Modeling Flow in Unsaturated,
Fractured Rock

"I'm caught in a dream
  Sometimes it ain't what it seems
  I'm all in a daze
  Can't find my way out of this maze
  I'm looking for clues
  And wanting a change in the rules..."   From the song "Fractured Love" by Def Leppard



I have been involved in analytical and numerical modeling of subsurface water for quite a few years now.  As indicated by the lyrics quoted above, my main interest is in finding new, improved conceptual models of flow in unsaturated, fractured rock.  The research presented below has been conducted in conjunction with the Applied Geosciences Department of the Idaho National Environmental and Engineering Laboratory (INEEL).  Funding for the simulations was provided through the generous support of the INEEL Subsurface Science Education Outreach Program, administered through the Idaho Water Resources Research Institute, and the Applied GeoSciences Department of INEEL.



 
A Comparison of Laboratory Testing with Model Simulations
The applicability of current conceptual models of unsaturated, fracture flow was explored by a comparison of laboratory tests and numerical simulations.  An experimental domain of a simplified fracture/matrix system was constructed from twelve limestone bricks stacked four wide and three high, separated by analog “fractures” whose apertures averaged from 1.5 x 10-4 m (vertical fractures) to 1.7 x 10-8 m (horizontal fractures).  Water was introduced to the top boundary at a rate of about 1 mL/min to each of the three vertically oriented fractures (for a total of 3 mL/min), and collected by fiberglass wicks at the bottom boundary.  These laboratory tests were simulated using four different conceptual models (isotropic and anisotropic equivalent continuum, dual porosity, and discrete fracture models).  Despite the simple and well-characterized nature of the experimental system, all of the conceptual models tested failed to reproduce critical aspects of the observed behavior.  This comparison implies that important physical processes are lacking from current descriptions of fracture flow in unsaturated media, and casts doubt on the ability of contemporary models to make useful predictions of subsurface flow and transport. 

 
Laboratory Experimental Results
The series of photos above show the progress of trial 3.  Water was injected over a period of 72 hours, at a rate of 3 mL/min (1 mL/min to each of the three analog fractures).  Contrast the following behavior visible in the photos with the modeling results below:
-Non-uniform wetting of the matrix blocks
-Focusing of flowpaths with increasing vertical distance from the injection points
-Matrix saturation lags fracture wetting front passage by a significant amount of time
The contrast between the behavior predicted by the models below and the experimental results above suggests that some critical physics is missing from current conceptual models of flow in unsaturated, fractured rock.  Identifying and including the necessary processes is an active area of research at the University of Idaho, and the Idaho National Engineering and Environmental Laboratory.

You can click on the plots below to get a full sized version with legible text...
 

Numerical Modeling Results: ECM (Isotropic Properties)
The Equivalent Continuum Model (ECM) combines the effects of both fractures and matrix into one "equivalent" medium.  As can be seen in the above images, the result averages flow over the domain.  Effects arising from sharp contrasts in properties are therefore lost.
 
 
Numerical Modeling Results: ECM (Anisotropic Properties)
The images above also were generated using an ECM, but in this case the hydraulic properties of the medium are direction dependent.  Although it appears in the plots that vertical fractures are explicitly included, the characteristic appearance of these simulations derives from the influences of gravity, point injection of water, anisotropy, and grid orientation.
 
 
Numerical Modeling Results: DFM 
The Discrete Fracture Model (DFM) is the most sophisticated and computationally intensive model presented here.  DFMs use two (or more) domains, each with its own hydraulic properties set: one domain for fractures, and one for matrix.  Although the DFM does a better job than the ECMs of resolving some of the effects of fractures on the flow field, it fails to reproduce many critical aspects observed in the laboratory tests shown above.
 

I'm on the lookout for a sharp graduate student or two, so if the above topics interest you give me a call (208/885-9259), or E-mail me at jfairley@uidaho.edu.
 
 
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