Permeability: Can It Flow

Part 1, Chapter 1: Rocks, Pores, and Fluids

Learning objectives

Define permeability as the ease of fluid flow through the rock
Explain that the pore throats, not the pore bodies, control permeability
Use Kozeny-Carman to relate permeability to porosity and grain size
Recognize that permeability spans many orders of magnitude

What Permeability Is

Porosity says how much fluid a rock holds; permeability says how easily that fluid moves. It is the constant $k$ in Darcy's law, which sets the flow rate $q$ through a rock of area $A$ and length $L$ under a pressure drop $\Delta P$ for a fluid of viscosity $\mu$ :

q = \frac{k A \,\Delta P}{\mu L}

Permeability is measured in darcies, though most reservoir rock is quoted in millidarcies (mD). At fixed pressure, doubling the permeability doubles the flow.

Drag porosity and grain size and watch the permeability marker swing across the log scale, and the flow arrows respond.

Throats, Not Bodies

Flow is throttled at the pore throats, the narrow necks between pores, not in the wide pore bodies. Since throat size scales with grain size, permeability depends very steeply on the grain size. The Kozeny-Carman relation captures it: $k \propto \frac{\phi^3}{(1-\phi)^2}, d^2$ . Cube the porosity, square the grain size. Halve the grain size and permeability falls four-fold; that is why a coarse sand and a fine silt of the same porosity can differ by orders of magnitude.

Porosity Is Not Permeability

A rock can be porous yet barely permeable. Chalk can hold 40 percent porosity in pores so tiny, and so poorly connected, that nothing flows; a fractured tight rock can flow well on almost no matrix porosity. There is a general poro-permeability trend, but the scatter spans orders of magnitude, because connectivity and throat size, not pore volume, govern flow. Keeping porosity and permeability as separate questions, how much is there versus can it move, is one of the first habits of a good log analyst.

References

Asquith, G. and Krygowski, D. (2004). Basic Well Log Analysis, 2nd ed. AAPG Methods in Exploration 16.
Tiab, D. and Donaldson, E. (2015). Petrophysics, 4th ed. Gulf Professional Publishing.