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Using the Experimental Cross-Association Energy and Artificial Neural Network for Modeling the Phase Equilibrium of Carbon Dioxide–Water System: What Advances Can Be Achieved?

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Abstract

In this work, first, the phase equilibrium of the CO2/water system has been conducted by using two equations of state, including Two-State and perturbed chain statistical association fluid theory equations of state. The experimental value of cross-association energy (exists in the previous studies) is used for this study to model the equilibrium composition CO2 in the aqueous phase. Two strategies are applied to carbon dioxide. In the first strategy, carbon dioxide can only have cross-association with water, so it has no self-association. The second strategy considers CO2 as both self and cross-associating fluid. Also, an additional equation is used for the cross-association section which reduces the number of adjustable parameters. The results of this study show that the first strategy is successful for all cases, and it is accurate while the second strategy is unsuccessful for Two-State equation of state. Moreover, the application of the first strategy and experimental cross-association energy makes the model independent of simplicity of the model and number of adjustable parameters. Then with the sufficient amount of datasets, machine learning techniques were applied to predict the solubility of CO2 in the water with high accuracy. The results are in good agreement with the experimental data with the correlation coefficient (R) of 0.999 and mean-square root of 4.45e−6 for multilayer perceptron network, which means that the network can predict the solubility for the wide range of temperature and pressure.

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Abbreviations

\(\tilde{a}\) :

Reduced Helmholtz energy

A :

Helmholtz energy

a :

Parameter in the energy term

AAD:

Average absolute deviation

b :

Co-volume parameter

d :

Temperature-dependent segment diameter

D ij :

Universal constants

E ij :

Association energy

EoS:

Equation of state

\(g\) :

Radial distribution function

k :

Boltzmann constant

k ij :

Binary interaction parameter

m :

Number of segments per chain

\(\overline{m }\) :

Mean segment number per molecule

M :

Number of association sites per molecule

N :

Number of molecules

n :

Number of moles

N A :

Avogadro’s constant

N C :

Number of compounds

N P :

Number of data

R :

Iideal gas constant [8.3145 J·(mol·K)−1]

PC-SAFT:

Perturbed chain statistical associating fluid theory

SRK:

Soave–Redlich–Kwong

T r :

Reduced temperature

x,y :

Mole fraction

VLE:

Vapor–liquid equilibrium

X A :

Mole fraction of molecules NOT bonded at site A

Z :

Compressibility factor

\(\Delta^{AB}\) :

Association strength

\(\varepsilon^{AB}\) :

Association energy

\(\in\) :

(Energy parameter) depth of the dispersion potential [J]

\(\eta\) :

Packing fraction, reduced segment density

\(\rho\) :

Mole density

\(\kappa^{AB}\) :

Volume of association

\(\sigma\) :

Segment diameter [\(^\circ A\)] (temperature-independent)

\(\zeta\) :

Partial volume fraction

\(\upsilon_{ij}\) :

Association volume

assoc:

Association

calc:

Calculated

chain:

Chain

disp:

Dispersion

exp:

Experimental

hc:

Hard chain

hs:

Hard sphere

id:

Ideal

sat:

Saturated

seg:

Segment

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Authors and Affiliations

  1. Iranian Institute of Research & Development in Chemical Industries (IRDCI)-ACECR, Tehran, Iran

    Zahra Rahmani & Shahin Khosharay

  2. School of Mechanical Engineering, Shiraz University, Shiraz, Iran

    Ehsan Davani

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  1. Zahra Rahmani
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  2. Ehsan Davani
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The authors have no financial or proprietary interests in any material discussed in this article. ZR: methodology, investigation, software, formal analysis, and validation. ED: investigation, software, formal analysis, and validation. SK: methodology, writing original draft, writing—review and editing, supervision. There is no funding for this study.

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Correspondence to Shahin Khosharay.

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Rahmani, Z., Davani, E. & Khosharay, S. Using the Experimental Cross-Association Energy and Artificial Neural Network for Modeling the Phase Equilibrium of Carbon Dioxide–Water System: What Advances Can Be Achieved?. Int J Thermophys 45, 24 (2024). https://doi.org/10.1007/s10765-023-03316-w

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