Assessing the Impact of Preprocessing and Conversion Technologies on the Sustainable Aviation Fuel Supply from Forest Residues in the Southeast U.S.A.

Abstract

Forest residues have been suggested as potential feedstock for sustainable aviation fuel (SAF) production through different pathways. However, the bulky density and scatter distribution require efficient size-reduction processes to enhance the feedstock supply. Thus, this study analyzes the impact of alternative preprocessing and conversion technologies on the SAF supply chains from logging residues (the predominant share of forest residues) using a two-stage mixed-integer linear programming model. The model determines the optimal location of biomass preprocessing depots, conversion facilities, and airports receiving SAF by minimizing the net present value of the total supply chain cost over 10 years. Using high-resolution spatial data in the Southeast U.S.A. as a case study, the results show that the technology and scale of the facilities heavily influenced the SAF’s breakeven cost and maximum supply quantity. The most economically efficient system that adopts a rotary shear milling system and pyrolysis conversion process could generate up to 650 million gallons of SAF from logging residues in the region, with nearly 62% of the SAF being produced from hardwood residues. Also, the most efficient system has an estimated breakeven cost of US$5.51 per gallon of SAF.

Keywords

aviation planning and analysis optimization alternative transportation fuels and technologies transportation network modeling and simulation

Commercial aviation has experienced a rapid rise over the past two decades, with tickets of all types sold increasing from 1.46 billion in 1998 to 4.54 billion in 2019 ( 1 ). Although the outbreak of COVID-19 had an unprecedented hit on the aviation industry, the International Air Transport Association (IATA) predicts that global passenger travel will return to the 2019 level of activity in 2024 and rise to 7.8 billion passenger journeys in 2040 at an average annual growth rate of 3.3% ( 2 ). While aviation has played an important role in the economic development, the growth in greenhouse gas (GHG) emissions from this sector has generated concerns ( 3 , 4 ). According to the Air Transport Action Group ( 5 ), the global aviation industry produced 915 million tons of carbon dioxide (CO₂) in 2019, which accounted for 2.1% of the total human-induced CO₂ emissions and 12% of global transport-sourced CO₂ emissions. The aviation industry could contribute to 22% of global GHG emissions by 2050 if no decarbonization action is taken ( 6 ). Thus, the global aviation industry has aimed to reduce GHG emissions by 50% by 2050 compared to 2005 levels ( 7 ), and the International Civil Aviation Organization (ICAO) reinforced the goal of net-zero CO₂ emissions from air transport during COP 27 in November 2022 ( 8 ).

Replacing conventional fossil-based jet fuel with sustainable aviation fuel (SAF) has been recommended as a major means to achieve the carbon neutrality goal ( 9 – 11 ). SAF can be produced from a variety of biomass feedstocks, including municipal solid waste, used cooking oil ( 12 ), wood wastes ( 13 , 14 ), energy crops ( 15 ), and forest residues ( 16 ). Under different conversion pathways, SAF could be mixed with conventional aviation fuel for aircraft without modifying the equipment. The carbon sequestration effect of biomass in the growth process reduces the life cycle GHG emissions compared to conventional aviation fuel ( 17 ). Thus, in September 2021, the U.S. Department of Energy, U.S. Department of Transportation, and U.S. Department of Agriculture launched a government-wide SAF Grand Challenge with a target of producing 3 billion gallons of SAF annually by 2030 and meeting all aviation fuel demand in the U.S.A. by 2050 to reach net-zero GHG emissions ( 18 ).

Previous studies have suggested forest residues (predominantly logging residues) as a feedstock for SAF because of the environmental and economic advantages ( 16 , 19 –21). Forest residues are woody biomass from the materials left over after forest harvesting, which include foliage, roots, and non-commercial log branches ( 22 ). Forest residues are not suitable for the primary wood products market ( 21 , 23 ), but can be converted to biofuels such as ethanol, biodiesel, electricity, and SAF ( 24 , 25 ). Traditionally, most of the forest residues are left to rot or burned at the sites where trees are harvested ( 26 – 28 ). Research has suggested that removing up to 70% of logging residues would not have significant impacts on nutrient availability for tree regeneration ( 29 , 30 ).

The southeast U.S.A., known as America’s wood basket, produces more than 50% of the nation’s forest products ( 26 ) and has plenty of logging residues that could be used to produce SAF. The region has been identified as a major area for supplying logging residues because of its abundant forestry resources and wood products ( 31 , 32 ). According to the U.S. Forest Service’s Timber Products Output (TPO) database, logging residues accounted for nearly 83% of total forest residues within the southeast U.S.A. in 2021 ( 33 ). By integrating various geographic data with ArcGIS 10.5, Pokharel et al. ( 30 ) estimated that the potentially recoverable logging residues within a 50-mi hauling distance from the procurement zones are roughly 23.14 million dry tons in the southeast states. Furthermore, the distributions of different kinds of logging residues in the southeast U.S.A. are varied. According to the TPO data, from 2011 to 2020, the estimated annual amount of hardwood and softwood logging residues were 65.70 and 55.59 million green tons, respectively, in the region. Kentucky, Tennessee, and Virginia are the top three states with the highest density of hardwood logging residues, while Georgia, South Carolina, and Louisiana have a higher density of softwood logging residues compared to other southeast states. Also, mills in the region are experienced in using forest residues to produce biofuels ( 34 ), and are familiar with the technologies of producing heat, electricity, biofuels, and chemicals from their residues ( 35 ).

Despite the rich forest resources in the southeast, the logistics and supply uncertainty are potential barriers to the commercialization of SAF produced from forest residues ( 36 ). Typically, forest residues are of low density, which results in higher transportation and preprocessing costs than field crops ( 37 , 38 ). Further, the supply of forest residues for SAF is not as consistent as dedicated energy crops because the availability of forest residues relies on market demand for timber products, therefore increasing the uncertainty of the investment for stakeholders. Thus, designing an optimal supply chain that integrates related activities has been identified as a key research question in utilizing forest residues for the mass production of transportation fuel ( 39 ).

Preprocessing and conversion technologies play a critical role in the cost and facility placement of SAF production. Preprocessing technologies extract and prepare feedstock for conversion into SAF and could influence the efficiency of feedstock conversion and overall cost of producing SAF ( 40 , 41 ). Similarly, the efficiency of conversion technologies directly affects the cost of SAF production. Different conversion pathways, such as gasification and pyrolysis, have varying efficiencies and costs ( 42 , 43 ). Higher conversion efficiencies generally result in lower operation costs but may require more advanced and expensive equipment. Also, a higher-throughput preprocessing technology and conversion pathway could produce the same level of output with less feedstock, resulting in a lower feedstock acquisition cost in the SAF supply chain.

The objective of this study is to determine the impact of various preprocessing and conversion technologies on the maximum supply quantity (MSQ) of SAF produced from logging residues and the associated displacement of the supply chain in the southeast U.S.A. Sawmill residues are another potential forest feedstock for SAF production, but sawmills also utilize the residues to generate energy for their operation. Thus, we focus on logging residues only in this study given their dominant share in forest residues. This study also assesses the breakeven cost (BEC) of producing SAF from different preprocessing and conversion technologies applied to logging residues. A two-stage mixed-integer programming model is applied to spatial data to determine the optimal supply chain by minimizing the associated BEC when meeting the SAF MSQ from logging residues in the region.

Design of a Logging Residue-Based Sustainable Aviation Fuel Supply Chain

Figure 1 illustrates the design of a two-stage logging residue-based SAF supply chain network that extends from forest harvesting to SAF delivery to airports. In the first stage, loggers pay landowners for the right to harvest trees (stumpage cost), deliver harvests to sawmills, and receive payment from the mills. The willingness to harvest (WTH), measuring the percentage of nonindustrial landowners’ lands to be harvested, is considered based on Butler et al. ( 44 ) to prevent an overestimate of the feedstock supply. Loggers decide the location and amount of harvest based on forest resources, the WTH of landowners, and the wood demand from sawmills. The harvesting decision then leads to the location and amount of available logging residues.

In the second stage, logging residues involve several interconnected operations: harvesting, transportation, preprocessing, storage, and conversion, all of which affect the cost of SAF production ( 45 ). Firstly, logging residues are collected from the site of tree harvesting and transported to woody biomass preprocessing centers (depot). Logging residue preprocessing at the depot includes chipping, sorting, drying, and size reduction to provide standardized feedstock ( 40 ) to the biomass conversion centers (biorefinery). Preprocessing is an important step for residues and can be accomplished using alternative technologies such as traditional hammermills and newly developed rotary shear technology ( 40 ). Logging residues can be chipped into manageable sizes at the harvesting sites or the depot. These residues are conveyed to the preprocessing equipment, where the residues’ moisture content and size are modified to meet conversion process feedstock specifications. Moisture content is reduced from around 50% to less than 10% through a drying process. Particle size is also reduced to conversion specifications, generally below 10 mm ( 46 ). The order of operations of drying and comminution is dependent on the selected equipment capabilities. This study examines two pathways: (a) drying then comminution with a hammermill and (b) comminution with a rotary shear then drying. After comminution, logging residues are sorted using screeners that ensure size uniformity within conversion-specified ranges. Residues smaller than the minimum acceptable sizes are discarded, and larger residues are recycled into the system for additional size reduction. In particular, pyrolysis conversion of woody biomass highly depends on feedstock particle size ( 47 ). At the biorefinery, SAF is produced from received preprocessed residues among other biofuels, such as diesel and naphtha, and then shipped to airports and blended with conventional aviation fuel at a given percentage.

Materials and Method

Figure 2 depicts the model’s structure with respect to inputs and outputs. Given the initial forest inventory and expected growth, sawmill demand and location, the distance matrix, and landowners WTH, the model will determine the optimal amount and location of forest harvested, as well as the amount of logging residue left behind by minimizing the total forest harvesting cost at the first stage. In the second stage, using the residue availability and location from the first stage, along with candidate sites for preprocessing and conversion facilities (considering technology parameters), airport location and demands, and the distance matrix, the model then determines the optimal location, scale, technology of preprocessing, and conversion facility, and the location and quantity of residues being harvested are determined. The SAF BEC is also estimated in the second stage.

Study Area

The study area comprises 10 southeastern states (Alabama, Arkansas, Georgia, Kentucky, Louisiana, Mississippi, North Carolina, South Carolina, Tennessee, and Virginia) with a buffer of 100 mi from the state borderline (Figure 3). This region is known for its abundance of trees, accounting for nearly one-third of the entire U.S. forest land, and as a major hub for the private sector’s industrial forest. Within this area, there are nearly 65 million acres of private corporate owned forest and 147 million acres of private noncorporate owned forest ( 48 ).

We disaggregated the study area into 14,040 hexagons as spatial units (50 square mi per hexagon) in this study to better capture the spatial variation in land resources and facility location. Federally owned lands (gray areas in Figure 3) were not considered as available forestry sources, and only privately owned lands were designated for forest harvesting in the analysis. In addition, there were 1541 sawmills (yellow circles in Figure 3), 529 industrial parks (potential locations for depots and biorefineries), and 22 major airports in the study area.

Forest inventory spatial data was gathered from the Forest Inventory and Analysis (FIA) database from the United States Department of Agriculture (USDA). The distribution of the initial forest inventory is presented in Figure 3 (dark green showing higher tree density), which is concentrated in the east-central part of the study area and in small areas in the southwest. The data source used in the mixed-integer linear programming model are summarized in Table 1.

Table 1.

Data Sources

Forest initial inventory	Forest Inventory and Analysis (FIA) data^a
Sawmills’ location and demand	Timber Product Output (TPO) data^b, USDA Forest Service ( 49 )
Forest inventory growth	ForSEAM model ( 50 )
Wood stumpage, harvesting, and transportation	U.S. Department of Energy ( 31 )
The ratio of logging residue over logs	Timber Product Output (TPO) data^b
Residue stumpage and harvesting cost	U.S. Department of Energy ( 31 )
Residue transportation cost	Trailer, fuel, and labor ( 51 )
Residue preprocessing facility	Capital cost, operational cost, and feedstock output–input ratio ( 52 )
Residue conversion facility	Capital cost, operational cost, and conversion feedstock output–input ratio: pyrolysis ( 43 ), Fischer–Tropsch ( 42 )
Industrial park’s location	English et al. ( 53 )

^aFIA database: https://apps.fs.usda.gov/fia/datamart/datamart.html.

TPO database: https://apps.fs.usda.gov/fia/datamart/datamart.html.

Estimating Logging Residues

The approach to estimating potential logging residues in the study area is illustrated in Figure 4. Based on the FIA sample database, four layers of timber are categorized: hardwood sawtimber, hardwood pulpwood, softwood sawtimber, and softwood pulpwood. Sawtimber is wood from trees with diameters greater than 11 in. for hardwood and greater than 9 in. for softwood, while pulpwood is wood from trees with diameters between 5 and 11 in. for hardwood and between 5 and 9 in. for softwood ( 32 ). We first interpolated the FIA sample data to generate the forest inventory level for the entire study area using the Kriging method ( 54 ) and further downscaled it into hexagon levels for each of the four layers. Next, wood demand for sawmills was approximated by the capacity of sawmills, which is categorized from size 1 to 6 ( 49 ). A k-nearest neighbors’ method was used to interpolate the demand for 263 newly opened sawmills after 2009. The demand was adjusted by a factor to ensure that the sum of mill demand in each state matches the data in the TPO database ( 55 ). Finally, the ratio of logging residue over wood harvested was calculated using the TPO data at the county level. The available logging residue data layer was then derived by multiplying the simulated wood harvests based on sawmill capacities with the ratio of logging residues over wood harvests for the feedstock quantity and location analysis at the first stage of modeling.

Mathematical Framework

Supply Chain Assumptions

The study aims to estimate how much SAF could be produced from logging residues using various preprocessing and conversion technologies. Two SAF conversion technologies, the Fischer–Tropsch process and the pyrolysis process, were considered in the study given logging residues as biomass feedstock. A range of biorefinery sizes was incorporated, including 60, 70, 80, 90, and 100 million gallons of SAF per year, to accommodate the scatter distribution of logging residues. For the preprocessing facility, we assumed that depots could select two different milling systems, a conventional hammermill or a more advanced rotary shear system ( 31 ), to produce 200,000 dry tons of preprocessed feedstock per year. Table 2 reports the yields of different scales and technologies in biorefineries and depots.

Table 2.

Key Parameters Used in the Model

Biorefinery	Technology
Biorefinery	Fischer–Tropsch ( 43 )	Pyrolysis ( 44 )
Capacity (MM gal)	Annual equivalent capital cost (MM US$/Year)^a
60	88.91	73.22
70	99.04	81.56
80	108.74	89.55
90	118.09	97.25
100	127.13	104.69
Operational cost (US$/gal)	2.17	1.96
Yield^b (gal/dry tons)	61.45	75.16
Share of SAF	50%	50%
Depot	Technology ( 53 )
	Hammermill	Rotary shear
Capacity (dry tons)	Annual equivalent capital cost (MM US$/Year)
200,000^c	3.85	4.17
Operational cost (US$/dry tons)	68.83	63.22
Throughput	60%	87%

Note: SAF = sustainable aviation fuel.

^aA economies of scale at 0.7 was used when calculating the annual equivalent capital cost of different capacities.

The biofuel outputs include: SAF, diesel, gasoline, and bunker fuel ( 43 , 44 ).

A minimum utilization rate of 70% was imposed.

To determine the impact of the technology at depot on the BEC and MSQ of SAF, three preprocessing options are considered. The three preprocessing options are as follows: (a) hammermill no depot (HND), which uses a hammermill attached to refineries; (b) hammermill at depot (HAD), which uses a hammermill at depots located at separate locations from the biorefinery; and (c) hammermill or rotary shear at depot (HRAD), which could use either a hammermill or rotary shear system at a depot located at separate locations. We also presumed that the distance boundary from the forest harvesting site to the sawmills, from the residue harvesting site to the depots, from the depots to the biorefinery, and from the biorefinery to the airport is 50, 50, 50, 75 mi, respectively, to reduce the computation demand for the optimization model. Definitions of the parameters and decision variables are listed in Table 3.

Table 3.

Definitions of Subscripts, Parameters, and Variables

	Definition
Indices
a	Type of forest inventory (hardwood saw, hardwood pulp, softwood saw, and softwood pulp)
c	Types of technology utilized in the depot (hammermill and rotary shear)
d	Biorefinery size
h	Locations for sawmills
i	Locations for forest inventory unit
j	Locations for logging residue unit
k	Industrial park sites for feedstock preprocessing facility (depot)
l	Industrial park sites for conversion facility (biorefinery)
m	Locations for airports
t	Index of time (year)
Parameters (values used in the study)
ADR	Airport annual demand growth rate (3%)
AF_iat	Available type a forest inventory to be harvested at site i in year t, MM cubic ft (0−96.52)
AR_jt	Available logging residues to be harvested at site j in year t, MM dry tons (0−2.13)
ATCDR_kl	Preprocessed feedstock transportation cost from depot k to biorefinery l, US$/dry tons (7.67−19.68)
ATCRA_lm	SAF transportation cost from biorefinery l to airport m, US$/gal (0.010−0.023)
ATCSD_ik	Raw feedstock transportation cost from residue harvesting site i to depot k, US$/dry tons (8.27−23.81)
ARHC_j	Logging residue harvesting cost at site j, US$/dry tons (17.20−17.37)
BCY	Biofuel conversion yield, gal/dry tons (values in Table 2)
C2D	Cubic ft to dry ton, dry tons/cubic ft (0.0365)^a
CB_d	Annual equivalent of capital expenditure for a size d biorefinery, US$/year (values in Table 2)
CD_c	Annual equivalent of capital expenditure for a depot with c technology, US$/year (values in Table 2)
CR	Commercial share of private forest (33.8%)
DA_m	The demand of SAF from airport m, MM gal/year (21−988)
DM_hat	The demand of type a log from sawmill h in year t, MM cubic ft (0.18−46.62)
FG_iat	Type a forest growth amount at site i in year t, MM cubic ft (0−0.55)
FI_iat	Private owned type a forest inventory at site i in year t, MM cubic ft (0−186.62)
H2A	Hexagon area to acre, acres/hexagon (32,000)
IRR	Discount interest rate (10%)
LA	Lower bound of SAF sent to a selected airport, MM gal (10)
LB_d	Lower bound of biofuels produced at a size d biorefinery, MM gal (values in Table 2)
LD	Lower bound of preprocessed feedstock produced at a depot, dry tons (140,000)
NCR	Non-commercial share of private forest (64%)
OB_d	Operational expenditure for a size d biorefinery, US$/gal (values in Table 2)
OD_c	Operational expenditure for a depot with c technology, US$/dry tons (values in Table 2)
RI_jt	Logging residue inventory at site j in year t, MM dry ton (0−3.04)
RP_c	Conversion factor of logging residues to preprocessed feedstock by c technology, % (values in Table 2)
RR_j	The ratio of logging residues to logs at site j, (0.95−100%)^a
RSC	Residue stumpage cost, US$/dry ton (9.83)
SS	Share of SAF in biofuel products (50%)
TSAF	Total SAF produced in 2030, MM gal (100−650)
UB_d	Upper bound of biofuels produced at a size d biorefinery, MM gal (values in Table 2)
UD	Upper bound of preprocessed feedstock sent from a depot, dry tons (values in Table 2)
UFHC_a	Unit forest harvesting cost for wood type a, US$/acre (843, 843, 834, and 834 for hardwood saw, hardwood pulp, softwood saw, and softwood pulp, respectively)
WTH	Willingness to harvest (45%)
Binary decision variables
DVA_m	Dummy variable that indicates whether any biorefinery has been assigned to airport m (1 yes, 0 otherwise)
DVB_ld	Dummy variable that indicates whether industrial park l has been selected as size d biorefinery l (1 yes, 0 otherwise)
DVD_kc	Dummy variable that indicates whether industrial park k has been selected as depot with c technology (1 yes, 0 otherwise)
Continuous decision variables
CC_t	Total conversion cost in year t, US$
PC_t	Total feedstock preprocessing cost in year t, US$
PVC	Present value of total cost along the residue supply chain over the study period, US$
RHC_t	Total feedstock harvesting cost of the second stage in year t, US$
SC_t	Total feedstock stumpage cost of the second stage in year t, US$
TCBA_t	Total transportation cost from biorefinery to airport in year t, US$
TCDB_t	Total transportation cost from depot to biorefinery in year t, US$
TCRD_t	Total transportation cost from residue harvesting site to depot in year t, US$
TRC_t	Total transportation cost of the second stage in year t, US$
XB_ldmt	Amount of biofuel sent from size d biorefinery l to airport m in year t, gal
XD_kcldt	Amount of preprocessed residue sent from depot k with c technology to size d biorefinery l in year t, dry tons
XF_ihat	Amount of type a log harvested at forest site i by loggers from sawmill h in year t, dry tons
XR_jkct	Amount of residue sent from residue site j to depot k with c technology in year t, dry tons
YA_mt	Amount of biofuel sent to airport m in year t, gal
YB_ldt	Amount of biofuel produced by size d biorefinery l in year t, gal
YD_kct	Amount of preprocessed residue produced by depot k with c technology in year t, dry tons

Note: SAF = sustainable aviation fuel.

^aThis ratio is estimated based on the Timber Products Output database.

First-Stage Model

In the first stage, loggers were assumed to seek areas that contain a greater number of large trees as the forest harvesting cost could be reduced at the forest inventory denser areas ( 56 ). Thus, minimization of the forest harvesting cost at the sawmill (FHC) for the first stage was modeled in Equations 1–6:

M i n : F H C_{t} = \sum_{i} \sum_{h} \sum_{a} (H 2 A \times U F H C_{a} \times X F_{i h a t} / A F_{i a t})

(1)

\sum_{i} X F_{i h a t} \geq D M_{h a t}

(2)

\sum_{h} X F_{ihat} \leq A F_{iat}

(3)

A F_{iat} = F I_{iat} \times (CR + NCR \times WTH)

(4)

F I_{i a (t + 1)} = F I_{i a t} - \sum_{h} X F_{i h a t} + F G_{i a t}

(5)

R G_{it} = R R_{i} \times C 2 D \times \sum_{h} \sum_{a} X F_{ihat}

(6)

Equation 1 presents the objective function that minimizes forest harvesting costs in each year under the assumption that the loggers make harvest decisions based on the current year’s forest inventory. Equation 2 ensures that sawmills’ wood demands are met, while Equation 3 ensures that the amount of log harvested that year cannot exceed the available forest inventory within the area. Equation 4 determines the amount of forest available for harvest in each area incorporating the WTH of the private landowners ( 57 ). We separated the private landowners into two categories (commercial and non-commercial) when calculating the forest inventory available for harvest. The inventory balance constraint in Equation 5 ensures that the forest inventory level at the end of period t equals the forest inventory level at the beginning of period t minus the amounts of forest harvest plus the forest growth (estimated with growth rates obtained from the ForSEAM model) ( 51 ). Equation 6 constrains that the new generated residues equal the product of the residue ratio (calculated by the ratio of residue to forest inventory on the TPO database) and the amount of harvested log in each hexagon.

Second-Stage Model

The objective of the second stage in Equation 7 is to minimize the net present value of the total cost associated with the logging residue-based supply chain, which includes the residue stumpage cost (SC_t), residue harvesting cost (RHC_t), residue preprocessing cost (PC_t), conversion cost (CC_t), and transportation cost (TRC_t):

Min : PVC = \sum_{t} (S C_{t} + RH C_{t} + P C_{t} + C C_{t} + TR C_{t}) \times {(1 + IRR)}^{- t}

(7)

TR C_{t} = TCR D_{t} + TCD B_{t} + TCB A_{t}

(8)

TCR D_{t} = SS \times \sum_{j} \sum_{k} \sum_{c} X R_{jkct} \times ATCS D_{jk}

(9)

TCD R_{t} = SS \times \sum_{k} \sum_{c} \sum_{d} \sum_{l} X D_{kcbldt} \times ATCD R_{kl}

(10)

TCR A_{t} = \sum_{l} \sum_{d} \sum_{m} X B_{ldmt} \times ATCR A_{lm}

(11)

The overall transportation cost (TCR_t) in Equation 8 includes three components: the green logging residue transportation costs from harvesting sites to depots (TCRD_t) in Equation 9, the preprocessed residues transportation costs from depots to biorefineries (TCDB_t) in Equation 10, and the SAF transportation costs from biorefineries to airports (TCBA_t) in Equation 11. Here, ATCSD_jk, ATCDR_kl, and ATCRA_lm are the average costs of transporting the corresponding feedstock or product between their origin and destination. Since SAF is not the only product from current conversion technology, Equations 9 and 10 consider the proportion of SAF in the total output (SS) to adjust the cost for SAF. We apply the same approach to the rest of the manuscript:

S C_{t} = SS \times RSC \times \sum_{j} \sum_{k} \sum_{c} X R_{jkct}

(12)

RH C_{t} = SS \times \sum_{j} \sum_{k} \sum_{c} (ARH C_{j} \times X R_{jkct})

(13)

P C_{t} = S S \times [\sum_{k} \sum_{c} (D V D_{k c} \times C D_{c}) + \sum_{k} \sum_{c} \sum_{d} \sum_{l} X D_{k c l d t} \times O D_{c}]

(14)

C C_{t} = \sum_{l} \sum_{d} (SS \times DV B_{ld} \times C B_{d} + Y B_{ld} \times O B_{d})

(15)

Equations 12–15 define the residue stumpage cost (SC_t), harvesting cost (RHC_t), preprocessing cost (PC_t), and conversion cost (CC_t), respectively.

Equation 16 ensures that the residue inventory (RI_jt) at the end of period t equals the residue inventory at the beginning of period t minus the amounts of residue sent to the depots $\sum_{k} \sum_{c} X R_{jkct}$ plus the amounts of residue generated during the first stage (RG_jt):

R I_{j (t + 1)} = R I_{jt} + R G_{jt} - \sum_{k} \sum_{c} X R_{jkct}

(16)

Equations 17–21 formulate all constraints relating to the depot. Under different equipment at the depots, Equation 17 guarantees a material balance ratio RP_c from input $\sum_{j} X R_{jkct}$ to output YD_kct (raw residues versus preprocessed residues) using different preprocessing technology c. Equations 18 and 19 define the lower bound (LD) and upper bound (UD) for annual output at a depot, where the lower bound is assumed to be 70% of the upper bound. Equation 20 makes sure that the output from the depot (YD_kct) and the quantity of feedstock transported to the biorefinery $\sum_{l} \sum_{d} X D_{kcldt}$ are identical. Equation 21 constrains that no more than one depot can be established in each hexagon:

Y D_{kct} = \sum_{j} X R_{jkct} \times R P_{c}

(17)

Y D_{kct} \geq LD \times DV D_{kc}

(18)

Y D_{kct} \leq UD \times DV D_{kc}

(19)

Y D_{kct} = \sum_{l} \sum_{d} X D_{kcldt}

(20)

\sum_{c} DV D_{kc} \leq 1

(21)

Equations 22–26 outline all biorefinery-related constraints. A mass balance (preprocessed residues versus SAF) is guaranteed under different equipment setups at conversion facility centers by Equation 22. Equations 23 and 24 define the lower $L B_{d}$ and upper bounds $U B_{d}$ of annual output in refineries of various sizes. Equation 25 ensures that the quantity of SAF transported to the airports $\sum_{m} X B_{ldmt}$ and the output of the biorefinery $Y B_{ldt}$ are the same. Equation 26 ensures that no more than one depot can be established in a spatial unit:

Y B_{ldt} = \sum_{k} \sum_{c} X D_{kcldt} \times BCY \times SS

(22)

Y B_{ldt} \geq L B_{d} \times DV B_{ld}

(23)

Y B_{ldt} \leq U B_{d} \times DV B_{ld}

(24)

Y B_{ldt} = \sum_{m} X B_{ldmt}

(25)

\sum_{d} DV B_{ld} \leq 1

(26)

Equations 27–30 present constraints on the airports. Equation 27 ensures that the amount of SAF shipped from the biorefinery $\sum_{l} \sum_{d} X B_{ldmt}$ and the quantity shipped to the airport $Y A_{mt}$ are identical. Equation 28 defines the minimum amount of SAF shipped to a selected airport (LA), while Equation 29 ensures that the amount of SAF shipped to an airport cannot surpass its demand. Equation 30 combines a minimum total SAF production in 2030 (TSAF) with a constant annual growth rate ( $ADR$ ):

Y A_{mt} = \sum_{l} \sum_{d} X B_{ldmt}

(27)

Y A_{mt} \geq LA \times DV A_{m}

(28)

Y A_{mt} \leq DV A_{m} \times D A_{m} \times {(1 + ADR)}^{t}

(29)

TSAF \times {(1 + ADR)}^{t} \leq \sum_{m} Y A_{mt}

(30)

Results and Discussion

First-Stage Results

Figure 5 provides information on how harvested areas have changed over time under this stage. Results show that loggers start the harvest areas with a high forest inventory given the lower harvesting cost. The darker areas indicate that more trees have been harvested during a particular year. Over time, more lighter areas are selected, suggesting that when the higher dense forests reduce, loggers gradually reach further areas with lower density for harvest. The total harvesting area has increased from 39,750 to 133,400 acres with an average annual growth rate of 14.40%. The location and amount of logging residues are then used as in the second-stage analysis.

Second-Stage Results

Figure 6 gives the maximum SAF production under each supply chain system. Driven by the throughput of the two conversion technologies shown in Table 2, the SAF MSQ from the pyrolysis process is apparently higher than that in the Fischer–Tropsch process. The MSQ of SAF produced from logging residues using the Fischer–Tropsch process under the HND, HAD, and HRAD preprocessing options are 250, 450, and 550 million gallons, respectively. This result suggests that applying the Fischer–Tropsch process to logging residues in the southeast region could supply 8.3%–18.3% of the national target of the SAF Grand Challenge in 2030 (3 billion gallons). When converting logging residues with the pyrolysis process, the respective SAF MSQ in the southeast of the three preprocessing options could reach 300, 550, and 650 million gallons, satisfying 10.0%–21.6% of the SAF Grand Challenge target in 2030. Among the three preprocessing options, the HRAD system outperforms the hammermill system (HND and HAD) with respect to the SAF MSQ, as the rotary shear has a higher system mass flow compared to the hammermill. Also, detaching the hammermill system from the biorefinery outperforms the attached hammermill system, as the former allows the collection of more logging residues farther away from biorefineries for SAF production. Figure 6 resembles a linear relationship between SAF production and the total supply chain cost, suggesting that the BEC of SAF is stable at varying production levels. Also, the flatter slope of the HRAD pyrolysis process system than the others denotes its cost advantage over other options at each output level.

Figure 7 shows the BEC of each MSQ case under the six evaluated systems. Apparently, the conversion process dominates the SAF cost produced from logging residues, followed by the preprocessing operation. The pyrolysis conversion process presents an economic advantage over the Fischer–Tropsch process because of its lower capital and operation cost. The pyrolysis conversion process reduces the BEC by about 24% compared to the Fischer–Tropsch conversion process under the evaluated systems. Using the same milling system (hammermill), locating the preprocessing system at separate depots rather than attached to the biorefinery (i.e., from HND to HAD) will increase the SAF BEC by US$ 0.19 per gallon (from US$7.38 to US$7.57) with the Fischer–Tropsch process, and by US$ 0.67 per gallon (from US$5.59 to US$5.81) with the pyrolysis process. The cost advantage is because there is no need to transport the preprocessed feedstock to the biorefinery when the preprocessing facilities are attached to the biorefinery. Switching from hammermill to rotary shear preprocessing technology (i.e., from HAD to HRAD) can reduce the SAF cost by about 5%. The improvement in the BEC when adopting the rotary shear technology is because of its higher throughput of on-spec material, resulting in a lower harvesting cost and transportation cost from field to depots. The most cost-effective logging residue supply chain utilizes rotary shear preprocessing technology and pyrolysis conversion process with an estimated SAF BEC at US$5.51 per gallon.

Figure 8 shows the feedstock flows for the SAF MSQ in each process system. The placement of the supply chains under the HND option is concentrated mainly in Georgia, North Carolina, Tennessee, and Virginia. The overall logging residue harvests in those four states for the HND Fischer–Tropsch and pyrolysis process system options are 13.1 and 11.7 million dry tons, respectively, accounting for more than 90% of the total. The overall residue harvested is lower for the pyrolysis technology because it has a relatively higher yield (see Table 2).

The SAF produced in the HND option are primarily shipped to Hartsfield-Jackson Atlanta (ATL), Raleigh-Durham (RDU), Norfolk (ORF), Washington D.C. Dulles (IAD), and Nashville (BNA). Compared to the Fischer–Tropsch pathway, the pyrolysis technique produced more SAF (285 versus 239 million gallons) with less raw residue (12.5 versus 13.3 million dry tons). When switching from the Fischer–Tropsch to the pyrolysis process, the amount of SAF received by all airports will increase, with Dulles and Hartsfield-Jackson Atlanta airports benefiting the most from such an increase.

After separating the depots from refineries (HAD), not only have the feedstock harvesting amounts for the original areas been increased, but Alabama and South Carolina have also been included in the feedstock harvest region. Detaching depots from the biorefinery can effectively expand the boundary for residue collection for a biorefinery, allowing regions with less density to reach enough supply of raw feedstock. Increasing the availability of raw feedstock leads to an expansion in SAF production and further to an increase in the number of airports to be served, that is, Charleston International Airport (CHS) and Charlotte Douglas International Airport (CLT).

Switching from detached hammermill (HAD) to rotary shear (HRAD) preprocessing technology at depots also heavily affects the feedstock harvest areas. Logging residues in Arkansas and Mississippi are harvested because of the higher throughput of rotary shear technology, which makes this area sufficient to produce SAF with a lower amount of feedstock. The increase of raw feedstock harvested and higher throughput of the depot has also led to an increase in SAF production and the number of airports that can be served, as the Memphis International Airport can be served with SAF now. Results clearly suggest that the HRAD pyrolysis process system has advantages over others with respect to both the MSQ and BEC. Figure 9 depicts the harvesting areas, optimal number of installed facilities, and selected airports for that system.

Given the advantage in the MSQ and BEC of the HRAD pyrolysis process system, we further examine the supply chain system with different sources of logging residues, that is, softwood and hardwood. As discussed earlier, the hardwood inventory is larger than that of softwood in the study area. Also, softwood residues are more common in the southeastern region of the study area, whereas hardwood residues are more prevalent in the northern region. Sorting out the sources of logging residues could better explain the supply chain placement. Our results suggest that the SAF MSQ from softwood logging residues could reach 250 million gallons, while hardwood logging residues can supply up to 400 million gallons of SAF. Also, an estimated US$ 0.21 advantage in the BEC is found for hardwood residues over softwood residues (US$5.47 versus US$5.68 per gallon), as the conversion cost is lowered from US$3.45 to US$3.24. The conversion cost advantage for hardwood residues is caused by a higher refinery utilization rate for hardwood residues over softwood residues, given the greater hardwood inventory/density in the area.

The supply chain of the SAF MSQ from softwood and hardwood residues using the HRAD pyrolysis process is presented in Figure 10. When using softwood residues alone for SAF, the supply chain placement is primarily in the southeastern region, while the supply chain placement moves toward the north and northwest area (i.e., Tennessee, North Carolina, and Virginia) when hardwood residues are used as the sole feedstock source. Also, more large-scale refineries are utilized when hardwood residues are used as feedstock compared to softwood residues because of the larger hardwood inventory and denser distribution. For instance, in northern Georgia, four 60-MM gal facilities are sited when using softwood residues as feedstock (Figure 10a), but two larger facilities (90 and 10 MM gal) are placed using hardwood residues (Figure 10b). Results indicate that the larger hardwood residue supply leads to a greater return to scale, lower BEC, and a higher MSQ over softwood. Also, a larger facility (e.g., 200 MM gal), rather than two smaller biorefineries in a cluster, could be placed in northern Georgia for SAF production from hardwood residues if the conversion technology is scaled up.

Conclusions

Driven by the increasing demand for decarbonization in the aviation sector, airlines and policymakers have set up a goal of net-zero carbon for commercial aviation by 2050. SAF from renewable feedstock, such as agricultural or forest residues, has been considered a crucial means to reduce carbon from aviation combustion in the near and medium term. In this study, we developed a two-stage mixed-integer linear programming model to analyze the potential supply and the BEC of SAF from logging residues from various preprocessing and conversion technologies in the southeast U.S.A. The model determines the optimal location of the feedstock collection area, and the location of facilities (depots, refineries, and airports) by minimizing the net present value of the total cost of the logging residue-based supply chain.

Results from various scenarios of feedstock preprocessing and SAF conversion processes in this study suggest that logging residues could produce between 250 and 650 million gallons of SAF annually in the southeast. The maximum SAF volume could vary when other preprocessing or conversion technologies are evaluated. Preprocessing technology and conversion processes are influential on the SAF production, cost, and the location of the supply chain system. The SAF supply chain system that detaches depots from biorefineries, utilizes rotary shear technology for size reduction at depots, and adopts the pyrolysis conversion process at the biorefineries is the most efficient among the evaluated systems. Such a system can potentially supply up to 650 million gallons from logging residues in the region, nearly 22% of the SAF Grand Challenge target in 2030 (i.e., 3 billion gallons of SAF production annually), with nearly 62% of the SAF production generated from hardwood residues. The estimated BEC of SAF from the system is around US$5.50 per gallon, much lower than the BEC from the system utilizing the hammermill and Fischer–Tropsch process (∼US$7.60 per gallon).

Our findings highlight the importance and relevance of enhancing the technologies utilized in the supply chain for SAF development. The estimated BECs of different preprocessing technologies and conversion processes range from US$5.50 to US$7.60 per gallon. SAF generally costs two to four times more than conventional jet fuels. In 2020–2021, the average price of SAF ranged from US$1412 to US$2140 per metric ton (or from US$5.4 to US$8.1 per gallon) ( 58 ). Thus, our estimated BEC using 2021 US$ falls into the range of the actual price of SAF.

Future studies may incorporate the impact of feedstock composition or quality on SAF or the biofuel supply chain and BEC. Different compositions or quality may affect the conversion cost or yields, which affects the supply chain. The implication of feedstock characteristics to SAF supply chain placement and challenges could be important considerations for further examination.

Footnotes

Author Contributions

The authors confirm contribution to the paper as follows: study conception and design: T.E. Yu; data collection: P. Li, D. Lanning; analysis and interpretation of results: P. Li, T.E. Yu, C. Trejo-Pech, J.A. Larson, B.C. English; draft manuscript preparation: P. Li, T.E. Yu; All authors reviewed the results and approved the final version of the manuscript.

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was partially funded by the US Federal Aviation Administration (FAA) Office of Environment and Energy as a part of ASCENT Project 1 and the US Department of Agriculture (USDA) National Institute of Food and Agriculture (NIFA), project award No. 2019-67019-29289.

ORCID iDs

Carlos Trejo-Pech

Burton C. English

David N. Lanning

Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the FAA or other ASCENT sponsor organizations and USDA-NIFA.

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