# Seawater Property Package

This package implements property relationships for seawater as provided in Sharqawy et al. (2010) and Nayar et al. (2016).

- This seawater property package:
supports only H2O (solvent) and TDS (solute) components

supports only liquid phase

is formulated on a mass basis

estimates molar basis properties based on an average molecular weight of sea salt

does not support dynamics

properties do not incorporate validity ranges for temperature and salinity

pressure-dependency of specific enthalpy is incorporated

assumes diffusivity of NaCl based on Bartholomew & Mauter (2019)

## Sets

Description |
Symbol |
Indices |
---|---|---|

Components |
\(j\) |
[‘H2O’, ‘TDS’] |

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 of seawater |
\(\rho\) |
dens_mass_phase |
[p] |
\(\text{kg/}\text{m}^3\) |

Mass density of pure water |
\(\rho_w\) |
dens_mass_solvent |
[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] |
\(\text{kg/}\text{m}^3\) |

Dynamic viscosity |
\(\mu\) |
visc_d_phase |
[p] |
\(\text{Pa}\cdotp\text{s}\) |

Osmotic coefficient |
\(\phi\) |
osm_coeff |
None |
\(\text{dimensionless}\) |

Specific enthalpy |
\(\widehat{H}\) |
enth_mass_phase |
[p] |
\(\text{J/kg}\) |

Enthalpy flow |
\(H\) |
enth_flow |
None |
\(\text{J/s}\) |

Saturation pressure |
\(P_v\) |
pressure_sat |
None |
\(\text{Pa}\) |

Specific heat capacity |
\(c_p\) |
cp_mass_phase |
[p] |
\(\text{J/kg/K}\) |

Thermal conductivity |
\(\kappa\) |
therm_cond_phase |
[p] |
\(\text{W/m/K}\) |

Latent heat of vaporization |
\(h_{vap}\) |
dh_vap_mass |
None |
\(\text{J/kg}\) |

Diffusivity |
\(D\) |
diffus_phase_comp |
[p] |
\(\text{m}^2\text{/s}\) |

Boiling point elevation |
\(BPE\) |
boiling_point_elevation_phase |
[p] |
\(\text{K}\) |

**The properties make use of the average molecular weight of sea salt, ≈ 31.40 g/mol, reported in the Reference-Composition Salinity Scale (Millero et al., 2008) to convert to moles.**

Description |
Symbol |
Variable |
Index |
Units |
---|---|---|---|---|

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 |
\(Cm\) |
molality_phase_comp |
[‘TDS’] |
\(\text{mole/kg}\) |

Osmotic pressure |
\(\pi\) |
pressure_osm_phase |
None |
\(\text{Pa}\) |

## Relationships

Description |
Equation |
---|---|

Component mass fraction |
\(x_j = \frac{M_j}{\sum_{j} M_j}\) |

Mass density |
Equation 8 in Sharqawy et al. (2010) |

Volumetric flowrate |
\(Q = \frac{\sum_{j} M_j}{\rho}\) |

Mass concentration |
\(C_j = x_j \cdotp \rho\) |

Dynamic viscosity |
Equations 22 and 23 in Sharqawy et al. (2010) |

Osmotic coefficient |
Equation 49 in Sharqawy et al. (2010) |

Specific enthalpy |
Equations 25-27 in Nayar et al. (2016) |

Enthalpy flow |
\(H = \sum_{j} M_j \cdotp \widehat{H}\) |

Component mole flowrate |
\(N_j = \frac{M_j}{MW_j}\) |

Component mole fraction |
\(y_j = \frac{N_j}{\sum_{j} N_j}\) |

Molality |
\(Cm = \frac{x_{TDS}}{(1-x_{TDS}) \cdotp MW_{TDS}}\) |

Osmotic pressure |
\(\pi = \phi \cdotp Cm \cdotp \rho_w \cdotp R \cdotp T\) [See note below] |

Saturation pressure |
Equations 5 and 6 in Nayar et al. (2016) |

Specific heat capacity |
Equation 9 in Sharqawy et al. (2010) |

Thermal conductivity |
Equation 13 in Sharqawy et al. (2010) |

Latent heat of vaporization |
Equations 37 and 55 in Sharqawy et al. (2010) |

Diffusivity |
Equation 6 in Bartholomew et al. (2019) |

Boiling point elevation |
Equation 36 in Sharqawy et al. (2010) |

Note: Osmotic pressure calculation (based on equation 48 in Nayar et al. (2016)) uses the density of water as a function of temperature (\(\rho_w\)) and the ideal gas constant (\(R\text{, 8.314 J/mol}\cdotp\text{K}\)), in addition to previously defined variables.

## Scaling

This seawater 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 will receive a warning if these are not set.

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

```
# relevant imports
import watertap.property_models.seawater_prop_pack as props
from idaes.core.util.scaling import calculate_scaling_factors
# relevant assignments
m = ConcreteModel()
m.fs = FlowsheetBlock(dynamic=False)
m.fs.properties = props.SeawaterParameterBlock()
# set scaling for component mass flowrate
m.fs.properties.set_default_scaling('flow_mass_phase_comp', 1, index=('Liq','H2O'))
m.fs.properties.set_default_scaling('flow_mass_phase_comp', 1e2, index=('Liq','TDS'))
# calculate scaling factors
calculate_scaling_factors(m.fs)
```

The default scaling factors are as follows:

1e-2 for temperature

1e-6 for pressure

1e-3 for mass density

1e3 for dynamic viscosity

1 for the osmotic coefficient

1e-5 for the specific enthalpy

1e-5 for saturation pressure

1e-3 for the specific heat capacity

1 for thermal conductivity

1e-6 for latent heat of vaporization

1e9 for diffusivity

1 for boiling point elevation

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

## References

K.G. Nayar, M.H. Sharqawy, L.D. Banchik, and J.H. Lienhard V, “Thermophysical properties of seawater: A review and new correlations that include pressure dependence,”Desalination, Vol.390, pp.1 - 24, 2016. https://doi.org/10.1016/j.desal.2016.02.024

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)

F.J. Millero, R. Feistel, D.G. Wright, T.J. McDougall, The composition of Standard Seawater and the definition of the Reference-Composition Salinity Scale, Deep-Sea Research Part I. 55 (2008) 50–72. https://doi.org/10.1016/j.dsr.2007.10.001.

T.V. Bartholomew, M.S. Mauter, Computational framework for modeling membrane processes without process and solution property simplifications, Journal of Membrane Science. 573 (2019) 682–693. https://doi.org/10.1016/j.memsci.2018.11.067.