Abstract
Non-Darcy behavior is important for describing fluid flow in porous media in situations where high velocity occurs. A criterion to identify the beginning of non-Darcy flow is needed. Two types of criteria, the Reynolds number and the Forchheimer number, have been used in the past for identifying the beginning of non-Darcy flow. Because each of these criteria has different versions of definitions, consistent results cannot be achieved. Based on a review of previous work, the Forchheimer number is revised and recommended here as a criterion for identifying non-Darcy flow in porous media. Physically, this revised Forchheimer number has the advantage of clear meaning and wide applicability. It equals the ratio of pressure drop caused by liquid–solid interactions to that by viscous resistance. It is directly related to the non-Darcy effect. Forchheimer numbers are experimentally determined for nitrogen flow in Dakota sandstone, Indiana limestone and Berea sandstone at flowrates varying four orders of magnitude. These results indicate that superficial velocity in the rocks increases non-linearly with the Forchheimer number. The critical Forchheimer number for non-Darcy flow is expressed in terms of the critical non-Darcy effect. Considering a 10% non-Darcy effect, the critical Forchheimer number would be 0.11.
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J.A. Andrade SuffixJr. U.M.S. Costa M.P. Almeida H.A. Makse H.E. Stanley (1998) ArticleTitleInertial effects on fluid flow through disordered porous media Phys. Rev. Lett. 82 IssueID26 5249–5252
J. Bear (1972) Dynamics of Fluids in Porous Media American Elsevier New York 125–129
Blick E.F. and Civan F. (1988). Porous media momentum equation for highly accelerated flow, SPE Reserv. Engng. 1048–1052.
H.C. Brinkman (1947) ArticleTitleA calculation of the viscous force exerted by a flowing fluid on a dense swarm of particles Appl. Sci. Res. A 1 27–34
InstitutionalAuthorNameCALSEP (2002) Help on PVTsim 12 Calsep Inc. Denmark 55–60
T.H. Chilton A.P. Colburn (1931) ArticleTitlePressure drop in packed tubes Ind Engng. Chem. 23 IssueID8 913–919 Occurrence Handle10.1021/ie50260a016
Civan, F. and Tiab, D.: 1991, Effects of external boundary conditions on steady and semi-steady radial flow equations based on Darcy, Forchheimer, Brinkman, and capillary-orifice models, SPE 22923, in: Proceedings of the SPE Annual Technical Conference, Dallas, Texas, USA, Oct. 6–9.
D. Cornell D.L. Katz (1953) ArticleTitleFlow of gases through consolidated porous media Indu. Engng. Chem. 45 IssueID10 2145–2152
J.P. Plessis ParticleDu J.H. Masliyah (1988) ArticleTitleMathematical modeling of flow through consolidated isotropic porous media Transport Porous Media 3 145–161 Occurrence Handle10.1007/BF00820342
S. Ergun (1952) ArticleTitleFluid flow through packed columns Chem. Engng. Prog. 48 IssueID2 89–94
R.E. Ewing R.D. Lazarov S.L. Lyons D.V. Papavassiliou J. Pasciak G. Qin (1999) ArticleTitleNumerical well model for non-Darcy flow through isotropic porous media Computat. Geosci. 3 185–204
G.H. Fancher J.A. Lewis (1933) ArticleTitleFlow of simple fluids through porous materials Ind. Engng. Chem. 25 IssueID10 1139–1147 Occurrence Handle10.1021/ie50286a020
Firoozabadi, A. and Katz, D. L.: 1979, An analysis of high-velocity gas flow through porous media, J. Petrol. Technol. 211–216.
P. Forchheimer (1901) ArticleTitleWasserbewegung durch boden Zeit. Ver.Deutsch. Ing. 45 1781–1788
V.A. Garanzha V.N. Konshin S.L. Lyons D.V. Papavassiliou G. Qin (2000) Validation of non-Darcy well models using direct numerical simulation Chen Ewing Shi (Eds) Numerical Treatment of Multiphase Flows in Porous Media, Lecture Notes in Physics, 552 Springer-Verlag Berlin 156–169
Geertsma, J.: 1974, Estimating the coefficient of inertial resistance in fluid flow through porous media, Soc. Petrol. Eng. J., 445–450.
Gidley, J. L.: 1991, A method for correcting dimensionless fracture conductivity for non-Darcy flow effect, SPE Prod. Engng. 391–394.
Green, L. Jr. and Duwez, P.: 1951, Fluid flow through porous metals, J. Appl. Mech. 39–45.
Guppy, K. H., Cinco-Ley, H. and Ramey, H. J.: 1982, Pressure buildup analysis of fractured wells producing at high flowrates, J. Petrol. Technol. 2656–2666.
M. Hassanizadeh W.G. Gray (1980) ArticleTitleGeneral conservation equations for multi-phase systems: 3 Constitutive theory for porous media flow Adv. Water Resour. 3 25–40 Occurrence Handle10.1016/0309-1708(80)90016-0
S.M. Hassanizadeh W.G. Gray (1987) ArticleTitleHigh velocity flow in porous media Transport Porous Media 2 521–531 Occurrence Handle10.1007/BF00192152
Holditch S.A. and Morse R.A. (1976). The effects of non-Darcy flow on the behavior of hydraulically fractured gas wells. J. Petrol. Technol. 1196–1179.
Li, D. and Engler, T. W.: 2001, Literature review on correlations of the non-Darcy coefficient, SPE 70015, in: Proceedings of the SPE Permian Basin Oil and Gas Recovery Conference, Midland, Texas, USA, May 15–16.
H. Ma D.W. Ruth (1993) ArticleTitleThe microscopic analysis of high Forchheimer number flow in porous media Transport Porous Media 13 139–160 Occurrence Handle10.1007/BF00654407
Martins, J. P., Milton-Taylor, D. and Leung, H. K.: 1990, The effects of non-Darcy flow in propped hydraulic fractures, SPE 20790, in: Proceedings of the SPE Annual Technical Conference, New Orleans, Louisiana, USA, Sept. 23–26.
Scheidegger, A. E.: 1974, The Physics of Flow through Porous Media (3rd edn), University of Toronto Press, 152–170.
F. Thauvin K.K. Mohanty (1998) ArticleTitleNetwork modeling of non-Darcy flow through porous media Transport Porous Media 31 19–37 Occurrence Handle10.1023/A:1006558926606
S. Whitaker (1969) ArticleTitleAdvances in theory of fluid motion in porous media Ind. Eng. Chem. 61 IssueID12 14–28 Occurrence Handle10.1021/ie50720a004
Zeng, Z., Grigg, R. and Ganda, S.: 2003, Experimental study of overburden and stress on non-Darcy gas flow in Dakota sandstone, SPE 84069, in: Proceedings of the SPE Annual Technical Conference, Denver, Colorado, USA, Oct. 5–8.
Zeng, Z., Grigg, R. B, and Gupta, D. B.: 2004, Laboratory investigation of stress-sensitivity of non-Darcy gas flow parameters, SPE 89431, in: Proceedings of the SPE/DOE Fourteenth Symposium on Improved Oil Recovery Conference, Tulsa, Oklahoma, USA, April 17–21.
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Zeng, Z., Grigg, R. A Criterion for Non-Darcy Flow in Porous Media. Transp Porous Med 63, 57–69 (2006). https://doi.org/10.1007/s11242-005-2720-3
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DOI: https://doi.org/10.1007/s11242-005-2720-3