$A$	Effective membrane area (m²)
$A_{\mathrm{w}}$	Water membrane transport parameter (m/atm s)
$b$	Friction factor of feed channel of the membrane module (atm s/m4)
$B_{\mathrm{s}}$	Dimethylphenol membrane transport parameter (m/s)
$C_{\mathrm{b}}$	Bulk dimethylphenol concentrations at the feed channel (kmol/m³)
$C_{\mathrm{f}}$	Inlet feed dimethylphenol concentrations (kmol/m³)
$C_{\mathrm{m}}$	Dimensionless dimethylphenol concentration in Equation (A5) in Table A1 of Appendix A (dimensionless)
$C_{\mathrm{p}}$	Permeate dimethylphenol concentration (kmol/m³)
$C_{\mathrm{w}}$	Dimethylphenol concentration at the membrane wall (kmol/m³)
$D_{\mathrm{b}}$	Dimethylphenol diffusion parameter at the feed side (m²/s)
$D_{\mathrm{p}}$	Dimethylphenol diffusion parameter at the permeate side (m²/s)
$d{e}_{\mathrm{b}}$	Equivalent diameters of the feed channel (m)
$d{e}_{\mathrm{p}}$	Equivalent diameters of the permeate channel (m)
$EC$	Specific energy consumption (kWh/m³)
$J_{\mathrm{s}}$	Dimethylphenol molar flux through the membrane pores (kmol/m² s)
$J_{\mathrm{w}}$	Permeate flux (m/s)
$k$	Mass transfer coefficient of dimethylphenol (m/s)
$L$	Membrane length (m)
$m_{\mathrm{f}}$	Parameter in Equations (A10) and (A11) in Table A1 of Appendix A
$P_{\mathrm{f}\left(\mathrm{in}\right)}$	Inlet pressure of the feed (atm)
$P_{\mathrm{f}\left(\mathrm{out}\right)}$	Retentate pressure exit the membrane module (atm)
$P_{\mathrm{p}}$	Permeate side pressure (atm)
$Q_{\mathrm{b}}$	Bulk feed flow rate (m³/s)
$Q_{\mathrm{f}}$	Inlet feed flow rate of the membrane module (m³/s)
$Q_{\mathrm{p}}$	Permeate flow rate of the membrane module (m³/s)
$Q_{\mathrm{r}}$	Retentate flow rate of the membrane module (m³/s)
$R$	Gas low constant (R = 0.082 atm m³/ K kmol)
$R{e}_{\mathrm{b}}$	Reynold number at the feed side (dimensionless)
$Rec$	Overall permeate recovery of a single membrane module (dimensionless)
$Rej$	Dimethylphenol rejection of a single membrane module (dimensionless)
$R{e}_{\mathrm{p}}$	Reynold number at the permeate side (dimensionless)
$T_{ }$	Feed temperature (°C)
$t_{\mathrm{f}}$	Height of feed channel of the membrane module (m)
$t_{\mathrm{p}}$	Height of permeate channel of the membrane module (m)
$U_{\mathrm{b}}$	Bulk feed velocity (m/s)
$W$	Membrane width (m)
Greek
${\mu }_{\mathrm{b}}$	Feed viscosity (kg/m s)
${\mu }_{\mathrm{p}}$	Permeate viscosity (kg/m s)
${\rho }_{\mathrm{b}}$	Feed density (kg/m³)
${\rho }_{\mathrm{p}}$	Permeate density (kg/m³)
${\rho }_{\mathrm{w}}$	Molal density of water (55.56 kmol/m³)
${\theta }_{ }$	Parameter in Equation (A24) in Table A1 of Appendix A