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It is a very common rule of thumb that permeability is a function of porosity but that assumption is a complete fallacy.
Consider a formation made up of hexagonally packed round bowling ball sized grains, the porosity of that formation would be approximately 26%. Consider another formation having hexagonally packed round 'BB' sized grains, the porosity of that formation would be approximately 26%. Both formations have vastly different grain sizes and correspondingly vastly different pore throat sizes but still have the same porosity.
Given the same pressure differential across each of the formation, a given fluid will flow through the formation with the larger pore throats more easily than the formation with smaller pore throats. Permeability is directly related to pore throat geometry and the tortuosity of the fluid flow path through any given rock.
Different formations can have the same porosity but because of pore throat geometry differences can have different fluid flow permeabilities. Permeability is not a function of porosity.
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