#################################################################################
# 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/"
#################################################################################
from pyomo.environ import (
Set,
Var,
Param,
check_optimal_termination,
Suffix,
Constraint,
NonNegativeReals,
value,
units as pyunits,
log,
)
from pyomo.dae import (
DerivativeVar,
)
from pyomo.common.config import ConfigBlock, ConfigValue, In, Bool
# Import Watertap cores
from watertap.core.util.initialization import check_solve, check_dof
# Import IDAES cores
from idaes.core import (
declare_process_block_class,
EnergyBalanceType,
MaterialBalanceType,
MomentumBalanceType,
UnitModelBlockData,
useDefault,
)
from idaes.core.util.constants import Constants
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
from idaes.core.util.misc import add_object_reference
import idaes.core.util.scaling as iscale
import idaes.logger as idaeslog
from enum import Enum
from watertap.core import ControlVolume1DBlock, InitializationMixin
from watertap.costing.unit_models.electrodialysis import cost_electrodialysis
__author__ = "Xiangyu Bi, Austin Ladshaw"
_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("Electrodialysis1D")
class Electrodialysis1DData(InitializationMixin, UnitModelBlockData):
"""
1D Electrodialysis Model
"""
# CONFIG are options for the unit model
CONFIG = ConfigBlock()
# These config args are common to any control volume
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.""",
),
)
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_Voltage,
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 calculated from the empirical equation."
"``LimitingCurrentDensityMethod.Theoretical``", "Limiting current density is calculated from a theoretical equation."
""",
),
)
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.}""",
),
)
CONFIG.declare(
"transformation_method",
ConfigValue(
default="dae.finite_difference",
description="Discretization method to use for DAE transformation",
doc="""Discretization method to use for DAE transformation. See Pyomo
documentation for supported transformations.""",
),
)
CONFIG.declare(
"transformation_scheme",
ConfigValue(
default="BACKWARD",
description="Discretization scheme to use for DAE transformation",
doc="""Discretization scheme to use when transforming domain. See
Pyomo documentation for supported schemes.""",
),
)
CONFIG.declare(
"finite_elements",
ConfigValue(
default=10,
domain=int,
description="Number of finite elements in length domain",
doc="""Number of finite elements to use when discretizing length
domain (default=10)""",
),
)
CONFIG.declare(
"collocation_points",
ConfigValue(
default=2,
domain=int,
description="Number of collocation points per finite element",
doc="""Number of collocation points to use per finite element when
discretizing length domain (default=2)""",
),
)
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()
self._validate_config()
# this creates blank scaling factors, which are populated later
self.scaling_factor = Suffix(direction=Suffix.EXPORT)
# Get the base units of measurement from the property definition
units_meta = self.config.property_package.get_metadata().get_derived_units
# Create essential sets
add_object_reference(
self, "component_set", self.config.property_package.component_list
)
add_object_reference(
self, "solute_set", self.config.property_package.solute_set
)
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)
self.membrane_set = Set(
initialize=["cem", "aem"]
) # cem = Cation-Exchange Membrane aem = Anion-Exchange Membrane
self.electrode_side_set = Set(initialize=["cathode_left", "anode_right"])
# Length var for building 1D control volume
self.cell_length = Var(
initialize=0.5,
bounds=(1e-3, 1e2),
units=pyunits.meter,
doc="Length of the electrodialysis cell/stack, in parallel to the convective flow",
)
# Control Volume for the Diluate channel:
self.diluate = ControlVolume1DBlock(
dynamic=self.config.dynamic,
has_holdup=self.config.has_holdup,
property_package=self.config.property_package,
property_package_args=self.config.property_package_args,
transformation_method=self.config.transformation_method,
transformation_scheme=self.config.transformation_scheme,
finite_elements=self.config.finite_elements,
collocation_points=self.config.collocation_points,
)
self.diluate.add_geometry(length_var=self.cell_length)
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,
)
# Below is declared the electrical power var and its derivative var,
# which is a performance metric of the entire electrodialysis stack.
# This var takes the "diluate" as the parent to utilize the discretization (as in Pyomo DAE) of this block for solving.
self.diluate.power_electrical_x = Var(
self.flowsheet().time,
self.diluate.length_domain,
initialize=0,
bounds=(0, 12100),
domain=NonNegativeReals,
units=pyunits.watt,
doc="Electrical power consumption of a stack",
)
self.diluate.Dpower_electrical_Dx = DerivativeVar(
self.diluate.power_electrical_x,
wrt=self.diluate.length_domain,
units=pyunits.watt,
)
add_object_reference(
self, "dens_mass", self.diluate.properties[0, 0].dens_mass_phase["Liq"]
)
add_object_reference(
self, "visc_d", self.diluate.properties[0, 0].visc_d_phase["Liq"]
)
# Apply the discretization transformation (Pyomo DAE) to the diluate block
self.diluate.apply_transformation()
# Control volume for the Concentrate channel
self.concentrate = ControlVolume1DBlock(
dynamic=self.config.dynamic,
has_holdup=self.config.has_holdup,
property_package=self.config.property_package,
property_package_args=self.config.property_package_args,
transformation_method=self.config.transformation_method,
transformation_scheme=self.config.transformation_scheme,
finite_elements=self.config.finite_elements,
collocation_points=self.config.collocation_points,
)
self.concentrate.add_geometry(length_var=self.cell_length)
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,
)
self.concentrate.apply_transformation()
# Add inlet and outlet as ports for Diluate and Concentrate
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)
# Create unit model parameters and vars
self.cell_pair_num = Var(
initialize=1,
domain=NonNegativeReals,
bounds=(1, 10000),
units=pyunits.dimensionless,
doc="cell pair number in a stack",
)
# Note: domain is set as Reals for optimizaiton convenience,
# although this var is technically integer.
# 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, parallel to the current/ion flux direction",
)
self.channel_height = Var(
initialize=0.0001,
units=pyunits.meter,
doc="The distance between 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.config.property_package.ion_set
| self.config.property_package.solute_set,
initialize=1e-10,
bounds=(1e-16, 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.config.property_package.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.total_areal_resistance_x = Var(
self.flowsheet().time,
self.diluate.length_domain,
initialize=1e-2,
bounds=(0, 100),
domain=NonNegativeReals,
units=pyunits.ohm * pyunits.meter**2,
doc="Total areal resistance of a stack ",
)
if self.config.operation_mode == ElectricalOperationMode.Constant_Current:
self.current_applied = Var(
self.flowsheet().time,
initialize=1,
bounds=(0, 1000),
units=pyunits.amp,
doc="Current across a cell-pair or stack, declared under the 'Constant Current' mode only",
)
self.current_density_x = Var(
self.flowsheet().time,
self.diluate.length_domain,
initialize=1,
bounds=(0, 1000),
units=pyunits.amp * pyunits.meter**-2,
doc="Current density accross the membrane as a function of the normalized length",
)
if self.config.operation_mode == ElectricalOperationMode.Constant_Voltage:
self.voltage_applied = 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.voltage_x = Var(
self.flowsheet().time,
self.diluate.length_domain,
initialize=100,
bounds=(0, 1000),
units=pyunits.volt,
doc="Voltage across a stack",
)
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
# Note that the power_electrical_x was declared under the diluate block
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.current_efficiency_x = Var(
self.flowsheet().time,
self.diluate.length_domain,
initialize=0.9,
bounds=(0, 1 + 1e-10),
units=pyunits.dimensionless,
doc="The overall current efficiency for deionization",
)
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,
self.diluate.length_domain,
initialize=0.01,
units=pyunits.meter * pyunits.second**-1,
doc="Linear velocity of flow",
)
self.velocity_concentrate = Var(
self.flowsheet().time,
self.diluate.length_domain,
initialize=0.01,
units=pyunits.meter * pyunits.second**-1,
doc="Linear velocity of flow",
)
# TODO: consider adding more performance as needed.
self._make_performance()
def _make_performance(self):
if (
self.config.has_nonohmic_potential_membrane
or self.config.has_Nernst_diffusion_layer
):
self.conc_mem_surf_mol_x = Var(
self.membrane_set,
self.electrode_side_set,
self.flowsheet().time,
self.diluate.length_domain,
self.config.property_package.ion_set,
initialize=500,
bounds=(0, 1e5),
units=pyunits.mol * pyunits.meter**-3,
doc="Membane surface concentration of components",
)
if self.config.has_nonohmic_potential_membrane:
self._make_performance_nonohm_mem()
if self.config.has_Nernst_diffusion_layer:
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,
self.diluate.length_domain,
doc="Express deltaP_term by the calculated pressure drop data, diluate.",
)
def eq_deltaP_diluate(self, t, x):
return self.diluate.deltaP[t, x] == -self.pressure_drop[t]
@self.Constraint(
self.flowsheet().time,
self.diluate.length_domain,
doc="Express deltaP_term by the calculated pressure drop data, concentrate.",
)
def eq_deltaP_concentrate(self, t, x):
return self.concentrate.deltaP[t, x] == -self.pressure_drop[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. "
)
# To require H2O must be in the component
if "H2O" not in self.component_set:
raise ConfigurationError(
"Property Package MUST constain 'H2O' as a component"
)
# -------- Add constraints ---------
@self.Constraint(
self.flowsheet().time,
self.diluate.length_domain,
doc="Calculate flow velocity in a single diluate channel",
)
def eq_get_velocity_diluate(self, t, x):
return (
self.velocity_diluate[t, x]
* self.cell_width
* self.channel_height
* self.spacer_porosity
* self.cell_pair_num
== self.diluate.properties[t, x].flow_vol_phase["Liq"]
)
@self.Constraint(
self.flowsheet().time,
self.diluate.length_domain,
doc="Calculate flow velocity in a single concentrate channel",
)
def eq_get_velocity_concentrate(self, t, x):
return (
self.velocity_concentrate[t, x]
* self.cell_width
* self.channel_height
* self.spacer_porosity
* self.cell_pair_num
== self.concentrate.properties[t, x].flow_vol_phase["Liq"]
)
@self.Constraint(
self.flowsheet().time,
self.diluate.length_domain,
doc="Calculate the total areal resistance of a stack",
)
def eq_get_total_areal_resistance_x(self, t, x):
if self.config.has_Nernst_diffusion_layer:
return self.total_areal_resistance_x[t, x] == (
(
self.membrane_areal_resistance["aem"]
+ self.membrane_areal_resistance["cem"]
+ (
self.channel_height
- self.dl_thickness_x["cem", "cathode_left", t, x]
- self.dl_thickness_x["aem", "anode_right", t, x]
)
* self.concentrate.properties[t, x].elec_cond_phase["Liq"] ** -1
+ (
self.channel_height
- self.dl_thickness_x["cem", "anode_right", t, x]
- self.dl_thickness_x["aem", "cathode_left", t, x]
)
* self.diluate.properties[t, x].elec_cond_phase["Liq"] ** -1
)
* self.cell_pair_num
+ self.electrodes_resistance
)
else:
return self.total_areal_resistance_x[t, x] == (
(
self.membrane_areal_resistance["aem"]
+ self.membrane_areal_resistance["cem"]
+ self.channel_height
* (
self.concentrate.properties[t, x].elec_cond_phase["Liq"]
** -1
+ self.diluate.properties[t, x].elec_cond_phase["Liq"] ** -1
)
)
* self.cell_pair_num
+ self.electrodes_resistance
)
@self.Constraint(
self.flowsheet().time,
self.diluate.length_domain,
doc="calcualte current density from the electrical input",
)
def eq_get_current_density(self, t, x):
if self.config.operation_mode == ElectricalOperationMode.Constant_Current:
return (
self.current_density_x[t, x] * self.cell_width * self.diluate.length
== self.current_applied[t]
)
else:
if self.config.has_nonohmic_potential_membrane:
if self.config.has_Nernst_diffusion_layer:
return (
self.current_density_x[t, x]
* self.total_areal_resistance_x[t, x]
+ (
self.potential_ohm_dl_x["cem", t, x]
+ self.potential_ohm_dl_x["aem", t, x]
+ self.potential_nonohm_dl_x["cem", t, x]
+ self.potential_nonohm_dl_x["aem", t, x]
+ self.potential_nonohm_membrane_x["cem", t, x]
+ self.potential_nonohm_membrane_x["aem", t, x]
)
* self.cell_pair_num
== self.voltage_applied[t]
)
else:
return (
self.current_density_x[t, x]
* self.total_areal_resistance_x[t, x]
+ (
self.potential_nonohm_membrane_x["cem", t, x]
+ self.potential_nonohm_membrane_x["aem", t, x]
)
* self.cell_pair_num
== self.voltage_applied[t]
)
else:
if self.config.has_Nernst_diffusion_layer:
return (
self.current_density_x[t, x]
* self.total_areal_resistance_x[t, x]
+ (
self.potential_ohm_dl_x["cem", t, x]
+ self.potential_ohm_dl_x["aem", t, x]
+ self.potential_nonohm_dl_x["cem", t, x]
+ self.potential_nonohm_dl_x["aem", t, x]
)
* self.cell_pair_num
== self.voltage_applied[t]
)
else:
return (
self.current_density_x[t, x]
* self.total_areal_resistance_x[t, x]
== self.voltage_applied[t]
)
@self.Constraint(
self.flowsheet().time,
self.diluate.length_domain,
doc="calcualte length_indexed voltage",
)
def eq_get_voltage_x(self, t, x):
if self.config.has_nonohmic_potential_membrane:
if self.config.has_Nernst_diffusion_layer:
return (
self.current_density_x[t, x]
* self.total_areal_resistance_x[t, x]
+ (
self.potential_ohm_dl_x["cem", t, x]
+ self.potential_ohm_dl_x["aem", t, x]
+ self.potential_nonohm_dl_x["cem", t, x]
+ self.potential_nonohm_dl_x["aem", t, x]
+ self.potential_nonohm_membrane_x["cem", t, x]
+ self.potential_nonohm_membrane_x["aem", t, x]
)
* self.cell_pair_num
== self.voltage_x[t, x]
)
else:
return (
self.current_density_x[t, x]
* self.total_areal_resistance_x[t, x]
+ (
self.potential_nonohm_membrane_x["cem", t, x]
+ self.potential_nonohm_membrane_x["aem", t, x]
)
* self.cell_pair_num
== self.voltage_x[t, x]
)
else:
if self.config.has_Nernst_diffusion_layer:
return (
self.current_density_x[t, x]
* self.total_areal_resistance_x[t, x]
+ (
self.potential_ohm_dl_x["cem", t, x]
+ self.potential_ohm_dl_x["aem", t, x]
+ self.potential_nonohm_dl_x["cem", t, x]
+ self.potential_nonohm_dl_x["aem", t, x]
)
* self.cell_pair_num
== self.voltage_x[t, x]
)
else:
return (
self.current_density_x[t, x]
* self.total_areal_resistance_x[t, x]
== self.voltage_x[t, x]
)
# Mass Transfer for the Diluate
@self.Constraint(
self.flowsheet().time,
self.diluate.length_domain,
self.config.property_package.phase_list,
self.config.property_package.component_list,
doc="Mass transfer term diluate channel",
)
def eq_mass_transfer_term_diluate(self, t, x, p, j):
if j == "H2O":
if self.config.has_Nernst_diffusion_layer:
return (
self.diluate.mass_transfer_term[t, x, p, j]
== (
-self.cell_width
* (
self.water_trans_number_membrane["cem"]
+ self.water_trans_number_membrane["aem"]
)
* (
self.current_density_x[t, x]
/ Constants.faraday_constant
)
- self.cell_width
* self.diluate.properties[
0, self.diluate.length_domain.first()
].dens_mass_solvent
/ self.config.property_package.mw_comp[j]
* (
self.water_permeability_membrane["cem"]
+ self.water_permeability_membrane["aem"]
)
* (
self.concentrate.properties[t, x].pressure_osm_phase[p]
* (
1
+ self.current_density_x[t, x]
/ self.current_dens_lim_x[t, x]
)
- self.diluate.properties[t, x].pressure_osm_phase[p]
* (
1
- self.current_density_x[t, x]
/ self.current_dens_lim_x[t, x]
)
)
)
* self.cell_pair_num
)
else:
return (
self.diluate.mass_transfer_term[t, x, p, j]
== (
-self.cell_width
* (
self.water_trans_number_membrane["cem"]
+ self.water_trans_number_membrane["aem"]
)
* (
self.current_density_x[t, x]
/ Constants.faraday_constant
)
- self.cell_width
* self.diluate.properties[
0, self.diluate.length_domain.first()
].dens_mass_solvent
/ self.config.property_package.mw_comp[j]
* (
self.water_permeability_membrane["cem"]
+ self.water_permeability_membrane["aem"]
)
* (
self.concentrate.properties[t, x].pressure_osm_phase[p]
- self.diluate.properties[t, x].pressure_osm_phase[p]
)
)
* self.cell_pair_num
)
elif j in self.config.property_package.ion_set:
if self.config.has_Nernst_diffusion_layer:
return (
self.diluate.mass_transfer_term[t, x, p, j]
== (
-self.cell_width
* (
self.ion_trans_number_membrane["cem", j]
- self.ion_trans_number_membrane["aem", j]
)
* (self.current_utilization * self.current_density_x[t, x])
/ (
self.config.property_package.charge_comp[j]
* Constants.faraday_constant
)
+ self.cell_width
* (
self.solute_diffusivity_membrane["cem", j]
/ self.membrane_thickness["cem"]
* (
self.conc_mem_surf_mol_x[
"cem", "cathode_left", t, x, j
]
- self.conc_mem_surf_mol_x[
"cem", "anode_right", t, x, j
]
)
+ self.solute_diffusivity_membrane["aem", j]
/ self.membrane_thickness["aem"]
* (
self.conc_mem_surf_mol_x[
"aem", "anode_right", t, x, j
]
- self.conc_mem_surf_mol_x[
"aem", "cathode_left", t, x, j
]
)
)
)
* self.cell_pair_num
)
else:
return (
self.diluate.mass_transfer_term[t, x, p, j]
== (
-self.cell_width
* (
self.ion_trans_number_membrane["cem", j]
- self.ion_trans_number_membrane["aem", j]
)
* (self.current_utilization * self.current_density_x[t, x])
/ (
self.config.property_package.charge_comp[j]
* Constants.faraday_constant
)
+ self.cell_width
* (
self.solute_diffusivity_membrane["cem", j]
/ self.membrane_thickness["cem"]
+ self.solute_diffusivity_membrane["aem", j]
/ self.membrane_thickness["aem"]
)
* (
self.concentrate.properties[t, x].conc_mol_phase_comp[
p, j
]
- self.diluate.properties[t, x].conc_mol_phase_comp[
p, j
]
)
)
* self.cell_pair_num
)
else:
return (
self.diluate.mass_transfer_term[t, x, p, j]
== (
self.cell_width
* (
self.solute_diffusivity_membrane["cem", j]
/ self.membrane_thickness["cem"]
+ self.solute_diffusivity_membrane["aem", j]
/ self.membrane_thickness["aem"]
)
* (
self.concentrate.properties[t, x].conc_mol_phase_comp[p, j]
- self.diluate.properties[t, x].conc_mol_phase_comp[p, j]
)
)
* self.cell_pair_num
)
# Mass Transfer for the Concentrate
@self.Constraint(
self.flowsheet().config.time,
self.diluate.length_domain,
self.config.property_package.phase_list,
self.config.property_package.component_list,
doc="Mass transfer term concentrate channel",
)
def eq_mass_transfer_term_concentrate(self, t, x, p, j):
return (
self.concentrate.mass_transfer_term[t, x, p, j]
== -self.diluate.mass_transfer_term[t, x, p, j]
)
# Performance Metrics calculation
@self.Constraint(
self.flowsheet().config.time,
self.diluate.length_domain,
doc="Electrical power consumption of a stack",
)
def eq_power_electrical(self, t, x):
if x == self.diluate.length_domain.first():
self.diluate.power_electrical_x[t, x].fix(0)
return Constraint.Skip
else:
return (
self.diluate.Dpower_electrical_Dx[t, x]
== self.voltage_x[t, x]
* self.current_density_x[t, x]
* self.cell_width
* self.diluate.length
)
@self.Constraint(
self.flowsheet().config.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[
t, self.diluate.length_domain.last()
].flow_vol_phase["Liq"]
== self.diluate.power_electrical_x[t, self.diluate.length_domain.last()]
)
@self.Constraint(
self.flowsheet().config.time,
self.diluate.length_domain,
self.config.property_package.phase_list,
doc="Overall current efficiency evaluation",
)
def eq_current_efficiency_x(self, t, x, p):
return (
self.current_efficiency_x[t, x]
* self.current_density_x[t, x]
* self.cell_width
* self.cell_pair_num
== -sum(
self.diluate.mass_transfer_term[t, x, p, j]
* self.config.property_package.charge_comp[j]
for j in self.cation_set
)
* Constants.faraday_constant
)
@self.Constraint(
self.flowsheet().config.time,
doc="Water recovery by mass",
)
def eq_recovery_mass_H2O(self, t):
return (
self.recovery_mass_H2O[t]
* (
self.diluate.properties[
t, self.diluate.length_domain.first()
].flow_mass_phase_comp["Liq", "H2O"]
+ self.concentrate.properties[
t, self.diluate.length_domain.first()
].flow_mass_phase_comp["Liq", "H2O"]
)
== self.diluate.properties[
t, self.diluate.length_domain.last()
].flow_mass_phase_comp["Liq", "H2O"]
)
def _make_performance_nonohm_mem(self):
self.potential_nonohm_membrane_x = Var(
self.membrane_set,
self.flowsheet().time,
self.diluate.length_domain,
initialize=0.01, # to inspect
bounds=(-50, 50),
units=pyunits.volt,
doc="Nonohmic potential across a membane",
)
@self.Constraint(
self.membrane_set,
self.electrode_side_set,
self.flowsheet().time,
self.diluate.length_domain,
self.ion_set,
doc="calcualte current density from the electrical input",
)
def eq_set_surface_conc(self, mem, side, t, x, 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_x[mem, side, t, x, j]
== self.concentrate.properties[t, x].conc_mol_phase_comp[
"Liq", j
]
)
else:
return (
self.conc_mem_surf_mol_x[mem, side, t, x, j]
== self.diluate.properties[t, x].conc_mol_phase_comp["Liq", j]
)
else:
return Constraint.Skip
@self.Constraint(
self.membrane_set,
self.flowsheet().time,
self.diluate.length_domain,
doc="Calculate the total non-ohmic potential across an iem; this takes account of diffusion and Donnan Potentials",
)
def eq_potential_nonohm_membrane_x(self, mem, t, x):
if (
not self.config.has_Nernst_diffusion_layer
) and x == self.diluate.length_domain.first():
self.potential_nonohm_membrane_x[mem, t, x].fix(0)
return Constraint.Skip
return self.potential_nonohm_membrane_x[mem, t, x] == (
Constants.gas_constant
* self.diluate.properties[t, x].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_x[mem, "cathode_left", t, x, j]
for j in self.ion_set
)
/ sum(
self.conc_mem_surf_mol_x[mem, "anode_right", t, x, j]
for j in self.ion_set
)
)
) # Note: the log argument is taken as *total ion concentration* while in the original equation as *electrolyte concentration*
# This is mathematically valid as the ratio eliminate the difference and electro-neutrality stands.
def _make_performance_dl_polarization(self):
self.current_dens_lim_x = Var(
self.flowsheet().time,
self.diluate.length_domain,
initialize=500,
bounds=(0, 10000),
units=pyunits.amp * pyunits.meter**-2,
doc="Limiting Current Density accross the membrane as a function of the normalized length",
)
self.potential_nonohm_dl_x = Var(
self.membrane_set,
self.flowsheet().time,
self.diluate.length_domain,
initialize=0.01, # to inspect
bounds=(-50, 50),
units=pyunits.volt,
doc="Nonohmic potential in two diffusion layers on the two sides of a membrane",
)
self.potential_ohm_dl_x = Var(
self.membrane_set,
self.flowsheet().time,
self.diluate.length_domain,
initialize=0.01, # to inspect
bounds=(0, 50),
units=pyunits.volt,
doc="Ohmic potential in two diffusion layers on the two sides of a membrane",
)
self.dl_thickness_x = Var(
self.membrane_set,
self.electrode_side_set,
self.flowsheet().time,
self.diluate.length_domain,
initialize=0.0005,
bounds=(0, 1e-2),
units=pyunits.m,
doc="Thickness of the diffusion layer",
)
if (
self.config.limiting_current_density_method
== LimitingCurrentDensityMethod.InitialValue
):
@self.Constraint(
self.flowsheet().time,
self.diluate.length_domain,
doc="Calculate length-indexed limiting current density",
)
def eq_current_dens_lim_x(self, t, x):
return self.current_dens_lim_x[t, x] == (
self.config.limiting_current_density_data
* pyunits.amp
* pyunits.meter**-2
/ sum(
self.diluate.properties[t, 0].conc_mol_phase_comp["Liq", j]
for j in self.cation_set
)
* sum(
self.diluate.properties[t, x].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="emprical parameter b to calculate limitting 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="emprical parameter a to calculate limitting current density",
)
@self.Constraint(
self.flowsheet().time,
self.diluate.length_domain,
doc="Calculate length-indexed limiting current density",
)
def eq_current_dens_lim_x(self, t, x):
return self.current_dens_lim_x[
t, x
] == self.param_a * self.velocity_diluate[t, x] ** self.param_b * sum(
self.config.property_package.charge_comp[j]
* self.diluate.properties[t, x].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()
@self.Constraint(
self.flowsheet().time,
self.diluate.length_domain,
doc="Calculate length-indexed limiting current density",
)
def eq_current_dens_lim_x(self, t, x):
return self.current_dens_lim_x[
t, x
] == 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[t, x].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]
* self.diluate.properties[t, x].conc_mol_phase_comp["Liq", j]
for j in self.cation_set
)
@self.Constraint(
self.membrane_set,
self.electrode_side_set,
self.flowsheet().time,
self.diluate.length_domain,
self.config.property_package.ion_set,
doc="Establish relationship between interfacial concentration polarization ratio and current density",
)
def eq_conc_polarization_ratio(self, mem, side, t, x, j):
if (mem == "cem" and side == "cathode_left") or (
mem == "aem" and side == "anode_right"
):
return self.conc_mem_surf_mol_x[
mem, side, t, x, j
] / self.concentrate.properties[t, x].conc_mol_phase_comp["Liq", j] == (
1 + self.current_density_x[t, x] / self.current_dens_lim_x[t, x]
)
else:
return self.conc_mem_surf_mol_x[
mem, side, t, x, j
] / self.diluate.properties[t, x].conc_mol_phase_comp["Liq", j] == (
1 - self.current_density_x[t, x] / self.current_dens_lim_x[t, x]
)
@self.Constraint(
self.membrane_set,
self.flowsheet().time,
self.diluate.length_domain,
doc="Calculate the total non-ohmic potential across the two diffusion layers of an iem.",
)
def eq_potential_nonohm_dl(self, mem, t, x):
if mem == "cem":
return self.potential_nonohm_dl_x[mem, t, x] == (
Constants.gas_constant
* self.diluate.properties[t, x].temperature
/ Constants.faraday_constant
* (
sum(
self.diluate.properties[t, x].trans_num_phase_comp["Liq", j]
/ self.config.property_package.charge_comp[j]
for j in self.cation_set
)
+ sum(
self.diluate.properties[t, x].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_x[mem, "anode_right", t, x, j]
for j in self.ion_set
)
* sum(
self.concentrate.properties[t, x].conc_mol_phase_comp[
"Liq", j
]
for j in self.ion_set
)
* sum(
self.conc_mem_surf_mol_x[mem, "cathode_left", t, x, j]
for j in self.ion_set
)
** -1
* sum(
self.diluate.properties[t, x].conc_mol_phase_comp["Liq", j]
for j in self.ion_set
)
** -1
)
)
else:
return self.potential_nonohm_dl_x[mem, t, x] == (
Constants.gas_constant
* self.diluate.properties[t, x].temperature
/ Constants.faraday_constant
* (
sum(
self.diluate.properties[t, x].trans_num_phase_comp["Liq", j]
/ self.config.property_package.charge_comp[j]
for j in self.cation_set
)
+ sum(
self.diluate.properties[t, x].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_x[mem, "anode_right", t, x, j]
for j in self.ion_set
)
* sum(
self.diluate.properties[t, x].conc_mol_phase_comp["Liq", j]
for j in self.ion_set
)
* sum(
self.conc_mem_surf_mol_x[mem, "cathode_left", t, x, j]
for j in self.ion_set
)
** -1
* sum(
self.concentrate.properties[t, x].conc_mol_phase_comp[
"Liq", j
]
for j in self.ion_set
)
** -1
)
)
@self.Constraint(
self.membrane_set,
self.flowsheet().time,
self.diluate.length_domain,
doc="Calculate the total ohmic potential across the two diffusion layers of an iem.",
)
def eq_potential_ohm_dl_x(self, mem, t, x):
if mem == "cem":
return self.potential_ohm_dl_x[mem, t, x] == (
Constants.faraday_constant
* (
sum(
self.diluate.properties[t, x].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[t, x].trans_num_phase_comp["Liq", j]
/ self.config.property_package.charge_comp[j]
for j in self.cation_set
)
)
** -1
* self.diluate.properties[t, x].equiv_conductivity_phase["Liq"]
** -1
* log(
sum(
self.conc_mem_surf_mol_x[mem, "anode_right", t, x, j]
for j in self.ion_set
)
** -1
* sum(
self.concentrate.properties[t, x].conc_mol_phase_comp[
"Liq", j
]
for j in self.ion_set
)
** -1
* sum(
self.conc_mem_surf_mol_x[mem, "cathode_left", t, x, j]
for j in self.ion_set
)
* sum(
self.diluate.properties[t, x].conc_mol_phase_comp["Liq", j]
for j in self.ion_set
)
)
)
else:
return self.potential_ohm_dl_x[mem, t, x] == (
-Constants.faraday_constant
* (
sum(
self.diluate.properties[t, x].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[t, x].trans_num_phase_comp["Liq", j]
/ self.config.property_package.charge_comp[j]
for j in self.cation_set
)
)
** -1
* self.diluate.properties[t, x].equiv_conductivity_phase["Liq"]
** -1
* log(
sum(
self.conc_mem_surf_mol_x[mem, "anode_right", t, x, j]
for j in self.ion_set
)
* sum(
self.diluate.properties[t, x].conc_mol_phase_comp["Liq", j]
for j in self.ion_set
)
* sum(
self.conc_mem_surf_mol_x[mem, "cathode_left", t, x, j]
for j in self.ion_set
)
** -1
* sum(
self.concentrate.properties[t, x].conc_mol_phase_comp[
"Liq", j
]
for j in self.ion_set
)
** -1
)
)
@self.Constraint(
self.membrane_set,
self.electrode_side_set,
self.flowsheet().time,
self.diluate.length_domain,
doc="Calculate the total non-ohmic potential across the two diffusion layers of an iem.",
)
def eq_dl_thickness(self, mem, side, t, x):
if mem == "cem" and side == "cathode_left":
return self.dl_thickness_x[mem, side, t, x] == (
Constants.faraday_constant
* (
sum(
self.diluate.properties[t, x].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[t, x].trans_num_phase_comp["Liq", j]
/ self.config.property_package.charge_comp[j]
for j in self.cation_set
)
)
** -1
* sum(
self.concentrate.properties[t, x].conc_mol_phase_comp["Liq", j]
for j in self.cation_set
)
* self.current_dens_lim_x[t, x] ** -1
)
elif mem == "cem" and side == "anode_right":
return self.dl_thickness_x[mem, side, t, x] == (
Constants.faraday_constant
* (
sum(
self.diluate.properties[t, x].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[t, x].trans_num_phase_comp["Liq", j]
/ self.config.property_package.charge_comp[j]
for j in self.cation_set
)
)
** -1
* sum(
self.diluate.properties[t, x].conc_mol_phase_comp["Liq", j]
for j in self.cation_set
)
* self.current_dens_lim_x[t, x] ** -1
)
elif mem == "aem" and side == "cathode_left":
return self.dl_thickness_x[mem, side, t, x] == (
-Constants.faraday_constant
* (
sum(
self.diluate.properties[t, x].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[t, x].trans_num_phase_comp["Liq", j]
/ self.config.property_package.charge_comp[j]
for j in self.cation_set
)
)
** -1
* sum(
self.diluate.properties[t, x].conc_mol_phase_comp["Liq", j]
for j in self.cation_set
)
* self.current_dens_lim_x[t, x] ** -1
)
else:
return self.dl_thickness_x[mem, side, t, x] == (
-Constants.faraday_constant
* (
sum(
self.diluate.properties[t, x].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[t, x].trans_num_phase_comp["Liq", j]
/ self.config.property_package.charge_comp[j]
for j in self.cation_set
)
)
** -1
* sum(
self.concentrate.properties[t, x].conc_mol_phase_comp["Liq", j]
for j in self.cation_set
)
* self.current_dens_lim_x[t, x] ** -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, 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 Sc",
)
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 = Var(
self.flowsheet().time,
initialize=1e4,
units=pyunits.pascal * pyunits.meter**-1,
doc="pressure drop per unit of length",
)
self.pressure_drop_total = Var(
self.flowsheet().time,
initialize=1e6,
units=pyunits.pascal,
doc="pressure drop over an entire ED stack",
)
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
and self.config.limiting_current_density_method
== LimitingCurrentDensityMethod.Theoretical
):
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 per unit length",
)
def eq_pressure_drop(self, t):
return (
self.pressure_drop[t]
== self.dens_mass
* self.friction_factor
* self.velocity_diluate[0, 0] ** 2
* 0.5
* self.hydraulic_diameter**-1
)
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_total(self, t):
return (
self.pressure_drop_total[t] == self.pressure_drop[t] * self.cell_length
)
# Intialization routines
[docs] def initialize_build(
self,
state_args=None,
outlvl=idaeslog.NOTSET,
solver=None,
optarg=None,
fail_on_warning=False,
ignore_dof=False,
):
"""
General wrapper for electrodialysis_1D 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)
fail_on_warning : boolean argument to fail or only produce warning upon unsuccessful solve (default=False)
ignore_dof : boolean argument to ignore when DOF != 0 (default=False)
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 intial conditions over the 1D length from the state vars
for k in self.keys():
for set in self[k].diluate.properties:
if ("flow_mol_phase_comp" or "flow_mass_phase_comp") not in self[
k
].diluate.properties[set].define_state_vars():
raise ConfigurationError(
"Electrodialysis1D unit model requires "
"either a 'flow_mol_phase_comp' or 'flow_mass_phase_comp' "
"state variable basis to apply the 'propogate_initial_state' method"
)
if "temperature" in self[k].diluate.properties[set].define_state_vars():
self[k].diluate.properties[set].temperature = value(
self[k].diluate.properties[(0.0, 0.0)].temperature
)
if "pressure" in self[k].diluate.properties[set].define_state_vars():
self[k].diluate.properties[set].pressure = value(
self[k].diluate.properties[(0.0, 0.0)].pressure
)
if (
"flow_mol_phase_comp"
in self[k].diluate.properties[set].define_state_vars()
):
for ind in self[k].diluate.properties[set].flow_mol_phase_comp:
self[k].diluate.properties[set].flow_mol_phase_comp[ind] = (
value(
self[k]
.diluate.properties[(0.0, 0.0)]
.flow_mol_phase_comp[ind]
)
)
if (
"flow_mass_phase_comp"
in self[k].diluate.properties[set].define_state_vars()
):
for ind in self[k].diluate.properties[set].flow_mass_phase_comp:
self[k].diluate.properties[set].flow_mass_phase_comp[ind] = (
value(
self[k]
.diluate.properties[(0.0, 0.0)]
.flow_mass_phase_comp[ind]
)
)
if hasattr(self[k], "conc_mem_surf_mol_x"):
for mem in self[k].membrane_set:
for side in self[k].electrode_side_set:
for j in self[k].ion_set:
self[k].conc_mem_surf_mol_x[
mem, side, set, j
].set_value(
self[k]
.diluate.properties[set]
.conc_mol_phase_comp["Liq", j]
)
for set in self[k].concentrate.properties:
if ("flow_mol_phase_comp" or "flow_mass_phase_comp") not in self[
k
].concentrate.properties[set].define_state_vars():
raise ConfigurationError(
"Electrodialysis1D unit model requires "
"either a 'flow_mol_phase_comp' or 'flow_mass_phase_comp' "
"state variable basis to apply the 'propogate_initial_state' method"
)
if (
"temperature"
in self[k].concentrate.properties[set].define_state_vars()
):
self[k].concentrate.properties[set].temperature = value(
self[k].concentrate.properties[(0.0, 0.0)].temperature
)
if (
"pressure"
in self[k].concentrate.properties[set].define_state_vars()
):
self[k].concentrate.properties[set].pressure = value(
self[k].concentrate.properties[(0.0, 0.0)].pressure
)
if (
"flow_mol_phase_comp"
in self[k].concentrate.properties[set].define_state_vars()
):
for ind in self[k].concentrate.properties[set].flow_mol_phase_comp:
self[k].concentrate.properties[set].flow_mol_phase_comp[ind] = (
value(
self[k]
.concentrate.properties[(0.0, 0.0)]
.flow_mol_phase_comp[ind]
)
)
if (
"flow_mass_phase_comp"
in self[k].concentrate.properties[set].define_state_vars()
):
for ind in self[k].concentrate.properties[set].flow_mass_phase_comp:
self[k].concentrate.properties[set].flow_mass_phase_comp[
ind
] = value(
self[k]
.concentrate.properties[(0.0, 0.0)]
.flow_mass_phase_comp[ind]
)
if hasattr(self[k], "conc_mem_surf_mol_x"):
for mem in self[k].membrane_set:
for side in self[k].electrode_side_set:
for j in self[k].ion_set:
self[k].conc_mem_surf_mol_x[
mem, side, set, j
].set_value(
self[k]
.concentrate.properties[set]
.conc_mol_phase_comp["Liq", j]
)
self[k].total_areal_resistance_x[set].set_value(
(
self[k].membrane_areal_resistance["aem"]
+ self[k].membrane_areal_resistance["cem"]
+ self[k].channel_height
* (
self[k].concentrate.properties[set].elec_cond_phase["Liq"]
** -1
+ self[k].diluate.properties[set].elec_cond_phase["Liq"]
** -1
)
)
* self[k].cell_pair_num
+ self[k].electrodes_resistance
)
# ---------------------------------------------------------------------
# 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.")
# ---------------------------------------------------------------------
if not ignore_dof:
check_dof(self, fail_flag=fail_on_warning, logger=init_log)
# Initialize concentrate block
flags_concentrate = self.concentrate.initialize(
outlvl=outlvl,
optarg=optarg,
solver=solver,
state_args=state_args,
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)))
check_solve(
res,
logger=init_log,
fail_flag=fail_on_warning,
checkpoint="Initialization Step 3",
)
# ---------------------------------------------------------------------
# Release state
self.diluate.release_state(flags_diluate, outlvl)
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()
units_meta = self.config.property_package.get_metadata().get_derived_units
# 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.cell_width, warning=True) is None:
iscale.set_scaling_factor(self.cell_width, 1)
if iscale.get_scaling_factor(self.cell_length, warning=True) is None:
iscale.set_scaling_factor(self.cell_length, 1)
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.membrane_thickness, warning=True) is None:
iscale.set_scaling_factor(self.membrane_thickness, 1e4)
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.solute_diffusivity_membrane, warning=True)
is None
):
iscale.set_scaling_factor(self.solute_diffusivity_membrane, 1e10)
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)
if (
iscale.get_scaling_factor(self.water_permeability_membrane, warning=True)
is None
):
iscale.set_scaling_factor(self.water_permeability_membrane, 1e4)
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.electrodes_resistance, warning=True) is None:
iscale.set_scaling_factor(self.electrodes_resistance, 1e4)
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[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, "voltage_applied") and (
iscale.get_scaling_factor(self.voltage_applied, warning=True) is None
):
iscale.set_scaling_factor(self.voltage_applied, 1)
if hasattr(self, "current_applied") and (
iscale.get_scaling_factor(self.current_applied, warning=True) is None
):
iscale.set_scaling_factor(self.current_applied, 1)
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, 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, 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
):
sf = iscale.get_scaling_factor(
self.pressure_drop
) * iscale.get_scaling_factor(self.cell_length)
iscale.set_scaling_factor(self.pressure_drop_total, sf)
# For vars below, the users can choose but not required to provide scaling factors.
# No warnings if no providing.
for ind in self.total_areal_resistance_x:
if (
iscale.get_scaling_factor(
self.total_areal_resistance_x[ind], warning=False
)
is None
):
sf = (
iscale.get_scaling_factor(self.membrane_areal_resistance) ** 2
+ iscale.get_scaling_factor(self.channel_height) ** 2
* (
iscale.get_scaling_factor(
self.diluate.properties[ind].elec_cond_phase["Liq"]
)
** -2
+ iscale.get_scaling_factor(
self.concentrate.properties[ind].elec_cond_phase["Liq"]
)
** -2
)
) ** 0.5 * iscale.get_scaling_factor(self.cell_pair_num)
iscale.set_scaling_factor(self.total_areal_resistance_x[ind], sf)
for ind in self.current_density_x:
if (
iscale.get_scaling_factor(self.current_density_x[ind], warning=False)
is None
):
if (
self.config.operation_mode
== ElectricalOperationMode.Constant_Current
):
sf = (
iscale.get_scaling_factor(self.current_applied)
/ iscale.get_scaling_factor(self.cell_width)
/ iscale.get_scaling_factor(self.cell_length)
)
iscale.set_scaling_factor(self.current_density_x[ind], sf)
else:
sf = iscale.get_scaling_factor(
self.voltage_applied
) / iscale.get_scaling_factor(self.total_areal_resistance_x[ind])
iscale.set_scaling_factor(self.current_density_x[ind], sf)
for ind in self.voltage_x:
if iscale.get_scaling_factor(self.voltage_x[ind], warning=False) is None:
sf = iscale.get_scaling_factor(
self.current_density_x[ind]
) * iscale.get_scaling_factor(self.total_areal_resistance_x[ind])
iscale.set_scaling_factor(self.voltage_x[ind], sf)
if iscale.get_scaling_factor(self.spacer_porosity, warning=False) is None:
iscale.set_scaling_factor(self.spacer_porosity, 1)
if hasattr(self, "conc_mem_surf_mol_x"):
for ind in self.conc_mem_surf_mol_x:
if iscale.get_scaling_factor(self.conc_mem_surf_mol_x[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_x[ind],
iscale.get_scaling_factor(
self.concentrate.properties[
ind[2], ind[3]
].conc_mol_phase_comp["Liq", ind[4]]
),
)
else:
iscale.set_scaling_factor(
self.conc_mem_surf_mol_x[ind],
iscale.get_scaling_factor(
self.diluate.properties[
ind[2], ind[3]
].conc_mol_phase_comp["Liq", ind[4]]
),
)
if hasattr(self, "current_dens_lim_x"):
if iscale.get_scaling_factor(self.current_dens_lim_x) is None:
if (
self.config.limiting_current_density_method
== LimitingCurrentDensityMethod.InitialValue
):
for ind in self.current_dens_lim_x:
sf = (
self.config.limiting_current_density_data**-1
* sum(
iscale.get_scaling_factor(
self.diluate.properties[
ind[0], 0
].conc_mol_phase_comp["Liq", j]
)
** 2
for j in self.cation_set
)
** -0.5
* sum(
iscale.get_scaling_factor(
self.diluate.properties[ind].conc_mol_phase_comp[
"Liq", j
]
)
** 2
for j in self.cation_set
)
** 0.5
)
iscale.set_scaling_factor(self.current_dens_lim_x[ind], sf)
elif (
self.config.limiting_current_density_method
== LimitingCurrentDensityMethod.Empirical
):
for ind in self.current_dens_lim_x:
sf = 25**-1 * sum(
iscale.get_scaling_factor(
self.diluate.properties[ind].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_x[ind], sf)
elif (
self.config.limiting_current_density_method
== LimitingCurrentDensityMethod.Theoretical
):
for ind in self.current_dens_lim_x:
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[ind].conc_mol_phase_comp[
"Liq", j
]
)
** 2
for j in self.cation_set
)
** 0.5
)
iscale.set_scaling_factor(self.current_dens_lim_x[ind], sf)
if hasattr(self, "potential_nonohm_membrane_x"):
if iscale.get_scaling_factor(self.potential_nonohm_membrane_x) is None:
for ind in self.potential_nonohm_membrane_x:
sf = (
value(Constants.faraday_constant)
* value(Constants.gas_constant) ** -1
* 298.15**-1
)
iscale.set_scaling_factor(self.potential_nonohm_membrane_x[ind], sf)
if hasattr(self, "potential_nonohm_dl_x"):
if iscale.get_scaling_factor(self.potential_nonohm_dl_x) is None:
for ind in self.potential_nonohm_dl_x:
sf = (
value(Constants.faraday_constant)
* value(Constants.gas_constant) ** -1
* 298.15**-1
)
iscale.set_scaling_factor(self.potential_nonohm_dl_x[ind], sf)
if hasattr(self, "potential_ohm_dl_x"):
if iscale.get_scaling_factor(self.potential_ohm_dl_x) is None:
for ind in self.potential_nonohm_dl_x:
sf = (
96485**-1
* sum(
iscale.get_scaling_factor(
self.diluate.properties[0, 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_x[ind], sf)
if hasattr(self, "dl_thickness_x"):
if iscale.get_scaling_factor(self.dl_thickness_x) is None:
for ind in self.dl_thickness_x:
sf = (
96485**-1
* sum(
iscale.get_scaling_factor(
self.diluate.properties[0, 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_x[ind, j])
** 2
for j in self.cation_set
)
** 0.5
* iscale.get_scaling_factor(
self.current_density_x[ind[2], ind[3]]
)
** -1
)
iscale.set_scaling_factor(self.dl_thickness_x[ind], sf)
for ind in self.diluate.power_electrical_x:
if (
iscale.get_scaling_factor(
self.diluate.power_electrical_x[ind], warning=False
)
is None
):
iscale.set_scaling_factor(
self.diluate.power_electrical_x[ind],
iscale.get_scaling_factor(self.voltage_x[ind])
* iscale.get_scaling_factor(self.current_density_x[ind])
* iscale.get_scaling_factor(self.cell_width)
* iscale.get_scaling_factor(self.cell_length),
)
for ind in self.diluate.Dpower_electrical_Dx:
if (
iscale.get_scaling_factor(
self.diluate.Dpower_electrical_Dx[ind], warning=False
)
is None
):
iscale.set_scaling_factor(
self.diluate.Dpower_electrical_Dx[ind],
iscale.get_scaling_factor(self.diluate.power_electrical_x[ind]),
)
if (
iscale.get_scaling_factor(self.specific_power_electrical, warning=False)
is None
):
iscale.set_scaling_factor(
self.specific_power_electrical,
3.6e6
* iscale.get_scaling_factor(
self.diluate.power_electrical_x[
0, self.diluate.length_domain.last()
]
)
* (
iscale.get_scaling_factor(
self.diluate.properties[
0, self.diluate.length_domain.last()
].flow_vol_phase["Liq"]
)
* iscale.get_scaling_factor(self.cell_pair_num)
)
** -1,
)
# Set up constraint scaling
for ind, c in self.eq_get_total_areal_resistance_x.items():
iscale.constraint_scaling_transform(
c, iscale.get_scaling_factor(self.total_areal_resistance_x[ind])
)
for ind, c in self.eq_get_current_density.items():
if self.config.operation_mode == ElectricalOperationMode.Constant_Current:
iscale.constraint_scaling_transform(
c, iscale.get_scaling_factor(self.current_applied[ind[0]])
)
else:
iscale.constraint_scaling_transform(
c, iscale.get_scaling_factor(self.voltage_applied[ind[0]])
)
for ind, c in self.eq_get_voltage_x.items():
iscale.constraint_scaling_transform(
c, iscale.get_scaling_factor(self.voltage_x[ind])
)
for ind, c in self.eq_get_velocity_diluate.items():
iscale.constraint_scaling_transform(
c,
iscale.get_scaling_factor(
self.diluate.properties[ind].flow_vol_phase["Liq"]
),
)
for ind, c in self.eq_get_velocity_concentrate.items():
iscale.constraint_scaling_transform(
c,
iscale.get_scaling_factor(
self.concentrate.properties[ind].flow_vol_phase["Liq"]
),
)
if hasattr(self, "eq_Re"):
iscale.constraint_scaling_transform(
self.eq_Re, iscale.get_scaling_factor(self.N_Re)
)
if hasattr(self, "eq_Sc"):
iscale.constraint_scaling_transform(
self.eq_Sc, iscale.get_scaling_factor(self.N_Sc)
)
if hasattr(self, "eq_Sh"):
iscale.constraint_scaling_transform(
self.eq_Sh, iscale.get_scaling_factor(self.N_Sh)
)
if hasattr(self, "eq_pressure_drop"):
for i, c in self.eq_pressure_drop.items():
iscale.constraint_scaling_transform(
c, iscale.get_scaling_factor(self.pressure_drop)
)
if hasattr(self, "eq_deltaP_diluate"):
for i, c in self.eq_deltaP_diluate.items():
iscale.constraint_scaling_transform(
c, iscale.get_scaling_factor(self.pressure_drop)
)
if hasattr(self, "eq_deltaP_concentrate"):
for i, c in self.eq_deltaP_concentrate.items():
iscale.constraint_scaling_transform(
c, iscale.get_scaling_factor(self.pressure_drop)
)
if hasattr(self, "eq_hydraulic_diameter"):
for i, c in self.eq_hydraulic_diameter.items():
iscale.constraint_scaling_transform(
c, iscale.get_scaling_factor(self.hydraulic_diameter)
)
if hasattr(self, "eq_pressure_drop_total"):
for i, c in self.eq_pressure_drop_total.items():
iscale.constraint_scaling_transform(
c, iscale.get_scaling_factor(self.pressure_drop_total)
)
if hasattr(self, "eq_friction_factor"):
iscale.constraint_scaling_transform(
self.eq_friction_factor, iscale.get_scaling_factor(self.friction_factor)
)
if hasattr(self, "eq_potential_nonohm_membrane_x"):
for ind, c in self.eq_potential_nonohm_membrane_x.items():
iscale.constraint_scaling_transform(
c, iscale.get_scaling_factor(self.potential_nonohm_membrane_x[ind])
)
if hasattr(self, "eq_current_dens_lim_x"):
for ind, c in self.eq_current_dens_lim_x.items():
iscale.constraint_scaling_transform(
c, iscale.get_scaling_factor(self.current_dens_lim_x[ind])
)
if hasattr(self, "eq_conc_polarization_ratio"):
for ind, c in self.eq_conc_polarization_ratio.items():
iscale.constraint_scaling_transform(c, 1)
if hasattr(self, "eq_potential_nonohm_dl_x"):
for ind, c in self.eq_potential_nonohm_dl_x.items():
iscale.constraint_scaling_transform(
c, iscale.get_scaling_factor(self.potential_nonohm_dl_x[ind])
)
if hasattr(self, "eq_potential_ohm_dl_x"):
for ind, c in self.eq_potential_ohm_dl_x.items():
iscale.constraint_scaling_transform(
c, iscale.get_scaling_factor(self.potential_ohm_dl_x[ind])
)
if hasattr(self, "eq_dl_thickness_x"):
for ind, c in self.eq_dl_thickness_x.items():
iscale.constraint_scaling_transform(
c, iscale.get_scaling_factor(self.dl_thickness_x[ind])
)
for ind, c in self.eq_mass_transfer_term_diluate.items():
if ind[3] == "H2O":
sf_osm = (
1e-3
* 0.018
* iscale.get_scaling_factor(self.water_permeability_membrane)
* (
(
iscale.get_scaling_factor(
self.diluate.properties[
(ind[0], ind[1])
].pressure_osm_phase[ind[2]]
)
)
** 2
+ (
iscale.get_scaling_factor(
self.diluate.properties[
(ind[0], ind[1])
].pressure_osm_phase[ind[2]]
)
)
** 2
)
** 0.5
)
sf_eleosm = value(Constants.faraday_constant)
iscale.constraint_scaling_transform(
c,
(sf_osm**2 + sf_eleosm**2) ** 0.5
* iscale.get_scaling_factor(self.cell_pair_num),
)
elif ind[3] in self.config.property_package.ion_set:
sf_diff = (
iscale.get_scaling_factor(self.solute_diffusivity_membrane)
/ iscale.get_scaling_factor(self.membrane_thickness)
* (
(
(
iscale.get_scaling_factor(
self.concentrate.properties[
(ind[0], ind[1])
].conc_mol_phase_comp[ind[2], ind[3]]
)
)
** 2
+ (
iscale.get_scaling_factor(
self.diluate.properties[
(ind[0], ind[1])
].conc_mol_phase_comp[ind[2], ind[3]]
)
)
** 2
)
** 0.5
)
)
sf_elemig = value(Constants.faraday_constant)
iscale.constraint_scaling_transform(
c,
(sf_diff**2 + sf_elemig**2) ** 0.5
* iscale.get_scaling_factor(self.cell_pair_num),
)
else:
iscale.constraint_scaling_transform(
c,
iscale.get_scaling_factor(self.solute_diffusivity_membrane)
/ iscale.get_scaling_factor(self.membrane_thickness)
* (
(
(
iscale.get_scaling_factor(
self.concentrate.properties[
(ind[0], ind[1])
].conc_mol_phase_comp[ind[2], ind[3]]
)
)
** 2
+ (
iscale.get_scaling_factor(
self.diluate.properties[
(ind[0], ind[1])
].conc_mol_phase_comp[ind[2], ind[3]]
)
)
** 2
)
** 0.5
)
* iscale.get_scaling_factor(self.cell_pair_num),
)
for ind, c in self.eq_mass_transfer_term_concentrate.items():
if ind[3] == "H2O":
sf_osm = (
1e-3
* 0.018
* iscale.get_scaling_factor(self.water_permeability_membrane)
* (
(
iscale.get_scaling_factor(
self.diluate.properties[
(ind[0], ind[1])
].pressure_osm_phase[ind[2]]
)
)
** 2
+ (
iscale.get_scaling_factor(
self.diluate.properties[
(ind[0], ind[1])
].pressure_osm_phase[ind[2]]
)
)
** 2
)
** 0.5
)
sf_eleosm = value(Constants.faraday_constant)
iscale.constraint_scaling_transform(
c,
(sf_osm**2 + sf_eleosm**2) ** 0.5
* iscale.get_scaling_factor(self.cell_pair_num),
)
elif ind[3] in self.config.property_package.ion_set:
sf_diff = (
iscale.get_scaling_factor(self.solute_diffusivity_membrane)
/ iscale.get_scaling_factor(self.membrane_thickness)
* (
(
(
iscale.get_scaling_factor(
self.concentrate.properties[
(ind[0], ind[1])
].conc_mol_phase_comp[ind[2], ind[3]]
)
)
** 2
+ (
iscale.get_scaling_factor(
self.diluate.properties[
(ind[0], ind[1])
].conc_mol_phase_comp[ind[2], ind[3]]
)
)
** 2
)
** 0.5
)
)
sf_elemig = value(Constants.faraday_constant)
iscale.constraint_scaling_transform(
c,
(sf_diff**2 + sf_elemig**2) ** 0.5
* iscale.get_scaling_factor(self.cell_pair_num),
)
else:
iscale.constraint_scaling_transform(
c,
iscale.get_scaling_factor(self.solute_diffusivity_membrane)
/ iscale.get_scaling_factor(self.membrane_thickness)
* (
(
(
iscale.get_scaling_factor(
self.concentrate.properties[
(ind[0], ind[1])
].conc_mol_phase_comp[ind[2], ind[3]]
)
)
** 2
+ (
iscale.get_scaling_factor(
self.diluate.properties[
(ind[0], ind[1])
].conc_mol_phase_comp[ind[2], ind[3]]
)
)
** 2
)
** 0.5
)
* iscale.get_scaling_factor(self.cell_pair_num),
)
for ind, c in self.eq_power_electrical.items():
iscale.constraint_scaling_transform(
c, iscale.get_scaling_factor(self.diluate.power_electrical_x[ind])
)
for ind, c in self.eq_specific_power_electrical.items():
iscale.constraint_scaling_transform(
c, iscale.get_scaling_factor(self.specific_power_electrical)
)
for ind, c in self.eq_current_efficiency_x.items():
iscale.constraint_scaling_transform(
c,
iscale.get_scaling_factor(self.current_density_x[ind[0], ind[1]])
* iscale.get_scaling_factor(self.cell_width),
)
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.diluate.power_electrical_x[
time_point, self.diluate.length_domain.last()
],
"Specific electrical power consumption, ED stack (kW*h/m**3)": self.specific_power_electrical[
time_point
],
"Water recovery by mass": self.recovery_mass_H2O[time_point],
"Channel inlet velocity, diluate (m/s)": self.velocity_diluate[
time_point, self.diluate.length_domain.first()
],
"Channel inlet velocity, concentrate (m/s)": self.velocity_concentrate[
time_point, self.diluate.length_domain.first()
],
},
"exprs": {},
"params": {},
}
def get_power_electrical(self, time_point=0):
return self.diluate.power_electrical_x[
time_point, self.diluate.length_domain.last()
]
@property
def default_costing_method(self):
return cost_electrodialysis