what is the name of the flows out of the system (on the feed side of the membrane, and on the other side?)
on the feed side: name depends on what you’re interested in
retentate
reject
concentrate
residue
on the other side: permeate
what is the principal behind membrane separations?
separation of gaseous or liquid mixtures using a semi-permeable membrane (selective barrier)
NOT eqm staged process
transport of species through the membrane involves what types of driving forces?
gradients of pressure or conc
three physical features of an ideal membrane
thin
no holes or weak spots
structurally strong to withstand P drops
what is an asymmetric or composite membrane?
thin membrane with highly porous thicker layer to add support for pressure drops but add little resistance to flow (usually porous ceramic metals/polymers)
name /describe three main configurations of membrane separators
flat sheets
spiral (most common)
hollow fibres
define volume concentration ratio VCR
VCR = V(in) / V(retentate)
ie. vol in and vol out on the same side, not through membrane
Because for a membrane not permeable to the solute, the only way the conc is changing is by solvent passing membrane, which is why the volume retained is an indication of concentration.
describe a semi batch filtration set up
retentate is recirculated (goes to storing tank), feed comes out of tank back into separator
BUT conc of solute in feed increases over time
describe a fed batch filtration set up
same as semi batch, membrane separator where retentate goes to tank, but fresh feed is continually added to the tank
extends the number of times the retentate is recirculated
describe the setup of a continuous membrane separator system
MOST COMMON APPROACH INDUSTRIALLY
tank and separator.
fresh feed into tank, vol FR of F0
some of the retentate is recycled back into the tank, some is removed, F(R)
what is the volume concentration ratio VCR for a continuous membrane separator system in terms of molar flow rates?
VCR = F0 / F(R) = F(R) + F(P) / F(R)
where F0 is the vol feed rate (added to tank)
and F(R) is the rate at which retentate is removed from the separator (rest is recycled)
F(P) is rate permeate is removed
expression for VOLUMETRIC flux of permeate, J, through the membrane
J = Q(P) / A
= N / π(m)
where Q(P) is the volumetric FR of permeate, and this is CHANGING
A is transfer area
N is molar flux, divide by molar density for volumetric flux
define molar flux of permeate, N(P)
N(P) = Q(P) * π(m) / A
Q(P): vol FR permeate
π(m): molar density of permeate
in liquid systems, total molar conc C(T) is used instead of π(m)
define selectivity for a membrane separator
πΌ = Km,A / Km,B
ie. the ratio of permeabilities of the membrane to the two components
in ultrafiltration and reverse osmosis, selectivity is expressed as a solute retention fraction, R:
Retention R = C(f) - C(P) / C(f)
this is the APPARENT retention fraction, based on conc bulk in feed C(f)
true retention fraction, R(true)
for ultrafiltration/reverse osmosis
R(true) = C(w) - C(P) / C(w)
instead of bulk feed conditions, take conc at wall, C(w)
what does the cut off molecular weight describe?
for porous membranes
the RMM of solutes at which 90% rejection by the membrane occurs
(does not tell you about the shape of membrane “holes” etc)
define the recovery (and the symbol!)
recovery, S = Q(P) / Q(1)
where Q(P) is vol FR on permeate side
Q(1) is the INLET feed fr
formally, what is the driving force for the mass transfer in a membrane separator?
how is this approximated for liquids and gases?
difference in fugacity is the driving force
liquids: approximate as βC of each component
gas: βP for each component
on the feed side, which is greater out of C(f) bulk and C(w) wall for some species A?
C(w) < C(f) in the absence of concentration polarisation.
Due to feed side film transfer resistance
relationship between permeability and resistance for a membrane
resistance = 1 / K
inverses of each other.
the mass transfer of some species A across a membrane can be approximated as a series of resistances. what are they for a symmetric membrane?
from the feed side:
C(w) < C(f), decreases over the feed film resistance
Km, some film permeability
Conc increases to bulk C(P) over the permeate film resistance
expression for the overall resistance for the mass transfer of species A across a symmetric membrane
1/K(O,j) = 1/k(f,j) + 1/K(m,j) + 1/k(p,j)
K(O,j) is the overall permeability of the system for component j
other k: feed film, membrane and permeate film coefficients
in GAS SEPARATION, what can the overall permeability, K(O,j) be approximated as?
the membrane coefficient dominates.
film mass resistances ignored.
K(O,j) = K(m,j)
