Estimation of isosteric heat of adsorption from generalized Langmuir isotherm

Hamid, Usman; Vyawahare, Pradeep; Chen, Chau‐Chyun

doi:10.1007/s10450-023-00379-x

Cited by 11 publications

(13 citation statements)

References 35 publications

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“…This translates to values of τ iϕ in the range of −(1−3.5), which is within the bounds observed by others. 18,19 For Sips, the value of m 0 tends to be in the expected range of 1−2, 4 and the values of m observed at reasonable temperatures were also largely in this range. Only the value of m 0 for CO 2 (m COd 2 0 = 4.46) on zeolite H-mordenite was found to be well outside this range.…”

Section: ■ Results and Discussionmentioning

confidence: 80%

“…As such, even for unary adsorbate systems, the isotherm must be treated as a mixture. The total surface area is related to the effective molar area and saturation capacity according to eq . , A 0 a ϕ ≡ n ϕ 0 = q i n i 0 = ∑ j = 1 C q i n i + n ϕ …”

Section: Theorymentioning

confidence: 99%

“…The total surface area is related to the effective molar area and saturation capacity according to eq 12. 18,19…”

Section: And C I )mentioning

confidence: 99%

“…In eq 15, τ ij is the 'i − j' binary interaction parameter reflecting the difference in interaction strength, and α is the nonrandomness parameter that is assigned a value of 0.3 as in the classical NRTL model for bulk liquid. 25 The expression for the isosteric enthalpy of adsorption for a unary adsorbate system is given by eq 19.…”

Section: And C I )mentioning

confidence: 99%

“…Equation 19 contains the partial derivatives of lnγ i with respect to temperature because the binary interaction parameters exhibit a temperature dependence: the mathematical forms of the derivatives are available in the literature. 19 By observation, the Langmuir equation is recovered when γ i = γ ϕ = 1, and as such, information on heterogeneity should be contained in the activity coefficient model. Because the surface is always "saturated", whether by adsorbates or phantom molecules, the authors chose to use the symmetric convention for defining the activity coefficients, such that γ i → 1 as x i → 1 and γ ϕ → 1 as x ϕ → 1.…”

Section: And C I )mentioning

confidence: 99%

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Comparison of Heterogeneous Langmuirian Models for Mixed-Gas Adsorption Equilibria

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Hamid

Otulana

et al. 2023

Ind. Eng. Chem. Res.

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Mixed-gas adsorption remains a very active area of research, where newly proposed adsorption equilibrium models need to be compared to standards in the field. The generalized Langmuir (gL) isotherm, proposed by Hamid et al. to address adsorption of different size molecules on heterogeneous adsorbents without requiring evaluation of the Gibbs isotherm, has thus far been tested mainly against the adsorbed solution theory (AST). The gL isotherm was shown to be thermodynamically consistent and gave either better or similar representation than AST models. Here, the gL isotherm is contrasted with the Dual-Process Langmuir isotherm popularized by Ritter and his co-workers and the Loading Ratio Correlation popularized for simple mixtures, both of which are considered the "standard" models for process simulation. The comparison is based on their theoretical roots, interpretations, and representation of the equilibrium loading and the isosteric enthalpy of adsorption of unary, binary, and ternary mixtures of various gaseous adsorbates on different adsorbents over a range of experimental pressures and temperatures.

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Section: ■ Results and Discussionmentioning

confidence: 80%

Section: Theorymentioning

confidence: 99%

“…The total surface area is related to the effective molar area and saturation capacity according to eq 12. 18,19…”

Section: And C I )mentioning

confidence: 99%

Section: And C I )mentioning

confidence: 99%

Section: And C I )mentioning

confidence: 99%

See 3 more Smart Citations

Comparison of Heterogeneous Langmuirian Models for Mixed-Gas Adsorption Equilibria

Sees

Hamid

Otulana

et al. 2023

Ind. Eng. Chem. Res.

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Addressing spreading pressure dependence of real adsorbed solution theory with generalized Langmuir isotherm

Vyawahare,

Hamid,

Sees

et al. 2023

Adsorption

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A developed dual-site Langmuir model to represent the high-pressure methane adsorption and thermodynamic parameters in shale

Hu,

Zhang,

Liu

et al. 2023

Int J Coal Sci Technol

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Comprehending the mechanism of methane adsorption in shales is a crucial step towards optimizing the development of deep-buried shale gas. This is because the methane adsorbed in shale represents a significant proportion of the subsurface shale gas resource. To properly characterize the methane adsorption on shale, which exhibits diverse mineral compositions and multi-scale pore sizes, it is crucial to capture the energy heterogeneity of the adsorption sites. In this paper, a dual-site Langmuir model is proposed, which accounts for the temperature and pressure dependence of the density of the adsorbed phase. The model is applied to the isothermals of methane adsorption on shale, at pressures of up to 30 MPa and temperatures ranging from 40 to 100 °C. The results show that the proposed model can describe the adsorption behavior of methane on shale more accurately than conventional models, which assume a constant value for the density of adsorbed phase. Furthermore, the proposed model can be extrapolated to higher temperatures and pressures. Thermodynamic parameters were analyzed using correctly derived equations. The results indicate that the widely used, but incorrect, equation would underestimate the isosteric heat of adsorption. Neglecting the real gas behavior, volume of the adsorbed phase, and energy heterogeneity of the adsorption sites can lead to overestimation of the isosteric heat of adsorption. Furthermore, the isosteric heat evaluated from excess adsorption data can only be used to make a rough estimate of the real isosteric heat at very low pressure.

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Estimation of isosteric heat of adsorption from generalized Langmuir isotherm

Cited by 11 publications

References 35 publications

Comparison of Heterogeneous Langmuirian Models for Mixed-Gas Adsorption Equilibria

Comparison of Heterogeneous Langmuirian Models for Mixed-Gas Adsorption Equilibria

Addressing spreading pressure dependence of real adsorbed solution theory with generalized Langmuir isotherm

A developed dual-site Langmuir model to represent the high-pressure methane adsorption and thermodynamic parameters in shale

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