A Review on Fundamentals and Capturing Petroleum Fluid Hysteresis Through Experiments
Abstract - 161
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Keywords

Viscosity
Hysteresis
Wettability
Capillary pressure
Interfacial tension

How to Cite

1.
Elhaj M. A Review on Fundamentals and Capturing Petroleum Fluid Hysteresis Through Experiments. Int. J. Petrol. Technol. [Internet]. 2023 Sep. 7 [cited 2024 Feb. 22];10:39-52. Available from: https://avantipublishers.com/index.php/ijpt/article/view/1411

Abstract

Hysteresis is proven to have a significant role in petroleum fluids and other disciplines for better understanding and evaluation. This shows a need to be explicit about precisely what is meant by the word "hysteresis." For a long time, the term hysteresis has been used and has attracted the attention of most researchers and investigators. Despite its common usage, hysteresis is used in different disciplines to mean different things. Thus, hysteresis has many definitions depending on the book or paper's area of interest. While various definitions of the term 'hysteresis' have been suggested, this paper will focus on the definition in the oil and gas industry. Hysteretic impacts petroleum fluids either positively or negatively. Therefore, accurately estimating fluid properties curves is vital in evaluating hydrocarbon recovery processes. This paper addresses and discusses a comprehensive review of the hysteresis of different petroleum fluid properties and their applications. This paper reviews many fluid properties of hysteresis and investigates them experimentally. Numerous laboratory studies in hysteresis are present in the literature and critically reviewed and highlighted in this research. This paper aims to review the experimental processes of fluid hysteresis extensively. To satisfy this aim, this paper offers insights into and explanations for experiments that have been used in fluid hysteresis. The outcomes highlight some missing concepts of the existing models and experimental processes for fluid hysteresis. Furthermore, this paper tracks the current development of hysteresis and gives insight into the future trends in the application of hysteresis.

https://doi.org/10.15377/2409-787X.2023.10.4
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References

Mayergoyz I. Mathematical models of hysteresis and their application. Elsevier Inc. 1986; 22: 603-8. https://doi.org/10.1109/TMAG.1986.1064347

Cross R, Grinfeld M, Lamba H. Hysteresis and economics. IEEE Control Syst. 2009; 29: 30-43. https://doi.org/10.1109/MCS.2008.930445

Noori HR. Hysteresis phenomena in biology. Springer; Heidelberg: 2014. https://doi.org/10.1007/978-3-642-38218-5

Paska Y, Haick H. Interactive effect of hysteresis and surface chemistry on gated silicon nanowire gas sensors. ACS Appl Mater Interfaces. 2012; 4: 2604-17. https://doi.org/10.1021/am300288z

Mielke A, Theil F. A mathematical model for rate-independent phase transformations with hysteresis. Universit at Hannover Welfengarten, 1999.

Wheeler SJ, Sharma RS, Buisson MSR. Coupling of hydraulic hysteresis and stress–strain behaviour in unsaturated soils. Géotechnique. 2003; 53: 41-54. https://doi.org/10.1680/geot.2003.53.1.41

Lotfollahi M, Kim I, Beygi MR, Worthen AJ, Huh C, Johnston KP, et al. Experimental studies and modeling of foam hysteresis in porous media. SPE Improved Oil Recovery Conference, Tulsa, Oklahoma, USA, April 2016, SPE-179664-MS. https://doi.org/10.2118/179664-MS

Teklu TW, Zhou Z, Li X, Abass H. Cyclic permeability and porosity hysteresis in mudrocks - Experimental study. 50th US Rock Mechanics / Geomechanics Symposium June 26-29, 2016, Houston: 2016, ARMA-2016-108.

Spiteri EJ, Juanes R. Impact of relative permeability hysteresis on the numerical simulation of WAG injection. J Pet Sci Eng. 2006; 50: 115–39. https://doi.org/10.1016/j.petrol.2005.09.004

Fatemi SM, Sohrabi M. Experimental and theoretical investigation of water/gas relative permeability hysteresis: Applicable to water alternating gas (WAG) injection and gas storage processes. Abu Dhabi International Petroleum Exhibition and Conference November 11–14, 2012, Abu Dhabi: SPE; 2012; SPE-161827-MS. https://doi.org/10.2118/161827-MS

Elhaj M, Imtiaz SA, Naterer GF, Zendehboudi S. Production Optimization of Hydrocarbon Reservoirs by Entropy Generation Minimization. J Nat Gas Sci Eng. 2020; 83: 103538. https://doi.org/10.1016/j.jngse.2020.103538.

Elhaj MA, Imtiaz SA, Naterer GF, Zendehboudi S. Entropy Generation Minimization of Two-Phase Flow Irreversibilities in Hydrocarbon Reservoirs. Energies (Basel), 2023; 16(10): 4096. https://doi.org/10.3390/en16104096.

Elhaj MA, Enamul Hossain M, Imtiaz SA, Naterer GF. Hysteresis of wettability in porous media: a review. J Pet Explor Prod Technol. 2020; 10: 1897-905. https://doi.org/10.1007/s13202-020-00872-x

Elhaj MA, Miah MI, Hossain ME. State-of-the-art on capillary pressure hysteresis: Productive techniques for better reservoir performance. Upstream Oil Gas Technol. 2021; 7: 100040. https://doi.org/10.1016/j.upstre.2021.100040

Jang H, Lee J, Han Lee J, Seo S, Park B-G, Myong Kim D, et al. Analysis of hysteresis characteristics of silicon nanowire biosensors in aqueous environment. Appl Phys Lett. 2011; 99: 1–4. https://doi.org/10.1063/1.3669409

Kawashima T, Saitoh T, Komori K, Fujii M. Synthesis of Si nanowires with a thermally oxidized shell and effects of the shell on transistor characteristics. Thin Solid Films. 2009; 517: 4520-6. https://doi.org/10.1016/j.tsf.2008.12.042

Elhaj MA, Hashan M, Hossain ME. A critical review and future trend on relative permeability hysteresis. Society of Petroleum Engineers June 25–26, 2018; SPE-191260-MS. https://doi.org/10.2118/191260-MS

Elhaj MA, Barri A, Hashan M, Hossain ME. State of the art on porosity and permeability hysteresis: Useful techniques for hydrocarbon recovery. Society of Petroleum Engineers - SPE Kingdom of Saudi Arabia Annual Technical Symposium and Exhibition 2018, Dammam: 2018, SPE-192409-MS. https://doi.org/10.2118/192409-MS

Elhaj MA, Enamul Hossain M, Imtiaz SA, Naterer GF. Hysteresis of wettability in porous media: a review. J Pet Explor Prod Technol 2020; 10: 1897-905. https://doi.org/10.1007/s13202-020-00872-x

Hashan M, Jahan LN, Uz Zaman T, Elhaj M, Imtiaz S, Hossain ME. Modelling of fluid flow in a petroleum reservoir using an engineering approach. SPE Trinidad and Tobago Section Energy Resources Conference 25-26 June, Port of Spain, Trinidad and Tobago: 2018, SPE-191153-MS. https://doi.org/10.2118/191153-MS

Ahmadzadeh PH, Masihi M, Al-Ajmi A, Al-Wahaibi T, Al-Wahaibi Y. Experimental study of the effects of IFT and hysteresis on resistivity and capillary pressure of carbonate rocks. Energy Sources, Part A: Recovery, Utilization, and Environmental Effects. 2015; 37: 1346-53. https://doi.org/10.1080/15567036.2011.567232

Heriot-watt MS. Cyclic hysteresis of three-phase relative permeability curves applicable to WAG injection under low gas/oil IFT: Effect of immobile water saturation, injection scenario and rock permeability. EAGE Annual Conference & Exhibition incorporating SPE Europec June 10–13, 2013, London: 2013; SPE-164918-MS. https://doi.org/10.2118/164918-MS

Okazawa T, Serres AJ, Rancier DG, Corry KE. Novel push-pull displacement method to determine relative permeability hysteresis in heavy oil reservoirs. SPE Annual Technical Conference and Exhibition September 30–October 3, 2001, New Orleans: 2001; SPE-71501-MS. https://doi.org/10.2118/71501-MS

Teklu TW, Zhou Z, Li X, Abass H. Experimental investigation on permeability and porosity hysteresis in low-permeability formations. The SPE Low Perm Symposium held in Denver May 5–6, 2016, Denver: 2016; SPE-180226-MS. https://doi.org/10.2118/180226-MS

Morris KA. What is hysteresis? Appl Mech Rev. 2011; 64(5): 050801. https://doi.org/10.1115/1.4007112

Morrow NR, Cram PJ, McCaffery FG. Displacement studies in dolomite with wettability control by octanoic acid. Soc Pet Eng J. 1973; 13: 221-32. https://doi.org/10.2118/3993-PA

Fatemi SM, Sohrabi M, Jamiolahmady M, Ireland S. Experimental and theoretical investigation of gas/oil relative permeability hysteresis under low oil/gas interfacial tension and mixed-wet conditions. Energy Fuels. 2012; 26: 4366-82. https://doi.org/10.1021/ef300386b

Shahverdi H, Sohrabi M. An improved three-phase relative permeability and hysteresis model for the simulation of a water-alternating-gas injection. SPE J. 2013; 18: 841-50. https://doi.org/10.2118/152218-PA

Sinha S, Braun EM, Determan MD, Passey QR, Leonardi SA, Boros JA, et al. Steady-state permeability measurements on intact shale samples at reservoir conditions - Effect of stress, temperature, pressure, and type of gas. SPE Middle East Oil and Gas Show and Conference March 10–13, 2013, Manama: 2013; SPE-164263-MS. https://doi.org/10.2118/164263-MS

Shahrokhi O, Fatemi M, Sohrabi M, Ireland S, Ahmed K, et al. Assessment of three phase relative permeability and hysteresis models for simulation of water-alternating-gas WAG injection in water-wet and mixed-wet systems. SPE Improved Oil Recovery Symposium April 12–16, Tulsa: 2014; SPE-169170-MS. https://doi.org/10.2118/169170-MS

Total SA. Comparison of history-matched water flood, tertiary polymer flood relative permeabilities and evidence of hysteresis during tertiary polymer flood in very viscous oils. Society of Petroleum Engineers - SPE Asia Pacific Enhanced Oil Recovery Conference, EORC 2015, Tulsa: 2015; SPE-174682-MS. https://doi.org/10.2118/174682-ms

Miah MI, Elhaj MA, Ahmed S, Hossain ME. Modeling of temperature distribution and oil displacement during thermal recovery in porous media: A critical review. Fuel 2018; 226: 423-40. https://doi.org/10.1016/j.fuel.2018.04.018

Zhu H. View of study on the influence law of temperature profile of water injection well. Int J Pet Technol. 2023; 10: 1-13.

Hansong M, Luo H, Haitao L, Yuxing X, Qin Z, Ying L. Study on the influence law of temperature profile of vertical wells in gas reservoirs. Int J Pet Technol. 2022; 9: 54-66. https://doi.org/10.15377/2409-787X.2022.09.7

Van Geel PJ, Sykes JF. The importance of fluid entrapment, saturation hysteresis and residual saturations on the distribution of a lighter-than-water non-aqueous phase liquid in a variably saturated sand medium. J Contam Hydrol. 1997; 25: 249-70. https://doi.org/10.1016/S0169-7722(96)00038-1

Fatemi SM, Sohrabi M, Jamiolahmady M, Ireland S. Cyclic hysteresis in three-phase relative permeability applicable to WAG injection: Water-wet and mixed-wet systems under low gas/oil IFT. SPE Annual Technical Conference and Exhibition, San Antonio: 2012; SPE-159816-MS. https://doi.org/10.2118/159816-MS

Irmak AE, Taşarkuyu E, Coşkun A, Acet M, Samancioʇlu Y. Magnetic and electrical transport properties of La0.65Ca0.30Pb0.05Mn0.90Cu0.10O3 compounds: Thermal hysteresis. Physica B Condens Matter. 2015; 411: 56-63. https://doi.org/10.1016/j.physb.2015.04.027

Longbiao L. Effects of loading type, temperature and oxidation on mechanical hysteresis behavior of carbon fiber-reinforced ceramic-matrix composites. Eng Fract Mech. 2017; 169: 336-53. https://doi.org/10.1016/j.engfracmech.2016.10.010

Angeli D, Ferrell JE, Sontag ED. Detection of multistability, bifurcations, and hysteresis in a large class of biological positive-feedback systems. Proc Natl Acad Sci. 2004; 101: 1822-7. https://doi.org/10.1073/pnas.0308265100

Chatterjee A, Kaznessis YN, Hu W-S. Tweaking biological switches through a better understanding of bistability behavior. Curr Opin Biotechnol. 2008; 19: 475-81. https://doi.org/10.1016/j.copbio.2008.08.010

Qiao L, Nachbar RB, Kevrekidis IG, Shvartsman SY. Bistability and oscillations in the Huang-Ferrell model of MAPK signaling. PLoS Comput Biol. 2007; 3: 1819-26. https://doi.org/10.1371/journal.pcbi.0030184

Georgescu-Roegen N. The Entropy Law and the Economic Process. vol. 10. Cambridge: Harvard University Press; 1985. https://doi.org/10.4159/harvard.9780674281653

Gocke M. Various concepts of hysteresis applied in economics. J Econ Surv. 2002; 16: 167-88. https://doi.org/10.1111/1467-6419.00163

DelMonte DW, Kim T. Anatomy and physiology of the cornea and related structures. J Cataract Refract Surg. 2011; 37: 588-98. https://doi.org/10.1016/j.jcrs.2010.12.037

Wang X. Effects of low-salinity waterflooding on capillary pressure hysteresis. SPE Improved Oil Recovery Conference, Tulsa: 2016; SPE-179562-MS. https://doi.org/10.2118/179562-MS

Kleppe J, Delaplace P, Lenormand R, Hamon G, Chaput E. Representation of capillary pressure hysteresis in reservoir simulation. Proceedings of the SPE Annual Meeting, San Antonio: 1997; SPE-38899-MS. https://doi.org/10.2118/38899-MS

Bouchard AJ, Hawkins JT. Reservoir-engineering implications of capillary-pressure and relative-permeability hysteresis. Log Analyst. 1992; 33: 415–20.

Brown HW. Capillary pressure investigations. J Pet Technol. 1951; 3: 67–74. https://doi.org/10.2118/951067-G

Jain V, Bryant S, Sharma M. Influence of wettability and saturation on liquid-liquid interfacial area in porous media. Environ Sci Technol. 2003; 37: 584–91. https://doi.org/10.1021/es020550s

Braun EM, Holland RF. Relative permeability hysteresis: Laboratory measurements and a conceptual model. SPE Reser Eng. 1995; 10: 222-8. https://doi.org/10.2118/28615-PA

Carlson FM. Simulation of relative permeability hysteresis to the nonwetting phase. SPE Annual Technical Conference and Exhibition October 4–7, 1981, San Antonio, Texas: October 1981; SPE-10157-MS. https://doi.org/10.2118/10157-MS

Denoyelle LC, Lemonnier P. Simulation Of CO2 huff “n” puff using relative permeability hysteresis. The 62nd Annual Technical Conference and Exhibition of the Society of Petroleum Engineers September 27–30, Dallas: 1987; SPE-16710-MS. https://doi.org/10.2118/16710-MS

Benner FC, Dodd CG, Bartell FE. Evaluation of effective displacement pressures for petroleum oil-water silica systems. In: Drilling and Production Practice, New York: 1942; p.169-77.

Bedrikovetsky P, Marchesin D, Oil MS, Academy G. Mathematical model for immiscible displacement honouring hysteresis. SPE Latin America/Caribbean Petroleum Engineering Conference, April 23-26, 1996. Port-of-Spain, Trinidad: SPE-36132-MS. https://doi.org/10.2118/36132-MS

Mantia MRTRW, Fegley E. Prediction of hysteresis performance of storage reservoirs. SPE Gas Technology Symposium March 15-18, Calgary, Alberta, Canada: 1998. SPE-39992-MS. https://doi.org/10.2118/39992-MS

Al-Kaabi AU, Mimoune K, Al-Yousef HY. Effect of hysteresis on the Archie saturation exponent. Middle East Oil Show and Conference March 15-18, Bahrain: 1997, SPE-37738-MS. https://doi.org/10.2118/37738-ms

Nguyen B-L, Bruining J, Slob EC. Hysteresis in dielectric properties of fluid-saturated porous media. SPE Asia Pacific Improved Oil Recovery Conference October 25-26, Kuala Lumpur: 1999; SPE-57305-MS. https://doi.org/10.2118/57305-MS

Kossack CA. Comparison of reservoir simulation hysteresis options. SPE Annual Technical Conference and Exhibition October 1-4, Dallas: 2000, SPE-63147-MS. https://doi.org/10.2118/63147-MS

Bartell FE, Cardwell PH. Reproducible contact angles on reproducible metal surfaces. I. Contact angles of water against silver and gold1. J Am Chem Soc. 1942; 64: 494-7. https://doi.org/10.1021/ja01255a007

Denney D. Relative permeability hysteresis: Water-alternating-gas injection and gas storage. J Pet Technol. 2013; 65: 90–2. https://doi.org/10.2118/0813-0090-JPT

Michaels AS, Lummis RC. Contact angle hysteresis on aquagels. AIChE/SPE Joint Symposium on Wetting and Capillarity in Fluid Displacement Processes May 17-20, Kansas City, Missouri, USA: 1959, SPE-1274-G. https://doi.org/10.2118/1274-G

Grundke K, Pöschel K, Synytska A, Frenzel R, Drechsler A, Nitschke M, et al. Experimental studies of contact angle hysteresis phenomena on polymer surfaces — Toward the understanding and control of wettability for different applications. Adv Colloid Interface Sci. 2015; 222: 350–76. https://doi.org/10.1016/j.cis.2014.10.012

Extrand CW. Contact angles and their hysteresis as a measure of liquid-solid adhesion. Langmuir. 2004; 20: 4017–21. https://doi.org/10.1021/la0354988

Gao L, McCarthy TJ. Contact angle hysteresis explained. Langmuir. 2006; 22: 6234–7. https://doi.org/10.1021/la060254j

Extrand CW. Model for contact angles and hysteresis on rough and ultraphobic surfaces. Langmuir. 2002; 18: 7991–9. https://doi.org/10.1021/la025769z

Extrand CW. Contact angles and hysteresis on surfaces with chemically heterogeneous islands. Langmuir. 2003; 19: 3793–6. https://doi.org/10.1021/la0268350

Reyssat M, Quéré D. Contact angle hysteresis generated by strong dilute defects. J Phys Chem B. 2009; 113: 3906–9. https://doi.org/10.1021/jp8066876

Moradi S, Englezos P, Hatzikiriakos SG. Contact angle hysteresis of non-flattened-top micro/nanostructures. Langmuir. 2014; 30: 3274–84. https://doi.org/10.1021/la500277n

Restagno F, Poulard C, Cohen C, Vagharchakian L, Léger L. Contact angle and contact angle hysteresis measurements using the capillary bridge technique. Langmuir. 2009; 25: 11188–96. https://doi.org/10.1021/la901616x

Gardner GHF, Acheson WP. Dynamic measurements of capillary pressure. SPE Production Research Symposium April 12-13, Tulsa, Oklahoma: 1962, SPE-301-MS. https://doi.org/10.2118/301-MS

Omoregie ZS. Factors affecting the equivalency of different capillary pressure measurement techniques. SPE Formation Evaluation. 1988; 3: 147–55. https://doi.org/10.2118/15384-PA

Dernaika M, Bjorn Wilson O, M. Skjæveland S. Drainage capillary pressure and resistivity index from short-wait porous plate experiments. European Association of Geoscientists & Engineers; GEO 2010, Mar 2010, cp-248-00221. https://doi.org/10.3997/2214-4609-pdb.248.224

Kee ST, Lee SH, Park WT. Submerged porous plate wave absorber. Proceedings of the 31st IAHR World Congress September 11-16, Seoul: 2005 p. 595–9.

Wang X, Alvarado V. Analysis of capillary pressure and relative permeability hysteresis under low-salinity waterflooding conditions. Fuel. 2016; 180: 228–43. https://doi.org/10.1016/j.fuel.2016.04.039

Masalmeh SK. Experimental measurements of capillary pressure and relative permeability hysteresis. Paper SCA. 2001; 23: 17–9.

Purcell WR. Interpretation of capillary pressure data. J Pet Technol. 1950; 2: 369-71. https://doi.org/10.2118/950369-G

Cao X, Pop IS. Two-phase porous media flows with dynamic capillary effects and hysteresis: Uniqueness of weak solutions. Comput Math Appl. 2015; 69: 688–95. https://doi.org/10.1016/j.camwa.2015.02.009

Ajufo AO, Daneshjou DH, Warne JD. Capillary pressure characteristics at overburden pressure using the centrifuge method. SPE Gas Technology Symposium June 28-30, Calgary, Alberta, Canada: 1993, SPE-26148-MS. https://doi.org/10.2118/26148-MS

Van Spronsen E. Three-phase relative permeability measurements using the centrifuge method. SPE Enhanced Oil Recovery Symposium April 4-7, Tulsa, Oklahoma, 1982, SPE-10688-MS. https://doi.org/10.2118/10688-MS

Paper T, Subject IS, Correction TO. The effects of sulfonate molecular and salt concentration on the interfacial tension of oil -brine-surfactant systems by. Society of Petroleum Engineers, 1976.

Hough EW, Rzasa MJ, Wood BB, Oil S, Co G. Interfacial tensions at reservoir pressures and temperatures; Apparatus and the water-methane system. J Pet Trans. 1951; 3: 57-60. https://doi.org/10.2118/951057-G

Chimienti ME, Illiano SN, Najurieta HL. Influence of temperature and interfacial tension on spontaneous imbibition process. SPE Latin American and Caribbean Petroleum Engineering Conference Proceedings April 21–23, Caracas, Venezuela: 1999, SPE-53668-MS. https://doi.org/10.2118/53668-ms

Ghorbani M, Mohammadi AH. Effects of temperature, pressure and fluid composition on hydrocarbon gas - oil interfacial tension (IFT): An experimental study using ADSA image analysis of pendant drop test method. J Mol Liq. 2017; 227: 318–23. https://doi.org/10.1016/j.molliq.2016.11.110

Peltonen LJ, Yliruusi J. Surface pressure, hysteresis, interfacial tension, and CMC of four sorbitan monoesters at water–air, water–hexane, and hexane–air interfaces. J Colloid Interface Sci. 2000; 227: 1–6. https://doi.org/10.1006/jcis.2000.6810

Jubb G, McCurrie R. Hysteresis and magnetic viscosity in a Nd-Fe-B permanent magnet. IEEE Trans Magn. 1987; 23: 1801–5. https://doi.org/10.1109/TMAG.1987.1065064

Stamps RL. Dynamic magnetic hysteresis and anomalous viscosity in exchange bias systems. Phys Rev B. 2000; 61: 12174–80. https://doi.org/10.1103/PhysRevB.61.12174

Murshed SMS, Estellé P. A state of the art review on viscosity of nanofluids. Renew Sustain Energy Rev. 2017; 76: 1134–52. https://doi.org/10.1016/j.rser.2017.03.113

Nguyen CT, Desgranges F, Roy G, Galanis N, Maré T, Boucher S, et al. Temperature and particle-size dependent viscosity data for water-based nanofluids – Hysteresis phenomenon. Int J Heat Fluid Flow. 2007; 28: 1492–506. https://doi.org/10.1016/j.ijheatfluidflow.2007.02.004

Nguyen CT, Desgranges F, Galanis N, Roy G, Maré T, Boucher S, et al. Viscosity data for Al2O3–water nanofluid—hysteresis: is heat transfer enhancement using nanofluids reliable? Int J Thermal Sci. 2008; 47: 103–11. https://doi.org/10.1016/j.ijthermalsci.2007.01.033

Daungthongsuk W, Wongwises S. A critical review of convective heat transfer of nanofluids. Renew Sustain Energy Rev. 2007; 11: 797-817. https://doi.org/10.1016/j.rser.2005.06.005

Chein R, Huang G. Analysis of microchannel heat sink performance using nanofluids. Appl Therm Eng. 2005; 25: 3104–14. https://doi.org/10.1016/j.applthermaleng.2005.03.008

Maïga SEB, Palm SJ, Nguyen CT, Roy G, Galanis N. Heat transfer enhancement by using nanofluids in forced convection flows. Int J Heat Fluid Flow. 2005; 26: 530–46. https://doi.org/10.1016/j.ijheatfluidflow.2005.02.004

El Bécaye Maïga S, Tam Nguyen C, Galanis N, Roy G, Maré T, Coqueux M. Heat transfer enhancement in turbulent tube flow using Al2O3 nanoparticle suspension. Int J Numer Methods Heat Fluid Flow. 2006; 16: 275–92. https://doi.org/10.1108/09615530610649717

Palm SJ, Roy G, Nguyen CT. Heat transfer enhancement with the use of nanofluids in radial flow cooling systems considering temperature-dependent properties. Appl Therm Eng. 2006; 26: 2209-18. https://doi.org/10.1016/j.applthermaleng.2006.03.014

Cho YI. Hydrodynamic and heat transfer study of dispersed fluid with submicron metallic oxide particles. Exp Heat Transf. 1998; 11: 151–70. https://doi.org/10.1080/08916159808946559

Xuan Y, Li Q. Investigation on convective heat transfer and flow features of nanofluids. J Heat Transf. 2003; 125: 151-5. https://doi.org/10.1115/1.1532008

Walz M, Wolff M, Voss N, Zabel H, Magerl A. Micellar crystallization with a hysteresis in temperature. Langmuir. 2010; 26: 14391-s4. https://doi.org/10.1021/la102415x

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