Theoretical tool for evaluating induction periods of calcium sulfate scaling on reverse osmosis membranes

Abraham Sagiv, Xianhui Li, Raphael Semiat, Hilla Shemer

Research output: Contribution to journalArticlepeer-review


The objective of the study was to provide an evaluation tool for the induction period of reverse osmosis membrane scaling by calcium sulfate. The proposed tool may be used as a preventive measure against severe and irreversible membrane scaling. Scaling experiments were conducted at different Reynolds numbers (Re) and calcium sulfate concentrations, that is, various saturation indices (SI). The observed induction periods were determined at the onset of the permeate flux decline. A computational fluid dynamics model was developed to determine the induction period based on two adjustable parameters describing the balance between deposition and removal rates to and from the membrane surface. These parameters were derivate by fitting the model to the experimental results. For a given membrane permeability, solution SI and Re number, a theoretical permeate flux and induction period were calculated using the model. In addition, the model output included the membrane surface coverage by the calcium sulfate scale. Finally, evaluated induction periods (EIP) were determined, considering the average standard deviation between the observed and theoretical induction periods. The average surface coverage fraction of scaling during the induction periods was found to be 0.066 ± 0.034. The EIP decreases with the supersaturation of the solution and increases with the Re number. EIP values were found to be less than the observed induction periods, satisfying safe operating conditions from both economic and membrane integrity aspects.

Original languageEnglish
Pages (from-to)64-71
Number of pages8
JournalDesalination and Water Treatment
StatePublished - May 2022
Externally publishedYes


  • Crystallization
  • Desalination
  • Flux decline
  • Membrane fouling
  • Scale deposition


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