Solution Diffusion Medel in Membrane Technology

1. SOLUTION-DIFFUSION (SD)
MODEL
- ADIL AGLODIYA
-SATISH MOVALIYA

2. • Its one of the earliest models proposed for RO
• The model is based on the principle of membrane
diffusion through a dense layer
• The SD model can be written as:
Jw = [(Dwm Cwm Vm /RTδ)*(ΔP-ΔП)] --------------(1)
= Aw (ΔP-ΔП)--------------------------(2)
Where ,
Dwm = membrane water diffusivity (m2/s)
Cwm = membrane water concentration (kg solvent / m3)
Vm = molar volume of solvent
Aw = water permeability (constant)

3. ΔP = P1-P2 is the hydrostatic pressure difference
with P1 exerted on feed and P2 on product
solution
ΔП = П1-П2 is the difference of osmotic pressure of
the feed solution to that of product solution
• In case of dilute organics with negligible
osmotic pressure this model fails to predict flux
behavior

4. • Above fig a schematic diagram of solvent and solute
transport in reverse osmosis process, where c1 and c2
are the feed side and permeate side solute
concentration

5. • For diffusion of solute through membrane the flux
equation can be written as:
Js= [(Dsm Ks /δ)*(c1-c2)]--------------------(3)
= As (c1-c2)---------------------------------(4)
Where,
As = Dsm Ks /δ
Js = solute flux (kg solvent / s m2)
Dsm = Diffusivity of solute in membrane (m2/s)
Ks = distribution coefficient
As = solute permeability constant (m/s)

6. • Under steady state condition, the solute diffusing
through the membrane must be equal to the amount
of solute leaving the permeate solution
Js = (Jw c2)/cw2 ------------------------(5)
where, cw2 is the concentration of solvent in permeate
stream (kg solvent/m3)
• Permeability constants for membrane are
determined experimentally for a particular type of
membrane.
• For cellulose acetate membranes, water permeability
constants = 1×10-4 to 5×10-4 kg solvent/s.m2.atm

7. • For the solute permeability constants As of
cellulose acetate membranes, some relative
typical values are as follows:
NaCl = 4 × 10-7
BaCl2 = 1.6 × 10-7
MgCl2 = 2.2 × 10-7
CaCl2 = 2.4 ×10-7

8. SOLUTE REJECTION
• This is defined as the fraction of solute remaining in
the feed stream.
• In RO solute rejection, R is defined as the ratio of
concentration difference of the solute across the
membrane to the bulk concentration of solute on the
feed side.
• R = (c1-c2)/c1 --------------------------(6)
• = 1- (c2/c1) ----------------------------(7)
Substituting eqn (1) and (3) into eqn (5)
[(Dsm Ks /δ)*(c1-c2)] = [(Dwm Cwm Vm /RTδ)*(ΔP-ΔП)]*(c2/cw2)
----------(8)

9. • Above eqn can be solved for c2 and c1, then value
can be substitued in eqn (6)
• Where B (atm-1)= (Dwm Cwm Vm )/ (Dsm Ks cw2 RT)
B must be determine experimentally for each type of
membrane.