Prediction of membrane flux in membrane bioreactors through dimensionless analysis and correlations

Abstract

Membrane flux (J, m³/m²·s) is a key design and operation parameter of membrane bioreactor (MBR) wastewater treatment plants. In this study, the impact of mixed liquor properties (mixed liquor density (ρ, kg/m³), mixed liquor dynamic viscosity (μ_s, kg/m.s)), hydrodynamic conditions (mixed liquor cross-flow velocity V_m in tubular MBRs or air-mixed liquor two-phase cross-low velocity V_am in the riser zone of the filtration tank of submerged MBRs, generalized as V (m/s)), trans-membrane pressure ΔP (Pa), membrane module geometry (tubular membrane channel diameter (D_t) or the hydraulic diameter (D_s) of the submerged bioreactor filtration riser zone, generalized as D (m)), and membrane filtration characteristics (total membrane filtration resistance (R_t, 1/m)) on membrane flux J in MBRs was analyzed and investigated using the dimensionless analysis and correlation approach. Four dimensionless groups, the ratio of membrane flux J to mixed liquor or air-mixed liquor generalized cross-flow velocity V (J/V), Reynolds number of mixed liquor (ρVD/μ_s), Euler number of mixed liquor (ΔP/(ρV²), and a new dimensionless group, fouling number of mixed liquor, (μ_sR_t/(ρV)), were derived to correlate the impact of these parameters on membrane flux J in MBRs as seen in Equation (i):(i)J/V = m(ρVD/μ_s)^a (ΔP/(ρV²))^b (μ_sR_t/(ρV))^c

Based on experimental data of MBRs from the literature, the coefficients (m, a, b, c) in Equation (i) were calibrated. The J/V values predicted using Equation (i) are in reasonably good agreement with the experimental J/V values from the literature with a typical relative error smaller than 20 % in most cases. Sensitivity analysis showed that trans-membrane pressure, ΔP, and total membrane filtration resistance, R_t, are the two most important parameters affecting the prediction of the derived dimensionless correlations (J/V) for both side-stream tubular MBRs and submerged MBRs. These new dimensionless group correlations provide a new mathematical tool for representing in-depth insights of how mixed liquor properties, hydrodynamic conditions, membrane module geometry, and total membrane filtration characteristics affect membrane flux J in MBRs. They can then be used to predict the membrane performance and to guide the optimal design and operation of MBR plants.