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Isolated buoyant convection in a two-layered porous medium with an inclined permeability jump

Published online by Cambridge University Press:  09 September 2020

K. S. Bharath Open the ORCID record for K. S. Bharath [Opens in a new window] ,
C. K. Sahu Open the ORCID record for C. K. Sahu [Opens in a new window]  and
M. R. Flynn Open the ORCID record for M. R. Flynn [Opens in a new window]
K. S. Bharath*
Affiliation:
Department of Mechanical Engineering, University of Alberta, EdmontonT6G 1H9, Canada
C. K. Sahu
Affiliation:
BP Institute for Multiphase Flow, University of Cambridge, Madingley Rise, CambridgeCB3 0EZ, UK
M. R. Flynn
Affiliation:
Department of Mechanical Engineering, University of Alberta, EdmontonT6G 1H9, Canada
*
†Email address for correspondence: [email protected]
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Abstract

The migration of dense fluid through a saturated, layered porous medium leads to two end-member examples of buoyancy-driven flow, namely plumes and gravity currents. Herein we develop an integrated theoretical model to study this scenario for the special case where the boundary between the permeable layers, in a two-layered porous medium, is inclined at an angle to the horizontal. Far from being a routine detail, the inclination of the permeability jump leads to a symmetry-breaking: up- and downdip flows have different volume fluxes and travel different distances, possibly substantially different distances, before becoming arrested at the point where plume inflow balances basal draining. Our model predicts these associated run-out lengths and the transient approach thereto. Predictions are validated with measurements from similitude laboratory experiments, in which the upper and lower layers are comprised of glass beads of different diameters. Experiments are conducted for a range of inclination angles and also a range of plume source conditions. The experimental data suggest a complicated structure for the gravity currents, whose boundaries are blurred by dispersion in a manner not captured by our (sharp interface) model. This observation has particular significance in predicting the lateral spread of contaminated fluid through real geological formations, particularly in instances where for example groundwater contamination is of particular concern.

JFM classification

Convection: Convection in porous media Low-Reynolds-number flows: Porous media Geophysical and Geological Flows: Gravity currents
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 902 , 10 November 2020 , A22
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Copyright
© The Author(s), 2020. Published by Cambridge University Press

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References

REFERENCES

Acton, J. M., Huppert, H. E. & Worster, M. G. 2001 Two-dimensional viscous gravity currents flowing over a deep porous medium. J. Fluid Mech. 440, 359–380.CrossRefGoogle Scholar
Bachu, S., Buschkuehle, B. E., Haug, K. & Michael, K. 2008 a Subsurface characterization of the Pembina-Wabamun acid-gas injection area. Energy Resources Conservation Board, ERCB/AGS Special Report 93, Available at: https://ags.aer.ca/publications/SPE_093.html.Google Scholar
Bachu, S., Buschkuehle, B. E., Haug, K. & Michael, K. 2008 b Subsurface characterization of the Edmonton-Area acid-gas injection operations. Energy Resources Conservation Board, ERCB/AGS Special Report 92, Available at: https://ags.aer.ca/publications/SPE_092.html.Google Scholar
Bear, J. 1972 Dynamics of Fluids in Porous Media. Dover.Google Scholar
Carman, P. G. 1937 Fluid flow through granular beds. Chem. Engng Res. Des. 75, S32–S48.CrossRefGoogle Scholar
Clennell, M. Ben 1997 Tortuosity: a guide through the maze. Geol. Soc. Spec. Publ. 122 (122), 299–344.CrossRefGoogle Scholar
De Loubens, R. & Ramakrishnan, T. S. 2011 Analysis and computation of gravity-induced migration in porous media. J. Fluid Mech. 675, 60–86.CrossRefGoogle Scholar
Delgado, J. M. P. Q. 2007 Longitudinal and transverse dispersion in porous media. Chem. Engng Res. Des. 85 (9 A), 1245–1252.CrossRefGoogle Scholar
Dong, W. & Selvadurai, A. P. S. 2006 Image processing technique for determining the concentration of a chemical in a fluid-saturated porous medium. Geotech. Testing J. 29 (5), 385–391.Google Scholar
Dullien, F. A. L. 1979 Porous Media: Fluid Transport and Pore Structure. Academic Press.Google Scholar
Espinoza, D. N. & Santamarina, J. C. 2017 $\textrm {CO}_{2}$ breakthrough—Caprock sealing efficiency and integrity for carbon geological storage. Intl J. Greenh. Gas Control 66(September), 218–229.CrossRefGoogle Scholar
Farcas, A. & Woods, A. W. 2009 The effect of drainage on the capillary retention of $\textrm {CO}_{2}$ in a layered permeable rock. J. Fluid Mech. 618, 349–359.CrossRefGoogle Scholar
Fitts, J. P. & Peters, C. A. 2013 Caprock fracture dissolution and $\textrm {CO}_{2}$ leakage. Rev. Mineral. Geochem. 77 (1), 459–479.CrossRefGoogle Scholar
Freeze, A. R. & Cherry, J. A. 1979 Groundwater. Prentice-Hall.Google Scholar
Ghanbarian, B., Hunt, A. G., Ewing, R. P. & Sahimi, M. 2013 Tortuosity in porous media: a critical review. Soil Sci. Soc. Am. J. 77 (5), 1461–1477.CrossRefGoogle Scholar
Goda, T. & Sato, K. 2011 Gravity currents of carbon dioxide with residual gas trapping in a two-layered porous medium. J. Fluid Mech. 673, 60–79.CrossRefGoogle Scholar
Hesse, M. A. & Woods, A. W. 2010 Buoyant dispersal of $\textrm {CO}_{2}$ during geological storage. Geophys. Res. Lett. 37 (1), 1–5.CrossRefGoogle Scholar
Homsy, G. M. 1987 Viscous fingering in porous media. Annu. Rev. Fluid Mech. 19 (1987), 271–311.CrossRefGoogle Scholar
Huppert, H. E. & Woods, A. W. 1995 Gravity-driven flows in porous layers. J. Fluid Mech. 292, 55–69.CrossRefGoogle Scholar
Jing, J., Yang, Y., Tang, Z. & Wang, F. 2019 Impacts of salinity on $\textrm {CO}_{2}$ spatial distribution and storage amount in the formation with different dip angles. Environ. Sci. Pollut. Res. 26 (22), 22173–22188.CrossRefGoogle Scholar
Khondaker, A. N., Al-Layla, R. I. & Husain, T. 1990 Groundwater contamination studies—the state-of-the-art. Crit. Rev. Environ. Control 20 (4), 231–256.CrossRefGoogle Scholar
MacKay, J. C. D. 2009 Sustainable Energy – Without the Hot Air. UIT Cambridge Ltd.Google Scholar
MacMinn, C. W. & Juanes, R. 2013 Buoyant currents arrested by convective dissolution. Geophys. Res. Lett. 40 (10), 2017–2022.CrossRefGoogle Scholar
McPherson, B. & Matthews, V. 2013 A ten step protocol and plan for CCS site characterization, based on an analysis of the rocky mountain region, USA. The University of Utah DOE Award Number: DE-FE0001812. Available at: https://www.osti.gov/servlets/purl/1158546.CrossRefGoogle Scholar
Neufeld, J. A. & Huppert, H. E. 2009 Modelling carbon dioxide sequestration in layered strata. J. Fluid Mech. 625, 353–370.CrossRefGoogle Scholar
Nordbotten, J. M. & Celia, M. A. 2006 Similarity solutions for fluid injection into confined aquifers. J. Fluid Mech. 561, 307–327.CrossRefGoogle Scholar
Parker, M. E., Northrop, S., Valencia, J. A., Foglesong, R. E. & Duncan, W. T. 2011 $\textrm {CO}_2$ management at ExxonMobil's LaBarge field, Wyoming, USA. Energy Procedia 4, 5455–5470.CrossRefGoogle Scholar
Pegler, S. S., Huppert, H. E. & Neufeld, J. A. 2016 Stratified gravity currents in porous media. J. Fluid Mech. 791, 329–357.CrossRefGoogle Scholar
Pritchard, D., Woods, A. W. & Hogg, A. J. 2001 On the slow draining of a gravity current moving through a layered permeable medium. J. Fluid Mech. 444, 23–47.CrossRefGoogle Scholar
Rayward-Smith, W. J. & Woods, A. W. 2011 Dispersal of buoyancy-driven flow in porous media with inclined baffles. J. Fluid Mech. 689, 517–528.CrossRefGoogle Scholar
Roes, M. A. 2014 Buoyancy-driven convection in a ventilated porous medium. Master's thesis, University of Alberta.Google Scholar
Saffman, P. G. & Taylor, S. G. 1958 The penetration of a fluid into a porous medium or Hele-Shaw cell containing a more viscous liquid. Proc. R. Soc. Lond. A 245 (1242), 312–329.Google Scholar
Sahu, C. K. & Flynn, M. R. 2015 Filling box flows in porous media. J. Fluid Mech. 782 (2015), 455–478.CrossRefGoogle Scholar
Sahu, C. K. & Flynn, M. R. 2017 The effect of sudden permeability changes in porous media filling box flows. Transp. Porous Media 119 (1), 95–118.CrossRefGoogle Scholar
Sahu, C. K. & Neufeld, J. A. 2020 Dispersive entrainment into gravity currents in porous media. J. Fluid Mech. 886, A5.CrossRefGoogle Scholar
Tang, Y., Yang, R. & Bian, X. 2014 A review of $\textrm {CO}_{2}$ sequestration projects and application in China. Sci. World J. 2014, 1–11.Google Scholar
Vella, D. & Huppert, H. E. 2006 Gravity currents in a porous medium at an inclined plane. J. Fluid Mech. 555, 353–362.CrossRefGoogle Scholar
Vella, D., Neufeld, J. A., Huppert, H. E. & Lister, J. R. 2011 Leakage from gravity currents in a porous medium. Part 2. A line sink. J. Fluid Mech. 666, 414–427.CrossRefGoogle Scholar
Wooding, R. A. 1963 Convection in a saturated porous medium at large Rayleigh number or Peclet number. J. Fluid Mech. 15 (1961), 527–544.CrossRefGoogle Scholar
Woods, A. W. 2014 Flow in Porous Rocks: Energy and Environmental Applications. Cambridge University Press.Google Scholar
Woods, A. W. & Mason, R. 2000 The dynamics of two-layer gravity-driven flows in permeable rock. J. Fluid Mech. 421, 83–114.CrossRefGoogle Scholar
Zheng, Z., Guo, B., Christov, I. C., Celia, M. A. & Stone, H. A. 2015 Flow regimes for fluid injection into a confined porous medium. J. Fluid Mech. 767, 881–909.CrossRefGoogle Scholar