Numerical investigation on wellbore temperature and pressure during carbon dioxide fracturing

In the present study, a transient 2D model considering the factors of CO2 thermal properties, viscous heating source, Joule-Thomson effect, axial and radial heat transfer is proposed to investigate the wellbore temperature and pressure. The temperature governing equations are solved numerically by using the method of Alternating Direction Implicit (ADI). Based on the law of conservation of energy, the viscous heating source is reasonably considered as the thermal energy converted by mechanical energy. The wellbore temperature and pressure are analyzed based on the investigation of the tubing and annulus injection well with the diameter of 50.3 mm and depth of 3600 m. The simulation results of our model are in good agreement with the field data. The analysis results show that the bottom hole temperature increases first and then decreases as injection time increases. Large injection rate results in low bottom hole pressure and negative axial pressure gradient. The critical depth increases as injection time increases. Compared with tubing injection, tubing and annulus injection decreases critical depth and increases the duration of wellbore unsteady flow and heat transfer process. The solid heat conduction in axial direction significantly affects the wellbore temperature and pressure distributions.