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The miscible displacement with fluid-solid dissolution reaction in a porous medium is a typical process in many industrial applications, such as underground-water pollution decontamination, and oil recovery or geological sequestration of carbon dioxide. It is a significant problem in engineering and physics applications. As is well known, the dissolution reaction can change the structure of the porous medium, which will have a great influence on the miscible displacement process. However, the relationship between the displacement process and the dissolution reaction in a porous medium has not been fully studied. In this study, the miscible displacement with dissolution in a porous medium is simulated by a lattice Boltzmann method (LBM). The study focuses on the influence of the internal structure change on the displacement process, and the further quantitative analyzing of the changes of the porosity and displacement efficiency by changing the Damkohler number (Da) and the Pèlcet number (Pe). The results show that when Da is large enough, the dissolution reaction will generate a few wormholes in the porous medium, and the displacement fluid will leave the porous medium along the wormholes, resulting in the decrease of the displacement efficiency. As Da increases, the reaction goes faster, the rate of change in porosity increases, and the wormholes become wider, thereby indeed yielding a larger displacement efficiency. With the increase of Pe, the fingerings develop faster, the rate of change in porosity decreases, and the displacement efficiency decreases as well.
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图 1 系统初始状态示意图
Figure 1. Schematic illustration of the initial state of the system
图 2 两平板间的互溶驱替问题初始状态示意图
Figure 2. Schematic illustration of the initial status of the miscible displacement of two parallel plates.
图 3 4种工况下的互溶驱替现象和平均浓度分布图
Figure 3. Miscible displacement phenomena and the average concentration distributions of four different cases.
图 4 不同网格下横界面(a)平均浓度和(b)平均速度随时间的演变图
Figure 4. Time evolution of the transverse-average concentration (a) and transverse-average velocity (b) with different grids.
图 5 3种工况下不同时刻多孔介质内流体浓度场瞬时图
Figure 5. Snapshots of the concentration field in porous media at different times under three cases.
图 6
$ Da = 4 $ , 8的浓度场图($ t = 0.7324 $ )Figure 6. Concentration contours for
$Da \,{=}\, 4$ , 8 at$t \,{=}\, 0.7324$ 
图 7 不同Da数下, (a), (b)多孔介质孔隙率和(c), (d)驱替效率随时间的变化图
Figure 7. Time evolutions of (a), (b) the porosity and (c), (d) displacement efficiency for different Damkohler numbers.
图 8
$ t = 0.2441 $ 时不同Pe数下的浓度场瞬时图 (a)$ Pe = $ $ 5 $ ; (b)$ Pe = 65 $ ; (c)$ Pe = 524 $ Figure 8. Snapshots of the concentration field at
$ t = 0.2441 $ : (a)$ Pe = 5 $ ; (b)$ Pe = 65 $ ; (c)$ Pe = 524 $ .
图 9 不同Pe数下多孔介质内水平方向上的平均浓度
Figure 9. Average concentration along the horizontal direction of the porous media for different Pèclet numbers.
图 10 不同Pe数下多孔介质的(a)孔隙率和(b)驱替效率随时间的变化
Figure 10. Time evolutions of (a) porosity and (b) displacement efficiency for different Pèlcet numbers.
图 11 不同初始孔隙率下, 多孔介质(a)孔隙率和(b)驱替效率随时间的变化情况
Figure 11. Time evolutions of (a) porosity and (b) displacement efficiency for different initial porosities.
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[1] Cubillas P, Kohler S, Prieto M, Causserand C, Oelkers E H 2005 Geochim. Cosmochim. Acta 69 5459
Google Scholar
[2] Chen Y, Valocchi A J, Kang Q, Viswanathan H S 2019 Water Resour. Res. 55 11144
Google Scholar
[3] Smith M M, Sholokhova Y, Hao Y, Carroll S A 2013 Adv. Water Resour. 62 370
Google Scholar
[4] Saffman P G, Taylor G I 1958 Proc. R. Soc. London, Ser. A 245 312
Google Scholar
[5] Zimmerman W B, Homsy G M 1992 Phys. Fluids A 4 2348
Google Scholar
[6] Wit A D, Homsy G M 1999 Phys. Fluids. 11 949
Google Scholar
[7] Nagatsu Y, Ishii Y, Tada Y, Wit A D 2014 Phys. Rev. Lett. 113 024502
Google Scholar
[8] Békri S, ThoverT J F, Adler P M 1995 Chem. Eng. Sci. 50 2765
Google Scholar
[9] Luo H, Quintard M, Debenest G, Laouafa F 2012 Comput. Geosci. 16 913
Google Scholar
[10] Oltéan C, Golfier F, Buès M A 2013 J. Geophys. Res. 118 2038
Google Scholar
[11] Soulaine C, Roman S, Kovscek A, Tchelepi H A 2017 J. Fluid Mech. 827 457
Google Scholar
[12] Abadi R H H, Rahimian M H 2018 Int. J. Heat Mass Transfer 127 704
Google Scholar
[13] 娄钦, 李涛, 杨茉 2018 物理学报 67 234701
Google Scholar
Lou Q, Li T, Yang M 2018 Acta Phys. Sin. 67 234701
Google Scholar
[14] 胡晓亮, 梁宏, 王会利 2020 物理学报 69 044701
Google Scholar
Huo X L, Liang H, Wang H L 2020 Acta Phys. Sin. 69 044701
Google Scholar
[15] He X, Li N, Goldstein B 2000 Mol. Simul. 25 145
Google Scholar
[16] Kang Q, Zhang D, Chen S, He X 2002 Phys. Rev. E 65 036318
Google Scholar
[17] Kang Q, Lichtner P C, Zhang D 2006 J. Geophys. Res. 111 B05203
[18] 张婷, 施保昌, 柴振华 2015 物理学报 15 154701
Google Scholar
Zhang T, Shi B C, Chai Z H 2015 Acta Phys. Sin. 15 154701
Google Scholar
[19] Ju L, Zhang C H, Guo Z L 2020 Int. J. Heat Mass Transfer 150 119314
Google Scholar
[20] Meng X H, Sun H R, Guo Z L, Yang X F 2020 Adv. Water Resour. 142 103640
[21] Rakotomalala N, Salin D, Watzky P 1997 J. Fluid Mech. 338 277
Google Scholar
[22] Islam M N, Azaier J 2007 J. Porous Media 10 357
Google Scholar
[23] 刘高洁, 郭照立, 施保昌 2016 物理学报 65 014702
Google Scholar
Liu G J, Guo Z L, Shi B C 2016 Acta Phys. Sin. 65 014702
Google Scholar
[24] Pan C, Luo L S, Miller C T 2006 Comput. Fluids 35 898
Google Scholar
[25] 郭照立, 郑楚光 2009 格子Boltzmann方法的原理及应用 (第一版) (北京: 科学出版社) 第66页
Guo Z L, Zheng C G 2009 Theory and Applications of Lattice Boltzmann Method (Vol. 1) (Beijing: Science Press) p66 (in Chinese)
[26] Laddy A J C 1994 J. Fluid Mech. 271 285
Google Scholar
[27] Wang J, Wang D, Lallemand P, Luo L S 2013 Comput. Math. Appl. 65 262
Google Scholar
[28] Zhang T, Shi B C, Guo Z L, Chai Z H, Lu J H 2012 Phys. Rev. E 85 016701
Google Scholar
[29] Li C, Kang Q, Viswanathan H S, Tao W Q 2014 Water Resour. Res. 50 9343
Google Scholar
[30] Wang H, Alvarado V, Bagdonas D A, McLaughlin J F, Kaszuba J P, Grana D, Campbell E, Ng K 2021 Int. J. Greenhouse Gas Control 107 103283
Google Scholar
[31] 霍吉祥, 宋汉周, 杜京浓, 管清晨 2015 岩土力学与工程学报 5 1013
Google Scholar
Huo J X, Song H Z, Du J N, Guan Q C 2015 J. Rock. Mech. Eng. 5 1013
Google Scholar
[32] Meng X H, Guo Z L 2016 Int. J. Heat Mass Transfer 100 767
Google Scholar
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