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@@ -10,4 +10,4 @@ Property Models | |
| coagulation | ||
| ASM1 | ||
| ASM2D | ||
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| mc_aq_sol | ||
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| Multi-Component Aqueous Solution (MCAS) Property Package | ||
| ========================================================= | ||
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| This property package implements property relationships for an aqueous solution that may contain multiple neutral and/or ionic solutes. | ||
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| 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. | ||
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| Classes | ||
| ------- | ||
| .. currentmodule:: watertap.property_models.multicomp_aq_sol_prop_pack | ||
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| .. autoclass:: MCASParameterBlock | ||
| :members: | ||
| :noindex: | ||
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| .. autoclass:: MCASParameterData | ||
| :members: | ||
| :noindex: | ||
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| .. autoclass:: _MCASStateBlock | ||
| :members: | ||
| :noindex: | ||
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| .. autoclass:: MCASStateBlockData | ||
| :members: | ||
| :noindex: | ||
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| Sets | ||
| ---- | ||
| .. csv-table:: | ||
| :header: "Description", "Symbol", "Members" | ||
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| "AqueousPhase", ":math:`p`", "{'Liq'}" | ||
| "component_list", ":math:`j`", "{'H2O', solute_list :sup:`1`}" | ||
| "solute_set", ":math:`j`", "{neutral species in solute_list} :sup:`2`" | ||
| "ion_set", ":math:`j`", "{ionic species in solute_list}" | ||
| "cation_set", ":math:`j`", "{cationic species in solute_list}" | ||
| "anion_set", ":math:`j`", "{anionic species in solute_list}" | ||
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| **Notes** | ||
| :sup:`1` solute_list is provided by a necessary configuration to use this property package. | ||
| :sup:`2` In the implementing codes, the "solute_set" was declared to include only neutral species for current programming convenience; in other places throughout this document, "solute" by itself includes both ionic and neutral species solvated by water. | ||
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| State variables | ||
| --------------- | ||
| .. csv-table:: | ||
| :header: "Description", "Symbol", "Coded Var Name", "Index", "Unit" | ||
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| "Component molar flow rate", ":math:`N`", "flow_mol_phase_comp", "[p, j]", ":math:`\text{mol s}^{-1}`" | ||
| "Temperature", ":math:`T`", "temperature", "None", ":math:`\text{K}`" | ||
| "Pressure", ":math:`P`", "pressure", "None", ":math:`\text{Pa}`" | ||
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| Calculated Properties | ||
| --------------------- | ||
| .. csv-table:: | ||
| :header: "Description", "Symbol", "Coded Var Name", "Index", "Unit", "Calculation Methods" | ||
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| "Component mass flow rate", ":math:`M`", "flow_mass_phase_comp", "[p, j]", ":math:`\text{kg s}^{-1}`", ":math:`M=Nm_N`" | ||
| "Component charge-equivalent molar flow rate", ":math:`\tilde{N}`", "flow_equiv_phase_comp", "[p, j]", ":math:`\text{mol s}^{-1}`", ":math:`\tilde{N}=N\left|z\right|`" | ||
| "Component charge-equivalent molar concentration", ":math:`\tilde{n}`", "conc_equiv_phase_comp", "[p, j]", ":math:`\text{mol m}^{-3}`", ":math:`\tilde{n}=n\left|z\right|`" | ||
| "Component mass fraction", ":math:`x`", "mass_frac_phase_comp", "[p, j]", ":math:`\text{dimensionless}`", ":math:`x_j=\frac{M_j}{\sum_j{M_j}}`" | ||
| "Mass density of aqueous phase", ":math:`\rho`", "dens_mass_phase", "[p]", ":math:`\text{kg m}^{-3}`", ":math:`\rho=1000 \text{kg m}^{-3}` or :math:`\rho=\rho_w + \textbf{f} \left(\sum_{j\in solute}{x_j}, T\right)` :sup:`1`" | ||
| "Mass density of solvent water", ":math:`\rho_w`", "dens_mass_w_phase", "[p]", ":math:`\text{kg m}^{-3}`",":math:`\rho_w=\textbf{f}\left(T\right)` :sup:`1`" | ||
| "Phase volumetric flowrate", ":math:`Q`", "flow_vol_phase", "[p]", ":math:`\text{m}^3\text{ } \text{s}^{-1}`", ":math:`Q=\frac{\sum_j{N_j m_{Nj}}}{\rho}`" | ||
| "Total volumetric flowrate", ":math:`Q_{tot}`", "flow_vol", "None", ":math:`\text{m}^3\text{ } \text{s}^{-1}`",":math:`Q_{tot}=\sum_p{Q_p}`" | ||
| "Component molar concentration", ":math:`n`", "conc_mol_phase_comp", "[p, j]", ":math:`\text{mol m}^{-3}`",":math:`nm_N=m`" | ||
| "Component mass concentration", ":math:`m`", "conc_mass_phase_comp", "[p, j]", ":math:`\text{kg m}^{-3}`",":math:`m=\rho x`" | ||
| "Component molar fraction", ":math:`y`", "mole_frac_phase_comp", "[p, j]", ":math:`\text{dimensionless}`", ":math:`y_j=\frac{N_j}{\sum_j{N_j}}`" | ||
| "Component molality", ":math:`b`", "molality_phase_comp", "[p, j]", ":math:`\text{mol kg}^{-1}`",":math:`b=\frac{N}{N_{H_2O} m_{N\text{H_2O}}}`" | ||
| "Component diffusivity", ":math:`D`", "diffus_phase_comp", "[p, j]", ":math:`\text{m}^2 \text{ } \text{s}^{-1}`", ":math:`D=` input from users" | ||
| "Dynamic viscosity", ":math:`\mu`", "visc_d_phase", "[p]", ":math:`\text{Pa s}`", ":math:`\mu=` input from users" | ||
| "Kinematic viscosity", ":math:`\nu`", "visc_k_phase", "[p]", ":math:`\text{m}^2 \text{ s}^{-1}`",":math:`\nu=\mu\rho^{-1}`" | ||
| "Phase osmotic pressure", ":math:`\Pi`", "pressure_osm_phase", "[p]", ":math:`\text{Pa}`",":math:`\Pi=RT\sum_{j\in solute}{n_j}`" | ||
| "Component stokes radius", ":math:`r_h`", "radius_stokes_comp", "[j]", ":math:`\text{m}`", ":math:`r_h=` input from users" | ||
| "Component molecular weight", ":math:`m_N`", "mw_comp", "[j]", ":math:`\text{kg mol}^{-1}`",":math:`m_N=` input from users" | ||
| "Ion component electrical mobility", ":math:`\mu_e`", "elec_mobility_phase_comp", "[p,j]", ":math:`\text{m}^2\text{ }\text{V}^{-1}\text{ }\text{s}^{-1}`", ":math:`\mu_e=` input from users or :math:`\mu_e=\frac{D\left|z\right|F}{RT}`" | ||
| "Ion component transport number", ":math:`t`", "trans_num_phase_comp", "[p, j]", ":math:`\text{dimensionless}`", ":math:`t=` input from users or :math:`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", ":math:`\Lambda`", "equiv_conductivity_phase", "[p]", ":math:`\text{m}^2 \text{ } \Omega^{-1} \text{ mol}^{-1}`", ":math:`\Lambda=` input from users or :math:`\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", ":math:`\lambda`", "elec_cond_phase", "[p]", ":math:`\Omega^{-1} \text{ m}^{-1}`", ":math:`\lambda=\Lambda\sum_{j\in cation}{\left|z_j\right|n_j}`" | ||
| "Ion component charge", ":math:`z`", "charge_comp", "[j]", ":math:`\text{dimensionless}`", ":math:`z=` input from users" | ||
| "Component activity coefficient", ":math:`\gamma`", "act_coeff_phase_comp", "[j]", ":math:`\text{dimensionless}`", ":math:`\gamma=` input from users" | ||
| "Dielectric constant", ":math:`\epsilon`", "dielectric_constant", "none", ":math:`\text{dimensionless}`", ":math:`\epsilon=` input from users" | ||
| "Debye-Huckel constant", ":math:`A`", "deby_huckel_constant", "none", ":math:`\text{dimensionless}`", ":math:`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", ":math:`I`", "ionic_strength_molal", "none", ":math:`\text{mol kg}^{-1}`", ":math:`I=0.5\sum_{j\in ion}{z_j^2b_j}`" | ||
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| **Notes** | ||
| :sup:`1` :math:`\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). | ||
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| Physical/chemical constants | ||
| --------------------------- | ||
| .. csv-table:: | ||
| :header: "Description", "Symbol", "Value", "Unit" | ||
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| "Idea gas constant", ":math:`R`", "8.3145", ":math:`\text{J mol}^{-1} \text{K}^{-1}`" | ||
| "Faraday constant", ":math:`F`", "96485.33", ":math:`\text{C mol}^{-1}`" | ||
| "Avogadro constant", ":math:`N_A`", "6.022e23", ":math:`\text{dimensionless}`" | ||
| "Boltzmann constant", ":math:`k`", "1.381e-23", ":math:`\text{J K}^{-1}`" | ||
| "Vacuum permittivity", ":math:`\epsilon_0`", "8.854e-12", ":math:`\text{F m}^{-1}`" | ||
| "Elementary charge", ":math:`\textbf{e}`", "1.602e-19", ":math:`\text{C}`" | ||
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| Scaling | ||
| ------- | ||
| A comprehensive scaling factor calculation method is coded in this property package. Among the state variables (:math:`N, T, \text{and } p`), default scaling factors for :math:`T` and :math:`p` were set and do not need users' input, while, for :math:`N`, usually require a user input via an interface. The coding interface to set defalut scaling factor for :math:`N` and call the scaling calculation for other variables is the following. | ||
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| .. code-block:: | ||
| 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: | ||
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| .. code-block:: | ||
| 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. | ||
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| Reference | ||
| --------- | ||
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| 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 ) | ||
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| Bard, A. J., Faulkner, L. R., & White, H. S. (2022). Electrochemical methods: fundamentals and applications. John Wiley & Sons. | ||
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