Short note: Porosity and permeability

Porosity

Porosity ($n$) is the ratio of the volume of voids to the total volume of rock or soil, usually in %.

$$n = \frac{V_v}{V}\times 100$$

• Primary porosity: pores between grains formed at deposition (sand, gravel).
• Secondary porosity: joints, fractures, solution cavities developed later.
• Depends on shape, packing and sorting; well-sorted rounded sand 30-40%, clay up to 50-60%, granite below 1%.
• Porosity measures storage capacity, not the ability to transmit water.

Permeability

Permeability is the ability of a rock or soil to transmit fluid through its interconnected pores. It is expressed as hydraulic conductivity $K$ (m/s) from Darcy's law, $Q = K A i$.

• Depends on pore size, connectivity, grain size, fractures and fluid viscosity.
• Gravel $10^{-2}$ m/s, sand $10^{-4}$ m/s, silt $10^{-6}$ m/s, clay $10^{-9}$ m/s.

Relation

A rock can be porous but impermeable (clay) because the pores are small and not connected. Good aquifers need both high porosity and high permeability.

Importance

Porosity and permeability control groundwater storage and yield, seepage under dams, reservoir leakage, drainage of slopes and foundation behaviour.