Summary
Prudent decision making in subsurface assets requires reservoir uncertainty
quantification. In a typical uncertainty-quantification study, reservoir models
must be updated using the observed response from the reservoir by a process
known as history matching. This involves solving an inverse problem, finding
reservoir models that produce, under simulation, a similar response to that of
the real reservoir. However, this requires multiple expensive multiphase-flow
simulations. Thus, uncertainty-quantification studies employ optimization
techniques to find acceptable models to be used in prediction. Different
optimization algorithms and search strategies are presented in the literature,
but they are generally unsatisfactory because of slow convergence to the
optimal regions of the global search space, and, more importantly, failure in
finding multiple acceptable reservoir models. In this context, a new approach
is offered by estimation-of-distribution algorithms (EDAs). EDAs are
population-based algorithms that use models to estimate the probability
distribution of promising solutions and then generate new candidate
solutions.
This paper explores the application of EDAs, including univariate and
multivariate models. We discuss two histogram-based univariate models and one
multivariate model, the Bayesian optimization algorithm (BOA), which employs
Bayesian networks for modeling. By considering possible interactions between
variables and exploiting explicitly stored knowledge of such interactions, EDAs
can accelerate the search process while preserving search diversity. Unlike
most existing approaches applied to uncertainty quantification, the Bayesian
network allows the BOA to build solutions using flexible rules learned from the
models obtained, rather than fixed rules, leading to better solutions and
improved convergence. The BOA is naturally suited to finding good solutions in
complex high-dimensional spaces, such as those typical in reservoir-uncertainty
quantification.
We demonstrate the effectiveness of EDA by applying the well-known synthetic
PUNQ-S3 case with multiple wells. This allows us to verify the methodology in a
well-controlled case. Results show better estimation of uncertainty when
compared with some other traditional population-based algorithms.
© 2012. Society of Petroleum Engineers
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History
- Original manuscript received:
7 April 2011
- Meeting paper published:
24 May 2011
- Revised manuscript received:
18 October 2011
- Manuscript approved:
8 November 2011
- Published online:
23 August 2012
- Version of record:
12 September 2012
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