1887

Abstract

Summary

This paper presents the analytical solution of four-component gas/oil displacements under constant pressure boundary conditions. All the previous studies in gas/oil displacement problems have been accomplished under the assumption of constant flux boundaries. In practice however, gas flooding projects are often conducted with constant injection pressure and constant producing well pressure. In this work, a novel generation of Buckley-Leverett’s classic fractional flow theory is applied to solve the problem of four-component gas/oil displacements under constant pressure boundaries.

Conservation of mass in a one-dimensional, dispersion-free medium, for a four-component gas/oil displacement system leads to a set of partial differential equations. The solution of the corresponding initial value problem under constant flux boundary conditions consists of rarefaction waves, shock waves and constant states connecting the injection state to the production state. In incompressible systems with constant pressure boundaries, the total volumetric flux is a function of time and hence, the classical Buckley-Leverett theory is not valid. However, the saturation wave structure obtained from the constant flux boundary condition problem can be used in the solution of the associated problem with constant pressure boundaries by determining the flux analytically as a function of time.

The solution for a four-component gas/oil displacement case study is presented. The determination of time dependent volumetric flux from the solution of the constant flux problem is demonstrated. Results are also obtained using a numerical approach and are compared to the analytical results. This indicates that the analytical solution is indistinguishable from the numerical solution as the number of grid blocks in the numerical method approaches infinity. However, a very fine grid is needed for an acceptable solution.

Loading

Article metrics loading...

/content/papers/10.3997/2214-4609.20141792
2014-09-08
2020-01-18
Loading full text...

Full text loading...

References

  1. Buckley, S. E., and Leverett, M. C.
    , [1941] Mechanism of fluid displacement in sands, Trans. Aime, 146, 107.
    [Google Scholar]
  2. Johansen, T., and Winther, R.
    , [1988] The solution of the Riemann problem for a hyperbolic system of conservation laws modeling polymer flooding, SIAM journal on mathematical analysis, 19(3), 541–566.
    [Google Scholar]
  3. , [1989] The Riemann problem for multicomponent polymer flooding, SIAM Journal on Mathematical Analysis, 20(4), 908–929.
    [Google Scholar]
  4. , [1990] Mathematical and numerical analysis of a hyperbolic system modeling solvent flooding, In 2nd European Conference on the Mathematics of Oil Recovery.
    [Google Scholar]
  5. Johansen, T., Wang, Y., Orr, F. M.Jr, and Dindoruk, B.
    , [2005] Four-component gas/oil displacements in one dimension: part I: global triangular structure, Transport in porous media, 61(1), 59–76.
    [Google Scholar]
  6. Johansen, T., and James, L. A.
    , [2014] Solutions of Multi-Component, Two-Phase Reimann Problems with Constant Pressure Boundaries, http://www.engr.mun.ca/research/eor/publications/.
  7. LaForce, T., and Johns, R. T.
    , [2004] Analytical theory for three-phase partially miscible flow in ternary systems, In SPE/DOE Symposium on Improved Oil Recovery. Society of Petroleum Engineers.
    [Google Scholar]
  8. , [2005] Analytical solutions for surfactantâĂŘenhanced remediation of nonaqueous phase liquids, Water resources research, 41(10).
    [Google Scholar]
  9. LaForce, T., Jessen, K., and Orr, F. M.Jr
    , [2008] Four-component gas/water/oil displacements in one dimension: Part I. structure of the conservation law, Transport in Porous Media, 71(2), 199–216.
    [Google Scholar]
  10. Monroe, W. W., Silva, M. K., Larson, L. L., and Orr, F. M.Jr
    , [1990] Composition paths in four-component systems: effect of dissolved methane on 1D CO2 flood performance, SPE Reservoir Engineering, 5(03), 423–432.
    [Google Scholar]
  11. Orr, F. M.
    , [2007] Theory of gas injection processes, Copenhagen, Tie-Line Publications.
    [Google Scholar]
  12. Wachmann, C.
    , [1964] A mathematical theory for the displacement of oil and water by alcohol, Society of Petroleum Engineers Journal, 4(03), 250–266.
    [Google Scholar]
  13. Wang, Y., Dindoruk, B., Johansen, T., and ORRF. M., Jr
    , [2005] Four-component gas/oil displacements in one dimension: part II: analytical solutions for constant equilibrium ratios, Transport in porous media, 61(2), 177–192.
    [Google Scholar]
  14. Welge, H. J., Johnson, E. F., Ewing, S. P.Jr, and Brinkman, F. H.
    , [1961] The linear displacement of oil from porous media by enriched gas, Journal of Petroleum Technology, 13 (08), 787–796.
    [Google Scholar]
http://instance.metastore.ingenta.com/content/papers/10.3997/2214-4609.20141792
Loading
/content/papers/10.3997/2214-4609.20141792
Loading

Data & Media loading...

This is a required field
Please enter a valid email address
Approval was a Success
Invalid data
An Error Occurred
Approval was partially successful, following selected items could not be processed due to error