**1. Introduction**

Society depends heavily on energy to support nearly all of its activities. Not surprisingly, the world is currently facing an unrivaled colossal energy threat. Alongside with the increase in global population, energy demand and consumption are projected to increase by 30% by 2040 [1]. However, fossil fuel resources such as oil, gas and coal, are unevenly distributed among nations and are now rapidly depleting. This thus raises issues on energy security and sustainability [2]. Furthermore, the continued use of fossil fuels has resulted in both health and environmental problems due to hazardous air emissions [3]. Recent studies assert that disastrous environmental problems will occur if the world does not reduce the emission of greenhouse gases (GHGs), making global warming a crucial issue. Hence, governments and policy makers are trying to take steps towards minimizing causes of global warming and climate change [4].

Because of these, the development of more sustainable and renewable sources of energy (e.g., solar, biomass, hydro, geothermal, and wind) as well as innovative strategies for cleaner production, and e fficient utilization of products is a necessity. Energy derived from biomass plays an important role in this. It is a clean, natural, renewable energy source. If one considers its entire life cycle, burning biomass results in net zero carbon emissions since CO2 was initially sequestered from the atmosphere during its growth. Furthermore, countries may utilize indigenous resources to replace current coal demand, thereby reducing dependency on conventional fossil fuels.

Even though the use of biomass for energy production has risen in the past few years, dedicated biomass-fired power plants remain to have small capacities (e.g., typically only 100 MW [5]) because of di fficulties associated with seasonal availability, inherent quality variations, and the wide geographical distribution of feedstock supply. To deal with varying biomass quality, advanced technologies for pre-treatment are used, such as drying, pelletization, torrefaction, and pyrolysis. These technologies can help reduce the moisture and ash contents, and bulk density of biomass feedstock without compromising their energy content significantly. Pre-treatment can thus improve the durability of biomass thereby reducing the costs associated to their storage and transport [6]. Nonetheless, performing pre-treatment entails additional costs and can result in additional environmental impacts, which may not be necessarily favorable for the system as a whole [7].

Co-firing of biomass with coal is a more practical interim approach towards increasing the utilization of renewable energy sources. This strategy requires minimal modification of existing power plants and allows for the continued use of high capacity coal power plants. Furthermore, biomass can easily be integrated into the energy supply chain by utilizing the existing infrastructure for fuel storage, transport and handling [4]. Biomass co-firing also improves the net energy and emissions balance of energy generation because it will require less coal to meet energy demands and thus less emissions associated with the mining and transportation of coal [8]. Biomass co-firing also provides an alternative to open field burning where the latter results in the generation of pollutants such as dioxins and furans because of uncontrolled burning conditions [9].

According to Ba et al. [10], the planning and managemen<sup>t</sup> of biomass and biomass co-firing supply chains have generally been modelled numerically using two main approaches: (1) simulation and (2) optimization models. Although, simulation modelling has the advantage of being highly flexible with the capability of handling stochastic events in complex supply chains, it is critiqued because of its inability to design large-scale optimal supply chains considering multiple objectives, which is usually the case in biomass co-firing supply chains.

Zandi Atashbar et al. [7] in a recent review, provided a critical analysis of various mathematical modelling approaches which have been used for biomass supply chains. Zandi Atashbar et al. [7] identified that the predominant objective among existing studies focused on minimizing overall costs, while some researchers define their objective function as to maximize overall profits or net present value (NPV). Most studies optimize based only on a single objective which may either be economic, environmental, or social. In fact, Shang [11] comments that existing epidemic modelling studies are similarly limited to considering single objectives. Environmental impact has usually been measured based on emissions, while the number of local jobs created has been used to measure the performance of the social objective. More recently, there have been limited studies focused on multi-objective optimization of biomass co-firing supply chains [7]. Pérez-Fortes et al. [12] asserts that the consideration of multiple objectives in the optimization of biomass co-firing supply chains is crucial because the design of such systems necessitates the satisfaction of conflicting goals, particularly those associated with economic and environmental factors. Multi-objective optimization models allow for the consideration of varied priorities of several stakeholders and balance the tradeoffs that exist between the objectives.

Only three studies dealing with multiple objectives in biomass co-firing were presented in literature. Mohd Idris et al. [13] and Gri ffin et al. [14] proposed a biomass co-firing supply chain optimization model that minimized the cost and emissions of the system, while Pérez-Fortes et al. [12] formulated a model in which decisions were assessed based on minimum NPV losses and maximum environmental impact annual savings. All three studies approached the problem by solving the economic and environmental objective functions separately.

Thus far, no studies have been able to optimize both the economic and environmental objectives simultaneously. Savic [15] explains that single objective optimization is only useful as a tool to allow decision makers to understand the nature of a problem. However, it cannot yield a set of alternative solutions that account for the trade-o ffs between conflicting objectives. Furthermore, considering only economic costs in optimizing a supply chain may result in a design which fails to consider critical processes and options to achieve the lowest cost at the expense of environmental sustainability. Alternatively, when a system is optimized in terms of environmental benefits, costs may be dramatically inflated making the solution impractical for implementation. Goal programming is an appropriate approach to simultaneously account for two or more conflicting objectives. It has been applied to several multi-objective optimization problems, demonstrating its e fficiency and e ffectiveness as an approach for tackling such problems [16]. The goal programming optimal solution for an industrial water network design problem was compared against other approaches used to solve multi-objective optimization problems, such as M-TOPSIS, LMS-TOPSIS, reference point method. Their results showed that although all approaches were able to obtain points on the Pareto front, the goal programming approach consistently obtained the best Pareto optimal solution with minimal computational e ffort [17].

Furthermore, there have been limited studies on the impact of feedstock quality [18] on the design of an optimal supply chain network. Most models overlook considering quality related issues, lowering logistics costs and emissions artificially. Scale-up scenarios become an important consideration when technologies expand from laboratory to commercial use. For instance, consider the implications of a conversion technology, which was rated to work with feedstock having a moisture content of about 10%, which in reality needs to work with fuels with moisture content of more than 25%. Moreover, significant financial losses will ensue when two batches of feedstock yield considerably di fferent amounts of energy. Several case studies establish that both scenarios are highly likely to take place in practice [19].

Pérez-Fortes et al. [12] has identified the following critical fuel properties: bulk density, moisture content, lower heating value, and ash content. For biomass, the bulk density and lower heating values are typically low while the moisture content is typically high. These properties are interdependent and affect different phases of the supply chain. Low heating values for example, will require more biomass to satisfy the needed energy while the low bulk density will need higher capacity vehicles or storage units [7]. High moisture and ash content will decrease the lower heating value [20]. Furthermore, with the ash in biomass feedstock being more alkaline that those from coal, fouling problems can potentially decrease the efficiency of boilers [21]. Biomass use must be managed carefully to avoid these effects [22].

Mohd Idris et al. [13] and Dundar et al. [4] identified the optimal blending ratios for fuels to satisfy a minimum biomass percentage regulation. Pérez-Fortes et al. [12] attempted to address the impact of biomass properties on the supply chain by integrating the pretreatment options into the optimization model. Required quality levels for the feedstock were considered but the impact of fuel properties during combustion were not captured. However, conversion technology usually ends up working with feedstock that do not follow the rated requirements, causing a corresponding decrease in yield or in the life of the equipment. In particular, fouling of heat transfer surfaces can become problematic. The impact of storage on the quality of biomass was also neglected in the study.

To address these gaps, a mathematical optimization model focused on a biomass co-firing network that simultaneously optimizes the economic and environmental objectives of the system is developed. Costs associated with retrofitting, storage, transport and pre-treatment are considered and the impact of biomass properties on blending ratio decisions, conversion e fficiencies and equipment life are also taken into account. Capturing these parameters increase the complexity of the model, but the solutions obtained provide more realistic insights into the behavior of the system and can be more reliable for decision-making.

The rest of the paper is organized as follows: Section 2 gives the formal problem statement. Section 3 gives a description of the system considered, while the MINLP model formulation is described in Section 4. The model capabilities are illustrated with a case study and scenario analysis in Sections 5 and 6. Finally, conclusions and prospects for future work are given in Section 7.

## **2. Problem Definition**

The formal problem statement can be stated as follows:






• The coal power plant *l* will have upper (*Lul* ) and lower (*Lll*) coal displacement limits if retrofitted, maximum allowable ash content (*aUl*), and upper (*mUl*) and lower (*mLl*) moisture content limits;

The problem may be visualized using the superstructure in Figure 1 where biomass and coal are obtained from their respective supply locations, biomass is pre-treated and then co-fired with coal in the identified powerplants. The objective is to determine the optimal allocation of biomass from the sources to the pretreatment facilities (*wijt*), allocation of processed biomass from the pretreatment facilities to the coal power plant (*xjlt*), the amount of coal that should be transported from the coal source to the power plant (*yklt*), the choice of which power plant should be retrofitted (*Rl*), when the pretreatment facilities (*Fjt*) and coal power plants (*Alt*) should be operating, and when the biomass option is implemented in the power plant (*Olt*) to achieve the simultaneous reduction in costs and environmental emissions. The solution should also indicate if the biomass should be stored in a pretreatment facility during period *t* (*Sjt*) and how much to keep in inventory (*Ijt*), if a power plant (*Clt*) or pretreatment facility (*Pjt*) should increase its capacity in another time period and by how much the capacities of the power plants (*f clt*) and pretreatment facilities (*f pjt*) should be increased.

**Figure 1.** Network superstructure.

#### **3. System Definition**

Biomass waste must be allocated from a set of source locations *i* ∈ *I* to a set of existing coal power plants *l* ∈ *L* to partially displace coal consumption. Coal is supplied to these plants by *k* ∈ *K* coal supply locations. Coal power plants generate electricity by co-firing biomass with coal to satisfy certain demands. Each biomass supply location provides biomass with certain properties, which is improved through pre-treatment in a given set of facilities *j* ∈ *J* before they are brought to the coal power plants for combustion. Biomass may be stored in pre-treatment facilities prior to transport.

#### *3.1. Biomass Co-Firing Network*

The biomass and coal sources have predefined supply capacities which vary between periods. Different biomass source localities also experience variations in the biomass properties due to climate differences. The carbon dioxide emissions from the cultivation and harvesting of biomass residues may be neglected since baseline conditions still require these operations and focus is given to emissions generated as a consequence of using the residues for co-firing.

Biomass are transported to pre-treatment facilities to improve their quality. Each facility performs a specific pre-treatment process, but can only process a certain amount of biomass each period. In addition, each process addresses only a set of properties and improves them only to certain extents. After pre-treatment, the biomass may be: (1) kept in storage until the succeeding period or (2) transported to coal power plants for co-firing. Storing biomass may result in deterioration and additional holding costs.

The model will also decide whether each existing coal power plant must be retrofitted for co-firing. Retrofitting a power plant will require capital investments. For plants that will be retrofitted, the model decides when the retrofit is implemented, when co-firing is activated, and where the biomass and coal will be sourced from. Each power plant has processing capacities, fuel property limits, and electricity demands that need to be satisfied. Equipment degradation is expressed as a function of the volume and quality of the feedstock they process. Higher usage rates or processing of feedstock with unsuitable quality levels will accelerate the degradation of the equipment. Unlike previous studies which model fuel property limits of power plants as hard constraints, this model allows for flexible feedstock properties and instead accounts for the impact of feedstock quality on equipment efficiency and environmental emissions.

#### *3.2. Economic Considerations*

The system considers six cost components: (1) feedstock costs, (2) capital costs, (3) transportation costs, (4) fixed operating costs, (5) variable operating costs, and (6) holding costs. Feedstock costs represent the cost of purchasing biomass waste (*pbit*) and coal (*pckt*) from their respective sources during a

specific period, expressed in cost per kiloton. Capital costs include the investment costs for retrofitting the handling systems of existing coal power plants (*icl*) to accept diverse feedstocks and costs to expand the capacities of the pretreatment facility (*ecpjt*) and the coal power plant (*ecclt*). Expansion costs are also based on the increase in capacity of pretreatment facilities (*epjt*) and coal power plants (*eclt*). Transportation costs refer to the costs incurred in transporting biomass from the source (*tcrijt*) and pre-treatment facility (*tcpjlt*); and in transporting coal (*tccklt*). Fixed operating costs represent the costs brought about by operating the coal power plants (*occlt*), using the co-firing option (*bclt*), operating the pre-treatment facilities (*ocpjt*), and storing biomass (*scjt*). Variable operating costs include two types of costs, namely (1) pre-treatment costs (*pcjt*) and (2) combustion costs for coal (*rclt*) and biomass (*rblt*) expressed as a cost per feedstock kiloton. Pre-treatment cost represents the cost of treating biomass to improve the properties of the biomass, while combustion cost is the cost to process and generate power from biomass and coal. Lastly, holding cost (*hjt*) refers to the cost to store biomass across each period.

#### *3.3. Environmental Considerations*

CO2 emissions from transportation (e.g., of biomass (*tepjlt*) and coal (*tecklt*)), combustion (e.g., of biomass (*ceblt*) and coal (*ceclt*)), and biomass pre-treatment are the environmental emissions considered in the system. The use of biomass is preferred from an environmental standpoint because emissions released are significantly less when burning biomass compared to coal. Pre-treating biomass to improve its properties also result in greenhouse gas emissions (*pejt*).

#### **4. Model Formulation**

The following section presents the model formulation for the biomass co-firing network described. A MINLP model is developed for the network, which aims to make investment and operational decisions that simultaneously minimizes the costs and environmental emissions while satisfying energy demand and capacity constraints. The model also considers the impact of fuel properties on the efficiency and life of the conversion equipment. Table 1 shows the indices, as well as the relevant parameters and variables used in the model.


**Table 1.** Notations.




**Table 1.** *Cont*.
