Recent progress in multiscale and mesoscopic reservoir simulation

Abstract Physical phenomena can be modeled at varying degrees of complexity and at different scales. Multiscale modeling and computation provides a framework for constructing mathematical and computational models of such phenomena, by examining the connection between models at different scales, based on fundamental principles, and based on mathematical theory of approximation. Recently, mesoscopic algorithms have been proposed and widely accepted in petroleum industry and lattice Boltzmann method (LBM) is the most famous one. The word mesoscopic is used to describe the flow property with regarding to certain Knudsen number range and the capability of capturing both macroscopic phenomena and microscopic interactions. LBM is proved to have super parallelization property and easy to implement using fully explicit scheme. Complex boundary can be treated well in LBM and numerous mechanisms can be coupled easily. Meanwhile, generalized multiscale finite element method has also been developed with the usage of certain upscaling technique such as proper orthogonal decomposition. In this chapter, we will start from the concepts and properties of upscaling techniques and then step into the application on discretized numerical methods. Multipoint flux approximation methods are also an option to conclude multiscale properties in one scheme. Finally, LBM is presented with rigorous derivations and modified schemes for specific engineering cases are presented to show the coupling with various mechanisms.