$C$	Concentration (mol m−3)
$C_{mean}$	Mean value of $C$ (mol m−3)
$c_k$	Membrane coefficient based on the Knudsen diffusion model (mol m−2 Pa−1 s−1)
$c_M$	Membrane coefficient based on the molecular diffusion model (kg m−2 Pa−1 s−1)
$c_m$	Membrane permeation coefficient (mol m−2 Pa−1 s−1)
$D_b$	Diffusion coefficient of CO2 in MEA (m2 s−1)
$d_{h,i}$	Equivalent hydraulic diameter of channel (m), i = spiral, empty
$Er$	Accuracy deviation of experimental results from the theoretical predictions
$E$	absorption flux enhancement
$f_F$	Fanning friction factor
$H_C$	Dimensionless Henry’s constant
$H_i$	Hydraulic dissipate energy (J kg−1), i = spiral, empty
$I_E$	Absorption flux enhancement
$I_P$	Power consumption relative index
${\omega }_i$	Molar flux (mol m−2 s−1)
$k_a$	Mass-transfer coefficient in the gas feed stream (m s−1)
$k_b$	Mass-transfer coefficient in the liquid absorbent side (m s−1)
$K_{ex}$	Equilibrium constant
${K^{\prime }}_{ex}$	Reduced equilibrium constant
$K_m$	Overall mass-transfer coefficient of membrane (m s−1)
$\mathcal{\ell }{w}_{f,j}$	Friction loss (J kg−1), j = CO2, MEA
$L$	Channel length (m)
$L_{spiral}$	Length of spiral wired channel (m)
$M_W$	Average molecular weight of CO2 and N2 gas mixture (kg mol−1)
Nexp	Number of experimental measurements
$P_1$	Saturation vapor pressure in the gas feed flow side (Pa)
$P_2$	Saturation vapor pressure in the liquid absorbent flow side (Pa)
$q_a$	Volumetric flow rate of the gas feed stream (m3 s−1)
$q_b$	Volumetric flow rate of the MEA absorbent side (m3 s−1)
$R$	Gas constant (8.314 J mol−1 K−1)
Re	Reynolds number
$r_i$	Radius of inner tube (m)
$r_o$	Radius of shell (m)
rp	Membrane pore radius (m)
Sc	Dimensionless Schmidt number
ShS	Enhanced dimensionless Sherwood number
$S{h}_{lam}$	Dimensionless Sherwood number for laminar flow
Wp	Pitch width (m)
$\omega$	Absorption flux (mol m−2 s−1)
${\left|Y_m\right|}_{\mathcal{\ell }n}$	Natural log mean CO2 mole fraction in the membrane
$z$	Axial coordinate along the flow direction (m)
Greek letters
${\alpha }^S$	Mass-transfer enhancement factor
$\beta$	Aspect ratio of the channel
${\delta }_m$	Thickness of membrane (µm)
$\epsilon$	Membrane porosity
$\overline{\nu }$	Average velocity (m s−1)
${\rho }_i$	Density (kg m−3), i = CO2, MEA
${\gamma }_m$	Concentration polarization coefficients
Subscripts
1	Membrane surface on MEA side
$2(l)$	Liquid phase on membrane surface on MEA side
$2 ( g)$	Gas phase on membrane surface on MEA side
a	The gas feed flow channel
b	The liquid absorbent flow channel
cal	Calculated results
spiral	Inserting spiral wires as promoters
empty	Empty channel
exp	Experimental results
in	Inlet
out	Outlet
theo	Theoretical predictions
Superscripts
con	Concurrent-flow operations
counter	Countercurrent-flow operations