Abstract: During liquid carbon dioxide fracturing operations, it has been discovered that the manifestation of formation fracture initiation pressure is not prominent. The delay in on-site monitoring of breakdown initiation is prone to causing excessive injection of carbon dioxide, thereby escalating the risk of tubing rupture. Based on the wellbore temperature-pressure coupling model, this study establishes a dynamic pressure ramping rate model during liquid carbon dioxide injection. The proposed model incorporates the dynamic variation of volume compressibility and systematically investigates the influence pattern of pressure ramping rate on fracture initiation pressure. The research results indicate the followings: A distinct time-delay effect in carbon dioxide fracturing was observed. According to the model calculations, when the injection rate of carbon dioxide is 4.3 m³/min, the fracture initiation pressure is 14.85% lower than that in the mini-fracturing test (hydraulic fracturing), and the breakdown initiation delay time is approximately 3.5 minutes; The injection rate was found to exert different effects on the bottom-hole temperature and pressure. As the injection rate increases, the bottom-hole temperature decreases. The bottom-hole pressure varies in a parabolic manner with the injection rate, and the critical injection rate of 1.5 m³/min is the turning point at which the bottom-hole pressure transitions from increasing to decreasing; The pressure ramping rate was observed to rise with an increase in the injection rate. Nevertheless, an excessively high injection rate leads to a reduction in the bottom-hole pressure, making it arduous for the formation to fracture. When the pumping displacement exceeds 4.3 m³/min, the frictional pressure loss increases significantly. Therefore, the optimal injection rate should be regulated within the range of 1.5-4.3 m³/min. Through this theoretical research, novel supporting theories have been provided for the rock fracture initiation pressure model of liquid carbon dioxide fracturing, which plays a supporting role in the safety assessment of carbon dioxide fracturing.