Advertisement

Transport in Porous Media

, Volume 79, Issue 3, pp 377–392 | Cite as

Oil Displacement for One-Dimensional Three-Phase Flow with Phase Change in Fractured Media

  • Hai-Shan Luo
  • Xiao-Hong WangEmail author
Article

Abstract

In this article, the numerical simulations for one-dimensional three-phase flows in fractured porous media are implemented. The simulation results show that oil displacement in matrix is dominated by oil–water capillary pressure only under certain conditions. When conditions are changed to decrease the amount of water entering into the fractured media from the boundary of the flow field, water in fracture may be vaporized to superheated steam. In these cases, the appearance of superheated steam in fracture rather than in matrix will decrease the fracture pressure and generate the pressure difference between matrix and fracture, which results in oil flowing from matrix to fracture. Assuming that oil is wetting to steam, the matrix steam–oil capillary pressure will decrease the matrix oil-phase pressure as the matrix steam saturation increases. After the steam–oil capillary pressure finally exceeds the pressure difference due to the appearance of superheated steam in fracture, the oil displacement in matrix will stop. It is also shown that variations of the water relative permeability curve in matrix do not result in different mechanisms for oil displacement in matrix. The simulation results suggest that the amount of liquid water supply from the boundary of flow field fundamentally influence the mechanisms for oil displacement in matrix.

Keywords

Fluid flows in porous media Multi-phase flows Fractured media Steam injection Oil recovery 

Nomenclature

CPα

α-Phase isobaric specific heat (J/kg °C)

E

Exchange of energy between fracture and matrix (J/m3s)

K

Intrinsic permeability (m2)

Krα

α-Phase relative permeability

Krog

Oil-phase relative permeability in oil–gas two-phase system

Krow

Oil-phase relative permeability in oil–water two-phase system

Hα

α-Phase enthalpy (J/kg)

Pα

α-Phase pressure (Pa)

Pc(og)

Gas–oil capillary pressure (Pa)

Pc(ow)

Oil–water capillary pressure (Pa)

Qα

α-Phase filtration velocity (m/s)

qα

Exchange of the mass between fracture and matrix for the α-phase (kg /m3s)

R

Gas constant (J/mol K)

Sα

α-Phase saturation

t

Time (s)

T

Temperature (K)

Uα

α-Phase internal energy (J/kg)

Greek Letters

ϕ

Porosity

λα

α-Phase thermal conductivity (W/m °C)

μα

α-Phase dynamic viscosity (Pa s)

ρα

α-Phase density (kg/m3)

σ

Fracture-matrix transfer shape factor (/m2)

Subscripts and Superscripts

φi

Value of variable ϕ at the i-th grid

φ(f)

Value of variable ϕ in fracture

φ(m)

Value of variable ϕ in matrix

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Aziz K., Ramesh A.B., Woo P.T.: Fourth SPE comparative solution project: comparison of steam injection simulators. J. Pet. Technol. 39(12), 1576–1584 (1987). doi: 10.2118/13510-PA Google Scholar
  2. Brooks R.H., Corey A.T.: Properties of porous media affecting fluid flow. J. Irrig. Drain. Div. Proc. Am. Soc. Civ. Eng. 92(IR2), 61–88 (1966)Google Scholar
  3. Chen, W.H., Wasserma, M.L., Fitzmorris, R.E.: A thermal simulator for naturally fractured reservoirs. Paper presented at the 9th SPE symposium on reservoir simulation, San Antonio, TX, 1–4 February 1987Google Scholar
  4. Dindoruk, M.D.S., Aziz, K., Brigham, W., Castanier, L.: A study of steam injection in fractured media. Dissertation, Stanford University, California (1996)Google Scholar
  5. Gilman J.R.: An efficient finite-difference method for simulating phase segregation in the matrix blocks in double-porosity reservoirs. Soc. Pet. Eng. J. 1(4), 403–413 (1986)Google Scholar
  6. Gilman, J.R., Kazemi, H.: Improve calculations for viscous and gravity displacement in matrix blocks in dual-porosity simulators. Paper presented at the 9th SPE symposium on reservoir simulation, San Antonio, TX, 1–4 February 1987Google Scholar
  7. Hill, A.C., Thomas, G.W.: A new approach for simulating complex fractured reservoirs. Paper presented at the SPE Middle east oil technical conference and exhibition, Bahrain, 11–14 March 1985Google Scholar
  8. Honarpour M.M., Koederitz F., Herbert A.: Relative Permeability of Petroleum Reservoirs. CRC Press, Boca Raton, FL (1986)Google Scholar
  9. Kazemi K., Merrill L.S. Jr, Porterfield K.P., Zeman P.R.: Simulation of water-oil flow in naturally fractured reservoirs. Soc. Pet. Eng. J. 16(6), 317–326 (1976)Google Scholar
  10. Kazemi H., Merrill L.S. Jr: Numerical simulation of water imbibition in fractured cores. Soc. Pet. Eng. J. 16, 175–182 (1979)Google Scholar
  11. Lee B.Y.Q., Tan T.B.S.: Application of a multiple porosity/permeability simulator in fractured reservoir simulation. Soc. Pet. Eng. J. 27, 181–192 (1987)Google Scholar
  12. Lim K.T., Aziz K.: Matrix-fracture transfer shape factors for dual-porosity simulators. J. Pet. Sci. Eng. 13, 169–178 (1995). doi: 10.1016/0920-4105(95)00010-F CrossRefGoogle Scholar
  13. Noetinger B., Estebenet T., Landereau P.: Up-scaling of double porosity fractured media using continuous-time random walks methods. Transp. Porous Media 39, 315–337 (2000). doi: 10.1023/A:1006639025910 CrossRefGoogle Scholar
  14. Oballa V., Coombe D.A., Buchanan W.L.: Factors affecting the thermal response of naturally fractured reservoirs. J. Can. Pet. Technol 32(8), 31–42 (1993)Google Scholar
  15. Pruess K., Narasimhan T.N.: A practical method for modelling fluid and heat flow in fractured porous media. Soc. Pet. Eng. J. 25(1), 14–26 (1985)Google Scholar
  16. Pruess, K., Wu, Y.-S.: A new semi-analytical method for numerical simulation of fluid and heat flow in fractured reservoirs. Paper presented at the SPE symposium on reservoir simulation, Houston, TX, 6–8 February 1989Google Scholar
  17. Quintard M., Whitaker S.: One- and two-equation models for transient diffusion processes in two-phase systems. Adv. Heat Transf. 23, 369–464 (1993)Google Scholar
  18. Reis, J.C.: Oil recovery mechanisms in fractured reservoirs during steam injection. Paper presented at the SPE/DOE symposium on enhanced oil recovery, Tulsa, OK, 22–25 April 1990Google Scholar
  19. Sandler S.I.: Chemical and Engineering Thermodynamics. Wiley, New York (1977)Google Scholar
  20. Schmidt E.: Properties of Sater and Steam in S.I. Units. Springer, Berlin (1982)Google Scholar
  21. Stone H.L.: Estimation of three-phase relative permeability and residual oil data. J. Pet. Technol. 12(4), 52–61 (1973)Google Scholar
  22. Thomas L.K., Dixon T.N., Pierson R.G.: Fractured reservoir simulation. Soc. Pet. Eng. J. 23(1), 42–54 (1983)Google Scholar
  23. Udell K.S.: Heat transfer in porous media heated from above with evaporation, condensation, and capillary effects. J. Heat Transf. 105, 485–492 (1983)CrossRefGoogle Scholar
  24. Van Golf-Racht T.D.: Fundamentals of Fractured Reservoir Engineering. Elsevier, Amsterdam (1982)Google Scholar
  25. Warren J.E., Root P.J.: The behavior of naturally fractured reservoirs. Soc. Pet. Eng. J. 3(5), 245–255 (1963)Google Scholar
  26. Wu Y.S., Pruess K.: A multiple-porosity method for simulation of naturally fractured petroleum reservoirs. Soc. Pet. Eng. J. 3, 327–336 (1988)Google Scholar
  27. Wu Y.S., Pruess K.: Numerical simulation of non-isothermal multiphase tracer transport in heterogeneous fractured porous media. Adv. Water Resour. 23, 699–723 (2000). doi: 10.1016/S0309-1708(00)00008-7 CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  1. 1.Department of Thermal Science and Energy EngineeringUniversity of Science and Technology of ChinaHefeiPeople’s Republic of China

Personalised recommendations