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nanofiltration_ZO.rst

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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
.. index::
   pair: watertap.unit_models.nanofiltration_ZO;nanofiltration_ZO


.. currentmodule:: watertap.unit_models.nanofiltration_ZO

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}}

Class Documentation