Thermoporoelasticity via homogenization: Modeling and formal two-scale expansions. (May 2019)

• Record Type: Journal Article
• Authors: van Duijn, C.J.; Mikelić, Andro; Wheeler, Mary F.; Wick, Thomas
• Is Part Of: International journal of engineering science. Volume 138(2019:May)
• Page Start: 1
• Page End: 25
• Publication Date: 2019-05
• Subjects: Two-scale expansions -- Porous media -- Linear thermoelasticity -- Fluid-structure interaction -- Heat transfer -- Upscaling; Engineering -- Periodicals; Ingénierie -- Périodiques; Engineering; Periodicals; 620
• DOI: 10.1016/j.ijengsci.2019.02.005
• Languages: English
• ISSNs: 0020-7225

Abstract

Abstract: In this paper we derive a macroscopic model for thermoporoelasticity from the pore scale linearized fluid-structure and energy equations. We consider the continuum mechanics thermodynamically compatible pore scale equations corresponding to realistic rock mechanics parameters. They are upscaled using two-scale asymptotic expansions. For the upscaled equations a Lyapunov functional (a generalization of Biot's free energy) is constructed and the well-posedness of the model is discussed. Possible applications to large time numerical simulations are pointed out.