#####################################################################################################
# “PrOMMiS” was produced under the DOE Process Optimization and Modeling for Minerals Sustainability
# (“PrOMMiS”) initiative, and is copyright (c) 2023-2026 by the software owners: The Regents of the
# University of California, through Lawrence Berkeley National Laboratory, et al. All rights reserved.
# Please see the files COPYRIGHT.md and LICENSE.md for full copyright and license information.
#####################################################################################################
"""
Property package for the multi-component diafiltration membrane.
Author: Molly Dougher
"""
from pyomo.common.config import ConfigValue, ListOf
from pyomo.environ import Param, Set, Var, units
from idaes.core import (
MaterialFlowBasis,
Phase,
PhysicalParameterBlock,
StateBlock,
StateBlockData,
declare_process_block_class,
)
from idaes.core.util.exceptions import ConfigurationError
from idaes.core.util.initialization import fix_state_vars
[docs]
@declare_process_block_class("MultiComponentDiafiltrationSoluteParameter")
class MultiComponentDiafiltrationSoluteParameterData(PhysicalParameterBlock):
"""
Property Package for the multi-component diafiltration membrane.
Currently includes the following solutes:
Li (lithium ion, +)
Co (cobalt ion, 2+)
Al (aluminum ion, 3+)
Cl (chloride ion, -)
"""
CONFIG = PhysicalParameterBlock.CONFIG()
CONFIG.declare(
"cation_list",
ConfigValue(
domain=ListOf(str),
default=["Li", "Co"],
doc="List of cations present in the system",
),
)
CONFIG.declare(
"anion_list",
ConfigValue(
domain=ListOf(str),
default=["Cl"],
doc="List of anions present in the system",
),
)
[docs]
def build(self):
super().build()
if len(self.config.anion_list) > 1:
raise ConfigurationError(
"The multi-component diafiltration unit model only supports systems with a common anion"
)
self.liquid = Phase()
self.component_list = Set(
initialize=self.config.cation_list + self.config.anion_list
)
# ion valence
charge_dict = {
"Li": 1,
"Co": 2,
"Al": 3,
"Cl": -1,
}
# infinite dilution solute diffusion coefficient
# source: https://www.aqion.de/site/diffusion-coefficients
# assumption: no hindered transport (D_bulk = D_membrane)
boundary_layer_diffusion_coefficient_dict = {
"Li": 3.71, # mm2 / h
"Co": 2.64, # mm2 / h
"Al": 2.01, # mm2 / h
"Cl": 7.31, # mm2 / h
}
membrane_diffusion_coefficient_dict = {
"Li": 3.71, # mm2 / h
"Co": 2.64, # mm2 / h
"Al": 2.01, # mm2 / h
"Cl": 7.31, # mm2 / h
}
# thermal reflection coefficient, related to solute rejection
sigma_dict = {
"Li": 1,
"Co": 1,
"Al": 1,
"Cl": 1,
}
# partition coefficient at the solution-membrane interfaces
# Reference: https://doi.org/10.1126/sciadv.adu8302
# Assumptions:
# membrane fixed charge is negative (Donnan effects are incorporated)
# monovalent ions of similar size (i.e., Na and Li) behave similarly
# H,Li is estimated from the data in Fig 1D (Na) of above reference at 200 mM
# H,Co (divalent) is estimated as one order of magnitude smaller than H,Li (monovalent)
# H,Al (trivalent) is estimated as two orders of magnitude smaller than H,Li (monovalent)
# H,Cl is estimated from the data in Fig 1C of above reference at 200 mM
# while H on the retentate and permeate sides can differ, we assume them to be equal for now
partition_coefficient_dict = {
"retentate": {
"Li": 0.4,
"Co": 0.04,
"Al": 0.004,
"Cl": 0.01,
},
"permeate": {
"Li": 0.4,
"Co": 0.04,
"Al": 0.004,
"Cl": 0.01,
},
}
if self.config.cation_list == ["Li"]:
salt_system = "Li_Cl"
elif self.config.cation_list == ["Co"]:
salt_system = "Co_Cl2"
elif self.config.cation_list == ["Al"]:
salt_system = "Al_Cl3"
elif self.config.cation_list == ["Li", "Co"]:
salt_system = "Li_Co_Cl3"
elif self.config.cation_list == ["Li", "Al"]:
salt_system = "Li_Al_Cl4"
elif self.config.cation_list == ["Co", "Al"]:
salt_system = "Co_Al_Cl5"
elif self.config.cation_list == ["Li", "Co", "Al"]:
salt_system = "Li_Co_Al_Cl6"
num_solutes_dict = {
"Li_Cl": {
"Li": 1,
"Cl": 1,
},
"Co_Cl2": {
"Co": 1,
"Cl": 2,
},
"Al_Cl3": {
"Al": 1,
"Cl": 3,
},
"Li_Co_Cl3": {
"Li": 1,
"Co": 1,
"Cl": 3,
},
"Li_Al_Cl4": {
"Li": 1,
"Al": 1,
"Cl": 4,
},
"Co_Al_Cl5": {
"Co": 1,
"Al": 1,
"Cl": 5,
},
"Li_Co_Al_Cl6": {
"Li": 1,
"Co": 1,
"Al": 1,
"Cl": 6,
},
}
# create subset of property dictionaries to initialize parameters
def _subset(mapping_dict):
return {ion: mapping_dict[ion] for ion in self.component_list}
initialize_charge_dict = _subset(charge_dict)
initialize_boundary_layer_diffusion_coefficient_dict = _subset(
boundary_layer_diffusion_coefficient_dict
)
initialize_membrane_diffusion_coefficient_dict = _subset(
membrane_diffusion_coefficient_dict
)
initialize_sigma_dict = _subset(sigma_dict)
initialize_partition_coefficient_retentate_dict = _subset(
partition_coefficient_dict["retentate"]
)
initialize_partition_coefficient_permeate_dict = _subset(
partition_coefficient_dict["permeate"]
)
initialize_num_solutes_dict = _subset(num_solutes_dict[salt_system])
# initialize properties
self.charge = Param(
self.component_list,
units=units.dimensionless,
initialize=initialize_charge_dict,
)
self.boundary_layer_diffusion_coefficient = Param(
self.component_list,
units=units.mm**2 / units.h,
initialize=initialize_boundary_layer_diffusion_coefficient_dict,
)
self.membrane_diffusion_coefficient = Param(
self.component_list,
units=units.mm**2 / units.h,
initialize=initialize_membrane_diffusion_coefficient_dict,
)
self.sigma = Param(
self.component_list,
units=units.dimensionless,
initialize=initialize_sigma_dict,
)
self.partition_coefficient_retentate = Param(
self.component_list,
units=units.dimensionless,
initialize=initialize_partition_coefficient_retentate_dict,
)
self.partition_coefficient_permeate = Param(
self.component_list,
units=units.dimensionless,
initialize=initialize_partition_coefficient_permeate_dict,
)
self.num_solutes = Param(
self.component_list,
units=units.dimensionless,
initialize=initialize_num_solutes_dict,
doc="Moles of ions dissociated in solution per mole of salt(s)",
)
self._state_block_class = MultiComponentDiafiltrationSoluteStateBlock
class _MultiComponentDiafiltrationSoluteStateBlock(StateBlock):
def fix_initialization_states(self):
"""
Fixes state variables for state blocks.
Returns:
None
"""
fix_state_vars(self)
[docs]
@declare_process_block_class(
"MultiComponentDiafiltrationSoluteStateBlock",
block_class=_MultiComponentDiafiltrationSoluteStateBlock,
)
class MultiComponentDiafiltrationSoluteStateBlockData(StateBlockData):
"""
State block for multi-component diafiltration membrane
"""
[docs]
def build(self):
super().build()
self.flow_vol = Var(
units=units.m**3 / units.h,
initialize=10,
bounds=(1e-20, None),
)
self.conc_mol_comp = Var(
self.component_list,
units=units.mol / units.m**3,
initialize=1e-5,
bounds=(1e-20, None),
)
[docs]
def get_material_flow_terms(self, p, j):
return self.flow_vol * self.conc_mol_comp[j]
[docs]
def get_material_flow_basis(self):
return MaterialFlowBasis.mole
[docs]
def define_state_vars(self):
return {"flow_vol": self.flow_vol, "conc_mol_comp": self.conc_mol_comp}
