Multiple regression modelling of bed expansion and backwashing pressure drop in pressurised porous media filters for microirrigation and comparison with semi-analytical models

Abstract Although the expansion of the fluidised bed is a key parameter for defining the optimal working condition of a pressurised porous media filter for microirrigation operating in backwashing mode, there are no ready to use tools available at the user level to calculate it. Complex machine learning models have previously been applied to predict the height of the expanded bed, but simpler methods are required to promote the practical use of bed expansion calculations. Therefore, the capabilities of simpler and easier to both implement and generalise multiple linear regression (MLR) models to forecast both the height of the fluidised bed and the backwashing filter pressure drop were investigated, with input variables being the porous medium type, the initial packed bed height, the underdrain design, and the superficial velocity. In addition, semi-analytical equations and a simplified computational fluid dynamics (CFD) model for calculating the expanded bed height as a function of porous medium properties were tested. The exponential model provided the best fit ( $$\:{R}^{2}\:$$ = 0.971) for the pressure drop, while the power model the best fit ( $$\:{R}^{2}$$ = 0.954) for the bed expansion. A simple semi-analytical expression reproduced the observed trend, but less efficiently than the MLR models. In terms of energy consumption, the results highlighted the relevance of improving the underdrain design, as well as avoiding operation at the point of maximum hydrodynamic shear stress, despite being the optimum condition for particle removal. Bed expansion values of 30–40% represented a reasonable compromise between power consumption and shear stress level.