Thermal efficiency of well bore during steaming with bare tubing without packer

It is often practiced that steam injection tubing is bared and with no packer. So the well head must be closed and the tubing interconnects with annular space at well bottom. Under this condition, temperature and pressure in annular, as well as thermal efficiency of well bore are all different from that with packer used. Thermodynamic theory is used to calculated temperature distribution and thermal efficiency of the well bore under assumption that annular space is full of vapor, and that saturated steam temperature (pressure) in the tubing and annular space are balanced at bottom hole. It is found that, compared with packer being used, temperature of casing inner surface and cement sheath outer surface is about 70 degrees C and 60 degrees C higher respectively, over-all heat loss is about 40%similar to 50% higher. When steam injection rate being low, over-all heat loss increases, and pressure has much more impact on mass dryness fraction which can be less than 10% at bottom hole. Steam injection rate has less impact on casing temperature than steam pressure does. https://link.springer.com/content/pdf/10.1007/978-3-540-75995-9_156.pdf