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]

\(\text{K}\)

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

\(\text{Pa}\)

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.

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.