Where Does Up-Scaling Begin? Let’s Put Geology Back into Geostatistics

Christian J. Heine
Saudi Aramco, Dhahran, Saudi Arabia

Historically, a geocellular model was considered ‘good’, if the porosity distribution of the interpolated grid ‘matched’ the porosity distribution of the input well data. While in some cases this might be an acceptable result; in a reservoir where contacts between bed units are sharp, attributes such as porosity tend to get ‘smoothed’ across the bed boundary and become part of the statistics.

‘Let the up scaling begin’ – Logging tools such as gamma-ray, sonic, density and neutron measure varying volumes of rock and have varying depths of investigation in the wellbore. Gamma-ray, for example measures a three foot window for each recorded sample and samples are recorded every ½ foot. This translates into 3-samples of transition measurement on each side of a sharp bed contact. If the reservoir unit being measured is not at least four feet thick, a logging tool may never achieve a true reading of the reservoir property.

‘You do the math’ –The Early Permian eolian Unayzah ‘A’ reservoir is a good example of a rock unit with sharp contacts between beds and will be used to illustrate the point. For example, if 100 feet of the Unayzah ‘A’ reservoir is logged and the reservoir consisted of alternating five-foot dune facies (reservoir) and five-foot playa facies (non-reservoir), the 100 feet logged interval would have 19 bed boundaries. Using a conservative 1-1/2 feet of ‘transition porosity’ measured above and below each boundary, 60 of the 100 feet of logged interval would have a transitional porosity value. This ‘smoothing’ of the log data can be seen in the frequency histograms derived for porosity using logs only. An extreme example of smoothing in a thinly bedded reservoir is visible in turbidities, where sand and shale beds are typically less than a foot thick and the log porosity measurement shows little character.

It’s a numbers game

‘Good’ – Take the same 100 feet of log porosity and group by facies, the facies-based porosity histograms show that there is a distinct relationship between facies and porosity. But still there is a significant overlap in porosity between each reservoir facies.

‘Better’ – Take the same 100 feet of logs and this time derive the porosity histograms from core data grouped by facies. The result is a tightly controlled histogram of the reservoir property. These facies based, externally derived histograms from core will tighten the porosity range for each reservoir facies and shift the mean higher for the dune facies and lower for the playa facies, thus reducing the overlap seen in the log and facies derived histograms.

‘Best’ – Attribute histograms can be further refined by mapping facies regions in map view for each reservoir zone, based on a geological or geophysical understanding of the reservoir. Separate histograms can then be derived for each region using only the data from wells that fall within each mapped facies region. These histograms are then applied to the facies region during the property modeling process. This reduces the numerical dispersion or ‘smoothing’ often seen when the reservoir statistics are built for, and applied to the entire layer… The resulting geocellular model shows distinctly sharper contacts between layers and an overall better looking porosity distribution when visualized in map view.

AAPG Search and Discovery Article #90101 © 2010 AAPG Foundation Distinguished Lecturer Series 2009-2010