Suscripción a Biblioteca: Guest
Portal Digitalde Biblioteca Digital eLibros Revistas Referencias y Libros de Ponencias Colecciones
Journal of Porous Media
Factor de Impacto: 1.752 Factor de Impacto de 5 años: 1.487 SJR: 0.43 SNIP: 0.762 CiteScore™: 2.3

ISSN Imprimir: 1091-028X
ISSN En Línea: 1934-0508

Volumes:
Volumen 23, 2020 Volumen 22, 2019 Volumen 21, 2018 Volumen 20, 2017 Volumen 19, 2016 Volumen 18, 2015 Volumen 17, 2014 Volumen 16, 2013 Volumen 15, 2012 Volumen 14, 2011 Volumen 13, 2010 Volumen 12, 2009 Volumen 11, 2008 Volumen 10, 2007 Volumen 9, 2006 Volumen 8, 2005 Volumen 7, 2004 Volumen 6, 2003 Volumen 5, 2002 Volumen 4, 2001 Volumen 3, 2000 Volumen 2, 1999 Volumen 1, 1998

Journal of Porous Media

DOI: 10.1615/JPorMedia.2019028855
pages 831-849

FAST AND INEXPENSIVE 2D-MICROGRAPH BASED METHOD OF PERMEABILITY ESTIMATION THROUGH MICRO-MACRO COUPLING IN POROUS MEDIA

Bamdad Barari
Laboratory for Flow and Transport Studies in Porous Media, Department of Mechanical Engineering, University of Wisconsin-Milwaukee, 3200 Cramer St., Milwaukee, WI, 53211
Saman Beyhaghi
Laboratory for Flow and Transport Studies in Porous Media, Department of Mechanical Engineering, University of Wisconsin-Milwaukee, 3200 Cramer St., Milwaukee, WI, 53211
Krishna Pillai
Mechanical Engineering Department EMS Building, 3200 N. Cramer Street, Room 945 College of Engineering and Applied Science University of Wisconsin, Milwaukee,WI 53211

SINOPSIS

The closure formulation, developed as a part of the derivation of Darcy's law proposed by Whitaker (1998), is used to develop a method based on two-dimensional (2D) micrographs for estimating the full in-plane (2D) permeability tensor of a porous medium without requiring multiple flow simulations in different directions. The governing equations were solved in the pore space of a representative elementary volume (REV) using the finite-element (FE) method via COMSOL Multiphysics software. The permeabilities of two distinct porous media created from cellulose nanofibers (CNF) and sintered polymer beads were then estimated numerically. In order to use real micrographs in such simulations, scanning electron microscopy (SEM) pictures of the CNF and polymer-wick porous media were considered. The mesh-size independence studies were conducted to find the appropriate FE mesh for computations. A falling-head permeameter was used for measuring the experimental permeability in order to test the accuracy of the permeability results obtained by numerical simulation. Unequal diagonal terms of the permeability tensor pointed to the presence of anisotropicity in CNF; such characterization is a benefit of the proposed method. A good agreement between the numerical permeability results and the experimental results confirmed the accuracy of the proposed micro-macro coupling based method in estimating this crucial property using 2D micrographs. This 2D closure-formulation based permeability estimation, which is faster, less expensive, and less troublesome than its three-dimensional (3D) counterpart, has the potential to emerge as a powerful characterization tool in the arsenal of porous-media scientists and researchers.

REFERENCIAS

  1. Anderson, T.B. and Jackson, R., A Fluid Mechanical Description of Fluidized Beds, Ind. Eng. Chem. Fundam, vol. 6, pp. 527-539, 1967.

  2. Ankerfors, M. and Lindstrom, T., Nanocellulose Developments in Scandinavia, Paper and Coating Chemistry Symposium (PCCS), Hamilton, ON, Canada, 2009.

  3. Barari, B., Ellingham, T.K., Ghamhia, I.I., Pillai, K.M., El-Hajjar, R., Turng, L., and Sabo, R., Mechanical Characterization of Scalable Cellulose Nano-Fiber based Composites Made Using Liquid Composite Molding Process, Composites Part B: Eng., vol. 84, pp. 277-284, 2016.

  4. Barari, B. and Pillai, K.M., Search for a "Green" Composite Material: An Attempt to Fabricate Cellulose Nano-Fiber Composites Using Liquid Composite Molding, J. Indian Inst. Sci., vol. 95, no. 3, pp. 313-320, 2015.

  5. Bear, J., Dynamics of Fluids In Porous Media, New York: Elsevier, 1972.

  6. Bear, J. and Bachmat, Y., Introduction to Modeling of Transport Phenomena in Porous Media, Dordrecht: Kluwer Academic, 1990.

  7. Belhouideg, S. and Lagache, M., Prediction of the Effective Permeability Coefficient in Random Porous Media Using the Finite Element Method, J. Porous Media, vol. 17, no. 9, pp. 819-830, 2014.

  8. Bennethum, L. and Cushman, J., Multiscale, Hybrid Mixture Theory for Swelling Systems, Int. J. Eng. Sci, vol. 34, no. 2, pp. 125-145, 1996.

  9. Bernard, D., Nielsen, 0., Salvo, L., and Cloetens, P., Permeability Assessment by 3D Interdendritic Flow Simulations on Micro-tomography Mappings of Al-Cu Alloys, Mater. Sci. Eng.: A, vol. 392, no. 1, pp. 112-120,2005.

  10. Beyhaghi, S. and Pillai, K.M., Estimation of Tortuosity and Effective Diffusivity Tensors Using Closure Formulation in a Sintered Polymer Wick during Transport of a Nondilute, Multi-Component Liquid-Mixture, Special Topics Rev. Porous Media: Int. J., vol. 2, no. 4, pp. 267-282, 2011.

  11. Blunt, M.J., Bijeljic, B., Dong, H., Gharbi, O., Iglauer, S., Mostaghimi, P., Paluszny, A., and Pentland, C., Pore-Scale Imaging and Modelling, Adv. Water Resour., vol. 51, pp. 197-216,2013.

  12. Bruschke, M. and Advani, S., Flow of Generalized Newtonian Fluids across a Periodic Array of Cylinders, J. Rheology, vol. 37, no. 3, pp. 479-498, 1993.

  13. Bultreys, T., De Boever, W., and Cnudde, V., Imaging and Image-Based Fluid Transport Modeling at the Pore Scale in Geological Materials: A Practical Introduction to the Current State-of-the-Art, Earth-Sci. Rev., vol. 155, pp. 93-128, 2016.

  14. Davit, Y., Quintard, M., and Debenest, G., Equivalence between Volume Averaging and Moments Matching Techniques for Mass Transport Models in Porous Media, Int. J. Heat Mass Transf., vol. 53, pp. 4985-4993, 2010.

  15. Gebart, B., Permeability of Unidirectional Reinforcements for RTM, J. Composite Mater., vol. 26, no. 8, pp. 1100-1133,1992.

  16. Golfier, F., Wood, B.D., Orgogozo, L., Quintard, M., and Bues, M., Biofilms in Porous Media: Development of Macroscopic Transport Equations via Volume Averaging with Closure for Local Mass Equilibrium Conditions, Adv. Water Resour., vol. 32, no. 3, pp. 463-485, 2009.

  17. Gray, W.G., General Conservation Equations for Multi-Phase Systems: Constitutive Theory Including Phase Change, Adv. Water Resour., vol. 6, pp. 130-140, 1983.

  18. Gray, W. and Lee, P., On the Theorems for Local Volume Averaging of Multiphase Systems, Int. J. Multiphase Flow, vol. 3, no. 4, pp. 333-340, 1977.

  19. Gray, W.G. and Miller, C., Thermodynamically Constrained Averaging Theory Approach for Modeling Flow and Transport Phenomena in Porous Medium Systems: 1. Motivation and Overview, Adv. Water Resour, vol. 28, no. 2, pp. 161-180,2005.

  20. Guibert, R., Horgue, P., Debenest, G., and Quintard, M., A Comparison of Various Methods for the Numerical Evaluation of Porous Media Permeability Tensors from Pore-Scale Geometry, Math. Geosci., vol. 48, pp. 329-347, 2016.

  21. Guibert, R., Nazarova, M., Horgue, P., Hamon, G., Creux, P., and Debenest, G., Computational Permeability Determination from Pore-Scale Imaging: Sample Size, Mesh and Method Sensitivities, Transp. Porous Media, vol. 107, no. 3, pp. 641-656,2015.

  22. Hassanizadeh, M. and Gray, W., General Conservation Equations for Multi-Phase Systems: 1. Averaging Procedure, Adv. Water Resour, vol. 2, pp. 131-144, 1979.

  23. He, Y.Q. and Sykes, J., On the Spatial-Temporal Averaging Method for Modeling Transport in Porous Media, Transp. Porous Media, vol. 22, no. 1, pp. 1-51, 1996.

  24. Howes, F.A. and Whitaker, S., The Spatial Averaging Theorem Revisited, Chem. Eng. Sci., vol. 40, pp. 1387-1392, 1985.

  25. Hsu, C.T., A Closure Model for Transient Heat Conduction in Porous Media, J. Heat Transf., vol. 121, no. 3, pp. 733-739, 1999.

  26. Kim, J.H., Ochoa, J.A., and Whitaker, S., Diffusion in Anisotropic Porous Media, Transport Porous Media, vol. 2, pp. 327-356, 1987.

  27. Lasseux, D., Abbasian Arani, A.A., and Ahmadi, A., On the Stationary Macroscopic Inertial Effects for One Phase Flow in Ordered and Disordered Porous Media, Phys. Fluids, vol. 23, no. 7, pp. 73-103, 2011.

  28. Lux, J., Ahmadi, A., Gobbe, C., and Delisee, C., Macroscopic Thermal Properties of Real Fibrous Materials: Volume Averaging Method and 3D Image Analysis, Int. J. Heat Mass Transf., vol. 49, no. 11, pp. 1958-1973, 2006.

  29. Masoodi, R. and Pillai, K.M., Wickingin Porous Materials: Traditional and Modern Modeling Approaches, Boca Raton, FL: CRC Press, 2012.

  30. Masoodi, R., Pillai, K.M., and Varanasi, P.P., Darcy's Law based Models for Liquid Absorption in Polymer Wicks, AIChE J, vol. 53, pp. 2769-2782, 2007.

  31. Mls, J., On the Existence of the Derivative of the Volume Average, Transp. Porous Media, vol. 2, pp. 615-621, 1987.

  32. Mostaghimi, P., Blunt, M., and Bijeljic, B., Computations of Absolute Permeability on Micro-CT Images, Math. Geosci., vol. 45, no. 1,pp. 103-125,2013.

  33. Nakayama, A., Kuwahara, F., Sugiyama, M., andXu, G., A Two-Energy Equation Model for Conduction and Convection in Porous Media, Int. J. Heat Mass Transf, vol. 44, no. 22, pp. 4375-4379,2001.

  34. Pillai, K.M., Single-Phase Flows in Swelling, Liquid-Absorbing Porous Media: A Derivation of Flow Governing Equations using the Volume Averaging Method with a Nondeterministic, Heuristic Approach to Assessing the Effect of Solid-Phase Changes, J. Porous Media, vol. 17, no. 10, pp. 915-935, 2014.

  35. Piller, M., Schena, G., Nolich, M., Favretto, S., Radaelli, F., and Rossi, E., Analysis of Hydraulic Permeability in Porous Media: from High Resolution X-Ray Tomography to Direct Numerical Simulation, Transport Porous Media, vol. 80, no. 1, pp. 57-78, 2009.

  36. Quintard, M., Diffusion in Isotropic and Anisotropic Porous Systems: Three-Dimensional Calculations, Transp. Porous Media, vol. 11, no. 2, pp. 187-199, 1993.

  37. Quintard, M., Bletzacker, L., Chenu, D., and Whitaker, S., Nonlinear, Multicomponent, Mass Transport in Porous Media, Chem. Eng. Sci, vol. 61, pp. 2643-2669, 2006.

  38. Rasband, W.S., ImageJ, Bethesda, Maryland: U.S. National Institutes of Health, http://imagej.nih.gov/ij/, 1997-2014.

  39. Sabo, R.C., Elhajjar, R., Clemons, C., and Pillai, K., Characterization and Processing ofNanocellulose Thermosetting Composites, in Handbook of Polymer Nanocomposites. Processing, Performance and Application, Volume C, J.K. Pandey, H. Takagi, A.N. Nakagaito, and H.-J. Kim, Eds., Heidelberg: Springer, pp. 265-295,2015.

  40. Saito, T., Hirota, M., Tamura, N., Kimura, S., Fukuzumi, H., Heux, L., and Isogai, A., Individualization of Nano-Sized Plant Cellulose Fibrils by Direct Surface Carboxylation Using TEMPO Catalyst under Neutral Conditions, Biomacromolecules, vol. 10, no. 7, pp. 1992-1996,2009.

  41. Slattery, J.C., Flow of Viscoelastic Fluids through Porous Media, AIChEJ., vol. 13, no. 6, pp. 1066-1071, 1967.

  42. ThermoFisher Scientific, Avizo for Materials Science, accessed from https://www.thermofisher.com/us/en/home/industrial/electron-microscopy/electron-microscopy-instruments-workflow-solutions/3d-visualization-analysis-software/avizo-materials-science.html, 2019.

  43. Vignoles, G.L., Coindreau, O., Ahmadi, A., and Bernard, D., Assessment of Geometrical and Transport Properties of a Fibrous C/C Composite Preform as Digitized by X-Ray Computerized Microtomography: Part II. Heat and Gas Transport Properties, J. Mater. Res., vol. 22, no. 6, pp. 1537-1550, 2007.

  44. Whitaker, S., Diffusion and Dispersion in Porous Media, AIChEJ., vol. 13, no. 3, pp. 420-427,1967.

  45. Whitaker, S., Advances in Theory of Fluid Motion in Porous Media, Industrial Eng. Chem.,vol. 61,no. 12, pp. 14-28, 1969.

  46. Whitaker, S., A Simple Geometrical Derivation of the Spatial Averaging Theorem, Chem. Eng. Educ., vol. 19, no. 1, pp. 50-52, 1985.

  47. Whitaker, S., The Method of Volume Averaging, Dordrecht: Springer, 1998.

  48. Wildenschild, D. and Sheppard, A.P., X-Ray Imaging and Analysis Techniques for Quantifying Pore-Scale Structure and Processes in Subsurface Porous Medium Systems, Adv. Water Res., vol. 51, pp. 217-246, 2013.

  49. Zhang, S. and Klimentidis, R., P. Barthelemy (1) - (1) Visualization Sciences Group, and ExxonMobil Upstream Research Co., Porosity and Permeability Analysis on Nanoscale FIB-SEM 3D Imaging of Shale Rock, SCA Symposium, 2011.


Articles with similar content:

PREDICTION OF THE EFFECTIVE PERMEABILITY COEFFICIENT IN RANDOM POROUS MEDIA USING THE FINITE ELEMENT METHOD
Journal of Porous Media, Vol.17, 2014, issue 9
Soufiane Belhouideg, Manuel Lagache
A 3D PROGRESSIVE MATERIAL DAMAGE MODEL FOR FE SIMULATION OF MACHINING A UNIDIRECTIONAL FRP COMPOSITE
Composites: Mechanics, Computations, Applications: An International Journal, Vol.8, 2017, issue 2
Ming Luo, Baohai Wu, Yanli He, Ying Zhang
LES OF COMLEX TURBULENT FLOWS WITH HIGH ORDER ACCURACY FINITE VOLUME METHOD
TSFP DIGITAL LIBRARY ONLINE, Vol.5, 2007, issue
Guixiang Cui, Lan Xu, Zhaoshun Zhang, Rui-Feng Shi
COMPUTATIONAL STUDY OF FLUID FLOW THROUGH AN IDEALIZED FRACTURE UNDER CONFINING STRESSES
Journal of Porous Media, Vol.18, 2015, issue 5
Goodarz Ahmadi, Alberto Roman
An Improved Capillary Bundle Model by Using Tortuosity and Parameters Extracted from Pore Network Model
International Heat Transfer Conference 15, Vol.40, 2014, issue
Yu Liu, Yongchen Song, Lingyu Chen, Xinhuan Zhou, Lanlan Jiang, Meiheriayi Mutailipu