Abstract: Based on the basic law of thermodynamics, the law of the entropy increase and the law of minimum energy, the transformation of macroscopic kinetic energy, potential energy, and internal energy of a system was considered, and the quantitative relationship between gas holdup of up-flow gas-liquid-solid three-phase bed and system conditions such as fluid velocity, viscosity and catalyst physical properties was established. On the basis of universal laws of thermodynamics, the concept of “variation order” of related physical quantity was proposed, cold model tests were carried out under different operating conditions and different catalyst loading schemes, and the effects of physical properties of fluid and catalyst on gas holdup was systematically studied. The established gas holdup model was used to fit the experimental data under various conditions and various catalysts loading schemes. The average relative deviation of the model was less than 5%, the parameters were reasonable and could well reflect the effects of gas-liquid-solid properties on gas holdup. The establishment of an excellent model to describe gas holdup in a gas-liquid-solid three-phase up-flow fixed bed reactor is of great significance to the study of up-flow hydrogenation process.

Key words: gas holdup, up-flow reactor, variation order, model, gas-liquid-solid properties