Skip to main content
SpringerLink
Log in

Non-Darcy Flow of Water Through a Packed Column Test

  • Published:
Transport in Porous Media Aims and scope Submit manuscript

Abstract

As the flow velocity and Reynolds number increase in rockfilled porous media, the flow deviates from Darcy conditions and enters into a new phase known as non-Darcy conditions. Due to a linear relationship between hydraulic gradient and the flow velocity in Darcy formula, the flow can be analyzed with no difficulty. However, as the velocity increases the Darcy law is violated, the flow becomes turbulent, making the analysis more challenging. In this paper a laboratory packed column was built to study high-velocity flow through granular materials and new experimental data have been obtained. The laboratory experiments include application of for six different sizes of rounded aggregates and using different hydraulic gradients to assess the flow behavior. Using new experimental data, the validity of four widely-used head-loss equations were evaluated. The results indicated that the Sidiropoulou et al. (Hydrol Process 21:534–554, 2007) and Ergun’s head-loss equations yield satisfactory results comparing to other available relationships.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

References

  • Bari, R.: The hydraulics of buried streams. MASc thesis, Department of Civil Engineering, Technical University of Nova Scotia, Halifax, NS, Canada (1997)

  • Bari, R., Hansen, D.: Application of gradually-varied flow algorithms to simulate buried streams. IAHR J. Hydraul. Res. 40(6), 673–683 (2002)

    Article  Google Scholar 

  • Barr, D.W.: Turbulent flow through porous media. Ground Water 39(5), 646–650 (2001)

    Article  Google Scholar 

  • Basak, P.: Steady non-Darcian seepage through embankments. ASCE J. Irrig. Drain. Eng. 102(4), 435–443 (1976)

    Google Scholar 

  • Basak, P.: Non-Darcy flow and its implications to seepage problems. ASCE J. Irrig. Drain. Eng. 103(4), 459–473 (1977)

    Google Scholar 

  • Bear, J.: Dynamics of fluids in porous media. Elsevier Science, New York (1972)

    Google Scholar 

  • Bordier, C., Zimmer, D.: Drainage equations and non-Darcian modeling in coarse porous media or geosynthetic materials. J. Hydrol. 228, 174–187 (2000)

    Article  Google Scholar 

  • Chapokpour, J., Amiri-Tokaldany, E., Sedghi-Asl, M.: Estimation of friction coefficient in sediment contained flow through rockfill. Int. J. Eng. 26(2), 85–94 (2013)

    Google Scholar 

  • Cheng, N.-S., Hao, Z., Tan, S.K.: Comparison of quadratic and power law for nonlinear flow through porous media. Exp. Therm. Fluid Sci. 32, 1538–1547 (2008)

    Article  Google Scholar 

  • Ergun, S.: Fluid flow through packed columns. Chem. Eng. Prog. 48, 89–94 (1952)

    Google Scholar 

  • Fand, R.M., Thinakaran, R.: The influence of the wall on flow through pipes packed with spheres. ASME J. Fluids Eng. 122(3), 84–88 (1990)

    Article  Google Scholar 

  • Forchheimer, P.: Wasserbewegung durch boden. Zeit. Ver. Deutsch. Ing. 45, 1781–1788 (1901)

    Google Scholar 

  • Gikas, G.D., Yiannakopoulou, T., Tsihrintzis, V.A.: Modeling of non-point source pollution in a mediterranean drainage basin. Environ. Model. Assess. 11, 219–233 (2006)

    Article  Google Scholar 

  • Greenly, B.T., Joy, D.M.: One-dimensional finite-element model for high flow velocities in porous media. ASCE J. Geotech. Eng. 122(10), 789–796 (1996)

    Article  Google Scholar 

  • Hansen, D.: The behavior of flowthrough rockfill dams. Ph.D. thesis, Department of Civil Engineering, University of Ottawa, Ottawa, Ontario (1992)

  • Hill, R.J., Koch, D.L.: The transition from steady to weakly turbulent flow in a close-packed ordered array of spheres. J. Fluid Mech. 465, 59–97 (2002)

    Google Scholar 

  • Hosseini, S.M., Joy, D.M.: Development of an unsteady model for flow through coarse heterogeneous porous. Int. J. River Basin Manag. 5(4), 253–265 (2007)

    Article  Google Scholar 

  • Huang, K., Wan, J.W., Chen, C.X., He, L.Q., Mei, W.B., Zhang, M.Y.: Experimental investigation on water flow in cubic arrays of spheres. J. Hydrol. 492, 61–68 (2013)

    Article  Google Scholar 

  • Klauder, W.S.: Experimentelle Untersuchung der Anströmung von Vertikalfilterbrunnen. Universität Aachen -Germany, Aachen (2010). Ph-D thesis-

    Google Scholar 

  • Kovacs, G.: Developments in water science seepage hydraulics, vol. 10. Elsevier, Amsterdam (1977)

    Google Scholar 

  • Mathias, S., Butler, A., Zhan, H.: Approximate solutions for Forchheimer flow to a well. ASCE J Hydraul. Eng. 134(9), 1318–1325 (2008)

    Article  Google Scholar 

  • Moutsopoulos, K.N.: One-dimensional unsteady inertial flow in phreatic aquifers, induced by a sudden change of the boundary head. Transp. Porous Media. 70, 97–125 (2007)

    Google Scholar 

  • Moutsopoulos, K.N.: Exact and approximate analytical solutions for unsteady fully developed turbulent flow in porous media and fractures for time dependent boundary conditions. J. Hydrol. 369(1–2), 78–89 (2009)

    Article  Google Scholar 

  • Moutsopoulos, K.N., Tsihrintzis, V.A.: Approximate analytical solutions of the Forchheimer equation. J. Hydrol. 309(1–4), 93–103 (2005)

    Article  Google Scholar 

  • Moutsopoulos, K.N., Papaspyros, J.N.E., Tsihrintzis, V.A.: Experimental investigation of inertial flow processes in porous media. J. Hydrol. 374, 242–254 (2009)

    Article  Google Scholar 

  • Panfilov, M., Fourar, M.: Physical splitting of non-linear effects in high-velocity stable flow through porous media. Adv. Water Res. 29(1), 30–41 (2006)

    Article  Google Scholar 

  • Panfilov, M., Oltean, C., Panfilova, I., Buès, M.: Singular nature of nonlinear macroscale effects in high-rate flow through porous media. Comptes Rendus Mecanique 331(1), 41–48 (2003)

    Article  Google Scholar 

  • Salehi, R.: An empirical study on hydraulic conductivity for turbulent flow through porous media. M.Sc. Thesis. Department of Irrigation and Reclamation, University of Tehran, Tehran, Iran (2003)

  • Samani, H.M.V., Samani, J.M.V., Shaiannejad, M.: Reservoir routing using steady and unsteady flow through Rockfill Dams. J. Hydraul. Eng. 129(6), 448–454 (2003)

    Article  Google Scholar 

  • Sedghi-Asl, M., Rahimi, H.: Adoption of Manning’s equation to 1D non-Darcy flow problems. J. Hydraul. Res. 49(6), 814–817 (2011)

    Article  Google Scholar 

  • Sen, Z.: Nonlinear flow toward wells. J. Hydraul. Eng. 115(2), 193–209 (1989)

    Article  Google Scholar 

  • Sidiropoulou, M.G., Moutsopoulos, K.N., Tsihrintzis, V.A.: Determination of Forchheimer equation coefficients \(a\) and \(b\). Hydrol. Process. 21(4), 534–554 (2007)

    Article  Google Scholar 

  • Skjetne, E., Auriault, J.L.: High-velocity laminar and turbulent flow in porous media. Transp. Porous Media. 36(2), 131–147 (1999)

    Google Scholar 

  • Sophocleous, M.: Interactions between groundwater and surface water: the state of the science. Hydrogeol. J. 10(1), 52–67 (2002)

    Article  Google Scholar 

  • Sophocleous, M.A.: Stream-floodwave propagation through the Great Bend alluvial aquifer, Kansas: field measurements and numerical simulations. J. Hydrol. 124, 207–228 (1991)

    Article  Google Scholar 

  • Venkataraman, P., Rao, P.R.M.: Darcian, transitional and turbulent flow through porous media. J. Hydraul. Eng. 124, 840–846 (1998)

    Article  Google Scholar 

  • Wen, Z., Huang, G., Zhan, H.: An analytical solution for non-Darcian flow in a confined aquifer using the power law function. Adv. Water Res. 31, 44–55 (2008a)

    Google Scholar 

  • Wen, Z., Huang, G., Zhan, H., Li, J.: Two-region non-Darcian flow toward a well in a confined aquifer. Adv. Water Res. 31(5), 818–827 (2008b)

  • Wen, Z., Huang, G.-H., Zhan, H.-B.: Non-Darcian flow toward a finite-Diameter vertical well in a confined aquifer. Pedosphere 18(3), 288–303 (2008c)

  • Wen, Z., Huang, G., Zhan, H.: Non-Darcian flow in a single confined vertical fracture toward a well. J. Hydrol. 330(3–4), 698–708 (2006)

    Article  Google Scholar 

  • Yamada, H., Nakamura, F., Watanabe, Y., Murakami, M., Nogami, T.: Measuring hydraulic permeability in a streambed using the packer test. Hydrol. Process. 19, 2507–2524 (2005)

    Article  Google Scholar 

  • Zeng, Z., Grigg, R.: A criterion for non-Darcy flow in porous media. Transp. Porous Media 63, 57–69 (2006)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Soil Science, Faculty of Agriculture, Yasouj University, P.O. Box: 353, Yasouj , 75918-74831, Iran

    Mohammad Sedghi-Asl

  2. Department of Irrigation and Reclamation Engineering, University College of Agricultural and Natural Resources, University of Tehran, Karaj, Iran

    Hassan Rahimi & Reza Salehi

Authors
  1. Mohammad Sedghi-Asl
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hassan Rahimi
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Reza Salehi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mohammad Sedghi-Asl.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Sedghi-Asl, M., Rahimi, H. & Salehi, R. Non-Darcy Flow of Water Through a Packed Column Test. Transp Porous Med 101, 215–227 (2014). https://doi.org/10.1007/s11242-013-0240-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11242-013-0240-0

Keywords

Search

Navigation