Research Papers

Estimation of CO2 Diffusivity in Brine by Use of the Genetic Algorithm and Mixed Kernels-Based Support Vector Machine Model

[+] Author and Article Information
Qihong Feng, Zhe Jiang

School of Petroleum Engineering,
China University of Petroleum (East China),
Qingdao 266580, Shandong, China

Ronghao Cui

School of Petroleum Engineering,
China University of Petroleum (East China),
Qingdao 266580, Shandong, China
e-mail: ronghao.cui1993@gmail.com

Sen Wang

School of Petroleum Engineering,
China University of Petroleum (East China),
Qingdao 266580, Shandong, China
e-mail: fwforest@gmail.com

Jin Zhang

School of Petroleum Engineering,
China University of Petroleum (East China),
Qingdao 266580, Shandong, China

1Corresponding authors.

Contributed by the Petroleum Division of ASME for publication in the JOURNAL OF ENERGY RESOURCES TECHNOLOGY. Manuscript received July 13, 2018; final manuscript received October 6, 2018; published online November 19, 2018. Assoc. Editor: Daoyong (Tony) Yang.

J. Energy Resour. Technol 141(4), 041001 (Nov 19, 2018) (11 pages) Paper No: JERT-18-1524; doi: 10.1115/1.4041724 History: Received July 13, 2018; Revised October 06, 2018

Diffusion coefficient of carbon dioxide (CO2), a significant parameter describing the mass transfer process, exerts a profound influence on the safety of CO2 storage in depleted reservoirs, saline aquifers, and marine ecosystems. However, experimental determination of diffusion coefficient in CO2-brine system is time-consuming and complex because the procedure requires sophisticated laboratory equipment and reasonable interpretation methods. To facilitate the acquisition of more accurate values, an intelligent model, termed MKSVM-GA, is developed using a hybrid technique of support vector machine (SVM), mixed kernels (MK), and genetic algorithm (GA). Confirmed by the statistical evaluation indicators, our proposed model exhibits excellent performance with high accuracy and strong robustness in a wide range of temperatures (273–473.15 K), pressures (0.1–49.3 MPa), and viscosities (0.139–1.950 mPa·s). Our results show that the proposed model is more applicable than the artificial neural network (ANN) model at this sample size, which is superior to four commonly used traditional empirical correlations. The technique presented in this study can provide a fast and precise prediction of CO2 diffusivity in brine at reservoir conditions for the engineering design and the technical risk assessment during the process of CO2 injection.

Copyright © 2019 by ASME
Your Session has timed out. Please sign back in to continue.


Ota, M. , Saito, T. , Aida, T. , Watanabe, M. , Sato, Y. , Smith, R. L. , and Inomata, H. , 2007, “ Macro and Microscopic CH4-CO2 Replacement in CH4 Hydrate Under Pressurized CO2,” AIChE J., 53(10), pp. 2715–2721. [CrossRef]
Bai, D. , Zhang, X. , Chen, G. , and Wang, W. , 2012, “ Replacement Mechanism of Methane Hydrate With Carbon Dioxide From Microsecond Molecular Dynamics Simulations,” Energy Environ. Sci., 5(5), pp. 7033–7041. [CrossRef]
Pruess, K. , 2006, “ Enhanced Geothermal Systems (EGS) Using CO2 as Working Fluid—A Novel Approach for Generating Renewable Energy With Simultaneous Sequestration of Carbon,” Geothermics, 35(4), pp. 351–367. [CrossRef]
Zhang, L. , Cui, G. , Zhang, Y. , Ren, B. , Ren, S. , and Wang, X. , 2016, “ Influence of Pore Water on the Heat Mining Performance of Supercritical CO2 Injected for Geothermal Development,” J. CO2 Util., 16, pp. 287–300. [CrossRef]
Cui, G. , Ren, S. , Rui, Z. , Ezekiel, J. , Zhang, L. , and Wang, H. , 2018, “ The Influence of Complicated Fluid-Rock Interactions on the Geothermal Exploitation in the CO2 Plume Geothermal System,” Appl. Energy, 227, pp. 49–63. [CrossRef]
Mohamed, I. M. , He, J. , and Nasr-El-Din, H. A. , 2012, “ Experimental Analysis of CO2 Injection on Permeability of Vuggy Carbonate Aquifers,” ASME J. Energy Resour. Technol., 135(1), p. 013301. [CrossRef]
Cui, G. , Wang, Y. , Rui, Z. , Chen, B. , Ren, S. , and Zhang, L. , 2018, “ Assessing the Combined Influence of Fluid-Rock Interactions on Reservoir Properties and Injectivity During CO2 Storage in Saline Aquifers,” Energy, 155, pp. 281–296. [CrossRef]
Rau, G. H. , and Caldeira, K. , 1999, “ Enhanced Carbonate Dissolution: A Means of Sequestering Waste CO2 as Ocean Bicarbonate,” Energy Convers. Manage., 40(17), pp. 1803–1813. [CrossRef]
Chen, B. , and Reynolds, A. C. , 2018, “ CO2 Water-Alternating-Gas Injection for Enhanced Oil Recovery: Optimal Well Controls and Half-Cycle Lengths,” Comput. Chem. Eng., 113, pp. 44–56. [CrossRef]
Li, A. , Ren, X. , Fu, S. , Lv, J. , Li, X. , Liu, Y. , and Lu, Y. , 2018, “ The Experimental Study on the Flooding Regularities of Various CO2 Flooding Modes Implemented on Ultralow Permeability Cores,” ASME J. Energy Resour. Technol., 140(7), p. 072902. [CrossRef]
Ren, B. , Zhang, L. , Huang, H. , Ren, S. , Chen, G. , and Zhang, H. , 2015, “ Performance Evaluation and Mechanisms Study of Near-Miscible CO2 Flooding in a Tight Oil Reservoir of Jilin Oilfield China,” J. Nat. Gas Sci. Eng., 27, pp. 1796–1805. [CrossRef]
Li, S. , Li, B. , Zhang, Q. , Li, Z. , and Yang, D. , 2018, “ Effect of CO2 on Heavy Oil Recovery and Physical Properties in Huff-n-Puff Processes Under Reservoir Conditions,” ASME J. Energy Resour. Technol., 140(7), p. 072907. [CrossRef]
Mutoru, J. W. , Leahy-Dios, A. , and Firoozabadi, A. , 2011, “ Modeling Infinite Dilution and Fickian Diffusion Coefficients of Carbon Dioxide in Water,” AIChE J., 57(6), pp. 1617–1627. [CrossRef]
Farajzadeh, R. , Zitha, P. L. , and Bruining, J. , 2009, “ Enhanced Mass Transfer of CO2 Into Water: Experiment and Modeling,” Ind. Eng. Chem. Res., 48(13), pp. 6423–6431. [CrossRef]
Trevisan, L. , Pini, R. , Cihan, A. , Birkholzer, J. T. , Zhou, Q. , and Illangasekare, T. H. , 2014, “ Experimental Investigation of Supercritical CO2 Trapping Mechanisms at the Intermediate Laboratory Scale in Well-Defined Heterogeneous Porous Media,” Energy Procedia, 63, pp. 5646–5653. [CrossRef]
Cadogan, S. P. , Hallett, J. P. , Maitland, G. C. , and Trusler, J. M. , 2014, “ Diffusion Coefficients of Carbon Dioxide in Brines Measured Using 13C Pulsed-Field Gradient Nuclear Magnetic Resonance,” J. Chem. Eng. Data, 60(1), pp. 181–184. [CrossRef]
Vivian, J. E. , and King, C. J. , 1964, “ Diffusivities of Slightly Soluble Gases in Water,” AIChE J., 10(2), pp. 220–221. [CrossRef]
Mazarei, A. F. , and Sandall, O. C. , 1980, “ Diffusion Coefficients for Helium, Hydrogen, and Carbon Dioxide in Water at 25 °C,” AIChE J., 26(1), pp. 154–157. [CrossRef]
Maharajh, D. M. , and Walkley, J. , 1973, “ The Temperature Dependence of the Diffusion Coefficients of Ar, CO2, CH4, CH3Cl, CH3Br, and CHCl2F in Water,” Can. J. Chem., 51(6), pp. 944–952. [CrossRef]
Tamimi, A. , Rinker, E. B. , and Sandall, O. C. , 1994, “ Diffusion Coefficients for Hydrogen Sulfide, Carbon Dioxide, and Nitrous Oxide in Water Over the Temperature Range 293-368 K,” J. Chem. Eng. Data, 39(2), pp. 330–332. [CrossRef]
Frank, M. J. , Kuipers, J. A. , and van Swaaij, W. P. , 1996, “ Diffusion Coefficients and Viscosities of CO2 + H2O, CO2 + CH3OH, NH3 + H2O, and NH3 + CH3OH Liquid Mixtures,” J. Chem. Eng. Data, 41(2), pp. 297–302. [CrossRef]
Ng, W. Y. , and Walkley, J. , 1969, “ Diffusion of Gases in Liquids: The Constant Size Bubble Method,” Can. J. Chem., 47(6), pp. 1075–1077. [CrossRef]
Jähne, B. , Heinz, G. , and Dietrich, W. , 1987, “ Measurement of the Diffusion Coefficients of Sparingly Soluble Gases in Water,” J. Geophys. Res., 92(C10), pp. 10767–10776. [CrossRef]
Hirai, S. , Okazaki, K. , Yazawa, H. , Ito, H. , Tabe, Y. , and Hijikata, K. , 1997, “ Measurement of CO2 Diffusion Coefficient and Application of LIF in Pressurized Water,” Energy, 22(2–3), pp. 363–367. [CrossRef]
Guzmán, J. , and Garrido, L. , 2012, “ Determination of Carbon Dioxide Transport Coefficients in Liquids and Polymers by NMR Spectroscopy,” J. Phys. Chem. B, 116(20), pp. 6050–6058. [CrossRef] [PubMed]
Liger-Belair, G. , Prost, E. , Parmentier, M. , Jeandet, P. , and Nuzillard, J. M. , 2003, “ Diffusion Coefficient of CO2 Molecules as Determined by 13C NMR in Various Carbonated Beverages,” J. Agric. Food Chem., 51(26), pp. 7560–7563. [CrossRef] [PubMed]
Maharajh, D. , 1973, “ Solubility and Diffusion of Gases in Water,” Ph.D. thesis, Simon Fraser University, Burnaby, BC, Canada.
Versteeg, G. F. , and Van Swaalj, W. , 1988, “ Solubility and Diffusivity of Acid Gases (Carbon Dioxide, Nitrous Oxide) in Aqueous Alkanolamine Solutions,” J. Chem. Eng. Data, 33(1), pp. 29–34. [CrossRef]
Himmelblau, D. M. , 1964, “ Diffusion of Dissolved Gases in Liquids,” Chem. Rev., 64(5), pp. 527–550. [CrossRef]
Thomas, W. J. , and Adams, M. J. , 1965, “ Measurement of the Diffusion Coefficients of Carbon Dioxide and Nitrous Oxide in Water and Aqueous Solutions of Glycerol,” Trans. Faraday Soc., 61, pp. 668–673. [CrossRef]
Brignole, E. A. , and Echarte, R. , 1981, “ Mass Transfer in Laminar Liquid Jets: Measurement of Diffusion Coefficients,” Chem. Eng. Sci., 36(4), pp. 705–711. [CrossRef]
Nijsing, R. , Hendriksz, R. H. , and Kramers, H. , 1959, “ Absorption of CO2 in Jets and Falling Films of Electrolyte Solutions, With and Without Chemical Reaction,” Chem. Eng. Sci., 10(1–2), pp. 88–104. [CrossRef]
Tan, K. K. , and Thorpe, R. B. , 1992, “ Gas Diffusion Into Viscous and Non-Newtonian Liquids,” Chem. Eng. Sci., 47(13–14), pp. 3565–3572. [CrossRef]
Tham, M. J. , Bhatia, K. K. , and Gubbins, K. F. , 1967, “ Steady-State Method for Studying Diffusion of Gases in Liquids,” Chem. Eng. Sci., 22(3), pp. 309–311. [CrossRef]
Vivian, J. E. , and Peaceman, D. W. , 1956, “ Liquid-Side Resistance in Gas Absorption,” AIChE J., 2(4), pp. 437–443. [CrossRef]
Pratt, K. C. , Slater, D. H. , and Wakeham, W. A. , 1973, “ A Rapid Method for the Determination of Diffusion Coefficients of Gases in Liquids,” Chem. Eng. Sci., 28(10), pp. 1901–1903. [CrossRef]
Bodnar, L. H. , and Himmelblau, D. M. , 1962, “ Continuous Measurement of Diffusion Coefficients of Gases in Liquids Using Glass Scintillators,” Int. J. Appl. Radiat. Isot., 13(1), pp. 1–6. [CrossRef]
Choudhari, R. , and Doraiswamy, L. K. , 1972, “ Physical Properties in Reaction of Ethylene and Hydrogen Chloride in Liquid Media. Diffusivities and Solubilities,” J. Chem. Eng. Data, 17(4), pp. 428–432. [CrossRef]
Reddy, K. A. , and Doraiswamy, L. K. , 1967, “ Estimating Liquid Diffusivity,” Ind. Eng. Chem. Fundam., 6(1), pp. 77–79. [CrossRef]
Lu, W. , Guo, H. , Chou, I. M. , Burruss, R. C. , and Li, L. , 2013, “ Determination of Diffusion Coefficients of Carbon Dioxide in Water Between 268 and 473 K in a High-Pressure Capillary Optical Cell With in Situ Raman Spectroscopic Measurements,” Geochim. Cosmochim. Acta, 115, pp. 183–204. [CrossRef]
Cadogan, S. P. , Maitland, G. C. , and Trusler, J. M. , 2014, “ Diffusion Coefficients of CO2 and N2 in Water at Temperatures Between 298.15 K and 423.15 K at Pressures Up to 45 MPa,” J. Chem. Eng. Data, 59(2), pp. 519–525. [CrossRef]
Jang, H. W. , Yang, D. , and Li, H. , 2018, “ A Power-Law Mixing Rule for Predicting Apparent Diffusion Coefficients of Binary Gas Mixtures in Heavy Oil,” ASME J. Energy Resour. Technol., 140(5), p. 052904. [CrossRef]
Shi, Y. , Zheng, S. , and Yang, D. , 2017, “ Determination of Individual Diffusion Coefficients of Alkane Solvent(s)–CO2–Heavy Oil Systems With Consideration of Natural Convection Induced by Swelling Effect,” Int. J. Heat Mass Transfer, 107, pp. 572–585. [CrossRef]
Zheng, S. , and Yang, D. , 2017, “ Experimental and Theoretical Determination of Diffusion Coefficients of CO2-Heavy Oil Systems by Coupling Heat and Mass Transfer,” ASME J. Energy Resour. Technol., 139(2), p. 022901. [CrossRef]
Zheng, S. , and Yang, D. , 2017, “ Determination of Individual Diffusion Coefficients of C3H8/n-C4H10/CO2/Heavy-Oil Systems at High Pressures and Elevated Temperatures by Dynamic Volume Analysis,” SPE J., 22, pp. 799–816. [CrossRef]
Li, H. A. , Sun, H. , and Yang, D. , 2017, “ Effective Diffusion Coefficients of Gas Mixture in Heavy Oil Under Constant-Pressure Conditions,” Heat Mass Transfer, 53(5), pp. 1527–1540. [CrossRef]
Zheng, S. , Sun, H. , and Yang, D. , 2016, “ Coupling Heat and Mass Transfer for Determining Individual Diffusion Coefficient of a Hot C3H8–CO2 Mixture in Heavy Oil Under Reservoir Conditions,” Int. J. Heat Mass Transfer, 102, pp. 251–263. [CrossRef]
Zheng, S. , Li, H. A. , Sun, H. , and Yang, D. , 2016, “ Determination of Diffusion Coefficient for Alkane Solvent–CO2 Mixtures in Heavy Oil With Consideration of Swelling Effect,” Ind. Eng. Chem. Res., 55(6), pp. 1533–1549. [CrossRef]
Li, H. , and Yang, D. , 2016, “ Determination of Individual Diffusion Coefficients of Solvent/CO2 Mixture in Heavy Oil With Pressure-Decay Method,” SPE J., 21(1), pp. 131–143. [CrossRef]
Sun, H. , Li, H. , and Yang, D. , 2014, “ Coupling Heat and Mass Transfer for a Gas Mixture–Heavy Oil System at High Pressures and Elevated Temperatures,” Int. J. Heat Mass Transfer, 74, pp. 173–184. [CrossRef]
Yang, D. , Tontiwachwuthikul, P. , and Gu, Y. , 2006, “ Dynamic Interfacial Tension Method for Measuring Gas Diffusion Coefficient and Interface Mass Transfer Coefficient in a Liquid,” Ind. Eng. Chem. Res., 45(14), pp. 4999–5008. [CrossRef]
Othmer, D. F. , and Thakar, M. S. , 1953, “ Correlating Diffusion Coefficient in Liquids,” Ind. Eng. Chem., 45(3), pp. 589–593. [CrossRef]
Wilke, C. R. , and Chang, P. , 1955, “ Correlation of Diffusion Coefficients in Dilute Solutions,” AIChE J., 1(2), pp. 264–270. [CrossRef]
Moultos, O. A. , Tsimpanogiannis, I. N. , Panagiotopoulos, A. Z. , and Economou, I. G. , 2016, “ Self-Diffusion Coefficients of the Binary (H2O + CO2) Mixture at High Temperatures and Pressures,” J. Chem. Thermodyn., 93, pp. 424–429. [CrossRef]
Cadogan, S. , 2015, “ Diffusion of CO2 in Fluids Relevant to Carbon Capture, Utilisation and Storage,” Ph.D. thesis, Imperial College London, London. https://core.ac.uk/download/pdf/77007460.pdf
Shokrollahi, A. , Arabloo, M. , Gharagheizi, F. , and Mohammadi, A. H. , 2013, “ Intelligent Model for Prediction of CO2–Reservoir Oil Minimum Miscibility Pressure,” Fuel, 112, pp. 375–384. [CrossRef]
Le Van, S. , and Chon, B. H. , 2018, “ Effective Prediction and Management of a CO2 Flooding Process for Enhancing Oil Recovery Using Artificial Neural Networks,” ASME J. Energy Resour. Technol., 140(3), p. 032906. [CrossRef]
Zhang, J. , Feng, Q. , Zhang, X. , Zhang, X. , Yuan, N. , Wen, S. , Wang, S. , and Zhang, A. , 2015, “ The Use of an Artificial Neural Network to Estimate Natural Gas/Water Interfacial Tension,” Fuel, 157, pp. 28–36. [CrossRef]
Khaksar Manshad, A. , Rostami, H. , Moein Hosseini, S. , and Rezaei, H. , 2016, “ Application of Artificial Neural Network–Particle Swarm Optimization Algorithm for Prediction of Gas Condensate Dew Point Pressure and Comparison With Gaussian Processes Regression–Particle Swarm Optimization Algorithm,” ASME J. Energy Resour. Technol., 138(3), p. 032903. [CrossRef]
Paul, A. , Bhowmik, S. , Panua, R. , and Debroy, D. , 2018, “ Artificial Neural Network-Based Prediction of Performances-Exhaust Emissions of Diesohol Piloted Dual Fuel Diesel Engine Under Varying Compressed Natural Gas Flowrates,” ASME J. Energy Resour. Technol., 140(11), p. 112201. [CrossRef]
Chen, B. , Harp, D. R. , Lin, Y. , Keating, E. H. , and Pawar, R. J. , 2018, “ Geologic CO2 Sequestration Monitoring Design: A Machine Learning and Uncertainty Quantification Based Approach,” Appl. Energy, 225, pp. 332–345. [CrossRef]
Kamari, A. , Arabloo, M. , Shokrollahi, A. , Gharagheizi, F. , and Mohammadi, A. H. , 2015, “ Rapid Method to Estimate the Minimum Miscibility Pressure (MMP) in Live Reservoir Oil Systems During CO2 Flooding,” Fuel, 153, pp. 310–319. [CrossRef]
Tatar, A. , Barati-Harooni, A. , Najafi-Marghmaleki, A. , Najafi-Marghmaleki, A. , Mohebbi, A. , Ghiasi, M. M. , Mohammadi, A. H. , and Hajinezhad, A. , 2016, “ Comparison of Two Soft Computing Approaches for Predicting CO2 Solubility in Aqueous Solution of Piperazine,” Int. J. Greenhouse Gas Control, 53, pp. 85–97. [CrossRef]
Linstrom, P. J. , and Mallard, W. G. E. , 2016, “ NIST Chemistry WebBook,” National Institute of Standards and Technology, Gaithersburg, MD, accessed Aug. 17, 2016, NIST Standard Reference Database No. 69, http://webbook.nist.gov
Cortes, C. , and Vapnik, V. , 1995, “ Support-Vector Networks,” Mach. Learn., 20(3), pp. 273–297.
Vapnik, V. , 1995, The Nature of Statistical Learning Theory, Springer, New York.
Boser, B. E. , Guyon, I. M. , and Vapnik, V. N. , 1992, “ A Training Algorithm for Optimal Margin Classifiers,” Fifth Annual Workshop on Computational Learning Theory, Pittsburgh, PA, July 27–29, pp. 144–152.
Drucker, H. , Burges, C. J. , Kaufman, L. , Smola, A. , and Vapnik, V. , 1997, “ Support Vector Regression Machines,” Advances in Neural Information Processing Systems 9, MIT Press, Cambridge, MA, pp. 155–161.
Geng, Y. , Chen, J. , Fu, R. , Bao, G. , and Pahlavan, K. , 2016, “ Enlighten Wearable Physiological Monitoring Systems: On-Body of Characteristics Based Human Motion Classification Using a Support Vector Machine,” IEEE Trans. Mobile Comput., 15(3), pp. 656–671. [CrossRef]
Lee, Y. J. , and Mangasarian, O. L. , 2001, “ SSVM: A Smooth Support Vector Machine for Classification,” Comput. Optim. Appl., 20, pp. 5–22. [CrossRef]
Bian, X. Q. , Han, B. , Du, Z. M. , Jaubert, J. N. , and Li, M. J. , 2016, “ Integrating Support Vector Regression With Genetic Algorithm for CO2-Oil Minimum Miscibility Pressure (MMP) in Pure and Impure CO2 Streams,” Fuel, 182, pp. 550–557. [CrossRef]
Filgueiras, P. R. , Portela, N. A. , Silva, S. R. , Castro, E. V. , Oliveira, L. M. , Dias, J. C. , Neto, A. C. , Romão, W. , and Poppi, R. J. , 2016, “ Determination of Saturates, Aromatics, and Polars in Crude Oil by 13C NMR and Support Vector Regression With Variable Selection by Genetic Algorithm,” Energy Fuels, 30(3), pp. 1972–1978. [CrossRef]
Fiacco, A. V. , and McCormick, G. P. , 1964, “ The Sequential Unconstrained Minimization Technique for Nonlinear Programing, A Primal-Dual Method,” Manag. Sci., 10(2), pp. 360–366. [CrossRef]
Smola, A. J. , and Schölkopf, B. , 2004, “ A Tutorial on Support Vector Regression,” Stat. Comput., 14(3), pp. 199–222. [CrossRef]
Schölkopf, B. , and Burges, C. J. , 1999, Advances in Kernel Methods: Support Vector Learning, MIT Press, Cambridge, MA.
Tehrany, M. S. , Pradhan, B. , and Jebur, M. N. , 2014, “ Flood Susceptibility Mapping Using a Novel Ensemble Weights-of-Evidence and Support Vector Machine Models in GIS,” J. Hydrol., 512, pp. 332–343. [CrossRef]
Smits, G. F. , and Jordaan, E. M. , 2002, “ Improved SVM Regression Using Mixtures of Kernels,” International Joint Conference on Neural Networks, Vol. 3, pp. 2785–2790.
Holland, J. H. , 1992, “ Genetic Algorithms,” Sci. Am., 267(1), pp. 66–72. [CrossRef]
Khadse, A. , Blanchette, L. , Kapat, J. , Vasu, S. , Hossain, J. , and Donazzolo, A. , 2018, “ Optimization of Supercritical CO2 Brayton Cycle for Simple Cycle Gas Turbines Exhaust Heat Recovery Using Genetic Algorithm,” ASME J. Energy Resour. Technol., 140(7), p. 071601. [CrossRef]
Salmachi, A. , Sayyafzadeh, M. , and Haghighi, M. , 2013, “ Infill Well Placement Optimization in Coal Bed Methane Reservoirs Using Genetic Algorithm,” Fuel, 111, pp. 248–258. [CrossRef]
Velez-Langs, O. , 2005, “ Genetic Algorithms in Oil Industry: An Overview,” J. Pet. Sci. Eng., 47(1–2), pp. 15–22. [CrossRef]
Davis, L. , 1991, Handbook of Genetic Algorithms, Van Nostrand Reinhold, New York.
Chatterjee, S. , and Hadi, A. S. , 2015, Regression Analysis by Example, Wiley, New York.
Rousseeuw, P. J. , and Leroy, A. M. , 2005, Robust Regression and Outlier Detection, Wiley, New York.
Mohammadi, A. H. , Eslamimanesh, A. , Gharagheizi, F. , and Richon, D. , 2012, “ A Novel Method for Evaluation of Asphaltene Precipitation Titration Data,” Chem. Eng. Sci., 78, pp. 181–185. [CrossRef]
Mohammadi, A. H. , Gharagheizi, F. , Eslamimanesh, A. , and Richon, D. , 2012, “ Evaluation of Experimental Data for Wax and Diamondoids Solubility in Gaseous Systems,” Chem. Eng. Sci., 81, pp. 1–7. [CrossRef]
Feng, Q. , Zhang, J. , Zhang, X. , and Wen, S. , 2015, “ Proximate Analysis Based Prediction of Gross Calorific Value of Coals: A Comparison of Support Vector Machine, Alternating Conditional Expectation and Artificial Neural Network,” Fuel Process. Technol., 129, pp. 120–129. [CrossRef]
Togun, N. K. , and Baysec, S. , 2010, “ Prediction of Torque and Specific Fuel Consumption of a Gasoline Engine by Using Artificial Neural Networks,” Appl. Energy, 87(1), pp. 349–355. [CrossRef]
Pradhan, B. , and Lee, S. , 2010, “ Landslide Susceptibility Assessment and Factor Effect Analysis: Backpropagation Artificial Neural Networks and Their Comparison With Frequency Ratio and Bivariate Logistic Regression Modelling,” Environ. Modell. Software, 25(6), pp. 747–759. [CrossRef]
Li, Q. , Meng, Q. , Cai, J. , Yoshino, H. , and Mochida, A. , 2009, “ Predicting Hourly Cooling Load in the Building: A Comparison of Support Vector Machine and Different Artificial Neural Networks,” Energy Convers. Manage., 50(1), pp. 90–96. [CrossRef]
Sorgun, M. , Murat Ozbayoglu, A. A. , and Evren Ozbayoglu, M. M. , 2014, “ Support Vector Regression and Computational Fluid Dynamics Modeling of Newtonian and Non-Newtonian Fluids in Annulus With Pipe Rotation,” ASME J. Energy Resour. Technol., 137(3), p. 032901. [CrossRef]
Pradhan, B. , 2013, “ A Comparative Study on the Predictive Ability of the Decision Tree, Support Vector Machine and Neuro-Fuzzy Models in Landslide Susceptibility Mapping Using GIS,” Comput. Geosci., 51, pp. 350–365. [CrossRef]
Rostami, A. , Hemmati-Sarapardeh, A. , and Shamshirband, S. , 2018, “ Rigorous Prognostication of Natural Gas Viscosity: Smart Modeling and Comparative Study,” Fuel, 222, pp. 766–778. [CrossRef]


Grahic Jump Location
Fig. 1

Schematic showing the fundamentals of SVM. The square dots represent support vectors. The circular dots are normal points. The full line denotes the hyperplane and the ε-tube is the region between two dotted lines.

Grahic Jump Location
Fig. 2

Function curves of the polynomial kernel (a), the RBF kernel (b), and the mixed kernel (c). x = 0.2 is the test point in three types of kernels. As an example of mixed kernel functions, d = 1 and γ = 10 are set.

Grahic Jump Location
Fig. 3

Computational procedure of the MKSVM-GA technique

Grahic Jump Location
Fig. 4

Mean square error and average uptime of the MKSVM-GA model in different population size and evolutionary generations

Grahic Jump Location
Fig. 5

Illustration of the Williams plot

Grahic Jump Location
Fig. 6

Prediction performance of the proposed MKSVM-GA model: (a) cross plot of the estimated results versus experimental diffusion coefficients of CO2 in brine; (b) comparison of each experimental and predicted data points

Grahic Jump Location
Fig. 7

Distribution of the residuals between predicted and experimental diffusion coefficients of CO2. The columns are instances and the solid curve is the normal distribution curve. Std Dev represents the standard deviation of residuals.

Grahic Jump Location
Fig. 8

Williams plot used for the detection of outliers

Grahic Jump Location
Fig. 9

Illustration of the structure of a typical three-layered feed forward ANN model

Grahic Jump Location
Fig. 10

The minimum MSE with variation of number of neurons in the hidden layer

Grahic Jump Location
Fig. 11

Comparison of the training performance between the MKSVM-GA model and the ANN model

Grahic Jump Location
Fig. 12

Comparison of the prediction performance between the MKSVM-GA model and the ANN model

Grahic Jump Location
Fig. 13

Absolute error curves of the MKSVM-GA model, the ANN model, and four empirical correlations

Grahic Jump Location
Fig. 14

Comparison of the prediction performances between the MKSVM-GA model and four empirical correlations: (a) Othmer and Thakar; (b) Wilke and Chang; (c) Lu et al.; (d) Cadogan et al. Squares and triangles represent the values predicted using the MKSVM-GA model and empirical correlations, respectively.



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In