Estimating the parameters of a two-phase sludge filtration model

Abstract

Numerous filtering models contain constants or parameters that are difficult to measure but can be determined through model calibration and other methods. Using linear regression techniques, models predicting the filtration parameters of a two-phase exponential filtration model were built and calibrated. These parameters include initial filtrate flow volume V1, slow phase filtrate V2, constants for the first phase k1, the slow phase k2, and the transition phase k3. On a total of 27 distinct experimental setups with varied applied pressure, solids content, and slurry volume, filtration experiments were conducted. The experimental data were employed to calibrate the two-phase model, and the resulting filtering parameters were retrieved and summarized. It was considered that the beginning and final stages of filtration were a function of the pressure, solids concentration, slurry volume, and the interplay of the variables. On the resultant linear model, dimension reduction and recalibration were performed to provide an improved model. Before and after dimension reduction, the linear model's R2 and R2adj values for V1 were 0.744 and 0.649, and 0.743 and 0.666, respectively. Before and after dimension reduction, the linear model for V2 yielded R2 and R2adj values of 0.961 and 0.947, and 0.961 and 0.953, respectively. The linear model for the rate constants k1, k2, and k3 showed respective R2 values of 0.631, 0.978, and 0.825. The estimated parameters were used in the two-phase model to predict measured data, and it compared favourably with R2 value ranging from 0.74 to 0.99.