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Erschienen in:
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2018 | OriginalPaper | Buchkapitel

1. Porous Media

verfasst von : Jacob Bear

Erschienen in: Modeling Phenomena of Flow and Transport in Porous Media

Verlag: Springer International Publishing

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Abstract

The chapter starts by defining a porous medium and discusses the continuum description of phenomena and flow and transport of extensive quantities such as mass, momentum and energy at the microscopic and macroscopic continuum levels. The derivation of the unscaled continuum description at the macroscopic level by volume and mass averaging is presented and discussed, although the book is based primarily on deriving the continuum description of transport in porous media by the phenomenological approach. Scales of description are discussed for inhomogeneous porous media. The general procedure for mathematical modeling is presented.

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Nächstes Kapitel Some Elements of Thermodynamics
Fußnoten
1
Contributed by Dr. Jonathan Ajo-Franklin, LBNL.
 
2
Dr. George J. Moridis of LBNL co-authored Sects. 1.3.3–1.3.6.
 
Literatur
Abdassah D, Ershaghis I (1986) Triple-porosity system for representing naturally fractured reservoirs. SPE Form Eval 1:113–127CrossRef
Adler PM, Thovert J-M (1999) Fractures and networks. Kluwer Academic Publishers, Dordrecht, 429 p
Aguilera R (1995) Naturally fractured reservoirs, 2nd edn. Pennwell Books, Tulsa, 520 p
Al-Ghamdi A, Ershaghi I (1996) Pressure transient analysis of dually fractured reservoirs. SPE J 1(1):93–100CrossRef
Armstrong RT, Ott H, Georgiadis A, Rucker M, Schwing A, Berg S (2014) Subsecond pore-scale displacement processes and relaxation dynamics in multiphase flow. Water Resour Res 50:9162–9176CrossRef
Bachmat Y, Bear J (1964) The general equation of hydrodynamic dispersion in homogeneous isotropic porous mediums. J Geophys Res 69:2561–2567CrossRef
Bakhvalov N, Panasenko G (1989) Homogenisation: averaging processes in periodic media. Kluwer Publishing Company, DordrechtCrossRef
Barenblatt GI, Zheltov IP, Kochina IN (1960) Basic concepts in the theory of seepage of homogeneous liquids in fissured rocks. J Appl Math Mech (PMM) 24:852–864
Bear J (1972) Dynamics of fluids in porous media. American Elsevier, 764 p (also published by Dover Publications, 1988; translated into Chinese)
Bear J, Bachmat Y (1991) Introduction to modeling phenomena of transport in porous media. Kluwer Publishing Company, Dordrecht, 553 p
Bear J, Cheng AH-D (2010) Modeling groundwater flow and contaminant transport. Springer, Berlin, 834 p
Bear J, Zaslavsky D, Irmay S (1968) Physical principles of water percolation and seepage. UNESCO, 465 p
Bear J, Tsang CF, de Marsily G (eds) (1993) Flow and contaminant transport in fractured rock. Academic Press Inc, San Diego, 560 p
Bensoussan A, Lions JL, Papanicolaou G (1978) Asymptotic analysis of periodic structures. North-Holland, Amsterdam
Berg S, Ott H, Klapp SA, Schwing A, Neiteler R, Brusse N, Makurat A, Leu L, Enzmann F, Schwarz J-O, Kersten M, Irvine S, Stanpanoni M (2013) Real-time 3D imaging of Haines jumps in porous media flow. Proc Nat Acad Sci 110(10):3755–3759CrossRef
Blunt MJ (2001) Flow in porous media - pore-network models and multiphase flow, current opinion. Colloid Interface Sci 6:197–207
Blunt MJ, Bijeljic B, Dong H, Gharbi O, Iglauer S, Mostaghimi P, Paluszny A, Pentland C (2013) Pore-scale imaging and modelling. Adv Water Resour 51:197–216CrossRef
Boussinesq J (1904) Recherches théoriques sur l’ecoulement des nappes d’eau infiltrées dans les sol, et sur le débit des sources. CRH Acad Sci, Paris, J Math Pure et Appl 10:5–78 (1903), 1(0):363–394
Celia M, Reeves PC, Ferrand LA (1995) Recent advances in pore scale models for multiphase flow in porous media. Rev Geophys 33:1049–1057CrossRef
Cipolla C, Mack M, Maxwell S (2010) Reducing exploration and appraisal risk in low-permeability reservoirs using microseismic fracture mapping. In: SPE 137437, presented at the Canadian unconventional resources and international petroleum conference, Calgary, Canada, October, 10–21, 2010
Cnudde V, Boone MN (2013) High-resolution X-ray computed tomography in geosciences: a review of the current technology and applications. Earth Sci Revs 123:1–17CrossRef
Courant R, Hilbert D (1962) Methods of mathematical physics. Wiley Interscience, N.Y., 560 p
Coussy O (2004) Poromechanics. Wiley, New York, 312 p
Coussy O (2007) Revisiting the constitutive equations of unsaturated porous solids using a Lagrangian saturation concept. Int J Numer Anal Meth Geomech 31(15):1675–1694CrossRef
Cushman JH (1997) The physics of fluids in hierarchial porous media. Kluwer Academic Publishers., Dordrecht, 467 p
Dagan G (1989) Flow and transport in porous formations. Springer, New York, 465 p
Dagan G, Neuman SP (eds) (1997) Subsurface flow and transport: a stochastic approach. Cambridge University Press, Cambridge, 241 p
Debye P, Anderson HR Jr, Brumberger H (1957) Scattering by an inhomogeneous solid II. The correlation function and its application. Appl Phys 28(6):679–683CrossRef
Doughty C (1999) Investigation of conceptual and numerical approaches for evaluating moisture, gas, chemical, and heat transport in fractured unsaturated rock. J Contam Hydrol 38(1–3):69–106CrossRef
Dupuit J (1863) Études Théoriques et Pratiques sur les Mouvementdes des Eaux dans les Cannaux Découverts et à Travers les Terrains Perméables, 1st edn 1948, 2nd edn. Dunod, Paris, 304 p
Eringen AC (1980) Mechanics of continua, 2nd edn. Krieger Publishing Company, Malabar, 592 p
Feller W (1957) An introduction to probability theory and its applications, 2nd edn. Wiley, New York
Forchheimer P (1886) Uber die Ergiebigkeit von Brunnenanlagen und Sickerschlitzen. Hannover Zeitz. d. Archit u Ing Ver 8(2):538–564
Forchheimer P (1901) Wasserbewegung durch boden. Z Ver Deutsch Ing 45:1782–1788
Fredrich JT (1999) 3D imaging of porous media using laser scanning confocal microscopy with application to microscale transport processes. Phys Chem Earth (A) 24(7):551–561CrossRef
Gelhar LW (1993) Stochastic subsurface hydrology. Prentice-Hall, Englewood Cliffs
Gelhar LW, Axnes CL (1983) Three dimensional stochastic analysis of macrodispersion in aquifers. Water Resour Res 19:161–180CrossRef
Gray WG (1975) A derivation of the equations for multi-phase transport. Chem Eng Sci 30:229CrossRef
Gray WG, Hassanizadeh SM (1989) Averaging theorems and averaged equations for transport of interface properties in multiphase systems. Int J Multiphase Flow 15:81–95CrossRef
Hassanizadeh SM (1986a) Derivation of basic equations of mass transport in porous media; Part I. Macroscopic balance laws. Adv Water Resour 9:196–206CrossRef
Hassanizadeh SM (1986b) Derivation of basic equations of mass transport in porous media; Part II. Generalized Darcy’s law and Fick’s law. Adv Water Resour 9:207–222CrossRef
Hassanizadeh M, Gray W (1979a) General conservation equations for multiphase systems: 1. Averaging procedure. Adv Water Resour 2:131–144
Hassanizadeh M, Gray W (1979b) General conservation equations for multiphase systems: 2. Mass, momentum, energy and entropy equations. Adv Water Resour 2:191–203
Hassanizadeh SM, Gray WG (1980) General conservation equations for multi-phase systems, 3. Constitutive theory for porous media flow. Adv Water Resour 3:25–40CrossRef
Hassanizadeh SM, Gray WG (1990) Mechanics and thermodynamics of multiphase flow in porous media including interphase boundaries. Adv Water Res 13:169–186CrossRef
Holzer L, Cantoni M (2011) Review of FIB-tomography. Nano-fabrication using focused ion and electron beams: principles and applications. Oxford University Press, Oxford
Jikov VV, Kozlov SM, Oleinik OA (1994) Homogenization of differential operators and integral functionals. Springer, BerlinCrossRef
Joekar-Niasar V, Hassanizadeh SM, Leijnse A (2008) Insights into the relationships among capillary pressure, saturation, interfacial area and relative permeability using pore-scale network modelling. Trans Porous Media 74:201–219CrossRef
Joekar-Niasar V, Hassanizadeh SM, Dahle HK (2010) Dynamic pore-network modeling of drainage in two-phase flow. J Fluid Mech 655:38–71CrossRef
Kjetil N, Ringrose SR (2008) Identifying the representative elementary volume for permeability of heterolithic deposits using numerical rock models. Math Geosci 40:753–771CrossRef
Leal LG (2007) Advanced transport phenomena: fluid mechanics and convective transport processes, Cambridge University Press, Cambridge
Lions J-L (1981) Some methods in the mathematical analysis of systems and their control. Kexue Chubanshe Science Press, Beijing
Low PF (1961) Physical chemistry of clay-water interactions. Adv Agron 13:269–327CrossRef
Low PF (1976) Viscosity of interlayer water in montmorillonite. Soil Sci Soc Am J 40:500–505CrossRef
MacDowell AA, Parkinsona DY, Habouba A, Schaiblea E, Nasiatkaa JR, Yeea CA, Jamesona JR, Ajo-Franklina JB, Brodersenb CA, McElronec AJ (2012) X-ray micro-tomography at the advanced light source, developments in X-ray tomography VIII. In: Stock SR (ed) Proceedings of SPIE, p 850618
Marle CM (1981) Multiphase flow in porous media. Editions Technip, Paris, 267 p
Marsden JE, Tromba A (2003) Vector calculus, 5th edn. W. H. Freeman, New York, 790 p
Mikelic A (2000) Homogenization theory and applications to filtration through porous media. In: Fasano A (ed) Filtration in porous media and industrial application, vol 1734. Lecture notes in mathematics. Springer, Berlin, pp 127–214
Molins S, Trebotich D, Steefel CI, Shen C (2012) An investigation of the effect of pore-scale flow on average geochemical reaction rates using direct numerical simulation. Water Resour Res 48(3)
Molins S, Trebotich D, Yang L, Ajo-Franklin J, Ligocki TJ, Shen C, Steefel CI (2014) Pore-scale controls on calcite dissolution rates from flow-through laboratory and numerical experiments. Environ Sci Tech 48(13):7453–7460CrossRef
Murdoch AI, Hassanizadeh SM (2002) Macroscale balance relations for bulk, interfacial, and common line systems in multiphase flow through porous media on the basis of molecular considerations. Int J Multiph Flow 28:1091–1123CrossRef
Muskat M (1949) Physical principles of oil production. McGraw-Hill, New York, 922 p
Nayfeh AH (2000) Perturbation methods. Wiley, New York, 437 p
Parker JG (1986) Hydrostatics of water in porous media. In: Sparks DL (ed) Soil physical chemistry. CRC Press, Boca Raton
Qin C, Hassanizadeh SM (2013) Multiphase flow through multilayers of thin porous media: General balance equations and constitutive relationships for a solid-gas-liquid three-phase system, Int J Heat Mass Tran, 70: 693–708
Qin C, Hassanizadeh SM (2015) A new approach to modelling water flooding in a polymer electrolyte fuel cell. Int J Hydrog Energy 40(8):3348–3358CrossRef
Raeini AQ, Blunt MJ, Bijeljic B (2014) Direct simulations of two-phase flow on micro-CT images of porous media and upscaling of pore-scale forces. Adv Water Resour 74:116–126CrossRef
Raoof A, Hassanizadeh SM (2012) A new formulation for pore-network modeling of two-phase flow. Water Resour Res 48:13
Raoof A, Hassanizadeh SM, Leijnse A (2010) Upscaling transport of adsorbing solutes in porous media: pore network modeling. Vadose Zone J 9:624–636CrossRef
Richards LA (1931) Capillary conduction of liquids through porous medium. Physics 1:318–333CrossRef
Rubin Y (2003) Applied Stochastic Hydrogeology. Oxford University Press, Oxford, 391 p
Sanchez-Palencia E (1974) Comportement local et macroscopique d’un type de milieu physiques héterogénes. Int J Eng Sci 12:331–352CrossRef
Sanchez-Palencia E (1980) Non-homogeneous media and vibration theory, vol 127. Lecture notes in physics. Springer, N.Y
Schluter S, Sheppard A, Brown K, Wildenschild D (2014) Image processing of multiphase images obtained via X-ray microtomography: a review. Water Resour Res 50:3615–3639CrossRef
Selyakov VI, Kadet VV (1996) Percolation models for transport in porous media. Kluwer Academic Publishers, Dordrecht, 241 p
Stock SR (2008) Recent advances in X-ray micro-tomography applied to materials. Intern Mater Rev 53(3):129–181CrossRef
Strobl M, Manke I, Kardjilov N, Hilger A, Dawson M, Banhart J (2009) Advances in neutron radiography and tomography. J Phys D Appl Phys 42(24):3001–3022CrossRef
Sun N-Z (1999) Inverse problems in groundwater modeling, 2nd edn. Springer, Berlin, 338 p
Sun N-Z, Sun A (2015) Model calibration and parameter estimation: for environmental and water resource systems. Springer, Berlin, 621 p
Sutton RP, Cox SA, Barre, RD (2010) SPE paper 138447 presented at the SPE tight gas completions conference held in San Antonio, Texas, USA, 2–3 November 2010
Ten Dam A, Erentz C (1970) Kizildere geothermal field, Western Anatolia. Geothermics 2(1):124–129 U.S. EIA, 2011CrossRef
Thewlis J (ed) (1973) Concise dictionary of physics. Pergamon Press, Oxford, 248 p
Truesdell C (1977) Rational thermodynamics. Springer, Berlin, 578 p
Warlick DN (2006) Gas shale and CBM development in North America. Oil Gas J 3(11):1–8
Warren JE, Root PJ (1963) The behavior of naturally fractured reservoirs. J Soc Pet Eng 3:245–255CrossRef
Whitaker S (1999) The method of volume averaging. Kluwer Acad. Publishers, Dordrecht, 219 p
Wildenschild D, Sheppard AP (2013) X-ray imaging and analysis techniques for quantifying pore-scale structure and processes in subsurface porous medium systems. Adv Water Resour 51:217–246CrossRef
Williams BB, Gidley JL, Schechter RS (1979) Acidizing fundamentals. Soc Petrol Eng Monograph Ser. 6(2):124 p
Wu YS, Liu HH, Bodvarsson GS (2004) A triple-continuum approach for modeling flow and transport processes in fractured rock. J Contam Hydrol 73(1):145–179CrossRef
Wu YS, Efendiev Y, Kang Z, Ren Y (2006) A multiple-continuum approach for modeling multiphase flow in naturally fractured vuggy petroleum reservoirs. In: SPE. Beijing Conference
Yaglom AM (1965) Theory of stationary random functions. Prentice Hall, Englewood Cliff
Zhang D, Zhang R, Chen S, Soll WE (2000) Pore scale study of flow in porous media: scale dependency, REV, and statistical REV. Geophys Res Lett 27(8):1195–1198CrossRef
Metadaten
Titel
Porous Media
verfasst von
Jacob Bear
Copyright-Jahr
2018
Buch
Modeling Phenomena of Flow and Transport in Porous Media

Print ISBN: 978-3-319-72825-4

Electronic ISBN: 978-3-319-72826-1

Copyright-Jahr: 2018

DOI
https://doi.org/10.1007/978-3-319-72826-1_1