

24

26 28 Switching time, ts (s)

30

32

ts = 21 s CH4 O2 C2H4 C2H6 CO/CO2

0.8 0.6

0.08 0.06 0.04

0.4 0.02

0.2 0.0

34

CC2H6, CC2H4, mol/m3

CCH4, CO2, CCO/CO2, mol/m3

1.0

0.00 F

Ra

E Ex C Position along columns

0.04

0.5

0.02

ts = 33 s

2.5 2.0

2

0.6 0.4

Experimental Simulation

0.2 20

22

24

26 28 30 Switching time, ts (s)

32

34

0.6 0.4 0.2 22

24

26 28 30 Switching time, ts (s)

Ra

E Ex C Position along columns

Fig. 7. Effect of switching time on steady state concentration profiles after 100 switching periods.

Experimental Simulation

20

0.00 F

1.0 0.8

0.0

CC2H6, CC2H4, mol/m3

2

1.0

CCH , CO , CCO/CO , mol/m3

SC2

0.8

YC2

1.5

0.12 CH4 O2 0.10 C2H4 C2H6 0.08 CO/CO2 0.06

4

1.0

32

34

Fig. 6. Effect of the switching time on the performance of the SCMCR after 100 switching periods.

Table 6 Effects of operating variables on XCH4 , SC2 and YC2 . XCH4 (%)

SC2 (%)

YC2 (%)

Figure

Reference runa

69.3

71.0

49.0

5c

ts = 21 s ts = 33 s QP = 1.5×10−6 m3 /s QP = 2.5×10−6 m3 /s  = 0.1  = 0.5  = 0.25  = 2.0 Rf = 2.0 Rf = 3.0  = 0.01  = 0.15  = 0.25  = 0.8

51.0 54.5 35.3 56.2 65.4 47.1 72.1 68.9 93.0 59.5 56.8 63.2 69.6 69.2

93.0 65.6 68.5 71.5 84.2 99.9 74.4 74.0 66.6 77.6 75.8 75.0 74.2 74.1

37.0 36.0 24.0 38.9 45.8 29.5 50.8 48.7 58.5 44.4 41.4 45.2 49.3 48.9

7a 7b 8a 8b 9a 9b 10a 10b 11a 11b – – – –

– Were not measured or plotted. a The operating conditions for the reference run are listed in Table 4. Operating parameters are the same as those of the reference run unless mentioned.

the concentration of unreacted CH4 and O2 are much higher than that of 30 s in section R2 (Fig. 5(c)). This explains the low conversion (51%) at short ts . Moreover, negligible amount of carbon dioxide is produced at shorter ts , which elucidates high selectivity (93%) in the extract stream. At longer ts , more CO/CO2 is generated in the section P as illustrated in Fig. 7(b) due to the enough reaction time of CH4 and O2 . Although a portion of CO/CO2 is collected at raffinate stream, still larger amount of CO/CO2 remains in the system and therefore, lowers the selectivity. 4.3.2. Effect of flow rate in section P, QP Selection of suitable QP is very important for the operation of SCMCR process since all the other internal flow rates are determined based on QP . In this SCMCR system, the main task of section P is to retain strongly adsorbed components (adsorption of C2 ) so that they do not breakthrough at the raffinate port where portion of the weakly adsorbed component is removed to increase the purity at extract. Part of unreacted CH4 , O2 (if present) and side products (CO/CO2 ) flow into section Q, where the column flow rate QQ [ = (1−)QP ] should be small enough to prevent these species breaking through into section R. The primary role of section Q is, therefore, retaining species currently in this section. Section R1 has the maximum flow rate, QR1 [ = (1−+) QP ]. The higher fluid phase velocity is beneficial to the performance of section R, which is responsible for desorbing C2 as well as unreacted CH4 , O2 so that C2 can be collected at extract port and this section is clean before the next port switching. The flow rate in section S, QS [ = (1−)QP ], is lower than QR1 after extract is removed as product. However, QS should be large enough to desorb CH4 and oxides of carbon from section S to be mixed with feed as the recycle to section P at the same time C2 should be retained in section S. For a particular ts , there seems to have a particular QP for which XCH4 and YC2 reach maximum and SC2 gets to maximum. This is particularly true for switching time near the breakthrough time.

0.02

0.2

0.01 0.00

0.0

CCH4, CO2, CCO/CO2, mol/m3

0.02

0.0

0.00

0.2

0.01 0.00

0.0

Ra

Ex C E Position along columns

E Ex C Position along columns

1.5

0.12 CH4 O2 0.10 C2H4 0.08 C2H6 CO/CO2 0.06

1.0

0.04

0.5

0.02

3.0

2

0.02

Ra

0.5

2

0.4

F

0.04

2.0

F

0.6

QP = 2.5×10-6 m3/s (150 ml/min)

0.8

1.0

2.5

E Ex C Position along columns 0.05 CH4 O2 0.04 C2H4 C2H6 CO/CO2 0.03

1.0

1.5

β = 0.1

4

Ra

CCH , CO , CCO/CO , mol/m3

F

CC2H6, CC2H4, mol/m3

CCH4, CO2, CCO/CO2, mol/m3

0.8

0.12 CH4 O2 0.10 C2H4 C2H6 0.08 CO/CO2 0.06

3.0

β = 0.5

2.5 2.0

0.0

CC2H6, CC2H4, mol/m3

0.4

QP = 1.5×10-6 m3/s (90 ml/min)

CCH4, CO2, CCO/CO2, mol/m3

0.6

0.05 CH4 O2 0.04 C2H4 C2H6 CO/CO2 0.03

1.0

CC2H6, CC2H4, mol/m3

P.K. Kundu et al. / Chemical Engineering Science 64 (2009) 5143 -- 5152

CC2H6, CC2H4, mol/m3

5150

0.00 F

Ra

E Ex C Position along columns

Fig. 8. Effect of QP on steady state concentration profiles after 100 switching periods with (a) QP = 1.5×10−6 m3 /s, XCH4 = 35.25%, SC2 = 68.5%, YC2 = 24.0%; (b) QP = 2.5×10−6 m3 /s, XCH4 = 56.2%, SC2 = 71.5%, YC2 = 38.9%.

Fig. 9. Effect of raffinate flow rate on steady state concentration profiles after 100 switching periods with (a)  = 0.1, XCH4 = 65.4%, SC2 = 84.2%, YC2 = 45.8%; (b)  = 0.5, XCH4 = 47.1%, SC2 = 99.9%, YC2 = 29.5%.

However, the increased fluid phase flow rate deteriorates the performance of section P, which plays the central role in the reaction. When the fluid phase flow rate is increased, the residence time is not sufficient for methane and oxygen to be completely consumed as well as adsorption of the products. Hence, the unconverted reactants will breakthrough at the raffinate port and thereby decrease XCH4 and YC2 . As QP increases, QQ also increases (for a particular ). Since higher QQ deteriorates column performance, unconverted reactant as well as CO/CO2 will travel with fluid phase and breakthrough at section R1. Thus YC2 suffers for high flow rate in section P. Performance of sections R and S improves when QP is increased. On the other hand, when QP is small, performance of sections P and Q enhances but performance of section S worsens. QS is not enough to desorb unreacted CH4 and side products CO/CO2 . They appear at the extract port in the next switching and thereby deteriorate overall performance. Table 6 lists the XCH4 , SC2 and YC2 values achieved at different QP . Fig. 9 depicts the effect of QP on the concentration profiles of the five components at pseudo-steady sate (N = 100). All other parameters are held same as shown earlier in Fig. 5(c). It is evident from Fig. 8 that performance of sections P and Q is deteriorated with increasing flow rate but enhanced performance in section S is found (Fig. 8(b)). On the contrary, performance of sections P and Q improves while section S worsens at lower QP (Fig. 8(a)).

selectivity and purity does not hamper. Heavier component can easily be retained in section Q. Cocurrent operation in this section is expected at optimal condition where anything elutes in section Q will travel with solid phase when column switches. Fig. 9 illustrates the effect of  on the concentration profiles of the five components at pseudo-steady sate (N = 100). All other parameters are kept the same as shown in Fig. 5(c). From the concentration profiles (Fig. 9(a) and (b)), it is clear that performance of section Q improves when  is increased (compared to Fig. 5(c)). From Table 6 it can be seen that when  increased to 0.1 from reference value of 0.034, SC2 increases to 84.2%, but XCH4 decreases to 65.4%. Little effect on YC2 is observed. Again when  is further increased to 0.5, which indicates that half of the fluid stream is withdrawn as raffinate, SC2 increases to 99.9% but XCH4 and YC2 decrease to 47.1% and 29.5% respectively. When  is further increased, selectivity remains unchanged at 99.9% though XCH4 and YC2 tend to decrease. For low switching time, this is not true because products are lost through the raffinate port before they get completely adsorbed.

4.3.3. Effect of raffinate flow rate/carrier gas removed,  The selection of , i.e., the flow rate ratio between raffinate and carrier gas, is important for the SCMCR performance also. For a particular QP , the value of QQ depends on the selection of . The higher the value of , the lower the QQ . Optimum QQ promotes adsorption of lighter components in section Q, and thereby, avoiding their elution to section R1. When  is further increased, significant reactant is lost through raffinate port, which reduces conversion, though

4.3.4. Effect of eluent flow rate,  Though relative separation factor for ethane and ethylene to methane and carbon dioxide (KC2 H6 /KCO/CO2 =8.96 and KC2 H4 /KCO/CO2 = 7.46) is quite large, the complete regeneration of the solid adsorbent is crucial for the successful separation of products. A high eluent flow rate helps in effectively cleaning the columns in section R by desorbing completely the strongly adsorbed component C2 . With a smaller switching time, section R1 is not completely regenerated because of tailing of its concentration front, and methane and oxides of carbon will appear at the extract port because of incomplete desorption in section S. On the other hand, with a longer switching time, product will breakthrough from section P and there will be some loss of products which is not desired. Therefore, the only way to further improve separation performance is to completely

0.5

0.02

0.0

1.5 1.0

0.04

0.5

0.02

0.0

0.00

CCH4, CO2, CCO/CO2, mol/m3

γ = 2.0

2.5 2.0

F

Ra

0.04

0.5

0.02 0.00 F

0.12 CH4 O2 0.10 C2H4 C2H6 0.08 CO/CO2 0.06

3.0

1.0

E Ex C Position along columns

Ra

3.0

E Ex C Position along columns

Fig. 10. Effect of eluent flow rate on steady state concentration profiles after 100 switching periods with (a)  = 0.25, XCH4 =72.1%, SC2 =74.4%, YC2 =50.8%; (b)  = 2.0, XCH4 = 68.9%, SC2 = 74.0%, YC2 = 48.7%.

regenerate section R1 by accurately adjusting the desorbent (solvent) flow rate. However, increase of purity is possible with further increase of eluent flow rate but that does not pay off due to the unnecessary operating cost associated with high eluent flow rate. Fig. 10 illustrates the effect of  on the concentration profiles for the five components at pseudo-steady sate (N = 100). When  is increased to 2.0 (compared to 1.7 in Fig. 5(c)), performance are almost same. When  is reduced to 0.25, it is obvious that section R1 is not completely regenerated (Fig. 10(a)). However, XCH4 , SC2 and YC2 do not change much with  as shown in Table 6. A slight decrease in conversion is expected since some unreacted methane that is not desorbed from section S is lost in the extract stream with higher eluent flow rate. There should be an optimal (a minimum) eluent flow rate beyond which performance does not improve with increase of eluent flow rate. 4.3.5. Effect of methane to oxygen ratio in make-up feed, Rf The feed ratio of methane to oxygen, Rf , has a strong effect on XCH4 and SC2 . Simulation results indicate that XCH4 decreases while SC2 and oxygen conversion increase as Rf increases; and product distribution has a more complex relationship with Rf . Running the system in an increasingly lean oxygen environment (higher Rf ), XCH4 decreases, meanwhile, SC2 increases because less amount of side products CO/CO2 are generated with less available O2 . In addition, when Rf increases, YC2 increases at low temperature but decreases at high temperature. Fig. 11 illustrates the effect of Rf on the concentration profiles of the five components at pseudo-steady sate (N = 100). If point 1 and 2 are compared, it is apparent that less oxides of carbon are produced when Rf is 3.0 instead of 2.0. Table 6 compares the SCMCR performance in terms of XCH4 , sC2 and YC2 at different Rf values. It is observed that XCH4 and YC2 can reach up to 93.0% and 58.5%

CCH4, CO2, CCO/CO2, mol/m3

Ra

1

1.5

0.0

0.00 F

2.0

Ex C E Position along columns

Rf = 3.0

2.5 2.0 1.5 2

1.0

0.12 CH4 O2 0.10 C2H4 C2H6 0.08 CO/CO2 0.06 0.04

0.5

0.02

0.0

2 4

0.04

2.5

0.12 CH4 O2 0.10 C2H4 C2H6 0.08 CO/CO2 0.06

2 6

1.0

Rf = 2.0

CC H , CC H , mol/m3

1.5

3.0 CCH4, CO2, CCO/CO2, mol/m3

2.0

0.12 CH4 O2 0.10 C2H4 C2H6 0.08 CO/CO2 0.06

CC2H6, CC2H4, mol/m3

γ = 0.25

CC2H6, CC2H4, mol/m3

CCH4, CO2, CCO/CO2, mol/m3

2.5

5151

CC2H6, CC2H4, mol/m3

P.K. Kundu et al. / Chemical Engineering Science 64 (2009) 5143 -- 5152

0.00 F

Ra

Ex C E Position along columns

Fig. 11. Effect of make-up methane to oxygen feed ratio on steady state concentration profiles after 100 switching periods with (a) Rf = 2.0, XCH4 = 93.0%, SC2 = 66.6%, YC2 = 58.5%; (b) Rf = 3.0, XCH4 = 59.5%, SC2 = 77.6%, YC2 = 44.4%.

respectively when Rf is 2.0 and fall to 59.5% and 44.4% when Rf is 3.0. SC2 , on the contrary, increases from 66.6% to 77.6% when Rf changes from 2.0 to 3.0. Optimal value of Rf is thus vital in operating SCMCR where conversion and selectivity will balance each other. 5. Conclusions The simulated countercurrent moving bed chromatographic reactor is a valuable process unit to improve reaction conversion. Oxidative coupling of methane reaction in SCMCR has been investigated in this paper. In order to obtain the various process parameters, a kinetic model was first developed which can best describe the associated kinetics of OCM in SCMCR. Adsorption isotherm parameters were then derived based on the available experimental breakthrough curves acquired using single adsorption column. The proposed mathematical model of SCMCR demonstrated extremely good predictions of the available experimental results. It is evident that the proposed mathematical model is robust and reliable and can describe the dynamic behavior of the SCMCR under various operating conditions. The effects of the different operating variables such as switching time, flow rate in section P, feed flow rate, raffinate flow rate, eluent flow rate, and methane to oxygen make-up fed ratio on the concentration profiles of the five components were investigated as well as the conversion of CH4 ; selectivity and yield to C2 H6 and C2 H4 were explained with respect to the trend for each of the single effect. A high conversion of CH4 , high selectivity and yield to C2 H6 and C2 H4 and nearly complete conversion of the limiting reactant, O2 can be achieved in SCMCR by selecting proper operating conditions. It is found that conversion reached as high as 93.0% and selectivity and yield reached 99.9% and 58.5% respectively, although not all simultaneously. It is also found that some of the process parameters not only alter the conversion, selectivity

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P.K. Kundu et al. / Chemical Engineering Science 64 (2009) 5143 -- 5152

and yield profoundly but also act in conflicting manners. There is a complex interplay between the parameters; when one improves, the other worsens. It is difficult to find a set of optimal conditions by trial and error because a desirable change in one performance criterion results in an unfavorable change in another desired variable. Systematic multi-objective optimization has to be carried out so that a set of optimal operating and design conditions can be found at which maximum conversion, selectivity and yield occurs. Notation C D k K Km Ko LR LS Ncol q Rf SC2 ts TR TS u XCH4 YC2 Z

concentration in the mobile phase, mol/m3 apparent axial dispersion coefficient, m2 /s reaction rate constant, mol/m3 /s adsorption desorption equilibrium constant reaction kinetic constant for methane, KPa−1 reaction kinetic constant for oxygen, KPa−1 length of reactor, m length of separator, m total number of the columns concentration in the stationary phase, mol/m3 methane to oxygen ration in feed selectivity of C2 (C2 H6 and C2 H4 ) at extract port, % switching time, s temperature of reactor, ◦ C temperature of separator, ◦ C superficial velocity, m/s conversion of methane, % yield of C2 (C2 H6 and C2 H4 ), % axial distance, m

Greek letters

      

fraction of feed fraction of raffinate withdrawn fraction of desorbent injected fraction of carrier gas injected porosity stoichiometric coefficient section

Superscripts and Subscripts Ex F i j N R Ra S

extract feed component index column index number of port switching reactor raffinate separator

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