Transport in Porous Media

, Volume 128, Issue 1, pp 29–43 | Cite as

Measurement and Quantification of Diffusion-Induced Compositional Variations in Absence of Convective Mixing at Reservoir Conditions

  • Ram R. RatnakarEmail author
  • Birol Dindoruk
  • Greg Odikpo
  • Edward J. Lewis


We present numerical and experimental investigation on the existence of diffusion-induced compositional variations in a reservoir fluid in the absence of convective mixing. New pressure-decay experimental data are presented for ethane in contact with stock tank oil, and the values of diffusivity and solubility parameters are obtained by using the one-dimensional transient diffusion model and integral-based regression method. We show the variation in oil composition through composition-height measurements at the end of the experiment. Finally, the diffusion model with estimated parameters is used to predict the compositional variations, where comparisons show excellent agreement with the measurements, validating the parameter estimation technique and quantifying the compositional variations in the oil phase caused by diffusion.


Modeling and experiments Compositional variations Early and late transient solutions Diffusivity Solubility 



Stock tank oil


Gas chromatography


Late transient solution


Early transient solution



The authors wish to thank Shell International Exploration and Production Inc. for granting the permission to publish the work.


  1. Adelstein, S.J., Manning, F.J. (eds.): Isotopes for Medicine and the Life Sciences. Committee on Biomedical Isotopes and Institute of Medicine. National Academic Press, Washington (1995)Google Scholar
  2. Anthea, M., Hopkins, J., Johnson, S., et al.: Cells Building Blocks of Life, pp. 66–67. Prentice Hall, Upper Saddle River (1997)Google Scholar
  3. Bird, R.B., Stewart, W.E., Lightfoot, E.N.: Transport Phenomena, 2nd edn. Wiley, Hoboken (2001)Google Scholar
  4. Boustani, A., Maini, B.B.: The role of diffusion and convective dispersion in vapor extraction process. J. Can. Pet. Technol. 40, 68 (2001)CrossRefGoogle Scholar
  5. Campbell, B.T., Orr, F.M.: Flow visualization of CO2-crude oil mixtures. Soc. Pet. Eng. J. 25(5), 665–678 (1985)CrossRefGoogle Scholar
  6. Civan, F., Rasmussen, M.L.: Accurate measurement of gas diffusivity in oil and brine under reservoir conditions. SPE-67319-MS (2001)Google Scholar
  7. Civan, F., Rasmussen, M.L.: Improved measurement of gas diffusivity for miscible gas flooding under nonequilibrium versus equilibrium conditions. SPE-75135-MS (2002)Google Scholar
  8. Civan, F., Rasmussen, M.L.: Analysis and interpretation of gas diffusion in quiescent reservoir, drilling and completion fluids: equilibrium versus non-equilibrium models. SPE-84072-MS (2003)Google Scholar
  9. Creux, P., Meyer, V., Cordelier, P.R., et al: Diffusivity in heavy oils. SPE-97798-MS (2005)Google Scholar
  10. Dindoruk, B.: Emerging oil regions: Brazil, the Arctic, and West Africa—and the role of fluid properties. The Way Ahead 7, 15–17 (2011)CrossRefGoogle Scholar
  11. Dindoruk, B., Kindi, A.: A case study of dynamic modeling of multiple regionally-extensive reservoirs using a unified fluid description. J. Pet. Sci. Eng. 78, 748–758 (2011)CrossRefGoogle Scholar
  12. Etminan, S.R, Maini, B.B., Hassanzadeh, H., Chen, Z.J.: Determination of concentration dependent diffusivity coefficient in solvent gas heavy oil systems. SPE-124832-MS (2009)Google Scholar
  13. Froment, G.F., Bischoff, K.B.: Chemical Reactor Analysis and Design, 2nd edn. Wiley, Hoboken (1990)Google Scholar
  14. Grogan, A.T., Pinczewski, W.V.: The role of molecular diffusion processes in tertiary CO2 flooding. J. Pet. Technol. 38(5), 591–602 (1987)CrossRefGoogle Scholar
  15. Harstad, K., Bellan, J.: High-pressure binary mass diffusion coefficients for combustion applications. Ind. Eng. Chem. Res. 43(2), 645–654 (2004)CrossRefGoogle Scholar
  16. Heck, R.M., Farrauto, R.J.: Catalytic Air Pollution Control: Commercial Technology. Wiley, Hoboken (2009)CrossRefGoogle Scholar
  17. Huang, E.T.S., Tracht, J.H.: The displacement of residual oil by carbon dioxide. SPE-4735-MS (1974)Google Scholar
  18. Jackson, R.: Transport in Porous Catalyst. Chemical Engineering Monographs, vol. 4. Elsevier Science Ltd, Amsterdam (1977)Google Scholar
  19. Kumar, P., Gu, T., Grigoriadis, K., et al.: Spatio-temporal dynamics of oxygen storage and release in a three-way catalytic converter. Chem. Eng. Sci. 111, 180–190 (2014)CrossRefGoogle Scholar
  20. Li, X., Yortsos, Y.C.: Theory of multiple bubble growth in porous media by solute diffusion. Chem. Eng. Sci. 50(8), 1247 (1995)CrossRefGoogle Scholar
  21. Neogi, P.: Diffusion in Polymers. Marcel Dekker Inc, New York (1996)Google Scholar
  22. Policarpo, N.A., Ribeiro, P.R.: Experimental measurement of gas–liquid diffusivity. Braz. J. Pet. Gas 5(3), 171–188 (2011)CrossRefGoogle Scholar
  23. Ratnakar, R.R., Balakotaiah, V.: Coarse-graining of diffusion–reaction models with catalyst archipelagos. Chem. Eng. Sci. 110, 44–54 (2014)CrossRefGoogle Scholar
  24. Ratnakar, R.R., Balakotaiah, V.: Reduced order multimode transient models for catalytic monoliths with micro-kinetics. Chem. Eng. J. 260, 557–572 (2015)CrossRefGoogle Scholar
  25. Ratnakar, R.R., Dindoruk, B.: Measurement of gas diffusivity in heavy oils and bitumens by use of pressure-decay test and establishment of minimum time criteria for experiments. SPE J. 20, 1–167 (2015)CrossRefGoogle Scholar
  26. Ratnakar, R.R., Dindoruk, B.: On the exact representation of pressure decay tests: new modeling and experimental data for diffusivity measurement in gas–oil/bitumen systems. SPE-181514-MS (2016)Google Scholar
  27. Ratnakar, R.R., Dindoruk B.: Analysis and interpretation of pressure-decay tests for gas/bitumen and oil/bitumen systems: methodology development and application of new linearized and robust parameter-estimation technique using laboratory data. SPE J. SPE-181514-PA (2018)Google Scholar
  28. Ratnakar, R.R., Bhattacharya, M., Balakotaiah, V.: Reduced order models for describing dispersion and reaction in monoliths. Chem. Eng. Sci. 83, 77–92 (2012)CrossRefGoogle Scholar
  29. Ratnakar, R.R., Kalia, N., Balakotaiah, V.: Modeling, analysis and simulation of wormhole formation in carbonate rocks with in situ cross-linked acids. Chem. Eng. Sci. 90, 179–199 (2013)CrossRefGoogle Scholar
  30. Riazi, M.R.: A new method for experimental measurement of diffusion coefficients in reservoir fluids. J. Pet. Sci. Eng. 14, 235–250 (1996)CrossRefGoogle Scholar
  31. Sachs, W.: The diffusional transport methane in liquid water: method and result of experimental investigation at elevated pressure. J. Pet. Sci. Eng. 21, 53–164 (1998)CrossRefGoogle Scholar
  32. Sheikha, H., Pooladi-Darvish, M., Mehrotra, A.K.: Development of graphical methods for estimating the diffusivity coefficient of gases in bitumen from pressure-decay data. Energy Fuels 19, 2041–2049 (2005)CrossRefGoogle Scholar
  33. Shelton, J.L., Schneider, F.N.: The effects of water injection on miscible flooding methods using hydrocarbons and carbon dioxide. Soc. Pet. Eng. J. 15(3), 217–226 (1975)CrossRefGoogle Scholar
  34. Stalkup, F.J.: Displacement of oil by solvent at high water saturation. Soc. Pet. Eng. J. 10(4), 337–348 (1970)CrossRefGoogle Scholar
  35. Ting, D., Dindoruk, B., Ratulowski, J.: Numerical investigation of gravitational compositional grading in hydrocarbon reservoirs using centrifuge data. SPE Reserv. Eval. Eng. 12, 793–802 (2009)CrossRefGoogle Scholar
  36. Yang, C., Gu, Y.: Diffusion coefficients and oil swelling factor of carbon dioxide, methane, ethane, propane, and their mixtures in heavy oil. Fluid Phase Equilib. 243, 64 (2006)CrossRefGoogle Scholar
  37. Yanze, Y., Clemens, T.: The role of diffusion for nonequilibrium gas injection into a fractured reservoir. SPE Reserv. Eval. Eng. 15(1), 60–71 (2012)CrossRefGoogle Scholar
  38. Zamanian, E., Hemmati, M., Beiranvand, M.S.: Determination of gas-diffusion and interface-mass-transfer coefficients in fracture-heavy oil saturated porous matrix system. Nafta Sci. J. 63, 351–358 (2012)Google Scholar
  39. Zhang, Y.P., Hyndman, C.L., Maini, B.B.: Measurement of gas diffusivity in heavy oils. J. Pet. Sci. Eng. 25, 37–47 (2000)CrossRefGoogle Scholar

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© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Shell International Exploration and Production Inc.HoustonUSA

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