Gas Mass Transport Model for Microfractures Considering the Dynamic Variation of Width in Shale Reservoirs
- Fanhui Zeng (Southwest Petroleum University) | Fan Peng (Southwest Petroleum University) | Jianchun Guo (Southwest Petroleum University) | Zhenhua Rui (Southwest Petroleum University and Massachusetts Institute of Technology) | Jianhua Xiang (PetroChina Company Limited Southwest Oil and Gas Field Branch)
- Document ID
- Society of Petroleum Engineers
- SPE Reservoir Evaluation & Engineering
- Publication Date
- February 2019
- Document Type
- Journal Paper
- 1,265 - 1,281
- 2019.Society of Petroleum Engineers
- micro-fracture width variation, microfractures, influencing factors, shale gas reservoir, gas mass transport
- 3 in the last 30 days
- 202 since 2007
- Show more detail
- View rights & permissions
|SPE Member Price:||USD 5.00|
|SPE Non-Member Price:||USD 35.00|
Microfractures are commonly observed in shale reservoirs. During the shale gas-production process, stress sensitivity induces a change in the width of the microfractures, which is a significant factor that affects shale gas mass transport. By using research methods based on desorption theory and elastic-plastic mechanics, a shale gas mass transport model that considers the dynamic variations in the microfracture width is established in this paper. This model comprehensively fuses the surface diffusion model, slip flow model, Knudsen diffusion model, and cubic grid model. The reliability of this model is verified using molecular simulations, which do not include surface diffusion. The shale gas is considered as pure methane. Then, the different contributions of the gas mass transport mechanisms to the total mass transport are discussed in detail. The results demonstrate the following findings: (1) The studied flows are well-simulated by the proposed model. (2) Stress sensitivity results in a decrease in gas mass transport when the formation pressure exceeds 3.4 MPa, and the minimum value is approximately 0.45 times smaller than that when the width change is not considered. Moreover, stress sensitivity results in an increase in gas mass transport when the formation pressure is lower than 3.4 MPa, and the maximum value is approximately 4.5 times higher than that when the width change is not considered. (3) Shale gas mass transport is positively associated with the Young’s modulus and Poisson’s ratio, whereas it is negatively associated with the microfracture compressibility. When the formation pressure is less than 4 MPa, shale gas transport is positively correlated with the desorption capacity, whereas when the formation pressure exceeds 4 MPa, the effect of different desorption capacities on gas transport is nearly consistent. (4) When the microfracture width is at nanoscale and the reservoir pressure is lower than 15 MPa, surface diffusion has an obvious effect on the shale gas mass transport process. When the contribution of surface diffusion to the total shale gas mass transport is relatively small, the contributions of slip flow and Knudsen flow to shale gas mass transport exhibit the trend of “shifting each other.” When the surface diffusion contribution is larger, a reduction in its contribution leads to simultaneous initial increases in the contributions of slip flow and Knudsen flow to shale gas mass transport, and then these flows begin “shifting each other.”
|File Size||869 KB||Number of Pages||17|
Binder, K., Horbach, J., Kob, W. et al. 2004. Molecular Dynamics Simulations. J. Phys.: Condens. Matter 16 (5): S429. https://doi.org/10.1088/0953-8984/16/5/006/.
Bradley, H. B. 1987. Petroleum Engineering Handbook, first edition. Richardson, Texas: Society of Petroleum Engineers.
Cercignani, C. 1977. Theory and Application of the Boltzmann Equation. Phys. Today 30 (1): 66–68. https://doi.org/10.1063/1.3037373.
Chalmers, G. R., Bustin, R. M., and Power, I. M. 2012. Characterization of Gas Shale Pore Systems by Porosimetry, Pycnometry, Surface Area, and Field Emission Scanning Electron Microscopy/Transmission Electron Microscopy Image Analyses: Examples From the Barnett, Woodford, Haynesville, Marcellus, and Doig Units. AAPG Bull. 96 (6): 1099–1119. https://doi.org/10.1306/10171111052.
Chen, J., and Xiao, X. 2014. Evolution of Nanoporosity in Organic-Rich Shales During Thermal Maturation. Fuel 129 (4): 173–181. https://doi.org/10.1016/j.fuel.2014.03.058.
Cui, X., Bustin, A. M. M., and Bustin, R. M. 2010. Measurements of Gas Permeability and Diffusivity of Tight Reservoir Rocks: Different Approaches and Their Applications. Geofluids 9 (3): 208–223. https://doi.org/10.1111/j.1468-8123.2009.00244.x.
Darabi, H., Ettehad, A., Javadpour, F. et al. 2012. Gas Flow in Ultra-Tight Shale Strata. J. Fluid Mechs. 710 (12): 641–658. https://doi.org/10.1017/jfm.2012.424.
Dong, J. J., Hsh, J. Y., Wu, W. J. et al. 2010. Stress-Dependence of the Permeability and Porosity of Sandstone and Shale From TCDP Hole-A. Int. J. Rock Mech. Min. Sci. 47 (7): 1141–1157. https://doi.org/10.1016/j.ijrmms.2010.06.019.
Dong, C., Pan, Z., and Ye, Z. 2015. Dependence of Gas Shale Fracture Permeability on Effective Stress and Reservoir Pressure: Model Match and Insights. Fuel 139: 383–392. https://doi.org/10.1016/j.fuel.2014.09.018.
Fathi, E. and Akkutlu, I. Y. 2012. Mass Transport of Adsorbed-Phase in Stochastic Porous Medium With Fluctuating Porosity Field and Nonlinear Gas Adsorption Kinetics. Transp. Porous Med. 91 (1): 12–20. https://doi.org/10.1007/s11242-011-9830-x.
Fathi, E., Akkutlu, I. Y. 2014. Multi-Component Gas Transport and Adsorption Effects During CO2 Injection and Enhanced Shale Gas Recovery. Int. J. Coal Geol. 123 (2): 52–61. https://doi.org/10.1016/j.coal.2013.07.021.
Freeman, C. M., Moridis, G. J., and Blasingame, T. A. 2011. A Numerical Study of Microscale Flow Behavior in Tight Gas and Shale Gas Reservoir Systems. Transp. Porous Med. 90 (1): 253–268. https://doi.org/10.2118/141125-STU.
Gad-el-hak, M. 1999. The Fluid Mechanics of Microdevices—The Freeman Scholar Lecture. J. Fluids Eng. 121 (1): 5–33. https://doi.org/10.1115/1.2822013.
Javadpour, F. 2009. Nanopores and Apparent Permeability of Gas Flow in Mudrocks (Shales and Siltstone). J Can Pet Technol 48 (8): 16–21. PETSOC-09-08-16-DA. https://doi.org/10.2118/09-08-16-DA.
Javadpour, F., Fisher, D., and Unsworth, M. 2007. Nanoscale Gas Flow in Shale Gas Sediments. J Can Pet Technol 46 (10): 55–61. PETSOC-07-10-06. https://doi.org/10.2118/07-10-06.
Kang, S. M., Fathi, E., Ambrose, R. J. et al. 2010. Carbon Dioxide Storage Capacity of Organic-Rich Shales. SPE J. 16 (4): 842–855. SPE-134583-PA. https://doi.org/10.2118/134583-PA.
Karniadakis, G., Beskok, A., and Aluru, N. 2005. Microflows and Nanoflows: Fundamentals and Simulation, first edition. New York: Springer Verlag.
Kazemi, M. and Takbiri-Borujeni, A. 2015. An Analytical Model for Shale Gas Permeability. Int. J. Coal Geol. 146 (3): 188–197. https://doi.org/10.1016/j.coal.2015.05.010.
Kazemi, M. and Takbiri-Borujeni, A. 2016. Non-Equilibrium Molecular Dynamics Simulation of Gas Flow in Organic Nanochannels. J. Nat. Gas Sci. Eng. 33: 1087–1094. https://doi.org/10.1016/j.jngse.2016.05.068.
Kogan, M. N. 1961. Rarefied Gas Dynamics. Phys. Today 14 (9): 90–92. https://doi.org/10.1007/978-1-4899-6381-9.
Levine, J. R. 1996. Model Study of The Influence of Matrix Shrinkage on Absolute Permeability of Coal Bed Reservoirs. Geol. Soc. London Spec. Publ. 109 (1): 197–212. https://doi.org/10.1144/GSL.SP.1996.109.01.14.
Loeb, L. B. 1934. The Kinetic Theory of Gases, second edition. New York: McGraw-Hill Co. Inc.
Loyalka, S. and Hamoodi, S. 1990. Poiseuille Flow of a Rarefied Gas in a Cylindrical Tube: Solution of Linearized Boltzmann Equation. Phys. Fluids A 2 (11): 2061–2065. https://doi.org/10.1063/1.858220.
Peng, Y., Liu, J., Pan, Z. et al. 2015. A Sequential Model of Shale Gas Transport Under the Influence of Fully Coupled Multiple Processes. J. Nat. Gas Sci. Eng. 27 (3): 808–821. https://doi.org/10.1016/j.jngse.2015.09.031.
Piekos, E. S. and Breuer, K. S. 1996. Numerical Modeling of Micromechanical Devices Using the Direct Simulation Monte Carlo Method. J. Fluids Eng. 118 (3): 464–469. https:/doi.org/10.1115/1.2817781.
Rahmanian, M. R., Solano, N., and Aguilera, R. 2010. Storage and Output Flow From Shale and Tight Gas Reservoirs. Presented at the SPE Western Regional Meeting, Anaheim, California, 27–29 May. SPE-133611-MS. https://doi.org/10.2118/133611-MS.
Robertson, E. P. and Christiansen, R. L. 2004. Optically-Based Strain Measurement of Coal Swelling and Shrinkage. Proc., International Coalbed Methane Symposium, Tuscaloosa, Alabama, 3–7 May.
Robertson, E. P. and Christiansen, R. L. 2006. A Permeability Model for Coal and Other Fractured, Sorptive-Elastic Media. SPE J. 13 (3): 314–324. SPE-104380-PA. https://doi.org/10.2118/104380-PA.
Roy, S., Raju, R., Chuang, H. F. et al. 2003. Modeling Gas Flow Through Microchannels and Nanopores. J. Appl. Chem. 93 (8): 4870–4879. https://doi.org/10.1063/1.1559936.
Shahri, M. R., Aguilera, R., and Kantzas, A. 2012. A New Unified Diffusion-Viscous Flow Model Based on Pore Level Studies of Tight Gas Formations. SPE J. 18 (1): 38–49. SPE-149223-MS. https://doi.org/10.2118/149223-MS.
Shi, J., Zhang, L., Li, Y. et al. 2013. Diffusion and Flow Mechanisms of Shale Gas Through Matrix Pores and Gas Production Forecasting. Presented at the SPE Unconventional Resources Conference, Calgary, 5–7 November. SPE-167226-MS. https://doi.org/10.2118/167226-MS.
Singh, H., Javadpour, F., Ettehadtavakkol, A. et al. 2013. Nonempirical Apparent Permeability of Shale. SPE Res Eval & Eng 17 (3): 414–424. SPE-170243-PA. https://doi.org/10.2118/170243-PA.
Slider, H. C. 1983. Worldwide Practical Petroleum Reservoir Engineering Methods, second edition. Tulsa, Oklahoma: Penn Well Publishing Company.
Sone, Y. and Hasegawa, M. 1987. Poiseuille and Thermal Transpiration Flows of A Rarefied Gas Through A Rectangular Pipe. J. Vac. Soc. Jpn. 30: 425–428. https://doi.org/10.3131/jvsj.30.425.
Thompson, S. L. and Owens, W. R. 1975. A Survey of Flow at Low Pressures. Vacuum 25 (4): 151–156. https://doi.org/10.1016/0042-207X(75)91404-9.
Wang, S., Javadpour, F., and Feng, Q. 2016. Molecular Dynamics Simulations of Oil Transport Through Inorganic Nanopores in Shale. Fuel 171: 74–86. https://doi.org/10.1016/j.fuel.2015.12.071.
Williams, M. M. R. 1971. Mathematical Methods in Particle Transport Theory, first edition. London: Wiley-Interscience.
Wu, K. and Chen, Z. 2016. Review of Gas Transport in Nanopores in Shale Gas Reservoirs. J. Pet. Technol. Bull. 1 (1): 91–127.
Wu, K., Li, X., and Chen, Z. 2015a. A Model for Gas Transport Through Nanopores of Shale Gas Reservoirs. Acta Petrolei Sinica 36 (7): 837–848, 889. https://doi.org/10.7623/syxb201507008.
Wu, K., Li, X., Chen, Z. et al. 2015b. Gas Transport Behavior Through Micro Fractures of Shale and Tight Gas Reservoirs. Chinese J. Theo. Appl. Mech. 47 (6): 955–964. https://doi.org/10.6052/0459-1879-15-141.
Wu, K., Li, X., Wang, C. et al. 2015c. Model for Surface Diffusion of Adsorbed Gas in Nanopores of Shale Gas Reservoirs. Ind. Eng. Chem. Res. 54 (12): 3225–3236. https://doi.org/10.1021/ie504030v.
Yao, Y. and Zhou, S. 1988. The Mechanical Property of Coal Containing Gas. J. China Univ. of Min. Tec. 2 (1): 4–10.