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A Comprehensive Review of Saline Water Correlations and Data-Part I: Thermodynamic Properties

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Abstract

Thermodynamic properties in a format of correlations, models, and data are reviewed for saline water. Even though seawater properties were reviewed in the literature, different essential parametric conditions are considered in this paper, such as multi-component (ions) concentration and high salinity, in addition to temperature and pressure. The thermodynamic properties are tabulated to include solution concentration, density, specific heat capacity, latent heat of vaporization, boiling point elevation, vapor pressure, specific enthalpy, and specific entropy. Other thermophysical properties such as viscosity, surface tension, electrical conductivity, thermal conductivity, osmotic coefficient, activity coefficient, and thermal expansivity are discussed in the accompanying part II paper. This part aims at being a comprehensive reference source of these properties for all the saline water types, in which Na and Cl are the major constituents, including brackish water, seawater, and high saline water from basins, lakes, produced water from oil and gas hydraulic fracturing, and so on. The correlations are listed in tabular forms and evaluated in terms of accuracy against available experimental data. Guidelines for selecting some correlations are discussed as well. New correlations with high accuracy for NaCl-specific enthalpy and specific entropy are proposed for a salinity range of 0–260 g/kg (0–6 molal) at ambient conditions.

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Abbreviations

C :

Concentration, mol/m3

C P :

Specific heat, J/kg K

C Pw :

Partial heat capacity of water in solution, J/kg K or cal/g K

ϕ C P :

Apparent heat capacity, J/kg K

co, c1, c2, c3, c4 :

Constants

D :

Static dielectric constant of solvent

d s :

Density of salt, kg/m3

e :

Unit electrical charge, 1.602 × 10−19 C

F :

Faraday’s constant, 9.649 × 104 C/mol

G ex :

Excess Gibbs energy, kJ

g :

Specific Gibbs energy, kJ/kg

h :

Enthalpy of saline water, kJ/kg

ϕh, ϕL :

Apparent enthalpy, kJ/kg

\(\bar{h}\) :

Partial enthalpy, kJ/kg

I :

Ionic strength

K :

Salt-dependent parameter

K f :

Compressibility factor

K ATM :

Compressibility factor at atmospheric pressure

K b :

Boltzmann constant, 1.3805 × 10−23 J/K

L :

Latent heat of vaporization, kJ/kg

m :

Molality, mol/kg

m i :

Molality of ith ion, mol/kg

M w :

Molar mass of water, g/mol

M i :

Molar mass of ionic species, g/mol

N A :

Avogadro number, 6.023 × 1023

n :

Number of ions

P :

Pressure, MPa or bar

p :

Vapor pressure, MPa or bar

p w :

Vapor pressure of pure water, MPa or bar

R :

Universal gas constant, kJ/mol.K

S :

Salinity, g/kg

s :

Specific entropy, J/kg.K

\(\bar{s}\) :

Partial specific entropy, J/kg.K

ϕ s :

Apparent specific entropy, J/kg.K

T :

Temperature, oC or K

u :

Ionic mobility, m2/V.s

V :

Specific volume, m3/kg

v :

Molar volume, m3/mol

x :

Mole fraction

Z :

Ionic charge, C

ATM:

Atmospheric pressure and temperature

BPE:

Boiling point elevation

ED:

Electrodialysis

EDR:

Electrodialysis reversal

FO:

Forward osmosis

HDH:

Humidification–dehumidification

MD:

Membrane distillation

MSE:

Mean square error

MSF:

Multi-stage flash desalination

MEE:

Multi-effect evaporation

MVC:

Mechanical vapor compression

ppm:

Parts per million

ppt:

Parts per thousand

ppb:

Parts per billion

RO:

Reverse osmosis

STP:

Standard temperature and pressure

α :

Empirical factor for density model

λ :

Equivalent conductivity, S/m

µ :

Viscosity of saline water, kg/m s

ρ :

Density of saline water, kg/m3

Φ :

Osmotic coefficient

A:

Anion

C:

Cation

e:

Electrical

f:

Liquid form

g:

Gaseous/vapor form

R:

Relative

S:

Salt

W:

Water

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Acknowledgement

The authors acknowledge the support provided by King Fahd University of Petroleum & Minerals through the project IN171048.

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Author notes

  1. These authors (Muhammad M. Generous, Naef A. A. Qasem) contributed equally to this work.

Authors and Affiliations

  1. Department of Mechanical Engineering, King Fahd University of Petroleum and Minerals, Dhahran, 31261, Saudi Arabia

    Muhammad M. Generous, Bilal A. Qureshi & Syed M. Zubair

  2. Department of Aerospace Engineering, King Fahd University of Petroleum and Minerals, Dhahran, 31261, Saudi Arabia

    Naef A. A. Qasem

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  1. Muhammad M. Generous
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Correspondence to Syed M. Zubair.

Appendices

Appendix A. Saline Water Concentration

1.1 A.1. Salinity

Salinity can be defined as masses, in a gram, of all solutes per kg of solution. Therefore, the concentration in terms of salinity can be expressed as:

$${\text{Salinity}} = \frac{{\sum {\text{Mass}}\;{\text{of}}\;{\text{the}}\;{\text{solute}}}}{{{\text{Mass}}\;{\text{of}}\;{\text{the}}\;{\text{solution}}}}$$

The example in Table 10 below calculates seawater salinity from its compositions.

Table 10 Example to estimate salinity form standard seawater composition
Full size table

Therefore, the salinity of seawater is 35.169 g/kg based on the data listed in Table 10. The same procedure can be applied to determine the salinity of any solution with any given quantity of impurities.

1.2 A.2. Molarity and Molality

Molarity or mole concentration is the ratio of moles of solute per volume in a liter of solution. It is represented by the “M.” It can be expressed as:

$${\text{Molarity}}\;\left( M \right) = \frac{{{\text{Moles}}\;{\text{of}}\;{\text{Solute}}}}{{{\text{Volume}}\;{\text{of}}\;{\text{Solution}}}}$$

In the case of a multi-species solution, the molarity of each component is determined separately. The molarity is calculated by using molarity and charge of each component, as expressed in the following relation:

$$M = \frac{1}{2}\mathop \sum \limits_{i = 1}^{n} M_{i} Z_{i}^{2}$$
(A.2.1)

where \(M_{i}\) and \(Z_{i}\) are molarity and charge of a given component.

Molality is the ratio of moles of solute per kg of solvent (water). It is denoted by “m” and written as:

$${\text{Molality}}\;\left( m \right) = \frac{{{\text{Moles}}\;{\text{of}}\;{\text{Solute}}}}{{{\text{Mass}}\;{\text{of}}\;{\text{solvent}}}}$$

An example to calculate the molality and molarity of seawater based on data listed in Table 10 is as follows:

The molar mass of seawater = 58.44 g/mol

Molality (m) = 35.169/58.44 = 0.6 mol/kg (molal)

Density of seawater (ρsw) = 1.025 kg/Liter

Molarity (M) = 0.6 × 1.025 = 0.615 mol/Liter

Appendix B. Data

See Tables 11, 12, 13, 14, 15, 16.

Table 11 Composition of saline water [101]
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Table 12 Ionic volumes and values of \(\alpha_{i}\) at 298.15 K for Lam et al. [34] density model
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Table 13 Values of constants c0 to c4 for Laliberte correlation [96]
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Table 14 Constants used in modified Debye-Hϋckel calculation of heat capacities [71]
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Table 15 Values of As, Bs, Cs, Ds and Es [96]
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Table 16 K-values
Full size table

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Generous, M.M., Qasem, N.A.A., Qureshi, B.A. et al. A Comprehensive Review of Saline Water Correlations and Data-Part I: Thermodynamic Properties. Arab J Sci Eng 45, 8817–8876 (2020). https://doi.org/10.1007/s13369-020-05019-y

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