Membrane Distillation (1D)

This Membrane Distillation (MD) unit model:
  • supports the following configurations:

    • DCMD (Direct Contact Membrane Distillation)

    • VMD (Vacuum Membrane Distillation)

    • GMD (Permeate Gap/Conductive Gap Membrane Distillation)

  • is 1-dimensional

  • supports steady-state only

  • assumes heat loss in equipment is negligible

  • assumes permeate exits the membrane pores with zero salinity

  • assumes no concentration polarization for the cold channel

  • assumes complete vapor condensation for the cold channel (in DCMD and GMD)

  • accounts for vapor expansion in VMD

  • assumes linear temperature change across gap channel (in GMD)

  • assumes no pressure change and temperature polarization in VMD vaccuum channel

Degrees of Freedom

In addition to the hot channel and cold channel inlet state variables (i.e, temperature, pressure, and component flowrates) for the DCMD and GMD configurations, the MD model has at least 4 degrees of freedom for all configurations that should be fixed for the unit to be fully specified. Typically, the following variables are fixed:

  • Membrane permeability coefficient

  • Membrane thickness

  • Membrane thermal conductivity

  • Recovery or membrane area

Additional degress of freedom:

  • VMD introduces vacuum pressure at the cold side.

  • GMD introduces gap thermal conductivity and gap thickness.

Configuring the MD unit to calculate temperature polarization, concentration polarization, mass transfer coefficient, and pressure drop would result in five additional degrees of freedom. In this case, in addition to the previously fixed variables, we typically fix the following variables to fully specify the unit:

  • Hot channel spacer porosity

  • Hot channel height

  • Cold channel spacer porosity (in DCMD and GMD)

  • Cold channel height (in DCMD and GMD)

  • Membrane length or membrane width

Model Structure

The MD model consists of a separate MDchannel1Dblock for each channel depending on the configuration:

  • DCMD: Includes hot channel and cold channel.

  • VMD: Includes hot channel and vacuum (cold) channel.

  • GMD: Includes hot channel, gap channel, and cold channel.

  • hot and cold channels in all configurations includes bulk properties StateBlocks indexed by time and space which are used for mass, energy, and momentum balances

  • hot channel in all configurations, cold channel in DCMD and GMD, and gap channel in GMD includes StateBlocks indexed by time and space for the conditions at the membrane interface and gap interface

  • hot channel in all configurations, cold channel in DCMD, and gap channel in GMD includes StateBlocks indexed by time and space for Vapor properties at the membrane interface (for DCMD and VMD configurations).

Sets

Description

Symbol

Indices

Time

\(t\)

[0]

Space

\(x\)

None

Phases

\(p\)

[‘Liq’, ‘Vap’]

Components

\(j\)

[‘H2O’, solute]*

*Solute depends on the imported property model.

Variables

Refer to the Variables section in the 0D MD model.

Equations

Refer to the Equations section in the 0D MD model.

Class Documentation