Computational fluid dynamics (CFD) analysis of micro-reactor performance: Effect of various configurations

Chemical Engineering Science 75 (2012) 85–95

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Computational fluid dynamics (CFD) analysis of micro-reactor performance: Effect of various configurations Hui An a, Ang Li a, Agus P. Sasmito b,n, Jundika C. Kurnia a,b, Sachin V. Jangam a,b, Arun S. Mujumdar a,b a b

Department of Mechanical Engineering, National University of Singapore, 9 Engineering Drive 1, Singapore 117576, Singapore Minerals Metals and Materials Technology Centre (M3TC), National University of Singapore, 9 Engineering Drive 1, Singapore 117576, Singapore

a r t i c l e i n f o

abstract

Article history: Received 13 October 2011 Received in revised form 22 February 2012 Accepted 3 March 2012 Available online 18 March 2012

The objective of this study is to examine via mathematical modeling several microreactor configurations which may yield enhanced overall performance. A computational fluid dynamic analysis was carried out for a microreactor in the form of a square cross-section channel of eight different configurations. These include parallel, pin-hole, wavy, oblique fin, serpentine, coiled, coiled with serpentine and coiled with double serpentine channel geometries. The performance of these microchannels in terms of the flow field and reaction rates was investigated numerically using a commercial package Fluent, and compared with that of a conventional straight microchannel of the same crosssection as well as other reactor geometries reported in the literature. This study was carried out for a single phase catalytic reaction between methane over a range of Reynolds numbers and selected geometric parameters. The reactor performance was compared in terms of the figure of merit (FoM) based on reaction throughput per unit pumping power and catalyst active area. The pinhole channel design was found to give the best overall performance over the range of Reynolds numbers studied. The effect was more pronounced at higher Reynolds numbers. It was observed that for each geometry a higher Reynolds number results in lower FoM. The relative advantages and limitations of the various micro-channel configurations examined are discussed in the light of the numerical results obtained. & 2012 Elsevier Ltd. All rights reserved.

Keywords: Coil Channel Figure of merit Pressure drop Reaction rate Single phase reaction

1. Introduction Micro-reactors are attracting considerable attention in recent years in chemical and pharmaceutical industries. Such reactors have inner dimensions of the structure in the order of millimeters or smaller. A number of impressive advantages of micro structured devices over the conventional chemical reactors have been demonstrated. One of the noticeable one is the very high area-tovolume ratio which offers considerably enhanced heat exchange and mass transport rates. However, in several microreactor designs the expected conversion cannot be achieved which may be attributed to poor mixing of the reactants. This is caused by non-uniform spread of reactants within the micro-channels or uneven distribution of flow between adjacent microreactors if the design utilizes parallel channels (Rebrov et al., 2011). These issues can result in considerable differences in heat and mass transfer and ultimately different reaction behavior within the reactor. Numerous studies have been reported which investigate enhanced performance of several innovative micro-reactor n Corresponding author. Present affiliation: Department of Mechanical Engineering, Masdar Institute of Science and Technology, Masdar City, P.O. Box 54224, Abu Dhabi, United Arab Emirates. Tel.: þ 971 2 810 9320. E-mail address: [email protected] (A.P. Sasmito).

0009-2509/$ - see front matter & 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ces.2012.03.004

designs. Since the flow in micro-reactors is typically laminar, as a result of the small dimensions, this allows precise computer simulation on the chemical reactions to evaluate strategies to overcome the aforementioned limitations. The small scale also allows much easier control of the process parameters such as temperature, pressure and flow rate etc., and hence, reduces the inherent danger in carrying out highly exothermic or explosive ¨ chemical reactions (Jahnisch et al., 2003; Watts and Haswell, 2005). Most of the reported studies concentrate on modifying a single micro-channel while another commonly tested design of choice is an array of micro-channels arranged in parallel with a common inlet with outlet channels perpendicular to them. Fazeli and Behnam (2010) carried out a computational fluid dynamic study of a hydrogen production reaction from steam reforming of methanol used in fuel cell application. They studied wall-coated straight and zig-zag micro-channel reactors. They concluded that the zig-zag arrangement improves heat and mass transfer rates in laminar fluid flow regime. It was also observed that a higher conversion of methanol results in lower temperatures which better for insulation. Kumar et al. (2007) and Mandal et al. (2011) introduced the concept of curved or inverted microreactors; these designs were found to perform much better than the straight micro-channels.

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The multi-channel type of structure with parallel channels is easy to manufacture but suffers from poor flow distribution (Amador et al., 2004). A fractal tree-like network structure frequently observed in natural organs (Bejan and Errera, 1997; Chen and Cheng, 2002) and a regular bifurcation shape (Amador et al., 2004), by contrast, are able to provide more uniform flow distribution with lower pressure loss in the structure. Coiledshape micro-reactors have been demonstrated to offer high heat and mass transfer rates as a result of the presence of secondary flows (Sasmito et al., 2012 and Kurnia et al., in press). Agrawal and Nigam (2001) found that the performance of coiled reactors lies in between the plug and laminar tube flow reactors under premix inlet conditions. Another microreactor design introduces posts or baffles (Chung et al., 2011) inside the channel to enhance mixing and reaction rate. Adeosun and Lawal (2010) proposed a new reactor design called ‘‘multilaminated/elongational flow micromixer’’ to enhance the mixing and reaction performance. Posts in catalytic reactors are often coated or directly made of catalysts and exhibit very high surface area (Ni et al., 2005; Yeom et al., 2009). A well designed posted structure can provide a narrow residence time distribution of gas and lead to higher reaction rates under carefully controlled conditions (Deshmukh et al., 2004; Regatte and Kaisare, 2011). Yu et al. (2008) studied a novel multichannel microreactor with omega-shaped microchannels and compared the performance with a straight and zig-zag type of designs both experimentally and via computational fluid dynamic modeling. This study was carried out for a Fischer–Tropsch reaction. They observed that the omega-shaped micro-reactor had the longest residence time amongst the three designs tested. Their experimental findings showed that the conversion rate for the omega-shaped design was much higher than other two designs for all inlet reactant ratios. Furthermore, various shapes of channel cross-section (Ramanathan et al., 2004; Arrighetti et al., 2007; Pan et al., 2008; Carvalho et al., 2009) of micro-reactors such as triangle, rectangle, square, circular, sinusoidal and hexagonal have been tested to evaluate their effect on the performance of microreactors. Arrighetti et al. (2007) carried out a 3D numerical simulation of heat and mass transfer in a catalytic converter of three different cross-sections viz., sinusoidal, square and hexagonal. The Nusselt number profile was observed to be nonuniform along the cross-section especially for the sinusoidal design although this geometry showed the best performance in terms of heat exchange and total conversion. Ramanthan et al. (2004) solved the governing convection–diffusion equations with wall reaction for a fully developed laminar flow in monolithic reactors of six different cross-sections having both smooth and sharp corners. It was observed that the geometries with sharp corners have non-uniform temperature distribution and lower reaction rates. Recently, Kurnia et al. (2011b) carried out a numerical evaluation of the hydrodynamic and heat transfer in an in-plane coil geometry of six different cross-section tubes and a straight tube of square cross-section. They found that the figure of merit (refer to Kurnia et al., in press for definition) for the straight tube of square cross-section and a trapezoidal one—among the six cross-sections studied for in-place coils—were significantly higher than those other cases for two different fluids tested, viz. air and water. They observed that rectangular, triangular and half circular cross-sections for in-plane coil geometry show poor heat transfer performance with higher pressure drop as well. As discussed earlier, apart from reactor geometry the flow configuration also plays an important role in determining the performance of a micro-reactor. Axial and cross-flow are the two typical flow configurations implemented in micro-reactor design. Ajmera et al. (2002) studied fixed-bed micro-reactors and found that the cross-flow configuration can offer high throughput at

lower pressure loss compared to the axial flow configuration. However, cross-flow imposes considerable flow maldistribution resulting in low reaction rate (Regatte and Kaisare, in press). Uniform flow distribution is essential for efficient reactant conversion (Saber et al., 2010). Rebrov et al. (2011) carried out an extensive review of flow distribution and heat transfer in single phase microreactors. They reported that the simulated and experimental results match well for single channels. However the accuracy is poor for multi-channel reactors because of the maldistribution. Rebrov et al. (2011) also provide guidelines for design of a multi-channel microreactor which includes adjusting the thickness of the channel walls and using non-uniform coolant flow to efficiently reduce the non-uniform temperature distribution. Despite several studies on the micro-reactor designs, there is still room for further improvement by evaluating new microchannel configuration which is a theme of this work. The present work deals with a computational fluid dynamic study of the performance of various multichannel microreactors. Essentially, various channel configurations are examined to understand their flow characteristics, heat transfer and reaction rates in the laminar regime.

2. Physical model As shown in Fig. 1, eight micro-reaction channel designs involving tubes of square cross-section were simulated viz., parallel, pin-hole, wavy channel, oblique fin, serpentine, coiled with outer inlet/outlet, coiled with serpentine and coiled with double serpentine. All channels have the same cross-section and dimensions (1 mm  1 mm). In this model, gaseous methane and air is assumed to be well mixed before entering the channel through the inlet. The reactions at the channel wall consist of multi-step reactions: adsorption, surface reaction and desorption. The detailed multi-step reaction mechanism and the relevant reaction rate constants are listed in Table 1. The surface species are calculated from site balance equations, while the surface reactions create sources of bulk phase, which determine their deposition rate on the surface.

3. Mathematical model The fluid flow is assumed to be steady, laminar and Newtonian follows the ideal gas condition, whereas the wall is coated with platinum catalyst to allow for catalytic reaction occur. Since this work relates only to laminar flow, a precise numerical solution is adequate to simulate the reality very closely. 3.1. Governing equations In the reaction channel, the conservation equations of mass, momentum, species and energy are given as (Sasmito et al., 2012)

rru ¼ 0 rru  u ¼ rp þ r

ð1Þ h

i 2 3

mðru þðruÞT Þ  mðruÞI

 ð2Þ

rðruoi Þ ¼ rðrDi roi Þ þ Ri,gas,surf ace

ð3Þ

rðrcp uTÞ ¼ rðkef f rTÞ þ Stemp,surf ace

ð4Þ

In above equations, r is the fluid density, u is the fluid velocity, p is the pressure, m is the dynamic viscosity, T is temperature, is the mass fraction of species i, Di is the diffusion coefficient of species i, Ri,gas,surface is the mass consumed or produced by reactions at the catalytic surface, cp is the specific heat of a gas

H. An et al. / Chemical Engineering Science 75 (2012) 85–95

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Fig. 1. Micro-reactor configuration design: (a) parallel; (b) pin-hole; (c) wavy; (d) oblique fin; (e) serpentine; (f) coiled; (g) coiled with serpentine and (h) coiled with double serpentine.

Table 1 Surface reaction mechanisms. No

Reaction

Ar

br

Er (J/kmol)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

H2 þ2Pt(s) ) 2H(s) 2H(s) ) H2 þ 2Pt(s) O2 þ 2Pt(s) ) 2O(s) O2 þ 2Pt(s) ) 2O(s) 2O(s) ) O2 þ2Pt(s) H2OþPt(s) ) H2O(s) H2O(s) ) H2Oþ Pt(s) OH þPt(s) ) OH(s) OH(s) ) OH þPt(s) H(s)þ O(s) ) OH(s) þ Pt(s) H(s)þ OH(s) ) H2O(s) þPt(s) OH(s)þ OH(s) ) H2O(s) þ O(s) CO þPt(s) ) CO(s) CO(s) ) CO þPt(s) CO2(s) ) CO2 þ Pt(s) CO(s)þ O(s) ) CO2(s) þ Pt(s) CH4 þ 2Pt(s) ) CH3(s) þH(s) CH3(s) þ Pt(s) ) CH2(s) þ H(s) CH2(s) þ Pt(s) ) CH(s)þ H(s) CH(s)þ Pt(s) ) C(s) þ H(s) C(s)þ O(s) ) CO(s) þ Pt(s) CO(s)þ Pt(s) ) C(s) þO(s) OH(s)þ Pt(s) ) H(s) þO(s) H2O(s) þPt(s) ) H(s) þOH(s) H2O(s) þO(s) ) OH(s)þ OH(s)

4.36e7 3.7e20 1.8e17 2.01e14 3.7e20 2.37e8 1e13 3.25e8 1e13 3.7e20 3.7e20 3.7e20 7.85e15 1e13 1e13 3.7e20 2.3e16 3.7e20 3.7e20 3.7e20 3.7e20 1e17 1.56e18 1.88e18 4.45e20

0.5 0  0.5 0.5 0 0.5 0 0.5 0 0 0 0 0.5 0 0 0 0.5 0 0 0 0 0 0 0 0

0 6.74e7 0 0 2.13e8 0 4.03e7 0 1.93e8 1.15e7 1.74e7 4.82e7 0 1.25e8 2.05e7 1.05e8 0 2e7 2e7 2e7 6.28e7 1.84e8 1.15e7 1.74e7 4.82e7

mixture, keff is the effective thermal conductivity and Si,gas,surface is heat release/absorb due to reactions at the catalytic surface. In this study, the conservation of energy in the solid is not considered.

3.2. Chemical reactions The reaction model considers the chemical reactions to occur only on the channel wall only, and the reactions involving surface deposition are defined as distinct surface reactions and hence treated differently from bulk phase reactions involving the same species. In the same way, the chemical species deposited on surfaces are treated as distinct from the same chemical species in the bulk gas (Li, 2009). In this model, seven gaseous species (CH4, O2, H2, H2O, CO, CO2 and N2), one bulk/solid species (Pt(b)) and eleven surface species (H(s), Pt(s), O(s), OH(s), H2O(s), CH3(s), CH2(s), CH(s), C(s), CO(s), CO2(s)) are considered. The gas phase species and surface species can be produced and consumed by surface reactions and the general expression is given by: Ng X i¼1

g 0i,r Gi þ

Nb X i¼1

0

bi,r Bi þ

Ns X i¼1

Kr

s0i,r Si "

Ng X i¼1

g 00i,r Gi þ

Nb X i¼1

00

bi,r Bi þ

Ns X

s00i,r Si

i¼1

ð5Þ

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H. An et al. / Chemical Engineering Science 75 (2012) 85–95

Here, Gi represents the gas phase species, Bi represents the solid species, and Si represents the surface adsorbed species. Kr, 0 bi,r , s0i,r are the stoichiometric coefficients for the three reactant 00 species respectively, and g 00i,r , bi,r , s00i,r are the stoichiometric coefficients for the three product species respectively. Kr is the overall reaction rate constant. The rate of reaction is given by Rr ¼ kf ,r

Ng Y

g 0i,r

s0i,r

½Gi wall ½Si wall

ð6Þ

i¼1

where kf,r is the reaction rate constant which is calculated using the Arrhenius equations given by: kf ,r ¼ Ar T br eEr =RT

ð7Þ

and ½Gi wall is the molar concentration on the wall. So the net molar rate of consumption or production for each species i is represented by: Nrxn X

R^ i,gas ¼

ðg 00i,r g 0i,r ÞRr

i ¼ 1,2,3,:::,Ng

r¼1

R^ i,bulk ¼

Nrxn X

00

0

ðbi,r bi,r ÞRr

i ¼ 1,2,3,:::,N b

r¼1 Nrxn X

R^ i,site ¼

ðs00i,r s0i,r ÞRr

i ¼ 1,2,3,:::,Ns

ð8Þ

r¼1

@oi,wall _ dep oi,wall ¼ M w,i R^ i,gas m @n

@½Si wall ¼ R^ i,site @t

i ¼ 1,2,3,:::,Ns

i ¼ 1,2,3,:::,Ng

_ dep ¼ m

while the gas mixture specific heat capacity cp is calculated by: X oi cp,i , ð17Þ cp ¼ i

where ki and cp,i are thermal conductivity and specific heat capacity for each species which can be found in Kaviany (2001) and Deutschmann et al. (2000), respectively. 3.3.2. Reactor performance To ensure the fidelity of comparison between various microchannel designs, the concept of the figure of merit (FoM) is introduced to evaluate the effect of Reynolds number and the effect of geometry on the pressure drop and reaction rate. FoM is defined as the ratio of the mass consumption rate per unit pumping power required given by:

M w,i R^ i,bulk

ð10Þ

ð11Þ

and ½Si wall is the site species concentration on the wall, defined as: ½Si wall ¼ rsite zi

ð12Þ

where rsite is the site density of the catalyst and zi is the site coverage of species i. The gas concentration at the wall is calculated from the species mass fraction which is expressed by:

rwall oi,wall M w,i

_ r,out _ r,in m m , Awall Ppump

ð13Þ

ð18Þ

where Awall is the area of catalytic surface and Ppump is the pumping power that is required to drive the fluid flow through the channel, calculated by Ppump ¼

i¼1

½Gi wall ¼

The multi-component gas mixture thermal conductivity is defined as: X kef f ¼ ki oi , ð16Þ

ð9Þ

_ dep is the rate of mass deposition or etching due to where m surface reaction which is given by: Nb X

b

FoM ¼

Furthermore, it is assumed that on the wall surface the mass flux of each gas species is balanced by its rate of production/ consumption which is given by:

rwall Di

where xa,b are the mole fractions of species a and b, and Fa, b is given by the expression below: 2 32 0 11=2    1=4 ðgÞ M 1 M a 1=2 6 m b 7 a Fa, b ¼ pffiffiffi 1 þ ð15Þ 41 þ @ ðgÞ A 5 Mb Ma 8 m

1

Zpump

Q Dp

ð19Þ

In the above equation, Zpump is pump efficiency, Q is the volume flow rate of the fluid, and Dp is the pressure drop. 3.4. Boundary conditions The following boundary conditions were applied

 Inlet: The mixture of air and methane is assumed to be well mixed before entering the micro-channels. The inlet mixture flow velocity and inlet temperature are: u ¼ uin ,

T ¼ T in ,

oO2 ¼ oin oCH4 ¼ oin oH2 ¼ oin ð20Þ O2 , CH4 , H2

 Outlet: At the outlet, the pressure is specified. The stream wise gradient of temperature and the species mass fraction are both set equal to zero. p ¼ pout ,

nrT ¼ nroi ¼ 0

ð21Þ

 Channel wall: At the walls of the channels, the surface reaction 3.3. Constitutive relations 3.3.1. Thermodynamic properties of the working fluid The working fluid is assumed to be well mixed mixture of air and methane. The miscible species mixture follows the ideal gas law. The thermodynamic properties of the working fluid are calculated as follows: The fluid mixture viscosity m is calculated as: X xa m a P m¼ with a, b ¼ CH4 ,H2 ,O2 ,H2 O,CO,CO2 ,N2 ð14Þ b xa Fa, b a

is taken into account and is resolved using Eq. (9). We specify no slip condition and constant wall temperature at the wall. Thus, u ¼ 0,

nroi ¼ 0,

nrT ¼ 0

ð22Þ

3.5. Numerical methodology The computational domains shown in Fig. 1 were created using AutoCAD 2010. The commercial pre-processor software GAMBIT 2.3.16 was used for building the mesh, labeling boundary

H. An et al. / Chemical Engineering Science 75 (2012) 85–95

90

70 60 50 40 30 20 10 0

4. Results and discussion The boundary conditions and relevant geometric parameters of the eight configurations tested are listed in Tables 2 and 3. Initially, validation of the mathematical model used in this study was carried out. Comparison was made with the experimental data reported by Bond et al. (1996). The simulations were carried out for the same geometry as the one used by Bond et al. (1996) for two different stoichiometric ratios at the inlet (0.18 and 0.39). It can be seen from Fig. 2 that the present simulation results show close agreement with the experimental data especially at the higher stoichiometric ratio where the mathematical models developed by Bond et al. (1996) and Canu (2001) deviate significantly from the data. This may be due to the fact that our mathematical model takes into account temperature dependency Table 2 Base case and operating parameters. Parameter Inlet flow velocity Inlet flow velocity Inlet flow velocity Inlet flow velocity Inlet temperature Outlet pressure Wall temperature

(Re (Re (Re (Re

100) 500) 1000) 1500)

Symbol

Value

Unit

uin uin uin uin T in pout T wall

1 5 10 15 300 101,325 1290

m/s m/s m/s m/s K Pa K

Table 3 Geometric parameters. Parameter

Symbol Value

Channel width Channel height Oblique fin angle Oblique fin width Oblique fin pitch Number of sinusoidal wave Amplitude of sinusoidal wave Total length of parallel channel Total length of serpentine channel Total length of wavy channel Total length of oblique fin channel Total length of coiled channel with outer inlet/outlet Total length of coiled channel with inner inlet/outlet Total length of coiled channel with serpentine Total length of coiled channel with double serpentine

wch hch

Unit

wob pob nwv Awv Lpa Lse Lwv Lob Lco

1  10  3 1  10  3 26 4.49  10  4 3.06  10  3 10 5.10  10  4 1.376 1.351 1.486 1.376 1.428

m m 1 m m – m m m m m m

Lci

1.428

m

Lcs Lcd

1.428 1.428

m m

yob

exp stoich 0.18 Bond et al. exp stoich 0.39 Bond et al. Present sim stoich 0.18 Present sim stoich 0.39 Sim stoich 0.18 Canu et al. Sim stoich 0.39 Canu et al. Sim stoich 0.18 Bond et al. Sim stoich 0.39 Bond et al.

80 Methane conversion rate (%)

conditions and determining the computation domains. Three mesh designs (2.5  105, 5  105, 1  106) compared in terms of computed pressure, temperature and velocity to ensure a mesh independent solution. The results show that a (5  105) mesh solution differs only about 1% in terms of p, u, and oi with a finer mesh 1  106, whereas a 2.5  105 mesh gives a deviation of 7% compared to the finest mesh. Hence, the 5  105 mesh was used to obtain solution with reasonable computational time. Based on Eqs. (1)–(4) and the boundary conditions shown in Table 2, the finite volume solver Fluent 6.3.26 was used to solve the constitutive relations consisting of eleven dependent variables r,u,v,w, oCH4 , oH2 , oo2 , oH2 O , oCO2 , oCO and T. The gas properties and chemical reaction mechanism were obtained using ChemKIN software. A user defined function (UDF) file was also created using C language to account for temperature dependence of the thermo-physical properties of the fluid.

89

0

1

2

3

4 5 Length (cm)

6

7

8

Fig. 2. Validation with experimental data at low and high inlet stoichiometry.

of the fluid properties. In the following sections, the effect of geometry on the performance of different configurations (Fig. 1) under high flow rate (Reynolds number 1500) is addressed first in order to identify which reactor configuration performs better. 4.1. Effect of channel configuration Geometry is one of the key factors which determine the performance of a micro-reactor. Flow distribution as a result of reactor structure has a direct impact on the reaction rate. Maldistribution reduces the fraction of species to be converted. Fig. 3 shows the computed velocity contours along the mid-plane of the flow channel (i.e. z ¼5  10  4 m) of each reactor configuration at a Reynolds number of 1500. It is observed that the serpentine (Fig. 3e), a rectangular coiled (Fig. 3f) and the two hybrid coiled (Fig. 3g and h) designs have higher velocity magnitudes across their configuration compared to the parallel (Fig. 3a), pin-hole (Fig. 3b), wavy (Fig. 3c) and oblique fin (Fig. 3d) shapes which, however, have overall velocity magnitude approximately one order smaller. Moreover, the latter four structures also shown higher velocity at branches near the inlet and outlet but the central branches have lower velocity (although not appreciable in the pin-hole configuration). This is similar to the flow behavior in a posted micro-reactors simulated by Regatte and Kaisare (2011). Both phenomena are attributed to the geometry of the reactor whose cross-flow configuration leads to uneven distribution of reactants inside the parallel, pin-hole, wavy and oblique fin configurations; the rest have only one channel path throughout the reactor with no flow distribution involved. To improve the distribution of the species, one may taper the inlet and outlet of the parallel, pin-hole, wavy and oblique fin designs (see Regatte and Kaisare, in press). A regular bifurcation shape (Amador et al., 2004) can also be implemented to obtain more even flow distribution. The fractional conversion of the species shows an inverse trend to the velocity contour plots of the reactor configuration at z¼5  10  4 m and Re  1500 for each configuration with same inlet conditions. The mass fraction of CH4 for all four ‘‘coiled’’ designs (Fig. 4e–h) decreases monotonically along the channel length, as shown in Fig. 4. The outlet mass fraction of CH4 for these four reactors has a very small value, which implies that the reaction is almost complete within each channel. The parallel (Fig. 4a), wavy (Fig. 4c) and oblique fin (Fig. 4d) configurations, however, exhibit uneven mass distribution. The consumption rate

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Fig. 3. Velocity contours at z ¼5  10  4 m for (a) parallel; (b) pin-hole; (c) wavy; (d) oblique fin; (e) serpentine; (f) coiled; (g) coiled with serpentine and (h) coiled with double serpentine for Re  1500.

of CH4 for these reactors is not as good as that obtained in the serpentine and coil-based configurations. This can be inferred from the computed results at the outlet; the wavy and oblique fin channels yield mass fractions of CH4 one order-of-magnitude larger than the other five designs while the parallel channel reactor has CH4 mass fraction which is two orders-of-magnitude larger. In contrast to these three rectilinear designs, the pin-hole configuration displays very low CH4 concentration (similar to that for coiled reactors) although the distribution is uneven in each parallel channel. The consumption contour of O2 for each reactor is similar to that for CH4. This large deviation in the three rectilinear configurations can be explained by the difference in residence times of the species. It is obvious that the longer the residence time, better the conversion. For the three rectilinear designs (the parallel, wavy and oblique fin), chemical conversion

occurs in a short length of the central branches. As observed in Fig. 3 the velocities are very low in these areas, the reactants present longer residence time and hence result in better reaction rate. The branches near the entrance or exit, by contrast, are not long enough to provide adequate residence time for reaction due to the higher velocities as compared to central branches. Thus the maldistribution of velocity lowers the overall reaction performance of these multi-channel configurations. On the other hand, single channel design implemented in all coil-based configurations in general has much longer traveling distance and therefore longer effective residence time for reactants, despite higher velocity. Hence the configurations of micro-reactor with long single channel design such as serpentine and coil are more efficient for chemical reaction. In case of the pin-hole configuration, although the velocity distribution and the CH4 concentration is uneven in each parallel channel, the total surface

H. An et al. / Chemical Engineering Science 75 (2012) 85–95

91

Fig. 4. Mole fraction of CH4 at z ¼ 5  10  4 m for (a) parallel; (b) pin-hole; (c) wavy; (d) oblique fin; (e) serpentine; (f) coiled; (g) coiled with serpentine and (h) coiled with double serpentine for Re  1500.

area available is significantly larger which in turn allows for higher conversion rates. Although high velocities result in better conversion, they lead to high pressure drop across the micro-reactors. Fig. 5 illustrates the pressure distribution across the reactor configurations discussed. The serpentine (Fig. 5e) and the three coil-based channels (Fig. 5f-h) which have high velocities reveal a significant pressure difference between the inlet and the outlet. A large pumping power is needed to drive the fluid in these channels. By contrast, the pumping power required for the parallel, pin-hole, wavy and oblique fin configurations is much lower (Fig. 5a–d). The inlet pressures in these configurations are approximately 30 times smaller than the coiled based channels while the outlet pressure is held the same. The pin-hole and oblique fin configurations require smallest pressure drop among all the rectilinear configurations as these have a larger number of branch channels through which the fluid can flow at lower velocities.

4.2. Effect of Reynolds number The effect of Reynolds number on reactor performance was evaluated in the laminar regime for 100, 500, 1000 and 1500. A desirable micro-channel design should be able to yield higher reaction rate at lower pumping power. Fig. 6 presents pressure drop results for various micro-channel designs at several Reynolds numbers. As expected, the pressure drop increases with Reynolds number in all cases. We can also see that the coiled-base designs (Fig. 6b) require much greater pressure drop compared with those of rectilinear design (Fig. 6a) at a given Reynolds number. Furthermore, among the rectilinear designs, the pressure drop for the pinhole design is lower than that for other three designs, viz., parallel, oblique-fin and wavy channels. It should be noted that if the flow channel not split, the pressure drop is much higher than that for a split geometry since the fluid is forced to flow over much longer passages.

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Fig. 5. Pressure distribution at z¼ 5  10  4 m for (a) parallel; (b) pin-hole; (c) wavy; (d) oblique fin; (e) serpentine; (f) coiled; (g) coiled with serpentine and (h) coiled with double serpentine for Re  1500.

Fig. 6. Pressure drop for each design at various Reynolds numbers (a) rectilinear designs; (b) coiled-base designs.

H. An et al. / Chemical Engineering Science 75 (2012) 85–95

Another key point of interest is the reaction rate; here it is presented in terms of fractional conversion. Fig. 7 depicts the fractional conversion of methane for various micro-channel designs at different Reynolds numbers. The coiled-based designs, as shown in Fig. 7b, give the highest conversion ranging from 98.8 to 100%. This can be expected due to their longer flow passages which in turn provide longer time for reaction to occur. On the other hand, the reaction rate for the serpentine channel design is slightly lower compared to that in the coiled-based design. However, it is still much higher compared to that for oblique fin, wavy channel and parallel channels, especially at the higher Reynolds numbers. If the rectilinear designs are considered (Fig. 7a), the rate of reaction is the highest for the pinhole design. This is due to the fact that the pin-hole design has the highest reaction surface compared to the other rectilinear design within the same total cross-section of a reactor. However, this effect is more pronounced at higher Reynolds numbers. The reaction rates for rectilinear designs do not differ much at lower Reynolds number values although the pressure drop decreases significantly. This provides clear evidence that all the rectilinear designs are also effective at lower Reynolds numbers. As shown in Fig. 1a, the parallel channel design is the simplest geometry, and the distance from inlet to outlet is also the shortest. Hence, the reaction time in the parallel channel design would be the shortest and the conversion would be the lowest as reflected in Fig. 7a. The fluid velocity and hence the mass flow rate at the inlet for different micro-channel designs increase linearly with Reynolds

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number since the cross sectional area for different designs is same. For the coiled-based designs, the conversion is almost complete even at the highest Reynolds number. Hence it should be noted that the consumption rate increases linearly with the Reynolds number as shown in Fig. 8b. However, at higher Reynolds numbers, the conversion for the rectilinear designs drops significantly which results in a drop in mass consumption rate compared to that in the coil-based designs at the same Reynolds number. This explains the deviation of the consumption versus Reynolds number curves for oblique-fin, parallel and wavy channels (Fig. 8a) except for the pin-hole geometry, where the consumption is comparable with coiled geometries. To discuss the combined effect of reaction rate and pressure drop for different channel designs, the ‘‘Figure of Merit’’ concept is introduced to compare the effectiveness of the reactor designs per unit pumping power (see Eq. (20)). Table 4 lists the calculated figure of merit for various reaction channel designs at different Reynolds numbers. As the Reynolds number increases, the figure of merit decreases. This is due to the fact that for coil-based designs, the pressure drop values increases significantly as the Reynolds number is increased, whereas for rectilinear designs, the reaction rate decreases notably with respect to the increased Reynolds number. It can also be seen that the coil-based channel designs have lower FoM. This is because coil-based channels require the highest pressure drop as shown in Fig. 6b. On the other hand, the parallel, pin-hole, wavy and oblique fin channels give much higher FoM values, up to around two order of

Fig. 7. Reaction rate for each design at various Reynolds numbers (a) rectilinear designs; (b) coiled-base designs.

Fig. 8. Mass consumption rate for each design at various Reynolds numbers (a) rectilinear designs; (b) coiled-base designs.

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Table 4 Figure of merit for various configurations of micro-channel reactors. Channel design

Parallel Pinhole Wavy Oblique Serpentine Coil Coil serpentine Coil double serpentine

Reynolds number 100

500

1000

1500

1449249 3977763 967993 1664785 32457 31902 32032 31902

43372 114234 30988 62379 1462 1314 1332 1332

7561 19782 5930 11749 315 278 278 278

183 6530 1953 3941 130 111 111 111

Ri Si si0 , si00 Stemp T U X

Greek letters

br

r m R

magnitude compared to those for coiled and serpentine channel designs. This results from a lower pressure drop. Amongst the four rectilinear designs tested, the pin-hole design has the highest FoM for all Reynolds number values. When designing reaction channels, careful consideration has to be given to the conversion and the pumping power required. When the yield is of more important, one may consider coil-based or the serpentine channel design; e.g. in production of pharmaceutical products yield is more important than pumping power. However, if pumping power is a major concern, the oblique fin design would be a good choice.

5. Conclusion A computational fluid dynamic analysis is carried out to investigate the conversion and pumping power required for microreactors of various designs over a range of Reynolds numbers. Four rectilinear channel designs, parallel, pin-hole, wavy, oblique fin and four coil-based designs were modeled. The reaction performance of micro-channels is discussed in terms of the figure of merit. Coil-based reactor designs give much higher conversion at all Reynolds numbers compared to those of rectilinear designs but also impose a significantly higher pressure drop penalty. As s result, the figures of merit for coil-based designs are much lower than those for other geometries. However, for application where pumping power is not an issue, the coil-based designs are desirable to obtain high conversion. The pin-hole design gives very good conversion -comparable to coils and with excellent figure of merit amongst the configurations tested. The pin-hole design has good potential for application as an innovative micro-reactor.

Nomenclature Ar Bi bi0 , bi00 cp Di Er Gi gi0 , gi00 keff kf,r M _ dep m p Q R

pre-exponential factor bulk/solid species, mol stoichiometric coefficient for bulk reactant, and product specific heat, Jkg  1 K  1 diffusivity of species I, ms  2 activation energy for the reaction, Jkg mol gas species, mol stoichiometric coefficient for gas reactant and product effective thermal conductivity, Wm  1 K  1 reaction rate constant using Arrhenius expression mean molecular mass net rate of mass deposition, kg pressure, pa volume flow rate, m3 s  1 universal gas constant, Jkg  1 mol  1 K  1

reaction rate of species i, kgm  3 surface-adsorbed/site species, mol stoichiometric coefficient for site reactant and product heat release/absorb due to reactions, Wm  3 temperature, K velocity, ms  1 mol fraction

Zpump oi

temperature exponent density, kg m  3 dynamic viscosity, Kg m  1 s  1 rate of rth reaction pump efficiency mass fraction of species i

Subscripts b dep eff g i r r, in r, out s temp

bulk deposition effective gas species i rth wall surface reaction reactant at inlet reactant at outlet solid/site temperature

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