An Introduction to Petroleum Reservoir Simulation is aimed toward graduate students and professionals in the oil and gas industry working in reservoir simulation. It begins with a review of fluid and rock properties and derivation of basic reservoir engineering mass balance equations. Then equations and approaches for numerical reservoir simulation are introduced. The text starts with simple problems (1D, single phase flow in homogeneous reservoirs with constant rate wells) and subsequent chapters slowly add complexities (heterogeneities, nonlinearities, multi-dimensions, multiphase flow, and multicomponent flow). Partial differential equations and finite differences are then introduced but it will be shown that algebraic mass balances can also be written directly on discrete grid blocks that result in the same equations. Many completed examples and figures will be included to improve understanding. An Introduction to Petroleum Reservoir Simulation is designed for those with their first exposure to reservoir simulation, including graduate students in their first simulation course and working professionals who are using reservoir simulators and want to learn more about the basics. Presents basic equations and discretization for multiphase, multicomponent transport in subsurface media in a simple, easy-to-understand manner - Features illustrations that explain basic concepts and show comparison to analytical solutions and commercial simulators - Includes dozens of completed example problems on a small number of grid blocks - Offers pseudocode and exercises to allow the reader to develop their own computer-based numerical simulator that can be verified against analytical solutions and commercial simulators Covers the basics of reservoir simulation for students and professionals who are new to the field An Introduction to Petroleum Reservoir Simulation is aimed toward graduate students and professionals in the oil and gas industry working in reservoir simulation. It begins with a review of fluid and rock properties and derivation of basic reservoir engineering mass balance equations. Then equations and approaches for numerical reservoir simulation are introduced. The text starts with simple problems (1D, single phase flow in homogeneous reservoirs with constant rate wells) and subsequent chapters slowly add complexities (heterogeneities, nonlinearities, multi-dimensions, multiphase flow, and multicomponent flow). Partial differential equations and finite differences are then introduced but it will be shown that algebraic mass balances can also be written directly on discrete grid blocks that result in the same equations. Many completed examples and figures will be included to improve understanding. An Introduction to Petroleum Reservoir Simulation is designed for those with their first exposure to reservoir simulation, including graduate students in their first simulation course and working professionals who are using reservoir simulators and want to learn more about the basics. Matthew T. Balhoff is a Professor in the Hildebrand Department of Petroleum and Geosystems Engineering and Director of the Center for Subsurface Energy and the Environment at UT-Austin. He co-leads the Industrial Affiliates Program on Chemical Enhanced Oil Recovery. Dr. Balhoff received his BS (2000) and PhD (2005) in chemical engineering from Louisiana State University. He became an SPE Distinguished member in 2017 and is a winner of the 2017 SPE Southwestern North America Regional Reservoir Description and Dynamics Award, 2014 SPE International Young Member Service Award, and 2012 SPE International Teaching Fellow Award. Dr. Balhoff has over 70 peer-reviewed publications in the areas of numerical reservoir simulation, pore-scale modelling, enhanced oil recovery, carbon storage, and unconventional resource production. He has taught dozens of undergraduate and graduate courses on numerical reservoir simulation, reservoir engineering, and fluid properties.