History matching of approximated lithofacies models under uncertainty |
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Authors: | Thomas Romary |
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Institution: | 1.Center of Geosciences and Geoengineering/Geostatistics,Mines ParisTech,Fontainebleau CEDEX,France |
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Abstract: | In history matching of lithofacies reservoir model, we attempt to find multiple realizations of lithofacies configuration
that are conditional to dynamic data and representative of the model uncertainty space. This problem can be formalized in
the Bayesian framework. Given a truncated Gaussian model as a prior and the dynamic data with its associated measurement error,
we want to sample from the conditional distribution of the facies given the data. A relevant way to generate conditioned realizations
is to use Markov chains Monte Carlo (MCMC). However, the dimensions of the model and the computational cost of each iteration
are two important pitfalls for the use of MCMC. Furthermore, classical MCMC algorithms mix slowly, that is, they will not
explore the whole support of the posterior in the time of the simulation. In this paper, we extend the methodology already
described in a previous work to the problem of history matching of a Gaussian-related lithofacies reservoir model. We first
show how to drastically reduce the dimension of the problem by using a truncated Karhunen-Loève expansion of the Gaussian
random field underlying the lithofacies model. Moreover, we propose an innovative criterion of the choice of the number of
components based on the connexity function. Then, we show how we improve the mixing properties of classical single MCMC, without
increasing the global computational cost, by the use of parallel interacting Markov chains. Applying the dimension reduction
and this innovative sampling method drastically lowers the number of iterations needed to sample efficiently from the posterior.
We show the encouraging results obtained when applying the methodology to a synthetic history-matching case. |
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