Wellbore temperature and pressure calculation model for supercritical carbon dioxide jet fracturing

A new numerical calculation model for wellbore temperature and pressure for SC-CO₂ jet fracturing was proposed in this research. In our model, the impact of tubing, casing, and cement on heat transfer, and the heat generated by fluid friction losses are all taken into consideration. The CO₂ physical properties are calculated by the Span–Wagner and Vesovic models. Based on our calculation model, the factors that may affect the wellbore temperature and pressure are discussed. The results indicated that ignoring the influence of the cement sheath thermal resistance on heat transfer would lead to a wellbore temperature higher than the actual value. The wellbore CO₂ pressure is always higher than its critical value, but the CO₂ temperature at the jet point in some cases is lower than its critical value. The wellbore CO₂ temperature is increased with the increase in injection temperature and cement sheath thermal conductivity and the decrease in annulus injection rate and coiled tubing injection rate. However, the decrease in the coiled tubing injection rate and increase in the cement sheath thermal conductivity are the only effective ways to ensure that the CO₂ temperature at the jet point exceeds its critical value.