Experimental evidence of scale-dependent hydraulic conductivity for fully developed turbulent flow in a single fracture

Summary This study uses laboratory experiments to investigate scale dependent hydraulic conductivity of fully developed turbulent flow in a single fracture under different fracture surface roughness, fracture apertures, and hydraulic gradients. The hydraulic conductivity for fully developed turbulent flow is defined as K  =  V 2 / J , where V and J are absolute values of the flow velocity and the hydraulic gradient, respectively. Three different surface roughness (fine, medium, and coarse), three different fracture apertures (1.0 mm, 2.0 mm, and 2.5 mm), and five different hydraulic gradients have been tested. Experimental evidence shows that K values generally increase with scale in a linear fashion. Surface roughness and fracture apertures appear to have the most significant influence upon the scale-dependency of K , which is less sensitive to hydraulic gradients. In general, a higher hydraulic gradient will lead to a lower K value at a given scale. The scale-dependency of K might be a manifestation of two-dimensional torturous flow within a rough surface fracture.

[1]  S. P. Neuman,et al.  Type curve interpretation of a cross‐hole pneumatic injection test in unsaturated fractured tuff , 2001 .

[2]  J. Carrera.  An overview of uncertainties in modelling groundwater solute transport , 1993 .

[3]  Hongbin Zhan,et al.  Theoretical and experimental studies of coupled seepage-pipe flow to a horizontal well , 2003 .

[4]  S. P. Neuman,et al.  Steady-state analysis of cross-hole pneumatic injection tests in unsaturated fractured tuff , 2003 .

[5]  Dirk Schulze-Makuch,et al.  Variations in hydraulic conductivity with scale of measurement during aquifer tests in heterogeneous, porous carbonate rocks , 1998 .

[6]  Yu-Shu Wu.  An approximate analytical solution for non-Darcy flow toward a well in fractured media , 2002 .

[7]  R. Sidle,et al.  Mass transport and scale-dependent hydraulic tests in a heterogeneous glacial till–sandy aquifer system , 2001 .

[8]  James J. Butler,et al.  Relationship Between Pumping‐Test and Slug‐Test Parameters: Scale Effect or Artifact? , 1998 .

[9]  RISK ASSESSMENT METHODOLOGY FOR KARST AQUIFERS: (2) SOLUTE-TRANSPORT MODELING , 1997 .

[10]  Jesús Carrera,et al.  Scale effects in transmissivity , 1996 .

[11]  W. Illman.  Strong field evidence of directional permeability scale effect in fractured rock , 2006 .

[12]  Shemin Ge,et al.  A governing equation for fluid flow in rough fractures , 1997 .

[13]  D. Cherkauer,et al.  Scale Dependency of Hydraulic Conductivity Measurements , 1995 .

[14]  A. Hunt.  Some comments on the scale dependence of the hydraulic conductivity in the presence of nested heterogeneity , 2003 .

[15]  Dirk Schulze-Makuch,et al.  Scale Dependency of Hydraulic Conductivity in Heterogeneous Media , 1999 .

[16]  S. P. Neuman,et al.  Generalized scaling of permeabilities: Validation and effect of support scale , 1994 .

[17]  Chin-Fu Tsang,et al.  Channel model of flow through fractured media , 1987 .

[18]  Weidong Zhao,et al.  Experimental study of turbulent unconfined groundwater flow in a single fracture , 2005 .

[19]  C. W. Drake,et al.  Regional groundwater flow model construction and wellfield site selection in a karst area, Lake City, Florida , 1999 .

[20]  B. Berkowitz.  Characterizing flow and transport in fractured geological media: A review , 2002 .

[21]  X. Sanchez‐Vila,et al.  An evaluation of Jacob's Method for the interpretation of pumping tests in heterogeneous formations , 1998 .

[22]  R. J. Hopkirk,et al.  Observation and simulation of non‐Darcian flow transients in fractured rock , 1997 .

[23]  Garrison Sposito,et al.  Scale Dependence and Scale Invariance in Hydrology , 1998 .

[24]  Vittorio Di Federico,et al.  Multifaceted nature of hydrogeologic scaling and its interpretation , 2003 .

[25]  E. Sudicky,et al.  The interpretation of a tracer experiment conducted in a single fracture under conditions of natural groundwater flow , 1999 .

[26]  Vincent C. Tidwell,et al.  Upscaling experiments conducted on a block of volcanic tuff: Results for a bimodal permeability distribution , 1999 .

[27]  Brian R. Zurbuchen,et al.  Support volume and scale effect in hydraulic conductivity: Experimental aspects , 2000 .

[28]  Chin-Fu Tsang,et al.  Flow and Contaminant Transport in Fractured Rock , 1993 .

[29]  David J. Brush,et al.  Fluid flow in synthetic rough‐walled fractures: Navier‐Stokes, Stokes, and local cubic law simulations , 2003 .

[30]  C. Clauser.  Permeability of crystalline rocks , 1992 .

[31]  C. Rovey.  Assessing flow systems in carbonate aquifers using scale effects in hydraulic conductivity , 1994 .

[32]  Walter A Illman,et al.  Asymptotic Analysis of Cross‐Hole Hydraulic Tests in Fractured Granite , 2006, Ground water.

[33]  Guanhua Huang,et al.  Non-Darcian flow in a single confined vertical fracture toward a well , 2006 .

[34]  Vincent C. Tidwell,et al.  Laboratory method for investigating permeability upscaling , 1997 .