Including a Regional Trend in Reservoir Modelling Using the Truncated Gaussian Method

Abstract

When studying the geometry of petroleum reservoirs, we have to integrate different kinds of data (wells and seismic) as well as geological knowledge. Usually, wells show the fine vertical variation of lithofacies, but are less precise about horizontal variations. On the another hand, seismic data give a good idea of the horizontal evolution but we lose information on the vertical variability. A realistic reservoir model has to take this into account.

Until now, we have been able to model vertical variability with HERESIM. Here we show that the truncated gaussian model can be used to model horizontal variability or both horizontal and vertical variability. This can be achieved by using both horizontal and vertical non stationary proportions with a stationary gaussian random function. We present the extension of the method in detail, focusing on how to perform structural analysis, which is possible because the gaussian is still stationary, even if the lithofacies show strong non stationarities. Thus we work with coherent non stationary models for the simple and cross variograms of lithofacies. This methodology is illustrated on examples.