PARAMETER ESTIMATION AND MODELING OF SPIRAL-WOUND

It may be noted that when σ= 1, the SK model mathematically is reduced to a two-parameter model such as the solution-diffusion model. The membrane characteristics used for simulation are given in Appendix B. The effect of the variation of the feed parameters and σ on the permeate flow rate and concentration are shown in Figs. 5-8. For simulation purposes the membrane hydrodynamic permeability and the solute permeability are taken as 20.8x10 -13 m3/m2.s.Pa and 1.11xl0 -7 m*s respectively.
In Graph 1, the permeate flow rate is seen to decrease with increasing feed concentration. This is because the osmotic pressure increases with increasing feed concentration. This reduces the driving force for the mass transfer, thus leading to lower volumetric flux. The value of the permeate flow rate can also be seen to be increasing as σ decreases. This is along the expected lines as lower σ values imply lower contribution of the osmotic pressure in the flux, Eq. (3).
From Graph 2 the value of (Cpt/Cf) x 100 falls with an increasing feed flow rate from 5 x 10-5 to 20 x 10 -5 m3/s, and after this the (Cp,/Cf) x 100 values almost remain constant when the feed flow rate is increased beyond 20x10-5 m3/s. This is because, as the velocity in feed channel is increased, the mass transfer coefficient also increases and thus the concentration polarization decreases, leading to lower permeate concentrations. But at a higher feed flow rate the concentration polarization becomes negligible, and therefore the permeate concentration does not change noticeably. The value of (Cpt/Cf) × 100 changes quite noticeably with respect to σ. This is because for lower σ values the membrane is leaky and allows more solute to pass through it compared to tight membranes where σ values are


Graph 1: Permeate flow rate Vs Feed concentration



Graph 2: Ratio of permeate to feed concentration Vs. Feed flowrate

closer to 1. At a feed flow rate of 5x 10-5 m3/s, the differences in the (Cpt/Cf) × 100 values for σ = 1 and σ = 0.9 can be almost 400%.
Since the driving force for mass transfer increases for higher feed pressures, the permeate flow rate is seen to increase with increasing feed pressure, as shown in Graph 3. However, the effect on permeate flow rate with respect to σ is not significant. On the other hand, the value of (Cpt/Cf)xl00 decreases significantly as the feed pressure is increased up to 20 bar, and after that the permeate concentration decreases marginally with increasing feed pressure for σ values up to 0.98 where as for lower values of σ , the permeate concentrations


Graph 3: Permeate flow rate Vs. Feed pressure

actually increase with increasing feed pressures. From the above results and discussion, the role of the reflection coefficient (σ) can be investigated.
It is noticed that for membranes with a higher reflection coefficient, both the permeate flow rates the permeate concentrations are lower. As the value of σ decreases, the permeate concentration goes up and the permeate flow rates are also increased.


Graph 4: Ratio of permeate to feed concentration Vs. Feed pressure

In conclusion, it can be said that the membranes with high reflection coefficients have lower permeabilities but higher selectivities.