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Foamy Oil Flow in Porous Media

  • D. D. Joseph
  • A. M. Kamp
  • R. Bai
Part of the The IMA Volumes in Mathematics and its Applications book series (IMA, volume 131)

Abstract

Certain heavy oils which foam under severe depressurization give rise to increased recovery factor and an increased rate of production under solution gas drive. These oils not only stabilize foam, but also stabilize dispersion of gas bubbles at lower volume ratios. The way this phenomenon is related to the chemistry of the oil and its viscosity is presently not understood. We present here a mathematical model of reservoir flow of foamy oil which depends only on the velocity through Darcy’s law, the pressure and the dispersed gas fraction. The theory governs only in situations in which the bubbles do not coalesce to produce the percolation of free gas. In this theory the bubbles move with the oil as they evolve. The main empirical content of the theory enters through the derivation of solubility isotherms which can be obtained from PVT data; modeling of nucleation, coalescence, bubble drag laws and transfer functions are avoided. The local pressure difference and dispersed gas fraction are in equilibrium on the solubility isotherm. In a pressure drawdown the time taken for the system to return to equilibrium is described by a rate law characterized by an empirical relaxation time (rate constant). The resulting systems of equations can be reduced to a coupled pair of nonlinear PDE’s for the dispersed gas fraction and pressure difference, which can further be reduced in the equilibrium case to a second order evolution equation for the pressure difference. This system of equations can also be derived from usual theory of two-phase flow in a porous media based on relative permeability under the assumption that the bubbles and oil move in lock step. We propose a reformulation of the conventional theory in which the concept relative permeability of the porous media is replaced with the more familiar concept of an effective phase viscosity. The equations of our relaxation theory are solved numerically, and the mixture viscosity function and relaxation time are selected to match the sand pack experiments of Maini and Sarma [1994].

Keywords

Porous Medium Relative Permeability Viscosity Function Solubility Isotherm Pressure Drawdown 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [1]
    Claridge, E. L. and Prats, M. June 19-21, 1995. “A Proposed Model and Mechanism for Anomalous Foamy Heavy Oil Behavior,” paper SPE 29243 presented at the International Heavy Oil Symposium, Calgary, AB Proc., 9–20; also the unsolicited manuscript of SPE (USMS) 29243, 1994.Google Scholar
  2. [2]
    Firoozabadi, A., Ottesen, B., & Mikkelsen, M. December 1992, “Measurement of Supersaturation and Critical Gas Saturation,” SPE Formation Evaluation, 337–344.Google Scholar
  3. [3]
    Huerta, M., Otero, C., Rico, A., Jimenez, I., De Mirabal, M. & Rojas, G. October 6-9, 1996. “Understanding Foamy Oil Mechanisms for Heavy Oil Reservoirs during Primary Production,” paper SPE 36749, presented at the 1996 SPE Annual Technical Conference and Exhibition, Denver, Colorado, 671–685.Google Scholar
  4. [4]
    Joseph, D. D. and Renardy, Y. 1992. Fundamentals of Two-Fluid Dynamics, Vol. I: Mathematical Theory and Applications, Vol. II: Lubricated Transport, Drops and Miscible Liquids, Springer.Google Scholar
  5. [5]
    Kraus, W. P., Mccaffrey, W. J., & Boyd, G. W. 1993. “Pseudo-Bubble Point Model for Foamy Oils,” paper CIM 93-94 presented at the 44th Annual Technical Conference of the Petroleum Society of CIM, Calgary, AB, May 9-12.Google Scholar
  6. [6]
    Lebel, J. P. March 2, 1994. “Performance implications of various reservoir access geometrics,” Paper presented at the 11 th Annual Heavy Oil & Oil Sands Tech. Symp.Google Scholar
  7. [7]
    Leibenson, L. S. 1941. The motion of gas-saturated fluid in a porous media. Bulletin, USSR Acad. Science, ser. geography & geophysics, No.3.Google Scholar
  8. [8]
    Maini, B. B. June 1996. “Foamy Oil Flow in Heavy Oil Production,” JCPT 35(6): 21–24.Google Scholar
  9. [9]
    Maini B. B. & Sarma, H. 1994. “Role of Nonpolar Foams in Production of Heavy Oils,” in: “Advances in Chemistry Series” 242: 405–420.Google Scholar
  10. [10]
    De Mirabal, M., Gordillo, R., Fuenmayor, M., Rojas, G., Rodriguez H. & Sanchez, R. April 23-26, 1996. “Integrated Study for the Characterization and Development of the MFB-53 Reservoir, North Hamaca-Orinoco Belt, Venezuela,” paper SPE 36095, presented at the Fourth Latin American & Caribbean Petroleum Engineering Conference, Port-of-Spain, Trinidad & Tobago.Google Scholar
  11. [11]
    Peng, D. Y., Fu, C. T., Bird, G. W. & Hsi, C. August, 4-9, 1991. “Effect of Gas components on thermodynamic properties of Alberta Heavy Crudes and Bitumens,” in: 5th Unitar Heavy Crude & Tar Sands International Conference, Caracas, Venezuela, Proc. 1: 47–55.Google Scholar
  12. [12]
    Pooladi-Darvish M. & Firoozabadi, A. June 11, 1997. “Solution gas drive in heavy oil reservoirs,” paper no. 97-113, presented at the 48th Annual Technical meeting of the Petroleum Society of CIM in Calgary, Canada.Google Scholar
  13. [13]
    Sheng, J.J., Hayes, R. E., Maini A. B. & Tortike, W. S. 1996. A dynamic model to simulate foamy oil flow in porous media, SPE 36750.Google Scholar
  14. [14]
    Sheng, J.J., Maini, B. B., Hayes R. E. & Tortike, W. S. May 1999a. “Critical Review of foamy Oil Flow,” Transport in Porous Media, 35(2): 157–187.Google Scholar
  15. [15]
    Sheng, J.J., Hayes, R. E., Maini, B. B. & Tortike, W. S. May 1999b. “Modeling Foamy Oil Flow in Porous Media,” Transport in Porous Media, 35(2): 227–258.Google Scholar
  16. [16]
    Svrcek, W.Y. & Mehrotra, A. K. 1982. Gas solubility, viscosity and density measurements for Athabasca bitumen, J. Canadian Petroleum Technology, 21(4): 31–38.Google Scholar

Copyright information

© Springer Science+Business Media New York 2002

Authors and Affiliations

  • D. D. Joseph
    • 1
  • A. M. Kamp
    • 2
  • R. Bai
    • 1
  1. 1.Dept. of Aerospace Engng. & Mech.University of MinnesotaMinneapolisUSA
  2. 2.PDVSA IntevepCaracasVenezuela

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