The fluid in the annulus is in a variable mass flow state under the lost circulation condition, significantly affecting wellbore pressure distribution and the heat transfer efficiency between wellbore and formation. Therefore, based on the hydrodynamics and energy conservation law, a coupling model of transient wellbore temperature and pressure field under lost circulation conditions is established, which fully considers the casing program, bottom hole assembly, and heat source generated in drilling, as well as the influence of the temperature and pressure coupling in wellbore on the physical parameters of drilling fluid. The calculation results of the model in this paper are in good agreement with the field measured data and the previous research results, which verifies the rationality and accuracy of the model in this paper. The effects of the loss rate and the lost circulation zone location on the wellbore temperature and pressure distribution are analyzed, and the variation rule of the physical parameters of drilling fluid under the lost circulation condition is studied. The numerical simulation results show that the density and viscosity of drilling fluid in the annulus and bottom hole pressure increase with the increase in the circulation time; the annulus temperature decreases gradually with the increase in cycle time and tends to become stable after 8 h of the cycle. The annulus temperature and bottom hole pressure decrease with the increase in loss rate and closeness of the loss zone to the well bottom. When the loss zone is in the upper open-hole section, an inflection point consistent with the location of the loss zone appears on the annular temperature difference curve between the loss circulation and the nonloss circulation, and the position of the loss zone can be judged according to the inflection point.

The correct reference is as follows: "(6) Hajidavalloo, E.; Daneh-Dezfuli, A.; Falavand Jozaei, A. Effect of temperature variation on the accurate prediction of bottom-hole pressure in well drilling.