## 2 The Quick Preliminary Design Model
### CO\({}_{2}\) Capture System  
The use of a DMFC involves the production of CO\({}_{2}\), which must be treated. An intuitive solution would be its ejection to the outside, but this method has serious drawbacks. First, it is not energy-free, as CO\({}_{2}\) must be compressed in order to be ejected. The compressor needed for great depths would be necessarily heavy and robust. Moreover, this method lacks the necessary stealth for some missions due to the presence of bubbles and the noise produced during the ejection process. Some works study the feasibility of ejecting the CO\({}_{2}\) while minimizing the energy consumption [36; 37; 38], but they have not been considered here because of their complexity, in addition to the previously mentioned difficulties.  
In this work, a Carbon dioxide Capture System (CO\({}_{2}\)CS), which uses a physical adsorbent material, is considered. Physical adsorbents make use of van der Waals forces to retain the molecules of a flow stream [39]. The adsorption process is a quiet mechanism making the CO\({}_{2}\)CS proposed very suitable for its use in AUVs. A blower circulates the CO\({}_{2}\) produced through the adsorbent material where it is captured. Adsorption is an exothermic process and the generated heat must be evacuated. This effect is achieved by the excess stream that passes through a heat exchanger where it is cooled. It is subsequently blended with the CO\({}_{2}\) stream coming from the anode gas separator and redirected to the CO\({}_{2}\)CS again. The system is easily regenerable as the captured CO\({}_{2}\) can be released by heating and increasing the pressure. The calculations were carried out using two different materials: Zeolite 13X and Mg-MOF-74. Zeolites are microporous aluminosilicate minerals, characterized by their wide contact surface combined with high porosity and high thermal stability. Among all the zeolites, Zeolite 13X was chosen as it presents the highest adsorption capacity for CO\({}_{2}\)[40]. Mg-MOF-74 is a Metal-Organic Framework material (MOF) that combines an organic structure (framework) with active nodes consisting of metal ions. This MOF presents the highest capture capacity for CO\({}_{2}\) in accordance with the work of [PERSON] et al. [41] but, unlike Zeolite 13X, it is more expensive and its higher affinity to water makes necessary an excellent device for separating the CO\({}_{2}\) produced by the fuel cell from the aqueous stream transporting it [42].  
To calculate the amount of adsorbent needed, \(m_{ads}\), DMFC-AUV\(\backslash\)QpDM makes use of the adsorption isotherm curves published by [PERSON] et al. [43]. These curves indicate the capture capacity of a material under certain conditions of pressure, \(p_{ads}\), and temperature, \(T_{ads}\). In the case of the adsorption of CO\({}_{2}\) by Zeolite 13X or Mg-MOF-74 the uptake capacity decreases as temperature increases. In the worst scenario, \(T_{ads}\) was taken equal to 318 K as this is the higher temperature of the isotherms available.  
Figure 6: Connection schema for two fuel cell stacks. 1  
The capture capacity of Mg-MOF-74 is 2.4 times greater than the capacity of Zeolite 13X at 318 K (45 \({}^{\circ}\)C) and 100 kPa, 8 molCO2/gMOF versus 3.25 molCO2/gZeolite. However, the density of Mg-MOF-74 is also higher: 0.909 kg/m3 [44] versus 0.689 kg/m3 [45].  
To facilitate the circulation of the CO2 and allow its uniform distribution inside the CO2 CO, the absorbents are used in a bead format with a diameter equal to 2.5 mm. This involves a maximum packing density equal to 74.048 % in accordance with the Kepler conjecture [46].