April 12 – Menel Rahrah: Mathematical modelling of fast, high volume infiltration in poroelastic media using finite elements

Menel Rahrah: Friday 12 April at 14:30, A315 Inria Paris.

Fast, High Volume Infiltration (FHVI) is a new method to quickly infiltrate large amounts of fresh water into the shallow subsurface. This infiltration method would have a great value for the effective storage of rainwater in the underground, during periods of extreme precipitation. To describe FHVI, a model for aquifers is considered in which water is injected. Water injection induces changes in the pore pressure and deformations in the soil. Furthermore, the interaction between the mechanical deformations and the flow of water gives rise to a change in porosity and permeability, which results in nonlinearity of the mathematical problem. Assuming that the deformations are very small, Biot’s theory of linear poroelasticity is used to determine the local displacement of the skeleton of a porous medium, as well as the fluid flow through the pores. The resulting problem needs a considerate numerical methodology in terms of possible nonphysical oscillations. Therefore, a stabilised Galerkin finite element method based on Taylor-Hood elements is developed. Subsequently, the impact of mechanical oscillations and pressure pulses on the amount of water that can be injected into the aquifer is investigated. In addition, a parameter uncertainty quantification is applied using Monte Carlo techniques and statistical analysis, to quantify the impact of variation in the parameters (such as the unknown oscillatory modes and the soil characteristics) on the model output. Since the assumption that the deformations are very small can be violated by imposing large mechanical oscillations, the difference between the linear and the nonlinear poroelasticity equations is analysed in a moving finite element framework using Picard iterations.

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