Abstract
When a wetting fluid is being displaced by a non-wetting gas in a capillary tube, a thin film of the wetting fluid is often left on the tube walls. To snap off the non-wetting gas, sufficient wetting fluid has to be collected in the pore throat, which will form a liquid lens that across the throat like a bridge, and a smaller gas bubble can be generated by snap-off. A number of researches have been conducted to study the phenomenon of snap-off both theoretically and experimentally. However, some dynamic characteristics of snap-off still remain unclear. In this work, a geometric model of pore throat and liquid collar formed in it was established, and multiple data sets of liquid collar shape were calculated. Following the principle that an interface system has a tendency of reducing its surface area, an evolvement path of liquid collar shape was concluded from the contour maps of calculation outcomes. Then a model of liquid flowing in film was derived, and the flow rate of liquid flowing from film into collar was calculated. Finally, the coalescence time of liquid collar calculated by model is almost the same with the measured time by experiment, and the film thickness utilized in model calculation is within a reasonable range of the experiment result, which proves a considerable reasonability and precision of the model. The liquid collar model in this work provides a new idea and reference for studying the morphological and dynamic characteristics of liquid collar in pore throat during snap-off.
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References
Abu Alsaud M, Riaz A, Tchelepi H (2016) Multiscale level-set method for accurate modeling of two-phase immiscible flow with deposited thin-films on solid surfaces. J Comput Phys 333:297–320. https://doi.org/10.1016/j.jcp.2016.12.038
Bennett PC, Cardenas WDB (2014) Extended roof snap-off for a continuous nonwetting fluid and an example case for supercritical CO2. Adv Water Resour 64(1):34–46. https://doi.org/10.1016/j.advwatres.2013.12.001
Beresnev IA, Deng W (2010) Theory of breakup of core fluids surrounded by a wetting annulus in sinusoidally constricted capillary channels. Phys Fluids 22(1):57. https://doi.org/10.1063/1.3294887
Beresnev IA, Li W, Vigil RD (2009) Condition for break-up of non-wetting fluids in sinusoidally constricted capillary channels. Transp Porous Media 80(3):581–604. https://doi.org/10.1007/s11242-009-9381-6
Bretherton FP (2006) The motion of long bubbles in tubes. J Fluid Mech 10(2):166–188
Cheng L, Liu H, Huang S, Wu K, Chen X, Wang D, Xiong H (2018) Environmental and economic benefits of solvent-assisted steam-gravity drainage for bitumen through horizontal well: a comprehensive modeling analysis. Energy 164:418–431. https://doi.org/10.1016/j.energy.2018.08.216
Deng W, Balhoff M, Cardenas MB (2016) Influence of dynamic factors on nonwetting fluid snap-off in pores. Water Resour Res 51(11):9182–9189. https://doi.org/10.1002/2015WR017261
Gauglitz PA, Radke CJ (1990) The dynamics of liquid film breakup in constricted cylindrical capillaries. J Colloid Interface Sci 134(1):14–40. https://doi.org/10.1016/0021-9797(90)90248-M
Gauglitz PA, Laurent CMS, Radke CJ (1988) Experimental determination of gas-bubble breakup in a constricted cylindrical capillary. Ind Eng Chem Res 27(7):1282–1291. https://doi.org/10.1021/ie00079a032
Hammond PS (1983) Nonlinear adjustment of a thin annular film of viscous fluid surrounding a thread of another within a circular cylindrical pipe. J Fluid Mech 137(137):363–384. https://doi.org/10.1017/S0022112083002451
Han Y, Shikazono N, Kasagi N (2011) Measurement of liquid film thickness in a micro parallel channel with interferometer and laser focus displacement meter. Int J Multiphase Flow 37(1):36–45. https://doi.org/10.1016/j.ijmultiphaseflow.2010.08.010
He J (2015) Study on the physical properties of foam characterization and the foam flooding. Doctoral dissertation, Northeast Petroleum University
Kovscek AR, Radke CJ (1996) Gas bubble snap-off under pressure-driven flow in constricted noncircular capillaries. Colloids Surf A Physicochem Eng Asp 117(1):55–76. https://doi.org/10.1016/0927-7757(96)03637-0
Lamanna JM, Bothe JV, Zhang FY, Mench MM (2014) Measurement of capillary pressure in fuel cell diffusion media, micro-porous layers, catalyst layers, and interfaces. J Power Sources 271:180–186. https://doi.org/10.1016/j.jpowsour.2014.07.163
Legait (1983) Laminar flow of two phases through a capillary tube with variable square cross-section. J Colloid Interface Sci 96(1):28–38. https://doi.org/10.1016/0021-9797(83)90005-X
Liu J, Xia R, Li B, Feng Q (2007) Directional motion of droplets in a conical tube or on a conical fibre. Chin Phys Lett 24(11):3210–3213. https://doi.org/10.1088/0256-307X/24/11/052
Meng X, Sheng JJ (2016) Experimental and numerical study of huff-n-puff gas injection to re-vaporize liquid dropout in shale gas condensate reservoirs. J Nat Gas Sci Eng 35:444–454. https://doi.org/10.1016/j.jngse.2016.09.002
Meng Y, Li X, Jiang M, Feng D, Zhang T, Zhang Z (2018) Experimental research on three dimensional flow characteristics of multiple horizontal fractures utilizing an innovative experiment apparatus. Arab J Geosci 11(10):243. https://doi.org/10.1007/s12517-018-3589-0
Pang Z (2008) Seepage mechanisms & applications of steam (gas) foam compound flooding. Doctoral dissertation, China University of Petroleum-Beijing.
Raeini AQ, Bijeljic B, Blunt MJ (2014) Numerical modelling of sub-pore scale events in two-phase flow through porous media. Transp Porous Media 101(2):191–213. https://doi.org/10.1007/s11242-013-0239-6
Riazi M, Sohrabi M, Bernstone C, Jamiolahmady M, Ireland S (2011) Visualisation of mechanisms involved in coinjection and storage in hydrocarbon reservoirs and water-bearing aquifers. Chem Eng Res Des 89(9):1827–1840. https://doi.org/10.1016/j.cherd.2011.03.009
Roman S, Soulaine C, Alsaud MA, Kovscek A, Tchelepi H (2016) Particle velocimetry analysis of immiscible two-phase flow in micromodels. Adv Water Resour 95:199–211. https://doi.org/10.1016/j.advwatres.2015.08.015
Roman S, Abu-Al-Saud MO, Tokunaga T, Wan J, Kovscek AR, Tchelepi HA (2017) Measurements and simulation of liquid films during drainage displacements and snap-off in constricted capillary tubes. J Colloid Interface Sci 507:279. https://doi.org/10.1016/j.jcis.2017.07.092
Roof JG (1970) Snap-off of oil droplets in water-wet pores. Soc Petrol Eng. https://doi.org/10.2118/2504-PA
Sapin P, Duru P, Fichot F, Prat M, Quintard M (2014) Pore-scale experimental study of boiling in porous media. In: 15th International Heat Transfer Conference–IHTC-15, Kyoto
Soulaine C, Horgue P, Franc J, Quintard M (2015) Gas-liquid flow modeling in columns equipped with structured packing. AICHE J 60(10):3665–3674. https://doi.org/10.1002/aic.14550
Sun F, Yao Y, Chen M, Li X, Zhao L, Meng Y, Sun Z, Zhang T, Feng D (2017a) Performance analysis of superheated steam injection for heavy oil recovery and modeling of wellbore heat efficiency. Energy 125:795–804. https://doi.org/10.1016/j.energy.2017.02.114
Sun F, Yao Y, Li X, Yu P, Ding G, Zou M (2017b) The flow and heat transfer characteristics of superheated steam in offshore wells and analysis of superheated steam performance. Comput Chem Eng 100:80–93. https://doi.org/10.1016/j.compchemeng.2017.01.045
Sun Z, Li X, Shi J, Yu P, Huang L, Xia J, Sun F, Zhang T, Feng D (2017c) A semi-analytical model for drainage and desorption area expansion during coal-bed methane production. Fuel 204:214–226. https://doi.org/10.1016/j.fuel.2017.05.047
Sun Z, Li X, Shi J, Zhang T, Sun F (2017d) Apparent permeability model for real gas transport through shale gas reservoirs considering water distribution characteristic. Int J Heat Mass Transf 115:1008–1019. https://doi.org/10.1016/j.ijheatmasstransfer.2017.07.123
Sun F, Yao Y, Li X (2018a) The heat and mass transfer characteristics of superheated steam coupled with non-condensing gases in horizontal wells with multi-point injection technique. Energy 143:995–1005. https://doi.org/10.1016/j.energy.2017.11.028
Sun Z, Shi J, Wu K, Li X (2018b) Gas flow behavior through inorganic nanopores in shale considering confinement effect and moisture content. Industrial & Engineering Chemistry Research 57(9):3430–3440. https://doi.org/10.1021/acs.iecr.8b00271
Sun Z, Shi J, Zhang T, Wu K, Feng D, Sun F, Huang L, Hou C, Li X (2018c) A fully-coupled semi-analytical model for effective gas/water phase permeability during coal-bed methane production. Fuel 223:44–52. https://doi.org/10.1016/j.fuel.2018.03.012
Sun Z, Shi J, Wang K, Miao Y, Zhang T, Feng D, Sun F, Wang S, Han S, Li X (2018d) The gas-water two phase flow behavior in low-permeability CBM reservoirs with multiple mechanisms coupling. Journal of Natural Gas Science and Engineering 52:82–93. https://doi.org/10.1016/j.jngse.2018.01.027
Sun F, Yao Y, Li G, Li X (2018e) Geothermal energy development by circulating CO2 in a U-shaped closed loop geothermal system. Energy Convers Manag 174:971–982. https://doi.org/10.1016/j.enconman.2018.08.094
Sun F, Yao Y, Li G, Li X (2018f) Geothermal energy extraction in CO2 rich basin using abandoned horizontal wells. Energy 158:760–773. https://doi.org/10.1016/j.energy.2018.06.084
Sussman M, Smereka P, Osher S (1994) A level set approach for computing solutions to incompressible two-phase flow. Academic Press Professional, Inc https://doi.org/10.1006/jcph.1994.1155
Tibirica CB, Nascimento FJD, Ribatski G (2010) Film thickness measurement techniques applied to micro-scale two. Exp Thermal Fluid Sci 34(4):463–473. https://doi.org/10.1016/j.expthermflusci.2009.03.009
Xu J, Tao J (2001) The fluid-flow rule at laminar-flow in ring-shape-channel. J Fuyang Teach Coll (Nat Sci) 18(2):17–19. https://doi.org/10.14096/j.cnki.cn34-1069/n.2001.02.006
Xu C, Kang Y, Chen F, You Z (2017) Analytical model of plugging zone strength for drill-in fluid loss control and formation damage prevention in fractured tight reservoir. J Pet Sci Eng 149:686–700. https://doi.org/10.1016/j.petrol.2016.10.069
Yang B, Kang Y, You L, Li X, Chen Q (2016) Measurement of the surface diffusion coefficient for adsorbed gas in the fine mesopores and micropores of shale organic matter. Fuel 181:793–804. https://doi.org/10.1016/j.fuel.2016.05.069
Yang B, Kang Y, Li X, You L, Chen M (2017) An integrated method of measuring gas permeability and diffusion coefficient simultaneously via pressure decay tests in shale. Int J Coal Geol 179:1–10. https://doi.org/10.1016/j.coal.2017.05.010
Yun W, Kovscek AR (2015) MicroVisual investigation of polymer retention on the homogeneous pore network of A micromodel. J Pet Sci Eng 128:115–127. https://doi.org/10.1016/j.petrol.2015.02.004
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Meng, Y., Li, X., He, M. et al. A semi-analytical model research of liquid collar shape and coalescence in pore throat during snap-off. Arab J Geosci 12, 468 (2019). https://doi.org/10.1007/s12517-019-4613-8
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DOI: https://doi.org/10.1007/s12517-019-4613-8