This property package implements property relationships for an aqueous solution that may contain multiple neutral and/or ionic solutes.
- The MCAS property package
- sets H2O as the solvent;
- supports multiple solute components including ions and neutral molecules;
- supports only liquid phase;
- uses temperature, pressure, and either molar flowrate (mol/s) or mass flowrate (kg/s) as state variables;
- does not support dynamics.
For usage examples, please refer to the associated :ref:`"how-to" documentation for MCAS<mcas_how_to>`.
| Description | Symbol | Indices |
|---|---|---|
| Components | j | component_list=['H2O', solute_list 1] |
| Phases | p | ['Liq'] |
| solute_set | j | [all components in component_list except H2O] |
| cation_set | j | [cationic components in component_list] |
| anion_set | j | [anionic components in component_list] |
| neutral_set | j | [neutral components in component_list] |
| ion_set | j | [cationic and anionic components in component_list] |
Note
1 solute_list must be provided by the user via the necessary configuration option, solute_list.
Figure 1. Hierarchy of the Pyomo sets constructed in the MCAS property package. Here, types are declared for the species in component list, or sometimes auto-assigned considering other input such as charge; e.g., the chloride anion would be contained in anion_set, ion_set, solute_set, and component_list.
| Description | Symbol | Variable | Index | Units |
|---|---|---|---|---|
| Temperature | T | temperature | None | \text{K} |
| Pressure | P | pressure | None | \text{Pa} |
The material_flow_basis configuration option can be used to select the desired state variable for flow basis.
If material_flow_basis is set to MaterialFlowBasis.molar (the default setting), component molar flowrates will be used:
| Description | Symbol | Variable | Index | Units |
|---|---|---|---|---|
| Component molar flowrate | N | flow_mol_phase_comp | [p, j] | \text{mol s}^{-1} |
If material_flow_basis is set to MaterialFlowBasis.mass, component mass flowrates will be used:
| Description | Symbol | Variable | Index | Units |
|---|---|---|---|---|
| Component mass flowrate | M | flow_mass_phase_comp | [p, j] | \text{kg s}^{-1} |
| Description | Symbol | Parameter | Index | Units |
|---|---|---|---|---|
| Component molecular weight 1 | m_N | mw_comp | [j] | \text{kg mol}^{-1} |
| Stokes radius of solute | r_h | radius_stokes_comp | [j] | \text{m} |
| Molar volume of solute | V | molar_volume_phase_comp | [p, j] | \text{m}^3 \text{ mol}^{-1} |
| Dynamic viscosity | \mu | visc_d_phase | [p] | \text{Pa s} |
| Bulk diffusivity of solute | D | diffus_phase_comp | [p, j] | \text{m}^2 \text{ s}^{-1} |
| Ion charge | z | charge_comp | [j] | \text{dimensionless} |
| Dielectric constant of water | \epsilon | dielectric_constant | None | \text{dimensionless} |
| Debye Huckel constant b | b | debye_huckel_b | None | \text{kg mol}^{-1} |
| Hayduk Laudie correlation constant | \chi_{1} | hl_diffus_cont | None | \text{dimensionless} |
| Hayduk Laudie viscosity coefficient | \chi_{2} | hl_visc_coeff | None | \text{dimensionless} |
| Hayduk Laudie molar volume coefficient | \chi_{3} | hl_molar_volume_coeff | None | \text{dimensionless} |
Note
1 Component molecular weight data is now set as a requirement when instantiating the MCAS property model. Hence, the user must provide these data in the mw_data configuration option.
Additionally, a warning will be displayed if charge data are not provided via the charge configuration option, in case the user intended to include ions in the solute_list but forgot to provide charge. However, this warning can be ignored if neutral molecules were the only solutes intended for inclusion in solute_list.
| Description | Symbol | Variable | Index | Units |
|---|---|---|---|---|
| Component charge-equivalent molar flowrate | \tilde{N} | flow_equiv_phase_comp | [p, j] | \text{mol s}^{-1} |
| Component charge-equivalent molar concentration | \tilde{n} | conc_equiv_phase_comp | [p, j] | \text{mol m}^{-3} |
| Component mass fraction | x | mass_frac_phase_comp | [p, j] | \text{dimensionless} |
| Mass density of aqueous phase | \rho | dens_mass_phase | [p] | \text{kg m}^{-3} |
| Mass density of solvent water | \rho_w | dens_mass_solvent | [p] | \text{kg m}^{-3} |
| Phase volumetric flowrate | Q | flow_vol_phase | [p] | \text{m}^3\text{ } \text{s}^{-1} |
| Total volumetric flowrate | Q_{tot} | flow_vol | None | \text{m}^3\text{ } \text{s}^{-1} |
| Component molar concentration | n | conc_mol_phase_comp | [p, j] | \text{mol m}^{-3} |
| Component mass concentration | m | conc_mass_phase_comp | [p, j] | \text{kg m}^{-3} |
| Component molar fraction | y | mole_frac_phase_comp | [p, j] | \text{dimensionless} |
| Component molality | b | molality_phase_comp | [p, j] | \text{mol kg}^{-1} |
| Kinematic viscosity | \nu | visc_k_phase | [p] | \text{m}^2 \text{ s}^{-1} |
| Phase osmotic pressure | \Pi | pressure_osm_phase | [p] | \text{Pa} |
| Ion component electrical mobility | \mu_e | elec_mobility_phase_comp | [p,j] | \text{m}^2\text{ }\text{V}^{-1}\text{ }\text{s}^{-1} |
| Ion component transport number | t | trans_num_phase_comp | [p, j] | \text{dimensionless} |
| Phase equivalent conductivity | \Lambda | equiv_conductivity_phase | [p] | \text{m}^2 \text{ } \Omega^{-1} \text{ mol}^{-1} |
| Phase electrical conductivity | \lambda | elec_cond_phase | [p] | \Omega^{-1} \text{ m}^{-1} |
| Component activity coefficient | \gamma | act_coeff_phase_comp | [j] | \text{dimensionless} |
| Debye-Huckel constant A | A | deby_huckel_constant | none | \text{dimensionless} |
| Ionic Strength | I | ionic_strength_molal | none | \text{mol kg}^{-1} |
| Mass diffusivity of solute | D | diffus_phase_comp | [p, j] | \text{m}^2 \text{ s}^{-1} |
| Description | Equation |
|---|---|
| Component charge-equivalent molar flowrate | \tilde{N}=N\left|z\right| |
| Component charge-equivalent molar concentration | \tilde{n}=n\left|z\right| |
| Component mass fraction | x_j=\frac{M_j}{\sum_j{M_j}} |
| Mass density of aqueous phase | \rho=1000 \text{ kg m}^{-3} or \rho=\rho_w + \textbf{f} \left(\sum_{j\in solute}{x_j}, T\right) 1 |
| Mass density of solvent water | \rho_w=\textbf{f}\left(T\right) 1 |
| Phase volumetric flowrate | Q=\frac{\sum_j{N_j m_{Nj}}}{\rho} |
| Total volumetric flowrate | Q_{tot}=\sum_p{Q_p} |
| Component molar fraction | y_j=\frac{N_j}{\sum_j{N_j}} |
| Component molality | b=\frac{N}{N_{H_2O} m_{N\text{H_2O}}} |
| Kinematic viscosity | \nu=\mu\rho^{-1} |
| Phase osmotic pressure | \Pi=RT\sum_{j\in solute}{n_j} |
| Ion component electrical mobility 2 | \mu_e=\frac{D\left|z\right|F}{RT} |
| Ion component transport number 3 | t_j=\frac{\left|z_j\right|\mu_{ej} n_j}{\sum_{j\in ion}{\left|z_j\right|\mu_{ej} n_j}} |
| Phase equivalent conductivity 4 | \Lambda=\frac{\sum_{j\in ion}{F\left|z_j\right|\mu_{ej} n_j}}{\sum_{j\in cation}{\left|z_j\right|n_j}} |
| Phase electrical conductivity | \lambda=\Lambda\sum_{j\in cation}{\left|z_j\right|n_j} |
| Debye-Huckel constant | A=\frac{\left(2 \pi N_A\right)^{0.5}}{log(10)} \left(\frac{\textbf{e}^2}{4 \pi \epsilon \epsilon_0 kT}\right)^{\frac{3}{2}} |
| Ionic strength | I=0.5\sum_{j\in ion}{z_j^2b_j} |
| Component mass diffusivity 5 | D\text{ specified in data argument} or D \text{ }[\text{m}^2 \text{ s}^{-1}]=\frac{\chi_{1}}{(\mu \text{ }[\text{cP}])^{\chi_{2}}(V \text{ }[\text{cm}^3 \text{ mol}^{-1}])^{\chi_{3}}} |
Note
1 \textbf{f}(\cdot) refers to empirical correlations of phase or solvent mass density to seawater salinity and temperature following the study of Sharqawy et al. (2010).
2 Electrical mobility can either be (1) specified when the user provides data via the elec_mobility_data configuration option or (2) calculated by setting the elec_mobility_calculation configuration option to ElectricalMobilityCalculation.EinsteinRelation.
3 Transport number can either be (1) specified when the user provides data via the trans_num_data configuration option or (2) calculated by setting the trans_num_calculation configuration option to TransportNumberCalculation.ElectricalMobility.
4 Phase equivalent conductivity can either be (1) specified when the user provides data via the equiv_conductivity_phase_data configuration option or (2) calculated by setting the equiv_conductivity_calculation configuration option to EquivalentConductivityCalculation.ElectricalMobility.
5 Diffusivity can either be (1) specified when the user provides data via the diffusivity_data configuration option or (2) calculated by the correlation defined in Hayduk, W., & Laudie, H. (1974). For the latter, the diffus_calculation configuration option must be set to DiffusivityCalculation.HaydukLaudie.
| Description | Symbol | Value | Unit |
|---|---|---|---|
| Idea gas constant | R | 8.3145 | \text{J mol}^{-1} \text{K}^{-1} |
| Faraday constant | F | 96485.33 | \text{C mol}^{-1} |
| Avogadro constant | N_A | 6.022e23 | \text{dimensionless} |
| Boltzmann constant | k | 1.381e-23 | \text{J K}^{-1} |
| Vacuum permittivity | \epsilon_0 | 8.854e-12 | \text{F m}^{-1} |
| Elementary charge | \textbf{e} | 1.602e-19 | \text{C} |
A comprehensive scaling factor calculation method is coded in this property package. Among the state variables (N, T, \text{and } p), default scaling factors for T and p were set and do not need users' input, while, for N, usually require a user input via an interface. The coding interface to set defalut scaling factor for N and call the scaling calculation for other variables is the following.
m.fs.properties.set_default_scaling('flow_mol_phase_comp', 1e2, index=('Liq','{component name}'))
# m is the model name, and fs is the instanced flowsheet block of m.
calculate_scaling_factors(m)
Users also have the authority to set a scaling factor for non-state variables via the following codes:
import idaes.core.util.scaling as iscale #import the needed utility package
...
iscale.set_scaling_factor(m.fs.properties.{property_name}, 100)
Proper scaling of variables is, in many cases, crucial to solver's performance in finding an optimal solution of a problem. While designing scaling can have a mathematical sophistication, a general rule is to scale all variables as close to 1 as possible, e.g., in the range of 1e-2 to 1e2.
.. currentmodule:: watertap.property_models.multicomp_aq_sol_prop_pack
.. autoclass:: MCASParameterBlock
:members:
:noindex:
.. autoclass:: MCASParameterData
:members:
:noindex:
.. autoclass:: _MCASStateBlock
:members:
:noindex:
.. autoclass:: MCASStateBlockData
:members:
:noindex:
M.H. Sharqawy, J.H.L. V, S.M. Zubair, Thermophysical properties of seawater: a review of existing correlations and data, Desalination and Water Treatment. 16 (2010) 354–380. https://doi.org/10.5004/dwt.2010.1079. (2017 corrections provided at http://web.mit.edu/seawater )
Bard, A. J., Faulkner, L. R., & White, H. S. (2022). Electrochemical methods: fundamentals and applications. John Wiley & Sons.
Hayduk, W., & Laudie, H. (1974). Prediction of diffusion coefficients for nonelectrolytes in dilute aqueous solutions. AIChE Journal, 20(3), 611–615. https://doi.org/10.1002/aic.690200329