Nanofiltration (ZO)
- This nanofiltration (NF) unit model
is a zero-order model that enables the user to specify performance in terms of membrane solvent flux and solute/ion rejection
supports a single liquid phase only
supports steady-state only
assumes isothermal conditions
Degrees of Freedom
The zero-order NF model has at least 7 degrees of freedom that should be fixed for the unit to be fully specified. Typically, the following variables are fixed:
solvent mass flow rate at the inlet
inlet temperature
inlet pressure
solvent volumetric flux of the membrane
permeate pressure
There are 2 degrees of freedom for each solute in a given property model:
solute rejection of the membrane
solute mass flow rate at the inlet
Note, when a set of solutes comprises ions and includes more than one ion pair, the solute rejection of one ion could be left unfixed to satisfy an electroneutrality constraint. In this case, the last degree of freedom can be eliminated by fixing another variable such as volumetric recovery rate or membrane area.
Model Structure
This NF model consists of 1 ControlVolume0DBlock for the feed-side of the membrane and 1 StateBlock (properties_permeate) for the permeate exiting the NF membrane module. The feed-side includes 2 StateBlocks (properties_in and properties_out) which are used for mass and momentum balances.
Sets
Description |
Symbol |
Indices |
|---|---|---|
Time |
\(t\) |
[0] |
Phases |
\(p\) |
[‘Liq’] |
Components |
\(j\) |
[‘H2O’, ‘Solute’]* |
*Solute depends on the imported property model, and more than one solute can be provided; ions can be represented as solutes in a given property model to be recognized by this NF model.
Variables
Description |
Symbol |
Variable Name |
Index |
Units |
|---|---|---|---|---|
Mass density of solvent |
\(\rho_{solvent}\) |
dens_solvent |
[p] |
\(\text{kg/}\text{m}^3\) |
Solvent volumetric flux across membrane |
\(J_{solv}\) |
flux_vol_solvent |
[t, j] |
\(\text{m}^3\text{/m}^2\text{/s}\) |
Membrane area |
\(A_m\) |
area |
None |
\(\text{m}^2\) |
Component recovery rate |
\(R_j\) |
recovery_mass_phase_comp |
[t, p, j] |
\(\text{dimensionless}\) |
Volumetric recovery rate |
\(R_{vol}\) |
recovery_vol_phase |
[t, p] |
\(\text{dimensionless}\) |
Observed solute rejection |
\(r_j\) |
rejection_phase_comp |
[t, p, j] |
\(\text{dimensionless}\) |
Mass transfer to permeate |
\(M_p\) |
mass_transfer_phase_comp |
[t, p, j] |
\(\text{kg/s}\) |
Equations
Description |
Equation |
|---|---|
Solvent mass transfer |
\(M_{p, solv} = A_m J_{solv} \rho_{solvent}\) |
Component recovery rate |
\(R_j = \frac{M_{p,j}}{M_{f,in,j}}\) |
Volumetric recovery rate |
\(R_{vol} = \frac{Q_{p}}{Q_{f,in}}\) |
Observed solute rejection |
\(r_j = 1 - \frac{C_{p}}{C_{f,in}}\) |