Estimation of distribution algorithms for reservoir history-matching optimisation
Author(s)
Petrovska, Iryna
Type
Thesis
Abstract
Reservoir modelling is widely used in the oil and gas industry to quantify the risk
associated with alternative production scenarios. However, reservoir models themselves
still contain a high level of uncertainty because of the typically very limited,
sparse and multiscale field knowledge available. History-matching (HM) reduces
this uncertainty by constraining the reservoir model to the available dynamic field data.
History-matching is an example of a typical non-linear inverse problem which
yields the existence of not one but multiple solutions, which all satisfy available data
constraints. In inverse problem theory Monte Carlo methods are regarded as the
most accurate methods for generating a family of problem solutions and capturing
posterior distributions of model parameters by exhaustive exploration of parameter
space. However these methods are very rarely applicable to HM problems because
they are too time and cost consuming.
While other stochastic inversion techniques have successfully overcome the runtime
issue Monte Carlo methods have, none of them has provided a deliberate estimation
of the posterior probabilities one would expect from Monte Carlo methods.
This thesis introduces an innovative application of a member of a class of Estimation
of Distribution Algorithms - a histogram-based Population-Based Incremental
Learning algorithm, to the problem of reservoir history-matching optimisation. It is shown that while avoiding an exhaustive exploration of parameter space the proposed
algorithm is capable of producing the approximations of the marginal posterior
distributions of model parameters which can be interpreted as their uncertainty
estimates.
We also suggest a new extension of histogram-based PBIL for pair-wise conditional
probabilities sampling. The developed extended version of the histogrambased
PBIL is the first attempt to explicitly capture possible dependencies between
reservoir model parameters and use them to perform conditional sampling of the
solution space. None of the currently used algorithms and techniques for reservoir
history-matching optimisation explicitly utilizes this dependency information.
associated with alternative production scenarios. However, reservoir models themselves
still contain a high level of uncertainty because of the typically very limited,
sparse and multiscale field knowledge available. History-matching (HM) reduces
this uncertainty by constraining the reservoir model to the available dynamic field data.
History-matching is an example of a typical non-linear inverse problem which
yields the existence of not one but multiple solutions, which all satisfy available data
constraints. In inverse problem theory Monte Carlo methods are regarded as the
most accurate methods for generating a family of problem solutions and capturing
posterior distributions of model parameters by exhaustive exploration of parameter
space. However these methods are very rarely applicable to HM problems because
they are too time and cost consuming.
While other stochastic inversion techniques have successfully overcome the runtime
issue Monte Carlo methods have, none of them has provided a deliberate estimation
of the posterior probabilities one would expect from Monte Carlo methods.
This thesis introduces an innovative application of a member of a class of Estimation
of Distribution Algorithms - a histogram-based Population-Based Incremental
Learning algorithm, to the problem of reservoir history-matching optimisation. It is shown that while avoiding an exhaustive exploration of parameter space the proposed
algorithm is capable of producing the approximations of the marginal posterior
distributions of model parameters which can be interpreted as their uncertainty
estimates.
We also suggest a new extension of histogram-based PBIL for pair-wise conditional
probabilities sampling. The developed extended version of the histogrambased
PBIL is the first attempt to explicitly capture possible dependencies between
reservoir model parameters and use them to perform conditional sampling of the
solution space. None of the currently used algorithms and techniques for reservoir
history-matching optimisation explicitly utilizes this dependency information.
Date Issued
2009-01
Date Awarded
2009-02
Copyright Statement
Attribution NoDerivatives 4.0 International Licence (CC BY-ND)
Advisor
Carter, Jonathan
Sponsor
Schlumberger AbTC
Creator
Petrovska, Iryna
Publisher Department
Earth Science and Engineering
Publisher Institution
Imperial College London
Qualification Level
Doctoral
Qualification Name
Doctor of Philosophy (PhD)