- Email: [email protected]
Effect of harvest region shape, biomass yield, and plant location on optimal biofuel facility size
Forest Policy and Economics 111 (2020) 102053
Contents lists available at ScienceDirect
Forest Policy and Economics journal homepage: www.elsevier.com/locate/forpol
Effect of harvest region shape, biomass yield, and plant location on optimal biofuel facility size Timothy L. Jenkinsa,1, Enze Jinb, John W. Sutherlandb,
T
⁎
a
Department of Mechanical Engineering - Engineering Mechanics, Sustainable Futures Institute, Michigan Technological University, 1400 Townsend Drive, Houghton, MI 49931, USA b Environmental and Ecological Engineering, Purdue University, 364 Potter Engineering Center, 500 Central Drive, West Lafayette, IN 47907, USA
ARTICLE INFO
ABSTRACT
Keywords: Forest biomass Biofuel Optimal facility size Taxicab geometry Tortuosity
The development of biofuel production facilities using renewable biomass faces many hurdles. One of these is determining the appropriate size of the facility under different uncertain conditions. Facility size is affected by many factors including transportation cost rate, biomass yields, facility location, and the availability of harvest region. This research focuses on understanding the impact of varying harvest yields that are typical with utilizing forest resources and the use of factors to account for actual road routes instead of Euclidean distance. The results suggest that use of realistic travel distances tends to lower the optimal facility size and increase the unit cost per liter of fuel. Varying harvesting yields do have an effect, but this is more a relation of actual location of the facility and less to do with varying yield across the region from which the biomass is harvested.
1. Introduction Cellulosic biofuel generated from agricultural waste and woody biomass have been identified as an advanced renewable fuel compared to the conventional biofuel. The market of cellulosic biofuels is driven by the Renewable Fuel Standard (RFS) that was regulated in the Energy Independence and Securing Act (EISA). The revised RFS requires that 16 billion gallons of cellulosic biofuels will be used for transportation fuel by 2022 (Environmental Protection Agency, 2010). However, the production of cellulosic biofuels cannot meet the demand for the compliance with the RFS2 due to the delayed commercialization of cellulosic biofuels in the U.S. Feedstock availability and economic viability are the major obstacles for commercializing cellulosic biofuels (Jin et al., 2019). Many characters such as facility size and bioconversion efficiency play significant roles in the economic performance of a biorefinery. Facility size optimization has been carried out by many studies (Gallagher and Johnson, 2018; Larasati et al., 2012; Zhao et al., 2015) for determining the least costly cellulosic biofuel production. One of the challenges with many facility size optimization models is that the models are developed around the premise of a circular servicing zone with the facility at the center and all distances normalized to an average haul distance (Overend, 1982). Previously, Jenkins and Sutherland (2014) developed a model to characterize the cost of producing forest
biomass-based fuel as a function of land/resource availability, transportation cost rate, material holding cost, and the economies of scale associated with building and operating a production facility. A relation was developed for the cost per unit of fuel output and a numerical procedure was employed to find the optimal plant size of the biofuel facility. This model was developed with the premise that the biofuel facility would be located at the center of a circular harvest region with uniformly distributed biomass availability. This form is similar to work by (Jenkins, 1997; Kumar et al., 2003; Wright and Brown, 2007). A finding of the study was that for forest-based biofuels, the optimal plant sizes may need to be very large, much larger than currently operating biofuel facilities that use corn or sugar cane (Jenkins and Sutherland, 2014). Moreover, the authors analyzed the sensitivity of this unit cost/ optimal plant size relationship to small changes in several model variables. This further work identified that several variables were significant, including variable transportation cost rate, conversion rate, and operational costs. In addition, several joint effects of factors interacted to impact the optimal facility size. For example, the effect of variable transportation cost on optimal facility size is stronger given a high conversion rate versus a lower one. One outcome of this further study was that for certain combinations of variables optimal facility sizes would be closer to those that are in operation today. Moreover, Huang et al. (2009) identified that the plant size has a significant effect on the feedstock delivered cost.
Corresponding author. E-mail address: [email protected] (J.W. Sutherland). 1 Present address: Department of Engineering Technology, Trine University, Angola, IN, USA. ⁎
https://doi.org/10.1016/j.forpol.2019.102053 Received 15 April 2019; Received in revised form 9 November 2019; Accepted 13 November 2019 1389-9341/ © 2019 Published by Elsevier B.V.
Forest Policy and Economics 111 (2020) 102053
T.L. Jenkins, et al.
To reflect the practical locations of facilities and transportation distance, several studies have combined the geographic information system (GIS) with the optimization model. Zhang et al. (2017) developed a GIS-based optimization approach to the optimal bioethanol facility size by minimizing the delivered biomass cost. Vukašinović and Gordić (2016) utilized the GIS-based optimization model to identify the types and locations of the most cost-effective bioenergy facilities in a certain region of Serbia. However, the previous studies fail to estimate the practical harvest and transportation distances by using Euclidean distance method. There are still some unanswered questions: i) would the use of rectilinear distance or a tortuosity factor (Overend, 1982; Sultana and Kumar, 2012) that compensates for real road distances reduce or enlarge the optimal facility size and thus the unit cost and transportation distance? ii) how does a change in the shape of the biomass harvest region affect both transportation distance and optimal facility size? iii) what impact does non uniform biomass density have on unit cost, transportation distance, and facility size? The answers to these questions are the basis for the analysis reported in this paper. A case study of the Upper Peninsula (U.P.) of Michigan was developed with forest resource data from a GIS based system (Froese et al., 2008) to answer the questions above.
Fig. 1. Representation of the Euclidean and Metro (rectilinear) distance from the production facility to a harvest site.
used to determine the unit cost optimal facility size using a circular harvest region as discussed next. It should be noted that the costs to build, operate the facility and bioconversion efficiency were taken as constants as a base case and scaled as the size of the plant changed. Changes in bioconversion efficiency could result in different scale factors, which is not considered in this research. In the prior work (Jenkins and Sutherland, 2014), several key assumptions were made. First, the model was based on the assumption that all transportation distances were calculated by using the Euclidean (straight line) distance, dE, between the plant and each harvest area as shown in Fig. 1. Based on the Euclidean distance from the processing facility to the elemental harvest areas, the average travel distance, d, part of the second element on the right hand side (RHS) of Eq. (1), is calculated as Eq. (2). One outcome of the Euclidean distance assumption and the use of average distance is the fact that the harvest region corresponding to the optimal facility size must be circular. The second assumption was that the annual biomass equivalent yield, YE, across the whole region of interest is uniformly constant, which is commonly used in the literature (Aden et al., 2002; Huang et al., 2009). This equivalent yield is the product of the land availability fraction and the yield per acre of forest biomass. In fact, the biomass yield varies across a region. The United States Forest Service provides data on forest resources on a county level basis (U.S. Department of Agriculture, 2013). Moreover, owing to the presence of bodies of water, restricted lands, and other natural/man-made features, a given geographic region may have no forest resources available for harvest as shown in Fig. 2. In this study, these two assumptions were changed to represent the real situation of transportation distance and biomass productivity.
2. Methodology This study applies evolutionary algorithm to determine the optimal facility size by minimizing the unit cost of producing forest-based biofuels. The new model is developed based on the existing discrete cost model and replaces the transportation cost of Euclidean distance with Metro distance. 2.1. Discrete cost model for facility operation In the previous work, an analytical expression for the unit cost of producing forest-based biofuels was developed by Jenkins and Sutherland (2014). The total production cost of forest-based biofuels is comprised of biomass gate cost, delivery cost, storage cost, facility construction cost, and facility operation cost (see details in Appendix A). The expression of production cost is shown in Eq. (1):
CU =
CP 1 I 1 + (TR d + TF ) + H M + YP YP YP 2 YP
+
d=
2 3
CBL AF FT
FT /YP BBL
FT 100 YE YP
+
OBL FT
FT / YP BBL
(1)
1 2
(2) −1
In Eq. (1), CU is the unit cost ($ L ), CP the unit cost of securing biomass in a form ready for transportation to the processing facility ($ mt−1), YP is the conversion rate from biomass to fuel (liter mt−1), TR is the variable transportation cost rate ($ mt−1 km−1), TF is the fixed component of the transportation cost rate ($ mt−1), YE is the equivalent biomass yield (mt ha−1), FT is the annual production rate of the facility (L yr−1), H is the unit holding cost ($ mt−1), IM is a proportionality factor, ϕ expresses the fraction of the year during which deliveries are restricted or not permitted, CBL is the cost of constructing a baseline facility ($) with an annual biomass processing capacity associated with BBL (mt yr−1), AF is a factor that annualizes the construction cost, α (value < 1) is a factor that describes the EOS (economy of scale) effect, OBL is the annual operational cost ($ yr−1) with a shape parameter β (value < 1) that describes the operational EOS effect. This model was
2.2. Evolutionary algorithm In this study, discrete approach is used to calculate the empirical transportation networks. In real transportation networks, trucks do not generally follow Euclidean (shortest, direct) paths. Instead, trucks typically move on existing roads (generally cannot move on a Euclidean path), or travel on roads that follow natural terrain features like valleys and waterways. The geographical transportation distance is actually longer than the Euclidean path. Understanding the importance of how
2
Forest Policy and Economics 111 (2020) 102053
T.L. Jenkins, et al.
Fig. 2. Illustration of Non-Uniform Biomass Density (numbers in the cells are the sustainable amount of biomass that can be harvested per year, mt yr−1).
the less direct routes affect the potential size and therefore the costs associated with production facilities is critical. The truck travel distance using rectilinear path, as opposed to following Euclidean paths, is often referred to as the Manhattan, taxi-cab, or metro distance (Black, 2006.). Using this metro (rectilinear) distance approach, the delivery distance expression to each elemental harvest area for the model is
dRi = (|x i
xs| + |yi
ys |),
optimization (Deb, 2001 & Spall, 2005). Our approach begins by proposing a location for the biofuel facility, say the yellow colored section with zero biomass in Fig. 2. The selected biofuel facility then is desired to find the unit cost for N sections (small harvest areas) near itself. The location plays an important role in determining the facility size by the tradeoff of transportation cost and biomass availability. However, this assumption is used to simplify the comparison between the results of traditional and evolutionary optimization methods. The first step in finding the unit cost is to calculate the transportation cost for the specified sections. To arrive at this cost, for each harvestable section, the available biomass, Bi, is multiplied by the metro distance (Eq. (3)), dRi, from the center of that harvest area to the center of the section containing the processing facility. Then, these N biomass-distance combinations are summed together, multiplied by the variable transportation cost rate (TR) and combined with the fixed transportation cost for the total biomass of the N sections, BT. The total transportation cost is then divided by the annual fuel production rate, FT, associated with the biomass for the N sections. This is shown in Eq. (4).
(3)
where (xs, ys) is the position of the biofuel facility, (xi, yi) is the center of the ith harvest area, and dRi is the rectilinear distance from the ith harvest area to the biofuel facility. This distance is also illustrated in Fig. 1. Calculus was applied to the analytical expression of Eq. (1) to determine the optimal facility size for a plant producing forest biofuels (Jenkins and Sutherland, 2014). To accommodate landscape features such as those noted above and allow the equivalent yield to vary across a region of interest, this paper employs a discrete area approach (as opposed to the calculus-based, continuous approach utilized previously by the authors). To solve the discrete optimization, a well-established evolutionary algorithm is employed, which is similar to genetic
Fig. 3. a–c). Representations of the expanding harvest area by section from the processing facility. 3a (upper left) shows the four harvest areas within 1.61 km of the facility, 3b (upper right) the 3.22 km from the facility and 3c (upper middle) the harvest areas that are 4.83 km from the facility.
3
Forest Policy and Economics 111 (2020) 102053
T.L. Jenkins, et al.
Table 1 Base case parameters. Biomass cost ($ mt−1) Trans rate ($ mt-1 km−1) Fixed transport cost ($ mt-1) Base size construction Cost ($) Base size operation Cost ($ yr−1) Biomass base (mt) Conversion rate (liter mt−1)
CP TR TF CBL OBL BBL YP
39.68 0.10 4.29 224,261,881 28,928,505 1,104,951 187.77160
YE IM Φ H α β AF
Equiv. yield (mt ha−1) Base level inventory Inven. build-up rate Unit hold cost ($ mt−1) EOS – construction EOS – operation Annualization factor
0.11209 0.04 0.10857 7.94 0.7 0.8 20
Table 2 Euclidean distance solutions for base case parameters.
(
1 TR FT
N i
Modeling approach
Facility size (L)
Unit cost ($ L−1)
Continuous biomass with analytical optimization (Eq. (1)) Discrete biomass with genetic optimization (Eq. (5))
316,578,018 317,019,841
0.4937 0.4937
)
(Bi dRi ) + BT TF ,
minimum cost is found. The procedure for expanding the harvest areas is shown in Fig. 3. Fig. 3a) - c) graphically show the elemental areas considered for successive iterations of the optimization. From the facility, the distance to the center of each harvest area is shown with red lines. The optimization considers all harvest sections starting with those closest to the facility and working outward, 1.60934 km (1 mile) at a time. Fig. 3a shows that 4 elemental areas are considered (the area containing the biofuel facility is not considered). Fig. 3b has 12 elemental areas, and Fig. 3c has 24 elemental areas. The search procedure continues until the minimum unit cost value is determined. Rather than simply incrementing the harvest areas considered by 1.60934 km at a time to search for the minimum unit cost, the actual method utilized was a genetic algorithm. The implemented genetic optimization method is well suited for solving search problems of this type. The optimization model in this new form, using metro distance and observed values for recoverable biomass, conforms more closely to real transportation networks and to harvest areas containing forest resources. The next step is to compare results from the proposed optimization method to those obtained from other approaches for simple cases.
(4)
where BT = ∑iNBi and FT = BT ∙ YP = (∑iNBi) ∙ YP. With the new transportation cost function defined, a new expression for the unit biofuel cost is found by replacing the second element of the unit cost equation of Eq. (1) with Eq. (4).
CU =
(
CP 1 + TR YP FT
+
CBL AF FT
N i
)
(Bi dRi) + BT TF + H
FT /YP BBL
+
OBL FT
IM 1 + YP 2 YP
FT / YP BBL
(5)
2.3. Optimal plant size determination With Eq. (5) now established as a function of metro distance, the optimal facility size with the corresponding unit cost can be found for a given processing facility location. Starting with a biofuel processing facility location like the one noted in Fig. 2, nearby elemental harvest areas are considered and the unit cost per liter is calculated. Then, harvest areas further and further away are considered in an iterative fashion using an evolutionary algorithm, where for each harvest area, the unit cost is calculated. These unit costs are compared until the Table 3 Genetic optimization for discrete biomass areas for base case parameters. Facility size (euclidean distance)
Unit cost
317,019,841 (L)
0.4937
($ L−1)
Facility size (metro distance)
Unit cost
230,708,549 (L)
0.5124
($ L−1)
Table 4 Long and narrow (bounded) land area with uniform biomass. −1
Situation
Facility size (metro distance)
Unit cost ($ L
Narrow strip central location Narrow strip other location
178,808,123 (L) 114,925,980 (L)
0.5156 0.5312
Fig. 4. Representation of a bounded rectangular land area showing two facility locations; one in the center of the area and one in the upper left quarter of the area. The harvest boundaries for each facility location are shown with red lines with the green area associated with the upper left facility location. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
)
4
Forest Policy and Economics 111 (2020) 102053
T.L. Jenkins, et al.
Fig. 5. Biomass availability across Michigan's Upper Peninsula.
Fig. 6. Details of a harvest region (red rectangle) within Fig. 5. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
5
Forest Policy and Economics 111 (2020) 102053
T.L. Jenkins, et al.
2.4. Assessment of the proposed optimization method
site. This is to be compared to the analytical solution obtained from Eq. (1). It is to be noted that the analytical optimization uses a continuous formulation. Table 2 shows the outcomes of the two solutions. According to the results shown in Table 2, the harvest region formed using optimization with discrete, 2.58999 sq. km (1 sq. mile) sections, and the Euclidean driving distance gives a nearly identical result, within 0.14%, to the analytical optimization solution that employs a continuous distribution of biomass. This small difference demonstrates that the proposed discrete approach to calculating the optimal unit cost
With the unit cost relationship defined and using the base case data from Table 1, the proposed genetic optimization method for discrete sections of biomass was assessed. As the first step in the assessment, the proposed optimization scheme was used to find the minimum unit cost for the base case data when using the Euclidean travel distance (found using the Pythagorean Theorem to convert the metro distance, dRi, to Euclidean distance) from the elemental harvest sections to the plant
Fig. 7. a. County level forest resource availability in the U.P for residues only. Data courtesy of Michigan Forest Biomass Information System, http://fbis.mtu.edu/ FBISV2/. b. County level forest resource availability in the U.P for all saleable logs and residues. Data courtesy of Michigan Forest Biomass Information System, http://fbis.mtu.edu/FBISV2/.
6
Forest Policy and Economics 111 (2020) 102053
T.L. Jenkins, et al.
is virtually the same as the analytical solution and provides support to pursue additional optimal facility size solutions using the metro distance method.
Table 3 indicate that this facility size is about 22% smaller than the facility size obtained with the Euclidean driving distance. The base case results in Table 3 assumed that the facility was located at the center of a substantial harvest region, similar to the analytical solution found in Jenkins and Sutherland (2014).
2.5. Metro distance optimal plant size With the genetic optimization method using a discrete biomass distribution providing comparable results to those for the calculusbased solution, the data in Table 1 were used to determine the optimal facility size using the metro transportation distance. Results shown in
2.6. Bounded harvest region The potential harvesting region has essentially been unbounded; however, the optimal harvest region may be circular (Euclidean travel
Fig. 8. a. Contour plot showing optimal facility size for residue only. b. Contour plot showing unit cost in $ per liter for residues only. c. Contour plot showing maximum one-way transportation distance in km for locations across the U.P. based on the residues only availability.
7
Forest Policy and Economics 111 (2020) 102053
T.L. Jenkins, et al.
Fig. 8. (continued)
3. Case analysis: U.P. of Michigan
distance), rectangular (rectilinear travel distance) or something else entirely. By way of example, attention now shifts to a bounded rectangular harvest region configuration, and possible facility site locations within the region as shown in. The land area considered was long and narrow, and consisted of a matrix of elemental areas that are 271 units (1 unit is 1 sq. mi or 2.59 sq. km in size) high by 451 units wide (436.31 km by 726.11 km). This shape is similar in scope to the proposed case area: Michigan's Upper Peninsula. Two facility site locations within this potential harvest area will be considered. In the first situation the facility was assumed to be located at the center of the potential harvest region (R136, C226); the second situation assumed that a facility location was well away from the center (R84, C56). To achieve a solution for this circumstance, all the elemental harvest areas were assumed to contain an equal amount of biomass again (except for the area that contained the facility – this area was assumed to have no biomass). Table 4 shows the results for the two facility locations. It is to be noted that these results have once again relied on the parameter values in Table 1. Fig. 4 also illustrates these results, with the yellow dot showing the centered location and the red dot the facility location away from the center of the region. The red borders provide the maximum one-way distance from the processing facility to the furthest most elemental harvest locations within the larger bounded harvest area identified with the black border. The results in Table 4, when compared to Table 3 – metro distance, illustrate that with changing land shapes and facility location, the optimal facility size is affected. For a location at the center of the bounded land area, the optimal facility size is reduced by 22.5% relative to the unbounded metro distance facility size in Table 3. When the facility is located away from the center of the land area, the optimal facility size is reduced by nearly 50%, again relative to the metro distance facility size in Table 3. Next, the case analysis for the Upper Peninsula of Michigan will explore other harvest region shape and location circumstances.
The U.P. of Michigan was selected for the case analysis because of the strong history of forest products extraction, unique land shape, and diversity of land ownership (Leatherberry and Spencer, 1996). In this case, the biomass density is not uniformed and varies across the region. Further, owing to the differences in land fertility and tree type on each elemental harvest area (259 hectare section), the yield of biomass varies across the harvest region. This presents a real issue for siting and sizing processing facilities since the varying nature of equivalent yield does play a significant role (Jenkins and Sutherland, 2014). As depicted in Fig. 5 and in more detail in Fig. 6, there could also be a number of places where biomass is not present. Fig. 6 shows a portion of Baraga County (upper left) and Marquette County in the U.P. of Michigan. Each sections biomass value is determined by taking the aforementioned county level biomass availability data and dividing the total availability by the number of harvestable sections in the county. This availability is then applied to all the potentially harvestable sections in that county. Fig. 6 shows the values for two counties as noted in metric tons per square kilometer. Fig. 7a and b illustrate the variability of yield for two biomass assessment types, residues only (tops and limbs) and for all saleable logs and residues, respectively. The legend for the density per square kilometer is provided in the lower left of each figure. These two sets of biomass resource availability values will be used to assess how the optimal unit biofuel cost changes for various locations across the U.P., and how the associated facility size varies. 3.1. Facility location assessment The optimization model, Eq. (5), is now used to determine for each potential facility location the optimal facility size, unit cost of producing each liter of biofuel, and the required one-way transportation distance from the farthest harvest site to the processing facility. To
8
Forest Policy and Economics 111 (2020) 102053
T.L. Jenkins, et al.
accomplish this, the U.P. is divided into sections, with each section containing resource being a potential site for a facility. The algorithm then accepts as input this “map” of the U.P. and runs the optimization repeatedly for each potential location and provides as output a series of “maps” containing the optimal facility size, unit cost, and farthest oneway transportation distance to service that facility location. There were 13,200 potential locations in the U.P. region. It is also possible to perform the optimization for a specific location (section) instead of for many locations across an entire region of interest, though this was not explored here. The intent of this research is to show that by changing
the location of where the biofuel facility could be located, the optimal size will differ and resolves question iii posed earlier. 4. Results and discussion Two model runs were made for the forest resource levels indicated previously. The contour plots in Fig. 8a–c show the optimal facility sizes, unit cost per liter, and maximum one-way travel distance for residues only. The results of best facility size are derived from the cost model with the consideration of various costs and locations. The white
Fig. 9. a. Contour plot showing optimal facility size for all log and residues. b. Contour plot showing unit cost in $ per liter for all log and residues. c. Contour plot showing maximum one-way transportation distance in km for locations across the U.P. based on all log and residues availability.
9
Forest Policy and Economics 111 (2020) 102053
T.L. Jenkins, et al.
Fig. 9. (continued)
areas represent either federal lands whose resources are not available for use in producing renewable fuels or urban areas like cities and towns. As expected, the locations where the smallest facilities occur are on the east and west ends of the peninsula, with the smallest optimal facility size located on the far eastern end near the town of Sault Saint Marie as marked on Fig. 8a. The largest facility sizes are near Marquette, in the north central part of the peninsula. As can be seen in Fig. 8a, several sites are in the range of 164.4 to 176.8 million liters. The range of facility size for the residue only biomass availability goes from 52.689 to 176.805 million liters (13.919 to 46.707 million gallons) (see Fig. 8a). The one-way delivery distance ranges from 168.99 to 340.89 km (105.01 to 211.82 miles). The unit costs range from 0.49 to 0.61 dollars per liter (1.8687 to 2.2938 $ per gallon). The smallest optimal facility sizes have delivery ranges of up to 265.34 km and unit costs of up to 0.59 $/liter, whereas the largest sizes have delivery ranges of up to 228.25 km and 0.51 $/liter. Fig. 9a–c show the optimal facility sizes, unit cost per liter, and maximum one-way collection distance for all logs and residues. Similar to the residue only results, the largest facilities are near the north central part of the peninsula (Marquette) and the smallest facilities are on the east end near Sault Saint Marie. However, there are some notable differences which are discussed next. The ranges of facility sizes for the log and residue biomass availability are substantially larger. The smallest facility is 134.570 million liters and the largest is 397.325 million liters. These are 2.6 and 2.25 times larger than the smallest and largest residue only biomass optimal facility sizes, respectively. The one-way delivery distance ranges from 143.24 to 257.25 km (89.01 to 159.85 miles). These distances are 15.24 and 24.54% smaller than the residue only distance results. The unit costs range from 0.45 to 0.54 dollars per liter (1.72 to 2.20 $ per gallon). These costs are 7.86 and 10.71% lower. The smallest optimal facility sizes have delivery ranges of up to 207.58 km and unit costs of up to 0.52 $/liter, whereas the largest sizes have delivery ranges of up to 183.3205 km and 0.47 $/liter. The case of log and residues indicates
a larger harvest region of biomass feedstock. Compared to the case of residue only, the optimal facility size could be enlarged and the unit cost decreases due to less harvest and transportation distances. Given the model outcomes illustrated in the above case, it is worth noting that a previous assessment was conducted by the author using GIS based assessment. In Fig. 10, the areas in red in the center of Marquette County, shown as darkest green, are close to the larger optimal facility locations identified in Figs. 8a and 9a. The value of GISbased analysis has been shown to be fruitful (Zhang et al., 2011) by using the extensive capabilities of GIS systems to study spatially distributed data. 5. Conclusions This study employs the metro distance approach to examine the effects of various biomass yield, harvest region shape, and plant location on the optimal biofuel facility size. Three questions were posed to direct the model development and address the uniqueness of forest biomass as a feedstock for biofuels. First, the use of metro (rectilinear) distance tends to reduce the optimal facility size. However, the associated unit cost and delivery distances are more a function of the facility size. For example, beyond the optimal facility production capacity, the unit cost tends to be lower as processing output increases as more of the fixed costs are distributed over higher production output. Delivery distance is a function of biomass yield as much as it is the facility size. However, metro distances are longer than Euclidean distances. In addition, the shape of the harvest region does impact facility size. Unbounded circular harvest regions tend to provide much larger optimal plant sizes than bounded regions, especially regions with unique shapes like the U.P. of Michigan. Further, non-uniform biomass density also plays a role in optimizing facility size. The distribution of the biomass over large areas tends to reduce the optimal size of the biofuel facility. Given the impact of transportation cost rate on optimal facility size this is consistent.
10
Forest Policy and Economics 111 (2020) 102053
T.L. Jenkins, et al.
Fig. 10. GIS based assessment of possible locations for ethanol production facilities in the northern Lower Peninsula and U.P. of Michigan. (This work was previously produced by the author for a graduate school course project.)
Declaration of Competing Interest
Acknowledgments
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
The authors gratefully acknowledge the support from a project (CBET-0524872) funded by the National Science Foundation Materials Use: Science, Engineering & Society (MUSES) program.
11
Forest Policy and Economics 111 (2020) 102053
T.L. Jenkins, et al.
Appendix A The unit cost model shown in Eq. (1) was developed in a previous paper by Jenkins and Sutherland (2014). The term definitions and model development provide additional background for the reader. The model has five elements as shown in Eq. (A.1a):
Facility Facility Total = Biomass + Delivery + Storage + + , Cost Gate Cost Cost Cost Construction Cost Operation Cost
(A.1a)
or, symbolically as (A.1b)
C T = CB + CD + CS + CF + COP These five elements on the right hand side (RHS) are then broken down as follows:
(A.2)
CB = CP BT ,
where CP is the whole cost ($/mt) of buying, harvesting, preprocessing, and handling the forest biomass and BT is the required amount of biomass (mt).
CD = TR
2 3
BT 100 YE
1/2
+ TF
BT
(A.3)
where TR the transportation cost rate ($/mt/km),the one-way delivery distance (km) is stated in terms of BT and equivalent yield, YE, for a round harvesting region the facility at the center, and TF is the fixed transport cost ($/mt).
CS = H BINV = H IM BT +
1 [BT 2
]
(A.4)
where H is the unit holding cost ($/mt/yr) and BINV is the average amount of biomass in storage during the year. The latter is expressed in terms of IM and ϕ, the minimum on-hand inventory and the fraction of the year during which deliveries could be restricted or not permitted.
CF =
CBL AF
BT BBL
(A.5)
where CBL is the cost of building a baseline facility ($) with an annual biomass handling capability, BBL (tonnes/year), AF is a parameter that annualizes the construction cost, and α is a factor that defines the EOS effect.
COP = OBL
BT BBL
(A.6)
where OBL is the baseline facility operating cost ($) also associated with BBL (mt/year), and β is the EOS effect factor that describes this cost element. These five elements when combined together and substituted into Eq. (A1b) gives:
CT = (CP BT ) + BT TR
2 3
BT 100
1 2
YE
+ TF + H IM
BT +
1 (BT 2
) +
CBL AF
BT BBL
+ OBL
BT BBL
(A.7)
Of course the desire is to express Eq. (A.7) in terms of FT, the annual production rate and on a unit cost basis. FT and BT are related by the production yield, YP: (A.8)
FT = BT YP BT = FT / YP and so CU expressed as a function of FT becomes
CU =
CP 1 2 + TR YP YP 3
FT 100 YE YP
1 2
+ TF + H
IM 1 + YP 2 YP
+
CBL AF FT
FT / YP BBL
+
OBL FT
FT / YP BBL
(A.9)
Huang, H.J., Ramaswamy, S., Al-Dajani, W., Tschirner, U., Cairncross, R.A., 2009. Effect of biomass species and plant size on cellulosic ethanol: a comparative process and economic analysis. Biomass Bioenergy 33, 234–246. https://doi.org/10.1016/j. biombioe.2008.05.007. Jenkins, B.M., 1997. A comment on the optimal sizing of a biomass utilization facility under constant and variable cost scaling. Biomass Bioenergy 13, 1–9. https://doi.org/ 10.1016/S0961-9534(97)00085-8. Jenkins, T.L., Sutherland, J.W., 2014. A cost model for forest-based biofuel production and its application to optimal facility size determination. For. Policy Econ. 38, 32–39. https://doi.org/10.1016/j.forpol.2013.08.004. Jin, E., Mendis, G.P., Sutherland, J.W., 2019. Spatial agent-based modeling for dedicated energy crop adoption and cellulosic biofuel commercialization. Biofuels Bioprod. Biorefin. https://doi.org/10.1002/bbb.1973. Kumar, A., Cameron, J.B., Flynn, P.C., 2003. Biomass power cost and optimum plant size in western canada. Biomass Bioenergy 24, 445–464. https://doi.org/10.1016/S09619534(02)00149-6. Larasati, A., Liu, T., Epplin, F.M., 2012. An analysis of logistic costs to determine optimal size of a biofuel refinery. EMJ Eng. Manag. J. 24, 63–72. https://doi.org/10.1080/ 10429247.2012.11431956. Leatherberry, E.C., Spencer, J.S., 1996. Michigan forest statistics, 1993. Michigan for.
References Aden, A., Ruth, M., Ibsen, K., Jechura, J., Neeves, K., Sheehan, J., Wallace, B., Montague, L., Slayton, A., Lukas, J., 2002. Lignocellulosic Biomass to Ethanol Process Design and Economics Utilizing Co-Current Dilute Acid Prehydrolysis and Enzymatic Hydrolysis for Corn Stover. NREL/TP-510-32438. Black, P.E., 2006. Manhattan distance. In: Black (Ed.), Dictionary of algorithms and data structures. 18. NIST, pp. 2012. http://xlinux.nist.gov/dads/. Deb, K., 2001. Multi-Objective Optimization Using Evolutionary Algorithms. vol. 16 John Wiley & Sons. Environmental Protection Agency, 2010. Environmental Protection Agency 40 CFR part 80 Regulation of Fuels and Fuel Additives: Changes to Renewable Fuel Standard Program; Final Rule / Rules and Regulations. Federal Register. https://doi.org/10. 1111/j.1365-2753.2009.01147.x. Froese, R.E., Waterstraut, J.R., Johnson, D.M., Shonnard, D.R., Whitmarsh, J.H., Miller, C.A., 2008. Lignocellulosic ethanol: is it economically and financially viable as a fuel source? Environ. Qual. Manag. https://doi.org/10.1002/tqem.20194. Gallagher, P., Johnson, D., 2018. Some new ethanol technology : cost competition and adoption effects in the petroleum market. Energy J. 20, 89–120.
12
Forest Policy and Economics 111 (2020) 102053
T.L. Jenkins, et al. Stat. 1993. https://doi.org/10.5962/bhl.title.80981. Overend, R.P., 1982. The average haul distance and transportation work factors for biomass delivered to a central plant. Biomass 2, 75–79. https://doi.org/10.1016/ 0144-4565(82)90008-7. Spall, J.C., 2005. Introduction to stochastic search and optimization. In: Introduction to Stochastic Search and Optimization, https://doi.org/10.1002/0471722138. Sultana, A., Kumar, A., 2012. Optimal siting and size of bioenergy facilities using geographic information system. Appl. Energy 94, 192–201. https://doi.org/10.1016/j. apenergy.2012.01.052. U.S. Department of Agriculture, 2013. Forest Inventory Data Online (FIDO). Vukašinović, V., Gordić, D., 2016. Optimization and GIS-based combined approach for the determination of the most cost-effective investments in biomass sector. Appl. Energy 178, 250–259. https://doi.org/10.1016/j.apenergy.2016.06.037.
Wright, M., Brown, R.C., 2007. Establishing the optimal sizes of different kinds of biorefineries. Biofuels Bioprod. Biorefin. https://doi.org/10.1002/bbb.25. Zhang, F., Johnson, D.M., Sutherland, J.W., 2011. A GIS-based method for identifying the optimal location for a facility to convert forest biomass to biofuel. Biomass Bioenergy 35, 3951–3961. https://doi.org/10.1016/j.biombioe.2011.06.006. Zhang, F., Wang, J., Liu, S., Zhang, S., Sutherland, J.W., 2017. Integrating GIS with optimization method for a biofuel feedstock supply chain. Biomass Bioenergy 98, 194–205. https://doi.org/10.1016/j.biombioe.2017.01.004. Zhao, L., Zhang, X., Xu, J., Ou, X., Chang, S., Wu, M., 2015. Techno-economic analysis of bioethanol production from lignocellulosic biomass in China: dilute-acid pretreatment and enzymatic hydrolysis of corn Stover. Energies 8, 4096–4117. https://doi. org/10.3390/en8054096.
13
Contents lists available at ScienceDirect
Forest Policy and Economics journal homepage: www.elsevier.com/locate/forpol
Effect of harvest region shape, biomass yield, and plant location on optimal biofuel facility size Timothy L. Jenkinsa,1, Enze Jinb, John W. Sutherlandb,
T
⁎
a
Department of Mechanical Engineering - Engineering Mechanics, Sustainable Futures Institute, Michigan Technological University, 1400 Townsend Drive, Houghton, MI 49931, USA b Environmental and Ecological Engineering, Purdue University, 364 Potter Engineering Center, 500 Central Drive, West Lafayette, IN 47907, USA
ARTICLE INFO
ABSTRACT
Keywords: Forest biomass Biofuel Optimal facility size Taxicab geometry Tortuosity
The development of biofuel production facilities using renewable biomass faces many hurdles. One of these is determining the appropriate size of the facility under different uncertain conditions. Facility size is affected by many factors including transportation cost rate, biomass yields, facility location, and the availability of harvest region. This research focuses on understanding the impact of varying harvest yields that are typical with utilizing forest resources and the use of factors to account for actual road routes instead of Euclidean distance. The results suggest that use of realistic travel distances tends to lower the optimal facility size and increase the unit cost per liter of fuel. Varying harvesting yields do have an effect, but this is more a relation of actual location of the facility and less to do with varying yield across the region from which the biomass is harvested.
1. Introduction Cellulosic biofuel generated from agricultural waste and woody biomass have been identified as an advanced renewable fuel compared to the conventional biofuel. The market of cellulosic biofuels is driven by the Renewable Fuel Standard (RFS) that was regulated in the Energy Independence and Securing Act (EISA). The revised RFS requires that 16 billion gallons of cellulosic biofuels will be used for transportation fuel by 2022 (Environmental Protection Agency, 2010). However, the production of cellulosic biofuels cannot meet the demand for the compliance with the RFS2 due to the delayed commercialization of cellulosic biofuels in the U.S. Feedstock availability and economic viability are the major obstacles for commercializing cellulosic biofuels (Jin et al., 2019). Many characters such as facility size and bioconversion efficiency play significant roles in the economic performance of a biorefinery. Facility size optimization has been carried out by many studies (Gallagher and Johnson, 2018; Larasati et al., 2012; Zhao et al., 2015) for determining the least costly cellulosic biofuel production. One of the challenges with many facility size optimization models is that the models are developed around the premise of a circular servicing zone with the facility at the center and all distances normalized to an average haul distance (Overend, 1982). Previously, Jenkins and Sutherland (2014) developed a model to characterize the cost of producing forest
biomass-based fuel as a function of land/resource availability, transportation cost rate, material holding cost, and the economies of scale associated with building and operating a production facility. A relation was developed for the cost per unit of fuel output and a numerical procedure was employed to find the optimal plant size of the biofuel facility. This model was developed with the premise that the biofuel facility would be located at the center of a circular harvest region with uniformly distributed biomass availability. This form is similar to work by (Jenkins, 1997; Kumar et al., 2003; Wright and Brown, 2007). A finding of the study was that for forest-based biofuels, the optimal plant sizes may need to be very large, much larger than currently operating biofuel facilities that use corn or sugar cane (Jenkins and Sutherland, 2014). Moreover, the authors analyzed the sensitivity of this unit cost/ optimal plant size relationship to small changes in several model variables. This further work identified that several variables were significant, including variable transportation cost rate, conversion rate, and operational costs. In addition, several joint effects of factors interacted to impact the optimal facility size. For example, the effect of variable transportation cost on optimal facility size is stronger given a high conversion rate versus a lower one. One outcome of this further study was that for certain combinations of variables optimal facility sizes would be closer to those that are in operation today. Moreover, Huang et al. (2009) identified that the plant size has a significant effect on the feedstock delivered cost.
Corresponding author. E-mail address: [email protected] (J.W. Sutherland). 1 Present address: Department of Engineering Technology, Trine University, Angola, IN, USA. ⁎
https://doi.org/10.1016/j.forpol.2019.102053 Received 15 April 2019; Received in revised form 9 November 2019; Accepted 13 November 2019 1389-9341/ © 2019 Published by Elsevier B.V.
Forest Policy and Economics 111 (2020) 102053
T.L. Jenkins, et al.
To reflect the practical locations of facilities and transportation distance, several studies have combined the geographic information system (GIS) with the optimization model. Zhang et al. (2017) developed a GIS-based optimization approach to the optimal bioethanol facility size by minimizing the delivered biomass cost. Vukašinović and Gordić (2016) utilized the GIS-based optimization model to identify the types and locations of the most cost-effective bioenergy facilities in a certain region of Serbia. However, the previous studies fail to estimate the practical harvest and transportation distances by using Euclidean distance method. There are still some unanswered questions: i) would the use of rectilinear distance or a tortuosity factor (Overend, 1982; Sultana and Kumar, 2012) that compensates for real road distances reduce or enlarge the optimal facility size and thus the unit cost and transportation distance? ii) how does a change in the shape of the biomass harvest region affect both transportation distance and optimal facility size? iii) what impact does non uniform biomass density have on unit cost, transportation distance, and facility size? The answers to these questions are the basis for the analysis reported in this paper. A case study of the Upper Peninsula (U.P.) of Michigan was developed with forest resource data from a GIS based system (Froese et al., 2008) to answer the questions above.
Fig. 1. Representation of the Euclidean and Metro (rectilinear) distance from the production facility to a harvest site.
used to determine the unit cost optimal facility size using a circular harvest region as discussed next. It should be noted that the costs to build, operate the facility and bioconversion efficiency were taken as constants as a base case and scaled as the size of the plant changed. Changes in bioconversion efficiency could result in different scale factors, which is not considered in this research. In the prior work (Jenkins and Sutherland, 2014), several key assumptions were made. First, the model was based on the assumption that all transportation distances were calculated by using the Euclidean (straight line) distance, dE, between the plant and each harvest area as shown in Fig. 1. Based on the Euclidean distance from the processing facility to the elemental harvest areas, the average travel distance, d, part of the second element on the right hand side (RHS) of Eq. (1), is calculated as Eq. (2). One outcome of the Euclidean distance assumption and the use of average distance is the fact that the harvest region corresponding to the optimal facility size must be circular. The second assumption was that the annual biomass equivalent yield, YE, across the whole region of interest is uniformly constant, which is commonly used in the literature (Aden et al., 2002; Huang et al., 2009). This equivalent yield is the product of the land availability fraction and the yield per acre of forest biomass. In fact, the biomass yield varies across a region. The United States Forest Service provides data on forest resources on a county level basis (U.S. Department of Agriculture, 2013). Moreover, owing to the presence of bodies of water, restricted lands, and other natural/man-made features, a given geographic region may have no forest resources available for harvest as shown in Fig. 2. In this study, these two assumptions were changed to represent the real situation of transportation distance and biomass productivity.
2. Methodology This study applies evolutionary algorithm to determine the optimal facility size by minimizing the unit cost of producing forest-based biofuels. The new model is developed based on the existing discrete cost model and replaces the transportation cost of Euclidean distance with Metro distance. 2.1. Discrete cost model for facility operation In the previous work, an analytical expression for the unit cost of producing forest-based biofuels was developed by Jenkins and Sutherland (2014). The total production cost of forest-based biofuels is comprised of biomass gate cost, delivery cost, storage cost, facility construction cost, and facility operation cost (see details in Appendix A). The expression of production cost is shown in Eq. (1):
CU =
CP 1 I 1 + (TR d + TF ) + H M + YP YP YP 2 YP
+
d=
2 3
CBL AF FT
FT /YP BBL
FT 100 YE YP
+
OBL FT
FT / YP BBL
(1)
1 2
(2) −1
In Eq. (1), CU is the unit cost ($ L ), CP the unit cost of securing biomass in a form ready for transportation to the processing facility ($ mt−1), YP is the conversion rate from biomass to fuel (liter mt−1), TR is the variable transportation cost rate ($ mt−1 km−1), TF is the fixed component of the transportation cost rate ($ mt−1), YE is the equivalent biomass yield (mt ha−1), FT is the annual production rate of the facility (L yr−1), H is the unit holding cost ($ mt−1), IM is a proportionality factor, ϕ expresses the fraction of the year during which deliveries are restricted or not permitted, CBL is the cost of constructing a baseline facility ($) with an annual biomass processing capacity associated with BBL (mt yr−1), AF is a factor that annualizes the construction cost, α (value < 1) is a factor that describes the EOS (economy of scale) effect, OBL is the annual operational cost ($ yr−1) with a shape parameter β (value < 1) that describes the operational EOS effect. This model was
2.2. Evolutionary algorithm In this study, discrete approach is used to calculate the empirical transportation networks. In real transportation networks, trucks do not generally follow Euclidean (shortest, direct) paths. Instead, trucks typically move on existing roads (generally cannot move on a Euclidean path), or travel on roads that follow natural terrain features like valleys and waterways. The geographical transportation distance is actually longer than the Euclidean path. Understanding the importance of how
2
Forest Policy and Economics 111 (2020) 102053
T.L. Jenkins, et al.
Fig. 2. Illustration of Non-Uniform Biomass Density (numbers in the cells are the sustainable amount of biomass that can be harvested per year, mt yr−1).
the less direct routes affect the potential size and therefore the costs associated with production facilities is critical. The truck travel distance using rectilinear path, as opposed to following Euclidean paths, is often referred to as the Manhattan, taxi-cab, or metro distance (Black, 2006.). Using this metro (rectilinear) distance approach, the delivery distance expression to each elemental harvest area for the model is
dRi = (|x i
xs| + |yi
ys |),
optimization (Deb, 2001 & Spall, 2005). Our approach begins by proposing a location for the biofuel facility, say the yellow colored section with zero biomass in Fig. 2. The selected biofuel facility then is desired to find the unit cost for N sections (small harvest areas) near itself. The location plays an important role in determining the facility size by the tradeoff of transportation cost and biomass availability. However, this assumption is used to simplify the comparison between the results of traditional and evolutionary optimization methods. The first step in finding the unit cost is to calculate the transportation cost for the specified sections. To arrive at this cost, for each harvestable section, the available biomass, Bi, is multiplied by the metro distance (Eq. (3)), dRi, from the center of that harvest area to the center of the section containing the processing facility. Then, these N biomass-distance combinations are summed together, multiplied by the variable transportation cost rate (TR) and combined with the fixed transportation cost for the total biomass of the N sections, BT. The total transportation cost is then divided by the annual fuel production rate, FT, associated with the biomass for the N sections. This is shown in Eq. (4).
(3)
where (xs, ys) is the position of the biofuel facility, (xi, yi) is the center of the ith harvest area, and dRi is the rectilinear distance from the ith harvest area to the biofuel facility. This distance is also illustrated in Fig. 1. Calculus was applied to the analytical expression of Eq. (1) to determine the optimal facility size for a plant producing forest biofuels (Jenkins and Sutherland, 2014). To accommodate landscape features such as those noted above and allow the equivalent yield to vary across a region of interest, this paper employs a discrete area approach (as opposed to the calculus-based, continuous approach utilized previously by the authors). To solve the discrete optimization, a well-established evolutionary algorithm is employed, which is similar to genetic
Fig. 3. a–c). Representations of the expanding harvest area by section from the processing facility. 3a (upper left) shows the four harvest areas within 1.61 km of the facility, 3b (upper right) the 3.22 km from the facility and 3c (upper middle) the harvest areas that are 4.83 km from the facility.
3
Forest Policy and Economics 111 (2020) 102053
T.L. Jenkins, et al.
Table 1 Base case parameters. Biomass cost ($ mt−1) Trans rate ($ mt-1 km−1) Fixed transport cost ($ mt-1) Base size construction Cost ($) Base size operation Cost ($ yr−1) Biomass base (mt) Conversion rate (liter mt−1)
CP TR TF CBL OBL BBL YP
39.68 0.10 4.29 224,261,881 28,928,505 1,104,951 187.77160
YE IM Φ H α β AF
Equiv. yield (mt ha−1) Base level inventory Inven. build-up rate Unit hold cost ($ mt−1) EOS – construction EOS – operation Annualization factor
0.11209 0.04 0.10857 7.94 0.7 0.8 20
Table 2 Euclidean distance solutions for base case parameters.
(
1 TR FT
N i
Modeling approach
Facility size (L)
Unit cost ($ L−1)
Continuous biomass with analytical optimization (Eq. (1)) Discrete biomass with genetic optimization (Eq. (5))
316,578,018 317,019,841
0.4937 0.4937
)
(Bi dRi ) + BT TF ,
minimum cost is found. The procedure for expanding the harvest areas is shown in Fig. 3. Fig. 3a) - c) graphically show the elemental areas considered for successive iterations of the optimization. From the facility, the distance to the center of each harvest area is shown with red lines. The optimization considers all harvest sections starting with those closest to the facility and working outward, 1.60934 km (1 mile) at a time. Fig. 3a shows that 4 elemental areas are considered (the area containing the biofuel facility is not considered). Fig. 3b has 12 elemental areas, and Fig. 3c has 24 elemental areas. The search procedure continues until the minimum unit cost value is determined. Rather than simply incrementing the harvest areas considered by 1.60934 km at a time to search for the minimum unit cost, the actual method utilized was a genetic algorithm. The implemented genetic optimization method is well suited for solving search problems of this type. The optimization model in this new form, using metro distance and observed values for recoverable biomass, conforms more closely to real transportation networks and to harvest areas containing forest resources. The next step is to compare results from the proposed optimization method to those obtained from other approaches for simple cases.
(4)
where BT = ∑iNBi and FT = BT ∙ YP = (∑iNBi) ∙ YP. With the new transportation cost function defined, a new expression for the unit biofuel cost is found by replacing the second element of the unit cost equation of Eq. (1) with Eq. (4).
CU =
(
CP 1 + TR YP FT
+
CBL AF FT
N i
)
(Bi dRi) + BT TF + H
FT /YP BBL
+
OBL FT
IM 1 + YP 2 YP
FT / YP BBL
(5)
2.3. Optimal plant size determination With Eq. (5) now established as a function of metro distance, the optimal facility size with the corresponding unit cost can be found for a given processing facility location. Starting with a biofuel processing facility location like the one noted in Fig. 2, nearby elemental harvest areas are considered and the unit cost per liter is calculated. Then, harvest areas further and further away are considered in an iterative fashion using an evolutionary algorithm, where for each harvest area, the unit cost is calculated. These unit costs are compared until the Table 3 Genetic optimization for discrete biomass areas for base case parameters. Facility size (euclidean distance)
Unit cost
317,019,841 (L)
0.4937
($ L−1)
Facility size (metro distance)
Unit cost
230,708,549 (L)
0.5124
($ L−1)
Table 4 Long and narrow (bounded) land area with uniform biomass. −1
Situation
Facility size (metro distance)
Unit cost ($ L
Narrow strip central location Narrow strip other location
178,808,123 (L) 114,925,980 (L)
0.5156 0.5312
Fig. 4. Representation of a bounded rectangular land area showing two facility locations; one in the center of the area and one in the upper left quarter of the area. The harvest boundaries for each facility location are shown with red lines with the green area associated with the upper left facility location. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
)
4
Forest Policy and Economics 111 (2020) 102053
T.L. Jenkins, et al.
Fig. 5. Biomass availability across Michigan's Upper Peninsula.
Fig. 6. Details of a harvest region (red rectangle) within Fig. 5. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
5
Forest Policy and Economics 111 (2020) 102053
T.L. Jenkins, et al.
2.4. Assessment of the proposed optimization method
site. This is to be compared to the analytical solution obtained from Eq. (1). It is to be noted that the analytical optimization uses a continuous formulation. Table 2 shows the outcomes of the two solutions. According to the results shown in Table 2, the harvest region formed using optimization with discrete, 2.58999 sq. km (1 sq. mile) sections, and the Euclidean driving distance gives a nearly identical result, within 0.14%, to the analytical optimization solution that employs a continuous distribution of biomass. This small difference demonstrates that the proposed discrete approach to calculating the optimal unit cost
With the unit cost relationship defined and using the base case data from Table 1, the proposed genetic optimization method for discrete sections of biomass was assessed. As the first step in the assessment, the proposed optimization scheme was used to find the minimum unit cost for the base case data when using the Euclidean travel distance (found using the Pythagorean Theorem to convert the metro distance, dRi, to Euclidean distance) from the elemental harvest sections to the plant
Fig. 7. a. County level forest resource availability in the U.P for residues only. Data courtesy of Michigan Forest Biomass Information System, http://fbis.mtu.edu/ FBISV2/. b. County level forest resource availability in the U.P for all saleable logs and residues. Data courtesy of Michigan Forest Biomass Information System, http://fbis.mtu.edu/FBISV2/.
6
Forest Policy and Economics 111 (2020) 102053
T.L. Jenkins, et al.
is virtually the same as the analytical solution and provides support to pursue additional optimal facility size solutions using the metro distance method.
Table 3 indicate that this facility size is about 22% smaller than the facility size obtained with the Euclidean driving distance. The base case results in Table 3 assumed that the facility was located at the center of a substantial harvest region, similar to the analytical solution found in Jenkins and Sutherland (2014).
2.5. Metro distance optimal plant size With the genetic optimization method using a discrete biomass distribution providing comparable results to those for the calculusbased solution, the data in Table 1 were used to determine the optimal facility size using the metro transportation distance. Results shown in
2.6. Bounded harvest region The potential harvesting region has essentially been unbounded; however, the optimal harvest region may be circular (Euclidean travel
Fig. 8. a. Contour plot showing optimal facility size for residue only. b. Contour plot showing unit cost in $ per liter for residues only. c. Contour plot showing maximum one-way transportation distance in km for locations across the U.P. based on the residues only availability.
7
Forest Policy and Economics 111 (2020) 102053
T.L. Jenkins, et al.
Fig. 8. (continued)
3. Case analysis: U.P. of Michigan
distance), rectangular (rectilinear travel distance) or something else entirely. By way of example, attention now shifts to a bounded rectangular harvest region configuration, and possible facility site locations within the region as shown in. The land area considered was long and narrow, and consisted of a matrix of elemental areas that are 271 units (1 unit is 1 sq. mi or 2.59 sq. km in size) high by 451 units wide (436.31 km by 726.11 km). This shape is similar in scope to the proposed case area: Michigan's Upper Peninsula. Two facility site locations within this potential harvest area will be considered. In the first situation the facility was assumed to be located at the center of the potential harvest region (R136, C226); the second situation assumed that a facility location was well away from the center (R84, C56). To achieve a solution for this circumstance, all the elemental harvest areas were assumed to contain an equal amount of biomass again (except for the area that contained the facility – this area was assumed to have no biomass). Table 4 shows the results for the two facility locations. It is to be noted that these results have once again relied on the parameter values in Table 1. Fig. 4 also illustrates these results, with the yellow dot showing the centered location and the red dot the facility location away from the center of the region. The red borders provide the maximum one-way distance from the processing facility to the furthest most elemental harvest locations within the larger bounded harvest area identified with the black border. The results in Table 4, when compared to Table 3 – metro distance, illustrate that with changing land shapes and facility location, the optimal facility size is affected. For a location at the center of the bounded land area, the optimal facility size is reduced by 22.5% relative to the unbounded metro distance facility size in Table 3. When the facility is located away from the center of the land area, the optimal facility size is reduced by nearly 50%, again relative to the metro distance facility size in Table 3. Next, the case analysis for the Upper Peninsula of Michigan will explore other harvest region shape and location circumstances.
The U.P. of Michigan was selected for the case analysis because of the strong history of forest products extraction, unique land shape, and diversity of land ownership (Leatherberry and Spencer, 1996). In this case, the biomass density is not uniformed and varies across the region. Further, owing to the differences in land fertility and tree type on each elemental harvest area (259 hectare section), the yield of biomass varies across the harvest region. This presents a real issue for siting and sizing processing facilities since the varying nature of equivalent yield does play a significant role (Jenkins and Sutherland, 2014). As depicted in Fig. 5 and in more detail in Fig. 6, there could also be a number of places where biomass is not present. Fig. 6 shows a portion of Baraga County (upper left) and Marquette County in the U.P. of Michigan. Each sections biomass value is determined by taking the aforementioned county level biomass availability data and dividing the total availability by the number of harvestable sections in the county. This availability is then applied to all the potentially harvestable sections in that county. Fig. 6 shows the values for two counties as noted in metric tons per square kilometer. Fig. 7a and b illustrate the variability of yield for two biomass assessment types, residues only (tops and limbs) and for all saleable logs and residues, respectively. The legend for the density per square kilometer is provided in the lower left of each figure. These two sets of biomass resource availability values will be used to assess how the optimal unit biofuel cost changes for various locations across the U.P., and how the associated facility size varies. 3.1. Facility location assessment The optimization model, Eq. (5), is now used to determine for each potential facility location the optimal facility size, unit cost of producing each liter of biofuel, and the required one-way transportation distance from the farthest harvest site to the processing facility. To
8
Forest Policy and Economics 111 (2020) 102053
T.L. Jenkins, et al.
accomplish this, the U.P. is divided into sections, with each section containing resource being a potential site for a facility. The algorithm then accepts as input this “map” of the U.P. and runs the optimization repeatedly for each potential location and provides as output a series of “maps” containing the optimal facility size, unit cost, and farthest oneway transportation distance to service that facility location. There were 13,200 potential locations in the U.P. region. It is also possible to perform the optimization for a specific location (section) instead of for many locations across an entire region of interest, though this was not explored here. The intent of this research is to show that by changing
the location of where the biofuel facility could be located, the optimal size will differ and resolves question iii posed earlier. 4. Results and discussion Two model runs were made for the forest resource levels indicated previously. The contour plots in Fig. 8a–c show the optimal facility sizes, unit cost per liter, and maximum one-way travel distance for residues only. The results of best facility size are derived from the cost model with the consideration of various costs and locations. The white
Fig. 9. a. Contour plot showing optimal facility size for all log and residues. b. Contour plot showing unit cost in $ per liter for all log and residues. c. Contour plot showing maximum one-way transportation distance in km for locations across the U.P. based on all log and residues availability.
9
Forest Policy and Economics 111 (2020) 102053
T.L. Jenkins, et al.
Fig. 9. (continued)
areas represent either federal lands whose resources are not available for use in producing renewable fuels or urban areas like cities and towns. As expected, the locations where the smallest facilities occur are on the east and west ends of the peninsula, with the smallest optimal facility size located on the far eastern end near the town of Sault Saint Marie as marked on Fig. 8a. The largest facility sizes are near Marquette, in the north central part of the peninsula. As can be seen in Fig. 8a, several sites are in the range of 164.4 to 176.8 million liters. The range of facility size for the residue only biomass availability goes from 52.689 to 176.805 million liters (13.919 to 46.707 million gallons) (see Fig. 8a). The one-way delivery distance ranges from 168.99 to 340.89 km (105.01 to 211.82 miles). The unit costs range from 0.49 to 0.61 dollars per liter (1.8687 to 2.2938 $ per gallon). The smallest optimal facility sizes have delivery ranges of up to 265.34 km and unit costs of up to 0.59 $/liter, whereas the largest sizes have delivery ranges of up to 228.25 km and 0.51 $/liter. Fig. 9a–c show the optimal facility sizes, unit cost per liter, and maximum one-way collection distance for all logs and residues. Similar to the residue only results, the largest facilities are near the north central part of the peninsula (Marquette) and the smallest facilities are on the east end near Sault Saint Marie. However, there are some notable differences which are discussed next. The ranges of facility sizes for the log and residue biomass availability are substantially larger. The smallest facility is 134.570 million liters and the largest is 397.325 million liters. These are 2.6 and 2.25 times larger than the smallest and largest residue only biomass optimal facility sizes, respectively. The one-way delivery distance ranges from 143.24 to 257.25 km (89.01 to 159.85 miles). These distances are 15.24 and 24.54% smaller than the residue only distance results. The unit costs range from 0.45 to 0.54 dollars per liter (1.72 to 2.20 $ per gallon). These costs are 7.86 and 10.71% lower. The smallest optimal facility sizes have delivery ranges of up to 207.58 km and unit costs of up to 0.52 $/liter, whereas the largest sizes have delivery ranges of up to 183.3205 km and 0.47 $/liter. The case of log and residues indicates
a larger harvest region of biomass feedstock. Compared to the case of residue only, the optimal facility size could be enlarged and the unit cost decreases due to less harvest and transportation distances. Given the model outcomes illustrated in the above case, it is worth noting that a previous assessment was conducted by the author using GIS based assessment. In Fig. 10, the areas in red in the center of Marquette County, shown as darkest green, are close to the larger optimal facility locations identified in Figs. 8a and 9a. The value of GISbased analysis has been shown to be fruitful (Zhang et al., 2011) by using the extensive capabilities of GIS systems to study spatially distributed data. 5. Conclusions This study employs the metro distance approach to examine the effects of various biomass yield, harvest region shape, and plant location on the optimal biofuel facility size. Three questions were posed to direct the model development and address the uniqueness of forest biomass as a feedstock for biofuels. First, the use of metro (rectilinear) distance tends to reduce the optimal facility size. However, the associated unit cost and delivery distances are more a function of the facility size. For example, beyond the optimal facility production capacity, the unit cost tends to be lower as processing output increases as more of the fixed costs are distributed over higher production output. Delivery distance is a function of biomass yield as much as it is the facility size. However, metro distances are longer than Euclidean distances. In addition, the shape of the harvest region does impact facility size. Unbounded circular harvest regions tend to provide much larger optimal plant sizes than bounded regions, especially regions with unique shapes like the U.P. of Michigan. Further, non-uniform biomass density also plays a role in optimizing facility size. The distribution of the biomass over large areas tends to reduce the optimal size of the biofuel facility. Given the impact of transportation cost rate on optimal facility size this is consistent.
10
Forest Policy and Economics 111 (2020) 102053
T.L. Jenkins, et al.
Fig. 10. GIS based assessment of possible locations for ethanol production facilities in the northern Lower Peninsula and U.P. of Michigan. (This work was previously produced by the author for a graduate school course project.)
Declaration of Competing Interest
Acknowledgments
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
The authors gratefully acknowledge the support from a project (CBET-0524872) funded by the National Science Foundation Materials Use: Science, Engineering & Society (MUSES) program.
11
Forest Policy and Economics 111 (2020) 102053
T.L. Jenkins, et al.
Appendix A The unit cost model shown in Eq. (1) was developed in a previous paper by Jenkins and Sutherland (2014). The term definitions and model development provide additional background for the reader. The model has five elements as shown in Eq. (A.1a):
Facility Facility Total = Biomass + Delivery + Storage + + , Cost Gate Cost Cost Cost Construction Cost Operation Cost
(A.1a)
or, symbolically as (A.1b)
C T = CB + CD + CS + CF + COP These five elements on the right hand side (RHS) are then broken down as follows:
(A.2)
CB = CP BT ,
where CP is the whole cost ($/mt) of buying, harvesting, preprocessing, and handling the forest biomass and BT is the required amount of biomass (mt).
CD = TR
2 3
BT 100 YE
1/2
+ TF
BT
(A.3)
where TR the transportation cost rate ($/mt/km),the one-way delivery distance (km) is stated in terms of BT and equivalent yield, YE, for a round harvesting region the facility at the center, and TF is the fixed transport cost ($/mt).
CS = H BINV = H IM BT +
1 [BT 2
]
(A.4)
where H is the unit holding cost ($/mt/yr) and BINV is the average amount of biomass in storage during the year. The latter is expressed in terms of IM and ϕ, the minimum on-hand inventory and the fraction of the year during which deliveries could be restricted or not permitted.
CF =
CBL AF
BT BBL
(A.5)
where CBL is the cost of building a baseline facility ($) with an annual biomass handling capability, BBL (tonnes/year), AF is a parameter that annualizes the construction cost, and α is a factor that defines the EOS effect.
COP = OBL
BT BBL
(A.6)
where OBL is the baseline facility operating cost ($) also associated with BBL (mt/year), and β is the EOS effect factor that describes this cost element. These five elements when combined together and substituted into Eq. (A1b) gives:
CT = (CP BT ) + BT TR
2 3
BT 100
1 2
YE
+ TF + H IM
BT +
1 (BT 2
) +
CBL AF
BT BBL
+ OBL
BT BBL
(A.7)
Of course the desire is to express Eq. (A.7) in terms of FT, the annual production rate and on a unit cost basis. FT and BT are related by the production yield, YP: (A.8)
FT = BT YP BT = FT / YP and so CU expressed as a function of FT becomes
CU =
CP 1 2 + TR YP YP 3
FT 100 YE YP
1 2
+ TF + H
IM 1 + YP 2 YP
+
CBL AF FT
FT / YP BBL
+
OBL FT
FT / YP BBL
(A.9)
Huang, H.J., Ramaswamy, S., Al-Dajani, W., Tschirner, U., Cairncross, R.A., 2009. Effect of biomass species and plant size on cellulosic ethanol: a comparative process and economic analysis. Biomass Bioenergy 33, 234–246. https://doi.org/10.1016/j. biombioe.2008.05.007. Jenkins, B.M., 1997. A comment on the optimal sizing of a biomass utilization facility under constant and variable cost scaling. Biomass Bioenergy 13, 1–9. https://doi.org/ 10.1016/S0961-9534(97)00085-8. Jenkins, T.L., Sutherland, J.W., 2014. A cost model for forest-based biofuel production and its application to optimal facility size determination. For. Policy Econ. 38, 32–39. https://doi.org/10.1016/j.forpol.2013.08.004. Jin, E., Mendis, G.P., Sutherland, J.W., 2019. Spatial agent-based modeling for dedicated energy crop adoption and cellulosic biofuel commercialization. Biofuels Bioprod. Biorefin. https://doi.org/10.1002/bbb.1973. Kumar, A., Cameron, J.B., Flynn, P.C., 2003. Biomass power cost and optimum plant size in western canada. Biomass Bioenergy 24, 445–464. https://doi.org/10.1016/S09619534(02)00149-6. Larasati, A., Liu, T., Epplin, F.M., 2012. An analysis of logistic costs to determine optimal size of a biofuel refinery. EMJ Eng. Manag. J. 24, 63–72. https://doi.org/10.1080/ 10429247.2012.11431956. Leatherberry, E.C., Spencer, J.S., 1996. Michigan forest statistics, 1993. Michigan for.
References Aden, A., Ruth, M., Ibsen, K., Jechura, J., Neeves, K., Sheehan, J., Wallace, B., Montague, L., Slayton, A., Lukas, J., 2002. Lignocellulosic Biomass to Ethanol Process Design and Economics Utilizing Co-Current Dilute Acid Prehydrolysis and Enzymatic Hydrolysis for Corn Stover. NREL/TP-510-32438. Black, P.E., 2006. Manhattan distance. In: Black (Ed.), Dictionary of algorithms and data structures. 18. NIST, pp. 2012. http://xlinux.nist.gov/dads/. Deb, K., 2001. Multi-Objective Optimization Using Evolutionary Algorithms. vol. 16 John Wiley & Sons. Environmental Protection Agency, 2010. Environmental Protection Agency 40 CFR part 80 Regulation of Fuels and Fuel Additives: Changes to Renewable Fuel Standard Program; Final Rule / Rules and Regulations. Federal Register. https://doi.org/10. 1111/j.1365-2753.2009.01147.x. Froese, R.E., Waterstraut, J.R., Johnson, D.M., Shonnard, D.R., Whitmarsh, J.H., Miller, C.A., 2008. Lignocellulosic ethanol: is it economically and financially viable as a fuel source? Environ. Qual. Manag. https://doi.org/10.1002/tqem.20194. Gallagher, P., Johnson, D., 2018. Some new ethanol technology : cost competition and adoption effects in the petroleum market. Energy J. 20, 89–120.
12
Forest Policy and Economics 111 (2020) 102053
T.L. Jenkins, et al. Stat. 1993. https://doi.org/10.5962/bhl.title.80981. Overend, R.P., 1982. The average haul distance and transportation work factors for biomass delivered to a central plant. Biomass 2, 75–79. https://doi.org/10.1016/ 0144-4565(82)90008-7. Spall, J.C., 2005. Introduction to stochastic search and optimization. In: Introduction to Stochastic Search and Optimization, https://doi.org/10.1002/0471722138. Sultana, A., Kumar, A., 2012. Optimal siting and size of bioenergy facilities using geographic information system. Appl. Energy 94, 192–201. https://doi.org/10.1016/j. apenergy.2012.01.052. U.S. Department of Agriculture, 2013. Forest Inventory Data Online (FIDO). Vukašinović, V., Gordić, D., 2016. Optimization and GIS-based combined approach for the determination of the most cost-effective investments in biomass sector. Appl. Energy 178, 250–259. https://doi.org/10.1016/j.apenergy.2016.06.037.
Wright, M., Brown, R.C., 2007. Establishing the optimal sizes of different kinds of biorefineries. Biofuels Bioprod. Biorefin. https://doi.org/10.1002/bbb.25. Zhang, F., Johnson, D.M., Sutherland, J.W., 2011. A GIS-based method for identifying the optimal location for a facility to convert forest biomass to biofuel. Biomass Bioenergy 35, 3951–3961. https://doi.org/10.1016/j.biombioe.2011.06.006. Zhang, F., Wang, J., Liu, S., Zhang, S., Sutherland, J.W., 2017. Integrating GIS with optimization method for a biofuel feedstock supply chain. Biomass Bioenergy 98, 194–205. https://doi.org/10.1016/j.biombioe.2017.01.004. Zhao, L., Zhang, X., Xu, J., Ou, X., Chang, S., Wu, M., 2015. Techno-economic analysis of bioethanol production from lignocellulosic biomass in China: dilute-acid pretreatment and enzymatic hydrolysis of corn Stover. Energies 8, 4096–4117. https://doi. org/10.3390/en8054096.
13