  We propose a method for calculating the effective permeability of
two-dimensional self-affine permeability fields based on generalizing the
one-dimensional concept of a bottleneck. We test the method on fracture faults
where the local permeability field is given by the cube of the aperture field.
The method remains accurate even when there is substantial mechanical overlap
between the two fracture surfaces. The computational efficiency of the method
is comparable to calculating a simple average and is more than two orders of
magnitude faster than solving the Reynolds equations using a finite-difference
scheme.
