A biobjective chance constrained optimization model to evaluate the economic and environmental impacts of biopower supply chains

Abstract

Generating electricity by co-combusting biomass and coal, known as biomass cofiring, is shown to be an economically attractive option for coal-fired power plants to comply with emission regulations. However, the total carbon footprint of the associated supply chain still needs to be carefully investigated. In this study we propose a stochastic biobjective optimization model to analyze the economic and environmental impacts of biopower supply chains. We use a life cycle assessment approach to derive the emission factors used in the environmental objective function. We use chance constraints to capture the uncertain nature of energy content of biomass feedstocks. We propose a cutting plane algorithm which uses the sample average approximation method to model the chance constraints and finds high confidence feasible solutions. In order to find Pareto optimal solutions we propose a heuristic approach which integrates the $\epsilon$-constraint method with the cutting plane algorithm. We show that the developed approach provides a set of local Pareto optimal solutions with high confidence and reasonable computational time. We develop a case study using data about biomass and coal plants in North and South Carolina. The results indicate that, cofiring of biomass in these states can reduce emissions by up to 8%. Increasing the amount of biomass cofired will not result in lower emissions due to biomass delivery.

Appendix: Life cycle assessment

1.1 Basic assumptions

• Two categories of sustainable biomass considered for the study: forest management residues and wood processing residues.

• We do not take into account the environmental impacts due to direct and indirect land use change (forest residues and urban wood waste have marginal land use change impacts).

• We assume that the $\hbox {CO}_2$ uptake during the biomass growth is equal to the amount that is emitted during the combustion at the power plant (biogenic carbon is not tracked in the analysis).

• GHG emissions due to transmission of power from plants to final users were not included in the analysis.

• We assume if the biomass is not utilized for cofiring and remains in the environment, the $\hbox {CH}_4$ emissions related to natural biodegradation would contribute to the life cycle GHG emissions.

1.2 Main steps of the LCA

To meet the ISO14040 (2006) standards for LCA, our analysis is carried out in the following four distinct steps.

Goal and scope definition The goal of the LCA analysis is to determine the life cycle environmental impacts of biomass cofiring. This analysis is intended to provide useful information for electric utility companies that want to use biomass as a renewable fuel to be cofired with coal in their coal-fired power plants. In this analysis we are only looking at use phase emissions from the power plants. Utility companies may be required to report GHG emissions throughout the fuel supply chain to comply with regulations or to receive renewable energy credits.¹ The functional unit considered for this analysis is the mass amount of biomass used at coal plants (Ton).

The life cycle boundary for our analysis includes the following three main phases:

• Phase 1: Raw material acquisition includes the activities related to collection and processing of biomass, and coal extraction. It begins with acquiring solid biomass and coal mining, and ends with biomass and coal ready for transport.

• Phase 2: Fuel transportation includes transport of coal and biomass from the point of acquisition to the energy conversion facility.

• Phase 3: Energy conversion facility includes operation of the power plant and any modifications necessary to process and cofire biomass to generate electricity.

Inventory analysis In this step, we analyze the input/output data associated with biomass cofiring supply chain and operations. The total life cycle emissions inventory accounts for raw material acquisition and preprocessing, coal and biomass transportation, and emissions at coal plants due to electricity generation and related operations. The total GHG emissions from each unit process is fed to the optimization model. The life cycle inventory entries, per functional unit of utilized biomass, is obtained from literature, several databases, and previous LCA analyses. We have used standard environmental databases that store emission data for similar processes, such as, EPA’s Emissions & Generation Resource Integrated Database (eGRID) and the US Life Cycle Inventory Database (USLCI) by National Renewable Energy Laboratory (NREL 2012). To conduct LCA, Argonne National Lab’s GREET Life Cycle Analysis$^{\textregistered }$ tool (Wang 2008) is used. More details about the life cycle inventory entries and assumptions are provided in the “Appendix”.

Impact assessment and integration of LCA in the optimization model In third step, results of the life cycle inventory analysis are translated into potential environmental contributions. The main metric used for quantifying environmental concerns is global warming potential. In this work, emissions of two GHG gases $\hbox {CO}_2$ and $\hbox {CH}_4$ are grouped together in a single indicator in terms of carbon dioxide equivalent emissions ($\hbox {CO}_2$-equivalent/ton). The relative global warming potential of $\hbox {CH}_4$ to $\hbox {CO}_2$ is assumed to be 25 : 1 based on a time horizon of 100 years suggested as part of Kyoto Protocol (IPCC 2007).

The conventional LCA does not provide a systematic way to compare the environmental impacts of different supply chain decisions. An excellent approach to overcome this limitation is through integrating the outcomes of impact assessment into a multiobjective optimization framework. This allows decision makers to evaluate diverse supply chain design and operations alternatives that may be implemented to improve environmental performance while also assessing other aspects of the system such as economic and social impacts. In order to integrate the LCA into the optimization model we follow the approaches proposed by Azapagic and Clift (1999) where the functional input is represented by decision variables, and relative impact of each activity is represented by objective function coefficients. This method is defined as the “problem oriented” approach to Impact Assessment (Heijungs et al. 1992).

Interpretation In last step of LCA analysis, results of the biobjective optimization model are analyzed and a set of practical strategies, which may help with the improvement of environmental and economic performance, are recommended. Solving the optimization model results in a set of optimal trade-off (Pareto optimal) solutions. These solutions represent a range of operational alternatives to utilize biomass in order to achieve best possible emission reductions and economic benefits. The proposed optimization approach provides additional insights into biomass cofiring. The Pareto optimal solutions help us to understand the inherent trade-offs that exist between economic and environmental objectives.

1.3 Phase 1: Raw material acquisition

Extracting coal from the ground is the first phase of the fossil fuel life cycle. Mining and cleaning are the main processes to prepare coal to be transported to power plants. The emissions at this stage are mainly due to diesel emissions from mining and preparation equipment and methane ($\hbox {CH}_4$) emissions from the mine. The GHG estimations for coal mining are mainly adopted from Spath et al. (1999) and the Argonne National Laboratory’s GREET (Greenhouse gases, Regulated Emissions, and Energy use in Transportation) model. We consider the two main types of coal, bituminous and subbituminous, as each of the coal plants under the study uses either of the these types as their primary fuel. The subbituminous coal is relatively pure and can be prepared for transportation by removing large impurities and crushing it into smaller size pieces. The bituminous coal generally requires a jig washing process to separate heavier impurities Spath et al. (1999). The preparation of urban wood waste for cofiring is initially involved with the collection of waste, transferring to a depot, and crushing the matter into small pieces (wood chips). After transporting the wood chips to power plants, extra processes may be applied to make biomass a compatible fuel for combustion in PC boilers (e.g. drying or compression). We will consider the impact of these processes in the third phase. The collection of forest residues mainly done by skidders which gather the residues and pile them in a landing site. The average energy use for the collection of forest residues using medium sized grapple skidders is reported as 83.8 MBtu/dry Ton in Boardman et al. (2014). In the landing depot, branches and barks are removed from trees using a stroke-boom delimber or iron gate for larger trees. The delimbed trees are then loaded into a chipper. The energy use for debarking/delimbing and chipping using conventional methods are assumed to be 116.4 MBtu/dry Ton and 105.8 MBtu/dry Ton respectively (based on the report in Boardman et al. (2014)). The primary GHG impact of preprocessing phase arise from the use of diesel equipment and trucks. The carbon intensity of diesel fuel is assumed to be 95 kg $\hbox {CO}_2$-eq/MMBtu (Skone and Gerdes 2008).

1.4 Phase 2: Fuel transportation

We use the information provided in Boardman et al. (2014) to take into account the emissions due to coal transportation. In this model, it is assumed that 10% of coal is transported on a barge over 330 miles and the other 90% of coal is transported by train over 440 miles (Wang 2008). The amount of required coal for a year depends on the heating value of coal, plant characteristics, and cofiring strategy. It is assumed that biomass feedstock (in form of wood chips) is transported by diesel trucks from supplier facilities to coal plants. Based on the GHG conversion factors provided by UK’s Department for Environment, Food & Rural Affairs (DEFRA), the average emission rate of transporting wood is 0.275 kg $\hbox {CO}_2$-eq/Ton-mile (DEFRA 2016). Work by Bauer et al. (2010) evaluates the relationships that exist among vehicle fuel consumption, $\hbox {CO}_2$ emissions, and vehicle load for transporting different biomass feedstock. The specific parameter values for biomass transportation were obtained and validated using Argonne Greet Model (Wang 2008) and USLCI. The geographical distance from suppliers to plants are calculated based on the great-circle distance method.

1.5 Phase 3: Electricity generation

In this phase of the life cycle we consider all of the processes typically carried out at a coal-fired power plant including those related to biomass fuel preparation and handling. The coal plants of interest use the pulverized coal (PC) boilers for fuel combustion. The majority of existing US coal plants use PC boilers, and this type of boiler can handle higher ratios of biomass cofiring (Tillman et al. 2010). The US Environmental Protection Agency (EPA) provides the environmental characteristics of current electricity generation utilities in the Emission & Generation Resource Integrated Database (eGRID). We use eGRID to find the annual GHG emission rates of the coal plants under study. eGrid provides the data for annual $\hbox {CO}_2$ equivalent output emission rates (kg $\hbox {CO}_2$-eq/MWh) for existing power plants in US. Using the efficiency factor and heat input of the primary fuel used at each plant we can estimate the output emission per ton of coal used $M_{coal} = \frac{1~\hbox {MWh}}{\eta _0LHV_{coal}}$. Regarding the avoided emissions, according to Mann and Spath (2001) The total $\hbox {CO}_2$ and methane avoided per ton of biomass are 1.117 ton 0.065 ton respectively (using global warming potential of greenhouse gases relative to $\hbox {CO}_2$ it adds up to $1.117+25\,*\,0.065 = 2.742$ ton $\hbox {CO}_2$-eq per ton of biomass avoided. However, in determining the net greenhouse gas emission balance for this system, it is important to recognize that not all of the emissions and avoided emissions will occur at the same time. While $\hbox {CO}_2$ will be emitted at the power plant as soon as biomass is fired, the release of $\hbox {CO}_2$ and methane from mulch, and particularly from landfills, will be delayed. Because it is exposed to the elements, the time frame for complete decomposition of mulch would likely be on the order of just few years, and is reported to occur at a rate of 10% per year Harmon et al. (1996).

GREET$^{\textregistered }$ life cycle analysis tool (2015) is the main tool we used for LCA. A sample output for one of the plants with 763 MW capacity which uses pulverized coal boilers and bituminous coal as the primary fuel is presented in Table 7.

Table 7 A sample GREET$^{\textregistered }$ LCA impact results