Economic and Land-Use Optimization of Lignocellulosic-Based Bioethanol Supply Chains Under Stochastic Environment

Abstract

The ever increasing concerns such as energy security and climate change calls for a wide range of alternate renewable sources of energy. Bioethanol produced from lignocellulosic feedstock show enormous potential as an economically and environmentally sustainable renewable energy source. In recent years considerable research has focused on the economic feasibility of lignocellulosic-based biofuel supply chains while analytical understanding of land-usage for biomass cultivation has remained limited. Switchgrass is considered as one of the best lignocellulosic feedstock for bioethanol production that can be cultivated on both marginal land with arid soil and crop land. Switchgrass cultivated on crop land normally gives twice the yield when compared with marginal land: however, the higher yield is obtained due to higher input costs. Crop lands are a finite resource and their widespread use for growing energy crops rather than food crops like corn and wheat has resulted in land-use issues such as food versus fuel debate. Therefore, cultivation of switchgrass on marginal land is being studied intensively to minimize the use of crop land for biomass cultivation. This work proposes a novel dual-objective stochastic optimization model to maximize the expected profit and simultaneously minimize usage of crop land to cultivate switchgrass for a lignocellulosic-based bioethanol supply chain (LBSC) under uncertainties of biomass supply, bioethanol demand and bioethanol sale price. The model determines the optimum allocation of marginal land and crop land for switchgrass cultivation, biorefinery locations, and biomass processing capacity of biorefineries. The e–constraint method is applied to trade-off among the competing objectives of profit maximization and land-use minimization. In order to solve the proposed stochastic model efficiently and effectively, the Sample Average Approximation method is utilized. A case study based in the state of Alabama in the U.S. illustrates the application of the proposed stochastic model. In addition, sensitivity analyses are conducted to provide insights on the important factors that impact on the profitability and land usage in the LBSC.

Appendices

Appendix A: Nomenclature

Indices
e	Bioethanol demand zones (e = 1, …, E)
i	Lignocellulosic biomass supply zones (i = 1, …, I)
m	Lignocellulosic biomass feedstocks (m = 1, …, M)
r	Biorefinery locations (r = 1, …, R)
ω	Stochastic scenarios (ω = 1, …, N)
First stage decision variables
CP i	Crop land used for switchgrass cultivation at supply zone i (acres)
MG i	Marginal land used for switchgrass cultivation at supply zone i (acres)
K r	Biomass processing capacity of biorefinery at location r (tons/year)
Y r	{1, if biorefinery setup in location r; Else 0}
Second stage decision variables
F mir (ω)	Amount of biomass m sent from zone i to biorefinery r during scenario ω (tons)
X1 i (ω)	Crop land in supply zone i harvested for switchgrass (acres)
X2 i (ω)	Marginal land in supply zone i harvested for switchgrass (acres)
L r (ω)	Volume of unsubsidized ethanol sold from refinery r during scenario ω (gallons)
O e (ω)	Volume of unmet bioethanol requirement in demand zone e during scenario ω (gallons)
P re (ω)	Volume of subsidized ethanol from refinery r sent to zone e during scenario ω (gallons)
S r (ω)	Amount of bioelectricity produced by biorefinery r during scenario ω (MWh)
Z r (ω)	Volume of ethanol produced by biorefinery r during scenario ω (gallons)
Deterministic parameters
Θ1 i	Switchgrass cultivation cost parameter in supply zone i using crop land ($/acre)
Θ2 i	Switchgrass cultivation cost parameter in supply zone i using marginal land ($/acre)
A	Switchgrass yield ratio using crop land for cultivation
B1 i	Crop land area available for switchgrass cultivation in biomass supply zone i (acres)
B2 i	Marginal land area available for switchgrass cultivation in biomass supply zone i (acres)
υ i	Average switchgrass yield in biomass supply zone i using marginal land (tons/acre)
D ir	Distance between biomass supply zone i and biorefinery r (mile)
D re	Distance between biorefinery r and bioethanol demand zone e (mile)
G r	Annualized fixed cost of biorefinery at location r ($)
H r	Variable cost parameter of biorefinery at location r ($/ton)
lc i	Switchgrass harvest cost parameter in supply zone i ($/acre)
pp i	Switchgrass densification cost parameter in supply zone i ($/ton)
U r	Ethanol production cost parameter of biorefinery at location r ($/gallon)
ζ mi	Amount of biomass type m ≠ 1 available in supply zone i (tons)
η mir	Transport cost parameter of biomass m from supply zone i to biorefinery r ($/ton x mile)
ι r	Average sale price of unsubsidized bioethanol at location r ($/gallon)
κ m	Bioethanol yield parameter for biomass type m (gallons/ton)
λ mi	Purchase price of biomass type m ≠ 1 at supply zone i ($/ton)
μ m	Electricity yield parameter for biomass type m (MWh/ton)
ν e	Average bioethanol demand (energy equivalent to 20 % of gasoline requirement) in zone e (gallons)
ρ max	Maximum amount of biomass that can be processed by biorefinery r (tons/year)
ρ min	Minimum amount of biomass that must be processed by biorefinery r (tons/year)
τ re	Tax credit for bioethanol production in location r for consumption in demand zone e ($/gallon)
φ e	Penalty cost parameter for unmet bioethanol requirement at biofuel demand zone e ($/gallon)
χ r	Sale price of electricity at location r ($/MWh)
ψ re	Transport cost parameter of bioethanol from biorefinery r to biofuel demand zone e ($/gallon x mile)
w 1	Weight for marginal land usage
w 2	Weight for crop land usage
Stochastic parameters
ο(ω)	Supply level of switchgrass (cultivated on marginal and/or crop land) during scenario ω
π(ω)	Demand level of bioethanol during scenario ω
σ(ω)	Price level of bioenergy during scenario ω

Appendix B: Input Parameters

See Tables B1 and B2

Table B1 Values of stochastic parameters (Osmani and Zhang 2013)

Table B2 Values of key deterministic parameters (Zhang et al. 2012)