Generalization and Expansion of the Hermia Model for a Better Understanding of Membrane Fouling

One of the most broadly used models for membrane fouling is the Hermia model (HM), which separates this phenomenon into four blocking mechanisms, each with an associated parameter n. The original model is given by an Ordinary Differential Equation (ODE) dependent on n. This ODE is solved only for these four values of n, which limits the effectiveness of the model when adjusted to experimental data. This paper aims extend the original Hermia model to new values of n by slightly increasing the complexity of the HM while keeping it as simple as possible. The extended Hermia model (EHM) is given by a power law for any n ≠ 2 and by an exponential function at n = 2. Analytical expressions for the fouling layer thickness and the accumulated volume are also obtained. To better test the model, we perform model fitting of the EHM and compare its performance to the original four pore-blocking mechanisms in six micro- and ultrafiltration examples. In all examples, the EHM performs consistently better than the four original pore-blocking mechanisms. Changes in the blocking mechanisms concerning transmembrane pressure (TMP), crossflow rate (CFR), crossflow velocity (CFV), membrane composition, and pretreatments are also discussed.