Recovery of Valuable Solutes from Organic Solvent/Water Mixtures via Direct Contact Membrane Distillation (DCMD) as a Non-Heated Process

. 2021 Jul 23;11(8):559. doi: 10.3390/membranes11080559

Symbols	Description	Units
A	Total membrane bore surface area	m²
B	Geometric factor determined by pore structure	–
$C_{c 0}$	Solute concentration in cooling water before operation	wt%
$C_{c}$	Solute concentration in cooling water after operation	wt%
$C_{o s 0}$	Organic solvent concentration of cooling water before operation	wt%
$C_{f 0}$	Solute concentration in the feed before operation	wt%
$C_{f}$	Solute concentration in the feed after operation	wt%
$C_{o s}$	Organic solvent concentration of cooling water after operation	wt%
$C_{o s v}$	Concentration of organic solvent in vapor	%
$A_{i}$ , $B_{i}$ , $C_{i}$	Constants of Antoine’s equation of component i	–
$a_{i j}$ , $a_{j i}$ , $b_{i j}$ , $b_{j i}$	parameter coefficients for calculate Wilson parameter	–
F	Concentration factor	fold
$J_{o s}$	Permeate vapor flux of organic solvent through the membrane	kg/m²·h
$J_{p}$	Total permeate vapor flux (water and organic solvents) through the membrane	kg/m²·h
$J_{s}$	Flux of total leaking solute through the membrane	g/m²·h
$LEP$	Liquid Entry Pressure	MPa
$m_{f 0}$	Amount of solute in the feed before operation	kg
$m_{f}$	Amount of solute in the feed after operation	kg
$Δ m_{s}$	Difference of the amount of solute contained in cooling water before and after operation	kg
$P_{feed}$	Saturated vapor pressure of the feed side	kPa
$P_{permeate}$	Saturated vapor pressure of the permeation side	kPa
$P_{i}^{0}$	Vapor pressure of pure liquid of component i	kPa
$P_{i}$	Partial vapor pressure of component i	kPa
$r_{m a x}$	Maximum pore radius of the membrane	μm
$T$	Absolute temperature	K
t	Operating time	hour
$W_{c}$	Weight of cooling water after operation,	kg
$W_{c 0}$	Weight of cooling water before operation	kg
$W_{f 0}$	Weight of the feed before operation	kg
$W_{f}$	Weight of the feed after operation	kg
$W_{p}$	Weight of permeate	kg
$W_{o s}$	Weight of permeated organic solvent through membrane	kg
α	the vapor permeation coefficient	kg/m²·h·kPa
$β$	solute retention ratio in the feed	%
$γ_{i}$	activity coefficient of component i	–
$σ_{L}$	surface tension of liquid	–
$θ$	contact angle	°
$Λ_{i j}$ , $Λ_{j i}$	Wilson parameters of the binary mixture of components i and j	–
$χ_{i}$	molar fraction of component i	–