The Poro-Perm Crossplot
Learning objectives
- Plot permeability on a log axis against porosity on a linear axis
- Recognize the straight line as the exponential law k = A times 10^(b phi)
- Quantify the scatter as the irreducible permeability uncertainty
- Sort by rock type before fitting (parallel facies lines)
The Workhorse Plot
The most-used permeability tool of all is just a graph. Plot core permeability on a log axis against core porosity on a linear axis, and the cloud of plugs falls along a straight line. A straight line on a semilog plot is an exponential law:
So a handful of core plugs fixes the slope and intercept, and from then on the line turns the log porosity, which is everywhere, into a permeability estimate, which would otherwise be only at the cored wells.
The Scatter Is Real
The plot is honest about its limits. The points do not sit on the line, they scatter about it, often by a factor of two or more, because porosity alone does not pin the throat size. That spread, shaded in the figure, is the irreducible uncertainty in any log permeability: read a porosity and the trend gives a single number, but the true value lives somewhere in a band around it. A permeability quoted without that band is overstating what a log can know.
Sort by Rock Type First
The scatter shrinks dramatically when the data are sorted. Different rock types fall on different, roughly parallel lines, a cleaner facies sitting a decade above a tighter one at the same porosity, as the dashed line shows. Pool them and the lines blur into one fat, useless trend; separate them by facies and each line tightens. That is why the most important step before fitting a poro-perm trend is to group the data by rock type, which leads straight to the flow-unit idea of the next section.
References
- Tiab, D. and Donaldson, E. C. (2015). Petrophysics, 4th ed. Gulf Professional Publishing.
- Amaefule, J. O. et al. (1993). Enhanced reservoir description: using core and log data to identify hydraulic flow units. SPE 26436.