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It was mentioned earlier that variogram-based techniques could be applied to discrete or continuous variables. Simulations are constrained by well data, variogram models, and histograms of the modelled variables. Uncertainties are quantified by generating a number of possible images or “realisations” all satisfying the above statistical constraints. The scarcity of well data, especially at field appraisal stage, explains the great uncertainty affecting the heterogeneity models. Therefore, any other available data, even if affected by uncertainty, must be used to better constrain the models in the inter-well volume.

A larger number of data can be acquired that provide a better control on heterogeneity modelling between wells (Fig. 95): together with well data, seismic and dynamic data are usually available. We will now see how such data can be used to constrain the heterogeneity models. Ideally, we would like (Fig. 96) to combine all available data in order to reduce the “sample space” or the number of geostatistical models compatible with the available data. Two main classes of approach will be discussed. Direct methods are used in situations where the constraining data can be written as a deterministic function of the simulated representation. For instance, the seismic response can be derived from an acoustic impedance model by 1D convolution or the well test permeability can be expressed as an average of the permeabilities in grid cells surrounding the well. On the other hand, indirect methods simply assume that some sort of statistical relationship exists between the variable simulated at one location and the constraining information.

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