Statistical Modelling 10 (2010), 89111
Bayesian calibration of hydrocarbon reservoir models using an approximate reservoir simulator in the prior specification
Ole Petter Lødøen
Department of Mathematical Sciences
Norwegian University of Science and Technology
Trondheim
Norway
Håkon Tjelmeland
Department of Mathematical Sciences
Norwegian University of Science and Technology
Trondheim
Norway
eMail: haakont@stat.ntnu.no
Abstract:
We consider prediction and uncertainty analysis for the ‘history matching’
problem in petroleum reservoir evaluation. Unknown reservoir properties
are represented on a fine three dimensional lattice. A ‘reservoir simulator’
takes the reservoir properties as input and gives production properties
as output. The history matching problem is to infer the reservoir
properties from the observed production history. To run the reservoir
simulator on the lattice size of interest is computer intensive,
and this severely limits the number of runs possible.
We formulate the problem in a Bayesian setting and, following suggestions
in the statistical literature, consider the reservoir simulator as an
unknown function. To obtain a realistic prior distribution for this
function, we propose to combine a coarse lattice (faster) version of
the simulator with parameters correcting for bias introduced by the
coarser lattice. We simulate from the resulting posterior by Markov
chain Monte Carlo (MCMC). We construct an artificial reference reservoir,
generate corresponding flow observations, and use our procedure to
evaluate the reservoir properties in the resulting posterior distribution.
Convergence and mixing are acceptable. The case study demonstrates how
the observed production history provides information about both the
reservoir properties and the bias correcting parameters included in
the prior specification.
Keywords:
approximate reservoir simulation; Bayesian statistics;
complex computer model; Markov chain Monte Carlo; parameter estimation;
production conditioning
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