A New Approach in Predicting Gas Adsorption Isotherms and Isosteric Heats Based on Two-Dimensional Equations of State

  • Ali Bakhtyari
  • Masoud MofarahiEmail author
Research Article - Chemical Engineering


The present study provides a modified approach in determining gas adsorption equilibria based on two-dimensional equations of state (2-D EOS). The proposed model utilizes temperature-dependent parameters in the general form of the 2-D EOS. These parameters were considered similar to other well-known isotherm models, such as Langmuir as specifics function of temperature. The proposed model was examined against various experimental single- and multi-component adsorption isotherm data. In most of the investigated cases, the proposed model reduces the error of predictions compared with temperature-independent two-dimensional equations of state. Moreover, utilizing temperature-dependent two-dimensional equations of state, isosteric heat of adsorption was theoretically obtained and compared with experimental heats of adsorption for different homogeneous and heterogeneous adsorption systems. Applying temperature-dependent parameters within 2-D EOS enables us to describe the heterogeneity of considered adsorption systems quite well. Predicted isosteric heats are in good accordance with the experimental data.


Gas adsorption equilibria Two-dimensional equations of state Isosteric heat Adsorption isotherm Thermodynamic prediction 



Two-dimensional equation of state


Specific molar volume of adsorbent (\(\hbox {m}^{2}/\hbox {mol}\))


Surface area per mass of adsorbent (\(\hbox {m}^{2}/\hbox {kg}\))


percentage of absolute average deviation


Fugacity (kPa)


Parameter of the TI 2-D EOS model (mol/kPa kg)


Parameter of the TD model (mol/kPa kg)


Parameter of the TD model parameter (\(\hbox {kPa\,m}^{3}/\)\(\hbox {mol}\))


2-D EOS constant (dimensionless)


Mass of adsorbent (kg)


Mole of components in adsorbed phase (mol)


Number of data points


Universal gas constant (\(\hbox {kPa}\,\hbox {m}^{3}/\hbox {mol}\,\hbox {K}\))


Terms in the isosteric heat of adsorption equations


Temperature (K)


Terms in the fugacity equations of adsorbed phase in the TI model

\(\bar{{T}}_1 ,\bar{{T}}_2\)

Terms in the fugacity equations of adsorbed phase in the TD model


2-D EOS constant (dimensionless)


2-D EOS constant (dimensionless)


Mole fraction in adsorbed phase (dimensionless)


Mole fraction in gas phase (dimensionless)


Compressibility factor of adsorbed phase (dimensionless)

\(\alpha \)

Parameter of the TI 2-D EOS model (kPa, \(\hbox {m}^{3}\,\hbox {kg/mol}^{2}\))

\(\alpha _{1}\)

Parameter of the TD model (kPa, \(\hbox {m}^{3}\,\hbox {kg/mol}^{2}\))

\(\alpha _{2}\)

Parameter of the TD model (kPa, \(\hbox {m}^{3}\,\hbox {kg/K\,mol}^{2}\))

\(\beta \)

Parameter of the TI 2-D EOS model (kg/mol)

\(\beta _{1}\)

Parameter of the TD model (kg/mol)

\(\beta _{2}\)

Parameter of the TD model (kg/mol K)

\(\theta \)

Fractional loading in the TI model (dimensionless)

\(\bar{{\theta }}\)

Fractional loading in the TD model (dimensionless)

\(\phi \)

Fugacity coefficient (dimensionless)

\(\pi \)

Spreading pressure (kPa m)

\(\varPsi \)

Deviation from ideality of isotherms in the TI model (dimensionless)

\({\varPsi }'\)

Deviation from ideality of Langmuir isotherm (dimensionless)

\(\bar{{\varPsi }}\)

Deviation from ideality of isotherms in the TD model (dimensionless)

\(\omega \)

Mole adsorbed per mass of adsorbent (mol/kg)



Adsorbed phase






Gas phase





Adsorbed phase


Components \(\textit{i,j}\) in mixture




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We thank the Persian Gulf University, for the financial support, and for granting the required approval for this study.

Supplementary material

13369_2019_3838_MOESM1_ESM.docx (155 kb)
Supplementary material 1 (docx 155 KB)


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Copyright information

© King Fahd University of Petroleum & Minerals 2019

Authors and Affiliations

  1. 1.Chemical Engineering DepartmentShiraz UniversityShirazIran
  2. 2.Department of Chemical Engineering, Faculty of Petroleum, Gas and Petrochemical EngineeringPersian Gulf UniversityBushehrIran
  3. 3.Department of Chemical and Biomolecular EngineeringYonsei UniversitySeoulRepublic of Korea

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