Poster Session - IFP Invited Poster

Multiple-Point Statistical Simulations Constrained by Continuous Auxiliary Data

T.L. Chugunova (1,2), L.Y. Hu (1)

(1) Reservoir Engineering Division, Institut Français du Pétrole, Rueil-Malmaison, France

(2) Centre de Géostatistique, Ecole Nationale Supérieur des Mines de Paris, France

Geostatistical simulation based on multiple-point statistics (MPS) has become a widespread tool for reservoir modeling. One of the important issues of using the MPS approach concerns the integration of auxiliary constraints derived, for instance, from seismic information. There exist two methods in the literature to MPS constrained simulations. One is based on an analytical approximation (the "-model") of the conditional probabilities, which involve auxiliary data. The degree of approximation of this method depends on the parameter  whose inference is difficult in practice. Also "-model" does not allow to constrain geostatistical simulation to some auxiliary data which defines, for ex., an orientation in space. Another method is based on the inference of these conditional probabilities directly from training images. This method classifies the auxiliary data into a few classes. This classification is in general arbitrary and therefore inconvenient in practice, especially in the case of continuous auxiliary constraints.

In this work, we propose an alternative method based on the direct inference of the conditional probabilities from the training images of principal and auxiliary variable. It allows continuous auxiliary data (facies proportion, object size, orientation etc.) to be integrated into MPS simulations. At the same time, it avoids the major inconveniences of the above two methods, namely the use of an approximate analytical model and the reduction of the auxiliary data into a limited number of classes. This method can be easily implemented in the existing MPS simulation codes. Numerical tests show the good performance of this method both in reproducing the geometrical features of the training image and in honoring the auxiliary data.

Key Words : geostatistical simulation, multiple-point statistics, auxiliary data constraint, non-stationarity.