Modeling Nanoparticle-Stabilized Foam Flow in Porous Media Accounting for Particle Retention and Permeability Reduction
DOI:
https://doi.org/10.69631/ipj.v2i1nr57Keywords:
Foam, Nanoparticles, Porous media, Particle retentionAbstract
This work presents a model for nanoparticle-stabilized foam flow in porous media, accounting for particle retention and the resulting permeability reduction. We present a semi-analytical solution under steady-state conditions, which allows for obtaining water saturation, foam apparent viscosity, and pressure drop profiles. We study different nanoparticle concentrations (in the presence and absence of salt) using retention parameters based on experimental data. When particle retention is neglected, the sweep efficiency of the porous medium improves compared to the case without nanoparticles, even at a low nanoparticle concentration (0.1 wt%). In contrast, when retention is accounted for, this enhancement is observed only at higher concentrations (0.5 wt% and 1.0 wt%). Neglecting nanoparticle retention generally underestimates pressure drop, especially in scenarios with significant retention. However, while retained nanoparticles increase pressure by reducing permeability, the loss of suspended nanoparticles decreases pressure by reducing the foam’s apparent viscosity. Consequently, when considering both nanoparticle loss and reduced permeability, the pressure drop is higher than in models that ignore retention. In contrast, omitting retention effects on permeability, the pressure drop is lower.
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Arain, Z.-U.-A., Al-Anssari, S., Ali, M., Memon, S., Bhatti, M. A., Lagat, C., & Sarmadivaleh, M. (2020). Reversible and irreversible adsorption of bare and hybrid silica nanoparticles onto carbonate surface at reservoir condition. Petroleum, 6(3), 277–285. https://doi.org/10.1016/j.petlm.2019.09.001
Ashoori, E., Marchesin, D., & Rossen, W. R. (2011). Roles of transient and local equilibrium foam behavior in porous media: Traveling wave. Colloids and Surfaces A: Physicochemical and Engineering Aspects, 377(1–3), 228–242. https://doi.org/10.1016/j.colsurfa.2010.12.042
Babakhani, P., Bridge, J., Doong, R., & Phenrat, T. (2017). Continuum-based models and concepts for the transport of nanoparticles in saturated porous media: A state-of-the-science review. Advances in Colloid and Interface Science, 246, 75–104. https://doi.org/10.1016/j.cis.2017.06.002
Bedrikovetsky, P. (2013). Mathematical theory of oil and gas recovery: with applications to ex-USSR oil and gas fields (Vol. 4). Springer Science & Business Media.
Bedrikovetsky, P., Marchesin, D., Shecaira, F., Souza, A. L., Milanez, P. V., & Rezende, E. (2001). Characterisation of deep bed filtration system from laboratory pressure drop measurements. Journal of Petroleum Science and Engineering, 32(2–4), 167–177. https://doi.org/10.1016/S0920-4105(01)00159-0
Bennetzen, M. V., & Mogensen, K. (2014). Novel applications of nanoparticles for future enhanced oil recovery. All Days, IPTC-17857-MS. https://doi.org/10.2523/IPTC-17857-MS
Borazjani, S., Dehdari, L., & Bedrikovetsky, P. (2020). Exact solution for tertiary polymer flooding with polymer mechanical entrapment and adsorption. Transport in Porous Media, 134(1), 41–75. https://doi.org/10.1007/s11242-020-01436-7
Collins, R. E. (1976). Flow of fluids through porous materials. Petroleum Publishing, Tulsa, OK. OSTI ID:7099752
Danelon, T., Paz, P., & Chapiro, G. (2024a). The mathematical model and analysis of the nanoparticle-stabilized foam displacement. Applied Mathematical Modelling, 125, 630–649. https://doi.org/10.1016/j.apm.2023.10.022
Danelon, T., Rocha, B. M., Dos Santos, R. W., & Chapiro, G. (2024b). Sensitivity analysis and uncertainty quantification based on the analytical solution for nanoparticle-stabilized foam flow in porous media. Geoenergy Science and Engineering, 242, 213285. https://doi.org/10.1016/j.geoen.2024.213285
Daneshfar, R., Ashoori, S., & Soltani Soulgani, B. (2024). Transport and retention of silica nanoparticles in glass-bead columns: Effects of particle size, type, and concentration of ionic species. Scientific Reports, 14(1), 685. https://doi.org/10.1038/s41598-023-51119-8
Daryasafar, A., & Shahbazi, K. (2018). Using nanotechnology for CO2-foams stabilization for application in enhanced oil recovery. International Journal of Energy for a Clean Environment, 19(3–4), 217–235. https://doi.org/10.1615/InterJEnerCleanEnv.2018026111
Du, D., Zhao, D., Li, Y., Wang, F., & Li, J. (2021). Parameter calibration of the stochastic bubble population balance model for predicting NP-stabilized foam flow characteristics in porous media. Colloids and Surfaces A: Physicochemical and Engineering Aspects, 614, 126180. https://doi.org/10.1016/j.colsurfa.2021.126180
Eftekhari, A. A., & Farajzadeh, R. (2017). Effect of foam on liquid phase mobility in porous media. Scientific Reports, 7(1), 43870. https://doi.org/10.1038/srep43870
Eide, Ø., Fernø, M., Bryant, S., Kovscek, A., & Gauteplass, J. (2020). Population-balance modeling of CO2 foam for CCUS using nanoparticles. Journal of Natural Gas Science and Engineering, 80, 103378. https://doi.org/10.1016/j.jngse.2020.103378
Espinosa, D., Caldelas, F., Johnston, K., Bryant, S. L., & Huh, C. (2010). Nanoparticle-stabilized supercritical CO2 foams for potential mobility control applications. SPE Improved Oil Recovery Symposium, SPE-129925-MS. https://doi.org/10.2118/129925-MS
Façanha, J. M. F., Lopes, L. F., Fritis, G., Godoy, P., Weber Dos Santos, R., Chapiro, G., & Perez-Gramatges, A. (2022). Bubble-growth regime for confined foams: Comparison between N2–CO2/foam and CO2/foam stabilized by silica nanoparticles. Journal of Petroleum Science and Engineering, 218, 111006. https://doi.org/10.1016/j.petrol.2022.111006
Fadili, A., Murtaza, A., & Zitha, P. (2022). Injectivity decline by nanoparticles transport in high permeable rock. Journal of Petroleum Science and Engineering, 211, 110121. https://doi.org/10.1016/j.petrol.2022.110121
Farajzadeh, R., Bedrikovetsky, P., Lotfollahi, M., & Lake, L. W. (2016). Simultaneous sorption and mechanical entrapment during polymer flow through porous media. Water Resources Research, 52(3), 2279–2298. https://doi.org/10.1002/2015WR017885
Hajiabadi, S. H., Bedrikovetsky, P., Mahani, H., Khoshsima, A., Aghaei, H., Kalateh-Aghamohammadi, M., & Habibi, S. (2020). Effects of surface modified nanosilica on drilling fluid and formation damage. Journal of Petroleum Science and Engineering, 194, 107559. https://doi.org/10.1016/j.petrol.2020.107559
Herzig, J. P., Leclerc, D. M., & Goff, P. Le. (1970). Flow of suspensions through porous media—Application to deep filtration. Industrial & Engineering Chemistry, 62(5), 8–35. https://doi.org/10.1021/ie50725a003
Hirasaki, G. J., & Lawson, J. B. (1985). Mechanisms of foam flow in porous media: apparent viscosity in smooth capillaries. Society of Petroleum Engineers Journal, 25(02), 176-190. https://doi.org/10.2118/12129-PA
Issakhov, M., Khanjani, M., Muratkhozhina, A., Pourafshary, P., Aidarova, S., & Sharipova, A. (2024). Experimental and data-driven analysis for predicting nanofluid performance in improving foam stability and reducing mobility at critical micelle concentration. Scientific Reports, 14(1), 7856. https://doi.org/10.1038/s41598-024-58609-3
Kam, S. I. (2008). Improved mechanistic foam simulation with foam catastrophe theory. Colloids and Surfaces A: Physicochemical and Engineering Aspects, 318(1–3), 62–77. https://doi.org/10.1016/j.colsurfa.2007.12.017
Keykhosravi, A., Bedrikovetsky, P., & Simjoo, M. (2022). Experimental insight into the silica nanoparticle transport in dolomite rocks: Spotlight on DLVO theory and permeability impairment. Journal of Petroleum Science and Engineering, 209, 109830. https://doi.org/10.1016/j.petrol.2021.109830
Kovscek, A. R., Patzek, T. W., & Radke, C. J. (1995). A mechanistic population balance model for transient and steady-state foam flow in Boise sandstone. Chemical Engineering Science, 50(23), 3783–3799. https://doi.org/10.1016/0009-2509(95)00199-F
Li, Q., & Prigiobbe, V. (2020). Modeling nanoparticle transport in porous media in the presence of a foam. Transport in Porous Media, 131(1), 269–288. https://doi.org/10.1007/s11242-019-01235-9
Li, S., Li, Z., & Wang, P. (2016). Experimental study of the stabilization of CO2 foam by sodium dodecyl sulfate and hydrophobic nanoparticles. Industrial & Engineering Chemistry Research, 55(5), 1243–1253. https://doi.org/10.1021/acs.iecr.5b04443
Li, Y., Wang, Y., Pennell, K. D., & Abriola, L. M. (2008). Investigation of the transport and deposition of fullerene (C60) nanoparticles in quartz sands under varying flow conditions. Environmental Science & Technology, 42(19), 7174–7180. https://doi.org/10.1021/es801305y
Rahman, A., Torabi, F., & Shirif, E. (2023). Surfactant and nanoparticle synergy: Towards improved foam stability. Petroleum, 9(2), 255–264. https://doi.org/10.1016/j.petlm.2023.02.002
Rodriguez, E., Roberts, M. R., Yu, H., Huh, C., & Bryant, S. L. (2009). Enhanced migration of surface-treated nanoparticles in sedimentary rocks. SPE Annual Technical Conference and Exhibition, SPE-124418-MS. https://doi.org/10.2118/124418-MS
Roebroeks, J., Eftekhari, A. A., Farajzadeh, R., & Vincent-Bonnieu, S. (2015, April 14). Nanoparticle stabilized foam in carbonate and sandstone reservoirs. IOR 2015 - 18th European Symposium on Improved Oil Recovery, Dresden, Germany. https://doi.org/10.3997/2214-4609.201412121
Rognmo, A. U., Horjen, H., & Fernø, M. A. (2017). Nanotechnology for improved CO2 utilization in CCS: Laboratory study of CO2-foam flow and silica nanoparticle retention in porous media. International Journal of Greenhouse Gas Control, 64, 113–118. https://doi.org/10.1016/j.ijggc.2017.07.010
Rognmo, A. U., Al-Khayyat, N., Heldal, S., Vikingstad, I., Eide, Ø., et al (2020). Performance of silica nanoparticles in co2 foam for EOR and CCUS at tough reservoir conditions. SPE Journal, 25(01), 406–415. https://doi.org/10.2118/191318-PA
Sameni, A., Pourafshary, P., Ghanbarzadeh, M., & Ayatollahi, S. (2015). Effect of nanoparticles on clay swelling and migration. Egyptian Journal of Petroleum, 24(4), 429–437. https://doi.org/10.1016/j.ejpe.2015.10.006
Sharma, M. M., & Yortsos, Y. C. (1987). Transport of particulate suspensions in porous media: Model formulation. AIChE Journal, 33(10), 1636–1643. https://doi.org/10.1002/aic.690331007
Simjoo, M. ., Dong, Y. ., Andrianov, A. ., Talanana, M. ., & Zitha, P. L. J. . L. J. (2013). Novel insight into foam mobility control. SPE Journal, 18(03), 416–427. https://doi.org/10.2118/163092-PA
Simjoo, M., & Zitha, P. L. J. (2015). Modeling of foam flow using stochastic bubble population model and experimental validation. Transport in Porous Media, 107(3), 799–820. https://doi.org/10.1007/s11242-015-0468-y
Singh, R., & Mohanty, K. K. (2015). Synergy between nanoparticles and surfactants in stabilizing foams for oil recovery. Energy & Fuels, 29(2), 467–479. https://doi.org/10.1021/ef5015007
Sun, Q., Li, Z., Li, S., Jiang, L., Wang, J., & Wang, P. (2014). Utilization of surfactant-stabilized foam for enhanced oil recovery by adding nanoparticles. Energy & Fuels, 28(4), 2384–2394. https://doi.org/10.1021/ef402453b
Sun, Q., Liu, W., Li, S., Zhang, N., & Li, Z. (2021). Interfacial rheology of foam stabilized by nanoparticles and their retention in porous media. Energy & Fuels, 35(8), 6541–6552. https://doi.org/10.1021/acs.energyfuels.0c03680
Tang, J., Castañeda, P., Marchesin, D., & Rossen, W. R. (2019). Three‐phase fractional‐flow theory of foam‐oil displacement in porous media with multiple steady states. Water Resources Research, 55(12), 10319–10339. https://doi.org/10.1029/2019WR025264
Tufenkji, N., & Elimelech, M. (2004). Deviation from the classical colloid filtration theory in the presence of repulsive DLVO interactions. Langmuir, 20(25), 10818–10828. https://doi.org/10.1021/la0486638
Wang, Y., Li, Y., Fortner, J. D., Hughes, J. B., Abriola, L. M., & Pennell, K. D. (2008). Transport and retention of nanoscale c60 aggregates in water-saturated porous media. Environmental Science & Technology, 42(10), 3588–3594. https://doi.org/10.1021/es800128m
Yekeen, N., Idris, A. K., Manan, M. A., Samin, A. M., Risal, A. R., & Kun, T. X. (2017). Bulk and bubble-scale experimental studies of influence of nanoparticles on foam stability. Chinese Journal of Chemical Engineering, 25(3), 347–357. https://doi.org/10.1016/j.cjche.2016.08.012
Yekeen, N., Manan, M. A., Idris, A. K., Padmanabhan, E., Junin, R., Samin, A. M., Gbadamosi, A. O., & Oguamah, I. (2018). A comprehensive review of experimental studies of nanoparticles-stabilized foam for enhanced oil recovery. Journal of Petroleum Science and Engineering, 164, 43–74. https://doi.org/10.1016/j.petrol.2018.01.035
Yu, H., Kotsmar, C., Yoon, K. Y., Ingram, D. R., Johnston, K. P., Bryant, S. L., & Huh, C. (2010). Transport and retention of aqueous dispersions of paramagnetic nanoparticles in reservoir rocks. SPE Improved Oil Recovery Symposium, SPE-129887-MS. https://doi.org/10.2118/129887-MS
Zavala, R. Q., Lozano, L. F., Zitha, P. L. J., & Chapiro, G. (2022). Analytical solution for the population-balance model describing foam displacement. Transport in Porous Media, 144(1), 211–227. https://doi.org/10.1007/s11242-021-01589-z
Zeinijahromi, A., Farajzadeh, R., (Hans) Bruining, J., & Bedrikovetsky, P. (2016). Effect of fines migration on oil–water relative permeability during two-phase flow in porous media. Fuel, 176, 222–236. https://doi.org/10.1016/j.fuel.2016.02.066
Zhang, T. (2012). Modeling of nanoparticle transport in porous media. PhD thesis, The University of Texas at Austin. http://hdl.handle.net/2152/ETD-UT-2012-08-6044
Zhang, T., Murphy, M., Yu, H., Huh, C., & Bryant, S. L. (2016). Mechanistic model for nanoparticle retention in porous media. Transport in Porous Media, 115(2), 387–406. https://doi.org/10.1007/s11242-016-0711-1
Zhang, T., Murphy, M. J., Yu, H., Bagaria, H. G., Yoon, K. Y., Neilson, B. M., Bielawski, C. W., Johnston, K. P., Huh, C., & Bryant, S. L. (2015). Investigation of nanoparticle adsorption during transport in porous media. SPE Journal, 20(04), 667–677. https://doi.org/10.2118/166346-PA
Zitha, P. L. J., & Du, D. X. (2010). A new stochastic bubble population model for foam flow in porous media. Transport in Porous Media, 83(3), 603–621. https://doi.org/10.1007/s11242-009-9462-6

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Copyright (c) 2025 Tatiana Danelon, Rouhi Farajzadeh, Pavel Bedrikovetsky, Grigori Chapiro

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Shell Brasil
Grant numbers ANP 23518-4 -
Conselho Nacional de Desenvolvimento Científico e Tecnológico
Grant numbers 306970/2022-8;405366/2021-3 -
Fundação de Amparo à Pesquisa do Estado de Minas Gerais
Grant numbers APQ-00206-24