Study of factors affecting shale gas adsorption by simplified local density-Peng

Abstract

Shale gas has become an important source of natural gas, and a significant portion of gas in the reservoir exists in an adsorbed state. Thus, knowledge of gas adsorption behavior is important to estimate original gas in place and shale gas production. In this paper, shale gas adsorption affecting factors which include temperature, pressure, pore type, and diameters were studied quantitatively and systematically using simplified local density model. It was found that the main affecting factors were temperature, pore type, diameter, and pressure; type I kerogen has the lowest and type III kerogen has the largest excess adsorption gas capacity; due to the interaction energy between gas molecules and pore wall molecules, gas has the highest local density near the pore wall and the lowest density in the middle of the pore under a certain pressure and temperature; the increment of gas density as temperature decreases near the pore wall is significant, but the bulk methane gas density shows a very small change due to temperature change; the ratio of excess adsorption gas to free gas declines and its rate slows down as pressure increases; when the pore diameter increased from 1.5 to 5 nm, the ratio of excess adsorption gas to the total gas amount decreases rapidly; the excess adsorption gas of type III kerogen takes up 89% of the total gas amount with diameter of 1.5 nm and takes 70% of the total gas amount with diameter increases to 5 nm; the excess adsorption gas of type I kerogen takes 71% of the total gas amount with diameter of 1.5 nm and takes up 43% of the total gas amount with diameter increases to 5 nm. Local gas density in different kinds of pores under different conditions also provided a way to calculate gas transport in pores that take adsorption gas into consideration.

Keywords

Shale gas adsorption simplified local density-Peng–Robinson affecting factors kerogen

Introduction

Shale gas reservoir has become an important source of natural gas, and a significant portion of the gas in this reservoir exists in an adsorbed state. Thus, knowledge of gas adsorption behavior is important to estimate gas in place. Researchers all over the world have done many studies on shale gas adsorption characteristics and influence factors. Lu et al. (1995), who measured isothermal adsorption curves of Devonian shale samples by experiments, found that the amount of the adsorbed phase depended on the pressure and temperature. Chalmers and Bustin (2008) investigated the geological controls on methane sorption capacity for the Lower Cretaceous Buckinghorse Formation and equivalent strata in northeastern British Columbia and drew a conclusion that total organic content (TOC) was the most significant control on methane sorption capacity and other important factors included the kerogen type, maturity, and clay content, in particular, abundance of illite. Zhang et al. (2012) conducted a series of methane adsorption experiments on bulk organic-rich shale and their isolated kerogen at different temperatures and pressures and found that the total amount of methane adsorbed was directly proportional to the TOC and was related to kerogen type. Liming et al. (2012) studied the methane adsorption of clay rocks which is the main components of shale and the results show that clay mineral type greatly affects CH₄ sorption capacity under experimental conditions. All the obtained conclusions above were based on experiments qualitatively. In this paper, we study shale gas adsorption influence factors quantitatively and systematically using simplified local density (SLD) model, including temperature, pressure, pore type, diameters, and so on. The SLD model which was first developed by Rangarajan et al. (1995) can be used to describe the adsorption behavior of pure gases. It has been successfully used in several studies on gas adsorption on activated carbon and coal (Fitzgerald et al., 2003, 2006; Mohammad et al., 2011). Recently, it was used in shale gas adsorption (Chareonsuppanimit et al., 2012, 2015, 2016), and yet the conclusions were not systematically and quantitatively obtained.

Simplified local density adsorption model

The SLD model envisions the adsorbent to be composed of rectangular-shaped slits and the adsorbate molecules reside within these two surface slits (Figure 1).

Figure 1.

Slit pore of SLD model (Fitzgerald et al., 2003). SLD: simplified local density.

A molecule within a slit has interactions with both walls of the adsorbent slit. The SLD model accounts for both fluid–fluid and fluid–solid interactions in the slit-shaped pore. Several researchers have used different equations of state within the SLD framework (Chen et al., 1997; Soule et al., 2001; Yang and Lira, 2012), and the Peng–Robinson equation of state (PR EOS) is used in this study. At equilibrium, the chemical potential of the fluid μ is expressed as the sum of the fluid–fluid and fluid–solid potentials at a position “z” between the slit surfaces

μ (z) = μ_{ff} (z) + μ_{fs} (z) = μ_{bulk}

(1)

where subscript “bulk” refers to the bulk fluid and “ff” and “fs” refer to the fluid–fluid and fluid–solid interactions, respectively. The equation shows how the chemical potential of the adsorbed fluid reflects the proximity of the fluid to the molecular wall of the adsorbent. Thus, the SLD model considers the inhomogeneity of the adsorbed phase in describing the molecular interactions of the adsorbed fluid with the adsorbent. The chemical potential of the bulk fluid can be expressed in terms of fugacity as

μ_{bulk} = μ_{0} (T) + RT \ln (\frac{f_{bulk}}{f_{0}})

(2)

where subscript “0” designates an arbitrary reference state and “f” refers to fugacity. Similarly, the chemical potential from fluid–fluid interactions is given as

μ_{ff} (z) = μ_{0} (T) + RT \ln (\frac{f_{ff} (z)}{f_{0}})

(3)

where “f_ff(z)” is fluid fugacity at position z and “f₀” refers to the same arbitrary reference state as in equation (2). The fluid–solid interactions in the model are accounted for through a potential energy function. In particular, the fluid–solid potential is given as

μ_{fs} (z) = N_{a} [ψ^{fs} (z) + ψ^{fs} (L - z)]

(4)

where “N_a” is Avogadro’s number and “ψ(z)” and “ψ(L–z)” are the fluid–solid interactions for the two surfaces of a slit of length L.

Substituting equations (2), (3), and (4) into equation (1), the equilibrium relationship for adsorption within the slit is

f_{ff} (z) = f_{bulk} e^{(- \frac{ψ^{fs} (z) + ψ^{fs} (L - z)}{kT})}

(5)

where k is the Boltzmann’s constant. The fluid–solid interaction, ψ^fs(z), was represented by Lee’s partially integrated 10–4 potential

ψ^{fs} (z) = 4 π n ɛ_{fs} σ_{fs}^{2} (\frac{σ_{fs}^{10}}{5 (z + σ_{ss} / 2)^{10}} - \frac{1}{2} \sum_{i = 1}^{4} \frac{σ_{fs}^{4}}{(z + σ_{ss} / 2 + (i - 1) \cdot σ_{ss}) 4})

(6)

where ɛ_fs is the fluid–solid interaction energy parameter, and ρ_atoms = 0.382 atoms/Å². The parameters σ_ff and σ_ss signify, respectively, the molecular diameter of the adsorbate and the slit pore molecular interplanar distances. The fluid–solid molecular diameter σ_fs is defined as

σ_{fs} = \frac{σ_{ff} + σ_{ss}}{2}

(7)

Applying the SLD model, the excess adsorption (n^ex) is given as

n^{ex} = \frac{A}{2} \int_{x_{0}}^{x_{1}} (ρ (z) - ρ_{bulk}) d z

(8)

where n^ex is the excess adsorption of adsorbate in number of moles per unit mass of adsorbent and A is the surface area of the adsorbate on a particular solid. The lower limit in equation (8) is 1/2σ_ff, which is 1/2 of the diameter of an adsorbed molecule touching the left plane surface. The upper limit is L − 1/2σ_ff, the location of an adsorbed molecule touching the right plane surface. The local density is assumed to be zero for the distances less than 1/2σ_ff away from the wall. The left and right sides of the slit each comprise half of the total surface area, A/2. The PR EOS (Peng and Robinson, 1976) was used to calculate the bulk fluid density and fugacity. The EOS, expressed in terms of density, is given as

\frac{P}{ρ_{bulk} RT} = \frac{1}{(1 - ρ_{bulk} b)} - \frac{a (T) ρ_{bulk}}{RT [1 + (1 - \sqrt{2}) ρ_{bulk} b] [1 + (1 + \sqrt{2}) ρ_{bulk} b]}

(9)

where

a (T) = \frac{0.457535 α (T) R^{2} T_{c}^{2}}{p_{c}}

(10)

b = \frac{0.077796 {RT}_{C}}{p_{C}}

(11)

T_c and p_c refer to the critical fluid temperature and pressure, respectively. The term, α(T), in equation (12) was calculated using the following expression (Gasem et al., 2001)

α (T) = e^{((A + {BT}_{r}) (1 - T_{r}^{C + D ω + E ω^{2}}))}

(12)

where A, B, C, D, and E are correlation parameters and their values are 2.0, 0.8145, 0.134, 0.508, and −0.0467, respectively.

The fugacity of the bulk fluid using PR EOS is

\ln \frac{f_{bulk}}{p} = \frac{b ρ_{bulk}}{1 - b ρ_{bulk}} - \frac{a (T) ρ_{bulk}}{RT (1 + 2 b ρ_{bulk} - b^{2} ρ_{bulk}^{2})} - \ln [\frac{p}{RT ρ_{bulk}} - \frac{pb}{RT}] - \frac{a (T)}{2 \sqrt{2} bRT} \ln [\frac{1 + (1 + \sqrt{2}) ρ_{bulk} b}{1 + (1 - \sqrt{2}) ρ_{bulk} b}]

(13)

For the adsorbing fluid, the fugacity for fluid–fluid interactions is

\ln \frac{f_{ff} (z)}{p} = \frac{b ρ (z)}{1 - b ρ (z)} - \frac{a (z) ρ (z)}{RT (1 + 2 b ρ (z) - b^{2} ρ^{2} (z))} - \ln [\frac{p}{RT ρ (z)} - \frac{pb}{RT}] - \frac{a (z)}{2 \sqrt{2} bRT} \ln [\frac{1 + (1 + \sqrt{2}) ρ (z) b}{1 + (1 - \sqrt{2}) ρ (z) b}]

(14)

The parameter a(z) in equation (14) varies with the position within the slit. Chen et al. (1997) provided equations for a(z), which depends on the ratio of slit length L to the molecular diameter σ_ff as follows:

For L/σ_ff ≥ 3, a(z) is given by

\frac{a (z)}{a_{bulk}} = \frac{3}{8} [\frac{z}{σ_{ff}} + \frac{5}{6} - \frac{1}{3 (\frac{L - z}{σ_{ff}} - 0.5)^{3}}] for 0.5 \leq \frac{z}{σ_{ff}} \leq 1.5

(15)

\frac{a (z)}{a_{bulk}} = \frac{3}{8} [\frac{8}{3} - \frac{1}{3 (\frac{z}{σ_{ff}} - 0.5)^{3}} - \frac{1}{3 (\frac{L - z}{σ_{ff}} - 0.5)^{3}}] for 1.5 \leq \frac{z}{σ_{ff}} \leq \frac{L}{σ_{ff}} - 1.5

(16)

\frac{a (z)}{a_{bulk}} = \frac{3}{8} [\frac{L - z}{σ_{ff}} + \frac{5}{6} - \frac{1}{3 (\frac{L - z}{σ_{ff}} - 0.5)^{3}}] for \frac{L}{σ_{ff}} - 1.5 \leq \frac{z}{σ_{ff}} \leq \frac{L}{σ_{ff}} - 0.5

(17)

For 2 < L/σ_ff < 3, a(z) is given by

\frac{a (z)}{a_{bulk}} = \frac{3}{8} [\frac{z}{σ_{ff}} + \frac{5}{6} - \frac{1}{3 (\frac{L - z}{σ_{ff}} - 0.5)^{3}}] for 0.5 \leq \frac{z}{σ_{ff}} \leq \frac{L}{σ_{ff}} - 0.5

(18)

\frac{a (z)}{a_{bulk}} = \frac{3}{8} (\frac{L}{σ_{ff}} - 1) for \frac{L}{σ_{ff}} - 0.5 \leq \frac{z}{σ_{ff}} \leq 1.5

(19)

\frac{a (z)}{a_{bulk}} = \frac{3}{8} [\frac{L - z}{σ_{ff}} + \frac{5}{6} - \frac{1}{3 (\frac{L - z}{σ_{ff}} - 0.5)^{3}}] for 1.5 \leq \frac{z}{σ_{ff}} \leq \frac{L}{σ_{ff}} - 0.5

(20)

For 1.5 ≤ L/σ_ff ≤ 2, a(z) is given by

\frac{a (z)}{a_{bulk}} = \frac{3}{8} (\frac{L}{σ_{ff}} - 1)

(21)

For 1 ≤ L/σ_ff < 1.5, a(z) is given by

\frac{a (z)}{a_{bulk}} = \frac{3}{16}

(22)

And a_bulk is given by

a_{bulk} = \frac{27}{64} \frac{R^{2} T_{c}^{2}}{p_{c}}

(23)

Database employed for adsorption modeling over large temperature ranges

Gas mainly adsorbs in organic carbons and clay minerals of shale, and the organic carbons in shale are always in a state of kerogen. A database was compiled for methane adsorption on three kinds of kerogen and four kinds of clay minerals over significant temperature ranges. The experimental data come from literature. Table 1 provides details of the database used in this work. Table 2 provides the geochemical characteristics of three kinds of kerogen.

Table 1.

Database and SLD regression parameters for methane adsorption on kerogen and clay minerals.

Absorbent	Temperature (℃)	L (nm)	A (m²/g)	ɛ_fs/k (K)	Reference
Type I kerogen	35.4	1.15	300.0	29.8	Zhang et al. (2012)
	50.4	1.15	300.0	28.8	Zhang et al. (2012)
	65.4	1.15	300.0	27.8	Zhang et al. (2012)
Type II kerogen	35.4	1.15	300.0	38.7	Zhang et al. (2012)
	50.4	1.15	300.0	38.0	Zhang et al. (2012)
	65.4	1.15	300.0	35.0	Zhang et al. (2012)
Type III kerogen	35.4	2.00	300.0	50.2	Zhang et al. (2012)
	50.4	2.00	300.0	49.2	Zhang et al. (2012)
	65.4	2.00	300.0	47.2	Zhang et al. (2012)
Illite	35.0	1.20	25.0	50.0	Hartman et al. (2008)
Illite	50.0	1.20	25.0	47.0	Hartman et al. (2008)
Illite/smectite mixed	35.4	1.15	63.1	53.5	Liming et al. (2012)
	50.4	1.15	63.1	52.5	Liming et al. (2012)
	65.4	1.15	63.1	51.5	Liming et al. (2012)
Smectite	35.4	1.50	76.4	58.2	Liming et al. (2012)
	50.4	1.50	76.4	57.2	Liming et al. (2012)
	65.4	1.50	76.4	55.8	Liming et al. (2012)
Chlorite	35.4	1.15	22.0	42.6	Liming et al. (2012)
Chlorite	50.4	1.15	22.0	40.6	Liming et al. (2012)

Table 2.

Geochemical characteristics of three kinds of kerogen (Zhang et al., 2012).

Kerogen type	Type I	Type II	Type III
S1 (mg HC/g rock)	5.7	8.7	4.1
S2 (mg HC/g rock)	180.2	109.2	175.3
S3 (mg CO₂/g rock)	23.6	1.04	4.8
S2/S3	8	105	36
Tmax (℃)	440	430	429
Ro (%)	0.56c	0.58c	0.56c
HI	872	636	239
OI	114	6	7
PI	0.03	0.07	0.02

HI: hydrocarbon generation index; OI: oxygen index; PI: PI = S1/(S1 + S2).

The following methodology was used in this work:

The SLD model parameters (namely surface area, A; slit length, L; solid–fluid interaction energy, ɛ_fs/k) were first regressed to obtain precise representations of the adsorption data. For a given adsorbate/adsorbent pair, data at all temperatures were regressed to obtain the parameters.

The regressed values of ɛ_fs/k were then used to develop a generalized model to account for the influence of temperature on gas adsorption capacity.

The generalized values of ɛ_fs/k from the above step were then used in the SLD model to obtain predictions for the various temperature and pore diameters.

Results and discussion

SLD model representations for gas adsorption on kerogens and clay minerals

The SLD model was used to match gas adsorption data on several kerogens from the literature. Table 1 presents the model parameters for each of the experimental data used in this research. The regression results produced parameters that characterize adsorbent surface properties such as the surface area, effective pore width, and solid–fluid interaction energy. These regressed parameters were within the range as expected of kerogens and clay minerals. The regressed parameter ɛ_fs/k of each adsorbent shows a good linear relationship with temperature, which agrees with the conclusion of Nasehzadeh et al. (2002). Figures 2 and 3 illustrate the excessive adsorption of experimental data and SLD model results on kerogen and clay minerals, respectively. For three kinds of kerogen, type III has the highest adsorption capacity and type І has the lowest adsorption capacity. For the different kinds of clay minerals, the smectite has the highest adsorption capacity while the chlorite has the lowest adsorption capacity.

Figure 2.

SLD model representations of methane adsorption on: (a) type I kerogen, (b) type II kerogen, and (c) type III kerogen (points are data from Zhang et al. (2012)). SLD: simplified local density.

Figure 3.

(a) SLD model representations of methane adsorption on smectite (points are data from Liming et al. (2012)), (b). SLD model representations of methane adsorption on illite (points are data from Hartman et al. (2008)), (c) SLD model representations of methane adsorption on smectite/illite mixed (points are data from Liming et al. (2012)), and (d) SLD model representations of methane adsorption on chlorite (points are data from Liming et al. (2012)). SLD: simplified local density.

Impact of temperature on gas adsorption

Local molecular density in pores can be obtained by equation (14). The ratio of excess adsorption gas to free gas then can be given by

\frac{n^{exc}}{n^{free}} = \frac{\int_{x_{0}}^{x_{1}} (ρ (z) - ρ_{bulk}) d z}{\int_{x_{0}}^{x_{1}} ρ_{bulk} d z}

(24)

And the ratio of excess adsorption gas to total gas in a pore is given by

\frac{n^{exc}}{n^{total}} = \frac{\int_{x_{0}}^{x_{1}} (ρ (z) - ρ_{bulk}) d z}{\int_{x_{0}}^{x_{1}} ρ (z) d z}

(25)

Take type I kerogen for an example, the local gas density in a pore with diameter of 2 nm at a fixed pressure of 1 MPa under temperature of 35.4, 50.4, and 65.4℃, respectively, is given in Figure 4. It is shown that there is a peak density near the pore face. The local gas density in the middle of the pore is the lowest. The increment of density as temperature decreases near the pore face is significant, but the bulk gas density shows a very small change due to temperature change.

Figure 4.

Local gas densities of a 2 nm pore at a fixed pressure of 1 MPa under different temperatures.

Impact of pressure on gas adsorption

Figure 5 demonstrates the local gas density of various kerogen pores with a fixed diameter of 1.5 nm and a fixed temperature of 35.4℃ under different pressures. It is shown that the gas peak density and the bulk density increase as pressure increases. The ratio of excess adsorption gas to free gas using equation (24) is shown in Figure 6. It can be seen that in a specific pore the ratio declines and its rate slows down as pressure increases. It can be inferred that with the pressure increasing continuously the excess gas adsorption may reach a very low level and the gas in the pore can all be considered as free gas. Zuo et al. (2016) drew the same conclusion in their experiment. So using Langmuir equation to calculate excess gas adsorption of shale is not valid when the pressure is very high, and the gas-in-place calculation should also take this into consideration.

Figure 5.

Local gas density of pores at a fixed diameter of 1.5 nm and temperature of 35.4℃ under different pressure: (a) type I kerogen, (b) type II kerogen, and (c) type III kerogen.

Figure 6.

Ratio of excess adsorption gas to free gas under different pressures with a fixed diameter of 1.5 nm and a fixed temperature of 35.4℃.

Impact of pore type and diameter on gas adsorption

From Figures 2 and 3, it can be seen that the gas excess adsorption capacity varies with different kinds of matters by experimental data. Because type I kerogen and type III kerogen have the lowest and the largest excess gas adsorption capacity, respectively, the peak gas density of type I kerogen is the lowest and type III kerogen is the highest under the same condition when compared to the other two kinds of kerogens from Figure 5. The ratio of excess adsorption gas to free gas is also impacted by pore types too. From Figure 6 it can be seen that the type I kerogen has the lowest ratio and type III kerogen has the highest ratio under the same conditions of temperature, pressure, and pore diameter. And the ratio decline rate is the highest as the pressure of type III kerogen increases. Pore diameters also have a great impact on gas adsorption. Figure 7 illustrates the ratio of excess adsorption gas to free gas with various pore diameters under 35.4℃ and 4 MPa. The ratio of excess adsorption gas to free gas declines as pore diameter increases and pores of different types have different ratios under the same condition. The ratio of excess adsorption gas to total gas amount in different pores with different pore diameters calculated by equation (25) is shown in Figure 8. As is shown, when the pore diameter increased from 1.5 to 5 nm, the ratio of excess adsorption gas to the total gas amount decreases rapidly. The excess adsorption gas of type III kerogen takes up 89% of the total gas amount with diameter of 1.5 nm and takes 70% of the total gas amount with diameter increases to 5 nm, and the reduction ratio due to increase of pore diameter is 21%. The excess adsorption gas of type I kerogen takes 71% of the total gas amount with diameter of 1.5 nm and takes up 43% of the total gas amount with diameter increases to 5 nm, and the reduction ratio due to increase of pore diameter is 39%.

Figure 7.

Ratio of excess adsorption gas to free gas with various pore diameters under 35.4℃ and 4 MPa.

Figure 8.

Ratio of excess adsorption gas to total gas amount with various pore diameters under 35.4℃ and 4 MPa.

Conclusions

The experimental data from literature were regressed, and the SLD model parameters, surface area, slit length, and solid–fluid interaction energy were obtained. It was found that the SLD-PR method can well represent isothermal curves of kerogen and clay minerals. The solid–fluid interaction energy showed a linear relationship with temperature and it provided gas adsorption on kerogen and clay minerals over a wide range of temperature. The gas local densities in pores under different conditions were calculated by SLD method. The excess gas adsorption amount and free gas under different conditions were also calculated from gas local densities. It was found that the main factors that affected the shale adsorption gas were temperature, pore type and diameter, pressure, and clay content.

Footnotes

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: The authors wish to express their thanks to the Chinese government for funding this work (2011ZX05018-005).

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Study of factors affecting shale gas adsorption by simplified local density-Peng–Robinson method

Abstract

Keywords

Introduction

Simplified local density adsorption model

Database employed for adsorption modeling over large temperature ranges

Results and discussion

SLD model representations for gas adsorption on kerogens and clay minerals

Impact of temperature on gas adsorption

Impact of pressure on gas adsorption

Impact of pore type and diameter on gas adsorption

Conclusions

Footnotes

Declaration of conflicting interests

Funding

References