Multiscale Finite Element Technique for Mathematical Modelling of Multi-physics Processes in Heterogeneous Media

Abstract

AbstractIn real-life applications, it is not always possible to decouple multiple physical processes occurring simultaneously in the medium, thus indirect methods based on, for example, electromagnetic measurements may be used to adequately describe the macroscopic behavior of the studied objects. We consider a multiscale problem of modelling the electromagnetic field in the hydrocarbon-bearing rock under the thermal and mechanical effects. The goal of this study is to develop a unified approach to modelling the multi-physical processes in geological media, such as oil reservoirs and carbon deposits. Geological media are characterized by the presence of multiple geometrical scales and highly heterogeneous physical properties. We use upscaling techniques and the effective characteristics of the media that adequately reflect its macroscopic behavior. We carry out mathematical modelling of the processes of heat and mass transfer, elastic deformation and mesoscale electromagnetic interactions with regard to the complex internal structure of the media. Our algorithm for the macroscopic description of the behavior of the geological media is based on the methods of the effective medium theory and numerical homogenization techniques. We present the results of the mathematical modelling of heat and mass transfer, elastic deformation and electromagnetic field in a heterogeneous medium, obtained using the computational schemes based on the multiscale finite element methods.KeywordsHeterogeneous mediumMulti-physics processesMultiscale non-conforming finite element methodsNumerical homogenization