Scale up validation tests for Buckingham Pi theorem applied to leaf test experiments for iron ore slurry

Abstract

Bench tests were conducted on ore slurry filtration using the leaf test method, varying scales, pressures, and water/solids ratios. These results were compared with analytical outcomes derived from applying the dimensionless Buckingham pi method to the general equation of slurry filtration with incompressible cakes under constant pressure. The aim was to validate the tests by corroborating experimental findings with calculated parameters for scale-up purposes. Vacuum pressure was employed to facilitate slurry dewatering, forming a cake comprising solids from the slurry. This cake’s thickness evolved over time, introducing specific resistivity that impeded filtering efficiency. Parameters such as cake resistance and filter media resistance were computed. Filtrate volume was measured over time to determine the filtration rate. These values were then adjusted using factors obtained through dimensional analysis. These factors facilitated comparisons to validate the feasibility of employing the Buckingham pi method for predicting slurry filtration results at larger scales. The results indicated lower errors when analyzing the filtrate rate over time with a solids/water ratio of 20/80%. When evaluating cake resistance, the method yielded lower errors at a ratio of 70/30%, while results for medium resistance were inconclusive. It’s important to consider the ratio and associated errors when predicting the behavior of an industrial filter based on bench test results, aiming to achieve theoretical scaled filtration rates and cake resistances. However, it’s not advisable to rely on the Buckingham pi method for scale-up purposes when evaluating medium resistance.

Keywords:

• Slurry
• filtration
• leaf test
• Buckingham Pi
• scale up

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported in part by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - Brasil (CAPES) - Finance Code 001. The work was also financing by Pontifícia Universidade Católica de Minas Gerais - PUC Minas, Fundação de Amparo à Pesquisa do Estado de Minas Gerais - FAPEMIG (grants PPM-00650-18 and 11231), and Conselho Nacional de Desenvolvimento Científico e Tecnológico - CNPq (grant 302175/2022-9).