- 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
pair: watertap.unit_models.nanofiltration_ZO;nanofiltration_ZO
watertap.unit_models.nanofiltration_ZO
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.
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.
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.
Description | Symbol | Variable Name | Index | Units |
---|---|---|---|---|
Mass density of solvent | ρsolvent | dens_solvent | [p] | kg/m3 |
Solvent volumetric flux across membrane | Jsolv | flux_vol_solvent | [t, j] | m3/m2/s |
Membrane area | Am | area | None | m2 |
Component recovery rate | Rj | recovery_mass_phase_comp | [t, p, j] | dimensionless |
Volumetric recovery rate | Rvol | recovery_vol_phase | [t, p] | dimensionless |
Observed solute rejection | rj | rejection_phase_comp | [t, p, j] | dimensionless |
Mass transfer to permeate | Mp | mass_transfer_phase_comp | [t, p, j] | kg/s |
Description | Equation |
---|---|
Solvent mass transfer | Mp, solv = AmJsolvρsolvent |
Component recovery rate | |
Volumetric recovery rate | |
Observed solute rejection |
watertap.unit_models.nanofiltration_ZO