Microhole technology is a novel technology for wellbore diameters less than 88.9 mm and uses coiled tubing (CT) as the tubing string for downhole operations. The CT cannot rotate in the downhole due to the small diameter of the microhole, so that a sliding force is needed to trip the CT into the microhole. As a result, high friction is generated between the CT and the wellbore. Problems such as buckling and even lock-up occur under compressive loads, which severely impairs downhole operations of the CT in the microhole. In this work, a detailed analysis is made of CT operating conditions in a small-diameter vertical wellbore. The critical buckling loads and associated contact loads on CT strings of different diameters are calculated using well-developed models, and a study is made of the dependence of the critical buckling loads and corresponding contact loads on various parameters. The results show that the critical buckling load increases with CT diameter and that coil pitch width increases with CT diameter and a decrease in the annular clearance between the CT and the wellbore wall. The contact load between the CT and the wellbore wall increases with an increase in the axial compressive load and decreases with an increase in CT diameter. To reduce friction and contact loads and to trip the CT smoothly into vertical microholes, a larger-diameter CT and a smaller compressive load should be used while maintaining adequate annular clearance.