Prediction of unstable fluid displacements in porous media using the Karhunen-loeve (K-L) decomposition

In Situ

Volumn 21, Issue 4, 1997, Pages 331-356

  Gharbi, Ridha B ^a   Smaoui, Nejib ^a   Peters, Ekwere J ^b  

^a KUWAIT UNIVERSITY   (Kuwait)

^b The University of Texas at Austin   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CORRELATION METHODS; EIGENVALUES AND EIGENFUNCTIONS; ENHANCED RECOVERY; FLOW PATTERNS; MAGNETIC RESONANCE IMAGING; MATRIX ALGEBRA; NUMERICAL METHODS; POROUS MATERIALS;

KARHUNEN-LOEVE DECOMPOSITION; UNSTABLE FLUID DISPLACEMENTS;

UNSTEADY FLOW;

EID: 0031268245     PISSN: 01462520     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (64)

1. Blackwell, R.J., J.R. Rayne and W.M., Terry: "Factors Influencing the Efficiency of Miscible Displacement," Trans., AIME (1959) 216, 1-8.
2. Habermann, B.: "The Efficiency of Miscible Displacement as a Function of Mobility Ratio," Trans., AIME (1960) 219, 264-272.
3. Homsy, G.M.: "Viscous Fingering in Porous Media," Ann. Rev. Fluid Mech (1987) 19, 271-311.
4. Peters, E.J. and W.D. Hardham: "Visualization of Fluid Displacements in Porous Media Using Computed Tomography Imaging," J. Pet. Sci. Eng. (May, 1990) 4, No.2, 155-168.
5. Peters, E.J. and N. Afzal: "Characterization of Heterogeneities in Permeable Media with Computed Tomography Imaging," J. Pet. Sci. Eng. (June, 1992) 7, No.3/4, 283-296.
6. Allen, E. and D.V. Boger: "The Influence of Rhedogical Properties on Mobility Control in Polymer-Augmented Waterflooding," paper SPE 18097, presented at the 63rd Annual Technical Conference and Exhibition of SPE, Houston, TX, October 2-5, 1988.
7. Chuoke, R.L., P. van Meurs, and C. van der Poel: "The Instability of Slow, Immiscible, Viscous Liquid-Liquid Displacements in Permeable Media," Trans., AIME (1959) 216, 188-194.
8. Croes, G.A. and N. Schwarz: "Dimensionally Scaled Experiments and the Theories on the Water-Drive Process," Trans., AIME (1955) 204, 35-42.
9. Giordano, R.M., S.J. Salter, and K.K. Mohanty: "The Effects of Permeability Variations on Flow in Porous Media", paper SPE 14365, presented at the 60th Annual Technical Conference and Exhibition of SPE, Las Vegas, NV, September 22-25, 1985.
10. Peters, E.J. and C.A. Reid: "A Microcomputer-Based Imaging System for the Visualization of Fluid Displacements," J. Pet. Tech. (May, 1990) 42, 558-563.
11. Christie, M.A., A.D.W. Jones, and A.H. Muggeridge: "Comparison Between Laboratory Experiments and Detailed Simulations of Unstable Miscible Displacement Influenced by Gravity," paper presented at the North Sea Oil and Gas Reservoirs Conference, Trondheim, Norway, May 8-10, 1989.
12. Dumore, J.M.: "Stability Considerations in Downward Miscible Displacements," Trans., AIME (1964) 231, 356-364.
13. Hall, H.N. and T.M. Geffen: "A Laboratory Study of Solvent Flooding," Trans., AIME (1957) 210, 48-57.
14. Lee, K.S. and E.L. Claridge: "Areal Sweep Efficiency of Pseudoplastic Fluids in a Five-Spot Hele-Shaw Model," Soc. Pet. Eng. J. (March, 1968) 8, 52-62.
15. Mahaffey, J.L., W.M. Rutherford, and C.S. Matthews: "Sweep Efficiency by Miscible Displacement in a Five-Spot," Soc. Pet. Eng. J. (March, 1966) 6, 73-80.
16. Peters, E.J., W.H. Broman, Jr., and J.A. Broman: "A Stability Theory for Miscible Displacement," paper SPE 13167, presented at the 59th Annual Technical Conference and Exhibition of SPE, Houston, TX, September 16-19, 1984.
17. 2 Flooding," Soc. Pet. Eng. J. (October, 1984) 24, 508-520.
18. 2 Displacements of Reservoir Oils from Long Berea Cores: Laboratory and Simulation Results," paper SPE 14306, presented at the 60th Annual Technical Conference and Exhibition of SPE, Las Vegas, NV, September 22-25, 1985.
19. Khataniar, S.: "A Numerical Study of the Performance of Unstable Displacements in Heterogeneous Media," Ph.D Dissertation, The University of Texas, Austin (1991).
20. Vinegar, H.J. and S.L. Wellington: "Tomographic Imaging of Three-Phase Flow Experiments," Rev. Sci. Instrum. (January, 1987)58, No. 1, 96-107.
21. Vinegar, H.J.: "X-Ray CT and NMR Imaging of Rocks," J. Pet. Tech. (March, 1986) 38, 257-259.
22. Withjack, E.M. and I. Ackervoll: "Computed Tomography Studies of 3-D Miscible Displacement Behavior in a Laboratory Five-Spot Model," paper SPE 18096, presented at the 63rd Annual Technical Conference and Exhibition of SPE, Houston, TX, October 2-5, 1988.
23. Edelstein, W.A., H.J. Vinegar, P.N. Tutunjian, P.B. Roemer, and O.M. Mueller: "NMR Imaging for Core Analysis," paper SPE 19272, presented at the 63rd Annual Technical Conference and Exhibition of SPE, Houston, TX, October 2-5, 1988.
24. Honarpour, M.M., K.R. McGee, M.E. Crocker, N.L. Maerefat, and B. Sharma: "Detailed Core Description of a Dolomite Sample from the Upper Madison Limestone Group, " paper SPE 15174, presented at the Rocky Mountain Regional Meeting of SPE, Billings, MT, May 19-21, 1986.
25. Bergosh, J.L. and G.D. Lord: "New Developments in the Analysis of Cores From Naturally Fractured Reservoirs", paper SPE 16805, presented at the 62nd Annual Technical Conference and Exhibition of SPE, Dallas, TX, September 27-30, 1987.
26. Wellington, S.L. and H.J. Vinegar: "X-Ray Computerized Tomography," J Pet. Tech. (August, 1987) 39, 885-898.
27. Kantzas, A.: "Investigation of Physical Properties of Porous Rocks and Fluid Flow Phenomena in Porous Media Using Computer Assisted Tomography," In Situ (1991) 14, No.1, 77-132.
28. Afzal, N.: "Investigation of Heterogeneities and Fluid Displacements in Porous Media Using Computed Tomography," M.S. Thesis, The University of Texas, Austin (1992).
29. Heller, J.P.: "Onset of Instability Patterns Between Miscible Fluids in Porous Media," J. Appl. Phys. (March, 1966) 37, 1566-1579.
30. Peters, E.J. and D.L. Flock: "The Onset of Instability During Two-Phase Immiscible Displacement in Porous Media," Soc. Pet. Eng. J. (April, 1981) 21, 249-258; Trans., AIME (1981) 271.
31. Peters, E.J. and D.L. Flock: "The Onset of Instability During Two-Phase Immiscible Displacement in Porous Media," Soc. Pet. Eng. J. (April, 1981) 21, 249-258; Trans., AIME (1981) 271.
32. Chikhliwala, E.D and Y.C. Yortsos: "Theoretical Investigations on Finger Growth by Linear and Weakly Nonlinear Stability Analysis," paper SPE 14367, presented at the 60th Annual Technical Conference and Exhibition of SPE, Las Vegas, NV, September 22-25, 1985.
33. Koval, E.J.: "A Method for Predicting the Performance of Unstable Miscible Displacement in Heterogeneous Media," J. Pet. Tech. (June, 1963) 3, 145-154.
34. Todd, M.R. and W.J. Longstaff: "The Development, Testing, and Application of a Numerical Simulator for Predicting Miscible Flood Performance," Trans., AIME (1972) 253, 874-882.
35. Fayers, F.J.: "An Approximate Model with Physically Interpretable Parameters for Representing Miscible Viscous Fingering," SPE Res. Eng. (May, 1988) 3, 551-558.
36. Fayers, F.J. and T.M. Newley: "Detailed Validation of an Empirical Model for Fingering With Gravity Effects," SPE Res. Eng. (May, 1988) 3, 542-550.
37. Nghiem, L.X., Y.K. Li, and R.K. Agarwal: "A Method for Modeling Incomplete Mixing in Compositional Simulation of Unstable Displacements," paper SPE 18439, presented at the 11th SPE Symposium on Reservoir Simulation , Houston, TX, February 6-8, 1989.
38. Odeh, A.S.: "A Proposed Technique for Simulation of Viscous Fingering in One-Dimensional Immiscible Flow," SPE Res. Eng. (August, 1989) 4, 304-308.
39. Young, L.C.: "The Use of Dispersion Relationship to Model Adverse Mobility Ratio Miscible Displacements," paper SPE/DOE 14899, presented at the 5th Joint SPE/DOE Symposium on Enhanced Oil Recovery, Tulsa, OK, April 20-23, 1986.
40. Christie, M.A. and D.J. Bond: "Detailed Simulation Of Unstable Processes in Miscible Flooding," SPE Res. Eng. (November, 1987) 2, 514-522.
41. Christie, M.A.: "High-Resolution Simulation Of Unstable Flows in Porous Media," SPE Res. Eng. (August, 1989) 4, 297-303.
42. Christie, M.A., A.H. Muggeridge, and J.J. Barley: "3D Simulation of Viscous Fingering and WAG Schemes," paper SPE 21238, presented at the 11th SPE Symposium on Reservoir Simulation, Anaheim, CA, February 17-20, 1991.
43. Araktingi, U.G. and F.M. Orr, Jr.: "Viscous Fingering in Heterogeneous Porous Media," paper SPE 18095, presented at the 63rd Annual Technical Conference and Exhibition of SPE, Houston, TX, October 2-5, 1988.
44. Araktingi, U.G. and F.M. Orr, Jr.: "Viscous Fingering, Gravity Segregation, and Reservoir Heterogeneity in Miscible Displacements in Vertical Cross Sections," paper SPE/DOE 20176, presented at the Joint SPE/DOE 7th Symposium on Enhanced Oil Recovery, Tulsa, OK, April 22-25, 1990.
45. Moissis, D.E., C.E. Miller, and M.F. Wheeler: "Simulation of Miscible Viscous Fingering Using a Modified Method of Characteristics: Effects of Gravity and Heterogeneity," paper SPE 18440, presented at the 11th SPE Symposium on Reservoir Simulation, Houston, TX, February 6-8, 1989.
46. Davies, G.W., A.D.W. Jones, and A.H. Muggeridge: "Miscible Displacements in a Heterogeneous Rock: Detailed Measurements and Accurate Predictive Simulation," paper SPE 22615, presented at the 66th Annual Technical Conference and Exhibition of SPE, Dallas, TX, October 6-9, 1991.
47. Peaceman, D.W. and H.H. Rachford Jr.: "Numerical Calculation of Multidimensional Miscible Displacement," J. Pet. Tech. (December, 1962) 14,327-339; Trans., AIME (1962) 225.
48. Peaceman, D.W. and H.H. Rachford Jr.: "Numerical Calculation of Multidimensional Miscible Displacement," J. Pet. Tech. (December, 1962) 14,327-339; Trans., AIME (1962) 225.
49. Li, P.: "Nuclear Magnetic Resonance Imaging of Fluid Displacements in Porous Media," Ph.D Dissertation, The University of Texas, Austin (1997).
50. Majors, P.D., P. Li, and E.J. Peters: "NMR Imaging of Immiscible Displacements in Porous Media," paper SPE 30557, presented at the 70th Annual Technical Conference and Exhibition of SPE, Dallas, TX, October 22-25, 1995.
51. Hotelling, H. (1953): "Analysis of Complex Statistical Variables in Principal Components," J. Exp. Psy. 24, 417 (1953).
52. Gonzalez, R.C. and P. Wintz: Digital Image Processing, 2nd Edition Addison Wesley, Reading, MA (1987) 122-130.
53. Lorenz, E.N.: "Deterministic Nonperiodic Flow," J. Atmos. Sci. (1963) 20, 130-141.
54. Brooks, C.L., M. Karplus, and B.M. Pettitt: Proteins: A Theoretical Perspective of Dynamics. Structure and Thermodynamics, Wiley Publishing Co., New York (1988).
55. Harman, H.: Modern Factor Analysis, University of Chicago Press, Chicago (1960).
56. Lumley, J. L.: "The Structure of Inhomogeneous Turbulent Flows," Atmospheric Turbulence and Radio Wave Propagation, A.M. Yaglom and V.I. Tatarski (eds.), Moskow: Nauka (1967) 166-178.
57. Armbruster, D., B. Nicolaenko, N. Smaoui, and P. Chossat: "Analyzing Bifurcations in the Kolmogorov Flow Equations," Dynamics Bifurcations and Symmetries, P. Chossat (ed.), NATO ASI, Cargese, Kluwer (1993).
58. Armbruster, D., B. Nicolaenko, N. Smaoui and P. Chossat: "Symmetries and Dynamics for the 2-d Navier Stokes Flow," Physica D (1996) 95, 81-93.
59. Smaoui, N.: "Karhunen-Loève Analysis on the 2-d Navier Stokes Flow," Bulletin of the American Physical Society (November, 1995) 40, No. 12, 2005.
60. Smaoui, N. and A.A. Garrouch: "A New Approach Combining Karhunen-Loève Decomposition and Artificial Neural Network for Estimating Tight Gas Sand Permeability," paper in press, J. Pet. Sci. Eng. (1996).
61. Sirovich, L.: "Turbulence and the Dynamics of Coherent Structures-Part III: Dynamics and Scaling," Quarterly of App. Math. (October, 1987) 45, 538-590.
62. Berkooz, G., P. Holmes, and J.L. Lumley: "The Proper Orthogonal Decomposition in the Analysis of Turbulent Flow," Ann. Rev. Fluid Mech. (1993) 25, No. 75, 539-575.
63. Crane, F.E., H.A. Kendall, and G.H. Gardner: "Some Experiments in the Flow of Miscible Fluids of Unequal Density Through Porous Media," Soc. Pet. Eng. J. (December, 1963) 3, 277-280.
64. van der Poel, C.: " Effect of Lateral Diffusivity on Miscible Displacement in Horizontal Reservoirs," Trans., AIME (1962) 225, 317-326.