.. _VAGMD_base_homepage: Vacuum Air Gap Membrane Distillation ==================================== .. code-block:: python 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. .. csv-table:: :header: "Variables", "Variable name", "Symbol", "Valid range", "Units" "Feed salinity", "``feed_props.conc_mass_phase_comp['Liq', 'TDS']``", ":math:`X_{f}`", "35 - 292", ":math:`\text{g/L}`" "Feed temperature", "``feed_props.temperature``", ":math:`T_{f}`", "20 - 30", ":math:`\text{°C}`" "Feed flow rate", "``steam_props.temperature``", ":math:`FFR`", "400 - 1100", ":math:`\text{L/hr}`" "Condenser inlet temperature", "``condenser_in_props.temperature``", ":math:`T_{cond,in}`", "20 - 30", ":math:`\text{°C}`" "Evaporator inlet temperature", "``evaporator_in_props.temperature``", ":math:`T_{evap,in}`", "60 - 80", ":math:`\text{°C}`" "Cooling water inlet temperature", "``cooling_in_props.temperature``", ":math:`T_{cooling,in}`", "20 - 30", ":math:`\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 :sup:`2` or * ``AS26C7.2L`` length of 7.2 m with an area of 25.92 m :sup:`2` * ``cooling_system_type``: Selection between ``closed`` or ``open`` * ``closed``: the condenser inlet temperature is forced to be constant and the cooling water temperature (:math:`T_{cooling,in}`) can be adjusted. * ``open``: the cooling process is available at a constant water temperature (:math:`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 ---- .. csv-table:: :header: "Description", "Symbol", "Indices" "Time", ":math:`t`", "[0]" "Phases", ":math:`p`", "['Liq']" "Components", ":math:`j`", "['H2O', 'TDS']" Variables --------- The system configuration variables should be fixed at the default values, which correspond to a single Aquastill module: .. csv-table:: :header: "Description", "Symbol", "Variable Name", "Value", "Units" "Pump efficiency", ":math:`\eta`", "``pump_efficiency``", "0.6", ":math:`\text{dimensionless}`" "Heat exchanger area", ":math:`A_{hx}`", "``heat_exchanger_area``", "1.34", ":math:`\text{m}^2`" "Cooling water volumetric flow rate", ":math:`q_{cool}`", "``cooling_flow_rate``", "1265", ":math:`\text{L/hr}`" "Overall heat transfer coefficient", ":math:`U`", "``thermal_heat_transfer_coeff``", "3168", ":math:`\text{W}/\text{m}^2\text{/K}`" The following performance variables are derived from the surrogate equations: .. csv-table:: :header: "Description", "Symbol", "Variable Name", "Units" "Permeate flux", ":math:`J_{perm}`", "``permeate_flux``", ":math:`\text{L/m}^2\text{/hr}`" "Pressure drop of the feed flow", ":math:`\Delta P_{feed}`", "``feed_flow_pressure_drop``", ":math:`\text{Pa}`" "Pressure drop of the feed flow", ":math:`\Delta P_{cool}`", "``cooling_flow_pressure_drop``", ":math:`\text{Pa}`" "Evaporator outlet temperature", ":math:`T_{evap,out}`", "``evaporator_out_props.temperature``", ":math:`\text{K}`" "Condenser outlet temperature", ":math:`T_{cond,out}`", "``condenser_out_props.temperature``", ":math:`\text{K}`" Equations --------- .. csv-table:: :header: "Description", "Equation" "Permeate flow rate", ":math:`q_{perm} = J_{perm} \times A`" "Brine volumetric flow rate", ":math:`q_{brine} = q_{feed} - q_{perm}`" "Brine salinity", ":math:`X_{brine} = \cfrac{q_{feed} X_{feed}}{q_{brine}}`" "Cooling power requirement", ":math:`P_{cooling} = R_{hot} * (T_{f} - T_{cond,in})`" "Thermal resistance on the hot side", ":math:`R_{hot} = q_{cool,in} \times \rho_{heater} \times C_{p, heater}`" "Thermal resistance on the cold side", ":math:`R_{cold} = q_{cool,in} \times \rho_{cooler} \times C_{p, cooler}`" "Number of transfer units", ":math:`\text{NTU} = \cfrac{\eta A_{hx}}{R_{hot}}`" "Effectiveness of the heat exchanger", ":math:`\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: .. csv-table:: :header: "Description", "Equation" "Inlet cooling watet temperature", ":math:`T_{cond,in} = T_{feed} - \cfrac{P_{cooling}}{\epsilon R_{hot}}`" "Outlet cooling water temperature (``closed``)", ":math:`T_{cond,out} = T_{cond,in} + \cfrac{R_{hot} (T_{feed} - T_{cond,in})}{R_{cold}}`" "Outlet cooling water temperature (``open``)", ":math:`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.