This property package implements property relationships for an aqueous solution that may contain multiple neutral and/or ionic solutes.
- This MCAS property package
- sets H2O as the solvent;
- supports multiple solute components including ions and neutral molecules;
- supports only liquid phase;
- uses molar flow rate (in mol/s), temperature and pressure as the initial state variables;
- does not support dynamics.
| Description | Symbol | Indices |
|---|---|---|
| Components | j | ['H2O', component_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] |
- Notes
- 1 component_list is provided by a necessary configuration to use this property package.
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 |
|---|---|---|---|---|
| Component molar flow rate | N | flow_mol_phase_comp | [p, j] | \text{mol s}^{-1} |
| Temperature | T | temperature | None | \text{K} |
| Pressure | P | pressure | None | \text{Pa} |
| Description | Symbol | Parameter | Index | Units |
|---|---|---|---|---|
| Component molecular weight | 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_param | [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} |
| Description | Symbol | Variable | Index | Units |
|---|---|---|---|---|
| Component mass flow rate | M | flow_mass_phase_comp | [p, j] | \text{kg s}^{-1} |
| Component charge-equivalent molar flow rate | \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 flow rate | \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 | \mu_e=\frac{D\left|z\right|F}{RT} |
| Ion component transport number | 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 | \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 | 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}}} 2 |
- Notes
- 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 Diffusivity specified in diffus_phase_comp_param or calculated by the correlation defined in Hayduk, W., & Laudie, H. (1974).
| 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