On the asymptotic flux of ultrapermeable seawater reverse osmosis membranes due to concentration polarisation
Section snippets
Asymptotic flux, as compared to asymptotic energy consumption
Even with infinitely permeable reverse osmosis membranes, there are finite limits on the flux that can be achieved in the future. We quantify the asymptotic limit on flux imposed by concentration polarisation – the phenomenon whereby solvent flux through the membrane results in the elevation of solute concentration, and hence osmotic pressure, at the membrane surface. We show that the limiting flux depends linearly on the mass transfer coefficient in the feed water channel and also in a
Asymptotic limits on flux at infinitesimal (or low) recovery
We seek to understand why concentration polarisation imposes a finite limit on flux. One way to do so is to combine a solution-diffusion model [9] for membrane permeability and a stagnant film model1 [11] for concentration polarisation, and to do this for infinitesimal recovery – whereby the quantity of product water removed from the feed is small enough to consider the feed osmotic pressure constant. For
Asymptotic flux of a single stage seawater reverse osmosis process
A common implementation of seawater reverse osmosis systems today is in a single stage configuration where the recovery is roughly in the range of 30–50% (Fig. 5a).3 We now derive an expression for the asymptotic flux in such systems, which is somewhat different
Mass transfer coefficients for UPMs
Fane et al. [8] have pointed out the importance of limiting the modified (or transverse) Péclet number, , in order to control concentration polarisation for UPMs. The nondimensionalizations of the preceding section may be used to isolate this variable as a function of other parameters. Specifically, Eq. (15) can be written as [cf. Eq. (17)]Similarly, Eq. (23) may be writtenBoth results show that for any given feed
Implications and limitations
There are several factors that can limit increases in the operating flux of RO, including concentration polarisation, fouling, scaling by sparingly soluble salts (whether compounded by effects of concentration polarisation or not), and increased viscous pressure in the feed channel due to increased flow rates. The purpose of this note is provide an explanation for the flux asymptote that arises due to concentration polarisation when employing ultrapermeable membranes. The simple formulas
Acknowledgements
The authors would like to thank Dr. Gregory P. Thiel for insightful discussion of this note.
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