## 3 Results and Discussion
### Base Scenario  
This process configuration has been set to obtain the energy requirements of the plant in the base scenario. Demanded energy was parametrized as a function of the inlet temperature of the reactor and the glycerol mass fraction, which was the selected feedstock in this study. Then, the energy exchanged in the preheater, where the effluent from the reactor is the 'hot fluid' and the feed stream is the 'cold fluid', was analyzed. In the scope of this work, heat exchanger calculations have been performed using a reference value for the overall heat exchanger transfer coefficient (0.85 kW/m\({}^{2}\).K) [46] and determining the temperature of the two outlet streams based on the heat and material balances. Thus, by imposing a minimum pinch point temperature of 25 \({}^{\circ}\)C, an average area is obtained for each glycerol mass fraction considered. This design area is calculated to ensure that there is no temperature cross between hot and cold streams throughout the heat exchanger. The values for the areas ranged from 8.3 m\({}^{2}\) (10 wt.% glycerol) to 8.9 m\({}^{2}\) (30 wt.% glycerol). When selecting these data as the mean value to operate under these conditions, the outlet temperature of the 'hot fluid' leaving the preheater ranged from 212 \({}^{\circ}\)C to 223 \({}^{\circ}\)C. Figure 4a represents the variation of the thermal power exchanged in the preheater, observing an increase in the thermal power exchanged at low glycerol concentrations. Likewise, Figure 4b shows the thermal power required in the heater to achieve the reactor inlet temperature set. In this case, the energy requirement decreases as the amount of gasified glycerol increases. The total energy required for heating the feed stream (from ambient conditions) is represented by the sum of the thermal power exchanged in the preheater and that supplied in the heater. Clearly, the reduction in glycerol concentration and the increase in reactor inlet temperature maximize the exchanged thermal power in the preheater. This result comes from the great influence of the heat capacity variation of the mixture of glycerol and water on the thermal energy exchange. Figure 5 shows the mass heat capacity of the glycerol-water mixture with a concentration of 10 wt.% and 30 wt.%. There are differences between both concentrations, especially around the supercritical region, where the maximum heat capacity for 10 wt.% glycerol is 30.0 kJ/kg K at 390.1 \({}^{\circ}\)C, while for 30 wt.% glycerol, the maximum value decreases to 15.8 kJ/kg K at 406.2 \({}^{\circ}\)C.  
Figure 4: **(a)** Thermal power exchanged in the preheater; **(b)** Additional thermal power required in the heater to achieve the reactor inlet temperature in a range from 450 to 600 \({}^{\circ}\)C. Both figures are parametrized as functions of the glycerol mass fraction in the feed stream. It is also important to analyze the behavior of the outlet temperature of the reactor with respect to the inlet temperature, as shown in Figure 6. In all cases, there is an increase in the temperature of the reactor outlet stream with respect to the reactor inlet. When the glycerol mass concentration remains constant, this temperature difference decreases as the reactor inlet temperature increases. For example, operating at 20 wt.% glycerol, when the reactor inlet temperature is set at 450 \({}^{\circ}\)C, the temperature of the effluent leaving the reactor is 494.1 \({}^{\circ}\)C, thus, increasing the temperature in 44.1 \({}^{\circ}\)C. However, when the reactor inlet temperature is 600 \({}^{\circ}\)C, the temperature at the reactor outlet increases in 30.7 \({}^{\circ}\)C. Likewise, when the glycerol concentration increases, the temperature change between the reactor inlet and the outlet increases substantially. For example, operating at the lowest glycerol concentration (10 wt.%), the temperature changes from 15.3 \({}^{\circ}\)C to 0.2 \({}^{\circ}\)C throughout the reactor, when the reactor inlet temperature varies from 450 to 600 \({}^{\circ}\)C, respectively.