Abstarct: The intricate displacement of Newtonian and non-Newtonian fluids in porous media, spanning multiple phases, holds pivotal significance in applications like enhanced oil recovery (EOR) and mitigating water resource contamination. These flows, governed by viscosity differentials and interfacial tension, engender intricate patterns at the interface, destabilizing flow. A comprehensive understanding of chemical flooding within uniform porous media remains elusive despite existing literature. Numerical simulations often rely on simplified equations, such as Darcy's law and its adaptations, for both Newtonian and non-Newtonian fluids. However, these equations might inadequately capture non-Newtonian behavior. Few studies tackle the comprehensive nonlinear momentum equations, particularly Navier-Stokes and Cauchy equations, applied to immiscible two-phase flows in micro-scale porous media models. We employ the level-set method to investigate Newtonian and non-Newtonian fluid displacements to address this. This method's proficiency in tracking phase interfaces yields more realistic outcomes than simplified equations. Our study evaluates oil displacement efficiency using seawater, aqueous sodium dodecyl sulfate solution, and a shear-thinning non-Newtonian polystyrene-baxsed fluid within the micro-model. We rigorously analyze parameters like displacing fluid injection rate, viscosity, and mobility ratios, as well as the power-law index 'n' in the non-Newtonian Carreau model. Our investigation delves into displacement parameters and Saffman-Taylor instability intricately. Results underscore the superior performance of shear-thinning non-Newtonian fluids within the micro-model's sweep range relative to other considered chemical factors. Notably, our findings demonstrate a significantly prolonged breakthrough time of 34 seconds for polystyrene injection at 0.5 mL/h, in contrast to the 21 seconds achieved with seawater