$a_z$	geometric ratio $L/R_1$
$c_p$	specific heat $[J/molK]$ or $[J/kgK]$
d	characteristic dimension of packed bed particles $\left[m\right]$
${\mathcal{D}}_{rr}$	radial dispersion coefficient $\left[m^2/s\right]$
${\mathcal{D}}_{zz}$	axial dispersion coefficient $\left[m^2/s\right]$
$\mathcal{D}$	diffusion coefficient $\left[m^2/s\right]$
$\mathbb{D}$	effective dispersion tensor $\left[m^2/s\right]$
f	average molar weight $[kg/mol]$
$J_h^m$	hydrogen mass flux through the membrane $[k{g}_{H_2}/\left(m^2·s\right)]$
$J_h^{m\ast }$	hydrogen molar flux through the membrane $[mo{l}_{H_2}/\left(m^2·s\right)]$
k	reaction rate constant $[mol/\left(m^3·s·Pa\right)]$
$k_e$	effective heat conductivity $[W/mK]$
$K_{eq}$	equilibrium constant $\left[P{a}^2\right]$
L	reactor length $\left[m\right]$
$\mathbf{n}$	unit vector normal to the membrane surface $\left[-\right]$
P	pressure $\left[Pa\right]$
$P_i$	partial pressure of the i-th component $\left[Pa\right]$
$P_L$	outlet pressure $\left[Pa\right]$
$P_U$	reference pressure $\left(\mu U{R}_1/\kappa \right)$ $\left[Pa\right]$
${\mathbb{P}}_m$	membrane permeability $[k{g}_{H_2}/\left(m^2·s·P{a}^{0.5}\right)]$
${\dot{Q}}_{wall}$	heat flux between catalyst and reactor wall $[W/m^2]$
${\dot{Q}}_{permeate}$	heat flux between catalyst and permeate $[W/m^2]$
r	radial coordinate $\left[m\right]$
$r_i$	volume-specific mass rate of production of the i-th component $[kg/\left(m^3·s·Pa\right)]$
$\mathcal{R}$	gas constant $[J/\left(mol·K\right)]$
$R_1$	inner reactor radius $\left[m\right]$
$R_2$	outer reactor radius $\left[m\right]$
$R_m$	volume-specific molar rate of methane consumption $[mol/\left(m^3·s·Pa\right)]$
T	temperature $\left[K\right]$
U	inlet gas velocity $\left[m/s\right]$
$U_m$	heat transfer coefficient between permeate and retentate $[W/m^{2}K]$
$U_w$	heat transfer coefficient between wall and retentate $[W/m^{2}K]$
$\mathbf{v}$	mass average velocity $\left[m/s\right]$
${\mathbf{v}}^{\ast }$	molar average velocity $\left[m/s\right]$
$W_i$	molar weight of the i-th component $[kg/mol]$
z	axial coordinate $\left[m\right]$
Greek symbols
$\alpha$	dimensionless outlet pressure $\left(P_L/P_U\right)$
$\beta$	ratio between characteristic and inlet velocities $\left(\kappa P_{atm}/\left(\mu R_{1}U\right)\right)\left[-\right]$
$\gamma$	dimensionless permeability parameter $\left({\mathbb{P}}_{m}RT{P}_{atm}^{-1/2}/W_{h}U\right)$
$\mathsf{\Gamma }$	$2\gamma /\left(a_r^2-1\right)$
$\delta$	membrane thickness $\left[m\right]$
$\eta$	proximity to reaction equilibrium $\left[-\right]$
$\kappa$	packed bed permeability $\left[m^2\right]$
$\mu$	gas viscosity $\left[Pa·s\right]$
${\mathsf{\Pi }}_{H_2}$	dimensionless permeate flow rate
$\rho$	gas density $\left[kg/m^3\right]$
${\rho }_i$	density of the i-th component $\left[kg/m^3\right]$
$\sigma$	geometric ratio, $R_2/R_1$
$\tau$	packed bed tortuosity factor $\left[-\right]$
${\nu }_i$	stoichiometric coefficient of the i-th component $\left[-\right]$
$\Phi$	intrinsic membrane permeability
${\omega }_i$	mass fraction of the i-th component $\left[-\right]$
$\mathsf{\Omega }$	linear combination of hydrogen and methane densities $\left(-{\nu }_m{\tilde{\rho }}_h+{\nu }_h{\tilde{\rho }}_m\right)$ $\left[-\right]$
$\mathsf{\Psi }$	hydrogen recovery (permeated hydrogen/produced hydrogen) $\left[-\right]$
${\mathsf{\Psi }}_s$	separator-base yield (permeated hydrogen/inlet hydrogen) $\left[-\right]$
$\mathsf{\Theta }$	inhibition factor
Dimensionless parameters
$\mathrm{Da}$	Damkholer number $\left(RTk{R}_1/U\right)$
${\mathrm{Da}}^{\ast }$	modified Damkholer number $\left(\mathrm{Da}/\mathsf{\Gamma }\right)$
${\tilde{\mathcal{D}}}_{rr}$	dimensionless radial dispersion $\left({\mathcal{D}}_{rr}/\mathcal{D}\right)$
$\tilde{\mathbb{D}}$	dimensionless dispersion tensor $\left(\mathbb{D}/\mathcal{D}\right)$
$l_p$	characteristic length of permeation $2\sqrt{{\rho }_h^0}/\mathsf{\Gamma }$
$Pe$	Peclet number $\left(U{R}_1/\mathcal{D}\right)$
$P{e}_m$	molecular Peclet number $\left(Ud/D\right)$
$P{e}_r^{eff}$	effective radial Peclet number $\left(Ud/{\mathcal{D}}_{rr}\right)$
$P{e}_z^{eff}$	effective axial Peclet number $\left(Ud/{\mathcal{D}}_{zz}\right)$
$Re$	Reynolds number $\rho U{R}_1/\mu$
$Sc$	Schmidt number $\mu /\left(\rho \mathcal{D}\right)$
Subscripts
c	carbon dioxide
h	hydrogen
m	methane
w	water
i	i-th component