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Induction times induced in an RO system by antiscalants delaying. Induction time model, страница 10

A  —

B  —

Frequency factor, m!2 s!1

Constant relating J and J, m!2

CP            —

Concentration polarization ratio, dimensionless

[Ca]          —

Concentration of Ca ion in the bulk of the solution, mol/L

[Ca]w               —

Concentration of Ca ion prevailing on the membrane surface,

mol/L

J               —

Nucleation rate, m!2 s!1

Jv                        —

Permeate flux, L/m2 h

k               —

Mass transfer coefficient, m/s

(KNSP)CaSO4 —

Solubility product of CaSO4, mol2/L2

Lp

—

Real permeability, L/m2 h bar

Sb

—

Supersaturation ratio in the bulk of the solution, dimensionless

Sw

—

Supersaturation ratio prevailing on the membrane surface, dimensionless defined by Eq. (6)

[SO4]

—

Concentration of SO4 ion in the bulk of the solution, mol/L

[SO4]w

—

Concentration of SO4 ion prevailing on the membrane surface, mol/L

T

Greek

—

Absolute temperature, °K

< 

—

Number of ions of crystallizing salt molecules

N

—

Wetting angle parameter

F

—

Crystal surface energy, mJ/m2

Feff1

—

Effective crystal surface energy defined by Eq. (4), mJ/m2

Feff2

—

Effective crystal surface energy based on < = 1, mJ/m2

J

—

Induction time, s

Lm

—

Molecular volume of crystalline phase, m3/mol

Acknowledgments

This study was undertaken in the framework of the EC Joule Programme Project JOE3-CT970053 performed by Suez-Lyonnaise des Eaux, CPERI of the University of Thessaloniki, AGBAR of Barcelona, Mekorot-Water Company and the Grand Water Research Institute (GWRI) of the Technion–Israel Institute of Technology. Thanks are due to the GWRI and to Professor Malcolm Chaikin for their invaluable support in providing the infrastructure of the Rabin Desalination Laboratory. This work forms part of the research undertaken by A.D. in partial fulfillment of the requirements of a Ph.D. degree.

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