Optimal biomass-harvesting model for biobutanol biorefineries

The Energy Independence and Security Act (EISA) 2007 mandate the use of 21 billion gallons of advanced biofuels including 16 billion gallons of cellulosic biofuels by the year 2022. While much previous advanced biofuel related research has focused on cellulosic ethanol, advanced drop-in-biofuels such as biobutanol and renewable diesel are gaining significant attention because of their attractive combustion properties, compatibility with existing vehicle fleet, fuel distribution, and retailing infrastructure. While corn ethanol production has increased fast enough to keep up with the mandates, production of cellulosic and advanced biofuels has been well below the targets despite significant government support. A number of pilot and demonstration scale advanced biofuel facilities have been set up, but commercial scale facilities are yet to become operational. Scaling up this new biofuel sector poses significant economic and logistical challenges for regional planners and biofuel entrepreneurs in terms of feedstock supply assurance, supply chain development, bioefinery establishment, and setting up transport, storage and distribution infrastructure. Economies of scale in processing mean that, future cellulosic biorefineries are expected to be large-scale facilities using multiple sources of feedstocks. Assuring a reliable supply of feedstock in adequate quantity and appropriate quality at reasonable cost and low environmental impacts is a key factor driving emergence of a sustainable bioenergy sector. Assuming that a biorefinery is set up in a region that has more than adequate biomass potential, biorefinery managers then face the problem of contracting with producers for the actual supply quantities of feedstock over the expected operational life time of the biorefinery. These supply contracts specify the quantities of different feedstocks (e.g. agricultural crops, perennial grasses, woody biomass), the timing of the deliveries, and the geographical location of production. In other words, through these supply contracts, the biorefinery managers essentially have an opportunity to design the biomass harvest-shed both temporally and spatially. Considerations in determining the optimal mix of these supply contracts include: (i) lowering procurement costs (harvest, baling, transport, storage, and seasonal costs), (ii) maximizing fuel yields and minimizing conversion costs, (iii) reducing in greenhouse gas (GHG) emissions to qualify as a cellulosic biofuel under the federal renewable fuels standard or similar regulations, and possibly for tradable GHG credits, and (iv) meeting contracting constraints to assure supply, for example while annual crop producers may be willing to supply under annual contracts, perennial grass producers may demand longer term contracts with varying quantities matching the temporal yield patterns. In addition to the above criteria used by biorefinery managers, regional planners may impose additional constraints related to protection of ecosystem services, habitat protection, water resources, traffic patterns, and congestion. In this article, we develop a multi-period optimization model aimed determining the optimal mix of woody biomass, annual crops and perennial grasses for a biorefinery, taking into account the necessary contract terms, feedstock costs, transport costs, GHG emissions and other environmental impacts, production capacity constraints etc. The decision variables of the optimization model are the acreages of various feedstocks (woody biomass, 3 annual crops and perennial grasses) that are contracted for harvesting during each month of a 25 year planning horizon. While the model is structured to be applicable to a generic biorefinery regardless of location, we parameterize the model using information for a hypothetical biorefinery located in the Midwest, producing biobutanol. Two versions of the model are developed, one optimizing the private costs faced by the biorefinery manager, and a second version taking the perspective of a regional planner with additional optimization criteria and social constraints. Mathematical programming software GAMS and solver program MINOS are used to code and solve the formulated optimization programs. A growing body of literature has previously addressed issues surrounding the supply of biomass feedstock for biofuel production (e.g. Epplin et al., 2007; Mapemba et al., 2007; Mapemba et al., 2008; Sokhansanj et al., 2009; Khanna et al., 2010; Kang et al., 2010). While drawing on previous research, the models developed in this article have several novel features. (i) Existing studies treat the available biomass quantities in the region as exogenously given and then try to minimize procurement costs. In comparison, this model treats biomass acreage to be harvested as an endogenous decision variable subject to overall biomass availability constraints. (ii) Unlike most existing studies, in this model transport costs are endogenously determined as a function of harvesting decisions. (iii) The temporal yield patterns of energy crops are modeled explicitly unlike many other studies which use steady state average yields. (iv) GHG emissions are also endogenously determined based on feedstock sourcing decisions. (v) The legal, institutional, and ecosystem sustainability constraints that are necessary from a regional planning perspective are also incorporated. (vi) While almost all previous studies model cellulosic ethanol biorefineries, this model is specifically aimed at biobutanol biorefineries. As a result, these models provide better insights into the realities of biomass procurement, especially for the emerging drop-in advanced biofuel production.