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 fractured 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 fractured 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 are 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.

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