# Multilevel Markov Chain Monte Carlo (MLMCMC) For Uncertainty Quantification

- Authors
- Doaa Elsakout (Heriot-Watt University, UK) | Mike Christie (Heriot-Watt University, UK) | Gabriel Lord (Heriot-Watt University, UK)
- DOI
- https://doi.org/10.2118/175870-MS
- Document ID
- SPE-175870-MS
- Publisher
- Society of Petroleum Engineers
- Source
- SPE North Africa Technical Conference and Exhibition, 14-16 September, Cairo, Egypt
- Publication Date
- 2015

- Document Type
- Conference Paper
- Language
- English
- ISBN
- 978-1-61399-392-7
- Copyright
- 2015. Society of Petroleum Engineers
- Disciplines
- 5 Reservoir Desciption & Dynamics, 5.5 Reservoir Simulation
- Keywords
- Uncertainty quantification, Markov Chain Monte Carlo, Multilevel Markov Chain Monte Carlo, Reservoir simulation, Bayesian approach
- Downloads
- 1 in the last 30 days
- 330 since 2007

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Uncertainty quantification is an important task in reservoir simulation studies used for decision making. There have been many techniques proposed in the SPE literature for quantifying uncertainty, such as Markov chain Monte Carlo (MCMC).

MCMC is statistical method for sampling from an arbitrary probability distribution to quantifying uncertainty in reservoir simulation. The major difficulty in applying MCMC methods is high computational cost.

The purpose of this paper is to demonstrate the performance of a new technique – Multilevel Markov Chain Monte Carlo (MLMCMC) – for quantifying uncertainty in reservoir simulation with less computional cost compared to Standard MCMC.

MLMCMC algorithm is based on decomposing the desired results into a set of components calculated with different level of coarsening level. This technique demonstrated a speed up and provided a forecast with no significant loss in accuracy compared to Standard MCMC. It makes Monte Carlo estimation a feasible technique for uncertainty quanti?cation in reservoir simulation applications.

There are only a few applications of MLMCMC in the petroleum industry as it is a new technique. We show results for two fields. The first is Teal South in the Gulf of Mexico and the second is Scapa in a North Sea.

File Size | 1 MB | Number of Pages | 12 |

DECC, 2015. Department of Energy and Climate Change. [Online] Available at: https://www.og.decc.gov.uk/pprs/full_production.htm