Gravity Effect on Two-Phase Immiscible Flows in Communicating Layered Reservoirs

详细信息    查看全文

• 作者：Xuan Zhang (1)
  Alexander Shapiro (1) ash@ktdtu.dk
  Erling H. Stenby (1)
• 关键词：Upscaling – ; Two ; phase flow – ; Viscous ; dominant regime – ; Gravity – ; Waterflooding
• 刊名：Transport in Porous Media
• 出版年：2012
• 出版时间：April 2012
• 年：2012
• 卷：92
• 期：3
• 页码：767-788
• 全文大小：936.9 KB
• 参考文献：1. Bedrikovetsky P.: Mathematical Theory of Oil and Gas Recovery. Kluwer Academic Publishers, (1993)
  2. Bird N.R.A., Perrier E., Rieu M.: The water retention function for a model of soil structure with pore and solid fractal distributions. Eur. J. Soil Sci. 51, 55–63 (2000)
  3. Bj酶rnar氓, T.I., Aker, E.: Comparing equations for two-phase fluid flow in porous media. In: COMSOL conference, Hannover (2008)
  4. Corey A.T., Rathjens C.H.: Effect of stratification on relative permeability. J. Petroleum Technol. 8(12), 69–71 (1956)
  5. Dietz, D.N.: A Theoretical Approach to the Problem of Encroaching and Bypassing Edge Water. Konikl. Ned. Akad. Wetenschap (1953)
  6. Diaz-Viera, M.A., Lopez-Falcon, D.A., Moctezuma-Berthier, A., Ortiz-Tapia, A.: COMSOL implementation of a multiphase fluid flow model in porous media. In: COMSOL conference, Boston (2008)
  7. Dulofsky, L.J.: Upscaling of geocellular models for reservoir flow simulation: a review of recent progress. In: The 7th international forum on reservoir simulation, Baden (2003)
  8. Dykstra, H., Parsons, R.L.: The prediction of oil recovery by waterflooding. In: Secondary Oil Recovery of Oil in the United States, 2nd Edn, API, pp. 160–174 (1950)
  9. El-Khatib, N.: The effect of crossflow on waterflooding of stratified reservoirs. In: SPE Middle East Oil Technical Conference and Exhibition, Manama (1983)
  10. El-Khatib N.: Waterflooding performance of communicating stratified reservoir with log-normal permeability distribution. SPE Reservoir Eval. Eng. 2(6), 542–549 (1999)
  11. Gelfand I.M.: Some problems of the theory of quasi-linear equations. Usp. Mat. Nauk. 24 2(86), 87–158 (1959)
  12. Hearn, C.L.: Simulation of Stratified Water Flooding by Pseudo Relative Permeability Curves. SPE 2929 (1971)
  13. Hiatt, W.N.: Injected-fluid coverage of multiwell reservoir with permeability stratification. In: Spring Meeting of the Pacific Coast District, Division of Production, Los Angeles (1958)
  14. Hunt A.G.: Percolation Theory for Flow in Porous Media. P33, The Lecture Notes in Physics. Springer, Berlin (2005)
  15. Kanevskaya R.D.: Asymptotic Analysis of the Effect of Capillary and Gravity Forces on the 2D Transport of Two-Phase Systems in a Porous Medium. Fluid Dyn 4, 557–563 (1988)
  16. Katz M.L., Tek M.R.: A theoretical study of pressure distribution and fluid flux in bounded stratified porous systems with crossflow. SPE J. 2(1), 68–82 (1962)
  17. Kurbanov A.K.: On some generalization of the equations of flow of a two-phase liquid in porous media. collected research papers on oil recovery. VNINeft 15, 32–38 (1961)
  18. Kurbanov A.K., Atanov G.A.: On the problem of oil displacement by water from heterogeneous reservoirs. oil and gas of Tyumen. Collect. Res. 13, 36–38 (1972)
  19. Longino, B.L., Kueper, B.H.: Retention of dense nonaqueous phase liquid (DNAPL) in fractured rock. In: 2nd North American Rock Mechanics Symposium, Montreal (1996)
  20. Martin, J.C.: Partial integration of equations of multiphase flow. SPE J. (December), 8(4), 370–380 (1968)
  21. Pau G.S.H., Bell J.B., Pruess K., Almgren A.S., Lijewski M.J., Zhang K.: High-resolution simulation and characterization of density-driven flow in CO2 storage in saline aquifers. Adv. Water Resour. 33, 443–455 (2010)
  22. Tyler S.W., Wheatcraft S.W.: Fractal processes in soil water retention. Water Resour. Res. 26, 1045–1054 (1990)
  23. Tyler S.W., Wheatcraft S.W.: Fractal scaling of soil particle size distributions—analysis and imitations. Soil Sci. Soc. Am. J. 56, 362–369 (1992)
  24. Yokoyama, Y., Lake, L.W.: The effects of capillary pressure on immiscible displacements in stratified porous media. Paper SPE 10109 presented at the society of petroleum engineers fall technical conference and exhibition, San Antonio (1981)
  25. Yortsos Y.C.: A theoretical analysis of vertical flow equilibrium. Transp. Porous Med. 18, 107–129 (1995)
  26. Zapata, V.J., Lake, L.W.: A Theoretical analysis of viscous crossflow. Paper SPE 10111 presented at the society of petroleum engineers fall technical conference and exhibition, San Antonio (1981)
  27. Zhang, X., Shapiro, A., Stenby, E.H.: COMSOL implementation for upscaling of two-phase immiscible flows in communicating layered reservoir. In: COMSOL conference, Paris (2010)
  28. Zhang, X., Shapiro, A., Stenby, E.H.: Upscaling of two-phase immiscible flows in communicating stratified reservoirs. Transp. Porous Med. 1287 (2011)
• 作者单位：1. Technical University of Denmark, Building 229, 2800 Lyngby, Denmark
• 刊物类别：Earth and Environmental Science
• 刊物主题：Earth sciences
  Geotechnical Engineering
  Industrial Chemistry and Chemical Engineering
  Civil Engineering
  Hydrogeology
  Mechanics, Fluids and Thermodynamics
  
• 出版者：Springer Netherlands
• ISSN：1573-1634

文摘

An upscaling method is developed for two-phase immiscible incompressible flows in layered reservoirs with good communication between the layers. It takes the effect of gravity into consideration. Waterflooding of petroleum reservoirs is used as a basic example for application of this method. An asymptotic analysis is applied to a system of 2D flow equations for incompressible fluids at high-anisotropy ratios, but low to moderate gravity ratios, which corresponds to the most often found reservoir conditions. The 2D Buckley–Leverett problem is reduced to a system of 1D parabolic equations in a layered reservoir. For low-gravity ratios, it can further be reduced to a system of hyperbolic equations. The number of the 1D equations in the system is equal to the number of layers in the reservoir. The method is tested on different examples of displacement in a layer-cake reservoir. Different combinations of gravity-viscous and anisotropy ratios are tested. Solutions by our method are compared with the results of 2D simulations carried out by the COMSOL solver. The results are comparable, especially if the layers of the reservoirs are further subdivided into sublayers, in order to account better for gravity segregation. The effects of gravity are analyzed.