Estimating Aqueous Nanofluids Viscosity via GEP Modeling: Correlation Development and Data Assessment

Document Type : Research Article


1 Department of Petroleum Engineering, Amirkabir University of Technology (AUT), P.O. Box 158754413 Tehran, I.R. IRAN

2 Department of Petroleum Engineering, Petroleum University of Technology (PUT), P.O. Box 6198144471 Ahwaz, I.R. IRAN

3 Department of Chemical and Petroleum Engineering, Sharif University of Technology, P.O. Box 113659465 Tehran, I.R. IRAN


This study focuses on developing a new method that represents user-accessible correlation for the estimation of water-based nanofluids viscosity. For this, an evolutionary algorithm, namely Gene Expression Programming (GEP), was adapted based on a wide selection of literature published databanks including 819 water-based nanofluids viscosity points. The developed model utilized the base fluid viscosity as well as volume fraction and size of the nanoparticles as the inputs of the model. Several statistical parameters integrated with graphical plots were employed in order to assess the accuracy of the proposed GEP-based model. Results of the evaluation demonstrate fairly enough accuracy of the developed model with statistical parameters of AARD%=11.7913, RMSE=0.3567, and SD=0.1851. Furthermore, the trend analysis indicates that the GEP calculated points satisfactorily follow the trend of the nanofluid viscosity variation as a function of different model inputs. To provide more verification, the proposed GEP model was compared with some literature theoretical and empirical correlations leading to the supremacy of the developed model here. The applied sensitivity analysis reveals that the highest impact value is assigned to the volume fraction of the nanoparticle. Moreover, the outlier’s detection by Williams’ technique illustrates that about 96.5% of the GEP estimates are in the applicability domain resulting in the validity of the proposed model in this study. At last, the results of this study demonstrate that the new method here outperforms other literature-published correlations from the standpoint of accuracy and reliability.


Main Subjects

[1] Meybodi M.K., Daryasafar A., Koochi M.M., Moghadasi J., Meybodi R.B., Ghahfarokhi A.K., A Novel Correlation Approach for Viscosity Prediction of Water Based Nanofluids of Al2O3, TiO2, SiO2 and CuO, Journal of the Taiwan Institute of Chemical Engineers, 58: 19-27 (2016).
[2] Soleimani H., Baig M.K., Yahya N., Khodapanah L., Sabet M., Demiral B.M.R., et al., Impact of Carbon Nanotubes Based Nanofluid on Oil Recovery Efficiency Using Core Flooding, Results in Physics, 9:39-48 (2018).
[3] Gharibshahi R., Jafari A., Numerical Investigation of controllable Parameters effect on Nanofluid Flooding in a Random Pore Generated Porous Medium. Iranian Journal of Chemistry and Chemical Engineering (IJCCE), 40(3): 780-795 (2021).
[4] Moghadasi R., Rostami A., Hemmati-Sarapardeh A., Application of Nanofluids for Treating Fines Migration During Hydraulic Fracturing: Experimental Study and Mechanistic Understanding. Advances in Geo-Energy Research, 3(2):198-206 (2019).
[5] Moghadasi R., Rostami A., Tatar A., Hemmati-Sarapardeh A., An Experimental Study of Nanosilica Application in Reducing Calcium Sulfate Scale at High Temperatures During High and Low Salinity Water Injection, Journal of Petroleum Science and Engineering, 179: 7-18 (2019).
[6] Moghaddaszadeh N., Esfahani J.A., Mahian O., Performance Enhancement of Heat Exchangers Using Eccentric Tape Inserts and Nanofluids, Journal of Thermal Analysis and Calorimetry, 137(3):865-877 (2019).
[7] Motahari K., Barati S., Optimization of Nusselt Number of Al2O3/Water Nanofluid Using Response Surface Methodology, Iranian Journal of Chemistry and Chemical Engineering (IJCCE), 38(3):309-317 (2019).
[8] Aghajanzadeh M.R., Ahmadi P., Sharifi M., Riazi M., Wettability Alteration of Oil-Wet Carbonate Reservoir Using Silica-Based Nanofluid: an Experimental Approach, Journal of Petroleum Science and Engineering (2019).
[9] Ali N., Teixeira J..A., Addali A., A Review on Nanofluids: Fabrication, Stability, and Thermophysical Properties. Journal of Nanomaterials (2018).
[10] Choi S.U, Eastman J.A., "Enhancing Thermal conductivity of Fluids with Nanoparticles”. Argonne National Lab., IL (United States) (1995).
[11] Bashirnezhad K., Bazri S., Safaei M.R., Goodarzi M., Dahari M., Mahian O., et al. Viscosity of Nanofluids: a Review of Recent Experimental Studies, International Communications in Heat and Mass Transfer, 73: 114-123 (2016).
[12] Gupta N.K., Tiwari A.K., Ghosh S.K., Heat Transfer Mechanisms in Heat Pipes Using Nanofluids– A Review, Experimental Thermal and Fluid Science, 90:84-100 (2018).
[13] Jana S., Salehi-Khojin A., Zhong W-H., Enhancement of Fluid Thermal Conductivity by the Addition of Single and Hybrid Nano-Additives, Thermochimica Acta, 462(1-2): 45-55 (2007).
[14] Heidari E., Sobati M.A., Movahedirad S., Accurate Prediction of Nanofluid Viscosity Using a Multilayer Perceptron Artificial Neural Network (MLP-ANN). Chemometrics and Intelligent Laboratory Systems, 155: 73-85 (2016).
[15] Murshed S.S., Estellé P., A State of the Art Review on Viscosity of Nanofluids, Renewable and Sustainable Energy Reviews, 76: 1134-1152 (2017).
[16] Mishra P.C., Mukherjee S., Nayak S.K., Panda A., A Brief Review on Viscosity of Nanofluids, International Nano Letters, 4(4):109-120 (2014).
[17] Anoop K., Sundararajan T., Das S.K., Effect of Particle Size on the Convective Heat Transfer in Nanofluid in the Developing Region, International Journal of Heat and Fluid Flow, 52(9-10): 2189-2195 (2009).
[18] Das S.K., Putra N., Roetzel W., Pool Boiling Characteristics of Nano-Fluids. International Journal of Heat and Fluid Flow, 46(5):851-862 (2003).
[19] Hadadian M., Samiee S., Ahmadzadeh H., Goharshadi E.K., Nanofluids for Heat Transfer Enhancement – A Review, Physical Chemistry Research, 1(1):1-33 (2013).
[20] Duan F., Kwek D., Crivoi A., Viscosity Affected by Nanoparticle Aggregation in Al2O3-Water Nanofluids, Nanoscale Research Letters, 6(1): 248 (2011).
[21] Syam Sundar L., Singh M.K., Sousa A.C.M., Investigation of Thermal Conductivity and Viscosity of Fe3O4 Nanofluid for Heat Transfer Applications, International Communications in Heat and Mass Transfer, 44: 7-14 (2013).
[22] Xian-Ju W., Xin-Fang L., Influence of pH on Nanofluids' Viscosity and Thermal Conductivity, Chinese Physics Letters, 26(5):056601 (2009).
[23] Wang X., Xu X., S. Choi S.U., Thermal Conductivity of Nanoparticle-Fluid Mixture, Journal of Thermophysics Heat Transfer, 13(4):474-480 (1999).
[24] Abareshi M., Sajjadi S.H., Zebarjad S.M., Goharshadi E.K., Fabrication, Characterization, and Measurement of Viscosity of α-Fe2O3-Glycerol Nanofluids, Journal of Molecular Liquids, 163(1): 27-32 (2011).
[25] Drzazga M., Gierczycki A., Dzido G., Lemanowicz M., Influence of Nonionic Surfactant Addition on Drag Reduction of Water Based Nanofluid in a Small Diameter Pipe, Chinese Journal of Chemical Engineering, 21(1):104-108 (2013).
[26] Duangthongsuk W., Wongwises S., Measurement of Temperature-Dependent Thermal Conductivity and Viscosity of TiO2-Water Nanofluids, Experimental Thermal and Fluid Science, 33(4):706-714 (2009).
[27] Nguyen C., 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, International Journal of Heat and Fluid Flow, 28(6):1492-506 (2007).
[28] He Y., Jin Y., Chen H., Ding Y., Cang D., Lu H., Heat Transfer and Flow Behaviour of Aqueous Suspensions of TiO2 Nanoparticles (Nanofluids) Flowing Upward Through a Vertical Pipe, International Journal  of Heat and Fluid Flow, 50(11-12):2272-2281 (2007).
[29] Namburu P.K., Kulkarni D.P., Misra D., Das D.K., Viscosity of Copper Oxide Nanoparticles Dispersed in Ethylene Glycol and Water Mixture, Experimental Thermal and Fluid Science, 32(2):397-402
[30] Chevalier J., Tillement O., Ayela F., Rheological Properties of Nanofluids Flowing Through Microchannels, Applied physics letters, 91(23): 233103 (2007).
[31] Lu W-Q., Fan Q-M., Study for the Particle's Scale Effect on Some Thermophysical Properties of Nanofluids by a Simplified Molecular Dynamics Method, Engineering Analysis with Boundary Elements, 32(4):282-289 (2008).
[32] Hemmati-Sarapardeh A., Varamesh A., Husein M.M., Karan K., On the Evaluation of the Viscosity of Nanofluid Systems: Modeling and Data Assessment, Renewable and Sustainable Energy Reviews, 81: 313-29 (2018).
[33] Einstein A., Eine Neue Bestimmung Der Moleküldimensionen, Annalen der Physik, 324(2): 289-306 (1906).
[34] Brinkman H., The Viscosity of Concentrated Suspensions and Solutions, The Journal of Chemical Physics, 20(4): 571-571 (1952).
[35] Hatschek E., The General Theory of Viscosity of Two-Phase Systems, Transactions of the Faraday Society, 9: 80-92 (1913).
[36] Nielsen L.E., Generalized Equation for the Elastic Moduli of Composite Materials, Journal of Applied Physics, 41(11):4626-4627 (1970).
[37] Sundar L.S., Sharma K.V., Naik M.T., Singh M.K., Empirical and Theoretical Correlations on Viscosity of Nanofluids: A Review, Renewable and Sustainable Energy Reviews, 25:670-686 (2013).
[38] Sharma A.K., Tiwari A.K., Dixit A.R., Rheological Behaviour of Nanofluids: A Review, Renewable and Sustainable Energy Reviews, 53:779-791 (2016).
[39] Tseng W.J., Lin K-C., Rheology and Colloidal Structure of Aqueous TiO2 Nanoparticle Suspensions, Materials science engineering: A, 355(1-2): 186-192 (2003).
[40] Chandrasekar M., Suresh S., Chandra Bose A., Experimental Investigations and Theoretical Determination of Thermal Conductivity and Viscosity of Al2O3/Water Nanofluid, Experimental Thermal and Fluid Science, 34(2):210-216 (2010).
[41] Chen H., Ding Y., He Y., Tan C., Rheological Behaviour of Ethylene Glycol Based Titania Nanofluids, Chemical physics letters, 444(4-6):333-337 (2007).
[44] Saghafi H.R., Rostami A., Arabloo M., Evolving New Strategies to Estimate Reservoir Oil Formation Volume Factor: Smart Modeling and Correlation Development, Journal of Petroleum Science and Engineering, 181:106180 (2019).
[45] Rostami A., Shokrollahi A., Accurate Prediction of Water Dewpoint Temperature in Natural Gas Dehydrators Using Gene Expression Programming Approach, Journal of Molecular Liquids, 243:196-204 (2017).
[46] Rostami A., Hemmati-Sarapardeh A., Shamshirband S., Rigorous Prognostication of Natural Gas Viscosity: Smart Modeling and Comparative Study, Fuel, 222: 766-778 (2018).
[47] Rostami A., Kalantari-Meybodi M., Karimi M., Tatar A., Mohammadi A.H., Efficient Estimation of Hydrolyzed Polyacrylamide (HPAM) Solution Viscosity for Enhanced Oil Recovery Process by Polymer Flooding, Oil & Gas Sciences and Technology–Revue d’IFP Energies Nouvelles, 73 :22 (2018).
[48] Karkevandi-Talkhooncheh A., Rostami A., Hemmati-Sarapardeh A., Ahmadi M., Husein M.M., Dabir B., Modeling Minimum Miscibility Pressure During Pure and Impure CO2 Flooding Using Hybrid of Radial Basis Function Neural Network and Evolutionary Techniques, Fuel, 220:2702-2282 (2018).
[49] Dargahi-Zarandi A., Hemmati-Sarapardeh A., Shateri M., Menad N.A., Ahmadi M., Modeling Minimum Miscibility Pressure of Pure/Impure CO2-Crude Oil Systems Using Adaptive Boosting Support Vector Regression: Application to Gas Injection Processes, Journal of Petroleum Science and Engineering, 184:106499 (2020).
[50] Benamara C., Gharbi K., Nait Amar M., Hamada B., Prediction of Wax Appearance Temperature Using Artificial Intelligent Techniques, Arabian Journal for Science and Engineering, 45(2):1319-1330 (2020).
[51] Benamara C., Nait Amar M., Gharbi K., Hamada B., Modeling Wax Disappearance Temperature Using Advanced Intelligent Frameworks, Energy & Fuels, 33(11):10959-10968 (2019).
[52] Menad N.A., Noureddine Z., Hemmati-Sarapardeh A., Shamshirband S., Mosavi A., Chau K-w., Modeling Temperature Dependency of Oil-Water Relative Permeability in Thermal Enhanced Oil Recovery Processes Using Group Method of Data Handling and Gene Expression Programming, Engineering Applications of Computational Fluid Mechanics, 13(1):724-743 (2019).
[53] Nguyen C.T., 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. International Journal of Heat and Fluid Flow, 28(6):1492-506 (2007).
[54] Pastoriza-Gallego M.J., Casanova C., Legido Ja., Piñeiro M.M., CuO in Water Nanofluid: Influence of Particle Size and Polydispersity on Volumetric Behaviour and Viscosity, Fluid Phase Equilibria, 300(1-2):188-196 (2011).
[55] Pak B.C., Cho Y.I., Hydrodynamic and Heat Transfer Study of Dispersed Fluids With Submicron Metallic Oxide Particles, Experimental Heat Transfer an International Journal, 11(2):151-70 (1998).
[56] Kwek D., Crivoi A., Duan F., Effects of Temperature And Particle Size on the Thermal Property Measurements of Al2O3− Water Nanofluids, Journal of Chemical Engineering Science, 55(12):5690-5695 (2010).
[57] Tavman I., Turgut A., Chirtoc M., Schuchmann H., Tavman S., Experimental Investigation of Viscosity and Thermal Conductivity of Suspensions Containing Nanosized Ceramic Particles, Archives of Materials Science,100(100) (2008).
[58] Duangthongsuk W., Wongwises S., An Experimental Study on the Heat Transfer Performance and Pressure Drop of TiO2-Water Nanofluids Flowing under a Turbulent Flow Regime, International Journal of Heat and Mass Transfer, 53(1):334-344 (2010).
[59] Fedele L., Colla L., Bobbo S., Viscosity and Thermal Conductivity Measurements of Water-Based Nanofluids Containing Titanium Oxide Nanoparticles, International Journal of Refrigeration, 35(5):1359-1366 (2012).
[60] Pastoriza-Gallego M.J., Casanova C., Páramo R., Barbés B., Legido J.L., Piñeiro M.M., A Study on Stability and Thermophysical Properties (Density and Viscosity) of Al2O3 in Water Nanofluid, Journal of Applied Physics, 106(6):064301 (2009).
[61] Lee J-H., Hwang K.S., Jang S.P., Lee B.H., Kim J.H., Choi S.U.S., et al. Effective Viscosities and Thermal Conductivities of Aqueous Nanofluids Containing Low Volume Concentrations of Al2O3 Nanoparticles, International Journal of Heat and Mass Transfer, 51(11):2651-2656 (2008).
[62] Turgut A., Tavman I., Chirtoc M., Schuchmann H.P., Sauter C., Tavman S., Thermal Conductivity and Viscosity Measurements of Water-Based TiO2 Nanofluids, International Journal of Thermophysics, 30(4):1213-1226 (2009).
[65] Holland J., “Adaptation in Natural and Artificial Systems”, University of Michigan Press. Ann Arbor (1975).
[66] Cramer N.L., A Representation For The Adaptive Generation of Simple Sequential Programs. "Proceedings of the First International Conference on Genetic Algorithms", 183-187 (1985).
[67] Ferreira C., Gene Expression Programming: A New Adaptive Algorithm for Solving Problems, "arXiv preprint cs/0102027", (2001).
[69] Rostami A., Arabloo M., Kamari A., Mohammadi A.H., Modeling of CO2 Solubility in Crude Oil During Carbon Dioxide Enhanced Oil Recovery Using Gene Expression Programming, Fuel, 210:768-782 (2017).
[70] Rostami A., Baghban A., Mohammadi A.H., Hemmati-Sarapardeh A., Habibzadeh S., Rigorous Prognostication of Permeability of Heterogeneous Carbonate Oil Reservoirs: Smart Modeling and Correlation Development, Fuel, 236:110-123 (2019).
[71] Gramatica P., Principles of QSAR Models Validation: Internal and External, QSAR & Combinatorial Science, 26(5):694-701 (2007).
[72] Hemmati-Sarapardeh A., Ameli F., Dabir B., Ahmadi M., Mohammadi A.H., On the Evaluation of Asphaltene Precipitation Titration Data: Modeling and Data Assessment, Fluid Phase Equilibria, 415: 88-100 (2016).
[73] Goodall C.R., “13 Computation Using the QR Decomposition”. "Handbook of Statistics", Elsevier, p. 467-508 (1993).
[74] Thomas C.U., Muthukumar M., Three-Body Hydrodynamic Effects on Viscosity of Suspensions of Spheres, The Journal of Chemical Physics, 94(7): 5180-5189 (1991).
[75] Ward S., Properties of Well-Defined Suspensions of Solids in Liquids, Journal of Oil and Colour Chemists Association, 38(9):   -   (1955).
[76] Lundgren T.S., Slow Flow Through Stationary Random Beds and Suspensions of Spheres, Journal of Fluid Mechanics, 51(2): 273-299 (1972).
[77] Batchelor G., The Effect of Brownian Motion on The Bulk Stress in a Suspension of Spherical Particles, Journal of Fluid Mechanics, 83(1): 97-117 (1977).
[78] Abedian B., Kachanov M., On the Effective Viscosity of Suspensions, International Journal of Engineering Science, 48(11): 962-965 (2010).
[79] Marquardt D.W., An Algorithm for Least-Squares Estimation of Nonlinear Parameters. Journal of the Society for Industrial and Applied Mathematics, 11(2):431-441 (1963).