Adsorption of Methane on Shale: Statistical Physics Model and Site Energy Distribution Studies

Duan, Shuo; Gu, Min; Tao, Mengmeng; Xian, Xuefu

doi:10.1021/acs.energyfuels.9b03746

Cited by 16 publications

(17 citation statements)

References 47 publications

(167 reference statements)

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“…This number is defined as n (Mobarak et al 2019b;Yazidi et al 2019). The partition function of grand canonical for one adsorption site can be expressed as (Duan et al 2020):…”

Section: Monolayer Model With One Energymentioning

confidence: 99%

“…92 allows these models to be written as a function of ε*. With the differentiating the expression Q e (ε*) with respect to ε*, the approximate SED is obtained (Carter et al 1995;Duan et al 2020;Yan and Niu 2017):…”

Section: Site Energy Distributionmentioning

confidence: 99%

“…The integral of Eq. 93 which represents the area under the distribution curve is equal to the adsorption amount at saturation Q sat (Duan et al 2020;Yan and Niu 2017):…”

Section: Site Energy Distributionmentioning

confidence: 99%

“…On the other hand, the SED curve defines the frequency of appearance of the accessible adsorption sites with specific adsorption energy. Its derivation, defined as the "adsorbent site energy heterogeneity σ e * " (also named the standard deviation of site energy distribution) allows examining the heterogeneity of adsorption site from an energetic point of view, using the following relation (Duan et al 2020): ( 92)…”

Section: Site Energy Distributionmentioning

confidence: 99%

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Calculation of adsorption isotherms by statistical physics models: a review

2021

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Adsorption is a major basic and applied phenomenon in many scientific disciplines. In particular, the design of adsorbents to remove pollutants from wastewater requires advanced knowledge of adsorption isotherms, which are useful tools to identify physicochemical factors that control adsorption performance. Recent modeling of adsorption isotherms has focused on the use of statistical physics. Here, we review the major adsorption isotherm models based on statistical physics. We discuss steric, energetic, and thermodynamic parameters.

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“…This number is defined as n (Mobarak et al 2019b;Yazidi et al 2019). The partition function of grand canonical for one adsorption site can be expressed as (Duan et al 2020):…”

Section: Monolayer Model With One Energymentioning

confidence: 99%

Section: Site Energy Distributionmentioning

confidence: 99%

“…The integral of Eq. 93 which represents the area under the distribution curve is equal to the adsorption amount at saturation Q sat (Duan et al 2020;Yan and Niu 2017):…”

Section: Site Energy Distributionmentioning

confidence: 99%

Section: Site Energy Distributionmentioning

confidence: 99%

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Calculation of adsorption isotherms by statistical physics models: a review

2021

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“…3 The main component of shale gas is CH 4 , which is usually stored in underground shale in three different states: free state, adsorbed state, and dissolved state, 4 where the amount of adsorbed gas accounts for up to 85% of the total shale gas reservoir. 5 At a depth of 1500−2500 m underground in Longmaxi Formation shale gas field in China, it was found that the reservoir temperature was approximately 330−360 K, and the gas pressure could well reach 38 MPa. 6 In addition, analysis of the thermodynamic characteristics in the adsorbed phase, based on the results of isothermal adsorption, could improve the understanding of adsorption behavior and enhance the development of shale gas resources.…”

Section: Introductionmentioning

confidence: 99%

Study on the Adsorption and Thermodynamic Characteristics of Methane under High Temperature and Pressure

Gao

et al. 2020

Energy Fuels

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The understanding of the adsorption and thermodynamic characteristics of methane adsorbed by shale under high pressure and high temperature (HPHT) is of great significance for evaluating deep shale gas reserves and for optimizing shale gas development. In this study, a strict framework for analyzing the adsorption−thermodynamic characteristics of methane adsorption in shale under HPHT conditions was proposed. Further, data processing and explanation of the framework were carried out through reference to published experimental data. When real gas behavior and phase density changes were considered, the temperaturedependent parameters were corrected on the dual-site Langmiur model (DSL) model to reflect the absolute adsorption isotherm at each temperature. These were successfully calculated by combining those with the global fitting method. Compared with other adsorption models that reflected surface heterogeneity, the modified DSL model was found to well characterize the adsorption behavior of shale under HPHT conditions. The thermodynamic potentials of the methane adsorption process were further calculated from the results obtained from the modified DSL model. It was found that in the two groups of shale samples with different total organic carbon (TOC) contents, the change law of isosteric enthalpy with adsorption capacity was different. The abnormal entropy change behavior of methane adsorption in shale with higher TOC content was explained, and a new position concerning the long-standing controversy relating to entropy change was put forward. In addition, both the total entropy and internal energy during the methane adsorbed phase under HPHT increased with an increase in adsorption capacity, and the total entropy in the adsorbed phase revealed a positive relationship with temperature. By introducing a thermodynamic graphic method to draw a clearer and more intuitive U a −n a −S a three-dimensional surface, more thermodynamic potential information could be obtained. The framework proposed in this study could also be used to help future research on the influence of basic physical parameters on adsorption and thermodynamic properties and to provide a foundation for improving the evaluation of deep shale gas reserves.

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Statistical physics modelling of adsorption isotherms of water vapour on shale: Stereographic, energetic and thermodynamic investigations

Duan,

Shen,

et al. 2024

Asia-Pacific J Chem Eng

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Understanding the mechanisms of shale–water interaction by water vapour adsorption is crucial for predicting shale gas productivity. In this study, equilibrium adsorption data of water vapour on four different shales of the Sichuan Basin at three temperatures (298, 308, and 318 K) were measured using static gravity techniques. The water vapour adsorption isotherms were simulated by three statistical physics models. Steric parameters, including the number of water vapour molecules adsorbed per site (n), monolayer adsorption amount (q0), and adsorption energy (ΔEa), and thermodynamic parameters such as configuration entropy (Sa), internal energy (Eint), and free energy (Ga) derived from the selected model were used to explain the adsorption mechanism. The model analyses suggest that the adsorbed water vapour molecules are attached to the shale surface in a multi‐anchorage manner. The adsorption of the first layer shows a Type I characteristics, while the adsorption of the subsequent layer is of Type III. The calculated adsorption energies indicate that the physical adsorption takes place on the water vapour molecules on the shale, and the main interaction forces are hydrophilic bonding forces and van der Waals forces. Negative Eint and Ga values indicate that the spontaneous properties are for water vapour adsorption and that the system requires the release of energy to capture the water vapour molecules.

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Adsorption of Methane on Shale: Statistical Physics Model and Site Energy Distribution Studies

Cited by 16 publications

References 47 publications

Calculation of adsorption isotherms by statistical physics models: a review

Calculation of adsorption isotherms by statistical physics models: a review

Study on the Adsorption and Thermodynamic Characteristics of Methane under High Temperature and Pressure

Statistical physics modelling of adsorption isotherms of water vapour on shale: Stereographic, energetic and thermodynamic investigations

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