Permeability Calculator: Timur and Coates-Denoo Equations from Porosity and Swi
Permeability from Porosity and Irreducible Water Saturation
Poro-Perm Profile Across Zones
| Zone | Porosity (percent) | Swi (percent) | Timur k (mD) |
|---|
Solve Required Porosity or Water Saturation
Estimate permeability from porosity and irreducible water saturation using the Timur and Coates-Denoo equations, build a poro-perm profile across several zones, or solve the porosity or water saturation a target permeability would require. Everything updates live.
Permeability from Porosity and Irreducible Water Saturation
Permeability controls how easily oil, gas, and water move through a reservoir rock, and since it cannot always be measured directly from every foot of a well, petrophysicists lean on empirical correlations that estimate permeability from porosity and irreducible water saturation logs. This tool covers a quick estimate from the Timur and Coates-Denoo equations, a poro-perm profile across multiple zones with a log scale chart, and a reverse solve for the porosity or water saturation a target permeability would require.
Start with the quick convert tab for a single permeability estimate from porosity and irreducible water saturation. Build a poro-perm profile to compare permeability across several zones in a well. Or solve backward, find the porosity or Swi a target permeability would require given the other variable.
The Timur and Coates-Denoo Equations
The Timur equation estimates permeability in millidarcies as k equals 0.136 times porosity to the power 4.4, divided by irreducible water saturation squared, with both porosity and Swi entered as percent rather than a fraction. It was developed from laboratory measurements on 155 sandstone core samples from three North American oil fields and remains one of the most widely cited poro-perm correlations in petrophysics.
The Coates-Denoo equation, closely related to the Wyllie and Rose relationships, expresses the square root of permeability as 100 times porosity squared times the ratio of movable water to irreducible water, with porosity and Swi entered as a fraction. Both equations are empirical, sandstone specific, and tend to agree reasonably well across typical reservoir porosity and saturation ranges while diverging more at extremes.
Why Two Equations Instead of One
No single permeability correlation works everywhere, since the true relationship between pore geometry and fluid flow depends on grain size, sorting, cementation, and clay content in ways a two variable formula cannot fully capture. Running both the Timur and Coates-Denoo equations side by side, and comparing the result to core data where it exists, gives a useful sense of how much uncertainty surrounds a log derived permeability estimate before it feeds into a completion or reserves decision.
Reading a Poro-Perm Profile
Permeability commonly spans several orders of magnitude within a single well, from a fraction of a millidarcy in a tight streak to several thousand millidarcies in a high quality channel sand, which is why poro-perm profiles are almost always plotted on a logarithmic scale. As a general guide, less than 10 millidarcies is considered fair, 10 to 100 millidarcies is high, 100 to 1000 millidarcies is very high, and above 1000 millidarcies is exceptional reservoir quality, though these thresholds shift somewhat by rock type and operator convention.
Common Mistakes
Applying a sandstone derived correlation like Timur or Coates-Denoo directly to carbonate reservoirs, where vuggy or fracture dominated porosity can produce very different permeability than an equivalent intergranular sandstone porosity would suggest.
Forgetting that Timur expects porosity and Swi as percent while Coates-Denoo in this tool expects the same log readings converted internally to a fraction, a unit mismatch that can produce permeability estimates off by orders of magnitude if entered incorrectly elsewhere.
Treating an empirical permeability estimate as equivalent to a core measurement or a well test derived value, when it should really be used as a first pass screening tool pending calibration against real data from the field.
Ignoring that these correlations were built on irreducible water saturation specifically, not total water saturation, so applying them in a zone that is still producing water can understate the actual flow capacity.
Who Uses This
Petrophysicists estimating permeability from wireline logs in wells without core or NMR data available.
Reservoir engineers building a poro-perm model to rank zones for completion or stimulation design.
Geologists comparing reservoir quality across multiple wells or fields using a consistent permeability estimate.
Students and early career professionals learning how porosity and water saturation logs translate into a flow capacity estimate.
Try It Above
Use the quick convert tab for a single permeability estimate from porosity and Swi, move to the poro-perm profile tab to compare permeability across multiple zones on a log scale chart, or use the solve tab when you need the porosity or water saturation a target permeability would require.
Related Calculators and References
See also the Permeability Converter for taking a reservoir permeability in millidarcy across into hydraulic conductivity in m/s or cm/s, where the fluid and its temperature start to matter.
Continue building your workflow with the AVO Intercept-Gradient Calculator. For background on the formulas used above, see University of Leeds Petrophysics Course Notes: Permeability.