Water tools

Membrane resistance in series: clean, reversible and irreversible fouling

Flux over transmembrane pressure is a resistance. Measured at three moments, new, just after cleaning and just before cleaning, it separates the membrane itself from the fouling a clean removes and the fouling it does not.

Clean-water flux of the new membraneL/m²·h

At transmembrane pressurebar

At temperature°C

Flux just after chemical cleaningL/m²·h

At transmembrane pressurebar

At temperature°C

Flux just before chemical cleaningL/m²·h

At transmembrane pressurebar

At temperature°C

Resistances

Clean membrane resistance

0.3810¹² m⁻¹

Irreversible fouling

1.3810¹² m⁻¹

Chemically reversible fouling

2.9510¹² m⁻¹

Total before cleaning

4.7110¹² m⁻¹

Membrane share of total

Irreversible share

29%

Reversible share

63%

Permeability

Specific flux, new membrane at 20 °C

944L/m²·h·bar

Specific flux, before cleaning at 20 °C

76L/m²·h·bar

How it works

Darcy form: flux over transmembrane pressure and viscosity is a resistance, and resistances add in series:

J = \frac{Δ P}{μ κ} κ = \frac{Δ P}{μ J} κ_{t o t a l} = κ_{m} + κ_{i r r} + κ_{r e v}

(1)

The new membrane with clean water gives κ_m; the state just after chemical cleaning adds the irreversible part; the state just before cleaning adds the chemically reversible part. Fluxes are first normalised to 20 °C:

J_{20} = J {1.03}^{20 - T}

(2)

where

$J$: flux, m³/m²·s
$Δ P$: transmembrane pressure, Pa
$μ$: water viscosity, kg/m·s
$κ$: resistance coefficient, 1/m
$κ_{m}$: clean membrane resistance
$κ_{i r r}$: irreversible fouling resistance, left after chemical cleaning
$κ_{r e v}$: chemically reversible fouling resistance
$J_{20}$: flux normalised to 20 °C, L/m²·h
$T$: measured temperature, °C

Full-scale plants run at constant flux, so fouling shows as rising TMP; the resistance view makes the trend comparable across temperatures. The 1.03 factor corrects viscosity only and is accurate within 5% between 1 and 28 °C. The same decomposition applies to MBR membranes, where the cake and pore-blocking terms can be isolated with a backwash step.

Membrane resistance in series: clean, reversible and irreversible fouling

How it works

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