Multicontinuum Homogenization for Heterogeneous Poroelastic Media

In this talk, we discuss the multicontinuum homogenization approach. The multicontinuum homogenization represents a general framework for deriving multicontinuum models in heterogeneous high-contrast media. The method consists of several key steps. First, the microscopic solution field is expanded in terms of macroscopic variables that represent average solutions in the corresponding continua. Next, we formulate cell problems with appropriate constraints to capture various homogenized effects for each continuum. Finally, under suitable assumptions, we rigorously derive the multicontinuum equations.
As a primary application, we focus on a poroelasticity problem in heterogeneous high-contrast media. Using the multicontinuum homogenization approach, we derive a generalized multicontinuum poroelasticity model for an arbitrary number of continua. The obtained multicontinuum model extends and generalizes existing multiple-network poroelasticity models.