Vacuum Air Gap Membrane Distillation

from watertap_contrib.reflo.unit_models import VAGMDSurrogateBase

This Vacuum Air Gap Membrane Distillation (VAGMD) 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

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

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	Units
Feed salinity	feed_props.conc_mass_phase_comp['Liq', 'TDS']	\(X_{f}\)	35 - 292	\(\text{g/L}\)
Feed temperature	feed_props.temperature	\(T_{f}\)	20 - 30	\(\text{°C}\)
Feed flow rate	steam_props.temperature	\(FFR\)	400 - 1100	\(\text{L/hr}\)
Condenser inlet temperature	condenser_in_props.temperature	\(T_{cond,in}\)	20 - 30	\(\text{°C}\)
Evaporator inlet temperature	evaporator_in_props.temperature	\(T_{evap,in}\)	60 - 80	\(\text{°C}\)
Cooling water inlet temperature	cooling_in_props.temperature	\(T_{cooling,in}\)	20 - 30	\(\text{°C}\)

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 modes will be selected in the model by specifying the following configuration arguments:

CO:sup:2

• module_type: Selection between two available Aquastill MD modules:

  • AS7C1.5L length of 1.5 m and an area of 7 m ² or

  • AS26C7.2L length of 7.2 m with an area of 25.92 m ²

• cooling_system_type: Selection between closed or open

  • closed: the condenser inlet temperature is forced to be constant and the cooling water temperature (\(T_{cooling,in}\)) can be adjusted.

  • open: the cooling process is available at a constant water temperature (\(T_{cooling,in}\)) and condenser inlet temperature is variable

• 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.

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 correspond to a single Aquastill module:

Description	Symbol	Variable Name	Value	Units
Pump efficiency	\(\eta\)	pump_efficiency	0.6	\(\text{dimensionless}\)
Heat exchanger area	\(A_{hx}\)	heat_exchanger_area	1.34	\(\text{m}^2\)
Cooling water volumetric flow rate	\(q_{cool}\)	cooling_flow_rate	1265	\(\text{L/hr}\)
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	\(J_{perm}\)	permeate_flux	\(\text{L/m}^2\text{/hr}\)
Pressure drop of the feed flow	\(\Delta P_{feed}\)	feed_flow_pressure_drop	\(\text{Pa}\)
Pressure drop of the feed flow	\(\Delta P_{cool}\)	cooling_flow_pressure_drop	\(\text{Pa}\)
Evaporator outlet temperature	\(T_{evap,out}\)	evaporator_out_props.temperature	\(\text{K}\)
Condenser outlet temperature	\(T_{cond,out}\)	condenser_out_props.temperature	\(\text{K}\)

Equations

Description	Equation
Permeate flow rate	\(q_{perm} = J_{perm} \times A\)
Brine volumetric flow rate	\(q_{brine} = q_{feed} - q_{perm}\)
Brine salinity	\(X_{brine} = \cfrac{q_{feed} X_{feed}}{q_{brine}}\)
Cooling power requirement	\(P_{cooling} = R_{hot} * (T_{f} - T_{cond,in})\)
Thermal resistance on the hot side	\(R_{hot} = q_{cool,in} \times \rho_{heater} \times C_{p, heater}\)
Thermal resistance on the cold side	\(R_{cold} = q_{cool,in} \times \rho_{cooler} \times C_{p, cooler}\)
Number of transfer units	\(\text{NTU} = \cfrac{\eta A_{hx}}{R_{hot}}\)
Effectiveness of the heat exchanger	\(\epsilon = \cfrac{1 - \text{exp}\left( {1-\text{NTU}\cfrac{R_{hot}}{R_{cold}}}\right)}{1-\cfrac{R_{hot}}{R_{cold}}\text{exp}\left(1-\text{NTU}\cfrac{R_{hot}}{R_{cold}}\right)}\)

Cooling water properties will be calculated based on the cooling system type:

Description	Equation
Inlet cooling watet temperature	\(T_{cond,in} = T_{feed} - \cfrac{P_{cooling}}{\epsilon R_{hot}}\)
Outlet cooling water temperature (closed)	\(T_{cond,out} = T_{cond,in} + \cfrac{R_{hot} (T_{feed} - T_{cond,in})}{R_{cold}}\)
Outlet cooling water temperature (open)	\(T_{cond,out} = T_{cond,in} + \cfrac{P_{cooling}}{R_{cold}}\)

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.