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A cost model for forest-based biofuel production and its application to optimal facility size determination
Forest Policy and Economics 38 (2014) 32–39
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A cost model for forest-based biofuel production and its application to optimal facility size determination Timothy L. Jenkins a,⁎, John W. Sutherland b a b
Department of Mechanical Engineering-Engineering Mechanics, Sustainable Futures Institute, Michigan Technological University, 1400 Townsend Drive, Houghton, MI 49931, USA Division of Environmental and Ecological Engineering, Purdue University, Potter Engineering Center, Room 322, 500 Central Drive, West Lafayette, IN 47907, USA
a r t i c l e
i n f o
Article history: Received 21 November 2009 Received in revised form 5 August 2013 Accepted 7 August 2013 Available online 26 September 2013 Keywords: Economics Forest biomass Biofuel Optimal facility size Unit cost
a b s t r a c t With continued concerns regarding the use of fossil fuels and energy security, there is increasing interest in biofuels. However, owing to worries over the use of agricultural feedstocks for biofuel, forest biomass as a feedstock has been investigated for some time and appears to be a promising alternative. Current corn-based ethanol facilities range in size from a few million to over 380 million liters (100 million gallons) per year with associated construction costs near $117 million for the latter sized capacity. On the other hand, the economics for forest biomass to biofuel facilities are different and there appears to be a lack of understanding about the cost optimal size for the processing facility and the associated investment. With this in mind, a mathematical model is developed to describe the total annual costs of a forest biomass to biofuel facility using the Upper Peninsula of Michigan as the case study area. The model includes terms associated with forest resource harvesting and collection, transportation, storage, and facility construction and operation costs. The model is used to establish a relationship for the optimal size of a production facility, that is, the facility size that provides the minimum unit cost. The effect of various factors on the optimal facility size and the associated biofuel unit cost are examined, especially transportation cost rate and equivalent yield. The results indicate these two factors do impact optimal size and unit cost. © 2013 Elsevier B.V. All rights reserved.
1. Introduction While corn and sugar cane are the primary feedstocks for producing first generation biofuels, other feedstocks include sorghum, wheat, sugar beets, soybeans, and cellulose. Many now believe that second and third generation biofuels may eventually dominate renewable biofuel production (NSF, 2008). Regardless of the biofuel type, the use of cellulose found in plant fibers (e.g., trees, grasses, crop wastes, and municipal solid waste) is gaining acceptance and several production facility projects have been proposed or initiated to produce biofuels (Rendleman and Shapouri, 2007; Greer, 2008). One advantage of cellulose over other feedstocks is that a food versus fuel tradeoff need not be made (Runge and Senauer, 2007). Another is the apparent abundance of these resources (USDA/DOE, 2005). In this study we will focus on forest resource material, e.g., forest residues (limbs, treetops, etc.) unused for pulp and paper harvesting and slash removals produced in the process of thinning operations undertaken to improve stand growth and reduce fire hazards (Graham et al., 2004). It is estimated that the U.S. has 112.5 million tonnes (124 million tons) of forest residues and other sources available annually for conversion to energy and bio-based ⁎ Corresponding author at: Department of Engineering Technology, Trine University, Angola, IN 46703, USA. Tel.: +1 260 665 4660; fax: +1 260 665 4816. E-mail address: [email protected] (T.L. Jenkins). 1389-9341/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.forpol.2013.08.004
fuels like ethanol (USDA/DOE, 2005). These values do not include any forest resources used for fuelwood, residues from wood processing mills, or urban wood wastes that could also be utilized. Walsh (2008) has estimated that in the U.S. there are 57.15 million tonnes (63 million tons) of forest residues from logging operations and 22.4 million tonnes (24.7 million tons) from other removals available annually. Additionally, it is estimated that as much as 403.7 million tonnes (445 million tons) of woody biomass from fuel treatment removals, to maintain healthy forests and limit catastrophic forest fires, are available in the western United States alone (Rummer et al., 2003; Ince et al., 2006). One of the issues associated with the production of biofuels from woody biomass (forest resources) is having a facility size that minimizes overall cost per unit of production. Several researchers have developed cost models (Wooley et al., 1999; Aden et al., 2002; Wyman, 2003; Lambert and Middleton, 2010) that have been used to find the best size of a biofuel production facility. In Wooley et al. (1999), the size of the facility was determined based on prior process economic analysis and reasonable feedstock delivery distances. Aden et al. (2002) provided an update to the earlier work by Wooley and Wyman that extended the analysis to include conversion to sugars, but again the study only considered baseline sizes. A more recent study by Lambert and Middleton (2010) developed a mixed integer programming model to evaluate the profitability of a field-to-refinery supply system. The focus in their work was on herbaceous crop residues and the
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decentralization of pretreatment facilities from biofuel refineries using North Dakota as a study area. However, the refinery sizes used were based on data from Aden et al. (2002), and only three sizes were used as inputs. Other models focused more on best facility size (Nguyen and Prince, 1996; Graham et al., 1997; Jenkins, 1997; Noon et al., 2002; Searcy and Flynn, 2008), and considered corn stover, switchgrass, and some regional forest resources. One limitation of these studies was that the facility sizes were specified a priori and not solved for. Further, little attention has been paid to storage costs that incorporate possible seasonal limitations to biomass transport into cost models. Finally, a study by Gan and Smith (2011) modeled the optimum plant size but assumed that certain costs were independent of plant size. Further, Gan and Smith (2011) combined facility construction and operation costs and assumed both had equal economy of scale characteristics. In spite of the importance of woody biomass as a key long-term component of any biofuel portfolio, less attention has been focused on cost models utilizing forest resources and the associated cost optimal facility size issue. The cost structure for biofuel facilities based on cellulosic biomass material is very different from that based on corn (Kocoloski et al., 2011); cellulosic biomass facilities are more expensive. With this in mind, in Section 2 a model for the total cost of biofuel production from woody biomass is developed. Section 3 will define the unit cost and this will be used in Section 4 to determine the cost optimal facility size. Similar to Gan and Smith (2011), this model formulation will address what the optimum size should be in the absence of a capital constraint. Finally, Section 5 will summarize the results and provide decision-makers insight into selecting a facility size that minimizes the unit cost of biofuel production. 2. Cost model for biofuel production A cost model for biofuel production must consider expenditures associated with biomass harvesting and collection, transportation, storage, and plant construction and operation. With this in mind, the total annual cost for producing biofuel from woody biomass may be expressed as: Storage Biomass Delivery Facility Total þ þ þ ¼ Cost Gate Cost Cost Construction Cost Cost Facility ; þ Operation Cost
cost of the biomass as the product of Cp and the amount of biomass, BT, consumed annually by the facility. 2.2. Delivery cost The movement of biomass from the forest to the processing facility will require transportation and thus incur an expense. For the purpose of model tractability in the present work, several assumptions were made. First, the harvest area is assumed to be circular; a similar assumption was used by Wright and Brown (2007), and Huang et al. (2009). Additionally, the distribution of forest resources is considered to be uniform over the entire land area, the facility is located at the center of the harvest area, and all resource deliveries to the facility occur in straight line distances, meaning there are no considerations for road networks or course deviations. This is different from Overend (1982) who included a tortuosity factor to compensate for these deviations. Thus, the delivery cost is given by: C D ¼ BT ðT R d þ T F Þ;
2.2.1. Shape and size of harvesting region As has been noted, it is assumed that the feedstock harvesting area is circular in shape and the biofuel production facility is located at the center of this circular area (refer to Fig. 1). A radius, R, defines the size of the harvesting region. Consider a very small harvest site in this region whose area is (r · dr · dθ). The distance traveled from the center of the circle to this site is r, where delivery routes are assumed to occur in straight line paths from source to plant. To determine the average delivery distance for a harvesting region with a radius of R (km), the one-way distances for all small harvest
ð1aÞ
ð1bÞ
Each of the variables on the right hand side (RHS) of Eq. (1b) can be expressed in terms of BT, the amount of biomass (tonnes) required by the facility each year to produce biofuels, where it is assumed that the facility will operate at full capacity. It should be noted that when the amount of biomass is referenced throughout the remainder of the paper, these amounts refer to dry weight. A closer examination of each of these five cost components of Eq. (1b) is provided below. 2.1. Biomass cost The cost of biomass, CB, includes expenses associated with purchasing woody materials from the landowner, harvesting, and field preprocessing. Eq. (2) considers the costs of purchasing, harvesting, and pre-processing biomass feedstock: C B ¼ C p BT ;
ð2Þ
where CP is the unit cost of securing biomass in a form ready for transportation to the processing facility. Eq. (2) expresses the total
ð3Þ
where TR is the variable transportation cost rate ($/tonne/km), d is the average one-way delivery distance (km) from the harvest site to the facility, and TF is the fixed component of the cost rate ($/tonne). The fixed rate cost was determined by Hicks (2009) from logger tariff rates and includes loading and unloading as well as other nondistance related costs. The delivery distance, d, depends on the size and shape of the area that will support the processing facility, and the per hectare yield of the forestland.
or, symbolically as C T ¼ C B þ C D þ C s þ C F þ C OP :
33
Fig. 1. Circular harvesting region with processing facility at center.
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sites within the region must be added via integration (and weighted by the size of the small site), and then divided by the area of the harvesting region, viz., 2π
d¼
R
∫0 ∫0 r ðr dr dθÞ 2
πR :
ð4Þ
Upon evaluating the expression on the RHS of Eq. (4), the average one-way delivery distance is found to be 2 d ¼ R: 3
ð5Þ
As is evident, the cost model terms presented to this point have all been expressed in terms of the amount of biomass to be processed annually, BT. Likewise, since d depends on the size of the harvesting region, it can also be defined in terms of BT. To accomplish this, R can be expressed as: R¼
1=2 1=2 A BT ¼ ; π 100 Y A LA π
ð6Þ
where A is the size of the harvest area in square kilometers. To include BT, the area A must be equated to hectares (using the hectares to square kilometer conversion factor of 100); the relation also includes the fraction of land available for forest harvesting, LA, and the average annual sustainable biomass harvest yield (tonnes/ha/year), YA. 2.2.2. Equivalent yield Here we introduce the concept of equivalent yield, YE, to describe the amount of biomass that may be sustainably recovered across the entire harvesting region on a per hectare basis. As the name suggests, the equivalent yield is a product of the average sustainable harvest yield per hectare of forested land (YA) and the amount of forestland available for harvesting (LA): Y E ¼ Y A LA :
ð7Þ
Forest resources are not typically harvested in large continuous sections of land like corn or sugar cane which are the current sources for biofuel (ethanol). Instead trees are collected in smaller plots or stands using several methods including thinning (Andersson et al., 2002; Leinonen, 2004), selective harvesting, and controlled understory reductions (Bolding et al., 2003; Graham et al., 2004). Clear cutting of forest land is also possible (i.e., completely harvested), but such practices are generally not believed to be environmentally sound or sustainable except for certain tree species. Further, unlike corn or sugar cane which grows back fully every year, most forests take decades to regenerate. Thus, the annual per hectare yield for forest residue resources would be less than that for row crops and grasses. Therefore, equivalent yield for forest resources expresses the average amount of biomass that may be sustainably harvested annually per hectare within the region of interest. Consequently, for the delivery cost portion of the model, YE replaces the product of YA and LA in Eq. (6) to give R¼
BT π 100 Y E
1=2
:
and replacing d in Eq. (3) with Eq. (9) gives the annual delivery cost as: 1=2 2 BT þTF : C D ¼ BT T R 3 π 100 Y E
2.3. Storage cost Considerations of inventory (or storage) costs are standard issues for decision-makers concerned with discrete parts manufacturing (Starr and Miller, 1962; Stevenson, 1996). Such decision-makers recognize that some on-hand inventory is needed in case of supply chain disruptions in components or changes in production rates. In the case of biomass processing, similar arguments can be made. For example, road restrictions or harsh weather conditions may mean that while year-round operation of a processing facility is desired, year-round harvesting and delivery cannot occur, as is typical in the Upper Peninsula of Michigan. Fig. 2 shows how the on-hand availability of stored biomass may be allowed to build up during the year, and then used during a period where road restrictions do not permit consistent biomass transportation (e.g., in the Upper Peninsula of Michigan trucks are prohibited on some roads during “spring breakup” or spring thaw). Fig. 2 also suggests that there is always some minimum on-hand inventory that is proportional to BT. This on-hand inventory is based on the proportionality factor, Im, and is determined based on conditions related to storage capacity, facility production rate, and feedstock characteristics. Furthermore, the figure indicates that owing to potential road restrictions associated with a spring thaw, there will need to be some significant biomass available when deliveries are restricted or not permitted. The ratio, ϕ, expresses the fraction of the year during which deliveries are restricted or not permitted and is expressed as: ϕ¼
Operational Days−Delivery Days Operational Days
1=2 2 BT ; 3 π 100 Y E
1 BINV ¼ IM BT þ ½BT ϕ; 2
ð12Þ
and thus, the cost associated with storage is 1 C S ¼ H BINV ¼ H IM BT þ ½BT ϕ ; 2 where H is the unit holding cost ($/tonnes/yr).
ð8Þ
ð9Þ
ð11Þ
Based on Fig. 2, the average amount of biomass in storage during the year is
Finally, the average one-way delivery distance (km) expressed in terms of the annual biomass consumed by the biofuel facility becomes
d¼
ð10Þ
Fig. 2. One possible scenario for biomass storage as a function of time.
ð13Þ
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35
2.4. Facility construction and operating costs
3. Unit cost and optimal facility size
These cost terms describe all the expenses associated with designing and constructing a biomass processing facility and operating the facility on an annual basis. The facility construction cost, which is dependent on the size of the facility, can also be converted into an annual cost. This cost should reflect economy of scale (EOS), e.g., a doubling of the plant size does not translate into a doubling of the construction costs. Alpert (1959) proposed a relation to reflect the effect of economy of scale on the cost. This relationship has been used by others (Lieberman, 1987; Jenkins, 1997; Wooley et al., 1999; Searcy and Flynn, 2008, Gan and Smith, 2011) to address the facility size problem for biofuels production. With some modification, the recent work of Froese et al., 2008 provides a basis for calculating an annualized cost, CF, for constructing a facility with a capacity that requires an annual biomass resource demand of BT:
The foregoing cost model development provides a structure to identify the relationship between annual production rate and total cost. This relationship, when further refined to a unit cost relationship as described in this section, is similar to the long run average cost. Long run average cost is an economic relationship that assumes no fixed costs. In the mathematical model defined in Eq. (18) total cost depends on a number of factors, like equivalent yield. Therefore, it is appropriate to identify values for the RHS of Eq. (18) using a case analysis. These values will be used to adapt the model to a real situation and will assist in exploring solutions to the minimum cost optimal facility size problem.
α C BL BT ; CF ¼ AF BBL
The study area which inspired and formed the basis for our case analysis was the Upper Peninsula of Michigan (U.P.); the U.P. has an abundant supply of forest biomass (Miller et al., 2007) and a biofuel production facility is being proposed there. We will use data from the U.P. to populate our model with values and develop optimal plant size solutions. The range of harvest yields and land availability in the U.P. provide for a range of equivalent yields as discussed previously. Therefore, we will evaluate the cost behavior across a wide array of equivalent yield values in the model. In discussing residue collection with loggers in the U.P., the consensus was that residue (tops and limbs) harvest yields can range from 4 to 9 tonnes per hectare (2–4 tons/acre) for selective cut stands (Nelson, 2007, 2010). However, if residue is collected from a given stand in one year, the site may not be visited again for 10–15 years. Thus, across a large region, the annual sustainable yield per hectare could range from 0.26 (4 mt/15 yr) to 0.9 (9 mt/10 yr) tonnes per hectare per year. Given this range, a base case harvest yield value of 0.56 tonnes per hectare (0.25 tons/acre) was assumed. Of course, yields for circumstances other than forest residue collection may be much larger; for example, short rotation woody crops, like hybrid willow and poplar, can produce between 6.5 and 22.5 tonnes per hectare (3–10 tons/acre) per year. So, in exercising our model for cost optimal facility size we will consider a wide range of harvest yields from 0.26 to 22.5 tonnes per hectare. Selecting a representative value for forestland availability involved a similar assessment to that considered above for harvest yield. Using the U.P., for example, the amount of forest land held by corporations and government entities is about 2.5 million hectares (6.2 million acres) while the total land area is 4.26 million hectares (10.5 million acres) (Miller et al., 2007). Because the U.S. government states that forest residue resources from federal lands do not count under the RFS biofuel definition (EISA, 2007), they are not considered available. Thus, the amount of forest land available in this case reduces to 1.7 million hectares (4.2 million acres) from the 2.5 million total. This total still does not account for protected lands within parks or reserves or individual private land owners (who may be unwilling to sell their resources for use in biofuels) (Becker et al., 2009). Perhaps the upper limit on land availability for this region might therefore be 40%. But, the actual availability could be much lower, say as low as 10%. Our assumption for the base case will be 20% for forest land availability. Combining both harvest yield and land availability, we believe an equivalent yield range, identified as 0.028 to 4.5 tonnes/ha, is representative of the true availability across any forested region of interest. In order to address the economy of scale effect, values for the construction and operation costs of the biomass facility are also introduced. The cost of constructing a biofuel (ethanol) facility with a baseline processing capacity of 1,104,951 tonnes/yr (1,218,000 tons/yr) was reported to be $224.2 million (Froese et al., 2008). Assuming a useful life of 20 years, the value for AF is 20. Values for the EOS factor, α, are typically between 0.6 and 0.8 (for large chemical processing facilities) (Lieberman, 1987; Searcy and Flynn, 2008), and using the facility size/
ð14Þ
where CBL is the cost of constructing a baseline facility ($) with an annual biomass processing capacity associated with BBL (tonnes/year), AF is a factor that annualizes the construction cost, and α (value b1) is a factor that describes the EOS effect. Like facility construction costs, operating costs can also follow EOS; as additional equipment and capacity are added, more production workers, maintenance needs, and administrative personnel are required — but, the costs of these additions may not double if capacity doubles. Several ethanol facilities of known size were used to develop the EOS relationship, with shape parameter β (value b1), between facility size and operating cost. The term associated with annual operating expenses is COP. This cost also depends on the amount of biomass, BT, similar to the construction cost noted earlier: C OP ¼ OBL
BT BBL
β
:
ð15Þ
2.5. Cost model summary The various cost components associated with producing biofuel have been described in this section. Replacing the terms in Eq. (1b) with the expressions that have been developed produces: ! 1 2 2 BT 1 C T ¼ ðC P BT Þ þ BT T R þ T F þ H I M BT þ ðBT ϕÞ 3 π 100 Y E 2 α β C BT BT þ OBL ð16Þ þ BL AF BBL BBL
Eq. (16) provides the total annual cost associated with operating a processing facility that converts forest biomass to biofuel. This development assumes the annual biomass demand (BT) is equal to the amount of biomass required to achieve 100% utilization of the processing facility. Most often, the size or capacity of a processing facility is expressed in L/yr (gallons/yr) or an annual production rate, FT. The annual biofuel production rate, FT, and the annual biomass demand, BT, are related by: F T ¼ BT Y P or BT ¼ F T =Y P ;
ð17Þ
where YP is the conversion rate from biomass to fuel, and again the assumption is that the facility will operate at 100% capacity. Thus, Eq. (16) may be rewritten as a function of FT: CT ¼
! 1 2 F F 2 FT F 1 FT CP T þ T T R þ T F þ H IM T þ ϕ 3 π 100 Y E Y P YP YP YP 2 YP C BL F T =Y P α F T =Y P β þ þ OBL ð18Þ AF BBL BBL
3.1. Case analysis
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cost survey data of the USDA (Shapouri and Gallagher, 2005), the value for α was estimated to be 0.7. Data for the known ethanol plant sizes provided a reasonable approximation for β of 0.8 (Nguyen and Prince, 1996; Shapouri and Gallagher, 2005). The baseline operational cost, OBL, for a facility using approximately 1,104,951 tonnes/yr is $28,928,505 per year (Froese et al., 2008). The general conditions for this base case are summarized in Table 1. The values in the table are as noted in this section and from the previous work of Aden et al., (2002), Walsh, 2008, and Hicks, 2009. Several of the values from Table 1 may be substituted into Eq. (18) to give 1=2 F FT FT 0:0376 T R þ 4:29 C T ¼ 39:68 T þ YP YP YP YE 0:7 F 224; 261; 881 F T =Y P · þ0:6873 T þ YP 1; 104; 951:01 20 0:8 F T =Y P þ28; 928; 505 1; 104; 951:01
ð19Þ
Fig. 3 displays the total annual cost and long run average cost per unit of fuel as a function of the annual biofuel produced, FT. 3.2. Model for the biofuel unit cost If one is interested in producing biofuels at a minimum cost per liter, then the total cost, expressed by Eq. (19) and presented in Fig. 3, must be divided by the amount of biofuel produced annually, FT. Eq. (20) shows this unit cost relation: CU ¼
! 1 2 39:68 T FT 4:29 0:6873 þ 0:0376 R þ þ YP YP YE YP YP YP 0:7 0:8 224; 261; 881 F T =Y P 28; 928; 505 F T =Y P þ þ 20 F T FT 1; 104; 951:01 1; 104; 951:01
ð20Þ To explore the effect of changes in the unfixed variables of Eq. (20), Figs. 4 and 5 were created. Fig. 4 shows how the one-way delivery distance as described by Eq. (9), changes as a function of the biofuel production rate (FT) for various equivalent yields (YE). In Fig. 4, the distance does not increase linearly as a function of either biomass demand or equivalent yield. Rather, a doubling of the demand translates into a doubling of the harvesting area, which means an increase in the delivery distance by a factor of 1.414 or 41.4%. Fig. 5 illustrates the unit cost behavior for different values of the transportation cost rate. As might be expected, as the transportation cost rate increases, the unit cost goes up. Careful examination of the figure also shows that as the transportation cost rate increases, the optimal
Fig. 3. Average and total annual cost as a function of biofuel production for U.P. case.
facility size (i.e., the size with minimum unit cost) decreases. The unit cost curves for lower transportation cost rates appear relatively flat; changes in the facility size near the optimum have little effect on the unit cost. Finally, the behavior of biofuel unit cost as a function of annual biofuel production for several equivalent yields ranging from 0.028 tonnes/ ha (0.0125 tons/acre) to 1.816 tonnes/ha (0.8100 tons/acre) is shown in Fig. 6. An examination of Fig. 6, like Figs. 4 and 5, reveals that there is a facility size (or production rate, FT, at full facility capacity) that produces a minimum unit cost for each equivalent yield. This is the optimal facility size, FO. In Fig. 6, it is observed that as the equivalent yield increases, the optimal facility size that produces the minimum unit cost also increases. The unit costs are also smaller as these optimal facility sizes increase for each equivalent yield. It is further observed that the cost curves for equivalent yields above 0.112 tonnes per hectare are relatively flat across a wide range of facility sizes (or production rates). So, while an optimal facility size that produces minimum unit cost does exist for equivalent yields greater than 0.112 tonnes per hectare, the cost behavior is fairly insensitive to facility size changes in a wider range near the optimum. 4. Optimal size behavior Figs. 5 and 6 showed the cost behaviors (unit cost versus facility size) for different transportation cost rates and equivalent yields. From these
Table 1 Parameter values for U.P. case. Base case $ 39.68 $ 0.10 $ 4.29
OBL BBL
Biomass Cost ($/tonne) Trans Rate ($/tonne/km) Fixed Transport Cost ($/tonne) Yield (tonnes/ha) Land Available Equiv Yield (tonnes/ha) Base Size Construction Cost Base size operation cost Biomass base, tonnes
YP
Yield (L/tonne)
187.77160
CP TR TF YA LA YE CBL
⁎All costs in 2005 US $.
Min days on hand Total op days Total delivery days
14 350 312
base level inventory Inven. build-up rate Unit holding cost EOS — construction
0.04 0.10857 $ 7.94 0.7
0.56043 0.2 0.11209 $ 224,261,881.00
IM ϕ H α
$ 28,928,505.00 1,104,951.01
β EOS — operation AF Annualization factor
0.8 20
Fig. 4. One-way delivery distance as a function of biofuel production and equivalent yield.
T.L. Jenkins, J.W. Sutherland / Forest Policy and Economics 38 (2014) 32–39
Fig. 5. Unit cost as a function of biofuel production for various delivery rate costs.
figures, general observations may be made about how equivalent yield and transportation cost rate affect the minimum unit cost and the corresponding facility size. Of course, other parameters may also have a role in determining the optimal plant size in terms of the unit cost. To characterize this unit cost–facility size relationship, the minimum of Eq. (20) with respect to facility size may be found using calculus. This requires taking the derivative of the unit cost equation with respect to the annual biofuel production rate, then setting the resulting expression equal to zero, and then solving for FT. The derivative of the unit cost with respect to the annual biofuel production is ! 3 1 2 39:68 T FT 4:29 0:6873 þ þ 0:0376 R þ þ 6 7 ∂ 6 YP YP YP YP YP YE 7 : 6 0:7 0:8 7 5 ∂F T 4 224; 261; 881 F T =Y P 28; 928; 505 F T =Y P þ 20 F T FT 1; 104; 951:01 1; 104; 951:01 2
ð21Þ After taking the derivative and simplifying, we obtain: ∂C U 197:92771 84:66064 0:01881 T R ¼ − 1:3 0:7 − 1:2 0:8 þ ¼ 0; ∂F T FP YP FP YP Y P ð F T Y E Y P Þ0:5
ð22Þ
Rearranging Eq. (22) gives 0:8 0:7 0:01881 T R Y Y −197:92771 P −84:66064 P ¼ 0: 0:5 FT FT ðY E Þ
ð23Þ
Fig. 6. Unit cost as a function of biofuel production for various equivalent yields.
37
It is evident from an examination of Eqs. (22) and (23) that the biomass resource cost (CB) and the storage cost (CS) do not influence the optimal plant size, since these variables have vanished from the equations. However, as has been noted the equivalent yield and delivery cost rate do affect the optimal plant size. The value of FT that makes Eq. (23) equal zero is termed the optimal plant size, FO. Owing to the form of the equation, FO must be solved for numerically and this plant size provides the minimum unit cost value. Fig. 7 shows a contour plot that displays the effect of equivalent yield and delivery cost rate on the optimal plant size from the numerical solution. Contours for the facility size range from 200 million to 3500 million liters (52 million to 925 million gallons) per year. While both equivalent yield and transportation cost rate influence the optimum size, the plot suggests that the yield has a slightly more important role. This is particularly evident at the yield values greater than 0.528 tonnes per hectare (0.24 tons per acre). At lower yield values, changes in the transportation cost rate have little effect on the facility size. Fig. 8 provides a companion contour plot to that of Fig. 7. It illustrates the behavior of the minimum unit cost (corresponding to the optimal plant size) as a function of equivalent yield and transportation cost rate. Contours ranging from $0.38 to $0.50 are displayed. Both the equivalent yield and the transportation cost rate influence the unit cost, and the plot suggests that the yield may have a slightly stronger effect. At lower yield values, changes in the transportation cost rate play a minor role in influencing the unit cost. 5. Summary and conclusions For a variety of reasons, biofuels are and will continue to be an energy source for transportation. A model has been developed for biofuel production cost; the model includes expenditures associated with biomass, logistics (transportation and storage), and facility construction and operation. A transportation cost relation was developed based on the assumption of a circular harvesting region with a processing facility located at its center. The expenses associated with delivery between the processing site and the harvesting locations were characterized using one-way distances. Biomass storage and associated costs are critically important, especially in locations where disruptions in supply are likely. The storage component of the cost model was constructed to insure a consistent on-hand supply of biomass for both short-lived supply chain disruptions as well as longer term delivery interruptions due to such issues as seasonal road restrictions. The model also includes costs of construction and processing facility operation, which include economies of scale. Data from the literature and personal communications were used to define conditions for a base case scenario.
Fig. 7. Contours of optimal facility size (L/year) as a function of equivalent yield and transportation rate.
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References
Fig. 8. Biofuel unit cost ($/liter) as a function of equivalent yield and transportation cost rate.
The behavior of the unit cost model as a function of changes to the conditions associated with a base case was examined. For example, the dependencies of the biofuel unit cost and facility size based on biomass gate and storage costs were explored. The unit cost function was then minimized with respect to facility size to find the optimal facility size. Contour plots were then constructed to reveal how the transportation cost rate and equivalent yield affect the optimal plant size and corresponding biofuel unit cost. Based on the cost model and the relation for the optimal facility size that have been developed, the following conclusions may be drawn: • As suggested by Fig. 4, for high equivalent yields, an increase in the biomass production (facility size) can be accommodated by a relatively modest increase in delivery distance. However, for low yields, an increase in the facility size will result in a dramatic increase in delivery distance. • While the biomass gate and storage cost affect the actual unit cost of biofuel, they do not influence the optimal size of the production facility. • Both equivalent yield and transportation cost rate influence the facility size, with the contour plot suggesting that perhaps the yield has a slightly more important role. • The contours for unit cost are similar in appearance to those for facility size. Both equivalent yield and transportation cost rate affect the unit cost, with the yield having a slightly larger effect. The developed model for producing biofuel from forest biomass predicts the total cost as a function of such factors as equivalent biomass yield, transportation cost rate, facility size, biomass resource inputs, storage, and facility construction and operation expenses. This cost model has been used to establish a relation for the size of a facility that produces the minimum biofuel unit cost. It should be noted that the cost model in no way guarantees producer profitability. There may be situations where even at the minimum unit cost, insufficient revenue is generated to make a profit based on market conditions. However, the cost model relationship does provide insight into the importance of key factors on the size and cost of constructing and operating a biofuel production facility from forest biomass and will aid decision-makers in determining a course of action within the renewable biofuel industry. Acknowledgments The authors gratefully acknowledge the support from a project (CBET-0524872) funded by the National Science Foundation through the Materials Use: Science, Engineering & Society (MUSES) program.
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. National Renewable Energy Laboratory (NREL/TP-510-32438, June 2002). Alpert, S.B., 1959. Economy of scale in the metal removal industry. J. Ind. Econ. 7 (3), 175–181 (Jul.). Andersson, G., Asikainen, A., Björheden, R., Hall, P.W., Hudson, J.B., Jirjis, R., Mead, D.J., Nurmi, J., Weetman, G.F., 2002. Chapter 3: Production of forest energy. In: Richardson, J., Björheden, R., Hakkila, P., Lowe, A.T., Smith, C.T. (Eds.), Bioenergy From Sustainable Forestry: Guiding Principles and Practice. Kluwer Academic Publishers, pp. 49–123. Becker, D.R., Skog, K., Hellman, A., Halvorsen, K.E., Mace, T., 2009. An outlook for sustainable forest bioenergy production in the Lake States. Energy Policy 37 (12), 5687–5693. Bolding, C., Lanford, B., Kellogg, L., 2003. Forest fuel reduction: current methods and future possibilities. Proceedings of the 2003 COFE (7-10 September. Bar Harbor, ME: 5 pp.). Energy Independence and Security Act of 2007 (EISA), 2007. Pub. L. No. 110-140, 121 Stat. 1492, 1783-84 (Dec. 19, 2007), codified at 42 U.S.C. §17381. Froese, R.E., Waterstraut, J.R., Johnson, D.M., Shonnard, D.R., Whitmarsh, J.H., Miller, C.M., 2008. Lignocellulosic ethanol: is it economically and financially viable as a fuel source? Environ. Qual. Manag. 18 (1), 23–45. Gan, J., Smith, C.T., 2011. Optimal plant size and feedstock supply radius: A modeling approach to minimize bioenergy production costs. Biomass and Bioenergy 35 (8), 3350–3359. Graham, R.L., Liu, W., Downing, M., Noon, C.E., Daly, M., Moore, A., 1997. The effect of location and facility demand on the marginal cost of delivered wood chips from energy crops: a case study of the state of Tennessee. Biomass Bioenergy 13 (3), 117–123. Graham, R.T., McCaffrey, S., Jain, T.B., 2004. Science basis for changing forest structure to modify wildfire behavior and severity. Gen. Tech. Rep. RMRS-GTR-120. Department of Agriculture, Forest Service, Rocky Mountain Research Station, Fort Collins, CO: U.S. (43 pp.). Greer, D., 2008. Commercializing cellulosic ethanol. November BioCycle 49 (11), 47 (http://www.jgpress.com/archives/_free/001764.html. Accessed August 10, 2009). Hicks, J., 2009. Modeling the multi-modal transport of logs and the effects of changing fuel prices. Master thesis Civil and Environmental Engineering Department, Houghton, Michigan Technological University. 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 (2), 234–246. Ince, P.J., Kramp, A., Spelter, H., Skog, K., Dykstra, D., 2006. FTM-West: fuel treatment market model for the U.S. West. Draft Manuscript. Jenkins, B.M., 1997. A comment on the optimal sizing of a biomass utilization facility under constant and variable cost scaling. Biomass Bioenergy 13 (1/2), 1–9. Kocoloski, M., Griffin, W.M., Matthews, H.S., 2011. Impacts of facility size and location decisions on ethanol production cost. Energy Policy 39 (1), 47–56. Lambert, D.K., Middleton, J., 2010. Logistical design of a regional herbaceous crop residuebased ethanol production complex. Biomass Bioenergy 34, 91–100. Leinonen, A., 2004. Harvesting technology of forest residues for fuel in the USA and Finland, Espoo 2004. VTT Tiedotteita. Research Notes, 2229 (132 pp. + app. 10 pp.). Lieberman, M.B., 1987. Market growth, economies of scale, and plant size in the chemical processing industries. J. Ind. Econ. 36 (2), 175–191. Miller, C.A., Froese, R.E., Leefers, L.A., 2007. Consequences of corporate timberland ownership change in Michigan's Upper Peninsula. 2007 SAF National Convention, October 23-27 at Portland, OR. National Science Foundation (NSF), 2008. Breaking the Chemical and Engineering Barriers to Lignocellulosic Biofuels: Next Generation Hydrocarbon Biorefineries. In: Huber, George W. (Ed.), University of Massachusetts Amherst. National Science Foundation. Chemical, Bioengineering, Environmental, and Transport Systems Div (Washington D.C. 180 pp.). Nelson, B., 2007. Marvin Nelson Forest Products, Inc. Personal Communications, July 2007. Nelson, B., 2010. Marvin Nelson Forest Products, Inc. Personal Communications, September 2010. Nguyen, M.H., Prince, R.G.H., 1996. A simple rule for bioenergy conversion plant size optimization: bioethanol from sugar cane and sweet sorghum. Biomass Bioenergy 10, 361–365. Noon, C.E., Zhan, F.B., Graham, R.L., 2002. GIS-based analysis of marginal price variation with an application in the identification of candidate ethanol conversion plant locations. Netw. Spat. Econ. 2 (1), 79–93. Overend, R.P., 1982. The average haul distance and transportation work factors for biomass delivered to a central plant. Biomass 2, 75–79. Rendleman, C.M., Shapouri, H., 2007. New technologies in ethanol production, AER-842, USDA. Office of Energy Policy and New Uses. Rummer, B., Prestemon, J., May, D., Miles, P., Vissage, J., McRoberts, R., Liknes, G., Shepperd, W.D., Ferguson, D., Elliot, W., Miller, S., Teutebuch, S., Barbour, J., Fried, J., Stokes, B., Bilek, E., Skog, K., 2003. A Strategic Assessment of Forest Biomass and Fuel Reduction Treatments in Western States. USDA Forest Service (April). Runge, C.F., Senauer, B., 2007. How biofuels could starve the poor. Foreign Aff. 86, 41–54. Searcy, E., Flynn, P., 2008. The impact of biomass availability and processing cost on optimum size and processing technology selection. Appl. Biochem. Biotechnol. 154 (1-3), 92–107 (2009 May). Shapouri, H., Gallagher, P., 2005. USDA’s 2002 Ethanol Cost-of-Production Survey. United States Department of Agriculture, Agricultural Economic Report Number 841. (July). Starr, M.K., Miller, D.W., 1962. Inventory Control: Theory and Practice. Prentice-Hall, Englewood Cliffs, NJ.
T.L. Jenkins, J.W. Sutherland / Forest Policy and Economics 38 (2014) 32–39 Stevenson, W.J., 1996. Production/operations management, 5th ed. Irwin. U.S. Department of Agriculture, U.S. Department of Energy (USDA/DOE), 2005. A billionton feedstock supply for bioenergy and bioproducts industry: technical feasibility of annually supplying 1 billion dry tons of biomass (DOE/GO-102995-2135; ORNL/ TM2005/66). Walsh, M., 2008. U.S. cellulosic biomass feedstock supplies and distribution. M & E Biomass. (http://ageconsearch.umn.edu/bitstream/7625/2/U.S.%20Biomass%20Supplies. Pdf, accessed February 16, 2009).
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Wooley, R., Ruth, M., Sheehan, J., Ibsen, K., 1999. Lignocellulosic Biomass to Ethanol Process Design and Economics Utilizing Co-Current Dilute Acid Prehydrolysis and Enzymatic Hydrolysis Current and Futuristic Scenarios. NREL report TP-580-26157, July http://www.ott.doe.gov/biofuels/process_engineering.html. Wright, M., Brown, R.C., 2007. Establishing the optimal sizes of different kinds of biorefineries. Biofuels, Bioprod. Biorefin. 1 (3), 191–2000. Wyman, C.E., 2003. Potential synergies and challenges in refining cellulosic biomass to fuels chemicals, and power. Biotechnol. Program 254–262.
Contents lists available at ScienceDirect
Forest Policy and Economics journal homepage: www.elsevier.com/locate/forpol
A cost model for forest-based biofuel production and its application to optimal facility size determination Timothy L. Jenkins a,⁎, John W. Sutherland b a b
Department of Mechanical Engineering-Engineering Mechanics, Sustainable Futures Institute, Michigan Technological University, 1400 Townsend Drive, Houghton, MI 49931, USA Division of Environmental and Ecological Engineering, Purdue University, Potter Engineering Center, Room 322, 500 Central Drive, West Lafayette, IN 47907, USA
a r t i c l e
i n f o
Article history: Received 21 November 2009 Received in revised form 5 August 2013 Accepted 7 August 2013 Available online 26 September 2013 Keywords: Economics Forest biomass Biofuel Optimal facility size Unit cost
a b s t r a c t With continued concerns regarding the use of fossil fuels and energy security, there is increasing interest in biofuels. However, owing to worries over the use of agricultural feedstocks for biofuel, forest biomass as a feedstock has been investigated for some time and appears to be a promising alternative. Current corn-based ethanol facilities range in size from a few million to over 380 million liters (100 million gallons) per year with associated construction costs near $117 million for the latter sized capacity. On the other hand, the economics for forest biomass to biofuel facilities are different and there appears to be a lack of understanding about the cost optimal size for the processing facility and the associated investment. With this in mind, a mathematical model is developed to describe the total annual costs of a forest biomass to biofuel facility using the Upper Peninsula of Michigan as the case study area. The model includes terms associated with forest resource harvesting and collection, transportation, storage, and facility construction and operation costs. The model is used to establish a relationship for the optimal size of a production facility, that is, the facility size that provides the minimum unit cost. The effect of various factors on the optimal facility size and the associated biofuel unit cost are examined, especially transportation cost rate and equivalent yield. The results indicate these two factors do impact optimal size and unit cost. © 2013 Elsevier B.V. All rights reserved.
1. Introduction While corn and sugar cane are the primary feedstocks for producing first generation biofuels, other feedstocks include sorghum, wheat, sugar beets, soybeans, and cellulose. Many now believe that second and third generation biofuels may eventually dominate renewable biofuel production (NSF, 2008). Regardless of the biofuel type, the use of cellulose found in plant fibers (e.g., trees, grasses, crop wastes, and municipal solid waste) is gaining acceptance and several production facility projects have been proposed or initiated to produce biofuels (Rendleman and Shapouri, 2007; Greer, 2008). One advantage of cellulose over other feedstocks is that a food versus fuel tradeoff need not be made (Runge and Senauer, 2007). Another is the apparent abundance of these resources (USDA/DOE, 2005). In this study we will focus on forest resource material, e.g., forest residues (limbs, treetops, etc.) unused for pulp and paper harvesting and slash removals produced in the process of thinning operations undertaken to improve stand growth and reduce fire hazards (Graham et al., 2004). It is estimated that the U.S. has 112.5 million tonnes (124 million tons) of forest residues and other sources available annually for conversion to energy and bio-based ⁎ Corresponding author at: Department of Engineering Technology, Trine University, Angola, IN 46703, USA. Tel.: +1 260 665 4660; fax: +1 260 665 4816. E-mail address: [email protected] (T.L. Jenkins). 1389-9341/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.forpol.2013.08.004
fuels like ethanol (USDA/DOE, 2005). These values do not include any forest resources used for fuelwood, residues from wood processing mills, or urban wood wastes that could also be utilized. Walsh (2008) has estimated that in the U.S. there are 57.15 million tonnes (63 million tons) of forest residues from logging operations and 22.4 million tonnes (24.7 million tons) from other removals available annually. Additionally, it is estimated that as much as 403.7 million tonnes (445 million tons) of woody biomass from fuel treatment removals, to maintain healthy forests and limit catastrophic forest fires, are available in the western United States alone (Rummer et al., 2003; Ince et al., 2006). One of the issues associated with the production of biofuels from woody biomass (forest resources) is having a facility size that minimizes overall cost per unit of production. Several researchers have developed cost models (Wooley et al., 1999; Aden et al., 2002; Wyman, 2003; Lambert and Middleton, 2010) that have been used to find the best size of a biofuel production facility. In Wooley et al. (1999), the size of the facility was determined based on prior process economic analysis and reasonable feedstock delivery distances. Aden et al. (2002) provided an update to the earlier work by Wooley and Wyman that extended the analysis to include conversion to sugars, but again the study only considered baseline sizes. A more recent study by Lambert and Middleton (2010) developed a mixed integer programming model to evaluate the profitability of a field-to-refinery supply system. The focus in their work was on herbaceous crop residues and the
T.L. Jenkins, J.W. Sutherland / Forest Policy and Economics 38 (2014) 32–39
decentralization of pretreatment facilities from biofuel refineries using North Dakota as a study area. However, the refinery sizes used were based on data from Aden et al. (2002), and only three sizes were used as inputs. Other models focused more on best facility size (Nguyen and Prince, 1996; Graham et al., 1997; Jenkins, 1997; Noon et al., 2002; Searcy and Flynn, 2008), and considered corn stover, switchgrass, and some regional forest resources. One limitation of these studies was that the facility sizes were specified a priori and not solved for. Further, little attention has been paid to storage costs that incorporate possible seasonal limitations to biomass transport into cost models. Finally, a study by Gan and Smith (2011) modeled the optimum plant size but assumed that certain costs were independent of plant size. Further, Gan and Smith (2011) combined facility construction and operation costs and assumed both had equal economy of scale characteristics. In spite of the importance of woody biomass as a key long-term component of any biofuel portfolio, less attention has been focused on cost models utilizing forest resources and the associated cost optimal facility size issue. The cost structure for biofuel facilities based on cellulosic biomass material is very different from that based on corn (Kocoloski et al., 2011); cellulosic biomass facilities are more expensive. With this in mind, in Section 2 a model for the total cost of biofuel production from woody biomass is developed. Section 3 will define the unit cost and this will be used in Section 4 to determine the cost optimal facility size. Similar to Gan and Smith (2011), this model formulation will address what the optimum size should be in the absence of a capital constraint. Finally, Section 5 will summarize the results and provide decision-makers insight into selecting a facility size that minimizes the unit cost of biofuel production. 2. Cost model for biofuel production A cost model for biofuel production must consider expenditures associated with biomass harvesting and collection, transportation, storage, and plant construction and operation. With this in mind, the total annual cost for producing biofuel from woody biomass may be expressed as: Storage Biomass Delivery Facility Total þ þ þ ¼ Cost Gate Cost Cost Construction Cost Cost Facility ; þ Operation Cost
cost of the biomass as the product of Cp and the amount of biomass, BT, consumed annually by the facility. 2.2. Delivery cost The movement of biomass from the forest to the processing facility will require transportation and thus incur an expense. For the purpose of model tractability in the present work, several assumptions were made. First, the harvest area is assumed to be circular; a similar assumption was used by Wright and Brown (2007), and Huang et al. (2009). Additionally, the distribution of forest resources is considered to be uniform over the entire land area, the facility is located at the center of the harvest area, and all resource deliveries to the facility occur in straight line distances, meaning there are no considerations for road networks or course deviations. This is different from Overend (1982) who included a tortuosity factor to compensate for these deviations. Thus, the delivery cost is given by: C D ¼ BT ðT R d þ T F Þ;
2.2.1. Shape and size of harvesting region As has been noted, it is assumed that the feedstock harvesting area is circular in shape and the biofuel production facility is located at the center of this circular area (refer to Fig. 1). A radius, R, defines the size of the harvesting region. Consider a very small harvest site in this region whose area is (r · dr · dθ). The distance traveled from the center of the circle to this site is r, where delivery routes are assumed to occur in straight line paths from source to plant. To determine the average delivery distance for a harvesting region with a radius of R (km), the one-way distances for all small harvest
ð1aÞ
ð1bÞ
Each of the variables on the right hand side (RHS) of Eq. (1b) can be expressed in terms of BT, the amount of biomass (tonnes) required by the facility each year to produce biofuels, where it is assumed that the facility will operate at full capacity. It should be noted that when the amount of biomass is referenced throughout the remainder of the paper, these amounts refer to dry weight. A closer examination of each of these five cost components of Eq. (1b) is provided below. 2.1. Biomass cost The cost of biomass, CB, includes expenses associated with purchasing woody materials from the landowner, harvesting, and field preprocessing. Eq. (2) considers the costs of purchasing, harvesting, and pre-processing biomass feedstock: C B ¼ C p BT ;
ð2Þ
where CP is the unit cost of securing biomass in a form ready for transportation to the processing facility. Eq. (2) expresses the total
ð3Þ
where TR is the variable transportation cost rate ($/tonne/km), d is the average one-way delivery distance (km) from the harvest site to the facility, and TF is the fixed component of the cost rate ($/tonne). The fixed rate cost was determined by Hicks (2009) from logger tariff rates and includes loading and unloading as well as other nondistance related costs. The delivery distance, d, depends on the size and shape of the area that will support the processing facility, and the per hectare yield of the forestland.
or, symbolically as C T ¼ C B þ C D þ C s þ C F þ C OP :
33
Fig. 1. Circular harvesting region with processing facility at center.
34
T.L. Jenkins, J.W. Sutherland / Forest Policy and Economics 38 (2014) 32–39
sites within the region must be added via integration (and weighted by the size of the small site), and then divided by the area of the harvesting region, viz., 2π
d¼
R
∫0 ∫0 r ðr dr dθÞ 2
πR :
ð4Þ
Upon evaluating the expression on the RHS of Eq. (4), the average one-way delivery distance is found to be 2 d ¼ R: 3
ð5Þ
As is evident, the cost model terms presented to this point have all been expressed in terms of the amount of biomass to be processed annually, BT. Likewise, since d depends on the size of the harvesting region, it can also be defined in terms of BT. To accomplish this, R can be expressed as: R¼
1=2 1=2 A BT ¼ ; π 100 Y A LA π
ð6Þ
where A is the size of the harvest area in square kilometers. To include BT, the area A must be equated to hectares (using the hectares to square kilometer conversion factor of 100); the relation also includes the fraction of land available for forest harvesting, LA, and the average annual sustainable biomass harvest yield (tonnes/ha/year), YA. 2.2.2. Equivalent yield Here we introduce the concept of equivalent yield, YE, to describe the amount of biomass that may be sustainably recovered across the entire harvesting region on a per hectare basis. As the name suggests, the equivalent yield is a product of the average sustainable harvest yield per hectare of forested land (YA) and the amount of forestland available for harvesting (LA): Y E ¼ Y A LA :
ð7Þ
Forest resources are not typically harvested in large continuous sections of land like corn or sugar cane which are the current sources for biofuel (ethanol). Instead trees are collected in smaller plots or stands using several methods including thinning (Andersson et al., 2002; Leinonen, 2004), selective harvesting, and controlled understory reductions (Bolding et al., 2003; Graham et al., 2004). Clear cutting of forest land is also possible (i.e., completely harvested), but such practices are generally not believed to be environmentally sound or sustainable except for certain tree species. Further, unlike corn or sugar cane which grows back fully every year, most forests take decades to regenerate. Thus, the annual per hectare yield for forest residue resources would be less than that for row crops and grasses. Therefore, equivalent yield for forest resources expresses the average amount of biomass that may be sustainably harvested annually per hectare within the region of interest. Consequently, for the delivery cost portion of the model, YE replaces the product of YA and LA in Eq. (6) to give R¼
BT π 100 Y E
1=2
:
and replacing d in Eq. (3) with Eq. (9) gives the annual delivery cost as: 1=2 2 BT þTF : C D ¼ BT T R 3 π 100 Y E
2.3. Storage cost Considerations of inventory (or storage) costs are standard issues for decision-makers concerned with discrete parts manufacturing (Starr and Miller, 1962; Stevenson, 1996). Such decision-makers recognize that some on-hand inventory is needed in case of supply chain disruptions in components or changes in production rates. In the case of biomass processing, similar arguments can be made. For example, road restrictions or harsh weather conditions may mean that while year-round operation of a processing facility is desired, year-round harvesting and delivery cannot occur, as is typical in the Upper Peninsula of Michigan. Fig. 2 shows how the on-hand availability of stored biomass may be allowed to build up during the year, and then used during a period where road restrictions do not permit consistent biomass transportation (e.g., in the Upper Peninsula of Michigan trucks are prohibited on some roads during “spring breakup” or spring thaw). Fig. 2 also suggests that there is always some minimum on-hand inventory that is proportional to BT. This on-hand inventory is based on the proportionality factor, Im, and is determined based on conditions related to storage capacity, facility production rate, and feedstock characteristics. Furthermore, the figure indicates that owing to potential road restrictions associated with a spring thaw, there will need to be some significant biomass available when deliveries are restricted or not permitted. The ratio, ϕ, expresses the fraction of the year during which deliveries are restricted or not permitted and is expressed as: ϕ¼
Operational Days−Delivery Days Operational Days
1=2 2 BT ; 3 π 100 Y E
1 BINV ¼ IM BT þ ½BT ϕ; 2
ð12Þ
and thus, the cost associated with storage is 1 C S ¼ H BINV ¼ H IM BT þ ½BT ϕ ; 2 where H is the unit holding cost ($/tonnes/yr).
ð8Þ
ð9Þ
ð11Þ
Based on Fig. 2, the average amount of biomass in storage during the year is
Finally, the average one-way delivery distance (km) expressed in terms of the annual biomass consumed by the biofuel facility becomes
d¼
ð10Þ
Fig. 2. One possible scenario for biomass storage as a function of time.
ð13Þ
T.L. Jenkins, J.W. Sutherland / Forest Policy and Economics 38 (2014) 32–39
35
2.4. Facility construction and operating costs
3. Unit cost and optimal facility size
These cost terms describe all the expenses associated with designing and constructing a biomass processing facility and operating the facility on an annual basis. The facility construction cost, which is dependent on the size of the facility, can also be converted into an annual cost. This cost should reflect economy of scale (EOS), e.g., a doubling of the plant size does not translate into a doubling of the construction costs. Alpert (1959) proposed a relation to reflect the effect of economy of scale on the cost. This relationship has been used by others (Lieberman, 1987; Jenkins, 1997; Wooley et al., 1999; Searcy and Flynn, 2008, Gan and Smith, 2011) to address the facility size problem for biofuels production. With some modification, the recent work of Froese et al., 2008 provides a basis for calculating an annualized cost, CF, for constructing a facility with a capacity that requires an annual biomass resource demand of BT:
The foregoing cost model development provides a structure to identify the relationship between annual production rate and total cost. This relationship, when further refined to a unit cost relationship as described in this section, is similar to the long run average cost. Long run average cost is an economic relationship that assumes no fixed costs. In the mathematical model defined in Eq. (18) total cost depends on a number of factors, like equivalent yield. Therefore, it is appropriate to identify values for the RHS of Eq. (18) using a case analysis. These values will be used to adapt the model to a real situation and will assist in exploring solutions to the minimum cost optimal facility size problem.
α C BL BT ; CF ¼ AF BBL
The study area which inspired and formed the basis for our case analysis was the Upper Peninsula of Michigan (U.P.); the U.P. has an abundant supply of forest biomass (Miller et al., 2007) and a biofuel production facility is being proposed there. We will use data from the U.P. to populate our model with values and develop optimal plant size solutions. The range of harvest yields and land availability in the U.P. provide for a range of equivalent yields as discussed previously. Therefore, we will evaluate the cost behavior across a wide array of equivalent yield values in the model. In discussing residue collection with loggers in the U.P., the consensus was that residue (tops and limbs) harvest yields can range from 4 to 9 tonnes per hectare (2–4 tons/acre) for selective cut stands (Nelson, 2007, 2010). However, if residue is collected from a given stand in one year, the site may not be visited again for 10–15 years. Thus, across a large region, the annual sustainable yield per hectare could range from 0.26 (4 mt/15 yr) to 0.9 (9 mt/10 yr) tonnes per hectare per year. Given this range, a base case harvest yield value of 0.56 tonnes per hectare (0.25 tons/acre) was assumed. Of course, yields for circumstances other than forest residue collection may be much larger; for example, short rotation woody crops, like hybrid willow and poplar, can produce between 6.5 and 22.5 tonnes per hectare (3–10 tons/acre) per year. So, in exercising our model for cost optimal facility size we will consider a wide range of harvest yields from 0.26 to 22.5 tonnes per hectare. Selecting a representative value for forestland availability involved a similar assessment to that considered above for harvest yield. Using the U.P., for example, the amount of forest land held by corporations and government entities is about 2.5 million hectares (6.2 million acres) while the total land area is 4.26 million hectares (10.5 million acres) (Miller et al., 2007). Because the U.S. government states that forest residue resources from federal lands do not count under the RFS biofuel definition (EISA, 2007), they are not considered available. Thus, the amount of forest land available in this case reduces to 1.7 million hectares (4.2 million acres) from the 2.5 million total. This total still does not account for protected lands within parks or reserves or individual private land owners (who may be unwilling to sell their resources for use in biofuels) (Becker et al., 2009). Perhaps the upper limit on land availability for this region might therefore be 40%. But, the actual availability could be much lower, say as low as 10%. Our assumption for the base case will be 20% for forest land availability. Combining both harvest yield and land availability, we believe an equivalent yield range, identified as 0.028 to 4.5 tonnes/ha, is representative of the true availability across any forested region of interest. In order to address the economy of scale effect, values for the construction and operation costs of the biomass facility are also introduced. The cost of constructing a biofuel (ethanol) facility with a baseline processing capacity of 1,104,951 tonnes/yr (1,218,000 tons/yr) was reported to be $224.2 million (Froese et al., 2008). Assuming a useful life of 20 years, the value for AF is 20. Values for the EOS factor, α, are typically between 0.6 and 0.8 (for large chemical processing facilities) (Lieberman, 1987; Searcy and Flynn, 2008), and using the facility size/
ð14Þ
where CBL is the cost of constructing a baseline facility ($) with an annual biomass processing capacity associated with BBL (tonnes/year), AF is a factor that annualizes the construction cost, and α (value b1) is a factor that describes the EOS effect. Like facility construction costs, operating costs can also follow EOS; as additional equipment and capacity are added, more production workers, maintenance needs, and administrative personnel are required — but, the costs of these additions may not double if capacity doubles. Several ethanol facilities of known size were used to develop the EOS relationship, with shape parameter β (value b1), between facility size and operating cost. The term associated with annual operating expenses is COP. This cost also depends on the amount of biomass, BT, similar to the construction cost noted earlier: C OP ¼ OBL
BT BBL
β
:
ð15Þ
2.5. Cost model summary The various cost components associated with producing biofuel have been described in this section. Replacing the terms in Eq. (1b) with the expressions that have been developed produces: ! 1 2 2 BT 1 C T ¼ ðC P BT Þ þ BT T R þ T F þ H I M BT þ ðBT ϕÞ 3 π 100 Y E 2 α β C BT BT þ OBL ð16Þ þ BL AF BBL BBL
Eq. (16) provides the total annual cost associated with operating a processing facility that converts forest biomass to biofuel. This development assumes the annual biomass demand (BT) is equal to the amount of biomass required to achieve 100% utilization of the processing facility. Most often, the size or capacity of a processing facility is expressed in L/yr (gallons/yr) or an annual production rate, FT. The annual biofuel production rate, FT, and the annual biomass demand, BT, are related by: F T ¼ BT Y P or BT ¼ F T =Y P ;
ð17Þ
where YP is the conversion rate from biomass to fuel, and again the assumption is that the facility will operate at 100% capacity. Thus, Eq. (16) may be rewritten as a function of FT: CT ¼
! 1 2 F F 2 FT F 1 FT CP T þ T T R þ T F þ H IM T þ ϕ 3 π 100 Y E Y P YP YP YP 2 YP C BL F T =Y P α F T =Y P β þ þ OBL ð18Þ AF BBL BBL
3.1. Case analysis
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T.L. Jenkins, J.W. Sutherland / Forest Policy and Economics 38 (2014) 32–39
cost survey data of the USDA (Shapouri and Gallagher, 2005), the value for α was estimated to be 0.7. Data for the known ethanol plant sizes provided a reasonable approximation for β of 0.8 (Nguyen and Prince, 1996; Shapouri and Gallagher, 2005). The baseline operational cost, OBL, for a facility using approximately 1,104,951 tonnes/yr is $28,928,505 per year (Froese et al., 2008). The general conditions for this base case are summarized in Table 1. The values in the table are as noted in this section and from the previous work of Aden et al., (2002), Walsh, 2008, and Hicks, 2009. Several of the values from Table 1 may be substituted into Eq. (18) to give 1=2 F FT FT 0:0376 T R þ 4:29 C T ¼ 39:68 T þ YP YP YP YE 0:7 F 224; 261; 881 F T =Y P · þ0:6873 T þ YP 1; 104; 951:01 20 0:8 F T =Y P þ28; 928; 505 1; 104; 951:01
ð19Þ
Fig. 3 displays the total annual cost and long run average cost per unit of fuel as a function of the annual biofuel produced, FT. 3.2. Model for the biofuel unit cost If one is interested in producing biofuels at a minimum cost per liter, then the total cost, expressed by Eq. (19) and presented in Fig. 3, must be divided by the amount of biofuel produced annually, FT. Eq. (20) shows this unit cost relation: CU ¼
! 1 2 39:68 T FT 4:29 0:6873 þ 0:0376 R þ þ YP YP YE YP YP YP 0:7 0:8 224; 261; 881 F T =Y P 28; 928; 505 F T =Y P þ þ 20 F T FT 1; 104; 951:01 1; 104; 951:01
ð20Þ To explore the effect of changes in the unfixed variables of Eq. (20), Figs. 4 and 5 were created. Fig. 4 shows how the one-way delivery distance as described by Eq. (9), changes as a function of the biofuel production rate (FT) for various equivalent yields (YE). In Fig. 4, the distance does not increase linearly as a function of either biomass demand or equivalent yield. Rather, a doubling of the demand translates into a doubling of the harvesting area, which means an increase in the delivery distance by a factor of 1.414 or 41.4%. Fig. 5 illustrates the unit cost behavior for different values of the transportation cost rate. As might be expected, as the transportation cost rate increases, the unit cost goes up. Careful examination of the figure also shows that as the transportation cost rate increases, the optimal
Fig. 3. Average and total annual cost as a function of biofuel production for U.P. case.
facility size (i.e., the size with minimum unit cost) decreases. The unit cost curves for lower transportation cost rates appear relatively flat; changes in the facility size near the optimum have little effect on the unit cost. Finally, the behavior of biofuel unit cost as a function of annual biofuel production for several equivalent yields ranging from 0.028 tonnes/ ha (0.0125 tons/acre) to 1.816 tonnes/ha (0.8100 tons/acre) is shown in Fig. 6. An examination of Fig. 6, like Figs. 4 and 5, reveals that there is a facility size (or production rate, FT, at full facility capacity) that produces a minimum unit cost for each equivalent yield. This is the optimal facility size, FO. In Fig. 6, it is observed that as the equivalent yield increases, the optimal facility size that produces the minimum unit cost also increases. The unit costs are also smaller as these optimal facility sizes increase for each equivalent yield. It is further observed that the cost curves for equivalent yields above 0.112 tonnes per hectare are relatively flat across a wide range of facility sizes (or production rates). So, while an optimal facility size that produces minimum unit cost does exist for equivalent yields greater than 0.112 tonnes per hectare, the cost behavior is fairly insensitive to facility size changes in a wider range near the optimum. 4. Optimal size behavior Figs. 5 and 6 showed the cost behaviors (unit cost versus facility size) for different transportation cost rates and equivalent yields. From these
Table 1 Parameter values for U.P. case. Base case $ 39.68 $ 0.10 $ 4.29
OBL BBL
Biomass Cost ($/tonne) Trans Rate ($/tonne/km) Fixed Transport Cost ($/tonne) Yield (tonnes/ha) Land Available Equiv Yield (tonnes/ha) Base Size Construction Cost Base size operation cost Biomass base, tonnes
YP
Yield (L/tonne)
187.77160
CP TR TF YA LA YE CBL
⁎All costs in 2005 US $.
Min days on hand Total op days Total delivery days
14 350 312
base level inventory Inven. build-up rate Unit holding cost EOS — construction
0.04 0.10857 $ 7.94 0.7
0.56043 0.2 0.11209 $ 224,261,881.00
IM ϕ H α
$ 28,928,505.00 1,104,951.01
β EOS — operation AF Annualization factor
0.8 20
Fig. 4. One-way delivery distance as a function of biofuel production and equivalent yield.
T.L. Jenkins, J.W. Sutherland / Forest Policy and Economics 38 (2014) 32–39
Fig. 5. Unit cost as a function of biofuel production for various delivery rate costs.
figures, general observations may be made about how equivalent yield and transportation cost rate affect the minimum unit cost and the corresponding facility size. Of course, other parameters may also have a role in determining the optimal plant size in terms of the unit cost. To characterize this unit cost–facility size relationship, the minimum of Eq. (20) with respect to facility size may be found using calculus. This requires taking the derivative of the unit cost equation with respect to the annual biofuel production rate, then setting the resulting expression equal to zero, and then solving for FT. The derivative of the unit cost with respect to the annual biofuel production is ! 3 1 2 39:68 T FT 4:29 0:6873 þ þ 0:0376 R þ þ 6 7 ∂ 6 YP YP YP YP YP YE 7 : 6 0:7 0:8 7 5 ∂F T 4 224; 261; 881 F T =Y P 28; 928; 505 F T =Y P þ 20 F T FT 1; 104; 951:01 1; 104; 951:01 2
ð21Þ After taking the derivative and simplifying, we obtain: ∂C U 197:92771 84:66064 0:01881 T R ¼ − 1:3 0:7 − 1:2 0:8 þ ¼ 0; ∂F T FP YP FP YP Y P ð F T Y E Y P Þ0:5
ð22Þ
Rearranging Eq. (22) gives 0:8 0:7 0:01881 T R Y Y −197:92771 P −84:66064 P ¼ 0: 0:5 FT FT ðY E Þ
ð23Þ
Fig. 6. Unit cost as a function of biofuel production for various equivalent yields.
37
It is evident from an examination of Eqs. (22) and (23) that the biomass resource cost (CB) and the storage cost (CS) do not influence the optimal plant size, since these variables have vanished from the equations. However, as has been noted the equivalent yield and delivery cost rate do affect the optimal plant size. The value of FT that makes Eq. (23) equal zero is termed the optimal plant size, FO. Owing to the form of the equation, FO must be solved for numerically and this plant size provides the minimum unit cost value. Fig. 7 shows a contour plot that displays the effect of equivalent yield and delivery cost rate on the optimal plant size from the numerical solution. Contours for the facility size range from 200 million to 3500 million liters (52 million to 925 million gallons) per year. While both equivalent yield and transportation cost rate influence the optimum size, the plot suggests that the yield has a slightly more important role. This is particularly evident at the yield values greater than 0.528 tonnes per hectare (0.24 tons per acre). At lower yield values, changes in the transportation cost rate have little effect on the facility size. Fig. 8 provides a companion contour plot to that of Fig. 7. It illustrates the behavior of the minimum unit cost (corresponding to the optimal plant size) as a function of equivalent yield and transportation cost rate. Contours ranging from $0.38 to $0.50 are displayed. Both the equivalent yield and the transportation cost rate influence the unit cost, and the plot suggests that the yield may have a slightly stronger effect. At lower yield values, changes in the transportation cost rate play a minor role in influencing the unit cost. 5. Summary and conclusions For a variety of reasons, biofuels are and will continue to be an energy source for transportation. A model has been developed for biofuel production cost; the model includes expenditures associated with biomass, logistics (transportation and storage), and facility construction and operation. A transportation cost relation was developed based on the assumption of a circular harvesting region with a processing facility located at its center. The expenses associated with delivery between the processing site and the harvesting locations were characterized using one-way distances. Biomass storage and associated costs are critically important, especially in locations where disruptions in supply are likely. The storage component of the cost model was constructed to insure a consistent on-hand supply of biomass for both short-lived supply chain disruptions as well as longer term delivery interruptions due to such issues as seasonal road restrictions. The model also includes costs of construction and processing facility operation, which include economies of scale. Data from the literature and personal communications were used to define conditions for a base case scenario.
Fig. 7. Contours of optimal facility size (L/year) as a function of equivalent yield and transportation rate.
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T.L. Jenkins, J.W. Sutherland / Forest Policy and Economics 38 (2014) 32–39
References
Fig. 8. Biofuel unit cost ($/liter) as a function of equivalent yield and transportation cost rate.
The behavior of the unit cost model as a function of changes to the conditions associated with a base case was examined. For example, the dependencies of the biofuel unit cost and facility size based on biomass gate and storage costs were explored. The unit cost function was then minimized with respect to facility size to find the optimal facility size. Contour plots were then constructed to reveal how the transportation cost rate and equivalent yield affect the optimal plant size and corresponding biofuel unit cost. Based on the cost model and the relation for the optimal facility size that have been developed, the following conclusions may be drawn: • As suggested by Fig. 4, for high equivalent yields, an increase in the biomass production (facility size) can be accommodated by a relatively modest increase in delivery distance. However, for low yields, an increase in the facility size will result in a dramatic increase in delivery distance. • While the biomass gate and storage cost affect the actual unit cost of biofuel, they do not influence the optimal size of the production facility. • Both equivalent yield and transportation cost rate influence the facility size, with the contour plot suggesting that perhaps the yield has a slightly more important role. • The contours for unit cost are similar in appearance to those for facility size. Both equivalent yield and transportation cost rate affect the unit cost, with the yield having a slightly larger effect. The developed model for producing biofuel from forest biomass predicts the total cost as a function of such factors as equivalent biomass yield, transportation cost rate, facility size, biomass resource inputs, storage, and facility construction and operation expenses. This cost model has been used to establish a relation for the size of a facility that produces the minimum biofuel unit cost. It should be noted that the cost model in no way guarantees producer profitability. There may be situations where even at the minimum unit cost, insufficient revenue is generated to make a profit based on market conditions. However, the cost model relationship does provide insight into the importance of key factors on the size and cost of constructing and operating a biofuel production facility from forest biomass and will aid decision-makers in determining a course of action within the renewable biofuel industry. Acknowledgments The authors gratefully acknowledge the support from a project (CBET-0524872) funded by the National Science Foundation through the Materials Use: Science, Engineering & Society (MUSES) program.
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. National Renewable Energy Laboratory (NREL/TP-510-32438, June 2002). Alpert, S.B., 1959. Economy of scale in the metal removal industry. J. Ind. Econ. 7 (3), 175–181 (Jul.). Andersson, G., Asikainen, A., Björheden, R., Hall, P.W., Hudson, J.B., Jirjis, R., Mead, D.J., Nurmi, J., Weetman, G.F., 2002. Chapter 3: Production of forest energy. In: Richardson, J., Björheden, R., Hakkila, P., Lowe, A.T., Smith, C.T. (Eds.), Bioenergy From Sustainable Forestry: Guiding Principles and Practice. Kluwer Academic Publishers, pp. 49–123. Becker, D.R., Skog, K., Hellman, A., Halvorsen, K.E., Mace, T., 2009. An outlook for sustainable forest bioenergy production in the Lake States. Energy Policy 37 (12), 5687–5693. Bolding, C., Lanford, B., Kellogg, L., 2003. Forest fuel reduction: current methods and future possibilities. Proceedings of the 2003 COFE (7-10 September. Bar Harbor, ME: 5 pp.). Energy Independence and Security Act of 2007 (EISA), 2007. Pub. L. No. 110-140, 121 Stat. 1492, 1783-84 (Dec. 19, 2007), codified at 42 U.S.C. §17381. Froese, R.E., Waterstraut, J.R., Johnson, D.M., Shonnard, D.R., Whitmarsh, J.H., Miller, C.M., 2008. Lignocellulosic ethanol: is it economically and financially viable as a fuel source? Environ. Qual. Manag. 18 (1), 23–45. Gan, J., Smith, C.T., 2011. Optimal plant size and feedstock supply radius: A modeling approach to minimize bioenergy production costs. Biomass and Bioenergy 35 (8), 3350–3359. Graham, R.L., Liu, W., Downing, M., Noon, C.E., Daly, M., Moore, A., 1997. The effect of location and facility demand on the marginal cost of delivered wood chips from energy crops: a case study of the state of Tennessee. Biomass Bioenergy 13 (3), 117–123. Graham, R.T., McCaffrey, S., Jain, T.B., 2004. Science basis for changing forest structure to modify wildfire behavior and severity. Gen. Tech. Rep. RMRS-GTR-120. Department of Agriculture, Forest Service, Rocky Mountain Research Station, Fort Collins, CO: U.S. (43 pp.). Greer, D., 2008. Commercializing cellulosic ethanol. November BioCycle 49 (11), 47 (http://www.jgpress.com/archives/_free/001764.html. Accessed August 10, 2009). Hicks, J., 2009. Modeling the multi-modal transport of logs and the effects of changing fuel prices. Master thesis Civil and Environmental Engineering Department, Houghton, Michigan Technological University. 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 (2), 234–246. Ince, P.J., Kramp, A., Spelter, H., Skog, K., Dykstra, D., 2006. FTM-West: fuel treatment market model for the U.S. West. Draft Manuscript. Jenkins, B.M., 1997. A comment on the optimal sizing of a biomass utilization facility under constant and variable cost scaling. Biomass Bioenergy 13 (1/2), 1–9. Kocoloski, M., Griffin, W.M., Matthews, H.S., 2011. Impacts of facility size and location decisions on ethanol production cost. Energy Policy 39 (1), 47–56. Lambert, D.K., Middleton, J., 2010. Logistical design of a regional herbaceous crop residuebased ethanol production complex. Biomass Bioenergy 34, 91–100. Leinonen, A., 2004. Harvesting technology of forest residues for fuel in the USA and Finland, Espoo 2004. VTT Tiedotteita. Research Notes, 2229 (132 pp. + app. 10 pp.). Lieberman, M.B., 1987. Market growth, economies of scale, and plant size in the chemical processing industries. J. Ind. Econ. 36 (2), 175–191. Miller, C.A., Froese, R.E., Leefers, L.A., 2007. Consequences of corporate timberland ownership change in Michigan's Upper Peninsula. 2007 SAF National Convention, October 23-27 at Portland, OR. National Science Foundation (NSF), 2008. Breaking the Chemical and Engineering Barriers to Lignocellulosic Biofuels: Next Generation Hydrocarbon Biorefineries. In: Huber, George W. (Ed.), University of Massachusetts Amherst. National Science Foundation. Chemical, Bioengineering, Environmental, and Transport Systems Div (Washington D.C. 180 pp.). Nelson, B., 2007. Marvin Nelson Forest Products, Inc. Personal Communications, July 2007. Nelson, B., 2010. Marvin Nelson Forest Products, Inc. Personal Communications, September 2010. Nguyen, M.H., Prince, R.G.H., 1996. A simple rule for bioenergy conversion plant size optimization: bioethanol from sugar cane and sweet sorghum. Biomass Bioenergy 10, 361–365. Noon, C.E., Zhan, F.B., Graham, R.L., 2002. GIS-based analysis of marginal price variation with an application in the identification of candidate ethanol conversion plant locations. Netw. Spat. Econ. 2 (1), 79–93. Overend, R.P., 1982. The average haul distance and transportation work factors for biomass delivered to a central plant. Biomass 2, 75–79. Rendleman, C.M., Shapouri, H., 2007. New technologies in ethanol production, AER-842, USDA. Office of Energy Policy and New Uses. Rummer, B., Prestemon, J., May, D., Miles, P., Vissage, J., McRoberts, R., Liknes, G., Shepperd, W.D., Ferguson, D., Elliot, W., Miller, S., Teutebuch, S., Barbour, J., Fried, J., Stokes, B., Bilek, E., Skog, K., 2003. A Strategic Assessment of Forest Biomass and Fuel Reduction Treatments in Western States. USDA Forest Service (April). Runge, C.F., Senauer, B., 2007. How biofuels could starve the poor. Foreign Aff. 86, 41–54. Searcy, E., Flynn, P., 2008. The impact of biomass availability and processing cost on optimum size and processing technology selection. Appl. Biochem. Biotechnol. 154 (1-3), 92–107 (2009 May). Shapouri, H., Gallagher, P., 2005. USDA’s 2002 Ethanol Cost-of-Production Survey. United States Department of Agriculture, Agricultural Economic Report Number 841. (July). Starr, M.K., Miller, D.W., 1962. Inventory Control: Theory and Practice. Prentice-Hall, Englewood Cliffs, NJ.
T.L. Jenkins, J.W. Sutherland / Forest Policy and Economics 38 (2014) 32–39 Stevenson, W.J., 1996. Production/operations management, 5th ed. Irwin. U.S. Department of Agriculture, U.S. Department of Energy (USDA/DOE), 2005. A billionton feedstock supply for bioenergy and bioproducts industry: technical feasibility of annually supplying 1 billion dry tons of biomass (DOE/GO-102995-2135; ORNL/ TM2005/66). Walsh, M., 2008. U.S. cellulosic biomass feedstock supplies and distribution. M & E Biomass. (http://ageconsearch.umn.edu/bitstream/7625/2/U.S.%20Biomass%20Supplies. Pdf, accessed February 16, 2009).
39
Wooley, R., Ruth, M., Sheehan, J., Ibsen, K., 1999. Lignocellulosic Biomass to Ethanol Process Design and Economics Utilizing Co-Current Dilute Acid Prehydrolysis and Enzymatic Hydrolysis Current and Futuristic Scenarios. NREL report TP-580-26157, July http://www.ott.doe.gov/biofuels/process_engineering.html. Wright, M., Brown, R.C., 2007. Establishing the optimal sizes of different kinds of biorefineries. Biofuels, Bioprod. Biorefin. 1 (3), 191–2000. Wyman, C.E., 2003. Potential synergies and challenges in refining cellulosic biomass to fuels chemicals, and power. Biotechnol. Program 254–262.