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Journal of Heat Transfer | Volume 134 | Issue 1 | Research Paper
Research Papers: Porous Media

Tomography-Based Determination of Effective Transport Properties for Reacting Porous Media

[+] Author and Article Information
Sophia Haussener1

Department of Mechanical Engineering, EPFL, 1015 Lausanne, SwitzerlandSophia.haussener@epfl.ch

Iwan Jerjen, Peter Wyss

Department of Electronics/Metrology,   EMPA Material Science and Technology, Überlandstrasse 129, 8600 Dübendorf, Switzerland

Aldo Steinfeld

Department of Mechanical and Process Engineering, ETH Zurich, 8092 Zurich, Switzerland; Solar Technology Laboratory,  Paul Scherrer Institute, 5232 Villigen, Switzerland

1

Corresponding author.

J. Heat Transfer 134(1), 012601 (Oct 27, 2011) (8 pages) doi:10.1115/1.4004842 History: Received April 16, 2011; Accepted July 30, 2011; Published October 27, 2011; Online October 27, 2011
Article
References
Figures
Tables
Citing Articles

The effective heat and mass transport properties of a porous packed bed of particles undergoing a high-temperature solid–gas thermochemical transformation are determined. The exact 3D geometry of the reacting porous media is obtained by high-resolution computed tomography. Finite volume techniques are applied to solve the governing conservation equations at the pore-level scale and to determine the effective transport properties as a function of the reaction extent, namely, the convective heat transfer coefficient, permeability, Dupuit–Forchheimer coefficient, tortuosity, and residence time distributions. These exhibit strong dependence on the bed morphological properties (e.g., porosity, specific surface area, particle size) and, consequently, vary with time as the reaction progresses.
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References

1
von Zedtwitz, P., and Steinfeld, A., 2003, “The Solar Thermal Gasification of Coal—Energy Conversion Efficiency and CO2 Mitigation Potential,” Energy, 28 , pp. 441–456.  [CrossRef]
2
Schunk, L., Haeberling, P., Wepf, S., Wuillemin, D., Meier, A., and Steinfeld, A., 2008, “A Receiver-Reactor for the Solar Thermal Dissociation of Zinc Oxide,” ASME J. Solar Energy Eng., 130 , p. 0210091.  [CrossRef]
3
Piatkowski, N., Wieckert, C., and Steinfeld, A., 2009, “Experimental Investigation of a Packed-Bed Solar Reactor for the Steam-Gasification of Carbonaceous Feedstocks,” Fuel Process. Technol., 90 , pp. 360–366.  [CrossRef]
4
Whitaker, S., 1999, “The Method of Volume Averaging,” "Theory and Applications of Transport in Porous Media", Vol. 13 , J.Bear, ed., Kluwer Academic Publishers.
5
Gnielinski, V., 1978, Gleichung zu Berechnung der Wärme- und Stoffaustausches in durchströmten ruhenden Kugelschüttungen bei mittleren und grossen Pecletzahlen, Verfahrenstechnik, 12 , pp. 363–366.
6
Wakao, N., and Kaguei, S., 1982, "Heat and Mass Transfer in Packed Beds", Gordon and Breach Science Publishers.
7
Gunn, D., 1978, “Transfer of Heat and Mass to Particles in Fixed and Fluidized Beds,” Int. J. Heat Mass Transfer, 21 , pp. 467–476.  [CrossRef]
8
Saidi, M., Rasouli, F., and Hajaligol, M., 2006, “Heat Transfer Coefficient for a Packed Bed of Shredded Materials at Low Peclet Numbers,” Heat Transfer Eng., 27 , pp. 41–49.  [CrossRef]
9
Kaviany, M., 1995, "Principles of Heat Transfer in Porous Media", Springer-Verlag, New York.
10
Dullien, F., 1979, "Porous Media Fluid Transport and Pore Structure", Academic Press, New York.
11
Kuwabara, S., 1959, “The Forces Experienced by Randomly Distributed Parallel Circular Cylinder or Spheres in a Viscous Flow at Small Reynolds Numbers,” J. Phys. Soc. Jpn., 14 , pp. 527–532.  [CrossRef]
12
Sparrow, E., and Loeffler, A., 1959, “Longitudinal Laminar Flow Between Cyclinders Arranged in a Regular Array,” Am. Inst. Chem. Eng., 5 , pp. 325–330.
13
Happel, J., and Brenner, H., 1986, "Low Reynolds Number Hydrodynamics", Martinus Nijhoff Publishers.
14
Torquato, S., 1990, “Relationship Between Permeability and Diffusion Controlled Trapping Constant of Porous Media,” Phys. Rev. Lett., 64 , pp. 2644–2646.  [CrossRef]
15
Macdonald, I. F., El-Sayed, M. S., Mow, K., and Dullien, F. A. L., 1979, “Flow Through Porous Media—The Ergun Equation revisited,” Ind. Eng. Chem. Fundam., 18 , pp. 199–208.  [CrossRef]
16
Ward, J., 1964, “Turbulent Flow in Porous Media,” J. Am. Soc. Civ. Eng., 90 , pp. 1–12.
17
Petrasch, J., Meier, F., Friess, H., and Steinfeld, A., 2008, “Tomography Based Determination of Permeability, Dupuit-Forchheimer Coefficient, and Interfacial Heat Transfer Coefficient in Reticulate Porous Ceramics,” Int. J. Heat Fluid Flow, 29 , pp. 315–326.  [CrossRef]
18
Haussener, S., Coray, P., Lipiński, W., Wyss, P., and Steinfeld, A., 2010, “Tomography-Based Heat and Mass Transfer Characterization of Reticulate Porous Ceramics for High-Temperature Processing,” ASME J. Heat Trans., 132 , p. 023305.  [CrossRef]
19
Ferréol, B., and Rothman, D., 1995, “Lattice-Boltzmann Simulation of Flow Through Fontainebleau Sandstone,” Transp. Porous Media, 20 , pp. 3–20.  [CrossRef]
20
Humby, S., 1999, “Modelling of Flow and Colloids in Porous Media,” Ph.D. thesis, University of Surrey, Guildford, UK.
21
Auzerai, F., Dunsmuir, J., Ferréol, B., Martys, N., Olson, J., Ramakrishnan, T., Rothmann, D., and Schwartz, L., 1996, “Transport in Sandstone: A Study Based on Three Dimensional Microtomography,” Geophys. Res. Lett., 23 , pp. 3–20.  [CrossRef]
22
Brensdorf, J., Brenner, G., and Dust, F., 2000, “Numerical Analysis of the Pressure Drop in Porous Media Flow With Lattice Boltzmann (BGK) Automata,” Comput. Phys. Commun., 129 , pp. 247–255.  [CrossRef]
23
Spanne, P., Thovert, J., Jacquin, C., Lindquist, W., Jones, K., and AdlerP., 1994, “Synchrotron Computed Microtomography of Porous Media: Topology and Transport,” Phys. Rev. Lett., 73 , pp. 2001–2004.  [CrossRef]
24
Haussener, S., Lipiński, W., Wyss, P., and Steinfeld, A., 2010, “Tomography-Based Analysis of Radiative Transfer in Reacting Packed Beds Undergoing a Solid-Gas Thermochemical Transformation,” ASME J. Heat Trans., 132 , p. 061201.  [CrossRef]
25
Streun, A., Böge, A., Dehler, M., Gough, C., Joho, W., Korhonen, T., Lüdeke, A., Marchand, P., Muñoz, Pedrozzi, M., Rivkin, L., Schilcher, T., Schlott, V., Schulz, L., and Wrulich, A., 2001, “Commissioning of the Swiss Light Source,” "Proceedings of the 2001 Particle Accelerator Conference", P.Lucas and S.Webber, eds., IEEE, Piscataway, pp. 224–226.
26
Stampanoni, M., Groso, A., Isenegger, A., Mikuljian, G., Chen, Q., Bertrand, A., Henein, S., Betemps, R., Frommherz, U., Böhler, P., Meister, D., Lnage, M., and Abela, R., 2006, “Trends in Synchrotron-Based Tomographic Imaging: The SLS Experience,” Proc. SPIE, 6318 , pp. M-1–M-14.  [CrossRef]
27
Ansys Inc., 2009, Ansys CFX-12.0, www.ansys.com.
28
Mousa, A., 1984, “Prediction of Gas-Particle Heat Transfer Coefficients by Pulse Technique,” Ind. Eng. Chem. Process. Des. Dev., 23 , pp. 805–808.  [CrossRef]
29
Darcy, H., 1856, "Les Fontaines Publiques sur le movement des eaux", Dalmont, Paris.
30
Forchheimer, P., 1901, “Water Movement Through Ground,” Zeitschrift des Vereins Deutscher Ingenieure, 45 , pp. 1782–1788.
31
Kyan, C., Wasan, D., and Kintner, R., 1970, “Flow of Single-Phase Fluids Through Fibrous Beds,” Ind. Eng. Chem. Fundam., 9 , pp. 596–603.  [CrossRef]
32
Rumpf, H., and Gupte, A., 1971, “Influence of Porosity and Particle Size Distribution in Resistance Law of Porous Flow,” Chem. Eng. Technol., 43 , pp. 367–375.  [CrossRef]
33
Itoh, S., 1983, “The Permeability of a Random Array of Identical Rigid-Spheres,” J. Phys. Soc. Jpn., 52 , pp. 2379–2388.  [CrossRef]
34
Davis, R., and Stone, H., 1993, “Flow Through Beds of Porous Particles,” Chem. Eng. Sci., 48 , pp. 3993–4005.  [CrossRef]

Figures

Grahic Jump Location
+CT scans of samples of the packed bed of tire shreds at three reaction extents: (a) initially at XC  = 0; (b) after pyrolysis at XC  = 0.68 (char); and (c) after gasification at XC  = 1 (ash). The edge length is 5.2 mm.
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CT scans of samples of the packed bed of tire shreds at three reaction extents: (a) initially at XC  = 0; (b) after pyrolysis at XC  = 0.68 (char); and (c) after gasification at XC  = 1 (ash). The edge length is 5.2 mm.
Figure 1

CT scans of samples of the packed bed of tire shreds at three reaction extents: (a) initially at XC  = 0; (b) after pyrolysis at XC  = 0.68 (char); and (c) after gasification at XC  = 1 (ash). The edge length is 5.2 mm.

Grahic Jump Location
+Schematic of the DPLS domain, consisting of a square duct containing a sample of the packed bed, and inlet and outlet regions
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Schematic of the DPLS domain, consisting of a square duct containing a sample of the packed bed, and inlet and outlet regions
Figure 2

Schematic of the DPLS domain, consisting of a square duct containing a sample of the packed bed, and inlet and outlet regions

Grahic Jump Location
+Mesh cutting plane of the computational domain of the initial packed bed. The packed bed region is enlarged. Parts of the inlet and outlet regions are visible at the top and bottom.
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Mesh cutting plane of the computational domain of the initial packed bed. The packed bed region is enlarged. Parts of the inlet and outlet regions are visible at the top and bottom.
Figure 3

Mesh cutting plane of the computational domain of the initial packed bed. The packed bed region is enlarged. Parts of the inlet and outlet regions are visible at the top and bottom.

Grahic Jump Location
+Re dependent Nu numbers for the packed bed at XC  = 0, 0.68, and 1 (initial, char, and ash) and at Pr = 0.1, 1, and 1. The symbols indicate numerically calculated Nu numbers and the solid line the fits given by Eq. 8 and Table 2.
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Re dependent Nu numbers for the packed bed at XC  = 0, 0.68, and 1 (initial, char, and ash) and at Pr = 0.1, 1, and 1. The symbols indicate numerically calculated Nu numbers and the solid line the fits given by Eq. 8 and Table 2.
Figure 4

Re dependent Nu numbers for the packed bed at XC  = 0, 0.68, and 1 (initial, char, and ash) and at Pr = 0.1, 1, and 1. The symbols indicate numerically calculated Nu numbers and the solid line the fits given by Eq. 8 and Table 2.

Grahic Jump Location
+Nu correlations for packed beds given by Gnielinski (ɛ = 0.61 and 0.74) [5], Wakao [6], Gunn (ɛ   = 0.61 and 0.74) [7], Saidi [8], and of present study for Pr   = 0.1 (a) and for Pr   = 1 (b)
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Nu correlations for packed beds given by Gnielinski (ɛ = 0.61 and 0.74) [5], Wakao [6], Gunn (ɛ   = 0.61 and 0.74) [7], Saidi [8], and of present study for Pr   = 0.1 (a) and for Pr   = 1 (b)
Figure 5

Nu correlations for packed beds given by Gnielinski (ɛ = 0.61 and 0.74) [5], Wakao [6], Gunn (ɛ   = 0.61 and 0.74) [7], Saidi [8], and of present study for Pr   = 0.1 (a) and for Pr   = 1 (b)

Grahic Jump Location
+Dimensionless pressure drop, Πpg , as a function of Re for the three samples of the packed bed at XC  = 0, 0.68, and 1 (initial, char, and ash)
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Dimensionless pressure drop, Πpg , as a function of Re for the three samples of the packed bed at XC  = 0, 0.68, and 1 (initial, char, and ash)
Figure 6

Dimensionless pressure drop, Πpg , as a function of Re for the three samples of the packed bed at XC  = 0, 0.68, and 1 (initial, char, and ash)

Grahic Jump Location
+Residence time distribution at Re = 1 for the reacting packed bed at XC  = 0, 0.68, and 1 (initial, char, and ash)
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Residence time distribution at Re = 1 for the reacting packed bed at XC  = 0, 0.68, and 1 (initial, char, and ash)
Figure 8

Residence time distribution at Re = 1 for the reacting packed bed at XC  = 0, 0.68, and 1 (initial, char, and ash)

Grahic Jump Location
+Tortuosity distribution at Re = 1 for the reacting packed bed at at XC  = 0, 0.68, and 1 (initial, char, and ash)
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Tortuosity distribution at Re = 1 for the reacting packed bed at at XC  = 0, 0.68, and 1 (initial, char, and ash)
Figure 9

Tortuosity distribution at Re = 1 for the reacting packed bed at at XC  = 0, 0.68, and 1 (initial, char, and ash)

Grahic Jump Location
+K and FDP numerically determined by DPLS with those calculated by models for packed beds with Kinner  = 10−10 m2 and for (a): ɛ = 0.61, d = 1.14 mm; (b): ɛ = 0.74, d = 0.97 mm; and (c): ɛ = 0.65, d = 0.42 mm. FDP is calculated by MacDonald (grey, Eq. 28) and by Ward (black, Eq. 29)
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K and FDP numerically determined by DPLS with those calculated by models for packed beds with Kinner  = 10−10 m2 and for (a): ɛ = 0.61, d = 1.14 mm; (b): ɛ = 0.74, d = 0.97 mm; and (c): ɛ = 0.65, d = 0.42 mm. FDP is calculated by MacDonald (grey, Eq. 28) and by Ward (black, Eq. 29)
Figure 7

K and FDP numerically determined by DPLS with those calculated by models for packed beds with Kinner  = 10−10 m2 and for (a): ɛ = 0.61, d = 1.14 mm; (b): ɛ = 0.74, d = 0.97 mm; and (c): ɛ = 0.65, d = 0.42 mm. FDP is calculated by MacDonald (grey, Eq. 28) and by Ward (black, Eq. 29)

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