2020/04/20 by Menel Rahrah, Rahrah, Menel, Luis A. Lopez-Peña +5
Engineering · Environmental Science · #FOS: Mathematics #Groundwater flow and contamination studies #Lattice Boltzmann Simulation Studies #Numerical Analysis (math.NA) #Soil and Unsaturated Flow
paper · pdf · doi:10.48550/arxiv.2004.09373
openalex publication_date 2020/04/20 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28
Water injection in the aquifer induces deformations in the soil. These\nmechanical deformations give rise to a change in porosity and permeability,\nwhich results in non-linearity of the mathematical problem. Assuming that the\ndeformations are very small, the model provided by Biot's theory of linear\nporoelasticity is used to determine the local displacement of the skeleton of a\nporous medium, as well as the fluid flow through the pores. In this continuum\nscale model, the Kozeny-Carman equation is commonly used to determine the\npermeability of the porous medium from the porosity. The Kozeny-Carman relation\nstates that flow through the pores is possible at a certain location as long as\nthe porosity is larger than zero at this location in the aquifer. However, from\nnetwork models it is known that percolation thresholds exist, indicating that\nthe permeability will be equal to zero if the porosity becomes smaller than\nthese thresholds. In this paper, the relationship between permeability and\nporosity is investigated. A new permeability-porosity relation, based on the\npercolation theory, is derived and compared with the Kozeny-Carman relation.\nThe strongest feature of the new approach is related to its capability to give\na good description of the permeability in case of low porosities. However, with\nthis network-inspired approach small values of the permeability are more likely\nto occur. Since we show that the solution of Biot's model converges to the\nsolution of a saddle point problem for small time steps and low permeability,\nwe need stabilisation in the finite element approximation.\n