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Abstract This study investigated the effects of various types of paddles on the oxygen gas holdup in different regions at a temperature of 403 K, oxygen partial pressure of 0.6 MPa, and agitation rate of 500 r/min. The results illustrate that the application of a self-priming agitator can significantly promote a bubble holdup in a solution. Furthermore, experiments determining the effects of the agitation rate, temperature, and oxygen partial pressure on the gas holdup were carried out, where the gas holdup increased from 0.03% to 1.59% with an agitation rate of 200 to 700 r/min, from 0.83% to 1.06% with a temperature of 363 to 423 K, and from 0.50% to 1.27% with an oxygen pressure of 0.1 to 0.8 MPa. The kinetics of oxygen pressure acid leaching of marmatite using various types of paddles were also studied. The activation energies of Zn leaching when using various types of paddles were determined to be 53.23, 56.30, 59.76, and 67.58 kJ mol−1, which shows that the processes were controlled through the surface chemical reactions. Based on a comparison of the activation energies, the self-priming type agitator was shown to be optimal. Finally, a similar criteria relationship of a self-priming agitator was established using the principle of homogeneity and Buckingham's theorem. Comprehensively, an empirical equation of a gas holdup was deduced based on experimental data and a similarity theory, where the criterion equation was determined to be ε = 7.20 × 10−10 n 2.63 T -1.52 P g 0.45. It can be seen from the formula that the agitation rate has the greatest impact on the gas holdup during the pressure leaching process using a self-priming agitator. Highlights • A transparent quartz autoclave and various types of paddle were used to study the gas holdup. • The gas holdup was studied under the condition of high temperature and high pressure. • The high-speed camera was used to investigate the bubble behavior at different condition. • The application of self-priming agitator could significantly promote bubble holdup and kinetics in solution. • The similar criteria relationship of self-priming agitator was established by Homogeneous Principle and Buckingham's theorem. [ABSTRACT FROM AUTHOR]