Vacuum Air-gapped Membrane Distillation - base model (VAGMD-base)
- This Vacuum Air-gapped Membrane Distillation - base (VAGMD-base) unit model
supports steady-state only
represents a single module from Aquastill
is a surrogate model
is verified against the operation data in Plataforma Solar de Almeria (PSA)
Degrees of Freedom
The VAGMD model has at least 6 degrees of freedom that should be fixed for the unit to be fully specified.
Variables |
Variable name |
Symbol |
Valid range |
Unit |
|---|---|---|---|---|
Feed salinity |
feed_props.conc_mass_phase_comp[‘Liq’, ‘TDS’] |
\(X_{f}\) |
35 - 292 |
\(\text{g/}\text{L}\) |
Feed temperature |
feed_props.temperature |
\(T_{f}\) |
20 - 30 |
\(^o\text{C}\) |
Feed flow rate |
steam_props.temperature |
\(FFR\) |
400 - 1100 |
\(\text{L}/\text{h}\) |
Condenser inlet temperature |
condenser_in_props.temperature |
\(TCI\) |
20 - 30 |
\(^o\text{C}\) |
Evaporator inlet temperature |
evaporator_in_props.temperature |
\(TEI\) |
60 - 80 |
\(^o\text{C}\) |
Cooling water inlet temperature |
cooling_in_props.temperature |
\(T_{cooling,in}\) |
20 - 30 |
\(^o\text{C}\) |
The cooling water inlet temperature is not required when cooling system type is set to “closed”. See details in Design Configurations below.
Design configurations
Different operation mode will be selected in the model by specifying the following configuration key-value pairs:
module_type: Selection between two available Aquastill MD modules:
AS7C1.5L or AS26C7.2L. The first one has a length of 1.5 \(m\)
and an area of 7 \(m^2\), while the latter has a length of 7.2 \(m\)
with an area of 25.92 \(m^2\).
cooling_system_type: Selection between closed or open.
In the closed cooling circuit, the condenser inlet temperature (TCI) is forced to be
constant and the cooling water temperature (\(T_{cooling,in}\)) can be adjusted.
In the open cooling circuit, the cooling process is available at a constant water
temperature (\(T_{cooling,in}\)) and condenser inlet temperature (TCI) varies.
high_brine_salinity: True or False, indicates whether the brine salinity
is high (> 175.3 g/L) or not. It can be inferred given a feed salinity.
Different surrogate equations will be applied based on the module_type and
high_brine_salinity specifications.
Model Structure
This VAGMD model consists of 11 StateBlocks and 2 Ports as in parenthesis below:
Feed flow (feed)
Permeate flow
Evaporator inlet flow
Evaporator outlet flow (brine)
Condenser inlet flow
Condenser outlet flow
Cooling inlet flow
Cooling outlet flow
Average status in the cooler
Average status in the heater
Average status in the condenser
Sets
Description |
Symbol |
Indices |
|---|---|---|
Time |
\(t\) |
[0] |
Phases |
\(p\) |
[‘Liq’] |
Components |
\(j\) |
[‘H2O’, ‘TDS’] |
Variables
The system configuration variables should be fixed at the default values, which are corresponded to a single Aquastill module:
Description |
Symbol |
Variable Name |
Value |
Units |
|---|---|---|---|---|
Pump efficiency |
\(\eta\) |
pump_efficiency |
0.6 |
\(\text{dimensionless}\) |
Heat exchanger area |
\(A_{exchanger}\) |
heat_exchanger_area |
1.34 |
\(\text{m}^2\) |
Cooling water volumetric flow rate |
\(v_{cooling}\) |
cooling_flow_rate |
1265 |
\(\text{L}/\text{h}\) |
Overall heat transfer coefficient |
\(U\) |
thermal_heat_transfer_coeff |
3168 |
\(\text{W}/(\text{m}^2 \text{K})\) |
The following performance variables are derived from the surrogate equations:
Description |
Symbol |
Variable Name |
Units |
|---|---|---|---|
Permeate flux |
\(PFlux\) |
permeate_flux |
\(\text{L} / (\text{m}^2\text{/h})\) |
Pressure drop of the feed flow |
\(\Delta P_{feed}\) |
feed_flow_pressure_drop |
\(Pa\) |
Pressure drop of the feed flow |
\(\Delta P_{cool}\) |
cooling_flow_pressure_drop |
\(Pa\) |
Evaporator outlet temperature |
\(TEO\) |
evaporator_out_props.temperature |
\(K\) |
Condenser outlet temperature |
\(TCO\) |
condenser_out_props.temperature |
\(K\) |
Equations
Description |
Equation |
|---|---|
Permeate flow rate |
\(v_{permeate} = PFlux \times A\) |
Brine volumetric flow rate |
\(v_{brine} = v_{feed} - v_{permeate}\) |
Brine salinity |
\(X_{brine} = \frac{v_{feed} X_{feed}}{v_{brine}}\) |
Cooling power requirement |
\(P_{cooling} = R_{hot} * (T_{f} - TCI)\) |
Thermal resistance on the hot side |
\(R_{hot} = v_{cooling,in} \times \rho_{heater} \times C_{p, heater}\) |
Thermal resistance on the cold side |
\(R_{cold} = v_{cooling,in} \times \rho_{cooler} \times C_{p, cooler}\) |
Number of transfer units |
\(NTU = \frac{\eta A_{exchanger}}{R_{hot}}\) |
Effectiveness of the heat exchanger |
\(\epsilon = \frac{1 - e^{1-NTU\frac{R_{hot}}{R_{cold}}}}{1-\frac{R_{hot}}{R_{cold}}e^(1-NTC\frac{R_{hot}}{R_{cold}})}\) |
Cooling water properties will be calculated based on the cooling system type：
Description |
Equation |
|---|---|
Inlet cooling watet temperature |
\(TCI = T_{feed} - \frac{P_{cooling}}{\epsilon R_{hot}}\) |
Outlet cooling water temperature (closed) |
\(TCO = TCI + \frac{R_{hot} (T_{feed} - TCI)}{R_{cold}}\) |
Outlet cooling water temperature (open) |
\(TCO = TCI + \frac{P_{cooling}}{R_{cold}}\) |
Surrogate equations and the corresponding coefficients for different number of effects can be found in the unit model class.
References
[1] J.A. Andres-Manas, I. Requena, G. Zaragoza, Characterization of the use of vacuum enhancement in commercial pilot-scale air gap membrane distillation modules with different designs, Desalination 528 (2022), 115490, https://doi.org/10.1016/j.desal.2021.115490.
[2] J.A. Andres-Manas, A. Ruiz-Aguirre, F.G. Acien, G. Zaragoza, Performance increase of membrane distillation pilot scale modules operating in vacuum-enhanced airgap configuration, Desalination 475 (2020), 114202, https://doi.org/10.1016/j.desal.2019.114202.