Techno-Economic Analysis of Cellulosic Butanol Production from Corn

Jun 28, 2016 - Biobutanol has fuel properties comparable to those of gasoline; however, its commercial production through acetone–butanol–ethanol ...
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Techno-economic Analysis of Cellulosic Butanol Production from Corn Stover through Acetone-Butanol-Ethanol (ABE) Fermentation Nawa Raj Baral, and Ajay Shah Energy Fuels, Just Accepted Manuscript • DOI: 10.1021/acs.energyfuels.6b00819 • Publication Date (Web): 28 Jun 2016 Downloaded from http://pubs.acs.org on June 29, 2016

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Techno-economic Analysis of Cellulosic Butanol Production from Corn Stover through Acetone-Butanol-Ethanol (ABE) Fermentation Nawa Raj Baral1, 2, Ajay Shah1,* 1

Department of Food, Agricultural and Biological Engineering, The Ohio State University,

Wooster, Ohio, USA. 2

Department of Mechanical Engineering, Institute of Engineering, Tribhuvan University,

Kathmandu, Nepal. * Corresponding Author: 110 FABE Building, 1680 Madison Avenue, Wooster, OH 44691, Phone: 330-263-3858, Email: [email protected]

Abstract Biobutanol has comparable fuel properties to gasoline; however, its commercial production through acetone-butanol-ethanol (ABE) fermentation from lignocellulosic biomass is still encumbering due to low product yield, energy extensive recovery method and butanol toxicity to microbes. Recent development of simultaneous saccharification, vacuum fermentation and recovery technique has potentials to reduce these problems and improve butanol yield, which has gained significant attention as an emerging alternative way for ABE fermentation. Thus, the main objective of this study was to assess the techno-economic feasibility of commercial-scale ABE fermentation for a 113.4 million liter/year (30 million gallon/year) butanol production and identify operational targets for process improvement. Commercial dilute sulfuric acid pretreatment and corn stover feedstock were used in this study. Experimental data on the pretreatment of corn stover, and the ABE fermentation and recovery were gathered from recent publications. Process modeling and economic analyses were performed using a modeling

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software-SuperPro Designer. Estimated butanol production costs were $1.8 and 1.5 per liter without and with byproducts credits. Butanol recovery was identified to be the most sensitive parameter followed by sugar utilization in the fermentation reactor, feedstock cost, corn stover to sugars conversion rate and heat recovery. Furthermore, optimizing these sensitive operating parameters could reduce the butanol production cost to $0.6/liter, which is competitive with current gasoline price; however, achieving these targets will require further research and development efforts on the ABE fermentation.

Keywords: Techno-economic analysis; ABE fermentation; dilute sulfuric acid pretreatment; vacuum fermentation and recovery; stillage utilization

Introduction Fluctuation in crude oil prices, environmental issues and depletion of fossil fuel resources are primary reasons for the production of alternative fuels from renewable biomass. Butanol is an attractive renewable liquid transportation biofuel, which is superior to ethanol in terms of fuel properties such as high calorific value, low freezing point, high hydrophobicity, low flammability and corrosiveness.1–5 Additionally, butanol is amenable to pipeline distribution and it can be used with or without blending with gasoline in existing vehicles without any modification.6,7 Furthermore, butanol is an important chemical solvent for paints, polymers and plastics industries, whose global market was 2.8 million tons in 2008.3 Thus, production of butanol is supported by governments around the globe including the United States (US), which mandates annual production of 16 billion gallons of cellulosic biofuels out of total 36 billion gallons of renewable biofuels by 2022.8 The cellulosic butanol can be produced from agricultural residues,

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forestry wastes, grasses, wastepaper and municipal wastes due to their availability, low cost and has no food deficiency issues like crops grain.5,9,10

Among lignocelluloses, corn stover is a viable feedstock for bioenergy production due to immediate availability and ease of cultivation.11 Cellulose, hemicellulose and lignin are major constituents of corn stover, where cellulose fibers are surrounded by a hemicellulose and both bonded by strong lignin barrier.9,12 While the lignin component of corn stover cannot be used by the solventogenic Clostridia, cellulose and hemicellulose can be transformed into fermentable sugars, which can be further metabolized by solventogenic Clostridia to produce butanol. Thus, pretreatment process is essential to produce fermentable sugars, such as glucose, xylose and galactose,9,12,13 by enhancing enzyme accessible surface area by changing structure of biomass and degrees of polymerization14,15. In addition to fermentable sugars pretreatment process could also produce fermentation inhibitors such as 5-hydroxymethylfurfural (HMF), furfural, acetic, ferulic, glucuronic and phenolic compounds. 1,4,9 These microbial inhibitors reduce butanol production requiring detoxification to reduce or eliminate effect of these during fermentation.

The fermentable sugars produced from pretreatment and successive enzymatic hydrolysis process are metabolized by Clostridium species during acetone-butanol-ethanol (ABE) fermentation. While Saccharomyces cerevisiae cannot utilize C5 sugars in conventional ethanol fermentation system, Clostridium species can metabolize both hexose (C6) and pentose (C5) sugars efficiently in ABE fermentation. A major problem of current ABE fermentation is low yield (i.e., based on current state of technology, butanol yield is about half that of ethanol), product inhibition, low productivities, multiple end products, low product concentration and

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energy intensive downstream processes.1,4,9 Although theoretical butanol yield is about 20% less than the theoretical ethanol yield, its energy value is about 32 % higher than that of the ethanol.7 Another concern associated with butanol production is that butanol concentration of more than 13 g/L is highly toxic to microorganisms that catalyze its production.2 This toxic effect could be reduced through process improvements, such as continuous fermentation and recovery methods, and selection of butanol tolerant strain(s).2,3,6,10 Clostridium acetobutylicum ATCC 824 and Clostridium beijerinckii NCIMB 8052, and their mutant strains are the main microbes that can metabolize fermentable sugars during ABE fermentation. 1,3,4,17,18 Under batch fermentation, these can produce ABE from corn stover at a concentration of 12.1 to 26.3 g/L.17 For instance, two commonly used strains, C. beijerinckii P260 and C. beijerinckii BA101, are mutant of C. beijerinckii NCIMB 8052.3,4,17 These strains are used in batch, fed batch and continuous fermenter to produce ABE. Contamination and failure to switch from acidogenic to solventogenic phase are severe problems in ABE fermentation as these lead to overall fermentation system cleaning and complete loss of a fermentation batch.1 The maximum ABE concentration of 26.27 g/L with yield of 0.44 g/g and productivity 0.31g/l/h has been achieved in batch fermentation of sulfuric acid pretreated corn stover using C. beijerinckii P260.19

Current n-butanol yield from fermentable sugars is in-between 15-25 wt% ,7 which can be improved through simultaneous saccharification, fermentation and recovery.20,21 This integrated system could minimize butanol toxicity to solventogenic Clostridia.10,22 One of the recent progresses on ABE fermentation is continuous vacuum fermentation and recovery. Vacuum recovery removes ABE in gas phase at the fermentation temperature, which is formed in the fermentation reactor due to the lower working pressure of 0.94-0.98 MPa23 when compared to

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standard atmospheric pressure. Implementation of this method for ABE recovery was initially ignored, while this method was widely used in ethanol fermentation.24–28 One of the reasons is more suitability of vacuum fermentation for recovering product that has the lower boiling point than water.29 However, a recent insight on heteroazeotropic mixture of butanol and water at concentration of 99 wt% pure water was assumed to be recovered. This water was assumed to be delivered to boiler. Apart from recovered water, additional feed water to boiler was assumed to be delivered directly from the well. The steam from boiler was assumed to be sent to multistage steam turbine where electricity and process steams can be obtained. Credit for high and medium temperature steam was assigned, while low temperature steam and condensed water were assumed to be mixed with recovered water from wastewater treatment section and recycled back to the boiler.

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Analyses Process economics Several economic parameters used to estimate investment and operating costs as well as economic analysis are summarized in Table 2. The model biorefinery for butanol production through ABE fermentation was assumed to be operated 330 days per year and 24 h per day based on previous techno-economic studies.16,48,49 Equipment purchase cost data were obtained from previous studies, including NREL16,35 and DOE/NETL50. Following the mass and energy balance analysis of different process equipment, their sizes and quantities were determined. Based on the estimated equipment sizes obtained from the process model and equipment sizes and costs used in the previous reports, 16,35,48,49,51

a reasonable equipment prices were obtained. Then, the estimated equipment

price of each equipment was further adjusted to the analysis year (2015) using in-built function of the software.34 Apart from equipment purchase price, an installation factor for different process equipment was assigned based on previous literatures48,49 and modelling software34 used in this study. Then, the fixed costs that are associated with a process, i.e., the total capital investment (TCI), was calculated as the sum of following cost items: direct fixed capital (DFC), working capital, and start-up cost. The DFC includes direct cost (equipment purchase, installation, piping, instrumentation, electrical, insulation, buildings, yard improvement, and auxiliary facilities cost) and the associated indirect costs (construction, engineering, contractor's fee, and contingency). The working capital is the tied-up funds required to operate the biorefinery, and accounts for raw materials, consumables, labor and utilities. Similarly, the start-up cost is a one-time investment to

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prepare a new plant for operation.34 The percentage of different cost parameters are presented in Table 2.

Apart from capital investment, annual operation cost was estimated as the sum of the facility-dependent cost, raw materials, labor-dependent cost, heating/cooling utilities and electricity. The facility dependent cost is the cost related to the use of a facility, which was estimated as the sum of the costs associated with equipment maintenance (10% of purchase cost), depreciation of the fixed capital cost (Table 2), and miscellaneous costs such as insurance (1% of DFC), local (property) taxes (2% DFC) and factory overhead expenses (5% of DFC).34 Apart from the facility dependent cost, material cost, such as price of feedstock and other input materials, was gathered from previous studies. The average price used to deliver the corn stover to the biorefinery gate ($/kg) was estimated to be 0.11 excluding overheads.34 Sulfuric acid, ammonia, enzyme and waste treatment chemicals prices at the biorefinery gate ($/kg)16 of 0.02, 0.09, 0.82 and 0.03, respectively, were used in this study. The labor hour required for each unit operations were gathered from literatures34, 48-50. Labor rate ($/h) was assumed to be $69/h34 including basic rate, benefits, supervision, operating supplies and administration. Steam, cooling water and chilled water were assumed for heating and cooling agents and their costs ($/t) were assumed to be 12, 0.4, 0.05, respectively34. The price of electricity was assumed to be $0.07/kWh52 for industrial use. Finally, butanol production cost was estimated based on the plant service life of 30 years.16

In addition to total cost of butanol production, net cost was estimated assuming credit for byproducts. A credit of $12/t34 was assigned for high temperature steam (~278˚C) and

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medium temperature steam (~250˚C). Additionally, credit of $0.07/kWh was assigned for electricity generation from steam turbine-generator system. While recovery of acetone and butanol were > 99 wt% on the final product, ethanol concentration on the final product was ~54 wt% even after dehydration using molecular sieve due to its low input concentration of ~4 wt%. This suggests another distillation column followed by molecular sieve is required to recover ethanol. Thus, credit of $1/kg was assigned for acetone7 and the credit for ethanol was excluded in this study.

Sensitivity analysis and optimization Average values for different operating parameters used in this study are discussed so far. After the base case estimation of the butanol production cost, sensitivity analysis on it was performed. Due to uncertainty of several input variables (Figure 8), sensitivity analysis was performed with ± 20% variation of the base case value to identify the most influencing parameter on butanol production cost. Different parameters used for sensitivity analysis were butanol recovery, sugar utilization rate and loss, solid and sulfuric acid loading ratio, feedstock cost, severity factor, heat recovery plant size, boiler and turbine-generator efficiency, retention time for reactors and moisture content (Figure 8). Apart from the sensitivity analysis, optimum butanol production cost was estimated using optimistic data for the most sensitive input parameters, which is discussed in the optimization section.

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Results and discussion Material and energy balance The estimated corn stover feedstock requirement for 113.4 MLPY (30 MGPY) butanol production was ~115 t/h. This feedstock requirement is ~2 folds more than ethanol production with same feedstock and biorefinery capacity36 because the estimated butanol production rate, as discussed earlier, is about half of the corn stover to ethanol conversion rate of ~80 gal/ton.16 With this conversion rate, ~ 6.4 t dry corn stover was estimated to be required to produce 1000 liter butanol. Apart from corn stover, water was found to be major input material with overall requirement of ~ 19t/kilo-liter butanol (Figure 4). Out of which, ~ 13 t of water was found to be required for upstream processes, i.e., pretreatment and fermentation, and apart from recovered water, ~6 t of additional water was found to be required for stillage utilization section to produce process steam and electricity. About 87% of the upstream process water was recovered through waste water treatment process and remaining 13% water was contained in the waste sludge. Air was another important input, which was found to be required ~32 t for stillage utilization from one kilo-liter butanol production. Air was mainly utilized for combustion of lignin and biogas in the boiler. In additional to boiler, aerobic bio-oxidation and solid liquid separation units also required air. Other input materials required for different units to produce one kilo-liter butanol are illustrated in Figure 4. These additional chemicals include sulfuric acid, ammonia, enzyme, nutrients and Clostridium strain. About 2t of these chemicals was found to be required to produce 1kilo-liter butanol. In addition to butanol, ~123 kg of acetone and ~30 kg of ethanol were also recovered from the vacuum ABE fermentation and recovery system evaluated in this study. The overall butanol to acetone ratio considering both glucose and xylose estimated in this study is about 6.6, which is higher than the average estimated butanol to acetone ratio of 5.6

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from the previous studies2, 23 considering glucose only. This is mainly due to assuming the same sugar utilization rates for both glucose and xylose because less acetone is produced from xylose when compared to the same amount of glucose utilized to produce acetone. The higher acetone yield by reducing ABE losses during recovery and separation processes could change overall butanol production cost through vacuum fermentation as acetone is a main byproduct of the ABE fermentation system.

The net external energy and process energy required for each unit of ABE fermentation system are also illustrated in Figure 4. Both electrical energy and energy associated with heating and cooling agents were considered for the net external energy. On the other hand, the process energy includes enthalpy of materials, which is dependent on mass and temperature of the material. The pretreatment unit was found to be the most energy intensive step requiring ~55% of the total external energy required for the overall ABE fermentation system. This energy was mainly required for pretreatment reactor. Apart from pretreatment section, ~23% of the total external energy was found to be required for recovery section to separate ABE using distillation column. Third most energy intensive unit of this system was stillage utilization unit. This unit requires ~18% of the total external energy to recover process water using evaporator, separate solid- liquid stillage and deliver air for aerobic bio-oxidation as well as boiler. Other energy intensive processes were fermentation unit followed by corn stover preparation and detoxification unit. These different units were found to be required ~4% of total external energy, where major energy contributors were fermentation reactor and hammer mill.

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The net external energy requirement is dependent on the amount of waste heat recovery. This heat recovery not only affects the heating agent requirement but also capital cost of the system due to decrease in the retention time in the reactors with increased temperature of the substrate.36 The decrease in retention time decreases the quantity of reactors requirement. On the other hand, heat exchanger cost will increase due to the requirement of more heat exchange area to increase heat recovery. Thus, there should be a good tradeoff among heat recovery, capital cost and operating cost. In this study, ~85% of the waste heat was assumed to be recovered using heat exchangers, which decreased the amount of external energy requirement, specifically, pretreatment, stillage utilization and recovery sections (Figure 4).

Overall ~11400 kWh of net external energy was required to produce one kilo-liter butanol through vacuum ABE fermentation and recovery system. Considering this external energy and ~26730 kWh heating value of dry corn stover as energy inputs as well as ~16605 kWh energy value of butanol, electricity and steam as the energy outputs, ~44% energy conversion efficiency was obtained through ABE fermentation system used in this study. The energy conversion efficiency of vacuum ABE fermentation system was found to be increased to 46% considering energy contained in the acetone, which is one of the major byproducts. Additionally, considering the energy value of ethanol can further improve the energy conversion efficiency; however, ethanol was not considered in this study due to their lower concentration and the higher water content of 50 wt% requiring additional external energy to produce fuel ethanol. Moreover, this efficiency could be further increased through the utilization of efficient process equipment and optimization of vacuum ABE fermentation mainly butanol and acetone yields from corn stover. Further optimization techniques are discussed in detail in the optimization section.

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Capital investment, operating and butanol production cost Total capital investment for a 113.4 MLPY (30 MGPY) cellulosic butanol production plant was estimated to be ~$410 million. The major contributor to capital investment cost was direct fixed capital cost, which shared ~92 % of the total capital investment cost. This result in ~$379 million for direct fixed capital cost, out of which ~62 % required for equipment, buildings materials and auxiliary facilities; ~25 % required for engineering and construction; and remaining ~13 % required for contractor’s fee and contingency. The purchase and installation of hammer mills, storage bins and tanks, pretreatment and fermentation reactors, distillation columns, anaerobic digesters, boilers, steam turbines and heat exchangers were the major contributors to the total direct fixed cost. The details of equipment costs, installation cost, and other contributors to the fixed cost are summarized in the supplementary document (S-1, 2). In addition to the direct fixed capital cost, remaining ~8 % of total capital investment cost was estimated to be required for working capital and startup cost. These different components of capital investment and their contribution for butanol production are summarized in Figure 5.

Annual operating cost required to produce butanol was estimated to be $1.76/liter and its components are summarized in Figure 6. Feedstock and other input material costs were the major contributors to the annual operating cost, which was estimated to be ~47 % of the total annual operating cost. Corn stover itself contributed ~40 % of the total operating cost. In addition to input materials, facility dependent cost shared ~32 % of total operating cost followed by ~15 % for utilities and ~6 % for labor. Details of the operating costs are provided in the supplementary document-S3.

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About 40 % contribution of corn stover to butanol production cost (Figure 7) suggests feedstock logistics is very crucial for sustainability of cellulosic biorefinery. Apart from logistics, stillage utilization section required ~22 % of the total butanol production cost, followed by ~ 11 % required for both pretreatment, and hydrolysis and fermentation, ~10 % required for recovery and ABE separation, 5 % required for preparation and ~1% required for detoxification process. These costs are summarized in Figure 7. The total estimated butanol production cost of $1.76/liter could be further reduced to $1.47/liter including byproducts credit (Figure 7). The major byproducts considered in this study were acetone, process steam and electricity.

Comparison between butanol and ethanol production costs from other previous studies While several techno-economic studies on ethanol fermentation are available, there are only few techno-economic studies on ABE fermentation specifically using lignocellulosic feedstock; some of the main studies are summarized in Table 3. Thus, a result of this study is also compared with the ethanol production as ethanol and butanol are two viable biofuels. Table 3 summarizes the comparison of the butanol cost obtained in this study with ethanol and butanol costs from other previous studies. The net butanol production cost found in this study was ~1.7 folds higher than previous estimate ($0.88/liter),7 while total byproducts credit assigned in this study was ~2 folds less than the same study ($0.58/liter butanol). These variations in this study may be due to corn stover price, different ABE fermentation systems and products yield, neglecting credit of ethanol and analysis year.

The differences in the assumptions in this and the previous study7 has both positive and negative impact on the butanol production cost. For instance, corn stover price used in this study is ~2

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fold more than the previous study7 that causes the increase in the butanol production cost. On the other hand, they considered continuous fermentation and recovery, while this study considered vacuum fermentation and recovery, which is supposed to be less expensive than the previous system. While sugar utilization to produce butanol considered in this study was based on experimental data on vacuum ABE fermentation2,23 and was ~ 1.2 folds higher than previous study,7 ethanol and acetone yields were ~2 folds less than their assumed sugar utilization rate of 4.5 and 27 %, respectively. In addition yield, due to lower concentration of ethanol ~ 50 % water retained in the final product even with distillation followed by molecular sieve separation, thus credit of ethanol was neglected in this study. Addition of two distillation columns before the molecular sieve separation may results fuel ethanol with >99 % concentration; however, recovery of fuel ethanol was neglected in this study due to low yield of 30 kg/kilo-liter butanol (Figure 4). These also increase the unit butanol production cost by reducing byproducts credit.

The butanol production cost found in this study is also higher than previous estimates of $1.1/liter from wheat straw 58 and $0.48/liter from corn stover4. A low butanol production cost ($0.48/liter) reported in the previous study4 may be due to the lower feedstock cost and capital investment when compared to other studies (Table 3). They also reported that feedstock cost is the most influencing parameter for butanol production cost. On the other hand, the cost estimated in this study is lower than previously estimated corn grain based butanol production cost of $1.9/liter.1 These variations may be due to variations in feedstock type, feedstock cost, butanol yield and process technology.

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Furthermore, the estimated butanol production cost in this study was higher than estimated cellulosic ethanol costs (Table 3) While ethanol and butanol can be produced through same route and almost similar level of process equipment and materials (apart from microorganism and nutrient requirements), major variation in production cost is due to their yield (Table 3). Duque et al.59 evaluates techno-economic feasibility of 10 agro-industrial residues yielding ethanol from 0.009 to 0.264 kg/kg of residues. They found the average ethanol production cost of $0.65/liter, which is highly dependent on ethanol yield. However, butanol production cost per unit energy is very competitive with ethanol production cost per unit energy (Table 3). The following sections identify and discuss some key influencing parameters on butanol production cost and possible ways to reduce the current estimated cost of butanol from corn stover to make it competitive with ethanol.

Sensitivity analysis Sensitivity of the butanol production cost through ABE fermentation is summarized in Figure 8. Butanol recovery was found to be the most sensitive input parameter. When butanol recovery decreased from 95 to 90 wt% butanol production cost was increased by ~7 %. Another most influencing input parameter to butanol production cost was sugars utilization to produce butanol in the fermentation reactor. The sugar utilization is also inversely proportional to the butanol production cost. While these two input parameters alter butanol production cost by mainly increasing or decreasing final product amount, solid loading ratio, which is another sensitive parameter, influences the on capital and operating costs. Decrease in solid loading ratio could increase number of reactor and heat exchanger requirement and amount of heating or cooling agent requirement due to high volume of water to be handled. Thus, it is essential to design these

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equipment such that all the heat exchangers and reactors are fully utilized. Apart from these parameters, feedstock cost, severity factor and heat recovery were the other most sensitive parameters (Figure 8). While the feedstock cost is directly proportional to butanol production cost, heat recovery impacts inversely to butanol production cost. High heat recovery can reduce utility requirement, thus, reduces butanol production cost. Heat recovery also causes the increase in the equipment cost as high heat exchanger area is required to recover large amount of heat energy, which can also increase the butanol production cost. Thus, an optimum heat recovery is very crucial to reduce the overall butanol production cost. The severity factor, which is the function of temperature and time, impacts on sugar conversion during pretreatment and enzymatic hydrolysis as well as heating and cooling agent requirement, thus, impacts on butanol production cost. Other input parameters considered in this study were the least sensitive to unit butanol production cost (Figure 8).

Optimization of butanol production cost The butanol production cost obtained in this study could be reduced through the improvement on the most sensitive parameters discussed in the previous section. Previous studies2,23 found 95-98 wt% ABE recovery through vacuum fermentation and recovery system. Thus, overall butanol recovery of 98 wt% was assumed in this study although all recovered butanol could not be separated. Thus, this is an optimistic assumption at the present state of technology and can be improved with research and development efforts in ABE recovery and separation methods. In addition to butanol recovery, previous studies2,23 found ~19-25 wt% butanol from glucose. The maximum value of glucose utilization rate (i.e., 25 wt%) and the same rate for xylose were assigned as an optimistic butanol yield from the fermentable sugars. The Clostridium species can

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metabolize both glucose and xylose effectively, thus, same sugar utilization rate for xylose was assumed for analysis in this study. Even with this sugar to butanol conversion rate and considering other byproducts of ABE fermentation, such as acetone and ethanol, 100% sugars utilization could not be achieved. About 19 wt% glucose and ~24 wt % xylose were found in the waste stream, which is very close to the total sugar loss (including glucose and xylose) of ~22 wt % reported in the previous techno-economic study.16 Thus, further research efforts are required not only to increase sugars utilization to produce butanol but also to improve overall sugar utilization.

Another sensitive input parameter was solid loading ratio. An optimistic solid loading ratio of 40 wt% was assumed in the model to estimate the optimistic butanol production cost although most of the experimental data used in this study and summarized in Figure 2 and 3 were conducted at ~10 wt% solid loading ratio. Previous study16 assumed 30 wt% solid loading ratio for commercial biofuel production and recent experimental studies60,61 with higher loading ratio (2036 wt%) encouraged to consider the optimistic solid loading ratio of 40 wt%. The corn stover supply cost could be reduced by optimizing the feedstock transportation and field operation,33 thus, corn stover cost at the biorefinery gate was assumed to be $64/t. This cost was also used in the previous techno-economic studies.7,16

Severity factor is another sensitive parameter. Sugars yield, and operating and capital costs are dependent on it. An optimum severity factor of 2.6 with glucose and xylose yield of 85 wt% each during enzymatic hydrolysis was assumed in this study. Although mean value obtained from the best fit curve (Figure 3) is