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History Matching and Uncertainty Quantification with Produced Water Chemistry

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History Matching and Uncertainty Quantification with Produced Water Chemistry
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    MSc (Petroleum Engineering) Project Report 2012/2013 Obinna Nwafor H00137989 History Matching and Uncertainty Quantification with Produced Water Chemistry Heriot-Watt University Institute of Petroleum Engineering Supervisor    -     i Declaration: I… Obinna Nwafor …onfim tht thi wok bmittd fo mnt i my own and is expressed in my own words. Any uses made within it of the works of other authors in any form (e.g. ideas, equations, figures, text, tables, programs) are properly acknowledged at the point of their use. A list of the references employed is included. Signd…………………………..   Dt…… 20 … August, 2013 ……    ii Acknowledgements I would like expressly my profound gratitude to my Supervisor Oscar Vasquez for his tireless effort in guiding me through this work. He has taken me from reservoir studies, and mixed in a little bit of chemistry and lots mathematics. Without his kind reassurance, I would not have come this far. My gratitude also g o to th whol “Untinty” research group at IPE, Heriot-Watt University, led  by Mike Christie. I am very grateful to Mike, especially for those solutions he throws my way at the moments my wits were fully spent. Vasily Demyanova has been to me a great teacher and guide, especially with the woolly concepts of uncertainty quantification. He never once got deterred by my “ silly ”  questions, which popped out every morning. I am truly thankful. Dan Arnolds has been invlbl to m in thing “ndtnding” tht n wy. He takes time to lead them back-in, ensuring they were securely tucked into their beds. I would not have had the coura g to tk on “mthmtil optimition” withot th encouragement from Eric Mackay. I am truly thankful to his insight, especially those words about ft “job pnttion.” My gtitd lo go to th Chplin of Hiot -Watt University, Alastair Donald, every Sunday I found my way back to him for the spiritual fodder that kept me going. I appreciate Epistemy Ltd for the Raven software used for this study, and the Computer Support Team who kept the systems running in spite of the mounting pressure. I wish to acknowledge all my lectures and tutors at the IPE over the last one year, they gave me a little bit of themselves, which I have put together in this work. My parents, especially mother, my sisters and brother in-law have been a rock to me throughout my one year stay in Edinburgh which culminated in this work. Thank you for being there, caring and offering your words and resources. I thank the Almighty God for his grace every step of the way.  iii Abstract   History matching is used in reservoir calibration. Conventional history matching could be improved  by addition of more constraints to be matched. The injected sea water, produced as part of associated water could have the potential of serving as an additional constraint. Such data can be obtained cheaply by using ion in sea water as natural tracers. This study aims to determine the extent of improvement to history matching and reduction of uncertainty in forecasts brought about by the addition of injected sea water production data to the history matching process. The study was carried out using the PUNQS3 reservoir model. It is a synthetic reservoir model that has been used for similar studies and severally to test out methods in history matching and uncertainty quantification. The uncertain parameters in the PUNQS3 model are the porosity and permeability. Two cases of automatic history matching were carried out. One involved the use of injected sea water tracer production data as additional constraint. The other involved using only the conventional  production data. The automatic history matching was based on multi-objective particle swarm optimization (PSO). Which is a nature inspired stochastic optimization technique. The uncertainty quantification was done using Neighbourhood Approximation method (NA-Bayes) based on a Bayesian framework. The result for the two cases was compared on the basis of advance of their  pareto front of models ensemble towards lower misfit values. The quality of history matching and size of uncertainty were also considered. They all show indications that addition of injected sea water  production data improves the history matching process, reduced uncertainty in forecast, as well as creates a more robust uncertainty quantification. However the improvements were not large, but could be more significant for more complex reservoir history matching problems.
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