Semiempirical kinetic modelling of water desalination by electrodialysis processes

ABSTRACT

Water desalination was performed by electrodialysis (ED) in batch recirculation mode by means of cationic and anionic membranes containing sulfonate and ammonium groups, respectively. Variations in sodium chloride (NaCl) concentration in dilute compartment versus time during ED experiments were recorded at different voltages, flow rates, and feed concentrations. ED experiments were modelled by means of a semiempirical kinetic model. A good agreement is found between experimental data and the model.

KEYWORDS:

• Electrodialysis
• desalination
• modelling
• NaCl

Nomenclature

N	=	Flux of ions (mol/m2 s)
A	=	Membrane area (m2)
I	=	Current intensity (A)
F	=	Faraday constant (C/mol)
t	=	Time (s)
n	=	Number of moles transferred (mol)
C	=	Concentration of ions at the bulk (mol/m3)
Cs	=	Concentration of ions at the membrane surface (mol/m3)
K	=	Mass transfer constant (m/s)
Sh	=	Sherwood number
Re	=	Reynolds number
SC	=	Schmidt number
y	=	Thickness of dilute compartment (m)
D	=	Coefficient of diffusion (m2/s)
l	=	Channel length (m)
u	=	Flow velocity (m/s)
Q	=	Flow rate of dilute compartment (m3/s)
E	=	Applied potential (V)
Nc	=	Number of cell pair
Rcp	=	Electrical resistance of cell pair (Ω)
Ram	=	Resistance of anion exchange membrane (Ω)
Rcm	=	Resistance of cation exchange membrane (Ω)
Rd	=	Resistance of dilute compartment (Ω)
Rc	=	Resistance of concentrate compartment (Ω)
VD	=	Volume of dilute solution (m3)
Ea	=	Activation energy (J/mol)
R	=	Gaz constant (J/mol K)
T	=	Temperature (K)

Greek letters

α	=	= , C A−1m−3
η	=	Current efficiency
ρ	=	Density (kg/m3)
μ	=	Dynamic viscosity (Pa s)
δ	=	Boundary layer thickness (m)
β	=	= α 3.3 (C A −1 m3 s−1)

Subscripts

ED	=	Electrodialysis
D	=	Dilute
C	=	Concentrate
s	=	Second
Mod	=	Model
Exp	=	Experimental