Nanofluid Injection in Poroelastic Media: Possible Applications in Environmental Science

Nanofluids are innovative materials consisting of a suspension of nanoparticles in a fluid, such as water or oil. They are commonly used in engineering and medicine because of their thermal conductivity, which makes them particularly efficient for cooling, heat transport, and tumor treatment. In recent times, the unique properties of nanofluids have led to their use for environmental application. This includes oil extraction processes, the treatment of contaminated water and soil, and the improvement of the seismic response of the soil during strong seismic events. Although these applications are very different from each other, it is necessary in all cases to inject the nanoparticles into the soil. However, predicting the distribution of particles a priori, considering the injection parameters, is very difficult due to the intrinsic complexity of the subsoil and uncertainty regarding parameters such as porosity and elastic properties. One possible solution is to use numerical simulations on digital twins of the area of interest. These simulations are computationally expensive, and are affected, in the specific case, by a high level of uncertainty, due to the lack of specific information on soil stratigraphy. In this paper, we present and discuss a mathematical model that describes the injection of nanofluid into the soil, taking into account its natural poroelasticity, which is often neglected. The subsequent drift and diffusion of the particles, as well as their interaction with the surrounding medium through absorption and desorption processes, can be described using the same model, but with different boundary and initial conditions. After introducing the model, we discuss in detail the effects of poroelasticity and the role of injection parameters on particle distribution. We also present some (semi−)analytical representations of the model that could be useful for the preliminar calibration of the numerical simulations and, potentially, of the injection process.