Sorption of Methane, Carbon Dioxide, and Their Mixtures on Shales

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Sorption of methane, carbon dioxide and their mixtures on shales from Sichuan Basin, China Rongrong Qi, Zhengfu Ning, Qing Wang, Yan Zeng, Liang Huang, Shuang Zhang, and Huaming Du Energy Fuels, Just Accepted Manuscript • DOI: 10.1021/acs.energyfuels.7b03429 • Publication Date (Web): 05 Feb 2018 Downloaded from http://pubs.acs.org on February 6, 2018

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Sorption of methane, carbon dioxide and their mixtures on shales from Sichuan Basin, China Rongrong Qi a,b*, Zhengfu Ning a,b, Qing Wang a,b, Yan Zeng a,b, Liang Huang a,b, Shuang Zhang b, Huaming Du a,b a

b

State Key Laboratory of Petroleum Resources and Prospecting in China University of Petroleum, Beijing, P. R. China

Ministry of Education Key Laboratory of Petroleum Engineering in China University of Petroleum, Beijing, P. R. China

Abstract: High pressure sorption isotherms of pure CH4 and CO2 at 80 ℃ and CH4 / CO2 mixtures at 30 and 80 ℃ on shale samples from Sichuan Basin, China, were measured by a modified volumetric method. The multicomponent sorption measurements were

conducted on the mixtures with feed gas compositions of 79.50 % and 48.62 % CH 4. The sorption isotherms of pure CH4 and CO2 were fitted by a modified Langmuir equation, and the sorption isotherms of the total and individual component of CH4 / CO2 mixtures were fitted by an Extended Langmuir (EL) equation. Qualitative and quantitative characterizations of selective sorption of

CH4 and CO2 were discussed at different temperatures and gas compositions. The results indicate that the sorption capacity of pure CO2 is larger than that of pure CH4, with the Langmuir sorption capacity of pure CO2 being approximately 2.5 times of pure CH4. However, higher sorption amount of CH4 than CO2 is obtained in competitive sorption of mixed gas with feed gas composition of 79.50 % CH4, suggesting that sorption behavior of individual component under competitive condition depends not only on the sorption affinity of the component, but also on the partial pressure of the component in the mixture. The separation factors calculated from multicomponent sorption data are in a range of 1.0 – 2.5, which are far less than that calculated from single gas sorption data,

indicating that the presence of CH4 greatly weakens the preferential sorption of CO2. On the contrary, increasing temperature and CO2 content in the mixture will promote preferential sorption of CO2. Key Words: Methane; Carbon dioxide; Sorption; Selectivity; Mixture gas

1. INTRODUCTION The growing interest in shale gas as an important unconventional energy resource during the past decades has led to increased exploration and production activities and has stimulated considerable research interest 1. Since a large proportion of gas in shale, approximately 20 - 85 % in some U.S. shale basins 2, 3, is in an adsorbed state, knowledge of sorption behavior is required to meet the need of resource assessment and exploitation 4. Much investigate effort had been undertaken to measure sorption isotherms of single

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Page 2 of 32

CH4 and CO2 on shales with different total organic carbon (TOC) content, thermal maturity, organic matter type, clay minerals and pore structure

1, 5-11

micropore volume

. The main results indicated that sorption capacity of shales had a positive relationship with TOC content and

5-7, 9, 12

. Clay minerals had a contribution to CH4 sorption in shales lacking organic matter

CO2 was always greater than that of CH4, and the former was 1.9 - 6.9 times of the latter

13

. Sorption amount of

4, 14-16

. CH4 displacement by injected CO2

looks plausible during CO2-enhanced shale gas recovery. However, the feasibility should be confirmed by multicomponent sorption measurements since the CO2-enhanced shale gas recovery depends on the relative affinity of CO2 and CH4 in their mixture 17, 18. Also, the mechanism of CO2 injection to increase CH4 gas recovery, either by lowering the CH4 partial pressure, or by competitive sorption, should be studied in the competitive sorption state. Thus, sorption measurements of the mixed gas will be the basic for the feasibility

studies of the CO2-enhanced shale gas recovery, and will have certain guiding significance for future injection strategies. The main findings on competitive sorption can be summarized as follows: The total sorption amount of CO2 / CH4 mixtures ranged between pure CH4 and CO2

19

, and increased with an increase of CO2 concentration in the feed gas

20

. Distinct variations

existed in preferential sorption behaviors depending on sample properties, moisture, pressure and temperature conditions, ranging

from preferential sorption of CH4 in the low pressure range and preferential sorption of CO2 over the entire pressure range Samples contained more micropores may denote the highest degree of preferential sorption of CO2

15, 20-24

.

15

. Temperature and moisture

tended to reduce the selective sorption of CO2 at low pressures (< 4MPa) 24. Preferential sorption of CO2 appeared to get weaker with increasing pressure 20. In terms of the above studies, preferential sorption of CO2 compared to CH4 was the most frequently published. However, Busch observed preferential sorption of CH4 at lower pressures in his series of studies 21-23, but failed to give explanations for this phenomenon. Selectivity factors were calculated to characterize the relative sorption affinity of CH4 and CO2 25, 26. However, most of these factors were obtained from single component sorption data. Selectivity factors obtained from competitive sorption and

their comparisons with the factors calculated from single component sorption were not yet systematically studied on shales.

The heterogeneous nature and hierarchical pore structures of the shales made the representation of competitive sorption

phenomena in these systems quite difficult

27

. Data for the mixture gas adsorption were not as much available as pure gas. Thus,


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studies on competitive sorption tended to be based on single gas sorption experiments. Much effort had been undertaken to describe 28

multicomponent gas sorption from pure component isotherm data by certain models in earlier studies. The EL

most commonly used due to its simplicity and low computational cost

equation was the

29-32

. The applicability of the model to shale still required

systematic single and multicomponent experiments to confirm.

The focus of this work was to study the competitive sorption of CH 4 and CO2. Sorption measurements of CH4, CO2 and their mixtures were carried out using a volumetric method. EL equation was applied to fit the measured sorption isotherms of the mixtures.

Effect of temperature, pressure and shale composition on preferential sorption of CH 4 and CO2 was discussed. Separation factors under competitive and noncompetitive conditions were calculated as a function of pressure to quantitatively characterize selective

sorption. This study was expected to extend the small existing data for competitive sorption on shales and provide a basic for the

feasibility studies of the CO2-enhanced shale gas recovery.

2. EXPERIMENTAL SECTION 2.1. Samples Three shale samples were obtained from Changning County of Sichuan Basin, China. The Sichuan Basin, located in the southwest of China, is a prolific hydrocarbon region and is currently China’s largest gas-producing region

33

. Four sets of main

hydrocarbon source rocks, which were Lower Cambrian marine shale, Upper Ordovician–Lower Silurian marine shale, Lower

Permian marine carbonate source rocks, and Upper Permian coal-bearing mudstone, had developed in the basin

34

. The samples

studied in our work were outcrops collected from the Wufeng-Longmaxi Formation of the Upper Ordovician–Lower Silurian age.

Detailed information on the stratigraphy, geology, and petroleum potential of these shales can be obtained in Refs.

33-35

.

2.2. Characterization of the Shale Sample The compositions of shale samples were characterized first before sorption measurements. All samples were ground to powder

and then assessed experimentally using X-ray diffraction (XRD) analysis and total organic carbon (TOC) content tests. The experimental details were described in Ref. 36.


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The pore structures of samples were characterized by liquid N2 adsorption experiment at 77 K. The experiment was conducted on an ASAP2460 Surface and Pore Size Analyzer basing on the standard static volumetric method. About 8 g powdered samples were outgassed at 110 ℃ for 10 h under a vacuum of 5 μmHg to remove the bound and capillary water adsorbed in the clays. The

BET specific surface area (BET SSA) was calculated at a relative pressure (p/p0) range of 0.05-0.30. The total pore volumes (TPV) of the samples were calculated by the adsorption capacity of liquid nitrogen at p/p0 ~ 1, according to Gurvich's rule 36. The average pore diameters (APD) were obtained from BET SSA and TPV calculated above.

2.3. Measurement of High Pressure Sorption Isotherms 2.3.1. Sorption Equipment A volumetric sorption equipment shown in Figure 1 was applied to study the sorption behavior of single and multi-component

sorption in this paper. The device mainly comprised a reference cell (RC), a sample cell (SC), and an intermediate zone (MZ)

between the two cells. Both RC and SC were made of stainless steel, and equipped with high precision pressure transducers with an accuracy of 0.03 % (PAA-35XHTT provided by Keller, max pressure 40 MPa, temperature range -20 - 150 ℃). MZ was composed of pipelines (1/8’’) between valve 2 (V2), valve 3 (V3) and valve 4 (V4). The RC, SC and MZ were placed in an oil bath to keep temperature constant, and an immersion temperature detector with an accuracy of 0.1 ℃ (provided by Omega, PT100, temperature range -20 - 150 ℃) was used to determine the temperature of the experiment system. A gas chromatograph (GC) was employed to

analyze the composition of the mixtures during the multicomponent sorption.

Figure 1. Scheme of high-pressure gas sorption set-up.


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The reference volume (Vref), sample volume (Vsam), intermediate volume (Vmid) and void volume (Vvoid) were respectively defined as follows: Vref consisted of the volume of RC, the pipeline volume between V1 and V2 and the dead volume of the pressure transducer; Vsam was the sum of the volume of SC, MZ and dead space of pressure transducer; Vmid referred to the pipeline volume between V2, V3 and V4; Vvoid referred to the volume not occupied by the sample frame in the sample volume. Vref and Vsam were determined by helium expansion using stainless steel balls of known volume as a reference1. The helium, which was an inert gas, was

supposed to be no-sorbing in this paper

1, 11

. Conduct the helium expansion experiment at 30 ℃ and at the pressure range of 0 – 10

MPa, according to the law of conservation of mass, there was, H injH Vref  equ (Vref  Vsam  V ) e

(1)

e

Convert the equation above to the form as y = kx + b, there was,

V =

H H equ  inj Vref  Vsam H equ e

e

(2)

e

He are the helium densities refer to injection pressure of RC and equilibrium pressure after RC and SC Where, injHe and equ

connected, kg/m3;

V is

the volume of the stainless steel ball, cm3. Change the number of the balls (i.e. change

V )

and repeat

helium expansion experiment three times, Vref and Vsam can be respectively obtained by the slope k and intercept b of the fitting curve of equation (2). He was the helium The measurement processes of Vmid and Vvoid were similar to that of the Vref and Vsam. In determining Vmid, equ

density at equilibrium pressure after RC and MZ connected, that is, H injH Vref  equ (Vref  Vmid ) e

e

(3)

In the determination of Vvoid, stainless steel balls were replaced by shale powder, that is, H injH Vref  equ (Vref  Vvoid ) e

e

The determined Vref, Vsam and Vmid were 159.15 cm3, 306.71 cm3 and 5.33 cm3, respectively.

2.3.2. Sorption Measurements Samples were first crushed to finer than 100 mesh (0.15 mm) and dried at 110 °C overnight. Then the powered rocks were


(4)

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placed in the sample cell, and kept drying for 4 hours at 110 °C in the oil bath to remove the moisture from the air during sample

loading. A degassing process with a vacuum pump evacuating for 1 h was needed before the apparatus was ready for sorption

experiments. (1) Single Component Sorption High pressure gas was charged into the RC, and was then transferred gradually from RC to SC. RC and SC remained

disconnected throughout the measurements. The sorption capacity (nads) was measured by the difference between the amount of gas transferred into the SC (ntrans) and the unabsorbed gas (nunadsorbed) in the void volume:

nads  ntrans  nunadsorbed  ntotal  nresidual  nunadsorbed  ( injVref  ref Vref  equVvoid ) / Mm

(5)

Where ntotal stands for the total amount of gas injected to the RC, mmol/g; nresidual refers to the amount of gas residual in the RC, mmol/g; ρinj, ρref and ρequ are the densities of the gas injected to the RC, the gas residual in the RC and the gas in the void volume respectively, kg/m3; Vref, Vvoid are the reference volume and void volume respectively, cm3. M is the molar mass of gas, g/mol; m is the mass of the sample loaded in sample cell, g. (2) Multi-component Sorption The sorption procedure of multi-component was roughly the same as the single component. The sorption capacity of component

i (nads(i)) in the mixture was given as follows:

nads (i )  ntrans zi  nunadsorced yi  (ntotal  nresidual ) zi  nunadsorbed yi

(6)

nresidual   ref Vref / M z m

(7)

nunadsorbed  equVvoid / M y m

(8)

Where

Of which, zi and yi are the mole fractions of the component i in feed gas and free gas, respectively; Mz and My, which refer to the mixed gas molar masses of the feed gas and free gas, were calculated with the molar masses of the single component: NC

M z   zi M i i 1


(9)

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NC

M y   yi M i

(10)

i 1

Where Mi is the molar mass of component i, g/mol; NC is the number of the components. Since the sorption capacities of individual component in the mixtures were different, gas compositions were constantly changing

during sorption process. Therefore, compositions of the mixed gases were required to retest at each sorption equilibrium point. The

gas sample used for composition measurements (nreduc) was taken from MZ:

nreduc  equVmid / M y m

(11)

The total amount of gas in the system continued to reduce due to the sampling from MZ. Thus, the total amount of gas at the nth

sorption equilibrium was calculated as following: n

n 0 ntotal  ntotal   nreduc ( j )

(12)

j 1

Where, j refers to the number of sampling; the original total amount of gas was calculated as follows: 0 ntotal  injVref / M z m

(13)

2.3.3. Error Analysis The physical quantities in the sorption experiments can be divided into measured and calculated quantities. The measured

quantities, such as temperature, pressure, mass and gas molar composition, can be directly measured from the experiment; while the

calculated quantities, such as the gas density and adsorption capacity, are calculated from a set of measured quantities through a

certain function. The uncertainty of measured quantities can be determined by the accuracy of the instrument or by repeating

experiments several times, and the uncertainty of calculated quantities can be obtained basing on the multivariate error propagation

theory

37

. That is, for a given quantity y, which is calculated from a set of individual measured quantities (x1, x2,..., xNV), the

uncertainty  y can be expressed as follows:

 y 2 2  )  xi  i 1  xi 

NV

 y2   ( Where, NV is the number of the individual measured quantities;

 x is the standard deviation of the measured quantity xi. i

(1) Error in the Measured Quantities


(14)

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Calibrations were performed before the sorption experiment. The temperature transducers were calibrated against a platinum

resistance reference thermometer provided by Minco and the pressure transducers were calibrated against an automatic pressure

calibrator provided by Mensor. The GC was calibrated against standard gas sample at feed gas concentrations. After calibration the uncertainties of the measured quantities were set as follows: temperature, 0.1 ℃; pressure, 0.012 MPa; mass of sample, 0.0001 g,

which can be ignored for its value is too small. The uncertainties of the mixture-gas composition and volumes (Vref, Vsam, Vmid, Vvoid) were determined by repeating the experiments several times and finding the standard deviation. The uncertainties of the mixture-gas composition and volumes are listed as follows: composition of the mixed gas, 0.0005 mole fraction; volumes, 0.01 cm3.

(2) Error in the Calculated Quantities

Calculated quantities in this paper include density and sorption amount. Among them, the density can be expressed as follows: =

p ZRT

(15)

Where, Z is the gas compression factor.

Based on the error propagation theory, the error of the density can be expressed as follows: 2

   2    2    2  p   T    Z  T   Z   p  2

2

 2 = 

2

(16)

 1 1 Z  2 1 Z  2 2 1 2 1  2  2    p     T      Z  T Z T  Z  p Z p  2

2

Where, the error of the compression factor can be obtained by accurate equations of state under certain temperature and pressure

for single component gas and under certain temperature, pressure and molar composition for the mixed gas.

According to the formula (5), the error of the pure component sorption capacity was expressed as following：  nads    inj

 n2   ads

2

 2  n   inj   ads    ref

2

 2  n   ref   ads   equ

2

 2  n   equ   ads   Vref

2

 2  n  2   Vref   ads   Vvoid  Vvoid   2

(17)

2 V  V     ref  2  equ  2 V  =  ref   2inj   ref   2ref   void   2equ   inj   Vref     Vvoid Mm Mm Mm Mm          Mm  2

2

2

2

According to the formula (6) - (13), the error of sorption capacity of component i in the mixed gas can be calculated： 2



2 nads ( i )



2

2

2

2

 n   n   n   nads (i )  2  nads (i )  2   ads (i )   n2total   ads (i )   n2residual   ads (i )   z2i     nunadsorbed     yi  ntotal   nresidual   zi   nunadsorbed   yi 



2  zi2  n2total   n2residual   ntotal  nresidual   z2i  yi2 n2unadsorbed  nunadsorbed  y2i 2


(18)

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Here， 2

2

n  n 0   n 0   n 0    n20    n2reduc ( j )   total   2inj   total   V2ref   total   M2 z     V  total j 1  M z   inj   ref  2 2 2  n  n   n   n     reduc ( j )   2equ ( j )   reduc ( j )   V2mid   reduc ( j )   M2 y       j 1   equ ( j )   Vmid   M y    2 2 2 2 2  n V     V  V      V  =  ref   2inj   inj   V2ref   inj 2 ref   M2 z    mid   2equ ( j )   equ ( j )   V2mid   equ ( j2) mid   M m  M m j 1  M y m  y y  M zm   M zm   Mz m      2

 n2

total

 n2

residual

 n   residual   ref 

2

2

 2  n   ref   residual   Vref

(19)

2  2    M y    

 2  n  2   Vref   residual   M z  M  z   2

(20)

 V      V    ref   2ref   ref   V2ref   ref 2 ref   M2 z  M zm   M zm   Mz m  2

 n2

unadsorbed

2

 n   unadsorbed   equ 

2

2

 2  n  n  2   equ   unadsorbed   Vvoid   unadsorbed  Vvoid    M y

2

2

2

V      V   void   2equ   equ   V2void   equ 2 void M m M m  M m y  y   y   NC

2

 2   M y 

2

 2   M y  NC

 M2    M i2 z2  zi2 M2    M i2 z2 z

i 1

i

i

NC

NC

i 1

i

i

i 1

i

In the equations of (22) and (23), the errors of molar masses were assumed to zero and the mole fraction errors of component i in the feed (  z ) and free gas (  y ) were equal to the uncertainties of the mixture-gas composition. i

i

(3) Error Analysis Results The error analysis results are presented in Table 1. The average uncertainties are 5.04 % – 6.26 % (0.0024 – 0.0026 mmol/g) for pure CH4 sorption measurements and 6.95 % - 8.72 % (0.0076 – 0.0082 mmol/g) for pure CO2 sorption measurements. The higher uncertainties for CO2 sorption may be due to the higher uncertainty in the CO2 compressibility factor, especially in the supercritical area. In general, the uncertainties for total gas are smaller than that for individual components in the multicomponent sorption measurements (except for mixture with 79.50 % CH4 at 80 ℃). The uncertainty for the sorption of individual component with stronger sorption affinity is lower than that with weaker sorption affinity, regardless of the composition of the feed gas.


(22)

i

i 1

 M2    M i2 y2  yi2 M2    M i2 y2 y

(21)

(23)

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Page 10 of 32

Table 1. Expected uncertainties in the single and multicomponent sorption measurements Mixture System

a

CH4

σ

%σ

a

Feed gas composition (%)

CO2

σ

b

%σ

a

σ

b

% σb

a

1

2

3

1

2

3

1

2

3

1

2

3

1

2

3

1

2

3

Pure CH4 (80 ℃)

\

\

\

\

\

\

\

0.0024

0.0026

0.0026

5.82

5.04

6.26

\

\

\

\

\

\

Pure CO2 (80 ℃)

\

\

\

\

\

\

\

\

\

\

\

\

\

0.0082

0.0076

0.0078

8.16

6.95

8.72

CH4/CO2 (30 ℃)

79.50 / 20.50

0.0065

0.0072

0.0067

7.79

7.71

7.15

0.0063

0.0069

0.0064

9.76

9.62

8.98

0.0017

0.0019

0.0017

9.06

8.72

8.16

CH4/CO2 (80 ℃)

79.50 / 20.50

0.0047

0.0048

0.0051

7.40

6.33

7.16

0.0045

0.0046

0.0049

10.53

9.17

10.11

0.0013

0.0013

0.0014

6.52

5.89

4.13

CH4/CO2 (30 ℃)

48.62 / 51.38

0.0068

0.0074

0.0071

7.24

8.00

6.93

0.0047

0.0051

0.0049

10.72

10.58

10.53

0.0049

0.0054

0.0052

8.63

9.68

8.67

σ is the average absolute uncertainty (mmol/g); b % σ is the average absolute percent uncertainty.


Page 11 of 32 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

2.4. Density Calculations The densities of the pure and mixed gases mentioned above were calculated from the NIST Standard Reference Database 23, using the REFPROP Version 9.0 software 38.

3. Results and Discussions 3.1. Characterizations of the Shale 3.1.1. Composition Analysis TOC content and mineral compositions of the shales are presented in Table 2. The TOC content of the shale samples ranged between

2.28 and 3.61 wt. % with an average value of 3.07 wt. %. The mineral compositions of the samples were mainly clay minerals, detrital

minerals (mainly quartz and feldspar) and authigenic minerals (mainly carbonate and pyrite). The clay minerals, which had a certain

contribution to the gas sorption, had a moderate content between 15.7 and 27.4 wt. %. All montmorillonite in clay minerals were

transformed into illite, and the relative content of illite were close to 100 wt. %.

3.1.2. Pore Structure Figure 2a shows the adsorption-desorption isotherms of N2 at 77 K. The isotherms are of type IV according to IUPAC classification 39

. Type IV isotherms are characterized by monolayer sorption or pore filling at low pressures, multilayer sorption at moderate pressures

and capillary condensation at high pressures 36. At the relative pressure of about 0.4, the desorption curve deviates from the sorption curve and a hysteresis loop is formed. The type of the hysteresis loop is H3 39, which indicating slit-shaped pores. The characteristic pore structure parameters of the shale samples are shown in Table 2. The BET SSA ranges between 13.86 – 19.12 m2/g, and the TPV is in a range of 0.016 – 0.026 cm3/g. Both the BET SSA and the TPV are positively corrected with TOC content, indicating that the BET SSA and the TPV of shales are mainly provided by organic matter. The APD ranges between 4.72 – 5.56 nm and

has no relationship with TOC content.

The pore size distributions of shale samples calculated from N2 adsorption branch by Barrett–Joyner–Halenda (BJH) method are shown in Figure 2b. Pore size distributions obtained from N2 desorption branch tend to show a false peak around 4 nm. The peak is caused by the Tensile Strength Effect (TSE) 40, and is primarily determined by the nature of the adsorbent rather than pore characteristics


Energy & Fuels

of the material

36

. The pore sizes of the samples show wide distribution from micropore, mesopore to macropore, of which micro- and

meso- pores account for the majority. As the TOC content increases, the distribution of micropores increases, further indicating that

micropores are mainly provided by organic matter.

Table 2. Compositions and pore structures of the shale samples. Relative content of clay

Pore structure

XRD minerals (%)

TOC Sample

Formation (wt.%)

Quartz+feldspar

Carbonates+pyrite

Total clays

BET SSA Illite

(wt.%)

(wt.%)

(wt.%)

1

Wufeng

2.28

72.6

/

27.4

2

Longmaxi

3.31

55.4

27.4

3

Longmaxi

3.61

41.7

42.6

16 14

Chlorite

TPV

APD

2

3

(m /g)

(cm /g)

(nm)

2

6

13.86

0.016

4.72

17.2

94

/

6

14.19

0.020

5.56

15.7

100

/

/

19.12

0.026

5.44

0.0035

1 2 3

1 2 3

0.0030 0.0025

dV/dD (cm3/g/nm)

12 10 8 6 4

0.0020 0.0015 0.0010 0.0005

2 0 0.0

Kaolinite

92

18

Adsorbed amount (cm3/g)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 12 of 32

0.2

0.4

0.6

0.8

1.0

0.0000 1

Relative pressure (p/p0)

10

100

1000

Pore diameter (nm)

(a)

(b)

Figure 2. (a) Low-pressure N2 adsorption-desorption isotherms and (b) pore size distributions of shale samples calculated from the adsorption branch of N2 isotherms by BJH method.

3.2. Single Component Sorption Sorption measurements of single CH4 up to 20 MPa and CO2 up to 15 MPa on shale samples were carried out at 80 °C. To verify the repeatability of the measurements, sorption tests were conducted on the same sample successively twice (run 1 and run 2) in the same

experiment condition. The results are shown in Figure 3. From the Figure we can see that the isotherms of the two runs were almost

overlapped.


Page 13 of 32

0.09 0.08

Excess sorption (mmol/g)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

0.07 0.06

Run 1 Run 2

0.05 0.04 0.03 0.02 0.01 0.00 0

2

4

6

8

10

12

14

16

18

20

22

Pressure (MPa)

Figure 3. Repeated sorption experiments of CH4 on sample 2 at 50 ℃ The excess sorption isotherms of single CH4 and CO2 and their fitting results obtained by a modified Langmuir equation (equation (24)) are presented in Figure 4 and Table 3. All excess sorption isotherms exhibit maxima, and show a slight decrease for CH 4 and dramatic decrease for CO2 at higher pressures (Figure 4). The maxima have no relationship with TOC content (Table 3). Pressures corresponding to the sorption maxima are higher for CH4 than CO2 (Table 3, CH4: 10.68 - 15.19 MPa, CO2: 7.99 - 8.93 MPa). Actually, gases with higher sorption affinity tend to reach sorption saturation more quickly, and therefore have smaller pressures corresponding to

sorption maxima.

nads  nL

 gas p (1  ) ads p  pL

(24)

Where, nL is the Langmuir maximum sorption, mmol/g; pL is the Langmuir pressure, MPa; p is the equilibrium pressure, MPa; ρads and ρgas are the densities of the adsorbed and free gases, respectively, kg/cm3. As a comparison, both Langmuir 3-parameter (nL, pL, ρads) and 2-parameter (nL, pL) equations were applied to fit the isotherms. In Langmuir 2-parameter equations, the adsorbed phase densities of CH4 were employed to be 421 kg/m3 (liquid density at boiling-point 41) and CO2 adsorbed phase densities were obtained by graphical estimate of the excess sorption isotherms

41

(Figure 5). The fitting results

are evaluated by average absolute deviations (%AAD) 30:

 n

NPTS

% AAD=100

k 1

c ads , k

e e  nads , k  / nads ,k

(25)

NPTS

e c and nads are the calculated and experimental sorption capacities for the kth sorption equilibrium, mmol/g; NPTS is Where, nads ,k ,k


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Page 14 of 32

the sorption equilibrium point.

Generally, the Langmuir 3-parameter equations fit sorption data well, with %AAD within 5 % (Table 3, Figure 4). Whereas, the

Langmuir 2-parameter equations fail to fit part of the data with %AAD exceeding 5 % (e.g. CH4 sorption at sample 1 and CO2 sorption at sample 2 and 3). Thus, the fitting results of the Langmuir 3-parameter equations are chosen for subsequent discussion. When the adsorbed density is assumed as a fitting parameter, nL is 0.134 – 0.146 mmol/g for CH4 and 0.339 – 0.371 mmol/g for CO2. These values were compared with the data reported in the literatures normalized to TOC content, and turned out to be in a reasonable range (Figure 6).

Samples with larger Langmuir sorption capacity have higher adsorbed phase density and lower Langmuir pressure. No relationship

between nL and TOC content is observed in the study, indicating that inorganic matter may contribute to the sorption capacity of shale with lower TOC content.


Page 15 of 32 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46

Energy & Fuels

Table 3. Experimental and fitting results of single CH4 and CO2 at 80 °C. Sample

CH4 isotherm at 80 °C

Langmuir 3-parameters


nmax (mmol/g)

Pressure at nmax (mmol/g)

nL (mmol/g)

pL(MPa)

ρads (kg/m )

%AAD

nL (mmol/g)

pL(MPa)

ρads (kg/m3)

%AAD

1

0.059

10.68

0.141

7.68

327

4.03

0.109

5.52

421

5.68

2

0.073

14.44

0.146

6.73

365

1.07

0.133

5.82

421

0.71

3

0.059

15.19

0.134

7.88

311

2.41

0.108

5.85

421

1.14

Sample

CO2 isotherm at 80 °C

3


Langmuir 2-parameters 3

nmax (mmol/g)

Pressure at nmax (mmol/g)

nL (mmol/g)

pL (MPa)

ρads (kg/m )

%AAD

nL (mmol/g)

pL (MPa)

ρads (kg/m3)

%AAD

1

0.152

8.93

0.365

7.09

681

4.79

0.279

4.82

908

4.03

2

0.156

7.99

0.371

6.72

694

4.55

0.291

5.05

997

6.46

3

0.139

8.48

0.339

7.21

652

4.16

0.249

4.28

787

5.60


Energy & Fuels

0.07

0.18

CH4



0.05 0.04 0.03

Sample 1 3-parameter 2-parameter

0.02

CO2

0.16

0.06

0.01

0.14 0.12 0.10 0.08


0.06 0.04 0.02 0.00

0.00 0

2

4

6

8

10

12

14

16

18

20

22

0

24

2

4

6

(a)

10

12

14

16

(d) 0.18

0.09

CH4

0.08 0.07 0.06 0.05


0.04 0.03

CO2

0.16



8

Pressure (MPa)

Pressure (MPa)

0.02 0.01

0.14 0.12 0.10 0.08


0.06 0.04 0.02

0.00 0

2

4

6

8

10

12

14

16

18

20

0.00

22

0

2

4

Pressure (MPa)

6

8

10

12

14

16

Pressure (MPa)

(b)

(e)

0.07

0.16

CH4

CO2

0.14


0.06


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 16 of 32

0.05 0.04 0.03


0.02 0.01

0.12 0.10 0.08


0.06 0.04 0.02 0.00

0.00 0

2

4

6

8

10

12

14

16

18

20

0

2

4

6

8

10

12

Pressure (MPa)

Pressure (MPa)

(c)

(f)

Figure 4. Sorption isotherms and fitting results of single CH4 (a, b and c) and CO2 (d, e and f) at 80 °C.


14

16

Page 17 of 32

0.18

0.18

Sample 2

Sample 1

Linear Region

Linear Region 0.15



0.15

0.12

0.09

0.06

0.03

908

0.12

0.09

0.06

997

0.03

0.00

0.00 0

100

200

300

400

500

600

700

800

900

0

1000

100

200

300

400

500

600

700

800

900 1000 1100

Gas density (kg/m3)

Gas density (kg/m3)

(a)

(b)

0.16


Sample 3

Linear Region

0.14 0.12 0.10 0.08 0.06 0.04

787 0.02 0.00 0

100

200

300

400

500

600

700

800

900

Gas density (kg/m3)

(c) Figure 5. Graphical method for estimating the adsorbed phase density: sorption isotherms of CO2 at 80 ℃. 60

12

CO2

CH4 10

Sorption capacity (mmol/g TOC)

Sorption capacity (mmol/g TOC)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

8

6

4

2

0

50

40

30

20

10

0 Data1

Data2

Data3

Data4

Data5

Data6 This study

Data1

Data3

Data source

Data4

Data7

This study

Data source

(a)

(b)

Figure 6. Comparisons between the single gas sorption data of this study and the literatures: data 1 is the maximum sorption amount calculated by Dubinin–Asthakov (DA) model 15; data 2 36, data 3 16, data 4 14, data 5 42, data 6


11

and data 7

43

are Langmuir maximum

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Page 18 of 32

sorption; the sorption amount units of data 4, 5, 7 are converted from scf/t to mmol/g using an equation of 1mmol/g=834.7 scf/t

36

; all

sorption amounts are expressed as a function of TOC .

As can be seen from Figure 4, both CH4 and CO2 excess sorption isotherms exhibit maximum. Li et al. attributed this phenomenon to the change of the ratios of gas phase density to adsorbed density (ρgas / ρads)

44

. The sorption capacity measured in the experiments is

excess sorption (nex), while what make sense in practice is absolute sorption (nabs), the relationship between the two is as follows:

   nex  nabs 1  gas   ads 

(26)

At low pressures (low gas phase densities) the density ratios are negligible and the excess sorption capacity is approximately equal to

the absolute sorption; while at higher pressures, especially at supercritical pressures the density ratios become dominant term, and excess sorption capacities begin to decrease 44. We can also see from Figure 4 that the decline of sorption amount of CO2 at higher pressures is more pronounced than that of CH4. This may be due to that the CO2 density increases nonlinearly with pressure (especially in supercritical state), while the CH4 density increases approximately linearly with pressure

24

, resulting in larger density ratios of CO2 and thus more

dramatic decrease of CO2 sorption isotherms than CH4 in supercritical state. A great deal of researches on the sorption-induced swelling of coals had been reported

45-49

. Coal is well known to swell in the

presence of CO2 due to its glassy, strained, cross-linked macromolecular structure 50. The volumetric strains associated with swelling can reach 15 % on coals

48

. However, the expansion of shale induced by sorption is much smaller than that of coal. Chen et al. (2015)

investigated the strain behavior of the shale in CH4 at different pore pressures. Their results indicated that the CH4 sorption induced swelling was at a magnitude of 0.1 % volumetrically at 10 MPa 51. Lahann et al. (2013) investigated the influence of CO2 sorption to the pore structure and mineralogy of the New Albany Shale at pressures ranging from 0.69 MPa to 24.1 MPa. In their study, the BET SSA,

BJH mesopore volumes, micropore surface area and micropore volumes were determined by an ASAP 2020 porosimeter before and after

CO2 sorption. Their results showed that the adsorbed CO2 did not have a measurable influence on these characteristic pore structure parameters of the shale samples 52. Actually, we have measured the helium void volumes before and after CO2 sorption experiments. The change in the void volumes under the two experimental conditions is only about 0.17 cm3 (0.13 % of the void volume).To quantitatively

characterize the effect of the slight swelling on CO2 sorption, swelling data of pure carbon and clay minerals from Heller et al. (2014)


14

Page 19 of 32

were adopted to correct the CO2 sorption isotherms at each pressure step by assuming that the void volume of the sample cell was decreased by the volume equivalent to the volumetric swelling of shale. In the calculation CO2 was assumed to be adsorbed only on organic matter and clay minerals. The volumetric swelling strain data of illite were used to replace that of clay minerals, due to high

degree of illitetization of the rocks in this study. The volumetric swelling of pure carbon is 2.5 - 3.9 times of illite (Figure 7a). When CO2 excess sorption is corrected by swelling, the excess sorption remains almost unchanged with the amount of change within its experimental

uncertainty (Figure 7b), indicating that the effect of swelling on the sorption of shale may be negligible. 0.18

0.20

Illite Pure carbon Bulk shale

0.16

0.15


Volumetric Swelling (cm3)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

0.10

0.05

0.14 0.12 0.10

Uncorrected Corrected

0.08 0.06 0.04

0.00

0.02 0

2

4

6

8

10

12

14

16

0

Pressure (MPa)

2

4

6

8

10

12

14

16

Pressure (MPa)

(a)

(b)

Figure 7. (a) Volumetric swelling of illite, pure carbon and bulk shale of sample 2 as a function of pressure (calculated from XRD data and TOC content of sample 2 and volumetric swelling strain data from literature 14; the densities used in the calculation were 2.70 g/cm3 for illite and 2.28 g/cm3 for pure carbon); (b) excess sorption isotherms for sample 2 at 80 ℃ showing the effect of swelling.

3.3. Multi-component Sorption Sorption isotherms of CH4 / CO2 mixtures were measured on shale samples at 30 and 80 °C up to 20 MPa. Two different CH4 / CO2 mixture compositions (79.50 % / 20.50 %, 48.62 % / 51.38 %) were used in these experiments. The excess sorption data of total (CH4 + CO2) and individual component were presented in Figure 8. From Figure 8 we can see that the excess sorption isotherms of both total and individual component exhibit maxima, just like sorption isotherms of single component. The total sorption amounts are between single

CH4 and CO2, and increase with increasing CO2 concentration in the mixtures (Figure 4, 8a - c). The shapes of sorption isotherms of total gas are found to be similar to that of individual component with either higher concentration or stronger sorption affinity. For example, the


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Page 20 of 32

shape of total sorption isotherm is similar to that of CH4 component in mixture with 79.50 % CH4 (higher concentration, Figure 8a - f), and similar to CO2 component in mixture with approximate equivalent content of CH4 and CO2 (stronger sorption affinity, Figure 8g - i). Additionally, a higher sorption amount of CH4 in CH4 / CO2 mixture with 79.50 % CH4 is observed (Figure 8a - f), which is inconsistent with the results of single component sorption indicating larger sorption amount of CO2. However, when the two individual components have approximately equal content, an expected higher sorption amount of CO2 is obtained (Figure 8g - i). This indicates that the sorption behavior of individual component under competitive condition may depend not only on the sorption affinity of the single component, but

also on the partial pressure of the component in the mixture.

Lee et al. (2013) conducted competitive sorption of CO2 / CH4 mixtures with about 80 % CO2 in the feed gas on anthracite coal, and found that the total excess sorption amounts and isotherm shapes of the mixtures were similar to those of single CO2 24. Lee’s research, combined with the conclusions of this paper, further prove that the sorption behavior of the total gas is greatly affected by the component

with higher sorption affinity and its partial pressure in the mixture. On the other hand, the higher sorption amount of CH4 compared to CO2 is observed in CH4 / CO2 mixture with 79.95 % CH4 in this study. Similar finding was reported by Sudibandriyo, who conducted CH 4 / CO2 mixture measurements on activated carbon with a series of gas compositions, and found a more sorption amount of CH4 in mixture with about 80 % CH4 41. However, under similar gas composition, higher sorption amount of CO 2 was also obtained

15, 31

. In fact, from

equation (6) we can see that the relative magnitude of sorption amount of CH4 and CO2 depends only on their proportions in the feed gas (zi) and free gas (yi), for the sorption values (ntotoal, nresidual, nunadsorbed) are equal for CH4 and CO2 throughout the experiment. In that respect, higher sorption amount of both CH4 and CO2 may occur depending on the feed gas composition and the preferential sorption of the component.


Page 21 of 32

0.10

0.12

0.04

0.02

0.08

0.06

0.04

0.02

0

2

4

6

8

10

12

14

16

18

20

0

22

2

4

6

8

12

14

16

18

20

Total CH4

0

0.04

0.02

0.00 10

12

14

16

18

20

0.12

0.10 0.08 0.06 0.04 0.02 0.00

22

0

2

4

6

8

10

12

14

16

18

20

Sample 1

CO2

0.06 0.04 0.02

2

4

6

8

10

12

14

16

18

Pressure (MPa)

(g) CH4 / CO2=48.62 % / 51.38 %, 30 ℃

20

20

22

Sample 3

0.06 0.04 0.02

2

4

6

8

10

12

14

16

18

20

22

0.16

Total CH4

0.14

0.12 0.10 0.08 0.06 0.04 0.02

0.00

18

0.08

Sample 2



0.08

16

(f) CH4 / CO2=79.50% / 20.50 %, 30 ℃

CO2

0.10

14

Pressure (MPa)

Total CH4

0.14

0.12

12

0.10

0

0.16

Total CH4

10

0.00

22

(e) CH4 / CO2=79.50% / 20.50 %, 30 ℃

0.16

8

CO2

Pressure (MPa)

(d) CH4 / CO2=79.50% / 20.50 %, 30 ℃

0

6

Total CH4

Sample 2

Pressure (MPa)

0.14

4

(c) CH4 / CO2=79.50 % / 20.50 %, 80 ℃



0.06

8

2

CO2

CO2

6

0.02

0.14

0.12

4

0.04

Pressure (MPa)

Total CH4

Sample 1

0.08

2

0.06

22

0.14

0.12


10

(b) CH4 / CO2=79.50 % / 20.50 %, 80 ℃

(a) CH4 / CO2=79.50 % / 20.50 %, 80 ℃

0

0.08

Pressure (MPa)

Pressure (MPa)

0.10

CO2

0.00

0.00

0.00

Sample 3

Total CH4

0.10

CO2


0.06

Sample 2

Total CH4

0.10

CO2



0.08

0.12

Sample 1

Total CH4


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

Sample 3

CO2

0.12 0.10 0.08 0.06 0.04 0.02

0.00 0

2

4

6

8

10

12

14

16

18

Pressure (MPa)

(h) CH4 / CO2=48.62 % / 51.38 %, 30 ℃

20

0

2

4

6

8

10

12

14

16

18

20

Pressure (MPa)

(i) CH4 / CO2=48.62 % / 51.38 %, 30 ℃

Figure 8. Sorption isotherms of total and individual components in CH4 / CO2 mixtures at different temperatures and compositions. The EL 28 model was used to fit the measured sorption isotherms of mixed gas in this study. Sorption parameters of single CH 4 and CO2 obtained by Langmuir 3-parameter equation (Table 3) were used as input parameters for the model. Since the experimental data are excess sorption while theoretical calculations yield absolute sorption 53, the sorption data measured in this study need to be corrected for

absolute sorption before model fitting. For mixed gases consisting of components 1 and 2, the absolute mole fraction of component 1 in adsorbed phase, x1abs , was calculated from the excess sorption data of the experiment, according to the method proposed by Sudibandriyo


Energy & Fuels 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 22 of 32

et al. (2003) 41:

x1abs  1  x2abs 

1excess ads (2)   gas ( y1  1excess ) ads (2)   gas ( y1  1excess )(1  ads (2) / ads (1) )

(27)

Where, 1excess is the fractional component excess sorption, which is defined as the ratio of the excess adsorbed amount of component 1 to the total excess adsorbed amount

41

; ρads(1) and ρads(2) are the adsorbed phase densities of pure component, kg/m3; ρads

(kg/m3) is the adsorbed phase density of the mixed gas, which is calculated by the adsorbed phase densities of the pure component with the assumption of ideal mixing in the adsorbed phase 41:

1

 ads



x1abs

 ads (1)



x2abs

 ads (2)

(28)

The absolute sorption of component 1 can be calculated as following:

n1abs  n abs x1abs

(29)

Here, the absolute sorption of the total gas, nabs, is calculated by equation (26), where nex, ρgas and ρads refer to the excess sorption, gas phase density and adsorbed phase density of the total gas, respectively.

Figure 9 and Table 4 show the EL model fitting results of CH4 / CO2 mixture (79.50 % CH4 in feed gas) at 80 °C. Entirely, the measured data can be modeled by EL equation with %ADD ranging between 5.19 and 22.85. Application of EL model to gas mixture

sorption implies that separation factors are constant for all pressures because they correspond to the ratios of the Langmuir constants for

the single component isotherms

22

. However, the compositions of the gas mixture constantly change due to the preferential sorption of

CO2 (discussed in section 3.4). Therefore, the separation factor could not be a constant. This may be one source of fitting error of EL model.


Page 23 of 32

0.16

0.14

Total Exp. Total Cal. CH4 Exp.

0.12

CH4 Cal.

Absolute sorption (mmol/g)


0.16

CO2 Exp.

0.10

CO2 Cal.

0.08 0.06 0.04 0.02

Sample 1

0.00 0

2

4

6

8

10

12

14

16

18

20

22

0.14


0.12

CH4 Cal. CO2 Exp.

0.10

CO2 Cal.

0.08 0.06 0.04 0.02

Sample 2

0.00 0

2

4

6

Pressure (MPa)

8

10

12

14

16

18

20

22

Pressure (MPa)

(a)

(b)

0.16


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

0.14


0.12

CH4 Cal. CO2 Exp.

0.10

CO2 Cal.

0.08 0.06 0.04 0.02

Sample 3

0.00 0

2

4

6

8

10

12

14

16

18

20

22

Pressure (MPa)

(c) Figure 9. EL model fitting results of CH4 / CO2 mixture (79.50 % / 20.50 %) at 80 ℃. Table 4. Fitting performance of EL model on sorption of CH4 / CO2 (79.50 % / 20.50 %) mixtures at 80 ℃ %AAD Sample

nmixture

nCH4

nCO2

1

11.83

6.92

22.80

2

5.19

13.56

21.91

3

9.86

17.41

22.85

3.4. Preferential Sorption 3.4.1. Comparison of Feed Gas and Gas Phase Composition Preferential sorption of CH4 / CO2 mixtures with 79.50 % CH4 in feed gas was discussed at 30 and 80 °C. Previous studies had indicated that preferential sorption was independent of gas composition

15, 21, 22

, thus the mixtures with one composition was enough to

study the preferential sorption behavior.


Energy & Fuels

In Figure 10, the compositions of free gas at different pressures are compared with the feed gas. The CO 2 / CH4 mole ratios are represented as a function of pressure and the horizontal dashed line indicates the molar ratio of feed gas. The mole ratios lower than those

of the feed gas indicate preferential sorption of CO2 in the mixture; otherwise, CH4 is preferentially adsorbed. In all cases, the CO2 / CH4 mole ratios are reduced from the feed gas, indicating a preferential sorption of CO 2 (Figure 10a – f). However, the extent of the preferential sorption and its trend with pressure depend on temperature. In the low pressure range (< 6 MPa), the extent of preferential sorption of CO2 at 80 ℃ is larger than that at 30 ℃. Namely, temperature tends to strengthen the preferential sorption of CO2 in that pressure range. At higher pressures (> 6 MPa), the mole ratios at both temperatures increase with the pressure and gradually approach the feed gas at the end of the experiments. The change in the compositions is due to the higher sorption capacity of

CO2 than CH4. As the pressure increases, the sorption tends to be saturated and the difference between the sorption amount of CO2 and CH4 becomes smaller. Thus, the compositions of the mixture approach feed gas at higher pressures 24. 0.28

0.28

CO2/CH4 mole ratio

0.26

CO2/CH4 mole ratio

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 24 of 32

0.26

0.24

Sample 1 (30 ℃) Feed gas

0.24


0.22

0.20

0.22

0.18 0

2

4

6

8

10

12

14

16

18

20

22

0

2

Pressure (MPa)

4

6

8

10

12

14

Pressure (MPa)

(a)

(d)


16

18

20

22

Page 25 of 32

0.28

0.28

0.26

CO2/CH4 mole ratio

CO2/CH4 mole ratio

0.27

0.26

0.25

0.24


0.23

0

2

4

6

8

10

12

14

16

0.24


0.22

0.20

0.22 18

20

22

0.18

24

0

2

4

6

Pressure (MPa)

8

0.27

0.26

CO2/CH4 mole ratio

0.28

0.26

0.25

0.24


2

4

6

8

10

14

16

18

20

22

12

14

18

20

22

0.24


0.22

0.20

0.22 0

12

(e)

0.28

0.23

10

Pressure (MPa)

(b)

CO2/CH4 mole ratio

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

16

18

20

22

0.18 0

2

Pressure (MPa)

4

6

8

10

12

14

16

Pressure (MPa)

(c)

(f)

Figure 10. Comparisons of feed gas composition and CO2 / CH4 mole ratios of free gas as a function of pressure.

3.4.2. Separation Factor Selectivity, which is a measure of relative affinity of components to the adsorbent in the mixture, is quantitatively characterized by

the separation factors. To compare the relative sorption capacity of CH4 and CO2 gas, separation factors under competitive and noncompetitive conditions were calculated. For competitive sorption, the composition of the mixture changes constantly due to the

differences in the sorption affinity of the components to the adsorbent; components with high sorption capacity are enriched in the

adsorbed phase, and the other components with weaker sorption capacity are concentrated in the free gas phase. Thus, in competitive sorption the CO2 / CH4 separation factors can be expressed by the compositions of the mixtures in adsorbed and free gas phase 54:


Energy & Fuels 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

SCO2 /CH4 

Page 26 of 32

xCO2 / yCO2

(30)

xCH4 / yCH4

Where, xCO and yCO are the molar fractions of CO2 in the adsorbed and free gas phase respectively. 2 2 The separation factors under noncompetitive condition were calculated by the methodology proposed by Myers

53

. The core of the

method was to calculate Gibbs free energy of desorption basing on pure gas sorption equilibrium at given temperature and pressure. The

Gibbs free energy of desorption mentioned above was considered as the chemical potential of the solid adsorbent relative to its clean state

at the same temperature

55

. To calculate the free energy of desorption analytically, the Langmuir- virial equation, which can provide an

analytical expression for the sorption isotherms, was applied 53:

p

n exp(C1n  C2 n 2 +...) K

(31)

Where, n is absolute sorption amount of the pure component, mmol/g; K is Henry constant, mmol/g/MPa; C1, C2, C3 are virial coefficients, as many virial coefficients as required to fit the data points. Based on the Langmuir- virial equation, Gibbs free energy of desorption can be expressed as follows 56: G =RT 

p

0

n 1 2   dp  RT  n  C1n 2  C2 n3  ...  p 2 3  

(32)

At constant pressure, the difference in pure gas free energies can be expressed as an integral form 57:

nCO2 1  nCH 4 GCO2  GCH 4  RT    0 y  CH 4 yCO2

 dyCH 4  nRT ln SCO2 / CH 4 

(33)

Here, SCO / CH is the mean selectivity at constant pressure and temperature; n is the average sorption of CH4 and CO2, mmol/g. 2

4

The separation factors as a function of pressure under competitive (multicomponent sorption) and noncompetitive (single component sorption) conditions are described in Figure 11. Separation factors

SCO2 / CH 4 greater

than 1 suggest preferential sorption of CO2; the greater

the SCO / CH is, the stronger the CO2 is preferentially adsorbed. From Figure 11 we can see that the selectivity of CO 2 over CH4 ( SCO / CH ) is 2

2

4

4

greater than 1 in all cases, indicating that CO2 has a stronger sorption affinity than CH4 in both competitive and noncompetitive sorption conditions. Actually, selectivity is affected by both kinetic diameter and sorption energy of the gas molecules

58

. CO2 can enter a wider

range of pores than CH4 due to its relatively smaller kinetic diameter (CH4: 0.38 nm, CO2: 0.33 nm). Moreover, the sorption energy of CO2 is more than that of CH4 in the pores with widths less than 0.36 nm and larger than 0.46 nm


58

. Therefore, CO2 shows preferential

Page 27 of 32 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

sorption in both competitive and noncompetitive conditions. The separation factors range between 1.0 – 2.5 under competitive condition and 3.0 – 5.0 under noncompetitive condition. The

results that selectivity of CO2 under competitive condition is far less than that under noncompetitive condition suggesting the presence of CH4 gas will greatly inhibit the preferential sorption of CO2. This may be due to that the amount of gas adsorbed in a mixed gas is not only related to the sorption affinity but also to the partial pressure of the gas (see discussion in section 3.3). After all, the enhancement of

CH4 by CO2 injection is achieved by both competitive sorption of CH4 and CO2 on the same sorption sites and lowing of the CH4 partial pressure in the mixture. Therefore, it is not reasonable to adopt the separation factors calculated from single sorption as a substitute for

separation factors in a mixed gas. In Figure 11, separation factors at 80 ℃ are higher than that at 30 ℃ in the mixtures with 20.50 % CO2; at 30 ℃, higher selectivity of CO2 was obtained in the mixtures with 51.38 % CO2 than that with 20.50 % CO2; separation factors in the mixtures at 80 ℃ and with 20.50 % CO2 are higher than mixtures at 30 ℃ and with 51.38 % CO2. From the above results we can see both temperature and gas composition affect selectivity, and the influence of the former is greater than the latter. Since the sorption of CH 4 and CO2 on shale is physical sorption, which is a spontaneous and exothermic process, the temperature can inhibit sorption. However, the influence of

temperature on CH4 and CO2 sorption is different, due to the difference in sorption thermodynamic properties of CH 4 and CO2. CO2 sorption can release more heat than CH4 due to its larger isosteric heat of sorption, which is a measure of the temperature change caused by sorption and desorption during a process in the energy balance

59

. The released heat from CO2 sorption results in the increase of the

temperature, which promotes the desorption of CH4 26, thus increases the separation factors of CO2 / CH4. As shown in Figure 11, the separation factors under noncompetitive condition show a first increase and then decrease trend with

pressure. Actually, the effects of gas sorption on porous adsorbents can be divided into energetic (binding energy) and entropic effects (packing effect) depending on the stage of sorption 24. Energetic effects are responsible for the growing selectivity of CO2 over CH4 at low coverage (low pressure), due to the stronger interaction of CO2 to shale than that of CH4. After the shale surface is saturated by the adsorbates with increasing pressure, the entropic effects (e.g. the adsorbates parking within the shale) begin to become important. The

entropic effects on CO2 sorption are more pronounced than CH4 sorption because the sorption amount decrease of pure CO2 is far more


Energy & Fuels

4.5

4.5

4.0

4.0

3.5

Pure gas (80 ℃) 20.50 % CO2 (80 ℃)

3.0

51.38 % CO2 (30 ℃)

3.0

2.5

20.50 % CO2 (30 ℃)

2.5

4 2

2.0

1.5

1.0

1.0

Sample 1

0.5

4

6

8

10

12

14

16

18

20

20.50 % CO2 (30 ℃)

Sample 2

0.5

0.0 2

51.38 % CO2 (30 ℃)

2.0

1.5

0

Pure gas (80 ℃) 20.50 % CO2 (80 ℃)

3.5

SCO /CH

2

SCO /CH

4

than that of pure CH4 at higher pressures (Figure 4). Therefore, the separation factors decrease at high pressure range.

22

0.0 0

2

Pressure (MPa)

4

6

8

10

12

14

16

18

20

22

Pressure (MPa)

(a)

(b)

5.0 4.5 4.0 3.5

Pure gas (80 ℃) 20.50 % CO2(80 ℃)

3.0

51.38 % CO2(30 ℃)

4

20.50 % CO2(30 ℃)

2.5

2

SCO /CH

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 28 of 32

2.0 1.5 1.0

Sample 3

0.5 0.0 0

2

4

6

8

10

12

14

16

18

20

22

Pressure (MPa)

(c)

Figure 11. Separation factors of CO2/CH4 as a function of pressure under competitive (multicomponent sorption) and noncompetitive (single component sorption) conditions.

4. Conclusions Single and multicomponent sorption of CH4 and CO2 gas were carried out on shale samples with an average of 3.07 wt. % TOC content at 30 and 80 ℃ up to 20 MPa. The Langmuir sorption capacity was 0.134 – 0.146 mmol/g for CH4 and 0.339 – 0.371 mmol/g for CO2. CO2 excess sorption isotherms showed a sharp decline in supercritical area. This may be due to the nonlinear increase of the CO2 gas density with pressure in the supercritical area. When the CO2 sorption isotherm was corrected by the sorption-induced swelling, no significant change was found in the curve.


Page 29 of 32 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

The total sorption amounts of CH4 / CO2 mixtures were between single CH4 and CO2, and increased with the increasing of CO2 concentration in the mixtures. The shapes of sorption isotherms of total gas were found to be similar to that of individual component with

either higher concentration or stronger sorption affinity. A higher sorption amount of CH4 in CH4 / CO2 mixture with 79.50 % CH4 was observed. However, when the two individual components had approximately equal content, an expected higher sorption amount of CO 2 was obtained. This indicates that the sorption behavior of individual component under competitive condition may depend not only on the

sorption affinity of the single component, but also on the partial pressure of the component in the mixture.

Preferential sorption of CO2 was observed in all competitive sorption of CH4 / CO2 mixtures with 79.50 % CH4 in the feed gas. Temperature tended to strengthen the preferential sorption of CO2 in low pressure range (< 6 MPa). At higher pressures (> 6 MPa), mole ratios at the two temperatures increased with the pressure and gradually approach the feed gas at the end of the experiments. Separation

factors calculated from multicomponent sorption were far lee than that calculated from single gas sorption, suggesting that the presence of

CH4 gas greatly inhibited the preferential sorption of CO2. On the contrary, increasing temperature and CO2 content in the mixture will promote preferential sorption of CO2.

Acknowledgements The authors would like to acknowledge the financial support of the National Natural Science Foundation of China (Grant No.

51274214, 51774298); Ministry of Education of China through the Science and Technology Research Major Project (Grant No. 311008);

State Key Laboratory of Petroleum Resources and Prospecting Independent Research Subject (Grant No. PRP/indep-3-1108).

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Page 32 of 32

Sorption of Methane, Carbon Dioxide, and Their Mixtures on Shales

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