Membrane Bioreactor (MBR) Flux, TMP & Fouling Calculator

Permeate flux through a microfiltration or ultrafiltration membrane is governed by Darcy's Law for flow through porous media, adapted to the resistance-in-series framework:

Where:

• $J$: Permeate flux ($m^3/(m^2 \cdot s)$ or $\text{LMH} = L/(m^2 \cdot h)$).
• $\Delta P_{TMP}$: Transmembrane Pressure ($Pa$ or $kPa$), defined as average feed/sludge hydrostatic pressure minus permeate suction pressure.
• $\mu(T)$: Dynamic water viscosity ($Pa \cdot s$), which increases exponentially as wastewater cools in winter.
• $R_m$: Intrinsic clean membrane resistance ($m^{-1}$), dictated by pore size, material morphology, and porosity.
• $R_c$: Dynamic cake layer resistance ($m^{-1}$), reversible solids deposited on the membrane surface, controlled by air scour.
• $R_p$: Pore constriction & adsorption resistance ($m^{-1}$), irreversible internal fouling requiring chemical Cleaning-in-Place (CIP).

Temperature Viscosity Normalization ($J_{20}$)

Because cold water is more viscous, operating at the same physical flux in winter requires much higher suction vacuum (TMP). To compare membrane health independent of seasonal thermal swings, flux is standardized to 20°C:

Air Scour Aeration Demand ($SAD_m$ & $SAD_p$)

Coarse bubble aeration is injected directly beneath membrane cassettes to induce intense shear stress and liquid vortex shedding along the fiber surface, scouring off accumulating biomass cake:

• Specific Aeration per Membrane Area ($SAD_m$): $Q_{air} = SAD_m \times A_{membrane} \quad [\text{Nm}^3/h]$. Typical range: $0.15 - 0.35 \text{ Nm}^3/(h \cdot m^2)$.
• Specific Aeration per Permeate Volume ($SAD_p$): $SAD_p = \frac{Q_{air}}{Q_{permeate}} \quad [\text{Nm}^3 \text{ air} / m^3 \text{ permeate}]$. Modern cyclic aeration systems achieve $SAD_p$ below 10.