In this study, hydrophobic associative polyacrylamide (HAPAM) was used in conjunction with the chemical flooding technique in a low-permeability carbonates reservoir. To test the efficacy of the proposed method, both a model and an experiment were created. Experiments were run to compare the relative permeability (Kr) curves, oil recovery rates, and rheological, physical, aging time, and petrophysical features of brine water and polymer flooding in a core. The purpose of these tests was to show how HAPAM can be used to boost oil recovery. Computer Modelling Group (CMG), a simulator, was then used. An oil-and-brine (or HAPAM solution) grid in three dimensions (3D) was developed. The validity of the suggested simulator was established by comparing its results to those obtained from commercial software and from most of the brine or polymer flooding experiments. The developed simulator was used to undertake additional research into the non-Newtonian flow of brine or polymer solution in porous media. The experimental consequences indicated that the polymer solution has a shear thinning viscosity curve and flow behavior index. Shear thinning, viscosity, shear resistance, aging time, density, surface tension, and interfacial tension, and the water wet relative permeability curve are all improved by the adding 1500 ppm HAPAM to brine water. Moreover, oil recovery was about 80%. There was a strong agreement between the results of the modeling study and the experiments.