96 1.5.1 Limit averaged equation for infinite number of scales, p.96 ,
126 3.2.2 Flow problem at the lowest scales, p.127 ,
129 3.3.1 Formulation of the flow problem at the second scale, p.129 ,
164 5.1.1 Problem setting, Parameters of the model, p.166 ,
Porous media: Geometry and transports, 1992. ,
Fractures and Fracture Network, 1999. ,
DOI : 10.1007/978-94-017-1599-7
Homogenization and Two-Scale Convergence, SIAM Journal on Mathematical Analysis, vol.23, issue.6, pp.1482-1518, 1992. ,
DOI : 10.1137/0523084
URL : https://hal.archives-ouvertes.fr/hal-01111805
Derivation of the Double Porosity Model of Single Phase Flow via Homogenization Theory, SIAM Journal on Mathematical Analysis, vol.21, issue.4, pp.823-826, 1990. ,
DOI : 10.1137/0521046
Homogenization of a degenerate triple porosity model with thin fissures, European Journal of Applied Mathematics, vol.16, issue.03, pp.335-359, 2005. ,
DOI : 10.1017/S0956792505006200
Homogenization of a single phase flow in a porous medium containing a thin layer, Math. Models Methods Appl, 2007. ,
On the homogenization of some double-porosity models with periodic thin structures, Applicable Analysis, vol.4, issue.10-11, pp.10-11, 2005. ,
DOI : 10.1007/978-1-4684-6787-1_10
URL : https://hal.archives-ouvertes.fr/hal-00865809
Averaging PDE With Fast Oscillating Coefficients, 1977. ,
Homogenization: Averaging Processes in Periodic Media, 1989. ,
On main representations in the theory of flow of homogeneous liquids in fractured rocks, Prikladnaya Mathematika i Mechanika, vol.24, issue.5, pp.852-864, 1960. ,
Theory of Non- Stationary Flow of Liquids and Gases Through Porous Media, 1972. ,
Theory of Fluid Flows Through natural Rocks, 1990. ,
DOI : 10.1007/978-94-015-7899-8
Block-geometry functions characterizing transport in densely fissured media, Journal of Hydrology, vol.77, issue.1-4, 1985. ,
DOI : 10.1016/0022-1694(85)90211-2
Modelling the effects of matrix diffusion on transport in densely fissured media, 1985. ,
Boundary conditions at a naturally permeable wall, Journal of Fluid Mechanics, vol.none, issue.01, pp.197-207, 1971. ,
DOI : 10.1017/S0022112067001375
Asymptotic analysis for periodic structures, 1978. ,
Laminar Flow in Channels with Porous Walls, Journal of Applied Physics, vol.3, issue.9, pp.1232-1235, 1953. ,
DOI : 10.1017/S0305004100019575
Effects of porous boundaries on the flow of fluids in systems of various geometries, Proceedings of the Second United Nations international Conference on the Peacefid Uses of Atomic Energy, pp.351-358, 1958. ,
Numerical experiments of the homogenization method for operators with periodic coefficients, Rapport de Recherche IRI, issue.277, pp.212-245, 1978. ,
A general double porosity model, C. R. Acad. Sci. Paris,. Sér. IIb, vol.327, pp.1245-1250, 1999. ,
Modè le de double porosité aléatoire, C.R. Acad. Sci. Paris, Sér. 1, pp.327-99, 1998. ,
Diffusion in Fissured Media, SIAM Journal on Mathematical Analysis, vol.16, issue.3, pp.500-509, 1985. ,
DOI : 10.1137/0516036
Peristaltic motion, Journal of Fluid Mechanics, vol.58, issue.04, pp.731-743, 1967. ,
DOI : 10.1017/S0022112067001156
Experimental study of tracer dispersion in sintered glass porous materials of variable compaction, Physics of Fluids, vol.31, issue.6, pp.1690-1698, 1987. ,
DOI : 10.1103/PhysRevB.31.5990
Contribution à l'étude expérimentale de l'écoulement radial d'un fluide visqueux incompressible entre deux disques parallèles, J. Mec, vol.5, pp.245-259, 1966. ,
Flow in Perforated Pipes: A Comparison of models and experiments Dead-end pore volume and dispersion in porous media, SPE Prod and Oper21 2, pp.302-311, 1964. ,
A general closure scheme for the method of volume averaging, Chemical Engineering Science, vol.41, issue.2, pp.227-235, 1986. ,
DOI : 10.1016/0009-2509(86)87003-8
Comparison between numerical simulations and experimental investigations of radial flows in rough fracture Advances in Fluid Mechanics III, pp.43-52, 2000. ,
Analytic Solutions for Determining Naturally Fractured Reservoir Properties by Well Testing, Society of Petroleum Engineers Journal, vol.16, issue.03, pp.117-122, 1976. ,
DOI : 10.2118/5346-PA
Flow through tubes with sinusoidal axial variations in diameter, AIChE Journal, vol.25, issue.4, pp.638-644, 1979. ,
DOI : 10.1002/aic.690250410
A Multiple- Porosity Model for A Single-Phase Flow Through Naturally-Fractured Porous Media, Computational and Applied Mathematics, vol.17, pp.19-48, 1998. ,
New Analytical Pressure-Transient Models to Detect and Characterize Reservoirs With Multiple Fracture Systems, SPE International Petroleum Conference in Mexico, pp.7-9, 2004. ,
DOI : 10.2118/92039-MS
Flow in fractured porous media, Water Resources Research, vol.78, issue.6, pp.558-566, 1977. ,
DOI : 10.1029/WR005i006p01273
A Proposed Model for Multiphase Flow Through Naturally Fractured Reservoirs, Society of Petroleum Engineers Journal, vol.22, issue.05, pp.669-680, 1983. ,
DOI : 10.2118/9940-PA
Computational Techniques for Fluid Dynamics Specific Techniques for Different Flow Categories, 1991. ,
The Use of Source and Green?s Functions in Solving Unsteady-Flow Problems in Reservoirs, SPE, vol.3818, pp.285-296, 1973. ,
Unsteady-State Pressure Distributions Created by a Well With a Single Infinite-Conductivity Vertical Fracture, Society of Petroleum Engineers Journal, vol.14, issue.04, pp.347-360, 1974. ,
DOI : 10.2118/4051-PA
A Study of Multiphase Flow Behavior in Vertical Wells, SPE Production Engineering, vol.3, issue.02, 1988. ,
DOI : 10.2118/15138-PA
Two-phase flow in vertical and inclined annuli, International Journal of Multiphase Flow, vol.18, issue.2, pp.279-293, 1992. ,
DOI : 10.1016/0301-9322(92)90089-Y
A Simplified Model for Oil/Water Flow in Vertical and Deviated Wellbores, p.143, 1994. ,
Diffusion models for fractured media, Journal of Mathematical Analysis and Applications, vol.147, issue.1, pp.69-80, 1990. ,
DOI : 10.1016/0022-247X(90)90385-S
Fundamental studies of fluid flow through a single fracture, 1976. ,
The interpretation of interference tests in naturally fractured reservoirs with uniform fracture distribution, SPE J, issue.12, pp.463-472, 1969. ,
Mathematical Handbook for Scientists and Engineers, 1968. ,
Homogenization of differential operators with closely periodic quickly oscillating coefficients, Mathematicheskii Sbornik. Novaya Seriia, pp.199-217, 1978. ,
Homogenization of random structures, Doklady Academii Nauk SSSR, vol.241, issue.5, pp.1016-1019, 1978. ,
Homogenization of random operators, Mathematicheskii Sbornik. Novaya Seriia, vol.109, issue.151 26, pp.188-202, 1979. ,
Conductivity of two-dimentional random media, Uspekhi Mathematicheskikh Nauk, pp.193-194, 1979. ,
Homogenization method and random walk in heterogeneous media, Uspekhi Mathematicheskikh Nauk, pp.61-120, 1985. ,
Geometric aspects of homogenization, Uspekhi Mathematicheskikh Nauk, pp.79-120, 1989. ,
Pressure Behavior of Horizontal Wells with Multiple Fractures, University of Tulsa Centennial Petroleum Engineering Symposium, pp.347-360, 1994. ,
DOI : 10.2118/27971-MS
A Nonlinear Approximation for the Pressure Behavior of Heterogeneous Reservoirs, SPE Journal, vol.1, issue.03, pp.229-241, 1996. ,
DOI : 10.2118/26456-PA
Pressure Behavior of Laterally Composite Reservoirs, SPE Formation Evaluation, vol.12, issue.01, pp.47-56, 1997. ,
DOI : 10.2118/24678-PA
Notes on somes computational aspects of homogenization in composite materials. Numerical methods in mathematical physics and optimal control, pp.5-19, 1978. ,
Stokes flow through a channel with wavy walls, Acta Mechanica, vol.69, issue.3-4, pp.151-182, 2006. ,
DOI : 10.1007/978-1-4612-0993-5
Boundary problems in domains with finely granulated boundaries (in Russian), 1974. ,
Unsteady-state behaviour of fractured reservoirs, SPE J, issue.1, pp.60-66, 1965. ,
Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations, Journal of Computational Physics, vol.79, issue.1, pp.12-49, 1988. ,
DOI : 10.1016/0021-9991(88)90002-2
Level Set Methods and Dynamic Implicit Surfaces, 2002. ,
DOI : 10.1115/1.1760520
General Wellbore Flow Model for Horizontal, Vertical, and Slanted Well Completions, SPE Journal, vol.3, issue.02, pp.124-133, 1998. ,
DOI : 10.2118/36608-PA
Single phase and multiphase fluid flow in horizontal wells, 1998. ,
A homogeneous model for gas???liquid flow in horizontal wells, Journal of Petroleum Science and Engineering, vol.27, issue.3-4, pp.119-128, 2000. ,
DOI : 10.1016/S0920-4105(00)00053-X
Averaging the parameters of mathematic models of heat, water and mass transport in an aggregated random-periodic porous medium. Mathematical methods of rock description and calculation of their effective propeties, pp.33-42, 1986. ,
Averaging the carcas constructions with random structures, Doklady AN SSSR, vol.244, issue.2, pp.335-337, 1988. ,
Phenomenon of Transient Boundary Layer in Underground Oil and Gas Reservoir Depletion Processes. Fluid Dynamics, pp.895-900, 1986. ,
Main Mode of Porous Flow in Highly Inhomogeneous Media, Soviet Physics Doclady, vol.35, issue.3, pp.225-227, 1990. ,
Structural Averaging of Porous Flow Processes in Heterogeneous Media. Fluid Dynamics, pp.112-120, 1993. ,
Averaged Model-Type Transition In Flows Through Multiple Heterogeneous Porous Media, C.R. Acad. Sci. Paris, Ser.II, pp.318-1437, 1994. ,
Macroscale models of flow through highly heterogeneous porous media, 2000. ,
DOI : 10.1007/978-94-015-9582-7
Singular nature of nonlinear macroscale effects in high-rate flow through porous media, Comptes Rendus M??canique, vol.331, issue.1, pp.41-48, 2003. ,
DOI : 10.1016/S1631-0721(02)00012-8
Macroscale model and viscous-inertia effects for Navier-Stokes flow in a radial fracture with corrugated walls, Journal of Fluid Mechanics, vol.504, pp.41-60, 2004. ,
Physical splitting of nonlinear effects in highvelocity stable flow through porous media, Advances in Water Ressources, pp.29-30, 2006. ,
High-Rate Navier-Stokes Flow in porous media: D'Alembert paradox and its solution The Netherlands, Proc. 2nd Biot Conference on Poromechanics, pp.521-526, 2002. ,
Asymptotic analysis of a double porosity model with thin fissures, Matematicheskii Sbornik, vol.194, issue.1, pp.121-146, 2002. ,
DOI : 10.4213/sm709
Asymptotic analysis of a double porosity model with thin fissures, English translation : Sbornik: Mathematics, pp.121-146, 0194. ,
DOI : 10.1070/SM2003v194n01ABEH000709
Multiscale Elliptic-Parabolic systems for Flow and Transport, Electronic Journal of Differential Equations, issue.147, pp.1-30, 2007. ,
Sur l'écoulement radial permanent d'un fluide visqueux incompressible entre deux plans parallèles fixes, J. Mec, vol.11, pp.377-395, 1963. ,
Poiseuille and his law, Anaesthesia, vol.1, issue.1, pp.273-5779509, 1976. ,
DOI : 10.1122/1.2116329
Handbook of Linear Partial Differential Equations for Engineers and Scientists, 2002. ,
DOI : 10.1201/9781420035322
Manzhirov Handbook of Integral Equations, 1998. ,
On the relationship between mechanical and hydraulic apertures in roughwalled fractures, J. Geophys. Res, vol.100, pp.12-629, 1995. ,
The existence of multiple solutions for the laminar flow in a uniformly porous channel with suction at both walls, Journal of Engineering Mathematics, vol.4, issue.1, pp.526-533, 1987. ,
DOI : 10.1007/BF01535424
On the boundary condition at the interface of a porous medium, 1971. ,
Non-homogeneous media and vibration theory. 129 of Lecture Notes in Physics, 1980. ,
Laminar radial flow betwen parallel plates, J. Appl. Mech, pp.594-596, 1963. ,
Boundary-layer Theory, 1968. ,
Laminar Flow in Channels with Porous Walls at High Suction Reynolds Numbers, Journal of Applied Physics, vol.26, issue.4, 1955. ,
DOI : 10.1063/1.1721476
Level Set Methods and Fast Marching Methods : Evolving Interfaces in Computational Geometry. Fluid Mechanics, Computer Vision, and Materials Science, 1999. ,
High-velocity flow in a rough fracture, Journal of Fluid Mechanics, vol.383, pp.1-28, 1999. ,
DOI : 10.1017/S0022112098002444
An Efficient, Interface-Preserving Level Set Redistancing Algorithm and Its Application to Interfacial Incompressible Fluid Flow, SIAM Journal on Scientific Computing, vol.20, issue.4, pp.1165-1191, 1999. ,
DOI : 10.1137/S1064827596298245
URL : https://hal.archives-ouvertes.fr/hal-01694576
The History of Poiseuille's Law, Annual Review of Fluid Mechanics, vol.25, issue.1, pp.1-19, 1993. ,
DOI : 10.1146/annurev.fl.25.010193.000245
Laminar flow in a uniformly porous channel, Aeronaut. Quart, vol.15, pp.299-310, 1964. ,
A front-tracking method for viscous, incompressible, multi-fluid flows, Journal of Computational Physics, vol.100, issue.1, pp.25-37, 1992. ,
DOI : 10.1016/0021-9991(92)90307-K
Radial inflow between two flat disks, Acta Mechanica, vol.31, issue.1-4, pp.109-118, 1995. ,
DOI : 10.1007/BF01212637
The Behavior of Naturally Fractured Reservoirs, Society of Petroleum Engineers Journal, vol.3, issue.03, pp.245-255, 1963. ,
DOI : 10.2118/426-PA
Laminar flow in a uniformly porous channel, J. Appl. Mech, vol.25, pp.613-617, 1958. ,
Laminar Pipe Flow With Injection and Suction Through a Porous Wall, Trans. ASME, vol.78, p.719, 1956. ,
DOI : 10.21236/AD0058831
Further Investigation of Laminar Flow in Channels with Porous Walls, Journal of Applied Physics, vol.56, issue.3, pp.267-269, 1956. ,
DOI : 10.1063/1.1722024
On the flow of a viscous fluid driven along a channel by suction at porous walls, Fluid Dynamics Research, vol.4, issue.3, pp.151-178, 1988. ,
DOI : 10.1016/0169-5983(88)90021-4
Effective transmissivity of two-dimensional fracture networks, International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, vol.33, issue.4, pp.433-438, 1996. ,
DOI : 10.1016/0148-9062(95)00067-4
Purely accelerating and decelerating flows within two flat disks, Acta Mechanica, vol.113, issue.1-4, pp.151-161, 1997. ,
DOI : 10.1007/BF01178407
Average Volumetric Concentration in Two-Phase Flow Systems, Journal of Heat Transfer, vol.87, issue.4, p.453, 1969. ,
DOI : 10.1115/1.3689137