Upscaling the Steam-Assisted-Gravity-Drainage Model for Heterogeneous Reservoirs
- Ali Takbiri-Borujeni (West Virginia University) | Vahid Mohammadnia (Infosys) | Mahdi Mansouri-Boroujeni (University of Orléans) | Hossein Nourozieh (Computer Modelling Group) | Payam Kavousi Ghahfarokhi (West Virginia University)
- Document ID
- Society of Petroleum Engineers
- SPE Journal
- Publication Date
- August 2019
- Document Type
- Journal Paper
- 1,681 - 1,699
- 2019.Society of Petroleum Engineers
- Upscaling, SAGD
- 20 in the last 30 days
- 81 since 2007
- Show more detail
- View rights & permissions
|SPE Member Price:||USD 12.00|
|SPE Non-Member Price:||USD 35.00|
The effects of heterogeneities in the rock and fluid properties on the governing equations in modeling the steam-assisted-gravity-drainage (SAGD) process are investigated using a spectrum-based upscaling approach. In this approach, heterogeneity is included by assigning random perturbation fields to permeability and thermal diffusivity that hold the assumption of first and second orders of stationarity. Heat and mass-transport parameters and dependent variables (e.g., temperature and viscosity) that are affected by heterogeneity are represented by their mean and perturbations around the mean values. Substituting the perturbed variables and coefficients into the basic governing equations (heat-diffusion and Darcy equations) results in new sets of stochastic partial-differential equations that include mean and perturbation. Mean equations are essentially upscaled new governing equations that include the autocorrelations and cross correlations between different perturbed quantities. The cross correlations are derived by applying the Fourier-Stieltjes transform. Verification and validation of the developed results for the heat-diffusion equation are performed using numerical simulations with synthetic heterogeneities. The upscaled equations embrace the heterogeneity in permeability and thermal diffusivity and can predict the flow rate and shape of the steam chamber.
The upscaled model is compared with the homogeneous model, developed by Butler (1991), to quantify the effects of heterogeneities in permeability and thermal diffusivity on the SAGD efficiency. A case is studied by assigning harmonic distribution to the perturbations of thermal diffusivity and permeability. Different cases with different relationships between permeability and thermal-diffusivity fields are considered to investigate their effects on the oil flow rate. The results show that local perturbations decrease the oil flow rate. Furthermore, steam-chamber growth is retarded in a reservoir with local perturbations compared with homogeneous reservoirs.
The developed model can be used in the initial stages of SAGD development projects for long-range planning as a guide to find the upper and lower limits of production in reservoirs with heterogeneities.
|File Size||1 MB||Number of Pages||19|
Alali, N., Pishvaie, M. R., and Jabbari, H. 2009. A New Semi-Analytical Modeling of Steam-Assisted Gravity Drainage in Heavy Oil Reservoirs. J Pet Sci Eng 69 (3–4): 261–270. https://doi.org/10.1016/j.petrol.2009.09.003.
Azom, P. N. and Srinivasan, S. 2011. Modeling the Effect of Permeability Anisotropy on the Steam-Assisted Gravity Drainage (SAGD) Process. Presented at the Canadian Unconventional Resources Conference, Calgary, 15–17 November. SPE-149274-MS. https://doi.org/10.2118/149274-MS.
Bakr, A. A., Gelhar, L. W., Gutjahr, A. L. 1978. Stochastic Analysis of Spatial Variability in Subsurface Flows: 1. Comparison of One-and Three-Dimensional Flows. Water Resour Res 14 (2): 263–271. https://doi.org/10.1029/WR014i002p00263.
Biercuk, M., Llaguno, M. C., Radosavljevic, M. et al. 2002. Carbon Nanotube Composites for Thermal Management. Appl Phys Lett 80 (15): 2767–2769. https://doi.org/10.1063/1.1469696.
Butler, R. 1985. A New Approach to the Modelling of Steam-Assisted Gravity Drainage. J Can Pet Technol 24 (3): 42–51. PETSOC-85-03-01. https://doi.org/10.2118/85-03-01.
Butler, R., Jiang, Q., and Yee, C. 1999. Steam and Gas Push (SAGP)–3; Recent Theoretical Developments and Laboratory Results. Presented at the Annual Technical Meeting, Calgary, 14–18 June. PETSOC-99-23. https://doi.org/10.2118/99-23.
Butler, R. M. 1991. Thermal Recovery of Oil and Bitumen. Old Tappan, New Jersey: Prentice Hall.
Butler, R. M., Mcnab, G. S., and Lo, H. Y. 1981. Theoretical Studies on the Gravity Drainage of Heavy Oil During In-Situ Steam Heating. Can J Chem Eng 59 (4): 455–460. https://doi.org/10.1002/cjce.5450590407.
Chalaturnyk, R. and Li, P. 2004. When Is It Important to Consider Geomechanics in SAGD Operations? J Can Pet Technol 43 (4): 53–61. PETSOC-04-04-05. https://doi.org/10.2118/04-04-05.
Chen, Q. 2009. Assessing and Improving Steam-Assisted Gravity Drainage: Reservoir Heterogeneities, Hydraulic Fractures, and Mobility Control Foams. PhD dissertation, Stanford University, Stanford, California (May 2009).
Dehghanpour, H., Li, G., and Mojarad, M. 2014. Emulsion Flow at the Edge of a Steam Chamber. Presented at the SPE Heavy Oil Conference–Canada, Calgary, 10–12 June. SPE-170094-MS. https://doi.org/10.2118/170094-MS.
Durlofsky, L. J. 1991. Numerical Calculation of Equivalent Grid Block Permeability Tensors for Heterogeneous Porous Media. Water Resour Res 27 (5): 699–708. https://doi.org/10.1029/91WR00107.
Faradonbeh, M., Harding, T. G., Abedi, J. et al. 2017. Semianalytical Modeling of Steam/Solvent Gravity Drainage of Heavy Oil and Bitumen: Unsteady-State Model With Curved Interface. SPE Res Eval & Eng 20 (1): 134–148. SPE-170123-PA. https://doi.org/10.2118/170123-PA.
Farouq Ali, S. M. 1997. Is There Life After SAGD? J Can Pet Technol 36 (6): 20–24. PETSOC-97-06-DAS. https://doi.org/10.2118/97-06-DAS.
Freeze, R. A. 1975. A Stochastic-Conceptual Analysis on One-Dimensional Groundwater Flow in Non-Uniform Homogeneous Media. Water Resour Res 11 (5): 725–741. https://doi.org/10.1029/WR011i005p00725.
Gelhar, L. 1974. Stochastic Analysis of Phreatic Aquifers. Water Resour Res 10 (3): 539–545. https://doi.org/10.1029/WR010i003p00539.
Gelhar, L. W. and Axness, C. L. 1983. Three-Dimensional Stochastic Analysis of Macrodispersion in Aquifers. Water Resour Res 19 (1): 161–180. https://doi.org/10.1029/WR019i001p00161.
Gotawala, D. R. and Gates, I. D. 2010. On the Impact of Permeability Heterogeneity on SAGD Steam Chamber Growth. Nat Resour Res 19 (2): 151–164. https://doi.org/10.1007/s11053-010-9114-0.
Hassanzadeh, H. and Harding, T. 2016. Analysis of Conductive Heat Transfer During In-Situ Electrical Heating of Oil Sands. Fuel 178 (15 August): 290–299. https://doi.org/10.1016/j.fuel.2016.03.070.
Heidari, M., Hejazi, S. H., and Farouq Ali, S. M. 2017. Steam-Assisted Gravity-Drainage Performance With Temperature-Dependent Properties–A Semianalytical Approach. SPE J. 22 (3): 902–911. SPE-175036-PA. https://doi.org/10.2118/175036-PA.
Kisman, K. E. and Yeung, K. C. 1995. Numerical Study of the SAGD Process in the Burnt Lake Oil Sands Lease. Presented at the SPE International Heavy Oil Symposium, Calgary, Alberta, Canada, 19–21 June. SPE-30276-MS. https://doi.org/10.2118/30276-MS.
Kumar, D. 2014. Modeling Steam Assisted Gravity Drainage in Heterogeneous Reservoirs Using Different Upscaling Techniques. Master’s thesis, University of Texas at Austin, Austin, Texas (May 2014).
Larter, S., Adams, J., Gates, I. D. et al. 2006. The Origin, Prediction and Impact of Oil Viscosity Heterogeneity on the Production Characteristics of Tar Sand and Heavy Oil Reservoirs. Presented at the Canadian International Petroleum Conference, Calgary, 13–15 June. PETSOC-2006-134. https://doi.org/10.2118/2006-134.
Mielke, P., Bignall, G., and Sass, I. 2010. Permeability and Thermal Conductivity Measurements of Near Surface Units at the Wairakei Geothermal Field, New Zealand. Oral presentation given at the World Geothermal Congress, Bali, Indonesia, 25–29 April.
Nourozieh, H., Kariznovi, M., and Abedi, J. 2015. Density and Viscosity of Athabasca Bitumen Samples at Temperatures Up to 200°C and Pressures Up to 10 MPa. SPE Res Eval & Eng 18 (3): 375–386. SPE-176026-PA. https://doi.org/10.2118/176026-PA.
Peaceman, D. 1993. Representation of a Horizontal Well in Numerical Reservoir Simulation. SPE Advanced Technology Series 1 (1): 7–16. SPE-21217-PA. https://doi.org/10.2118/21217-PA.
Pooladi-Darvish, M., Tortike, W. S., and Farouq Ali, S. M. 1995. A New Semi-Analytical Model for Thermal Recovery Processes. Presented at the SPE Western Regional Meeting, Bakersfield, California, 8–10 March. SPE-29660-MS. https://doi.org/10.2118/29660-MS.
Popov, Y., Tertychnyi, V., Romushkevich, R. et al. 2003. Interrelations Between Thermal Conductivity and Other Physical Properties of Rocks: Experimental Data. In Thermo-Hydro-Mechanical Coupling in Fractured Rock, ed. H.-J. Kümpel, 1137–1161. Basel, Switzerland: Birkhäuser.
Reis, J. C. 1992. A Steam-Assisted Gravity Drainage Model for Tar Sands: Linear Geometry. J Can Pet Technol 31 (10): 14–20. PETSOC-92-10-01. https://doi.org/10.2118/92-10-01.
Robinson, B., Kenny, J., Hernandez-Hdez, I. L. et al. 2005. Geostatistical Modeling Integral to Effective Design and Evaluation of SAGD Processes of an Athabasca Oilsands Reservoir, A Case Study. Presented at the SPE International Thermal Operations and Heavy Oil Symposium, Calgary, 1–3 November. SPE-97743-MS. https://doi.org/10.2118/97743-MS.
Sharma, B. C., Khataniar, S., Patil, S. L. et al. 2002. A Simulation Study of Novel Thermal Recovery Methods in the Ugnu Tar Sand Reservoir, North Slope, Alaska. Presented at the SPE Western Regional/AAPG Pacific Section Joint Meeting, Anchorage, 20–22 May. SPE-76729-MS. https://doi.org/10.2118/76729-MS.
Sharma, J. and Gates, I. D. 2010. Multiphase Flow at the Edge of a Steam Chamber. Can J Chem Eng 88 (3): 312–321. https://doi.org/10.1002/cjce.20280.
STARS is a trademark of Computer Modelling Group Ltd.
Sun, T., Takbiri-Borujeni, A., Nourozieh, H. et al. 2019. Application of Peng-Robinson Equation of State for Modelling the Multiphase Equilibrium Properties in Athabasca Bitumen/Ethane Mixtures. Fuel 252 (September): 439–447. https://doi.org/10.1016/j.fuel.2019.04.106.
Vanegas, J. W. P., Deutsch, C. V., and Cunha, L. B. 2008. Uncertainty Assessment of SAGD Performance Using a Proxy Model Based on Butler’s Theory. Presented at the SPE Annual Technical Conference and Exhibition, Denver, 21–24 September. SPE-115662-MS. https://doi.org/10.2118/115662-MS.
Welty, C. and Gelhar, L. W. 1991. Stochastic Analysis of the Effects of Fluid Density and Viscosity Variability on Macrodispersion in Heterogeneous Porous Media. Water Resour Res 27 (8): 2061–2075. https://doi.org/10.1029/91WR00837.