Ethane Mixtures on Shale

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Competitive Sorption of Methane/Ethane Mixtures on Shale: Measurements and Modeling Yu Wang, Theodore T. Tsotsis, and Kristian Jessen Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.5b02850 • Publication Date (Web): 16 Oct 2015 Downloaded from http://pubs.acs.org on October 19, 2015

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Industrial & Engineering Chemistry Research

Competitive Sorption of Methane/Ethane Mixtures on Shale: Measurements and Modeling Yu Wang, Theodore T. Tsotsis and Kristian Jessen*, Mork Family Department of Chemical Engineering and Materials Science, University of Southern California

ABSTRACT

As the primary mechanism of gas storage in shale, sorption phenomena of CH4 and other hydrocarbons in the micropores and mesopores are critical to estimates of gas-in-place and of the long-term productivity from a given shale play. Since C2H6 is another important component of shale gas, besides CH4, knowledge of CH4-C2H6 binary mixture sorption on shale is of fundamental significance and plays a central role in understanding the physical mechanisms that control fluid storage, transport, and subsequent shale-gas production. In this work, measurements of pure component sorption isotherms for CH4 and C2H6 for pressures up to 114 bar and 35 bar, respectively, have been performed using a thermogravimetric method in the temperature range (40-60 oC), typical of storage formation conditions. Sorption experiments of binary (CH4-C2H6) gas mixtures containing up to 10% (mole fraction) of C2H6, typical of shale-gas compositions, for pressures up to 125 bar under the aforementioned temperature conditions have also been

* Corresponding author Email address: [email protected] ACS Paragon Plus Environment


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conducted. To the best of our knowledge, this is the first time that systematic measurements of CH4, C2H6 pure and binary mixture sorption on the Marcellus shale have been conducted, thus providing a comprehensive set of CH4-C2H6 competitive sorption data, which can help to improve the fundamental understanding of shale-gas storage mechanisms and its subsequent production. In the study, the Multicomponent Potential Theory of Adsorption (MPTA) approach is utilized to model the sorption data. The MPTA model is shown capable in representing the pure component sorption data, and also provides reasonable predictive capability when applied to predict the total sorption for CH4-C2H6 binary mixtures in shale over a range of compositions and temperatures.

KEYWORDS: Sorption of pure components and binary mixtures; CH4, C2H6; Gas Shale; MPTA modeling

ACS Paragon Plus Environment

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1. INTRODUCTION Gas shales have emerged as key hydrocarbon reservoirs in the past couple of decades or so, and have received renewed research attention in recent years in the context of reducing greenhouse gas emissions. The U.S. government's Energy Information Administration (EIA) predicts that by 2035 46% of the U.S. natural gas supply will come from shale gas.1 Sorption of gases in the complex shale matrix system is the key mechanism via which shale-gas is stored in such formations, and has as a result received attention in a number of previous studies related to shale gas recovery.2-5 Among these studies, much attention has been focused on the competitive adsorption of CH4/N2/CO2 gas mixtures on coals/shales, which bears a great importance for enhanced coal bed methane (ECBM) and CO2 storage applications.6-14 However, shale-gas (consisting primarily of methane and various other alkanes) sorption data on shale under realistic reservoir pressure and temperature conditions are still lacking. For example, as the second primary component in shale-gas, ethane is the alkane that is found in the largest concentrations in shale-gas, up to 15+ vol.%.15 The effective utilization of such hydrocarbon resource is of critical importance for the continued development of the industry, given today’s very low prices of natural gas. Therefore, the study of the adsorption characteristics of C2H6/CH4 mixtures is of key importance for the industry and generating such data is the key motivation behind this work. It is, in general, a challenge to model sorption in natural materials, such as shale, due to their heterogeneous nature and hierarchical pore structures (manifested, typically, by multi-modal pore size distributions), which makes the representation of competitive sorption phenomena in these systems quite difficult. Past modeling efforts, for example, have attempted to describe



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multicomponent gas sorption in shales from pure component isotherm data via the use of the extended Langmuir model (ELM), and also the Ideal Adsorbed Solution (IAS) theory, the main motivation behind such efforts being the simplicity and low/moderate computational cost of these commonly utilized methods.16-19 However, it has been demonstrated that neither of these models is capable of accurately describing the multicomponent sorption behavior that is relevant to coalbed methane recovery processes.20-21 Here, we test, instead, the accuracy of the Multicomponent Potential Theory of Adsorption (MPTA) approach for the calculation of gas sorption on shale. The choice of the MPTA method, which originated from the potential theory concept suggested by Polanyi22, is because it directly models excess adsorption data, which is a key advantage, while ELM/IAS require that one converts the excess adsorption data into absolute adsorption, and that entails significant, and completely untested (for the CH4/C2H6 pair in shale) assumptions about the density of the adsorbate layer. Furthermore, the MPTA model has been utilized before to model the sorption of gases and liquids in microporous materials with promising results.23-25 The organization of this paper is as follows: First, we describe the experimental approach and report the pure and binary sorption data of CH4, C2H6 on shale. Then, we employ the MPTA model to interpret and represent the sorption data, and we compare our predictions to the experimental observations. Finally, a discussion and conclusions section completes the manuscript.

2. SAMPLE PREPARATION AND EXPERIMENTAL APPROACH 2.1. Sample Preparation The shale sample used in this study is from the Marcellus formation in the Appalachian Basin. It was extracted from a depth of 7,802.5 ft. Prior to its use in the present sorption study, the sample


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was stored in a zip-lock bag as received to avoid further oxidation and water uptake. To reduce internal mass transfer limitation effects and to facilitate faster sorption of gases on the shale, the sample was ground and sieved. Sample particles with diameters in the range of 1-1.18 mm (US Mesh 16-18) were then collected and subsequently used in the sorption experiments. Prior to the initiation of these experiments, the sample was then evacuated at 120 oC for 24 hrs. We note that the evacuation process will, likely, also remove moisture from the shale samples that is normally present, at varying amounts, in the subsurface. In addition, to water other heavier hydrocarbons are also found in shale-gas. Their impact on the sorption properties of the C2H6/CH4 mixtures is beyond the scope of this manuscript, however, and will be addressed in our continuing studies of the sorption characteristics of shale materials. At the end of each sorption experiment, the sample was again regenerated under vacuum at 120 oC for 24 hrs. Such a procedure assures that all gases that may potentially remain adsorbed at the end of an experiment get desorbed prior to the initiation of the next experiment. This, then, guarantees reproducibility among duplicative runs, as discussed further in Sec. 3.1. 2.2. Experimental Approach The thermogravimetric analysis (TGA) technique is used for the measurement of the sorption data. The heart of the TGA set-up is a Magnetic Suspension Balance (Rubotherm, Germany), which is capable of measuring weight changes down to 1 µg. During an experiment, the weight change of the sample due to sorption is transmitted from the sorption chamber to the analytical balance in a contactless manner via the magnetic suspension mechanism. A sorption experiment consists of several steps: First, one must measure the weight of the empty sample container, M sc and its volume Vsc at the temperature of the experiment. This is accomplished by pressurizing the sorption chamber with the sample container alone (without the sample in place) in a step-wise



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manner using a flowing inert gas (Helium) and recording its apparent weight M sc ,app at various pressures. M sc ,app relates to M sc and Vsc according to the following relationship (the He density

ρ He in Eq. (1) is measured also in situ in the TGA set-up by using a reference stainless steel insert of known volume and weight): M sc ,app = M sc − ρ HeVsc .

(1)

By plotting M sc ,app vs. the He density ρ He , one can calculate both the M sc (as the intercept) and the Vsc (as the slope). The above experimental step is then repeated after the shale sample is placed into the sorption chamber to calculate the combined weight of the sample and the sample container, ( M s + M sc ), and their total volume ( V s + V sc ). In a third step, after evacuating once more the sample chamber at the eventual temperature of the experiment for 5 hrs, the sorption chamber is filled with the flowing gas to be studied, i.e., CH4, C2H6 or one of their mixtures at an initial pre-determined pressure and the apparent weight is monitored until it stabilizes. The chamber pressure is then raised in a step-wise manner consistent with steps 1 and 2 above. The

(

)

TGA again measures the apparent weight M ρ mb , T at the desired conditions (T, p):

(

)

(

M ρ mb , T = M s + M sc + m a − ρ mb Vs + Vsc + V a

)

,

(2)

where m a is the mass sorbed on the sample, V a is its volume, and ρ mb is the mass density of the bulk fluid (CH4, C2H6 or their mixtures) as measured in situ using the aforementioned method for measuring the He density. The experimental density values are quite accurate, as Figs. S1-S5 in the Supplemental Materials Section show that compare these values with modeling via the


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Peng-Robinson (PR) equation of state. By rearranging Eq. (2), one can directly obtain the measurable quantity, i.e., the excess sorbed mass m eas by the following Eq. (3):

(

)

(

)

m eas ρ mb , T = m a − ρ mb V a = M ρ mb , T − (M s + M sc ) + ρ mb (Vs + Vsc ) .

(3)

TGA (but also volumetric and chromatographic sorption) measurements cannot distinguish between amounts that are adsorbed and absorbed. For a solid material, an indication that absorption may be taking place is sample swelling26. However, for heterogeneous samples like shales consisting of both an inorganic backbone and potential organic inclusions it is not possible to accurately determine how much of the gas is adsorbed vs. absorbed in the shale material.

3. EXPERIMENTAL RESULTS 3.1. CH4 and C2H6 Pure Component Isotherms CH4 and C2H6 pure component sorption were measured on the shale sample at three different temperatures, namely, 40 oC, 50 oC and 60 oC. For each temperature, the weight and volume of the shale sample were measured. During the experiments, we observed that the shale sample undergoes a slight thermal expansion and volume change in response to the change in temperature. Specifically, the measured volume of the sample used in our TGA experiments, which weighs 2.2880 g, is 0.8414 cc, 0.8421 cc and 0.8439 cc, at the three different temperatures of 40 oC, 50 oC and 60 oC, respectively. The impact of this volume change is rather small, but it is also taken into account in the calculations of excess adsorption via Eqs. (2) and (3). CH4 and C2H6 pure component isotherms for pressures up to 114 bar and 35 bar, respectively, were obtained by the



experimental procedure discussed above, and are reported in Fig. 1 (and Figs. S6-S8, Tables S1-S3, in the Supplemental Section).

6

Excess sorption (mg/g)

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CH4 @ 40C CH4 @ 50C CH4 @ 60C C2H6 @ 40C C2H6 @ 50C C2H6 @ 60C

4

2

0 0

20

40

60

80

100

120

Pressure (bar)

Figure 1. CH4 and C2H6 pure component sorption on shale at 40, 50 and 60 oC. In the range of experimental pressures utilized (up to ~114 bar), as can be seen from Fig. 1 (and also Figs. S6-S8, Tables S1-S3, in the Supplemental Section), the CH4 sorption isotherm has approached an asymptotic behavior. However, the same is not true for C2H6 excess sorption, which for the pressure range utilized (up to ~ 35 bar) increases monotonically over the entire range of pressures. Several other studies on methane sorption on coal and shale samples have also reported similar behavior of maximum CH4 loadings attained ~100 bar.27-33 Prior studies, for example, have found that this maximum loading behavior happens when the gas reaches its supercritical fluid state and beyond.34-35 For CH4, Tc = -82.59 °C and pc = 45.99 bar, while for C2H6, Tc = 32.17 °C and pc = 48.72 bar, so our experimental observations are consistent with those of the prior studies. (Such maximum loading behavior is, of course, to be expected, based on the mathematical


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definition of excess adsorption, i.e., Eq. (7) in Sec. 4.1 below, at higher pressures, when the adsorbed layer is saturated and the density of the bulk phase fluid becomes non-negligible compared to that of the adsorbed gas). Clear from Fig. 1 are the notably different sorption affinities of the shale towards CH4 and C2H6, with C2H6 displaying the stronger affinity: The ratio of C2H6/CH4 excess sorption is quite large, varying between 1.5 and 2.5 (on a molar basis) over the common pressure range investigated. As noted in Sec. 2.1., upon the completion of one sorption experiment and prior to the initiation of another the shale sample is evacuated for 24 hrs at 120 oC. This has been shown to restore the surface of the sample to its original state via the desorption of any residual gases that may remain adsorbed. The regeneration approach that we have used has been found effective in assuring experimental reproducibility among the various runs. For example, Fig. 2 shows the results of two consecutive methane sorption runs at 60 oC. Between the runs the shale sample was subjected to the aforementioned regeneration step. The data in Fig. 2 indicate very good reproducibility between the two consecutive runs.



2


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1

Run 1 Run 2

0 0

20

40

60

80

100

120

Pressure (bar)

Figure 2. Reproducibility test of CH4 sorption on shale at 60 oC. 3.2. CH4 and C2H6 Pure Component Adsorption/Desorption Hysteresis Though adsorption isotherm data are of fundamental importance, from an engineering perspective desorption phenomena are of significance as well, as they dominate during the shale-gas recovery process. As part of this study, therefore, we have investigated the desorption characteristics of CH4 and C2H6 on the shale sample. Figs. 3 and 4, for example, show CH4 and C2H6 adsorption/desorption isotherms at 60 oC as measured with the TGA set-up.


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1.8 1.6


1.4 1.2 1.0

adsorption desorption

0.8 0.6 0.4 0.2 0.0 0

20

40

60

80

100

120

Pressure (bar)

Figure 3. CH4 adsorption/desorption isotherms on shale at 60 oC.

4


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3

2

adsorption desorption 1

0 0

5

10

15

20

25

30

35

40

Pressure (bar)

Figure 4. C2H6 adsorption/desorption isotherms on shale at 60 oC. Two interesting features are observed in Figs. 3 and 4: First, moderate hysteresis behavior is observed between the loading (adsorption) and unloading (desorption) curves. Second, the



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desorption isotherm does not return to the origin at p = 0 bar. Though in recent years hysteresis phenomena have been observed with microporous materials as well, they are typically associated with mesoporous systems (i.e., those containing pores in the range between 2 and 50 nm) with complex 3-D pore structures. It has been reported that sorption hysteresis in such materials is associated with liquid-gas phase transitions under porous confinement. It is thought, that during adsorption the pores are filled by the liquid in the order of increasing pore radii, while on desorption the dimension of the pore necks (narrowest parts of the pore structure) controls the emptying of the pores. This explains why adsorbed gas molecules get “stuck” in these mesoporous materials and consequently create the adsorption hysteresis. The shale sample studied here has a hierarchical pore structure (as the data in Table 1 indicate) characterized by microporous, mesoporous, and macroporous regions, but the largest fraction of the pore space (>76%) resides in the mesopore range. Table 1. Distribution of micropore, mesopore, and macropore volumes in the shale sample as measured by BETa.

a

Cumulative

Cumulative

Cumulative

Total pore

micropore ( 12 hrs. This may signify a part of the shale sample (perhaps an organic inclusion) where both these gases are held more tightly. Heating under vacuum at 120 oC for 24 hrs results in the desorption of these residual amounts and restores the sample in its original state (see Fig. 2). 3.3. Competitive Adsorption of CH4-C2H6 Binary Mixtures Sorption isotherms were also measured for binary mixtures of CH4-C2H6 on the shale sample at the same temperatures (i.e., 40 oC, 50 oC and 60 oC) as those employed for the single-gas experiments. Three different CH4-C2H6 binary gas compositions (90%-10%, 93%-7%, and 96%-4% mole fraction – certified pre-mixed gases purchased from Matheson) were used in these experiments, and the isotherms were measured by varying, in a step-wise manner, the total pressure of the mixture. Estimates of the rate of uptake indicate it to be < 0.2 % of the gas flow rate through the TGA chamber, meaning that the mixture composition stays virtually constant throughout the sorption experiment. Figs. 5-7 (and Tables S4-S6 in Supplemental Materials Section) report the total (CH4 + C2H6) excess sorption data measured for these mixtures.



2.5


2.0

1.5

90%-10% CH4-C2H6 93%-7% CH4-C2H6 96%-4% CH4-C2H6

1.0

0.5

0.0 0

20

40

60

80

100

120

140

Pressure (bar)

Figure 5. Sorption of CH4-C2H6 mixtures (90%-10%, 93%-7%, 96%-4%) on shale at 40 oC.

2.5

2.0


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1.5

1.0

90%-10% CH4-C2H6 93%-7% CH4-C2H6 96%-4% CH4-C2H6

0.5

0.0 0

20

40

60

80

100

120

140

Pressure (bar)

Figure 6. Sorption of CH4-C2H6 mixtures (90%-10%, 93%-7%, 96%-4%) on shale at 50 oC.


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2.5

2.0


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1.5

1.0

90%-10% CH4-C2H6 93%-7% CH4-C2H6 96%-4% CH4-C2H6

0.5

0.0 0

20

40

60

80

100

120

140

Pressure (bar)

Figure 7. Sorption of CH4-C2H6 mixtures (90%-10%, 93%-7%, 96%-4%) on shale at 60 oC. From Figs. 5-7, we observe an increase in the total excess sorption amount as the concentration of C2H6 in the binary mixture increases. This is consistent with the single-gas sorption data that indicate the preferential sorption of C2H6 over CH4 in the shale sample. In addition, we observe a maximum in the total excess loading at ~100 bar beyond which the total excess sorption amount starts to decrease, while this was not observed from the CH4 or the C2H6 pure component sorption isotherms. We attribute the maximum excess loading observed for binary mixtures to interactions between the two species in the sorbed phase, and defer additional discussion of this behavior to the modeling section below.

4. MULTICOMPONENT POTENTIAL THEORY Of ADSORPTION (MPTA) 4.1. MPTA Theory



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Based on the original potential theory of adsorption (PTA), originally suggested by Polanyi22, Shapiro and Stenby23 introduced the multicomponent potential theory of adsorption (MPTA). In this theory, the adsorbate is considered to be a separate phase subjected to an external attractive potential field ε i (z ) exerted by the adsorbent itself.36 For the ith component in the adsorbed phase, the isothermal equilibrium state is reached when the sorption potential on that component ε i (z ) exerted by the adsorbent at any position z within the adsorbed phase equals the difference between its chemical potential in the bulk phase µig ( p y , y ) and the chemical potential in the adsorbed phase µi ( p( z ), x( z ) ) at location z:

µ i ( p ( z ), x( z ) ) − ε i ( z ) = µ ig ( p y , y )

i = 1,..., nc .

(4)

In Eq. (4) above, p (z ) is the pressure in the sorbed phase, p y is the pressure in the bulk phase, x and y are the mole fractions of component i in the sorbed phase and bulk phase, respectively. Eq. (4) can be rewritten in the form of fugacities:

ln f i ( p( z ), x( z ) ) = ln f ig ( p y , y ) +

ε i (z ) RT

.

(5)

In order to determine the distribution of pressures p (z ) and mole fractions x (z ) in the sorbed phase, in addition to an appropriate equation of state (EOS) that describes the bulk and sorbed phases, one has to also assume a representation of the sorption potentials ε i (z ) . Traditionally, in MPTA the same EOS is used to describe both phases. Though this does not represent an intrinsic limitation for the theory since, in principle, one could use a different EOS to describe the adsorbed phase, in practice no such experimentally-validated EOS exist today.


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Shapiro and Stenby23 assumed in their original paper the following generalized Dubinin–Astakhov (DA) potential to describe sorption in porous media: 

ε i ( z ) = ε 0i  ln 

z0   z 

1β

,

(6)

where z 0 is the total pore volume of the adsorbent, ε 0 i is the characteristic potential for component i , and β is the so-called Dubinin exponent.24, 37 The DA potential has been shown adequate to describe microporous solids with a narrow pore-size distribution PSD.38 As the PSD becomes broader, the DA equation may no longer be applicable, however. In the MPTA approach, z 0 , ε 0 i and β are treated as adjustable parameters and can be regressed from modeling the relevant pure component sorption isotherms. A robust procedure for solving the MPTA equations is utilized here, that was first developed by Shojaei and Jessen36, and for which further details are provided in the Supplemental Materials Section. In the spirit of the original papers by Dubinin and coworkers39-41 and also Shapiro and coworkers23-25,

37

, the model

parameters are taken here to be temperature-independent. For example, Dubinin39-41 and coworkers, in their studies of the adsorption of vapors on various solids, reported that for a given adsorbate–adsorbent pair, when plotting the quantity ( z z 0 ) vs. ε , they obtained a nearly invariant curve for different temperatures. Generally good success has been obtained in fitting experimental data with temperature-invariant DA parameters by Shapiro and coworkers23-25, 37 as well. The excess sorption of component i , i.e., the difference between the actual amount sorbed and the amount that would exist under bulk-phase conditions in a volume of the pore space equal to that of the adsorbed phase is represented by the following integral:



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[

]

Γi = ∫ xi ( z )ρ ( z ) − yi ρ y dz . z0

0

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(7)

where z 0 is the total porous volume, ρ is the molar density of the sorbed phase, which can be estimated by an equation of state. Here the PR-EOS was employed to describe both the bulk phase and the adsorbed phase. As noted above, the PR-EOS has been shown to accurately describe the experimental bulk densities, see Figs. S1-S5 in the Supplemental Section and further discussion to follow. 4.2. Modeling of CH4 and C2H6 Pure Component Isotherms Using the original form of the MPTA model23, we extracted relevant model parameters, i.e., the characteristic energies, and the Dubinin exponent by matching the model to the pure component sorption isotherms. In the interest of integrating the experimental pore volume information from the shale characterization (Table 1) into the MPTA model, two different DA potential functions were utilized, one corresponding to the microporous region covering the pore volume from 0 to 0.0081 cc/g, and another to the meso- to macro-porous regions covering the pore volume from 0.0081 to 0.0346 cc/g. Specifically, we keep the functional form of the DA potential to be the same in both regions but allow the use of different characteristic parameters in each region. This is done by introducing the following potential relationships

 b  ε ( z ) = ε  ln 0   z  Ι i

Ι 0i

1

βΙ

+ ε iΠ (b0 ) ,

 z  ε (z ) = ε  ln 0   z  Π i

Π 0i

1

βΠ

,

0 < z ≤ b0

b0 < z ≤ z 0 ,


(8)

(9)

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where b0 represents the pore volume of the microporous region, and z0 is the total pore volume. Eq. (8) ensures continuity in the chemical potential in the transition from the microporous to the mesoporous region. The new composite potential function is used with fixed values of b0 and z0 set to 0.0081 and 0.0346 cc/g, respectively, as measured experimentally for this shale sample. In this form, a total of 6 parameters must be estimated simultaneously from the CH4, C2H6 pure-component isotherms. They include the energy parameters for each species in each region (a total of four parameters) and the Dubinin exponent for each region, taken to be independent of the species (a total of two additional parameters). We assume that in each porous region, the characteristic potential ε0 should vary among different components, because in the DA model it is interpreted as a measure of the affinity between the component and the adsorbent. However, we keep the Dubinin exponent (β) the same for all species in each porous region, since in the DA model is thought to provide a measure of the heterogeneity of the porous regions, and to thus be independent of the components (we allow it, however, to vary among the pore regions, as they are likely to have different degrees of heterogeneity). As noted above, we have used the PR-EOS42 in our calculations. The relevant PR-EOS model parameters are listed in Table 2, with the binary interaction coefficient between CH4 and C2H6 set to zero. As discussed previously, and also shown in Figs. S1-S5 in the Supplemental Materials Section, the PR-EOS calculations are in excellent agreement with both our single component and also binary mixture experimental density data. The six MPTA model parameters were fitted to the experimental pure component isotherms (54 points), and Table 3 reports the final MPTA parameters. Figs. 8-10 present the MPTA model representation of the CH4 and C2H6 pure component isotherms corresponding to the parameters listed in Table 3.



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Table 2. Peng-Robinson EOS model parameters. Critical temperature

Critical pressure

Acentric factor

Volume shift

Tc (K)

p c (bar)

ω (dimensionless)

S i (dimensionless)

CH4

190.56

45.99

0.011

-0.03463

C2H6

305.32

48.72

0.099

-0.34350

Table 3. MPTA model parameters obtained from pure component sorption isotherms at 40 oC, 50 o

C and 60 oC. MPTA

CH4

C2H6

ε 0Ι i R(K )

682.5

684.4

ε 0Πi R (K )

11.2

120.4

β Ι (− )

1.284

β Π (− )

0.314

b0 (cc gr )

0.0081

z 0 (cc gr )

0.0346


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5.5 5.0

CH4 Expt. C2H6 Expt. CH4 MPTA C2H6 MPTA


4.5 4.0 3.5 3.0 2.5 2.0 1.5 1.0 0.5 0.0 0

20

40

60

80

100

120

Pressure (bar)

Figure 8. Comparison of MPTA calculations and experimental observations for CH4 and C2H6 excess sorption on shale at 40 oC.

5.0 4.5


4.0


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


3.5 3.0 2.5 2.0 1.5 1.0 0.5 0.0 0

20

40

60

80

100

120

Pressure (bar)

Figure 9. Comparison of MPTA calculations and experimental observations for CH4 and C2H6 excess sorption on shale at 50 oC.



4.5 4.0


3.5


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

3.0 2.5 2.0 1.5 1.0 0.5 0.0 0

20

40

60

80

100

120

Pressure (bar)

Figure 10. Comparison of MPTA calculations and experimental observations for CH4 and C2H6 excess sorption on shale at 60 oC. We observe from Figs. 8-10 that the MPTA model is reasonably accurate in representing the CH4, C2H6 pure component sorption isotherms, with low/moderate Root-Mean-Square (RMS) errors (representing the standard deviation of the differences between predicted values and observed values) as listed in Table 4. Interestingly, the model predicts very similar amounts of CH4 and C2H6 sorbed in the microporous regions (note the very similar ε 0iΙ values in Table 3), with the significant differences in excess sorption between the two species resulting from differences in the amounts sorbed in the mesoporous regions.


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Table 4. RMS errors for CH4 and C2H6 isotherms at 40 oC, 50 oC and 60 oC. RMS error CH4

C2H6

40 oC

0.1147

0.1194

50 oC

0.0326

0.0819

60 oC

0.0758

0.1109

(mg/g)

4.3. Prediction of CH4-C2H6 Adsorption Behavior Based on the MPTA model parameters obtained from the pure component sorption isotherms at various temperatures, we applied the MPTA model, in a predictive mode, to calculate the binary sorption of CH4-C2H6 mixtures on shale at relevant conditions. In this work, we have studied binary mixtures with a CH4 molar content of 90%, 93% and 96%. Figs. 11-13 compare the model predictions for overall CH4-C2H6 binary excess sorption with experimental observations.



3.0


2.5

2.0

1.5

90%-10% CH4-C2H6 Expt. 93%-7% CH4-C2H6 Expt. 96%-4% CH4-C2H6 Expt. 90%-10% CH4-C2H6 MPTA 93%-7% CH4-C2H6 MPTA 96%-4% CH4-C2H6 MPTA

1.0

0.5

0.0 0

20

40

60

80

100

120

140

Pressure (bar)

Figure 11. Measured and calculated total CH4-C2H6 excess sorption on shale at 40 oC.

3.0

2.5


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 35

2.0

1.5


1.0

0.5

0.0 0

20

40

60

80

100

120

140

Pressure (bar)

Figure 12. Measured and calculated total CH4-C2H6 excess sorption on shale at 50 oC.


Page 25 of 35

3.0

2.5


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


2.0

1.5


1.0

0.5

0.0 0

20

40

60

80

100

120

140

Pressure (bar)

Figure 13. Measured and calculated total CH4-C2H6 excess sorption on shale at 60 oC. From Figs. 11-13, we observe that the MPTA approach does a decent job in predicting the qualitative trends of CH4-C2H6 binary excess sorption on shale, while the quantitative agreement for the mixture data is of moderate quality. The RMS errors for the binary mixtures are reported in Table 5. Despite the fact that the MPTA is the only continuum model in use today that can directly model excess adsorption data (the other approaches like the ELM and IAS require that one converts the excess adsorption data into absolute adsorption, and that entails significant assumptions about the density of the adsorbate layer), it itself has its own intrinsic limitations. It is, principally, intended to describe porous materials with narrow pore size distributions, and the shale materials studied here are, in fact, characterized by hierarchical structures with broad pore size distributions, as the BET data (Table 1) indicate. In addition, the Dubinin–Astakhov (DA) potential model, on which the MPTA model is based, is better suited for describing simple



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Page 26 of 35

inorganic materials (e.g., zeolites) or microporous carbons and not the chemically complex systems like shale. Table 5. RMS errors for CH4-C2H6 binary mixtures at 40 oC, 50 oC and 60 oC. RMS error

90%-10%

93%-7%

96%-4%

(mg/g)

CH4-C2H6

CH4-C2H6

CH4-C2H6

40 oC

0.2746

0.2566

0.1445

50 oC

0.2825

0.2153

0.1529

60 oC

0.2601

0.2289

0.1289

Due to the interactions and competitions between the two sorbed species, the CH4-C2H6 binary sorption demonstrates a maximum in excess loading for all cases, and the MPTA model is able to represent this feature. We note that the MPTA model tends to over-estimate the excess sorption, the difference between theory and experiments widening with an increasing mole fraction of C2H6 in the mixture. This implies that the interaction and competition between the two sorbed species become increasingly complicated with more evenly distributed composition of the bulk phase.

5. DISCUSSION AND CONCLUSIONS In the previous sections we have reported new experimental observations of excess sorption of CH4 and C2H6 and their binary mixtures for a range of pressures and temperatures. At these experimental conditions, the pure component isotherms do not show any extrema in the excess


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sorption as commonly observed for CO2 sorption in coal. In contrast, the sorption isotherms for the binary CH4/C2H6 mixtures exhibit extrema in the total excess loading, predominantly at high C2H6 concentrations and at low temperatures. Sorption hysteresis is observed for both the pure component isotherms, indicating a multi-modal pore size distribution. BET measurements (reported in Table 1) further support this interpretation by demonstrating that the sample’s pore volume consists of micropores, mesopores and macropores, with the mesopores commonly thought responsible for adsorption/desorption hysteresis. The sorption hysteresis is observed to be more significant for CH4 than for C2H6. This suggests that the common industry practice of using the loading curve to evaluate gas in place and to evaluate production dynamics may not be appropriate. Mineralogical analysis of these samples43 reveals that the shale sample is composed largely of clay and quartz (> 80 wt.% ), but also contains ~3 % of total organic content (TOC). The non-zero unloading at p = 0 bar is also consistent with the concept of a heterogeneous sample containing both organic and inorganic components with gases being held perhaps more tightly in the organic inclusions. The multi-porosity and inherent heterogeneous nature of shale presents a challenge for the successful application of MPTA (but also all other continuum, semi empirical-type theories)

to

model sorption phenomena. The MPTA model, in its original form, was first proposed for sorption calculations in microporous materials with narrow PSD, such as activated carbons and zeolites. The pore size distribution of a shale sample, however, is more widely dispersed, with micropores, mesopores and macropores all contributing to the overall porosity and adsorption in the sample. It is notable, therefore, that the model still manages to provide an adequate fit of the experimental



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Page 28 of 35

mixture data based solely on parameters that were estimated from monotonic pure component isotherms, and that is even capable of identifying the observed maximum in the total excess loading.

ACKNOWLEDGEMENT The authors gratefully acknowledge the financial support from the Research Partnership to Secure Energy for America (RPSEA) project 11122-71.

ASSOCIATED CONTENT Supporting Information Available: Supplemental data and simulations, and a description of the numerical approach utilized for the MPTA model. This material is available free of charge via the Internet at http://pubs.acs.org/.

REFERENCES


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Table of Contents (TOC) Graphic:


Ethane Mixtures on Shale

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