$a_s$	shell area of membranes (m2);
$A_{tot}$	total membrane surface (m2);
$c_{tot}$	total concentration (kmol·m−3);
$D_{0,H}$	diffusion pre-exponential factor (m2·s−1);
$D_{H_2,m}$	diffusivity of hydrogen in the mixture retentate side (m2·s−1);
$D_{eq}$	equivalent diameter of membranes (m);
$d$	channel depth (m);
$E_a$	activation energy for hydrogen permeation through metallic membranes (J·mol−1);
$E_D$	activation energy for the diffusion of hydrogen atoms (J·mol−1);
$F$	molar flow rate (kmol·h−1);
$F_G$	mass transfer coefficient (kmol·h−1·m−2);
$F_{OG}$	overall mass transfer coefficient (kmol·h−1·m−2);
$HRF$	hydrogen recovery factor;
$I{D}_s$	internal shell diameter (m);
$J_{H_2}$	hydrogen flux (kmol·h−1·m−2);
$\overline{J}$	average hydrogen flux (kmol·h−1·m−2);
$j_D$	mass transfer dimensional group;
$K_{H_2}$	hydrogen permeance (kmol·h−1·m−1·bar−0.5);
$\overline{K_{H_2}}$	average hydrogen permeance (kmol·h−1·m−2·bar−0.5);
$L$	membrane length (m);
$LHV$	lower heating value (kJ/Nm3);
$N_G$	natural gas (kg/h);
$N_m$	number of membranes;
$O{D}_t$	outside tube diameter (m);
$O{D}_M$	outside membrane diameter (m);
$P_{H_2}$	hydrogen permeability (kmol·h−1·m−1·bar−0.5);
$P_{H_2}^0$	permeability pre-exponential factor (kmol·h−1·m−1·bar−0.5);
$P_t$	tube pitch (m);
$p_{H_2}$	hydrogen partial pressure on the right/left interface (bar);
$r$	membrane internal radius (m);
$Re$	average Reynolds number;
$v$	average velocity of the mixture, retentate side (m·s−1);
$Sc$	average Schmidt number;
$w$	channel width (m);
$y_{H_2}$	hydrogen molar fraction on the retentate/lefth interface of i-esimo step;
Apices and Subscripts
$j$	H2O, CO, CO2, CH4;
LI	relative to the left-interface in the film theory;
m	relative to the mixture;
cp	concentration polarization;
ML	logarithm mean;
$P$	relative to the permeate;
$R$	relative to the retentate-side;
$R^{*}$	relative to concentration polarization;
M	relative to membrane;
$RI$	relative to the right-interface in the film theory;
$s$	relative to the shell-side;
t	tube-side;
Greekletter
δ	membrane thickness, (m);
${\mu }_m$	viscosity of mixture, retentate side (Pa·s);
${\rho }_m$	density of mixture, retentate side (kg·m−3);
$\Delta S_R^0$	standard enthalpy of the surface dissociation reaction (J·mol−1·K−1);
$\Delta H_R^0$	entropy change of the dissociation reaction (J·mol−1);