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Communication Dans Un Congrès Année : 2009

History matching by interacting MCMC

Thomas Romary


The history matching problem in reservoir engineering, which consists in matching the geostatistical model to production data, is an ill-posed inverse problem. Its resolution implies to infer the probability distribution of the geostatistical model conditioned to the dynamical data, considering both the geological a priori, expressed in the geostatistical model, and the adequacy with production data. The aim is then to generate a representative sample from this distribution. Geostatistical models are usually discretized on a grid of hundreds of thousands even millions of blocks. Classical methods aim at solving the inverse problem considering the value of the random field at each gridblock as parameters. The huge dimension of this problem makes it intractable in practice. Therefore, we need a parameterization technique that will be able to reduce the problem dimension. The first part of our work is devoted to studying a parameterization method of Gaussian-related geostatistical models, based on their Karhunen-Loève (KL) expansion. Then, according to both statistical and dynamical (with respect to fluid flow results) criteria, we quantify the dimension reduction offered by this decomposition. In a second part, we present the principles of Markov chain Monte-Carlo (McMC) methods. Particularly, we point out the defects of classical approaches when trying to solve a Bayesian inversion problem. We then introduce the interacting Markov chains methods whose advantages are exposed. Finally, the results obtained by using jointly both methods are exhibited in two reservoir characterization synthetic problems: the history matching of a permeability field, and the history matching of a lithofacies field.
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Dates et versions

hal-00583627 , version 1 (06-04-2011)


  • HAL Id : hal-00583627 , version 1


Thomas Romary. History matching by interacting MCMC. 4th international EnKF workshop, Jun 2009, Bergen, Norway. ⟨hal-00583627⟩
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