Skewness: Permeability Log-Normality, Reserve Distribution Asymmetry, and WCSB Petrophysical Statistics

Skewness is a measure of the degree to which a probability distribution departs from the bilateral symmetry of a normal distribution, describing whether the data lean to one side with a longer tail on the other. A perfectly symmetric distribution, such as the Gaussian or normal curve, has zero skewness: its mean, median, and mode coincide and the two tails mirror each other. A positively or right-skewed distribution has a long tail extending toward high values, so the mean is pulled above the median; a negatively or left-skewed distribution has a long tail toward low values and a mean below the median. In oilfield practice skewness is often expressed qualitatively, as simply right-skewed or left-skewed, but it can also be quantified through the third standardized statistical moment, which normalizes the average cubed deviation from the mean by the cube of the standard deviation. The concept matters enormously to petrophysics and reserves work because several of the most important rock and fluid properties are not normally distributed, and treating them as if they were leads to systematic error. Permeability is the textbook case: in most reservoir intervals permeability values are strongly right-skewed and approximately log-normal, meaning the logarithm of permeability is roughly normal while permeability itself has a long high-side tail dominated by a few very high values. Because of that asymmetry, the arithmetic mean of permeability is a poor and usually misleading summary statistic, since it is dragged upward by the high-permeability tail and overstates the typical rock; the geometric mean, computed in log space, is the appropriate central measure. Porosity, by contrast, is generally much closer to normally distributed within a single geologic layer, so its arithmetic mean is a reasonable summary. Recognizing the shape of a distribution before choosing a summary statistic is therefore not a statistical nicety but a guard against incorrect interpretation. Skewness also pervades reserves and volumetrics: the distribution of recoverable volumes across prospects or wells is typically right-skewed, which is exactly why the industry reports probabilistic reserves as P90, P50, and P10 rather than a single mean, and why the mean expected value usually exceeds the P50 median. In the Western Canadian Sedimentary Basin, where heterogeneous tight reservoirs such as the Montney, Duvernay, and Cardium show permeability spanning several orders of magnitude across short vertical and lateral distances, accounting for skewness is central to honest core analysis, log interpretation, geomodel population, and the reserve disclosures that fall under National Instrument 51-101 and the Canadian Oil and Gas Evaluation Handbook. A petrophysicist who averages skewed permeability arithmetically, or who fits a symmetric distribution to right-skewed recovery data, will systematically misstate both the typical rock quality and the spread of outcomes that investors and regulators rely on.

Why the Mean Misleads on Skewed Data

The practical danger of skewness is that the arithmetic mean stops representing the typical value. Consider a tight Montney interval where most core plugs measure permeability in the microdarcy to tens-of-microdarcy range, but a handful of microfractured plugs read in the millidarcy range. The arithmetic mean is pulled toward those few high readings and suggests rock far better than what dominates the interval. The geometric mean, equivalent to averaging the logarithms, returns a value representative of the bulk of the plugs. This is why core laboratories and petrophysicists report permeability statistics in log space and why geomodels populate permeability fields from log-normal distributions rather than normal ones.

Skewness in Volumetric and Reserve Estimates

Monte Carlo volumetric models multiply several uncertain inputs, area, net pay, porosity, saturation, and recovery factor, and the product of distributions is itself right-skewed even when the inputs are not. The output original-oil-in-place or recoverable-volume distribution therefore has a long high-side tail, so the mean exceeds the P50. Canadian evaluators reporting under COGEH express this directly through proved, proved-plus-probable, and proved-plus-probable-plus-possible categories, which correspond to high-confidence low estimates through low-confidence high estimates, an explicit acknowledgement that recoverable volumes are skewed rather than symmetric.

Related Terms

Skewness is one of several descriptive statistics applied to reservoir properties. It is most consequential for permeability, whose log-normal, right-skewed distribution forces the use of geometric rather than arithmetic averaging. It contrasts with porosity, which is typically near-normal within a layer. Skewness in recoverable volumes underpins probabilistic reserves reporting, where the asymmetry of outcomes is captured by the P90, P50, and P10 percentiles that evaluators disclose under Canadian standards.

Real-World WCSB Scenario

A Montney evaluation team reviewing 180 core-plug permeability measurements from a Karr-area horizontal initially reported an arithmetic mean permeability that implied attractive deliverability. A reservoir engineer flagged that the data were strongly right-skewed, with a small cluster of microfractured plugs reading orders of magnitude above the rest. Recomputing in log space, the geometric mean came in well below the arithmetic figure and matched the well's observed flowing behaviour far better.

The corrected statistic changed the type-curve assumptions and the booked reserve estimate filed under NI 51-101, lowering the expected per-well recovery to a defensible value. The episode reinforced the firm's standard practice: always test permeability and recovery data for skewness, average permeability geometrically, and report reserves probabilistically rather than as a single skew-blind mean.