Investigation of the dynamics of immiscible displacement of a ganglion in capillaries

Amgad Salama, Jianchao Cai, Jisheng Kou, Shuyu Sun, Mohamed F. El-Amin, Yi Wang

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Abstract


In this work the problem of displacing a ganglion of a fluid by another immiscible one in capillaries is investigated. A modeling approach is developed to predict the location of the ganglion with time. The model describes two patterns; namely, when the ganglion totally exists inside the tube, and when the advancing interface of the ganglion has broken through the exit of the tube. The model is valid for the case in which the ganglion is wetting as well as when it is nonwetting to the wall of the tube. It also considers the situation in which both the advancing and the receding interfaces assume, generally, different contact angles. For the special case when the displacement process is quasistatic, both the receding and the advancing contact angles may be considered the same. Under these conditions, interfacial tension force plays no role and the ganglion moves as a plug inside the tube with a constant velocity. When the viscosity ratio between the invading fluid and the ganglion is one (i.e., both phases are having the same viscosity) the motion reduces to the Hagen-Poiseuille flow in pipes. Once the advancing interface breaks through the exit of the tube, interfacial tension starts to take part in the displacement process and the ganglion starts to accelerate or decelerate according to the viscosity ratio. When the ganglion is nonwetting, interfacial tension becomes in the direction of the flow and is opposite to the flow otherwise. The model accounts for external forces such as pressure and gravity in addition to capillarity. A computational fluid dynamics analysis of this system is conducted for both types of wettability scenarios and shows very good match with the results of the developed model during both the two modes of flow patterns. This builds confidence in the developed modeling approach. Other cases have also been explored to highlight the effects of other scenarios.

Cited as: Salama, A., Cai, J., Kou, J., Sun, S., EI-Amin, M. F., Wang, Y. Investigation of the dynamics of immiscible displacement of a ganglion in capillaries. Capillarity, 2021, 4(2): 31-44, doi: 10.46690/capi.2021.02.02


Keywords


Imbibition, drainage, ganglion, capillarity, Lucas-Washburn model

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Abdus S., Iqbal, G. M., Buchwalter, J. L. Practical Enhanced Reservoir Engineering: Assisted With Simulation Soft-ware. Oklahoma, USA, Pennwell, 2008.

Ahmed, T. Principles of Waterflooding, in Reservoir Engineer-ing Handbook, edited by T. Ahmed, Gulf Professional Publishing, USA, pp. 901-1107, 2019.

Alemu, B. L., Aker, E., Soldal, M., et al. Influence of CO2 on rock physics properties in typical reservoir rock: A CO2 flooding experiment of brine saturated sandstone in a CT-scanner. Energy Procedia, 2011, 4: 4379-4386.

Almetwally, A. G., Jabbari, H. Finite-difference simulation of coreflooding based on a reconstructed CT scan; modeling transient oscillating and pulse decay permeability exper-iment. Journal of Petroleum Science and Engineering, 2020, 192: 107260.

Arab, D., Kantzas, A., Bryant, S. L. Water flooding of oil reservoirs: Effect of oil viscosity and injection velocity on the interplay between capillary and viscous forces. Journal of Petroleum Science and Engineering, 2020, 186: 106691.

Bageri, B. S., Adebayo, A. R., Al Jaberi, J., et al. Evaluating drilling fluid infiltration in porous media-comparing NMR, gravimetric, and X-ray CT scan methods. Journal of Petroleum Science and Engineering, 2021, 198: 108242.

Bao, K., Salama, A., Sun, S. Numerical investigation on the effects of a precursor wetting film on the displacement of two immiscible phases along a channel. Flow, Turbulence and Combustion, 2016, 96(3): 757-771.

Bao, K., Salama, A., Sun, S., Flow split characterization of two immiscible phases with different wettability scenarios: A numerical investigation using a coupled Cahn-Hilliard and Navier-Stokes system. International Journal of Multiphase Flow, 2018, 100: 172-185.

Batchelor, G. K. An introduction to fluid dynamics. Cam-bridge, United Kingdom, Cambridge university press, 2000.

Benilova, E. S. The dynamics of liquid films, as described by the diffuse-interface model. Physics of Fluids, 2020, 32(11): 112103.

Bijeljic, B., Markicevic, B., Navaz, H.K. Capillary climb dynamics in the limits of prevailing capillary and gravity force. Physical Review E, 2011, 83(5): 056310.

Blunt, M. J. Flow in porous media-pore-network models and multiphase flow. Current Opinion in Colloid and Interface Science, 2001, 6(3): 197-207.

Blunt, M. J., Jackson, M. D., Piri, M., et al. Detailed physics, predictive capabilities and macroscopic consequences for pore-network models of multiphase flow. Advances in Water Resources, 2002, 25(8-12), 1069-1089.

Cai, J., Hu, X., Standnes, D. C., et al. An analytical model for spontaneous imbibition in fractal porous media including gravity. Colloids and Surfaces A: Physicochemical and Engineering Aspects, 2012, 414: 228-233.

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., Yu, B., Zou, M., et al. Fractal analysis of invasion depth of extraneous fluids in porous media. Chemical Engineering Science, 2010, 65(18): 5178-5186.

Cnudde, V., Boone, M., Dewanckele, J., et al. 3D charac-terization of sandstone by means of X-ray computed tomography. Geosphere, 2011, 7(1): 54-61.

De Mello, E. V. L., da Silveira Filho, O. T. Numerical study of the Cahn-Hilliard equation in one, two and three dimensions. Physica A: Statistical Mechanics and its Applications , 2005, 347: 429-443.

Dullien, F. A. L., El-Sayed, M. S., Batra, V. K. Rate of capillary rise in porous media with nonuniform pores. Journal of Colloid and Interface Science, 1977, 60(3): 497-506.

Echakouri, M., Salama, A., Henni, A. Experimental and computational fluid dynamics investigation of the deterioration of the rejection capacity of the membranes used in the filtration of oily water systems, ACS ES&T Water, 2021, 1(3): 728-744.

Grunau, D., Chen, S., Eggert, K. A lattice Boltzmann model for multiphase fluid flows. Physics of Fluids A: Fluid Dynamics, 1993, 5(10): 2557-2562.

Guo, Z. Well-balanced lattice Boltzmann model for two-phase systems featured. Physics of Fluids. 2021, 33(3): 031709.

Hammecker, C., Mertz, J.D., Fischer, C., et al. A geometrical model for numerical simulation of capillary imbibition in sedimentary rocks. Transport Porous Media, 1993, 12(2): 125-141.

Huang, X., Zhou, W., Deng, D. Validation of pore network modeling for determination of two-phase transport in fibrous porous media. Scientific Reports, 2020, 10(1): 20852.

Jha, K. N. Residual oil in reservoirs and prospects. Energy Developments: New Forms, Renewables, Conservation, Pergamon, 1984, 41-48.

Joekar-Niasar, V., Hassanizadeh, S. M. Analysis of fundamen-tals of two-phase flow in porous media using dynamic pore-network models: A review. Critical Reviews in Environmental Science and Technology, 2012, 42(18): 1895-1976.

Joekar-Niasar, V., Hassanizadeh, S. M. Effect of fluids proper-ties on non-equilibrium capillarity effects: Dynamic pore-network modeling. International Journal of Multiphase Flow, 2011, 37(2): 198-214.

Lamura, A., Gonnella, G., Yeomans, J. M. A lattice Boltzmann model of ternary fluid mixtures. Europhysics Letters, 1999, 45(3): 314-320.

Lucas, R. Rate of capillary ascension of liquids. Kollid Z, 1918, 23(15): 15-22.

Madonna, C., Almqvist, B. S. G., Saenger, E. H. Digital rock physics: numerical prediction of pressure-dependent ul-trasonic velocities using micro-CT imaging. Geophysical Journal International, 2012, 189(3): 1475-1482.

Mogensen, K., Masalmeh, S. A review of EOR techniques for carbonate reservoirs in challenging geological settings. Journal of Petroleum Science and Engineering, 2020, 195: 107889.

Montazeri, H., Zandavi, S. H., Bazylak, A. Sharp interface models for two-phase flows: Insights towards new approaches. Computer Methods in Applied Mechanics and Engineering, 2017, 322: 238-261.

Nordhaug, H. F., Celia, M., Dahle, H. K. A pore network model for calculation of interfacial velocities. Advances in Water Resources, 2003, 26(10): 1061-1074.

Pan, L., Lou, J., Li, H., et al. A diffuse interface model for two-phase flows with phase transition. Physics of Fluids 2019, 31(9): 092112.

Payatakes, A. C. Dynamics of oil ganglia during immiscible displacement in water-wet porous media. Annual Review of Fluid Mechanics, 1982, 14(1): 365-393.

Qin, C. Z., van Brummelen, H. A dynamic pore-network model for spontaneous imbibition in porous media. Advances in Water Resources, 2019, 133: 103420.

Ramanathan, R., Shehata, A. M., Nasr-El-Din, H. A. Effect of rock aging on oil recovery during water-alternating-CO2 injection process: An interfacial tension, contact angle, coreflood, and CT scan study. Paper SPE 179674 presented at the SPE Improved Oil Recovery Conference, Tulsa, Oklahoma, USA, 11-13 April 2016.

Raoof, A., Hassanizadeh, S.M. A new method for generating pore-network models of porous media. Transport in Porous Media. 2010, 81(3): 391-407.

Raoof, A., Nick, H. M., Hassanizadeh, S. M., et al. Poreflow: A complex pore-network model for simulation of reactive transport in variably saturated porous media. Computers and Geosciences, 2013, 61: 160-174.

Regaieg, M., Moncorgé, A. Adaptive dynamic/quasi-static pore network model for efficient multiphase flow simulation. Computional Geosciences, 2017, 21(4): 795-806.

Salama, A. A generalized analytical model for estimating the rate of imbibition/drainage of wetting/nonwetting fluids in capillaries. Chemical Engineering Science, 2021a: 116788.

Salama, A. Coalescence of an oil droplet with a permeating one over a membrane surface: conditions of permeation, recoil, and pinning. Langmuir, 2021b, 37(12): 3672-3684.

Salama, A. Critical entry pressure of a droplet pinning over multitude of pore openings. Physics of Fluids, 2021c, 33(3): 032114.

Salama, A. Investigation of the onset of the breakup of a permeating oil droplet at a membrane surface in crossflow filtration: A new model and CFD verification. International Journal of Multiphase Flow, 2020a, 126: 103255.

Salama, A. On the breakup of a permeating oil droplet in crossflow filtration: Effects of viscosity contrast. Physics of Fluids, 2020b, 32(7): 072101.

Salama, A. On the estimation of the leaked volume of an oil droplet undergoing breakup in crossflow filtration: CFD investigation, scaling, and a macroscopic model. Separation and Purification Technology, 2020c, 252: 117459.

Salama, A. Simplified formula for the critical entry pressure and a comprehensive insight into the critical velocity of dislodgment of a droplet in crossflow filtration. Langmuir, 2020d, 36(32): 9634-9642.

Salama, A., Amin, M. F. E., Kumar, K., et al. Flow and transport in tight and shale formations: A review. Geofluids, 2017, 4251209.

Sato, Y., Ničeno, B. A sharp-interface phase change model for a mass-conservative interface tracking method. Journal of Computational Physics, 2013, 249: 127-161.

Sheng, J. J. Alkaline-polymer flooding, in Enhanced Oil Recovery Field Case Studies, edited by J. J. Sheng, Gulf Professional Publishing, USA, pp. 169-178, 2013.

Siebold, A., Nardin, M., Schultz, J., et al. Effect of dynamic contact angle on capillary rise phenomena. Colloids and Surfaces A: Physicochemical and Engineering Aspects, 2020, 161(1): 81-87.

Speight, J. G. Upgrading by hydrocracking, in Heavy Oil Recovery and Upgrading, edited by J. G. Speight, Gulf Professional Publishing, USA, pp. 467-528, 2019.

Tummons, E. N., Tarabara, V. V., Chew, J., et al. Behavior of oil droplets at the membrane surface during crossflow microfiltration of oil-water emulsions. Journal of Mem-brane Science, 2016, 500: 211-224.

Washburn, E. W. The dynamics of capillary flow. Physical Review, 1921, 17(3): 273-283.

Won, J., Lee, J., Burns, S.E. Upscaling polydispersed particle transport in porous media using pore network model. Acta Geotechnica, 2021, 16(2): 421-432.

Wu, P., Nikolov, A. D., Wasan, D. T. Capillary rise: Validity of the dynamic contact angle models. Langmuir, 2017, 33(32): 7862-7872.

Xiong, Q., Baychev, T. G., Jivkov, A. P. Review of pore network modelling of porous media: Experimental characterisations, network constructions and applications to reactive transport. Journal of Contaminant Hydrology, 2016, 192: 101-117.

Xu, X., Di, Y., Yu, H. Sharp-interface limits of a phase-field model with a generalized Navier slip boundary condition for moving contact lines. Journal of Fluid Mechanics, 2018, 849: 805-833.

Zhang, T., Salama, A., Sun, S., et al. Pore network modeling of drainage process in patterned porous media: A quasi-static study. Journal of Computational Science, 2015, 9: 64-69.

Zhong, H., Wang, X., Salama, A., et al. Quasistatic analysis on configuration of two-phase flow in Y-shaped tubes. Computers and Mathematics with Applications, 2014, 68(12): 1905-1914.

Zoubeik, M., Salama, A., Henni, A. A novel antifouling technique for the crossflow filtration using porous membranes: Experimental and CFD investigations of the periodic feed pressure technique. Water Research, 2018, 146: 159-176.


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