經由碳封存技術的啟發，本實驗為一組Hele-Shaw cell裝置類比二氧化碳在地下水層的對流現象。簡述孔隙介質流與類二維流體之間的關係及前人文獻的結果後，依此架設裝置及流體系統。在過錳酸鉀(KMnO4)粒子與水的交互作用下，清楚觀測到指頭狀對流的動態過程，並加以定性上的描述。我們分析指狀流在控制滲透率下的行為，此包括粗粒化過程、對流起始時間、指狀流平均距離，及溶解速率，此參數範圍相當於模擬雷利數(Ra) 2×〖10〗^4 ~ 8.26×〖10〗^6下的流體行為。透過計算努塞爾特數(Nu)得出，在此Ra區間，溶質的溶解速率不因Ra的改變有顯著的變化。

Inspired by the flow process of carbon capture and storage(CCS) technology in saline structure, we set up an analogy fluid system in homogeneous porous media to mimic the supercritical \ce{CO2} mixing dynamics with brine. Before getting into the details of the experiment, the theoretical background and previous works are presented first, and then the experimental setup of Hele-Shaw cell is shown. By observing the convective flow due to dissolution, the description of mixing dynamics is given. We also examine the coarsening process, onset time of convection, wavelength of fingers, and the rate of dissolution with Ra the Rayleigh number which is in the range of $2 \times 10^{4} \leq Ra \leq 8.26 \times 10^{6}$. Through calculating Nusselt number, $Nu$, the dimensionless convective flux, which is expected to predict the dissolution process, we find that the dissolution flux is not influenced significantly in this range of $Ra$ number. The result implies the geometrical structure plays a minor role in high $Ra$ for convective dissolution.

[1] O. Sohnel and P. Novotny. Densities of aqueous solutions of inorganic sub-
stances, volume 22. Elsevier Publishing Company, 1985.
[2] Guenter Ahlers, Siegfried Grossmann, and Detlef Lohse. Heat transfer and
large scale dynamics in turbulent rayleigh-benard convection. Rev. Mod.
Phys., 81(2):503, 2009.
[3] Susan Solomon, Gian-Kasper Plattner, Reto Knutti, and Pierre Friedlingstein.
Irreversible climate change due to carbon dioxide emissions. Proceedings
of the national academy of sciences, pages pnas{0812721106, 2009.
[4] B. Metz, O. Davidson, H. De Coninck, M. Loos, L. Meyer, et al. IPCC Special
Report On Carbon Dioxide Capture and Storage. Cambridge university press,
2005.
[5] A. Rucci, D. W. Vasco, and F. Novali. Monitoring the geologic storage of
carbon dioxide using multicomponent sar interferometry. Geophys. J. Int.,
193(1):197{208, 2013.
[6] R. Korbl and A. Kaddour. Sleipner vest CO2 disposal-injection of removed
CO2 into the utsira formation. Energy Convers. Manage., 36(6):509{512,
1995.
[7] FC Boait, NJ White, MJ Bickle, RA Chadwick, JA Neufeld, and HE Huppert.
Spatial and temporal evolution of injected co2 at the sleipner eld, north sea.
Journal of Geophysical Research: Solid Earth, 117(B3), 2012.
[8] A. Riaz, M. Hesse, H. A. Tchelepi, and F. M. Orr. Onset of convection in a
gravitationally unstable diusive boundary layer in porous media. J. Fluid
Mech., 548:87{111, 2006.
[9] J. Bear. Dynamics of Fluids in Porous Media. 1972.
[10] T. E. Faber. Fluid Dynamics for Physicists. Cambridge University Press,
1995. doi: 10.1017/CBO9780511806735.
[11] Hamid Emami Meybodi and Hassan Hassanzadeh. Stability analysis of twophase
buoyancy-driven
ow in the presence of a capillary transition zone.
Physical Review E, 87(3):033009, 2013.
[12] A. C. Slim and T. S. Ramakrishnan. Onset and cessation of time-dependent,
dissolution-driven convection in porous media. Phys. Fluids, 22(12):124103,
2010.
[13] J. J. Hidalgo, J. Fe, L. Cueto-Felgueroso, and R. Juanes. Scaling of convective
mixing in porous media. Phys. Rev. Lett., 109(26):264503, 2012.
[14] A. C. Slim. Solutal-convection regimes in a two-dimensional porous medium.
J. Fluid Mech., 741:461{491, 2014.
[15] G. S.H. Pau, J. B. Bell, K. Pruess, A. S. Almgren, M. J. Lijewski, and
K. Zhang. High-resolution simulation and characterization of density-driven

ow in CO2 storage in saline aquifers. Adv. Water Resour., 33(4):443{455,
2010.
[16] J. A. Neufeld, M. A. Hesse, A. Riaz, M. A. Hallworth, H. A. Tchelepi, and
H. E. Huppert. Convective dissolution of carbon dioxide in saline aquifers.
Geophys. Res. Lett., 37(22), 2010.
[17] H. E. Huppert and J. A. Neufeld. The
uid mechanics of carbon dioxide
sequestration. Annu. Rev. Fluid Mech., 46:255{272, 2014.
[18] M. L. Szulczewski, M. A. Hesse, and R. Juanes. Carbon dioxide dissolution
in structural and stratigraphic traps. J. Fluid Mech., 736:287{315, 2013.
[19] S. Backhaus, K. Turitsyn, and R. E. Ecke. Convective instability and mass
transport of diusion layers in a hele-shaw geometry. Phys. Rev. Lett., 106
(10):104501, 2011.
[20] P. A. Tsai, K. Riesing, and H. A. Stone. Density-driven convection enhanced
by an inclined boundary: Implications for geological CO2 storage. Phys Rev
E Rapid, 87(1):011003(R), 2013.
[21] A. C. Slim, M. M. Bandi, J. C. Miller, and L. Mahadevan. Dissolution-driven
convection in a hele-shaw cell. Phys. Fluids, 25(2):024101, 2013.
[22] J. Garcia. Fluid dynamics of carbon dioxide disposal into saline aquifers,
2003.
[23] A. Riaz and Y. Cinar. Carbon dioxide sequestration in saline formations:
Part i|review of the modeling of solubility trapping. J. Pet. Sci. Technol.,
124:367{380, 2014.
[24] R. E. Ecke and S. Backhaus. Plume dynamics in hele-shaw porous media
convection. Phil. Trans. R. Soc. A, 374(2078):20150420, 2016.