Heat transfer characteristics analysis and optimization of the Micro Packed Bed Bionic Reactor

Journal Pre-proof Heat transfer characteristics analysis and optimization of the Micro Packed Bed Bionic Reactor Wei-liao Liu Xi Li You-wei Cheng Li-jun Wang

PII:

S0255-2701(19)30402-7

DOI:

https://doi.org/doi:10.1016/j.cep.2019.107644

Reference:

CEP 107644

To appear in:

Chemical Engineering and Processing

Received Date:

10 April 2019

Revised Date:

6 August 2019

Accepted Date:

21 August 2019

Please cite this article as: Wei-liao Liu, Xi Li, You-wei Cheng, Li-jun Wang, Heat transfer characteristics analysis and optimization of the Micro Packed Bed Bionic Reactor, (2019), doi: https://doi.org/10.1016/j.cep.2019.107644

This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Published by Elsevier.

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Figure 1: (a) Schematic diagram of mammal circulatory system, (b) Simplified schematic

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diagram of the hierarchical channel system, (c) Elementary level of the FBBR.

Figure 2: Sectional view of the prototype elementary structure of the MPBBR.

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Page 1 of 36

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Figure 3: (a) Sectional view of the MPBBR elementary unit, 2D geometries and boundary

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conditions of x − y plane (b) and x − z plane (c).

Figure 4: Heat transfer interactions between (a) radial conduction and convection in the packed bed, (b) axial convection and radial conduction in the input channel, (c) axial conduction and reaction heat in the packed bed.

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Page 2 of 36

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Figure 5: Influence of wall thickness on the axial temperature distribution in the input channel

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and catalyst bed.

Figure 6: Influence of channel width on the axial temperature distribution in the input channel and catalyst bed.

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Page 3 of 36

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Figure 7: Sectional view of the MPBBR structure with back-turning input channel.

Figure 8: Heat transfer behavior and temperature profile in (a) the normal single input channel, (b) the back-turning input channel (2h = 3mm, N = 4, ww = 0.6mm, L = 10cm).

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Page 4 of 36

f oo

Figure 9: Axial distribution of channel temperature with and without back-turning channel

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Pr

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(2h = 3mm, N = 4, ww = 0.6mm, L = 10cm).

Figure 10: Relation between maximal bed temperature difference and bed length with and

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without back-turning channel (2h = 3mm, N = 4, ww = 0.6mm).

Figure 11: Comparisons of axial temperature distribution between other monolithic reactor investigations and the MPBBR (single input channel).

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Page 5 of 36

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Figure 12: Schematic and geometric parameters of the HRMC (unit:mm).

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Figure 13: Comparisons of axial temperature distribution between the HRMC and CMC.

Figure 14: Top view of the MPBBR structure with back-turning input channel.

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Page 6 of 36

f oo pr e-

Figure 15: Relation between the maximal temperature difference and bed length for different

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Pr

channel density (y0,CH4 = 1%).

Figure 16: Relation between the maximal temperature difference and bed length for different channel density (y0,CH4 = 0.5%).

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Page 7 of 36

f oo pr ePr al rn

Figure 17: Temperature profile for the whole elementary unit, framework domain, and catalyst

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bed domains under optimized conditions (y0,CH4 = 1%).

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Page 9 of 36

Introduction of the Micro Packed Bed Bionic Reactor (MPBBR) Mathematical modeling of MPBBR elementary structure unit Analysis of the heat transfer behaviors and auto-thermal function MPBBR design for the catalytic combustion of lean methane

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Optimization of structure and geometric parameters

Page 10 of 36

Heat transfer characteristics analysis and optimization of the Micro Packed Bed Bionic Reactor Wei-liao Liu, Xi Li∗, You-wei Cheng, Li-jun Wang

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College of Chemical and Biological Engineering, Zhejiang University, 38 Zheda road, Hangzhou 310027, People’s Republic of China

Abstract

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The Fixed Bed Bionic Reactor (FBBR) is a novel conceptual reactor using hierarchical flow channel networks to reduce the pressure drop in fixed beds so

e-

that fine catalysts can be used to enhance the catalyst effectiveness. The Micro Packed Bed Bionic Reactor (MPBBR) is a representative implementation of the FBBR designed for fast catalytic reactions with strong heat effect. In this

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work, the heat transfer behaviors of the MPBBR are qualitatively analyzed. By a typical application case, the catalytic combustion of lean methane, the influences of channel structure and geometric parameters on the heat transfer

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performance are quantitatively analyzed. An optimal MPBBR for such highly exothermic reaction uses porous silicon carbide ceramic monoliths as honeycomb

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framework. The single input channel is modified by add a back-turning channel. With the optimized channel structure and geometric parameters, the maximal

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temperature difference in the catalyst bed is maintained under 45o C, and the unit catalyst mass and unit reactor volume handling capacities are doubled and tripled, respectively. The MPBBR is proved to be a flexible and economical device with high performance heat transfer. Keywords:

Fixed bed bionic reactor, Heat transfer in porous channel, Auto-thermal function, Reactor optimization, Catalytic combustion of lean methane ∗ Corresponding

author Email address: [email protected] (Xi Li)

Preprint submitted to Chemical Engineering & Processing: Process IntensificationAugust 6, 2019

Page 11 of 36

Nomenclature

2

I~

direction vector

3

~u

velocity vector, m/s

4

B

permeability, m2

5

C

molar concentration, mol/m3

6

Cp

heat capacity at constant pressure, J/kg · K

7

D

diffusivity, m2 /s

8

dp

catalyst particle diameter, mm

9

h

half channel width, mm

10

K

thermal conductivity, W/m · K

11

L

bed length, cm

12

N

column number of catalyst bed

13

p

pressure, P a

14

QR

reaction heat, W/m3

15

R

reaction rate, mol/m3 · s

16

u

flow velocity in x-direction, m/s

17

v

flow velocity in y-direction, m/s

18

w

thickness, mm

19

Greek symbols

20



porosity

21

µ

dynamic viscosity, P a · s

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Pr

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pr

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f

1

2

Page 12 of 36

0

feed

25

b

catalyst bed

26

e

effective coefficient

27

g

gaseous reactant

28

L

longitudinal direction

29

s

solid material

30

T

transverse direction

31

w

permeable wall

32

1. Introduction

oo

24

pr

Subscript

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23

Pr

ρ

f

density, kg/m3

22

The Fixed Bed Bionic Reactor (FBBR) is a novel conceptual reactor. The

34

core idea of the FBBR is the use of hierarchical input and output channel net-

35

works to reduce the pressure drop in packed beds so that fine catalysts can be

36

used to enhance the catalyst effectiveness [1]. The FBBR structure is inspired

37

from the mammal circulatory system, which consists of artery and vein channel

38

networks and capillaries in Fig. 1(a). Fig. 1(b) is the simplified schematic di-

39

agram demonstrating the hierarchical channel system from aorta to vena cava.

40

The capillaries only exist between the lowest level of arteries and veins. The

41

FBBR adopts the distributed flow pattern which is realized by proper arrange-

42

ment of different levels of flow channels. The elementary structure level is shown

43

in Fig. 1(c). As the arrows indicate, the distributed reactant fluids flow verti-

44

cally into the close-ended input channels, penetrate the adjacent catalyst beds,

45

and leave through the nearest output channels. The input and output channels

46

are alternatively configured. The catalyst particles are packed in the space area

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33

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47

between adjacent channels. In this way the catalyst bed can be segmented to

48

rather thin layers and the infiltration velocity is greatly reduced due to large

49

contact surface between the channels and the beds, resulting in low flow resis-

50

tance and the applicability of fine catalysts. Based on different reaction conditions and production scales, there are sev-

52

eral kinds of implementations of the FBBR. The MPBBR is a representative

53

implementation and its elementary structure is formed by honeycomb frame-

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works. Fig. 2 shows a sectional view of the prototype structure of the MPBBR.

55

One end of a column is sealed to form input or output channel. The catalysts

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are packed and sealed in several columns between a pair of input and output

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channels to form the catalyst bed. The manufacture of the MPBBR is simple,

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since the honeycomb framework can be realized by wall-flow monoliths. Due

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to the small scale and compact structure of flow channels and catalyst beds,

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the heat transfer resistance is fundamentally reduced in the MPBBR. There-

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fore, with proper design to enhance the heat transfer performance, it may be

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an attractive option for fast catalytic reactions with strong heat effect.

Pr

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pr

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f

51

Several investigations were made upon heat transfer enhancement in uncon-

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ventional packed bed reactors. Vervloet et al. [2] compared several structured

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packing elements for tubular fixed bed reactors and suggested packed closed

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cross flow structure was good in heat transfer performance and catalyst hold-

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up. Visconti et al. [3] used highly conductive metal-foam to enhance the heat

68

conduction in the packed bed. Busse et al. [4] investigated the periodic open

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63

69

cellular structures and demonstrated their beneficial properties like high specific

70

surface area, low pressure drop, and adjustable heat transfer properties. How-

71

ever, the MPBBR has the small scale structure of flow channels and packed beds,

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of which the widths and thicknesses are in millimeter level. Thus it is difficult

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and uneconomical to embed other heat transfer structures like conductive foams

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or to use external heat exchange units like tube bundles, which means the heat

75

transfer enhancement in the MPBBR will be merely based on the optimization

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of the channel structure and geometric parameters. Therefore, it is important

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to study the heat transfer behaviors in the MPBBR and to quantitatively an4

Page 14 of 36

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alyze the influence of the channel structure and the geometric parameters on

79

the heat transfer performance, so that with proper choices of the structure and

80

geometric parameters, the temperature gradient in the beds can be limited to a

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tolerant range. The uncoupled flow and heat transfer research works can trace back to Prins

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et al. [5] for flow and heat transfer between parallel plates with constant wall

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temperature. Cess and Shaffer [6] consider the same problem with prescribed

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wall heat flux. Terrill [7] further considered flow and transfer between porous

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plates with small suction Reynolds numbers and Yeroshenko et al. [8] extended

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the results to large P eclet numbers with both suction and injection. Recent

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analytical studies focused on the heat transfer between porous parallel plates

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filled with a saturated porous medium and with asymmetric uniform heat flux

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[9, 10]. However, of all the previous works focused on heat transfer between

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parallel plates with given wall temperature or heat flux, none considered flow

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and heat transfer in the channels coupled with reaction heat. Rebrov et al. [11]

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and Haber et al. [12] investigated the heat transfer by numerical methods in the

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microstructured reactor, where the catalysts are coated on channel walls. The

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investigation upon heat transfer in a system coupled by porous parallel plates

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and adjacent packed bed with unprescribed wall heat flux boundary conditions

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is not reported in literatures. The transport phenomenon in this coupled system

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is complicated and nonlinear, so in this work, numerical simulations are used

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to quantitatively estimate the temperature distribution and to optimize the

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channel structure and geometric parameters.

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2. Model description and analysis

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2.1. Mathematical models of the MPBBR

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The 3D geometric model of an elementary unit is shown in Fig. 3(a) and

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the types of the boundary conditions are shown in the sectional views (Fig. 3

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(b) and (c)). The 3D model is divided into 3 kinds of domains: the free flow

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domains of the flow channels; the porous media domains of the packed beds;

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Page 15 of 36

the one single porous medium domain of the framework that contains all the

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permeable walls. The major assumption in the models are listed as follows:

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(1) The fluid is ideal gas and is incompressible.

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(2) Pseudo-homogeneous model is used.

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(3) The catalyst beds and the framework are considered as individual uniform

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porous media with constant porosity, permeability, and thermal conductivity.

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(4) The operation is adiabatic.

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2.1.1. Momentum transfer model

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The flow in the free channels is described by the stationary and incompress-

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ible Navier-Stokes equations, while the flow in porous media is described by

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the Brinkman equations with Forchheimer correction [13]. The coupled Stokes-

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Darcy-Brinkman model was used for coupled free and porous media flow [14, 15].

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The earlier studies of this coupled model by Beavers and Joseph [16] exhibited

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the existence of a slip velocity at the fluid/porous interface. An interface bound-

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ary condition was given by continuity to satisfy the slip velocity and shear stress

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at the interface [17]. However, Schmitz and Prat [18] showed that the slip effect

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can be neglected for low porosity surface like membrane. In the MPBBR, the

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permeable wall is also a kind of low porosity surface ( < 30%), so the slip effect

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is also neglected at the channel/wall interface. The momentum transfer model

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Pr

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rn

is expressed as eq. (1) & (2).    Continuity eq. : O · ~u = 0      F ree channel : ρ(~u · O)~u = O · [−pI~ + µ(O~u + (O~u)T )]

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  Catalyst bed : ρ2 (~u · O)~u = O · [−pI~ + µb (O~u + (O~u)T )] − Bµb ~u − βF |~u|~u   b    P ermeable wall : ρ (~u · O)~u = O · [−pI~ + µ (O~u + (O~u)T )] − µ ~u − β |~u|~u F 2w w Bw (1)

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Boundary conditions:    Inlet : ~u = u0 I~x   Outlet : p = ambient pressure     Channel/wall interf ace : ~u = (0, Bw Op · I~ , 0) y

(2)

µ

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Page 16 of 36

128

Here the inlet velocity is assumed to be perpendicular to the inlet surface and

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backflow is suppressed at the outlet surface. B is the permeability of the porous

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media estimated by eq. (3) [19]. B=

d2p 3 150(1 − )2

(3)

βF |~u|~u is the Forchheimer correction for turbulent drag contributions. βF is the

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non-Darcy flow coefficient estimated by an empirical correlation eq. (4) [20].

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βF = 5.5 × 10−12 B −1.47 −0.53 ρ 2.1.2. Mass transfer model

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(4)

The mass transfer is described by the convection and diffusion model. In

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the porous media, the effective diffusivity and mass dispersion are considered. The mass transfer model is expressed as eq. (5) & (6)    F ree channel : O · (−Di OCi ) + ~u · OCi = 0      Catalyst bed : O · (−(D + D )OC ) + ~u · OC = R e,i D,i i i i  P ermeable wall : O · (−(D + D )OC ) + ~u · OC = 0  e,i D,i i i      i = CH , O , H O, CO , N 4 2 2 2 2   Inlet : C = C i 0,i  Outlet : D OC = 0 i

(6)

i

The calculation correlations of different diffusivities are listed in Table 1. Here

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(5)

Boundary conditions:

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Pr

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P eM is the mass transfer Peclet Number P eM = ul/D and Sc is the Schmidt

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Number Sc = µ/ρD, where l is the characteristic length. For practical applica-

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tion cases of the MPBBR, 10 < P eM < 500 and 1 < Sc < 200.

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2.1.3. Energy transfer model

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The energy transfer is described by the convection and diffusion model. The

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third boundary conditions are given for the inlet surface and the channel/wall

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interface. In the porous media, the thermal dispersion is considered. The energy

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Table 1: Calculation correlations for diffusivities (unit:m2 /s).

Diffusivity in mixture [19] Di =

P P 1−yi ( Nj )/Ni (yj −yi Nj /Ni )/Dij

Binary diffusivity [19] Dij =

0.01T 1.75 (1/Mi +1/Mj )0.5 P P p[( Vi )1/3 +( Vj )1/3 ]2

De = τ Di

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Effective diffusivity [19]

Longitudinal (y-direction) dispersion coefficient [21] DL = P eM Di /(25Sc1.14 /P eM + 0.5)

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Transverse (x,z-direction) dispersion coefficient [21]

transfer model is expressed as eq. (7) & (8)    ρCp ~u · OT − O · (KOT ) = Q      F low channels : Q = 0, K = K , g   Catalyst beds : Q = QR , K = Ke,b + Kdisp      P ermeable wall : Q = 0, K = K + K e,w disp Boundary conditions:    Inlet : Kg OT · I~x = ρCp u0 (T − T0 )   Outlet : Kg OT = 0     Channel/wall interf ace : K OT · I~ = h ∆T e,w y w

(8)

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(7)

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Pr

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DT = (1 + (2.7 × 10−5 Sc + 12/P eM )−1 )Di

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The thermal conductivity of gaseous flow Kg is calculated by molar average.

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The effective thermal conductivities of porous media are estimated by Hadley’s

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correlations eq. (9) & (10) [22]. Ke 0.8 + (Ks /Kg )(1 − 0.8) 2(1 − )(Ks /Kg )2 + (1 + 2)(Ks /Kg ) = (1−α0 ) +α0 Kg 1 − 0.2(Ks /Kg − 1) (2 + )(Ks /Kg ) + 1 −  (9)

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where log α0 = −1.084 − 6.778( − 0.298)

0.298 ≤  ≤ 0.580

(10)

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Page 18 of 36

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The thermal dispersion coefficients are estimated by Saffman’s correlations eq. (11)

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& (12) [23]. DL P eH P eH 17 = [ln(122P eH ) − − ] Kg 6 200 12

(11)

DT 3P eH P e2H = + Kg 16 1000

(12)

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Here P eH is the heat transfer Peclet Number P eH = ulρCp /K, where l is the

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characteristic length. For practical application cases of the MPBBR, 0.01 <

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P eH < 0.5.

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hw is the effective heat transfer coefficient at channel/wall interface, which

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is determined by the channel Nusselt number N u. Terrill and Yeroshenko [7, 8]

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studied the heat transfer in flow between parallel porous plates and gave a

161

correlation for N u as eq. (13). hw is then estimated by eq. (14), where δ is the

162

thickness of the heat transfer layer.

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N u = 3.77 + P eH + 0.087P e2H + 0.01Rew 163

164

(13) (14)

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hw = N uKg /δ

(P eH < 3)

2.2. Model credibility discussion

The assumptions listed in section 2.1 are all common assumptions. No

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practical application case for the Bionic Reactor is under very high pressure

167

or low temperature so the ideal gas assumption should be valid. The pseudo-

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168

homogeneous model and the uniform porous media assumption are commonly

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used in the simulation studies of gas-solid catalytic reactions in packed beds

170

[24, 25, 26, 27]. The MPBBR is an adiabatic reactor and can be considered as

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an integration of many individual elementary units, so it is reasonable to assume

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adiabatic operation in the elementary unit.

173

The coupled Stokes-Darcy-Brinkman model with negligible interface bound-

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ary condition was commonly used for membrane processes [28, 29]. Damak [30]

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proved that this model was accurate enough for a membrane process with chan-

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nel Reynolds number between 300 and 1000 and infiltration Reynolds number 9

Page 19 of 36

between 0.1 and 0.3. The flow in the MPBBR may cover a larger range of

178

Reynolds number, so the Forchheimer correction for turbulent drag contribution

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is also considered. Thus the model is still valid when the infiltration deviates

180

from Darcy flow. The convection and diffusion models of mass and energy trans-

181

fer for coupled domains with different physical properties are commonly used

182

in microchannel and membrane reactors [31, 32, 33, 34].The basic behaviors of

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the mass and energy transfer of the MPBBR are similar to the membrane and

184

microchannel reactors and the effective diffusivities and thermal conductivities

185

are estimated respectively for free flow and porous domains. The mass and

186

thermal dispersions are also considered for the porous domains. Therefore, the

187

current model can be considered of enough credibility.

188

2.3. Flow distribution criterion

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The flow distribution characteristics was studied analytically in a 2D model

190

in the authors’ earlier publication [1]. A dimensionless parameter Pr (Eq. (15))

191

was identified to be the key factor that determining the flow distribution unifor-

192

mity. Another parameter, the infiltration Reynolds number Rew , was demon-

193

strated to play a second role. Relations between Pr , Rew and the relative

194

maximal infiltration velocity difference σmax were obtained from the analytical

195

solution of the model, and this holds for the flow distribution in the MPBBR.

196

However, in the previous work, the influence of the permeable walls were ne-

197

glected. In this work, the 3D geometric model of an elementary unit in Fig. 3(a)

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Pr

189

shows that a catalyst bed consists of several columns of channels, so the influ-

199

ence of the permeable wall should be considered. Therefore, some corresponding

200

modifications need to be made in the expression of Pr .

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Pr =

u0 ρBb L µhwb

(15)

hvw ρ µ

(16)

201

Rew = 202

Assuming that the catalyst consists of N columns of channel, then the

203

total pressure difference between the input and output channel is estimated by

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Page 20 of 36

204

eq. (17). ∆p = N

205

2hvw µ ww vw µ + (N + 1) Bb Bw

(17)

Thus the expression of Pr number of the MPBBR is modified as Eq. (18). Pr =

u0 ρBbw L 2h2 µN

(18)

2hN ww (N + 1) −1 + ) Bb Bw

(19)

oo

Bbw = (

f

206

207

where the permeabilities of the packed bed and porous wall are esitimated by

208

Eq. (3), and Bbw can be considered as the average unit permeability. The modified Pr number now includes all the independent geometric pa-

210

rameters and physical properties. Since the Pr number is the key parameter

211

that determines the flow distribution uniformity, it should always be an indis-

212

pensable criterion of the optimal design of the MPBBR.

213

2.4. Heat transfer behaviors in the MPBBR

Pr

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Although analytic solutions are unavailable for the coupled mathematical

215

model of the MPBBR, several heat transfer interactions can be demonstrated

216

by Fig. 4 to help comprehending the heat transfer behaviors.

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In a common case where the reaction is exothermic and the feed fluid is

218

cold, the radial conduction and convection are in opposite directions, as shown

219

in Fig. 4(a). In a conventional fixed bed reactor, the large size catalyst bed

220

with high infiltration velocity will result in large heat conduction resistance and

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217

221

the domination of the convection of the cold inflow. Thus the feed fluid must

222

be sufficiently preheated to avoid extinction. Whereas, in the MPBBR, the bed

223

size and infiltration velocity can be one or two orders of magnitude lower for

224

the heat conduction to become dominant, resulting in a smaller temperature

225

gradient in the catalyst bed. Thus in the MPBBR, cold feed can be directly

226

used without preheating which is essential for the realization of the auto-thermal

227

function, since the reaction heat can be neutralized by the sensible heat increase

228

of the cold feed. However, the axial temperature difference along the input

229

channel will be inevitable because of the interaction between axial convection 11

Page 21 of 36

and radial conduction in Fig. 4(b), which is denoted by the channel Peclet

231

Number P e = ρCp uh/K. The characteristic length h here refers to the input

232

channel width, meaning that a wider input channel will be in favor of limiting

233

the radial conduction so that the axial difference in the channel temperature

234

can be reduced. By contrast, the interaction between the axial conduction and

235

reaction heat in the packed bed is more intuitional in Fig. 4(c). A higher bed

236

heat conductivity or a shorter bed length can generally result in a more uniform

237

bed temperature distribution.

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230

The aforementioned heat transfer behaviors imply that thinner and shorter

239

catalyst bed and wider input channel can result in perfect uniformity of tem-

240

perature distribution. However, there are other indispensable restrictions to

241

follow, like the Pr number, the pressure drop, the catalyst packing fraction, the

242

handling capacity, and the manufacture feasibility as well. In section 3, an ap-

243

plication case will be introduced to quantitatively estimate the influence of the

244

channel structure and geometric parameters on the temperature distribution

245

uniformity as well as to demonstrate the optimization of the MPBBR.

246

3. Analysis and optimization of application case

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Pr

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pr

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The catalytic combustion of lean methane (concentration of 0.5 – 1v%) is a

248

representative fast catalytic highly exothermic reaction. The present industrial

249

processes use the catalytic flow reversal reactors (CFRR) loaded with cordierite

250

monoliths [35, 36]. The Reverse-Flow Operation for the catalytic combustion

251

requires a vast amount of room for thermal storage media, resulting in a catalyst

252

packing fraction of lower than 25%. Since the space velocity is as high as

253

36000h−1 , to maintain a low pressure drop, large catalyst particles have to be

254

used. In the CFRR, Raschig rings with a characteristic length of 7.5mm are

255

used and its catalyst effectiveness is only about 42.1%. In this situation, to

256

improve the handling capacity and in the meantime satisfy the heat transfer

257

requirement, the MPBBR appears to be an ideal substitution.

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Page 22 of 36

258

3.1. Advantages and operation conditions for the MPBBR

259

Since the pressure drop is fundamentally reduced in the MPBBR, under

260

the same level of pressure drop as the CFRR, fine catalysts with much higher

261

effectiveness can be used. To eliminate the resistance of the intra-particle dif-

262

fusion, 0.18mm fine catalysts are used and its catalyst effectiveness can reach

263

over 90%. The adiabatic temperature rise of this reaction is about 340o C for 1v%

265

concentration of methane, so it is feasible to use cold feed without preheating

266

and take advantage of the auto-thermal function of the MPBBR. Thus the

267

thermal storage media are no longer needed and the catalyst packing fraction

268

can be increased. In recent investigations, high performance catalysts have been

269

found for low temperature catalytic combustion. The ignition temperature is

270

lower than 350o C and over 99% conversion of methane can be achieved under

271

570o C [37, 38]. Therefore, the inlet temperature is set to be 230o C for the heat

272

balance.

Pr

e-

pr

oo

f

264

In the following sections, the heat transfer characteristics will be quantita-

274

tively analyzed based on the numerical solutions to the coupled mathematical

275

model equations of the MPBBR (Eq. (1) – (14)) through Comsol M ultiphysicsT M .

276

The feed stream for the simulations contains 79v% N2 , 20v% O2 ,1v% CH4 , and

277

the inlet temperature and pressure are 230o C and 0.103M P a. The inlet velocity

278

condition varies based on different geometric parameters.

rn

al

273

3.2. Material selection for the honeycomb framework

Jo u 279

280

The cordierite ceramic is a commonly used material for monoliths. It has

281

good permeability and mechanical strength. However, for porosity of 24%,

282

the cordierite wall thermal conductivity is only 1.5W/(mK) [39, 40], which is

283

evidently not applicable for such highly exothermic reaction. For higher thermal

284

conductivity, the metal foam and metal matrix composites (MMCs) seem to be

285

a better option, since the specific thermal conductivities range from 10W/(mK)

286

to over 100W/(mK) for different metals [41]. Whereas, the defects are that the

287

performance of metal foam and MMCs can’t hold under high temperature (over 13

Page 23 of 36

400o C) and the manufacture is rather expensive. Thus the porous silicon carbide

289

ceramic tends to be a wise choice, for it is a high temperature resistant and

290

economic material with considerable thermal conductivity. According to Liu &

291

Tuan [42], the thermal conductivity of such material prepared by mixing coarse

292

SiC particles with a small amount of sodium silicate can reach 19W/(mK), even

293

though the porosity is as high as 40%.

294

3.3. Heat transfer characteristics analysis

oo

f

288

Since the inlet temperature is 120o C lower than the ignition temperature,

296

and on the other hand, the catalytic activity shows a typical decrease above

297

580o C for the P d/Cex Zr1−x O2 catalyst [37], the temperature control of the

298

MPBBR should be precise enough to avoid extinction or deactivation of cat-

299

alysts. This requires reasonable optimizations of the channel structure and

300

geometric parameters. The geometric parameters to be optimized include the

301

total catalyst bed thickness wb , the whole channel width 2h, the wall thickness

302

ww , and the bed length L.

Pr

e-

pr

295

Based on the qualitative judgement in section 2.4, thinner bed thickness

304

is in favor of better heat transfer performance and lower pressure drop, while

305

some trial simulations show that the axial temperature difference in the cata-

306

lyst bed is the main contribution to the non-uniformity of temperature, so for

307

the practical interests, the determination of wb should concern more about the

308

catalyst packing fraction and handling capacity. According to the pressure drop

rn

al

303

restriction, wb can be at most set to be 12mm to maintain the same level of

310

pressure drop as that in the CFRR. The corresponding infiltration velocity is

311

0.12m/s, which is fast enough to eliminate the resistance of the inter-particle

312

diffusion.

Jo u 309

313

The prototype of the honeycomb framework uses single column as input

314

channel (Fig. 2). Trial simulations show that the main temperature difference is

315

in the axial direction. Thus to quantitatively estimate the non-uniformity of the

316

axial temperature distribution, simulations are carried out for elementary units

317

with L = 10cm, 2h = 3, ww = 0.5, 0.6, 0.8mm, and L = 10cm, ww = 0.6, 2h = 14

Page 24 of 36

2, 3, 4mm. Fig. 5 indicates that the wall thickness has little influence on the

319

channel temperature Tc distribution, whereas the axial difference of the bed

320

temperature Tb decreases as the wall thickness increases. This is predictable

321

because the SiC framework is the main contributor of the heat transfer, and

322

thicker wall will lead to higher equivalent heat conductivity, especially in the

323

axial direction [43, 44]. Fig. 6 indicates that the axial channel temperature

324

difference is significantly affected by the channel width. As discussed in section

325

2.4, the axial heat convection become dominant in a wider flow channel, so the

326

channel temperature will be more uniform. We can also tell from the variation

327

of the Tb curves that reducing the channel temperature difference is an effective

328

way to have a more uniform bed temperature distribution. However, merely

329

increasing the width of channels and walls will not be acceptable for catalyst

330

packing fraction or reactor manufacture feasibility.

e-

pr

oo

f

318

Since a large temperature rise will always exist in the first pass through

332

the input channel, the input channel can be modified by adding a back-turning

333

channel (see Fig. 7). The fabrication of the input channel modification is simple.

334

Such back-turning channels can be simply formed by cutting off some lower parts

335

of the adjacent walls of an input channel. The cold inflow will be provided with a

336

second pass through the channel and more heat exchanging area before entering

337

the catalyst bed. Thus the bed temperature difference will be determined by

338

the more uniform temperature gradient in the back-turning channel. Fig. 8

339

shows the different heat transfer behaviors and temperature profiles with and

Jo u

rn

al

Pr

331

340

with out back-turning channel (the figure is widened in y-direction to exhibit the

341

details of temperature profile). To demonstrate the effect of the back-turning

342

channel more intuitively, the axial distribution curves of channel temperature

343

are shown in Fig. 9. The maximal temperature difference in the single input

344

channel is about 220o C, while that in the back-turning input channel is about

345

120o C. Therefore by adding the back-turning channel, the channel temperature

346

difference can be nearly halved.

15

Page 25 of 36

Table 2: Geometric and operations parameters for monolithic reactors.

Vin (m/s)

y0,CH4

Conv.CH4

∆Tmax (o C)

Mei [45]

φ2.5mm × 2.54cm

427

1

0.68%

> 99%

150

Cominos [46]

φ1.2mm × 10cm

450

7.75

2%

81.5%

467

Hwang [47]

φ1.5mm × 8cm

594

7.3

3.5%

43%

396

f

Tin (o C)

3.4. Simulation results validation

oo

347

Channel size

This investigation has not been funded, so the experimental validations

349

may not be available at the present stage, but will be the priority in the future

350

works. Therefore, the simulation results can only be validated by the results of

351

some similar investigations.

pr

348

Although the flow pattern in the MPBBR is the axial free flow in the

353

channel and radial infiltration in the bed, the axial heat transfer behaviors is

354

similar to those in the monolithic reactors. The axial temperature distributions

355

in different monolithic reactors with coated Pt/alumina catalyst are shown in

356

Fig. 11. The corresponding geometric and operation parameters are listed in

357

table 2. The temperature distribution pattern in different monolithic reactors

358

are similar. A rapid growth of temperature exists near the entrance region and

359

the temperature gradient is small in the rest part. Although the combustion

360

temperature is low in the MPBBR due to the use of low temperature combustion

361

catalysts, the distribution pattern is similar. The difference is that the rapid

rn

al

Pr

e-

352

temperature growth is shifted into the input channel.

Jo u 362

363

Yan et al. [48] studied the heat transfer in a heat recirculation meso-

364

combustor (HRMC). The structure of the HRMC (Fig. 12) is similar to that of

365

the back-turning channel in the MPBBR. Yan et al. compared the temperature

366

profile between the HRMC and the conventional meso-combustor under the

367

conditions of Tin = 227o C, Vin = 0.5m/s, y0,CH4 = 3.5%, and the conversion

368

of methane is larger than 80%. Fig. 13 shows the temperature profiles at the

369

centerlines of the combustors. Due to the preheating inlet channels, the axial

370

temperature difference in the HRMC is only a quarter of that in the CMC.

16

Page 26 of 36

Table 3: Geometric parameters for different channel density.

cpsi

2h(mm)

Nb

ww (mm)

fw (v%)

fc (v%)

a

29

4

3

0.73

28.5

42.9

b

50

3

4

0.6

30.5

46.3

c

79

2.4

5

0.46

29.6

50.2

d

117

2

6

0.35

27.6

54.3

e

95

2

6

0.6

40.8

oo

f

Structure No.

44.4

Comparing Fig. 13 and Fig. 9, we can see similar heat transfer enhancement

372

characteristics.

373

3.5. Optimization of the geometric parameters

e-

pr

371

Now that we have proved the benefits of adding back-turning channels,

375

we can ulteriorly optimize the geometric parameters for the MPBBR elemen-

376

tary unit for 1v% & 0.5v% CH4 . For 0.5% concentration of methane, the

377

inlet temperature is set to be 405o C. The optimization should also consider

378

the manufacture feasibilities. The size of honeycomb monoliths are commonly

379

denoted by the channels per square inch (cpsi). Table 3 shows the geometric

380

parameters of some commercially available honeycomb monoliths. Channels

381

thinner than 2mm are not considered because the catalyst particle diameter is

382

0.18mm, whereas the channel width to diameter ratio should be at least 10:1.

383

The wall volume fraction fw and the catalyst packing fraction fc are calculated

Jo u

rn

al

Pr

374

384

by Eq. (20) and Eq. (21) respectively, based on the geometric relations denonted

385

in Fig. 14.

(2h + ww )2 − (2h)2 (2h + ww )2

(20)

hwb (h + ww /2)(2h + ww )(N + 2)

(21)

fw =

386

fc = 387

17

Page 27 of 36

388

Simulations are carried out to give the relations between the maximal tem-

389

perature difference and bed length for different channel density in Fig. 15 &

390

16. For the combustion of 1v% methane, it can be concluded from relation

392

curves a, b, c, d in Fig. 15 that with higher wall volume fraction, the maximal

393

temperature difference is reduced. However, the rule is not followed by structure

394

e. In addition, the maximal temperature differences seem to grow much faster

395

with L than expected for structure c and d. This is because thinner channel

396

width will increase the value of Pr and reduce the channel P eclet N umber.

397

Higher Pr will result in non-uniformity of infiltration velocity and thus of reac-

398

tion load, whereas lower P eclet N umber means relatively stronger radial heat

399

conduction in the input channel and larger axial difference of channel temper-

400

ature. Thus in the perspective of uniformizing the temperature distribution,

401

structure b tends to the best choice.

e-

pr

oo

f

391

As mentioned earlier, the activity of P d/Cex Zr1−x O2 catalyst will decrease

403

above 580o C and simulations show that when the maximal temperature differ-

404

ence in the bed exceed 50o C, the total methane conversion will be lower than

405

99%. Therefore, to be conservative, the threshold of the maximal temperature

406

difference is set to be 45o C.

al

Pr

402

From the dashed line of 45o C in Fig. 15, the maximal bed length for

408

different channel densities can be read. Although the catalyst packing fraction

409

is higher for structure c and d, the bed length cannot exceed 8.5cm, which

Jo u

rn

407

410

is not favorable to the handling capacity and manufacture feasibility (most

411

commercially available monoliths are longer than 10cm). Thus structure b is

412

finally chosen as the optimal channel density for the combustion of 1v% methane

413

and the maximal bed length can reach 12.2cm.

414

For the combustion of 0.5v% methane, from the relation curves in Fig. 16, it

415

can be seen that structure a, instead of b, has the best heat transfer performance.

416

This is because the heat effect is reduced due to lower concentration of methane

417

and the temperature distribution is mainly determined by the value of Pr . Thus,

418

for sturcture a, the maximal bed length can reach about 24cm. However, the 18

Page 28 of 36

catalyst packing fraction of structure a is the lowest, whereas our optimal design

420

principle is to achieve as high packing fraction as possible. Therefore, from the

421

dashed line in Fig. 16, structure c is finally chosen as the optimal channel

422

density for the combustion of 0.5v% methane and the maximal bed length can

423

reach 11.6cm.

424

3.6. Performance comparison between the MPBBR and CFRR

f

419

Detailed performance comparisons between CFRR and MPBBR for the

426

combustion of 1v% methane are listed in Table 4 and the detailed temperatuer

427

profiles in the MPBBR elementary unit are shown in Fig. 17. Due to the

428

distributed flow pattern in the MPBBR, the pressure drop doesn’t exceed that in

429

the CFRR, despite that the catalyst beds are packed with 0.18mm fine particles.

430

Since the catalyst effectiveness and catalyst packing fraction are both doubled,

431

the handling capacities per unit mass of catalyst and unit volume of reactor are

432

significantly increased. In this situation, to achieve the same handling capacity,

433

the MPBBR takes only half mass of catalysts and one third volume of reactor

434

used in the CFRR. For the heat transfer performance, the MPBBR realizes the

435

auto-thermal function without any external heat removal units and the maximal

436

temperature difference is maintained under 45 o C. More importantly, such high

437

performance catalytic combustion reactor of lean methane can be converted to

438

a compact modular mobile device to meet the demands of various scales of

439

exhaust gas treatment.

Jo u

rn

al

Pr

e-

pr

oo

425

440

4. Conclusion

441

The FBBR is a novel concept packed bed reactor with hierarchical channel

442

network and distributed flow pattern, which is designed for fast catalytic reac-

443

tions. The MPBBR is a representative implementation of the FBBR with the

444

capability of enhancing heat transfer performance for highly exothermic reac-

445

tions. The distribution uniformity of flow and temperature is the main challenge

446

of the optimal design. In this work, the heat transfer behaviors are qualitatively

19

Page 29 of 36

Table 4: Performance comparisons between MPBBR and CFRR [49].

MPBBR

Methane conversion (%)

>99

99.4

Catalyst particle diameter (mm)

7.5

0.18

Catalyst effectiveness (%)

42.1

90.1

Catalyst packing fraction (%)

>25

46.3

Maximal temperature difference in the bed (o C)

200

44.3

Total pressure drop (P a)

2500

2030

Unit mass handling capacity (kg CH4/kg Cat · h)

0.095

0.201

Unit volume handling capacity (kg CH4/m3 Cat · h)

14.7

50.7

pr

oo

f

CFRR

analyzed. In the input channel, the axial heat convection should be enhanced

448

while the radial heat conduction should be weakened to reduce the difference

449

in the bed entrance temperature. In the packed bed, the axial heat conduc-

450

tion should be enhanced to match the generation rate of reaction heat, whereas

451

the radial heat conduction should be dominant comparing to the radial heat

452

convection to realize the auto-thermal function.

Pr

e-

447

In the application case, numerical simulations give quantitative analysis

454

for the influence of channel structure and geometric parameters on the heat

455

transfer performance. The modified input channel with a back-turning chan-

456

nel can effectively uniformize the bed temperature distribution by reducing the

457

axial difference of channel temperature. The optimal channel density and ge-

458

ometric parameters are determined as 50 cpsi, and 2h = 3mm, N = 4, ww =

459

0.6mm, L = 12.2cm for the combustion of 1v% methane, and 79 cpsi, and

460

2h = 2.4mm, N = 5, ww = 0.46mm, L = 11.6cm for the combustion of 0.5v%

461

methane. The performance comparison between the CFRR demonstrates that

462

only half mass of catalysts and one third volume of reactor are needed based on

463

unit handling capacity. Therefore, with the flow and temperature distribution

464

uniformity under control, the MPBBR is proved to be an effective and economi-

465

cal alternative for many fast catalytic reactions. Further investigations and case

Jo u

rn

al

453

20

Page 30 of 36

466

studies will be carried out upon more industrial processes.

467

Acknowledgements

468

This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

470

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oo

472

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