Multiphase Linear Flow in Tight Oil Reservoirs
- S. Hamed Tabatabaie (IHS Global Canada Limited) | Mehran Pooladi-Darvish (Futech Energy Corporation and University of Calgary)
- Document ID
- Society of Petroleum Engineers
- SPE Reservoir Evaluation & Engineering
- Publication Date
- February 2017
- Document Type
- Journal Paper
- 184 - 196
- 2017.Society of Petroleum Engineers
- Boltzmann transformation, Linear Flow, Similarity Solution, Tight Oil, Multi-phase flow
- 86 in the last 30 days
- 462 since 2007
- Show more detail
- View rights & permissions
|SPE Member Price:||USD 10.00|
|SPE Non-Member Price:||USD 30.00|
The main objective of this work is to gain a general understanding of the performance of tight oil reservoirs during transient linear two-phase flow producing at constant flowing pressure. To achieve this, we provide a theoretical basis to explain the effect of different parameters on the behavior of solution-gas-drive unconventional reservoirs. It is shown that, with the Boltzmann transformation, the highly nonlinear partial-differential equations (PDEs) governing two-phase flow through porous media can be converted to two nonlinear ordinary-differential equations (ODEs). The resulting ODEs simplify the calculation of the reservoir performance and avoid the tedious calculation inherent in solving the original PDEs. Thus, the proposed model facilitates sensitivity studies and rapid evaluation of different hypotheses. Moreover, successful conversion of the highly nonlinear PDEs (in terms of distance and time) to the ODEs (in terms of the Boltzmann variable) implies that the saturation and pressure are unique functions of the Boltzmann variable, and as a result, saturation is a unique function of pressure. This transformation enables us to explain (a) the constant gas/oil ratio (GOR) that has been observed in some hydraulically fractured tight oil reservoirs and (b) the straight-line plot of 1=qo and 1=qg vs. √t during constant-pressure two-phase production.
An approximate analytical model is also developed. It is shown that the proposed approximate solution can be converted to a form similar to the well-known equations for single-phase flow, which enhances our understanding of two-phase-flow behavior.
Extensive sensitivity studies are performed to examine the utility of the proposed model in predicting the performance of tight oil reservoirs. The applicability of the conclusions to the boundary-dominated flow period is investigated. On the basis of numerous simulation studies, it is shown that the impact of various parameters on boundary-dominated flow can be predicted with the transient solution, without the need for running multiple numerical simulations.
|File Size||1 MB||Number of Pages||13|
Ayala, L. F. and Kouassi, J. P. 2007. The Similarity Theory Applied To the Analysis of Multiphase Flow in Gas-Condensate Reservoirs. Energy & Fuels 21 (3): 1592–1600. http://dx.doi.org/10.1021/ef060505w.
Behmanesh, H., Hamdi, H., and Clarkson, C. R. 2013. Production Data Analysis of Liquid Rich Shale Gas Condensate Reservoirs. Presented at the SPE Unconventional Resources Conference Canada, Calgary, 5–7 November. SPE-167160-MS. http://dx.doi.org/10.2118/167160-MS.
Bøe, A., Skjaeveland, S. M., and Whitson, C. H. 1989. Two-Phase Pressure Test Analysis. SPE Form Eval 4 (4). SPE-10224-PA. http://dx.doi.org/10.2118/10224-PA.
Burnell, J. G., McNabb, A., Weir, G. J. et al. 1989. Two-Phase Boundary Layer Formation in a Semi-Infinite Porous Slab. Transport in Porous Media 4 (4): 395–420. http://dx.doi.org/10.1007/BF00165781.
Burnell, J. G., Weir, G. J., and Young, R. 1991. Self-Similar Radial Two-Phase Flows. Transport in Porous Media 6 (4): 359–390. http://dx.doi.org/10.1007/BF00136347.
Fetkovich, M. J. 1973. The Isochronal Testing of Oil Wells. Presented at the 48th Annual Fall Meeting of the Society of Petroleum Engineers of AIME, Las Vegas, Nevada, 30 September–3 October. SPE-4529-MS. http://dx.doi.org/10.2118/4529-MS.
Kissling, W., McGuinness, M., McNabb, A. et al. 1992. Analysis of One-Dimensional Horizontal Two-Phase Flow in Geothermal Reservoirs. Transport in Porous Media 7 (3): 223–253. http://dx.doi.org/10.1007/BF01063961.
Martin, J.C. 1959. Simplified Equations of Flow in Gas Drive Reservoirs and the Theoretical Foundation of Multiphase Pressure Buildup Analyses. In Transactions of the Society of Petroleum Engineers, Vol. 216, 321–323, SPE-1235-G. Richardson, Texas: SPE.
Muskat, M. and Meres, M. W. 1936. The Flow of Heterogeneous Fluids Through Porous Media. Journal of Applied Physics 7 (9): 346–363. http://dx.doi.org/10.1063/1.1745403.
O’Sullivan, M. J. 1981. A Similarity Method for Geothermal Well Test Analysis. Water Resources Research 17 (2): 390–398. http://dx.doi.org/10.1029/WR017i002p00390.
Perrine, R. L. 1956. Analysis of Pressure-buildup Curves. In Drilling and Production Practice API-56-482.
Raghavan, R. 1976. Well Test Analysis: Wells Producing by Solution Gas Drive. SPE J. 16 (4): 196–208. SPE-5588-PA. http://dx.doi.org/10.2118/5588-PA.
Ramey Jr., H. J. 1964. Rapid Methods for Estimating Reservoir Compressibilities. J Pet Technol 16 (4): 447–454. SPE-772-PA. http://dx.doi.org/10.2118/772-PA.
Tabatabaie, S. H. 2014a. Unconventional Reservoirs: Mathematical Modeling of Some Non-linear Problems. PhD thesis, University of Calgary (August).
Tabatabaie, S. H. 2014b. Unconventional Reservoirs: Mathematical Modeling of Some Non-linear Problems. PhD thesis, University of Calgary, Chapter 7, Appendix 7-B.
Tabatabaie, S. H. 2014c. Unconventional Reservoirs: Mathematical Modeling of Some Non-linear Problems. PhD thesis, University of Calgary, Chapter 7, Appendix 7-A.
Whitson, C. H. and Sunjerga, S. 2012. PVT in Liquid-Rich Shale Reservoirs. Presented at the SPE Annual Technical Conference and Exhibition, San Antonio, Texas, 8–10 October. SPE-155499-MS. http://dx.doi.org/10.2118/155499-MS.
Wyckoff, R. D., and Botset, H. G. 1936. The Flow of Gas-Liquid Mixtures Through Unconsolidated Sands. Physics 7 (9): 325–345. http://dx.doi.org/10.1063/1.1745402.