Temperature effect on gas adsorption capacity in different sized pores of coal: Experiment and numerical modeling

Accepted Manuscript Temperature effect on gas adsorption capacity in different sized pores of coal: Experiment and numerical modeling Yu Liu, Yanming Zhu, Shimin Liu, Wu Li, Xin Tang PII:

S0920-4105(18)30206-7

DOI:

10.1016/j.petrol.2018.03.021

Reference:

PETROL 4762

To appear in:

Journal of Petroleum Science and Engineering

Received Date: 11 July 2017 Revised Date:

4 February 2018

Accepted Date: 3 March 2018

Please cite this article as: Liu, Y., Zhu, Y., Liu, S., Li, W., Tang, X., Temperature effect on gas adsorption capacity in different sized pores of coal: Experiment and numerical modeling, Journal of Petroleum Science and Engineering (2018), doi: 10.1016/j.petrol.2018.03.021. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

ACCEPTED MANUSCRIPT 1

Temperature Effect on Gas Adsorption Capacity in Different Sized Pores of Coal:

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Experiment and Numerical Modeling

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Yu Liu a, b,c Yanming Zhu a, b,

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a

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Education, China University of Mining and Technology, Xuzhou, China

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b

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University, University Park, PA, USA

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Abstract: Accurate methane gas adsorption capacity estimation is key for the coalbed methane (CBM)

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reservoir gas-in-place assessment. As in situ, the reservoir pressure and temperature vary from one location

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to another. The temperature induced gas sorption capacity evaluation is important for the CBM and mining

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industry. In this study, grand canonical Monte Carlo (GCMC) simulation was used to investigate

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temperature effect on methane adsorption capacity and adsorbed methane density for different sized pores.

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Methane adsorption experiments were performed to show realistic temperature effect on methane

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adsorption capacity and the experimental data were used directly to validate the numerical model. The pore

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structure of coal was characterized by high-pressure mercury injection, low-pressure N2 gas adsorption,

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low-pressure CO2 gas adsorption. The simulation results revealed that, first, temperature influence on

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methane adsorption was more obvious in smaller pores than that in larger pores. Based on the

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characteristics of the temperature influence on methane adsorption, pores can be divided into three

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categories: 0.7-0.9 nm pores, 1.0-1.3 nm pores and pores larger than 1.4 nm. In the 0.7-0.9 nm group,

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methane adsorption capacity decreased by approximately 19% at 3MPa from 20°C to 100°C. In contrast,

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in the 1.0-1.3 nm pores and pores larger than 1.4 nm, methane adsorption capacity decreased by

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approximately 32% and 45%. Second, in 0.7 nm and 1.0 nm pores, methane adsorption capacity decreased

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linearly with an increase in temperature. In 4.0 nm pores methane adsorption capacity exhibited a negative

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exponential decrease with increasing temperature at low pressure (< 3 MPa). Third, when the pore size was

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the same, the temperature effect was more obvious at a lower pressure than that at a higher pressure. The

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experimental results indicated that methane adsorption capacity in the coal sample decreased linearly with

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temperature increasing, and temperature effect on reducing methane adsorption capacity was greater at low

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pressure. These experimental results were consistent with the simulation results. Based on simulation and

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experimental data, it was obvious that temperature-induced gas adsorption capacity variation was both

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pore size dependent and pressure dependent.

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Key words: Coalbed methane; temperature effect; methane adsorption; pore structure; GCMC;

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Shimin Liu c,* Wu Li a, b, , Xin Tang a, b

Key Laboratory of Coalbed Methane Resources & Reservoir Formation on Process, Ministry of

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School of Resources and Geosciences, China University of Mining and Technology, Xuzhou, China

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Department of Energy and Mineral Engineering, G3 Center and Energy Institute, The Pennsylvania State

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Corresponding author: Yanming Zhu, E-mail: [email protected]; Shimin Liu, E-mail: [email protected]

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1 Introduction As an unconventional gas, coalbed methane (CBM) is an important source of energy in the United

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States, China, Australia and other countries (Moore, 2012; Pan and Wood, 2015). In addition to the energy

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production, the methane extraction from mineable coal seams has an imperative benefit to reduce the

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explosion hazard in subsequent mining process. In coal, methane gas generally stored as free, adsorbed and

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absorbed (Liu and Harpalani, 2013; Clarkson and Bustin, 1999; Ian, 1987; Moore, 2012). Among these

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three states, adsorbed methane plays dominant role in the gas storage and production (Milewska-Duda et

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al., 2000). Understanding of methane sorption mechanism in coal is very important to estimate the gas

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content at various locations, which is crucial for the economically developing the gas resources (Bustin

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and Bustin, 2008). Coal seams are vertically buried at different depths, thus the pressure and temperature

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conditions of the coal formations are expected to vary from one seam to another. Efforts have been made

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to understand the influences of pressure and temperature on methane adsorption capacity on coal to map

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and quantify the gas volume (Bustin and Bustin, 2016). A large amount of work has been conducted to

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study the influence of temperature on methane adsorption capacity based on experimental methods as well

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as theoretical analysis (Guan et al., 2018; Azmi et al., 2006; Bustin and Bustin, 2008; Charoensuppanimit

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et al., 2015; Crosdale et al., 2008; Wang et al., 2015). Bustin and Bustin (2008), Sakurovs et al. (2008),

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and Crosdale et al. (2008) experimentally studied temperature effects on methane adsorption on coal, and

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found that methane adsorption capacity progressively decreases with the increase of temperature. Mosher

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et al. (2013) numerically simulated methane adsorption capacity for a 1.0 nm slit pore at different

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temperatures by grand canonical Monte Carlo (GCMC) method. The results indicated that the increase in

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temperature reduced the methane adsorption capacity by reducing the equivalent pressures, but the

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maximum number of adsorbed molecules remained constant as there was still space for adsorption in pores

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ACCEPTED MANUSCRIPT at higher temperatures (Mosher et al., 2013). Additionally, other adsorption models were proposed to

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explain the temperature effects on sorption capacity. Charoensuppanimit et al. (2015) extended simplified

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local density (SLD) model to define adsorption data and the extended SLD model can the effectively

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model the temperature-dependent sorption behavior of coal. The SLD model has also been successfully

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used in the field of methane adsorption and adsorption-induced swelling (Chareonsuppanimit et al., 2014;

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Chareonsuppanimit et al., 2012; Charoensuppanimit et al., 2015; Fitzgerald et al., 2003).

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Coal is a porous and heterogeneous medium. A wide range of pores in coal was involved in the coal

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matrix from micropores (<2 nm) to macropores (>50nm) (Zhao et al., 2018; Li et al., 2015; Liu et al., 2015;

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Pan et al., 2016; Swanson et al., 2015; Zhang et al., 2015; Zhang et al., 2010). Mesopores (2-50 nm) and

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micropores (< 2nm) provide the vast majority of the internal surface area and control the methane

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adsorption capacity (Li et al., 2015; Liu et al., 2015; Pan et al., 2016; Swanson et al., 2015; Zhang et al.,

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2010). The gas sorption characteristics is a pore-size dependent parameter. The gas sorption experiments

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always use coal samples with full spectrum of pores, thus gas sorption results are a superposition of

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methane adsorption for all involved pores. Numerical simulations are known to be helpful to elucidate the

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fundamental gas sorption mechanism for different pore size under various temperature conditions. In last

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four decades, numerical simulations have been widely adopted in gas adsorption studies on coal and/or

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active carbon, and substantial achievements have been made to advance the understanding of gas sorption

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(Firouzi et al., 2014; Liu et al., 2015; Mosher et al., 2013; Steele, 2002; Tan and Gubbins, 1990; Zhang et

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al., 2014).

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Previous numerical studies have primarily focused on gas sorption behaviors for a single size at

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different temperatures and the results demonstrate that the increase of temperature would reduce the

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methane adsorption amount in coal or active carbon (Mosher et al., 2013; Tan and Gubbins, 1990; Zhou et 3

ACCEPTED MANUSCRIPT al., 2000). Tan and Gubbins (1990) simulated temperature influence on methane adsorption in 0.95 nm,

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1.91 nm and 3.81 nm slit pores between 148 K and 296 K. However, the in situ temperature of coal

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formation is always greater than 303 K. Thus, systematic studies on the influence of temperature on

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methane adsorption capacity using combined numerical simulation and experimental measurement are

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demanded and these studies will shed light on the gas sorption mechanism for the complex coal pore

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structures.

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For numerical simulation and experimental methods, each has its own advantages and disadvantages.

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Numerical simulations can offer detailed information about methane adsorption capacity, adsorbed

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methane density, and many others. Experimental measurements can intuitively show final and real

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methane sorption capacity on coal and it will be an essential dataset for the simulation model validation.

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By combining numerical simulation and experimental measurements, we can get the detailed and realistic

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methane adsorption behavior in coal. In this study, we try to characterize temperature effect on methane

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adsorption capacity for various pore sizes within coal matrix. GCMC methods were used to simulate the

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temperature effect on methane adsorption capacity quantification and methane density distribution in slit

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pores for different sized pores. Finally, the pore size distributions of selected coal samples were

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characterized and followed by the methane adsorption capacity measurements at different temperatures.

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These experimental results were used to validate the numerical simulation results and comprehensively

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analyze temperature effect on methane adsorption in coal.

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2 Experiments and Simulation

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2.1 Sample preparation and Experiments

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A core sample, labeled as CS-1-1, was obtained at depth of 3452 m from northern part of Erdos Basin

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China. This coal sample is Permo-Carboniferous Taiyuan Formation. Coal petrographycial analysis was 4

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conducted and the vitrinite reflectance (Ro) is ~1.8%. The vitrinite content of the coal is 75%, which is the single dominant maceral component in this coal sample.

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High Pressure Methane isothermal adsorption measurements: In the methane isothermal adsorption

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experiment, coal was pulverized to 60-80 mesh. The isothermal adsorption equipment used in the study

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was the GAI-100 made by Core Laboratories Company US. The maximum test pressure is 69 MPa (10,000

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psi), and the maximum testing temperature is 177 °C. The volumetric method was used to obtain the

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methane adsorption quantity.

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High Pressure Mercury Injection (HPMI) Experiment: The AutoPore IV 9510 HPMI instrument is

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equipped at our home institution in the Key Laboratory of Coalbed Methane Resources and Reservoir

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Forming Processes at China University of Mining and Technology. The samples had been dried at 70-80°C

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for 12 hours before each experiment, and the sample quantity used in the experiment was ~1 cm3 bulk chip.

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The maximum mercury injection pressure was 60,000 psi.

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Low Pressure N2 Gas Adsorption (LP-N2-GA) Experiment: The LP-N2-GA experiment was conducted

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using a Micromeritics ASAP 2460 surface area and porosity analyzer at the Physical and Chemical Center

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of Beijing. The sample used in the experiment was 40-60 mesh pulverized powder which was dried for 8

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hours at 70°C. The instrument bath temperature was 77 K during the experiment. The density functional

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theory (DFT) model was used to calculate the pore size distribution based on the low pressure N2/CO2 gas

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adsorption data. DFT model has been proven to be an effective method to characterize pore size

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distribution of micropores and mesopores in coal (Neimark et al., 2009; Nie et al., 2015; Qi et al., 2017).

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More details about DFT model can be seen in elsewhere in the literature (Evans, 1992; Neimark et al.,

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2009).

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Low Pressure CO2 Gas Adsorption (LP-CO2-GA) Experiment: The LP-CO2-GA experiment was also

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ACCEPTED MANUSCRIPT conducted using Micromeritics ASAP 2460 at the Physical and Chemical Center of Beijing. The sample

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used was also 40-60 mesh powder. The powder sample was dried for 8 hours at 70°C prior to the analysis.

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The instrument bath temperature was set to be 0 °C. We also used the DFT model to calculate the pore size

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distribution information based on the low pressure CO2 gas adsorption data.

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2.2 Numerical simulation

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Fig. 1 The representative nanoscale pores in the coal sample through SEM images Slit pore model was adopted in our simulation work to simulate methane adsorption behavior under

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different temperature conditions. The justification of the slit pore model is that the coal is rich in nanoscale

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slit-like pores. The scanning electron microscope (SEM) was used to probe the coal sample and the results

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shown in Fig. 1. The lengths of these slit pores range from ~40 to ~100 nm, and the widths of these slit

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pores are slightly less than 8 nm as illustrated in Fig. 1. Based on the results of SEM images, it was

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believed that those silt pores can provide considerable internal pore surfaces within the coal matrix and

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have a profound influence on methane adsorption capacity for the coal. In fact, other shapes of nanoscale

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pores were also observed, but the frequency of non-silt pores was less than that of slit shape ones. This

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may be the reason why the previous studies on coal sorption simulation also use silt pores to represent the

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physical model of the coal pore structures (Liu et al., 2016; Mosher et al., 2013). The grand canonical Monte Carlo (GCMC) method was employed to simulate the gas sorption

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behaviors and this method has been tested to be a valid tool for this type of simulation studies (Gotzias et

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al., 2013; Liu et al., 2016; Mohammadhosseini et al., 2013; Zhang et al., 2014). During the numerical

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simulation, both the methane adsorption amount and adsorbed phase methane density were estimated

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based on the Lennard-Jones equation. The behavior of adsorbed methane molecules in nanopores is

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defined by both gas-solid and gas-gas interactions, which are all van der Waals forces (Mosher et al.,

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2013). The force field used in this work is the Condensed-phase Optimized Molecular Potentials for

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Atomistic Simulation Studies (COMPASS) field (Hu et al., 2010; Sun, 1998). In the COMPASS force field,

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van der Waals force is theoretically calculated by the Lennard-Jones 9-6 equation (Eq.1). For the atoms i

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and j, the potential energy of van de Waals force between two atoms can be calculated by Eq. 1 (Sun,

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1998).

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r0 r0 EvdW = ∑ε ij [2( ij )9 − 3( ij )6 ] rij rij ij

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(1)

rij0 and ε ij are the corresponding van der Waals parameters for the i, j atom pair; rij is the

where,

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distance between atom i and j. For the rij0 and

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calculate based on the parameter r 0 (radius of the atom) and

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atom, which would be found in relative references (Tan and Gubbins, 1990; Sun, 1998).

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ri 0,j = (

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( ri0 ) 6 − ( r j0 ) 6 2

ε ij = 2 ε i ε j (

εij between different atoms, Eqs. 2 and 3 can be used to ε

(depth of potential well) for the same

)1/ 6

( ri 0 ) 3 ·( r j0 ) 3 ( ri 0 ) 6 ·( r j0 ) 6

（2） )

（3）

It is essential and capable to define the total gas quantity, excess adsorption amount, bulk phase gas 7

ACCEPTED MANUSCRIPT amount and absolute adsorption in the simulation. Total gas quantity is the sum of all gas molecules within

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the pore system, including both the adsorbed frees gas molecules. Bulk phase gas is defined as the gas in

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the pore void space, and thus no adsorbed gas is involved within bulk gas. Excess adsorption, termed as

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Gibbs adsorption, equals to the total gas amount minus the bulk gas. Within the coal pore system, excess

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adsorption (Gibbs adsorption) is the amount in excess of what would be present if pores are completely

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filled with the bulk phase gas with absence of sorption quantity (Fitzgerald et al., 2003). To quantify the

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excess adsorption quantity, Eq.4 was proposed through the density correction (Fitzgerald et al., 2003;

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Krooss et al., 2002):

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nexcess = Va ⋅ ( ρ a − ρb ) = ntot − Vb ρb

(4)

where Va and Vb are the volumes of the adsorbed phase and bulk phase; ρa and ρa represent the methane

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densities of adsorbed phase and bulk phase respectively; nexcess is the amount of excess adsorption quantity.

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ρ represents the methane density. ntot is the amount of total gas. V refers to the volume. Based on the

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GCMC simulation, the total gas quantity can be estimated. Then excess adsorption amount can be

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estimated by subtracting the bulk gas amount (calculated by equation of state) from the total gas quantity.

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The density of bulk phase gas is calculated by the Peng-Robin equation of state (Peng and Robinson,

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1976).

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The intermolecular forces between gas molecule and pore wall result in the formulation of adsorbed

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gas layer. In other word, the generation of adsorbed gas layers is due to intermolecular potential energy

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between the pore wall and gas molecules (Fitzgerald et al., 2003; Tan and Gubbins, 1990; Zhou et al., 2000).

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Thus, the distribution of intermolecular potential energy between pore wall and gas molecules will be pivot

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to improve the mechanistic understanding of the adsorbed gas behavior nearby the pore walls. In a slit pore

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framework, the distribution of intermolecular potential energy between methane and a single pore wall can 8

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been theoretically estimated by Lee’s partially integrated 10-4 Lennard–Jones potential (Fitzgerald et al.,

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2003; Lee, 1988) as shown in Eq. 5:

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ψ ( z ) = 4πρ atomsε gsσ gs2 ⋅ 

 σ 10 gs 10

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ε gs = ε gg × ε ss

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σ gs =

 σ gs4 1 4 ∑ 4 2 i=1 {z + (i − 1)·σ ss } 

(5)

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 5( z )

−

σ gg + σ ss 2

(6) (7)

where, εgs, εgg and εss are the energy parameters of the gas-solid, gas-gas and solid-solid interactions. σgg

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and σss are the molecular diameters of methane and carbon, respectively. In this study, the values of σgg, σss,

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εgg/k, εss/k and ρatoms are 0.3758nm, 0.335nm, 148.1 K, 24.0K and 114nm-3, at which k is the Boltzmann's

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constant (k=1.38 × 10-23 J/K.).

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Fig.2 shows intermolecular potential energy distributions and methane density distributions in slit

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pores for different sizes. Based on the comparison between Fig. 2 (a) and (b), it is apparent that the highest

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adsorbed methane density always occurs at the position of lowest potential energy. Due to van der Waals

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force, methane molecules are more inclined to stay in the position with the lowest potential energy

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(Charoensuppanimit et al., 2015; Fitzgerald et al., 2003; Hasanzadeh et al., 2010). It should be noted that

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intermolecular potential energy between methane and pore wall does not correlate with temperature

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variation as described in Eq. 5. This can be interpreted that the position of the major adsorbed layer will be

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located at the same position regardless of temperature. As shown in Fig. 2, two symmetric densified

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methane adsorbed layers are located near outby of the pore wall for the pores in size between 1.0 and 4.0

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nm. However, for 0.7 nm slit pore, a single adsorbed layer was formed at center of the pore (Fig. 2), which

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is attributed to that only one lowest potential energy can be formed for 0.7 nm slit pore. Thus, in 0.7 nm

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slit pore, methane molecules tend to stay in the center of 0.7 nm slit pore (Fig.2).

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Methane adsorption features in various sized pores are known to be different (Liu et al., 2016; Mosher 9

ACCEPTED MANUSCRIPT et al., 2013; Tan and Gubbins, 1990) as shown in Fig. 2(b). According to the methane adsorption

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characteristics, pores of different sizes can be divided into three categories (Liu et al., 2016; Mosher et al.,

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2013). In this study, 0.7 nm, 1.0 nm and 4.0 nm slit pores were chosen to represent the three categories to

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investigate the temperature effect on methane adsorption capacities for different sized pores as shown in

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Fig. 2 (b). In 0.7 nm pores, a single adsorbed methane layer can be formed. In the 1.0 nm pores, there are

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two adsorbed methane layers in the slit pores: one adsorbed methane layer near each pore wall. The center

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of the slit pores could be affected by the pore walls. In the 4.0 nm slit pore, the pore volume is large

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enough for methane adsorption. For each side of the pore wall of 4.0 nm slit pores, the first adsorbed

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methane layer is near the pore wall, and the second methane density peak clearly occurs after a low density

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gap (Mosher et al., 2013) (illustrated in Fig. 2 (b)). A low-density gap is between these two layers.

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Fig. 2 The distribution of intermolecular potential energy between methane and pore wall in different sized

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slit pores (a) and methane density distribution in different sized slit pores from simulation results (b)

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3. Results and discussion

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3.1 Methane adsorption capacity in different sized pores at various temperatures

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From Fig. 3, it was found that excess methane adsorption capacity negatively correlates with the

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temperature for all sized pores. In 0.7 nm and 1.0 nm pores (Fig. 3 (a), (b)), excess methane adsorption

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capacity decreases linearly with increasing temperature from 0 °C to 100 °C. It was also found that the

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regressed linear slope between excess adsorption amount and temperature is a pressure dependent 11

ACCEPTED MANUSCRIPT parameter and the absolute slope value gradually increase with the continuous decrease of bulk gas

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pressure as shown in Fig. 3 (a, b). These results suggest that methane adsorption capacity decreases more

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rapidly for the lower pressure than for high pressures, In other words, the decremental of methane

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adsorption capacity is relative small for high pressure formations.

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Fig. 3 (c) shows the methane adsorption amount in 4.0 nm slit pores under different temperatures and

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different pressures. The influence of temperature on methane adsorption capacity in 4.0 nm pores is

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different from that smaller pores of 0.7 nm and 1.0 nm. In 4.0 nm pores, excess adsorption capacity

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exhibits a negative exponential decay with increasing temperature at low pressure (< 3MPa); this

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phenomenon is more obvious at lower pressure. When the pressure is larger than 3 MPa, methane

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adsorption capacity decreases linearly with increasing temperature in the 4.0 nm slit pores. Additionally,

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temperature has a more obvious influence on methane adsorption capacity at lower pressure in 4.0 nm, and

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this is also true for methane adsorption in the 0.7 nm and 1.0 nm slit pores.

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0

20

40

60

80

Temperature (°C)

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y=-0.051x+10.30 y=-0.046x+11.72 y=-0.042x+12.04 y=-0.032x+11.81

10

10

2

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1 MPa 3 MPa 5 MPa 10 MPa

12

12

4

16

8 6 4

1MPa y=10.68*e-x/94.89-0.32 3MPa y=17.73*e-x/193.69-3.70 5MPa y=15.31-0.070*x 10MPa y=15.82-0.055*x

16 14 12 10 8 6 4 2

2

100

Excess adsorption amount (mol/mol)

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y=-0.019x+8.29 y=-0.016x+8.69 y=-0.014x+8.75 y=-0.010x+8.63

Excess adsorption amount (mol/mol)

1MPa 3MPa 5MPa 10MPa

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Excess adsorption amount (mol/mol)

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0

20

40

60

Temperature (°C)

80

100

0

20

（ b）

（ a）

40

60

80

100

Temperature (°C) （ c）

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Fig. 3 Excess adsorption capacity in 0.7nm, 1.0nm, and 4.0 nm slit pores from 0 °C to 100 °C at different

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pressures (a: 0.7nm; b: 1.0nm; c: 4.0nm) (based on the simualtion results)

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Fig. 4 Reduction ratio of excess adsorption amount with increasing temperature from 20°C to 100°C at

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3MPa (based on simulation results)

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Based on the comparisons of the methane adsorption capacities for 0.7 nm, 1.0 nm and 4.0 nm pores,

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it was noted that the decreased quantity of methane adsorption with temperature increase for 0.7 nm pore

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system is much smaller than those of 1.0 nm and 4.0 nm pore systems at the same gas pressure. Fig. 4

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shows the reduction ratio of excess adsorption for different sized pore systems (0.7 nm, 0.9 nm, 1.0 nm,

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1.1 nm, 1.2 nm, 1.4 nm, 1.5 nm, 2.5 nm, 3.0 nm and 4.0 nm) for temperatures between 20 °C to 100 °C at

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constant 3 MPa methane pressure. In this study, reduction ratio was defined as “reduction ratio= (nexcess,

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20-nexcess,100)/nexcess, 20”

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adsorption amount at 100 °C). The higher reduction ratio suggests a greater temperature influence on

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methane adsorption amount. From Fig. 4, it was apparent that the reduction ratios of excess adsorption

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increase in stage-wise manner. The reduction ratio can be broken into three stages in related to pore size.

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In the first stage (0.7-0.9 nm), the methane adsorption amount decreases by approximately 19% from

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20 °C to 100 °C. In the second stage (1.0-1.3 nm), methane adsorption capacity decreases by

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approximately 32% and in the third stage (larger than 1.4 nm), the methane adsorption amount decreases

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by approximately 45%. The underlying reason for this patterned temperature-induced sorption reduction is

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(nexcess, 20 is excess adsorption amount at 20°C and nexcess,100 is excess

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ACCEPTED MANUSCRIPT attributed to different layers of adsorbed methane molecules occurring in slit pores for different stages

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(0.7-0.9 nm, 1.0-1.3 nm and larger than 1.4 nm). For the first stage as showed in Fig. 2, only one layer of

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adsorption-phase methane is contained in the slit pore, and in the second stage, two layers of

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adsorption-phase methane exist in the slit pore. In the third stage, three or four layers of methane exist in

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the slit pores. If there are more layers of adsorption-phase methane in the slit pore, temperature would have

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larger influences on methane adsorption.

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3.2 Temperature influence on methane density distributions in different sized pores

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We calculated methane density distributions in different sized pores at different temperatures through

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GCMC simulations as shown in Fig. 5. From Fig. 5 (a), we can find that the adsorbed methane density near

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the pore center deceases with a temperature increase from 10 °C to 90 °C. Adsorption is due to the

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interaction force between methane molecules and pore wall, and the number of methane molecules

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adsorbed is defined by the equilibrium of the potential energy between methane and pore wall and the

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kinetic energy of methane molecules. An increase in temperature will effectively elevate the average

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kinetic energy of methane molecules, but the potential energy between methane and pore wall keeps

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constant for different temperatures as theoretically depicted in Eq. 5. Thus, a portion of adsorbed methane

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molecules tend to kinetically active with a temperature raise and potentially escape from the adsorbed layer

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to the bulk free phase. Thus, the adsorbed phase density will decrease with an increase of system

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temperature.

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In 1.0 nm pores (Fig. 5 (b)), there are two adsorbed methane layers in the slit pores, both of which are

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near the pore walls. The densities of the two adsorbed methane layers decrease with a temperature raise as

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similar to the adsorbed methane in other sized pores. However, the density of methane at the center of the

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slit pore increases with the temperature increase. This is unexpected and opposite of the temperature effect 14

ACCEPTED MANUSCRIPT on the density of the bulk phase and density of the methane adsorbed layers near the pore walls for this

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size pore. In fact, when the first adsorbed methane layer formed, methane molecules in the center of 1.0

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nm pores would be affected by the first adsorbed layer (Zhou and Zhou, 2009). In addition to gravitational

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force, repulsion force also exists across the intermolecular force. And when the distance is close enough,

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the repulsion force overtakes the gravitation force. In the center of the 1.0 nm slit pores, methane

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molecules are so close with the first adsorbed methane layer that these methane molecules feel the

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repulsive force of first adsorbed methane layer. With temperature increasing, the density of first adsorbed

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methane layer decreases, and then repulsion force between the first adsorbed methane layer and the

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methane molecules in the center of 1.0 nm slit pores decreases. Thus, with temperature raise, the methane

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density in the center of 1.0 nm slit pores increases.

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Fig. 5 Methane density at different temperatures at 3MPa in pores of different sizes (a: 0.7nm; b: 1.0nm; c:

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4.0nm) (based on simulation results) Fig. 5 (c) shows the sorption behaviors of 4.0 nm slit pores. As expected, the methane density of the

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first adsorbed methane layer near the pore wall decreases with increasing temperature and this consists

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with the results from the other sized pores. The density of the second adsorbed methane layer decreases

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rapidly with the increasing temperature as shown in Fig. 5(c). When the temperature is higher than 70 °C,

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the second adsorbed methane layer no longer shows up. The maximum density in 0.7 nm pores decreases

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by 23% with increasing temperature from 10°C to 90°C. Correspondingly, the maximum density in 4.0 nm

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pores decreases by 50%. As the methane density of the adsorbed methane decreases more rapidly with

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increasing temperature in 4.0 nm pores, excess adsorption decreases more rapidly with increasing

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temperature in 4.0 nm pores compared with 0.7 nm pores, as shown in Figs. 3 and 4.

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3.3 Pores size distribution in coal samples

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As temperature effect on methane adsorption in different sized pores is different, it is crucial to

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characterize pore structures of the coal samples when we analyze ultimate influence of temperature of

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methane adsorption on coal. Figs. 6 and 5 show the information of pore size distribution of the chosen coal

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sample CS-1-1. From HPMI data, it can be found that pores with size less than 100 nm are dominant pores

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in term of the total pore volume, and pores smaller than 10 nm provide most of the total pore surface area.

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LP-N2-GA results show that the incremental pore volume initially increases and then decreases with pore

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width increasing. The variation characteristics of incremental pore surface area are different from that of

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incremental pore volume, as small pores would provide a higher surface area. From the LP-CO2-GA data

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in Figs. 6 and 7, we can see that pore volume distribution and pore surface distribution both show a

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bimodal distribution between 0.4 and 1.1 nm, and the two peaks are located at 0.55 nm and 0.85 nm,

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ACCEPTED MANUSCRIPT respectively. Comparing the data across HPMI, LP-N2-GA, and LP-CO2-GA, it can be seen that the pore

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volume and pore surface area of pores between 3 nm to 100 nm measured by LP-N2-GA are significantly

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smaller than those measured by HPMI, and there are similar phenomena shown in other studies (Okolo et

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al., 2015). Okolo et al. (2015) compared the porosities and surface areas of coal as measured by gas

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adsorption, mercury intrusion and SAXS techniques and found that many pores in coal are inaccessible to

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N2 at 77 K. In Fig. 6 and 7, through comprehensive analysis of the HPMI data, LP-N2-GA data and

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LP-CO2-GA data, it can be found that pores smaller than 10 nm provide most of the total surface area and

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pores smaller than 1.0 nm contributed more than 50% of the total surface area.

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Fig. 6 Pore volume distribution of the coal sample CS-1-1 from the data of HPMI, LP-N2-GA, and

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LP-CO2-GA experiments

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Fig. 7 Pore surface distribution of the coal sample CS-1-1 from the data of HPMI, LP-N2-GA, and

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LP-CO2-GA experiments

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Fig. 8 Experimental methane adsorption isotherms at four different temperatures

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For gas isotherm measurements, methane adsorption capacities were tested at 50 °C, 60 °C, 70 °C and

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80 °C and the results are shown in Fig. 8. With temperature increase, excess methane adsorption amounts

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decrease, which agrees with the results from other papers (Bustin and Bustin, 2008; Guan et al., 2018).

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Fig. 9 Temperature influence on methane adsorption capacity under different temperatures from the

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experimental data

In order to show temperature effect on methane adsorption capacity on coal under different pressures,

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the adsorption amounts for each pressure at different temperatures were plotted in Fig.9. It can be found

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that the methane adsorption capacity of the CS-1-1 coal sample decrease linearly with increasing

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temperature for all pressures. In Fig. 9, we can also see that the slopes of methane adsorption

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capacity-temperature curves at 2.0 MPa, 4.7 MPa, 6.8 MPa and 18 MPa are regressed to be -0.069, -0.064,

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-0.054, and -0.041, respectively. The slopes of the methane adsorption amount-temperature curves increase

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with an increase in pressure, suggesting that at higher pressure, temperature has weaker influences on the

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methane adsorption capacity in coal, and this is consistent with our previous numerical simulation results

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as shown in Fig. 5.

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The experimental results illustrate that methane adsorption amount decreases linearly with

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temperature increase for all pressures. This phenomenon agrees with the methane behavior in small pores 19

ACCEPTED MANUSCRIPT (pore size < 1.5 nm). According to the simulation results, methane adsorption amount decreases linearly

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with increasing temperature, both at low and high pressures within small pore systems. Additionally, in the

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coal sample CS-1-1, pores smaller than 1.0 nm account for more than half of the total pore surface area

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(Fig. 7). Thus, although large pores exist in the coal sample, the final results are more like the methane

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adsorption behavior in pores with size less than 1.5 nm.

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It is widely accepted that pores in coal have strong heterogeneity (Liu et al., 2017; Pan et al., 2016).

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Pores with different shapes and geochemical compositions exist within the coal matrix. The pore features

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of shape and geochemical composition with the coal matrix is also expected to influence methane

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adsorption capacity. In this study, we used the graphite slit pore as the simplified coal pore and this

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certainly introduces errors between reality and the simulated modeled results. In terms of atom

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composition of pore wall, although carbon element accounted for more than 90% of the total, N, H, O and

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other elements still occur in the coal macromolecular. The element compositions change continually from

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low to high rank coals during coalification process (Stach et al., 1982). The pore surface was known to be

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composed by different functional groups (Yu et al., 2016; Liu et al., 2017). These unique feature can

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determine the van de Waals force between pore wall and methane molecules and the force can be different

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since the localized physiochemical differences (Yu et al., 2016). Apart from the chemical composition

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difference, the shape and morphology of pores in coal are known to be complex, and methane adsorption

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behavior in pores of different shapes is expected to be different from one to another. Pantatosaki et al.

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(2004) studied gas adsorption in both cylindrical and slit pores, and concluded that the temperature had less

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influence on gas adsorption in cylindrical pores than that of silt pores. This is mainly because the intermolecular

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potential energy between pore wall and methane molecules is relatively large in cylindrical pores compared to

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silt pores. In addition, through analyzing temperature influence on methane adsorption in different sized and

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ACCEPTED MANUSCRIPT shaped pores, it was found that the temperature have less impact on methane adsorption in the pores where the

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interaction forces between pore wall and methane molecules are relatively large. In different types of pores, the

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larger interaction forces between pore wall and methane molecules, the less temperature-induced impact on

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methane adsorption capacity. The phenomenon can also been found through SLD model (Hasanzadeh et al.,

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2010; Charoensuppanimit et al., 2015; Fitzgerald et al., 2003).

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4 Conclusions:

Based on the simulation results and experimental data, the following conclusions can be made:

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1. For 0.7 nm and 1.0 nm slit pore systems, methane adsorption capacities linearly decrease with an

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increase of temperature for all pressures. For 4.0 nm silt pores, excess adsorption capacity exhibits a

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negative exponential decay with temperature increase at low pressures (< 3 MPa).

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2. The temperature effect on methane adsorption capacity is stronger within large pores than small pores.

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According to the features of the temperature effect on methane adsorption in pores of different sizes,

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pores can be divided into three categories: 0.7-0.9 nm pores, 1.0-1.3 nm pores and pores larger than

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1.4 nm. For 0.7-0.9nm pores, methane adsorption amount decreases by approximately 19% at 3 MPa

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from 20°C to 100°C, and that in 1.0-1.3 nm pores and pores larger than 1.4nm decrease by

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approximately 32% and 45%, respectively.

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3. HPMI, LP-N2-GA and LP-CO2-GA data show that pores smaller than 1.0 nm are dominant pore

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distribution and these pores contribute more than half of the total pore surface area. Methane

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isothermal adsorption experiments indicate that the methane adsorption capacity decreases linearly

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with an increase in temperature, and the temperature influence is less apparent at high pressure than at

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low pressure. These experimental results are consistent with the simulation results.

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4. The temperature-induced gas adsorption capacity variation is both pore size dependent and pressure 21

ACCEPTED MANUSCRIPT 387

dependent.

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Acknowledgments

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The authors sincerely thank the financial support of the National Natural Science Foundation of China (No.

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41472135), the Natural Science Foundation of Jiangsu Province (Grant No. BK20160243), the Scientific

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Research Foundation of the Key Laboratory of Coalbed Methane Resources and Reservoir Formation

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Process, Ministry of Education (China University of Mining and Technology) (No. 2015-04) and the

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Research and Innovation Project for College Graduates of Jiangsu Province (No. KYLX15_1396).

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Experiments and simulation were used to study temperature effect on adsorption Temperature influence on methane adsorption in different sized pores was simulated Experimental results were used to validate simulation results Temperature effect on adsorption capacity is both pore size and pressure dependent