An industry producing $k-$fertilizers is recycling process waters containing a $KCl$ content

of $3\mathrm{.}6\%($by mass$)$ by reverse osmosis, using $37m^2$ Filmtec SW$30-$HREL$400$ spiral

modules. The concentration of permeate in $KCl$ is $0\mathrm{.}025\%($by mass$),$ the pressures of

the feed, rejection and permeate currents are $8300,8100$ and $110$kPa respectively, the

feed flow is $100\frac{m^3}{d}$ and the recovery factor of Water is $44\%.$ The module has been

characterized with a mass transfer coefficient in the $KCl$ stream of ${10}^{-4}\frac{m}{s}.$

Calculate:

a$)KCl$ rejection $(r_s)$ and the $KCl$ concentration on the retentate $(C_{sr})$

b$)$ The value of concentration by polarization on the membrane surface $(gK\frac{K}{L})$

c$)$ Water flux $(mol\frac{s}{m^2}*s)$ considering the polarization by concentration

phenomenon

d$)$ Calculate what will be the net hydraulic pressure net $=P-($bar$)$

e$)$ Calculate the water permeance $($ Awmo$\frac{l}{s}*m^2$ bar$),$ the $KCl$ flux

and $KCl$ permeance $($Bs $\frac{m^3}{m^2}*s).$

Data: The osmotic pressure can be determined by the expression $(Pa)=7,722*T*Cl$

where $T[K]$ and $Cl[$moles ions $\frac{?}{m^3}].$