Elsevier

Journal of Membrane Science

Volume 520, 15 December 2016, Pages 560-565
Journal of Membrane Science

On the asymptotic flux of ultrapermeable seawater reverse osmosis membranes due to concentration polarisation

https://doi.org/10.1016/j.memsci.2016.07.028Get rights and content

Highlights

  • Concentration polarisation imposes a finite limit on RO flux.

  • Analytical expressions are provided for single stage and batch RO.

  • For seawater, the limit is four times typical flux today.

  • For brackish water, the limit is twenty times typical flux today.

Abstract

Just as thermodynamic considerations impose a finite limit on the energy requirements of reverse osmosis, concentration polarisation imposes a finite limit on flux, or equivalently, on system size. In the limit of infinite permeability, we show the limiting flux to be linearly dependent on the mass transfer coefficient and show this to be true for low recovery systems just as well as moderate and high recovery single stage and batch reverse osmosis system designs. At low recovery, the limiting flux depends on the logarithm of the ratio of hydraulic to bulk osmotic pressure and at moderate or higher recovery, the relationship with this pressure ratio is a little more complex but nonetheless can be expressed as an explicit analytical formula. For a single stage seawater reverse osmosis system operating at a hydraulic pressure, recovery ratio, and value of mass transfer coefficient that are typical today, the flux asymptote is roughly 60 L m−2 h−1 – roughly four times where average fluxes in seawater reverse osmosis systems currently stand.

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, J*=J/k, 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)]J(RR)k=(AmπFk)[PπFeJ(RR)/k1RR].Similarly, Eq. (23) may be writtenJbk=(AmπFk)[RRPπF+eJb/kln(1RR)]Both 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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