In membrane filtration processes, the decline in treatment performance caused by membrane fouling remains an unresolved challenge. Several fouling indices that can be evaluated using only a small amount of spot filtration data have been proposed, including the Silt Density Index (SDI), Modified Fouling Index (MFI), Fouling Mechanism Index (FMI), and Fouling Degree Index (FDI). All of these indices are evaluated based on the decrease in filtration rate during constant-pressure filtration tests.

In this study, we propose a Pressure-based Fouling Index (PFI) as a fouling indicator applicable to constant-rate filtration, derived from changes in filtration pressure. PFI evaluates membrane fouling from the variation in filtration pressure over a defined period and is expressed as PFI = 100(1 ̶ p_i/p_f)/t_t. Here, p_i is the pressure increase after filtering for t₀ = 5 min starting from the initial pressure p₀, and p_f is the pressure increase after filtering for the same duration t₀, but measured following an elapsed time of t_t = 15 min from the start of the test. Using the blocking filtration law dp/dv = kpⁿ, the filtration pressure p can be expressed as p = {p₀^1-n + k(1 ̶ n)(dv/dt)t}^1/(1-n). Accordingly, p_i = {p₀^1-n + k(1 ̶ n)(dv/dt)t₀}^1/(1-n) ̶ p₀, p_f = {p₀^1-n + k(1 ̶ n)(dv/dt)(t_t + t₀)}^1/(1-n) ̶ {p₀^1-n + k(1 ̶ n)(dv/dt)t_t}^1/(1-n), from which the relationship between PFI and the blocking indices n and k can be derived.

Sodium alginate, a polysaccharide, was used as the model foulant. Membrane filtration tests were conducted at a constant rate (dv/dt), and the time-dependent change in filtration pressure p was monitored. The blocking index n was found to depend on the change in membrane pore structure associated with fouling, and it remained [...]