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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] 1
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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
2
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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.
118 119 120 121 122 123
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∆)
124
(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)
136
Optionally, the derivative of pressure with respect to temperature can be determined if the functional
137
relation between the amount of substance adsorbed and pressure and temperature are provided. In this article, the 7
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139
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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:
