The Mathematics Of Reservoir Simulation

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

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.

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.

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.

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.

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.

Reservoir Simulation, written by experienced simulation users, was designed to help demystify the what's and whys of designing, editing, and analyzing reservoir simulations.

Petroleum Reservoir Simulation, Second Edition, introduces this novel engineering approach for petroleum reservoir modeling and operations simulations. Updated with new exercises, a new glossary and a new chapter on how to create the data to run a simulation, this comprehensive reference presents step-by-step numerical procedures in an easy to understand format. Packed with practical examples and guidelines, this updated edition continues to deliver an essential tool for all petroleum and reservoir engineers. Includes new exercises, a glossary and references Bridges research and practice with guidelines on introducing basic reservoir simulation parameters, such as history matching and decision tree content Helps readers apply knowledge with assistance on how to prepare data files to run a reservoir simulator

The development of naturally fractured reservoirs, especially shale gas and tight oil reservoirs, exploded in recent years due to advanced drilling and fracturing techniques. However, complex fracture geometries such as irregular fracture networks and non-planar fractures are often generated, especially in the presence of natural fractures. Accurate modelling of production from reservoirs with such geometries is challenging. Therefore, Embedded Discrete Fracture Modeling and Application in Reservoir Simulation demonstrates how production from reservoirs with complex fracture geometries can be modelled efficiently and effectively. This volume presents a conventional numerical model to handle simple and complex fractures using local grid refinement (LGR) and unstructured gridding. Moreover, it introduces an Embedded Discrete Fracture Model (EDFM) to efficiently deal with complex fractures by dividing the fractures into segments using matrix cell boundaries and creating non-neighboring connections (NNCs). A basic EDFM approach using Cartesian grids and advanced EDFM approach using Corner point and unstructured grids will be covered. Embedded Discrete Fracture Modeling and Application in Reservoir Simulation is an essential reference for anyone interested in performing reservoir simulation of conventional and unconventional fractured reservoirs. Highlights the current state-of-the-art in reservoir simulation of unconventional reservoirs Offers understanding of the impacts of key reservoir properties and complex fractures on well performance Provides case studies to show how to use the EDFM method for different needs

Publisher's Note: Products purchased from Third Party sellers are not guaranteed by the publisher for quality, authenticity, or access to any online entitlements included with the product. Develop, build, and deploy accurate mathematical models for hydrocarbon reservoirs This practical resource discusses the construction of reservoir models and the implementation of these models in both forward and inverse modes using numerical, analytical, empirical, and artificial intelligence techniques. Written by a pair of experts in the field, Reservoir Engineering Models: Analytical and Numerical Approaches clearly explains the complicated building processes of mathematical models and lays out cutting-edge solution protocols. Advanced chapters teach the assembly of complex physical processes using principles of physics, thermodynamics and mathematics. You will learn to optimize decision-making processes applicable to the management of field development and extraction activities. Coverage includes: •An introduction to reservoir engineering models•Mathematics of reservoir engineering•Reservoir engineering fundamentals•Hydrocarbon fluid models and thermodynamics•Reservoir engineering transport equations•Analytical and numerical reservoir engineering solutions•Proxy and hybrid models in reservoir engineering