Symbols
Am	Membrane area (m2)
D	Diffusion coefficient (m2 s−1)
dh	Hydraulic diameter (m)
$f_{glob}=\frac{d_h}{2\rho u_{eff}{}^2}\frac{\Delta p_{ch}}{L_m}$	Fanning friction factor
hch	Membrane channel height (m)
J	Mass flux (kg m−2 s−1, L m−2 h−1)
kmt	Mass transfer coefficient (m s−1)
Lm	Membrane length (m)
Lp	Membrane permeance (m Pa−1 s−1)
N	Number of envelopes
p	Pressure (Pa, bar)
$\Delta p_{tm}=p_{in}-p_a$	Transmembrane pressure (bar)
Q	Volumetric flow rate (m3 s−1)
$R=1-\frac{w_p}{w_w}$	Membrane intrinsic rejection
$R{e}_h=\frac{\rho u_{eff}{d}_h}{\mu }$	Hydraulic Reynolds number
RRO	Recovery ratio
$Sc=\frac{\mu }{\rho D}$	Schmidt number
$Sh=\frac{k_{mt}{d}_h}{D}$	Sherwood number
t	Time (s)
uavg	Inlet velocity (m s−1)
$u_{eff}=\frac{u_{avg0}}{\epsilon }$	Effective velocity (m s−1)
$\stackrel{\rightharpoonup }{v}$	Velocity vector (m s−1)
w	Solute mass fraction
x	Distance in the bulk flow direction, parallel to the membrane surface (m)
y	Distance from the bottom membrane surface, in the direction normal to the surface (m)
Greek letters
δch	Channel width (m)
ε	Porosity
$\gamma$	Concentration polarisation modulus
μ	Dynamic viscosity (kg m−1 s−1)
ηpump	Pump efficiency
${\eta }_R=\frac{p_0-p_a}{{\left(p_0-p_a\right)}_{ideal}}$	Retentate pressure recovery efficiency
π	Osmotic pressure (Pa)
${\pi }_0=\phi w_{b0}$	Inlet osmotic pressure (Pa)
φ	Osmotic pressure coefficient (Pa)
ψ	Ratio of volumetric flux to the impermeable mass transfer coefficient
ρ	Density (kg m−3)
σ	Reflection coefficient
Subscripts
b	Value at the inlet bulk conditions
f	Value for the feed
HB	Value for hypersaline brine
imp	Value for the impermeable wall condition
in	Value for the inlet
out	Value at the domain outlet
p	Value for the permeate
per	Value for the permeable wall condition
r	Value for the retentate/concentrate
SW	Value for seawater
w	Value on the feed side membrane surface (wall)