A mathematical model of motion of polymer systems with nanoaggregates in the pore space of an oil reservoir

A percolation-hydrodynamic model of the process of oil displacement by polymer solutions with nanoaggregates of various structures has been formulated and numerically implemented. The model allows taking into account the features of the pore space structure and the nature of the interaction of nanoaggregates with its surface during the filtration of the polymer solution. The possibility of achieving a higher oil recovery factor in the case of using polymers with hyperbranched nanomaterials compared to the classical polymer effect is shown. A cycle of laboratory studies was implemented to verify the results of theoretical calculations obtained using the model and compare them with the experimental data. The oil displacement process was modeled in terms of the composite model of a reservoir element assembled from 10 standard core samples taken from one oil-bearing reservoir. Theoretical estimates are in qualitative agreement with the results of the laboratory experiments also conducted with a composite reservoir model, and their quantitative difference is due to the use of the rheological law for Newtonian fluids in the mathematical model. The experimental results showed that the studied polymers are characterized by a pseudoplastic flow regime, therefore the effective viscosity of the polymer solution is higher than that assumed in the calculations. Based on the theoretical and experimental studies, it can be concluded that the application of polymer systems containing hyperbranched nanoaggregates leads to a significant increase in the residual resistance factor, where the formation of a stable polymer structure significantly decreases a porous medium’s permeability in flooded channels. The percolation-hydrodynamic model presented in this paper allows for a more adequate consideration of the physicochemical processes that occur during polymer flooding of oil-saturated reservoirs.