**5. Results and Discussion**

The optimization formulation is a mixed-integer nonlinear program (MINLP) with 68 variables. The solution of the relaxed problem with no bounds on the environmental or safety objectives (using the Global Solver of LINGO software) is shown by Figure 5. The global solution of the relaxed

optimization problem features a centralized facility and achieves a return on investment (ROI) of 11.8%/year. The GHG emissions of the relaxed problem is 291 <sup>×</sup> 103 tonnes CO2eq/year and the process risk index, HPSI, is 0.75 (high risk). As described in the methodology, the ε-constraintmethod was used to establish the tradeoffs among the various objectives. Using bounds of 285 <sup>×</sup> 103 tonnes CO2eq/year on the GHG emissions and 0.5 on HPSI (medium risk), another solution (shown by Figure 6) is generated, which is economically suboptimal but superior for the environmental and safety objectives. It has a common facility for cities (A and B) and a local facility in city C. The ROI for the common facility matches that of the global solution, but there is a decrease in the ROI for the facility in city C to 10.1%/year. Table 5 shows the GHG emissions and safety for the optimal and suboptimal solutions.

**Figure 5.** Economically optimum solution with a centralized facility (ROI is return on investment).

**Figure 6.** Suboptimal solution with centralized and decentralized facilities.


**Table 5.** Risk results for methanol transportation.

The results of the transportation risk analysis resulting from spillage/noncontainment due to accidents are shown by Table 5. The risk for transporting biomass was assumed to be negligible compared to the risk of transporting methanol (which involves loss of containment, toxicity, flammability, and explosion issues). For the optimal solution, transporting methanol to cities B and C by highway is safer than by railroad. The total risk factor using a highway gives a value of 634.14, while the total risk factor using a railroad is 801.24. The differences in risk are attributed to distance. Therefore, the lower risk factor for transporting methanol from a centralized facility is obtained by using the railroad to supply methanol to city B and by using the highway for city C, giving a value of 554.95. In the suboptimal solution, the use of highway as a transport medium is safer than railroad. Table 6 summarizes the carbon footprint and risk for the economically optimal and the suboptimal solutions. Although the economically optimal solution offers a higher ROI, it involves higher carbon footprint and higher risk. The decision makers should balance these conflicting objectives and select a strategy that reconciles the importance of the economic, environmental, and safety objectives. Alternatively, the decision makers may use an economic platform to incorporate sustainability, risk, and resilience into the ROI calculations [57–62].

**Table 6.** Greenhouse gas (GHG) emissions and risk for the optimal and suboptimal solutions.


### **6. Conclusions and Recommendations for Future Research**

This paper introduces a systematic approach to the design and comparison of centralized versus decentralized biorefining options. The paper provides the following new contributions: (1) a superstructure representation embedding all configurations of interest; (2) an optimization formulation with economic, environmental, and safety objectives that are solved using the ε-constraintmethod to establish the tradeoffs among the multiple objectives; and (3) incorporation of transportation risk (in addition to process risk using a new metric quantifying total process risk). Furthermore, a CAPEX cost correlation is developed for order-of-magnitude estimation purposes. This correlation offers the advantages of using few data (feed flowrate and number of functional steps) and enabling the explicit incorporation of cost functions in the optimization formulation without committing to the type of technology or the size of the plant. The limitation of this correlation is that its level of accuracy is an order-of-magnitude estimate and should therefore be used with caution, with the results checked using more detailed cost estimation methods once a detailed design is available. Alternatively, if more accurate cost correlations are available, they can be readily used in the optimization formulation, which does not depend on a specific correlation. A case study is solved to address centralized versus decentralized options for converting RDF to methanol. The centralized option showed better profitability but higher levels of carbon footprint and risk.

This work constitutes the basis for several future research directions. Specifically, the following topics are recommended for future research:


**Supplementary Materials:** The following are available online at http://www.mdpi.com/2227-9717/8/12/1682/s1, Figure S1: Data used in developing FCI correlation, Table S1: Summary of extracted data.

**Author Contributions:** All authors contributed to conceptualization, methodology, validation, formal analysis, investigation, data curation, writing—original draft preparation, writing—review and editing, and visualization. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Conflicts of Interest:** The authors declare no conflict of interest.

## **Nomenclature**


