×

The effect of a fissure on storage in a porous medium. (English) Zbl 1183.76889

Summary: We consider the two-dimensional buoyancy driven flow of a fluid injected into a saturated semi-infinite porous medium bounded by a horizontal barrier in which a single line sink, representing a fissure some distance from the point of injection, allows leakage of buoyant fluid. Our studies are motivated by the geological sequestration of carbon dioxide (CO\(_{2})\) and the possibility that fissures in the cap rock may compromise the safe long-term storage of \(CO_{2}\). A theoretical model is presented that accounts for leakage through the fissure using two parameters, which characterize leakage driven both by the hydrostatic pressure within the overriding fluid and by the buoyancy of the fluid within the fissure. We determine numerical solutions for the evolution of both the gravity current within the porous medium and the volume of fluid that has escaped through the fissure as a function of time. A quantity of considerable practical interest is the efficiency of storage, which we define as the amount of fluid remaining in the porous medium relative to the amount injected. This efficiency scales like \(t^{-1/2}\) at late times, indicating that the efficiency of storage ultimately tends to zero. We confirm the results of our model by comparison with an analogue laboratory experiment and discuss the implications of our two-dimensional model of leakage from a fissure for the geological sequestration of CO\(_{2}\).

MSC:

76S05 Flows in porous media; filtration; seepage
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Phillips, Geological Fluid Dynamics: Sub-Surface Flow and Reactions (2009) · Zbl 1177.76005
[2] DOI: 10.1017/S0022112007006623 · Zbl 1118.76065
[3] DOI: 10.1021/es035338i
[4] DOI: 10.1007/s11242-004-0670-9
[5] DOI: 10.1029/2003WR002997
[6] DOI: 10.1017/S0022112008004400 · Zbl 1156.76463
[7] DOI: 10.1017/S0022112008005703 · Zbl 1171.76447
[8] DOI: 10.1016/j.epsl.2006.12.013
[9] DOI: 10.1017/S0022112005006713 · Zbl 1081.76512
[10] Bear, Dynamics of Fluids in Porous Media (1972) · Zbl 1191.76001
[11] DOI: 10.1017/S0022112095001431 · Zbl 0862.76078
[12] Barenblatt, Scaling, Self-Similarity, and Intermediate Asymptotics (1996) · Zbl 0907.76002
[13] DOI: 10.1017/S002211200600930X · Zbl 1090.76022
[14] DOI: 10.1007/s00254-007-0946-9
[15] Happel, Low Reynolds Number Hydrodynamics: With Special Applications to Particulate Media (1991)
[16] DOI: 10.1029/94WR00952
[17] DOI: 10.1016/j.energy.2004.03.072
[18] DOI: 10.1063/1.1600733 · Zbl 1186.76026
[19] DOI: 10.1017/S0022112001004700 · Zbl 1107.76394
[20] DOI: 10.1017/S0022112008004527 · Zbl 1156.76447
[21] DOI: 10.1017/S0022112006009578 · Zbl 1090.76068
[22] DOI: 10.1017/S0022112008005223 · Zbl 1165.76376
[23] DOI: 10.1017/S002211200100516X · Zbl 1028.76048
[24] DOI: 10.1017/S0022112002008327 · Zbl 1031.76050
[25] DOI: 10.1021/es801135v
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.