Modelling and semi-analytical solutions for fingering instability during zero-dimensional nano floodings

Fingering instability, a pivotal phenomenon in multiphase flow within porous media, is thoroughly examined. It stems from the interplay of capillary and viscous forces, yielding distinctive finger-like patterns, and holds critical implications for oil recovery and environmental remediation. A comprehensive mathematical model, fortified by the Method of Directly Defining the inverse Mapping, is established. This study scrutinizes the efficacy of zero-dimensional nanoparticles: aluminium oxide, magnesium oxide, and silicon dioxide. Nano-powders were infused at 0.4% concentration in a brine solution, a pioneering approach to enhanced oil recovery. The model was established to identify the saturation of injected fluid where a layer of crude oil is positioned at an angle relative to the horizontal plane. This means that instead of being perfectly flat, the layer tilts or slopes in a particular direction. Such inclined formations are common in natural reservoirs, and understanding their geometry and properties is crucial for effective oil extraction and recovery processes.  Gravity now plays a more pronounced role in determining the direction of oil movement. Analysis of the resulting graph, generated through Maple 16, indicates that the injection of aluminium oxide leads to the highest saturation levels in comparison to the other fluids. Conversely, the use of magnesium oxide results in the lowest saturation. This finding underscores the potential significance of aluminium oxide in optimizing oil extraction techniques and contributes valuable insights into optimizing oil recovery processes and managing subsurface fluid dynamics, fostering advancements in enhanced oil recovery methodologies.