A simple method for correcting for the presence of minor gases when determining the adsorbed methane content in shale

Fuel 150 (2015) 334–338

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A simple method for correcting for the presence of minor gases when determining the adsorbed methane content in shale Chun-Yun Zhang a, Xin-Sheng Chai a,⇑, Xian-Ming Xiao b a b

State Key Laboratory of Pulp and Paper Engineering, South China University of Technology, Guangzhou, China State Key Laboratory of Organic Geochemistry, Guangzhou Institute of Geochemistry, Chinese Academy of Sciences, Guangzhou, China

h i g h l i g h t s  Develop an approach to use the HS-GC determined parameters in gas calculation.  Convert the adsorption equilibration partition coefficient to Langmuir constants.  The Langmuir constants of minor gases used in gas calculation are from HS-GC test.

a r t i c l e

i n f o

Article history: Received 28 October 2014 Received in revised form 11 February 2015 Accepted 12 February 2015 Available online 23 February 2015 Keywords: Correcting Minor gases Adsorbed methane content Langmuir isotherm

a b s t r a c t This paper demonstrates a novel approach for correcting for the presence of minor gases when determining the adsorbed methane content in shale. Based on the widely used Langmuir isotherm in calculating the adsorbed gas, an equation is derived that converts the adsorption equilibrium partition coefficient (Kd) and maximal amount of adsorbed gas (N) at low pressure to Langmuir pressure (pL). Headspace gas chromatography (HS-GC) is used to determine the Kd and N of the minor gas species present in the shale. The results indicate that the method satisfactorily accounts for the presence of minor gases when estimating the amount of adsorbed methane. This HS-GC method is much more efficient than the isothermal adsorption test currently used for the measurement of adsorption parameters of minor gas species in shale. Therefore, this new approach will improve the speed and accuracy of estimating the amount of adsorbed methane in shale deposits. Ó 2015 Elsevier Ltd. All rights reserved.

1. Introduction Natural gas production from hydrocarbon-rich shale formations, known as ‘‘shale gas’’, is one of the most rapidly growing new sources of energy. For example, in recent years, there has been rapid progress in the development of unconventional shale gas recovery in North America [1]. To produce similar results in China, which also has abundant estimated reserves of shale gas [2], additional research is needed, including development of techniques for effectively and efficiently estimating the amount of shale gas in particular formations. This information is vital for identifying locations of interest (i.e., enriched zones) that would justify the investment of resources to commercialize shale gas production. In addition to the free gas which dissociates with shale pores, the absorbed gas can account for 20–80% of the total gas ⇑ Corresponding author. Tel./fax: +86 20 87113713. E-mail address: [email protected] (X.-S. Chai). http://dx.doi.org/10.1016/j.fuel.2015.02.050 0016-2361/Ó 2015 Elsevier Ltd. All rights reserved.

entrapped in underground shale gas reservoirs [3,4]). When only methane (the major component of shale gas) is taken into consideration, the typical Langmuir equation [5] can be used, i.e.,

Ga ¼

GaL p p þ pL

ð1Þ

where two parameters (i.e., Langmuir volume (GaL) and Langmuir pressure (pL) of adsorbed methane) are required. Although these parameters can be obtained by the isothermal adsorption test [6,7], the experimental procedure required is complicated and time-consuming. In most cases, the problem is further complicated by the presence of several minor gas species (e.g., ethane and carbon dioxide) that coexist in shale. The neglecting of these coexisting minor gases results in an over-estimation of the absorbed methane in shale if the conventional Langmuir equation is used. In order to correct for the presence of minor gases, an extended Langmuir equation has been proposed to calculate the adsorbed methane gas (GMe a ) in shale [8–10]; i.e.,

335

C.-Y. Zhang et al. / Fuel 150 (2015) 334–338 Me GMe a ¼ GaL

y p  Me  P 1 þ ni¼1 ypiip pMe L

ð2Þ

system (Agilent 7890A, USA) and an automatic headspace sampler (DANI HS 86.50, Italy) were used for HS-GC measurement.

L

This expression is similar to Eq. (1), except that in addition to Me the Langmuir constants (i.e., GMe aL and pL ) for methane, the Langmuir pressures for the minor gas (i.e., piL ) are also required. Although the amounts of these minor gas species adsorbed in shale are much lower than that of methane, the same procedures must be individually performed for each gas species in the isothermal adsorption test [11]. Therefore, a significant amount of time is required to evaluate the amounts of all of the adsorbed gases in the shale samples. The isothermal adsorption test is designed to simulate the adsorption behavior of gases at various pressures. For methane, the isothermal adsorption test conducted at high pressure is necessary to obtain the Langmuir constants because of the high partial pressure of methane in most shale gas reservoirs [12]. For the minor gases, their partial pressures could be much lower than that of methane [12]. In that case, the adsorption behavior can be described by their partitioning coefficients between the vapor and solid phases when the linear sorption isotherm is valid, which can then be converted to parameters used in the Langmuir equation. This approach greatly reduces the time required to determine the amount of methane adsorbed in the shale. There are several methods that can be used for the determination of partition coefficients in a solid–vapor adsorption system [13–16], however are usually based on custom-designed devices. Recently, we have developed two novel methods, based on the commercial headspace gas chromatographic system (HS-GC), for the determination of the adsorption equilibrium partition coefficient and maximal amount of adsorbed gas for the minor gases adsorbed in shale [17,18]. Thus, the method lends itself to relatively easy standardization procedures. Compared with the isothermal adsorption test, all these methods are much more efficient for the determination of the adsorption-related parameters for the minor gases adsorbed on shale. However, in the practical applications, the key step is the conversion of the parameters measured by these efficient methods to the parameters that appear in the extended Langmuir equation. The objective of the present work was to develop a new approach to correct for the presence of the minor gases in calculating the adsorbed methane in shale, using the parameters that efficiently determined by HS-GC. The main focuses were on the error analysis of the Langmuir equation for calculating the adsorbed gas and the derivation of the conversion of adsorption equilibrium partition coefficients to adsorption constants in the Langmuir equation. The derived relationship was tested by application to a case study of calculating the content of adsorbed methane in a shale sample.

2. Experimental

3. Results and discussion 3.1. Error analysis When the Langmuir volume (GaL) and pressure (pL) of analyte(s) in the Langmuir equation, i.e., Eq. (1), are available, the volume of the adsorbed analyte(s) (Ga) at any pressure can be calculated. According to Eq. (1) and the propagation of uncertainty (or propagation of error) [19], the uncertainty of Ga (as relative standard deviation, RSD) can be expressed as

sG RSD ¼ a ¼ Ga

The shale samples were obtained from shale gas reservoir in both China (sample A and B) and North America (sample C). Each sample was ground and screened to 60–80 mesh; the average particle size was 214 lm. The key information, including specific surface area, Langmuir constant, adsorption equilibrium partition coefficient, and maximal adsorbed gas, were obtained from analysis of core samples using BET method, the Langmuir isothermal adsorption test and the HS-GC methods. 2.2. Apparatus and operations An electromagnetic ore grinder (DF-3, Huanan Instrument, China) was used in the preparation of the powder samples. A GC

ð3Þ

All symbols and definitions are listed in Table 1. Combine Eqs. (1) and (3) to have

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  2  2  2 1 1 pL RSD ¼ s2GaL þ s2pL þ s2p GaL p þ pL pðp þ pL Þ

ð4Þ

Thus, it can be seen from Eq. (4) that the error in the Ga measurement is a function of GaL, pL, and the pressurized pressure (p). Adopting the permitted uncertainties (i.e., 10%) in both GaL and pL measurement from Langmuir isotherm experiment and a margin of error of 0.01 MPa for the pressure [20], the standard errors (i.e., sGaL , spL , and sp) for GaL, pL, and p can be determined. Thus, the RSD of the Langmuir isotherm experiment at various pressures can be estimated using Eq. (4). The relationship between the RSD and the pressurized pressure is shown in Fig. 1. As shown in Fig. 1, the Langmuir isotherm experiment can provide a good measurement precision at higher pressure range, indicating that it is suitable to be used for the determination of the major gas (i.e., methane) at the subterranean pressure. However, a significant error can be expected when the Langmuir isotherm experiment is used for measuring the amount of a minor gas, such

Table 1 Symbols and definitions. Symbols

Definitions

Units

a b Ca Cg Ga, GaL

m2/g MPa1 g(gas)/m2 g(gas)/mL m3/t

M

Specific surface area Adsorption constant Gas concentration in the adsorbed phase Gas concentration in the vapor phase The adsorbed gas content and the Langmuir volume of gas, respectively The adsorbed methane and the Langmuir volume of methane, respectively Adsorption equilibrium partition coefficient Molecular weight of the gas species

N

Maximal amount of adsorbed gas

i pL, pMe L , pL

Langmuir pressure of universal gas, methane and the minor gases Formation pressure Molar gas constant Standard error of adsorbed gas and Langmuir volume, respectively. Standard error of Langmuir pressure and pressure, respectively Temperature Molar fraction of methane and minor gases in shale gas, respectively Fraction of coverage of shale pore surface by adsorbed gas

Me GMe a , GaL

Kd

2.1. Samples

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  2  2  2 @ ln Ga @ ln Ga @ ln Ga s2GaL þ s2pL þ s2p @GaL @pL @p

p R sGa , sGaL spL , sp T yMe, yi h

lmol/g (g/m2)/ (g/mL) g(gas)/ lmol lmol/ g(sample) MPa MPa J/lmol K lmol/ g(sample) MPa K

%

336

C.-Y. Zhang et al. / Fuel 150 (2015) 334–338

Fig. 1. Effect of pressure on the measurement error in the Langmuir isothermal test.

Fig. 2. Linear range of the adsorption isotherm.

as ethane and carbon dioxide, because of their lower partial pressures. Therefore, we can apply the efficient techniques that determine the adsorption parameters at lower pressure to these minor gases in shale. 3.2. Conversion of the parameters 3.2.1. Converting the partition coefficient to the adsorption constant or Langmuir pressure The definition of vapor–solid adsorption equilibrium partition coefficient (Kd) obtained by HS-GC method and the Langmuir isotherm equation are expressed, respectively, as the follows.

Kd ¼

Ca Cg

ð5Þ

and

bp h¼ 1 þ bp

Fig. 3. The relative error for the replacement of Eq. (6) by the linear equation (Eq. (7)) at different Kd values.

ð6Þ

When adsorption takes place at low partial pressure, e.g., when it meets bp  1 in Eq. (6), it agrees with the linear adsorption isotherm. Thus, we have

h ¼ bp

ð7Þ

According to the definition of h (i.e., the fraction of coverage of the shale pore surface by adsorbed gas) and the equation of the state of gas, we have

h¼

aC a NM

ð8Þ

C g RT M

ð9Þ

and

p¼

Merging Eqs. (5), (7), (8) and (9), and make an arrangement, the correlation of Kd and b in the linear adsorption isotherm range can be expressed as

b¼

aK d NRT

ð10Þ

Since the Langmuir pressure (pL) is defined as the pressure at which one half of the maximal amount adsorbed gas is obtained, i.e., h = 1/2, the following equation can be obtained from Eq. (6), i.e.,

pL ¼

1 b

ð11Þ

Substitute Eq. (11) to Eq. (10) to obtain the correlation of Kd and pL, i.e.,

pL ¼

NRT aK d

ð12Þ

3.2.2. Scope of the conversion equation Fig. 2 shows the difference between the curves drawn by Eqs. (6) and (7). It can be seen that the difference between these two models is not significant in the lower pressure range (e.g., <0.7 MPa) for the shale sample with b = 0.0926 MPa1 (from Sichuan province, China). Therefore, we can make the above conversion in this linear adsorption isotherm range. Since the partial pressures of the minor gas species are basically located in the linear range, we can use Eq. (12) to convert the Kd (obtained from HSGC measurement) to the Langmuir pressure (pL) for the minor gas species of involved. Fig. 3 shows the relationships between the relative errors and the pressures for shale samples with different Kds. It can be seen that the error is highly related to the Kd of species. At an error tolerance level of 10% (required in the standard isothermal adsorption test), the maximum range of pressures for the conversion equation are about 0.1, 0.5, and 1 MPa, for the sample with the Kd values of 0.05, 0.01, and 0.001, respectively. Therefore, the species with a larger Kd has a wide linear pressure range that is suitable for the application of the conversion. 3.3. New equation for calibrating the adsorbed methane Eq. (2) is an extended Langmuir equation for calculating the adsorbed methane gas in shale, in which the effect of multiple

337

C.-Y. Zhang et al. / Fuel 150 (2015) 334–338 Table 2 The core information of shale samples. Sample ID

Component

Ga,L, lmol/g

y, %

a

Kd, (g/m2)/(g/mL)

N, lmol/g

T, °C

p, MPa

10.8 5.14a 7.76a

– 0.0109b 0.0169b

– 115b 183b

82.2

20.8

pL, MPa a

A

Methane Ethane Carbon dioxide

94 3 2

70.8 – –

B

Methane Ethane Propane Butane Pentane

80 7 5 5 2

87.2a – – – –

3.33a 12.8a 38.4a 45.3a 10.2a

– 0.0106b 0.00658b 0.00533b 0.0226b

– 327b 719b 253b 509b

86.4

C

Methane Ethane Propane Carbon dioxide

86 7 3 3

81.9a – – –

8.16a 3.89a 4.25a 4.89a

– 0.00550b 0.0113b 0.00922b

– 106b 226b 183b

79.4

9.62

10.2

a, m2/g 5.6

7.9

10.1

a and b represent the isothermal adsorption test data and the HS-GC test data, respectively.

Table 3 The comparison of the adsorbed methane content in the shale samples calculated by the Langmuir (L), extended Langmuir (EL), and present (P) methods, respectively. Adsorbed methane, lmol/g

Samples

A B C

Relative difference, %

Present

Extended Langmuir

Langmuir

EL vs. P

L vs. EL

42.8 58.7 38.2

42.9 58.8 36.8

45.6 60.9 42.4

0.23 0.17 3.80

6.29 3.57 15.2

gas species (minor) coexisting in the sample is taken into consideration. Different from the traditional Langmuir isotherm test, the HS-GC method we developed can be used to efficiently determine the equilibrium partition coefficients (K id ) and maximal amount of adsorbed gas (Ni) of these minor gases [17,18]. Thus, we can use Eq. (12) to convert the parameters measured by HSGC to those required in Eq. (2). The item of the sum of the partial pressures of the species in the denominator in Eq. (2) can be written as n X yp i

piL i¼1

¼

n1 yMe p X yi p þ Me pL piL i¼1

ð13Þ

where the parameter (pMe L ) of methane cannot be converted by Eq. (12) due to its high pressure, which is obtained from Langmuir adsorption isotherm test. Since the Langmuir pressure (piL ) of the minor gas species can be derived from K id and Ni by Eq. (12), Eq. (13) can be further written as n X yp i

piL i¼1

¼

n1 yMe p X yi paK id þ Me Ni RT pL i¼1

ð14Þ

required in the calculation were obtained from analysis of core samples using rock characterization instruments, the Langmuir isothermal adsorption test and the HS-GC methods. The data are listed in Table 2. Based on the data in Table 2, the amounts of adsorbed methane in these samples can be calculated. Table 3 shows the comparison of results of the adsorbed methane content in the shale samples calculated by the different methods, i.e., Langmuir model (L), Extended Langmuir model (EL), and the present (P) method. It can be seen that the data calculated by the EL and P methods have a good match (RSD < 4%), indicating that the present method is justifiable to be used in the application. Clearly, if ignoring minor gases effect, more than 15% of the adsorbed methanol in the shale sample could be over-estimated, this will have a significant impact on any management decision regarding possible development of a particular resource. 4. Conclusions This study presents a new approach for correcting for the presence of minor gases when calculating the adsorbed methane in shale. A theoretical correlation was developed to convert the vapor–solid partition coefficient determined by HS-GC to the Langmuir constants that are related to the amount of adsorbed gases. We have also shown the circumstances under which this conversion yields results of acceptable precision. Based on the conversion, the HS-GC determined parameters can be easily used to correct for the presence of minor gases when estimating adsorbed methane based on the extended Langmuir model. A case study of three samples illustrates the value of the new approach when making a management decision regarding possible development of a particular resource. Acknowledgements

Substituting Eq. (14) into Eq. (2), we obtain

yMe p

Me GMe a ¼ GaL

pMe 1 þ ypMeMep þ L L

n1 X i¼1

yi paK id N i RT

!

ð15Þ

Eq. (15) is the new equation for calculating the adsorbed methane content in shale samples based on the Langmuir isotherm test, in which the effect of minor gases on methane adsorption is corrected by the parameters measured by HS-GC. 3.4. Applications Three samples (designated A, B and C) from shale gas wells in both China and North America were collected, and the parameters

This study was jointly supported by National key Basic Research Program of China (973 Program: 2012CB214705), the Natural Science Foundation of China (No. 21037001), and Research Fund for the Doctoral Program of Higher Education of China (No. 20110172110026). References [1] U.S., Energy Information Administration. Effect of increased natural gas exports on domestic energy markets; 2012. . [2] U.S., Energy Information Administration. World shale gas resources: An initial assessment of 14 regions outside the United States; 2011. . [3] Curtis JB. Fracture shale-gas systems. AAPG Bull 2002;86:1921.

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