Modeling of counter-current spontaneous imbibition in independent capillaries with unequal diameters
Abstract view|0|times PDF download|0|times
Abstract
Spontaneous imbibition is a crucial process for oil recovery from fractured and unconventional reservoirs. Herein, with the assumption of capillaries being independent, a new mathematical model for spontaneous imbibition is proposed and solved using a numerical method. The simulated results show that the wetting phase preferentially enters smaller capillaries where the advancement velocity is higher than that in larger ones, while the non-wetting phase can be displaced out in the larger capillaries. In addition, the effect of fluid viscosity ratio on counter-current imbibition is analyzed. The results show that imbibition velocity becomes higher with the increase in the viscosity ratio. When the viscosity of the non-wetting phase is larger than that of the wetting phase, the end pressure gradually increases as the imbibition front advances. In contrast, when the viscosity of the non-wetting phase is less than that of the wetting phase, the end pressure decreases with the infiltration. With a higher viscosity ratio of non-wetting and wetting phase, the heterogeneity of the interface advancement among different capillaries increases.
Cited as: Chen, K., Xu, H., Zhang, Z., Meng, Q., Zhang, T. Modeling of counter-current spontaneous imbibition in independent capillaries with unequal diameters. Capillarity, 2022, 5(6): 115-122. https://doi.org/10.46690/capi.2022.06.02
Keywords
Full Text:
PDFReferences
Abd, A. S., Elhafyan, E., Siddiqui, A. R., et al. A review of the phenomenon of counter-current spontaneous imbibition: Analysis and data interpretation. Journal of Petroleum Science and Engineering, 2019, 180: 456-470.
Bourblaux, B. J., Kalaydjian, F. J. Experimental study of cocurrent and countercurrent flows in natural porous media. SPE Reservoir Engineering, 1990, 5(3): 361-368.
Cai, J., Jin, T., Kou, J., et al. Lucas-Washburn equation-based modeling of capillary-driven flow in porous systems. Langmuir, 2021, 37(5): 1623-1636.
Cai, J., Perfect, E., Cheng, C., et al. Generalized modeling of spontaneous imbibition based on Hagen-Poiseuille flow in tortuous capillaries with variably shaped apertures. Langmuir, 2014, 30(18): 5142-5151.
Cai, J., Yu, B. A discussion of the effect of tortuosity on the capillary imbibition in porous media. Transport in Porous Media, 2011, 89: 251-263.
Cai, J., Yu, B., Zou, M., et al. Fractal characterization of spontaneous co-current imbibition in porous media. Energy & Fuels, 2010, 24(3): 1860-1867.
Cheng, Z., Gao, H., Ning, Z., et al. Inertial effect on oil/water countercurrent imbibition in porous media from a porescale perspective. SPE Journal, 2022, 27(3): 1619-1632.
Dong, M., Dullien, F. A. L., Dai, L., et al. Immiscible displacement in the interacting capillary bundle model part I. Development of interacting capillary bundle model. Transport in Porous Media, 2005, 59: 1-18.
Dong, M., Dullien, F. A. L., Dai, L., et al. Immiscible displacement in the interacting capillary bundle model part II. Applications of model and comparison of interacting and non-interacting capillary bundle models. Transport in Porous Media, 2006, 63: 289-304.
Foley, A. Y., Nooruddin, H. A., Blunt, M. J. The impact of capillary backpressure on spontaneous counter-current imbibition in porous media. Advances in Water Resources, 2017, 107: 405-420.
Gong, Y., Piri, M. Pore-to-core upscaling of solute transport under steady-state two-phase flow conditions using dynamic pore network modeling approach. Transport in Porous Media, 2020, 135(1): 181-218.
Gong, Y., Sedghi, M., Piri, M. Dynamic pore-scale modeling of residual trapping following imbibition in a rough-walled fracture. Transport in Porous Media, 2021, 140(1): 143-179.
Gorce, J. B., Hewitt, I. J., Vella, D. Capillary imbibition into converging tubes: Beating Washburn’s law and the optimal imbibition of liquids. Langmuir, 2016, 32(6): 1560-1567.
Haugen, Å., Fernø, M. A., Mason, G., et al. Capillary pressure and relative permeability estimated from a single spontaneous imbibition test. Journal of Petroleum Science and Engineering, 2014, 115: 66-77.
Kim, K., Kim, M., Oh, J. Core-scale investigation of the effect of heterogeneity on the dynamics of residual and dissolution trapping of carbon dioxide. Journal of Hydrology, 2021, 596: 126109.
Mason, G., Fischer, H., Morrow, N. R., et al. Correlation for the effect of fluid viscosities on counter-current spontaneous imbibition. Journal of Petroleum Science and Engineering, 2010, 72(1-2): 195-205.
Mason, G., Morrow, N. R. Developments in spontaneous imbibition and possibilities for future work. Journal of Petroleum Science and Engineering, 2013, 110: 268-293.
Meng, Q., Liu, H., Wang, J. A critical review on fundamental mechanisms of spontaneous imbibition and the impact of boundary condition, fluid viscosity and wettability. Advances in Geo-Energy Research, 2017a, 1(1): 1-17.
Meng, Q., Liu, H., Wang, J. Effect of viscosity on oil production by cocurrent and countercurrent imbibition from cores with two ends open. SPE Reservoir Engineering, 2017b, 20(2): 251-259.
Morrow, N. R., Mason, G. Recovery of oil by spontaneous imbibition. Current Opinion in Colloid & Interface Science, 2001, 6(4): 321-337.
Nooruddin, H. A., Blunt, M. J. Analytical and numerical investigations of spontaneous imbibition in porous media. Water Resources Research, 2016, 52(9): 7284-7310.
Pooladi-Darvish, M., Firoozabadi, A. Cocurrent and countercurrent imbibition in a water-wet matrix block. SPE Journal, 2000, 5(1): 3-11.
Qin, C. Z., Wang, X., Hefny, M., et al. Wetting dynamics of spontaneous imbibition in porous media: From pore scale to darcy scale. Geophysical Research Letters, 2022, 49(4): e2021GL097269.
Ruth, D., Bartley, J. A perfect-cross-flow model for two phase flow in porous media. Paper SCA2002-05 Presented at the International Society of Core Analysts Annual Meeting, Monterey, CA, USA, May, 2002.
Shen, A., Liu, Y., Farouq, S. M. A model of spontaneous flow driven by capillary pressure in nanoporous media. Capillarity, 2020, 3(1): 1-7.
Unsal, E., Mason, G., Ruth, D. W., et al. Co- and countercurrent spontaneous imbibition into groups of capillary tubes with lateral connections permitting cross-flow. Journal of Colloid and Interface Science, 2007, 315(1): 200-209.
Wang, J., Dong, M. Trapping of the non-wetting phase in an interacting triangular tube bundle model. Chemical Engineering Science, 2011, 66(3): 250-259.
Wang, Z., Li, H., Lan, X., et al. Formation damage mechanism of a sandstone reservoir based on micro-computed tomography. Advances in Geo-Energy Research, 2021, 5(1): 25-38.
Washburn, E. W. The dynamics of capillary flow. Physical Review, 1921, 17(3): 273-283.
Xiao, J., Luo, Y., Niu, M., et al. Study of imbibition in various geometries using phase field method. Capillarity, 2019, 2(4): 57-65.
Yang, Z., Liu, X., Li, H., et al. Analysis on the influencing factors of imbibition and the effect evaluation of imbibition in tight reservoirs. Petroleum Exploration and Development, 2019, 46(4): 779-785.
Zhang, X., Morrow, N. R., Ma, S. Experimental verification of a modified scaling group for spontaneous imbibition. SPE Reservoir Engineering, 1996, 11(4): 280-285.
Zhao, J., Qin, F., Fischer, R., et al. Spontaneous imbibition in a square tube with corner films: Theoretical model and numerical simulation. Water Resources Research, 2021, 57(2): e2020WR029190.
Zhou, Y., Pu, H., Zhong, X., et al. Visualized experiment of the imbibition oil recovery for the nano-particles in Hele-Shaw model. Petroleum Geology & Oilfield Development in Daqing, 2019, 38(6): 46-51. (in Chinese)
Refbacks
- There are currently no refbacks.
Copyright (c) 2022 The Author(s)
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.