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In the first part of this course, we have discussed the use of conditional simulations for generating realistic scenarios of the variations of a parameter between wells. One important characteristic of stochastic models is their ability, through the generation of multiple realisations, to quantify uncertainty or “non-uniqueness”. The approach is simple: the use of well data, plus statistical parameters (width/thickness ratio, variogram, …), even if complemented with seismic or production data, is not sufficient to deterministically characterise heterogeneities between wells: a large number of “possible” or “equiprobable” realisations match the well data, the geostatistical parameters, the seismic and the production data. The stochastic formalism allows the generation of such realisations, and the variability from one realisation to another gives a measure of how well or how poorly the distribution of the parameter of interest is constrained between wells.

Thus, the good new is that uncertainty can be naturally addressed and quantified through the stochastic formalism. But we will stress that this approach must be used with a full understanding of the assumptions that are made, in order to avoid an underestimation of the uncertainties. As an introduction to geostatistical uncertainty quantification, let us first discuss the basic Monte-Carlo approach used in applications such as Prospect Appraisal or Economic Evaluation.

A simple example of Monte-Carlo simulation is that of estimating the probability density function (pdf) associated with the volume of oil (OOIP) in a reservoir at exploration or appraisal stage. Let us assume that:

Gross-Rock Volume (GRV) is between 100 and 500 million barrels, with a mode at 300 million barrels.

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