Advertisement

Transport in Porous Media

, Volume 129, Issue 3, pp 811–836 | Cite as

Bubble Migration Velocity in a Uniform Pore Network

  • Saloumeh GhasemianEmail author
  • Amir Ahmadzadegan
  • Ioannis Chatzis
Article
  • 59 Downloads

Abstract

Gas bubbles can be generated naturally or introduced artificially in porous media. Gas bubble migration through porous media governs the rate of gas emission to the atmosphere as well as the hydraulic and mechanical properties of sediments. The migration of air bubbles through water-wet porous media of uniform geometry was studied using a glass micromodel. Experiments were conducted to measure the velocity of bubbles of various lengths rising in a glass micromodel saturated with different test liquids and varying elevation angles. The results showed a linear dependency of the average bubble velocity on the bubble length and the sine of inclination angle of the micromodel. Comparisons were made using experimental data for air bubbles rising in kerosene, Soltrol 170 and dyed white oil. The effective permeability of the micromodel for the gas bubble, Kg, was calculated for different systems at different inclination angles, assuming that the effective length for viscous dissipation is equal to the initial static bubble length. It was found that the calculated permeability of the medium for gas bubbles had an increasing trend with increasing the bubble length. To visualize the periodic nature of the flow of rising bubbles in a porous medium, the motion of the air bubbles in white oil was video recorded by a digital camera, reviewed and analyzed using PowerDVDTM11 software. The bubble shape, exact positions of the bubble front and bubble tail during motion and, hence, the dynamic bubble length were determined through image analysis. Numerical simulation was performed by modifying an existing simulation code for the rise velocity of a gas bubble and the induced pressure field while it migrates through the pore network. The results showed that the rise velocity of a gas bubble is affected by the grid size of the pore network in the direction perpendicular to the bubble migration. The findings of this study can have important implications for studies on the migration of injected gas bubbles in geoenvironmental applications, as well as fundamental studies on bubble transport and behavior in porous media.

Keywords

Porous medium Pore network model Bubble migration Micromodel Bubble velocity 

List of Symbols

DP

Depth of pore (m)

Dt

Tube diameter (m)

DT

Depth of throat (m)

g

Gravity acceleration (m s−2)

hc

Capillary height (m)

K

Intrinsic permeability (m2)

Kg

Effective permeability of the gas phase (m2)

kr

Relative permeability (m2)

L

Length (m)

Lb

Bubble length (m)

Lb,dynamic

Dynamic bubble length (m)

Lb0

Initial static bubble length (m)

Leff

Effective length (m)

Lt

Tube length (m)

Nb

Number of nodes

P

Pressure (kg m−1 s−2)

Pc

Capillary pressure (kg m−1 s−2)

Q

Volumetric flow rate (m3 s−1)

u

Velocity (m s−1)

WP

Pore width (m)

WT

Throat width (m)

Xf

Bubble front position (m)

Xt

Bubble tail position (m)

z

Hydrostatic height (m)

Greek Letters

α

Angle (°)

θ

Contact angle (°)

σ

Surface/interfacial tension (kg s−2)

ρ

Density (kg m−3)

µ

Dynamic viscosity (kg m−1 s−1)

Subscripts

A

Advancing

b

Bubble

dr

Drainage

cr

Critical

g

Gas

imb

Imbibition

inc

Inclination

l

Liquid

R

Receding

Notes

Acknowledgements

The authors acknowledge Jonathan D. Smith for providing us with his MATLAB® code.

References

  1. Ajaev, V.S., Homsy, G.M.: Modeling shapes and dynamics of confined bubbles. Annu. Rev. Fluid Mech. 38, 277–307 (2006)CrossRefGoogle Scholar
  2. Amos, R.T., Mayer, K.U.: Investigating ebullition in a sand column using dissolved gas analysis and reactive transport modeling. Environ. Sci. Technol. 40(17), 5361–5367 (2006)CrossRefGoogle Scholar
  3. Baird, A.J., Beckwith, C.W., Waldron, S., Waddington, J.M.: Ebullition of methane-containing gas bubbles from near-surface Sphagnum peat. Geophys. Res. Lett. 31(21), L21505 (2004)CrossRefGoogle Scholar
  4. Bear, J.: Dynamics of Fluids in Porous Media. Elsevier, New York, pp. 161–176, 687–702 (1972)Google Scholar
  5. Buchgraber, M., Kovscek, A.R., Castanier, L.M.: A study of microscale gas trapping using etched silicon micromodels. Transp. Porous Media 95(3), 647–668 (2012)CrossRefGoogle Scholar
  6. Chatzis, I.: Photofabrication technique of two-dimensional glass micromodels. PRRC report 82-12. New Mexico Institute of Mining and Technology, Socorro (1982)Google Scholar
  7. Chatzis, I.: Mobilization of residual oil mechanisms seen in micromodels. In: International Symposium of Core Analysis. Austin, USA (2011)Google Scholar
  8. Cihan, A., Corapcioglu, M.Y.: Effect of compressibility on the rise velocity of an air bubble in porous media. Water Resour. Res. 44(4), W04409 (2008)CrossRefGoogle Scholar
  9. Corapcioglu, M.Y., Cihan, A., Drazenovic, M.: Rise velocity of an air bubble in porous media: theoretical studies. Water Resour. Res. 40(4), W04214 (2004)CrossRefGoogle Scholar
  10. Dejam, M., Hassanzadeh, H.: Diffusive leakage of brine from aquifers during CO2 geological storage. Adv. Water Resour. 111, 36–57 (2018a)CrossRefGoogle Scholar
  11. Dejam, M., Hassanzadeh, H.: The role of natural fractures of finite double-porosity aquifers on diffusive leakage of brine during geological storage of CO2. Int. J. Greenh. Gas Control 78, 177–197 (2018b)CrossRefGoogle Scholar
  12. Dong, M., Chatzis, I.: An experimental investigation of retention of liquids in corners of a square capillary. J. Colloid Interface Sci. 273(1), 306–312 (2004)CrossRefGoogle Scholar
  13. Garrettson, B.A.: Bubble transport theory with application to the upper ocean. J. Fluid Mech. 59(1), 187–206 (1973)CrossRefGoogle Scholar
  14. Gutiérrez, B., Juarez, F., Ornelas, L., Zeppieri, S., Ramos, A.: Experimental study of gas–liquid two-phase flow in glass micromodels. Int. J. Thermophys. 29(6), 2126–2135 (2008)CrossRefGoogle Scholar
  15. Haberman, W.L., Morton, R.K.: An experimental investigation of the drag and shape of air bubbles rising in various liquids. In: Taylor, D.W. (ed.) Model Basin. Navy Department, Washington (1953)Google Scholar
  16. Hubert, M.K.: Darcy’s law and the field equations of the flow of underground fluids. Trans. AIME 207(7), 222–239 (1956)Google Scholar
  17. Iliuta, I., Larachi, F., Grandjean, B.P.A.: Residence time, mass transfer, and back-mixing of the liquid in trickle flow reactors containing porous particles. Chem. Eng. Sci. 54(18), 4099–4109 (1999)CrossRefGoogle Scholar
  18. Ioannidis, M.A., Chatzis, I., Payatakes, A.C.: A mercury porosimeter for investigating capillary phenomena and microdisplacement mechanisms in capillary networks. J Colloid Interface Sci. 143(1), 22–36 (1991)CrossRefGoogle Scholar
  19. Jafari, M., Cao, S.C., Jung, J.: Geological CO2 sequestration in saline aquifers: Implication on potential solutions of China’s power sector. Resour. Conserv. Recycl. 121, 137–155 (2017)CrossRefGoogle Scholar
  20. Johann, W., Siekmann, J.: Migration of a bubble with adsorbed film in a Hele–Shaw cell. Acta Astronaut. 5(9), 687–704 (1978)CrossRefGoogle Scholar
  21. Kim, J.-S., Jo, H.Y., Yun, S.-T.: Visualization of gaseous and dissolved CO2 migration in porous media. Environ. Earth Sci. 77(8), 301 (2018)CrossRefGoogle Scholar
  22. Lago, M., Huerta, M., Gomes, R.: Visualization study during depletion experiments of Venezuelan heavy oils using glass micromodels. J. Can. Pet. Technol. 41(1), 41–47 (2002)CrossRefGoogle Scholar
  23. Lenormand, R., Zarcone, C., Sarr, A.: Mechanisms of the displacement of one fluid by another in a network of capillary ducts. J. Fluid Mech. 135, 337–353 (1983)CrossRefGoogle Scholar
  24. Li, T.: Recovery of source non-aqueous phase liquids from groundwater using supersaturated water injection. Master’s thesis, University of Waterloo (2004)Google Scholar
  25. Luo, S., Xu, R., Jiang, P., Huang, X.: Visualization experimental investigations of supercritical CO2 inject into porous media with the fissure defect. Energy Procedia 4, 4411–4417 (2011)CrossRefGoogle Scholar
  26. Ma, Y., Kong, X.-Z., Scheuermann, A., Galindo-Torres, S.A., Bringemeier, D., Li, L.: Microbubble transport in water-saturated porous media. Water Resour. Res. 51, 4359–4373 (2015)CrossRefGoogle Scholar
  27. Mahabadi, N., Zheng, X., Yun, T.S., van Paassen, L., Jang, J.: Gas bubble migration and strapping in porous media: pore-scale simulation. J. Geophys. Res. Solid Earth 123, 1060–1071 (2018)CrossRefGoogle Scholar
  28. Maruvada, S.R.K., Park, C.-W.: Retarded motion of bubbles in Hele–Shaw cells. Phys. Fluids 8(12), 3229–3233 (1996)CrossRefGoogle Scholar
  29. Mashayekhizadeh, V., Ghazanfari, M.H., Kharrat, R., Dejam, M.: Pore-level observation of free gravity drainage of oil in fractured porous media. Transp. Porous Media 87(2), 561–584 (2011)CrossRefGoogle Scholar
  30. Mashayekhizadeh, V., Kharrat, R., Ghazanfari, M.H., Dejam, M.: An experimental investigation of fracture tilt angle effects on frequency and stability of liquid bridges in fractured porous media. Pet. Sci. Technol. 30(8), 807–816 (2012)CrossRefGoogle Scholar
  31. McCain Jr., W.D.: The Properties of Petroleum Fluids, 2nd edn. PennWell Publishing Co., Tulsa (1990)Google Scholar
  32. Mckellar, M., Warldlaw, N.C.: A method of making two-dimensional glass micromodels of pore systems. J. Can. Pet. Technol. 21(4), 39–41 (1982)CrossRefGoogle Scholar
  33. Nelson, L., Barker, J., Li, T., Thomson, N., Ioannidis, M.A., Chatzis, I.: A field trial to assess the performance of CO2-supersaturated water injection for residual volatile LNAPL recovery. J. Contam. Hydrol. 109(1–4), 82–90 (2009)CrossRefGoogle Scholar
  34. Niessner, J., Berg, S., Hassanizadeh, S.M.: Comparison of two-phase Darcy’s law with a thermodynamically consistent approach. Transp. Porous Media 88(1), 133–148 (2011)CrossRefGoogle Scholar
  35. Oldenburg, C.M., Lewicki, J.L.: On leakage and seepage of CO2 from geologic storage sites into surface water. Environ. Geol. 50(5), 691–705 (2006)CrossRefGoogle Scholar
  36. Ostrovsky, I., McGinnis, D.F., Lapidus, L., Eckert, W.: Quantifying gas ebullition with echosounder: the role of methane transport by bubbles in a medium-sized lake. Limnol. Oceanogr. Methods 6(2), 105–118 (2008)CrossRefGoogle Scholar
  37. Pankow, J.F., Johnson, R.L., Cherry, J.A.: Air sparging in gate wells in cut-off walls and trenches for control of plumes of volatile organic compounds (VOCs). Ground Water 31(4), 654–663 (1993)CrossRefGoogle Scholar
  38. Rillaerts, E., Joos, P.: The dynamic contact angle. Chem. Eng. Sci. 35(4), 883–887 (1980)CrossRefGoogle Scholar
  39. Roosevelt, S.E., Corapcioglu, M.Y.: Air bubble migration in a granular porous medium: experimental studies. Water Resour. Res. 34(5), 1131–1142 (1998)CrossRefGoogle Scholar
  40. Sandnes, B., Flekkøy, E.G., Knudsen, H.A., Maløy, K.J., See, H.: Patterns and flow in frictional fluid dynamics. Nat. Commun. 2, 288 (2011)CrossRefGoogle Scholar
  41. Selker, J.S., Niemet, M., McDuffie, N.G., Gorelick, S.M., Parlange, J.Y.: The local geometry of gas injection into saturated homogeneous porous media. Transp. Porous Media 68(1), 107–127 (2007)CrossRefGoogle Scholar
  42. Selva, B., Cantat, I., Jullien, M.-C.: Temperature-induced migration of a bubble in a soft microcavity. Phys. Fluids 23(5), 052002 (2011)CrossRefGoogle Scholar
  43. Smith, J.D.: Mobility of bubbles in porous media with application to non-aqueous phase liquid removal via saturated water injection. Master’s thesis, University of Waterloo (2005)Google Scholar
  44. Smith, J.D., Chatzis, I., Ioannidis, M.A.: A new technique to measure the breakthrough capillary pressure. J. Can. Pet. Technol. 44(11), 25–31 (2005)CrossRefGoogle Scholar
  45. Stark, J., Manga, M.: The motion of long bubbles in a network of tubes. Transp. Porous Media 40(2), 201–218 (2000)CrossRefGoogle Scholar
  46. Tohidi, B., Anderson, R., Clennell, M.B., Burgass, R.W., Biderkab, A.B.: Visual observation of gas-hydrate formation and dissociation in synthetic porous media by means of glass micromodels. Geology 29(9), 867–870 (2001)CrossRefGoogle Scholar
  47. Varas, G., Ramos, G., Géminard, J.-C., Vidal, V.: Flow and fracture in water-saturated, unconstrained granular beds. Front. Phys. 3, 44 (2015)CrossRefGoogle Scholar
  48. Whalen, S.C.: Biogeochemistry of methane exchange between natural wetlands and the atmosphere. Environ. Eng. Sci. 22(1), 73–94 (2005)CrossRefGoogle Scholar
  49. Wu, K., de Martín, L., Coppens, M.-O.: Pattern formation in pulsed gas-solid fluidized beds—the role of granular solid mechanics. Chem. Eng. J. 329, 4–14 (2017)CrossRefGoogle Scholar
  50. Yan, J., Luo, X., Wang, W., Toussaint, R., Schmittbuhl, J., Vasseur, G., Chen, F., Yu, A., Zhang, L.: An experimental study of secondary oil migration in a three-dimensional tilted porous. AAPG Bull. 96(5), 773–788 (2012)CrossRefGoogle Scholar
  51. Yang, G.Q., Du, B., Fan, L.S.: Bubble formation and dynamics in gas-liquid-solid fluidization—a review. Chem. Eng. Sci. 62(1–2), 2–27 (2007)CrossRefGoogle Scholar
  52. Zheng, X., Barrios, A., Perreault, F., Yun, T.S., Jang, J.: Interfacial tension and contact angle in a CO2–water/nanofluid-quartz system. Greenh Gases Sci Technol 8(4), 734–746 (2018)CrossRefGoogle Scholar

Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Department of Chemical EngineeringUniversity of WaterlooWaterlooCanada
  2. 2.Department of Mechanical and Mechatronics EngineeringUniversity of WaterlooWaterlooCanada

Personalised recommendations