**3. Methodology**

The main steps in the proposed methodology are shown in the flowchart of Figure 1. The methodology is streamlined via the following tasks:


**Figure 1.** Flowchart summarizing the methodology.

First, the various configurational alternatives are embedded through a superstructure representation that represents the basis for formulating the optimization program. In order to explicitly include cost optimization within the optimization formulation, a correlation is developed for estimating capital cost of the proposed biorefineries. Three objectives are considered using economic, environmental, and safety metrics. The ε-constraintmethod is used to solve the multiobjective optimization problem. The economic metric (e.g., maximizing return on investment) is used as the objective function while the safety and environmental objectives are placed in the constraints with certain bounds that are repeatedly altered to generate the tradeoff results. First, the relaxed optimization problem is solved for maximizing profit with no bounds on the safety and environmental metrics. Next, the safety and environmental bounds are added and the optimization program is solved to generate alternate configurations with tradeoffs that constitute the basis for decision making.

The following sections summarize the key steps used in setting up the optimization formulation and the solution approach.

### *3.1. Development of Superstructure and Optimization Formulation*

The first step is to create a superstructure that embeds the options of interest. Figure 2 shows the superstructure with centralized and decentralized options. A source–interception–sink representation [41] is used. Sources represent the biomass available from each region. Sinks represent the market demands in the various regions. The centralized and decentralized biorefineries represent the interceptors. Biomass may be processed within the same city in a decentralized facility or hauled to a larger centralized plant that accepts feedstock from multiple regions. The products may also be used locally or transported for sales in other regions. The flowrates of biomass and products assigned within the superstructure (represented by dashed arrows) as well as the throughput through each biorefinery are unknown and to be determined via the solution of the optimization formulation. A zero value indicates the absence of an option.

**Figure 2.** Superstructure of centralized and decentralized biorefining options.

Using the aforementioned superstructure, the optimization formulation is given below:

Maximize Profitability (e.g., return on investment (ROI)) (1)

Subject to:

$$\text{Annual Sales} = \sum\_{i=1}^{N\_{\text{Cities}}+1} \sum\_{j=1}^{N\_{\text{Troch}}} \sum\_{p=1}^{N\_{\text{Products}}} \mathbb{C}\_{p} \* \mathbf{R}\_{i,j,p} \tag{2}$$

where *Ri,j,p* is the production capacity of product p in the plant in city *i* using technology *j* (which is an optimization variable).

To ensure a practical capacity of each plant between a lower bound (LB) and an upper bound (UB), the following constraint is used:

$$LB \* I\_{i,j,p} \le R\_{i,j,p} \le LB \* I\_{i,j,p} \tag{3}$$

where *Ii,j,p* is a binary integer variable that takes the value of 1 when product *p* is produced in region/city *i* using technology j. Otherwise, it is zero.

To limit the number of facilities per city to a maximum number, the following constraint is used:

$$\sum\_{j=1}^{N\_{\text{Tach}}} \sum\_{p=1}^{N\_{\text{Products}}} I\_{i,j,p} \le \text{NPlants}\_i^{\text{max}} \; \forall i \tag{4}$$

The fixed capital investment (FCI) is given by:

$$FCI = \sum\_{i=1}^{N\_{\text{Cities}}+1} \sum\_{j=1}^{N\_{\text{Tcell}}} \sum\_{p=1}^{N\_{\text{Products}}} FCI\_{i,j,p} \tag{5}$$

The total capital investment (TCI) is given by

$$\text{TCI} = \text{FCI} + \text{WCI} \tag{6}$$

where WCI is the working capital investment. In this work, WCI is taken to be 15/85 of the FCI (El-Halwagi, 2017a).

The annual net profit (ANP) is expressed as (El-Halwagi, 2017a):

ANP = (Annual Sales − Annual OPEX − Annualized FCI) \* (1 − Tax Rate) + Annualized FCI (7)

The ε-constraintmethod is used to account for the environmental and safety objectives:

$$EM \le EM^{\text{Max}} \tag{8}$$

$$RM \le RM^{\text{Max}} \tag{9}$$

where *EM* and *RM* are the environmental and risk metrics, respectively, and Max designates an upper bound on the metric. The metrics may be selected from a wide variety of options [34,35,41]. The case study in this paper shows an example of the calculation and use of such metrics.

The process yield is:

$$G\_{i,j,p} = \mathcal{Z}(F\_{i,j,p}) \tag{10}$$

where ∅ is the yield function that depends on the feed characteristics and technology.

The availability of feedstock is:

$$F\_{\vec{l}} \le F\_{\vec{l}}^{\max} \,\,\forall \vec{l} \tag{11}$$

The market limitations are:

$$G\_{i,p} \le G\_{i,p}^{\max} \,\,\forall i \tag{12}$$

The flowrate of the biomass received in city *i*, for technology *j*, to produce product *p* is obtained from shipments coming from all cities. Therefore,

$$F\_{i,j,p} = \sum\_{i'=1}^{N\_{\text{Cities}}+1} F\_{i,i',j,p} \tag{13}$$

where *Fi*,*<sup>i</sup>* ,*j*,*<sup>p</sup>* is the biomass flowrate assigned from city *i* to city *i*' and technology *j* to produce product *p*.

Therefore, the sum of all shipments of biomass from a city is given by the shipments distributed from sources to sinks:

$$F\_i = \sum\_{j=1}^{N\_{\text{Toch}}} \sum\_{p=1}^{N\_{\text{Products}}} F\_{i,j,p} \,\forall i \tag{14}$$

The net production of product *p* is:

$$\mathbf{G}\_{i,p} = \sum\_{j=1}^{N\_{\text{Cyl}}} \mathbf{G}\_{i,j,p} - \sum\_{i'=1}^{N\_{\text{Critic}+1}} \mathbf{G}\_{i,i',p}^{Tnsported} \,\,\forall i,p \tag{15}$$

The first term on the right-hand side represents that total amount of product *p* generated by all technologies in city *i*. Product *p* may also be shipped to or from city *i*. The second term represents the net amount of product *p* shipped out of city *i.* The term *GTrasported i*,*i* ,*<sup>p</sup>* has a positive value when it is shipped out of city *i* and a negative value when it is shipped to city *i*.

#### *3.2. Capital Cost Estimation*

A convenient approach to including a parametric function for the estimation of CAPEX in the optimization formulation is to use a generic formulation that works for various biorefining technologies, feedstocks, and products. Because of the nature of this work intended to generate high-level directions for decision making, order-of-magnitude cost estimates are appropriate. Towards this end, we have carried out data analytics for the information extracted from 40 biorefineries. A functional form similar

to the correlation developed by Zhang and El-Halwagi [42] was used. The correlation relates the FCI to two main factors: process throughput (feed flowrate of biomass) and number of functional steps "*N*" (which represent primary operation such as separation, reaction, and waste treatment). The data sources are given in the Supplementary Materials.

The resulting correlation is expressed as:

$$\text{FCI (in USDM)} = 0.16 \ast N \ast \text{(Flowrate of biomass feed in 1000 tonnes/year)} \ast 0.84 \tag{16}$$

As indicated earlier, for the intended purposes of high-level decision making, an order-ofmagnitudes cost estimation has the proper level of accuracy [41,42].

#### *3.3. Life Cycle for RDF to Methanol Process*

The centralized vs. decentralized processing for the RDF to methanol process needs an account of emissions at different stages of the life cycle. A life cycle assessment framework [43] is used to compute these emissions. For the process, the system boundaries are considered to be at the processing plant gate, where the RDF is brought. For the transportation emissions, the latest U.S. Environmental Protection Agency (EPA) emission factors for transportation are considered from the Emission Factors for Greenhouse Gas Inventories [44].

#### *3.4. Safety Analysis*

Two types of risks are evaluated for the process and for transportation. A relative risk approach is used to compare and rank the risks of the various alternatives. For process risk, hazard identification is carried out using the Hazardous Process Stream Index (HPSI) [45]. The HPSI is proposed to define and compare the level of hazard of each stream. The estimation is based on five normalized indicators, which consider pressure, density, molar flowrate, heat of combustion, and flash point, as follows:

$$I\_P = \frac{\text{pressure value of individual stream}}{\text{average pressure for all streams}} \tag{17}$$

$$I\_{\rho} = \frac{\text{density value of individual stream}}{\text{average density for all streams}} \tag{18}$$

$$I\_{\rm MF} = \frac{\text{molar flow value of individual stream}}{\text{average molar flow for all streams}} \tag{19}$$

$$I\_{\Delta Hc} = \frac{\text{heat of combustion of individual stream}}{\text{average heat of combustion for all streams}} \tag{20}$$

$$I\_{Fp} = \frac{\text{flash point score of individual stream}}{\text{average flash point score for all streams}} \tag{21}$$

The result of *HPSI* is calculated through the following expression:

$$HPSI = \left(\frac{I\_P \cdot I\_{MF} \cdot I\_{\Delta Hc} \cdot I\_{FP}}{I\_P}\right) \cdot W \tag{22}$$

This index accounts for the relationship between the five dimensionless indicators of each process stream, and *W* is used as a scaling factor. As such, an increase in the capacity implies an increase in flowrate and inherently a more significant mass release in the case of loss of containment and its consequences. Therefore, *W* is defined as the ratio of the production capacity of the process with capacity *i* (*CPi*) to the reference process capacity (*CPbase*). It is worth noting that the proposed index takes into account the impact of process capacity. For the same process technology and flowsheet, the smallest-scale process risk is considered the reference if the production capacity is different.

$$\mathcal{W} = \frac{\text{CPi}}{\text{CP}\_{\text{base}}} \tag{23}$$

The process line with the highest value of HPSI poses the highest risk levels, reflecting the severity of the process stream in the loss of containment case, leading to a fire or explosion.

The relative process risk level is estimated from the HPSI value. A new normalization approach is proposed to enable the identification of relative risk using the following equation:

$$R\_i = \frac{HPSI\_i - HPSI\_{\min}}{HPSI\_{\max} - HPSI\_{\min}} \tag{24}$$

where *HPSIi* is the individual index value of the process streams, *HPSImin* is the smallest index value of the process streams, *HPSImax* is the maximum index value of the process streams, and *Ri* is the individual risk of the process streams.

Once the individual risk has been estimated, the total relative process risk (*RT*) is estimated by the arithmetic average of the individual risks as follows:

$$R\_T = \frac{\sum\_{i}^{n} R\_i}{PS} \tag{25}$$

where *PS* is the total number of process streams. The risk scale is defined according to Table 1.


**Table 1.** Risk scale based on the Hazardous Process Stream Index (HPSI).

If different process technologies are compared, HPSI must be assessed for each process using the same production capacity and then the assessment is carried out for the total relative process risk.

It is worth noting that alternate approaches for risk assessment may be used. For instance, an alternative approach to the aforementioned HPSI to determine the risk of the process at a different production scale is to consider the sum of the individual risks instead of the average used in this work. To classify risk based on summation, a risk scale may be defined to categorize/classify the different processes based on the sum.

For the methanol transportation risk analysis, the approach proposed by Zhang et al. (2018) is adopted. The following is a summary of the approach. Two transportation modes are considered: highway and railroad. Three variables were defined to assess the risk factor of methanol transportation using the two alternatives: (1) value loss per accident (*Ct*), (2) number of trips (*Nt*) per year, and (3) overall probability of accident as a function of distance (d) when methanol is moved among cities (*Pi*,*j*,*d*). The number of trips is calculated, dividing the maximum demand of each city by the load capacity of each transport. The overall probability of an accident during methanol transport is estimated by the product of general accident rate for transportation mode and the cumulative probability as a function of the natural logarithm of distance for methanol highway and railroad incidents. The product of these three variables provides the risk factor of each transport option
