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Adaptive Conditioning of Multiple-Point Statistical Facies Simulation to Flow Data with Probability Maps

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Abstract

Multiple-point statistics (MPS) provides a flexible grid-based approach for simulating complex geologic patterns that contain high-order statistical information represented by a conceptual prior geologic model known as a training image (TI). While MPS is quite powerful for describing complex geologic facies connectivity, conditioning the simulation results on flow measurements that have a nonlinear and complex relation with the facies distribution is quite challenging. Here, an adaptive flow-conditioning method is proposed that uses a flow-data feedback mechanism to simulate facies models from a prior TI. The adaptive conditioning is implemented as a stochastic optimization algorithm that involves an initial exploration stage to find the promising regions of the search space, followed by a more focused search of the identified regions in the second stage. To guide the search strategy, a facies probability map that summarizes the common features of the accepted models in previous iterations is constructed to provide conditioning information about facies occurrence in each grid block. The constructed facies probability map is then incorporated as soft data into the single normal equation simulation (snesim) algorithm to generate a new candidate solution for the next iteration. As the optimization iterations progress, the initial facies probability map is gradually updated using the most recently accepted iterate. This conditioning process can be interpreted as a stochastic optimization algorithm with memory where the new models are proposed based on the history of the successful past iterations. The application of this adaptive conditioning approach is extended to the case where multiple training images are proposed as alternative geologic scenarios. The advantages and limitations of the proposed adaptive conditioning scheme are discussed and numerical experiments from fluvial channel formations are used to compare its performance with non-adaptive conditioning techniques.

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Acknowledgments

The authors wish to thank the three anonymous reviewers of this manuscript for their constructive comments and valuable suggestions during the review process. The support for this work was provided in part by Department of Energy, Crisman Institute at Texas A&M, and the Viterbi School of Engineering at USC.

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Authors and Affiliations

  1. Petroleum Engineering, Texas A&M University, College Station, USA

    Morteza Khodabakhshi

  2. Mork Family Department of Chemical Engineering and Material Science, Viterbi School of Engineering, University of Southern California (USC), 925 Bloom Walk, HED 313, Los Angeles, CA, 90089, USA

    Behnam Jafarpour

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  1. Morteza Khodabakhshi
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  2. Behnam Jafarpour
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Correspondence to Behnam Jafarpour.

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Khodabakhshi, M., Jafarpour, B. Adaptive Conditioning of Multiple-Point Statistical Facies Simulation to Flow Data with Probability Maps. Math Geosci 46, 573–595 (2014). https://doi.org/10.1007/s11004-014-9526-1

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  • DOI: https://doi.org/10.1007/s11004-014-9526-1

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