This book describes the state of the art of the mathematical theory and numerical analysis of imaging. Some of the applications covered in the book include computerized tomography, magnetic resonance imaging, emission tomography, electron microscopy, ultrasound transmission tomography, industrial tomography, seismic tomography, impedance tomography, and NIR imaging.

Beginning with an overview of classical reservoir engineering and basic reservoir simulation methods, this book then progresses through a discussion of types of flows - single-phase, two-phase, black oil (three-phase), single phase with multi-components, compositional, and thermal. The author provides a thorough glossary of petroleum engineering terms and their units, along with basic flow and transport equations and their unusual features, and corresponding rock and fluid properties. The book also summarises the practical aspects of reservoir simulation, such as data gathering and analysis, and reservoir performance prediction. Suitable as a text for advanced undergraduate and first-year graduate students in geology, petroleum engineering, and applied mathematics; as a reference book; or as a handbook for practitioners in the oil industry. Prerequisites are calculus, basic physics, and some knowledge of partial differential equations and matrix algebra.

Presents numerical methods for reservoir simulation, with efficient implementation and examples using widely-used online open-source code, for researchers, professionals and advanced students. This title is also available as Open Access on Cambridge Core.

Discusses the need for sophisticated mathematical tools to deal with complex enhanced recovery procedures in the field of hydrocarbon extraction.

Numerical simulators for oil reservoirs have been developed over the last twenty years and are now widely used by oil companies. The research, however, has taken place largely within the industry itself, and has remained somewhat inaccessible to the scientific community. This book hopes to remedy the situation by means of its synthesized presentation of the models used in reservoir simulation, in a form understandable to both mathematicians and engineers.The book aims to initiate a rigorous mathematical study of the immiscible flow models, partly by using the novel `global pressure' approach in treating incompressible two-phase problems. A finite element approximation technique based on the global pressure variational model is presented, and new approaches to the modelling of various kinds of multiphase flow through porous media are introduced.Much of the material is highly original, and has not been presented elsewhere. The mathematical and numerical models should be of great interest to applied mathematicians, and to engineers seeking an alternative approach to reservoir modelling.

Reservoir Simulation: Machine Learning and Modeling helps the engineer step into the current and most popular advances in reservoir simulation, learning from current experiments and speeding up potential collaboration opportunities in research and technology. This reference explains common terminology, concepts, and equations through multiple figures and rigorous derivations, better preparing the engineer for the next step forward in a modeling project and avoid repeating existing progress. Well-designed exercises, case studies and numerical examples give the engineer a faster start on advancing their own cases. Both computational methods and engineering cases are explained, bridging the opportunities between computational science and petroleum engineering. This book delivers a critical reference for today's petroleum and reservoir engineer to optimize more complex developments. - Understand commonly used and recent progress on definitions, models, and solution methods used in reservoir simulation - World leading modeling and algorithms to study flow and transport behaviors in reservoirs, as well as the application of machine learning - Gain practical knowledge with hand-on trainings on modeling and simulation through well designed case studies and numerical examples.

The use of numerical reservoir simulation with high-speed electronic computers has gained wide acceptance throughout the petroleum industry for making engineering studies of a wide variety of oil and gas reservoirs throughout the world. These reservoir simulators have been designed for use by reservoir engineers who possess little or no background in the numerical mathematics upon which they are based. In spite of the efforts to improve numerical methods to make reservoir simulators as reliable, efficient, and automatic as possible, the user of a simulator is faced with a myriad of decisions that have nothing to do with the problem to be solved. This book combines a review of some basic reservoir mechanics with the derivation of the differential equations that reservoir simulators are designed to solve.