Petroleum resources continue to be the main source of energy in today’s civilization. It is important to predict petroleum production accurately in order to plan long-term energy management. Currently used predictive tools are inadequate for capturing the science of petroleum production. This book makes important fundamental advancement in modeling complex phenomena that are currently neglected or are added to the predictive tool with unjustified simplification. Various mathematical models that are used for characterizing phenomena, ranging from drilling to reservoir engineering, are considered. Also, presented are shortcomings, such as, the use of linear or linearized rheological and rock behavior models, unsustainable drilling practices, insufficient risk analysis models, and inaccurate description of the thermal effects in a petroleum reservoir. This book will lead to the development of more accurate reservoir simulation tools and comprehensive risk analysis methods. These methods can be used by petroleum engineers, mechanical engineers, chemical engineers, risk analysts, operating engineers, and graduate students to develop sustainable drilling and production operations.