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A Comprehensive Review of Saline Water Correlations and Data: Part II—Thermophysical Properties

  • Review-Mechanical Engineering
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Abstract

This paper reviews the thermophysical properties of saline water correlations and data. The key parameters that influence the properties are considered, such as multi-component composition, high salinity, temperature, and pressure. Since the thermodynamic properties are reviewed in part I of the paper, this part (# II) focuses on the thermophysical properties involving viscosity, surface tension, electrical conductivity, thermal conductivity, osmotic coefficient, activity coefficient, and thermal expansivity. The properties are comprehensive to include all saline water types, i.e., brackish water, seawater, high saline water from basins, lakes, produced water from oil and gas hydraulic fracturing, and so on. The correlations are summarized in tabular forms and assessed based on their accuracy against available experimental data. Besides, guidelines for choosing some correlations are also discussed. Since the thermal conductivity has no multi-component model, a novel and straightforward model is proposed with excellent accuracy.

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Abbreviations

a :

Activity

A φ :

Modified Debye–Hückel parameter (kg1/2/mol1/2)

A, B :

Constants used in McCleskey multi-component model for electrical conductivity

B ij, B ϕij :

Pitzer parameter, second virial coefficient (kg/mol)

B ij′:

Pitzer binary interaction parameter (kg2/mol)

b, s, n :

Parameters related to the Wang model for BPE calculations

C :

Concentration (mol/m3)

C ij, C ϕij :

Pitzer parameter, unlike-charged interactions (kg2/mol2)

Cl:

Chlorinity (g/kg)

C P :

Specific heat (J/kg.K)

D :

Diffusion coefficient (m2/s)

F :

Faraday’s constant (96,485.3329 A.s/mol)

F 1, F 2, F 3 :

Constants for Pawlowicz method

g :

Interference parameter in Pitzer equation for surface tension calculations

I :

Ionic strength (mol/kg)

K b :

Boltzmann constant (1.3805 × 10−23 J/K)

k :

Thermal conductivity (W/m.K)

K e :

Electrical conductivity (mS/m)

m :

Molality (mol/kg)

M :

Molarity (mol/L)

m s :

Mass of solute (g or kg)

N A :

Avogadro’s number (6.022 × 1023)

P :

Pressure (MPa or bar)

p :

Vapor pressure (MPa or bar)

R :

Universal gas constant (8.3145 J/mol.K)

S :

Salinity (g/kg)

T :

Temperature (°C or K)

u :

Ionic mobility (m2/V.s)

V :

Volume (m3)

Z :

Ionic charge (C)

∆:

Change

µ :

Viscosity of saline water (kg/m.s)

α :

Thermal expansivity (1/K) or Pitzer parameter (kg1/2/mol1/2)

β :

Thermal compressibility (1/Pa) or Pitzer parameter (kg/mol)

γ :

Activity coefficient

θ :

Pitzer parameter (kg/mol)

λ :

Equivalent conductivity (S.cm2/eq)

λ ij :

Pitzer parameter, uncharged interactions (kg/mol)

μ :

Chemical potential (kJ/mol)

ν :

Stoichiometric coefficient

ρ :

Density (kg/L)

σ :

Surface tension (N/m)

ϕ :

Osmotic coefficient

Φ ij, Φ ϕij :

Pitzer parameter, like-charged interactions (kJ/mol)

Φ ij′:

Pitzer parameter, like-charged interactions (kg2/mol2)

Ψ ijk :

Pitzer parameter, ternary interactions (kg2/mol2)

a, X :

Anion

c, M :

Cation

e:

Electrical

n, N :

Neutral species

p:

Isobaric

s :

Solute

S:

Salt

SW:

Seawater

R:

Relative

W:

Water

o:

Infinite dilution

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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. Naef A. A. Qasem and Muhammad M. Generous have contributed equally to this work.

Authors and Affiliations

  1. Department of Aerospace Engineering, King Fahd University of Petroleum & Minerals, Dhahran, 31261, Saudi Arabia

    Naef A. A. Qasem

  2. Department of Mechanical Engineering, King Fahd University of Petroleum & Minerals, Dhahran, 31261, Saudi Arabia

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

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  1. Naef A. A. Qasem
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  3. Bilal A. Qureshi
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Corresponding author

Correspondence to Syed M. Zubair.

Appendix

Appendix

See Tables 9, 10, 11, 12, 13, 14, 15, 16, and 17.

Table 9 Diffusion constants of inorganic cations [106]
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Table 10 Diffusion constants of inorganic anions [106]
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Table 11 Diffusion constants of organic anions [106]
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Table 12 Data of McCleskey et al. model for equations used to calculate individual ionic-molal conductivities \(\left( {{\text{mS}}\;{\text{kg}}/{\text{cm}}\;{\text{mol}}} \right)\) and for the ions applicable to natural waters (T is in °C) [101]
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Table 13 Data for Park method for seawater: partial equivalent ionic conductance of major ions in seawater at 23 °C, assuming the cation transference number of potassium chloride in seawater is 0.49 Ω/cm2 [100]
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Table 14 Ion-dependent numerical parameter [99]
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Table 15 Individual aqueous species considered in this study and parameters for calculating their contributions to thermal conductivity [59]
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Table 16 Coefficient (α) for selected aqueous ions [59]
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Table 17 Calculated results of surface tension and parameters for single-electrolyte aqueous solutions [113]
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Qasem, N.A.A., Generous, M.M., Qureshi, B.A. et al. A Comprehensive Review of Saline Water Correlations and Data: Part II—Thermophysical Properties. Arab J Sci Eng 46, 1941–1979 (2021). https://doi.org/10.1007/s13369-020-05020-5

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