First, solve for the mass transfer coefficient using the equation:

,

where

is the mass transfer coefficient,

is the rotational speed of the stirring bar (rad/s),

is the tank diameter (m),

is kinematic viscosity (

),

is the Schmidt number (dimensionless) and

is the diffusivity of the solute in water (

).

Then solve for the maximum solvent flux:

,

where

is maximum water flux through the membrane (

) and

is the density of water (

).

Solve for the solvent flux:

,

where

is mechanical pressure (atm),

is osmotic pressure (atm) and

is permeability of the membrane to the solvent (

).

A material balance is done for salt across the system to get the value for the mass fraction of salt in the outlet stream, which is the same as the retentate mass fraction inside the tank (given the tank is well mixed):

,

where

is inlet feed (kg/s),

is the mole fraction of salt in the inlet stream, and

is the area of the membrane (

).

To find how much of the feed exits as the permeate, an overall mass balance is done:

,

where

is the fraction of the feed that is purified and exits as the permeate, i.e., cut

(dimensionless).