Doaa Elsakout - Academia.edu (original) (raw)
Papers by Doaa Elsakout
Uncertainty quantification is an important task in reservoir simulation and is an active area of ... more 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 North Sea. 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. Dedicated to the souls of my parents... I would like to express my deepest gratitude to my supervisors, Prof. Mike Christie and Prof. Gabriel Lord for leaving me alone to study and be independent. Thanks for providing freedom to explore different ideas throughout my PhD journey. Also, I would like to thank the Uncertainty quantification group for improving my presentation skills and giving feedback. I would like to thank Uncertainty quantification sponsors for their useful comments on my work especially, Prof. Jonathan Carter. Furthermore, I would like to thank the examiners for this thesis, Prof Peter King and Dr. James Cruise for their useful comments and incredible feedback to improve the thesis. Moreover, thanks to computer support team and the best magician Jack Talbot for fixing software problem issues during my PhD. I would like to thank Ali Danesh Scholarship for funding my PhD study at Heriot-Watt University. I would like to thank the African Institute for Mathematical Science for providing funding to conference participation. Thanks to Faculty of Science, Cairo University for giving me a study leave to study PhD. I would like to thank my best friend Samah Alhafian for supporting me during my PhD study. Also, I would like to thank my friends Laila, Maha, Radiha, Razan, Alyaa, and Sohad for their effort to make me enjoying the time here in Edinburgh during my PhD. Moreover, my friends at Uncertainty quantification group Zainab, Alexandra, Junko and Behzad for supporting me during my study. Last but not least, I would first like to thank my mother without her continuous support and encouragement I never would have been able to achieve my goals. I dedicate this PhD for my parents' souls.
Uncertainty quantification is an important task in reservoir simulation and is an active area of ... more 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 ...
Day 2 Tue, September 15, 2015, 2015
Uncertainty quantification is an important task in reservoir simulation studies used for decision... more 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 techni...
International Journal of Applied and Computational Mathematics, 2020
Uncertainty quantification is an important task in reservoir simulation and is an active area of ... more 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 North Sea. 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. Dedicated to the souls of my parents... I would like to express my deepest gratitude to my supervisors, Prof. Mike Christie and Prof. Gabriel Lord for leaving me alone to study and be independent. Thanks for providing freedom to explore different ideas throughout my PhD journey. Also, I would like to thank the Uncertainty quantification group for improving my presentation skills and giving feedback. I would like to thank Uncertainty quantification sponsors for their useful comments on my work especially, Prof. Jonathan Carter. Furthermore, I would like to thank the examiners for this thesis, Prof Peter King and Dr. James Cruise for their useful comments and incredible feedback to improve the thesis. Moreover, thanks to computer support team and the best magician Jack Talbot for fixing software problem issues during my PhD. I would like to thank Ali Danesh Scholarship for funding my PhD study at Heriot-Watt University. I would like to thank the African Institute for Mathematical Science for providing funding to conference participation. Thanks to Faculty of Science, Cairo University for giving me a study leave to study PhD. I would like to thank my best friend Samah Alhafian for supporting me during my PhD study. Also, I would like to thank my friends Laila, Maha, Radiha, Razan, Alyaa, and Sohad for their effort to make me enjoying the time here in Edinburgh during my PhD. Moreover, my friends at Uncertainty quantification group Zainab, Alexandra, Junko and Behzad for supporting me during my study. Last but not least, I would first like to thank my mother without her continuous support and encouragement I never would have been able to achieve my goals. I dedicate this PhD for my parents' souls.
Uncertainty quantification is an important task in reservoir simulation and is an active area of ... more 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 ...
Day 2 Tue, September 15, 2015, 2015
Uncertainty quantification is an important task in reservoir simulation studies used for decision... more 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 techni...
International Journal of Applied and Computational Mathematics, 2020