Mathematical Modeling of Transport Processes

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Mathematical Modeling ofTransport Processes


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Mathematical Modeling ofTransport Processes

Editors: Agus P. Sasmito, Jundika C. Kurnia and

Sachin V. Jangam

2011


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Mathematical Modeling of Transport Processes

Copyright 2011

ISBN: 978-981-08-9179-4

All rights reserved. No part of this publication may be reproduced or

distributed in any form or by any means, or stored in a database or

retrieval system, without the prior written permission of thecopyright holder.


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FOREWORD

For a long time I have thought of and even planned to offer a new type of assignment leading

to some new pedagogy in teaching advanced level postgraduate course in Heat and MassTransfer. Essentially it is based on the well known and well-practiced Problem-based

learning (PBL) approach. Students are expected to self-learn based on carefully chosenproblems the solutions of which require groups of students to carry out appropriate

searches on their own. This experience is very valuable despite some inherent limitations

that should be covered elsewhere in the curriculum.

My idea was to let groups of students (in my case just 2) carry out independent and original

research project in transport phenomena and learn all aspects of carrying out a research

project from start to finish just in 3 months. In the current case the course was entitled Mass

Transport which included coupled heat transfer and reactions as well. Seven projects were

loosely defined so as to be original with no readymade solutions found by goggling. Most

projects required use of CFD software such as Fluent and MATLAB. My graduate students

agreed to be mentors for the 7 groups formed out of 14 students most PhD students in

mechanical engineering which I defined and sometimes refined the projectscope/objectives. Students were allowed to modify them with justification. Students wrote

technical report following a standard journal practice and then prepared suitable

PowerPoint presentations of about 20 minutes with 10 minutes for questions and

discussion. They were also told that selected papers could be reformatted and compiled as a

free e-book so as to provide a model for future generations of instructors and students whowish to follow the model.

In the classroom, lectures focused on basic concepts of conservation laws, control volumes

vs. systems, initial and boundary conditions, analytical solutions, dimensionless groups,

scaling of equations etc. Mentors trained most in use of CFD software as required. Students

were allowed to discuss problems and solutions with mentors and instructor but were

required to be as independent and original as possible. It is impossible to make all projectsof equal complexity or difficulty, of course.

The outcome of this effort is presented in this book upon reformatting and minor updates

for consistency. Readers will be impressed by both the breadth and depth achieved just in

about 3 months from start when most did not know what diffusion is and how a mass

transfer coefficient is defined as all had mechanical and civil engineering background.

My personal impression is that most students effectively went through the entire process

they need to go through during their PhD research. They even had experience to deliver

their paper in a conference like setting with an external Chairman and Co-Chairman.

I hope that the readers will find this documented experience of value in defining their ownpedagogical assignments. With some mentoring it seems to me that students can be

motivated to produce high quality work and learn several different aspects of research while

carrying out an essential course exercise.

I want to thank my PhD students Agus P. Sasmito, Jundika C. Kurnia and Sachin V. Jangam for

being such helpful and motivating mentors. We hope some of these term papers will be

refined and upgraded and submitted for journal publication as well.

Congratulations to everyone whose name appears in this e-book.

Arun S. Mujumdar

Professor

http//serve.me.nus.edu.sg/arun


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PREFACE

We are pleased at the opportunity to co-edit under Professor A.S. Mujumdar's guidance

this concise e-book which essentially records the outcome of a new pedagogical exerciseProf. Mujumdar designed and implemented for the first time in his module ME6203Mass Transport here at NUS. We are pleased to be a part to this unique experiment

which also has been very successful. We are all Professor Mujumdar's PhD students and

also mentors for the seven term paper projects that were assigned and completed

during January-March 2011.

Although given rather short time, students were able to jump-start their work as thetheme was specified to ensure there was opportunity to make a contribution to a new

area not covered in the lectures and indeed not available on "Google" searches either.Students had to define the problem and then develop mathematical descriptions

followed by numerical or analytical solutions (if possible). Some help was provided with

the numerical aspect. Focus was placed on processing and interpretation of results andon presenting it in the form of a technical journal paper. To simulate oral presentation

experience, the students were required to present their work to a larger audience offaculty and students as happens in a conference session. Numerous criteria were taken

into account for evaluation.

Professor Mujumdar terms this Research Project Based Learning" which probably

represents a paradigm shift in teaching of PhD students since they go through all key

aspects of what is needed to complete a PhD thesis. Readers can make their ownjudgment. We feel several of the term papers (as submitted) included here can be

enhanced further for journal publication. The copyrights of the content rest with

individual authors. This freely downloadable book is being brought out solely as aservice to faculty members all over the world who wish to follow this or a modifiedversion of the pedagogical model in their teaching.

We enjoyed working on this unique experiment and recommend it warmly. The only

caution is that it is a major effort for the faculty members and mentors who need to beextremely passionate and motivated about teaching.

Agus P. Sasmito

Jundika C. KurniaSachin V. Jangam

June 2011


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Index

Chapter No Title / Authors Page No

01 Numerical investigation of the performance of various

micro-reactor configurations

Hui An and Ang Li

01

02 Enhanced convective mixing for gaseous microreactors

M. Shaker and H. Ghaedamini

25

03 Modeling conjugate heat and mass transfer between a

laminar impinging jet and planar and curved thin slab of

wet solids

Tong Wei and Wang Yue

47

04 Numerical evaluation of pulsation effect on the reactionper-formance of a t-junction micro-mixer

Balaji Mohan and Jiang Puqing

61

05 Numerical analysis of single-particle combustion of coal

char

H. Osman and A. Ismail

83


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Hui An, Ang Li Numerical Investigation of the Performance of Various Micro-reactor configura-

tions


Chapter 1

Numerical investigation of the performance of various micro-

reactor configurations

Hui An1 and Ang Li2

Department of Mechanical Engineering, National University of Singapore,

9 Engineering Drive 1, Singapore

E-mail:

[email protected]

[email protected]

Contents

1.1. INTRODUCTION ................................................................................................................................ 3

1.2. MATHEMATICAL MODEL .............................................................................................................. 5

1.2.1. GOVERNING EQUATIONS ........................ ......................... ......................... ......................... .................. 6

1.2.2. CHEMICAL REATIONS ........................................................................................................................... 7

1.2.3. CONSTITUTIVE RELATIONS ............................................................................................................... 8

1.2.3.1. THERMODYNAMIC PROPERTIES OF THE WORKING FLUID ......................... ............... 8

1.2.3.2. REACTOR PERFORMANCE ........................ ..................... .......................... ......................... .......... 9

1.2.4. BOUNDARY CONDITIONS .................................................................................................................... 9

1.3. NUMERICS ........................................................................................................................................ 10

1.4. RESULTS AND DISCUSSIONS ...................................................................................................... 11

1.4.1. EFFECT OF CHANNEL CONFIGURATION ........................ ......................... ......................... .......... 11

1.4.2. EFFECT OF REYNOLDS NUMBER ........................ ......................... ......................... ......................... 17

1.5. CONCLUSION.................................................................................................................................... 21

NOMENCLATURE .................................................................................................................................... 21

REFERENCES ............................................................................................................................................ 22

Hui An and Ang Li. Numerical Investigation of the performance of various micro-reactor, Sasmito, A.P.; Kurnia,

J.C.; Jangam, S.V. and Mujumdar, A.S., 2011, ISBN 978-981-08-9179-4, Published in Singapore, pp. 1-24


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1.1. INTRODUCTION

Micro-reactor is a recent developing technology in chemical and pharmaceutical in-

dustries. It refers to the reactors with inner dimensions of the structure in the order of

millimetres and smaller. A number of impressive advantages have been demonstrated

on the micro-structured device over the conventional chemical reactors. It exposes high

area to volume ratio and offers high heat exchange and mass transport rate. Most of the

flows inside the micro-reactors are laminar in nature which allows precise computer

simulation on the chemical reactions. Its small scale also permits much easier control on

process parameters like temperature, pressure and flow rate, etc, and hence, reduces the

danger of highly exothermic or explosive chemical reactions (Jhnisch et al. 2003; Watts

and Haswell 2005).

Numerous research activities have been conducted to investigate the performance

of various micro-reactor designs. One of commonly used design choice is an array of mi-

cro-channels arranged in parallel with a common inlet and outlet channels perpendicu-

lar to them. This type of structure is easy to manufacture but expose poor flow distribu-

tion (Amador et al. 2004). A fractal tree-like network structure frequently observed

from natural organs (Bejan and Errera 1997; Chen and Peng 2002) and a regular bifur-

cation shape (Amador et al. 2004), on contrast, are able to provide more uniform flow

distribution and lower pressure loss in the structure. Coil-shape micro-reactor has been

demonstrated its ability of offering high heat and mass transfer as a result of the pres-

ence of secondary flows (Sasmito et al. 2011). Agrawal and Nigam (Agrawal and Nigam

2001) also found that its performance lies in between the plug and laminar tube flow

reactors under a premix inlet condition. Another type of design is to introduce posts or

baffles (Chung et al. 2011)inside the microreactor to enhance the mixing and reaction.

Posts in catalytic reaction are often coated or directly made of catalysts and exhibits

very high surface area (Ni et al. 2005; Yeom et al. 2009). A proper designed posted struc-

ture may provide narrow residence time distribution of gas and lead to high reaction

rate under carefully controlled condition (Deshmukh et al. 2004; Regatte and Kaisare

2011a). Furthermore, the shapes ofcross-section (Ramanathan et al. 2003; Arrighetti et

al. 2007; Carvalho et al. 2009, Kurnia et al 2011a)of the micro-reactors such as triangle,

rectangle, square, circular, sinusoidal and hexagonal have also been investigated to im-

prove the performance of micro-reactor.

Apart from the reactor geometry, flow configuration also plays an important role indetermining the performance of the micro-reactor. Axial- and cross-flow are two typical

flow configurations implemented in the micro-reactor design. Ajmera et al (Ajmera et al.

2002) studied fixed-bed micro-reactors and found out that cross-flow configuration can

offer high throughput in expense of less pressure loss than that of axial-flow. However,

cross-flow impose considerable flow mal-distribution, resulting in low reaction rate

(Regatte and Kaisare 2011b). A uniform flow distribution is essential to the rate of reac-

tant conversion(Saber et al. 2010).


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Figure 1.1. Micro-reactor configuration design: (a) parallel; (b) serpentine; (c) oblique fin; (e) coiled with

outer inlet/outlet; (f) coiled with inner inlet/outlet; (g) coiled with serpentine and (h) coiled with double

serpentine.

Micro-reactors generally work well for low Reynolds number. However, low Rey-nolds number leads to low throughput, while high flow rate impose a drop in chemical

a b

c dc

e f

g h


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reaction rate, which bottleneck the application of micro-structure in the industry. In this

paper the performance of a few configurations of micro-reactors are evaluated at both

low and high Reynolds number.Figure 1.1shows the configurations for parallel, serpen-

tine, wavy and oblique fin channels, two rectangular coiled channels with opposite flow

directions as well as two novel hybrid channels. Among all these designs, parallel, wavy

and oblique fin implements cross-flow configurations, whereas the rest are single-

channel. Moreover, the shape of oblique fin channel may be similar to that of micro-

reactor with parallelogrammic posts. In addition, a square shape cross-section for all the

configurations was used as it has better heat transfer behaviour over other design,

slightly higher total catalytic surface area as well as less requirement on manufacture

(Kurnia et al. 2011a)

The heat transfer capacity of these configurations has been evaluated in previous

work (Kurnia et al. 2011b) and the latter four designs has been demonstrated higher

rate and more uniform distribution over others. The reaction implemented to demon-

strate the concept is methane oxidation reaction with platinum as catalyst coated on theinner wall of surfaces (Li 2004;Deutschmann et al. 2000). Note that other type of reac-

tions can also be implemented within frame work derived here. It is assumed that the

species are well mixed at the inlet and constant well temperature of each configuration.

The numerical simulation is conducted by Fluent 6.3.26. The performance of eight con-

figurations in terms of reaction rate of species, pressure drop and Figure of Merit (de-

fined later) are evaluated under four Reynolds numbers (they are, 100, 500, 1000, 1500)

with an assumption of premix inlet condition.

1.2. MATHEMATICAL MODEL

The physical model which can be seen in Figure 1.1 comprises of eight micro-

reaction channel designs, e.g., parallel, serpentine, wavy channel, oblique fin, coiled with

outer inlet/outlet, coiled with inner inlet/outlet, coiled with serpentine and coiled with

double serpentine. All the channels have the same cross-section (1mmx1mm). In this

model, the methane and air is assumed to be well mixed before entering the channel

from the inlet. The reactions at the channel wall consist of multi-step reactions: adsorp-

tion reaction, surface reaction and desorption reaction. The detailed multi-step reaction

mechanism and its reaction rate constants are listed inTable 1.1.The wall is assumed tohave constant temperature, whereas the fluid is assumed to be steady, laminar, and

Newtonian. Since this work relates only to laminar flow, a precise numerical solution is

adequate to simulate the reality very closely.

Table 1.1. Surface reaction mechanism

No Reaction Ar r Er


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(J/kmol)

1 H2 + 2Pt(s) => 2H(s) 4.36e7 0.5 0

2 2H(s) => H2 + 2Pt(s) 3.7e20 0 6.74e7

3 O2 + 2Pt(s) => 2O(s) 1.8e17 -0.5 0

4 O2 + 2PT(s) => 2O(s) 2.01e14 0.5 0

5 2O(s) => O2 + 2Pt(s) 3.7e20 0 2.13e8

6 H2O + Pt(s) => H2O(s) 2.37e8 0.5 0

7 H2O(s) => H2O + Pt(s) 1e13 0 4.03e7

8 OH + Pt(s) => OH(s) 3.25e8 0.5 0

9 OH(s) => OH + Pt(s) 1e13 0 1.93e8

10 H(s) + O(s) => OH(s) + Pt(s) 3.7e20 0 1.15e7

11 H(s) + OH(s) => H2O(s) + Pt(s) 3.7e20 0 1.74e7

12 OH(s) + OH(s) => H2O(s) + O(s) 3.7e20 0 4.82e7

13 CO + Pt(s) => CO(s) 7.85e15 0.5 0

14 CO(s) => CO + Pt(s) 1e13 0 1.25e8

15 CO2(s) => CO2 + Pt(s) 1e13 0 2.05e7

16 CO(s) + O(s) => CO2(s) + Pt(s) 3.7e20 0 1.05e8

17 CH4 + 2Pt(s) => CH3(s) + H(s) 2.3e16 0.5 0

18 CH3(s) + Pt(s) => CH2(s) + H(s) 3.7e20 0 2e7

19 CH2(s) + Pt(s) => CH(s) + H(s) 3.7e20 0 2e7

20 CH(s) + Pt(s) => C(s) + H(s) 3.7e20 0 2e7

21 C(s) + O(s) => CO(s) + Pt(s) 3.7e20 0 6.28e7

22 CO(s) + Pt(s) => C(s) + O(s) 1e17 0 1.84e8

23 OH(s) + Pt(s) => H(s) + O(s) 1.56e18 0 1.15e7

24 H2O(s) + Pt(s) => H(s) + OH(s) 1.88e18 0 1.74e7

25 H2O(s) + O(s) => OH(s) + OH(s) 4.45e20 0 4.82e7

1.2.1. GOVERNING EQUATIONS

In the reaction channel, the conservation equations of mass, momentum, species

and energy are considered and given by

0 u (1)


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23

p

T

u u u u u I

(2)

i i i i

+ RD u

(3)

p eff tempc T k T S u (4)

In the above equations, is the fluid density, u is the fluid velocity, p is the pressure,

is the dynamic viscosity, T is temperature,i

is the mass fraction of species i ,i

D is

the diffusion coefficient of species i,i

R is the mass consumed or produced by reactions,

pc is the specific heat of the nano-fluid,

effk is the effective thermal conductivity and

tempS

is

heat release/absorb due to reactions.

1.2.2. CHEMICAL REATIONSThe reaction model considers the chemical reactions to be occurred 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 dis-

tinct from the same chemical species in the gas. In this model, seven gas 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 consi-

dered.

The gas phase species and surface species can be produced and consumed by sur-

face reactions and the general expression is given by:

' ' ' '' '' '', , , , , ,

1 1 1 1 1 1

g gb s b s r

N NN N N N K

i r i i r i i r i i r i i r i i r i

i i i i i i

g G b B s S g G b B s S

(5)

Here, iG represents the gas phase species, iB represents the solid species, and iS

represents the surface adsorbed species. rK ,',i rb ,

',i rs are the stoichiometric coefficients

for the three reactant species respectively, and '',i rg ,'',i rb ,

'',i rs are the stoichiometric coef-

ficients for the three product species respectively.r

K is the overall reaction rate con-

stant.

The rate of reaction is given

' ', ,

, wall wall1

g

i r i r

Ng s

r f r i i i

k G S

(6)

where ,f rk is the reaction rate constant which is calculated using the Arrhenius equa-

tions given by:

/

,

r rE RT

f r rk A T e

(7)


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andwalli

G is the molar concentration on the wall. So the net molar rate of consumption

or production for each species i is represented by:

rxn

rxn

rxn

'' ',gas , ,

1

'' ',bulk , ,

1

'' ',site , ,

1

1,2, 3,...,

1,2, 3,...,

1,2, 3,...,

N

i i r i r r g

rN

i i r i r r b

rN

i i r i r r s

r

R g g i N

R b b i N

R s s i N

(8)

Furthermore, it is assumed that on the wall surface the mass flux of each gas species

is balanced with its rate of production/consumption which is given by:

,wallwall dep i,wall , i,gas

1,2, 3,...,i

i w i g D m M R i N n

(9)

walli,site

1,2, 3,...,i

s

SR i N

t

(10)

where depm is the rate of mass deposition or etching due to surface reaction which is

given by:

dep , ,1

bN

w i i bulki

m M R

(11)

andwalli

S

is the site species concentration on the wall, defined as:

sitewalli iS z (12)

where site is the site density of the catalyst and iz is the site coverage of species i.

The gas concentration at the wall is calculated from the species mass fraction which

is expressed by:

wall i ,wall

wall,

i

w i

GM

(13)

1.2.3. CONSTITUTIVE RELATIONS

1.2.3.1. THERMODYNAMIC PROPERTIES OF THE WORKING FLUID

The working fluid is assumed to be well mixed air and methane. The thermody-

namic properties of the working fluid are calculated as follows:

The fluid density is given by the ideal gas law:

/pM RT (14)

where R is the universal gas constant and M is the molecular weight of the mixture flu-

id given by:


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4 2 2 2 2 2

4 2 2 2 2 2

1

CH H O H O CO NCO

CH H O H O CO CO N

MM M M M M M M

(15)

The fluid mixture viscosity is

4 2 2 2 2 2

,

with , = CH , H , O , H O, CO, CO , Nx

x

(16)

where ,x are the mole fractions of species and , and , is given by the expres-

sion below:

21 1

1/22(g) 4

,

(g)

11 1

8

MM

M M

(17)

The multi-component gas mixture thermal conductivity is defined as:

eff i ik k (18)

The gas mixture specific heat capacity pc is calculated by:

p i p,ii

c c (19)

1.2.3.2. REACTOR PERFORMANCE

In the later part of this paper, the results are discussed based on the figure of merit

(). To ensure the fidelity of comparison between various micro-channel designs, the

figure of merit is introduced to evaluate the effect of Reynolds number and the effect of

geometry on the pressure drop and reaction rate. is defined as the ratio of mass

consumption rate per unit pumping power required given by:

r,in r,out

pump

FoMP

(20)

where pumpP is the pumping power that is required to drive the fluid flow through the

channel, calculated by

1pump

pump

P Q p

(21)

In the above equation, pump is the pump efficiency, Q is the volume flow rate of the fluid,

and p is the pressure drop.

1.2.4. BOUNDARY CONDITIONS

The boundary conditions for the flow through the micro-channels are defined as

follows:


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Inlet: The mixture fluid of air and methane is assumed to be well mixed beforeentering the inlet of the micro-channels. We define the inlet mixture fluid flow

velocity and inlet temperature as:

2 4 22 4 2

in in inO O CH H

, , , ,in in CH H

u u T T (22)

Outlet: At the outlet, we specified the pressure. The stream wise gradient of thetemperature and the species mass fraction are both set to zero. The velocity is

not known a priori but needs to be iterated from the neighboring computational

cells.

out, 0ip p T n n (23)

Flow channel walls: at the walls of the channels, the surface reaction is taken intoaccount and is resolved based on Eq.9. We specify no slip condition and constant

wall temperature.

i0, 0T u (24)

1.3. NUMERICS

The computational domains shown inFigure 1.1were created using AutoCAD 2010.

The commercial pre-processor software GAMBIT 2.3.16 was used for building the mesh,

labeling boundary conditions and determining the computation domains. There are

three different amount of mesh (2.5 105, 5 1 05, 1 106) that were built and com-

pared in terms of pressure, temperature and velocity to ensure a mesh independent so-lution. The results show that a mesh amount of 5 1 05 only differs about 1% in terms

of p, u, and with the mesh amount of1 1 06, whereas a mesh amount of2.5 105

gives a deviation of 7% as compared to the finest mesh. Hence, a mesh amount of

5 1 05 was used for the numerical investigation purposes since it reduces the computa-

tional time and at the same time gives a reasonable accuracy on the results.

Based on equations 1-4 and the boundary conditions shown inTable 1.2, the finite

volume solver Fluent 6.3.26 was used to solve the constitutive relations consisting of

eleven dependent variables-,, ,,2,4,2,2,2,, and . The gas prop-

erties and chemical reaction mechanism was generated by using ChemKIN software; anda user defined function (UDF) file was also created using C language to account for tem-

perature dependence of the thermo-physical properties of the fluid.

Table 1.2. Base case and operating parameters

Parameter Symbol Value Unit

Inlet flow velocity (Re 100) 1 m/s




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Inlet temperature 300 K

Outlet pressure 101,325 Pa

Wall temperature 1290 K

1.4. RESULTS AND DISCUSSIONS

The computational fluid dynamic simulations were conducted for typical conditions

for micro-reactors. The boundary conditions and geometric parameters of the eight con-

figurations listed inTable 1.2andTable 1.3In the following, the effect of geometry on

the performance of the configurations under high flow rate (Reynolds number 1500) is

first addressed. Then an evaluation of the behaviour of every design affected variousReynolds number (100, 500, 1000, 1500) is performed. The concept of the Figure of

Merit is utilized to compare the conversion rate of reactants of all configurations at unit

pumping power.

1.4.1. EFFECT OF CHANNEL CONFIGURATION

Geometry is one of the key factors to determine the performance of the micro-

reactor. Flow distribution caused by reactor structure has a direct impact on the reac-

tion rate, and a mal-distribution reduces the fraction of species to be converted. Figure

1.2shows the simulated velocity contour at the middle of the flow channel (i.e. z = 5 x

10-4 m) of each reactor configuration at Reynolds number of 1500. It is observed that the

serpentine (Figure 1.2b), the two rectangular coiled (Figure 1.2e-f) and the two hybrid

coiled (Figure 1.2g-h) designs have higher velocity magnitude across their configuration

compared to the parallel (Figure 1.2a), wavy (Figure 1.2c) and oblique fin (Figure 1.2d)

shape which, however, have overall velocity magnitude approximately one order

smaller. Moreover, the latter three structures have also shown that higher velocity ap-

pears at branch channels near the inlet and outlet but the middle branches have lower

velocity, which in agreement with flow behaviour in a posted micro-reactors simulated

by Regatte and Kaisare(Regatte and Kaisare 2011b). Both phenomena attribute to the

structure of the reactor designs where cross-flow configuration leads to an uneven dis-

tribution of mass flow rate inside the parallel, wavy and oblique fin configurations, while

the rest have only one channel path throughout the configuration with now flow distri-

bution involved. To improve the distribution of the species, one may tapper the inlet and

outlet of the parallel, wavy and oblique fin designs (see(Regatte and Kaisare 2011b)). A

regular bifurcation shape (Amador et al. 2004) (as introduced early) can also be imple-

mented to obtain a more even flow distribution.

Table 1.3. Geometric parameters

Parameter Symbol Value Unit

Channel Widthch

w 1 x 10-3 m


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Channel Heightch

h 1 x 10-3 m

Oblique fin angleob 26

o

Oblique fin widthob

w 4.49 x 10-4 m

Oblique fin pitchob

p 3.06 x 10-3 m

Number of sinusoidal wavewv

n 10

Amplitude of sinusoidal wavewvA 5.10 x 10

-4 m

Total length of parallel channelpa

L 1.376 m

Total length of serpentine channelseL 1.351 m

Total length of wavy channel wvL 1.486 m

Total length of oblique fin channelob

L 1.376 m

Total length of coiled channel with outer

inlet/outletco

L 1.428 m

Total length of coiled channel with inner

inlet/outletci

L 1.428 m

Total length of coiled channel with serpentinecs

L 1.428 m

Total length of coiled channel with double serpen-tine

cdL 1.428 m


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a b

c d

e f

g h

Figure 1.2. Velocity contours at z = 5 x 10-4 m for (a) parallel; (b) serpentine; (c) oblique fin; (e)

coiled with outer inlet/outlet; (f) coiled with inner inlet/outlet; (g) coiled with serpentine and (h)

coiled with double serpentine for Re 1500.


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a b

c d

e f

g hFigure 1.3. Mass fraction of CH4 at z = 5 x 10-4 m for (a) parallel; (b) serpentine; (c) oblique fin; (e)


coiled with double serpentine for Re 1500.

Reaction rate of species shows an inverse trend to the velocity contour of reactor

configuration. At z = 5 x 10-4 m and Re 1500 for each configuration with same inlet


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condition. The mass fraction of CH4 of the serpentine (Figure 1.3b) and four coil based

designs (Figure 1.3e-h) continuously reduce along the channels, as shown inFigure 1.3.

The outlet mass fraction of CH4 for these five reactors presents a very small value, which

implies that the reaction is almost complete inside the channels. The parallel (Figure

1.3a), wavy (Figure 1.3c) and oblique fin (Figure 1.3d) configurations, however, exhibituneven mass distribution. The reaction rate of CH4 of these reactors is not as good as the

serpentine and coil based configurations, as the results show that at the outlet the wavy

and oblique fin channel has the mass fraction of CH4 one order of magnitude larger than

five designs and the parallel channel gives two orders of magnitude larger. The reaction

contour of O2 of each reactor is similar to that of CH4. This large deviation can be ex-

plained by the residence time of the species. Thermodynamically speaking, the longer

the residence time is, the better the conversion rate. Infinitely long residence time may

lead to almost full species conversion. From kinetic point of view, however, this is not

feasible as it requires extremely low flow rate. For the three rectilinear designs (the pa-

rallel, wavy and oblique fin), species finish the chemical conversion in a short channeldistance at their middle branches. As observed inFigure 1.2that velocity is very low at

these areas, the reactants present longer residence time and hence better reaction rate.

The branches near the entrance or exit, on contrast, are not long enough to accommo-

date the species for reaction due to the higher velocity noted as compared to middle

branches. Thus the mal-distribution of velocity abates the overall reaction performance

of these multi-channel configurations. On the other hand, single channel implemented in

serpentine and coil based configuration in general has much longer travelling distance

and therefore longer effective residence time for reactants, despite of high velocity.

Hence the configurations of micro-reactor with long single channel design such as ser-

pentine and coil are more efficient for the chemical reaction.

High velocity can result considerable pressure drop across the micro-reactors.Fig-

ure 1.4illustrates the pressure distribution across the reactor configurations introduced

in this paper. The serpentine (Figure 1.4b) and the four coil based channels (Figure 1.4e-

h) which have large velocity reveal a significant difference between inlet and outlet. A

large amount of pumping power is needed to push the fluid to flow in these channels. On

contrast, the requirement of pumping power is much less for the parallel (Figure 1.4a),

wavy (Figure 1.4c) and oblique fin (Figure 1.4d). Their inlet pressures are one approxi-

mately 30 times smaller than the coiled based channels. This can be explained by the

fact that micro-reactors with branch channels distribute the mass flow rate so that the

friction loss is small in branch channels. This also explains that oblique fin has the small-

est pressure drop among all the configurations as it has the largest number of branch

channels.


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a b

c d

e f

g hFigure 1.4. Pressure distribution at z = 5 x 10-4 m for (a) parallel; (b) serpentine; (c) oblique fin; (e)


coiled with double serpentine for Re 1500


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1.4.2. EFFECT OF REYNOLDS NUMBER

Another key factor for investigation in this study is the effect of Reynolds number,

as it directly affects the flow behavior and hence the reaction rate and the pumping

power that is required. In this study, four different Reynolds numbers 100, 500, 1000

and 1500 were used for investigation.

a)

b)

Figure 1.5. Pressure drop for each design at various Reynolds numbers (a) rectilinear designs; (b)

coiled- base designs.


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tions


a)

b)

Figure 1.6. Reaction rate for each design at various Reynolds numbers (a) rectilinear designs; (b) coiled-

base designs.

For similar micro-channel designs, we always would like to keep the pressure drop to

be the minimum, as it directly affects the operating cost. Hence, a good microchannel

design in our study should be able to maintain the reaction rate, and at the same time,

lower the pressure drop.Figure 1.5shows the pressure drop for different micro-channel

designs at various Reynolds numbers. As expected, the pressure drop increases as the

Reynolds number increases for all the designs. This is because larger Reynolds number

means larger flow rate, and will require higher pressure difference to drive the fluidflow. We can also see that coiled-base designs (Figure 1.5b) require higher pressure


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drop compared with that for rectilinear designs (Figure 1.5a) at the same Reynolds

number. This can be explained by the more complex flow patterns inside the channel

and the longer flow passages. Furthermore, among the rectilinear designs, the pressure

drop for the serpentine channel is one order of magnitude higher than that of parallel,

oblique-fin and wavy channels. We can note that if the flow channel does not split, thepressure drop is much higher than that with flow splitting since the fluid is forced to

flow in a much longer passages.

Another point of interest is the reaction rate. A good micro-channel design not only

gives a lower pressure drop but also a higher reaction rate.Figure 1.6depicts the reac-

tion rate for various micro-channel designs at different Reynolds numbers. The coiled-

based designs, as shown inFigure 1.6b, gives the highest reaction rate ranges from 98.8

to 100%. This can be expected due to their longer flow passages which in turn provide

longer reaction duration. On the other hand, the reaction rate for the serpentine channel

design is slightly lower compared to that of the coiled-based design; however, it is still

much higher compared to that of oblique fin, wavy channel and parallel channels espe-

cially at higher Reynolds numbers. But at lower Reynolds numbers, the reaction rate for

the oblique-fin and wavy channels does not differ much compared to that of serpentine,

whilst the pressure drop reduce significantly. This provides a clear evidence that the

oblique-fin and wavy channels are also very effective when used at lower Reynolds

numbers. As shown inFigure 1.1a, the parallel channel design gives the simplest geome-

try, and the distance from the inlet to the outlet is also the shortest. Hence, the reaction

time in the parallel channel design would be the shortest and the reaction rate would be

the lowest as reflected inFigure 1.6a.

The fluid velocity and hence the mass fluid rate at the inlet for different micro-channel designs increases linearly with the Reynolds number since the cross sectional

area for different designs are the same. For the coiled-based designs, the reaction rates

are almost equal to one even at the highest Reynolds number; hence we can see the

mass consumption rate increases linearly with the Reynolds number as shown inFigure

1.7b. However, at higher Reynolds numbers, the reaction rate for the rectilinear designs

drops significantly which results in the drop of mass consumption rate compared to that

of the coiled-based designs at the same Reynolds number. This explains the deviation of

the mass consumption verses Reynolds number curves for oblique-fin, parallel and

wavy channels from that for the serpentine curve as shown inFigure 1.7a.

With respect to the reaction rate and the 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 1.4lists the calculated figure of me-

rit for various reaction channel designs at different Reynolds numbers. It can be seen

that as the Reynolds number increases, the figure of merit decreases. This is due to the

fact that for coil-based designs, the pressure drops increases significantly as the Rey-

nolds number increases, whereas for rectilinear designs, the reaction rate reduces large-

ly with respect to the increases of Reynolds number. It can also be found that the coil-

based channel designs have lower figure of merit. This is because coil-based channels

require the highest pressure drop as shown inFigure 1.5b. On the other hand, the paral-

lel, wavy channel and oblique fin channels give much higher figures of merit, up to


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tions


around two order of magnitude compared to those for coiled and serpentine channel

designs. This results from the lower pressure drop.

a)

b)

Figure 1.7. Mass consumption rate for each design at various Reynolds numbers (a) rectilinear designs;

(b) coiled- base designs.


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Table 1.4 Figure of merit for various channel designs at different Reynolds numbers

Channel Design Re 100 Re 500 Re 1000 Re 1500

Coiled with double serpentine 172.4 7.2 1.5 0.6

Coiled with serpentine 173.1 7.2 1.5 0.6

Coiled with inner inlet/outlet 172.5 7.2 1.6 0.6

Coiled with outer inlet/outlet 172.4 7.1 1.5 0.6

Parallel with oblique fins 11363.9 425.8 80.2 26.9

Parallel 7915.8 236.9 41.3 12.0

Serpentine 175.4 7.9 1.7 0.7

Parallel wavy 5501.0 176.1 33.7 11.1

When designing reaction channels, careful balance and consideration has to be given to

the reaction rate and the pumping power that is required. When the reaction rate is

more of the interest, one can consider coil-based designs and the serpentine channel

design. However, if pumping power is the major concern, the oblique fin design may be

the most ideal case for consideration.

1.5. CONCLUSION

A reaction modeling has been done to investigate the reaction rate and the pres-

sure drop for various reaction channel designs at different Reynolds numbers (100, 500,

1000, and 1500). Eight channel designs,-parallel, serpentine, wavy channel, oblique fin,

coild with inner inlet/outlet, coiled with outer inlet/outlet, coiled with serpentine, and

coiled with double serpentine were used for investigation. The reaction performance of

micro-channels is discussed in terms of the figure of merit. It was found that coil based

designs give much higher reaction rate at all Reynolds numbers compared to those of

rectilinear designs due to their complex flow patterns and longer flow passages, but they

also impose a significantly higher pressure drop penalty. As s result, the figures of meritfor coil-based designs are very much lower. However, for the application where pump-

ing power is not an issue, the coil-based design can be the ideal choices for applications.

NOMENCLATURE

Ar pre-exponential factor

Bi bulk/solid species, mol

bi , bi stoichiometric coefficient for bulk reactant, and product

cp specific heat, Jkg-1K-1

Di diffusivity of species I, ms-2

Er activation energy for the reaction, Jkgmol


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Gi gas species, mol

gi , gi stoichiometric coefficient for gas reactant and product

keff effective thermal conductivity, Wm-1K-1

kf,r reaction rate constant using Arrhenius expression

M mean molecular massdep net rate of mass deposition, kg

p pressure, pa

Q volume flow rate, m3s-1

R universal gas constant, Jkg-1mol-1K-1

Ri reaction rate of species i, kgm-3

Si surface-adsorbed/site species, mol

si , si stoichiometric coefficient for site reactant and product

Stemp heat release/absorb due to reactions, Wm-3

T temperature, K

U velocity, ms-1

X mol fraction

Greek letters

br temperature exponent

density, kgm-3m dynamic viscosity, Kgm-1s-1

rate of rth reactionhpump pump efficiency

mass fraction of species i

Subscripts

b bulk

dep deposition

eff effective

g gas

i species i

r rth wall surface reaction

r, in reactant at inlet

r, out reactant at outlet

s solid/site

temp temperature

REFERENCES

Agrawal, S. and K. D. P. Nigam, 2001, Modelling of a coiled tubular chemical reactor,

Chemical Engineering Journal, 84 (3), 437-444.Ajmera, S. K., C. Delattre, Schmidt, M.A., and Jense, K.F., 2002, Microfabricated cross-flow

chemical reactor for catalyst testing, Sensors Actuators B, 4155, 1-10.Amador, C., A. Gavriilidis, Angeli, P., 2004, Flow distribution in different microreactor

scale-out geometries and the effect of manufacturing tolerances and channel

blockage, Chemical Engineering Journal, 101(1-3), 379-390.


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Arrighetti, C., S. Cordiner, Mulone, V., 2007, Heat and mass transfer evaluation in the

channels of an automotive catalytic converter by detailed fluid-dynamic andchemical simulation,Journal of Heat Transfer, 129(4), 536-547.

Bejan, A. and M. R. Errera., 1997, Deterministic tree networks for fluid flow: Geometry

for minimal flow resistance between a volume and one point, Fractals, 5(4), 685-

695.Carvalho, A. T., R. R. Lima, Silva, L. M., Simoes, E. W., Silva, M. L. P., 2009, Three-

dimensional microchannels as a simple microreactor, Sensors and Actuators, B:Chemical, 137(1), 393-402.

Chen, Y. and P. Cheng., 2002, Heat transfer and pressure drop in fractal tree-like

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Chung, C. K., T. R. Shih, Chang, C. K., Lai, C. W., Wu, B. H., 2011, Design and experiments ofa short-mixing-length baffled microreactor and its application to microfluidic

synthesis of nanoparticles, Chemical Engineering Journal, 168 (2), 790-798.Deshmukh, S. R., A. B. Mhadeshwar, Vlachos, D. G., 2004, Microreactor modeling for

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Deutschmann, O., L. I. Maier, Riedel, U., Stroemman, A. H., Dibble, R. W., 2000, Hydrogen

assisted catalytic combustion of methane on platinum, Catalysis Today, 59(1-2),

141-150.Jhnisch, K., V. Hessel, Lowe, H., Baerns, M., 2003, Chemistry in microstructured reactors,

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heat transfer performance of various cooling channel designs, Applied Thermal

Engineering, 31(6-7), 1293-1304.Li, G., "Surface reactions in catalytic tubes." Fluent documentations.Ni, Z., E. G. Seebauer, Masel, R. I., 2005, Effects of microreactor geometry on performance:

Differences between posted reactors and channel reactors, IndustrialEngineering Chemistry Research, 44(12), 4267-4271.

Ramanathan, K., Balakotaiah, V., D. H. West, 2003, Geometry effects on ignition incatalytic monoliths, AIChE Journal, 50 (7), 1493-1509.

Regatte, V. R. and N. S. Kaisare, 2011a, Propane combustion in non-adiabaticmicroreactors: 1. Comparison of channel and posted catalytic inserts, Chemical

Engineering Science, 66(6), 1123-1131.

Regatte, V. R. and N. S. Kaisare, 2011, Propane combustion in non-adiabatic

microreactors: 2. Flow configuration in posted microreactors, ChemicalEngineering Science, DOI: 10.1016/j.ces.2011.01.002.Saber, M., J. M. Commenge, Falk, L., 2010, Microreactor numbering-up in multi-scale

networks for industrial-scale applications: Impact of flow maldistribution on thereactor performances, Chemical Engineering Science, 65(1), 372-379.

Sasmito, A. P., Kurnia, J. C., Mujumdar, A. S., 2011, Numerical evaluation of transportphenomena in a T-junction micro-reactor with coils of different

configurations,Industrial Engineering Chemistry Research, DOI:

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Watts, P. and S. J. Haswell, 2005, The application of microreactors for small scale organicsynthesis, Chemical Engineering and Technology, 28(3), 290-301.

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micropost-filled microreactors, Journal of Micromechanics and Microengineering,

19(6), 5025.


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Chapter 2

Enhanced Convective Mixing for Gaseous Microreactors

M. Shaker and H. Ghaedamini

Department of Mechanical Engineering, National University of Singapore

9 Engineering Drive 1, Singapore 117576

Contents

ABSTRACT .......................................................................................................................................................... 27

2.1. INTRODUCTION .................... ...................... ...................... ...................... ..................... ...................... ....... 27

2.2. SIMULATION METHOD .......................................................................................................................... 28

2.2.1. Mathematical Model and Numerical Procedure ............ ............ ............. ............. ............. ............. ......... 29

2.2.2. Basic of Chemical Reaction ............. ............. ............ ............. ............. ............. ............. ............. ............. .......... 31

2.2.3. Boundary Conditions ................... ............. ............. ............. ............. ............ ............. ............. ............. ............. .. 32

2.2.4. Computational Procedure ............ ............. ............. ............. ............. ............. ............. ............. ............. ............ 33

2.3. RESULTS AND DISCUSION ..................................................................................................................... 34

2.3.1. Stochiometric Ratio ............. ............. ............. ............. ............. ............. ............. ............. ............. ............ ........... 34

2.3.2. Pre-Mixing and Uniform Concentration ............ ............. ............. ............. ............. ............. ............. ........... 35

2.3.3. Effect of Redirection and Sudden Expansion ............ ............. ............. ............. ............. ............ ............. ... 35

2.3.4. Effect of Split and Recombination and Impingement ............. ............. ............ ............. ............. ........... 40

2.3.5. Effect of Reynolds Number on Yield ............. ............. ............. ............. ............. ............. ............. ............. ..... 41

2.4. CONCLUSIONS ........................................................................................................................................... 42

M. Shaker and H. Ghaedamini, Enhanced Convective Mixing for Gaseous Microreactors, in Mathematical

Modelling of Transport Processes, Ed. Sasmito, A.P.; Kurnia, J.C.; Jangam, S.V., 2011, ISBN - 978-981-08-

9179-4, Published in Singapore, pp. 25-46.


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Shaker and Ghaedamini Enhanced convective mixing for gaseous microreactors

Mathematical Modeling of Transport Processes 27

ABSTRACT

This study investigates the steady, laminar flow field and reaction rates of several con-

figurations of a semi-T shaped microreactor by numerical simulations, governing con-

servation equations of mass, momentum, energy and spices were solved using Fluent 6-

3. The reaction is a catalyst surface based gaseous one between methane and air. Micro-

channel geometries can be divided into some innovative circular and rectangular con-

figurations which are designed to study and compare several effects such as those due to

recirculation, redirection, splitting of the flow and impingement. It is observed that the

rectangular designs display a better performance considering reactant utilization and

desired yield. Configurations with splitting and impingement zones have better per-

formance at the expense of higher pressure drop. Effect of pre-mixing of the reactant is

also considered by changing the inlet design. Effect of Reynolds number is to reduce the

yield due to shorter residence time in the microreactor..

2.1. INTRODUCTION

High performance microreactors have received special attention these years as

miniaturization has emerged as a need in industrial and medical applications like Bio

Micro-Electro-Mechanical Systems (BioMEMS) and lab-on-a-chip Microsystems [Wang et

al., 2011]. using devices working at sub millimeter scale, improved mass and heat trans-

fer rates can be achieved which enable us to proceed with reactions which are precisely

controlled and give the opportunity to selectively control the reaction process and

products [Nguyen and Wu, 2005;Aoki and Mae, 2006a].

In a microreactors two phenomena occur; mixing and reaction. Mixing in micro-

reactor is an important factor which needs special attention. Good mixing in a microre-

actor will result in a good reaction rate which it is desirable. In order to enhance mixing,

two approaches can be followed, passive mixing and active mixing[Hessel et al., 2005].

In passive mixing, we make use of the energy of the flow by designing the shape of the

channel to stretch and fold the flow [Aoki and Mae, 2006]. Even in some cases this can

generate chaotic advection [Tabeling et al., 2004]. All these will increase the interfacial

area between fluid segments and hence reducing the diffusion length. In an active mi-

cromixer, external forces help to enhance the mixing [Lam et al., 2005] this external

force can be a simple rotation [Dinh and Ogami, 2009], pulsation of the flow [Tesar,

2009], or an electrically exited flow[ Meisel and Ehrhard, 2006]. A recent review of sin-

gle phase micromixers has been by Kumar et al. which includes the recent improve-

ments and achievements in micromixers and microreactors[Kumar et al. 2011].

In the case of mixing at microchannels, due to the laminar regime in microchan-

nels, diffusion is the governing mode of mixing and mass transport[Aubin et al., 2010].

As a result, proposing special shapes which can enhance advection mixing is desirable.

This can be achieved by forcing the flow to go through special channel shapes which

manipulate the flow and by creating vortices in the flow field; it increases the contact

area between the species and reduces the diffusion length. For this purpose, methods

like splitting and rejoining the flow, chaotic mixing etc. can be implemented. It should be

noted that when the flow regime is laminar, the mixing is controlled by the diffusion.Hence to have better mixing, reducing the diffusion length scale is the target. This can be


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28 Mathematical Modelling of Transport Processes

achieved by adding some recirculation areas to the flow field, splitting and recombina-

tion of the fluid flow and etc.

Surely it is not possible to have a perfect design but it should be possible to have

a design which is least imperfect. In a microreactor, mixing and reaction occur at the

same time. The most optimum condition reaction completes exactly at the outlet of themicroreactor not sooner, the means that the residence time is equal to reaction time.

This is an ideal case and in our evaluations we will pay attention to it.

The case we examine via modeling in this investigation is a surface catalyst based gase-

ous reaction in a semi-T shaped microreactor. Due to the fact the diffusivity of gas

phases is relatively high; it is believed that T shaped micromixers are appropriate for

such applications. However, the numerical work on semi-T shaped microreactor shows

that, there is dependence on the mass flow volume and as the result Re. The reason is in

the fact that the reaction time scale and mixing time scale are the limiting factors which

at higher flow rates makes the T shaped microreactor efficiency to lower down. Thus, in

order to enhance flow mixing three geometric effects are to be considered.

Adding recirculation zones to the flow field by sudden expansions Adding recirculation and redirecting the flow Splitting and recombining the flow and impingement of streams

Based on the above three designs, eight types of semi-T shaped microchannels are mod-

elled which they can be classified as circular and rectangular designs.

2.2. SIMULATION METHOD

The model used in this investigation considers a semi-T shaped microreactor with eightdifferent designs to evaluate several phenomena which may enhance the mixing.Figure

2.1shows these eight designs. As one can see these reactor designs can be grouped into

two categorizes viz, circular and rectangular. With such designs the effect of recircula-

tion, cross section change, impingement and splitting of the flow streams can be com-

pared. Based on the main subject of this investigation, which is the study a gaseous re-

action, the model reaction of air with methane in the presence of a catalyst (platinum)

coated surface is chosen. This reaction is very well studied and the mechanism of the

chemical reactions can be obtained through available literature. The inlet design of the

reactor plays an important role in reaction rate and since we want to study the effect of

geometry on the efficiency. It was decided to reduce the negative effect of poor inlet de-sign by introducing the semi-T shaped microchannel fitted with two inlets for the air

and one inlet for methane. The reason for changing the inlet configuration is the fact that

by considering equal area for fuel and air inlet, it is necessary to increase the inlet veloc-

ity of air in order to obtain the necessary Stoichiometric ratio, defined with air to fuel

molar ratio of 9.52 for the reaction modelled in this study. Hence we changed the inlet

configuration and increased the inlet area for air as we need to feed much more air than

methane.Based on Fig.1, there are two inlets to the T shaped microchannel for air and

through the smaller inlet channel, the fuel enters the reactor. The reactants mix and re-

action occurs along the microchannel inside surface.


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Figure 2.1. Different two dimensional channel configurations

2.2.1. Mathematical Model and Numerical Procedure

Mixing and reaction which occur in a microchannel lead to different transport

phenomena such as diffusion, convective mass and heat transfer, adsorption and de-

sorption on the surface of the channel etc. In order to translate these physical phenom-

ena to a numerical model, three basic conservation equations are invoked:

Conservation of mass, the continuity equation:

() = 0 (1)

Conservation of momentum:

( ) = p + ( + () 23 ( )) (2)

Conservation of energy:

cpT = (keffT) + Stemp (3)

As the microchannel is a microreactor, chemical reaction and therefore conservation of

spices should be considered as the fourth conservation equation:


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(i) = (Dii) + Ri (4)

where, is the fluid density, u is the fluid velocity, p is the pressure, is the dynamic vis-

cosity, T is temperature,

iis the mass fraction of species i, D

iis the diffusion coefficient

of species i, Ri is the mass consumed or produced by reactions, cp is the specific heat,keffis the effective thermal conductivity and Stemp is heat release/absorption due toreaction.

Solving above four equations results in computation of the velocity, pressure and

temperature fields along channel length; also they lead to calculation of outlet mass frac-

tions of all spices including reactants and products.

In this study we assumed steady, laminar and Newtonian flow. Also it is assumed

that the miscible species mixture follows ideal gas law; so the thermodynamic proper-

ties of the mixture such as density (), viscosity (), thermal conductivity (keff) and heatcapacity (cp) defined as follow:

The fluid density is given by the ideal gas law:

= pM RT (5)

where R is the universal gas constant and M is the molecular weight of the mixture fluid

given by:

M = (CH

MCH+

H

MH+

O

MO+

HO

MHO+

CO

MCO+

CO

MCO+

M)1 (6)

The fluid mixture viscosity is computed from:

= x x, with , = CH4, H2, O2, H2O,CO,CO2, N2 (7)

where x,are the mole fractions of species and , and , is given by the expression

below:

, =1

8(1 +

M

M)1 2 [ 1 + (

()

())

(

M

M)

]2 (8)

The multi-component gas mixture thermal conductivity is computed using:

keff= kii (9)

The gas mixture specific heat capacity cp is calculated by:

cp = icp,ii (10)


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2.2.2. Basic of Chemical Reaction

The heterogeneous reaction model considers the chemical reactions to occur on

the channel surface only, and the reactions involving surface deposition are defined as

distinct surface reactions and hence treated differently from bulk phase reactions in-

volving the same species. In the same way, the chemical species deposited on surfacesare treated as distinct from the same chemical species. In this model, seven gas 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 [Deutschmann, O.; Maier, L. I.; Riedel, U.; Stroemman, A. H.; Dibble, R. W. ,

2000].

The gas phase species and surface species can be produced and consumed by surface

reactions and the general expression is given by:

gi,r GiNi=1 + bi,r Bi

Ni=1 + si,r Si

Ni=1

K gi,r GiNi=1 + bi,r BiNi=1 + si,r SiNi=1 (11)

where Gi represents the gas phase species, Bi represents the solid species, Si representsthe surface adsorbed species. gi,r

, bi,r , si,r

are the stoichiometric coefficients for thethree reactant species respectively, and gi,r

, bi,r , si,r

are the stoichiometric coefficientsfor the three product species respectively. Kr is the overall reaction rate constant.

The rate of reaction is given by:

r = kf,r [Gi]wallg,N

i=1 [Si]wallS, (12)

where kf,r is the reaction rate constant which is calculated using the Arrhenius equa-tions given by:

kf,r = ArTeE RT (13)

and [Gi]wall is the molar concentration on the wall. So the net molar rate of consumptionor production for each species i is represented by:

Ri,gas = (gi,r gi,r )Nnr=1 r i = 1,2,3, . . , Ng

Ri,bulk = (bi,r bi,r )Nnr=1 r i = 1,2,3, . . , NbR i,site = (si,r si,r )Nnr=1 r i = 1,2,3, . . , Ns

(14)

Furthermore, it is assumed that on the wall surface the mass flux of each gas species is

balanced with its rate of production/consumption which is given by:

wallDii,wall

n m depi,wall = M,iRi,gas

i = 1,2,3, . . , Ng(15)


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[S]t = R

i,site i = 1,2,3, . . , Ns (16)

where m dep is the rate of mass deposition or etching due to surface reaction which isgiven by:

m dep = M,iNi=1 R i,bulk (17)

and [Si]wall is the site species concentration on the wall, defined as:

[Si]wall = sitezi (18)

where site 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 isexpressed by:

[Gi]wall =,

M, (19)

2.2.3. Boundary Conditions

Besides specifying basic set of conservation equations and characteristic of flow, we

need to define the boundary conditions to solve the mathematical model equations.

Definition of the boundary conditions have been done for inlet, outlet and channel wall;

temperature, spices mass fraction and velocity are known parameter for the inlets, pres-sure and gradient of the temperature and gradient of the species mass fraction are

known for outlet and along channel wall, no slip condition and constant platinum sur-

face temperature are assumed as the boundary conditions.

Boundary conditions at inlet1. At air side :

= 0.01, 0.05, 0.1 ,1, 3,7 ,

= 300 ,

2 = 0.21 & 2 = 1 2

2. At methane side: = 0.01, 0.05, 0.1 ,1, 3,7 ,

= 300

,


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4 = 0.9 & 2 = 0.1

Boundary conditions at the outlet = 1 ,

= 0 & = 0

Boundary conditions along channel wall1. No-slip condition2. No species flux

= 1290 ,2.2.4. Computational Procedure

In order to solve the above coupled equations, a commercial software (FLUENT 6.3)

based on the finite volume scheme was implemented. For the grid production, the Gam-

bit code was used to produce the quad 2D mesh which is then imported to Fluent. The

pressure based solving procedure is then implemented while the first order upwind spa-

tial discretization was used. the SIMPLE scheme used for the pressure-velocity coupling.

The reaction equations mechanisms were imported from CHEMKIN to Fluent.Table 2.1

contains the surface reactions postulated. Iterations were done until the residuals of the

energy, continuity, momentum and species were less than 1e-6. Grid study was carried

out by reducing the mesh size until the difference in key variables between two similar

cases with different mesh sizes was less than 1%. This grid study showed that a mesh

size of 0.002 for the mapped quad element is suitable for all cases examined here.

Table 2.1. Surface reaction mechanism

[Deutschmann et al., 2000 ]

No Reaction Ar Br Er (J/kmol)

1 H2 + 2Pt(s) => 2H(s) 4.36e7 0.5 0

2 2H(s) => H2 + 2Pt(s) 3.7e20 0 6.74e7

3 O2 + 2Pt(s) => 2O(s) 1.8e17 -0.5 0

4 O2 + 2PT(s) => 2O(s) 2.01e14 0.5 0

5 2O(s) => O2 + 2Pt(s) 3.7e20 0 2.13e86 H2O + Pt(s) => H2O(s) 2.37e8 0.5 0

7 H2O(s) => H2O + Pt(s) 1e13 0 4.03e7

8 OH + Pt(s) => OH(s) 3.25e8 0.5 0

9 OH(s) => OH + Pt(s) 1e13 0 1.93e8

10 H(s) + O(s) => OH(s) +

Pt(s)

3.7e20 0 1.15e7

11 H(s) + OH(s) => H2O(s) +

Pt(s)

3.7e20 0 1.74e7

12 OH(s) + OH(s) => H2O(s) +

O(s)

3.7e20 0 4.82e7

13 CO + Pt(s) => CO(s) 7.85e15 0.5 014 CO(s) => CO + Pt(s) 1e13 0 1.25e8


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15 CO2(s) => CO2 + Pt(s) 1e13 0 2.05e7

16 CO(s) + O(s) => CO2(s) +

Pt(s)

3.7e20 0 1.05e8

17 CH4 + 2Pt(s) => CH3(s) +

H(s)

2.3e16 0.5 0

18 CH3(s) + Pt(s) => CH2(s) +H(s)

3.7e20 0 2e7

19 CH2(s) + Pt(s) => CH(s) +

H(s)

3.7e20 0 2e7

20 CH(s) + Pt(s) => C(s) + H(s) 3.7e20 0 2e7

21 C(s) + O(s) => CO(s) + Pt(s) 3.7e20 0 6.28e7

22 CO(s) + Pt(s) => C(s) + O(s) 1e17 0 1.84e8

23 OH(s) + Pt(s) => H(s) +

O(s)

1.56e18 0 1.15e7

24 H2O(s) + Pt(s) => H(s) +

OH(s)

1.88e18 0 1.74e7

25 H2O(s) + O(s) => OH(s) +OH(s)

4.45e20 0 4.82e7

2.3. RESULTS AND DISCUSION

For heterogeneous catalytic reactions, the desired reaction is defined in terms of the

maximum utilization of the reactants and hence maximum production of desirable spe-

cies. This naturally depends on the concentration of the fresh reactants which are in

contact with the catalyst to yield the desired species. Catalyst improves the reaction rate

by decreasing required activation energy of reaction. Thus, it is important that, as much

as possible, the reactants are in contact with the catalyst-coated surface simultaneously.

Therefore by increasing the contact area of micro-channel we should be able to enhance

yield of the desirable reaction.

In catalyst based micro reactors the basic mechanism of the reaction depends on

the near surface conditions. This includes adsorption, i.e. adsorption of fuel and oxygen

onto the platinum-coated surface, surface reactions, i.e. chemical reactions of the ad-

sorbed species, as well as the desorption reaction, i.e. desorption of the resulting prod-

ucts, which overall cause to heat release. Besides these phenomena, convective heat and

mass transfer between catalyst coated surface and gas boundary layer are the other

mechanisms which take place there. Therefore in addition to the effect of increased cata-lyst surface, increasing the diffusion rate, convective mass and heat transfer rates will

contribute to improved yield. Satisfying Stoichiometric ratio, pre-mixing and uniform

concentrations are the other factors which should be considered.

2.3.1. Stochiometric Ratio

For all reactions stoichiometric ratio is one of the key factors, because the exhaust

species will be different for different values of the coefficients. It is important to distin-

guish between rich and lean conditions of combustion. Beside the importance of the type

of exhaust products, lean combustion may lead to low fuel consumption which is one of

the features of the reaction.


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To investigate the effect of stoichiometric ratio, we modeled two reactions with O 2

inlet mass fractions of 0.21 and 1. Our results showed that changing the mass fraction of

O2 in inlet from 0.21 to 1 improved the CH4 and O2 (reactants) utilization by 3.48 and

1.24 times, respectively. Also, it changed the composition of the exhaust. In the first case

(mass fraction of O2=0.21) there was a higher percentage of carbon monoxide but by

increasing the mass fraction of O2, production of CO2 composition increased, which is

our desired product in combustion of methane.

2.3.2. Pre-Mixing and Uniform Concentration

To reach a uniform concentration of products at the outlet, an indicator of a com-

plete reaction, it is important that a uniform mixture of the reactants to be in contact

with catalyst surface. Non-uniform mixture would cause low air-to-fuel ratio on one side

of the catalytic surface and thus it leads to an increase in the production of undesirable

products at the surface. Thus, it is suggested that we first mix the reactants together and

then pass the mixture of reactants through the reactor zones (channel coated with cata-

lyst) to yield desired products. It would lead to uniform concentration at the outlet.

Without premixing of reactants a distinct concentration difference is observed at the

outlet of the reactor while much better uniformity in concentration is attained, as ex-

pected, with good premixing.

Figure 2.2. Effect of premixing on a T shaped microreactor-CO2 mass fraction fields

2.3.3. Effect of Redirection and Sudden Expansion

Figure 2.3 shows the consumption of CH4 as one of the reactants vs the Reynolds

number. Increment in area coated with catalyst and vortices which appear along chan-

nel walls because of sudden expansion will lead to increment in the rate of reactant

utilization comparing to strait T junction channel.

As can be seen, at small Re the utilization for all cases is near 100% which is rea-sonable since the mean residence time is much greater than diffusion time and the reac-


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tion time. This can be better seen from the CO2 mass fraction contour at Figure 2.4.

Therefore there is no difference in utilization of the reactants with different microchan-

nel geometries. The superiority of adding redirection to the flow field shows itself at

relatively higher Reynolds numbers. FromFigure 2.3, it can be seen that for Re greater

than 100, redirection of the flow will result in better utilization of reactants. Due to the

fact that redirection will increase the residence time as the flow has to go through a

longer path, also from the velocity profile (Figure 2.5) at Re=90 it is obvious that the

two dissimilar counter rotating vortices in a type2 configuration will occur at higher

Reynolds numbers which are stronger and thus, a shorter diffusion length plus greater

interfacial area will result in a better mixing.

Figure 2.3. CH4 utilization at different Reynolds number for rectangular designs

0

10

20

30

40

50

60

70

80

90

100

0 200 400 600 800

ch4Utilizatio

n%

Re. Number

Type 1

Type 2


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Figure 2.4. CO2 mass fraction contour plots for type1 configuration.


50/122



Figure 2.5. Velocity contour plots at Re=90 for a type1 and type2 configuration

Figure 2.6shows a similar trend for the circular types as the Reynolds number in-

creases. The redirection can increase the consumption of CH4 but it can be seen that in

comparison with rectangular design the increment is less. This is due to the fact that the

recirculation area in the circular design has reduced into one vortex instead of two,

which means smaller contact area and poorer mixing. This is obvious from theFigure

2.7which shows the velocity field.

0

10

20

30

40

50

60

70

80

90

100

0 100 200 300 400 500 600 700

ch4Utilization%

Re. Number

Type 3

Type 4


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Figure 2.6. CH4 utilization for circular designs

Figure 2.7. Velocity contours at Re=90 for a type3 and type4 configurations.

Figure 2.8shows the pressure drop of the first four types. It can be seen that the chan-

nels with more complicated flow structure, type 2 and 4, have a higher pressure drop.

By increasing the Reynolds number, pressure drop will increase but the increment of

circular designs is greater in compare with rectangular designs. A comparison between

rectangular and circular designs reveals that the rectangular shapes are superior as they

have the same order of utilization while the pressure drop is much lower.

Figure 2.8. Pressure drop

0

5000

10000

15000

20000

25000

30000

35000

0 50 100 150 200 250 300

PressureDrop(Pa)

Re. Number

Type 1

Type 2

Type 3

Type 4


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2.3.4. Effect of Split and Recombination and Impingement

In order to see the effect of splitting the flow, channel configuration of types 5 to 8

are designed to have even and uneven splitting of the flow which it gives us the oppor-

tunity to study the case with more generality.Figure 2.9shows the CH4 utilization of six

configurations, it is obvious that the splitting types which have more complicated ge-ometries have better performance. However, the results show that type 5 and 7 designs,

rectangular designs with splitting, have the highest reactant utilization among all the

microchannel geometries examined. The main trend of all configurations is that the

utilization of reactants decreases with increasing Reynolds number. There are several

implications here. First, splitting of the two reactant streams and their recombination in

type 5 to 8 geometries increases the contact area with the catalyst-coated surface and at

the same time increases the diffusion because splitting of fluid streams contributes to

mixing by increasing the interfacial area and by shortening the diffusion length. Increase

in both factors leads to increase in the reaction yield. Second, impingement of streams in

splitting configurations leads to increase of heat and mass transfer coefficients betweenthe catalyst-coated area and the gas flow, thus increasing the adsorption of reactants

and desorption of products. Third, centric and eccentric configurations have a same

production rate as it is obvious fromFigure 2.9andFigure 2.10. The reason is that for

two cases, resistance time as well as the diffusion length are as the same order and thus

equal utilization is observed however, pressure drop of centric configurations are less

than eccentric configurations, Figure 2.11. Fourth, with increasing Reynolds number,

the effect of vortex generation and impingement enhances the mass transfer and reac-

tion rates. However, increasing the Reynolds number also leads to shorter residence

time of fluid in the channel; fluid molecules may have not enough time to mix and react,

and can cause reduction of reaction rate. When the negative effect of residence time isgreater than the positive effect of impingement jet and vortex generation, the overall

rate of reactant utilization will decrease.

Figure 2.9. CH4 utilization vs. Reynolds number.

0

10

20

30

40

50

60

70

80

90

100

0 50 100 150 200 250 300

ch4

Utilization%

Re. Number

Type 1

Type 3

Type 5

Type 6

Type 7

Type 8


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Figure 2.10. Mass fraction of centric and eccentric configurations at Re=90.

Figure 2.11. Pressure drop of centric and eccentric designs.

2.3.5. Effect of Reynolds Number on Yield

Figure 2.12show that the Reynolds number has an effect on the type of the final prod-

ucts. There is higher percentage of carbon monoxide with increasing Re, which is not the

final desired product in combustion of methane. With increasing Re, since the residencetime of flow in microchannel decreases, this leads to incomplete reaction between

0

5000

10000

15000

20000

25000

30000

35000

40000

45000

0 50 100 150 200 250 300

PressureDrop(Pa)

Re. Number

Type 5

Type 6

Type 7

Type 8


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methane and air. It can be seen fromTable 2.1, CO2 will be generated when CO(s) and

O(s) react on the surface of catalyst. When there is not enough time for the presence of

flow in channel, some of the surface reactions of Table 1 will occur incompletely; there-

fore the ratio of co production to CO2 will increase. Interestingly type 1 microchannel

has minimum undesirable products at high flow rates. However, it should be noted that

the overall production of type1 is much less than in other configurations e.g. type 5 and

6. Moreover, the superiority of the

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