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ANISOTROPIC HYDROLOGY PART I - FRACTURE FLOW SYSTEMS
 

An On-Line Version of a Column First Published in the:
National Environmental Journal July./Aug. 1994 Vol. 4 No. 4 Page 25-26

by: David B. Vance

 Usually shallow water bearing zones underlying a site are in soil. However, in some cases they are in bedrock. In the latter, any significant groundwater flow occurs in fracture systems within the bedrock. If soils are fine grained (i.e. tills or clays) fractures may also play a dominant role in advective flow there. Much of the science of hydrogeology was developed with and was designed for use in granular porous media. This is due to the incentive to find and produce aquifers for large scale groundwater consumption. Fractured media in most instances will not produce groundwater on that scale. Fracture flow systems are also more complex to analyze and hydraulically respond differently than those in porous granular matrices. This column will touch on some of those differences.

To compare, under identical hydraulic gradients one square meter of granular material with a hydraulic conductivity of 8.1 x 10-2 cm/sec has the equivalent water conducting capacity of one fracture in one square meter of rock with an aperture of 1 mm. In granular media, grain size, shape, and degree of sorting are the prime microscale parameters that determine hydraulic character. Fracture density, orientation, aperture and type of rock matrix are the major parameters affecting groundwater flow in fractured media. The typical range for fracture aperture is from 0.2 to 25 mm and fracture spacing from 2 mm to 3 meters.

Individual fractures are not infinite in extent. Therefore where flow is supported, fracture density must be high enough to insure connectivity through the system. The fracture density required to sustain advective flow is termed the "percolation threshold". Below that threshold fractures may be connected, but only in small localized regions. Above, localized regions become interconnected and flow can take place. With an increase in fracture density the system becomes increasingly pervious.

An expression of the parameter that determines the percolation through fracture is N(LF)2, where N is fracture density and LF is equal to fracture length times pi/2. The percolation threshold has been found to fall around 0.3.

As an example, in an area underlain by metamorphic rocks with discrete water producing fracture systems:

  • fractures were approximately 0.5 meter in length;
  • with a density of 50 to 200 per 0.5 meter;
  • This gave values of NLF2 of 30 to 120, well above the percolation threshold of 0.3.

 Given adequate connectivity, the flow an individual fracture can support is proportional to the cube of the fracture aperture. This cube rule means that a few fractures with preferentially higher apertures can dominate the flow system and those are the ones most important to delineate. Typically fracture aperture will decrease with depth. Usually the highest flow rates occur in the upper 30 feet of a fracture system, with flow decreasing to near zero below depths of 100 feet.

To some degree all rocks or soils are reactive. In most igneous, metamorphic or fine grained sedimentary rocks geochemical reactions tend to seal a given fracture over time. In carbonates the opposite can be true, with the fracture aperture increasing with time (and the potential flow rate increasing with the cube of that aperture).

The hydrodynamics of fracture flow systems will approach those in porous media in systems where fractures are randomly oriented and density is high. These systems can be analyzed using conventional granular media methodologies. To use those methods on other fracture systems is an error with potentially significant consequences.

Characterization of a fracture flow system is potentially an expensive process. Ideally, data should be gathered on fracture length, orientation, aperture, and density. Additionally, information on hydraulic head, the porosity and hydraulic characteristics of the bulk matrix, the type of contaminants, and potential interactions between contaminants and the matrix are also important. Hydrogeologic characterization of fracture systems can be accomplished through coring, complex pumping tests, tracer tests, geophysical evaluation, or bore hole flow meters. In addition, evaluation of the hydrodynamics of a fracture system that has been defined with multiple orientations is mathematically extremely complex.

However, some level of useful knowledge can be inferred based on the structural setting of a site. The tectonic and depositional history of a given site is generally available in the geologic literature. The removal of overburden introduces stresses due to reduction of overburden pressure, uplift of the region and thermal stresses due to cooling, the net stress is extensional.

Fractures that form in the tensile stress field can be placed in two classes:

  • Unloading fractures, which include vertical fractures, indicating response to tensile stress in the horizontal plane and fractures horizontal or parallel to the topographic surface
  • Release fractures, that are fabric controlled in their orientation.

 If a site has undergone even a mild degree of tectonic deformation, structural analysis can be used as a powerful predictive tool for the orientation of the dominant fracture sets at a site. Several points are important to use this concept:

  • The deformational pattern observed in the large scale is replicated at medium, small and microscopic scales. For example the NE trend of the Appalachians is generally reflected as a NE oriented fabric at all scales.
  • Deformation imparts a fabric to the impacted rocks. This fabric imparts anisotropicity, which in turn will control subsequent fracture generation. For example fractures will tend to propagate perpendicular to a strong linear fabric element.
  • The stronger the degree of imprinted fabric the greater the density of fractures in the controlled orientations.
  • Depositional features such as bedding planes also impart anisotropic fabric.

 It is important to understand the differences between fractured and porous media with regards to contaminant fate and transport. First, rapid transport in preferred directions can occur through rocks that normally would be thought impervious. A more subtle point has to do with the lack of retardation. Retardation is a function of matrix and contaminant chemistry and surface area. As an estimate, a block of granular media will have a surface area 1,000 to 100,000 times greater than a similar block of fractured media. Contaminant retardation will be roughly proportional. Contaminants in fractures can be mobile over long distances or until they are transported into a granular media.

One last note to illustrate alternate thinking with regards to fracture flow systems, when drilling recovery wells in fractured terrain orient the well bore such that it is perpendicular to the major water bearing fracture set. The resulting well may not necessarily be vertical, but will maximize the potential to intersect flow bearing fractures. Next column, anisotropic granular flow systems.

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Copyright 2002 David B. Vance
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