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Investigation of methane diffusion in low-rank coals by a multiporous diffusion model
Journal of Natural Gas Science and Engineering 33 (2016) 97e107
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Investigation of methane diffusion in low-rank coals by a multiporous diffusion model Zhentao Li a, Dameng Liu a, *, Yidong Cai a, Yunlong Shi b a Coal Reservoir Laboratory of National Engineering Research Center of CBM Development & Utilization, China University of Geosciences, Beijing 100083, China b Key Laboratory of Ocean Circulation and Waves, Institute of Oceanology, Chinese Academy of Sciences, Qingdao 266071, China
a r t i c l e i n f o
a b s t r a c t
Article history: Received 26 January 2016 Received in revised form 4 May 2016 Accepted 5 May 2016 Available online 7 May 2016
To study the methane diffusion behaviors of low-rank coals (Ro,m of 0.45% and 0.58%), a combination of CO2 adsorption, N2 adsorption/desorption, and mercury intrusion porosimetry (MIP) measurements were used to characterize the pore structure of coals, and a new multiporous diffusion model was established to model methane diffusion under dry and moist conditions during the methane adsorption process. The results indicate that the pore structure of low-rank coal samples exhibits a multimodal pore size/volume distribution and has a greater percentage of microporosity and mesoporosity. The multiporous model provides a better fit than the bidisperse model, which deviates significantly from the data, especially during the initial diffusion stage. Based on the multiporous diffusion model, the macropore diffusivity (104~103 s1) is generally one to three orders of magnitude greater than the mesopore diffusivity (105~104 s1) and micropore diffusivity (106~105 s1). Moreover, both the macropore diffusivity and micropore diffusivity show a decreasing trend with increasing pressure, whereas a strong positive correlation exists between the mesopore diffusivities and pressure, indicating that the effect of pressure on methane diffusion in pores with different sizes is different during the adsorption process. This difference may be due to the competition between the different mechanisms of gaseous methane diffusion and the swelling of the coal matrix caused by gas adsorption. Furthermore, the moisturereduced methane diffusivities is mainly due to the moisture in the coal matrix that adsorbs to the pore surface and occupies the pore space, as well as changes the pore structure according to the effect of mineral swelling from the adsorbing moisture. Therefore, these results may have a significant implication for understanding the transport mechanism of methane in coals and the design of enhanced CBM recovery. © 2016 Elsevier B.V. All rights reserved.
Keywords: Gas diffusion Multiporous diffusion model Pore structure Pressure Moisture content
1. Introduction Coalbed methane (CBM) represents an alternative hydrocarbon resource that has attracted global attention in recent years. Compared to conventional natural gas reservoirs, coal reservoirs have unique characteristics, including a dual porosity system, pore structure, gas storage, and flow mechanisms. It has been confirmed that CBM is mainly adsorbed at the pore surface in the coal matrix and that gas is desorbed from the pore surface and diffuses from the pore system to the cleat/fracture systems during production (Clarkson and Bustin, 1999; Shi and Durucan, 2005; Cai et al.,
* Corresponding author. E-mail address: [email protected] (D. Liu). http://dx.doi.org/10.1016/j.jngse.2016.05.012 1875-5100/© 2016 Elsevier B.V. All rights reserved.
2014a,b). Commonly, gas transport in coals is divided into two stages: gas diffusion within the coal matrix and flow in the cleat system (Pillalamarry et al., 2011). Harpalani and Chen (1997) revealed that gas diffusion through the matrix is assumed to be concentration gradient driven and is usually modeled using Fick’s Second Law of Diffusion. Moreover, both Shi and Durucan (2003); Pan et al. (2010) found that gas diffusion within the coal matrix is dominated by three diffusion mechanisms in coals, including Fickian diffusion (molecule-molecule collisions dominate), Knudsen diffusion (molecule-wall collisions dominate) and Surface diffusion (transport through physically adsorbed layer). Due to the often significant heterogeneity of the pore structure, all three diffusion mechanisms play important roles in gas diffusion within the coal matrix (Xu et al., 2015; Yuan et al., 2014). A significant amount of work has been completed in modeling
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diffusion, and various diffusion models have been applied to characterize the diffusion process, such as the unipore model a re et al., 2010; Jian et al., 2012; Pone et al., 2009; Sv bov (Charrie a et al., 2012), the bidisperse model (Busch et al., 2004; Clarkson and Bustin, 1999; Cui et al., 2004; Shi and Durucan, 2003, 2005; Smith and Williams, 1984; Pan et al., 2010), and the Fickian diffusion-relaxation (FDR) model (Staib et al., 2013). Based on these models, one or two diffusion coefficients are obtained to describe the sorption kinetics of coals. By studying the gas diffusion of different rank coals, Crosdale et al. (1998); Clarkson and Bustin (1999) discovered that the unipore model is more suitable for vitrinite-rich bright coals, whereas the bidisperse model may be adequate to describe the sorption kinetics of some inertinite-rich dull or banded coals. This observation indicates that the coal composition may influence gas transport in the coal matrix and the pore structure plays an important role in accurately modeling gas transport through the coal matrix. Previous research using nuclear magnetic resonance suggests that the pore volume distribution of low-rank coals has a triple peak pattern (Cai et al., 2015). Moreover, based on experimental and mathematical simulations, many influencing factors on the diffusion coefficients have been discussed in recent studies. Pan et al. (2010), by studying the effects of matrix moisture on methane and carbon dioxide diffusion, discovered that the diffusion coefficients of dry coal are higher than those of wet coal and that the diffusion coefficients of CO2 are significantly higher than those of CH4 under the same conditions. However, a similar study by Wang et al. (2014) also found that diffusivity decreases with increasing moisture for Chinese anthracite, whereas for Chinese bituminous coal, diffusivity varies with the moisture following a U-shaped function. Furthermore, re et al. (2010) demonstrated that the calculated diffusion Charrie coefficients of CH4 and CO2 from the unipore model increase with increasing temperature and gas pressure on coals from the Lorraine Basin in France. However, it has been proposed that diffusion coefficients may have different trends depending on the model chosen, even when using the same data (Clarkson and Bustin, 1999; Shi and Durucan, 2005; Staib et al., 2013). In this work, we investigated the methane adsorption and diffusion behaviors in two Chinese low-rank coals through experimental study and modeling. The pore structure, as a factor of methane diffusion, is required. Therefore, the pore structure of the coal samples was first investigated via the CO2 adsorption, N2 gas adsorption/desorption, and mercury intrusion porosimetry (MIP) techniques. Then, a new multiporous diffusion model, based on the bidisperse model, was proposed to describe the methane diffusivity in the coal matrix. Finally, the effects of moisture and pressure on methane diffusion under dry and moist conditions were discussed in detail. 2. Material and methods 2.1. Coal samples and preparation The coal samples used in this work were collected from the Taian coal mine and Wangtian coal mine in the Baode mining area, Shanxi Province. The maximum vitrinite reflectance (Ro,m), petrographic, and proximate analyses for the coal samples were carried out in our laboratory, and the experimental procedures were the same as those of our previous work (Cai et al., 2011). The ranks of the two coals are lignite for Taian (TA) and long-flame coal for Wangtian (WT), with maximum vitrinite reflectance (Ro,m) reaching 0.45% (TA) and 0.58% (WT), respectively. The results of the petrographic and the proximate analysis are presented in Table 1. The coal lumps were pulverized and the particles between 0.18 and 0.25 mm were selected for CH4 adsorption and diffusion
experiments. The powder samples were divided into two parts. One part was dried in a 50 C vacuum oven for more than one week to remove any pre-existing moisture. The other part was used to prepare the moisture-equilibrated samples. The samples were prepared using a saturated K2SO4 solution, with a relative humidity of approximately 97%. The wet samples were weighed periodically during moisture-equilibrated process. Over a period of two months, the moisture of the coal samples reached an equilibrium state, as described in detail by Pan et al. (2010). The moisture content of coal samples is defined as:
w% ¼
mmoisture 100% mcoal
(1)
where w% is the moisture content, mmoisture is the total mass of water uptake in coal, mcoal is the total mass of the dry coal. The dry and moisture-equilibrated samples were prepared for CH4 isotherm adsorption and diffusion experiments. 2.2. Mercury intrusion porosimetry analysis Many methods, including scanning electron microscope (SEM), low-temperature N2 adsorption/desorption, MIP, and nuclear magnetic resonance (NMR) techniques, have been adopted to acquire the pore structure information. In this study, the pore structure and pore size distribution of the coal samples were investigated using the MIP method. The block sample was selected for MIP analysis following the rock capillary pressure measurement standard process (the Chinese Oil and Gas Industry Standard of SY/T 5346-2005) (Yao and Liu, 2012) and conducted using the PoreMasterGT60 (Quantachrome, US). The measurements run up to a pressure of 206 MPa, at which pore throats as small as four nm can be penetrated. Mercury intrusion/extrusion curves were obtained, and the cumulative mercury injection volume, pore radius, and pore size distribution could be inferred from the curves. The results of the MIP analysis are listed in Table 2. 2.3. CO2 adsorption and N2 adsorption/desorption analysis Although the MIP method is commonly used to characterize the pore size distribution of coal from a few nanometers to tens of micrometers, the pore compressibility of coals is inevitable at high pressures (normally higher than 20 MPa) (Patrick et al., 2004), which can easily lead to inaccurate results. Therefore, CO2 adsorption and N2 gas adsorption/desorption experiments are used to characterize pores with diameters less than 300 nm. The experiments were conducted using a modified Micromeritics ASAP2000 automated surface area analyzer. Prior to CO2 adsorption and N2 gas adsorption/desorption analyses, 0.18e0.25-mm particle size coal samples were sieved and dried at 105 C for 24 h in a vacuum oven to remove air, free water, and other impurities (Yao et al., 2008; Nie et al., 2015). The CO2 adsorption data (273.15 K or 0 C) were collected at a relative pressure (P/P0) range from 0.01 to 0.035, and the N2 gas adsorption/ desorption (77 K or 196.15 C) isotherms were measured at a relative pressure (P/P0) range from 0.01 to 0.995. As discussed by Clarkson et al. (2013), CO2 adsorption at 273 K can be used to investigate pores with diameters less than 1.5 nm and N2 adsorption at 77 K can be used to investigate pores with diameters greater than 1.7 nm. Furthermore, the CO2 adsorption data were interpreted using the Dubinin-Astakhov (D-A) and DubininRadushkevich (D-R) models, and the N2 adsorption/desorption data were analyzed using the Brunauer-Emmett-Teller (BET) and Barrett-Joyner-Halenda (BJH) theories. The results of the CO2 adsorption and N2 adsorption/desorption analysis are listed in
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Table 1 Results of the Ro,m, petrographic and proximate analysis of the coal samples. Ro,m (%)
Samples No.
TA-Lignite WT-Long-flame coal
Proximate analysis (%)
0.45 0.58
Petrographic analysis (%)
Mad
Aad
Vad
FCad
Vitrinite
Inertinite
Liptinite
Mineral
1.99 2.48
21.28 15.13
27.74 32.69
48.99 49.70
71.59 68.28
15.85 21.79
1.77 0.73
10.8 9.2
Note: Mad ¼ Moisture content (wt. %, air dry basis); Aad ¼ Ash yield (wt. %, air dry basis); Vdaf ¼ Volatile matter (wt. %, air dry basis).
Table 2 Pore structure characterization of coal samples from CO2 adsorption (273 K), low-pressure N2 adsorption/desorption (77 K) and MIP. Samples No.
TA-Lignite WT-Long-flame coal
Pores volume distribution (cm3/g) CO2 adsorption (273 K)
N2 adsorption/desorption (77 K)
<1.5 nm
1.7e2 nm
1.56 102 2.10 102
1.38 104 4.21 103 2.15 103 2.03 102 1.12 102 1.77 104 7.84 103 3.37 103 2.44 102 0.17 102
2e50 nm
MIP
>50 nm
<100 nm
Table 2. 2.4. Methane isotherm adsorption and diffusion measurements CH4 adsorption isotherm and diffusion experiments were conducted on a TerraTek Isotherm Measurement System (IS-300), which uses a manometric method. All experiments were carried out at 30 C, and the adsorption isotherms were measured up to a maximum gas pressure of approximately 7.0 MPa. The experimental procedures are those described by Busch and Gensterblum, 2011; Yao et al., 2008. During the experiment, pressure change with time was recorded every minute for the first 180 min after which the recording intervals increased to 10 min for the next 300 min. The adsorbed amount calculation from the experimental data follows the Chinese Technical Standard GB/T 19560-2004 (SAC, 2004). We use the Langmuir equation to fit the CH4 adsorption volumes of the coal samples under different moisture contents, and the Langmuir parameters are calculated using the Langmuir model, as follows:
V¼
BET surface area (m2/ Extrusion efficiency g) (%)
VL P PL þ P
(2)
where P is pressure (MPa), V is the CH4 adsorbed volume at pressure P (cm3/g), PL is the Langmuir pressure (MPa), and VL is the maximum adsorbed volume (cm3/g).
100 e1000 nm
>1000 nm 0.29 102 2.81 0.21 102 3.83
57.74 77.48
and Bustin, 1999). To better describe the behavior of the gas adsorption/desorption rate, Ruckenstein et al. (1971) developed the bidisperse model to fit the experimental data, which includes a fast macropore diffusion stage and a much slower micropore diffusion stage. For the first macropore diffusion stage, the uptake is given by: ∞ Ma 6 X 1 ¼1 2 exp Dae n2 p2 t 2 Ma∞ p n¼1 n
(4)
and the second slower micropore diffusion stage can be expressed as: ∞ Mi 6 X 1 ¼1 2 exp Die n2 p2 t 2 Mi∞ p n¼1 n
(5)
where Ma is the total amount of CH4 adsorbed in the macropores at time t, Ma∞ is the total amount of CH4 adsorbed in the macropores over infinite time, Dae is the macropore effective diffusivity and can be expressed as Dae ¼ Dr2a , Mi is the total amount of CH4 adsorbed in a the micropores at time t, Mi∞ is the total amount of CH4 adsorbed in the micropores over infinite time, and Die is the micropore effective i diffusivity and can be expressed as Die ¼ D . ri2 The total uptake at any time is the sum of the macrosphere uptake and the microsphere uptake. Therefore, Pan et al. (2010) determined that the overall uptake is:
3. Establishment of methane diffusion modeling Based on the assumptions of the isothermal conditions and homogenous pore structure, the analytical solution of the unipore model can be expressed as follows (Crank, 1975): ∞ Mt 6 X 1 2 2 ¼1 2 exp D n p t e M∞ p n¼1 n2
(3)
where Mt is the amount of gas adsorbed at time t and M∞ is the total amount of gas adsorbed at equilibrium pressure. De is the effective diffusivity and can be expressed as De ¼ rD2 , where r is the sphere radius. However, it has been reported that the unipore models may be inadequate for coals, with a bimodal pore distribution (Clarkson
Mt Ma þ Mi Ma M ¼ ¼b þ ð1 bÞ i M∞ Ma∞ þ Mi∞ Ma∞ Mi∞
(6)
a∞ where b ¼ Ma∞MþM is the ratio of the macropore adsorption to the i∞ total adsorption. Eq. (6) is different than the original bidisperse model derived by Ruckenstein et al. (1971), but they are based on the same assumptions. Because the pore structure of some coals is very complex, the gas diffusion stages cannot simply be divided into a fast macropore diffusion and a much slower micropore diffusion stage (Cai et al., 2014a,b; Clarkson et al., 2013). The gas diffusion in the coal matrix may consist of multiple diffusion processes, such as the two samples in this study. Thus, the overall uptake should be expressed as:
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stage in the low pressure region illustrates that the seepage-pores are not well developed in this coal, at only 13.59% (Fig. 1d). Moreover, due to the efficiency of mercury withdrawal reaching 77.48%, the open pores constitute a large ratio of the total pores and the pores are well connected.
n X M4 Mt ¼ M∞ 4¼1 M4∞
¼ v1
M4 M1 M þ v2 2 þ … þ 1 v1 v2 … v4 M1∞ M2∞ M4∞ (7)
We apply the bidisperse model and the multiporous diffusion model to match the experimental data and compare their applicability in determining the diffusion coefficients of low-rank coals. 4. Results and discussion 4.1. Pore structure of low-rank coals 4.1.1. Mercury intrusion porosimetry The mercury intrusion/extrusion curves and pore size distribution of two low-rank coal samples using MIP are shown in Fig. 1. For sample TA, the mercury injection curve has three distinct stages, including a straight-line stage, a platform stage, and a smooth curve stage (Fig. 1a). Based on the Washburn Equation (Washburn, 1921), the mercury injection process indicates that the adsorption-pores (<100 nm) and seepage-pores (>100 nm) are well developed in lignite. The pores with diameters less than 100 nm account for 59.07%, the pores with diameters greater than 100 nm account for 40.93%, and the pore size distribution of sample TA has a multimodal distribution (Fig. 1b). It is to note that the efficiency of mercury withdrawal is relatively low, only 57.74%, which indicates that a certain amount of semi-closed pores exists and that the pores are not well connected. As shown in Fig. 1c, the mercury injection curve of sample WT has two clear stages. The smooth curve stage in the high pressure region indicates that sample WT has a greater percentage of adsorption-pores, up to 86.41%, and the broken line
4.1.2. CO2 adsorption and N2 adsorption/desorption analysis Because of the compression effect on the coal matrix at the high pressure of the MIP, the CO2 adsorption and N2 adsorption/ desorption tests are combined to describe the characteristics of the adsorption-pores. Fig. 2a and c shows the isotherm results of the N2 adsorption/desorption analysis. As shown in Fig. 2a, the N2 adsorption/desorption isotherm of sample TA has a distinct hysteresis loop and the desorption curve declines dramatically at a relative pressure of 0.45, indicating a large number of ink-bottleshaped pores within the coal matrix, according to the theory of De Boer (1958). It is obvious that sample WT has a smaller hysteresis loops and the isotherms of the adsorption and desorption are reversible when P/P0 < 0.45, which indicates the existence of many wedge-shaped, cylindrical, and slit-shaped pores that have one side closed (Fig. 2c). This observation is consistent with the phenomenon from the MIP. The pore size classification of the International Union of Pure and Applied Chemistry (IUPAC, 1982) is used in this work: micropores (<2 nm), mesopores (2e50 nm) and macropores (>50 nm). The pore size distribution of the coal samples using the N2 adsorption/desorption and CO2 adsorption analyses is shown in Figs. 2 and 3 and indicates that the studied coal samples display a multimodal pore size distribution. The pore system of sample TA has a high volume of micropores (71.2%), moderately developed mesopores (19.1%) and slightly developed macropores (9.7%) (Table 2). This coal may be favorable for gas adsorption but unfavorable for gas flow due to the higher volume of micropores and poor connectivity. Moreover, the pore system of sample WT
Fig. 1. The mercury intrusion/extrusion curves and pore size distribution of coal samples by MIP.
Z. Li et al. / Journal of Natural Gas Science and Engineering 33 (2016) 97e107
Fig. 2. The adsorption/desorption isotherms and pore size distribution of coal samples by N2 adsorption/desorption analysis.
Fig. 3. The adsorption isotherms and pore size distribution of coal samples by CO2 adsorption analysis.
includes large developed micropores (65.4%), mesopores (24.2%) and macropores (10.4%). Due to the open pores and good connectivity, this pore structure is favorable for both gas adsorption and
flow.
101
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Fig. 4. The methane adsorption isotherms of dry samples and moisturized samples.
and diffusion properties of the coal matrix. In this study, the coal samples already developed many peaks in the pore size distribution results of the CO2 adsorption, N2 adsorption/desorption, and MIP. The micropores and mesopores are well developed in the lignite sample and long-flame coal sample (Figs. 1e3). Based on the trimodal pore structure of the coal samples, eq. (7) can be written as:
4.2. Methane adsorption isotherms Fig. 4 shows the CH4 adsorption isotherms of the dry and moisturized coals based on the isothermal adsorption experiments. Using the Langmuir adsorption law, the Langmuir parameters of the dry and moisturized coals are calculated (Table 3). The relative errors of the deviation of the Langmuir-predicted values were less than 2.0%, which are acceptable (Dutta et al., 2008). The CH4 adsorption volume increases from 8.08 cm/g3 to 14.50 cm/g3 when the moisture of the coal sample TA falls from 5.03% to 0.0% (Table 3). Similarly, the CH4 adsorption volume also increases from 7.32 cm/ g3 to 12.59 cm/g3 when the moisture of the coal sample WT falls from 4.63% to 0.0%. This observation indicates that the amount of moisture has a negative impact on the CH4 adsorption capacity of lignite and long-flame coals. The moisture may preferentially occupy the polar functional groups and adsorption space in lowrank coals, suggesting that the moisture significantly reduces the CH4 adsorption capacity (Busch and Gensterblum, 2011; Day et al., 2008; Gensterblum et al., 2013). Moreover, the gas adsorption capacity of coal is typically influenced by other factors, such as pressure, temperature, coal rank, and composition (Hildenbrand et al., 2006; Krooss et al., 2002). It is obvious that sample TA has a slightly higher CH4 adsorption capacity than that of sample WT (Fig. 4). Due to the similarity in volatile matter and fixed carbon content of the two samples, the slight difference of the CH4 adsorption capacity may be affected by coalification and the maceral composition, including vitrinite and liptinite content.
Mt Ma þ Me þ Mi Ma Me M ¼ ¼ va þ ve þ vi i M∞ Ma∞ þ Me∞ þ Mi∞ Ma∞ Me∞ Mi∞
(8)
where va þ ve þ vi ¼ 1, Me is considered to be the total amount of CH4 adsorbed in the mesopores at time t and P∞ 1 Me 6 2 2 n¼1 n2 expðDee n p tÞ. Me∞ ¼ 1 p2 According to eq. (8), the multiporous model can be translated into a code in MATLAB. First, the diffusion data is imported into the program. Then, the initial value is repeatedly set up to match data. In this process, the reasonable initial value is determined by the goodness of fitting. Finally, the diffusion coefficients can be obtained by using MATLAB to fit diffusion data. Figs. 5 and 6 show the bidisperse model and a modified multiporous model are applied to represent the experimental data. It is apparent from the figures that the multiporous model provides an excellent fit to the diffusion data of the two coal samples, whereas the bidisperse model deviates significantly from the data at the initial diffusion stage. This difference suggests that the bidisperse model may be inadequate to accurately characterize the diffusion behavior for some low-rank coals, which have a more complex pore structure and a greater percentage of microporosity and mesoporosity. Through studying the gas diffusion of dull coals, Clarkson and Bustin (1999) have reported that transition diffusion occurs from macroporedominated transport at an early time, to micropore-dominated transport at a later time. However, the bidisperse model ignored the transition diffusion stage, which occurs between the faster diffusion stage and the slower diffusion stage. In contrast, the transition diffusion stage is taken into account in the multiporous model, which agrees well with the diffusion data of the two coal
4.3. Estimation of methane diffusion coefficient When applied to some coals that have a distribution consisting mostly of macropores and micropores, the unipore model failed to accurately describe gas diffusion. Both Smith and Williams (1984); Clarkson and Bustin (1999) derived the bidisperse model, which has one diffusion coefficient for each pore size and can be used to describe gas diffusion in the coal matrix. This model indicates that the pore structure is an important factor that affects the adsorption
Table 3 Moisture content and CH4 isothermal adsorption results of coal samples. Samples No.
TA-Lignite WT-Long-flame coal
Salt solution
e K2SO4 e K2SO4
Relative humidity
0% 97% 0% 97%
Moisture content
0.0% 5.03% 0.0% 4.63%
CH4 isothermal adsorption results Langmuir volume (VL, cm3/g)
Langmuir pressure (PL, MPa)
Correlation coefficient
14.50 8.08 12.59 7.32
2.14 2.53 2.45 2.20
0.983 0.976 0.991 0.987
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Fig. 5. Fit curves of bidisperse model and multiporous model to sample TA data.
samples. The CH4 diffusion coefficients of both the bidisperse model and multiporous model are shown in Table 4. Based on the multiporous model, the order of magnitude of the macropore diffusivity is roughly between 104 and 103 s1, the mesopore diffusivity varies from 105 to 104 s1, and the micropore diffusivity varies from 106 to 105 s1. The macropore diffusivity is generally one to three orders of magnitude greater than the mesopore diffusivity and micropore diffusivity. In addition, the macropore diffusivities of the bidisperse model are between the macro- and mesopore diffusivities of the multiporous model, while the micropore diffusivities of the bidisperse model are close to those of the multiporous model, which are comparable to the results from Pan et al. (2010). Table 4 also summarizes the methane diffusivity fraction values (aa, ae and ai) of the multiporous model. For lignite sample TA, the macro-
diffusivity fraction ranges from 0.141 to 0.243, the mesodiffusivity fraction ranges from 0.131 to 0.248, and the microdiffusivity fraction ranges from 0.518 to 0.728. For long-flame coal sample WT, the macro-diffusivity fraction ranges from 0.102 to 0.253, the meso-diffusivity fraction ranges from 0.103 to 0.196, and the micro-diffusivity fraction ranges from 0.607 to 0.754. There is a significantly positive correlation between the methane diffusivity fractions and porosity fractions. This correlation suggests that the fraction of micro-, meso-, and macro-porosity is a very important factor that directly affects the determination of the diffusion coefficients. However, this conclusion is based on the two low-rank coal samples used in this paper, and more work is required to validate the model for application to other coals.
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Fig. 6. Fit curves of bidisperse model and multiporous model to sample WT data.
4.4. Effect of gas pressure and moistures on methane diffusion Fig. 7 shows the relationship between the methane diffusivities obtained from the multiporous model and equilibrium adsorption pressure of the low-rank coal samples. The CH4 macropore and micropore diffusivities tend to decrease with an increase in pressure, whereas a strong positive correlation exists between the CH4 mesopore diffusivities and gas pressure. The effects of the gas pressure on the methane diffusivities in the coal matrix may be related to the different mechanisms of gaseous methane diffusion and coal matrix swelling caused by gas adsorption. However, inconsistent conclusions are reported by Clarkson and Bustin (1999); Cui et al. (2004); Xu et al. (2015). Based on the gas molecular mean free path (l) and pore diameter (dp), the diffusion mechanisms can be divided into three types: Fickian diffusion (dp > 10l), transitional diffusion (0.1l < dp < 10l), and Knudsen
diffusion (dp < 0.1l) (Reeves and Pekot, 2001; Yan et al., 2008; Xu et al., 2015). Moreover, the mean free paths of the methane molecules can be described by the Maxwell distribution, which is expressed by:
KT
l ¼ pffiffiffi 2 2pd0 P where K is the Boltzmann constant (1.38 1023 J/K), T is the experimental temperature (K), d0 is the gas molecule diameter (m), and P is the pressure (Pa). Taking the equilibrium pressure 0.88 MPa as an example (the other cases are similar) and using the experimental conditions (T ¼ 303.15 K, d0,methane ¼ 0.33 nm), the primary diffusion mode is Fickian diffusion when the pore diameter is greater than 74.1 nm, whereas the primary diffusion mode is Kundsen diffusion for pore
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Table 4 Diffusivity of coal samples by different models. Sample
Moisture content (%) Equilibrium pressure (MPa) Bidisperse model
b TA-Lignite
0.0
5.03
WT-Long- flame coal 0.0
4.63
0.88 1.85 3.03 3.99 5.42 0.88 2.06 3.06 3.86 5.30 0.98 1.87 3.04 4.11 5.54 0.89 1.84 2.83 3.83 5.37
0.373 0.359 0.387 0.259 0.263 0.459 0.213 0.312 0.336 0.339 0.347 0.253 0.227 0.237 0.261 0.338 0.177 0.358 0.377 0.204
diameters smaller than 0.74 nm. Considering the pore size distribution in Figs. 1e3, it is suggested that the methane diffusion in macropores is mainly controlled by Fickian diffusion and Knudsen diffusion only occurs within micropores, whereas methane diffusion in mesopores is controlled by a combination of Fickian diffusion and transitional diffusion. Additionally, the swelling of the coal matrix with increasing methane adsorption pressure may narrow some pores, which increases the resistance to diffuse gas molecules. Therefore, the effect of pressure on methane diffusivity during the adsorption process is the competition between these two factors. In this work, the macropore and micropore diffusivities decrease with increasing pressure, indicating that the adsorption swelling effect of the coal matrix becomes dominant. As the pressure increases, the Fickian diffusion occurs in the smaller pore size within the mesopores, which results in the continual increase of the mesopore diffusivity. This observation suggests that the effect of pressure on the methane diffusion in pores with different pore sizes is different during the adsorption process. The presence of moisture is another factor on methane diffusion in coals, which may significantly reduce the methane diffusivities of low-rank coal samples at the same equilibrium pressure. This conclusion is consistent with other diffusion results obtained by Clarkson and Bustin (1999); Pan et al. (2010); Xu et al. (2015), who studied gas diffusion at different moisture levels. Similarly, the methane adsorption volume of the moist samples is far less than that of dry samples (Fig. 4). The main reason for this result is that moisture more easily adsorbs to the pore surface and occupies the pore space in the coal matrix, which is unfavorable for gas adsorption and diffusion. Moreover, the results show that the mesopore diffusivities are most affected by moisture, with a reduction of up to 50% (Table 4). This reduction in mesopore diffusivity may form clusters and even condensates in the mesopores of the low-rank coal matrix. Additionally, the moisture can swell clay minerals in coals, such as illite and montmorillonite, which possibly reduces the original pore volume and narrows the pore throats (Zhang et al., 2012; Yuan et al., 2014). In this study, the mineral proportions of the two low-rank coal samples were approximately 10% (Table 1), which could also significantly reduce the methane diffusivity in coals under moist conditions.
Dae (s1) 3.72 3.80 4.24 5.20 5.55 6.82 3.48 2.53 2.81 2.96 4.11 4.53 4.80 5.07 5.86 3.55 3.88 4.10 4.78 4.93
Multiporous model Die (s1)
4
10 104 104 104 104 105 104 104 104 104 104 104 104 104 104 104 104 104 104 104
1.31 1.29 1.27 1.24 1.25 9.79 1.23 9.61 9.58 9.03 1.16 1.02 9.06 1.04 1.06 1.00 9.74 9.48 8.90 9.97
va 5
10 105 105 105 105 106 105 106 106 106 105 105 106 105 105 105 106 106 106 106
0.193 0.203 0.243 0.166 0.141 0.161 0.164 0.161 0.166 0.192 0.201 0.135 0.138 0.170 0.196 0.182 0.102 0.214 0.253 0.165
Dae (s1) 1.85 1.62 1.50 1.33 1.30 1.30 9.14 7.75 5.34 5.17 2.00 1.73 1.66 1.58 1.56 1.62 1.44 1.35 1.21 1.16
ve 3
10 103 103 103 103 103 104 104 104 104 103 103 103 103 103 103 103 103 103 103
0.236 0.211 0.239 0.214 0.131 0.248 0.226 0.224 0.214 0.179 0.192 0.132 0.108 0.128 0.103 0.196 0.162 0.173 0.133 0.158
Dee (s1) 4.29 6.62 8.86 9.17 9.87 2.03 3.86 4.23 4.84 4.97 7.46 9.80 1.12 1.22 1.28 5.30 6.58 7.92 8.10 8.28
5
10 105 105 105 105 105 105 105 105 105 105 105 104 104 104 105 105 105 105 105
vi
Die (s1)
0.571 0.586 0.518 0.620 0.728 0.591 0.610 0.615 0.620 0.629 0.607 0.733 0.754 0.702 0.701 0.622 0.706 0.613 0.614 0.677
1.09 1.04 1.00 9.63 8.85 9.83 9.50 9.12 8.79 8.57 1.21 1.20 1.16 1.14 1.11 9.22 9.10 9.07 8.96 8.58
105 105 105 106 106 106 106 106 106 106 105 105 105 105 105 106 106 106 106 106
5. Conclusions In this study, two low-rank coals from China were used to study the diffusion behaviors that occur during the methane adsorption process. The low-rank coal samples exhibited a multimodal pore size/volume distribution and contained a large amount of micropores and mesopores, which is favorable for CBM adsorption and diffusion. The bidisperse diffusion model and multiporous diffusion model were applied to represent the experimental data for dry and moist coal samples. The results show that the multiporous model provides an excellent fit to the diffusion data of the two coal samples, whereas the bidisperse model deviates significantly from the data of the initial diffusion stage. This difference suggests that the gas diffusion stages are not only simply divided into a fast macropore diffusion stage and a much slower micropore diffusion stage but also consist of multiple diffusion processes, at least for the coals used in this study. Based on the multiporous model, the macropore diffusivity (104~103 s1) is generally one to three orders of magnitude greater than the mesopore diffusivity (105~104 s1) and micropore diffusivity (106 ~105 s1). The effects of the adsorption pressure and moisture on methane diffusion in low-rank coal samples are discussed in this work. With increasing adsorption pressure, both macropore diffusivity and micropore diffusivity have a decreasing trend, whereas a strong positive correlation exists between mesopore diffusivity and pressure. This difference may be related to the different mechanisms of gaseous methane diffusion and the swelling of the coal matrix caused by gas adsorption. This difference also indicates that the effect of pressure on methane diffusion in pores with different pore sizes is different during the adsorption process. Furthermore, the presence of moisture significantly reduces the methane diffusivities of low-rank coal samples in this work, which is consistent with the existing literature. The main reason for this observation is that the moisture more easily adsorbs to the pore surface and occupies the pore space in the coal matrix in addition to the effect of the mineral swelling of the adsorbing moisture. These findings may have important implications for gas diffusion modeling, and further study is required to test the applicability of the multiporous diffusion model.
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Fig. 7. CH4 diffusivities of dry and moist coal samples by using multiporous model (-D represents the dry sample, -M represents the moist sample).
Acknowledgments This research was funded by the National Natural Science Foundation of China (grant no. U1262104), Program for New Century Excellent Talents in University (grant no. NCET-11-0721), Research Program for Excellent Doctoral Dissertation Supervisor of Beijing (grant no. YB20101141501), Fundamental Research Funds for Central Universities (grant no. 35832015136) and Key Project of Coal-based Science and Technology in Shanxi Province-CBM accumulation model and reservoir evaluation in Shanxi province (grant no. MQ2014-01). The authors also thank Dr. Zhejun Pan for his constructive suggestions in revising the manuscript. References Busch, A., Gensterblum, Y., 2011. CBM and CO2-ECBM related sorption processes in coal: a review. Int. J. Coal Geol. 87, 49e71. Busch, A., Gensterblum, Y., Krooss, B.M., Littke, R., 2004. Methane and carbon dioxide adsorption-diffusion experiments on coal: upscaling and modeling. Int. J. Coal Geol. 60, 151e168. Cai, Y.D., Liu, D.M., Yao, Y.B., Li, J.Q., Qiu, Y.K., 2011. Geological controls on prediction
of coalbed methane of No. 3 coal seam in Southern Qinshui Basin, North China. Int. J. Coal Geol. 88, 101e112. Cai, Y.D., Liu, D.M., Yao, Y.B., Li, J.Q., Zheng, G.Q., 2014a. The evolution of petrophysical properties of coalbed methane reservoirs under the heat treatment. Earth Sci. Front. 21 (1), 240e248. Cai, Y.D., Pan, Z.J., Liu, D.M., Zheng, G.Q., Tang, S.H., Connell, L.D., Yao, Y.B., Zhou, Y.F., 2014b. Effects of pressure and temperature on gas diffusion and flow for primary and enhanced coalbed methane recovery. Energy Explor. Exploit. 32 (4), 604e619. Cai, Y.D., Liu, D.M., Pan, Z.J., Che, Y., Liu, Z.H., 2015. Investigating the effects of seepage-pores and fractures on coal permeability by fractal analysis. Transp. Porous Med. http://dx.doi.org/10.1007/s11242-015-0605-7. re, D., Pokryszka, Z., Behra, P., 2010. Effect of pressure and temperature on Charrie diffusion of CO2 and CH4 into coal from the Lorraine basin (France). Int. J. Coal Geol. 81, 373e380. Clarkson, C.R., Bustin, R.M., 1999. The effect of pore structure and gas pressure upon the transport properties of coal: a laboratory and modeling study. 2. Adsorption rate modeling. Fuel 78, 1345e1362. Clarkson, C.R., Solano, N., Bustin, R.M., Bustin, A.M.M., Chalmers, G.R.L., He, L., ski, A.P., Blach, T.P., 2013. Pore structure characterMelnichenko, Y.B., Radlin ization of North American shale gas reservoirs using USANS/SANS, gas adsorption, and mercury intrusion. Fuel 103, 606e616. Crank, J., 1975. The Mathematics of Diffusion, second ed. Oxford University Press, London. Crosdale, P.J., Beamish, B., Valix, M., 1998. Coalbed methane sorption related to coal
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coal. Energy Fuel 23, 4688e4695. Reeves, S., Pekot, L., 2001. Advanced reservoir modeling in desorption-controlled reservoirs. In: SPE Rocky Mountain Petroleum Technology Conference. SPE, Keystone, Colorado, pp. 21e23. Ruckenstein, E., Vaidyanathan, A.S., Youngquist, G.R., 1971. Sorption by solids with bidisperse pore structures. Chem. Eng. Sci. 26, 1305e1318. Shi, J.Q., Durucan, S., 2003. A bidisperse pore diffusion model for methane displacement desorption in coal by CO2 injection. Fuel 82, 1219e1229. Shi, J.Q., Durucan, S., 2005. Gas storage and flow in coalbed reservoirs: implementation of a bidisperse pore model for gas diffusion in coal matrix. SPE Reserv. Eval. Eng. 8 (2), 169e175. Smith, D.M., Williams, F.L., 1984. Diffusional effects in the recovery of methane from coalbeds. Soc. Pet. Eng. J. 24 (5), 529e535. Staib, G., Sakurovs, R., Gray, E.M.A., 2013. A pressure and concentration dependence of CO2 diffusion in two Australian bituminous coals. Int. J. Coal Geol. 116e117, 106e116. Standardization Administration of the People’s Republic of China (SAC), 2004. GB/T 19560e2004. Experimental Method of High-pressure Adsorption Isothermal to Coal-capacity Method (In Chinese). Standards Press of China, Beijing, China. a bova , M., Weishauptov Sv a, Z., Pribyl, O., 2012. The effect of moisture on the sorption process of CO2 on coal. Fuel 92, 187e196. Wang, K., Zang, J., Feng, Y.F., Wu, Y.Q., 2014. Effects of moisture on diffusion kinetics in Chinese coals during methane desorption. J. Nat. Gas Sci. Eng. 21, 1005e1014. Washburn, E.W., 1921. The dynamics of capillary flow. Phys. Rev. 17, 273e283. Xu, H., Tang, D.Z., Zhao, J.L., Li, S., Tao, S., 2015. A new laboratory method for accurate measurement of the methane diffusion coefficient and its influencing factors in the coal matrix. Fuel 158, 239e247. Yan, B.Z., Wang, Y.B., Ni, X.M., 2008. Coalbed methane diffusion characters based on nano-scaled pores under formation conditions. China Coal Soc. 33 (6), 657e660 (in Chinese). Yao, Y.B., Liu, D.M., 2012. Comparison of low-field NMR and mercury intrusion porosimetry in characterizing pore size distributions of coals. Fuel 95, 152e158. Yao, Y.B., Liu, D.M., Tang, D.Z., Tang, S.H., Huang, W.H., 2008. Fractal characterization of adsorption-pores of coals from North China: an investigation on CH4 adsorption capacity of coals. Int. J. Coal Geol. 73, 27e42. Yuan, W.N., Pan, Z.J., Li, X., Yang, Y.X., Zhao, C.X., Connell, L.D., Li, S.D., He, J.M., 2014. Experimental study and modelling of methane adsorption and diffusion in shale. Fuel 117, 509e519. Zhang, T.W., Ellis, G.S., Ruppel, S.C., Milliken, K., Yang, R.S., 2012. Effect of organicmatter type and thermal maturity on methane adsorption in shale-gas systems. Org. Geochem. 47, 120e131.
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Investigation of methane diffusion in low-rank coals by a multiporous diffusion model Zhentao Li a, Dameng Liu a, *, Yidong Cai a, Yunlong Shi b a Coal Reservoir Laboratory of National Engineering Research Center of CBM Development & Utilization, China University of Geosciences, Beijing 100083, China b Key Laboratory of Ocean Circulation and Waves, Institute of Oceanology, Chinese Academy of Sciences, Qingdao 266071, China
a r t i c l e i n f o
a b s t r a c t
Article history: Received 26 January 2016 Received in revised form 4 May 2016 Accepted 5 May 2016 Available online 7 May 2016
To study the methane diffusion behaviors of low-rank coals (Ro,m of 0.45% and 0.58%), a combination of CO2 adsorption, N2 adsorption/desorption, and mercury intrusion porosimetry (MIP) measurements were used to characterize the pore structure of coals, and a new multiporous diffusion model was established to model methane diffusion under dry and moist conditions during the methane adsorption process. The results indicate that the pore structure of low-rank coal samples exhibits a multimodal pore size/volume distribution and has a greater percentage of microporosity and mesoporosity. The multiporous model provides a better fit than the bidisperse model, which deviates significantly from the data, especially during the initial diffusion stage. Based on the multiporous diffusion model, the macropore diffusivity (104~103 s1) is generally one to three orders of magnitude greater than the mesopore diffusivity (105~104 s1) and micropore diffusivity (106~105 s1). Moreover, both the macropore diffusivity and micropore diffusivity show a decreasing trend with increasing pressure, whereas a strong positive correlation exists between the mesopore diffusivities and pressure, indicating that the effect of pressure on methane diffusion in pores with different sizes is different during the adsorption process. This difference may be due to the competition between the different mechanisms of gaseous methane diffusion and the swelling of the coal matrix caused by gas adsorption. Furthermore, the moisturereduced methane diffusivities is mainly due to the moisture in the coal matrix that adsorbs to the pore surface and occupies the pore space, as well as changes the pore structure according to the effect of mineral swelling from the adsorbing moisture. Therefore, these results may have a significant implication for understanding the transport mechanism of methane in coals and the design of enhanced CBM recovery. © 2016 Elsevier B.V. All rights reserved.
Keywords: Gas diffusion Multiporous diffusion model Pore structure Pressure Moisture content
1. Introduction Coalbed methane (CBM) represents an alternative hydrocarbon resource that has attracted global attention in recent years. Compared to conventional natural gas reservoirs, coal reservoirs have unique characteristics, including a dual porosity system, pore structure, gas storage, and flow mechanisms. It has been confirmed that CBM is mainly adsorbed at the pore surface in the coal matrix and that gas is desorbed from the pore surface and diffuses from the pore system to the cleat/fracture systems during production (Clarkson and Bustin, 1999; Shi and Durucan, 2005; Cai et al.,
* Corresponding author. E-mail address: [email protected] (D. Liu). http://dx.doi.org/10.1016/j.jngse.2016.05.012 1875-5100/© 2016 Elsevier B.V. All rights reserved.
2014a,b). Commonly, gas transport in coals is divided into two stages: gas diffusion within the coal matrix and flow in the cleat system (Pillalamarry et al., 2011). Harpalani and Chen (1997) revealed that gas diffusion through the matrix is assumed to be concentration gradient driven and is usually modeled using Fick’s Second Law of Diffusion. Moreover, both Shi and Durucan (2003); Pan et al. (2010) found that gas diffusion within the coal matrix is dominated by three diffusion mechanisms in coals, including Fickian diffusion (molecule-molecule collisions dominate), Knudsen diffusion (molecule-wall collisions dominate) and Surface diffusion (transport through physically adsorbed layer). Due to the often significant heterogeneity of the pore structure, all three diffusion mechanisms play important roles in gas diffusion within the coal matrix (Xu et al., 2015; Yuan et al., 2014). A significant amount of work has been completed in modeling
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diffusion, and various diffusion models have been applied to characterize the diffusion process, such as the unipore model a re et al., 2010; Jian et al., 2012; Pone et al., 2009; Sv bov (Charrie a et al., 2012), the bidisperse model (Busch et al., 2004; Clarkson and Bustin, 1999; Cui et al., 2004; Shi and Durucan, 2003, 2005; Smith and Williams, 1984; Pan et al., 2010), and the Fickian diffusion-relaxation (FDR) model (Staib et al., 2013). Based on these models, one or two diffusion coefficients are obtained to describe the sorption kinetics of coals. By studying the gas diffusion of different rank coals, Crosdale et al. (1998); Clarkson and Bustin (1999) discovered that the unipore model is more suitable for vitrinite-rich bright coals, whereas the bidisperse model may be adequate to describe the sorption kinetics of some inertinite-rich dull or banded coals. This observation indicates that the coal composition may influence gas transport in the coal matrix and the pore structure plays an important role in accurately modeling gas transport through the coal matrix. Previous research using nuclear magnetic resonance suggests that the pore volume distribution of low-rank coals has a triple peak pattern (Cai et al., 2015). Moreover, based on experimental and mathematical simulations, many influencing factors on the diffusion coefficients have been discussed in recent studies. Pan et al. (2010), by studying the effects of matrix moisture on methane and carbon dioxide diffusion, discovered that the diffusion coefficients of dry coal are higher than those of wet coal and that the diffusion coefficients of CO2 are significantly higher than those of CH4 under the same conditions. However, a similar study by Wang et al. (2014) also found that diffusivity decreases with increasing moisture for Chinese anthracite, whereas for Chinese bituminous coal, diffusivity varies with the moisture following a U-shaped function. Furthermore, re et al. (2010) demonstrated that the calculated diffusion Charrie coefficients of CH4 and CO2 from the unipore model increase with increasing temperature and gas pressure on coals from the Lorraine Basin in France. However, it has been proposed that diffusion coefficients may have different trends depending on the model chosen, even when using the same data (Clarkson and Bustin, 1999; Shi and Durucan, 2005; Staib et al., 2013). In this work, we investigated the methane adsorption and diffusion behaviors in two Chinese low-rank coals through experimental study and modeling. The pore structure, as a factor of methane diffusion, is required. Therefore, the pore structure of the coal samples was first investigated via the CO2 adsorption, N2 gas adsorption/desorption, and mercury intrusion porosimetry (MIP) techniques. Then, a new multiporous diffusion model, based on the bidisperse model, was proposed to describe the methane diffusivity in the coal matrix. Finally, the effects of moisture and pressure on methane diffusion under dry and moist conditions were discussed in detail. 2. Material and methods 2.1. Coal samples and preparation The coal samples used in this work were collected from the Taian coal mine and Wangtian coal mine in the Baode mining area, Shanxi Province. The maximum vitrinite reflectance (Ro,m), petrographic, and proximate analyses for the coal samples were carried out in our laboratory, and the experimental procedures were the same as those of our previous work (Cai et al., 2011). The ranks of the two coals are lignite for Taian (TA) and long-flame coal for Wangtian (WT), with maximum vitrinite reflectance (Ro,m) reaching 0.45% (TA) and 0.58% (WT), respectively. The results of the petrographic and the proximate analysis are presented in Table 1. The coal lumps were pulverized and the particles between 0.18 and 0.25 mm were selected for CH4 adsorption and diffusion
experiments. The powder samples were divided into two parts. One part was dried in a 50 C vacuum oven for more than one week to remove any pre-existing moisture. The other part was used to prepare the moisture-equilibrated samples. The samples were prepared using a saturated K2SO4 solution, with a relative humidity of approximately 97%. The wet samples were weighed periodically during moisture-equilibrated process. Over a period of two months, the moisture of the coal samples reached an equilibrium state, as described in detail by Pan et al. (2010). The moisture content of coal samples is defined as:
w% ¼
mmoisture 100% mcoal
(1)
where w% is the moisture content, mmoisture is the total mass of water uptake in coal, mcoal is the total mass of the dry coal. The dry and moisture-equilibrated samples were prepared for CH4 isotherm adsorption and diffusion experiments. 2.2. Mercury intrusion porosimetry analysis Many methods, including scanning electron microscope (SEM), low-temperature N2 adsorption/desorption, MIP, and nuclear magnetic resonance (NMR) techniques, have been adopted to acquire the pore structure information. In this study, the pore structure and pore size distribution of the coal samples were investigated using the MIP method. The block sample was selected for MIP analysis following the rock capillary pressure measurement standard process (the Chinese Oil and Gas Industry Standard of SY/T 5346-2005) (Yao and Liu, 2012) and conducted using the PoreMasterGT60 (Quantachrome, US). The measurements run up to a pressure of 206 MPa, at which pore throats as small as four nm can be penetrated. Mercury intrusion/extrusion curves were obtained, and the cumulative mercury injection volume, pore radius, and pore size distribution could be inferred from the curves. The results of the MIP analysis are listed in Table 2. 2.3. CO2 adsorption and N2 adsorption/desorption analysis Although the MIP method is commonly used to characterize the pore size distribution of coal from a few nanometers to tens of micrometers, the pore compressibility of coals is inevitable at high pressures (normally higher than 20 MPa) (Patrick et al., 2004), which can easily lead to inaccurate results. Therefore, CO2 adsorption and N2 gas adsorption/desorption experiments are used to characterize pores with diameters less than 300 nm. The experiments were conducted using a modified Micromeritics ASAP2000 automated surface area analyzer. Prior to CO2 adsorption and N2 gas adsorption/desorption analyses, 0.18e0.25-mm particle size coal samples were sieved and dried at 105 C for 24 h in a vacuum oven to remove air, free water, and other impurities (Yao et al., 2008; Nie et al., 2015). The CO2 adsorption data (273.15 K or 0 C) were collected at a relative pressure (P/P0) range from 0.01 to 0.035, and the N2 gas adsorption/ desorption (77 K or 196.15 C) isotherms were measured at a relative pressure (P/P0) range from 0.01 to 0.995. As discussed by Clarkson et al. (2013), CO2 adsorption at 273 K can be used to investigate pores with diameters less than 1.5 nm and N2 adsorption at 77 K can be used to investigate pores with diameters greater than 1.7 nm. Furthermore, the CO2 adsorption data were interpreted using the Dubinin-Astakhov (D-A) and DubininRadushkevich (D-R) models, and the N2 adsorption/desorption data were analyzed using the Brunauer-Emmett-Teller (BET) and Barrett-Joyner-Halenda (BJH) theories. The results of the CO2 adsorption and N2 adsorption/desorption analysis are listed in
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Table 1 Results of the Ro,m, petrographic and proximate analysis of the coal samples. Ro,m (%)
Samples No.
TA-Lignite WT-Long-flame coal
Proximate analysis (%)
0.45 0.58
Petrographic analysis (%)
Mad
Aad
Vad
FCad
Vitrinite
Inertinite
Liptinite
Mineral
1.99 2.48
21.28 15.13
27.74 32.69
48.99 49.70
71.59 68.28
15.85 21.79
1.77 0.73
10.8 9.2
Note: Mad ¼ Moisture content (wt. %, air dry basis); Aad ¼ Ash yield (wt. %, air dry basis); Vdaf ¼ Volatile matter (wt. %, air dry basis).
Table 2 Pore structure characterization of coal samples from CO2 adsorption (273 K), low-pressure N2 adsorption/desorption (77 K) and MIP. Samples No.
TA-Lignite WT-Long-flame coal
Pores volume distribution (cm3/g) CO2 adsorption (273 K)
N2 adsorption/desorption (77 K)
<1.5 nm
1.7e2 nm
1.56 102 2.10 102
1.38 104 4.21 103 2.15 103 2.03 102 1.12 102 1.77 104 7.84 103 3.37 103 2.44 102 0.17 102
2e50 nm
MIP
>50 nm
<100 nm
Table 2. 2.4. Methane isotherm adsorption and diffusion measurements CH4 adsorption isotherm and diffusion experiments were conducted on a TerraTek Isotherm Measurement System (IS-300), which uses a manometric method. All experiments were carried out at 30 C, and the adsorption isotherms were measured up to a maximum gas pressure of approximately 7.0 MPa. The experimental procedures are those described by Busch and Gensterblum, 2011; Yao et al., 2008. During the experiment, pressure change with time was recorded every minute for the first 180 min after which the recording intervals increased to 10 min for the next 300 min. The adsorbed amount calculation from the experimental data follows the Chinese Technical Standard GB/T 19560-2004 (SAC, 2004). We use the Langmuir equation to fit the CH4 adsorption volumes of the coal samples under different moisture contents, and the Langmuir parameters are calculated using the Langmuir model, as follows:
V¼
BET surface area (m2/ Extrusion efficiency g) (%)
VL P PL þ P
(2)
where P is pressure (MPa), V is the CH4 adsorbed volume at pressure P (cm3/g), PL is the Langmuir pressure (MPa), and VL is the maximum adsorbed volume (cm3/g).
100 e1000 nm
>1000 nm 0.29 102 2.81 0.21 102 3.83
57.74 77.48
and Bustin, 1999). To better describe the behavior of the gas adsorption/desorption rate, Ruckenstein et al. (1971) developed the bidisperse model to fit the experimental data, which includes a fast macropore diffusion stage and a much slower micropore diffusion stage. For the first macropore diffusion stage, the uptake is given by: ∞ Ma 6 X 1 ¼1 2 exp Dae n2 p2 t 2 Ma∞ p n¼1 n
(4)
and the second slower micropore diffusion stage can be expressed as: ∞ Mi 6 X 1 ¼1 2 exp Die n2 p2 t 2 Mi∞ p n¼1 n
(5)
where Ma is the total amount of CH4 adsorbed in the macropores at time t, Ma∞ is the total amount of CH4 adsorbed in the macropores over infinite time, Dae is the macropore effective diffusivity and can be expressed as Dae ¼ Dr2a , Mi is the total amount of CH4 adsorbed in a the micropores at time t, Mi∞ is the total amount of CH4 adsorbed in the micropores over infinite time, and Die is the micropore effective i diffusivity and can be expressed as Die ¼ D . ri2 The total uptake at any time is the sum of the macrosphere uptake and the microsphere uptake. Therefore, Pan et al. (2010) determined that the overall uptake is:
3. Establishment of methane diffusion modeling Based on the assumptions of the isothermal conditions and homogenous pore structure, the analytical solution of the unipore model can be expressed as follows (Crank, 1975): ∞ Mt 6 X 1 2 2 ¼1 2 exp D n p t e M∞ p n¼1 n2
(3)
where Mt is the amount of gas adsorbed at time t and M∞ is the total amount of gas adsorbed at equilibrium pressure. De is the effective diffusivity and can be expressed as De ¼ rD2 , where r is the sphere radius. However, it has been reported that the unipore models may be inadequate for coals, with a bimodal pore distribution (Clarkson
Mt Ma þ Mi Ma M ¼ ¼b þ ð1 bÞ i M∞ Ma∞ þ Mi∞ Ma∞ Mi∞
(6)
a∞ where b ¼ Ma∞MþM is the ratio of the macropore adsorption to the i∞ total adsorption. Eq. (6) is different than the original bidisperse model derived by Ruckenstein et al. (1971), but they are based on the same assumptions. Because the pore structure of some coals is very complex, the gas diffusion stages cannot simply be divided into a fast macropore diffusion and a much slower micropore diffusion stage (Cai et al., 2014a,b; Clarkson et al., 2013). The gas diffusion in the coal matrix may consist of multiple diffusion processes, such as the two samples in this study. Thus, the overall uptake should be expressed as:
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stage in the low pressure region illustrates that the seepage-pores are not well developed in this coal, at only 13.59% (Fig. 1d). Moreover, due to the efficiency of mercury withdrawal reaching 77.48%, the open pores constitute a large ratio of the total pores and the pores are well connected.
n X M4 Mt ¼ M∞ 4¼1 M4∞
¼ v1
M4 M1 M þ v2 2 þ … þ 1 v1 v2 … v4 M1∞ M2∞ M4∞ (7)
We apply the bidisperse model and the multiporous diffusion model to match the experimental data and compare their applicability in determining the diffusion coefficients of low-rank coals. 4. Results and discussion 4.1. Pore structure of low-rank coals 4.1.1. Mercury intrusion porosimetry The mercury intrusion/extrusion curves and pore size distribution of two low-rank coal samples using MIP are shown in Fig. 1. For sample TA, the mercury injection curve has three distinct stages, including a straight-line stage, a platform stage, and a smooth curve stage (Fig. 1a). Based on the Washburn Equation (Washburn, 1921), the mercury injection process indicates that the adsorption-pores (<100 nm) and seepage-pores (>100 nm) are well developed in lignite. The pores with diameters less than 100 nm account for 59.07%, the pores with diameters greater than 100 nm account for 40.93%, and the pore size distribution of sample TA has a multimodal distribution (Fig. 1b). It is to note that the efficiency of mercury withdrawal is relatively low, only 57.74%, which indicates that a certain amount of semi-closed pores exists and that the pores are not well connected. As shown in Fig. 1c, the mercury injection curve of sample WT has two clear stages. The smooth curve stage in the high pressure region indicates that sample WT has a greater percentage of adsorption-pores, up to 86.41%, and the broken line
4.1.2. CO2 adsorption and N2 adsorption/desorption analysis Because of the compression effect on the coal matrix at the high pressure of the MIP, the CO2 adsorption and N2 adsorption/ desorption tests are combined to describe the characteristics of the adsorption-pores. Fig. 2a and c shows the isotherm results of the N2 adsorption/desorption analysis. As shown in Fig. 2a, the N2 adsorption/desorption isotherm of sample TA has a distinct hysteresis loop and the desorption curve declines dramatically at a relative pressure of 0.45, indicating a large number of ink-bottleshaped pores within the coal matrix, according to the theory of De Boer (1958). It is obvious that sample WT has a smaller hysteresis loops and the isotherms of the adsorption and desorption are reversible when P/P0 < 0.45, which indicates the existence of many wedge-shaped, cylindrical, and slit-shaped pores that have one side closed (Fig. 2c). This observation is consistent with the phenomenon from the MIP. The pore size classification of the International Union of Pure and Applied Chemistry (IUPAC, 1982) is used in this work: micropores (<2 nm), mesopores (2e50 nm) and macropores (>50 nm). The pore size distribution of the coal samples using the N2 adsorption/desorption and CO2 adsorption analyses is shown in Figs. 2 and 3 and indicates that the studied coal samples display a multimodal pore size distribution. The pore system of sample TA has a high volume of micropores (71.2%), moderately developed mesopores (19.1%) and slightly developed macropores (9.7%) (Table 2). This coal may be favorable for gas adsorption but unfavorable for gas flow due to the higher volume of micropores and poor connectivity. Moreover, the pore system of sample WT
Fig. 1. The mercury intrusion/extrusion curves and pore size distribution of coal samples by MIP.
Z. Li et al. / Journal of Natural Gas Science and Engineering 33 (2016) 97e107
Fig. 2. The adsorption/desorption isotherms and pore size distribution of coal samples by N2 adsorption/desorption analysis.
Fig. 3. The adsorption isotherms and pore size distribution of coal samples by CO2 adsorption analysis.
includes large developed micropores (65.4%), mesopores (24.2%) and macropores (10.4%). Due to the open pores and good connectivity, this pore structure is favorable for both gas adsorption and
flow.
101
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Fig. 4. The methane adsorption isotherms of dry samples and moisturized samples.
and diffusion properties of the coal matrix. In this study, the coal samples already developed many peaks in the pore size distribution results of the CO2 adsorption, N2 adsorption/desorption, and MIP. The micropores and mesopores are well developed in the lignite sample and long-flame coal sample (Figs. 1e3). Based on the trimodal pore structure of the coal samples, eq. (7) can be written as:
4.2. Methane adsorption isotherms Fig. 4 shows the CH4 adsorption isotherms of the dry and moisturized coals based on the isothermal adsorption experiments. Using the Langmuir adsorption law, the Langmuir parameters of the dry and moisturized coals are calculated (Table 3). The relative errors of the deviation of the Langmuir-predicted values were less than 2.0%, which are acceptable (Dutta et al., 2008). The CH4 adsorption volume increases from 8.08 cm/g3 to 14.50 cm/g3 when the moisture of the coal sample TA falls from 5.03% to 0.0% (Table 3). Similarly, the CH4 adsorption volume also increases from 7.32 cm/ g3 to 12.59 cm/g3 when the moisture of the coal sample WT falls from 4.63% to 0.0%. This observation indicates that the amount of moisture has a negative impact on the CH4 adsorption capacity of lignite and long-flame coals. The moisture may preferentially occupy the polar functional groups and adsorption space in lowrank coals, suggesting that the moisture significantly reduces the CH4 adsorption capacity (Busch and Gensterblum, 2011; Day et al., 2008; Gensterblum et al., 2013). Moreover, the gas adsorption capacity of coal is typically influenced by other factors, such as pressure, temperature, coal rank, and composition (Hildenbrand et al., 2006; Krooss et al., 2002). It is obvious that sample TA has a slightly higher CH4 adsorption capacity than that of sample WT (Fig. 4). Due to the similarity in volatile matter and fixed carbon content of the two samples, the slight difference of the CH4 adsorption capacity may be affected by coalification and the maceral composition, including vitrinite and liptinite content.
Mt Ma þ Me þ Mi Ma Me M ¼ ¼ va þ ve þ vi i M∞ Ma∞ þ Me∞ þ Mi∞ Ma∞ Me∞ Mi∞
(8)
where va þ ve þ vi ¼ 1, Me is considered to be the total amount of CH4 adsorbed in the mesopores at time t and P∞ 1 Me 6 2 2 n¼1 n2 expðDee n p tÞ. Me∞ ¼ 1 p2 According to eq. (8), the multiporous model can be translated into a code in MATLAB. First, the diffusion data is imported into the program. Then, the initial value is repeatedly set up to match data. In this process, the reasonable initial value is determined by the goodness of fitting. Finally, the diffusion coefficients can be obtained by using MATLAB to fit diffusion data. Figs. 5 and 6 show the bidisperse model and a modified multiporous model are applied to represent the experimental data. It is apparent from the figures that the multiporous model provides an excellent fit to the diffusion data of the two coal samples, whereas the bidisperse model deviates significantly from the data at the initial diffusion stage. This difference suggests that the bidisperse model may be inadequate to accurately characterize the diffusion behavior for some low-rank coals, which have a more complex pore structure and a greater percentage of microporosity and mesoporosity. Through studying the gas diffusion of dull coals, Clarkson and Bustin (1999) have reported that transition diffusion occurs from macroporedominated transport at an early time, to micropore-dominated transport at a later time. However, the bidisperse model ignored the transition diffusion stage, which occurs between the faster diffusion stage and the slower diffusion stage. In contrast, the transition diffusion stage is taken into account in the multiporous model, which agrees well with the diffusion data of the two coal
4.3. Estimation of methane diffusion coefficient When applied to some coals that have a distribution consisting mostly of macropores and micropores, the unipore model failed to accurately describe gas diffusion. Both Smith and Williams (1984); Clarkson and Bustin (1999) derived the bidisperse model, which has one diffusion coefficient for each pore size and can be used to describe gas diffusion in the coal matrix. This model indicates that the pore structure is an important factor that affects the adsorption
Table 3 Moisture content and CH4 isothermal adsorption results of coal samples. Samples No.
TA-Lignite WT-Long-flame coal
Salt solution
e K2SO4 e K2SO4
Relative humidity
0% 97% 0% 97%
Moisture content
0.0% 5.03% 0.0% 4.63%
CH4 isothermal adsorption results Langmuir volume (VL, cm3/g)
Langmuir pressure (PL, MPa)
Correlation coefficient
14.50 8.08 12.59 7.32
2.14 2.53 2.45 2.20
0.983 0.976 0.991 0.987
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Fig. 5. Fit curves of bidisperse model and multiporous model to sample TA data.
samples. The CH4 diffusion coefficients of both the bidisperse model and multiporous model are shown in Table 4. Based on the multiporous model, the order of magnitude of the macropore diffusivity is roughly between 104 and 103 s1, the mesopore diffusivity varies from 105 to 104 s1, and the micropore diffusivity varies from 106 to 105 s1. The macropore diffusivity is generally one to three orders of magnitude greater than the mesopore diffusivity and micropore diffusivity. In addition, the macropore diffusivities of the bidisperse model are between the macro- and mesopore diffusivities of the multiporous model, while the micropore diffusivities of the bidisperse model are close to those of the multiporous model, which are comparable to the results from Pan et al. (2010). Table 4 also summarizes the methane diffusivity fraction values (aa, ae and ai) of the multiporous model. For lignite sample TA, the macro-
diffusivity fraction ranges from 0.141 to 0.243, the mesodiffusivity fraction ranges from 0.131 to 0.248, and the microdiffusivity fraction ranges from 0.518 to 0.728. For long-flame coal sample WT, the macro-diffusivity fraction ranges from 0.102 to 0.253, the meso-diffusivity fraction ranges from 0.103 to 0.196, and the micro-diffusivity fraction ranges from 0.607 to 0.754. There is a significantly positive correlation between the methane diffusivity fractions and porosity fractions. This correlation suggests that the fraction of micro-, meso-, and macro-porosity is a very important factor that directly affects the determination of the diffusion coefficients. However, this conclusion is based on the two low-rank coal samples used in this paper, and more work is required to validate the model for application to other coals.
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Fig. 6. Fit curves of bidisperse model and multiporous model to sample WT data.
4.4. Effect of gas pressure and moistures on methane diffusion Fig. 7 shows the relationship between the methane diffusivities obtained from the multiporous model and equilibrium adsorption pressure of the low-rank coal samples. The CH4 macropore and micropore diffusivities tend to decrease with an increase in pressure, whereas a strong positive correlation exists between the CH4 mesopore diffusivities and gas pressure. The effects of the gas pressure on the methane diffusivities in the coal matrix may be related to the different mechanisms of gaseous methane diffusion and coal matrix swelling caused by gas adsorption. However, inconsistent conclusions are reported by Clarkson and Bustin (1999); Cui et al. (2004); Xu et al. (2015). Based on the gas molecular mean free path (l) and pore diameter (dp), the diffusion mechanisms can be divided into three types: Fickian diffusion (dp > 10l), transitional diffusion (0.1l < dp < 10l), and Knudsen
diffusion (dp < 0.1l) (Reeves and Pekot, 2001; Yan et al., 2008; Xu et al., 2015). Moreover, the mean free paths of the methane molecules can be described by the Maxwell distribution, which is expressed by:
KT
l ¼ pffiffiffi 2 2pd0 P where K is the Boltzmann constant (1.38 1023 J/K), T is the experimental temperature (K), d0 is the gas molecule diameter (m), and P is the pressure (Pa). Taking the equilibrium pressure 0.88 MPa as an example (the other cases are similar) and using the experimental conditions (T ¼ 303.15 K, d0,methane ¼ 0.33 nm), the primary diffusion mode is Fickian diffusion when the pore diameter is greater than 74.1 nm, whereas the primary diffusion mode is Kundsen diffusion for pore
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Table 4 Diffusivity of coal samples by different models. Sample
Moisture content (%) Equilibrium pressure (MPa) Bidisperse model
b TA-Lignite
0.0
5.03
WT-Long- flame coal 0.0
4.63
0.88 1.85 3.03 3.99 5.42 0.88 2.06 3.06 3.86 5.30 0.98 1.87 3.04 4.11 5.54 0.89 1.84 2.83 3.83 5.37
0.373 0.359 0.387 0.259 0.263 0.459 0.213 0.312 0.336 0.339 0.347 0.253 0.227 0.237 0.261 0.338 0.177 0.358 0.377 0.204
diameters smaller than 0.74 nm. Considering the pore size distribution in Figs. 1e3, it is suggested that the methane diffusion in macropores is mainly controlled by Fickian diffusion and Knudsen diffusion only occurs within micropores, whereas methane diffusion in mesopores is controlled by a combination of Fickian diffusion and transitional diffusion. Additionally, the swelling of the coal matrix with increasing methane adsorption pressure may narrow some pores, which increases the resistance to diffuse gas molecules. Therefore, the effect of pressure on methane diffusivity during the adsorption process is the competition between these two factors. In this work, the macropore and micropore diffusivities decrease with increasing pressure, indicating that the adsorption swelling effect of the coal matrix becomes dominant. As the pressure increases, the Fickian diffusion occurs in the smaller pore size within the mesopores, which results in the continual increase of the mesopore diffusivity. This observation suggests that the effect of pressure on the methane diffusion in pores with different pore sizes is different during the adsorption process. The presence of moisture is another factor on methane diffusion in coals, which may significantly reduce the methane diffusivities of low-rank coal samples at the same equilibrium pressure. This conclusion is consistent with other diffusion results obtained by Clarkson and Bustin (1999); Pan et al. (2010); Xu et al. (2015), who studied gas diffusion at different moisture levels. Similarly, the methane adsorption volume of the moist samples is far less than that of dry samples (Fig. 4). The main reason for this result is that moisture more easily adsorbs to the pore surface and occupies the pore space in the coal matrix, which is unfavorable for gas adsorption and diffusion. Moreover, the results show that the mesopore diffusivities are most affected by moisture, with a reduction of up to 50% (Table 4). This reduction in mesopore diffusivity may form clusters and even condensates in the mesopores of the low-rank coal matrix. Additionally, the moisture can swell clay minerals in coals, such as illite and montmorillonite, which possibly reduces the original pore volume and narrows the pore throats (Zhang et al., 2012; Yuan et al., 2014). In this study, the mineral proportions of the two low-rank coal samples were approximately 10% (Table 1), which could also significantly reduce the methane diffusivity in coals under moist conditions.
Dae (s1) 3.72 3.80 4.24 5.20 5.55 6.82 3.48 2.53 2.81 2.96 4.11 4.53 4.80 5.07 5.86 3.55 3.88 4.10 4.78 4.93
Multiporous model Die (s1)
4
10 104 104 104 104 105 104 104 104 104 104 104 104 104 104 104 104 104 104 104
1.31 1.29 1.27 1.24 1.25 9.79 1.23 9.61 9.58 9.03 1.16 1.02 9.06 1.04 1.06 1.00 9.74 9.48 8.90 9.97
va 5
10 105 105 105 105 106 105 106 106 106 105 105 106 105 105 105 106 106 106 106
0.193 0.203 0.243 0.166 0.141 0.161 0.164 0.161 0.166 0.192 0.201 0.135 0.138 0.170 0.196 0.182 0.102 0.214 0.253 0.165
Dae (s1) 1.85 1.62 1.50 1.33 1.30 1.30 9.14 7.75 5.34 5.17 2.00 1.73 1.66 1.58 1.56 1.62 1.44 1.35 1.21 1.16
ve 3
10 103 103 103 103 103 104 104 104 104 103 103 103 103 103 103 103 103 103 103
0.236 0.211 0.239 0.214 0.131 0.248 0.226 0.224 0.214 0.179 0.192 0.132 0.108 0.128 0.103 0.196 0.162 0.173 0.133 0.158
Dee (s1) 4.29 6.62 8.86 9.17 9.87 2.03 3.86 4.23 4.84 4.97 7.46 9.80 1.12 1.22 1.28 5.30 6.58 7.92 8.10 8.28
5
10 105 105 105 105 105 105 105 105 105 105 105 104 104 104 105 105 105 105 105
vi
Die (s1)
0.571 0.586 0.518 0.620 0.728 0.591 0.610 0.615 0.620 0.629 0.607 0.733 0.754 0.702 0.701 0.622 0.706 0.613 0.614 0.677
1.09 1.04 1.00 9.63 8.85 9.83 9.50 9.12 8.79 8.57 1.21 1.20 1.16 1.14 1.11 9.22 9.10 9.07 8.96 8.58
105 105 105 106 106 106 106 106 106 106 105 105 105 105 105 106 106 106 106 106
5. Conclusions In this study, two low-rank coals from China were used to study the diffusion behaviors that occur during the methane adsorption process. The low-rank coal samples exhibited a multimodal pore size/volume distribution and contained a large amount of micropores and mesopores, which is favorable for CBM adsorption and diffusion. The bidisperse diffusion model and multiporous diffusion model were applied to represent the experimental data for dry and moist coal samples. The results show that the multiporous model provides an excellent fit to the diffusion data of the two coal samples, whereas the bidisperse model deviates significantly from the data of the initial diffusion stage. This difference suggests that the gas diffusion stages are not only simply divided into a fast macropore diffusion stage and a much slower micropore diffusion stage but also consist of multiple diffusion processes, at least for the coals used in this study. Based on the multiporous model, the macropore diffusivity (104~103 s1) is generally one to three orders of magnitude greater than the mesopore diffusivity (105~104 s1) and micropore diffusivity (106 ~105 s1). The effects of the adsorption pressure and moisture on methane diffusion in low-rank coal samples are discussed in this work. With increasing adsorption pressure, both macropore diffusivity and micropore diffusivity have a decreasing trend, whereas a strong positive correlation exists between mesopore diffusivity and pressure. This difference may be related to the different mechanisms of gaseous methane diffusion and the swelling of the coal matrix caused by gas adsorption. This difference also indicates that the effect of pressure on methane diffusion in pores with different pore sizes is different during the adsorption process. Furthermore, the presence of moisture significantly reduces the methane diffusivities of low-rank coal samples in this work, which is consistent with the existing literature. The main reason for this observation is that the moisture more easily adsorbs to the pore surface and occupies the pore space in the coal matrix in addition to the effect of the mineral swelling of the adsorbing moisture. These findings may have important implications for gas diffusion modeling, and further study is required to test the applicability of the multiporous diffusion model.
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Fig. 7. CH4 diffusivities of dry and moist coal samples by using multiporous model (-D represents the dry sample, -M represents the moist sample).
Acknowledgments This research was funded by the National Natural Science Foundation of China (grant no. U1262104), Program for New Century Excellent Talents in University (grant no. NCET-11-0721), Research Program for Excellent Doctoral Dissertation Supervisor of Beijing (grant no. YB20101141501), Fundamental Research Funds for Central Universities (grant no. 35832015136) and Key Project of Coal-based Science and Technology in Shanxi Province-CBM accumulation model and reservoir evaluation in Shanxi province (grant no. MQ2014-01). The authors also thank Dr. Zhejun Pan for his constructive suggestions in revising the manuscript. References Busch, A., Gensterblum, Y., 2011. CBM and CO2-ECBM related sorption processes in coal: a review. Int. J. Coal Geol. 87, 49e71. Busch, A., Gensterblum, Y., Krooss, B.M., Littke, R., 2004. Methane and carbon dioxide adsorption-diffusion experiments on coal: upscaling and modeling. Int. J. Coal Geol. 60, 151e168. Cai, Y.D., Liu, D.M., Yao, Y.B., Li, J.Q., Qiu, Y.K., 2011. Geological controls on prediction
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