Prediction of the bed expansion of a liquid fluidized bed bioreactor applied to wastewater treatment and biogas production

The high potential of water treatment and biogas production systems using liquid fluidization is still underexplored. The design of this equipment is usually done using the simple Richardson-Zaki equation for bed expansion predictions, which is powerful but overlooks the interactions between fluid and particles. In this work, an alternative method based on a force balance on the bed and drag correlations to estimate the bed porosity was proposed. The accuracy of the methods was assessed by comparing bed porosity estimations with experiments carried out in a wide range of regimes (Reynolds numbers between 498 and 18664), using 7 different particles with various diameters (2.66 to 6.37 mm) and densities (1022 to 3585 kg/m3). On average, the fitting between the Richardson-Zaki equation and the experimental results was improved by 60% when the wall effects were considered. The alternative approach using the drag correlations showed promising results, presenting a coefficient of determination higher than 80% for all particles, and better precision in 4 out of the 7 particles compared to Richardson-Zaki. The results show that, in general, both the Richardson-Zaki equation and the drag correlation approach can be used to predict the liquid fluidized bed expansion. However, the proposed approach using drag correlations showed more reliable results, especially when the Rong drag model was applied, with an average coefficient of determination of 0.92. Comparisons with other results in the literature confirm the extent and the scalability of the method. The use of the proposed method to estimate the liquid fluidized bed expansion allows for easier and safer applicability of the technology in areas such as wastewater treatment and biogas production.