--> Uncertainty distributions in practice: Which, How, What?

AAPG Asia Pacific Technical Symposium

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Uncertainty distributions in practice: Which, How, What?

Abstract

From the time that computer applications are being used in our industry for the probabilistic assessment of risks and volumes of undrilled prospects we have required to specify the uncertainty of geological input parameters such as reservoir thickness, net/gross, hydrocarbon saturation, column length, etcetera. We normally do this by using some type of mathematical distribution type. Modern probabilistic tools offer a wide – and for many explorers bewildering – range of distribution types to choose from: normal, lognormal, beta, stretched beta, uniform, triangular, double-triangular, gamma, etc. In addition to these the ‘good old’ histogram can be used also in most tools. Not all explorers have a good understanding of the offered distribution types and their differences. The workflow of the probabilistic tools we use requires us to first choose a distribution type, and to then specify a Low value (either Minimum or P90), a High value (either Maximum or P10) and a Middle value. These inputs determine the shape of the distribution. Somewhat confusing is that the lognormal distribution requires as ‘middle’ input a value for the Mean, while for other distribution types it must be the Mode. It all seems to be very much about statistics instead of being about geology. There is a common believe with many explorers that uncertainty distributions for subsurface parameters must in general be lognormal. This comes from observations by P.R Rose (2001) and others (Megill, 1984 and Capen, 1984, 1992) that “most important geotechnical parameters involved with oil and gas occurrences are lognormal”. And indeed, for many geological parameters it is valid that when sufficient measured data points are plotted, they tend to display a lognormal distribution; these are so-called variability distributions. This is then taken as evidence that our pre-drill uncertainty distributions for the same subsurface parameters must also be lognormal in shape. But is this correct? In Begg, Bratvold and Welsh (2014) the fundamental difference between variability and uncertainty distributions is discussed. Uncertainty distributions are representations of our degree of uncertainty of what is a precise single value in an undrilled prospect. Uncertainty distributions should be based on all available data plus geological models and understanding, but they are not representations of data. The width and shape of uncertainty distributions depend on the degree of our understanding and knowledge. As we acquire data and gain understanding, uncertainty distributions normally become narrower. This then means that there is no correct or wrong distribution; nor is there a correct or wrong distribution type. If we would have complete knowledge there would be no distribution; the parameter then becomes a single value (a spike): for example the prospect’s average porosity, its average reservoir thickness, the exact HC column length. In the subsurface there is no uncertainty – the uncertainty is in our heads. It is interesting to realize that variability distributions may actually get wider with more data; this will be the case when the values of newly collected data are higher or lower then the extremes of the previously collected data. It seems a basic truism that uncertainty distributions should cover all outcomes that are geologically possible and consistent with an oil or gas discovery. Nevertheless, very often, actual geological parameters in exploration wells fall outside the predicted pre-drill uncertainty range. Clearly, uncertainty tends to be grossly underestimated. For uncertainty distributions it is important that they are consistent with our geological understanding of the specific geological parameter. It is not about statistical concepts, but about pragmatically translating geological understanding into realistic numbers and ranges of numbers, whilst avoiding biases. Some simple guidelines will be presented that will allow explorers to focus on geology instead of on (possibly confusing) statistical concepts.