A mixed-dimensional model for direct current simulations in the presence of a thin high-resistivity liner

In this work, we present a mixed-dimensional mathematical model to obtain the electric potential and current density in direct current simulations when a thin liner is included in the modelled domain. The liner is used in landfill management to prevent leakage of leachate from the waste body into the underground and is made of a highly-impermeable high-resistivity plastic material. The electrodes and the liner have diameters and thickness, respectively, that are much smaller than their other dimensions, thus their numerical simulation might be too costly in an equi-dimensional setting. Our approach is to approximate them as objects of lower dimension and derive the corresponding equations. The obtained mixed-dimensional model is validated against laboratory experiments of increasing complexity to show the reliability of the proposed mathematical model. Our tests also show that configurations with current and voltage electrodes on either sides of the liner confining the landfill may be effective in detecting damages of the membrane.