Unsteady Flow Dynamics and Phase Transition Behavior of CO₂ in Fracturing Wellbores

This study presents a two-dimensional, transient model to simulate the flow and thermal behavior of CO₂ within a fracturing wellbore. The model accounts for high-velocity flow within the tubing and radial heat exchange between the wellbore and surrounding formation. It captures the temporal evolution of temperature, pressure, flow velocity, and fluid density, enabling detailed analysis of phase transitions along different tubing sections. The influence of key operational and geological parameters, including wellhead pressure, injection velocity, inlet temperature, and formation temperature gradient, on the wellbore’s thermal and pressure fields is systematically investigated. Results indicate that due to intense convective transport by the high-speed CO₂ flow, the temperature and velocity within the tubing are primarily governed by the inlet temperature and injection velocity, with relatively minor influence from radial heat transfer with the formation. The pressure, flow velocity, and density of CO₂ within the tubing are strongly dependent on wellhead conditions. Frictional losses and well depth contribute to pressure variations, particularly in the horizontal section of the wellbore, where a noticeable pressurization effect increases the fluid density. During injection, liquid CO₂ initially undergoes a rapid transition to a supercritical state, with the depth at which this phase change occurs stabilizing as injection progresses.