This thesis is submitted to University of SouthEastern Norway (USN) for the degree of Doctor of Philosophy to the Department of Electrical Engineering, Information Technology, and Cybernetics under the Faculty of Technology, Natural Sciences, and Maritime Sciences. The research work is funded by the Ministry of Education and Research of the Norwegian Government, for four years with 25% teaching duties and starting from September 2014. The work is mainly related to flow measurement in the return line of drilling fluid circulation while drilling. In any drilling operations, wellbore stability is the primary objective for safe and efficient drilling. The study focuses on the usage of the delta flow measurement (i.e., the difference between inflow and return flow) for maintaining the wellbore stability. An accurate return flow measurement is a comparatively challenging task, which is investigated in this study. For the return flow measurement, a simple and accurate flow measurement system using Venturi constriction is presented that may replace an existing uniform open channel. For the study, three different types of existing flow models are investigated. Different machine learning based flow models are developed. The models are tested in a flow loop available at USN, Campus Porsgrunn using synthetic drilling fluids with rheological properties that are comparable with water-based drilling mud. The experimental results show that the models are applicable for non-Newtonian fluid flow measurements. I hope the models will be of use in the real drilling operations for both inflow and outflow measurements. vii Acknowledgement I would like to express my sincere gratitude towards my supervisor Saba Mylvaganam for his help and support in this work. I would also like to thank my cosupervisor Håkon Viumdal for his valuable contribution. We three together as a team has successfully managed to complete this work in time. My sincere thanks also go to my co-supervisor Gerhard Nygaard for sharing his expert knowledge on drilling operations during the early period of the work. I am grateful to the University of SouthEastern Norway and the Ministry of Education and Research of the Norwegian Government for funding the work. I would like to thank Equinor ASA for providing and commissioning the flow loop with various types of sensors and control systems dedicated to flow studies. The economic support from the Research Council of Norway and Equinor ASA through project no. 255348/E30 "Sensors and models for improved kick/loss detection in drilling (Semi-kidd)" is gratefully acknowledged. I greatly appreciate and acknowledge the expert advice on drilling operations by Dr. Geir Elseth of Equinor. I thank my colleagues and friends; Rajan