$c_p$	specific heat (J·kg−1·K−1);
$d_c$	catalytic pellets diameter (m);
$d_i$	internal shell/tube diameter for MR and SR respectively (m);
$d_e$	outside shell/tube diameter for MR and SR respectively (m);
$D_{0,H}$	diffusion pre-exponential factor (m2·s−1);
$E_a$	activation energy for hydrogen permeation through metallic membranes (J·mol−1);
$E_D$	activation energy for the diffusion of hydrogen atoms (J·mol−1);
${\left(\frac{d{F}_{H_2}}{dz}\right)}_{prod.}$	rate of production of hydrogen (mol·m−1·s−1);
${\left(\frac{d{F}_{H_2}}{dz}\right)}_{perm.}$	rate of permeation of hydrogen (mol·m−1·s−1);
f	friction factor;
$F_G$	mass transfer coefficient (kmol·h−1·m−2);
$F_{OG}$	overall mass transfer coefficient (kmol·h−1·m−2);
GHSV	gas hourly space velocity (h−1);
$h_i$	convective heat transfer coefficient in packed bed (J· m−1·s−1·k−1);
$I{D}_s$	internal shell diameter (m);
$I{D}_t$	internal tube diameter (m);
$J_H{}_2$	hydrogen molar flux (mol·m−2·s)
$k_T$	thermal conductivity of tube (J·s−1·m−1·K−1);
$k_c$	thermal conductivity of catalyst (J·s−1·m−1·K−1);
$k_1$	steam reformer reaction rate constant;
$k_2$	water gas shift reaction rate constant;
$k_3$	overall steam reformer reaction rate constant;
$K_1$	steam reformer equilibrium constant (bar2);
$K_2$	water gas shift equilibrium constant;
$K_3$	overall steam reformer equilibrium constant (bar2);
$K_{CO}$	carbon monoxide adsorption equilibrium constant;
$K_{C{H}_4}$	methane adsorption equilibrium constant;
$K_{H_2}$	hydrogen adsorption equilibrium constant;
$K_{H_{2}O}$	steam adsorption equilibrium constant;
$\overline{K_{H_2}}$	average hydrogen permeance (kmol· h−1·m−2·bar−0.5);
$L$	reactor, membrane geometrical length (m);
$O{D}_s$	outside shell diameter (m);
$O{D}_t$	outside tube diameter (m);
$P$	operating pressure (bar);
$p_{CO}$	carbon monoxide partial pressure (bar);
$p_{C{H}_4}$	methane partial pressure (bar);
$p_{C{O}_2}$	carbon dioxide partial pressure (bar);
$p_{H_{2}O}$	steam partial pressure (bar);
$p_{H_2}$	hydrogen partial pressure (bar);
$P_{H_2}^0$	permeability pre-exponential factor (kmol·h−1·m−1·bar−0.5);
$P_{H_2}$	hydrogen permeability (kmol·h−1·m−1·bar−0.5);
$r_1$	steam reformer reaction rate (mol·kgc−1·s−1);
$r_2$	water gas shift reaction rate (mol·kgc−1·s−1);
$r_3$	overall steam reformer reaction rate (mol·kgc−1·s−1);
$r_i$	rate of disappearance of i-th reactions (kmoli-th·kgc−1·h−1);
$r_{C{H}_4}$	rate of disappearance of methane (kmolCH4·kgc−1·h−1);
$r_{C{O}_2}$	rate of production of carbon dioxide (kmolCH4·kgc−1·h−1);
$r_{H_2}$	rate of production of hydrogen (kmolCH4·kgc−1·h−1);
$Re$	Reynolds number;
S/C	steam to carbon ratio;
$T$	operating temperature (K);
$T_w$	tube wall temperature (K);
$u$	superficial velocity of gas mixture (m3·m−2·s−1);
$U$	overall mass transfer coefficient (J·m−2·K−1·s−1);
$X_{C{H}_4}$	methane conversion;
$X_{C{O}_2}$	carbon dioxide yield;
Apices and Subscripts
$c$	relative to the catalyst;
LI	relative to the left interface in the film theory;
M	relative to the membrane;
ML	logarithm mean;
P	relative to permeate side;
$R$	relative to the retentate side;
$RI$	relative to the right interface in the film theory;
r	relative to reactor;
$s$	relative to the shell-side;
t	relative to tube-side;
$z_i$	axial coordinates of mass/heat/momentum balances;
Greek Letters
$\epsilon$	void fraction of the bed;
$\delta$	membrane thickness, (m);
$\Delta H_i$	molar enthalpy of i-th reactions (J·mol−1);
$\Delta H_R^0$	standard enthalpy of the surface dissociation reaction (J·mol−1);
$\Delta S_R^0$	entropy change of the dissociation reaction (J·mol−1·K−1);
${\eta }_i$	efficiency factor of i-th reactions;
${\eta }_{C{H}_4}$	methane efficiency factor;
${\eta }_{C{O}_2}$	carbon dioxide efficiency factor;
${\rho }_g$	density of gas mixture (kg·m−3);
${\rho }_c$	density of catalytic bed (kgc·m−3);
Ω	cross section of the reactor (m3)