Effect of viscosity and heterogeneity on dispersion in porous media during miscible flooding processes

Abstract

In this paper, a mathematical model has been developed to quantitatively examine the effect of viscosity and heterogeneity on dispersion in porous media at the pore scale during miscible flooding processes. More specifically, the Navier-Stokes equation and advection-diffusion equation are coupled with supplementary equations to describe the solvent transport behaviour. Two-dimensional heterogeneous models are numerically developed as a function of porosity and permeability, assuming that the grain sizes satisfy normal distribution. In addition, the performance of miscible hydrocarbon gas injection in heterogeneous porous media is comprehensively evaluated. It is found that a larger aspect ratio (ratio of pore throat size) in the single non-flowing pore model results in a greater asymmetry of the concentration curve. As for single non-flowing pore models and heterogeneous models, the dispersion coefficients increase with the expansion of the non-flowing domain. Both the heterogeneity of porous media and the variable viscosity of th fluid mixture contribute to the asymmetry of the concentration curve in the heterogeneous model. A negative correlation is established between the sorting coefficients of pore throat size and the power-law coefficients. As for slug injection, the injected solvent slug size along the longitudinal direction does not effectively influence the longitudinal length of the mixing zone for a given porous medium and fluids, though the Peclet number and the porosity greatly affect the length and concentration distribution of the mixing zone.

Cited as: Bai, Z., Song, K., Fu, H., Shi, Y., Liu, Y., Chen, Z. Effect of viscosity and heterogeneity on dispersion in porous media during miscible flooding processes. Advances in Geo-Energy Research, 2022, 6(6): 460-471. https://doi.org/10.46690/ager.2022.06.03

References

Arshad, A., Al-Majed, A. A., Maneouar, H., et al. Carbon dioxide (CO2) miscible flooding in tight oil reservoirs: A case study. Paper SPE 127616 Presented at SPE Kuwait International Petroleum Conference and Exhibition, Kuwait City, Kuwait, 14-16 December, 2009.

Babaei, M., Joekar-Niasar, V. A transport phase diagram for pore-level correlated porous media. Advances in Water Resources, 2016, 92: 23-29.

Bakke, S., Øren, P.-E. 3-D pore-scale modeling of sandstones and flow simulations in the pore networks. SPE Journal, 1997, 2(2): 136-149.

Berkowitz, B., Cortis, A., Dentz, M., et al. Modeling non-Fickian transport in geological formations as a continuous time random walk. Reviews of Geophysics, 2006, 44(2): 2005RG000178.

Berkowitz, B., Scher, H. The role of probabilistic approaches to transport theory in heterogeneous media. Transport in Porous Media, 2001, 42(1): 241-263.

Bijeljic, B., Mostaghimi, P., Blunt, M. J. Insights into non-fickian solute transport in carbonates. Water resources research, 2013, 49(5): 2714-2728.

Bijeljic, B., Muggeridge, A. H., Blunt, M. J. Pore-scale modeling of longitudinal dispersion. Water resources research, 2004, 40(11): W11501.

Booth, R. Miscible flow through porous media. Oxford, University of Oxford, 2008.

Bretz, R. E., Orr, Jr. F. M. Interpretation of miscible displacements in laboratory cores. SPE Reservoir Engineering, 1987, 2(4): 492-500.

Bretz, R. E., Specter, R. M., Orr, Jr. Mixing during single phase flow in reservoir rocks: Models, effects of pore structure and interpretation of experiments, in Reservoir Characterization, edited by L. W. Lake and H. B. Carrol, Jr., Dallas, Texas, pp. 585-642, 1986.

Bretz, R. E., Specter, R. M., Orr Jr., F. M. Effect of pore structure on miscible displacement in laboratory cores. SPE Reservoir Engineering, 1988, 3(3): 857-866.

Brodie, J. A., Jhaveri, B. S., Moulds, T. P., et al. Review of gas injection projects in BP. Paper SPE 154008 Presented at SPE Improved Oil Recovery Symposium, Tulsa, Oklahoma, 14-18 April, 2012.

Cao, J., Kitanidis, P. K. Pore-scale dilution of conservative solutes: An example. Water Resources Research, 1998, 34(8): 1941-1949.

Correa, A. C., Pande, K. K., Ramey, H. J., et al. Computation and interpretation of miscible displacement performance in heterogeneous porous media. SPE Reservoir Engineering, 1990, 5(1): 69-78.

Delgado, J. M. P. Q. Longitudinal and transverse dispersion in porous media. Chemical Engineering Research and Design, 2007, 85(9): 1245-1252.

Derakhshanfar, M., Nasehi, M., Asghari, K. Simulation study of CO2-assisted waterflooding for enhanced heavy oil recovery and geological storage. Paper CMTC-151183-MS Presented at Carbon Management Technology Conference, Orlando, Florida, 7-9 February, 2012.

Dmitriev, N. M. Surface porosity and permeability of porous media with a periodic microstructure. Fluid Dynamics, 1995, 30(1): 64-69.

Dullien, F. A. L. Porous Media, Fluid Transport and Pore Structure. New York, USA, Academic Press, 1992.

Duncan, B., Urquhart, J., Roberts, S. Review of measurement and modelling of permeation and diffusion in polymers. Teddington, UK, National Physical Laboratory Report, 2005.

Fassnacht, H., McClure, E. M., Grant, G. E., et al. Downstream effects of the pelton-round butte hydroelectric project on bedload transport, channel morphology, and channel-bed texture, lower deschutes river, Oregon. Oregon Water Science and Application, 2003, 7: 175-207.

Fourar, M., Konan, G., Fichen, C., et al. Tracer tests for various carbonate cores using X-ray CT. Paper SCA200556 Presented at Annual International Symposium of the Society of Core Analysis, Toronto, Canada, 21-25 August, 2005.

Garmeh, G., Johns, R. T., Lake, L. W. Pore-scale simulation of dispersion in porous media. SPE Journal, 2009, 14(4): 559-567.

Ghazanfari, M. H., Kharrat, R., Rashtchian, D., et al. Statistical model for dispersion in a 2D glass micromodel. SPE Journal, 2010, 15(2): 301-312.

Gladkikh, M., Chen, J., Chen, S. Method of determining formation grain size distribution from acoustic velocities and NMR relaxation time spectrum. Paper SPWLA-2008-GGG Presented at SPWLA 49th Annual Logging Symposium, Austin, Texas, 25-28 May, 2008.

Golparvar, A., Zhou, Y., Wu, K., et al. A comprehensive review of pore scale modeling methodologies for multiphase flow in porous media. Advances in Geo-Energy Research, 2018, 2(4): 418-440.

Jha, R. K., John, A., Bryant, S. L., et al. Flow reversal and mixing. SPE Journal, 2009, 14(1): 41-49.

Mahnaz, H., Mitra, D., Muhammad, S. Pore-network simulation of unstable miscible displacements in porous media. Transport in Porous Media, 2016, 113(3): 511-529.

Maloney, D. R., Honarpour, M. M., Brinkmeyer, A. D. The effects of rock characteristics on relative permeability. Office of Scientific and Technical Information, United States, 1990.

Majdalani, S., Chazarin, J. P., Delenne, C., et al. Solute transport in periodical heterogeneous porous media: Importance of observation scale and experimental sampling. Journal of Hydrology, 2015, 520: 52-60.

Muhammad, K. A., Athari, A. O., Abubakar, J. A., et al. Influence of permeability and injection orientation variations on dispersion coefficient during enhanced gas recovery by CO2 injection. Energies, 2019, 12(12): 2328.

Panja, P., Velasco, R., Deo, M. Understanding and modeling of gas-condensate flow in porous media. Advances in Geo-Energy Research, 2020, 4(2): 173-186.

Peyman, M., Saeed, T., Steven, L. B., et al. Solvent diffusion and dispersion in partially saturated porous media: An experimental and numerical pore-level study. Chemical Engineering Science, 2018, 191: 300-317.

Sahimi, M., Rasaei, M. R., Haghighi, M. Gas injection and fingering in porous media, in Theory and Applications of Transport in Porous Media, edited by S. M. Hassanizadeh, Springer, Dordrecht, pp. 133-168, 2006.

Saied, A., Hejazi, S. H., Apostolos, K. Longitudinal dispersion in heterogeneous layered porous media during stable and unstable pore-scale miscible displacements. Advances in Water Resources, 2018, 119: 125-141.

Scholze, M., Boedeker, W., Faust, M., et al. A general best-fit method for concentration-response curves and the estimation of low-effect concentrations. Environmental Toxicology and Chemistry, 2001, 20(2): 448-457.

Sheng, G., Su, Y., Zhao, H., et al. A unified apparent porosity/permeability model of organic porous media: Coupling complex pore structure and multi-migration mechanism. Advances in Geo-Energy Research, 2020, 4(2): 115-125.

Song, C., Yang, D. Optimization of CO2 flooding schemes for unlocking resources from tight oil formations. Paper SPE 162549 Presented at SPE Canadian Unconventional Resources Conference, Calgary, Alberta, 30 October-1 November, 2012.

Srivastava, R. K., Huang, S. S., Dong, M. Laboratory investigation of Weyburn CO2 miscible flooding. Journal of Canadian Petroleum Technology, 2000, 39(2): 41-51.

Turta, A., Fisher, D., Singhal, A. K., et al. Variation of oil-solvent mixture viscosity in relation to the onset of asphaltene flocculation and deposition. Journal of Canadian Petroleum Technology, 1999, 38(13): PETSOC-99-13-46.

Wen, Y., Kantzas, A. Evaluation of heavy oil/bitumen-solvent mixture viscosity models. Journal of Canadian Petroleum Technology, 2004, 45(4): 56-61.

Yang, X., Lu, W., Jin, X., et al. Fractal theory-based seepage model of hershel-bulkley fluid in porous medium. Coal Geology & Exploration, 2020, 48(3): 122-127. (in Chinese)

Yang, X., Scheibe, T. D., Richmond, M. C., et al. Direct numerical simulation of pore-scale flow in a bead pack: Comparison with magnetic resonance imaging observations. Advances in Water Resources, 2013, 54: 228-241.