Non-Steady-State Coupled Model of Viscosity–Temperature–Pressure in Polymer Flooding Injection Wellbores

Polymer solutions play a crucial role in the polymer flooding process by influencing the flow characteristics of formation fluids and enhancing recovery efficiency. Their properties are influenced by the transient coupling of temperature, pressure, and viscosity, yet the underlying patterns remain unclear. This study establishes a non-steady-state coupling model of polymer temperature–pressure–viscosity in wellbores, solved numerically using a staggered-grid fully implicit scheme in Matlab. At a depth of 1000 m, the polymer viscosity is measured in the field as 102.12 mPa·s, while the simulated value is 107.46 mPa·s (4.97% error), indicating good agreement with the wellbore viscosity distribution. Wellbore temperature is the dominant factor, whereas injection pressure has minor effects. Injection flow rate governs heat exchange with the formation; low flow causes larger temperature and viscosity fluctuations, while high flow leads to insufficient heat transfer. With prolonged injection, wellbore temperature approaches dynamic equilibrium, viscosity decreases, and sand-carrying capacity weakens. These findings provide theoretical guidance for optimizing polymer flooding.