Porous hollow fibres made of polyvinylidene fluoride were employed as membrane contactor for carbon dioxide (CO2) absorption in a gas–liquid mode with methyldiethanolamine (MDEA) based nanofluid absorbent. Both theoretical and experimental works were carried out in which a mechanistic model was developed that considers the mass transfer of components in all subdomains of the contactor module. Also, the model considers convectional mass transfer in shell and tube subdomains with the chemical reaction as well as Grazing and Brownian motion of nanoparticles effects. The predicted outputs of the developed model and simulations showed that the dispersion of CNT nanoparticles to MDEA-based solvent improves CO2 capture percentage compared to the pure solvent. In addition, the efficiency of CO2 capture for MDEA-based nanofluid was increased with rising MDEA content, liquid flow rate and membrane porosity. On the other hand, the enhancement of gas velocity and the membrane tortuosity led to reduced CO2 capture efficiency in the module. Moreover, it was revealed that the CNT nanoparticles effect on CO2 removal is higher in the presence of lower MDEA concentration (5%) in the solvent. The model was validated by comparing with the experimental data, and great agreement was obtained.