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.