Water distribution characteristic and effect on methane adsorption capacity in shale clay

International Journal of Coal Geology 159 (2016) 135–154

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Water distribution characteristic and effect on methane adsorption capacity in shale clay Jing Li a, Xiangfang Li a, Xiangzeng Wang b, Yingying Li c, Keliu Wu a,d,⁎, Juntai Shi a, Liu Yang a, Dong Feng a, Tao Zhang a, Pengliang Yu a a

MOE Key Laboratory of Petroleum Engineering, China University of Petroleum (Beijing), Beijing 102249, PR China Shaanxi Yanchang Petroleum (Group) Corp. Ltd., Xi'an 710075, PR China CNOOC Research Institute Beijing, Beijing 100027, PR China d Chemical and Petroleum Engineering, University of Calgary, Calgary, Alberta T2N1N4, Canada b c

a r t i c l e

i n f o

Article history: Received 23 September 2015 Received in revised form 16 March 2016 Accepted 17 March 2016 Available online 2 April 2016 Keywords: Shale Clay Water saturation distribution Gas–liquid–solid interaction

a b s t r a c t Methane adsorption in shale is a gas–liquid–solid interaction rather than a gas–solid interaction by considering the initial water saturation in actual condition. As an important constituent of inorganic matter, clay minerals may affect gas-in-place of shale systems. Generally, Clay minerals are strongly hydrophilic with a water film bound on its surface, significantly reducing gas sorption capacity, which will lead to overestimate gas-in-place (GIP) of shale gas reservoir. In this work, we analyze the interactions between methane, water film and clay, and results reveal that: methane adsorption on clay (dry) is a typical gas–solid interaction; however, methane adsorption on clay bound water film should belong to gas–liquid interaction. Furthermore, a unified model is established to describe gas-water-clay interactions, in which, gas–solid Langmuir equation and gas–liquid Gibbs equation are integrated by water coverage coefficient. Meanwhile, a mathematical model is presented to quantify thickness of water films by considering surface force interactions between liquid film and clay. Our results show that, the water film thickness in shale clay pores mainly depends on relative humidity and pore size. Under a certain humidity condition (such as 0.98), the water saturation distribute in different sized pores mainly as: (i) capillary water in the small pores (b6 nm); (ii) water film in the larger pores. Thus, considering the water distribution characteristics, the effect of moisture on methane adsorption capacity is mainly for two aspects: (i) small pores (b 6 nm) blocked by water are invalid for methane adsorption, (ii) large pores bounded by water film change interaction characteristics for methane adsorption (from gas–solid interaction to the gas– liquid interaction). The overall effect could reduce the adsorption capacity by 80%–90%. © 2016 Elsevier B.V. All rights reserved.

1. Introduction Shale gas is a typical unconventional gas resource which is derived from the organic matter within the mudrock and kerogen through biogenic and/or thermogenic processes (Jarvie et al., 2007) The recoverable reserves of shale gas in the United States are estimated to be 24.4 × 1012 m3 (Wu et al., 2015c), and the gas production from a particular shale play will depend on its storage potential and transport properties (Wu et al., 2015a,b,c,d). However, unlike conventional reservoirs in which gas is stored primarily as compressed (“free”) gas in pores and fractures, a significant proportion of gas in shales can be stored as “sorbed” gas. Nano-scale pores present in shales result in large internal surface area available for molecular interactions between gas and solids, and the adsorbed gas content could be over than 50% estimated by Lu ⁎ Corresponding author at: MOE Key Laboratory of Petroleum Engineering, China University of Petroleum (Beijing), Beijing 102249, PR China. E-mail address: [email protected] (K. Wu).

http://dx.doi.org/10.1016/j.coal.2016.03.012 0166-5162/© 2016 Elsevier B.V. All rights reserved.

et al. (1995). Therefore, the estimation of initial adsorbed gas in place is one of the primary concerns to conduct shale gas reservoir study, and it is also important for reservoir-engineering analysis, such as gasproduction forecast (Li et al., 2014; Wu et al., 2014, 2015a,b,c,d). At present, the evaluation of adsorbed gas content is mainly based on the experiments studies in laboratory, and most of the experiments are carried out based on dry samples (Chareonsuppanimit et al., 2012; Gasparik et al., 2012; Yaguzhinsky et al., 2013; Zhang et al., 2012b) or moisture equilibrated samples according to ASTM (ASTM D1412–07, 2010) standard. However, a significant deviation in adsorption capacity evaluation is revealed between these two treatments. According to Ross and Bustin (2009) and Gasparik et al. (2014), methane adsorption capacity is seriously affected by moisture for both clay-rich and organic-rich shales, meanwhile the adsorption amount in moist condirions would reduce about 40%–90% compared with dry conditions. Unfortunately, water saturation or moisture always exist in shale under actual condition (Fang et al., 2014; Liu and Wang, 2013; Haghighi and Ahmad, 2013), which will lead to further difficulties

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to resources evaluation and prediction. In order to evaluate the shale adsorption capacity more reasonably, it is necessary to investigate the characteristic of gas and water distribution in initial condition. Gas shales are complex rocks, characterized by heterogeneity in composition and structure at all scales (Curtis et al., 2010). Furthermore, the wettability of various minerals (organic matter and inorganic matter) is significantly different, which results in mysterious water distribution characteristics in both organic and inorganic pores. According to present literatures, it is generally believed that the organic pore (or kerogen pore) formed during hydrocarbon generation process is hydrophobic (Odusina et al., 2011) and almost without water. While Hu et al. (2014) clarified that the water clusters could adsorb on hydrophilic sites such as functional group in organic pore by molecule simulation. Compared with organic matter, water adsorption in inorganic matter is much clearer. The inorganic pore especially for the clay mineral is always hydrophilic, thus the water molecules could bind on the clay particle or pore surface by hydrogen bond, electrostatic force and Van der Waals force. The CBW (clay bound Water) could reach 2.63–7.19% of the total simple volume by TRA (Tight Rock Analysis) technology (Boyer et al., 2006), and the irreducible water in the clay pore should not be ignored (Spears et al., 2011). Korb et al. (2014) analyzed sealed coring oil shale samples by NMRD technology and found that water mainly remains in the inorganic pore. It's generally believed that, besides organic matter, inorganic matter such as clay minerals may provide additional adsorption capacity of shale media due to high internal surface area (Aringhieri, 2004; Aylmore and Quirk, 1967b; Sondergeld et al., 2010; Ji et al., 2012; Curtis et al., 2011). Thus, under dry conditions, both inorganic and organic materials dominate methane adsorption amount. However, under moist conditions, the absorption capacity of pure clay mineral (illite, kaolinite and montmorillonite) will reduce by 80–95% (Ross and Bustin, 2009). Chalmers and Bustin (2010) indicated that water covering inorganic hydrophilic mineral surface would result in a loss of methane adsorption site in shale. Therefore, the moisture in inorganic minerals (especially for clay minerals) is one of the primary reasons that influence the adsorbed shale gas amount and make the gas resources overestimated. Simultaneously, the effect of water on adsorption capacity in shale clay is badly needed to be quantified. In this work, we assume that the water in organic pores can be neglected compared with water in inorganic pores. Thus, we mainly analyze the water distribution characteristic in different sized clay pores, and establish a new model for methane absorbed on shale clay with gas–liquid–solid three-phase interactions. It mainly includes: (i) proposing a mathematical model to quantify water films thickness based on surface force between film and clay; (ii) establishing a unified model for computing methane absorption capacity with different moisture content by integrating gas–solid interface adsorption and gas–liquid interface adsorption; (iii) performing experimental studies on low pressure nitrogen adsorption and methane adsorption on shale and clay samples with moisture equilibrated in different relative humidity conditions; (iv) analyzing water distribution characteristic and forecasting adsorption capacity of our studied samples by our model. This work provides an insight into the fundamental understanding on the effect of water (or moisture) on methane adsorption capacity and gives a path to evaluate the amount of gas present (gas-in-place, GIP) in shale systems more accurately. 2. Thickness of surface-bound water films 2.1. Sub-irreducible water saturation The removal of water saturation in gas reservoir takes place by two mechanisms (Mahadevan et al., 2005). First is the immiscible displacement of the water from the pores by the flowing gas, second is the evaporation of subsequent irreducible water by thermodynamic equilibrium of vapor and water film. For the conventional gas reservoir,

it is always in the condition of capillary pressure equilibrium and the initial water saturation is the results of displacement in the process of oil and gas migration (Hoffman, 2013). However, for unconventional gas reservoirs with very low permeability, such as shale gas and tight gas formations, they are in a state of capillary under-saturation where the initial water saturation is less than would be expected from conventional capillary mechanics for the pore system (Bennion et al., 2000; Bennion and Thomas, 2005). This condition is referred to as “sub-irreducible water saturation” or “ultra-low water saturation”. The degree of water saturation in shales and tight sands varies with lithology, pore scales, and porosities. Nevertheless, the most important control on water saturation is the extent of past hydrocarbon generation, which leads to water expulsion (Yves et al., 2015). Research for the formation mechanisms of “sub-irreducible water saturation” in unconventional reservoirs indicated that (Yao et al., 2014; Zhang et al., 2005), evaporation of water films bound on pore surface during hydrocarbon generation process is one of the primary reasons. Caused by increasing accumulation of hydrocarbon, such as methane, the relative humidity of gaseous phase in reservoir system will reduce, which will lead to evaporation of water from liquid film or capillary water into gaseous phase. Actually, experimental research (Mahadevan et al., 2005, 2006, 2007a,b; Kamath and Laroche, 2003) has shown that removal of irreducible water saturation takes place by evaporation when core sample is injected with dry gas continuously. For instance, the irreducible water saturation in sandstone samples (Swi = 23.90–25.43%) will further reduce to 12.4–14.7% by evaporation (Zuluaga et al., 2001). Meanwhile, “Moisture Equilibrium Method” is a prevalent way to restore initial water content in reservoirs with “sub-irreducible water saturation” and “Vapor Desorption Method” is always used to characterize high capillary pressure curves in reservoirs that are not in capillary pressure equilibrium (Newsham et al., 2003, 2004; Dernaika, 2010). Thus, the thermodynamic equilibrium between liquid water and vapor will play a key role in those extremely low-permeability formations. 2.2. Surface forces and disjoining pressure Comparing with the inorganic pores, water saturation or moisture in organic pores can be neglected (Sondergeld et al., 2010). Thus, in this work, we focus on the water film in inorganic pores (especially for clay material) and analyze the interaction between liquid phase (water film), gaseous phase (vapor and methane) and solid phase (pore surface). Here, we assume that: (1) the gaseous phase is constituted by methane and vapor, and other component can be ignored; (2) inorganic pore surface is strongly water-wet and it is firstly occupied by water molecules (water film) rather than methane molecules; (3) water film is incompressible and homogeneous; (4) methane molecules dissolved in water film can be ignored; (5) reservoir temperature maintains constant; (6) reservoir pressure and humidity system are unified. In the condition of “sub-irreducible water saturation”, the surface force that holds the liquid as a film completely covering the pore surface should be taken into consideration (Newsham et al., 2003, 2004). In our study, the disjoining pressure Π(h) proposed by Derjaguin et al. (1987) is employed to describe the surface interactions between liquid film, solid and gas phase during the vaporization processes of liquid water. The details of thermodynamic equilibrium between water film and vapor is shown in Appendix A and the relationship between surface attractive force and relative humidity can be described as: Π ðhÞ  V m ¼ −RT ln

Pv P0

ð1Þ

Where, Π(h) is disjoining pressure between solid surface and liquid film, which is related to the water film thickness, MPa; Vm is molar volume of water, cm3/mol; P0 is the saturated vapor pressure of liquid film, MPa; Pv is the partial pressure of water vapor, MPa; Pv/P0 is the relative

J. Li et al. / International Journal of Coal Geology 159 (2016) 135–154

humidity of gaseous phase, %; R is the gas constant, J/mol·K; T is the temperature, K. The total disjoining pressure is the sum of the London–Van der Waals force, Πm, the electrical force, Πe, and the structural force, Πs (Derjaguin et al., 1987). Π ðhÞ ¼ Π m ðhÞ þ Π e ðhÞ þ Π s ðhÞ

ð2Þ

repulsion of two surfaces (Derjaguin et al., 1987). Thus, the structural forces arise as a result of overlapping of structurally altered water boundary layers. Generally, structural forces are short-range interactions at a distance of less than 5 nm (Hunter and Chan, 1987; Takahashi and Kovscek, 2010). The calculation of structural component of the disjoining pressure can be approximately represented in a semiempirical equation with exponential form (Starov et al., 2007): Π s ðhÞ ¼ ke−λ h

2.2.1. London–Van der Waals Force London–Van der Waals force, also referred to as molecular or dispersion force, is the most investigated component of the disjoining pressure (Derjaguin et al., 1987). Various expressions with Πm often proportional to h− 3 were derived by Kralchevsky et al. (1996) and Iwamatsu and Horii (1996). The modern theory of Πm was developed based on a fluctuating electromagnetic field, and the molecular component for a film of uniform thickness h between two semiinfinite phases can be approximately given as (Starov et al., 2007): Π m ðhÞ ¼

AH 3

h

ð3Þ

Where, AH is the Hamaker constant in a gas/water/solid system and the characteristic value is 10−21–10− 20 J. Meanwhile, the Hamaker constant can be either positive or negative (Starov et al., 2007). Tuller et al. (1999) and Mattia et al. (2012) has used Hamaker constant with value of 1 × 10− 20 J to describe water adsorption on inorganic adsorbent, such as fine sandstone, silt and clay. Melrose (1982) and Takahashi and Kovscek (2010) have used the Hamaker constant ranging from 0.3 to 1 × 10−20 J in reservoir system, such as siliceous shale. In this study, value approximate to 10−20 J was used as the Hamaker constant for calculating the molecular component of the disjoining pressure in gas/water/clay system. 2.2.2. Electrical force Electrical force is always referred to the interaction between two surfaces with similarly or oppositely charged in an aqueous electrolyte solution (Derjaguin et al., 1987). The electrostatic component of the disjoining pressure is calculated from the solution of the Poisson– Boltzmann equation for the DDL with appropriate boundary conditions (Khilar and Fogler, 2010). In the case of oppositely charged surfaces and at relatively small distances, the approximate expression for the electrostatic component is (Starov et al., 2007): Π e ðhÞ ¼

εε0 ðζ 1 −ζ 2 Þ2 2 8π h

ð4Þ

Where, ε0 is electric constant in vacuum, F/m; ε is the relative dielectric permittivity of liquid, dimensionless; ζ1 and ζ2 are the electric potentials of the solid–liquid and liquid–air interfaces, respectively, mV. Generally, the electrostatic component of disjoining pressure will dominate the stability of wetting film on substance surface when the strong electrolyte solution is introduced, such as acidic or alkaline solutions with pH ranging from 3 to 12 in Takahashi and Kovscek, (2010)'s study. However, in our study, adsorbed film is assumed as pure water and the potentials difference between water-solid interface and water-air interface is used as △ζ = ζ1–ζ2 = 40–80 mV in the condition of contact angle less than 20°(Churaev, 1995a,b; Mattia et al., 2012). 2.2.3. Structural force Polarization of interfaces results in a change in orientational structure of polar liquids, such as water molecules, near to the solid–liquid interface (Derjaguin et al., 1987). These boundary layers with molecules structure changed is also referred as to ‘hydration layer’ for water. When two interfaces with hydration layers close to each of them (or even one of them), hydration layers will overlap and lead to an attraction or

137

ð5Þ

Where, where k is the coefficient for the strength of structural force, N/m2; λ is the characteristic length of water molecules, nm. The value of coefficient k depends on the wettability in gas/liquid/solid system. Based on research of Churaev (1995a,b), hydrophilic attraction (k N 0) takes place when contact angel of water on hydrophilic surface is less than 20°, and hydrophobic repulsion (k b 0) takes place when contact angel is higher than 40°. Meanwhile, in the region with contact angel 20° b θ b 40°, structural force can be neglected and stability of wetting film is dominated by molecular force and electrical force. In our study, the surface of inorganic matter, such as sandstone and clay, is strongly hydrophilic. Thus, a case of contact angel θ = 15°–20° with k = 0– 1 × 10− 7 N/m2 and λ = 1–2 nm (Churaev, 1995a,b) is used for calculation. 2.3. Water films in slit nanopores The components of shale clay minerals almost are kaolinite, montmorillonite and illite. For quantifying the water film thickness in actual shale clay pore, we need to take the effect of pore wall potential into account, which is related to pore structure. The research of Aylmore and Quirk (1967b) showed that the nanopores within clay particles are generally analogous slit shape consisted by crystal layers and slit pores with 1 nm found between crystal layers of Montmorillonite. The high magnification EMG scanning images of shale clay pore by Curtis et al. (2011) and Sondergeld et al. (2010) indicated the width of these slit pores range from 3–20 nm. Additionally, EMGs in our study (Fig. 1) also illustrate numerous slit like pores within inorganic substance of clay-rich samples. Thus, we simplify clay pore as slit in our research. In the case of slit pores, the mechanical equilibrium of water film is quite different from that of film on flat surface, and the effect of pore wall potential on the adsorption behavior of wetting film needs to be considered. Thus, isotherm of flat films, described by Eq. (1), must be corrected for an effect of mutual attraction of the films under the action of opposite slit surfaces. In Fig. 2 the model of a slit pore is represented, where H is the width of the slit pore and h is the film thickness on the pore walls. Except for the surface interaction Π1(h) between water film and surface on which water is adsorbed, we also need to take the Π2(h) and Π3(h) into account, which are interactions between water film and opposite surface, and interactions between two films adsorbed on the opposite walls, respectively. Considering the effects of Π2(h) and Π3(h), the effective disjoining pressure in slit pores is given as (Tuller et al., 1999; Churaev et al., 2000) Π slit ðhÞ ¼ Π 1 ðhÞ þ Π 2 ðhÞ þ Π 3 ðhÞ AH εε0 ðζ 1 −ζ 2 Þ2 h þ ke−λ Π 1 ðhÞ ¼ 3 þ 2 8π h h AH εε0 ðζ 1 −ζ 2 Þ2 Π 2 ðhÞ ¼ þ 3 8π ðH−hÞ2 ðH−hÞ AH  Π 3 ðhÞ ¼ 3 ðH−2hÞ

ð6Þ

Where Π1(h) is the disjoining pressure between water film and surface at the same side by considering both of the short-range (structural force Πs) and long-range interactions (molecular force

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Fig. 1. Slit pores within our clay-rich shale samples.

Πm and electrical force Πe), MPa; Π2(h) is the disjoining pressure between water film and surface at the opposite side by neglecting short-range interactions (structural force Πs) due to the relative long range between film and opposite clay layer, MPa; Π3(h) is the disjoining pressure between two water films by only considering molecular force Π m due to the potentials difference between the two similar films is zero, MPa; AH is the Hamaker constant for solid–gas–liquid interactions, J; A H* is the Hamaker constant for liquid–gas–liquid interactions, J. In the research of Tuller et al. (1999) and Churaev et al. (2000), AH* ranges from 1.3 × 10− 21 J to 1.9 × 10− 21 J, and we take AH* = 1.5 × 10− 21 J in this work. Thus, combined with Eqs. (1) and (6), the relationship between h, H and Pv/P0 in case of water film in slit pore is given by

Π 1 ðhÞ þ Π 2 ðhÞ þ Π 3 ðhÞ ¼ −

RT Pv  ln P0 Vm

ð7Þ

Furthermore, the water saturation Sw in single slit pore is given as follows Sw ¼

2h H

ð8Þ

Using AH = 1 × 10− 20 J; AH⁎ = 1.5 × 10−21 J; T = 298 K (25 °C); Vm = 18 × 10− 6 m3/mol; △ζ = 50 mV; ε0 = 8.85 × 10− 12F/m; ε = 81.5; k = 1 × 10−7 N/m2; λ = 1.5 nm. The water film thickness h and water saturation Sw changing with relative humidity P/P0 in different pores with width H = 2 nm, 5 nm, 10 nm and 50 nm are calculated by Eqs. (7) and (8) respectively. The results indicate that pore width has little influence on film thickness in slit pore (Fig. 3) while affect water saturation Sw significantly (Fig. 4). Meanwhile, the film thickness and water saturation grows fast near P/P0 = 1, which reveals a compelling evidence that surface forces, including long range intermolecular, electrostatic, and structural

Pw

h H

Pg

Water molecule in vapor phase Solid phase (clay)

Gaseous phase (methane and vapor)

Disjoining pressure Π1

Liquid phase (water film)

Disjoining pressure Π2

Fig. 2. Mechanical equilibrium between water film and vapor in slit pore.

Disjoining pressure Π3

J. Li et al. / International Journal of Coal Geology 159 (2016) 135–154

139

10

Adsorbed phase

H

Bulk phase

h (nm)

1

Methane molecular

0.1

H=50nm

H=10nm

H=5nm

H=2nm

Fig. 5. Schematics of gas–solid interface adsorption in slit pore.

Ji et al. (2012), we take the value of K ranging from 0.0041 to 0.0088 mmol/m2 in this study (Fig. 6).

0.01 0

0.5

1

Pv /P0 3.2. Gas–liquid interface interaction Fig. 3. Relationship between water film thickness and humidity in slits with different width.

interactions, play a significant role in stability of adsorbed film transition into condensed bulk liquid. As the slit width decreases, the scale of surface interactions increases, directly leading to a sharper growth of water saturation and a lower critical relative humidity for condensation. Especially for the pores with width less than 5 nm, condensation phenomenon is significant. Thus, this condensation phenomenon will lead to a significant difference of water saturation distributing inside different sized pores. The water saturation distribution characters will be further discussed in Section 5. 3. Interactions between methane, water film and clay 3.1. Gas–solid interface interaction Methane sorption on the surface of dry clay belongs to typical gas– solid interfacial interaction, which is controlled by the London dispersion force. Schematic of methane sorption on dry slit pore is shown in Fig. 5. Here, we take the layer spacing as H, and surface area of single layer as Aslit, thus the surface area of slit pore is 2Aslit. We also assume that Langmuir equation (Langmuir, 1917) is able to describe this interaction. Therefore, methane adsorption amount can be expressed by nad−dry ¼ 2Aslit  K 

P P þ PL

ð9Þ

Where, nad-dry is methane adsorption amount on dry clay surface, mmol/g; Aslit is specific surface area of single crystal layer area, m2/g; PL is Langmuir pressure, MPa; P is equilibrium pressure of gaseous phase, MPa; K is the maximum methane adsorption amount for unit area, mmol/m2. Ji et al. (2012) suggested that the maximum capacity of methane sorption on dry clay has a liner relationship on the specific surface area. According to experiments data from Ross and Bustin (2009) and

The experiment and theoretical study about methane sorption on moist clay is rare. Here, we take volatile organic compounds (VOC) sorption on the moist soil as reference. The theory of VOC sorption indicated that (Ho and Webb, 2006): under moist conditions, VOCs from the vapor phase distribute into soil matrices by (i) dissolution into the aqueous phase; (ii) adsorption at the gas–water vapor interface, which is gas–liquid interface interaction; (iii) absorption onto the mineral surface from aqueous phase, which is liquid–solid interface interaction; (iv) condensation of VOCs into pores. For case (i) and (ii), whether organic gas is dissolved or absorbed depends on the solubility itself. For example, the trichloroethylene vapor (TCE) with high aqueous solubility (1100 mg/L) would prefer to be in the aqueous phase rather than at the water–gas interface when partitioning on moist clay (Shimizu et al., 1994), while the paraxylene vapor with low solubility (198 mg/L) mainly adsorbs on water film (Hoff et al., 2002). Considering the extreme low solubility of methane in water (21.4 mg/L) (Fu et al., 1996), methane molecules should be mainly adsorbed on gas–liquid interface rather than dissolution. For case (iii), although a little part of methane molecules could be dissolved into water, however, due to the strong hydrophilicity of clay, the dissolved methane cannot be further adsorbed on clay surface from aqueous phase (solution with methane). Similarly, it also has been reported in molecular simulation results by Jin and Firoozabadi (2014), during competing of methane and water adsorption in clay pores, the first layer of pore surface is occupied by water molecules rather than methane. Thus, it's impossible for the dissolved methane molecules adsorbed on clay surface though liquid phase. For case (iv), due to the temperature in shale system is much higher than methane critical temperature (−80.4 °C/190.7 K), liquefaction or condensation of gaseous methane would not occur (super-critical condition). Based on the analysis above, methane molecules are likely to adsorb on water film binding on clay surface under moist conditions, which belongs to typical gas–liquid interaction rather than gas–solid interaction. 0.5

H=50nm

Maximum adsorption capacity (10-3mol/g)

1 H=10nm

Sw(i)

0.8 H=5nm

0.6

H=2nm

0.4 0.2

Smectite(Ross) Illite(Ross)

0.4

y = 0.0088x

0.3

Kaolinite(Ross) Chlorite(Ross)

y = 0.0054x (Ji)

Smectite(Ji)

0.2

y = 0.0041x

I-S mixed layer(Ji) Illite(Ji)

0.1

Kaolinite(Ji) Chlorite(Ji)

0 0

0 0

0.2

0.4

0.6

0.8

1

Pv /P0 Fig. 4. Relationship between water saturation and humidity in slits with different width.

20

40

60

80

Surface area (m2/g) Fig. 6. Relationship between methane maximum adsorption capacity and clay surface area.

140

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80

There are quantities of models to describe the behavior of VOC sorption on gas–liquid interface (Costanza and Brusseau, 1999). However, most of these models are semi-empirical and available in certain conditions. Meanwhile, the experiments condition for VOC adsorption is always below critical temperature of vapor phase, which is significantly different from the condition of methane adsorption in shale gas reservoir. Considering the limitation of the semi-empirical model for VOC sorption, we apply the widely used Gibbs adsorption model (Kondo and Ishikawa, 2006) to describe the interaction of methane and water film, the relationship between adsorption amount and surface tension is given by

ð10Þ

Where, Γ is methane adsorption amount on gas–liquid interface for unit area, mol/m2; γ is gas-water surface tension, mN/m; T is environment temperature, K; P is equilibrium pressure of gaseous phase, MPa; R is gas constant, 8.314 J/mol·K. Schematic of methane sorption on moist slit pore is shown in Fig. 7. Here, we assume that the water film thickness is homogeneous and we take the surface area of gas-water interface is 2Aslit. Thus, the adsorption amount on gas–liquid interface nad-wet can be described as
 ∂γ P   2Aslit ∂P T RT

ð11Þ

The relationship between gas-water surface tension γ and gaseous pressure P with different temperatures condition is described by experimental data from Jennings and Newman (1971). Furthermore, we fit these data by Eq. (12), as shown in Fig. 8. γ ¼ a  ln ðb þ P Þ þ c

ð12Þ

Where, a, b and c are fitting parameters, fitting results are shown in Table 1. Thus, combined with Eqs. (11) and (12), the relationship between the adsorption amount on gas–liquid interface and gaseous pressure can be expressed as: nad−wet ¼ 2Aslit 

(mN/m)

60 50 40

30 23.3 100 176.6

20 10

Fitting (23.3 ) Fitting (100 ) Fitting(176.6 )

0 0

10

20

30

40

P (MPa)


 ∂γ P  Γ¼− ∂P T RT

nad−wet ¼ Γ  2Aslit ¼ −

70

a P P  ¼ 2Aslit  Γ   RT P þ b P þ P

ð13Þ

Fig. 8. Relationship between surface tension and pressure with different temperatures.

3.3. Mixed interaction Ong and Lion (1991) indicated that, in the region from dry conditions to one monolayer coverage of water on the solid surface, direct solid-vapor sorption was evident with strong competition between water and trichloroethylene (TCE) molecules for adsorption sites on the sorbents; and in the region between a monolayer coverage to several layers of water molecules, likely interaction between TCE vapor and water includes sorption of TCE onto surface-bound water and limited TCE dissolution into adsorbed water. As reference, we take monolayer coverage of water molecules as limit. Thus, when the coverage of water on the solid surface is more than monolayer, the long-range forces between clay and methane is much lower than the short-range forces between water and methane, which will lead to a transition from gas–solid interface interaction into gas–liquid interface adsorption. However, when the coverage is less than monolayer, strong competition between water and methane molecules for adsorption sites on clay surface should be considered, which will result in a mixed adsorption of gas–solid interaction and gas–liquid interaction, as shown in Fig. 9. Defining the coverage coefficient of water molecules as: α ¼ AH2 O =Atotal

The methane adsorption amount under mixed adsorption condition can be described as nad−mix ¼ ð1−α Þ  nad−dry þ α  nad−wet

Where, Γ* is maximum adsorption amount of gas–liquid interface for unit area, mmol/m2; P* is the pressure constant, MPa. Based on the fitting results from Table 1, calculation results of Γ* is 0.00864 mmol/m2, and it's independent with temperature. However, P* is variable with temperature changing. When the temperature is 23.3 °C, 100 °C and 176.6 °C, the value of P* is 22.28 MPa, 50.13 MPa and 120.22 MPa, respectively. The Eq. (13) is similar to Langmuir equation formally. It should be noted that, if we use other equation to describe the relationship between surface tension γ and gaseous pressure P instead of Eq. (12), such as the polynomials, the form of Eq. (13) will change.

Water film Adsorbed phase

ð14Þ

ð15Þ

Here, we assume that the thickness of monolayer water film is 0.4 nm. Thus, water saturation Smon in slit pore under the monolayer water molecules coverage condition can be expressed by

Smon ¼

2h H

ð16Þ

Therefore, integrating gas–solid interactions and gas–liquid interactions by Eqs. (9), (13) and (15), the unified model to determine methane adsorption amount under different water saturation condition can be given by

H Bulk phase

h Fig. 7. Schematics of gas–liquid interface adsorption in slit pore.

8 P > > ¼ 2Aslit  K  ; Sw ¼ 0 n > < ad−dry P þ PL nad−mix ¼ ð1−α Þ  nad−dry þ α  nad−wet ; 0bSw ≤Smon > > P >  :n ; Smon ≤Sw ≤1 ad−wet ¼ 2Aslit  Γ  P þ P

ð17Þ

J. Li et al. / International Journal of Coal Geology 159 (2016) 135–154

141

Table 1 Fitting parameters of surface tension. Temperature

Parameter a

Parameter b

Parameter c

Fitting equation

23.3 °C 100 °C 176.6 °C

−21.41 −26.79 −32.29

22.28 50.13 120.22

139.0 161.0 194.0

γ = −21.41 × ln(22.28 + P) + 139 γ = −26.79 × ln(50.13 + P) + 161 γ = −30.91 × ln(120.22 + P) + 194

3.4. Model validation 3.4.1. Molecular simulation In this study, molecular simulation data by Jin and Firoozabadi (2014) is used to validate the unified model. In their works, GCMC simulations is used to investigate the effect of water on methane sorption in clay-like slit pores. The montmorillonite clay as 2:1 clay mineral was built as a simulation cell which contains two 32-clay unit cells. Each clay patch of 4.224 × 3.656 nm with a thickness of 0.656 nm is separated by a distance (H) to represent a clay nanopore. Meanwhile, the clay sheets are considered as rigid molecules and no bending potential is considered. Methane, and water molecules are simulated by using the Tra-PPE and SPC-E force field model, respectively. Pairwise additive Lennard-Jones (LJ) and Coulomb potentials are used to compute the interactions between particles by considering the both short and long-range intermolecular interactions as well as the electrostatic force. The simulation consists of 0.1 million MC cycles per absorbed molecule for equilibrium and 0.5 million MC cycles per absorbate molecule for sampling the density profiles. In their simulations, fixed number of water molecules is preloaded within the clay nanopores and sorption of methane is simulated by assuming that the pores are connected with a reservoir of pure methane with a given chemical potential. While the number of methane molecules varies depend on the given chemical potential (gas pressure of bulk phase) and the pre-adsorbed water molecules are allowed to move in order to reach equilibrium. All of the simulations are performed at system temperature of T = 298.15 K. Simulation results show that, due to the strong hydrophilicity of clay minerals, the water molecules remain within the pores and no water desorption is observed even at high gas fugacity. Meanwhile, during competing of methane and water adsorption on clay pores lager than 2 nm, the first layer of clay surface is occupied by water molecules and middle of the pore space is mainly accumulated by gas molecules. This meaningful finding in simulation process is similar to the assumption of gas-water-clay interactions in our conceptual model that methane mainly adsorb on water film rather than directly adsorbs on clay surface under moist conditions. In simulations, the average gas weight density ρCH4(Sim) in clay nanopores is given as:

ρCH4 ðSimÞ ¼

1  H

ZH ρðzÞdz

ð18Þ

0

Where ρ(z) is the weight density at distance z from one of the clay surface sheets, g/cm3.

Gas-liquid adsorption

The average water density in the pore ρH2O(Sim) is related to the number of water molecuels NH2O in the pores. In their simulations, it defined as: ρH2 OðSimÞ ¼

N H2 O  M H2 O H  Aslit  NA

Where Aslit is the surface area of single slit layer, NA is the Avogardo number and MH2O the water molar weight. 3.4.2. Computational model In this works, the simulation data of average density of methane ρCH4 adsorbed in slit pore with H = 4 nm under different water saturation condition (average density of water ρH2O = 0 g/cm3, 400 g/cm3 and 600 g/cm3) are used to validate our computational model. In our model, the average density of methane is simplified as the ratio of total gas content to pore volume. The total gas content is defined as the entire quantity of gas that resides in the pore space at a given temperature and pressure and includes both the gas in the center of the pore (‘free’ gas or bulk phase) as well as the gas adsorbed directly on the pore surface or water film (adsorbed phase) (Mosher et al., 2013). Compared with average gas density ρCH4(Sim) in simulation (Eq. (18)), the average density of methane in our model can be described as ρCH4 ¼

ðnad þ nbulk Þ  M CH4 Aslit  H

ð20Þ

As mentioned in Sections 3.1–3.2, the amount of adsorbed phase nadin dry or moist condition can be described as Eqs. (9) and (13), respectively. Meanwhile, the amount of bulk phase can be determined by real gas state equation. It should be noted that, due to the distance between methane molecules and the clay surface, the effective width H* for free gas accumulation is less than the distance H between two parallel slit layers in simulations. Similarly, Kaneko and Murata (1997) suggested that the effective or actual pore width for adsorbate uptake is less than the physical width measured from one wall to the opposite wall. The effective pore width can be described as:

slit

H  ¼ H−2Δ

ð21Þ

Where, Δ is the distance between pore wall and adsorbate molecules where the local density is assumed to be zero, nm. Kaneko and Murata (1997) indicated Δ = 0.12 nm in the case of N2-graphitic slit pore system. In DFT method to calculate density distribution of adsorbate (Chareonsuppanimit et al., 2012, 2015), this limited distance is suggested as 3/8σff (σff is the molecular diameter of the adsorbate, nm). The diameter of methane molecular is 0.373 nm in Jin and Firoozabadi (2014)’s simulation, and the invalid distance △ for gas

Bulk phase

h

ð19Þ

Gas-solid adsorption

Water film Fig. 9. Schematics of gas–liquid-solid interactions on the clay surface.

142

J. Li et al. / International Journal of Coal Geology 159 (2016) 135–154

90

accumulation can be calculated as about 0.14 nm. Thus, we take △ = 0.14 nm for calculation and the free gas content in the slit pore is given by:

(kg/m3)

70

ð22Þ

CH4

nbulk

P ¼  ðH−2ΔÞ  Aslit ZRT

w=0 w=400 w=600

80

Where, Z is the free gas compressibility factor, which is calculated by Peng-Robinson model (Peng and Robinson, 1976). Meanwhile, the relationship between the water film thickness h and average water molecules density ρH2O can be given by

60 50 40 30 20 10 0 0

ρH O H h ¼ 2  ρH2 O 2

1

2

ð23Þ

3

4

P (MPa)

5

6

Fig. 10. Comparison between calculation results and simulation results (ρCH4).

Where, ρ*H2O is liquid density; MCH4 is molar mass of methane. In this work, we take ρ*H2O = 1 g/cm3 and MCH4 = 16 g/mol for calculation. In dry condition (ρH2O = 0 g/cm3), combined with Eqs. (9), (18) and (20), the average density of methane in clay slit pore (ρH2O = 0 g/cm3) can be described as: ρCH4 ¼

w=0(Jin) w=400(Jin) w=600(Jin)

 
 nad−dry þ nbulk  M CH4 2K P H−2Δ P ¼ þ   Aslit  H H P þ PL H ZRT  MCH4

ð24Þ

In moist condition (ρH2O = 400 g/cm3 and 600 g/cm3), the effect of water films thickness on effective pore space also should be taken into consideration. Combined with Eqs. (14), (18) and (20), the average density of methane in the clay pore with pre-adsorbed water can be described as: ðnad−wet þ nbulk Þ  M CH4
 Aslit  H  2Γ P H−2ðΔ þ hÞ P  ¼   M CH4  þ H PþP H ZRT

ρCH4 ¼

ð25Þ

3.4.3. Results comparison As mentioned before, the average methane density ρCH4 in slit pore with different moisture content (ρH2O = 0 g/cm3, 400 g/cm3 and 600 g/cm3) can be calculated by Eqs. (24) and (25). Where, the parameters of methane adsorption on gas–solid interface (K and PL) are based on simulation data of methane sorption on dry clays by Jin and Firoozabadi (2013), and the parameters of methane adsorption on gas–liquid interface (Γ* and P*) are based on experiments data of gaswater surface tension by Jennings and Newman (1971) (details see in Section 3.2). Others are shown in Table 2. The comparison of calculation results and simulation results of average methane density ρCH4 under different conditions is shown in

Fig. 10. It can be found that the matching results are perfect for analytical solutions and published molecular simulation data, which indicates that our united model is able to describe the behavior of methane molecules adsorption on clay surface with pre-adsorbed water molecules. Furthermore, based on Eq. (26), the methane sorption amount on gas–liquid interface for unit area in simulation Γad can be descibed as a relationship bebween average methane density ρCH4 in moist conditions: Γ ad ¼


 nT −nbulk 1 ρCH4 ðSimÞ  H P  ðH−2Δ−2hÞ ¼  − 2Aslit MCH4 2 ZRT

ð26Þ

As shown in Fig. 11, the gas–liquid interface adsorption capacity Γad calculated by Eq. (26) can be basically matched with the results calculated by Gibbs adsorption model (Eq. (10)), which is used to describe gas-water interactions in this study. Meanwhile, it should be noted that, the value of Γad almost overlap in the condition of ρH2O = 400 g/cm3 and 600 g/cm3. If we take thickness of monolayer water film as 0.4 nm, for a slit pore with H = 4 nm, the average water molecules density ρH2O under the monolayer water molecules coverage condition is about 200 g/cm3. Thus, the coverage layer of water molecules in the moist condition with ρH2O = 400 g/cm3 and 600 g/cm3 is more than 1. This meaningful finding may indicate that the gas–liquid interface adsorption capacity will be a constant in slit pore or flat surface when the coverage of water molecules is more than monolayer, and it will be further discussed in Section 5. 4. Samples and experimental methods 4.1. Sample preparation Besides the theoretical study, we also conduct experimental study about adsorption of liquid nitrogen (N2), water (H2O) and methane 6

Table 2 Basic parameter for calculation of methane adsorption capacity.

Model

Symbol

Unit

Value

Temperature Pressure Pore size Water molar volume Maximum adsorption amount per unit area on gas–solid interface Langmuir pressure of gas–solid interface adsorption Maximum adsorption amount per unit area on gas–liquid interface Langmuir pressure of gas–liquid interface adsorption

T P H Vm K

K MPa nm m3/mol mmol/m2

298 0–40 4 18 × 10−6 0.0075

PL

MPa

2.5

ad

Parameter

(10-6mol/m2)

5

w=400(Jin)

4

w=600(Jin) 2.5 2 1.5 1 0.5 0

3 2 1

Γ*

mmol/m

2

0

2

4

6

0 0.00864

0

5

10

15

20

25

30

35

40

P (MPa) P*

MPa

22.28 Fig. 11. Comparison between calculation results and simulation results (Γad-slit).

J. Li et al. / International Journal of Coal Geology 159 (2016) 135–154

(CH4) for both natural clay samples and shale samples in this work. The clay mineral samples including montmorillonite and kaolinite were obtained from the Clay Mineral Society (in Beijing, China) as pure clay samples. The clay-rich shale samples were collected from the Yanchang Formation in Ordos Basin, China. The mineral composition of our clay-rich shale samples were derived from X-Ray diffraction (XRD) analysis of powder less than 200 mesh (i.e. b75 mm). The measurements were conducted on a Bruker D8 DISCOVER diffractometer (Co Ka-radiation, 45 kv, 35 mA) following the two independent processes of the CPSC procedure. The diffracted beam was measured with a scintillation detector with counting time of 20s for each step of 0.02°2θ. Diffraction patterns were recorded in the 2θ range from 2° to 76°. Meanwhile, for the determination of Total Organic carbon (TOC) content, shale samples were powdered less than 200 mesh (i.e. b75 mm) by using a laboratory disk mill. TOC data were measured via Leco CS-230 carbon analyzer. Before using carbon analyzer, about 100 mg sample was placed in a crucible with 5% HCl at 80 °C to remove inorganic carbon. Details of lithology and XRD mineralogical compositions of the studied samples are shown in Table 3. The shale sample (S) with total clay content of 39.7% and TOC of 1.8% is typically clay-rich shale while the montmorillonite (M) and kaolinite (K) in our study are regarded as pure clay samples. Following these analysis, all samples were crushed to 100–150 mesh (150–100 μm) and prepared to the adsorption of N2, H2O and CH4. 4.2. Water adsorption (moisture equilibration) analysis Measurements of water sorption isotherms in our study is referred to the moisture equilibrium method described in ASTM D1412–07 (2010). Both the crushed shale and clay samples (~10 g) with a particle size of 100–150 μm are placed in a sealed environment at constant humidity conditions at room temperature (~25 °C). In order to control the relative humidity RH% (or relative vapor pressure), we used different saturated salt solutions of known vapor pressure. Table 4 lists the salts used in the water sorption experiments and their corresponding Pv (vapor pressure) of the saturated solutions at 25 °C by ASTM E104–2002 (2007). Before the moisture equilibrium process, the drying process of clay and clay-rich shale samples are required. Due to the strongly electrostatic bound water on the clay surface, samples are dried at a higher temperature of 200 °C rather than the API recommended standard of 110 °C in our experiments. This condition ensures removal of any bound and capillary water adsorbed with the clays while avoiding irreversible changes to the structure of clays (Kuila, 2013). Meanwhile, the temperature of 200 °C is suggested to be the optimum for degassing clay rich samples (Drits and Mccarty, 2007; Środoń and Macarty, 2008). The dry weight (m dry) was measured after samples are dried in a 200 °C oven with vacuum for 24 h, and then equilibrated over a saturated salt solution in an evacuated desiccator. The moisture equilibration was performed at 9 different humidity levels (see Table 2) more than one month until weight constancy, starting at low relative humidity ~ 0.1 RH. The humidity was then increased stepwise up to ~ 1.0 RH. The moisture uptake

143

M% (in wt.%) was calculated by Eq. (27): M% ðRH Þ ¼

mmoist ðRHÞ−mdry mdry

ð27Þ

Where M% is the moisture content level; mmoist is the total mass of moist samples, g; mdry is the total mass of dry samples, g; the difference between mmoist and mdry is the mass of water uptake in samples. Compared with nitrogen adsorption or methane adsorption analysis, the moisture equilibration process always lasts for an extremely long time (nearly or even more than one month). Measurement of water sorption isotherms for single sample in such long time may lead to errors. Thus, to ensure that the moisture content measured in our procedure is correct, contrast test with about 10 g crushed samples is also performed in the same relative humidity condition. The average value of moisture content will be used when an obvious deviation exists between these two tests. 4.3. Low pressure nitrogen adsorption analysis Low pressure (77 K) N2 analyses are commonly used to characterize specific surface areas (SSA) and pore-size distributions (PSD) of porous media. The amount of gas molecules attached to a material surface at a given relative pressure (P/P0) depends on the local surface energies and geometrical properties of the porous matrix (Rouquerol et al., 1994). Our experiments of nitrogen sorption on clay and shale samples were conducted with a Quantachrome NOVA 2200e Surface Area and Pore Size Analyzer at State Key Laboratory of Petroleum Engineering in China. The isotherms were performed at 77 K (held constant with a liquid N2 bath) with 99.999% N2 used as the probe gas. Both the adsorption and desorption isotherms of N2 are performed with 72 points in a range of 0.001 ≤ P/P0 ≤ 0.995 with an equilibrium time of 10 h. As the relatively small sample holder, samples of about 0.5–0.8 g are used for the gas sorption. It should be noted that the effect of water saturation or moisture on SSA and PSD characters are critical parameters to be analyzed in this study. Thus, the experiments of low pressure nitrogen sorption on both dry and moist samples have been performed. In the process of nitrogen sorption on dry samples, besides the 24 hour drying procedure in a vacuum oven at 200 °C, an outgas procedure is also required at 200 °C for 3 h at a pressure of 1 × 10−4 MPa to drive off H2O and other adsorbed gases. However, in the process of nitrogen sorption on moist samples, the outgas procedure is held at room temperature (25 °C) just for 10 min at vacuum condition to drive off adsorbed gases while remain the most of pre-adsorbed water. Then the moist samples will be immediately immersed in liquid nitrogen at a temperature as low as − 196 °C. In such condition, the pre-adsorbed water can be regard as ice-like and the evaporation of bound water can be ignored. In our analyses, the specific surface areas are calculated using the Brunauer–Emmett–Teller (BET) method (Brunauer et al., 1938) and the pore size distributions are calculated using the Barrette–Joyner– Halenda (BJH) model (Barrett et al., 1951). The BET surface area is obtained based on isotherm data at relatively low P/P0 condition when a quasi-homogeneous layer of gas atoms (monolayer) is formed in the

Table 3 XRD mineralogical compositions of the studied samples. Sample

Quartz

K-feldspar

Na-feldspar

Calcite

Dolomite

Pyrite

Total clay

Clay compositions (%) M

I/S

I

K

C

S M K

17.0 / /

3.6 / /

19.6 / /

/ / /

/ / /

20.1 / /

39.7 100 100

/ 100 /

33 / /

55 / /

4 / 100

8 / /

M: Montmorillonite; I/S: I–S mixed layer; I:Illite; K: kaolinite; c:chlorite.

144

J. Li et al. / International Journal of Coal Geology 159 (2016) 135–154

Table 4 Salt solutions used in the water sorption experiments and their relative pressure at 25 °C. Saturated solution

ZnCl2

CH3COOK

MgCl2

MnCl2

NaCl

KCl

KNO3

K2SO4

DI water

Pv/P0 (RH)

0.1

0.23

0.32

0.56

0.75

0.85

0.94

0.98

1

material surface (Brunauer et al., 1938), and the gas adsorption data at P/P0 = 0.05–0.34 is used to compute the specific areas. Meanwhile, pore size distribution calculated from BJH model is derived from the Kelvin equation based on capillary condensation or evaporation. Due to the hysteresis loop between the adsorption and desorption branches of the N2 isotherms, PSDs obtained from different branches will change a lot. The published experimental studies has suggested that PSDs from adsorption analysis could not distinguish pore throats and bodies while PSDs from desorption analysis can clearly reflect the structure of narrow pores (Clarkson et al., 2012; Kuila, 2013; Schmitt et al., 2015) Thus, the desorption branch of isotherms is employed to determine the pore structure information. Finally, quantitative analysis of SSA and PSD are performed by NOVAwin 2 software directly.

adsorption in reservoir system is much higher than critical temperature itself (− 80.4 °C/190.7 K), and the condensation behavior of gaseous methane molecules would not occur. Therefore, the Langmuir model based on the “monomolecular” layer concept is commonly used in practice due to its simplicity and clear physical meaning of fitting parameters are clear. Meanwhile, the Langmuir equation could provide a good representation of the measured sorption data for coals (Crosdale et al., 2008), clays (Ji et al., 2012; Hartman et al., 2008) and even shales (Liu et al., 2016) in both dry condition and moist condition. As discussed in Section 3 theoretically, the adsorption amount of methane on gas/ clay interface and gas/water interface can be described as a model with Langmuir form. Thus, in this study, Langmuir equation is also employed to fit the experimental adsorption data of methane on both dry samples and moist samples.

4.4. High pressure methane adsorption analysis nad ¼ nLðfit Þ 

P P þ P Lðfit Þ

ð28Þ

Normalized N2 sorption volume

Where nad is the adsorption amount measured in experiments (excess adsorbed amount), mmol/g; P is equilibrium pressure of samples cells, MPa; PL(fit) and n L(fit) are the fitting parameter according to Langmuir model, corresponding to the Langmuir pressure and maximum sorption capacity, MPa and mmol/g.

1 Montmorillonite-adsorption (RH=0.00)

0.8

Montmorillonite-desorption (RH=0.00) Kaolinite-adsorption (RH=0.00)

0.6

Kaolinite-desorption (RH=0.00)

a) Montmorillonite and kaolinite

0.4 0.2 0 0

0.2

0.4 0.6 Relative pressure P/P0

0.8

1

1 Normalized N2 sorption volume

High pressure methane sorption isotherms was obtained using FYKT 1000 (made in China) isothermal adsorption apparatus according to GB/T 1560–2004 (China national standard) testing standard at State Key Laboratory of Petroleum Engineering in China. To compare our experimental data with the molecular simulation results by Jin and Firoozabadi (2014) at 298 K, the uniform temperature was required. Thus, isothermal adsorption experiments were conducted at 298 K (~25 °C) on dry as well as moisture-equilibrated samples with particle size of 100 ~ 150 μm and weight of 10 ~ 15 g. Meanwhile, the CH4 (of ultra-high purity, 99.999%) was used as the adsorbate gas and the range of experimental pressure was 0.5 ~ 18.5 MPa. The dry samples were heated in a vacuum oven at a constant temperature of 200 °C before being subjected to the gas adsorption test. The moistureequilibration samples were prepared in an evacuated desiccator under controlled relative humidity (RH) conditions using saturated salt solutions of ZnCl2 (0.1 RH), NaCl (0.75 RH), KNO3 (0.94 RH) and K2SO4 (0.98 RH). The high pressure methane adsorption procedure consisted of void volume measurement by helium (He) and adsorption isotherm measurement by methane (CH4). In the void volume measurement progress, the pretreated samples were placed in the sample cell and the adsorption system, including both reference and sample cells, was first pressurized with helium to 15 MPa. The void volume of the sample cell was determined by helium expansion and the void volume measurements at 25 °C were applied in the calculation of the corresponding CH4 adsorption isotherms. Then the experimental setup was evacuated and CH4 was introduced into the reference cell. During isotherm measurement, a certain amount of CH4 was charged into the reference cell. After equilibrium was reached, as assessed by monitoring pressure variations of b10−4 MPa within 10 min, the valve between the reference cell and the sample cell was opened, and the gas was expanded into the sample cell. By measuring the pressures before and after expansion, gas molar densities at different stages were calculated using an appropriate equation of state (EOS), and the amount of gas adsorbed at one pressure level could be determined. The isotherm was obtained by repeating these procedures until the measurement at the highest desired gas pressure was achieved. The equations to calculate adsorption amount nad (mol/g) are presented in several published works (Gasparik et al., 2014; Zhang et al., 2012b). For practical use, the measured sorption data are often represented by mathematical models based on various concepts of the sorption mechanism. Generally, the temperature for methane

Shale-adsorption (RH=0.00)

0.8

b) Shale

Shale-desorption (RH=0.00)

0.6 0.4 0.2 0 0

0.2

0.4 0.6 Relative pressure P/P0

0.8

1

Fig. 12. Normalized N2 isotherms of (a) montmorillonite and kaolinite; (b) shale.

J. Li et al. / International Journal of Coal Geology 159 (2016) 135–154

5. Results and discussion 5.1. Effect of water on pore size distribution characteristics 5.1.1. Nitrogen adsorption isotherms Fig. 12 depicts the normalized N2 isotherms of montmorillonite (M), kaolinite(K) and shale (S) under dry conditions (RH = 0.0), showing an evident hysteresis loop between adsorption/desorption branches. The reason of sorption hysteresis phenomenon is always complex and mystery. In the thermodynamic equilibrium of subcritical gas adsorption/desorption inside actual porous media, the energy change between adsorption (condensation) and desorption (evaporation) processes is irreversible due to the effect of irregular pore bodies on phase behavior, such as gas–liquid menisci formation or bubble nucleation (Ravikovitch and Neimark, 2002; Sergej, 2009). Meanwhile, the pore structures (pore body and throat), shape (slit and capillary), connectivity and surface roughness also dominate the sorption hysteresis characters (Evans et al., 1986). In this study, the four-type classification of hysteresis loops IUPAC recommended on the basis of De Boer's categories was used to determine pore structure information of our samples (Boer and Lippens, 1964; Sing, 1982). As shown in Fig. 12, the normalized N2 isotherms of montmorillonite (M), kaolinite (K) and shale (S) have illustrated two different shapes of hysteresis loops. For montmorillonite (M) and kaolinite (K), the shapes fall within types H4 with closure point of adsorption/desorption branches around P/P0 = 0.45. It mainly indicates that narrow slit-like pores are dominated in our clay samples (M and K). Meanwhile, the character of type I isotherms below P/P0 = 0.45 points out a potential microporosity in clays. However, for clayrich shale (S) samples, the adsorption/desorption branches are not closed until relative pressure P/P0 less than 0.1. It may demonstrate the presence of more complex pore structures (such as amorphous pore), poor connectivity between pore networks and less microporosity in our shale samples. Specially, the effect of pre-adsorbed water on N2 sorption isotherms is also discussed in our study. The isotherms of montmorillonite (M), kaolinite (K) and shale (S) under different moist conditions with relative humidity (RH) ranging from 0 to 0.98 is shown in Fig. 13. Without exception, the maximum N2 adsorption amount at P/P0 = 1 of all samples decrease with the increase of RH. It mainly attributes to a part of the pore surface or space is occupied by adsorbed water, and the effective surface are and pore volume for N2 uptake have reduced. However, the effect of water on N2 adsorption characters varies with different samples. It is obvious that the impact of pre-adsorbed water on clay samples (M and K) is more significant than on shale (S). For shale samples, in such competitive sorption condition (H2O and N2), clay nanopores display a strong affinity to water due to the attractive electrostatic force and the clay-bound water cannot be easily replaced by nitrogen (Zolfaghari and Dehghanpour, 2015a,b). Additionally, the temperature is extremely low in N2 sorption analysis (77 K) and the evaporation or diffusion of pre-adsorbed water is impossible. For shale samples, the interactions between water and organic matter is much weaker and water molecules may be even inaccessible to organic 30

Desorption (RH=0.00) Adsorption (RH=0.10)

135

a) Montmorillonite

Desorption (RH=0.10) Adsorption (RH=0.75) Desorption (RH=0.75)

90

Adsorption (RH=0.94) Desorption (RH=0.94) Adsorption (RH=0.98) Desorption (RH=0.98)

45 0 0

0.2

0.4 0.6 Relative pressure P/P0

0.8

1

nanopores in low RH condition (Striolo et al., 2003). The detail for water distribution characteristics of clay and shale will be discussed later in Section 5.2. Furthermore, compared with N2 sorption isotherms of dry condition and moist condition, hysteresis loops between adsorption and desorption branches, epically for clay samples, become narrow and flat. As mentioned above, the shape of hysteresis loop indicate the pore structure information. Thus, it can be inferred from the narrow loops in moist condition that the pre-adsorbed water in porous medium may reduce the roughness of pore surface and make the pore structure more uniform. 5.1.2. Effective Pore Size Distribution The effective pore size distributions of montmorillonite (M), kaolinite (K) and shale (S) under different moist condition with RH = 0.00, 0.10, 0.75, 0.94 and 0.98 deduced from N2 desorption isotherms are shown in Fig. 14. The results show that the pre-adsorbed water mainly reduce the effective volume of pores within 20 nm in both clay and shale. Especially for montmorillonite samples with strong hydrophilicity (Fig. 14a), the effective volume of fine pores within about 6 nm will ‘disappear’ in EPSD curves when the RH approaches to 0.98. Thus, it directly gives the evidence of ‘capillary condensation behavior’ in clay nanopores. However, this ‘disappear’ phenomenon has not occurred in clay-rich shale samples even RH higher than 0.98 (Fig. 14c). This remarkable phenomenon may be caused by the unapproachability of water molecules into micro and ultra-micro pores of organic matters, such as kerogen nanopores. Similarly, Firouzi et al. (2014b) indicated that pore size and surface chemistry may prevent the water from condensing in nanopores of coal and shale, and PSDs of these samples were unable to be measured by NMR cryoporometry. Experiments of low-pressure adsorption with carbon dioxide on dry and moistureequilibrated coal samples by Prinz and Littke (2005) showed that water is unable to penetrate the aromatic structures of the macromolecular networks. Meanwhile, complex graphite structures containing local charge and defect sites within pores, in addition to the inclusion of chemical functional groups inside the cavities, may be one of the primary reasons that affects gas and water distribution characters in coal and shale nanopores (Firouzi and Wilcox, 2013; Firouzi et al., 2014a). The molecular simulation results from Hu et al. (2015) showed that the accessibility of the kerogen nanopores for water depends on thermal maturity and surface roughness, and water hardly accesses into ultramicro pore of organic matter or pores without oxygenated functional groups. Here, our analysis method by low-pressure N2 sorption in this work may provide a new approach to understand the water distributions characteristics in clay and shale microporosity. Additionally, the effective specific surface area (ESSA) and effective pore volume (EPV) are also obtained from our experiments. The ESSA is assessed in the early stage of adsorption isotherms (P/P0 = 0.05 ~ 0.34) by BET model while EPV is calculated by assuming gas as liquid phase condensed in entire pore space at P/P0 ~ 1.0 and ρ = 0.808 cm3/g is used as density of liquid N2. Details for ESSA and EPV of analyzed samples are shown in Table 5. It also can be found that the effect of relative humidity (RH) on ESSA and EPV of clay samples is 20

Adsorption (RH=0.00) Desorption (RH=0.00)

Adsorption (RH=0.10)

N2 sorption volume SPT (cc/g)

Adsorption (RH=0.00)

N2 sorption volume SPT (cc/g)

N2 sorption volume SPT (cc/g)

180

145

b) Kaolinite

Desorption (RH=0.10)

20

Adsorption (RH=0.75) Desorption (RH=0.75) Adsorption (RH=0.94)

Desorption (RH=0.94)

10

Adsorption (RH=0.98) Desorption (RH=0.98)

0 0

0.2

0.4 0.6 Relative pressure P/P0

0.8

1

Adsorption (RH=0.00) Desorption (RH=0.00) Adsorption (RH=0.10)

15

Desorption (RH=0.10) Adsorption (RH=0.75)

c) Shale

Desorption (RH=0.75)

10

Adsorption (RH=0.94) Desorption (RH=0.94) Adsorption (RH=0.98) Desorption (RH=0.98)

5 0 0

0.2

Fig. 13. Low pressure N2 isotherms of (a) montmorillonite, (b) kaolinite and (c) shale with different RH.

0.4 0.6 Relative pressure P/P0

0.8

1

146

J. Li et al. / International Journal of Coal Geology 159 (2016) 135–154

RH=0.10

0.03

RH=0.75

RH=0.94 RH=0.98

0.02

a) Montmorillonite

0.01 0

Diferental pore volume (cc/g)

0.006

RH=0.00

Diferental pore volume (cc/g)

Deferential pore volume (cc/g)

0.04

RH=0.00 RH=0.10 RH=0.75

0.004

RH=0.94 RH=0.98

b) Kaolinite

0.002

20 Pore size (nm)

200

RH=0.00 RH=0.10

0.002

RH=0.75 RH=0.94

0.0015

RH=0.98

0.001

c) Shale

0.0005 0

0 2

0.0025

2

20 Pore size (nm)

200

2

20 Pore size (nm)

200

Fig. 14. Effective PSD curves of (a) montmorillonite, (b) kaolinite and (c) shale with different RH.

significant higher than shale samples. This phenomenon can be attributed to the inaccessibility of the kerogen material for water as mentioned above. 5.1.3. Prediction of Effective PSDs The surface forces, including intermolecular, electrostatic, and structural interactions, between water films and clay nanopores have been analyzed in Section 2. Subsequently, a mathematical model for calculation of water films thickness and water saturation in single slit pore is also presented based on disjoining pressure. Combined with Eqs. (7) and (8), for clay porous media with given pore size distribution, the water saturation Sw(i) in pores with different size as follows: Sw ðiÞ ¼

2  hðiÞ ¼ f ½HðiÞ; P v =P 0  HðiÞ

ð29Þ

relationship of pore throats and bodies, is more heterogeneous than montmorillonite and the condensed liquid (such as liquid N2) in pore throats will prevent the further condensation behaviors in pore bodies even in a high RH condition. Meanwhile, the basic parameters for calculating the surface force (disjoining pressure) of water/montmorillonite and water/kaolinite are listed in Table 6. Although clay minerals typically have a very high affinity to water molecules, the differences exist between clay minerals (Van Oss, 1995; Giese and Van Oss, 2002). Due to their active interlayer space in montmorillonite type clay minerals, the kaolinite type clay minerals have a lower surface affinity and surface area than montmorillonite (Meunier, 2005; Mcgregor et al., 2014). Thus, a lower Hamaker constant AH and hydration coefficient k is used to describe the molecular force and structural force between water film and kaolinite (Table 6). 5.2. Water adsorption and distribution characteristics

Where, Sw(i) is water saturation for single slit, %; h(i) is water film thickness for single slit, nm; H(i) is the width of slit, nm; Pv/P0 is the relative humidity, %. Further, the effective deferential pore volume Veff with pre-adsorbed water can be defined as:

Where, V(i) is the deferential pore volume under dry condition, cm /g; Sw(i) is the water saturation for single pore, %. The relationship between H(i) and Veff (i) can be represented as the effective pore size distribution (EPSD). Based on the PSD curves of montmorillonit (M) and kaolinite (K) samples under dry conditions (RH = 0.00), the EPSD curves under different moist condition with 0.10, 0.75, 0.94 and 0.98 can be calculated by Eq. (30). The comparison of calculated results and PSD curves interpreted from low pressure N2 sorption isotherms is shown in Fig. 15, and the calculated EPSD curves basically match our experimental data. Especially for montmorillonit (M), even the ‘disappear phenomenon’ in EPSD curves with RH = 0.98 can be also perfectly fitted by our model. Additionally, it also puzzled us a lot that this ‘disappear phenomenon’ didn't happen in experimental analysis of kaolinite (K) samples in such high RH condition, although EPSD curves with RH = 0.10, 0.75 and 0.94 can be fitted perfectly. A reasonable explanation may be that the pore structure of kaolinite, such as geometrical 3

Table 5 Effective specific surface area (ESSA) and effective pore volume of our studied samples. RH

0 0.1 0.75 0.94 0.98

Montmorillonite (M)

Kaolinite (K)

Shale (S)

ESSA (m2/g)

EPV (cm3/g)

ESSA (m2/g)

EPV (cm3/g)

ESSA (m2/g)

EPV (cm3/g)

51.768 42.561 41.062 33.357 17.351

0.277 0.223 0.202 0.171 0.133

6.002 5.352 4.852 3.92 3.098

0.042 0.035 0.028 0.014 0.012

5.536 5.346 5.772 4.453 4.442

0.029 0.028 0.026 0.02 0.018

Differential pore volume (cc/g)

ð30Þ

a) Montmorillonite

0.04

Experiment (RH=0.00) Experiment (RH=0.10) Experiment (RH=0.75)

0.03

Experiment (RH=0.94) Experiment (RH=0.98) Model (RH=0.10)

0.02

Model (RH=0.75) Model (RH=0.94) Model (RH=0.98)

0.01 0 2

Differential pore volume (cc/g)

V eff ðiÞ ¼ V ðiÞ  ½1−Sw ðiÞ

5.2.1. Water adsorption isotherms The water sorption isotherms measured by the moisture equilibration method are shown in Fig. 16(a–c) for montmorillonite, kaolinite and shale with RH ranging from 0.0 in dry condition to about 1.0 in

0.006

20 Pore size (nm)

b) Kaolinite

200

Experiment (RH=0.00) Experiment (RH=0.10)

0.005

Experiment (RH=0.75)

Experiment (RH=0.94)

0.004

Experiment (RH=0.98)

0.003

Model (RH=0.10) Model (RH=0.75)

0.002

Model (RH=0.94) Model (RH=0.98)

0.001 0 2

20 Pore size (nm)

200

Fig. 15. Prediction of effective PSD curves of (a) montmorillonite and (b) kaolinite.

J. Li et al. / International Journal of Coal Geology 159 (2016) 135–154

147

Table 6 Basic parameter for calculation water-clay interactions. Parameter

Symbol

Unit

Value (Montmorillonit)

Value (Kaolinite)

Reference value

Temperature Water molar volume Gas constant Hamaker constant (clay-water-air) Hamaker constant (water-air-water) Electric constant (vacuum) Water relative dielectric permittivity Electric potentials difference Coefficient of structural force Characteristic length of water

T Vm R AH AH* ε0 ε △ζ k λ

K m3/mol J/mol·K J J F/m – mV N/m2 nm

298 18 × 10−6 8.314 1.0 × 10−20 0.15 × 10−20 8.85 × 10−12 81.5 50 1 × 10−7 1.5

298 18 × 10−6 8.314 0.5 × 10−20 0.15 × 10−20 8.85 × 10−12 81.5 50 0.5 × 10−7 1.5

– – – 0.1–1.0 × 10−20(a) 0.13–0.19 × 10−20(b) – – 40–80(c) 0–2(d) 1.0– 2.5(d)

(a): by Starov et al. (2007). (b): by Tuller et al. (1999) and Churaev et al. (2000). (c): by Churaev (1995a) and Mattia et al. (2012). (d): by Churaev (1995a,b).

ð31Þ

Where, wm is the monolayer capacity of moisture uptake, wt.%; aw is the water activity which is equal to relative vapor pressure, aw = RH = Pv/P0; CGAB is an energy constant related to adsorption heat, dimensionless; k is a constant, dimensionless. The GAB equation reduces to the well-known BET when k = 1. As shown in Fig. 16 (the black dash line), the water isotherms in our study can be basically fitted by GAB model. The monolayer capacities (wm) of montmorillonite, kaolinite and shale calculated from the GAB model are 8%, 3% and 1.5%, respectively. These values are reached at RH approaches to 0.1 and they are lower than the relative pressure for formation of monolayer layer N2 (~ 0.30), which indicates a higher adsorption capacity of water than nitrogen for clay and clay-rich shale. Meanwhile, combined with the mathematic model for water saturation Sw(i) calculation in single pore (Eqs. (7), (8) and (30)), the water sorption isotherms of porous media also can be predicted by accumulating Sw(i) in each pores based on PSDs. Sw ¼

i¼n X

Sw ðiÞ 

i¼1

V ðiÞ VT

ð32Þ

Where, Sw is the total water saturation in porous media, %; VT is total pore volume of samples based on N2 sorption analysis, cm3/g; V(i) is the deferential pore volume under dry condition, cm3/g. Further, the moisture uptake can be obtained by M = VT · ρw · Sw with assuming destiny of adsorbed water ρw = 1.0 cm3/g, and these calculated water uptake curves of montmorillonite and kaolinite are plotted as red dash lines in Fig. 16. It should be noted that the water sorption isotherms directly measured in our experiments (black dash line) are much higher than

Moisture (w%)

M2_measured (I+O)

30%

120%

GBA Model (I+O)

100%

Data_PV-EPV (I)

80%

Calculated (I)

20%

60% 40%

10%

20% 0%

0% 0

0.2

0.4 0.6 0.8 Relative humidity (RH%)

10%

140%

a) Montmorillonite

1

K1_measured (I+O) K2_measured (I+O)

8% Moisture (w%)

M1_measured (I+O)

Water Saturation (%)

40%

5.2.2. Water distribution characteristics The significant deviation between water sorption isotherms determined by different methods shown in Fig. 16 likely suggests different water distribution characteristics within multi-scale porosity of clay. Based on the clay structures, three types of pores including interparticle pores, inter-crystal pores, and inter-layer pores within crystals (for montmorillonite) are always found in clay materials. (Aylmore and Quirk, 1967a; Jullien et al., 2005). The relationship of the three types of spaces is shown in Fig. 17. A clay particle is normally composed of numerous crystals aggregating together and the space exists between crystals within particles referred to inter-crystal pore. Especially for montmorillonite, each crystal can be further separated into bundles of TOT (tetrahedra-octohedra-tetrahedra) layers and the space between layers referred to inter-layer pore (Geatches and Wilcox, 2014a,b). Both of the inter-crystalline and inter-layer pores belong to intraparticle porosity (contrast to inter-particle porosity). Experimental evidence (Zhang et al., 2012a; Kuila and Prasad, 2013) shows that pores with diameter between 10 to 100 nm are dominant in the pore spaces between bundles of clay crystals, while pores with diameter account 5%

b) Kaolinite

200%

GBA Model (I+O)

Data_PV-EPV (I)

6%

150%

Calculated (I)

4%

100%

2%

50%

0%

0% 0

0.2

0.4 0.6 0.8 Relative humidity (RH%)

1

S1_measured (I+O) S2_measured (I+O)

4%

GBA Model (I+O)

160%

c) Shale

120%

Data_PV-EPV (I)

3%

GBA Model (I)

80%

2%

40%

1%

0%

Water Saturation (%)

wm  C GAB  aw ð1−kaw Þð1 þ ðC GAB −1Þkaw Þ

Moisture (w%)

M% ¼

the calculated results based on PSD curves (red dash line). It is mainly caused by the different distribution characters of adsorbed water in these two methods. In moisture equilibration process, water molecules access into porosity of both intra-particles and inter-particles of clay powders, thus the measured data represents total water adsorption amount or actual water adsorption capacity. However, the predicated isotherms based on PSD within 300 nm may mainly represent water uptake within microporosity of inter-particles and it will lead to an underestimate of moisture content in actual condition. Details for water distribution characters will be discussed later. Additionally, as shown in Table 5, the difference between effective pore volume (EPV) in moist condition and pore volume (PV) in dry condition by N2 adsorption analysis (PV-EPV) can be roughly regarded as volume of pre-adsorbed water within inter-particles space (ignoring water evaporation and pore volume changing). These water volume data have been further converted into moisture content and plotted in Fig. 16 as red circle points. As expected, the predicated isotherms based on PSD (red dash line) can be basically matched the water uptake date inferred from EPV (red circle points).

Water Saturation (%)

moist condition controlled by DI water. According to the IUPAC classification of sorption isotherms, both of the curves are typical type II isotherms which reflects a condensation behavior in high RH condition. In this study, the water isotherms were plotted with the moisture uptake M% (in wt%) against the RH and fitted by the 3-parameter Guggenheim–Anderson–de Boer (GAB) adsorption model (Boer, 1953)

0% 0

0.2

0.4 0.6 0.8 Relative humidity (RH%)

1

Fig. 16. Experimental and calculated water uptake isotherms of (a) montmorillonite, (b) kaolinite and (c) shale. (I + O) represents water uptake within both intra-particle pores and interparticle pores; (I) represents water uptake within inter-particle pores.

148

J. Li et al. / International Journal of Coal Geology 159 (2016) 135–154

Inter-particle space (macropore)

Intra-particle space (mesopore-micropore)

Inter-layer space (for montmorillonite)

Clay particle

Clay sheet Interlayer Cations

Water ‘bridge’ between clay particles

Water film

Capillary water

Water molecules Nano-scale

Micro-scale Fig. 17. Relationship of the three types of pores in clay.

(~1 nm) for the porosity within crystals of clay platelets. Otherwise, the macropores between the particles of clays are always lager than 100 nm, even reach up to 1 μm–20 μm. Thus, the PSD within 300 nm interpreted from N2 sorption analysis represents intra-particle space (mainly inter-crystal pores) and the water uptake isotherms based on PSD only reflect the water distribution inside a part of inter-particle pores. However, the moisture distribution in the space between clay particles should also be taken into account. Actually, the ‘agglomeration’ of clay powders is found during moisture equilibration process in our experiments especially under high RH conditions (Fig. 18). It directly shows the evidence of water sorption or even condensation (‘liquid bridge’) in external surface of clay particles. Therefore, it can be inferred that the PSD interpreted from water sorption isotherms by moisture equilibration method is larger than that of nitrogen sorption isotherms, because clay minerals have a higher affinity of adsorbing water and more pore space is occupied by moisture. Similar results have also been reported by Zolfaghari and Dehghanpour (2015a,b) from a comparative study of PSD in gas shales by water and nitrogen sorption isotherms. It have been reported that the intra-particle porosity of clay minerals, especially for pores less than 100 nm, can provide significant specific surface for gas adsorption in clay-rich shale reservoirs (Ross and Bustin, 2009; Kuila and Prasad, 2013). However, this conclusion is mainly drawn from the tests by dry clay or shale samples. Under moist conditions, ‘capillary condensation phenomenon’ in nanoporosity has been shown in the EPSD curves (Fig. 14) and the pores blocked by capillary water may be unavailable for gas adsorption. Thus, the water distribution characteristics with in intra-particle

Montmorillonite

porosity of shale clay may significantly affect gas storage potential. Based on Eq. (29) and water/montmorillonite interaction parameters in Table 6, the water saturation Sw(i) distribution curves with RH ranging from 0.10 to 0.99 are shown in Fig. 19. The results show that water saturation varies significantly in different sized pores even under the same relative humidity condition and it is much higher in pores with smaller width. As illustrated in Fig. 19, in moist condition with RH b 0.75, water saturation in all pores (3 ~ 300 nm) is less than 1.0, which indicates that only water film is bound on pore surface, without condensed water filling in pore. As RH increases, water film becomes unstable, and transforms into the condensed water filling pore space. Simultaneously, these pores with smaller size will be firstly blocked by condensed water while the bigger pores are likely bound by water film. In the region of RH ranging from 0.90 to 0.99, the pore with width of 3.07 nm to 8.33 nm will gradually be filled with capillary water. Thus, it is clearly showed by water saturation distribution curves that water distributes in different sized pores mainly as two forms: (i) capillary water condensed in the small pores or pore throats; (ii) water film bounding in the larger pores or pore bodies. Additionally, the effect of moisture on pores larger than 100 nm is slightly, which should be result of the difficulty for water condensation within these macropores. However, it should be noted that the all of the calculation results in Fig. 19 are based on slit pore model and this assumption may be only available to inter-crystal pore and inter-layer pore of clay minerals. The effects of pore shapes and structures, such as angular pore and cylindrical Pore, on the thickness and stability of water film have been discussed elsewhere (Churaev et al., 2000; Tuller et al., 1999). These effects can be significant in some cases and it may be the

Kaolinite

Fig. 18. ‘Agglomeration phenomenon’ of clay and shale powders during moisture equilibration process.

Shale

J. Li et al. / International Journal of Coal Geology 159 (2016) 135–154 Table 7 Langmuir fitting parameters for methane adsorption on montmorillonite.

RH=0.10 RH=0.50

0.8

RH=0.75

0.6

RH=0.94 RH=0.96

0.4

RH

Sw (inner-particle pores)

PL(fit) (MPa)

nL(fit) (mmol/g)

Montmorillonite (M)

0 0.1 0.75 0.94 0.98

0% 10.90% 23.10% 58.59% 82.36%

6.72 17.18 22.28 22.28 22.28

0.4839 0.4776 0.474 0.2326 0.1169

RH=0.98 RH=0.99

0.2 0 2

20 Pore size (nm)

200

Fig. 19. Water saturation distribution characteristics in clay pores with different total Sw.

primary reason for ‘liquid bridge’ existing within inter-particle macropores lager than 100 nm in our experiments. 5.3. Effect of water on methane adsorption characteristics 5.3.1. Methane adsorption isotherms To compare our experimental data with the molecular simulation results of by Jin and Firoozabadi (2014), a series of CH4 sorption isotherms on montmorillonite (M) with moisture equilibrated in different relative humidity conditions (RH = 0.0, 0.10, 0.75, 0.94, 0.98) were measured at pressures up to 18.5 MPa and at 25 °C. As shown in Fig. 20, the methane adsorption amount significantly decreases with increasing moisture content, especially for methane sorption in montmorillonite samples with higher RH. The details for effect of water on methane adsorption capacity will be further discussed below by combining with water distribution characters. As mentioned above, the Langmuir model is commonly used in practice and physical meaning of fitting parameters are almost clear. Further, the Langmuir model could perfectly match the measured sorption data both for (Crosdale et al., 2008), clays (Ji et al., 2012; Hartman et al., 2008) and shales (Liu et al., 2016) in dry and moist condition. Therefore, Langmuir equation is also employed to fit the experimental data of methane adsorption on both dry and moist clays. The fitting parameters Langmuir pressure PL(fit) and maximum sorption capacity nL(fit) are shown in Table 7, and the relationships between fitting parameters and water saturation within inter-particle pores are shown in Fig. 21. As illustrated in Fig. 21, both of the PL(fit) and nL(fit) decrease with the increasing of water saturation (moisture content) in our montmorillonite samples, which is consistent with the experimental data of shale and illite samples by Gasparik et al. (2012) and Hartman et al. (2008). It's worth noting that an inflection point is found in Fig. 21 at water saturation Sw around 23.1% (RH = 0.75). In a relative low moist condition with Sw less than 23.1%, the Langmuir pressure PL(fit) for

methane sorption increases significantly while the maximum sorption capacity nL(fit) changes slightly. However, in a relative high moist condition with Sw larger than 23.1%, nL(fit) reduces with Sw increasing and PL(fit) almost maintains constant. In Langmuir model, the parameter PL(fit) represents strength of interactions between adsorbent and adsorbate, and the parameter nL(fit) represents the maximum potential for adsorbate adsorption on adsorbent. Therefore, this meaningful finding may indicate two different mechanisms for water influencing methane adsorption capacity on clay. In low Sw or RH conditions, the water film firstly tends to cover the pore surface and it weakens the adsorption force between methane and clay. Meanwhile, the ‘capillary condensation’ does not happen in such condition and thin bond water film will not significantly reduce the effective surface area of samples and potential for gas storage. Actually, the ESSA values in Table 5 can certify our assumption. The ESSA of our montmorillonite samples reduces slightly from 51.768 m2 in dry condition to 41.062 m2 in moist condition with RH = 0.75. Nevertheless, in high Sw or RH conditions, more than monolayer water film already cover the pore surface, and the interactions between clay and gas change in to that between water and gas, thus the PL(fit) basically remain constant. Additionally, the condensed capillary water will block part of pore space and reduce the effective site for gas adsorption. It has been shown that the ESSA would further sharply reduce to 17.351 m2 at RH = 0.98. Thus, the ESSA data directly give the evidence of these two different mechanisms for methane adsorption on moist clay samples. 5.3.2. Adsorption on flat surface In order to further discuss the effect of water on methane adsorption, an ideal case of methane and water competitive adsorption on a flat clay surface is firstly analyzed (the specific surface area of this flat surface is assumed as SSA of montmorillonite in dry condition). In this condition, water blocking phenomenon couldn't occur, thus the methane adsorption capacity is mainly caused by transformation from gas–solid interaction to gas–liquid interaction. Obviously, the coverage coefficient of water molecules on solid surface plays a key role of describing methane adsorption characteristics under different moisture conditions. Based on Eq. (17) and basic parameters in Table 3, the methane absorption content with different water coverage coefficient α (0, 0.25, 0.5, 0.75

25

0.4

0.5

Data (Dry)

0.35

Data(0.10)

0.3

Data(0.75)

0.25

Data(0.94)

0.2

Data(0.98) Fitting(0.00)

0.15

Fitting(0.10)

0.1

Fitting(0.75)

0.05

Fitting(0.94)

0

Fitting(0.98)

0

5

10

15

20

P(MPa) Fig. 20. Isotherms and Langmuir fitting curves of methane adsorption on montmorillonite with different RH.

0.4

20

0.3 15 0.2 10

PL(fit)

nL(fit)

0.1

5

Maximum sorption capicity (mmol/g)

nad (mmol/g)

Sample

RH=0.90

Langmuir pressure (MPa)

Water saturation Sw(i)

1

149

0 0%

20%

40% 60% Water saturation (%)

80%

Fig. 21. Relationship between Langmuir pressure and maximum sorption capacity with water saturation Sw.

150

J. Li et al. / International Journal of Coal Geology 159 (2016) 135–154

0.1

0.4

Model(0.10)

0.3

Model(0.75)

0.25

Model(0.94)

0.2

Model(0.98)

nad (mmol/g)

nad (mmol/g)

0.08 0.06 0.04 0.02

Model(0.00)

0.35

Data (Dry)

0.15

Data(0.10)

0.1

Data(0.75)

0.05

Data(0.94)

0

0 0

5

10

15

Data(0.98)

0

20

5

10

15

20

P(MPa)

P(MPa) Fig. 22. Methane adsorption isothermal curves with pressure for different water coverage coefficient α.

Fig. 24. Methane adsorption isothermal curves with pressure for different water saturation Sw.

and 1.0) is calculated. As shown in Fig. 22, the methane adsorption amount decreases with increasing of water coverage coefficient, and capacity of methane adsorption on clay surface (α = 0) is larger than that of methane adsorption on water film (α = 1). Meanwhile, the relationship between ratio of nad-wet/nad-dry at 6 MPa (nad-wet and nad-dry is the capacity of methane absorption on moist clay and dry clay, respectively) and water coverage coefficient α is shown in Fig. 23. It should be found that the ratio of nad-wet/nad-dry is linear with the variation of α before α b 1, and this value will remain constant when more than monolayer water molecules cover the solid surface (α N 1). Comparing with the dry condition, methane absorption capacity is approximately reduced by 65% under the condition of adsorption on gas–liquid interface.

amount for single slit, mmol/g; A(i) is the specific surface area for single slit, m2/g; other parameters in Eq. (34) are seen in Table 5. Then, total methane adsorption amount nad in porous media can be calculated by accumulating nad(i) in different sized pores based on PSD curves, as follows

5.3.3. Adsorption in porous media Furthermore, the effect of water on methane adsorption capacity in porous media will be discussed in this section by combining with water distribution characteristics in different sized pores. The PSD and SSA information of our montmorillonite sample is used to analyze. Firstly, based on water saturation Sw(i) distribution in montmorillonite sample (the details for calculation of Sw(i) has be discussed above by Eq. (29)), the coverage coefficient of water molecules α(i) in pores with different size is calculated by Eq. (33) firstly, then the methane adsorption amount nad(i) in different sized pores can be obtianed by Eq. (34): α ðiÞ ¼ Sw ðiÞ=Smon ðiÞ  nad ðiÞ ¼ ð1−α ðiÞÞ  K 

ð33Þ  P P þ α ðiÞ  Γ     AðiÞ P þ PL PþP

ð34Þ

Where, α(i) is the coverage coefficient of water molecules for single slit, dimensionless; Smon(i) is water saturation with monolayer water molecules coverage pore surface, %; nad(i) is the methane adsorption

nad ¼

i¼n X

nad ðiÞ

ð35Þ

i¼1

Based on Eq. (35), the methane absorption isotherms on montmorillonite samples with moisture equilibrated in different RH condition (0.00, 0.10, 0.75, 0.94 and 0.98) can be calculated. The corresponding total water saturation Sw is 0%, 10.90%, 23.10%, 58.59% and 82.36%, respectively. Meanwhile, the calculated results by our model are compared with the experiential data under different RH conditions. As shown in Fig. 24, the calculated results basically match the experiential data. Compared with methane-water adsorption on a flat surface (Fig. 23), the impact of water on methane adsorption in porous media is more significant. Moreover, this influence becomes obvious when the RH is over 0.75. Combining with water distribution characters in Fig. 19, the ‘capillary condensation phenomenon’ in pores about 3 nm won't happen until RH reaches 0.90 and pores less than 6.76 nm, including major peak with H = 4.10 nm, will be filled by water in a higher moist condition with RH = 0.98. In such condition, these pores blocked by water will lose capacity to adsorb methane, which results in a sharp reduction on methane adsorption capacity. Meanwhile, the relationship between ratio of nad-wet/nad-dry and water saturation Sw is shown in Fig. 25, and the methane adsorption amount is also calculated in 6 MPa. The results indicate that the methane adsorption capacity is stepped variation with increasing of water saturation, which is significantly different from that in flat surface case. Thus, adsorption capacity in porous media with different moisture

1 Predication (this work)

1

Experimental Data (this work)

0.8

0.6

nwet/ndry

nwet/ndry

0.8

0.4 0.2

Boulder shale (by Chalmers) Hulcross shale (by Chalmers)

0.6

Gates shale (by Chalmers)

0.4

0.2

0 0

1

2

3

4

5

0 0

0.2

0.4

0.6

0.8

1

Sw Fig. 23. Relationship between ratio of nad-wet/nad-dry and water coverage coefficient α (P = 6 MPa).

Fig. 25. Relationship between ratio of nad-wet/nad-dry and water saturation Sw (P = 6 MPa).

J. Li et al. / International Journal of Coal Geology 159 (2016) 135–154

depends on both adsorption transformation mechanism and water blocking mechanism. In our study, the relationship between methane adsorption capacity and water saturation Sw in Fig. 25 can be divided into three stages. (i) In the region from dry conditions to Sw approaching to 13.5% (RH ≈ 0.3), the methane adsorption capacity decreases linearly with increasing of Sw. In this stage, the thickness of clay bound water film is less than 0.4 nm and the coverage of water molecules is below monolayer. Thus, adsorption transition mechanism from methane adsorption on solid surface to adsorption on water film surface is dominating the methane adsorption capacity. (ii) In the region with Sw ranging from 13.5% to 40% (RH from 0.30 to 0.90), methane adsorption capacity is almost constant with varying Sw. It can be explained by water saturation distribution characteristics in Fig. 19. In this stage, the water molecules coverage is over monolayer while water saturation is less than 1, and methane can be completely adsorbed on gas-water interface while no pores are filled by water. Thus the water saturation has no effect on methane adsorption capacity in this stage. (iii) In the region that Sw ranges from 40% to 100% (RH from 0.90 to 0.99), the methane adsorption capacity is further reduced until all of the pore space is occupied by water. In this stage, pores width within 8.33 nm (at RH ≈ 0.99) will be gradually filled with capillary water and these pores blocked by water will lose capacity to adsorption methane. Thus, water blocking mechanism dominates the methane adsorption capacity in this stage. Therefore, the effect of water on methane adsorption in porous media is mainly dominated by two aspects: (i) transition of methane adsorption characteristics (from gas–solid interaction to the gas–liquid interaction); (ii) reduction of methane adsorption available surface area (several pores blocked by capillary water). In our experimental study with P = 6 MPa and RH = 0.98 (Sw ≈ 80%), total reduction of methane absorption capacity is approximately 90%, including about 65% caused by transition mechanism and nearly 25% caused by blocking mechanism. Additionally, the experimental data of methane adsorption on clay-rich shale under different moisture conditions in 6 MPa by Chalmers and Bustin (2010) are used to compare with the calculation results by our model. The comparison of calculation results and experimental results is shown in Fig. 25, and it presents a same trend between each other. Thus, our analysis is reasonable and available for the mechanism of water and methane competitive adsorption in shale inorganic mineral (such as clay). 6. Conclusion In this paper, we analyzed the thermodynamic equilibrium between water film and vapor in clay pores, and presented a mathematical model to quantify water films thickness bound on clay surface based on disjoining pressure. Then, we investigated the three-phase interaction characteristics between methane, water film and clay surface. It should be noted that, methane adsorption on clay (dry) is a typical gas–solid interaction; however, methane adsorption on clay bound water film should belong to gas–liquid interaction. Base on adsorption theory, an integrated model for methane absorbed on shale clay by considering the gas–liquid-solid interactions was established. In this model, the water coverage coefficient was defined to describe the transition between gas–solid adsorption and gas–liquid adsorption. Furthermore, instead of single pore, a method was given to analysis the characteristics of water saturation distribution and its effect on methane absorption in porous media. Thus, our model can be applied to predict methane absorption capacity under different water saturation condition in shale system with a real pore size distribution. According to this study, the following key conclusions can be obtained: (1) The water saturation in shale clay pore mainly depends on relative humidity and pore size. With the same relative humidity condition, the pore size is smaller, the water saturation is higher. Thus, under a certain shale humidity system, water saturation in

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pores with different sizes is significantly different. Meanwhile, a capillary condensation phenomenon is also found in our work. The pore size is smaller, the critical relative humidity for condensation is lower. For slit pore, condensation occurs in pores less than 8.33 nm when relative humidity approaches to 0.99. (2) Considering the condensation phenomenon, the water saturation in actual condition mainly exists in two forms: a) capillary water in the small pores or throats; b) water film of certain thickness in the lager pores. (3) The interaction characteristics between methane, water film and clay are revealed as flows: a) methane adsorption on clay (dry) should be described by gas–solid interface Langmuir adsorption equation, b) methane adsorption on water film should be described by gas–liquid interface Gibbs adsorption equation, c) gas–liquid-solid interaction should be described by equation integrating ‘gas–solid’ and ‘gas–liquid’ interactions. (4) Considering the water distribution characteristics in porous media, the effect of water on methane adsorption is mainly dominated by two aspects: a) the interaction characteristics for methane adsorption are changed by water film bounded on pore surface; b) the available surface area for methane adsorption is reduced by capillary water blocking pore space. However, note that the clay pores in shale is only assumed as slit shape in this work. The effects of pore structure and shape on both water film thickness and methane adsorption capacity are not investigated. Meanwhile, the clay swelling phenomenon which will lead to a change of pore structure and pore space is also need to be further considered. The water molecules adsorbed on functional group in organic (kerogen) pores are also neglected in this study. The general model for covering organic pores, inorganic pores, mineral content, pore size distribution, and pore structure will be developed in the future. Acknowledgments We acknowledge the National Natural Science Foundation Projects of China (51490654), and the National Science and Technology Major Projects of China (2016ZX05042 and 2016ZX05039) to provide research funding. We also acknowledge Key Laboratory of Petroleum Engineering at China University of Petroleum in Beijing (CUP) for providing the facilities to perform experiments in this work. Appendix A. Thermodynamic equilibrium between water film and vapor In this work, thermodynamic equilibrium process between water film and vapor is shown in Fig. A1. We assume that, the gaseous phase is only constituted by methane and vapor, and none water film is adsorbed on the solid surface at initial stage T1. Thus, the system in this period is thermodynamically unstable and water molecules (vapor) from gaseous phase will adsorb on solid surface. In the next period T2, gas–liquid-solid interactions become thermodynamically stable and the water film thickness increases by △h. Transition of water molecules from vapor in gas phase to water film in liquid phase can be regarded as an adsorption process. In this study, gas phase is simplified as mixture of vapor and methane. Thus, the adsorption potential for unit mol vapor transition into liquid film can be described by G-M binary gas adsorption model (Grant and Manes, 2002): Z Δμ 1 ¼

P0 Pv

RT Pv dP ¼ −RT ln P0 P

ðA:1Þ

152

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T1

T2 h

Water molecule

Gaseous phase (methane and vapor)

Liquid phase (water film)

Solid phase (clay)

Fig. A1. Thermodynamic equilibrium process of water-vapor-clay interaction.

Where, P0 is the saturated vapor pressure, MPa; Pv is the partial pressure of water vapor, MPa; PV/P0 is the relative humidity of gaseous phase, %; R is the gas constant, J/mol·K; T is the temperature, K. Meanwhile, this free energy change can be also described as the work of pressure deference between gas phase and water film, △u2, which is given by the sum of two contributions: a positive energy term caused by water pressure and a negative energy term caused by gas pressure. Δμ 2 ¼ P w  A  Δh−P g  A  Δh

ðA:2Þ

Where A is water film surface area, m2; Pg is gas pressure, MPa; Pw is water pressure, MPa; △h is the water film thickness, mm. The DLVO theory indicates that (Tadros, 2013), pressure in thin liquid films (thickness usually less than 100 nm) is different from the pressure in the bulk liquid, and this difference is caused by the action of additional forces referred to surface or colloidal forces. Thus, in the case of zero capillary pressure, such as a flat surface, the water films pressure is different from gas pressure as well as bulk liquid pressure. The pressure difference between water films and gaseous phase, called disjoining pressure, is given by P w −P g ¼ Π ðhÞ

ðA:3Þ

Where, Π(h) is water film disjoining pressure related to the water film thickness, MPa. Combined with Eqs. (A.2) and (A.3), the chemical potential △u2 can be described as Δμ 2 ¼ Π ðhÞ  A  Δh

ðA:4Þ

For unit mol vapor transition into unit mol water film, based on the material balance, the relationship between thickness △h and molar volume of liquid Vm can be described as: Δh ¼

Vm A

ðA:5Þ

Combined with Eqs. (A.4) and (A.5), thus Δμ 2 ¼ Π ðhÞ  V m

ðA:6Þ

Noted that both chemical potentials △μ1 and △μ2 describe the energy change for phase transition of unit mol water from gaseous phase to liquid phase (water film). The chemical potential △μ1 is based on the thermodynamic equilibrium while △μ2 is based on the mechanical equilibrium. Therefore, the chemical potential △μ1 equals to △μ2. Combined with Eqs. (A.1) and (A.6), the relationship between water film and relative humidity can be described as Π ðhÞ  V m ¼ −RT ln

Pv P0

ðA:7Þ

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Further reading Jagannathan, M., Sharma, M.M., Yortsos, Y.C., 2006. Flow-through drying of porous media. AICHE J. 52 (52), 2367–2380. Li, K.X., Wang, C., Yu, W., Chen, Z., 2015. Model for surface diffusion of adsorbed gas in nanopores of shale gas reservoirs. Ind. Eng. Chem. Res. 54 (12).