## 1 Introduction
Research in membrane performance, materials and additives has been done with successful results, from a technical point of view [16; 17; 18], but their economic viability is not demonstrated [19]. The second main approach in membrane technology for CO\({}_{2}\) capture is the use of membrane contactors as a non-selective barrier, which is considered in this work due to its well-known advantages, such as flexibility on the operation, controlled and known interfacial area, easy and proportional scale-up, low energy needs, and no solvent drop dragging because of the precise separation of both phases [7]. The membrane role is to increase the surface for the mass transfer exchange between both phases; i.e., the feed gas and the absorption liquid--by the action of a driving force [20] and the principal parameter to evaluate the process is the overall mass transfer coefficient. Several absorption liquids are used in this field but a general concern is the regeneration of the absorption liquid or the valorization of CO\({}_{2}\). Large emissions of CO\({}_{2}\) into the atmosphere are a concern that could become an opportunity for the industry if a valuable compound can be produced at minimum cost. The approach of our work tries to recover CO\({}_{2}\) as sodium carbonate (Na\({}_{2}\)CO\({}_{3}\)), following previous works that showed the technical viability of the carbonate production as pure crystals [21; 22; 23; 24], independently of the amount of impurities on the NaOH-containing streams. This is particularly interesting in pulp and paper, water treatment, and certain chemical sectors where NaOH can be substituted for sodium carbonate (Na\({}_{2}\)CO\({}_{3}\)) in certain uses (preparing of white liquors, impurities removal of saturated salt solution, etc.) [25]. The reaction of CO\({}_{2}\) with sodium hydroxide (NaOH) to produce sodium carbonate (Na\({}_{2}\)CO\({}_{3}\)) is considered [26]:  
Overall reaction (R\({}_{1}\)): CO\({}_{2}\) + 2 NaOH \(\rightarrow\) Na\({}_{2}\)CO\({}_{3}\) + H\({}_{2}\)O  
Rate-determining reaction (R\({}_{2}\)): CO\({}_{2}\) + OH\({}^{-}\)\(\rightarrow\) HCO\({}_{3}\)\({}^{-}\)  
Ionic reaction (R\({}_{3}\)): HCO\({}_{3}\)\({}^{-}\) + OH\({}^{-}\)\(\rightarrow\) CO\({}_{3}\)\({}^{-}\) + H\({}_{2}\)O  
NaOH offers fast absorption, producing a valuable product with commercial interest in 2015, sodium carbonate world production rounded 53.4 millions of tons [25]. NaOH can be taken from the waste streams coming from Merox Towers [27] or from subproduct flows of chlor-alkali industry [28]. In this latter case, the use of NaOH-containing streams for CO\({}_{2}\) capture opens the opportunity to implement an integrated (membrane) process; i.e., CO\({}_{2}\) capture & sodium carbonate crystallization--for the valorization of the wastewater in an internal process loop on the chlor-alkaliindustry. The interest of this approach is given because the brines (NaCl streams), used as raw material in the electrodialysis for the NaOH production, require a previous purification using Na\({}_{2}\)CO\({}_{3}\). Thus, NaOH-containing streams would reach both the CO\({}_{2}\) removal and the carbonate production, leading to a self-sufficient industry. Furthermore, the footprint associated to the electricity generation (electrodialysis is the larger energy-consuming step) would be minimized. The main objective of this manuscript is to compare the performance of the membrane based-absorption with the conventional absorption system using NaOH aqueous solutions as the absorption solvent. The different species involved in the absorption process are monitored and the influence of the main parameters (concentration and flow rates of both gas and liquid phases) on the mass transfer are addressed.