Determination of Porosity in Shale by Double Headspace Extraction

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Rapid Determination of Porosity in Shale by Double Headspace Extraction GC Analysis Chun-Yun Zhang, Teng-Fei Li, Xin-Sheng Chai, Xianming Xiao, and Donald Barnes Anal. Chem., Just Accepted Manuscript • DOI: 10.1021/acs.analchem.5b03142 • Publication Date (Web): 13 Oct 2015 Downloaded from http://pubs.acs.org on October 13, 2015

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Analytical Chemistry

Rapid Determination of Porosity in Shale by Double Headspace Extraction GC Analysis Chun-Yun Zhang1, Teng-Fei Li2, Xin-Sheng Chai1,*, Xian-Ming Xiao2, and Donald Barnes3 1. State Key Laboratory of Pulp and Paper Engineering, South China University of Technology, Guangzhou, China 2. State Key Laboratory of Organic Geochemistry, Guangzhou Institute of Geochemistry, Chinese Academy of Sciences, Guangzhou, China 3. School of Environment and Energy, South China University of Technology, Guangzhou, China

Abstract: This paper reports on a novel method for the rapid determination of the shale porosity by double headspace extraction gas chromatography (DHE-GC). Ground core samples of shale were placed into headspace vials and DHE-GC measurements of released methane gas were performed at a given time interval. A linear correlation between shale porosity and the ratio of consecutive GC signals was established both theoretically and experimentally by comparing with the results from the standard helium pycnometry method. The results showed that: a) the porosity of ground core samples of shale can be measured within 30 min; b) the new method is not significantly affected by particle size of the sample; c) the uncertainties of measured porosities of nine shale samples by the present method were range from 0.31 – 0.46 p.u.; and d) the results obtained by the DHE-GC method are in a good agreement with those from the standard helium pycnometry method. In short, the new DHE-GC method is simple, rapid, and accurate, making it a valuable tool for shale gas-related research and applications. Keywords: shale gas; porosity; Double headspace extraction; gas chromatography

*Corresponding author. Tel/fax: +86-20-87113713; E-mail: [email protected] (X.-S. Chai)

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INTRODUCTION The commercial success of gas production from unconventional gas shales in North America has stimulated global interest in understanding this promising resource in China.1 It has been estimated that China has the world’s largest reserves of shale gas.2 To hasten the development of this important energy supply, many of shale’s properties, such as total organic content, mineral composition, gas content, porosity, and permeability, have been studied carefully.3-6 Porosity, reflecting the ability to accommodate and transport fluids in media,7 is one of the important parameters being used to evaluate the potential of a particular shale gas reservoir for development and production. Therefore, methods for the effective and efficient determination of the porosity of shale rock are important for the assessment and commercial exploration of shale gas reservoirs. Porosity is defined as the percentage of the pore (or the void) volume of a sample in the bulk volume. Traditionally, the porosity measurement is mainly based on fluid saturation and immersion techniques, in which the sample is pretreated by solvent extraction or heating, or a combination of both, to remove formation fluids, such as water and hydrocarbons. The pretreated sample is then saturated by a fluid of known density, low surface tension, and a high wetting tendency. Acetylene tetrachloride,8 deionized water,9 light hydrocarbons,10 and paraffin11 are typical fluids used in this method. By weighing the difference between the fully saturated and the dried sample, the pore volume of the sample can be determined. Coupled with the bulk volume, which is determined by fluid immersion and Archimedes’ Principle, the porosity of the sample can be calculated. This technique has been recommended as a standard porosity method by the American Petroleum Institute (API),12 the American Society for Testing and Materials (ASTM),13,14 and the International Society for Rock Mechanics (ISRM).15 Although some changes have been made regarding the saturation and immersion fluids and pretreatment conditions for various rock samples,8-11 the fundamental principle of the method has been maintained.

Besides

the complicated experimental procedures involved, a major problem of the method is 2


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that it underestimates the porosity due to the incomplete fluid intrusion into the fine pores of the system. Currently, the helium pycnometry method developed by the Gas Research Institute (GRI) is the technique for measuring shale porosity that is most favored in the energy industry.16-17

In this technique, the bulk volume of an untreated core

sample (～300 g) is measured by immersion in a fluid (often mercury) using Archimedes’ Principle.

The sample is then crushed and treated by both solvent

extraction (using hot toluene) for one to two weeks by the Dean Stark method18 and drying in an oven at 110oC for one to two weeks to completely remove the fluids from the pores. The grain volume (excluding the pore volume from the bulk volume) of the treated sample is measured by helium pycnometry and Boyle’s law; i.e., using helium penetration equilibration and pressure-volume calculations. The porosity is calculated by the ratio of the difference between bulk volume and grain volume of the sample to the bulk volume17.

Although the GRI method has a better measurement precision

than the fluid saturation and immersion techniques, it is still very complicated and time-consuming. More recently, nuclear magnetic resonance (NMR) has been proposed as a technique for measuring shale porosity.19-21 In this case, the shale porosity is directly calculated from the NMR signal of the hydrogen nuclei in water in the shale pores and fractures. Although sample crushing is not required in the NMR method, the inefficient sample treatment procedures of the solvent extraction and water saturation are still required.22 Moreover, the method is very sensitive to the NMR experimental parameters; e.g., echo time and waiting time.21

Therefore, an optimization of

instrument parameters must be performed for various rock samples, thereby making the measurement very complicated in addition to being expensive when the high cost of instrumentation, operation and maintenance are considered. In this paper, we propose a different approach, one based on headspace (HS) analysis as an effective technology for analysis of porosity of shale samples.

HS has

proven itself in numerous applications for analyzing volatile species in the presence of non-volatile interferences.23 Coupled with gas chromatography (GC), HS can be used to simultaneously determine multiple volatile species in samples.23 3


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works24-25 have described the application of HS-GC to the study of the adsorption behavior of gases in shale samples. Since there is a multiple headspace extraction (MHE) function available in most of commercial automated headspace samplers, a repeated monitoring of volatile species released from a given sample can be conducted by MHE-GC. Based on this monitoring function, we have previously developed a MHE-GC technique for the determination of the liquor viscosity,26 based on the fact that the mass transfer resistance of a tracer in a liquid sample is affected by liquor viscosity. In general, the pores in shale can be regarded as narrow channels with nano-scale diameters.27 The apparent resistance to the release of shale gas (mainly methane) in these channels is a function of the number and volume of these narrow channels, which is related to the porosity of the shale. Since the information of apparent transfer resistance is contained in the release rate of methane (as a tracer) in shale, it is possible to determine shale porosity by monitoring the methane release rate using MHE-GC. Because the tracer gas originates in shale, the complicated and time-consuming sample pre-measurement procedures for degassing and saturating that are a part of the previous methods described above are not required. The goal of this work was to develop a new method for the rapid determination of shale porosity based on the MHE function of headspace samplers, coupled with GC analysis. The main focus has been to identify the adequate, but minimal, number of extractions needed to make this measurement and to optimize the conditions for the determination. The method was evaluated by determining the porosity of a series of shale samples from the field.

EXPERIMENTAL Samples Nine core samples of shale were collected from three shale gas reservoirs located in Chongqing, China. The mineral and total organic content are listed in Table 1. The samples were ground and screened to 10-20, 20-40, and 60-80 meshes, and then stored in a desiccators at room temperature prior to analysis. 4


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Apparatus and operations A GC system (Agilent 7890A, USA) and an automatic headspace sampler (DANI HS 86.50, Italy) were used for the HS-GC measurements. The GC system was equipped with a flame ionization detector (FID) operating at a temperature of 250 oC and a DB-5 capillary column (Agilent, USA) operating at a temperature of 30oC for 3 min with nitrogen carrier gas (flow rate = 3mL/min). The injection port was operated at 250 oC in splitless mode. The headspace operating conditions were as follows: strong shaking for the sample equilibration at a temperature of 120oC for 10 min and multiple headspace sampling with an interval time of 20 min; vial pressurization time = 0.2min; and sample loop fill time = 0.2 min. The volume of the headspace sample vial and sampling loop were 21.6 mL and 3 mL, respectively. A helium pycnometer (Ultrapore-300, Temco, USA) was used for the porosity measurement as the reference method. The operating pressure was 200 psi, and the precision of the pressure sensor was 0.1 %. Preparations and procedures Porosity measurement using helium pycnometry. Core plugs (cylinder with diameter of 2.54 cm and height of 2 – 6 cm) were dried at 110 oC for 24 h, and the grain volume (VG) was measured by helium pycnometry at an initial pressure of 200 psi. For the bulk volume (VB), the sample was first sealed with paraffin (0.9 g/cm3), and weighed in air (mair), and then in water (mwater) with known density (ρwater). The bulk volume was then calculated by the following equation, i.e., VB =

mair − mwater

ρ water

(1)

The porosity ( φ ) of the sample was calculated from the grain volume and bulk volume; i.e.,

φ=

VB − VG ×100 VB

(2)

Porosity measurement using DHE-GC. One gram of ground core sample of shale with specific particle size (e.g. 10-20 meshes) in the range of 10-100 meshes was 5



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placed into the headspace sample vial and immediately sealed with a PTFE/silicone septum and an aluminum cap. Headspace extraction in the MHE mode, followed by GC analysis, was performed on the same sample vial at 120oC, with an equilibration time of 10 min and interval time of 20 min.

RESULTS AND DISCUSSION Theory of the method When the shale sample is placed in a closed headspace sample vial, the gas species entrapped in shale pores (solid phase) is released into the headspace (vapor phase), driven by the concentration difference of the gas in the two phases. According to the Darcy’s law which describes the fluid flow through porous media,28 the increasing rate of analyte concentration in the headspace phase is proportional to the mass transfer driving force, thus we have

dCg dt

= α ( Ce − Cg )

(3)

where the driving force of the mass transfer is the analyte concentration gradient between the actual state and the equilibrium state.

t is the mass transfer time. Ce

and Cg represent the analyte concentration in the headspace at the equilibrium state and the actual state, respectively. α is the mass transfer coefficient related to the pore system in the sample. Since the pores in the shale sample are extremely small (nano-scale diameters), the relationship between α and porosity ( φ ) of shale can be established according to a capillary model (describing the flow through small channels),29 i.e.,

α =βφ

(4)

where β is a coefficient that is related to the permeant fluid viscosity and the diameter distribution of pores. If the permeant gas is designated (e.g., methane as a tracer in the present work) and the uniformity of pores in shale sample is assumed, then β can be considered as 6


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a constant. Thus, α is proportional to the porosity. This relationship was also suggested in the study of shale permeability in previous studies.30-31 Substituting Eq. (4) into Eq. (3), and integrating Eq. (3) with the initial conditions, i.e., t = 0 , C g = 0 , we have

C g = Ce (1 − e− βφt )

(5)

In the MHE mode, headspace sampling is performed stepwise at given time intervals ( ∆t ), the concentration change of the released analyte in the headspace vial during the process is followed by GC measurement, and the analyte in the gas phase is stepwise removed at a constant ratio ( ϕ ) due to the headspace sampling. Thus, if we study the mass transfer process between any two consecutive MHE-GC measurements; e.g., i and i+1, the corresponding analyte concentrations at these two MHE-GC measurements are Cgi and Cgi +1 , respectively, and the analyte concentration in the headspace after the ith measurement is (1 − ϕ ) Cgi because of the mass lose during the sampling. According to Eq. (5), we have

(1 − ϕ ) Cgi = Ce (1 − e− βφt )

(6)

(

(7)

i

C gi +1 = Ce 1 − e

− βφ ( ti +∆t )

)

where ti and ti +1 are the mass transfer time at the ith and i+1th measurements, respectively. Merging Eqs (6) and (7), and making an arrangement, we have Cgi +1 C gi

(1 − ϕ ) (1 − e− βφ (t +∆t ) ) i

=

1 − e − βφti

(8)

Because the interval time between the measurements is very short compared to the time for equilibration, which often takes weeks or months in the direct method for determining shale gas content,32 the terms e ± βφ∆t → 1 . Thus, Eq. (8) can be further simplified as

7



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Cgi +1 C

i g

=

(

e βφ∆t (1 − ϕ ) e − βφ∆t − e e

− βφ∆t

(

1− e

− βφ ti

− βφ ( ti +∆t )

)

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) = (1 − ϕ ) e

βφ∆t

(9)

From Eq. (9), a linear relationship exists between the logarithm of the ratio of the analyte concentration in two consecutive measurements (i and i+1) separated by an interval of ∆t and sample porosity, i.e.,

φ=

ln (1 − ϕ ) 1 ln ( C gi +1 / C gi ) − β∆t β ∆t

(10)

Since the GC signal (A) in the HS-GC measurement is proportional to the concentration of the analyte in the vapor phase; i.e., Cgi = fAi , Eq. (10) can be written as

φ=

ln (1 − ϕ ) 1 ln ( Ai +1 / Ai ) − β ∆t β∆t

(11)

Thus, the porosity in the sample can be obtained using the GC signals from two consecutive measurements in the MHE testing.

Optimization of measurement conditions In this work, the shale samples were placed in a closed headspace and the methane trapped in shale pore channels was used as the tracer. By conducting MHE on a given headspace vial, the release of methane from that shale sample can be followed.

To obtain a good efficiency, sensitivity, and accuracy, conditions, such as

equilibration temperature, time, time interval and sample particle size should be optimized

Selection of headspace equilibration temperature. The release of the entrapped methane from shale sample is a very slow process at a room temperature. This property not only affects the efficiency of the method, but also reduces the detection sensitivity, especially for aged samples. However, the rate of release of the methane from shale can be greatly increased when the process is conducted at an elevated temperature.24,25 According to the proposed theory of the method, an elevated temperature should increase the diffusion-controlled mass transport of the methane in the shale. 8


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In the present work, we performed the testing for shale samples at 120 oC because the temperature is below the maximum tolerable temperature of the rubber septum that seals the headspace sample vial. Tests have shown that no leakage occurs from the vial as a consequence of the high pressure generated at this moderately high temperature.24,25

Equilibration time and interval time. A goal of the study is to develop a new method that is rapid compared to existing methods. In order to make sure that the studied mass transfer process takes place at the given temperature, it is necessary that the desired temperature (120oC) has been reached when the first HS-GC measurement is taken. Thus, the equilibration time should be longer enough to achieve this end. According to a previous study33 and reference heat capacity data34, we found that the target temperature for the given weight of shale sample can be achieved in 10 min. Therefore, we selected 10 min as the equilibration time for the first headspace extraction measurement. According to Eq. (5), a longer interval time will be helpful in obtaining a larger concentration change of the analyte between the two consecutive HS-GC measurements, thereby improving the detection sensitivity for the analyte. Fig. 1 shows the integrated methane release during the headspace equilibration at 120oC. The 20 min interval time (between 10 and 30 min) was chosen because the change in methane concentration was the greatest during this interval, which improves the sensitive of the measurement. Note that the total time for the analysis is roughly 30 min and can be accomplished with only two extractions; hence, the name “double headspace extraction-gas chromatography (DHE-GC)” for the method.

Selection of sample particle size. For a given weight of shale sample, smaller particle size generally provides larger exposed surface area and thus results in a higher rate of methane release from the solid sample, which is important for improving the sensitivity of the method.

Table 2 shows the effect of sample particle size on the

ratio of the methane signals between the first and second measurement; i.e., A2 / A1 in Eq. (11).

It can be seen that the differences in A2 / A1 for the measurement with

different particle sizes are not significant, indicating that the permeability of the shale 9



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sample is so poor that the release rate of the analyte is mainly determined by internal diffusion (in the nano-scale channels) processes, rather than by the desorption process on the pore surface.

In short, over the particle size range (10 - 100 meshes) studied,

the effect of sample particle size on the present method was not significant.

Method calibration As described in the experimental section, nine shale samples with various porosities ( φ ) (as measured by a reference method) were ground to obtain material in a specific particle size range.

These samples were then measured by DHE-GC using

the GC signals from the first and second MHE-GC measurements; i.e., A1 and A2. By plotting φ vs. ln ( A2 / A1 ) , a linear relationship between them was established, as shown in Fig. 2, whose equation is

φ = 6.62 ( ±0.43) ln ( A2 / A1 ) + 6.58 ( ±0.27 )

n = 16

(12)

which is of the form of Eq (11) and which can be used to calculate shale porosity from the two signals measured by DHE-GC. Fig. 2 shows that most of the data points in this study are located in the area with an uncertainty < 10 %.

The two most notable exceptions can be attributed to

significant measurement errors that occurred in the helium porosity determination16 or the heterogeneity in this particular sample that led to significant differences in the determinations by the two methods.

The results also confirm that there is no

significant difference when using different sample particle sizes (20-40 or 60-80 meshes) in the testing.

Method evaluation Measurement precision. The precision of the DHE-GC method was investigated by quintuplicate measurements of the same shale sample (Sample 7 in Table 1) with particle size of 10-20 meshes. The results in Table 3 show that the uncertainty (expressed as the relative standard deviation, RSD) of the ratio of the GC signals (i.e., A2/A1) is much smaller than the uncertainty in the individual measurement for either

10


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A1 or A2, indicating that the present method based on the relative measurement has a good precision. To evaluate the errors of porosity measured by the DHE-GC method, an uncertainty propagation analysis was employed as follows. According to Eq. (12), the uncertainty (as standard derivation) of φ is mainly from the slope ( S = 6.62 ), intercept ( I = 6.58 ), and the ratio (R) of the GC signals (i.e., R = A2 / A1 ). Thus, the standard error of φ can be expressed as 2

2

2

 ∂φ   ∂φ   ∂φ  2 sφ2 =   sS2 +   sI2 +   sR  ∂S   ∂I   ∂R 

(13)

where sφ , sS , sI , and sR represent the standard error of the porosity, the slop, the intercept, and the ratio of the two GC signals, respectively. Rearranging Eq. (13), we obtain sφ =

( ln ( R − (ϕ − 1) ))

2

2

  2 S s + s +   sR − − 1 R ϕ ( )   2 S

2 I

(14)

Using Eq. (14), the uncertainty of porosity can be calculated from S and the measured values of R and ϕ ( ϕ is a constant under the given operation conditions [23], which was calibrated beforehand).

From the measurements of nine core

samples with particle size of 10-20 meshes, the uncertainties of the porosities determined by the DHE-GC method were in the range from 0.31 to 0.46 p.u. (a unit equal to the percentage of pore space in a unit volume of rock.), which are smaller than 0.56 p.u. from helium pycnometry method reported by Luffel and Guidry.16

Correlation of DHE-GC results with those of the reference method. The porosities of nine core samples were measured by both the present method and the helium pycnometry method. The results are shown in Fig 3, in which the error range from DHE-GC method was calculated by Eq. (14). There is good agreement between the data obtained by the two methods, indicating that the DHE-GC method is suitable for the rapid determination of porosity in shale samples.

CONCLUSIONS 11



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A new method for rapid determination of shale porosity by DHE-GC method has been developed. Based on the ratio of GC signals from two successive headspace extraction-GC measurements, the shale porosity can be calculated from the two GC signals using a correlation between them. Investigation showed that the method is not significantly affected by the particle size of the sample. Since the method does not require extensive, time-consuming sample treatments, such as solvent extraction, heating, and drying, the DHE-GC method is simpler, more rapid and more efficient than the current standard helium pycnometric method. In short, the DHE-GC method is a new valuable tool available for shale gas-related research and production applications.

AUTHOR INFORMATION

Corresponding Author *E-mail: [email protected]

Notes The authors declare no competing financial interest.

ACKNOWLEDGEMENTS This study was jointly supported by National key Basic Research Program of

China (973 Program: 2012CB214705), and the Natural Science Foundation of China (No. 21576105).

REFERENCES (1) U.S., Energy Information Administration. Effect of increased natural gas exports on domestic energy markets. 2012, http://www.fossil.energy.gov/programs/gas rerulation/reports/feeialng.pdf. (2) U.S., Energy Information Administration. World shale gas resources: An initial assessment of 14 regions outside the United States. 2011, http://www.eia. gov/analysis/studies/ worldshalegas/pdf. (3) Chen, F.W.; Lu, S.F.; Ding, X. The Scientific World J. 2014, 1-9. (4) Yuan, W.N.; Pan, Z.J.; Li, X.; Yang, Y.X.; Zhao, C.X.; Connell, L.D.; Li, S.D.; He, 12


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J.M. Fuel 2014, 117, 509-519. (5) Tian, H.; Pan, L.; Xiao, X.M.; Wilkins, R.W.T.; Meng, Z.P.; Huang, B.J. Mar. Petrol. Geol. 2013, 48, 8-19. (6) Jiang, Y.L.; Xue, H.Q.; Wang, H.Y.; Liu, H.L.; Yan, G. Appl. Mech. Mater. 2013, 288, 333-337. (7) Tiab, D. Donaldson, E.C. Petrophysics. Elsever: Holand, 2004. (8) Barnes, K.B. A method for determining the effective porosity of a reservoir-rock. Vol. 10. School of Mineral Industries. State college: Pennsylvania, 1931. (9) Shapiro, L. Rapid analysis of silicate, carbonate and phosphate rocks, revised edition, vol. 1401 of USGS Bulletin. US Government Printing Office, 1975. (10) Howard, J.J. Clay. Clay Miner. 1991, 39, 355-361. (11) E.W. Washbum, E.N. Bunting, J. Am. Ceram. Soc., 1922, 5, 48-56. (12) American Petroleum Institute. Recommended practices for core analysis. API RP 40, 1998. (13) American Society for Testing and Materials. Standard test method for apparent porosity, water absorption, apparent specific gravity, and bulk density of burned refractory brick and shape for boling water. ASTM Standard C20-00, 2010. (14) American Society for Testing and Materials. Standard test method for apparent porosity, liquid absorption, apparent specific gravity, and bulk density of refractory shapes by vacuum pressure. ASTM Standard C830-00, 2011. (15) Franklin, J.; Vogler, U.; Szlavin, J.; Edmond, J.; Bieniawski, Z. Suggested methods for determining water content, porosity, density, absorption and related properties and swelling and slake-durability index properties. Pergamon Press: Oxford, 1981. (16) Luffel, D.L.; Guidry, F.K. J. Pet. Technol. 1992, 44, 1184-1190. (17) Luffel, D.L.; Guidry, F.K.; Crutis, J.B. J. Pet. Technol. 1992, 44, 1192-1197. (18) Dean, E.W.; Stark, D.D. Ind. Eng. Chem. 1920, 12, 486-490. (19) Sun, J.C.; Chen, J.P.; Yang, Z.M.; Liu, X.W.; Liu, Y.J. Sci. Technol. Rev. 2012, 30 25-30. (20) Yao, Y.B.; Liu, D.M. Fuel 2012, 95, 152-158. (21) Xu, H.; Tang, D.Z.; Zhao, J.L.; Li, S. Fuel 2015, 143, 47-54. 13



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(22) Chinese

petroleum

industry

standard.

Specification

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for

normalization

measurement of core NMR parameter in laboratory. SY/T 6490-2007, 2007. (23) Kolb, B.; Ettre, L.S. Static Headspace-Gas Chromatography-Theory and Practice. Wiley-VCH Press: New York, 2006. (24) Zhang, C.Y.; Hu, H.C.; Chai, X.S.; Pan, L.; Xiao, X.M. J. Chromatogr. A 2013, 1310, 121-125. (25) Zhang, C.Y.; Hu, H.C.; Chai, X.S.; Pan, L. Xiao, X.M. J. Chromatogr. A 2014, 1328, 80-84. (26) Hu, H.C.; Chai, X.S. J. Chromatogr. A 2013, 1320, 125-129. (27) Zhang, S. Klimentidis, R.E. Porosity and permeability analysis on nano-scale FIB-SEM 3D imaging of shale rock, International Symposium of the Society of Core Analysts, Texas, USA, 2011. (28) Brace, W.F.; Walsh, J.B.; Frangos, W.T. J. Geophys. Res. 1968, 73, 2225-2236. (29) Leonards, G.A. Engineering properties of soil, chapter 2, Foundation Engineering. McGraw-Hill Book Company, 1962. (30) Lapierre, C.; Leroueil, S. Can. Geotech. J. 1990, 27, 761-773. (31) Mesri, G.; Olson, R.E. Clay. Clay Miner. 1971, 19, 151-158. (32) Kissell, F.N.; Mcculloch, C.M.; Elder, C.H. US Bur. Mines, Rep. Invest. 1973, 7767, 17. (33) Chai, X.S.; Zhu, J.Y. J. Chromatogr. A 1998, 799, 207. (34) Ahrens, T.A. Rock physics & phase relations: a handbook of physical constants. American Geophysical Union: Washington, 1995.

14


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Table 1 Content of the shale samples Mineral composition, % Sample no.

TOC, % Quartz

Clay

Others

1

0.946

31.2

67.2

0.654

2

1.35

43.7

56.4

——

3

1.90

66.6

33.4

——

4

3.72

49.1

49.2

——

5

4.03

39.4

59.1

——

6

5.20

57.6

42.3

——

7

8.49

65.7

34.3

——

8

1.19

26.4

71.3

1.31

9

0.875

23.2

74.8

1.13

15



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Table 2

Page 16 of 22

Effect of particle size on the value of A2 / A1 * GC signals

Particle size, mesh A1

A2

A2/A1

10-20

26.1

23.0

0.881

20-40

27.5

23.3

0.847

40-60

23.9

20.9

0.874

60-80

26.8

22.0

0.821

80-100

26.5

22.2

0.838

*Sample 7 in Table 1 was used in the test.

16


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Table 3 The precision of the DHE-GC method Run no.

A1

A2

A2/A1

1

18.0

15.1

0.839

2

19.2

16.5

0.855

3

19.3

16.6

0.865

4

22.0

18.4

0.836

5

21.1

17.9

0.848

RSD, %

8.06

7.68

1.16

17



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

Figure Captions Fig. 1 The time-dependent release of methane during the headspace equilibration. Fig. 2 The relationship between the porosity measured by helium pycnometry and

ln ( A2 / A1 ) determined by DHE-GC. Fig. 3 The correlation between the porosity measured by the DHE-GC and the helium pycnometric method.

18


Page 18 of 22

Page 19 of 22

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Fig. 1 The time-dependent release of methane during the headspace equilibration 297x209mm (150 x 150 DPI)



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Fig. 2 The relationship between the porosity measured by helium pycnometry and DHE-GC. 297x209mm (150 x 150 DPI)


Page 20 of 22

ln(A2/A1) determined by

Page 21 of 22

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Fig. 3 The correlation between the porosity measured by the DHE-GC and the helium pycnometric method. 297x209mm (150 x 150 DPI)



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Graphic abstract for the manuscript 134x81mm (96 x 96 DPI)


Page 22 of 22

Determination of Porosity in Shale by Double Headspace Extraction

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