Support vector machine-based modeling of grafting hyperbranched polyethylene glycol on polyethersulfone ultrafiltration membrane for separation of oil–water emulsion

  • Hooman Adib
  • Ahmadreza RaisiEmail author
  • Behzad Salari


In present study, a new method based on the support vector machine (SVM) approach was employed to calculate the oil–water permeation flux and grafting yield of maleic anhydride and hyperbranched polyethylene glycol (PEG) on the polyethersulfone (PES) membrane surface. A set of 7 input/output experimental data was applied for training and testing the results of the model. The results of the developed SVM model showed good compliance with the experimental data, as the value of correlation index for the developed model is 0.96, 0.95 and 0.98 for the maleic anhydride and hyperbranched PEG grafting and oil–water permeation flux, respectively. The model was also validated against the kinetic reaction of benzophenone formation on the PES membrane which derives from combination of benzophenone formation reactions and the Lambert–Beer law. Also, to validate the SVM results, the oil–water permeation flux and antifouling characteristics of the modified and neat membranes were investigated, and based on the results, the SVM can be considered as a strong modeling approach in membrane process technologies.


Hyperbranched polyethylene glycol (PEG) Benzophenone Membrane fouling Support vector machine (SVM) 

List of symbols





Feed oil concentration


Permeate oil concentration


Permeate flux


Kernel function


Number of data


Normal vector


Weight of permeate


Input parameter


Simulation value


Experimental value



Lagrangian multiplier


Vector dot product


Regularization parameter


Precision threshold


Slack variable


Kernel parameter



Average absolute deviation


Artificial neural networks




Benzophenone formation rate


N,N-dimethyl formamide


Chemical oxygen demand


Fuzzy inference system


Genetic algorithm


Mean absolute error






Polyethylene glycol




Coefficient of determination





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Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Department of Chemical EngineeringAmirkabir University of Technology (Tehran Polytechnic)TehranIran
  2. 2.National Iranian Gas Company (NIGC), South Pars Gas Complex (SPGC)AsaluyehIran

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