The MBR Book: Principles and Applications of Membrane

2.1.4 Membrane process operation
2.1.4.1 Flux, pressure, resistance and permeability
The key elements of any membrane process relate to the influence of the following
parameters on the overall permeate flux:
(a) the membrane resistance,
(b) the operational driving force per unit membrane area,
(c) the hydrodynamic conditions at the membrane:liquid interface,
(d) the fouling and subsequent cleaning of the membrane surface.
The flux (normally denoted J) is the quantity of material passing through a unit area
of membrane per unit time. This means that it takes SI units of m 3 /m 2 /s, or simply
ms �1 , and is occasionally referred to as the permeate or filtration velocity. Other non-
SI units used are litres per m 2 per hour (or LMH) and m/day, which tend to give more
accessible numbers: MBRs generally operate at fluxes between 10 and 100 LMH. The
flux relates directly to the driving force (i.e. the TMP for conventional MBRs) and the
total hydraulic resistance offered by the membrane and the interfacial region adjacent
to it.
Although for conventional biomass separation MBRs the driving force for the
process is the TMP, for extractive or diffusive MBRs (Sections 2.3.2–2.3.3) it is respectively
the concentration or partial pressure gradient. Whereas with conventional
pressure-driven MBRs the permeate is the purified product, for extractive MBRs the
contaminants are removed from the water across the membrane under the influence
of a concentration gradient and are subsequently biologically treated, the
retentate forming the purified product. For diffusive bioreactors neither water nor
contaminants permeate the membrane: in this case the membrane is used to transport
a gas into the bioreactor.
Resistance R (/m) and permeability K (m/(s bar), or LMH/bar in non-SI units) are
inversely related. The resistance is given by:
P
R �
J
�
h
Fundamentals 29
(2.1)
where � is the viscosity (kg/(m s 2 )) and �P (Pa) the pressure drop, and can refer to
either the TMP (�P m Pa/bar in non-SI units) or individual components which contribute
to the pressure drop. Permeability is normally quoted as the ratio of flux to
TMP (hence J/�P m), the most convenient units being LMH/bar, and sometimes corrected
for temperature impacts on viscosity.
The resistance R includes a number of components, namely:
(a) the membrane resistance,
(b) the resistance of the fouling layer (adsorbed onto the membrane surface),
(c) the resistance offered by the membrane:solution interfacial region.