Multicontinuum Homogenization for Poroelasticity Model

Abstract

In this paper, we derive multicontinuum poroelasticity models using the multicontinuum homogenization method. Poroelasticity models are widely used in many areas of science and engineering to describe coupled flow and mechanics processes in porous media. However, in many applications, the properties of poroelastic media possess high contrast, presenting serious computational challenges. It is well known that standard homogenization approaches often fail to give an accurate solution due to the lack of macroscopic parameters. Multicontinuum approaches allow us to consider such cases by defining several average states known as continua. In the field of poroelasticity, multiple-network models arising from the multiple porous media theory are representatives of these approaches. In this work, we extend previous findings by deriving the generalized multicontinuum poroelasticity model. We apply the recently developed multicontinuum homogenization method and provide a rigorous derivation of multicontinuum equations. For this purpose, we formulate coupled constraint cell problems in oversampled regions to consider different homogenized effects. Then, we obtain a multicontinuum expansion of the fine-scale fields and derive the multicontinuum model supposing the smoothness of macroscopic variables. We present the most general version of equations and the simplified ones based on our numerical experiments. Numerical results are presented for different heterogeneous media cases and demonstrate the high accuracy of our proposed multicontinuum models.