Skip to content

Latest commit

 

History

History
120 lines (93 loc) · 5.91 KB

NaCl_T_dep.rst

File metadata and controls

120 lines (93 loc) · 5.91 KB
Raw

NaCl Property Package with Temperature Dependence

This package implements property relationships for an NaCl solution.

This NaCl property package:
  • supports only H2O (solvent) and NaCl (solute) components
  • supports only liquid phase
  • is formulated on a mass basis
  • is intended for non-isothermal applications
  • does not support dynamics

Sets

Description Symbol Indices
Components j ['H2O', 'NaCl']
Phases p ['Liq']

State variables

Description Symbol Variable Index Units
Component mass flowrate M_j flow_mass_phase_comp [p, j] \text{kg/s}
Temperature T temperature None \text{K}
Pressure P pressure None \text{Pa}

Properties

Description Symbol Variable Index Units
Component mass fraction x_j mass_frac_phase_comp [p, j] \text{dimensionless}
Mass density \rho dens_mass_phase [p] \text{kg/}\text{m}^3
Phase volumetric flowrate Q_p flow_vol_phase [p] \text{m}^3\text{/s}
Volumetric flowrate Q flow_vol None \text{m}^3\text{/s}
Mass concentration C_j conc_mass_phase_comp [p, j] \text{kg/}\text{m}^3
Component mole flowrate N_j flow_mol_phase_comp [p, j] \text{mole/s}
Component mole fraction y_j mole_frac_phase_comp [p, j] \text{dimensionless}
Molality Cm_{NaCl} molality_comp ['NaCl'] \text{mole/kg}
Solubility x_{sat_{NaCl}} solubility_comp ['NaCl'] \text{dimensionless}
Vapor Pressure P_{sat} pressure_sat None \text{Pa}
Dynamic viscosity \mu visc_d_phase [p] \text{Pa/s}
Thermal Conductivity k therm_cond_phase [p] \text{W/m/K}
Specific Heat Capacity C_p cp_mass_phase [p] \text{J/kg/K}
Solute diffusivity D diffus_phase_comp [p,'NaCl'] \text{m}^2\text{/s}
Osmotic coefficient \phi osm_coeff None \text{dimensionless}
Osmotic pressure \pi pressure_osm None \text{Pa}
Specific enthalpy \widehat{H} enth_mass_phase [p] \text{J/kg}
Enthalpy flow H enth_flow None \text{J/s}

Relationships

Description Equation
Component mass fraction X_j = \frac{M_j}{\sum_{j} M_j}
Mass density Equation 7 in Sparrow (2003)
Volumetric flowrate Q = \frac{\sum_{j} M_j}{\rho}
Mass concentration C_j = X_j \rho
Component mole flowrate N_j = \frac{M_j}{MW_j}
Component mole fraction y_j = \frac{N_j}{\sum_{j} N_j}
Molality Cm_{NaCl} = \frac{x_{NaCl}}{(1-x_{NaCl}) MW_{NaCl}}
Solubility Equation 5 in Sparrow (2003)
Vapor Pressure Equation 6 in Sparrow (2003)
Dynamic viscosity Regressed from Zaytsev & Aseev (1992)
Thermal Conductivity Regressed from Zaytsev & Aseev (1992)
Specific Heat Capacity Regressed from Zaytsev & Aseev (1992)
Solute diffusivity Regressed from Zaytsev & Aseev (1992)
Osmotic coefficient Regressed from Pitzer et. al. (1984)
Osmotic pressure \pi = i \phi Cm_{NaCl} \rho_w R T [See note 1 below]
Specific enthalpy Equation 8 in Sparrow (2003)
Enthalpy flow H = \sum_{j} M_j \widehat{H}

Note 1: Osmotic pressure calculation uses the van 't Hoff factor (i\text{, assumed to be 2}), density of water (as a function of temperature), gas constant (R\text{, 8.314 J/mol}\text{K}) in addition to previously defined variables.

Scaling

This NaCl property package includes support for scaling, such as providing default or calculating scaling factors for almost all variables. The only variables that do not have scaling factors are the component mass flowrate and the user must set them or the user will receive a warning.

The user can specify the scaling factors for component mass flowrates with the following:

The default scaling factors are as follows:

  • 1e-2 for temperature
  • 1e-6 for pressure
  • 1e-3 for mass density
  • 1e3 for dynamic viscosity
  • 1e9 for solute diffusivity
  • 1 for the osmotic coefficient
  • 1e-5 for the specific enthalpy
  • 1e-4 for the specific heat capacity
  • 1e-5 for vapor pressure
  • 1 for thermal conductivity
  • 1 for solubility

The scaling factors for other variables can be calculated based on their relationships with the other variables with the user supplied or default scaling factors.

References

Pitzer, Kenneth S., J. Christopher Peiper, and R. H. Busey. (1984). Thermodynamic Properties of Aqueous Sodium Chloride Solutions, Journal of Physical and Chemical Reference Data 13, no. 1 , 1–102. DOI: 10.1063/1.555709
Mostafa H. Sharqawy, John H. Lienhard V & Syed M. Zubair. (2010). Thermophysical properties of seawater: a review of existing correlations and data, Desalination and Water Treatment, 16:1-3, 354-380, DOI: 10.5004/dwt.2010.1079
Sparrow, Benjamin S. (2003). Empirical Equations for the Thermodynamic Properties of Aqueous Sodium Chloride, Desalination 159, no. 2, 161–70. DOI: 10.1016/S0011-9164(03)90068-3
Zaytsev Ivan Dmitrievich & Aseev G. G. (1992). Properties of aqueous solutions of electrolytes, CRC Press.