B$2.$ Sea water typically contains $0\mathrm{.}6M$ of dissolved salt $($mostly NaCl $).$

Fresh water, on the other hand, contains less than $1g{L}^{-1}$ of salt $($or

approximately $0\mathrm{.}017M$ of NaCl equivalent$).$

$($a$)$ If a single stage reverse osmosis $($RO$)$ unit is to be used to

produce fresh water from sea water, what is the minimum hydraulic

pressure difference required for the process? State any

assumptions made in the calculation.

$[15$ marks$]$

$($b$)$ A reverse osmosis unit requires a hydraulic pressure difference of

$50$ bar to reduce the salt content of sea water to $1g{L}^{-1}.$ Under this

operating condition, the flux of fresh water achieved is $80L{m}^{-2}{h}^{-1}.$

Assuming no mass transfer resistance, what is the permeance of

the RO membrane for water and salt, respectively?

$[10$ marks$]$

$($c$)$ The water permeance of the unit as specified by the manufacturer

is $4\mathrm{.}5L{m}^{-2}{h}^{-1}$ bar ${?}^{-1}.$ Assuming any difference between the

specified permeance and the permeance calculated in $($b$)$ arises

from mass transfer resistance on the feed side,

i$)$ Estimate the concentration of the salt near the surface of the

membrane on the feed side.

$[9$ marks$]$

ii$)$ Calculate the actual rejection coefficient and the polarisation

modulus. Is concentration polarisation significant?

iii$)$ Estimate the mass transfer coefficient.

$[7$ marks$]$

$[9$ marks$]$

Additional information:

You may estimate the osmotic pressure of a solution using the

following equation:

$=22\mathrm{.}6{\displaystyle \underset{?}{\overset{?}{}}}{c}_i$

${\displaystyle \underset{?}{\overset{?}{}}}{c}_i$ is the total molar concentration of all dissolved ions and non$-$ionic

molecules; and the osmotic pressure has the unit of bar.