# Investigation of the Gelation Process of a Polymer Composition Based on an Acrylic Polymer

## TL;DR

This paper studies how a polymer solution gels under different flow conditions and introduces a new mathematical model to describe the process.

## Contribution

A new approach using the Verhulst differential equation is proposed to model gelation dynamics under varying flow rates.

## Key findings

- The Verhulst equation with correction factors accurately models gelation under different shear rates.
- Nonlinear effects in gelation are linked to structural formation and destruction processes.
- Limitations of existing gel invasion models in simulators like UTCHEM and BPOPE are identified.

## Abstract

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.