|dc.description.abstract||Uncertainty quantification is an important task in reservoir simulation and is an
active area of research. The main idea of uncertainty quantification is to compute
the distribution of a quantity of interest, for example oil rate. That uncertainty,
then feeds into the decision making process.
A statistically valid way of quantifying the uncertainty is a Markov Chain Monte
Carlo (MCMC) method, such as Random Walk Metropolis (RWM). MCMC is a
robust technique for estimating the distribution of the quantity of interest. RWM is
can be prohibitively expensive, due to the need to run a huge number of realizations,
45% - 70% of these may be rejected and, even for a simple reservoir model it
may take 15 minutes for each realization. Hamiltonian Monte Carlo accelerates the
convergence for RWM but may lead to a large increase computational cost because
it requires the gradient.
In this thesis, we present how to use the multilevel concept to accelerate convergence
for RWM. The thesis discusses how to apply Multilevel Markov Chain Monte
Carlo (MLMCMC) to uncertainty quantification. It proposes two new techniques,
one for improving the proxy based on multilevel idea called Multilevel proxy (MLproxy)
and the second one for accelerating the convergence of Hamiltonian Monte
Carlo is called Multilevel Hamiltonian Monte Carlo (MLHMC).
The idea behind the multilevel concept is a simple telescoping sum: which represents
the expensive solution (e.g., estimating the distribution for oil rate on finest
grid) in terms of a cheap solution (e.g., estimating the distribution for oil rate on
coarse grid) and `correction terms', which are the difference between the high resolution
solution and a low resolution solution. A small fraction of realizations is then
run on the finer grids to compute correction terms. This reduces the computational
cost and simulation errors significantly.
MLMCMC is a combination between RWM and multilevel concept, it greatly reduces
the computational cost compared to the RWM for uncertainty quantification.
It makes Monte Carlo estimation a feasible technique for uncertainty quantification
in reservoir simulation applications. In this thesis, MLMCMC has been implemented
on two reservoir models based on real fields in the central Gulf of Mexico and in
MLproxy is another way for decreasing the computational cost based on constructing
an emulator and then improving it by adding the correction term between
the proxy and simulated results.
MLHMC is a combination of Multilevel Monte Carlo method with a Hamiltonian
Monte Carlo algorithm. It accelerates Hamiltonian Monte Carlo (HMC) and is faster
than HMC. In the thesis, it has been implemented on a real field called Teal South
to assess the uncertainty.||en_US