Effect of Variability on Average Rock-Mass Permeability


Fluid flow in fractured rocks has been a very difficult problem that has stymied many workers. A major cause of this problem is the disconnect between the geology of fracturcd rocks and the assumptions of Darcy's Law. Darcy's Law is based on the average permeability over a uniform mass of rock or soil, but the permeability of fracturcd rock is anything but uniform, and tends to be log-normally distributed with a high degree of variability. Darcy's Law requires the arithmetic mean permeability but log-normal distributions arc centered around the geometric mean. If the variability is low, the geometric mean will be close to the arithmetic mean so that the error is not serious. However, if the variability is high, as is typical of fractured rock, the geometric mean can be several orders of magnitude lower than the arithmetic mean, resulting in profound error and failed calculations. This paper shows how to obtain the arithmetic mean of the log-normal distribution so that permeability data from fractured rock can be used in Darcy's Law.

Meeting Name

48th US Rock Mechanics / Geomechanics Symposium: Rock Mechanics Across Length and Time Scales (2014: Jun. 1-4, Minneapolis, MN)


Geosciences and Geological and Petroleum Engineering

Keywords and Phrases

Flow of Fluids; Fluid Dynamic; Geomechanics; Geometry; Groundwater Flow; Mechanical Permeability; Mechanics; Normal Distribution; Reliability Analysis; Rock Mechanics; Seepage; Arithmetic Mean; Average Permeability; Fractured Rock; Geometric Mean; High Degree Of Variability; Log-Normal Distribution; Orders Of Magnitude; Rock-Mass Permeability

International Standard Book Number (ISBN)


Document Type

Article - Conference proceedings

Document Version


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© 2014 American Rock Mechanics Association (ARMA), All rights reserved.

Publication Date

01 Jun 2014