Effect of Permeability Anisotropy on the Production of Multi-Scale Shale Gas Reservoirs
Abstract
:1. Introduction
2. Calculation Model of Permeability Anisotropy for Shale Gas Reservoirs
3. Multi-Scale Seepage Non-Linear Model in Shale Gas Reservoirs
3.1. Knudsen Number and Multi-Scale Flow Regimes in Shale Gas Reservoirs
3.2. Apparent Permeability Model Valid for Different Flow Regimes
4. Gas and Water Transport Model in Multi-Scale Shale Gas Reservoirs
4.1. Gas Flow in Multiscale Shale Gas Reservoirs
4.1.1. Gas Flow in Multiscale Shales
4.1.2. Gas Flow in Hydraulic Fracture
4.2. Water Flow in Multiscale Shale Gas Reservoirs
4.2.1. Water Flow in Multiscale Shales
4.2.2. Water Flow in Hydraulic Fracture
4.3. Validation of the Developed Numerical Model
5. Results and Discussion
5.1. Effect of Permeability Anisotropy on Production Rate
5.2. Effects of Non-Darcy Effect in Multiscale Shales
5.3. Effect of Gas-Water Flow in Formation
6. Conclusions
- A new model of permeability anisotropy for shale gas reservoirs is presented to calculate permeability in an arbitrary direction in three dimensional space, and a numerical model which is valid for all flow regimes in multiscale shale gas reservoirs was developed. The simulation result showed that numerical model matches well with the field data of the Marcellus shale.
- The production rate and cumulative production increase with the decrease of dip and azimuth (supposing that the direction of horizontal well is parallel with the maximum permeability when azimuth is equal to 0°), but dip has a greater impact on production rate and cumulative production than azimuth. The effects of dip (azimuth) on production are small for angles less than 30°, moderate for dip (azimuth) between 30° and 60°, and large for dip (azimuth) greater than 60°. When dip (azimuth) increases to 90°, the production becomes the lowest.
- Different flow regimes in this three dimensional numerical model were classified by Knudsen number, and the effect of non-Darcy in multiscale shales on production rate was emphatically analyzed under different permeabilities of shales. The production rate of multi-stage fractured horizontal well increases with the permeability of shale. But the increase of gas production which considers the effects of non-Darcy flow in multiscale shales decreases with the increase of shale permeability, compared with the gas production rate only considering viscous flow.
- The effect of gas-water flow on the performance of multi-stage fractured horizontal wells was analyzed as well. Initial water saturation has a greater impact on gas production than relative permeability curves with different nanopore radii, and initial water saturation affects the production throughout the whole development process of shale gas reservoirs.
Acknowledgments
Author Contributions
Conflicts of Interest
Nomenclature
Latin | |
A1 | fitting adjustable coefficient, 7.9 [30] |
A2 | fitting adjustable coefficient, 9.0 × 10−6 [30] |
A3 | fitting adjustable coefficient, 0.28 [30] |
b | slippage coefficient |
Bg | gas volume factor |
Bw | water volume factor |
f(Kn) | permeability correction factor |
g | gravitational acceleration, m/s2 |
i, j, k | coordinates of grid block |
Ka | apparent permeability |
KH | permeability of hydraulic fracture |
KH0 | initial permeability of hydraulic fracture |
K∞ | absolute permeability |
kB | Boltzmann Constant, 1.3805 × 10−23 J/K |
krg | relative permeability of gas phase |
krw | relative permeability of water phase |
kδx | maximum permeability measured parallel to bedding plane |
kδy | minimum permeability measured parallel to bedding plane |
kδz | permeability measured perpendicular to bedding plane |
kn | permeability in an arbitrary direction |
Kn | Knudsen number |
M | molecular mass, kg/mol |
p | pressure, Pa |
pg | pressure of gas phase, Pa |
pgi | initial pressure of gas phase, Pa |
pL | Langmuir’s pressure, Pa |
pc | critical pressure of methane, 4.5992 × 106 Pa [30] |
pw | pressure of water phase, Pa |
qg | gas volume flux per unit volume of shale and per unit time |
qw | water volume flux per unit volume of shale and per unit time |
r | pore radius |
rh | equivalent hydraulic radius of pores |
rw | wellbore radius |
sg | gas saturation |
sw | water saturation |
T | temperature at formation condition, K |
Tc | critical temperature of methane, 190.564K [30] |
vg | gas flow rate, m/s |
vw | water flow rate, m/s |
Va | volume of adsorbed gas (standard condition) under formation pressure, m3/kg |
VL | Langmuir’s volume at standard condition, m3/kg |
wH | width of hydraulic fracture |
x, y, z | distance coordinates, m |
Z | gas compressibility factor |
Greek letters | |
α | dip |
αr | rarefication coefficient |
αs | stress-sensitivity coefficient, Pa−1 |
β | azimuth |
δx, δy, δz | directions of principal permeabilities |
gas molecule mean free path, m | |
μ | viscosity, Pa·s |
μg | gas viscosity, Pa·s |
μw | water viscosity, Pa·s |
ρbi | bulk density of shale at initial reservoir pressure, kg/m3 |
ρg | gas density, kg/m3 |
ρw | water density, kg/m3 |
σ | collision diameter of gas molecule |
τ | tortuosity of shale |
ϕ | porosity of shale |
Appendix A. Derivation of Calculation Model of Permeability Anisotropy in Two Dimensional Space
- (a)
- Vector composition: the reservoir is assumed to be homogeneous and isotropic, so the permeabilities in all directions are equal to k, while the permeability in the direction of k3 should be according to the character of vector composition, which is contrary to the assumption that permeabilities in all directions should be k.
- (b)
- Vector decomposition: the reservoir is assumed to be homogeneous and isotropic, and the permeabilities in all directions are equal to k, while the permeability in the direction of kω should be k·cosα according to the character of vector decomposition, which is contrary to the assumption that permeabilities in all directions are equal to k.
References
- Davis, R.A. Depositional Systems: An Introduction to Sedimentology and Stratigraphy, 2nd ed.; Prentice Hall: Upper Saddle River, NJ, USA, 1992. [Google Scholar]
- Deng, J.; Zhu, W.; Ma, Q. A new seepage model for shale gas reservoir and productivity analysis of fractured well. Fuel 2014, 124, 232–240. [Google Scholar] [CrossRef]
- Young, A.; Low, P.F.; McLatchie, A.S. Permeability studies of argillaceous rocks. J. Geophys. Res. 1964, 69, 4237–4245. [Google Scholar] [CrossRef]
- Kwon, O.; Kronenberg, A.K.; Gangi, A.F.; Johnson, B.; Herbert, B.E. Permeability of illite-bearing shale: 1. Anisotropy and effects of clay content and loading. J. Geophys. Res. 2004, 109, B10205. [Google Scholar] [CrossRef]
- Chemali, R.; Gianzero, S.; Su, S.M. The effect of shale anisotropy on focused resistivity Devices. In Proceedings of the SPWLA 28th Annual Logging Symposium, London, UK, 29 June–2 July 1987. [Google Scholar]
- Johnston, J.E.; Christensen, N.I. Seismic anisotropy of shales. J. Geophys. Res. 1995, 100, 5991–6003. [Google Scholar] [CrossRef]
- Safdar, K.; Sajjad, A.; Han, H. Importance of shale anisotropy in estimating insitu stresses and wellbore stability analysis in Horn river basin. In Proceedings of the Canadian Unconventional Resources Conference, Calgary, AB, Canada, 15–17 November 2011. [Google Scholar]
- Kocks, U.F.; Tome, C.N.; Wenk, H.R. Texture and Anisotropy: Preferred Orientations in Polycrystals and Their Effect on Materials Properties; Cambridge University: Cambridge, UK, 1998. [Google Scholar]
- Wenk, H.R.; Voltolini, M.; Mazurek, M.; Van Loon, L.R.; Vinsot, A. Preferred orientations in shales: Callvovo-oxfordian shale (France) and opalinus clay (Switzerland). Clays Clay Min. 2008, 56, 285–306. [Google Scholar] [CrossRef]
- Roy, S.; Raju, R. Modeling gas flow through microchannels and nanopores. J. Appl. Phys. 2003, 93, 4870–4879. [Google Scholar] [CrossRef]
- Wu, K.; Chen, Z.; Li, X. A model for multiple transport mechanisms through nanopores of shale gas reservoirs with real gas effect–adsorption-mechanic coupling. Int. J. Heat Mass Transf. 2016, 93, 408–426. [Google Scholar] [CrossRef]
- Wu, K.; Li, X.; Guo, C.; Wang, C.; Chen, Z. A unified model for gas transfer in nanopores of shale-gas reservoirs: coupling pore diffusion and surface diffusion. SPE J. 2016, 21, 1583–1611. [Google Scholar] [CrossRef]
- Javadpour, F. Nanopores and apparent permeability of gas flow in mudrocks (shales and siltstone). J. Can. Pet. Technol. 2009, 48, 16–21. [Google Scholar] [CrossRef]
- Ozkan, E.; Raghavan, R.S.; Apaydin, O.G. Modeling of fluid transfer from shale matrix to fracture network. In Proceedings of the SPE Annual Technical Conference and Exhibition, Florence, Italy, 19–22 September 2010. [Google Scholar]
- Shabro, V.; Torres-Verdin, C.; Javadpour, F. Numerical simulation of shale-gas production: From pore-scale modeling of slip-flow, Knudsen diffusion and Langmuir desorption to reservoir modeling of compressible fluid. In Proceedings of the SPE North American Unconventional Gas Conference and Exhibition, Woodlands, TX, USA, 14–16 June 2011. [Google Scholar]
- Swami, V.; Settari, A. A Pore Scale Gas Flow Model for Shale Gas Reservoir. In Proceedings of the Americas Unconventional Resources Conference, Pittsburgh, PA, USA, 5–7 June 2012. [Google Scholar]
- Huang, T.; Guo, X.; Chen, F. Modeling transient flow behavior of a multiscale triple porosity model for shale gas reservoirs. J. Nat. Gas Sci. Eng. 2015, 23, 33–46. [Google Scholar] [CrossRef]
- Ziarani, A.S.; Aguilera, R. Knudsen’s permeability correction for tight porous media. Transp. Porous Media 2012, 91, 239–260. [Google Scholar] [CrossRef]
- Beskok, A.; Karniadakis, G. A model for flows in channels pipes, and ducts at micro and nanoscales. Microsc. Thermophys. Eng. 1999, 3, 43–77. [Google Scholar]
- Civan, F.; Rai, C.S.; Sondergeld, C.H. Shale-gas permeability and diffusivity inferred by improved formulation of relevant retention and transport mechanisms. Transp. Porous Media. 2011, 86, 925–944. [Google Scholar] [CrossRef]
- Wang, J.; Liu, H.; Wang, L. Apparent permeability for gas transport in nanopores of organic shale reservoirs including multiple effects. Int. J. Coal Geol. 2015, 152, 50–62. [Google Scholar] [CrossRef]
- Yuan, Y.; Doonechaly, N.G.; Rahman, S. An analytical model of apparent gas permeability for tight porous media. Transp. Porous Media 2016, 111, 193–214. [Google Scholar] [CrossRef]
- Brown, M.; Ozkan, E.; Raghavan, R.; Kazemi, H. Practical solutions for pressure-transient responses of fractured horizontal wells in unconventional shale reservoirs. SPE Reserv. Eva. Eng. 2011, 14, 663–676. [Google Scholar] [CrossRef]
- Zhao, Y.; Zhang, L.; Zhao, J.; Luo, J.; Zhang, B. “Triple porosity” modeling of transient well test and rate decline analysis for multi-fractured horizontal well in shale gas reservoir. J. Pet. Sci. Eng. 2013, 110, 253–262. [Google Scholar] [CrossRef]
- Wang, H.T. Performance of multiple fractured horizontal wells in shale gas reservoirs with consideration of multiple mechanisms. J. Hydrol. 2014, 510, 299–312. [Google Scholar] [CrossRef]
- Cipolla, C.L.; Lolon, E.P.; Erdle, J.C.; Rubin, B. Reservoir modeling in shale-gas reservoirs. SPE Reserv. Eval. Eng. 2010, 13, 638–653. [Google Scholar] [CrossRef]
- Clarkson, C.R.; Nobakht, M.; Kaviani, D.; Ertekin, T. Production analysis of tight-gas and shale-gas reservoirs using the dynamic-slippage concept. SPE J. 2012, 17, 230–242. [Google Scholar] [CrossRef]
- Li, D.; Zhang, L.; Lu, D. Effect of distinguishing apparent permeability on flowing gas composition, composition change and composition derivative in tight-and shale-gas reservoir. J. Pet. Sci. Eng. 2015, 128, 107–114. [Google Scholar] [CrossRef]
- Civan, F. Effective correlation of apparent gas permeability in tight porous media. Transp. Porous Media 2010, 82, 375–384. [Google Scholar] [CrossRef]
- Wu, K.; Chen, Z.; Li, X. Flow behavior of gas confined in nanoporous shale at high pressure: Real gas effect. Fuel 2017, 205, 173–183. [Google Scholar] [CrossRef]
- Florence, F.A.; Rushing, J.A.; Newsham, K.E.; Blaingame, T.A. Improved permeability prediction relations for low permeability sands. In Proceedings of the 2007 SPE Rocky Mountain Oil & Gas Technology Symposium, Denver, CO, USA, 16–18 April 2007. [Google Scholar]
- Johnson, D.L.; Koplik, J.; Schwartz, L.M. New pore-size parameter characterizing transport in porous media. Phys. Rev. Lett. 1986, 57, 2564–2567. [Google Scholar] [CrossRef] [PubMed]
- Chen, P.; Jiang, S.; Chen, Y. An apparent permeability model of shale gas under formation conditions. J. Geophys. Eng. 2017, 14, 833–840. [Google Scholar] [CrossRef]
- Wang, J.; Luo, H.; Liu, H. An integrative model to simulate gas transport and production coupled with gas adsorption, non-Darcy flow, surface diffusion, and stress dependence in organic-shale reservoirs. SPE J. 2017, 22, 244–264. [Google Scholar] [CrossRef]
- Zhang, J.; Kamenov, A.; Zhu, D.; Hill, A.D. Laboratory measurement of hydraulic fracture conductivities in the Barnett Shale. In Proceedings of the SPE Hydraulic Fracturing Technology Conference, The Woodlands, TX, USA, 4–6 February 2013. [Google Scholar]
- Meyer, B.R.; Bazan, L.W.; Jacot, R.H. Optimization of multiple transverse hydraulic fractures in horizontal wellbores. In Proceedings of the SPE Unconventional Gas Conference, Pittsburgh, PA, USA, 23–25 February 2010. [Google Scholar]
- Yu, W.; Sepehrnoori, K. Simulation of gas desorption and geomechanics effects for uncomventional gas reservoirs. Fuel 2014, 116, 455–464. [Google Scholar] [CrossRef]
- Li, T.; Song, H.; Wang, J. An analytical method for modeling and analysis gas-water relative permeability in nanoscale pores with interfacial effects. Int. J. Coal Geol. 2016, 159, 71–81. [Google Scholar] [CrossRef]
- Wang, D.; Zhou, Y.; Ma, P.; Tian, T. Vector properties and calculation model for directional rock permeability. Rock Soil Mech. 2005, 26, 1294–1297. [Google Scholar]
Knudsen Number | Kn ≤ 0.001 | 0.001 < Kn ≤ 0.1 | 0.1 < Kn ≤ 10 | Kn > 10 |
---|---|---|---|---|
Flow regime | Continuum flow | Slip flow | Transition flow | Free-molecule flow |
Parameter | Value | Unit |
---|---|---|
Formation depth | 2400 | m |
Formation thickness | 50 | m |
Initial pressure | 32.0 | MPa |
Initial temperature | 355 | K |
Shale porosity | 0.065 | / |
Shale permeability | 6.0 × 10−4 | 10−3 μm2 |
Initial density of rock | 2460 | kg/m3 |
Langmuir pressure | 3.44 | MPa |
Langmuir volume | 5.66 | cm3/g |
Initial gas saturation | 0.75 | / |
Gas specific gravity | 0.58 | / |
Horizontal well length | 640 | m |
Hydraulic fracture spacing | 87 | m |
Half-length of hydraulic fracture | 68 | m |
Number of hydraulic fractures | 7 | / |
Stress-sensitivity coefficient | 1.5 × 10−8 | Pa−1 |
Wellbore pressure | 6 | MPa |
Wellbore radius | 0.1 | m |
© 2017 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).
Share and Cite
Huang, T.; Tao, Z.; Li, E.; Lyu, Q.; Guo, X. Effect of Permeability Anisotropy on the Production of Multi-Scale Shale Gas Reservoirs. Energies 2017, 10, 1549. https://doi.org/10.3390/en10101549
Huang T, Tao Z, Li E, Lyu Q, Guo X. Effect of Permeability Anisotropy on the Production of Multi-Scale Shale Gas Reservoirs. Energies. 2017; 10(10):1549. https://doi.org/10.3390/en10101549
Chicago/Turabian StyleHuang, Ting, Zhengwu Tao, Erpeng Li, Qiqi Lyu, and Xiao Guo. 2017. "Effect of Permeability Anisotropy on the Production of Multi-Scale Shale Gas Reservoirs" Energies 10, no. 10: 1549. https://doi.org/10.3390/en10101549