#################################################################################
# WaterTAP Copyright (c) 2020-2024, The Regents of the University of California,
# through Lawrence Berkeley National Laboratory, Oak Ridge National Laboratory,
# National Renewable Energy Laboratory, and National Energy Technology
# Laboratory (subject to receipt of any required approvals from the U.S. Dept.
# of Energy). All rights reserved.
#
# Please see the files COPYRIGHT.md and LICENSE.md for full copyright and license
# information, respectively. These files are also available online at the URL
# "https://github.com/watertap-org/watertap/"
#################################################################################
# Import Pyomo libraries
from pyomo.environ import (
Set,
Var,
check_optimal_termination,
Param,
Suffix,
NonNegativeReals,
value,
log,
Constraint,
units as pyunits,
)
from pyomo.common.config import Bool, ConfigBlock, ConfigValue, In
# Import IDAES cores
from idaes.core import (
declare_process_block_class,
MaterialBalanceType,
EnergyBalanceType,
MomentumBalanceType,
UnitModelBlockData,
useDefault,
)
from idaes.core.util.misc import add_object_reference
from watertap.core.solvers import get_solver
from idaes.core.util.tables import create_stream_table_dataframe
from idaes.core.util.config import is_physical_parameter_block
from idaes.core.util.exceptions import ConfigurationError, InitializationError
import idaes.core.util.scaling as iscale
import idaes.logger as idaeslog
from idaes.core.util.constants import Constants
from enum import Enum
from watertap.core import ControlVolume0DBlock, InitializationMixin
from watertap.costing.unit_models.electrodialysis import cost_electrodialysis
__author__ = " Xiangyu Bi, Austin Ladshaw, Kejia Hu"
_log = idaeslog.getLogger(__name__)
[docs]class LimitingCurrentDensityMethod(Enum):
InitialValue = 0
Empirical = 1
Theoretical = 2
[docs]class ElectricalOperationMode(Enum):
Constant_Current = 0
Constant_Voltage = 1
[docs]class PressureDropMethod(Enum):
none = 0
experimental = 1
Darcy_Weisbach = 2
[docs]class FrictionFactorMethod(Enum):
fixed = 0
Gurreri = 1
Kuroda = 2
[docs]class HydraulicDiameterMethod(Enum):
fixed = 0
spacer_specific_area_known = 1
conventional = 2
# Name of the unit model
[docs]@declare_process_block_class("Electrodialysis0D")
class Electrodialysis0DData(InitializationMixin, UnitModelBlockData):
"""
0D Electrodialysis Model
"""
# CONFIG are options for the unit model
CONFIG = ConfigBlock() #
CONFIG.declare(
"dynamic",
ConfigValue(
domain=In([False]),
default=False,
description="Dynamic model flag - must be False",
doc="""Indicates whether this model will be dynamic or not,
**default** = False. The filtration unit does not support dynamic
behavior, thus this must be False.""",
),
)
CONFIG.declare(
"has_holdup",
ConfigValue(
default=False,
domain=In([False]),
description="Holdup construction flag - must be False",
doc="""Indicates whether holdup terms should be constructed or not.
**default** - False. The filtration unit does not have defined volume, thus
this must be False.""",
),
)
CONFIG.declare(
"has_pressure_change",
ConfigValue(
default=False,
domain=In([True, False]),
description="Pressure change term construction flag",
doc="""Indicates whether terms for pressure change should be
constructed,
**default** - False.
**Valid values:** {
**True** - include pressure change terms,
**False** - exclude pressure change terms.}""",
),
)
CONFIG.declare(
"pressure_drop_method",
ConfigValue(
default=PressureDropMethod.none,
domain=In(PressureDropMethod),
description="Method to calculate the frictional pressure drop in electrodialysis channels",
doc="""
**default** - ``PressureDropMethod.none``
.. csv-table::
:header: "Configuration Options", "Description"
"``PressureDropMethod.none``", "The frictional pressure drop is neglected."
"``PressureDropMethod.experimental``", "The pressure drop is calculated by an experimental data as pressure drop per unit lenght."
"``PressureDropMethod.Darcy_Weisbach``", "The pressure drop is calculated by the Darcy-Weisbach equation."
""",
),
)
CONFIG.declare(
"friction_factor_method",
ConfigValue(
default=FrictionFactorMethod.fixed,
domain=In(FrictionFactorMethod),
description="Method to calculate the Darcy's friction factor",
doc="""
**default** - ``FrictionFactorMethod.fixed``
.. csv-table::
:header: "Configuration Options", "Description"
"``FrictionFactorMethod.fixed``", "Friction factor is fixed by users"
"``FrictionFactorMethod.Gurreri``", "Friction factor evaluated based on Gurreri's work"
"``FrictionFactorMethod.Kuroda``", "Friction factor evaluated based on Kuroda's work"
""",
),
)
CONFIG.declare(
"hydraulic_diameter_method",
ConfigValue(
default=HydraulicDiameterMethod.conventional,
domain=In(HydraulicDiameterMethod),
description="Method to calculate the hydraulic diameter for a rectangular channel in ED",
doc="""
**default** - ``HydraulicDiameterMethod.conventional``
.. csv-table::
:header: "Configuration Options", "Description"
"``HydraulicDiameterMethod.fixed``", "Hydraulic diameter is fixed by users"
"``HydraulicDiameterMethod.conventional``", "Conventional method for a rectangular channel with spacer porosity considered"
"``HydraulicDiameterMethod.spacer_specific_area_known``", "A method for spacer-filled channel requiring the spacer specific area data"
""",
),
)
CONFIG.declare(
"operation_mode",
ConfigValue(
default=ElectricalOperationMode.Constant_Current,
domain=In(ElectricalOperationMode),
description="The electrical operation mode. To be selected between Constant Current and Constant Voltage",
),
)
CONFIG.declare(
"limiting_current_density_method",
ConfigValue(
default=LimitingCurrentDensityMethod.InitialValue,
domain=In(LimitingCurrentDensityMethod),
description="Configuration for method to compute the limiting current density",
doc="""
**default** - ``LimitingCurrentDensityMethod.InitialValue``
.. csv-table::
:header: "Configuration Options", "Description"
"``LimitingCurrentDensityMethod.InitialValue``", "Limiting current is calculated from a single initial value of the feed solution tested by the user."
"``LimitingCurrentDensityMethod.Empirical``", "Limiting current density is caculated from the empirical equation: TODO"
"``LimitingCurrentDensityMethod.Theoretical``", "Limiting current density is calculated from a theoretical equation: TODO"
""",
),
)
CONFIG.declare(
"limiting_current_density_data",
ConfigValue(
default=500,
description="Limiting current density data input",
),
)
CONFIG.declare(
"has_nonohmic_potential_membrane",
ConfigValue(
default=False,
domain=Bool,
description="Configuration for whether to model the nonohmic potential across ion exchange membranes",
),
)
CONFIG.declare(
"has_Nernst_diffusion_layer",
ConfigValue(
default=False,
domain=Bool,
description="Configuration for whether to simulate the concentration-polarized diffusion layers",
),
)
CONFIG.declare(
"material_balance_type",
ConfigValue(
default=MaterialBalanceType.useDefault,
domain=In(MaterialBalanceType),
description="Material balance construction flag",
doc="""Indicates what type of mass balance should be constructed,
**default** - MaterialBalanceType.useDefault.
**Valid values:** {
**MaterialBalanceType.useDefault - refer to property package for default
balance type
**MaterialBalanceType.none** - exclude material balances,
**MaterialBalanceType.componentPhase** - use phase component balances,
**MaterialBalanceType.componentTotal** - use total component balances,
**MaterialBalanceType.elementTotal** - use total element balances,
**MaterialBalanceType.total** - use total material balance.}""",
),
)
CONFIG.declare(
"is_isothermal",
ConfigValue(
default=True,
domain=Bool,
description="""Assume isothermal conditions for control volume(s); energy_balance_type must be EnergyBalanceType.none,
**default** - True.""",
),
)
CONFIG.declare(
"energy_balance_type",
ConfigValue(
default=EnergyBalanceType.none,
domain=In(EnergyBalanceType),
description="Energy balance construction flag",
doc="""Indicates what type of energy balance should be constructed,
**default** - EnergyBalanceType.none.
**Valid values:** {
**EnergyBalanceType.useDefault - refer to property package for default
balance type
**EnergyBalanceType.none** - exclude energy balances,
**EnergyBalanceType.enthalpyTotal** - single enthalpy balance for material,
**EnergyBalanceType.enthalpyPhase** - enthalpy balances for each phase,
**EnergyBalanceType.energyTotal** - single energy balance for material,
**EnergyBalanceType.energyPhase** - energy balances for each phase.}""",
),
)
CONFIG.declare(
"momentum_balance_type",
ConfigValue(
default=MomentumBalanceType.pressureTotal,
domain=In(MomentumBalanceType),
description="Momentum balance construction flag",
doc="""Indicates what type of momentum balance should be constructed,
**default** - MomentumBalanceType.pressureTotal.
**Valid values:** {
**MomentumBalanceType.none** - exclude momentum balances,
**MomentumBalanceType.pressureTotal** - single pressure balance for material,
**MomentumBalanceType.pressurePhase** - pressure balances for each phase,
**MomentumBalanceType.momentumTotal** - single momentum balance for material,
**MomentumBalanceType.momentumPhase** - momentum balances for each phase.}""",
),
)
CONFIG.declare(
"property_package",
ConfigValue(
default=useDefault,
domain=is_physical_parameter_block,
description="Property package to use for control volume",
doc="""Property parameter object used to define property calculations,
**default** - useDefault.
**Valid values:** {
**useDefault** - use default package from parent model or flowsheet,
**PhysicalParameterObject** - a PhysicalParameterBlock object.}""",
),
)
CONFIG.declare(
"property_package_args",
ConfigBlock(
implicit=True,
description="Arguments to use for constructing property packages",
doc="""A ConfigBlock with arguments to be passed to a property block(s)
and used when constructing these,
**default** - None.
**Valid values:** {
see property package for documentation.}""",
),
)
def _validate_config(self):
if (
self.config.is_isothermal
and self.config.energy_balance_type != EnergyBalanceType.none
):
raise ConfigurationError(
"If the isothermal assumption is used then the energy balance type must be none"
)
[docs] def build(self):
# build always starts by calling super().build()
# This triggers a lot of boilerplate in the background for you
super().build()
# this creates blank scaling factors, which are populated later
self.scaling_factor = Suffix(direction=Suffix.EXPORT)
# Check configs for errors
self._validate_config()
# Create essential sets.
self.membrane_set = Set(initialize=["cem", "aem"])
self.electrode_side = Set(initialize=["cathode_left", "anode_right"])
add_object_reference(self, "ion_set", self.config.property_package.ion_set)
add_object_reference(
self, "cation_set", self.config.property_package.cation_set
)
add_object_reference(self, "anion_set", self.config.property_package.anion_set)
# Create unit model parameters and vars
self.water_density = Param(
initialize=1000,
units=pyunits.kg * pyunits.m**-3,
doc="density of water",
)
self.cell_pair_num = Var(
initialize=1,
domain=NonNegativeReals,
bounds=(1, 10000),
units=pyunits.dimensionless,
doc="cell pair number in a stack",
)
# electrodialysis cell dimensional properties
self.cell_width = Var(
initialize=0.1,
bounds=(1e-3, 1e2),
units=pyunits.meter,
doc="The width of the electrodialysis cell, denoted as b in the model description",
)
self.cell_length = Var(
initialize=0.5,
bounds=(1e-3, 1e2),
units=pyunits.meter,
doc="The length of the electrodialysis cell, denoted as l in the model description",
)
self.channel_height = Var(
initialize=0.0001,
units=pyunits.meter,
doc="The distance between the consecutive aem and cem",
)
self.spacer_porosity = Var(
initialize=0.7,
bounds=(0.01, 1),
units=pyunits.dimensionless,
doc='The prosity of spacer in the ED channels. This is also referred to elsewhere as "void fraction" or "volume parameters"',
)
# Material and Operational properties
self.membrane_thickness = Var(
self.membrane_set,
initialize=0.0001,
bounds=(1e-6, 1e-1),
units=pyunits.meter,
doc="Membrane thickness",
)
self.solute_diffusivity_membrane = Var(
self.membrane_set,
self.ion_set | self.config.property_package.solute_set,
initialize=1e-10,
bounds=(0.0, 1e-6),
units=pyunits.meter**2 * pyunits.second**-1,
doc="Solute (ionic and neutral) diffusivity in the membrane phase",
)
self.ion_trans_number_membrane = Var(
self.membrane_set,
self.ion_set,
bounds=(0, 1),
units=pyunits.dimensionless,
doc="Ion transference number in the membrane phase",
)
self.water_trans_number_membrane = Var(
self.membrane_set,
initialize=5,
bounds=(0, 50),
units=pyunits.dimensionless,
doc="Transference number of water in membranes",
)
self.water_permeability_membrane = Var(
self.membrane_set,
initialize=1e-14,
units=pyunits.meter * pyunits.second**-1 * pyunits.pascal**-1,
doc="Water permeability coefficient",
)
self.membrane_areal_resistance = Var(
self.membrane_set,
initialize=2e-4,
bounds=(1e-6, 1),
units=pyunits.ohm * pyunits.meter**2,
doc="Surface resistance of membrane",
)
self.electrodes_resistance = Var(
initialize=0,
bounds=(0, 100),
domain=NonNegativeReals,
units=pyunits.ohm * pyunits.meter**2,
doc="areal resistance of TWO electrode compartments of a stack",
)
self.current = Var(
self.flowsheet().time,
initialize=1,
bounds=(0, 1000),
units=pyunits.amp,
doc="Current across a cell-pair or stack",
)
self.voltage = Var(
self.flowsheet().time,
initialize=100,
bounds=(0, 1000),
units=pyunits.volt,
doc="Voltage across a stack, declared under the 'Constant Voltage' mode only",
)
self.current_utilization = Var(
initialize=1,
bounds=(0, 1),
units=pyunits.dimensionless,
doc="The current utilization including water electro-osmosis and ion diffusion",
)
# Performance metrics
self.current_efficiency = Var(
self.flowsheet().time,
initialize=0.9,
bounds=(0, 1),
units=pyunits.dimensionless,
doc="The overall current efficiency for deionizaiton",
)
self.power_electrical = Var(
self.flowsheet().time,
initialize=1,
bounds=(0, 12100),
domain=NonNegativeReals,
units=pyunits.watt,
doc="Electrical power consumption of a stack",
)
self.specific_power_electrical = Var(
self.flowsheet().time,
initialize=10,
bounds=(0, 1000),
domain=NonNegativeReals,
units=pyunits.kW * pyunits.hour * pyunits.meter**-3,
doc="Diluate-volume-flow-rate-specific electrical power consumption",
)
self.recovery_mass_H2O = Var(
self.flowsheet().time,
initialize=0.5,
bounds=(0, 1),
domain=NonNegativeReals,
units=pyunits.dimensionless,
doc="water recovery ratio calculated by mass",
)
self.velocity_diluate = Var(
self.flowsheet().time,
initialize=0.01,
units=pyunits.meter * pyunits.second**-1,
doc="Linear velocity of flow in the diluate",
)
self.velocity_concentrate = Var(
self.flowsheet().time,
initialize=0.01,
units=pyunits.meter * pyunits.second**-1,
doc="Linear velocity of flow in the concentrate",
)
# Fluxes Vars for constructing mass transfer terms
self.elec_migration_flux_in = Var(
self.flowsheet().time,
self.config.property_package.phase_list,
self.config.property_package.component_list,
units=pyunits.mole * pyunits.meter**-2 * pyunits.second**-1,
doc="Molar flux_in of a component across the membrane driven by electrical migration",
)
self.elec_migration_flux_out = Var(
self.flowsheet().time,
self.config.property_package.phase_list,
self.config.property_package.component_list,
units=pyunits.mole * pyunits.meter**-2 * pyunits.second**-1,
doc="Molar flux_out of a component across the membrane driven by electrical migration",
)
self.nonelec_flux_in = Var(
self.flowsheet().time,
self.config.property_package.phase_list,
self.config.property_package.component_list,
units=pyunits.mole * pyunits.meter**-2 * pyunits.second**-1,
doc="Molar flux_in of a component across the membrane driven by non-electrical forces",
)
self.nonelec_flux_out = Var(
self.flowsheet().time,
self.config.property_package.phase_list,
self.config.property_package.component_list,
units=pyunits.mole * pyunits.meter**-2 * pyunits.second**-1,
doc="Molar flux_out of a component across the membrane driven by non-electrical forces",
)
if (
self.config.has_nonohmic_potential_membrane
or self.config.has_Nernst_diffusion_layer
):
self.conc_mem_surf_mol_ioa = Var(
self.membrane_set,
self.electrode_side,
self.flowsheet().time,
self.ion_set,
initialize=500,
bounds=(0, 1e5),
units=pyunits.mol * pyunits.meter**-3,
doc="Membane surface concentration of components",
)
# Build control volume for the dilute channel
self.diluate = ControlVolume0DBlock(
dynamic=False,
has_holdup=False,
property_package=self.config.property_package,
property_package_args=self.config.property_package_args,
)
self.diluate.add_state_blocks(has_phase_equilibrium=False)
self.diluate.add_material_balances(
balance_type=self.config.material_balance_type, has_mass_transfer=True
)
self.diluate.add_energy_balances(
balance_type=self.config.energy_balance_type,
has_enthalpy_transfer=False,
)
if self.config.is_isothermal:
self.diluate.add_isothermal_assumption()
self.diluate.add_momentum_balances(
balance_type=self.config.momentum_balance_type,
has_pressure_change=self.config.has_pressure_change,
)
# den_mass and visc_d in diluate and concentrate channels are the same
add_object_reference(
self, "dens_mass", self.diluate.properties_in[0].dens_mass_phase["Liq"]
)
add_object_reference(
self, "visc_d", self.diluate.properties_in[0].visc_d_phase["Liq"]
)
# Build control volume for the concentrate channel
self.concentrate = ControlVolume0DBlock(
dynamic=False,
has_holdup=False,
property_package=self.config.property_package,
property_package_args=self.config.property_package_args,
)
self.concentrate.add_state_blocks(has_phase_equilibrium=False)
self.concentrate.add_material_balances(
balance_type=self.config.material_balance_type, has_mass_transfer=True
)
self.concentrate.add_energy_balances(
balance_type=self.config.energy_balance_type,
has_enthalpy_transfer=False,
)
if self.config.is_isothermal:
self.concentrate.add_isothermal_assumption()
self.concentrate.add_momentum_balances(
balance_type=self.config.momentum_balance_type,
has_pressure_change=self.config.has_pressure_change,
)
# Add ports (creates inlets and outlets for each channel)
self.add_inlet_port(name="inlet_diluate", block=self.diluate)
self.add_outlet_port(name="outlet_diluate", block=self.diluate)
self.add_inlet_port(name="inlet_concentrate", block=self.concentrate)
self.add_outlet_port(name="outlet_concentrate", block=self.concentrate)
# extension options
if self.config.has_nonohmic_potential_membrane:
self._make_performance_nonohm_mem()
if self.config.has_Nernst_diffusion_layer:
self.current_dens_lim_ioa = Var(
self.flowsheet().time,
initialize=500,
bounds=(0, 1000),
units=pyunits.amp * pyunits.meter**-2,
doc="Limiting current density across the membrane as a function of the normalized length",
)
self._make_performance_dl_polarization()
if (
not self.config.pressure_drop_method == PressureDropMethod.none
) and self.config.has_pressure_change:
self._pressure_drop_calculation()
@self.Constraint(
self.flowsheet().time,
doc="Pressure drop expression as calculated by the pressure drop data, diluate.",
)
def eq_deltaP_diluate(self, t):
return self.diluate.deltaP[t] == -self.pressure_drop_total[t]
@self.Constraint(
self.flowsheet().time,
doc="Pressure drop expression as calculated by the pressure drop data, concentrate.",
)
def eq_deltaP_concentrate(self, t):
return (
# self.concentrate.deltaP[t]
# == -self.pressure_drop[t] * self.cell_length
self.concentrate.deltaP[t]
== -self.pressure_drop_total[t]
)
elif self.config.pressure_drop_method == PressureDropMethod.none and (
not self.config.has_pressure_change
):
pass
else:
raise ConfigurationError(
"A valid (not none) pressure_drop_method and has_pressure_change being True "
"must be both used or unused at the same time. "
)
# Build Constraints
@self.Constraint(
self.flowsheet().time,
doc="Calculate flow velocity in a single diluate channel, based on the average of inlet and outlet",
)
def eq_get_velocity_diluate(self, t):
return self.velocity_diluate[
t
] * self.cell_width * self.channel_height * self.spacer_porosity * self.cell_pair_num == 0.5 * (
self.diluate.properties_in[0].flow_vol_phase["Liq"]
+ self.diluate.properties_out[0].flow_vol_phase["Liq"]
)
@self.Constraint(
self.flowsheet().time,
doc="Calculate flow velocity in a single concentrate channel, based on the average of inlet and outlet",
)
def eq_get_velocity_concentrate(self, t):
return self.velocity_concentrate[
t
] * self.cell_width * self.channel_height * self.spacer_porosity * self.cell_pair_num == 0.5 * (
self.concentrate.properties_in[0].flow_vol_phase["Liq"]
+ self.concentrate.properties_out[0].flow_vol_phase["Liq"]
)
@self.Constraint(
self.flowsheet().time,
self.config.property_package.phase_list,
doc="Current-Voltage relationship",
)
def eq_current_voltage_relation(self, t, p):
if self.config.has_Nernst_diffusion_layer:
total_areal_resistance = (
self.membrane_areal_resistance["aem"]
+ self.membrane_areal_resistance["cem"]
+ (
self.channel_height
- self.dl_thickness_ioa["cem", "cathode_left", t]
- self.dl_thickness_ioa["aem", "anode_right", t]
)
* 0.5**-1
* (
self.concentrate.properties_in[t].elec_cond_phase["Liq"]
+ self.concentrate.properties_out[t].elec_cond_phase["Liq"]
)
** -1
+ (
self.channel_height
- self.dl_thickness_ioa["cem", "anode_right", t]
- self.dl_thickness_ioa["aem", "cathode_left", t]
)
* 0.5**-1
* (
self.diluate.properties_in[t].elec_cond_phase["Liq"]
+ self.diluate.properties_out[t].elec_cond_phase["Liq"]
)
** -1
) * self.cell_pair_num + self.electrodes_resistance
else:
total_areal_resistance = (
self.membrane_areal_resistance["aem"]
+ self.membrane_areal_resistance["cem"]
+ self.channel_height
* (
0.5**-1
* (
self.concentrate.properties_in[t].elec_cond_phase["Liq"]
+ self.concentrate.properties_out[t].elec_cond_phase["Liq"]
)
** -1
+ 0.5**-1
* (
self.diluate.properties_in[t].elec_cond_phase["Liq"]
+ self.diluate.properties_out[t].elec_cond_phase["Liq"]
)
** -1
)
) * self.cell_pair_num + self.electrodes_resistance
# the average conductivity of each channel's inlet and outlet is taken to represent that of the entire channel
if self.config.has_nonohmic_potential_membrane:
if self.config.has_Nernst_diffusion_layer:
return (
self.current[t]
* (self.cell_width * self.cell_length) ** -1
* total_areal_resistance
+ (
self.potential_ohm_dl_ioa["cem", t]
+ self.potential_ohm_dl_ioa["aem", t]
+ self.potential_nonohm_dl_ioa["cem", t]
+ self.potential_nonohm_dl_ioa["aem", t]
+ self.potential_nonohm_membrane_ioa["cem", t]
+ self.potential_nonohm_membrane_ioa["aem", t]
)
* self.cell_pair_num
== self.voltage[t]
)
else:
return (
self.current[t]
* (self.cell_width * self.cell_length) ** -1
* total_areal_resistance
+ (
+self.potential_nonohm_membrane_ioa["cem", t]
+ self.potential_nonohm_membrane_ioa["aem", t]
)
* self.cell_pair_num
== self.voltage[t]
)
else:
if self.config.has_Nernst_diffusion_layer:
return (
self.current[t]
* (self.cell_width * self.cell_length) ** -1
* total_areal_resistance
+ (
self.potential_ohm_dl_ioa["cem", t]
+ self.potential_ohm_dl_ioa["aem", t]
+ self.potential_nonohm_dl_ioa["cem", t]
+ self.potential_nonohm_dl_ioa["aem", t]
)
* self.cell_pair_num
== self.voltage[t]
)
else:
return (
self.current[t]
* (self.cell_width * self.cell_length) ** -1
* total_areal_resistance
== self.voltage[t]
)
@self.Constraint(
self.flowsheet().time,
self.config.property_package.phase_list,
self.config.property_package.component_list,
doc="Equation for electrical migration flux_in",
)
def eq_elec_migration_flux_in(self, t, p, j):
if j == "H2O":
return self.elec_migration_flux_in[t, p, j] == (
self.water_trans_number_membrane["cem"]
+ self.water_trans_number_membrane["aem"]
) * (
self.current[t]
/ (self.cell_width * self.cell_length)
/ Constants.faraday_constant
)
elif j in self.ion_set:
return self.elec_migration_flux_in[t, p, j] == (
self.ion_trans_number_membrane["cem", j]
- self.ion_trans_number_membrane["aem", j]
) * (
self.current_utilization
* self.current[t]
/ (self.cell_width * self.cell_length)
) / (
self.config.property_package.charge_comp[j]
* Constants.faraday_constant
)
else:
self.elec_migration_flux_in[t, p, j].fix(0)
return Constraint.Skip
@self.Constraint(
self.flowsheet().time,
self.config.property_package.phase_list,
self.config.property_package.component_list,
doc="Equation for electrical migration flux_out",
)
def eq_elec_migration_flux_out(self, t, p, j):
if j == "H2O":
return self.elec_migration_flux_out[t, p, j] == (
self.water_trans_number_membrane["cem"]
+ self.water_trans_number_membrane["aem"]
) * (
self.current[t]
/ (self.cell_width * self.cell_length)
/ Constants.faraday_constant
)
elif j in self.ion_set:
return self.elec_migration_flux_out[t, p, j] == (
self.ion_trans_number_membrane["cem", j]
- self.ion_trans_number_membrane["aem", j]
) * (
self.current_utilization
* self.current[t]
/ (self.cell_width * self.cell_length)
) / (
self.config.property_package.charge_comp[j]
* Constants.faraday_constant
)
else:
self.elec_migration_flux_out[t, p, j].fix(0)
return Constraint.Skip
@self.Constraint(
self.flowsheet().time,
self.config.property_package.phase_list,
self.config.property_package.component_list,
doc="Equation for non-electrical flux_in",
)
def eq_nonelec_flux_in(self, t, p, j):
if j == "H2O":
if self.config.has_Nernst_diffusion_layer:
return self.nonelec_flux_in[
t, p, j
] == self.water_density / self.config.property_package.mw_comp[
j
] * (
self.water_permeability_membrane["cem"]
+ self.water_permeability_membrane["aem"]
) * (
self.concentrate.properties_in[t].pressure_osm_phase[p]
* (
1
+ self.current[t]
* (self.cell_width * self.cell_length) ** -1
/ self.current_dens_lim_ioa[t]
)
- self.diluate.properties_in[t].pressure_osm_phase[p]
* (
1
- self.current[t]
* (self.cell_width * self.cell_length) ** -1
/ self.current_dens_lim_ioa[t]
)
)
else:
return self.nonelec_flux_in[
t, p, j
] == self.water_density / self.config.property_package.mw_comp[
j
] * (
self.water_permeability_membrane["cem"]
+ self.water_permeability_membrane["aem"]
) * (
self.concentrate.properties_in[t].pressure_osm_phase[p]
- self.diluate.properties_in[t].pressure_osm_phase[p]
)
else:
if self.config.has_Nernst_diffusion_layer:
return self.nonelec_flux_in[t, p, j] == -(
self.solute_diffusivity_membrane["cem", j]
* self.membrane_thickness["cem"] ** -1
* (
self.conc_mem_surf_mol_ioa["cem", "cathode_left", t, j]
- self.conc_mem_surf_mol_ioa["cem", "anode_right", t, j]
)
+ self.solute_diffusivity_membrane["aem", j]
* self.membrane_thickness["aem"] ** -1
* (
self.conc_mem_surf_mol_ioa["aem", "anode_right", t, j]
- self.conc_mem_surf_mol_ioa["aem", "cathode_left", t, j]
)
)
else:
return self.nonelec_flux_in[t, p, j] == -(
self.solute_diffusivity_membrane["cem", j]
/ self.membrane_thickness["cem"]
+ self.solute_diffusivity_membrane["aem", j]
/ self.membrane_thickness["aem"]
) * (
self.concentrate.properties_in[t].conc_mol_phase_comp[p, j]
- self.diluate.properties_in[t].conc_mol_phase_comp[p, j]
)
@self.Constraint(
self.flowsheet().time,
self.config.property_package.phase_list,
self.config.property_package.component_list,
doc="Equation for non-electrical flux_out",
)
def eq_nonelec_flux_out(self, t, p, j):
if j == "H2O":
if self.config.has_Nernst_diffusion_layer:
return self.nonelec_flux_out[
t, p, j
] == self.water_density / self.config.property_package.mw_comp[
j
] * (
self.water_permeability_membrane["cem"]
+ self.water_permeability_membrane["aem"]
) * (
self.concentrate.properties_out[t].pressure_osm_phase[p]
* (
1
+ self.current[t]
* (self.cell_width * self.cell_length) ** -1
/ self.current_dens_lim_ioa[t]
)
- self.diluate.properties_out[t].pressure_osm_phase[p]
* (
1
- self.current[t]
* (self.cell_width * self.cell_length) ** -1
/ self.current_dens_lim_ioa[t]
)
)
else:
return self.nonelec_flux_out[
t, p, j
] == self.water_density / self.config.property_package.mw_comp[
j
] * (
self.water_permeability_membrane["cem"]
+ self.water_permeability_membrane["aem"]
) * (
self.concentrate.properties_out[t].pressure_osm_phase[p]
- self.diluate.properties_out[t].pressure_osm_phase[p]
)
else:
if self.config.has_Nernst_diffusion_layer:
return self.nonelec_flux_out[t, p, j] == -(
self.solute_diffusivity_membrane["cem", j]
* self.membrane_thickness["cem"] ** -1
* (
self.conc_mem_surf_mol_ioa["cem", "cathode_left", t, j]
- self.conc_mem_surf_mol_ioa["cem", "anode_right", t, j]
)
+ self.solute_diffusivity_membrane["aem", j]
* self.membrane_thickness["aem"] ** -1
* (
self.conc_mem_surf_mol_ioa["aem", "anode_right", t, j]
- self.conc_mem_surf_mol_ioa["aem", "cathode_left", t, j]
)
)
else:
return self.nonelec_flux_out[t, p, j] == -(
self.solute_diffusivity_membrane["cem", j]
/ self.membrane_thickness["cem"]
+ self.solute_diffusivity_membrane["aem", j]
/ self.membrane_thickness["aem"]
) * (
self.concentrate.properties_out[t].conc_mol_phase_comp[p, j]
- self.diluate.properties_out[t].conc_mol_phase_comp[p, j]
)
# Add constraints for mass transfer terms (diluate)
@self.Constraint(
self.flowsheet().time,
self.config.property_package.phase_list,
self.config.property_package.component_list,
doc="Mass transfer term for the diluate channel",
)
def eq_mass_transfer_term_diluate(self, t, p, j):
return (
self.diluate.mass_transfer_term[t, p, j]
== -0.5
* (
self.elec_migration_flux_in[t, p, j]
+ self.elec_migration_flux_out[t, p, j]
+ self.nonelec_flux_in[t, p, j]
+ self.nonelec_flux_out[t, p, j]
)
* (self.cell_width * self.cell_length)
* self.cell_pair_num
)
# Add constraints for mass transfer terms (concentrate)
@self.Constraint(
self.flowsheet().time,
self.config.property_package.phase_list,
self.config.property_package.component_list,
doc="Mass transfer term for the concentrate channel",
)
def eq_mass_transfer_term_concentrate(self, t, p, j):
return (
self.concentrate.mass_transfer_term[t, p, j]
== 0.5
* (
self.elec_migration_flux_in[t, p, j]
+ self.elec_migration_flux_out[t, p, j]
+ self.nonelec_flux_in[t, p, j]
+ self.nonelec_flux_out[t, p, j]
)
* (self.cell_width * self.cell_length)
* self.cell_pair_num
)
@self.Constraint(
self.flowsheet().time,
doc="Electrical power consumption of a stack",
)
def eq_power_electrical(self, t):
return self.power_electrical[t] == self.current[t] * self.voltage[t]
@self.Constraint(
self.flowsheet().time,
doc="Diluate_volume_flow_rate_specific electrical power consumption of a stack",
)
def eq_specific_power_electrical(self, t):
return (
pyunits.convert(
self.specific_power_electrical[t],
pyunits.watt * pyunits.second * pyunits.meter**-3,
)
* self.diluate.properties_out[t].flow_vol_phase["Liq"]
== self.current[t] * self.voltage[t]
)
@self.Constraint(
self.flowsheet().time,
doc="Overall current efficiency evaluation",
)
def eq_current_efficiency(self, t):
return (
self.current_efficiency[t] * self.current[t] * self.cell_pair_num
== sum(
self.diluate.properties_in[t].flow_mol_phase_comp["Liq", j]
* self.config.property_package.charge_comp[j]
- self.diluate.properties_out[t].flow_mol_phase_comp["Liq", j]
* self.config.property_package.charge_comp[j]
for j in self.config.property_package.cation_set
)
* Constants.faraday_constant
)
@self.Constraint(
self.flowsheet().time,
doc="Water recovery by mass",
)
def eq_recovery_mass_H2O(self, t):
return (
self.recovery_mass_H2O[t]
* (
self.diluate.properties_in[t].flow_mass_phase_comp["Liq", "H2O"]
+ self.concentrate.properties_in[t].flow_mass_phase_comp[
"Liq", "H2O"
]
)
== self.diluate.properties_out[t].flow_mass_phase_comp["Liq", "H2O"]
)
def _make_performance_nonohm_mem(self):
self.potential_nonohm_membrane_ioa = Var(
self.membrane_set,
self.flowsheet().time,
initialize=0.01, # to reinspect
bounds=(-50, 50),
units=pyunits.volt,
doc="Nonohmic potential across a membane",
)
# ioa = in-out average
@self.Constraint(
self.membrane_set,
self.electrode_side,
self.flowsheet().time,
self.ion_set,
doc="calcualte current density from the electrical input",
)
def eq_set_surface_conc_ioa(self, mem, side, t, j):
if not self.config.has_Nernst_diffusion_layer:
if (mem == "cem" and side == "cathode_left") or (
mem == "aem" and side == "anode_right"
):
return self.conc_mem_surf_mol_ioa[mem, side, t, j] == 0.5 * (
self.concentrate.properties_in[t].conc_mol_phase_comp["Liq", j]
+ self.concentrate.properties_out[t].conc_mol_phase_comp[
"Liq", j
]
)
else:
return self.conc_mem_surf_mol_ioa[mem, side, t, j] == 0.5 * (
self.diluate.properties_in[t].conc_mol_phase_comp["Liq", j]
+ self.diluate.properties_out[t].conc_mol_phase_comp["Liq", j]
)
else:
return Constraint.Skip
@self.Constraint(
self.membrane_set,
self.flowsheet().time,
doc="Calculate the total non-ohmic potential across an iem; this takes account of diffusion and Donnan Potentials",
)
def eq_potential_nonohm_membrane_ioa(self, mem, t):
return self.potential_nonohm_membrane_ioa[mem, t] == (
Constants.gas_constant
* self.diluate.properties_in[t].temperature
/ Constants.faraday_constant
* (
sum(
self.ion_trans_number_membrane[mem, j]
/ self.config.property_package.charge_comp[j]
for j in self.cation_set
)
+ sum(
self.ion_trans_number_membrane[mem, j]
/ self.config.property_package.charge_comp[j]
for j in self.anion_set
)
)
* log(
sum(
self.conc_mem_surf_mol_ioa[mem, "cathode_left", t, j]
for j in self.ion_set
)
/ sum(
self.conc_mem_surf_mol_ioa[mem, "anode_right", t, j]
for j in self.ion_set
)
)
)
def _make_performance_dl_polarization(self):
self.potential_nonohm_dl_ioa = Var(
self.membrane_set,
self.flowsheet().time,
initialize=0,
bounds=(-50, 50),
units=pyunits.volt,
doc="Nonohmic potential in two diffusion layers on the two sides of a membrane",
)
self.potential_ohm_dl_ioa = Var(
self.membrane_set,
self.flowsheet().time,
initialize=0.001,
bounds=(0, 50),
units=pyunits.volt,
doc="Ohmic potential in two diffusion layers on the two sides of a membrane",
)
self.dl_thickness_ioa = Var(
self.membrane_set,
self.electrode_side,
self.flowsheet().time,
initialize=0.0005,
bounds=(0, 1e-2),
units=pyunits.m,
doc="Thickness of the diffusion layer",
)
@self.Constraint(
self.flowsheet().time,
doc="Calculate limiting current density",
)
def eq_current_dens_lim_ioa(self, t):
if (
self.config.limiting_current_density_method
== LimitingCurrentDensityMethod.InitialValue
):
return self.current_dens_lim_ioa[t] == (
self.config.limiting_current_density_data
* pyunits.amp
* pyunits.meter**-2
/ sum(
self.diluate.properties_in[t].conc_mol_phase_comp["Liq", j]
for j in self.cation_set
)
* 0.5
* sum(
self.diluate.properties_in[t].conc_mol_phase_comp["Liq", j]
+ self.diluate.properties_out[t].conc_mol_phase_comp["Liq", j]
for j in self.cation_set
)
)
elif (
self.config.limiting_current_density_method
== LimitingCurrentDensityMethod.Theoretical
):
self._get_fluid_dimensionless_quantities()
return self.current_dens_lim_ioa[t] == (
self.N_Sh
* self.diffus_mass
* self.hydraulic_diameter**-1
* Constants.faraday_constant
* (
sum(
self.ion_trans_number_membrane["cem", j]
/ self.config.property_package.charge_comp[j]
for j in self.cation_set
)
- sum(
self.diluate.properties_in[t].trans_num_phase_comp["Liq", j]
/ self.config.property_package.charge_comp[j]
for j in self.cation_set
)
)
** -1
* sum(
self.config.property_package.charge_comp[j]
* 0.5
* (
self.diluate.properties_in[t].conc_mol_phase_comp["Liq", j]
+ self.diluate.properties_out[t].conc_mol_phase_comp[
"Liq", j
]
)
for j in self.cation_set
)
)
elif (
self.config.limiting_current_density_method
== LimitingCurrentDensityMethod.Empirical
):
self.param_b = Param(
initialize=0.5,
units=pyunits.dimensionless,
doc="empirical parameter b to calculate limiting current density",
)
self.param_a = Param(
initialize=25,
units=pyunits.coulomb
* pyunits.mol**-1
* pyunits.meter ** (1 - self.param_b)
* pyunits.second ** (self.param_b - 1),
doc="empirical parameter a to calculate limiting current density",
)
return self.current_dens_lim_ioa[
t
] == self.param_a * self.velocity_diluate[t] ** self.param_b * sum(
self.config.property_package.charge_comp[j]
* 0.5
* (
self.diluate.properties_in[t].conc_mol_phase_comp["Liq", j]
+ self.diluate.properties_out[t].conc_mol_phase_comp["Liq", j]
)
for j in self.cation_set
)
@self.Constraint(
self.membrane_set,
self.electrode_side,
self.flowsheet().time,
self.ion_set,
doc="Establish relationship between interfacial concentration polarization ratio and current density",
)
def eq_conc_polarization_ratio(self, mem, side, t, j):
if (mem == "cem" and side == "cathode_left") or (
mem == "aem" and side == "anode_right"
):
return self.conc_mem_surf_mol_ioa[mem, side, t, j] / (
0.5
* (
self.concentrate.properties_in[t].conc_mol_phase_comp["Liq", j]
+ self.concentrate.properties_out[t].conc_mol_phase_comp[
"Liq", j
]
)
) == (
1
+ self.current[t]
* (self.cell_width * self.cell_length) ** -1
/ self.current_dens_lim_ioa[t]
)
else:
return self.conc_mem_surf_mol_ioa[mem, side, t, j] / (
0.5
* (
self.diluate.properties_in[t].conc_mol_phase_comp["Liq", j]
+ self.diluate.properties_out[t].conc_mol_phase_comp["Liq", j]
)
) == (
1
- self.current[t]
* (self.cell_width * self.cell_length) ** -1
/ self.current_dens_lim_ioa[t]
)
@self.Constraint(
self.membrane_set,
self.flowsheet().time,
doc="Calculate the total non-ohmic potential across the two diffusion layers of an iem.",
)
def eq_potential_nonohm_dl_ioa(self, mem, t):
if mem == "cem":
return self.potential_nonohm_dl_ioa[mem, t] == (
Constants.gas_constant
* self.diluate.properties_in[t].temperature
/ Constants.faraday_constant
* (
sum(
self.diluate.properties_in[t].trans_num_phase_comp["Liq", j]
/ self.config.property_package.charge_comp[j]
for j in self.cation_set
)
+ sum(
self.diluate.properties_in[t].trans_num_phase_comp["Liq", j]
/ self.config.property_package.charge_comp[j]
for j in self.anion_set
)
)
* log(
sum(
self.conc_mem_surf_mol_ioa[mem, "anode_right", t, j]
for j in self.ion_set
)
* 0.5
* (
sum(
self.concentrate.properties_in[t].conc_mol_phase_comp[
"Liq", j
]
for j in self.ion_set
)
+ sum(
self.concentrate.properties_out[t].conc_mol_phase_comp[
"Liq", j
]
for j in self.ion_set
)
)
* sum(
self.conc_mem_surf_mol_ioa[mem, "cathode_left", t, j]
for j in self.ion_set
)
** -1
* (
0.5
* (
sum(
self.diluate.properties_in[t].conc_mol_phase_comp[
"Liq", j
]
for j in self.ion_set
)
+ sum(
self.diluate.properties_out[t].conc_mol_phase_comp[
"Liq", j
]
for j in self.ion_set
)
)
)
** -1
)
)
else:
return self.potential_nonohm_dl_ioa[mem, t] == (
Constants.gas_constant
* self.diluate.properties_in[t].temperature
/ Constants.faraday_constant
* (
sum(
self.diluate.properties_in[t].trans_num_phase_comp["Liq", j]
/ self.config.property_package.charge_comp[j]
for j in self.cation_set
)
+ sum(
self.diluate.properties_in[t].trans_num_phase_comp["Liq", j]
/ self.config.property_package.charge_comp[j]
for j in self.anion_set
)
)
* log(
sum(
self.conc_mem_surf_mol_ioa[mem, "anode_right", t, j]
for j in self.ion_set
)
* 0.5
* (
sum(
self.diluate.properties_in[t].conc_mol_phase_comp[
"Liq", j
]
for j in self.ion_set
)
+ sum(
self.diluate.properties_out[t].conc_mol_phase_comp[
"Liq", j
]
for j in self.ion_set
)
)
* sum(
self.conc_mem_surf_mol_ioa[mem, "cathode_left", t, j]
for j in self.ion_set
)
** -1
* (
0.5
* (
sum(
self.concentrate.properties_in[
t
].conc_mol_phase_comp["Liq", j]
for j in self.ion_set
)
+ sum(
self.concentrate.properties_out[
t
].conc_mol_phase_comp["Liq", j]
for j in self.ion_set
)
)
)
** -1
)
)
@self.Constraint(
self.membrane_set,
self.flowsheet().time,
doc="Calculate the total ohmic potential across the two diffusion layers of an iem.",
)
def eq_potential_ohm_dl_ioa(self, mem, t):
if mem == "cem":
return self.potential_ohm_dl_ioa[mem, t] == (
Constants.faraday_constant
* (
sum(
self.diluate.properties_in[t].diffus_phase_comp["Liq", j]
** -1
for j in self.ion_set
)
** -1
* len(self.ion_set)
)
* (
sum(
self.ion_trans_number_membrane[mem, j]
/ self.config.property_package.charge_comp[j]
for j in self.cation_set
)
- sum(
self.diluate.properties_in[t].trans_num_phase_comp["Liq", j]
/ self.config.property_package.charge_comp[j]
for j in self.cation_set
)
)
** -1
* self.diluate.properties_in[t].equiv_conductivity_phase["Liq"]
** -1
* log(
sum(
self.conc_mem_surf_mol_ioa[mem, "anode_right", t, j]
for j in self.ion_set
)
** -1
* 0.5**-1
* (
sum(
self.concentrate.properties_in[t].conc_mol_phase_comp[
"Liq", j
]
for j in self.ion_set
)
+ sum(
self.concentrate.properties_out[t].conc_mol_phase_comp[
"Liq", j
]
for j in self.ion_set
)
)
** -1
* sum(
self.conc_mem_surf_mol_ioa[mem, "cathode_left", t, j]
for j in self.ion_set
)
* 0.5
* (
sum(
self.diluate.properties_in[t].conc_mol_phase_comp[
"Liq", j
]
for j in self.ion_set
)
+ sum(
self.diluate.properties_out[t].conc_mol_phase_comp[
"Liq", j
]
for j in self.ion_set
)
)
)
)
else:
return self.potential_ohm_dl_ioa[mem, t] == (
-Constants.faraday_constant
* (
sum(
self.diluate.properties_in[t].diffus_phase_comp["Liq", j]
** -1
for j in self.ion_set
)
** -1
* len(self.ion_set)
)
* (
sum(
self.ion_trans_number_membrane[mem, j]
/ self.config.property_package.charge_comp[j]
for j in self.cation_set
)
- sum(
self.diluate.properties_in[t].trans_num_phase_comp["Liq", j]
/ self.config.property_package.charge_comp[j]
for j in self.cation_set
)
)
** -1
* self.diluate.properties_in[t].equiv_conductivity_phase["Liq"]
** -1
* log(
sum(
self.conc_mem_surf_mol_ioa[mem, "anode_right", t, j]
for j in self.ion_set
)
* 0.5
* (
sum(
self.diluate.properties_in[t].conc_mol_phase_comp[
"Liq", j
]
for j in self.ion_set
)
+ sum(
self.diluate.properties_out[t].conc_mol_phase_comp[
"Liq", j
]
for j in self.ion_set
)
)
* sum(
self.conc_mem_surf_mol_ioa[mem, "cathode_left", t, j]
for j in self.ion_set
)
** -1
* 0.5**-1
* (
sum(
self.concentrate.properties_in[t].conc_mol_phase_comp[
"Liq", j
]
for j in self.ion_set
)
+ sum(
self.concentrate.properties_out[t].conc_mol_phase_comp[
"Liq", j
]
for j in self.ion_set
)
)
** -1
)
)
@self.Constraint(
self.membrane_set,
self.electrode_side,
self.flowsheet().time,
doc="Calculate the total non-ohmic potential across the two diffusion layers of an iem.",
)
def eq_dl_thickness_ioa(self, mem, side, t):
if mem == "cem" and side == "cathode_left":
return self.dl_thickness_ioa[mem, side, t] == (
Constants.faraday_constant
* (
sum(
self.diluate.properties_in[t].diffus_phase_comp["Liq", j]
** -1
for j in self.ion_set
)
** -1
* len(self.ion_set)
)
* (
sum(
self.ion_trans_number_membrane[mem, j]
/ self.config.property_package.charge_comp[j]
for j in self.cation_set
)
- sum(
self.diluate.properties_in[t].trans_num_phase_comp["Liq", j]
/ self.config.property_package.charge_comp[j]
for j in self.cation_set
)
)
** -1
* 0.5
* (
sum(
self.concentrate.properties_in[t].conc_mol_phase_comp[
"Liq", j
]
for j in self.cation_set
)
+ sum(
self.concentrate.properties_out[t].conc_mol_phase_comp[
"Liq", j
]
for j in self.cation_set
)
)
* self.current_dens_lim_ioa[t] ** -1
)
elif mem == "cem" and side == "anode_right":
return self.dl_thickness_ioa[mem, side, t] == (
Constants.faraday_constant
* (
sum(
self.diluate.properties_in[t].diffus_phase_comp["Liq", j]
** -1
for j in self.ion_set
)
** -1
* len(self.ion_set)
)
* (
sum(
self.ion_trans_number_membrane[mem, j]
/ self.config.property_package.charge_comp[j]
for j in self.cation_set
)
- sum(
self.diluate.properties_in[t].trans_num_phase_comp["Liq", j]
/ self.config.property_package.charge_comp[j]
for j in self.cation_set
)
)
** -1
* 0.5
* (
sum(
self.diluate.properties_in[t].conc_mol_phase_comp["Liq", j]
for j in self.cation_set
)
+ sum(
self.diluate.properties_out[t].conc_mol_phase_comp["Liq", j]
for j in self.cation_set
)
)
* self.current_dens_lim_ioa[t] ** -1
)
elif mem == "aem" and side == "cathode_left":
return self.dl_thickness_ioa[mem, side, t] == (
-Constants.faraday_constant
* (
sum(
self.diluate.properties_in[t].diffus_phase_comp["Liq", j]
** -1
for j in self.ion_set
)
** -1
* len(self.ion_set)
)
* (
sum(
self.ion_trans_number_membrane[mem, j]
/ self.config.property_package.charge_comp[j]
for j in self.cation_set
)
- sum(
self.diluate.properties_in[t].trans_num_phase_comp["Liq", j]
/ self.config.property_package.charge_comp[j]
for j in self.cation_set
)
)
** -1
* 0.5
* (
sum(
self.diluate.properties_in[t].conc_mol_phase_comp["Liq", j]
for j in self.cation_set
)
+ sum(
self.diluate.properties_out[t].conc_mol_phase_comp["Liq", j]
for j in self.cation_set
)
)
* self.current_dens_lim_ioa[t] ** -1
)
else:
return self.dl_thickness_ioa[mem, side, t] == (
-Constants.faraday_constant
* (
sum(
self.diluate.properties_in[t].diffus_phase_comp["Liq", j]
** -1
for j in self.ion_set
)
** -1
* len(self.ion_set)
)
* (
sum(
self.ion_trans_number_membrane[mem, j]
/ self.config.property_package.charge_comp[j]
for j in self.cation_set
)
- sum(
self.diluate.properties_in[t].trans_num_phase_comp["Liq", j]
/ self.config.property_package.charge_comp[j]
for j in self.cation_set
)
)
** -1
* 0.5
* (
sum(
self.concentrate.properties_in[t].conc_mol_phase_comp[
"Liq", j
]
for j in self.cation_set
)
+ sum(
self.concentrate.properties_out[t].conc_mol_phase_comp[
"Liq", j
]
for j in self.cation_set
)
)
* self.current_dens_lim_ioa[t] ** -1
)
def _get_fluid_dimensionless_quantities(self):
self.diffus_mass = Var(
initialize=1e-9,
bounds=(1e-16, 1e-6),
units=pyunits.meter**2 * pyunits.second**-1,
doc="The mass diffusivity of the solute as molecules (not individual ions)",
)
self.hydraulic_diameter = Var(
initialize=1e-3,
bounds=(0, None),
units=pyunits.meter,
doc="The hydraulic diameter of the channel",
)
self.N_Re = Var(
initialize=50,
bounds=(0, None),
units=pyunits.dimensionless,
doc="Reynolds Number",
)
self.N_Sc = Var(
initialize=2000,
bounds=(0, None),
units=pyunits.dimensionless,
doc="Schmidt Number",
)
self.N_Sh = Var(
initialize=100,
bounds=(0, None),
units=pyunits.dimensionless,
doc="Sherwood Number",
)
if self.config.hydraulic_diameter_method == HydraulicDiameterMethod.fixed:
_log.warning("Do not forget to FIX the channel hydraulic diameter in [m]!")
else:
@self.Constraint(
doc="To calculate hydraulic diameter",
)
def eq_hydraulic_diameter(self):
if (
self.config.hydraulic_diameter_method
== HydraulicDiameterMethod.conventional
):
return (
self.hydraulic_diameter
== 2
* self.channel_height
* self.cell_width
* self.spacer_porosity
* (self.channel_height + self.cell_width) ** -1
)
else:
self.spacer_specific_area = Var(
initialize=1e4,
bounds=(0, None),
units=pyunits.meter**-1,
doc="The specific area of the channel",
)
return (
self.hydraulic_diameter
== 4
* self.spacer_porosity
* (
2 * self.channel_height**-1
+ (1 - self.spacer_porosity) * self.spacer_specific_area
)
** -1
)
@self.Constraint(
doc="To calculate Re",
)
def eq_Re(self):
return (
self.N_Re
== self.dens_mass
* self.velocity_diluate[0]
* self.hydraulic_diameter
* self.visc_d**-1
)
@self.Constraint(
doc="To calculate Sc",
)
def eq_Sc(self):
return self.N_Sc == self.visc_d * self.dens_mass**-1 * self.diffus_mass**-1
@self.Constraint(
doc="To calculate Sh",
)
def eq_Sh(self):
return self.N_Sh == 0.29 * self.N_Re**0.5 * self.N_Sc**0.33
def _pressure_drop_calculation(self):
self.pressure_drop_total = Var(
self.flowsheet().time,
initialize=1e6,
units=pyunits.pascal,
doc="pressure drop over an entire ED stack",
)
self.pressure_drop = Var(
self.flowsheet().time,
initialize=1e3,
units=pyunits.pascal * pyunits.meter**-1,
doc="pressure drop per unit of length",
)
if self.config.pressure_drop_method == PressureDropMethod.experimental:
_log.warning(
"Do not forget to FIX the experimental pressure drop value in [Pa/m]!"
)
else: # PressureDropMethod.Darcy_Weisbach is used
if not (self.config.has_Nernst_diffusion_layer == True):
self._get_fluid_dimensionless_quantities()
self.friction_factor = Var(
initialize=10,
bounds=(0, None),
units=pyunits.dimensionless,
doc="friction factor of the channel fluid",
)
@self.Constraint(
self.flowsheet().time,
doc="To calculate pressure drop over an stack",
)
def eq_pressure_drop_total(self, t):
return (
self.pressure_drop_total[t]
== self.dens_mass
* self.friction_factor
* self.velocity_diluate[0] ** 2
* 0.5
* self.hydraulic_diameter**-1
* self.cell_length
)
if self.config.friction_factor_method == FrictionFactorMethod.fixed:
_log.warning("Do not forget to FIX the Darcy's friction factor value!")
else:
@self.Constraint(
doc="To calculate friction factor",
)
def eq_friction_factor(self):
if (
self.config.friction_factor_method
== FrictionFactorMethod.Gurreri
):
return (
self.friction_factor
== 4 * 50.6 * self.spacer_porosity**-7.06 * self.N_Re**-1
)
elif (
self.config.friction_factor_method
== FrictionFactorMethod.Kuroda
):
return (
self.friction_factor
== 4 * 9.6 * self.spacer_porosity**-1 * self.N_Re**-0.5
)
@self.Constraint(
self.flowsheet().time,
doc="To calculate total pressure drop over a stack",
)
def eq_pressure_drop(self, t):
return (
self.pressure_drop[t]
== self.pressure_drop_total[t] * self.cell_length**-1
)
# initialize method
[docs] def initialize_build(
self,
state_args=None,
outlvl=idaeslog.NOTSET,
solver=None,
optarg=None,
):
"""
General wrapper for pressure changer initialization routines
Keyword Arguments:
state_args : a dict of arguments to be passed to the property
package(s) to provide an initial state for
initialization (see documentation of the specific
property package) (default = {}).
outlvl : sets output level of initialization routine
optarg : solver options dictionary object (default=None)
solver : str indicating which solver to use during
initialization (default = None)
Returns: None
"""
init_log = idaeslog.getInitLogger(self.name, outlvl, tag="unit")
solve_log = idaeslog.getSolveLogger(self.name, outlvl, tag="unit")
# Set solver options
opt = get_solver(solver, optarg)
# ---------------------------------------------------------------------
# Set the outlet has the same intial condition of the inlet.
for k in self.keys():
for j in self[k].config.property_package.component_list:
self[k].diluate.properties_out[0].flow_mol_phase_comp["Liq", j] = value(
self[k].diluate.properties_in[0].flow_mol_phase_comp["Liq", j]
)
self[k].concentrate.properties_out[0].flow_mol_phase_comp["Liq", j] = (
value(
self[k]
.concentrate.properties_in[0]
.flow_mol_phase_comp["Liq", j]
)
)
if hasattr(self[k], "conc_mem_surf_mol_ioa"):
for mem in self[k].membrane_set:
for side in self[k].electrode_side:
for j in self[k].ion_set:
self[k].conc_mem_surf_mol_ioa[mem, side, 0, j].set_value(
self[k]
.concentrate.properties_in[0]
.conc_mol_phase_comp["Liq", j]
)
# Initialize diluate block
flags_diluate = self.diluate.initialize(
outlvl=outlvl,
optarg=optarg,
solver=solver,
state_args=state_args,
hold_state=True,
)
init_log.info_high("Initialization Step 1 Complete.")
# ---------------------------------------------------------------------
# Initialize concentrate_side block
flags_concentrate = self.concentrate.initialize(
outlvl=outlvl,
optarg=optarg,
solver=solver,
state_args=state_args, # inlet var
hold_state=True,
)
init_log.info_high("Initialization Step 2 Complete.")
# ---------------------------------------------------------------------
# Solve unit
with idaeslog.solver_log(solve_log, idaeslog.DEBUG) as slc:
res = opt.solve(self, tee=slc.tee)
init_log.info_high("Initialization Step 3 {}.".format(idaeslog.condition(res)))
# ---------------------------------------------------------------------
# Release state
self.diluate.release_state(flags_diluate, outlvl)
init_log.info("Initialization Complete: {}".format(idaeslog.condition(res)))
self.concentrate.release_state(flags_concentrate, outlvl)
init_log.info("Initialization Complete: {}".format(idaeslog.condition(res)))
if not check_optimal_termination(res):
raise InitializationError(f"Unit model {self.name} failed to initialize")
def calculate_scaling_factors(self):
super().calculate_scaling_factors()
# Scaling factors that user may setup
# The users are highly encouraged to provide scaling factors for assessable vars below.
# Not providing these vars will give a warning.
if (
iscale.get_scaling_factor(self.solute_diffusivity_membrane, warning=True)
is None
):
iscale.set_scaling_factor(self.solute_diffusivity_membrane, 1e10)
if iscale.get_scaling_factor(self.membrane_thickness, warning=True) is None:
iscale.set_scaling_factor(self.membrane_thickness, 1e4)
if (
iscale.get_scaling_factor(self.water_permeability_membrane, warning=True)
is None
):
iscale.set_scaling_factor(self.water_permeability_membrane, 1e14)
if iscale.get_scaling_factor(self.cell_pair_num, warning=True) is None:
iscale.set_scaling_factor(self.cell_pair_num, 0.1)
if iscale.get_scaling_factor(self.cell_length, warning=True) is None:
iscale.set_scaling_factor(self.cell_length, 1e1)
if iscale.get_scaling_factor(self.cell_width, warning=True) is None:
iscale.set_scaling_factor(self.cell_width, 1e1)
if iscale.get_scaling_factor(self.channel_height, warning=True) is None:
iscale.set_scaling_factor(self.channel_height, 1e4)
if iscale.get_scaling_factor(self.spacer_porosity, warning=True) is None:
iscale.set_scaling_factor(self.spacer_porosity, 1)
if (
iscale.get_scaling_factor(self.membrane_areal_resistance, warning=True)
is None
):
iscale.set_scaling_factor(self.membrane_areal_resistance, 1e4)
if iscale.get_scaling_factor(self.electrodes_resistance, warning=True) is None:
iscale.set_scaling_factor(self.electrodes_resistance, 1e4)
if iscale.get_scaling_factor(self.current, warning=True) is None:
iscale.set_scaling_factor(self.current, 1)
if iscale.get_scaling_factor(self.voltage, warning=True) is None:
iscale.set_scaling_factor(self.voltage, 1)
if hasattr(self, "diffus_mass") and (
iscale.get_scaling_factor(self.diffus_mass, warning=True) is None
):
iscale.set_scaling_factor(self.diffus_mass, 1e9)
# The folloing Vars are built for constructing constraints and their sf are computed from other Vars.
iscale.set_scaling_factor(
self.elec_migration_flux_in,
iscale.get_scaling_factor(self.current)
* iscale.get_scaling_factor(self.cell_length) ** -1
* iscale.get_scaling_factor(self.cell_width) ** -1
* 1e5,
)
iscale.set_scaling_factor(
self.elec_migration_flux_out,
iscale.get_scaling_factor(self.current)
* iscale.get_scaling_factor(self.cell_length) ** -1
* iscale.get_scaling_factor(self.cell_width) ** -1
* 1e5,
)
for ind in self.nonelec_flux_in:
if ind[2] == "H2O":
sf = (
1e-3
* 0.018
* iscale.get_scaling_factor(self.water_permeability_membrane)
* iscale.get_scaling_factor(
self.concentrate.properties_in[ind[0]].pressure_osm_phase[
ind[1]
]
)
)
else:
sf = (
iscale.get_scaling_factor(self.solute_diffusivity_membrane)
/ iscale.get_scaling_factor(self.membrane_thickness)
* iscale.get_scaling_factor(
self.concentrate.properties_in[ind[0]].conc_mol_phase_comp[
ind[1], ind[2]
]
)
)
iscale.set_scaling_factor(self.nonelec_flux_in[ind], sf)
for ind in self.nonelec_flux_out:
if ind[2] == "H2O":
sf = (
1e-3
* 0.018
* iscale.get_scaling_factor(self.water_permeability_membrane)
* iscale.get_scaling_factor(
self.concentrate.properties_out[ind[0]].pressure_osm_phase[
ind[1]
]
)
)
else:
sf = (
iscale.get_scaling_factor(self.solute_diffusivity_membrane)
/ iscale.get_scaling_factor(self.membrane_thickness)
* iscale.get_scaling_factor(
self.concentrate.properties_out[ind[0]].conc_mol_phase_comp[
ind[1], ind[2]
]
)
)
iscale.set_scaling_factor(self.nonelec_flux_out[ind], sf)
iscale.set_scaling_factor(
self.power_electrical,
iscale.get_scaling_factor(self.current)
* iscale.get_scaling_factor(self.voltage),
)
for ind, c in self.specific_power_electrical.items():
iscale.set_scaling_factor(
self.specific_power_electrical[ind],
3.6e6
* iscale.get_scaling_factor(self.current[ind])
* iscale.get_scaling_factor(self.voltage[ind])
* iscale.get_scaling_factor(
self.diluate.properties_out[ind].flow_vol_phase["Liq"]
)
** -1,
)
for ind in self.velocity_diluate:
if (
iscale.get_scaling_factor(self.velocity_diluate[ind], warning=False)
is None
):
sf = (
iscale.get_scaling_factor(
self.diluate.properties_in[ind].flow_vol_phase["Liq"]
)
* iscale.get_scaling_factor(self.cell_width) ** -1
* iscale.get_scaling_factor(self.channel_height) ** -1
* iscale.get_scaling_factor(self.spacer_porosity) ** -1
* iscale.get_scaling_factor(self.cell_pair_num) ** -1
)
iscale.set_scaling_factor(self.velocity_diluate[ind], sf)
iscale.set_scaling_factor(self.velocity_concentrate[ind], sf)
if hasattr(self, "conc_mem_surf_mol_ioa"):
for ind in self.conc_mem_surf_mol_ioa:
if iscale.get_scaling_factor(self.conc_mem_surf_mol_ioa[ind]) is None:
if (ind[0] == "cem" and ind[1] == "cathode_left") or (
ind[0] == "aem" and ind[1] == "anode_right"
):
iscale.set_scaling_factor(
self.conc_mem_surf_mol_ioa[ind],
iscale.get_scaling_factor(
self.concentrate.properties_in[
ind[2]
].conc_mol_phase_comp["Liq", ind[3]]
),
)
else:
iscale.set_scaling_factor(
self.conc_mem_surf_mol_ioa[ind],
iscale.get_scaling_factor(
self.diluate.properties_in[ind[2]].conc_mol_phase_comp[
"Liq", ind[3]
]
),
)
if hasattr(self, "potential_nonohm_membrane_ioa"):
if iscale.get_scaling_factor(self.potential_nonohm_membrane_ioa) is None:
sf = (
value(Constants.faraday_constant)
* value(Constants.gas_constant) ** -1
* 298.15**-1
)
iscale.set_scaling_factor(self.potential_nonohm_membrane_ioa, sf)
if hasattr(self, "potential_nonohm_dl_ioa"):
if iscale.get_scaling_factor(self.potential_nonohm_dl_ioa) is None:
sf = (
value(Constants.faraday_constant)
* value(Constants.gas_constant) ** -1
* 298.15**-1
)
iscale.set_scaling_factor(self.potential_nonohm_dl_ioa, sf)
if hasattr(self, "potential_ohm_dl_ioa"):
if iscale.get_scaling_factor(self.potential_ohm_dl_ioa) is None:
sf = (
96485**-1
* sum(
iscale.get_scaling_factor(
self.diluate.properties_in[0].diffus_phase_comp["Liq", j]
)
** -2
for j in self.ion_set
)
** -0.5
* float(len(self.ion_set)) ** -1
)
iscale.set_scaling_factor(self.potential_ohm_dl_ioa, sf)
if hasattr(self, "dl_thickness_ioa"):
if iscale.get_scaling_factor(self.dl_thickness_ioa) is None:
for ind in self.dl_thickness_ioa:
sf = (
96485**-1
* sum(
iscale.get_scaling_factor(
self.diluate.properties_in[0].diffus_phase_comp[
"Liq", j
]
)
** -2
for j in self.ion_set
)
** -0.5
* len(self.ion_set) ** -1
* sum(
iscale.get_scaling_factor(
self.conc_mem_surf_mol_ioa[ind, j]
)
** 2
for j in self.cation_set
)
** 0.5
* iscale.get_scaling_factor(self.current) ** -1
* iscale.get_scaling_factor(self.cell_width)
* iscale.get_scaling_factor(self.cell_length)
)
iscale.set_scaling_factor(self.dl_thickness_ioa[ind], sf)
if hasattr(self, "spacer_specific_area") and (
iscale.get_scaling_factor(self.spacer_specific_area, warning=True) is None
):
iscale.set_scaling_factor(self.spacer_specific_area, 1e-4)
if hasattr(self, "hydraulic_diameter") and (
iscale.get_scaling_factor(self.hydraulic_diameter, warning=True) is None
):
iscale.set_scaling_factor(self.hydraulic_diameter, 1e4)
if hasattr(self, "N_Re") and (
iscale.get_scaling_factor(self.N_Re, warning=True) is None
):
sf = (
iscale.get_scaling_factor(self.dens_mass)
* iscale.get_scaling_factor(self.velocity_diluate[0])
* iscale.get_scaling_factor(self.hydraulic_diameter)
* iscale.get_scaling_factor(self.visc_d) ** -1
)
iscale.set_scaling_factor(self.N_Re, sf)
if hasattr(self, "N_Sc") and (
iscale.get_scaling_factor(self.N_Sc, warning=True) is None
):
sf = (
iscale.get_scaling_factor(self.visc_d)
* iscale.get_scaling_factor(self.dens_mass) ** -1
* iscale.get_scaling_factor(self.diffus_mass) ** -1
)
iscale.set_scaling_factor(self.N_Sc, sf)
if hasattr(self, "N_Sh") and (
iscale.get_scaling_factor(self.N_Sh, warning=True) is None
):
sf = (
10
* iscale.get_scaling_factor(self.N_Re) ** 0.5
* iscale.get_scaling_factor(self.N_Sc) ** 0.33
)
iscale.set_scaling_factor(self.N_Sh, sf)
if hasattr(self, "friction_factor") and (
iscale.get_scaling_factor(self.friction_factor, warning=True) is None
):
if self.config.friction_factor_method == FrictionFactorMethod.fixed:
sf = 0.1
elif self.config.friction_factor_method == FrictionFactorMethod.Gurreri:
sf = (
(4 * 50.6) ** -1
* (iscale.get_scaling_factor(self.spacer_porosity)) ** -7.06
* iscale.get_scaling_factor(self.N_Re) ** -1
)
elif self.config.friction_factor_method == FrictionFactorMethod.Kuroda:
sf = (4 * 9.6) ** -1 * iscale.get_scaling_factor(self.N_Re) ** -0.5
iscale.set_scaling_factor(self.friction_factor, sf)
if hasattr(self, "pressure_drop") and (
iscale.get_scaling_factor(self.pressure_drop, warning=True) is None
):
if self.config.pressure_drop_method == PressureDropMethod.experimental:
sf = 1e-5
else:
sf = (
iscale.get_scaling_factor(self.dens_mass)
* iscale.get_scaling_factor(self.friction_factor)
* iscale.get_scaling_factor(self.velocity_diluate[0]) ** 2
* 2
* iscale.get_scaling_factor(self.hydraulic_diameter) ** -1
)
iscale.set_scaling_factor(self.pressure_drop, sf)
if hasattr(self, "pressure_drop_total") and (
iscale.get_scaling_factor(self.pressure_drop_total, warning=True) is None
):
if self.config.pressure_drop_method == PressureDropMethod.experimental:
sf = 1e-5 * iscale.get_scaling_factor(self.cell_length)
else:
sf = (
iscale.get_scaling_factor(self.dens_mass)
* iscale.get_scaling_factor(self.friction_factor)
* iscale.get_scaling_factor(self.velocity_diluate[0]) ** 2
* 2
* iscale.get_scaling_factor(self.hydraulic_diameter) ** -1
* iscale.get_scaling_factor(self.cell_length)
)
iscale.set_scaling_factor(self.pressure_drop_total, sf)
if hasattr(self, "current_dens_lim_ioa"):
if iscale.get_scaling_factor(self.current_dens_lim_ioa) is None:
if (
self.config.limiting_current_density_method
== LimitingCurrentDensityMethod.InitialValue
):
sf = self.config.limiting_current_density_data**-1
iscale.set_scaling_factor(self.current_dens_lim_ioa, sf)
elif (
self.config.limiting_current_density_method
== LimitingCurrentDensityMethod.Empirical
):
sf = 25**-1 * sum(
iscale.get_scaling_factor(
self.diluate.properties_in[0].conc_mol_phase_comp["Liq", j]
)
** 2
for j in self.cation_set
) ** (0.5 * 0.5)
iscale.set_scaling_factor(self.current_dens_lim_ioa, sf)
elif (
self.config.limiting_current_density_method
== LimitingCurrentDensityMethod.Theoretical
):
sf = (
iscale.get_scaling_factor(self.N_Sh)
* iscale.get_scaling_factor(self.diffus_mass)
* iscale.get_scaling_factor(self.hydraulic_diameter) ** -1
* 96485**-1
* sum(
iscale.get_scaling_factor(
self.diluate.properties_in[0].conc_mol_phase_comp[
"Liq", j
]
)
** 2
for j in self.cation_set
)
** 0.5
)
iscale.set_scaling_factor(self.current_dens_lim_ioa, sf)
# Constraint scaling
for ind, c in self.eq_current_voltage_relation.items():
iscale.constraint_scaling_transform(
c, iscale.get_scaling_factor(self.membrane_areal_resistance)
)
for ind, c in self.eq_power_electrical.items():
iscale.constraint_scaling_transform(
c, iscale.get_scaling_factor(self.power_electrical)
)
for ind, c in self.eq_specific_power_electrical.items():
iscale.constraint_scaling_transform(
c, iscale.get_scaling_factor(self.specific_power_electrical[ind])
)
for ind, c in self.eq_elec_migration_flux_in.items():
iscale.constraint_scaling_transform(
c, iscale.get_scaling_factor(self.elec_migration_flux_in)
)
for ind, c in self.eq_elec_migration_flux_out.items():
iscale.constraint_scaling_transform(
c, iscale.get_scaling_factor(self.elec_migration_flux_out)
)
for ind, c in self.eq_nonelec_flux_in.items():
iscale.constraint_scaling_transform(
c, iscale.get_scaling_factor(self.nonelec_flux_in[ind])
)
for ind, c in self.eq_nonelec_flux_out.items():
iscale.constraint_scaling_transform(
c, iscale.get_scaling_factor(self.nonelec_flux_out[ind])
)
for ind, c in self.eq_mass_transfer_term_diluate.items():
iscale.constraint_scaling_transform(
c,
min(
iscale.get_scaling_factor(self.elec_migration_flux_in[ind]),
iscale.get_scaling_factor(
self.nonelec_flux_in[ind], self.elec_migration_flux_out[ind]
),
iscale.get_scaling_factor(self.nonelec_flux_out[ind]),
),
)
for ind, c in self.eq_mass_transfer_term_concentrate.items():
iscale.constraint_scaling_transform(
c,
min(
iscale.get_scaling_factor(self.elec_migration_flux_in[ind]),
iscale.get_scaling_factor(
self.nonelec_flux_in[ind], self.elec_migration_flux_out[ind]
),
iscale.get_scaling_factor(self.nonelec_flux_out[ind]),
),
)
if hasattr(self, "eq_potential_nonohm_membrane_ioa"):
for ind, c in self.eq_potential_nonohm_membrane_ioa.items():
iscale.constraint_scaling_transform(
c,
iscale.get_scaling_factor(self.potential_nonohm_membrane_ioa[ind]),
)
if hasattr(self, "eq_current_dens_lim_ioa"):
for ind, c in self.eq_current_dens_lim_ioa.items():
iscale.constraint_scaling_transform(
c, iscale.get_scaling_factor(self.current_dens_lim_ioa[ind])
)
if hasattr(self, "eq_potential_nonohm_dl_ioa"):
for ind, c in self.eq_potential_nonohm_dl_ioa.items():
iscale.constraint_scaling_transform(
c, iscale.get_scaling_factor(self.potential_nonohm_dl_ioa[ind])
)
if hasattr(self, "eq_potential_ohm_dl_ioa"):
for ind, c in self.eq_potential_ohm_dl_ioa.items():
iscale.constraint_scaling_transform(
c, iscale.get_scaling_factor(self.potential_ohm_dl_ioa[ind])
)
if hasattr(self, "eq_dl_thickness_ioa"):
for ind, c in self.eq_dl_thickness_ioa.items():
iscale.constraint_scaling_transform(
c, iscale.get_scaling_factor(self.dl_thickness_ioa[ind])
)
for ind, c in self.eq_recovery_mass_H2O.items():
iscale.constraint_scaling_transform(
c,
iscale.get_scaling_factor(
self.diluate.properties_out[ind].flow_mass_phase_comp["Liq", "H2O"]
),
)
for ind, c in self.eq_power_electrical.items():
iscale.constraint_scaling_transform(
c,
iscale.get_scaling_factor(self.power_electrical[ind]),
)
for ind, c in self.eq_specific_power_electrical.items():
iscale.constraint_scaling_transform(
c,
iscale.get_scaling_factor(self.specific_power_electrical[ind])
* iscale.get_scaling_factor(
self.diluate.properties_out[ind].flow_vol_phase["Liq"]
),
)
for ind, c in self.eq_current_efficiency.items():
iscale.constraint_scaling_transform(
c, iscale.get_scaling_factor(self.current[ind])
)
def _get_stream_table_contents(self, time_point=0):
return create_stream_table_dataframe(
{
"Diluate Channel Inlet": self.inlet_diluate,
"Concentrate Channel Inlet": self.inlet_concentrate,
"Diluate Channel Outlet": self.outlet_diluate,
"Concentrate Channel Outlet": self.outlet_concentrate,
},
time_point=time_point,
)
def _get_performance_contents(self, time_point=0):
return {
"vars": {
"Total electrical power consumption(Watt)": self.power_electrical[
time_point
],
"Specific electrical power consumption (kW*h/m**3)": self.specific_power_electrical[
time_point
],
"Current efficiency for deionzation": self.current_efficiency[
time_point
],
"Water recovery by mass": self.recovery_mass_H2O[time_point],
},
"exprs": {},
"params": {},
}
def get_power_electrical(self, time_point=0):
return self.power_electrical[time_point]
@property
def default_costing_method(self):
return cost_electrodialysis