Experimental study on gas slippage of Marine Shale in Southern China

Petroleum xxx (2016) 1e6

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Original article

Experimental study on gas slippage of Marine Shale in Southern China Ying Ren a, *, Xiao Guo a, Chuan Xie b, Hongqin Wu c a

State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation, Southwest Petroleum University, No. 8, Xindu Avenue, Xindu District, Chengdu 610500, China b Shunan Division of Southwest Oil and Gasfield Company, PetroChina, Sichuan, Luzhou 646000, China c Research Institute of Drilling Engineering, Sinopec Southwest Petroleum Engineering Company, Sichuan, Deyang 618000, China

a r t i c l e i n f o

a b s t r a c t

Article history: Received 11 January 2016 Received in revised form 4 March 2016 Accepted 22 March 2016

The shale gas reservoirs are composed of porous media of different length scales such as nanopores, micropores, natural fractures and hydraulic fractures, which lead to high heterogeneity. Gas flow from pores to fractures is under different flow regimes and in the control of various flow mechanisms. The gas slippage would have significant effects on gas flow in shale. To obtain the effect of slippage on gas flow in matrix and fractures, contrast experiments were run by using cores with penetration fractures and no fractures from Marine Shale in Southern China under constant confining pressure. The results showed that slippage effect dominates and increases the gas permeability of cores without fractures. To cores with penetration fractures, slippage effect is associated with the closure degree of fractures. Slippage dominates when fractures close under low pore pressure. Slippage weakens due to the fractures opening under high pore pressure. Fracture opening reduces the seepage resistance and slippage effect. The Forchheimer effect occurs and leads to a permeability reduction. Copyright © 2016, Southwest Petroleum University. Production and hosting by Elsevier B.V. on behalf of KeAi Communications Co., Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

Keywords: Shale gas Permeability Fracture Slippage Effective stress

1. Introduction As shale gas reservoirs are increasingly becoming major fossil energy in today's world, understanding the gas flow mechanism in these unconventional gas resources is crucial. The dynamics of gas flow in shale gas reservoirs has become an important research topic during the current decade in the oil and gas industry [1]. There are four types of porous media of different length scales in shale gas reservoirs: nanopores, micropores, natural fractures and hydraulically induced fractures [2]. Fig. 1 shows the pores in conventional and shale gas reservoirs. As presented in the

* Corresponding author. Tel.: þ86 18782943263. E-mail address: [email protected] (Y. Ren). Peer review under responsibility of Southwest Petroleum University.

Production and Hosting by Elsevier on behalf of KeAi

schematic figure, shale gas reservoirs contain more nanopores than conventional reservoirs. Radius of pore throats in gas shale sediments generally ranges from a few nanometers to a few micrometers [3]. These matrix pores make up the significant portion of reservoir space of natural gas. The complex fracture system composed of natural fractures and hydraulically induced fractures connects matrix pores, which forms a highpermeability network in gas shale. When gas flows from nanopores to fractures and from factures to wellbore, the flow mechanism varies due to the different length scales of flow channels. Gas flow in larger pores, throats and fractures generally follows Darcy equation, and in nanopores, slip flow and diffusion dominate [4]. The Knudsen number, a significant dimensionless parameter, is used to classify the flow regimes in porous media of different length scales. It is defined as the ratio of the gas mean free path l (m) and the pore radius r (m) [3].

Kn ¼

l r

(1)

http://dx.doi.org/10.1016/j.petlm.2016.03.003 2405-6561/Copyright © 2016, Southwest Petroleum University. Production and hosting by Elsevier B.V. on behalf of KeAi Communications Co., Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

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Y. Ren et al. / Petroleum xxx (2016) 1e6 100 1nm 10nm 100nm 500nm 1um 5um

The Knudsen number (Kn), dimensionless

10

free molecular flow

transitional flow

1

0.1

slip flow

0.01

0.001 continuum flow (no-slip flow) 0.0001 0.1

1

10 pressure (p), MPa

100

Fig. 2. Knudsen number as a function of pressure.

Klinkenberg slippage factor, MPa; p is the mean pore pressure, MPa. Table 1 presents various correlations for gas slippage factor b proposed in the subsequent work. Beskok and Karniadakis(1999) [17] developed a rigorous equation for volumetric flow through a micro tube.

 ka ¼ ð1 þ aKnÞ 1 þ Fig. 1. Pores in conventional (a) and shale gas (b) reservoirs [3].

a¼ The gas mean free path l is defined as

K T l ¼ pffiffiffi B 2 2pd p

(2)

in which KB is the Boltzmann constant, 1.3805  1023 J/K; T is temperature, K; p is pressure, Pa; d is the collision diameter of the gas molecule. For methane, d¼0.4  109 m. Different Knudsen numbers correspond to different flow regimes [5,6]: continuum flow (Kn < 0.001), slip flow (0.001 < Kn < 0.1), transitional flow (0.1 < Kn < 10), and free molecular flow (Kn > 10). Fig. 2 presents the Knudsen number as a function of pressure with various pore sizes ranging from 1 nm to 5 mm. The gas slippage typically occurs in the condition where the mean free path of the gas molecules is no more negligible compared to the average effective pore throat radius (0.001 < Kn < 0.1). The gas molecules would slip on the inner surfaces of the pores. This effect gives apparently higher permeability than the absolute permeability measured using a liquid [7,8]. Klinkenberg (1941) [9] first addressed the gas slippage in porous media and gave a linear correlation between the measured gas permeability and the reciprocal mean pore pressure.

  b ka ¼ k∞ 1 þ k p

(3)

where k∞ is the absolute permeability, mD; ka is the measured gas permeability (apparent permeability), mD; bk is the

 4Kn k∞ 1  bKn

  128 1 0:4 4Kn tan 15p2

(4a)

(4b)

where a is the dimensionless sparse coefficient, b is gas slippage factor and generally b z 1. Civan (2010) [13] improved Beskok and Karniadakis model and demonstrated a simple inverse power-law expression of the sparse coefficient a as given below

a¼

a0 A 1 þ Kn B

(5)

where A ¼ 0.170, B ¼ 0.434, a0 ¼ 1.358. Tang et al. (2005) [15] reported that the second-order term of the Knudsen number (Kn2) cannot be neglected for gas flow with relatively high Knudsen numbers. They presented a widely known model given as follows

ka ¼ k∞ 1 þ

A B þ p p2

! (6)

where A, B are constants that depend on gas properties and pore geometry. Zhu et al. (2007) [16] also recommended using a higher-order equation which can be written as

  a ka ¼ k∞ 1 þ Aep

(7)

Fathi et al. (2012) [18] proposed the following equation based on their numerical analysis.

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Y. Ren et al. / Petroleum xxx (2016) 1e6

3

Table 1 Various correlations for Klinkenberg gas slippage factor. Model

Correlation

Klinkenberg (1941) [9] Heid et al. (1950) [10] Jones and Owens (1979) [11] Sampath and Keighin (1982) [12] Florence et al. (2007) [7]

bk bk bk bk bk

Civan (2010) [13]

bk ¼ 0:0094ðk∞ =fÞ0:5

Nitrogen

Letham and Bustin (2015) [14]

bk ¼ 0:026ðk∞ Þ0:43

Nitrogen

" ka ¼ k∞

¼ 4clp=r ¼ 11:419ðk∞ Þ0:39 ¼ 12:639ðk∞ Þ0:33 ¼ 13:851ðk∞ =fÞ0:53 ¼ bðk∞ =fÞ0:5

  2  # b LKe 1þ p l

(8)

where LKe is a new length scale associated with the kinetic energy of the bouncing-back molecules. There are several ways [8] to measure shale permeability such as steady-state [1,19] and pressure pulse-decay [14,20] measurements. Experiment study of slippage is based on these measurements in different experimental conditions. Steadystate measurement is widely used to measure the permeability of porous media. Zhu et al. (2015) [21], Yang et al. (2015) [22] and Kang et al. (2015) [19] conducted steady-state flow experiments at constant confining pressure and constant net confining pressure. However, Steady-state measurement usually costs much time. Therefore, Brace et al. (1978) [23] proposed pulse-decay method based on unsteady-state flow mechanism, which greatly reduces the time of measurements. Fathi et al. (2012) [18] conducted a transient permeability measurement using crushed samples. Ren et al. (2015) [24] proposed an unsteady-state measurements considering slippage. In this paper, we presented a laboratory study on gas slippage by using low permeability shale samples. We characterized two types of cores from Qiongzhusi Formation and Longmaxi Formation of Marine Shale in Southern China. Cores with well-tended appearance are used to model shale matrix and cores with penetration fractures are used to model matrix affected by hydraulic fractures or macro natural fractures. We measured gas permeability by changing the pore pressure at constant confining pressure. Then we analyzed the difference of experiment results between two types of cores and showed the gas flow behavior in cores with fractures.

Comments

Units

c z 1, Air Air Air Air bNitrogen ¼ 43.345 bAir ¼ 44.106

bk: psi k∞: mD p: psi r: nm b: psi l: nm f: fraction bk: Pa k∞: m2 bk: MPa k∞: mD

showed that the facility possesses excellent sealing when confining pressure is over 5 MPa. Results of standard core showed that experimental data were within the accepted error range. Fig. 4 shows the diagram of the gas flow experiment. The core sample was enclosed in a rubber sleeve which was mounted in a core holding unit. We used nitrogen gas as the pore fluid and water as the confining fluid. In all our tests, the

2. Sample description We extracted eight intact core samples for gas flow experiments from Qiongzhusi Formation and Longmaxi Formation of Marine Shale in Southern China. Four cores numbered S1eS4 were with well-tended appearance and cores numbered S5eS8 were with penetration fractures (Fig. 3). The brittleness of shale makes it easy to make fractures. Fractures of cores S5eS8 generated during the process of increasing confining pressure in core holding unit. Then we heated these eight cores to 60  C to drive off any free fluid for 48 h.

Fig. 3. Photographs of cores for experiments.

3. Gas flow experiments and experimental setup We conducted gas flow experiments by using the HA-IIIAH2S-CO2 experimental facility of core. Iron core and standard core were tested respectively to verify the sealing and precision of the equipment before the measurements. Results of iron core

Fig. 4. Experimental diagram. 1. Nitrogen gas cylinder. 2. Pressure regulating valve. 3. Pressure sensor. 4. Core holding unit. 5. Temperature control chamber. 6. Confining pressure pump. 7. Soap film flowmeter. 8. Computer.

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Y. Ren et al. / Petroleum xxx (2016) 1e6

confining pressure was at 20 MPa and the downstream pressure was atmospheric pressure. The initial upstream pressure was at 0.2 MPa. Two pressure sensors and a flow sensor were used to detect and transmit experimental data so that we could observe and log it on the computer. We recorded the upstream pressure, downstream pressure and flow rate until the data remained stable. Then we increased the upstream pressure and conducted next stage of experiments. For cores S1eS4, we increased the upstream pressure by 0.2 MPa per stage; for cores S5eS8, we increased the upstream pressure by 0.1 MPa per stage. Computer recorded pressure, temperature and flow rate in real time, and it calculated the measured gas permeability by using the equation as follows:

2q p mL Kg ¼  20 0 2   104 A p1  p2

(9)

where q0 is outlet flow, cm3; m is gas viscosity, mPa$s; p0 is atmospheric pressure, MPa; A is cross-sectional area of core, cm2; L is length of core, cm; p1, p2 are the upstream pressure and downstream pressure, MPa; Kg is measured gas permeability, mD. The viscosity was corrected during the calculation for it would change with temperature and pressure. 4. Results and discussion 4.1. Gas slippage in S1eS4 Figs. 5 and 6 present gas flow rate as a function of differences of pressure squares. Overall, gas flow rate increases with the increase of differences of pressure squares and presents a convex trend. However, there are obvious differences between the curves. Gas flow rate in Fig. 6 ranges from 0 to 7.2 cm3/s while gas

flow rate in Fig. 5 ranges from 0 to 0.3 cm3/s, which indicates that fractures contributes much to the gas flow rate of cores S5eS8. Then, the trend of convex was related to the absolute permeability [21]. The curves of lower-permeability cores (S1eS4) are more like a straight line while curves of higher-permeability cores (S5eS8) would present an obvious convex trend. 4.2. Gas slippage in S1eS4 Klinkenberg curves of S1eS4 measured in this study are presented in Fig. 7. Four curves all follow a near-linear trend with varying amounts of scatter. Permeability increases linearly with incremental inverse pore pressure, which indicates that the slippage dominates in matrix at the experimental condition (pc ¼ 20 MPa, pp < 3 MPa, T ¼ 60  C). Permeability and slippage factor were calculated by comparing the linear fitting data with the Klinkenberg slippage model and we would discuss it in subsequent work. As presented in Fig. 8, permeability ranges from 0.05 mD to 0.5 mD which is a few orders of magnitude larger than that of S1eS4. The existence of fractures would improve shale permeability obviously. Moreover, Klinkenberg plots of S5eS8 follow an obvious non-linear relation which could be divided into two parts. In the left part of the curves (1/pp < 2 MPa1), there was dramatic increase. Then we saw an approximately linear rise and the slope of the section was close to that of S1eS4 when inverse pore pressure was over 2 MPa1. 4.3. Flow mechanism in shale matrix and fractures There was no penetration fractures in cores S1eS4, so gas flow in these samples could be seemed as flow in shale matrix in

Mesured Gas Permeability (ka), mD

0.0120

0.3000 0.2500

Gas flow rate (q), cm3/s

0.2000

0.0100

Experimental Data of S1 Experimental Data of S2 Experimental Data of S3 Experimental Data of S4

0.0080

0.1500 0.1000

0.0020

0.0500

0.0000 0.00

0.0000 0.00

Experimental Data of S2 Experimental Data of S4 Linear Fitting for S2 Linear Fitting for S4

0.0040

2.00 4.00 6.00 8.00 Differences of pressure squares (Δp2), MPa2

1.00

2.00 3.00 4.00 Inverse Pore Pressure (1/pp), MPa-1

5.00

6.00

10.00 Fig. 7. Klinkenberg plots of S1eS4.

0.6000 Mesured Gas Permeability (ka), mD

Fig. 5. Gas flow rate versus differences of pressure squares of samples S1eS4.

0.5000

7.2000

Experimental Data of S5 Experimental Data of S6 Experimental Data of S7 Experimental Data of S8

6.0000 Gas flow rate (q), cm3/s

Experimental Data of S1 Experimental Data of S3 Linear Fitting for S1 Linear Fitting for S3

0.0060

4.8000

0.4000 Experimental Data of S5 Experimental Data of S7 Liner Fitting for S7 Liner Fitting for S6

0.3000

3.6000

Experimental Data of S6 Experimental Data of S8 Liner Fitting for S8 Liner Fitting for S5

0.2000

2.4000

0.1000

1.2000

0.0000

0.0000 0.00

2.00 4.00 6.00 8.00 Differences of pressure squares (Δp2), MPa2

10.00

Fig. 6. Gas flow rate versus differences of pressure squares of samples S5eS8.

0.00

1.00

2.00

3.00

4.00

5.00

6.00

7.00

8.00

Inverse Pore Pressure (1/pp), MPa-1 Fig. 8. Klinkenberg plots of S5eS8.

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Y. Ren et al. / Petroleum xxx (2016) 1e6

4.4. Correlation for slippage factor b Slippage factor b and corrected permeability of measured cores were given by regressing linear experimental data to the Klinkenberg slippage model (Eq. (3)). As presented in Fig. 10, the slippage factor of S1eS4 ranges from 0.0526 MPa1 to 0.3333 MPa1 when permeability ranges from 0.0078 mD to 0.0012 mD. For pseudo-matrix flow (linear section in Fig. 7) of S5eS8, slippage factor ranges from 0.0316 MPa1 to 0.0431 MPa1 when permeability ranges from 0.0348 mD to 0.4167 mD. Fig. 10 indicates that slippage factor b negatively correlates with corrected permeability, which fits the equation as follows: b ¼ aKb. We conducted exponential fit and got the correlation between slippage factor b and corrected permeability: b ¼ 0:0233k0:246 . When corrected permeability is ∞ lower than 0.05 mD, slippage factor b decreases quickly with the increase of permeability [25].

(a) High effective stress (low pore pressure): Slip-flow + Darcy-flow

0.35

Slippage Factor (b), MPa

which gas slippage dominates. Measured gas permeability is as a linear function of inverse pore pressure. For cores S5eS8, existence of fractures complicates the flow mechanism. Fractures opening or closing is related to the effective stress which is defined as the difference between confining pressure and pore pressure. In this study, confining pressure was set as a constant 20 MPa, so effective stress negatively correlated with pore pressure. Fig. 9 presents different flow mechanisms of different stress condition in fractures. High effective stress (low pore pressure) would lead to closure of the fractures. However, fractures would not close completely for the anisotropy of shale and antideformation of filler. The flow mechanism was same as flow in shale matrix that gas slippage dominates and the matrix has higher permeability due to the unclosed fractures. We saw a linear correlation in this pseudo-matrix section. Contrarily, low effective stress (high pore pressure) would open the fractures, which would extend the flowing space. According to Eq. (1), the Knudsen number negatively correlated with pore radius r, so extension of flowing space causes a decrease of the Knudsen number, which reduces the contribution of gas slippage effect. Moreover, high pore pressure and wide flowing channels even lead to the occurrence of Forchheimer effect. A sharp decrease appears in this pseudo-fracture section.

5

0.3 Experimental data Exponentiation fit

0.25 0.2 0.15 0.1 0.05 0 0

0.1

0.2

0.3

0.4

0.5

Klinkenberg Corrected Pemeability (k ), mD Fig. 10. Exponentiation relation between slippage and permeability.

5. Conclusions Contrast experiments were run by using cores with penetration fractures and no fractures under constant confining pressure. The main conclusions in this paper are as follows: (1) Gas flow in shale matrix is in the control of gas slippage and follows the Klinkenberg model at the experimental conditions where the confining pressure is 20 MPa, the temperature was 60  C and the pore pressure is lower than 3 MPa. Slippage factor b ranges from 0.05 to 0.3. (2) Gas flow in core with fractures presented a two-section characteristic which is composed of pseudo-matrix section and fracture section. In pseudo-matrix section where inverse pore pressure is over 2 MPa1, permeability increases linearly and slowly with the incremental inverse pore pressure. In fracture section where inverse pore pressure is less than 2 MPa1, permeability increases rapidly with the incremental inverse pore pressure.

(b) Low effective stress (high pore pressure): Slip-flow + Darcy-flow + Forehheimer-flow

Fig. 9. Flow mechanism of different stress conditions in fractures.

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(3) Effective stress affects the opening and closing of fractures, which would have significant effects on gas flow. High effective stress causes fractures closing and enhances gas slippage, while low effective stress opens the fractures and weakens gas slippage. (4) A correlation between slippage factor b and corrected permeability was built. The correlation indicates that b changes little when permeability is higher than 0.05 mD, while b decreases sharply with the increase of permeability when permeability is lower than 0.05 mD.

Acknowledgments We would like to thank the National “973” Plan Project of China (No. 2013CB228002) for providing financial support to this research work.

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