# Evaluation of Algae-Based Biodiesel Production Topologies via Inherent Safety Index (ISI)
## 2 Materials and Methods
### Inherent Safety Analysis  
The inherent safety of the three pathways for biodiesel production from microalgae was evaluated following the inherent safety index (ISI) methodology proposed by [PERSON] [55]. The ISI technique is used to measure the inherent safety of chemical processes at the conceptual design stage to avoid and eliminate hazards [56]. The total inherent safety index \(\text{I}_{\text{TI}}\) includes two terms: chemical safety index \(\text{I}_{\text{CI}}\) and process safety index \(\text{I}_{\text{PI}}\) as shown in Equation (14). \[\text{I}_{\text{TI}}=\text{I}_{\text{CI}}+\text{I}_{\text{PI}} \tag{14}\]  
The first term is determined from the contribution of parameters such as reactions heat, toxicity, explosiveness, flammability, corrosiveness, and chemical interaction of the substances involved in the process. The second term is calculated from process parameters such as temperature, pressure, inventory, safety equipment, and safe process structure. Figure 5 depicts the criteria to evaluate \(\text{I}_{\text{CI}}\) and \(\text{I}_{\text{PI}}\). The chemical safety index and the process safety index are determined as shown in Equations (15) and (16), considering the sum of the subindices related to the criteria mentioned in Figure 5.  
\[\text{I}_{\text{CI}}=\text{I}_{\text{RM,max}}+\text{I}_{\text{BS,max}}+\text{I }_{\text{INT,max}}+(\text{I}_{\text{H}}+\text{I}_{\text{ex}}+\text{I}_{\text {box}})_{\text{max}}+\text{I}_{\text{COR,max}} \tag{15}\]  
\[\text{I}_{\text{PI}}=\text{I}_{\text{I}}+\text{I}_{\text{T,max}}+\text{I}_{ \text{P,max}}+\text{I}_{\text{EQ,max}}+\text{I}_{\text{ST,max}} \tag{16}\]  
where \(\text{I}_{\text{rmmax}}\) and \(\text{I}_{\text{rsmax}}\) are the main and side chemical reaction subindices, respectively, \(\text{I}_{\text{intmax}}\) is the chemical interaction subindex, \((\text{I}_{\text{H}}+\text{I}_{\text{ex}}+\text{I}_{\text{box}})_{\text{max}}\) is the dangerous substance subindex and \(\text{I}_{\text{cormax}}\) represents the corrosiveness subindex. \(\text{I}_{\text{I}}\) is the inventory subindex, \(\text{I}_{\text{Tmax}}\) and \(\text{I}_{\text{pmax}}\) are the subindices for process temperature and pressure, \(\text{I}_{\text{EQmax}}\) is the subindex for equipment risk and \(\text{I}_{\text{STmax}}\) is the subindex for process safe structure. Figure 4: Process diagram for biodiesel production from microalgae via hydrothermal liquefaction (HTL). The calculations under the ISI methodology are performed considering the worst-case scenario. The chemical reactivity subindex is determined for the main and side reactions according to the released reaction heat (\(\Delta\)H\({}_{\text{r}}\)). Equation (17) shows the expression to calculate the heat of reaction, where H\({}_{\text{fprod}}\) and H\({}_{\text{freeac}}\) are the standard enthalpy of formation for products and reactants, respectively. \[\Delta\text{H}_{\text{r}}=\Sigma\text{H}_{\text{fprod}}-\Sigma\text{H}_{\text{ freeac}} \tag{17}\]  
The chemical interaction sub-index evaluates undesirable reactions between chemicals and materials in the plant area. These reactions are not expected to take place inside the reactor, therefore, are not considered within the chemical reactivity subindex. The dangerous substance subindex is assessed according to the flammability (flashpoint), explosivity (Lower and Upper explosive limit), and toxicity (Threshold limit value--TLV). The corrosiones subindex is determined based on the construction material required for the equipment depending on the corrosive substances. The values assigned for the chemical safety sub-index are determined using specific weights, as shown in Table 1.  
The inventory subindex is measured by the mass flows in the equipment of inside battery limits area (ISBL) during a retention time of 1 h. The temperature and pressure subindices consider the maximum temperature and pressure registered in the process. Finally, the safety equipment subindex evaluates the most unsafe equipment within the