Abstract
For two-phase flows of immiscible displacement processes in porous media, we proposed a simplified model to capture the interfacial fronts, which is given by explicit expressions and satisfies the continuity conditions of pressure and normal velocity across the interface. A new similarity solution for the interfacial evolution in the rectangular coordinate system was derived by postulating a first-order approximation of the velocity distribution in the region that the two-phase fluids co-exist. The interfacial evolution equation can be explicitly expressed as a linear function, where the slope of the interfacial equation is simply related to the mobility ratio of two-phase fluids in porous media. The application of the proposed solutions to predictions of interfacial evolutions in carbon dioxide injected into saline aquifers was illustrated under different mobility ratios and operational parameters. For the purpose of comparison, the numerical solutions obtained by level set method and the similarity solutions based on the Dupuit assumptions were presented. The results show that the proposed solution can give a better approximation of interfacial evolution than the currently available similarity solutions, especially in the situation that the mobility ratio is large. The proposed approximate solutions can provide physical insight into the interfacial phenomenon and be readily used for rapidly screening carbon dioxide storage capacity in subsurface formations and monitoring the migration of carbon dioxide plume.
Similar content being viewed by others
References
Bachu S.: Screening and ranking of sedimentary basins for sequestration of CO2 in geological media in response to climate change. Environ. Geol. 44(3), 277–289 (2003). doi:10.1007/s00254-003-0762-9
Bear J.: Dynamics of Fluids in Porous Media. Dover Publications Inc, New York (1972)
Class H., Ebigbo A., Helmig R., Dahle H.K., Nordbotten J.M., Celia M.A., Audigane P., Darcis M., Ennis-King J., Fan Y.Q., Flemisch B., Gasda S.E., Jin M., Krug S., Labregere D., Beni A.N., Pawar R.J., Sbai A., Thomas S.G., Trenty L., Wei L.L.: A benchmark study on problems related to CO2 storage in geologic formations. Comput. Geosci. 13(4), 409–434 (2009). doi:10.1007/s10596-009-9146-x
Dentz M., Tartakovsky D.: Abrupt-interface solution for carbon dioxide injection into porous media. Transp. Porous Med. 51(7), 1–13 (2008)
Dentz, M., Tartakovsky, D.: Response to “Comments on abrupt-interface solution for carbon dioxide injection into porous media by Dentz and Tartakovsky (2008)” by Lu et al. Transport in Porous Media 79, 3 (2009). doi:10.1007/s11242-009-9363-8
Hesse M.A., Tchelepi H.A., Cantwell B.J., Orr F.M.: Gravity currents in horizontal porous layers: transition from early to late self-similarity. J. Fluid Mech. 577, 363–383 (2007). doi:10.1017/s0022112007004685
Hesse M.A., Orr F.M., Tchelepi H.A.: Gravity currents with residual trapping. J. Fluid Mech. 611, 35–60 (2008). doi:10.1017/s002211200800219x
Holloway S., Pearce J.M., Hards V.L., Ohsumi T., Gale J.: Natural emissions of CO2 from the geosphere and their bearing on the geological storage of carbon dioxide. Energy 32(7), 1194–1201 (2007)
Lu C., Lee S.-Y., Han W.S., McPherson B.J., Lichtner P.C.: Comments on “Abrupt-interface solution for carbon dioxide injection into porous media” by M. Dentz and D. Tartakovsky. Transp. Porous Med. 79, 9 (2009). doi:10.1007/s11242-009-9362-9
Liu Y.Z., Wang L., Yu B.: Sharp front capturing method for carbon dioxide plume propagation during injection into a deep confined aquifer. Energy Fuels 24, 1431–1440 (2010). doi:10.1021/ef9010498
MacMinn C.W., Juanes R.: A mathematical model of the footprint of the CO2 plume during and after injection in deep saline aquifer systems. Energy Procedia 1(1), 3429–3436 (2009a)
MacMinn C.W., Juanes R.: Post-injection spreading and trapping of CO2 in saline aquifers: impact of the plume shape at the end of injection. Comput. Geosci. 13(4), 483–491 (2009b). doi:10.1007/s10596-009-9147-9
Nordbotten J.M., Celia M.A.: Similarity solutions for fluid injection into confined aquifers. J. Fluid Mech. 561, 307–327 (2006). doi:10.1017/s0022112006000802
Nordbotten J.M., Kavetski D., Celia M.A., Bachu S.: Model for CO2 leakage including multiple geological layers and multiple leaky wells. Environ. Sci. Technol. 43(3), 743–749 (2009). doi:10.1021/es801135v
Okwen R.T., Stewart M.T., Cunningham J.A.: Analytical solution for estimating storage efficiency of geologic sequestration of CO2. Int. J. Greenhouse Gas Control 4(1), 102–107 (2010)
Pinder G.F., Gray W.G.: Essentials of Multiphase Flow and Transport in Porous Media. Wiley, Hoboken, NJ (2008)
Schnaar G., Digiulio D.C.: Computational modeling of the geologic sequestration of carbon dioxide. Vadose Zone J. 8(2), 389–403 (2009). doi:10.2136/vzj2008.0112
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Wang, L., Liu, Y. & Chu, K. A Simplified Model and Similarity Solutions for Interfacial Evolution of Two-Phase Flow in Porous Media. Transp Porous Med 93, 721–735 (2012). https://doi.org/10.1007/s11242-012-9979-y
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11242-012-9979-y