Abstract
Miscible displacement of two-phase fluids in rough fractures is relevant to some industrial processes, including enhanced oil recovery and geological carbon sequestration. When a less viscous fluid displaces another more viscous fluid, finger instability occurs. Previous works focused on miscible displacement in porous media or Hele-Shaw, but the experimental study was rarely reported for rough fractures. Here, we perform visualization experiments of water displacing glycerol in a transparent fracture model to investigate the effects of flow rate and diffusion in miscible displacement. We quantify the displacement patterns using the sweep efficiency, the mixing length, and the relative contact area. We observe two distinct displacement regimes: dominant finger regime and multiple fingers regime. A critical Peclet number Pe is obtained to identify such two regimes. Below the critical Pe, the channel forms, and the displacement is the dominant finger regime, which results in low sweep efficiency and linearly growth of mixing length at late time. Above this critical Pe, intensive tip-splitting events result in the formation of dendritic displacement pattern, and the displacement is multiple fingers regime, slowing down the growth rate of mixing length at late time and contributes to the higher sweep efficiency. Our work shows a critical Pe that separates the two distinct regimes and improves our understanding of the evolution of the miscible displacement fronts in rough fractures.
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References
Afshari, S., Hejazi, S.H., Kantzas, A.: Role of medium heterogeneity and viscosity contrast in miscible flow regimes and mixing zone growth: a computational pore-scale approach. Phys. Rev. Fluids 3, 54501 (2018). https://doi.org/10.1103/PhysRevFluids.3.054501
Al-Shalabi, E.W., Sepehrnoori, K., Pope, G.: Numerical modeling of combined low salinity water and carbon dioxide in carbonate cores. J. Pet. Sci. Eng. 137, 157–171 (2016). https://doi.org/10.1016/j.petrol.2015.11.021
Alzayer, A.N., Voskov, D.V., Tchelepi, H.A.: Relative permeability of near-miscible fluids in compositional simulators. Transp. Porous Media 122, 547–573 (2018). https://doi.org/10.1007/s11242-017-0950-9
Arshadi, M., Rajaram, H., Detwiler, R.L., Jones, T.: High-resolution experiments on chemical oxidation of DNAPL in variable-aperture fractures. Water Resour. Res. 51, 2317–2335 (2015). https://doi.org/10.1002/2014WR016159
Auradou, H., Hulin, J.-P., Roux, S.: Experimental study of miscible displacement fronts in rough self-affine fractures. Phys. Rev. E 63, 66306 (2001). https://doi.org/10.1103/PhysRevE.63.066306
Babadagli, T., Raza, S., Ren, X., Develi, K.: Effect of surface roughness and lithology on the water–gas and water–oil relative permeability ratios of oil-wet single fractures. Int. J. Multiph. Flow 75, 68–81 (2015). https://doi.org/10.1016/j.ijmultiphaseflow.2015.05.005
Benson, S.M., Cole, D.R.: CO2 sequestration in deep sedimentary formations. Elements 4, 325–331 (2008). https://doi.org/10.2113/gselements.4.5.325
Bertels, S.P., DiCarlo, D.A., Blunt, M.J.: Measurement of aperture distribution, capillary pressure, relative permeability, and in situ saturation in a rock fracture using computed tomography scanning. Water Resour. Res. 37, 649–662 (2001). https://doi.org/10.1029/2000WR900316
Blackwell, R.J., Rayne, J.R., Terry, W.M.: Factors influencing the efficiency of miscible displacement. Trans. AIME 217, 1–8 (1959). https://doi.org/10.2118/1131-G
Chen, Y.-F., Wu, D.-S., Fang, S., Hu, R.: Experimental study on two-phase flow in rough fracture: phase diagram and localized flow channel. Int. J. Heat Mass Transf. 122, 1298–1307 (2018). https://doi.org/10.1016/j.ijheatmasstransfer.2018.02.031
Chui, J.Y.Y., de Anna, P., Juanes, R.: Interface evolution during radial miscible viscous fingering. Phys. Rev. E 92, 041003 (2015). https://doi.org/10.1103/PhysRevE.92.041003
Connolly, M., Johns, R.T.: Scale-dependent mixing for adverse mobility ratio flows in heterogeneous porous media. Transp. Porous Media 113, 29–50 (2016). https://doi.org/10.1007/s11242-016-0678-y
D’Errico, G., Ortona, O., Capuano, F., Vitagliano, V.: Diffusion coefficients for the binary system glycerol + water at 25 °C. A velocity correlation study. J. Chem. Eng. Data 49, 1665–1670 (2004). https://doi.org/10.1021/je049917u
Detwiler, R.L., Pringle, S.E., Glass, R.J.: Measurement of fracture aperture fields using transmitted light: an evaluation of measurement errors and their influence on simulations of flow and transport through a single fracture. Water Resour. Res. 35, 2605–2617 (1999). https://doi.org/10.1029/1999WR900164
Dou, Z., Zhou, Z.F., Wang, J.G.: Three-dimensional analysis of spreading and mixing of miscible compound in heterogeneous variable-aperture fracture. Water Sci. Eng. 9, 293–299 (2016). https://doi.org/10.1016/j.wse.2017.01.007
Er, V., Babadagli, T.: Miscible interaction between matrix and fracture: a visualization and simulation study. SPE Reserv. Eval. Eng. 13, 109–117 (2010). https://doi.org/10.2118/117579-PA
Ershadnia, R., Wallace, C.D., Soltanian, M.R.: CO2 geological sequestration in heterogeneous binary media: Effects of geological and operational conditions. Adv. Geo-Energy Res. 4, 392–405 (2020)
Etrati, A., Frigaard, I.A.: Viscosity effects in density-stable miscible displacement flows: experiments and simulations. Phys. Fluids 30, 123104 (2018). https://doi.org/10.1063/1.5065388
Ghesmat, K., Azaiez, J.: Viscous fingering instability in porous media: effect of anisotropic velocity-dependent dispersion tensor. Transp. Porous Media 73, 297–318 (2008). https://doi.org/10.1007/s11242-007-9171-y
Hekmatzadeh, M., Dadvar, M., Sahimi, M.: Pore-network simulation of unstable miscible displacements in porous media. Transp. Porous Media 113, 511–529 (2016). https://doi.org/10.1007/s11242-016-0708-9
Hu, R., Zhou, C.-X., Wu, D.-S., Yang, Z., Chen, Y.-F.: Roughness control on multiphase flow in rock fractures. Geophys. Res. Lett. 46, 12002–12011 (2019). https://doi.org/10.1029/2019GL084762
Jiao, C., Maxworthy, T.: An experimental study of miscible displacement with gravity-override and viscosity-contrast in a Hele Shaw cell. Exp. Fluids 44, 781–794 (2008). https://doi.org/10.1007/s00348-007-0434-8
Kahrobaei, S., Farajzadeh, R., Suicmez, V.S., Bruining, J.: Gravity-enhanced transfer between fracture and matrix in solvent-based enhanced oil recovery. Ind. Eng. Chem. Res. 51, 14555–14565 (2012). https://doi.org/10.1021/ie3014499
Lee, H.-B., Yeo, I.W., Ji, S.-H., Lee, K.-K.: Wettability-dependent DNAPL migration in a rough-walled fracture. J. Contam. Hydrol. 113, 44–55 (2010). https://doi.org/10.1016/j.jconhyd.2009.12.006
Lu, M., Su, Y., Zhan, S., Almrabat, A.: Modeling for reorientation and potential of enhanced oil recovery in refracturing. Adv. Geo-Energy Res. 4, 20–28 (2020)
Malhotra, S., Sharma, M.M., Lehman, E.R.: Experimental study of the growth of mixing zone in miscible viscous fingering. Phys. Fluids 27, 14105 (2015). https://doi.org/10.1063/1.4905581
Mason, G., Morrow, N.R.: Developments in spontaneous imbibition and possibilities for future work. J. Pet. Sci. Eng. 110, 268–293 (2013). https://doi.org/10.1016/j.petrol.2013.08.018
Paterson, L.: Fingering with miscible fluids in a Hele Shaw cell. Phys. Fluids 28, 26–30 (1985). https://doi.org/10.1063/1.865195
Petitjeans, P., Chen, C.-Y., Meiburg, E., Maxworthy, T.: Miscible quarter five-spot displacements in a Hele-Shaw cell and the role of flow-induced dispersion. Phys. Fluids 11, 1705–1716 (1999). https://doi.org/10.1063/1.870037
Ruith, M., Meiburg, E.: Miscible rectilinear displacements with gravity override. Part 1. Homogeneous porous medium. J. Fluid Mech. 420, 225–257 (2000). https://doi.org/10.1017/S0022112000001543
Saffman, P.G., Taylor, G.: The penetration of a fluid into a porous medium or Hele-Shaw cell containing a more viscous liquid. Proc. R. Soc. Lond. A 245, 312–329 (1958). https://doi.org/10.1098/rspa.1958.0085
Sajjadi, M., Azaiez, J.: Scaling and unified characterization of flow instabilities in layered heterogeneous porous media. Phys. Rev. E Stat. Nonlinear Soft Matter Phys. 88, 33017 (2013). https://doi.org/10.1103/PhysRevE.88.033017
Shahnazari, M.R., Maleka Ashtiani, I., Saberi, A.: Linear stability analysis and nonlinear simulation of the channeling effect on viscous fingering instability in miscible displacement. Phys. Fluids 30, 34106 (2018). https://doi.org/10.1063/1.5019723
Shokri, H., Kayhani, M.H., Norouzi, M.: Nonlinear simulation and linear stability analysis of viscous fingering instability of viscoelastic liquids. Phys. Fluids 29, 33101 (2017). https://doi.org/10.1063/1.4977443
Tan, C.T., Homsy, G.M.: Stability of miscible displacements in porous media: rectilinear flow. Phys. Fluids 29, 3549–3556 (1986). https://doi.org/10.1063/1.865832
Tan, C.T., Homsy, G.M.: Stability of miscible displacements in porous media: radial source flow. Phys. Fluids 30, 1239–1245 (1987). https://doi.org/10.1063/1.866289
Tan, C.T., Homsy, G.M.: Simulation of nonlinear viscous fingering in miscible displacement. Phys. Fluids 31, 1330–1338 (1988). https://doi.org/10.1063/1.866726
Taylor, G.I.: Dispersion of soluble matter in solvent flowing slowly through a tube. Proc. R. Soc. Lond. A 219, 186–203 (1953). https://doi.org/10.1098/rspa.1953.0139
Videbæk, T.E., Nagel, S.R.: Diffusion-driven transition between two regimes of viscous fingering. Phys. Rev. Fluids 4, 33902 (2019). https://doi.org/10.1103/PhysRevFluids.4.033902
Yang, Z., Méheust, Y., Neuweiler, I., Hu, R., Niemi, A., Chen, Y.-F.: Modeling immiscible two-phase flow in rough fractures from capillary to viscous fingering. Water Resour. Res. 55, 2033–2056 (2019). https://doi.org/10.1029/2018WR024045
Zimmerman, W.B., Homsy, G.M.: Nonlinear viscous fingering in miscible displacement with anisotropic dispersion. Phys. Fluids A Fluid Dyn. 3, 1859–1872 (1991). https://doi.org/10.1063/1.857916
Acknowledgements
We acknowledge support from the National Key R&D Program of China (No. 2019YFC0605001) and the National Natural Science Foundation of China (Nos. 51925906, 51779188).
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XSC and RH designed and performed the experiments and data processing and wrote the manuscript. XSC, RH, WG, and YFC made scientific contributions to data interpretation and were actively involved in preparing the manuscript.
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Chen, XS., Hu, R., Guo, W. et al. Experimental Observation of Two Distinct Finger Regimes During Miscible Displacement in Fracture. Transp Porous Med 144, 175–188 (2022). https://doi.org/10.1007/s11242-021-01547-9
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DOI: https://doi.org/10.1007/s11242-021-01547-9