This paper proposes a general and rigorous theoretical framework for averaging the single-phase permeability, which has been validated by laboratory experiments. This approach uses powerful tools of statistical mechanics (field-theory), and provides exact results for log-normally distributed permeabilities, without any restriction about the width of this distribution.
On the other hand, laboratory experiments were performed on both a 3-D heterogeneous sandstone and a limestone blocks. Their overall (effective) permeabilities were measured first. Then they were both cut into 300 plugs, whose permeabilities were measured in turn, and later plotted on a histogram.
A very simple 3-D algebraic permeability composition formula is given, Keff=<k1/3 >3, in which the brackets correspond to an arithmetic mean. Its form differs significantly from the widely-used geometric mean, a well-known 2-D result.
In both cases, excellent agreement is observed between experimental results obtained for the overall permeability and the algebraic prediction given by our local permeability-composition formula.