Thermodynamic Characteristic of Methane Sorption on Shales from Oil

Aug 31, 2018 - Energy and Mineral Resources Group (EMR), Institute of Geology and Geochemistry of Petroleum and Coal, Lochnerstraße 4-20, RWTH ...
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Thermodynamic Characteristic of Methane Sorption on Shales from Oil, Gas and Condensate windows Feng Yang, Boyu Hu, Shang Xu, Qingbang Meng, and Bernhard M. Krooss Energy Fuels, Just Accepted Manuscript • DOI: 10.1021/acs.energyfuels.8b02140 • Publication Date (Web): 31 Aug 2018 Downloaded from http://pubs.acs.org on September 2, 2018

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Energy & Fuels

Thermodynamic Characteristic of Methane Sorption on Shales from Oil, Gas and Condensate windows

Feng Yang,a Boyu Hu,a Shang Xu,a,* Qingbang Meng,a Bernhard M. Krooss b

a

Key Laboratory of Tectonics and Petroleum Resources (China University of Geosciences),Ministry of

Education, Wuhan 430074, PR China b

Energy and Mineral Resources Group (EMR), Institute of Geology and Geochemistry of Petroleum and

Coal, Lochnerstr. 4-20, RWTH Aachen University, 52056 Aachen, Germany * Corresponding Author: [email protected]

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ABSTRACT: High-pressure methane sorption isotherms at 40–101 °C and pressures up to 25 MPa were

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measured on Jurassic lacustrine and Silurian marine shales from China. Shale samples span a thermal

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maturity range from low mature (oil window) to overmature (dry gas window). Low pressure CO2 and

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N2 adsorption techniques were used to quantify specific surface area, pore volume, and pore size

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distributions. Thermodynamic characteristic of methane sorption on shales was assessed based on the

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experimental multi-temperature isotherms. The effects of physical and chemical properties of shales on

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thermodynamic properties were analyzed and discussed. Finally, standard enthalpy of sorption was first

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introduced to evaluate the sorption affinity of methane on shales, and a general pattern describing the

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evolution of methane sorption as a function of thermal maturity was proposed.

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The Langmuir sorption capacity of these shales varies from 0.09 to 0.16 mmol/g. The low-TOC,

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clay-rich lacustrine shales have comparable methane sorption capacities than organic-rich, high

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thermal-maturity marine shales, though high thermal-maturity shale samples tend to have larger

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micropore volume than low mature shales. Clay minerals, especially I/S mixed layer minerals, contribute

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a lot to methane sorption of lacustrine shales in oil window. The isosteric heat of methane sorption on

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these shales decreases with increasing absorbed amount. The commonly used Clausius-Clapeyron

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equation, which neglects the real gas behavior and adsorbed volume, tends to overvalue the isosteric heat.

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The standard enthalpy of sorption reflects the comprehensive effect of physical and chemical properties

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of shales on gas sorption, and shows a parabolic-like pattern with thermal maturity. The standard enthalpy

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of sorption first decreases with increasing thermal maturity up to the condensate window shales (late

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mature, equilibrated vitrinite reflectance 1.0–1.1%) and subsequently increases toward the overmature

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shales.

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KEYWORDS: shale; sorption isotherm; thermodynamics; thermal maturation; heat of sorption

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1 Introduction

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The commercial success of recovering gas from unconventional reservoirs such as organic-rich shales has

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led to increased efforts in studying the sorption behavior of these natural porous materials [1–6]. Understanding

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gas sorption behavior in shales is crucial to an accurate assessment of gas-in-place (GIP) of shale gas systems. It

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is roughly estimated that 50−80% of the total amount of gas in several shale reservoirs in United States is

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considered to be stored as sorbed gas [7]. However, gas sorption on shales is complicated since shale is a kind of

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natural materials with strong heterogeneity. Shales are made up of organic matter, clay minerals, and other

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inorganic matters. At the same time, pore size distributions of shales extend over a wide range from nanometers

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to micrometers [8]. Complicated mineral compositions and variable pore sizes offer a great challenge to

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accurately predict methane sorption capacity in shales.

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Gas sorption on shales is a function of type and abundance of organic and inorganic matter, thermal

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maturation, and other external conditions (pressure, temperature, moisture content etc.) [9–15]. Hydrocarbon

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generation and storage are closely associated with the thermal maturation of organic matter in shales. Though

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significant progress has been made in analyzing the factors affecting methane sorption of shales, evolution of

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sorption capacity with thermal maturation is not fully understood [9–15]. Part of this is due to that the total

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organic matter carbon (TOC) content typically trumps the effect of other geological controls [16]. Previous

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studies on shales from North America and Europe have demonstrated the critical role of organic matter on

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methane sorption [8–15]. In order to extract the effect of thermal maturity, sorption data are commonly reported

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normalized to TOC content [10–17]. However, it is demonstrated that this approach can bring about significant

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errors due to the uncertainties in measured TOC values [18]. Furthermore, thermal evolution of organic matter is

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accompanied by changes in both physical properties (pore structure) and chemical compositions (function

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groups). Though high-resolution scanning electron microscopy (SEM) techniques have revealed various

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nano-scaled pores in organic matter [19–23], there seems to be no specific relationship between thermal maturity 3

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and porosity in organic matter considering the abundance and type of organic matter [22,23]. Several

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investigators found that even in the same shale sample, the organic porosity of different organic matter particles

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might be totally different [23]. What’s more, investigations on the maceral chemistry of coals have shown that

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low mature organic matter is rich in aliphatic and oxygen containing functional groups [24–26]. In contrast, high

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rank coals (anthracite) show the accumulation of condensed aromatic structures [24–26]. Variations in both pore

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structure and function groups of organic matter share a major challenge in fundamentally understanding the

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relationship between thermal maturity and methane sorption capacity.

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In addition to organic matter, clay minerals potentially help to gas sorption on shales. Literatures have

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documented the influences of clay minerals on sorption capacity of shales [27–29]. The contribution from clay

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minerals complicates the evolution of sorption behavior of shales with thermal maturity. Compared to marine

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shales, lacustrine shales are often clay rich and low in thermal maturation [30–33]. Unlike organic-rich shales, it

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is difficult to fully explain the variations in sorption capacity via TOC content alone in low-TOC, clay-rich

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shales [32]. It is important to compare gas sorption capacities of lacustrine and marine shales, since GIP from

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lacustrine shales accounts for roughly one third of total recoverable shale gas resource in China [34].

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Sorption is a process that adsorbate molecules accumulate on the adsorbent surface to reduce the potential

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energy. Experimental measured sorption data not only provide the absorbed amount, but also imply sorption heat

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in the sorption process [35, 36]. Though significant progress has been made on the evaluation of sorption

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capacity, there is relatively few detailed studies on the thermodynamic aspect of gas sorption on shales [6,10,13].

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The isosteric heats of bulk shales are reported to fall between the main organic and inorganic constituents of

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shales [10]. The isosteric heat of methane sorption on type III kerogen is thought to be higher than that of type I

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and type II kerogens because of more aromatic moieties [13]. To improve understanding of the interaction

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between shale and methane molecules, a thorough investigation on the thermodynamic process of methane

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sorption in these complex micro- and mesoporous materials is needed. 4

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This paper aims at shedding light on methane sorption on shales from the perspective of sorption

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thermodynamics. High-pressure sorption isotherms for methane on lacustrine and marine shales spanning

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different thermal maturity stages were measured up to pressures of 25 MPa, at temperatures from 40 to 101 °C

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using a manometric method. Thermodynamic parameters of methane sorption on shales were estimated

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according to the experimental multi-temperature sorption isotherms. The effects of physical and chemical

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properties of shales on the thermodynamic properties have been discussed. Finally, a general evolution pattern

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relating sorption heat to thermal maturity was proposed by the combination of our isotherms and those from

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North America and Europe.

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2 Thermodynamic frameworks

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2.1 Excess sorption and absolute sorption

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The measured quantity in all sorption experiments (manometric, volumetric, gravimetric, chromatographic,

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etc) is “Gibbsian surface excess adsorption” [37]. With the Gibbs definition of adsorption, the experimentally

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measured excess sorption can be written as:

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 =  −   ∙  =  1 − 





(1)

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Here nexc (mmol/g) is the Gibbs excess sorbed amount; nabs (mmol/g) is the absolute sorption; Vabs (g/mmol) is

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the volume of the adsorbed phase; ρgas and ρads are densities of the free phase and adsorbed phase, respectively,

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both expressed in the same units (e.g., kg/m3).

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Rigorous thermodynamic analysis relies on absolute sorption values. Unfortunately, the density and volume

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of the adsorbed phase cannot be experimentally measured. It is common to assume that the excess sorption

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approximates the absolute sorption in literatures [13,14,27]. Although this assumption is reasonable at low

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pressure conditions, it cannot be applicable in high-pressure studies. Under low pressure conditions, the volume

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occupied by the adsorbed phase is relatively small, thus the Gibbs excess sorption approximates the absolute

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sorption. However, the adsorbed volume is no longer negligible at high pressures. To determine the absolute 5

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amount of sorption and avoid the well-documented errors associated with equating excess sorption and absolute

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sorption, an adapted Langmuir function, which explicitly considering the volume of the adsorbed phase, was

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applied to fit the measured excess sorption data [10, 16, 38]: 

 =  1 − 

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 =   1 − 





(2)

Where =

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√

%

exp ( ) &

(3)

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Here nL (mmol/g) is the amount of substance adsorbed at infinite pressure, also known as the Langmuir

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volume; K (1/MPa) is the Langmuir constant; A (K1/2MPa-1) is a prefactor and E (kJ/mol) is a binding energy; R

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(kJ/(mol·K)) is the universal gas constant. Determining the absolute sorption quantity (nabs) is simple when the

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adsorbed gas density or the volume of the adsorption layer (Vads) is known. Since it is difficult to experimentally

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measure the adsorbed phase density, a number of assumptions have been presented to estimate it [39]. One of the

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general approaches is letting the adsorbed phase density to be an independent parameter in the fitted equation of

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choice. The adapted Langmuir equation has been shown to be suitable fitting equations for determining absolute

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sorption from excess isotherms since they are monotonically increasing and contain a relatively small number of

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fitting parameters to achieve a satisfactory fit to the sorption data [10–12]. The variables that remain unknown in

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Eq. (2) and Eq. (3) are the Langmuir volume nL, prefactor A, binding energy Ei, and adsorbed phase density ρads.

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These variables can be obtained by simultaneously performing multivariable nonlinear regression over the

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sorption data recorded at different temperatures.

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2.2 Isosteric enthalpy of sorption

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The isosteric enthalpy (heat) of sorption is one of the key thermodynamic variables for gas sorption systems.

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The isosteric heat is always captured by differentiating a series of sorption isotherms at constant loading using

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the popular Clausius-Clapeyron equation [40–42]. However, strictly speaking, the approach based on the

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Clausius-Clapeyron equation only applies to perfect gas. It has been noted that the extension of this method to 6

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the case of real gas will lead to considerable confusion [40, 43]. In this paper, we start from the basic

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thermodynamic theory to derive the general expressions of sorption thermodynamics, and then compare the

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results of the general and simplified equations.

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From the theory of thermodynamic equilibrium, the change in entropy of sorption (∆)  ) can be calculated as a function of sorption uptake, 

  

*+

, -,

=.

 -.

=.

∆,

(4)

 -.

Furthermore, the Gibbs free energy of the adsorbed phase (/  ) is equal to the Gibbs free energy of the gas phase (/ ) at thermodynamic equilibrium, in which case, the isosteric entropy of adsorption (∆)  ) is ∆/  = /  − / = ∆0  − 1∆)  = 0

(5)

∆0  = 1∆) 

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(6)

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The isosteric enthalpy of adsorption (∆0  ) is a widely used quantity to characterize the strength of

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binding interactions at a fixed temperature, pressure, and coverage. Typically it is determined using the isosteric

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method and reported as a positive value (34 ), the so-called isosteric heat in literatures [40–42],

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34 = −∆0  = −1∆)  = −T   

*+



6   −  7 = −T   

*+

8

9



−

9



:

(7)

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Eq. (7) does not include any assumption and is arguably the most important equation of sorption

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thermodynamics. A number of assumptions are proposed to simplify this expression. The most common one is

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assuming that the volume of adsorbed phase is negligible compared to the bulk phase, which yields:

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34 = −∆0  = −T  

 *+

If the bulk phase is assumed as ideal gas, i.e.,



6−  7 = −T   9



=

& 

 *+

8−

9



:

(8)

, Eq. (7) can be further simplified as the commonly

used Clausius-Clapeyron equation (where it also neglects the volume of adsorbed phase): 

34 = −∆0  = −T   

*+

−

& 

=

& ;  

  

*+

(9)

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Optionally, the derivative of pressure with respect to temperature can be determined if the functional

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relation between the amount of substance adsorbed and pressure and temperature are provided. In this article, the 7

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derivative is further treated based the Langmuir equation, and can be decomposed as follows: 

  

*+

B A + + >?   >C A +

(10)

In the case of Langmuir equation, the respective components of the derivative in Eq. (10) can be written as: