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采用格子Boltzmann方法研究了孔隙尺度下多孔介质内含流固溶解反应的互溶驱替过程, 重点研究了被驱替流体与驱替流体黏性差异较大的情况下, 溶解反应引起的多孔介质内部结构变化对驱替过程的影响; 定量分析了不同达姆科勒数及佩克莱数下多孔介质孔隙率和驱替过程驱替效率随时间的演变. 研究结果表明: 达姆科勒数较大时, 溶解反应的发生会在多孔介质内部生成虫洞, 导致一部分被驱替流体不能被波及, 驱替流体沿虫洞离开多孔介质, 造成驱替效率的减少. 在此基础上, 随着达姆科勒数的增大, 孔隙率变化越大, 生成的虫洞越宽, 最终驱替效率变大, 但仍小于无溶解反应时的驱替效率; 随着佩克莱数的增大, 指进增长速度越快, 孔隙率变化越小, 驱替效率越小.
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关键词:
- 多孔介质 /
- 互溶驱替 /
- 溶解反应 /
- 格子Boltzmann方法
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.[1] Cubillas P, Kohler S, Prieto M, Causserand C, Oelkers E H 2005 Geochim. Cosmochim. Acta 69 5459
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图 2 两平板间的互溶驱替问题初始状态示意图
Fig. 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
Fig. 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
Fig. 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
Fig. 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 $ )Fig. 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
Fig. 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 $ Fig. 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
Fig. 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
Fig. 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
Fig. 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 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 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 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 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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