1887
  1. Home
  2. Conferences
  3. Conference Proceedings
  4. IOR+ 2023
  5. Conference paper

Abstract

Summary

Solutions are investigated for counter-current spontaneous imbibition in dimensions between 1D and 3D for samples of different shape. The dimension and characteristic length of the sample are calculated based on relations with area per volume and derivative of area with respect to volume. This correctly produces linear, radial and spherical flow as special cases for symmetrical plugs, while for rectangular or cylindrical core plugs, a continuous range of dimensions are produced. This results in a novel characteristic length different from the traditional (Ma et al) as it accounts for flow conditions: imbibition into a cylinder is ∼1D if the height-to-radius ratio is small, ∼2D (radial) if the ratio is large (reproducing analytical limits) and ∼3D if the ratio is near 1.

The differential equation for counter-current imbibition in N-D is derived and investigated. The solutions are described by the same self-similar saturation profile at early times (when the imbibition front has not traveled very far). At later times the saturation profiles shape depends on distance from the inlet and the dimension. When the deviation from self-similarity at the inlet is affected by either the distance traveled by the front or the late time interaction with the closed boundary, the recovery profile will start to deviate from a stable early time behavior. During this early-time, recovery is proportional to square root of time, regardless of geometry, as long as imbibition occurs inwards. This is validated by literature and in-house experimental data with different geometry.

Deviation from self-similar behavior occurs sooner when the dimension is higher, as the imbibing saturations interact more strongly. The early time behavior can be calculated semi-analytically and permit scaling of all solutions without limiting assumptions on saturation functions. An approximate analytical solution is derived describing imbibition into the core plug as a piston-like displacement to demonstrate the effect of geometry (e.g. linear vs spherical) on recovery behavior. The impact of geometry on the advancing front and recovery profile is derived and captured in a new time scale. It is shown both generally and by the simple solution that early time recovery in N-D is N times faster than in 1-D when the system characteristic length is the same.

Counter-current experiments are among the most common multiphase experiments being performed and although the samples are rarely designed to give linear flow, they are modeled and interpreted based on mathematical descriptions assuming linear flow.

© EAGE Publications BV
Loading

Article metrics loading...

/content/papers/10.3997/2214-4609.202331078
2023-10-02
2024-10-11

  • From This Site

    /content/papers/10.3997/2214-4609.202331078
    dcterms_title,dcterms_subject,pub_keyword
    -contentType:Journal -contentType:Contributor -contentType:Concept -contentType:Institution
    10
    5
Loading full text...

Full text loading...

References

  1. 1.Abd, A. S., Elhafyan, E., Siddiqui, A. R., Alnoush, W., Blunt, M. J., & Alyafei, N. [2019]. A review of the phenomenon of counter-current spontaneous imbibition: Analysis and data interpretation. Journal of Petroleum Science and Engineering, 180, 456–470.
     [Google Scholar]
  2. 2.Abolghasemi, E., & Andersen, P. Ø. [2022]. The influence of adsorption layer thickness and pore geometry on gas production from tight compressible shales. Advances in Geo-Energy Research, 6(1), 4–22.
     [Google Scholar]
  3. 3.Alcantara, R., Santiago, L. H., Fuentes, G., Garcia, H., Romero, P., López, P., … & Martinez, M. I. [2019, March]. A dynamic characterization approach for a complex naturally fractured reservoir. In International Petroleum Technology Conference.
     [Google Scholar]
  4. 4.Amott, E. [1959]. Observations relating to the wettability of porous rock. Transactions of the AIME, 216(01), 156–162.
     [Google Scholar]
  5. 5.Andersen, P. Ø. [2019]. A simplified modelling approach for petroleum recovery by spontaneous imbibition in naturally fractured reservoirs. Journal of Natural Gas Science and Engineering, 63, 95–114.
     [Google Scholar]
  6. 6.Andersen, P. Ø., Nesvik, E. K., & Standnes, D. C. [2020]. Analytical solutions for forced and spontaneous imbibition accounting for viscous coupling. Journal of Petroleum Science and Engineering, 186, 106717.
     [Google Scholar]
  7. 7.Andersen, P. Ø. [2021a]. Early-and Late-Time Analytical Solutions for Cocurrent Spontaneous Imbibition and Generalized Scaling. SPE Journal, 26(01), 220–240.
     [Google Scholar]
  8. 8.Andersen, P. Ø. [2021b]. A semi-analytical solution for shale gas production from compressible matrix including scaling of gas recovery. Journal of Natural Gas Science and Engineering, 95, 104227.
     [Google Scholar]
  9. 9.AndersenP. Ø., SalomonsenL., SlevelandD. S. [2022]. Characteristic Forced and Spontaneous Imbibition Behavior in Strongly Water-Wet Sandstones Based on Experiments and Simulation. Energies, 15(10), 3531.
     [Google Scholar]
  10. 10.Andersen, P. Ø. [2023a]. Early-and late-time prediction of counter-current spontaneous imbibition and estimation of the capillary diffusion coefficient. Transport in Porous Media, 147(3), 573–604.
     [Google Scholar]
  11. 11.Andersen, P. Ø. [2023b]. Insights from Boltzmann transformation in solving 1D counter-current spontaneous imbibition at early and late time. Advances in Geo-Energy Research, 7(3), 164–175.
     [Google Scholar]
  12. 12.Anderson, W. G. [1987]. Wettability literature survey-part 4: Effects of wettability on capillary pressure. Journal of petroleum technology, 39(10), 1283–1300.
     [Google Scholar]
  13. 13.Aronofsky, J. S., Masse, L., & Natanson, S. G. [1958]. A model for the mechanism of oil recovery from the porous matrix due to water invasion in fractured reservoirs. Transactions of the AIME, 213(01), 17–19.
     [Google Scholar]
  14. 14.Bear, J. [1988]. Dynamics of Fluids in Porous Media. Courier Corporation.
     [Google Scholar]
  15. 15.Bourbiaux, B. J., & Kalaydjian, F. J. [1990]. Experimental study of cocurrent and countercurrent flows in natural porous media. SPE Reservoir Engineering, 5(03), 361–368.
     [Google Scholar]
  16. 16.Bratton, T., Canh, D. V., Van Que, N., Duc, N. V., Gillespie, P., Hunt, D., ... & Sonneland, L. [2006]. The nature of naturally fractured reservoirs. Oilfield Review, 18(2), 4–23.
     [Google Scholar]
  17. 17.Evans, H. P. [1947]. Volume of an n-dimensional sphere. The American Mathematical Monthly, 54(10), 592–594.
     [Google Scholar]
  18. 18.Fischer, H., & Morrow, N. R. [2006]. Scaling of oil recovery by spontaneous imbibition for wide variation in aqueous phase viscosity with glycerol as the viscosifying agent. Journal of Petroleum Science and Engineering, 52(1–4), 35–53.
     [Google Scholar]
  19. 19.Graham, J. W., & Richardson, J. G. [1959]. Theory and application of imbibition phenomena in recovery of oil. Journal of Petroleum Technology, 11(02), 65–69.
     [Google Scholar]
  20. 20.Karimaie, H., Torsæter, O., Esfahani, M. R., Dadashpour, M., & Hashemi, S. M. [2006]. Experimental investigation of oil recovery during water imbibition. Journal of Petroleum Science and Engineering, 52(1–4), 297–304.
     [Google Scholar]
  21. 21.Kazemi, H., Gilman, J. R., & Elsharkawy, A. M. [1992]. Analytical and numerical solution of oil recovery from fractured reservoirs with empirical transfer functions. SPE Reservoir Engineering, 7(02), 219–227.
     [Google Scholar]
  22. 22.Kleppe, J., & Morse, R. A. [1974, October]. Oil production from fractured reservoirs by water displacement. In SPE Annual Technical Conference and Exhibition? (pp. SPE-5084). SPE.
     [Google Scholar]
  23. 23.Leverett, M. [1941]. Capillary behavior in porous solids. Transactions of the AIME, 142(01), 152–169.
     [Google Scholar]
  24. 24.Li, G., Liu, Y., Mi, L., Song, L., Cheng, Z., Qian, Q., … & Pei, X. [2022]. Time-dependent shape factor for scaling of multi-dimensional counter-current imbibition with different boundary conditions. Journal of Petroleum Science and Engineering, 217, 110880.
     [Google Scholar]
  25. 25.Lohne, A., Nødland, O., Stavland, A., & Hiorth, A. [2017]. A model for non-Newtonian flow in porous media at different flow regimes. Computational Geosciences, 21, 1289–1312.
     [Google Scholar]
  26. 26.Ma, S., Morrow, N. R, & Zhang, X. [1997]. Generalized scaling of spontaneous imbibition data for strongly water-wet systems. Journal of Petroleum Science and Engineering, 18(3–4), 165–178.
     [Google Scholar]
  27. 27.Mason, G, Fischer, H., Morrow, N. R, Ruth, D. W., & Wo, S. [2009]. Effect of sample shape on counter-current spontaneous imbibition production vs time curves. Journal of Petroleum Science and Engineering, 66(3–4), 83–97.
     [Google Scholar]
  28. 28.Mason, G, & Morrow, N. R. [2013]. Developments in spontaneous imbibition and possibilities for future work. Journal of Petroleum Science and Engineering, 110, 268–293.
     [Google Scholar]
  29. 29.March, R, Doster, F., & Geiger, S. [2016]. Accurate early‐time and late‐time modeling of countercurrent spontaneous imbibition. Water Resources Research, 52(8), 6263–6276.
     [Google Scholar]
  30. 30.Mattax, C. C, & Kyte, J. R. [1962]. Imbibition oil recovery from fractured, water-drive reservoir. Society of Petroleum Engineers Journal, 2(02), 177–184.
     [Google Scholar]
  31. 31.McWhorter, D. B., & Sunada, D. K. [1990]. Exact integral solutions for two‐phase flow. Water Resources Research, 26(3), 399–413.
     [Google Scholar]
  32. 32.Meng, Q., Liu, H., & Wang, J. [2017]. Effect of viscosity on oil production by cocurrent and countercurrent imbibition from cores with two ends open. SPE Reservoir Evaluation & Engineering, 20(02), 251–259.
     [Google Scholar]
  33. 33.Meng, Q., Cai, J., & Wang, J. [2019]. Scaling of countercurrent imbibition in 2D matrix blocks with different boundary conditions. SPE Journal, 24(03), 1179–1191.
     [Google Scholar]
  34. 34.Qiao, Y., Andersen, P. Ø., Evje, S., & Standnes, D. C. [2018]. A mixture theory approach to model co-and counter-current two-phase flow in porous media accounting for viscous coupling. Advances in water resources, 112, 170–188.
     [Google Scholar]
  35. 35.Rottmann, K. [1960]. Mathematische Formelsammlung. Bibliographisches Institut-Hochschultaschenbuecher.
     [Google Scholar]
  36. 36.Roychaudhuri, B., Tsotsis, T. T., & Jessen, K. [2013]. An experimental investigation of spontaneous imbibition in gas shales. Journal of Petroleum Science and Engineering, 111, 87–97.
     [Google Scholar]
  37. 37.Ruth, D. W., Li, Y., Mason, G, & Morrow, N. R. [2007]. An approximate analytical solution for counter-current spontaneous imbibition. Transport in porous media, 66, 373–390.
     [Google Scholar]
  38. 38.Schmid, K. S., & Geiger, S. [2013]. Universal scaling of spontaneous imbibition for arbitrary petrophysical properties: water-wet and mixed-wet states and Handy’s conjecture. Journal of Petroleum Science and Engineering, 101, 44–61.
     [Google Scholar]
  39. 39.Standnes, D. C. [2004]. Experimental study of the impact of boundary conditions on oil recovery by co-current and counter-current spontaneous imbibition. Energy & fuels, 18(1), 271–282.
     [Google Scholar]
  40. 40.Standnes, D. C. [2006]. Spontaneous imbibition of water into cylindrical cores with high aspect ratio: Numerical and experimental results. Journal of Petroleum Science and Engineering, 50(2), 151–160.
     [Google Scholar]
  41. 41.Standnes, D. C, & Andersen, P. Ø. [2017]. Analysis of the impact of fluid viscosities on the rate of countercurrent spontaneous imbibition. Energy & fuels, 31(7), 6928–6940.
     [Google Scholar]
  42. 42.Tavassoli, Z., Zimmerman, R W., & Blunt, M. J. [2005]. Analytic analysis for oil recovery during counter-current imbibition in strongly water-wet systems. Transport in Porous Media, 58, 173–189.
     [Google Scholar]
  43. 43.Yildiz, H. O., Gokmen, M., & Cesur, Y. [2006]. Effect of shape factor, characteristic length, and boundary conditions on spontaneous imbibition. Journal of Petroleum Science and Engineering, 53(3–4), 158–170.
     [Google Scholar]
  44. 44.Zhou, X., Morrow, N. R, & Ma, S. [2000]. Interrelationship of wettability, initial water saturation, aging time, and oil recovery by spontaneous imbibition and waterflooding. SPE Journal, 5(02), 199–207.
     [Google Scholar]
  45. 45.Zhou, D., Jia, L., Kamath, J., & Kovscek, A. R [2002]. Scaling of counter-current imbibition processes in low-permeability porous media. Journal of Petroleum Science and Engineering, 33(1–3), 61–74.
     [Google Scholar]
/content/papers/10.3997/2214-4609.202331078
Loading
Counter-Current Spontaneous Imbibition in Different Geometries and Its Impact On Early- and Late Time Recovery Behavior
Conference Proceedings 2023, 1 (2023); https://doi.org/10.3997/2214-4609.202331078
/content/papers/10.3997/2214-4609.202331078
/content/papers/10.3997/2214-4609.202331078
Loading

Data & Media loading...

Most Cited This Month Most Cited RSS feed

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