Nonempirical Apparent Permeability of Shale
- Harpreet Singh (University of Texas at Austin) | Farzam Javadpour (University of Texas at Austin) | Amin Ettehadtavakkol (University of Texas at Austin) | Hamed Darabi (University of Texas at Austin)
- Document ID
- Society of Petroleum Engineers
- SPE Reservoir Evaluation & Engineering
- Publication Date
- August 2014
- Document Type
- Journal Paper
- 414 - 424
- 2014.Society of Petroleum Engineers
- 5.1 Reservoir Characterisation, 1.10 Drilling Equipment, 5.8.2 Shale Gas, 4.3.4 Scale
- ultratight porous media, unconventional reservoir, sorption, micro/nanofluid mechanism, nanopore
- 10 in the last 30 days
- 1,450 since 2007
- Show more detail
- View rights & permissions
|SPE Member Price:||USD 10.00|
|SPE Non-Member Price:||USD 30.00|
Physics of fluid flow in shale reservoirs cannot be predicted from standard flow or mass-transfer models because of the presence of nanopores, ranging in size from one to hundreds of nanometers, in shales. Conventional continuum-flow equations, such as Darcy's law, greatly underestimate the fluid-flow rate when applied to nanopore-bearing shale reservoirs. As a result of the existence of nanopores in shales, the molecular mean free path becomes comparable with the characteristic geometric scale, and we hypothesize that under this condition, Knudsen diffusion, in addition to correction for the slip boundary condition, becomes the dominant mechanism. Recently, a few models have been developed that use various empirical parameters to account for these modifications (Javadpour 2009; Civan 2010; Darabi et al. 2012). This paper aims to provide a different approach to modeling apparent permeability in shale reservoirs. The proposed model is analytical, free of any empirical coefficients, and has been derived without invoking the assumption of slip flow at the pore wall. Our model of apparent permeability represented by a single analytical equation, depends only on pore size, pore geometry, temperature, gas properties, and average reservoir pressure. The proposed model is valid for Knudsen numbers less than unity and it stands up under the complete operating conditions of a shale reservoir. Our model reasonably predicts results as reported by other models. Finally, the model shows that pore-surface roughness and mineralogy have a negligible influence on gas-flow rate, whereas pore geometry and pore size play a significant role in the proportion of diffusion in total flow rate. Our study shows that a combination of Darcy flow and Knudsen flow - ignoring the Klinkenberg effect - can describe gas flow for a range of Knudsen flow applicable to a shale-gas system.
|File Size||2 MB||Number of Pages||11|
Agrawal, A. and Prabhu, S.V. 2008. Survey on Measurement of Tangential Momentum Accommodation Coefficient. J. Vac. Sci. Technol. A 26 (4): 634–45. http://dx.doi.org/10.1116/1.2943641.
Aguilera, R. and Lopez, B. 2013. Evaluation of Quintuple Porosity in Shale Petroleum Reservoirs. Presented at SPE Eastern Regional Meeting, Pittsburgh, Pennsylvania, 20–22 August. SPE-165681-MS. http://dx.doi.org/10.2118/165681-MS.
Ambrose, R., Hartman, R., Diaz-Campos, M., et al. 2010. New Pore-Scale Considerations for Shale Gas in Place Calculations. Presented at SPE Unconventional Gas Conference, Pittsburgh, Pennsylvania, 23–25 February. SPE-131772-MS. http://dx.doi.org/10.2118/131772-MS.
Ambrose, R., Hartman, R., Diaz-Campos, M., et al. 2012. Shale Gas-in-Place Calculations Part I: New Pore-Scale Considerations.” SPE J. 17 (1): 219–229. SPE-131772-PA. http://dx.doi.org/10.2118/131772-PA.
Arkilic, E.B., Schmidt, M.A., and Breuer, K.S. 1997. Gaseous Slip Flow in Long Microchannels. J. Microelectromech. S. 6 (2): 167–178. http://dx.doi.org/10.1109/84.585795.
Azom, P. and Javadpour, F. 2012. Dual-Continuum Modeling of Shale and Tight Gas Reservoirs. SPE Annual Technical Conference and Exhibition, San Antonio, Texas, 8–10 October. SPE-159584-MS. http://dx.doi.org/10.2118/159584-MS.
Beskok, A. and Em Karniadakis, G. 1999. A Model for Flows In Channels, Pipes, and Ducts at Micro and Nano Scales. Microscale Therm. Eng. 3 (1): 43–77. http://dx.doi.org/10.1080/108939599199864.
Civan, F. 2010. Effective Correlation of Apparent Gas Permeability in Tight Porous Media. Transport Porous Med. 82 (2): 375–84. http://dx.doi.org/10.1007/s11242-009-9432-z.
Darabi, H., Ettehad, A., Javadpour, F., et al. 2012. Gas Flow in Ultra-Tight Shale Strata. J. Fluid Mech. 710 (November): 641–658. http://dx.doi.org/10.1017/jfm.2012.424.
Do, D.D. and Wang, K. 1998a. Dual Diffusion and Finite Mass Exchange Model for Adsorption Kinetics in Activated Carbon. AIChE J. 44 (1): 68–82. http://dx.doi.org/10.1002/aic.690440109.
Do, D.D. and Wang, K. 1998b. A New Model for the Description of Adsorption Kinetics in Heterogeneous Activated Carbon. Carbon 36 (10): 1539–1554. http://dx.doi.org/10.1016/S0008-6223(98)00145-6.
Fathi, E. and Yucel Akkutlu, I. 2012. Mass Transport of Adsorbed-Phase in Stochastic Porous Medium with Fluctuating Porosity Field and Nonlinear Gas Adsorption Kinetics. Transport Porous Med. 91 (1): 5–33. http://dx.doi.org/10.1007/s11242-011-9830-x.
Fathi, E., Tinni, A., and Yucel Akkutlu, I. 2012. Correction to Klinkenberg Slip Theory for Gas Flow in Nano-Capillaries. Int. J. Coal Geol. 103 (December): 51–59. http://dx.doi.org/10.1016/j.coal.2012.06.008.
Fenton, L. 1960. The Sum of Log-Normal Probability Distributions in Scatter Transmission Systems. IEEE T. Commun. 8 (1): 57–67. http://dx.doi.org/10.1109/TCOM.1960.1097606.
Freeman, C., Moridis, G., Michael, G., et al. 2012. Measurement, Modeling, and Diagnostics of Flowing Gas Composition Changes in Shale Gas Wells. Presented at SPE Latin America and Caribbean Petroleum Engineering Conference, Mexico City, Mexico, 16–18 April. SPE-153391-MS. http://dx.doi.org/10.2118/153391-MS.
Gad-el-Hak, M. 1999. The Fluid Mechanics of Microdevices—The Freeman Scholar Lecture. J. Fluids Eng. 121 (1): 5. http://dx.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. http://dx.doi.org/10.2118/09-08-16-DA.
Javadpour, F., Farshi, M., and Amrein, M. 2012. Atomic-Force Microscopy: A New Tool for Gas-Shale Characterization. J Can Pet Technol 51 (4): 236–243. SPE-161015-PA. http://dx.doi.org/10.2118/161015-PA.
Jensen, J., Hinkley, D., and Lake, L. 1987. A Statistical Study of Reservoir Permeability: Distributions, Correlations, and Averages. SPE Form Eval 2 (4): 461–468. SPE-14270-PA. http://dx.doi.org/10.2118/14270-PA.
Katsube, T. J. 1991. Petrophysical Characteristics of Shales from the Scotian Shelf. Geophysics 56 (10): 1681. http://dx.doi.org/10.1190/1.1442980.
Klinkenberg, LJ. 1941. The Permeability Of Porous Media To Liquids And Gases. In Drilling and Production Practice, 200–213. Washington, DC: American Petroleum Institute.
Loucks, R.G., Reed, R.M., Ruppel, S.C., et al. 2012. Spectrum of Pore Types and Networks in Mudrocks and a Descriptive Classification for Matrix-Related Mudrock Pores.” AAPG Bull. 96 (6): 1071–1098. http://dx.doi.org/10.1306/08171111061.
Milliken, K.L., Esch, W.L., Reed, R.M., et al. 2012. Grain Assemblages and Strong Diagenetic Overprinting in Siliceous Mudrocks, Barnett Shale (Mississippian), Fort Worth Basin, Texas. AAPG Bull. 96 (8): 1553–1578. http://dx.doi.org/10.1306/12011111129.
Peters, E.J. 2012. Advanced Petrophysics: Volume 2: Dispersion, Interfacial Phenomena/Wettability, Capillarity/Capillary Pressure, Relative Permeability. Austin, Texas: Live Oak Book Company.
Rathakrishnan, E. 2004. Gas Dynamics. New Delhi, India: Prentice-Hall of India Pvt. Ltd.
Revil, A., Woodruff, W. F., Torres-Verdín, C., et al. 2013. Complex Conductivity Tensor of Anisotropic Hydrocarbon-Bearing Shales and Mudrocks. Geophysics 78 (6): D403–D418. http://dx.doi.org/10.1190/geo2013-0100.1.
Rezaveisi, M., Javadpour, F., and Sepehrnoori, K. 2014. Modeling Chromatographic Separation of Produced Gas in Shale Wells. Int. J. Coal Geol. 121 (January): 110–22. http://dx.doi.org/10.1016/j.coal.2013.11.005.
Roy, S., Raju, R., Chuang, H.F., et al. 2003. Modeling Gas Flow through Microchannels and Nanopores. J. Appl. Phys. 93 (8): 4870–79. http://dx.doi.org/10.1063/1.1559936.
Ruthven, D.M. 1984. Principles of Adsorption and Adsorption Processes. Hoboken, New Jersey: John Wiley & Sons, Inc.
Ruzyla, K. 1986. Characterization of Pore Space by Quantitative Image Analysis. SPE Form Eval 1 (4): 389–398. SPE-13133-PA. http://dx.doi.org/10.2118/13133-PA.
Sakhaee-pour, A. and Bryant, S. 2011. Gas Permeability of Shale. Presented at SPE Annual Technical Conference and Exhibition, Denver, Colorado, 30 October–2 November. SPE-146944-MS. http://dx.doi.org/10.2118/146944-MS.
Salem, H.S. 1993. Geological Survey of Canada, Open File 2686. Ottawa, Canada: Natural Resources Canada.
Santos Rueda, J. and Yucel Akkutlu, I. 2012. Laboratory Measurement of Sorption Isotherm under Confining Stress with Pore Volume Effects. Presented at SPE Canadian Unconventional Resources Conference, Calgary, Alberta, Canada, 30 October–1 November. SPE-162595-MS. http://dx.doi.org/10.2118/162595-MS.
Shabro, V., Torres-Verdín, C., Javadpour, F., et al. 2012. Finite-Difference Approximation for Fluid-Flow Simulation and Calculation of Permeability in Porous Media. Transport Porous Med. 94 (3): 775–793. http://dx.doi.org/10.1007/s11242-012-0024-y.
Singh, H. and Azom, P. 2013. Integration of Nonempirical Shale Permeability Model in a Dual-Continuum Reservoir Simulator. Presented at SPE Unconventional Resources Conference Canada, Calgary, Alberta, Canada, 5–7 November. SPE-167125-MS. http://dx.doi.org/10.2118/167125-MS.
Singh, H. and Javadpour, F. 2013. A New Non-Empirical Approach to Model Transport of Fluids in Shale Gas Reservoirs. Proc., Unconventional Resources Technology Conference, Denver, Colorado, 12–14 August, 1258–1273. http://dx.doi.org/10.1190/urtec2013-127.
Vasina, E.N., Paszek, E. Jr., Nicolau, D.V. Jr., et al. 2009. The BAD Project: Data Mining, Database and Prediction of Protein Adsorption on Surfaces. Lab Chip 9 (7): 891–900. http://dx.doi.org/10.1039/B813475H.
Veltzke, T. and Thöming, J. 2012. An Analytically Predictive Model for Moderately Rarefied Gas Flow. J. Fluid Mech. 698 (May): 406–422. http://dx.doi.org/10.1017/jfm.2012.98.