Multiple-Point Simulations Constrained by Continuous Auxiliary Data |
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| Authors: | Tatiana L Chugunova Lin Y Hu |
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| Institution: | (1) Reservoir Engineering Division, IFP, 1 et 4 avenue de Bois-Préau, 92852 Rueil-Malmaison Cedex, France;(2) Centre de Géostatistique, Ecole des Mines de Paris, Paris, France |
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| Abstract: | An important issue of using the multiple-point (MP) statistical approach for reservoir modeling concerns the integration of
auxiliary constraints derived, for instance, from seismic information. There exist two methods in the literature for these
non-stationary MP simulations. One is based on an analytical approximation (the “τ-model”) of the conditional probabilities that involve auxiliary data. The degree of approximation with this method depends
on the parameter τ, whose inference is difficult in practice. The other 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 paper,
we propose an alternative method for performing non-stationary MP simulations. This method accounts for the data support in
the modeling procedure and allows, in particular, continuous auxiliary data to be integrated into MP simulations. This method
avoids the major limitations of the previous 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 MP simulation
codes. Numerical tests show good performance of this method both in reproducing the geometrical features of the training image
and in honouring the auxiliary data. |
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| Keywords: | Geostatistical simulation Multiple-point statistics Training image Data support Non-stationarity |
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