Modeling the height of high-pressure ebullated beds based on superficial energy

•Developed a model based on minimum energy for high-pressure ebullated beds.•The parameters of the model obtained in this work are analyzed for various energy.•The predictions of bed height are well in agreement with experiments.

Since the prediction of the height of fluidized beds, especially in high pressure multi-phase fluidized beds, depends mostly on empirical models in the reported literature, an attempt is preliminarily made in this work to develop a semi-empirical model for the behavior of bed expansion or contraction in high-pressure ebullated beds based on minimum energy principle. The model principally takes kinetic energy, potential energy, and energy balance resulted from interaction between different phases in the system into account. Reported experimental data are utilized to validate the model, and the obtained values of the model parameters basically reflect the contribution of kinetic energy, potential energy and surface interaction energy to the height of bed. A reasonably good agreement between the experimental data and the calculated height of ebullated bed is subsequently achieved, demonstrating that the model can be satisfactorily endowed with predictive capability within the reported experimental ranges.