The aim of this work is to describe the gelation process of a crosslinked polymer composition depending on its flow rate in free space and in pore space. The object of the study is a polymer solution based on partially hydrolyzed polyacrylonitrile and chromium acetate. A team of researchers has proposed a new approach to describing the kinetic viscosity curve of a crosslinked polymer system in a free volume. This approach takes into account oscillatory variations in the structural and mechanical characteristics relative to a smoothly increasing gelation curve. The nonlinear effects are linked to the processes of structural formation and, simultaneously, destruction due to mechanical, thermobaric, and chemical destruction under varying flow conditions. The proposed solution is based on the Verhulst differential equation and tested on five values of shear rates with the addition of correction factors. The article explains the processes of gel formation and the destruction of polymer compounds, and compares the equation of limited growth with the Kenneth Sorbie method, which is employed in the PC-GEL simulator. The limitations of the modern gel invasion model used in the UTCHEM and BPOPE simulator within the porous media (within a narrow gap) are revealed.
Raupov et al. (2026) studied this question.