Multiscale Parameterization of Petrophysical Properties for Efficient History-Matching
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Multiscale Parameterization of Petrophysical Properties for Efficient History-Matching Caroline Gardet · Mickaele Le Ravalec · Erwan Gloaguen
Received: 19 December 2012 / Accepted: 10 July 2013 © International Association for Mathematical Geosciences 2013
Abstract The prediction of fluid flows within hydrocarbon reservoirs requires the characterization of petrophysical properties. Such characterization is performed on the basis of geostatistics and history-matching; in short, a reservoir model is first randomly drawn, and then sequentially adjusted until it reproduces the available dynamic data. Two main concerns typical of the problem under consideration are the heterogeneity of rocks occurring at all scales and the use of data of distinct resolution levels. Therefore, referring to sequential Gaussian simulation, this paper proposes a new stochastic simulation method able to handle several scales for both continuous or discrete random fields. This method adds flexibility to history-matching as it boils down to the multiscale parameterization of reservoir models. In other words, reservoir models can be updated at either coarse or fine scales, or both. Parameterization adapts to the available data; the coarser the scale targeted, the smaller the number of unknown parameters, and the more efficient the history-matching process. This paper focuses on the use of variational optimization techniques driven by the gradual deformation method to vary reservoir models. Other data assimilation methods and perturbation processes could have been envisioned as well. Last, a numerical application case is presented in order to highlight the advantages of the proposed method for conditioning permeability models to dynamic data. For simplicity, we focus on two-scale processes. The coarse scale describes the variations in the trend while the fine scale characterizes local variations around the trend. The relationships between data resolution and parameterization are investigated. Keywords Geostatistical model · Reservoir simulation · Multiscale reservoir model · Sequential Gaussian simulation
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C. Gardet ( ) · M. Le Ravalec IFP Energies Nouvelles, 1 & 4 avenue de Bois Préau, 92852 Rueil-Malmaison, France e-mail: [email protected] E. Gloaguen INRS Eau Terre Environnement, 490, rue de la Couronne, Québec G1K 9A9 Canada
Math Geosci
1 Introduction The production of hydrocarbons is a complex problem dealing with the movement of fluids through porous, permeable geological formations. Permeability is one of the most important properties that governs fluid flows as it defines the capacity of rocks to transmit fluids. Thus, the characterization of the spatial variations in permeability is essential to understand and predicting fluid displacements. Two main issues then arise. The first one is related to the natural heterogeneity of rocks. Heterogeneity induces permeability variations over several orders of magnitudes between layers, but also within layers. The second major difficulty is the sparsity of the available data. Permeab
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