Porosity and Permeability Calculator

Porosity n is the ratio of void volume to total volume and can be obtained either directly, by measuring the void space, or indirectly from densities as n = 1 - (bulk density / grain density), since the grain density is the density of the mineral solids alone. Quartz-rich soils have a grain density near 2.65 g per cubic centimeter and most clays 2.70 to 2.80, so the density route is reliable provided the mineralogy is known. Typical total porosity runs about 25 to 40 percent in gravel, 25 to 50 percent in sand, 35 to 50 percent in silt, and 40 to 70 percent in clay, while consolidated rock varies from under 5 percent in intact granite to 5 to 30 percent in sandstone. Void ratio e = n / (1 - n) restates the same information relative to the solid volume and is preferred in geotechnical work because compression changes voids while the solid volume stays fixed. Specific yield, the portion that drains under gravity, is smaller than porosity because water is retained by capillarity: sand and gravel typically yield 15 to 30 percent, whereas clay may hold nearly all its water despite porosity above 50 percent. Permeability estimates translate pore geometry into flow capacity. The Kozeny-Carman equation models the medium as a bundle of tortuous capillaries and gives permeability proportional to n cubed divided by (1 - n) squared times the square of a characteristic grain diameter, divided by a shape and tortuosity constant conventionally taken as 180. The porosity term is extremely sensitive, so a rise from 0.30 to 0.40 roughly triples the estimate, and the grain-size term is squared, which is why small changes in the fine fraction dominate. The empirical Hazen expression, a coefficient times the square of the effective size d10 in millimeters, is an alternative for loose clean sands; the coefficient is unit-bearing, so 0.01 with d10 in millimeters returns hydraulic conductivity in meters per second, while a coefficient near 1 with the same input returns centimeters per second. Both correlations should be treated as order-of-magnitude estimates. They fail badly in clays, where electrical double-layer effects and adsorbed water reduce the mobile pore volume far below the geometric porosity, and in fractured or karstic rock, where a small connected fracture porosity can carry nearly all the flow while the matrix porosity carries almost none. That disconnect is the central reason porosity and permeability must be measured or estimated separately rather than derived from one another.

Systematic porosity and permeability work began where the economic stakes were highest, in water supply and petroleum. Oscar Meinzer of the United States Geological Survey formalized the vocabulary of aquifer storage in his 1923 Water-Supply Papers, including the distinction between specific yield, the water that drains by gravity, and specific retention, the water held against it, which remains the basis of well yield estimation. Around the same period laboratory methods for pore volume matured: Boyle's law gas pycnometry using helium to measure true grain volume, and mercury intrusion porosimetry founded on Edward Washburn's 1921 capillary equation and developed for reservoir rock characterization by W. R. Purcell in 1949. Gus Archie's 1942 paper relating formation resistivity to porosity gave the petroleum industry a way to read porosity from well logs rather than from cores. The permeability correlation carries the names of its two authors. Josef Kozeny, a hydraulics professor in Vienna, published the capillary-bundle derivation in 1927 in the proceedings of the Vienna Academy of Sciences, relating permeability to porosity and specific surface area. Philip Carman, working on fluid flow through granular beds in the late 1930s, tested the relation against packed-column data and published revisions in 1937 and 1938 in the Transactions of the Institution of Chemical Engineers that introduced the tortuosity correction and settled the numerical constant near 180 that is still used. The combined Kozeny-Carman equation spread from chemical engineering into soil physics, hydrogeology, and reservoir engineering, and it continues to serve as the standard first-order estimate for granular media even though the underlying capillary-bundle picture is known to be a considerable idealization of real pore networks.