Numerical simulation and optimisation of unconventional three-section simulated countercurrent moving bed chromatographic reactor for oxidative coupling of methane reaction

Numerical Simulation and Optimisation ofUnconventional Three-Section SimulatedCountercurrent Moving BedChromatographic Reactor for OxidativeCoupling of Methane ReactionProdip K. Kundu,1,2 Ajay K. Ray2 and Ali Elkamel1*

1. Department of Chemical Engineering, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1

2. Department of Chemical and Biochemical Engineering, University of Western Ontario, London, Ontario, Canada N6A 5B9

The simulated countercurrent moving-bed chromatographic reactor (SCMCR) has been reported to significantly enhance methane conversion andC2 product yield for oxidative coupling of methane (OCM) reaction, which is otherwise a low per pass conversion reaction. A mathematical modelof an unconventional three-section SCMCR for OCM was first developed and solved using numerically tuned kinetic and adsorption parameters.The model predictions showed good agreement with available experimental results of SCMCR for OCM. Effects of several process parameters onthe performance of SCMCR were investigated. A multi-objective optimisation problem was solved at the operating stage using state-of-the-artAI-based non-dominated sorting genetic algorithm with jumping genes adaptations (NSGA-II-JG), which resulted in Pareto Optimal solutions. Itwas found that the performance of the SCMCR could be significantly improved under optimal operating conditions.

Keywords: simulated moving bed reactor, multifunctional reactor, oxidative coupling of methane, optimisation, genetic algorithm, NSGA-II-JG,Pareto set

INTRODUCTION

Simulated moving bed (SMB) technology has been receiv-ing an increasing amount of attention in recent years asan alternative technique to elution chromatography and has

recently been widely applied in the petrochemical, biochemicaland fine chemical industries. Simulated countercurrent moving-bed chromatographic reactor (SCMCR) technology combines themore powerful and energy-saving separation technology of anSMB with a reversible chemical reaction usually in a seriesof interconnected columns packed with catalyst and adsorbent.Recent results have demonstrated that this integrated process canincrease process performance substantially, and at the same timecan improve process economics by reducing capital and operatingcosts, especially for the equilibrium limited reactions (Ray et al.,1994; Lode et al., 2001). A fixed bed is used in the SMB system andcountercurrent movement is simulated by successive switching ofthe feed and product take-off streams at timed intervals througha series of inlets located at intervals along a single column or

between a series of packed columns. The fixed bed is divided intoa number of segments with provision for adding feed to the streampassing from one segment to the next or of withdrawing a streamemerging from any segment. Feed enters in a particular columnfor a predetermined length of time, known as switching time andthen is shifted to next column. Product streams are also advancedsimultaneously. The shifting of the feed and product positions inthe direction of the fluid flow thus mimics movement of solidsin the opposite direction, simulating continuous countercurrentflow of fluid and solid phases while retaining advantages of con-tinuous countercurrent operation without the associated problems

∗Author to whom correspondence may be addressed.E-mail address: [email protected]. J. Chem. Eng. 89:1–12, 2011© 2011 Canadian Society for Chemical EngineeringDOI 10.1002/cjce.20663Published online in Wiley Online Library(wileyonlinelibrary.com).

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of actual movement of solids. SCMCR is a novel reactor by whichequilibrium (or otherwise) limited reactions can be forced towardscompletion through in situ separation of the products from thereactants as soon as the products are formed, and thus higherconversion, selectivity and yield relative to conventional processcan be achieved.

SCMCR has found its application in several categories of reac-tions, such as esterification (Duennebier et al., 2000; Lode et al.,2001), etherification (Zhang et al., 2001), hydrogenation (Rayet al., 1994), isomerisation (Hashimoto et al., 1983; Ching andLu, 1997), oxidative coupling of methane (Tonkovich and Carr,1994; Bjorklund et al., 2001), partial oxidation of methane(Bjorklund and Carr, 2002), reactions involving sugar (Azevedoand Rodrigues, 2001) and so on. Oxidative coupling of methane(OCM) is a reaction of industrial importance since it producesethylene and ethane (C2 products) which are precursor to manyother reaction products. But for OCM, conversion of methane perpass in a single reaction tube is extremely low (2–16%) whichdrives up the expense of a large scale operation. It was reportedthat in order to compete with existing technologies, C2 yields inexcess of 30% would be required for a commercially successfulprocess (Srivastava et al., 1992). Experimental investigation byincorporating OCM in SCMCR showed that methane conversion of79.6%, C2 selectivity of 73.2% and C2 yield higher than 58% canbe attained (Bjorklund et al., 2001); even though it is difficult toobtain a C2 yield in excess of 20–25% by other methods. An inte-grated reactor–separator, however, complicates the process designand plant operation. Although a reasonable number of experi-mental and simulation studies on SCMCRs were reported in theliterature, there are very few reported applications of SCMCRs inthe chemical industry because of the complexity of the processesand large amount of kinetic and physical parameters required.A more detailed understanding and criteria for operating SCM-CRs are needed before successful applications can be achieved.It is also essential to find out the optimal design and operatingconditions to successfully implement reactive SCMCR processeson industrial scale. However, single objective optimisation is notsufficient for real life design of complex process like SCMCR,a more realistic approach such as multiobjective optimisation(MOO) is deemed necessary for the design of SCMCR for OCM.

Several methods are available for solving MOO problems, forexample, the ε-constraint method, goal attainment method andgenetic algorithm (GA) (Holland, 1975; Goldberg, 1989; Deb,1995, 2001). GA is a nontraditional search and optimisationmethod that has become quite popular in engineering optimisa-tion. In MOO, a solution that is the best (global optimum) withrespect to all objectives might not exist. Instead, an entire setof optimal solutions exists which might be equally good. Thesesolutions are known as Pareto Optimal (or non-dominated) solu-tions. Non-dominated sorting GA (NSGA) is a modified versionof the simple GA, for multiple objectives. Non-domination refersto a solution being better in at least one objective than anothersolution. NSGA differs from the simple GA only in the way theselection operator works. NSGA uses a ranking selection methodto emphasise the good chromosomes and niche method to creatediversity in the population without losing a stable sub-populationof good chromosomes. NSGA-II is a further improvement of NSGA;it is an elitist NSGA using an elite-preservation strategy as wellas an explicit diversity-preserving mechanism. NSGA-II was usedto optimise an industrial fluidised-bed catalytic cracking unit(FCCU), which resulted in better convergence near the true ParetoOptimal front. An improved spread of Pareto Optimal solutionswas also found although a decrease in genetic diversity was

observed (Kasat et al., 2002). NSGA-II-JG combines the conceptof jumping genes with NSGA-II and the adaptation was used tooptimise the same FCCU. The adaptation was able to maintaingenetic diversity while at the same time reduce computation time(Kasat and Gupta, 2003). This optimisation approach has success-fully been applied for many chemical engineering applications(Bhaskar et al., 2001; Zhang et al., 2003, 2009; Subramani et al.,2004; Kurup et al., 2005; Tarafder et al., 2005; Bhutani et al., 2006;Agrawal et al., 2007; Kundu et al., 2009b).

The study here aims to provide insights into the operation ofthe unconventional three-section SCMCR for OCM by performinga systematic modelling and simulation process. A mathematicalmodel mimicking experimental conditions was developed andsolved using numerically tuned kinetic and adsorption param-eters. The model-predicted results were compared with that ofexperimental studies and finally the effects of various processparameters (switching time, inlet-outlet flow rates, methane tooxygen ratio in feed etc.) on the performance of SCMCR wereinvestigated. It was observed that there is a complex interplayamong various process parameters, and some of these processparameters not only alter conversion of methane, yield and selec-tivity of C2 products significantly, but also act in a conflictingmanner. It was possible to improve the performance by suitablyadjusting process parameters. However, it is not possible to max-imise the conversion and selectivity simultaneously. When onemaximises, other worsens. Further improvement is expected ifa systematic process optimisation is conducted using multipleobjectives. An operating stage MOO problem aiming at simulta-neously improving conversion of methane and selectivity of C2

products was solved using NSGA-II-JG. The method of optimisa-tion used in this work is very efficient and can easily be appliedto almost any other combination of objective functions.

OCM IN A SCMCR SYSTEMThe oxidative coupling reaction occurs catalytically at elevatedtemperature. The methane activates on the surface of the catalystand then couples to form ethane homogeneously in the gas phase.The reaction must take place at an oxygen lean environment toavoid forming complete oxidation products. However, per passconversion of methane in a single reactor is very low. In orderto augment the conversion of methane, two distinct approachescan be taken. One is to find the most effective catalyst so that thereaction can be carried out at less severe conditions and whichwill give reasonably high methane conversion as well as selectiv-ity. There are some paradoxical relations between conversion andselectivity. Catalysts which give a high conversion of methane donot always exhibit high selectivity to ethane and ethylene; andthose which give a high selectivity are not extremely active. Vari-ous efforts were taken to find out the active and selective catalystsfor OCM in microcatalytic reactors (Otsuka et al., 1986; Tonkovichand Carr, 1994; Kruglov et al., 1996; Bjorklund et al., 2001; Simonet al., 2007; Takanabe and Iglesia, 2009). It was found that oxidesof rare earth metals and heterogeneous catalysts of transition met-als are the most active and selective catalysts for OCM. The otherdirection to increase methane conversion aims at designing anovel reactor separator which will have considerable flexibility,that is separate reaction and separation columns, a controlled reac-tion, sweeping product stream and recycling of unused reactants.A novel SCMCR, first developed by Tonkovich et al. (1993) forOCM, showed an improved methane conversion, C2 (combinedethylene and ethane) selectivity and yield. There were four sec-tions in the original design, in which each SCMCR section consists

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Figure 1. Schematic of the SCMCR experimental arrangement for OCM.All valves labelled I are ON at once, then all valves labelled II and then allvalves labelled III (Bjorklund et al., 2001).

of a fixed bed reactor followed by a lower temperature adsorptionbed. Bjorklund et al. (2001) modified the original SCMCR designwhere only one fixed-bed reactor was used instead of the four byTonkovich et al. (1993). The single fixed-bed reactor diminishesthe possibility of reactor-to-reactor catalyst activity variations andreduces energy and construction costs upon scale-up. Figure 1demonstrates the schematic of the SCMCR experimental arrange-ment for OCM. The SCMCR has only three sections rather thanthe conventional four sections to reduce complexity and solidsinventory. The fixed-bed reactor is successively coupled to eachdownstream adsorber section by the SCMCR flow switching opera-tions. Make-up feed is introduced into the catalytic reactor section(CRS), which is the section of the SCMCR currently incorporatingthe fixed-bed reactor. Carrier gas, introduced one separation sec-tion upstream of the CRS, desorbs the reactants adsorbed duringthe previous switching cycle and adds them back to the CRS dur-ing the current switching period. Extra carrier gas, introduced twosections behind the CRS, strips off the strongly-adsorbed productsfrom the SCMCR. The products are taken off at an intermediatepoint in the adsorber because they are more strongly adsorbedon the adsorbent surfaces than methane. The fixed-bed reactoris packed with granular YBa2Zr3O9.5 catalyst and separators arepacked with activated charcoal as adsorbent. The reactor and sep-arators are operated at 850 and 100◦C, respectively.

MATHEMATICAL MODELS

Microreactor ModelThe YBa2Zr3O9.5 catalyst appears to have desirable characteristicsfor OCM. It was proved that this catalyst demonstrates excellentstability towards deactivation and remains both selective to C2

and active concerning oxygen conversion. A selectivity of 84% forC2 products in microreactor was obtained for a methane/oxygenratio of 11 at nearly complete oxygen conversion, making this cat-alyst attractive for commercial application (Kruglov et al., 1996).

However, the reaction mechanism and kinetics of OCM overYBa2Zr3O9.5 catalyst bed are extremely complicated and requireadvanced knowledge of the complex OCM heterogeneous andhomogeneous kinetics to allow for its quantitative prediction.There could be literally hundreds of elementary steps possible,all accompanied by pore diffusion and axial dispersion. Since rateconstants and activation energies for each of the steps are notwell known, a reliable and predictive reactor model is not pos-sible. By analysing the microreactor outlet products, the reactionover the YBa2Zr3O9.5 catalyst can be described by the followingoverall reactions:

2CH4 + 12

O2 → C2H6 + H2O (1a)

C2H6 + 12

O2 → C2H4 + H2O (1b)

2CH4 + O2 → C2H4 + 2H2O (1c)

CH4 + 32

O2 → CO + 2H2O (1d)

CH4 + 2O2 → CO2 + 2H2O (1e)

Based on the microreactor experimental results at temperatureof 1123 K, the reaction could be characterised by the followingempirical relations (Kruglov et al., 1996; Bjorklund et al., 2001),formulated by fitting the experimental data using Sigma Plotwhich is based on Marquardt (1963) method:

S = 0.555 Rf0.143 (2)

E = 4.24 y−0.279CH4

y0.526O2

(3)

where S is the C2 selectivity, Rf is the CH4/O2 mole ratio, E is theethylene-to-ethane ratio in the products and yCH4 and yO2 are themole fractions of methane and oxygen, respectively, in the feed.

Adsorber ModelThe adsorption and desorption dynamics of reactants and prod-ucts play a central role in the overall SCMCR performance.Experimental breakthrough curves were reported elsewhere(Bjorklund et al., 2001), and the adsorber model was used topredict the elution profiles for each of the components throughthe adsorber. The mass balance equations were written based onthe equilibrium-dispersive model, which assumes that the fluidphase and solid phase are always in equilibrium, contributionsof all the non-equilibrium effects are lumped together with anapparent axial dispersion coefficient, Di, and the apparent disper-sion coefficients of the solutes remain constant, independent ofthe concentration of the components (Guiochon et al., 1994). Themass balance partial differential equation for each species i for thenon-reactive breakthrough column can be expressed as follows:

∂Ci

∂t+

(1 − ε

ε

)∂qi

∂t+ u

ε

∂Ci

∂Z= Di

∂2Ci

∂Z2(4)

where C and q are the concentrations of species i in the mobileand stationary phases, respectively. u is the superficial velocitymobile phase, ε is the porosity of adsorbent; whereas, t and Z arethe two independent variables time and axial position (distance).

For the OCM reaction, there are up to six components in the sys-tem. It is difficult to precisely describe the adsorption isotherm for


such a system. Moreover, the concentrations of the components inthe system are quite low. Considering all these, it is proposed thata linear adsorption isotherm is accurate enough for the system,as follows:

qi = KiCi (5)

where K is the adsorption–desorption equilibrium constant.The initial and boundary conditions are given by:

Ci(t = 0) = 0 (6)

Ci(0 < t ≤ tp)Z=0 = Ci,f (7)

Ci(t > tp)Z=0 = 0 (8)

[∂Ci(t)

∂Z

]Z=0

= 0 (9)

where subscript f represents feed and p represents the width ofthe rectangular pulse (step function increase followed by stepdecrease at a later time).

The main objective here was to determine the apparent axialdispersion coefficient (D) and the adsorption–desorption equilib-rium constant (K) for each of the species, as well as the porosity(ε) of the adsorbent bed by fitting the experimental breakthroughcurve for each of the components to the solution of mathemati-cal model equations of a single adsorption column. State-of-the-artoptimisation method such as non-dominated sorting genetic algo-rithm (NSGA) was used in which the sum square errors betweenthe model predicted results and experimental values were min-imised. To use NSGA, the objective function (error function) wasfirst defined as:

Fi =m∑

j=1

(Cij,exp − Cij,mod)2 (10)

A reasonable range (upper and lower bounds) of K, D and ε

were assumed. A gene pool of 50 chromosomes was consideredand computations were carried out for 50 generations.

Mathematical Model for SCMCRWithout the instant of column switching, a SCMCR unit resem-bles a fixed bed chromatographic reactor. The dynamic model fora fixed bed chromatographic reactor, corresponding to each sin-gle column in the SCMCR unit, can be developed by adoptingan equilibrium dispersive model and finally incorporating cyclicport switching to model the SCMCR process. In addition, it isassumed that there is no separation occurring in the reactioncolumn and no reaction taking place in the separation column.Thermal effect was not considered in this work for the lack of therelative experimental data.

Unlike the design of a four section SCMCR (Kundu et al.,2009a), where there were four reactor columns and eight adsorp-tion columns; the unconventional three-section SCMCR has onlyone reactor column (section P). The configuration in Figure 1is simplified in Figure 2a by considering only two columns ineach section of M, R and H; one small separation column fol-lowed by a large one. Products take off point (point E) dividessection R in two sections, section R1 and R2. There are a totalof six adsorption columns (Ncol = 6) where periodic switching isperformed. Figure 2b represents the switching schedule. How-ever, the reactor is considered fixed, that is reactor input dependsupon section H and the reactor output stream is the feed for sec-tion M. In numerical simulations, experimental values of Rf andyi from independent catalytic reactor experiments were used toevaluate S and E (Equations 2 and 3). These were then used tocompute the inlet composition for the adsorber bed (column W1),and the adsorber model was used to compute the time-varyingadsorber composition. Reactor inlet/outlet stream specificationsare calculated in points A and B using material balance, algebraicrelations and volume corrections. The mass balance equations in

Figure 2. (a) Schematic diagram of the SCMCR systems and (b) principle of operation of SCMCR (switching schedule).


the adsorbers are given by:

∂C(N)ij

∂t+

(1 − ε

ε

)∂q

(N)ij

∂t+ u�

ε

∂C(N)ij

∂Z= Di

∂2C(N)ij

∂Z2(11)

for component i in the jth column during the Nth switchingperiod, where uϕ denotes the superficial flow rate in section ϕ

(with ϕ = M, R1, R2 and H).The adsorption isotherm is given by:

q(N)ij = KiC

(N)ij (12)

Initial conditions:

When N = 0, C(0)ij = 0; q

(0)ij = 0 (13a)

When N ≥ 1, C(N)i,j = C

(N-1)i,j+2 for j = 1 to (Ncol − 2) (13b)

C(N)i,j = C

(N−1)i,(j+2)−Ncol

for j = (Ncol − 1) to Ncol (13c)

Boundary conditions:Feed point to reactor, after volume correction (point A in Figure

2a)

Ci,CRS

∣∣Reactor inlet

= QH

QCRSC

(N)i,W6

∣∣Z=L

+ QF

QCRSCi,f (14a)

Reactor outlet point, after volume correction (point B in Figure2a)

C(N)i,W1

∣∣Z=0

= Ci,CRS

∣∣Reactor outlet

(14b)

Extra carrier gas injection point (point D in Figure 2a)

C(N)i,W3

∣∣Z=0

= QM − QP

QM − QP + QEC

(N)i,W2

∣∣Z=L

(14c)

Product takeoff point (point E in Figure 2a)

C(N)i,W4

∣∣Z=0

= C(N)i,W3

∣∣Z=L

(14d)

Carrier gas injection point (point F in Figure 2a)

C(N)i,W5

∣∣Z=0

= QH − QC

QHC

(N)i,W4

∣∣∣∣Z=L

(14e)

The mass balance equation (Equation 11), initial and boundaryconditions (Equations 12–14) and adsorption isotherm (Equation12) completely define the SCMCR system, and are reduced to a sys-tem of ordinary differential equations of initial value problem by

method of lines (Schiesser, 1991). In this technique, a PDE is firstdiscretised in space using the finite difference method (FDM) toconvert the system into a set of several coupled ODE-IVPs, and thesystem of resultant ODEs, which is usually stiff, was solved withDIVPAG subroutine in the IMSL library (which is based on Gear’smethod). Since periodic switching is performed on the system,the concentrations of all the components at every point withinthe columns are always changing. Whenever a switching is per-formed, a new initial value problem must be solved. However,a pseudo-steady state with a period equal to the switching timeis eventually attained. The objective of this work is to validatethe model predicted result with that of the reported experimentalresults. Subsequently, we will determine whether we can achievea higher conversion, selectivity and yield for OCM reaction inSCMCR through systematic optimisation. Therefore, the designof the SCMCR configuration and operating conditions to be usedtherein must be set such that conversion of CH4 (XCH4), yield (YC2)and selectivity (SC2) of the desired product (C2H6 + C2H4) are max-imised at the product withdrawal port. The above quantities aredefined as follows:

XCH4 = [2 × moles of C2(C2H6 + C2H4) + moles of C1(CO2 + CO)] collected in extract[moles of CH4 fed]

(15)

SC2 = [2 × moles of C2(C2H6 + C2H4) collected in extract][2 × moles of C2(C2H6 + C2H4) + moles of C1(CO2 + CO)]collected in extract

(16)

YC2 = [2 × moles of C2(C2H6 + C2H4) collected in extract][moles of CH4 fed]

(17)

RESULTS AND DISCUSSION

Effect of Adsorption and Reaction Kinetic ParametersFor the microcatalytic reactor model (Equations 2 and 3), find-ing out selectivity (S) and ethylene/ethane ratio (E) in the reactoroutlet are the two key factors. Experimental data are available interms of CH4/O2 mole ratio (Rf), and mole fractions of methane(yCH4) and oxygen (yO2) in the feed (Bjorklund et al., 2001). Fromthe reactor effluent analysis with a GC, experimental conversion(XCH4), selectivity (SC2), yield (YC2) and ethylene/ethane ratio(E) were reported. The kinetic model validates the microreactorexperimental results. Figure 3a represents the model predictedconversion, selectivity and yield with different Rf in the feed. Fig-ure 3b represents the model predicted E in the product streamwith different Rf and yCH4 in the feed. The kinetic model was usedto compute the inlet composition (composition for the first plate)for the adsorber.

Adsorption isotherm parameters of each component wereobtained by fitting the breakthrough curves of CH4, C2H6, C2H4,CO2 and CO in single adsorption column as shown in Figure 4.Experimental details of getting these breakthrough curves can befound elsewhere (Bjorklund et al., 2001). Since the porosity (ε)of the adsorbent in the separation column is not reported any-where, several values were tried to determine the fitting. Fittingwas found quite acceptable if the values are within the range of0.4 to 0.6. The best fit value for porosity was found to be 0.51.However, it was also found that for ε values within the aboverange, the K values for all the components tend to increase as ε

increases. The values of D are insensitive, and error do not showany clear relationship with ε (Table 1). The K and D values of


Figure 3. (a) Effect of methane/oxygen ratio on methane conversion, C2selectivity and C2 yield in the microcatalytic reactor. (b) Effect ofmethane/oxygen ratio on C2H4/C2H6 product ratio in the microcatalyticreactor.

the components obtained by using NSGA are shown in Table 2. Itcan be seen that most of the fitting curves in Figure 4 are in goodagreement with the experimental data.

Dynamic Behaviour of SCMCR PerformanceIt is apparent from Table 2 that the desired products (C2H4 andC2H6) are more strongly adsorbed on activated charcoal than thereactants and undesired products (CO and CO2). Methane startsto elute from the adsorber column after 23 s; reaches peak at 67 s;and its flow diminishes to zero at 107 s (Figure 4). Ethylene andethane start to elute the adsorber column after 160 and 225 s,respectively; continuous flow occurs until 361 s for C2H4 and 450 sfor that of C2H6. On the other hand, CO2 and CO take 71 and19 s, respectively to breakthrough; continuous flow occurs until

Table 1. Dependence of porosity in the adsorber bed with adsorptionequilibrium constant (K) and apparent dispersion coefficient (D) ofmethane

Porosity (ε) KCH4 DCH4 × 104 (m2/s) Error function (Fi )

0.4 18.53 40.94 0.02450.5 22.66 40.95 0.02830.6 25.17 40.95 0.0272

Table 2. Adsorption–desorption equilibrium constant (K) andapparent dispersion coefficient (D) for CH4, C2H6, C2H4, CO2 andCO (ε = 0.51)

Component i K D × 104 (m2/s)

CH4 22.66 40.95C2H6 250 2.3C2H4 185 3.6CO2 157.52 50.0CO 36 140.0

436 s for CO2 and 104 s for CO. It is apparent that with activatedcharcoal, CO2 is difficult to separate from C2 products because ofsimilar elution characteristics. Again, unreacted methane, swipedto the reactor by carrier gas (QC) from section H, contains CO,since they have similar elution properties. Breakthrough curvesfor ethylene and ethane are slender and they rise steeply to thepeak. This can be described by their low D values. Since ethy-lene and ethane have higher K values, the adsorption of the twocomponents on the activated charcoal is very strong and there-fore, they cannot completely elute within one switching period.Due to their higher K values, ethane and ethylene move moreslowly than methane, hence many additional columns and sec-tions are required to remove the products from the middle of eachseparation section.

Operating parameters for the SCMCR system are listed inTable 3. Figure 3 indicates that the SCMCR should be operatedat Rf = 25 to optimise the C2 selectivity. The SC2 increases as Rf

increases but XCH4 suffers at this operation. Again, XCH4 increasesas Rf decreases but SC2 worsens at this operation. On the otherhand, a low Rf value maximises E in the product stream. SCMCRcan be operated either at high Rf values to minimise the formationof undesired products (COX); or at low Rf values to favour C2H4

over C2H6 or can be operated at an intermediate optimal operatingconditions. The Rf in the feed was set to 25 for the first switchbut for the subsequent switches, the make-up Rf was kept 1.32in order to keep the operation consistent with the experiment.Operation in this manner keeps the ratio of methane and oxygenhigh enough to ensure the high selectivity of C2 products. Theaddition of a make-up feed, under ideal conditions, will presentidentical feed mixtures (with high Rf) to the reaction columnin every switching. The SCMCR design intention is to make theamount of O2 limiting so that methane or its product (C2H4 andC2H6) cannot be oxidised further and the selectivity remains high.The degree of decrease should be carefully chosen and justi-fied in order to achieve optimal operation. Under the operatingconditions used, conversion of CH4 can reach as high as 79.6%,while the selectivity and yield can reach 73.2% and 58.2%,respectively (Figures 5 and 6). This is much higher than the perpass conversion of 2–16% (Tonkovich and Carr, 1994) in a singlecolumn fixed bed reactor. The carrier gas (QC) flow rate was setat 1.0 × 10−6 m3/s (60 sccm) and a larger flow rate (four timesgreater than main carrier stream) was used in the product removalsection as extra carrier gas (QE) to completely remove all theproducts which are left in the column.

Countercurrent movement of the fluid and solid is simulated bySCMCR flow switching operations (controlled by valves). Flowthrough different adsorber columns is switched after a periodof time, which is known as switching time (ts). Controlling theflow through inlet and withdrawal ports after predetermined ts,actually mimics column advancing in the opposite direction ofthe fluid flow (clockwise), which is equivalent to move the solid


Figure 4. Experimental and model predicted breakthrough curves in the adsorber for (a) CH4, (b) C2H4, (c) C2H6, (d) CO2 and (e) CO.

in the opposite direction of fluid flow. However, C2H4 and C2H6

adsorb more strongly on the adsorbent than unreacted CH4. Effec-tive separation of the products is accomplished by appropriatelyselecting the switching time (and, hence the fluid phase velocity)in such a way that the more strongly adsorbed components travelwith the solid phase and breakthrough at section R, while thecomponents with the weaker affinity travel with the fluid phase.

Effect of Operating ParametersSwitching time (ts) plays a key role in determining the perfor-mance of a SCMCR unit. The model predicted results are comparedwith available experimental data at different ts in Figure 5.

Table 3. Operating parameters for the SCMCR system

SCMCR geometry Operating parameters

dR = 5 mm TR = 850◦CLR = 400 mm TS = 100◦CdS = 6.35 mm QC = 1.0 × 10−6 m3/sLS1 = 127 mm QE = 4.33 × 10−6 m3/sLS2 = 305 mm Rf = 25 (first switch), 1.32 (other switches)

QF(methane) = 0.025 × 10−6 m3/s

The figure reveals that the model predictions are in good agree-ment with the experimental results. At the reference conditions(Table 3), the XCH4 was found maximum 79.6% at ts of 401 s;whereas, the maximum XCH4 of 79.6% was achieved experimen-tally when ts was 391 s (Bjorklund et al., 2001). However, theslight discrepancies between the model prediction and experi-mental data can be explained. The complete reactor dynamics

Figure 5. Effect of switching time on the performance of the SCMCR.


and thermal effect on the reaction was not taken into accountfor the mathematical model, which could be the prime reason forinconsistency with the experimental data. Again in the mathemat-ical model, the pore diffusion within the adsorbent was neglectedwhich may be significant in the real operation of the SCMCR.

The effect of ts on XCH4 is quite pronounced. Both XCH4 and SC2

are a strong function of ts. An optimal ts exists which maximisesXCH4 . When the ts is a small fraction of the breakthrough time,XCH4 drops. This is expected since there is not enough time forall of the material, which adsorbed during the previous switchingcycle (section M), to desorb from the carrier section (section H).The extra non-desorbed material which remains behind the feedsection is lost at the extract port (point E), consequently deteri-orates the overall XCH4 . Again, it was found that at ts very closeto the breakthrough time, XCH4 drops. This is also expected sincewith the increase in the amount of feed, there is an increase inthe unreacted methane concentration in section M, and therefore,the concentration front no longer behaves linearly. The convectivevelocity of the material increases as a function of concentrationwhich results in a decrease in breakthrough time. The concen-trated reactant front moves with a faster convective velocity,which allows a significant amount of reactant to break throughthe separation column, and this material is lost through the purgestream as well as through the extract port. Operating SCMCR atan optimal ts is thus crucial in order to overcome reactant losseither through incomplete reactant desorption or early reactantbreakthrough. Thus XCH4 is a decreasing function at both ends ofthe ts spectrum due to the competing sources of methane losses.In Figure 5, XCH4 drops to 68.9% and 70.8% when ts is 251 and475 s, respectively; reaches a maximum at 401 s which can beconsidered the optimal ts.

The effect of ts on SC2 and YC2 is shown in Figure 6. The selec-tivity in the microreactor (equivalently, products available foradsorption in SCMCR) is determined by the actual Rf in the reac-tor sections (which is not constant in time). At the optimal ts, themajority of the methane originally fed to the SCMCR is retained inthe system and is recycled, maintaining a high Rf that is respon-sible for the high overall SC2 . At shorter ts, methane is lost fromthe system by incomplete desorption. Since the reactor model isbased on 100% oxygen conversion (limiting reactant), the feedstream in the next switch attains low Rf , which is responsible forlow SC2 . Again at ts higher than the optimal, SC2 decreases dueto low Rf which is the result of early reactant breakthrough andsubsequent loss of reactant through the purge stream. At longer

Figure 6. Model prediction for C2 selectivity and C2 yield at differentswitching time in the SCMCR.

Figure 7. Effect of CH4/O2 ratio in the make-up feed (Rf ) on theperformance of SCMCR.

ts, some products from section M can elute through the purgestream, which may also account for the low SC2 . The C2 yield isexpressed as the product of conversion and selectivity; and is seento have a similar trend with that of C2 selectivity.

The make-up of Rf has a strong effect on the SCMCR perfor-mance. Figure 7 shows the effect of this ratio on XCH4 and SC2 .The decrease in XCH4 and the increase in SC2 with increasing Rf

are readily understood. However, the product distribution has amore complex relationship with the feed ratio. Running the systemin an increasingly lean oxygen environment provides less of onebimolecular reactant, thus the conversion of the other decreases.When CH4/O2 in the make-up feed is larger than the stoichio-metric ratio, CH4 accumulates in the SCMCR until some of theexcess CH4 elutes with either the product or purge stream, and thenet conversion becomes smaller. Selectivity, on the other hand, isknown to increase with increasing Rf . When the reaction envi-ronment has less oxygen available, the reaction producing ethaneand ethylene are preferred to the undesired complete oxidationreaction which forms carbon oxides (COX), and thus, selectiv-ity increases. At higher Rf , the low conversion limits the yield,whereas at lower Rf , low selectivity limits the yield. The optimalvalue of Rf is thus vital in operating SCMCR where conversion andselectivity will balance each other. Overall, the model predictionsare quite good, however further improvement is sought throughMOO.

Operating Stage OptimisationThe MOO problem is solved for an existing set up and is describedmathematically by:

Max J1 = XCH4(ts, QE, QC, Rf) (18)

Max J2 = SC2(ts, QE, QC, Rf) (19)

Subject to

XCH4 ≥ 60% (20)

The choice of two objective functions J1 and J2 (Equations 18and 19), enables the simultaneous maximisation of the conver-sion of methane and selectivity of desired products (C2H4 + C2H6).These two objective functions were chosen as the base casesince this is the primary goal of OCM in the SCMCR. OCM isa low-conversion process, and per pass conversion of methanein an non-separative reactor is as low as 2–16% (Tonkovich


Figure 8. Optimisation technique for NSGA-II-JG.

and Carr, 1994). A methane conversion of more than 60% wasachieved experimentally in SCMCR by adjusting operating con-ditions (Bjorklund et al., 2001). Hence, we incorporated theinequality constraint to achieve conversion of methane greaterthan 60% for all feasible solutions. The inequality constraint(Equation 20) was incorporated using penalty functions. Figure 8represents the solution technique of the optimisation problem.Numerical parameter values used in NSGA-II-JG for the optimisa-tion study are listed in Table 4. More details of the optimisationsequence and computational parameters can be found elsewhere(Srinivas and Deb, 1994; Deb, 2001).

Four decision variables were used for this operating stage opti-misation study. They are switching time (ts), CH4/O2 ratio in thefeed (Rf), carrier gas flow rate (QC) and extra carrier gas flow rate(QE). The ts and Rf are the key parameters for effective operationin an SCMCR. The QC and QE are also important operating cost

Table 4. Computational parameters of NSGA-II-JG used inmulti-objective optimisation study

Parameters Value

No of generations, Ngen 50Population size, Npop 50Sub-string length coding for each decision variable, lsubstr 32Crossover probability, Pcross 0.7Mutation probability, Pmute 0.005Jumping gene probability, Pjump 0.15Seed for random number generator, Sr 0.45

parameters. Since a large volume of extra carrier gas (or eluent)is usually required as found out from the experiment, determin-ing an optimal eluent flow rate is essential. Since an existingsetup is being considered for this operating stage optimisation, allother parameters were fixed at their reference values as shown inTable 3.

The Pareto Optimal solution for the operating stage optimisa-tion problem, together with YC2 and the optimal values of the fourdecision variables corresponding to the points on the Pareto set,are shown in Figure 9a–f. Figure 9a shows the relation betweentwo objectives, XCH4 and SC2 . It is obvious that XCH4 cannot beimproved without penalising SC2 . The conversion of methane wasfound to be approximately 88% as shown in Figure 9a, comparedto maximum 79.6% reported in experiment (Bjorklund et al.,2001). It is not possible to maximise conversion and selectivity atthe same time. When one increases, other suffers. However, yieldappears to be concave with selectivity. A higher yield of 59.2%was found as shown in Figure 9b, in comparison to experimentallyattained maximum of 50%. A ts of approximately 370 s was foundoptimal for the operation as shown in Figure 9c. Figure 9d showsthat a higher QE was used in the operation. The QE should be suffi-ciently large enough for desorbing the adsorbed product, therebycompletely regenerating section R1. It was observed that the QE

should be above a minimum value, and performance does notimprove any further by increasing QE. Moreover, a large QE unnec-essarily increases the operating costs. A flow rate of 160–170 sccmof QE was found optimal for product removal and regeneratingsection R1, which shows 40% savings in carrier gas consump-tion. Figure 9e shows that QC is relatively insensitive in decidingthe Pareto Optimal solutions. A sufficient QC is required which


Figure 9. Pareto set and the corresponding decision variables for the operating stage optimisation problem.

can carry the unreacted adsorbed materials to the reactor fromthe previous switching cycle. It is apparent from Figure 9f thatthe Rf has a strong effect on the conversion and selectivity. WhenRf increases, selectivity increases as expected due to favourableconditions for reactions producing ethylene and ethane. WhenRf is lowered to 1.25 from 1.32 (reference value), XCH4 reaches88% with SC2at 61%, but drops to 63% with SC2 at 80% when Rf

is increased to 2.0. Searching optimal operating conditions thatmaximise conversion, selectivity and yield; mitigate reactant lossand minimise operating costs are vital for efficient operation ofSCMCR unit.

CONCLUSIONThe SCMCR can significantly enhance methane conversion andC2 product yield for OCM reaction. A mathematical model wasdeveloped and subsequently a systematic MOO problem of theSCMCR system for OCM reaction was solved using a robust, state-of-the-art AI-based non-traditional global optimisation technique;elitist non-dominated sorting genetic algorithm with adaptationsof jumping genes (NSGA-II-JG). The adopted kinetic model bestdescribed the associated kinetics of OCM in SCMCR. Adsorptionisotherm parameters were derived based on experimental break-through curves using a single adsorption column. The dynamicmodel of the SCMCR unit was developed by adopting an equilib-rium dispersive model that also incorporates cyclic port switching.The predicted results demonstrated good agreement with thephysical consequences of the variation of operating parameters. Itis evident that the model is robust, reliable and can describe the

dynamic behaviour of the SCMCR under various operating condi-tions. However, it was difficult to find a set of optimal conditionsby trial and error because a desirable change in one perfor-mance criterion results in an unfavourable change in anotherdesired variable. A systematic study of the optimal operation of anSCMCR for the OCM reaction was carried out aiming at enhancingmethane conversion while retaining high C2 products selectivity.A Pareto Optimal curve, which provides a set of optimal solutionsthat are equally good, was obtained. It was found that optimalperformance of the SCMCR is better in terms of achieving a betteryield of C2 products using less eluent.

NOTATIONSC concentration in the mobile phase (mol/m3)dR diameter of reactor (m)dS diameter of separator (m)D apparent axial dispersion coefficient (m2/s)E ethylene-to-ethane ratio in the productsK adsorption–desorption equilibrium constantLR length of reactor (m)LS length of separator (m)N number of the columnsq concentration in the stationary phase (mol/m3)Q fluid flow rate (m3/s)Rf methane to oxygen ratio in feedS microreactor C2 selectivitySC2 selectivity of C2 (C2H6 and C2H4) at extract port (%)ts switching time (s)


TR temperature of reactor (◦C)TS temperature of separator (◦C)u superficial velocity (m/s)W1–6 separator column notationXCH4 conversion of methane (%)YC2 yield of C2 (C2H6 and C2H4) (%)yCH4 mole fraction of methane in reactoryO2 mole fraction of oxygen in reactorZ axial distance (m)

Greek Lettersε porosityϕ section (M, R1, R2 or H)

Superscripts and Subscripts0 initialcol columnf feedi component indexj column indexN number of switching

ACKNOWLEDGEMENTSThis work was made possible by the facilities of the Shared Hier-archical Academic Research Computing Network (SHARCNET:www.sharcnet.ca).

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Manuscript received April 20, 2011; revised manuscriptreceived June 11, 2011; accepted for publication June 28, 2011.


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Numerical simulation and optimisation of unconventional three-section simulated countercurrent moving bed chromatographic reactor for oxidative coupling of methane reaction