ASSESSING THE IMPACT OF UNCERTAINTY ON
ETHANOL PRODUCTION OUTCOMES
A Master of Engineering Project
Presented to the Faculty of the Graduate School
of Cornell University
In Partial Fulfillment of the Requirements for the Degree of
Master of Engineering
Mariel B. Eisenberg
August 2011
Assessing the Impact of Uncertainty on Ethanol Production Outcomes
Mariel B. Eisenberg
Department of Biological and Environmental Engineering
Cornell University
August 2011
As research into cellulosic ethanol production advances, efficiencies are improving at
every step through the process. Review of relevant research shows significant variability in
parameter estimates for almost every unit process through both supply chain and conversion
process.
The objective of this study is an assessment of the impact of various parametric
uncertainties on the overall material requirements for ethanol production, specifically feedstock
requirements and land area for production of feedstock. The analysis is based on a generalized
input-output style model of ethanol production, with uncertainty introduced through a Monte
Carlo Simulation (MCS) framework. In the initial study, uncertainties in crop yield, storage loss,
sugar yield, and fermentation yield are considered. Results show the variation of crop yield has
the greatest effect on land area requirements; while variation of sugar yield has the greatest effect
on harvested switchgrass, given crop yield parameters. Further analysis will consider the impact
of these uncertainties on economic and energy flows in the system.
ii
ACKNOWLEDGEMENTS
I would like to thank my advisor, Lindsay Anderson, for her guidance throughout the
research process. Thank you to Professor Larry Walker for providing the switchgrass to ethanol
model on which this project is based.
I would also like to thank my family and friends for their unconditional love and support.
I am truly grateful for the joy you bring to my life everyday and for the encouragement you have
given me throughout this journey.
iii
TABLE OF CONTENTS
Chapter 1: Introduction ............................................................................................................... 1
1.1
General ............................................................................................................................ 1
1.2
Objectives ....................................................................................................................... 1
Chapter 2: Literature Review ...................................................................................................... 3
2.1
Switchgrass ..................................................................................................................... 3
2.2
Ethanol Production.......................................................................................................... 4
2.3
System Modeling ............................................................................................................ 5
Chapter 3: Model Development ................................................................................................... 9
3.1
Assumptions.................................................................................................................... 9
3.2
Parameters ..................................................................................................................... 10
3.3
Procedure ...................................................................................................................... 13
Chapter 4: Results and Discussion ............................................................................................ 16
4.1
Simulation Results ........................................................................................................ 16
4.2
Sensitivity Analysis ...................................................................................................... 18
Chapter 5: Conclusion ................................................................................................................ 21
References .................................................................................................................................... 23
Appendix A: Schematic Model.................................................................................................... 26
Appendix B: Switchgrass to Ethanol Library .............................................................................. 27
Appendix C: Matlab Code ........................................................................................................... 41
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Chapter 1: Introduction
1.1 General
This project investigates the impact of various parametric uncertainties on the overall
material requirements for ethanol production, specifically feedstock requirements and land.
Through this study, insight can be gained to determine which processes have the greatest impact
on uncertainty of outcomes. Processes are examined beginning with harvesting switchgrass,
proceeding through the conversion process, and addressing nutrient inputs and land area
requirements to produce the desired amount of ethanol. The primary processes that the harvested
switchgrass undergoes are pretreatment, enzymatic hydrolysis, and fermentation. Figure 1 below
summarizes the processes discussed in this report.
Figure 1 Summary of processes for conversion of switchgrass to ethanol
1.2 Objectives
The primary objective of this project is to estimate the impact of uncertainty on the
material input requirements for production of a targeted level of ethanol. The achievement of
this objective requires the following steps.
1. Determine parameters with the most significant uncertainty in the process of
producing ethanol from switchgrass.
2. Collect parameter data and characterize the nature of the uncertainty for each
parameter determined in step 1, in the form of range and distribution type.
1
3. Develop a model for the ethanol production process and method to incorporate
uncertainty into this model.
4. Conduct sensitivity analysis of uncertainty parameters on land area and harvest
switchgrass.
5. Determine range of land area and harvested switchgrass based on desired amount of
annual ethanol production.
2
Chapter 2: Literature Review
2.1 Switchgrass
Switchgrass (Panicum virgatum) is a native North American warm season perennial
grass, commonly cited as a potential dedicated bioenergy feedstock. Switchgrass has emerged as
a leading bioenergy feedstock due to this high-yielding, perennial grass’ broad cultivation range
and low agronomic input requirements. Switchgrass’ tolerance to heat, cold, and drought, as
well as it’s resistance to pests and diseases, has enabled a variety of ecotypes of switchgrass to
inhabit a wide range of climates and soil conditions throughout North America.
There are two general ecotypes of switchgrass: lowland and upland. Lowland ecotypes
are vigorous, tall, thick-stemmed and adaptable to wet conditions while the upland ecotypes are
shorter, thinner-stemmed, and better suited to drier conditions (Gunter et al., 1996). Examples of
lowland ecotypes are Alamo switchgrass; which is typically grown in the Deep South and midlatitudes, and Kanlow; an ecotype more tolerant of cold temperatures that is typically grown in
mid-latitudes (Groode, 2008).
Upland ecotypes include Cave-In-Rock, Blackwell, and
Trailblazer, which are all recommended for central and northern states.
Switchgrass is typically harvested once in the fall or winter after a killing freeze. After a
freeze, nutrients travel into the plants root system. This minimizes the harvest of plant nutrients,
and the need to replace such nutrients, while also maximizing switchgrass yield. Therefore, we
assume a single, late-season harvest to make switchgrass production a sustainable low-input
system (Larson et al., 2010). The assumed harvest period for switchgrass is between November
1 and March 1 (Larson et al., 2010).
3
2.2 Ethanol Production
Although there will be only one harvest per year, once after senescence, a refinery will
need a supply of feedstock throughout the year to produce ethanol. This is achieved by using
stored switchgrass during non-harvest periods. Therefore, storage of switchgrass is a significant
process in the switchgrass supply chain. According to Larson et al., it is assumed that one-third
of all harvested switchgrass is delivered to the biorefinery immediately after harvest in the
harvest season, while the remaining two-thirds is stored and uniformly delivered to the plant
during the non-harvest season, typically from March to October (2010).
The U.S. Department of Energy has identified switchgrass as a model herbaceous energy
crop (Keshwani, 2009). Benefits of switchgrass include its high yield, low water and nutritional
inputs, environmental benefits, and ability to thrive on marginal lands. Because conventional
farming equipment for seeding, crop management, and harvesting can be used, switchgrass can
easily be integrating into existing farms (Keshwani, 2009). In fact, the Oak Ridge National
Laboratory estimates that 171 million tons of switchgrass can be produced economically in the
United States, on an annual basis (Bals et al., 2010).
The main component in switchgrass is lignocellulose. Lignocellulose is composed of
cellulose, hemicellulose, and lignin, closely associated in a complex crystalline structure. The
conversion of lignocellulosic material to ethanol involves two main processes: hydrolysis of
cellulose to fermentable reducing sugars and fermentation of the sugars to ethanol. However,
because the cellulose and hemicellulose are not readily available for enzymatic hydrolysis, an
initial pretreatment step is required to increase accessibility of enzymes to the structural
carbohydrate fraction. Physical, chemical, and biological processes have all been used in
biomass pretreatment.
Ammonia fiber explosion is a physiochemical method of pretreatment to solubilize and
remove lignin and hemicellulose from the cellulose. In the AFEX process, biomass is treated
with liquid ammonia under high pressure (100 to 400 psi) and moderate temperatures (70 to
200°C) for less than 30 minutes (Bals et al. 2010). The pressure is then rapidly released,
4
exploding the fibrous mass.
This process decrystallizes the cellulose, hydrolyses the
hemicellulose, removes and depolymerizes lignin, and increases the size of micropores on the
cellulose surface (Bals et al. 2010). This process results in treated biomass that can reach close
to theoretical sugar yields due to increased susceptibility of lignocellulose to enzymatic
hydrolysis.
Following pretreatment, the cellulose and hemicellulose can be enzymatically
hydrolyzed, producing a mixture of fermentable sugars such as glucose and xylose. Enzymatic
hydrolysis proves to be an environmentally friendly alternative to using concentrated acid or
alkaline reagents through the use of carbohydrate degrading enzymes, both cellulases and
hemicellulases (Keshwani, 2009).
Based on complete hydrolysis of the cellulose and hemicellulose to monomeric sugars,
the maximum theoretical yield of reducing sugars is 800mg/g dry switchgrass (Dale et al. 1996).
Dale et al. reports that the maximum rates and yields of sugar occur at AFEX conditions of 90
degrees Celsius, ammonia loading of 1 gram per gram of biomass (ammonioa:biomass ratio of
1:1), and 15% moisture content. These AFEX-treated samples yield 4 to 5 times more sugar
compared with the untreated controls at the same enzyme loading.
The major advantage of SHF, compared to simultaneous saccharification and
fermentation (SSF), is that it is possible to carry out the hydrolysis and fermentation at their own
optimum conditions (Taherzadeh and Karimi, 2007). The resulting sugars can then be fermented
to produce ethanol. The fermented broth or mash is then further processed toward pure ethanol.
In order to assess the impact of various stages of this process, a method for modeling the overall
system is required.
2.3 System Modeling
The aforementioned processes involved in producing ethanol from switchgrass are
detailed in the input-output model in Appendix A. In systems modeling, input-output models are
5
used to represent interdependencies between stages of a system (Miller and Blair, 2009). Each
node of an input-output model may contain several equations that together complete the system
of equations that represents the whole model. With this type of model, each process of ethanol
production can be broken down by inputs and outputs. Each output becomes the input for the
subsequent process, demonstrating the interdependency between processes.
The figure below shows a snapshot of a small section of the switchgrass to ethanol inputoutput model. The figure shows the detail in each individual process and how each process
connects to the next. Each of the processes shown in Figure 2 represents a series of equations
for that particular process. Table 1 below summarizes these equations for the 4 processes in
Figure 2. Additionally, each process is connected at a node. At each node the output from the
previous process becomes the input for the subsequent process. Table 2 below summarizes the
process connectivity for the 4 processes by showing the nodal equations.
Process 10LIGNIN RECOVER/
FILTRATION
Process 11FERMENTATION
Process 9HYDROLYSIS
Process 8PRETREATMENT
Y4,11 = Yeast
Y3,10 = Water
Y3,11 = Yeast
Extract
Y2,9 = Enzyme
n3
Y1,12 =
Ferm.
Broth
n4
Y0,11 =
Ferm.
Broth
Y4,8 = Water
Y5,11 = CO2
P11
Y2,11 =
Bactopeptone
Y1,11 =
Sugar
Soln.
Y3,9 = Buffer
n6
n5
Y0,10 =
Sugar
Soln.
P10
Y2,10 =
Spent
Solids
Y1,10 =
Hydrolyzed
Biomass
Y4,10 =
Excess
Water
Y0,9 =
Hydrolyzed
Biomass
P9
Y1,9 =
Y0,8 =
Pretreated Pretreated
Biomass Biomass
Y3,8 =
Recycled
Ammonia
n7
P8
Y1,8 =
Reduced
SG
Y2,8 = Liquid
Ammonia
n8
Y1,20 = Make-up
Ammonia
Figure 2 Several processes of the switchgrass to ethanol input-output model
6
Y0,7 =
Reduced
SG
Process Equations
P8: k0,8*Y1,8 - Y0,8 = 0
P8: k2,8*Y1,8 - Y2,8 = 0
P8: k3,8*Y1,8 - Y3,8 = 0
P8: k4,8*Y1,8 - Y4,8 = 0
P9: k0,9*Y1,9 - Y0,9 = 0
P9: k2,9*Y1,9 - Y2,9 = 0
P9: k3,9*Y1,9 - Y3,9 = 0
P10: k0,10*Y1,10 - Y0,10 = 0
P10: k2,10*Y1,10 - Y2,10 = 0
P10: k3,10*Y1,10 - Y3,10 = 0
P10: k4,10*Y1,10 - Y4,10 = 0
P11: k0,11*Y1,11 - Y0,11 = 0
P11: k2,11*Y1,11 - Y2,11 = 0
P11: k3,11*Y1,11 - Y3,11 = 0
P11: k4,11*Y1,11 - Y4,11 = 0
Table 1 Select process equations for the switchgrass to ethanol input-output model
Process Connectivity Nodal Equations
n7: Y1,8 - Y0,7 = 0
n6: Y1,9 - Y0,8 = 0
n5: Y1,10 - Y0,9 = 0
n4: Y1,11 - Y0,10 = 0
n3: Y1,12 - Y0,11 = 0
Table 2 Nodal equations for process connectivity for select
process of the switchgrass to ethanol input-output model
Once a base-case system model is developed, an approach for incorporating uncertainty
is required. One such method is Monte Carlo Simulation (MCS). Monte Carlo simulation is a
stochastic technique used to incorporate uncertainty into a model (Manly, 2007). This method is
considered a sampling method because inputs are randomly generated from probability
distributions. Monte Carlo simulation can be applied to the input-output model to determine a
range of outcomes for land area and harvested switchgrass requirements.
With Monte Carlo simulation, the results are estimates, with a certain level of uncertainty
that must be considered (Seppale, 2008). To determine the results with the greatest likelihood of
certainty, multiple simulations should be done. Performing multiple simulations is the main
disadvantage of Monte Carlo simulation; however a computer program such as Matlab is a tool
that can be used to run thousands of simulations quickly and efficiently. The simulated results
7
can be presented as empirical probability distributions (histograms) displaying the range and
most probable values of output values. Monte Carlo simulation is an extremely useful technique
in that the range of outcomes accounts for a system’s variability.
After using random selection, the model runs through a given number of trials, generating
multiple results for each output. The final results can then be presented as empirical probability
distributions (histograms) displaying the range and most probable values of output values.
Monte Carlo simulation is an extremely useful technique in that the range of outcomes accounts
for a system’s variability.
8
Chapter 3: Model Development
The development of the simulation model is based on three main steps; first, the
definition of the material flow model of the system, second determination of the parametric
uncertainties to be modeled, and finally the combination of the mass flow model with probability
distributions to simulate the uncertain parameter values.
The material flows through the system are modeled using an input-output model of
ethanol production. The details of the input-output model are provided in Appendix A. The
parameters selected are discussed in greater detail in Section 3.2, and summarized in Table 3.
The parameters were input into the model to analyze uncertainties in switchgrass crop yield,
switchgrass storage loss, sugar yield, and fermentation yield through Monte Carlo Simulation.
The goal was to extract useful information in the resulting outputs of land area and harvested
switchgrass requirements.
To assess the importance of various uncertainties, sensitivity analyses were conducted on
the simulation results generated from the input-output model, as discussed in Section 4.2.
3.1 Assumptions
The results outlined in this report are based on a number of assumptions, outlined as
follows:
1. Single, late-season switchgrass harvest.
2. Switchgrass is stored throughout the year to provide continuous supply of feedstock
to plant for ethanol production.
3. Annual 95% ethanol production (stimulus variable) is set at 95,000,000 liters of
ethanol produced per year.
4. Method of pretreatment is ammonia fiber explosion (AFEX).
5. Separate hydrolysis and fermentation (SHF).
9
6. Assume average time in storage (t) of 200 days.
7. Parameter values described in Table 3.
8. Process 5 and process 15 intentionally left out to remain consistent with original
model.
3.2 Parameters
The parameters for each process are summarized in Table 3 and discussed in greater
detail below. Note that single values represent assumed constant values.
In a 2008 report, T. A. Groode identifies that crop yield, detailed in Process 1, is
normally distributed with a mean of 12.5 mt/ha and standard deviation 2.8 mt/ha.
This
distribution is used to determine the amount of land required to produce the desired amount of
ethanol per year. Nitrogen, phosphate, potassium and pesticide application rates are dependent
on crop yield, which determines land area. The coefficient values for the application rates
(kg/mt) are determined by multiplying the assumed application per area (kg/ha) by the crop yield
(ha/mt), as seen in Table 3.
10
Symbol
k1,1
k2,1
k3,1
k4,1
k5,1
Switchgrass Library
Milled SG
k1,2
0.9
mt hamermilled SG/mt harvested SG
Stored SG
k2,3
(see Appendix B)
mt stored hammermilled SG/mt hammermilled SG
Stored SG
k2,6
1
mt stored delivered SG/mt delivered SG
Reduced SG
k1,7
0.95
mt reduced SG/mt delivered SG
Pretreated SG
Liquid Ammonia
Recycled Ammonia
Water
k1,8
k2,8
k3,8
k4,8
1
1000
990
0.11
mt pretreated SG/mt reduced biomass
kg liquid ammonia/mt reduced biomass
liter recycled ammonia/mt reduced biomass
mt water/mt reduced biomass
Hydrolyzed BM
Enzymes
Buffer (Citrate)
k1,9
k2,9
k3,9
1
5000000
20000
mt hydrolyzed BM/mt pretreated biomass
FPU enzymes/mt pretreated biomass
liters buffer (citrate)/mt pretreated biomass
Sugar Solution
Spent Solids
Water
Excess Water
k1,10
k2,10
k3,10
k4,10
~U(1.667,1.8182)
0.629
(4900 l water/mt sugar soln)*(k1,10)
(7.258 mt excess H20/mt sugar soln)*(k1,10)
mt sugar solution/ mt hydrolyzed biomass
mt spent solids/ mt hydrolyzed biomass
liters water/ mt hydrolyzed biomass
mt excess water/ met hydrolyzed biomass
Fermentation Broth
Bactopepetone
Yeast Extract
Mutant Extract
Carbon Dioxide
k1,11
k2,11
k3,11
k4,11
k5,11
[((12.5)/(0.51*~U(0.9,0.94))]^-1)*(10^6)
(0.02 kg bactopeptone/liter broth)*(k1,11)
(0.01 kg yeast/liter broth)*(k1,11)
(0.0006 kg mutant yeast/liter broth)*(k1,11)
(0.489 kg carbon dioxide/liter broth)*(k1,11)
liters broth/ mt sugar solution
kg bactopeptone/ mt sugar solution
kg yeast/ mt sugar solution
kg mutant yeast/ mt sugar solution
kg carbon dioxide/ mt sugar solution
Dilute Ethanol
Yeast Cell Mass
k0,12
k2,12
1
0.003
liter dilute ethanol/ liter broth
kg yeast cell mass/ liter borth
Concentrated Ethanol
Waste Water
k1,13
k2,13
0.00125
1
liter concentrated ethanol/ liter dilute ethanol
liter waste water/ liter dilute ethanol
Stored Ethanol
k2,14
1
liter stored 95% ethanol/liter 95% ethanol
Ash
Water
Steam
Carbon Dioxide
k1,16
k2,16
k3,16
k4,16
0.05
5.64
5.64
3.8
mt ash/mt SG
mt water/mt SG
mt steam/mt SG
mt carbon dioxide/mt SG
Spent Steam
k1,17
1
mt spent steam/mt steam
Parameter
Nitrogen
Phosphate
Potassium
Pesticide
Land Area (Yield)
(112 kg/ha)*(k5,1)
(50 kg/ha)*(k5,1)
(112 kg/ha)*(k5,1)
(1.75 kg/ha)*(k5,1)
[~N(12.5,2.8)]
-1
Units
kg Nitrogen/mt biomass
kg Phosphate/mt biomass
kg Potassium/mt biomass
kg Pesticides/mt biomass
ha/mt biomass
Table 3 Input parameters, including constant and variable
During storage, biomass is lost due to fragile parts breaking off and due to fermentation
and breakdown of carbohydrate (Sokhansanj et al., 2006). According to Sokhansanj et al.,
storage loss is dependent on moisture content as seen in Equation 3.1 below. Moisture content is
randomly selected from the continuous uniform distribution with minimum 0.1 and maximum
0.25 (Bals et al., 2010).
11
k2,3max = 0.3792*Moisture Content + 0.0368
(3.1)
Equation 3.1 calculates the maximum dry matter loss, k2,3max. The following equation
assumes dry matter loss approaches a maximum value asymptotically, where t is time in storage
(days).
k2,3  1  [k2,3max * (1  e( t /180) )]
(3.2)
Equation 3.2 is used in the model to determine the overall switchgrass lost in storage
(k2,3). The original model neglects storage loss, setting k2,3 at a value of 1 mt/mt. Table 4 below
compares the results for the original switchgrass storage loss coefficient (k2,3) to 5,000
simulations varying the moisture content and determining k2,3 as seen above in Equations 3.1 and
3.2. The results show approximately 7% change in both land area and harvested switchgrass
requirements when accounting for switchgrass lost in storage, therefore, the model will account
for switchgrass storage loss as determined by Equations 3.1 and 3.2. Additionally, the coefficient
for switchgrass lost in storage calculated in Process 3, encompasses all storage loss. Therefore,
we neglect storage loss in Process 6 (k2,6 = 1) as seen in Table 3.
Land Area (Y5,1)
Harvest SG (Y0,1)
Mean (ha/yr)
SD (ha/yr)
Mean (mt/yr)
SD (mt/yr)
k2,3 = 1 (Original)
329,474.40
0
4,118,429.60
0
k2,3
(Randomly Selected)
354,440.01
4,272.60
4,423,167.89
51,929.13
% Change
7.04%
100%
6.89%
100%
Table 4 Effect of switchgrass storage loss on land area and harvested switchgrass
According to Dale et al., AFEX treated switchgrass will yield 550-600 mg sugar/g
biomass (1996). This range of expected sugar yield is represented by a continuous uniform
distribution in Process 10 in which each yield from 550-600 mg sugar/g biomass has the same
probability of occurring. Water and excess water in this material transformation process are
dependent on sugar yield. The coefficient values for water and excess water are determined by
multiplying the assumed rates, as seen in Table 3, by the randomly selected sugar yield.
12
The fermentation process is represented by Process 11. The theoretical yield of the
fermentation of pretreated switchgrass is 0.51 g ethanol/g sugars (Krishnan et al., 1999).
Fermentation conditions are set at 60 g Bactopeptone/L and 10 g yeast extract/L. Based on these
conditions, typical ethanol yields range from 0.46 to 0.48 g ethanol/g glucose, corresponding to
90-94% of the theoretical yield (Krishnan et al., 1999). This yield is randomly selected from a
continuous uniform distribution and k1,11 is calculated as seen in Table 3, based on the dilute
ethanol concentration of 12.5 g/L ethanol.
In the fermentation process 0.489 kg carbon
dioxide/kg sugar solution is produced (Xu et al., 2010). The coefficient values for bactopeptone,
yeast, and carbon dioxide are then determined by multiplying the assumed rates, as seen in Table
3, by the randomly selected fermentation yield.
3.3 Procedure
Using the model shown in Appendix A, a Matlab program was written to determine all
variables required to produce 95 million liters of ethanol per year. The program outputs the
response variables to an ExcelTM spreadsheet. Table 5 below lists the variables, symbols, and
units of the model. The main variables of interest are land area (Y5,1) and harvested switchgrass
(Y0,1). The program was then modified to account for the uncertainty parameters (see Appendix
C for Matlab code). The four main parameters of interest (k5,1, k2,3, k1,10, and k1,11) were varied
simultaneously to simulate all the possible outcomes of both land area and harvested switchgrass
to produce the desired amount of ethanol per year. Running multiple simulations generated a
range of land area and harvested switchgrass requirements.
In the 2010 report by Larson et al., an ethanol biorefinery annual capacity of 25 million
gallons (95 million liters) per year was assumed for the analysis. This figure was based on the
authors’ discussions with executives of Genera Energy LLC and DuPont Danisco Cellolusic
Ethanol LLC regarding the potential size of a first-generation commercial cellulosic ethanol
biorefinery (Larson et al., 2010). Therefore, the stimulus variable is set at 95 million liters of
95% ethanol per year (Y2,14).
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Then each parameter (k5,1, k2,3, k1,10, and k1,11) was varied independently while holding all
other parameters constant. This determined the effect each parameter directly has on land area
and harvested switchgrass requirements.
Linear regression was used to determine the
relationship between land area and harvested switchgrass and each parameter of interest. An
additional sensitivity analysis included independently setting each parameter to the high and low
values to create tornado diagrams for both land area and harvested switchgrass.
14
Symbol
Y0,1
Y1,1
Y2,1
Y3,1
Y4,1
Y5,1
Y0,2
Y1,2
Y1,3
Y2,3
Y0,4
Y1,6
Y2,6
Y0,7
Y1,7
Y0,8
Y1,8
Y2,8
Y3,8
Y4,8
Y0,9
Y1,9
Y2,9
Y3,9
Y0,10
Y1,10
Y2,10
Y3,10
Y4,10
Y0,11
Y1,11
Y2,11
Y3,11
Y4,11
Y1,11
Y0,12
Y1,12
Y2,12
Y0,13
Y1,13
Y2,13
Y1,14
Y0,16
Y1,16
Y2,16
Y3,16
Y4,16
Y0,17
Y1,17
Y1,20
Y1,21
Variable
Harvested Switchgrass
Nitrogen
Phosphate (P2O5)
Potassium (K20)
Pesticides
Land
Harvested Switchgrass
Hammer Milled Switchgrass
Hammer Milled Switchgrass
Switchgrass
Switchgrass Transport to Plant
Delivered Switchgrass
Delivered Switchgrass
Size Reduced Switchgrass
Delivered Switchgrass
Pretreated Biomass
Size Reduced Switchgrass
Liquid Ammonia
Recycled Ammonia
Water
Hydrolyzed Biomass
Pretreated Biomass
Enzymes
Citrate Buffer
Sugar Solution
Hydrolyzed Biomass
Spent Solids
Water
Excess Water
Fermentation Broth
Sugar Solution
Bactopeptone
Yeast Extract
Yeast
Carbon Dioxide (CO2)
Dilute Ethanol
Ferm. Broth
High Protein Bioprod
95% Ethanol
Dilute Ethanol
Waste Water
95% Ethanol
Spent Solids
Ash
Water
Steam
Carbon Dioxide (CO2)
Steam
Water
Make-up Ammonia
Make-up H20
Units
mt/yr
kg/yr
kg/yr
kg/yr
kg/yr
ha/yr
mt/yr
mt/yr
mt/yr
mt/yr
mt/yr
mt/yr
mt/yr
mt/yr
mt/yr
mt/yr
mt/yr
liter/yr
liter/yr
mt/yr
mt/yr
mt/yr
FPU/yr
liter/yr
mt/yr
mt/yr
mt/yr
liter/yr
liter/yr
liter/yr
mt/yr
kg/yr
kg/yr
kg/yr
kg/yr
liter/yr
liter/yr
kg/yr
liter/yr
liter/yr
liter/yr
liter/yr
mt/yr
mt/yr
mt/yr
mt/yr
mt/yr
mt/yr
mt/yr
liter/yr
mt/yr
Table 5 Name and symbol of variables
15
Chapter 4: Results and Discussion
4.1 Simulation Results
The four parameters of interest (k5,1, k2,3, k1,10, and k1,11) were varied simultaneously to
simulate the possible outcomes of both land area and harvested switchgrass to produce 95
million liters of ethanol per year.
For 5,000 simulations, land area (Y5,1) and harvested
switchgrass (Y0,2) is shown below in Figure 3 and Figure 4, respectively. Table 6 compares the
means and standard deviations of land area, harvested switchgrass, and the four parameters of
interest. The four parameters of interest, determined from the distributions detailed in Table 3,
are highlighted in gray in Table 6.
Land Area Y 5,1 (ha/yr)
0.7
0.6
Frequency (%)
0.5
0.4
0.3
0.2
0.1
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
2.2
6
x 10
Figure 3 Land Area (ha/yr) for varying parameters simultaneously
16
Harvested Switchgrass Y 0,1 (mt/yr)
0.2
0.18
0.16
Frequency (%)
0.14
0.12
0.1
0.08
0.06
0.04
0.02
0
4
4.1
4.2
4.3
4.4
4.5
4.6
4.7
4.8
4.9
6
x 10
Figure 4 Harvested Switchgrass (mt/yr) for varying parameters simultaneously
Mean
Standard Deviation
Land Area Y5,1 (ha/yr)
3.74E+05
1.04E+05
Harvest SG Y0,1 (mt/yr)
4.43E+06
1.35E+05
Land Area (Yield) k5,1 (ha/mt)
8.00E-02
2.00E-02
Storage Loss k2,3 (mt/mt)
9.30E-01
1.00E-02
Sugar Yield k1,10 (mt/mt)
5.70E-01
1.00E-02
Fermentation Yield k1,11 (l/mt)
3.75E+04
4.72E+02
Table 6 Results of varying all parameters simultaneously
Then each parameter (k5,1, k2,3, k1,10, and k1,11) was varied independently while holding all
other parameters constant. Table 7 below summarizes the resulting land area (ha/yr) and harvest
switchgrass (mt/yr) requirements for varying each parameter in column one independently while
holding all other parameters constant. The table shows the mean and stand deviations for 5,000
simulations. Note that the standard deviation of harvested switchgrass (Y0,1) is 0 mt/year when
varying coefficient k5,1 because land area requirement does not affect harvested switchgrass
requirement.
17
Land Area (Y5,1)
Harvest SG (Y0,1)
Mean (ha/yr)
SD (ha/yr)
Mean (mt/yr)
SD (mt/yr)
k5,1
3.77E+05
1.11E+05
4.43E+06
0.00E+00
k2,3
3.54E+05
4.25E+03
4.43E+06
5.31E+04
k1,10
k1,11
3.55E+05
3.54E+05
8.84E+03
4.45E+03
4.43E+06
4.43E+06
1.11E+05
5.56E+04
Table 7 Results of varying each parameter independently
4.2 Sensitivity Analysis
In order to assess the impact of the parametric uncertainties on the overall material
requirements for ethanol production, specifically feedstock requirements and land area for
production of feedstock, sensitivity analysis was performed through linear regression and
tornado diagrams.
Varying each parameter simultaneously produced the results seen in Figures 3 and 4
above.
To determine the effect each parameter directly has on land area and harvested
switchgrass requirements, linear regression was performed. Tables 8 and 9 below summarize the
results of the linear regression between land area and harvested switchgrass requirements,
respectively, against each parameter. Table 8 shows that crop yield, coefficient k5,1, has the
greatest slope and coefficient of determination for the linear regression and therefore, has the
greatest effect on land area requirements. Sugar yield, coefficient k1,10, has the greatest effect on
harvested switchgrass requirements as shown in Table 9 by the greatest slope and coefficient of
determination.
Slope
r2
k5,1
4.00E+06
9.87E-01
k2,3
-3.52E+05
1.40E-03
k1,10
-7.01E+05
9.40E-03
k1,11
-1.23E+01
3.10E-03
Table 8 Land area linear regression results
18
Slope
r2
k2,3
-5.00E+06
1.59E-01
k1,10
-8.00E+06
6.72E-01
k1,11
-1.11E+02
1.52E-01
Table 9 Harvested switchgrass linear regression results
A visual comparison of the relative impact of each of the uncertain parameters is
provided in Figure 5. This tornado plot shows the maximum and minimum land area (ha/year)
when independently varying switchgrass yield, storage loss, sugar yield, and fermentation yield.
Figure 6 shows the maximum and minimum harvested switchgrass when varying storage loss,
sugar yield, and fermentation yield.
Sensitivity Analysis
(k5,1) Crop Yield
(ha/mt)
20.9
4.1
(k1,10) Sugar Yield
(mt/mt)
0.60
0.55
(k1,11) Fermentation Yield
(l/mt)
0.94
0.90
(k2,3) Storage Yield
(mt/mt)
0.10
0.25
0
200,000
400,000
600,000
800,000
1,000,000
Land Area (ha/year)
Figure 5 Range of land area (ha/yr) when varying each parameter independently
19
Sensitivity Analysis
(k1,10) Sugar Yield
(mt/mt)
0.60
(k1,11) Fermentation Yield
(l/mt)
0.55
0.94
(k2,3) Storage Yield
(mt/mt)
0.90
0.25
0.10
4,100,000
4,200,000
4,300,000
4,400,000
4,500,000
4,600,000
4,700,000
Harvested Switchgrass (mt/year)
Figure 6 Range of harvested switchgrass (mt/yr) when varying each parameter independently
20
Chapter 5: Conclusion
Land area is most strongly affected by switchgrass yield. Table 7 shows that when
varying each parameter (k5,1, k2,3, k1,10, and k1,11) independently while holding all other
parameters constant, the standard deviation of land area when varying switchgrass yield (k5,1) is
approximately 110,000 ha/year, a value much greater than independently varying the other three
parameters. Land area dependence on switchgrass yield is also demonstrated by the linear
regression results between land area and each parameter shown in Table 8. The results show that
switchgrass yield (k5,1) has the greatest slope and coefficient of determination for the linear
regression. The tornado plot shown in Figure 5 also shows that switchgrass yield has the greatest
effect on land area requirements
The amount of harvested switchgrass depends on both the land area and crop yield.
However, independent of land area, harvested switchgrass has the greatest variation when
varying the sugar yield coefficient (k1,10). This is demonstrated in Table 7, in which harvested
switchgrass requirements has the largest standard deviation when varying sugar yield while
holding all other parameters constant. Both methods of sensitivity analyses also support that
harvested switchgrass has the greatest variation when changing sugar yield compared to the other
parameters. Table 9 shows that sugar yield (k1,10) has both the greatest slope and coefficient of
determination for the linear regression. The sensitivity analysis results shown in Figure 6 also
show that the range of harvested switchgrass is more dependent on sugar yield than fermentation
yield or storage yield.
Recent work at Oak Ridge National Laboratory estimates that approximately 171 million
tons of switchgrass can be produced annually in the United States (Bals et al., 2010). Putting
this in the context of this input-output model, this quantity of switchgrass can produce an average
of 3.75E+09 liters of 95% ethanol per year.
In the future, the results of this study should be expanded to assess the impact of these
uncertainties on economic and energy flows in the system. The conversion of lignocellulosic
feedstock to ethanol is an emerging technology and therefore there are many unknowns in the
21
context of long-term ethanol production. Hence, in the future, the model may be modified to
compare various ecotypes of switchgrass, nutrient inputs, and treatment methods. Additionally,
the model can be expanded as research emerges on value-added byproducts, such as extracting
proteins while simultaneously producing fermentable sugars from AFEX pretreated switchgrass
or utilizing hemicellulose, which makes up 20-25% of switchgrass, to improve the economics of
ethanol production (Keshwani and Cheng, 2009).
Sustainability of the process of converting switchgrass to ethanol depends on the
chemical and energy inputs. It is, therefore, critical that future research considers these factors in
the model. Energy consumption, greenhouse gas emissions, and petroleum displacement during
the life cycle of switchgrass-based ethanol can be incorporated into the model to evaluate the
potential of long-term, large-scale production of ethanol from this lignocellulosic biomass
(Groode, 2008).
22
References
Alizadeh, H. et al., 2005. Pretreatment of Switchgrass by Ammonia Fiber Explosion (AFEX).
Applied Biochemistry And Biotechnology, 121-124, pp.1133-1141.
Bals, B. et al., 2010. Evaluation of ammonia fibre expansion (AFEX) pretreatment for enzymatic
hydrolysis of switchgrass harvested in different seasons and locations. Biotechnology for
biofuels, 3(1), pp.1-11. Available at:
http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=2823726&tool=pmcentrez&r
endertype=abstract.
Casler, M.D., 2005. Ecotypic Variation among Switchgrass Populations from the Northern USA.
Library, 45(1), pp.338-398.
Chang, V.S. et al., 2001. Oxidative Lime Pretreatment of High-Lignin Biomass. Applied
Biochemistry And Biotechnology, 94(1), p.1=28.
Cundiff, J.S. et al., 2009. Logistic Constraints in Developing Dedicated Large-Scale Bioenergy
Systems in the Southeastern United States. Journal of Environmental Engineering,
135(11), pp.1086-1096. Available at:
http://link.aip.org/link/JOEEDU/v135/i11/p1086/s1&Agg=doi.
Dale, B. et al., 1996. Hydrolysis of lignocellulosics at low enzyme levels: Application of the
AFEX process. Bioresource Technology, 56(1), pp.111-116. Available at:
http://linkinghub.elsevier.com/retrieve/pii/0960852495001832.
Duffy, M. & Nanhou, V.Y., 2001. Costs of Producing Switchgrass for Biomass in Southern
Iowa. Iowa State University: University Extension, pp.1-12.
Ferrer, A. et al., 2002. Optimizing ammonia processing conditions to enhance susceptibility of
legumes to fiber hydrolysis: Florigraze rhizoma peanut. Applied Biochemistry and
Biotechnology, 98-100, pp.135-46. Available at:
http://www.ncbi.nlm.nih.gov/pubmed/12018243.
Groode, T.A., 2008. Biomass to Ethanol: Potential Production and Environmental Impacts.
Massachusetts Institute of Technology, Department of Mechanical Engineering, (2002),
p.185.
Gunter, L. E., Tuskan, G. A., Wullschleger, S. D., 1996. Diversity among populations of
switchgrass based on RAPD markers. Crop Sci. 36 (4), 1017–1022.
Holtzapple, M.T. et al., 1991. The Ammonia Freeze Explosion (AFEX) Process: A Practical
Lignocellulose Pretreatment. Applied Biochemistry And Biotechnology, 28/29, pp.59-74.
23
Keshwani, D.R. & Cheng, J.J., 2009. Switchgrass for Bioethanol and Other Value-Added
Applications: A Review. Bioresource Technology, 100, pp.1515-1523. Available at:
http://www.ncbi.nlm.nih.gov/pubmed/18976902.
Krishnan, M.S. et al., 1997. Fuel Ethanol Production from Lignocellulosic Sugars: Studies Using
a Genetically Engineered Saccharomyces Yeast. In ACS Symposium Series. pp. 74-92.
Krishnan, M.S., Ho, N.W.Y. & Tsao, G.T., 1999. Fermentation Kinetics of Ethanol Production
from Glucose and Xylose by Recombinant Saccharomyces. Applied Biochemistry And
Biotechnology, 77-79, pp.373-388.
Manly, Bryan F. J., 2007. Randomization, Bootstrap and Monte Carlo Methods in Biology 3rd
ed. Chapman & Hall/CRC. Boca Raton, Florida.
Miller, Ronald E. and Peter D. Blair, 2009. Input-Output Analysis: Foundations and
Extensions, 2nd edition. Cambridge University Press.
Mosier, N. et al., 2005. Features of promising technologies for pretreatment of lignocellulosic
biomass. Bioresource technology, 96(6), pp.673-86. Available at:
http://www.ncbi.nlm.nih.gov/pubmed/15588770.
Popp, M.P., 2007. Assessment of Alternative Fuel Production from Swithgrass: An Example
from Arkansas. Journal of Agricultural and Applied Economics, 39(2), pp.373-380.
Sanderson, M.A., Egg, R.P. & Wiselogel, A.E., 1997. Biomass Losses During Harvest and
Storage of Switchgrass. Biomass and Bioenergy, 12(2), pp.107-114.
Schmer, M.R. et al., 2008. Net energy of cellulosic ethanol from switchgrass. Proceedings of the
National Academy of Sciences of the United States of America, 105(2), pp.464-9.
Available at:
http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=2206559&tool=pmcentrez&r
endertype=abstract.
Seader, J.D. and Ernest J. Henley, 1990. Separation Process Principles.
Seppale, Tomi, 2008. Introduction to Monte Carlo Simulation and Modeling. Department of
Business Technology Helsinki School of Economics. Available at:
http://www.evira.fi/attachments/elaintauti_ja_elintarviketutkimus/riskinarviointi/food_saf
ety_simulation_evira.pdf
Shuler, M.L. and F. Kargi, 2002. Bioprocess Engineering: Basic Concepts 2nd ed. Prentice Hall.
Sokhansanj, S., Kumar, A. & Turhollow, A.F., 2006. Development and Implementation of
Integrated Biomass Supply Analysis and Logistsics Model (IBSAL). Biomass and
Bioenergy, 30(10), pp.838-847. Available at:
http://linkinghub.elsevier.com/retrieve/pii/S0961953406000912 [Accessed May 9, 2011].
24
Taherzadeh, M.J. & Karimi, K., 2007. Enzyme-Based Hydrolysis Processes for Ethanol from
Lignocellulosic Materials: A Review. BioResources, 2(4), pp.707-738.
Thomason, W.E. et al., 2004. Switchgrass Response to Harvest Frequency and Time and Rate of
Applied Nitrogen. Journal of Plant Nutrition, 27(7), pp.1199-1226. Available at:
http://www.informaworld.com/openurl?genre=article&doi=10.1081/PLN120038544&magic=crossref||D404A21C5BB053405B1A640AFFD44AE3 [Accessed
February 13, 2011].
Xu, Y., Isom, L. & Hanna, M., 2010. Adding Value to Carbon Dioxide from Ethanol
Fermentations. Bioresource technology, 101(10), pp.3311-9. Available at:
http://www.ncbi.nlm.nih.gov/pubmed/20110166.
25
Appendix A: Schematic Model
Sugar Yield k1,10 Varies
Uniformly
Y4,11 = Yeast
Y3,11 = Yeast
Extract
Y3,10 = Water
Y2,14 = 95%
Ethanol
Fermentation Yield
k1,11 Varies
Uniformly
P14
Y5,11 = CO2
Y1,14 = 95%
Ethanol
Y0,10 = Sugar
Soln.
n4
P10
Y4,10 =
Excess
Water
Y2,10 =
Spent
Solids
n14
Y0,13 = 95%
Ethanol
Y2,11 = Bactopeptone
P13
Y2,9 = Enzyme
n16
Y2,12 = High
Protein
Bioprod
Y0,8 =
Pretreated
Biomass
Y0,17 =
Steam
Y0,7 =
Reduced SG
n7
P7
P6
n8
Y1,20 = Make-up
Ammonia
t
Y2,8 = Liquid
Ammonia
P8
Y1,1 = N2
n13
Y3,1 = K2O
P1
Y0,2 =
Harvested
SG
`
Y0,1 =
Harvested
SG
Y1,2 =
Hammer
Milled SG
ns
Y3,8 =
Recycled
Ammonia
Tr
a
Y2,1 = P2O5
n12
26
Y1,6 =
Delivered
SG
P4
Stimulus Variable
P3
Y2,3 = SG
Uncertainty Parameters
Storage Loss k2,3
Varies Uniformly
Y5,1 = Land
n10
n11
Y1,3 =
Hammer
Milled SG
P2
Y4,1 =
Pesticides
Land Area (Yield) k5,1
Varies Normal Dist.
Y2,6 =
Delivered
SG
n9
Y1,8 =
Reduced
SG
P17
n15
Y2,13 = Waste
Water
Y1,7 =
Delivered SG
Y
0,
po 4 = S
rt
to G
Pl
an
Y1,16 =
Ash
n6
Y1,17 = Water
Y3,16 =
Steam
Y1,9 =
Pretreated
Biomass
Y4,8 = Water
P9
Y1,21 =
Make-up
Water
P16
n1
Y1,13 = Dilute
Ethanol
P12
Y3,9 = Buffer
Y2,16 =
Water
Y4,16 =
CO2
Y0,11 = Ferm.
Broth
n5
Y0,9 =
Hydrolyzed
Biomass
Y0,16 =
Spent
Solids
n2
n3
P11
Y1,10 =
Hydrolyzed
Biomass
Y0,12 = Dilute
Ethanol
Y1,12 = Ferm.
Broth
Y1,11 = Sugar
Soln.
Variables of Interest
Appendix B: Switchgrass to Ethanol Library
Process 1 – Switchgrass Cultivation
Flow Labels and Units
Y0,1 = Harvested Switchgrass, mt/ yr
Y1,1 = Nitrogen Usage, kg / yr
Y2,1 = Phosphate Usage, kg / yr
Y3,1 = Potassium Usage, kg / yr
Y4,1 = Pesticide Usage, kg / yr
Y5,1 = Land Under Cultivation, ha / yr
References
Technology Coefficients
k1,1 = kg Nitrogen / mt Biomass = (112)(k5,1)*
[1, 4, 5]
1. Casler, M.D., 2005. Ecotypic Variation among Switchgrass Populations from the Northern USA.
Library, 45(1), pp.338-398.
k2,1 = kg Phosphate / mt Biomass = (50)(k5,1)†
[3]
2. Groode, T.A., 2008. Biomass to Ethanol: Potential Production and Environmental Impacts.
Massachusetts Institute of Technology, Department of Mechanical Engineering, (2002), p.185.
k3,1 = kg Potassium / mt Biomass = (112)(k5,1)‡
[3]
k4,1 = kg Pesticides / mt Biomass = (1.75)(k5,1)§
[1]
k5,1 = Hectare / mt Biomass = Normal Distribution (μ=12.5, σ=2.8)
*k
1,1
†k
2,1
‡k
3,1
§k
4,1
3. Popp, M.P., 2007. Assessment of Alternative Fuel Production from Swithgrass: An Example from
Arkansas. Journal of Agricultural and Applied Economics, 39(2), pp.373-380.
4. Schmer, M.R. et al., 2008. Net energy of cellulosic ethanol from switchgrass. Proceedings of the
National Academy of Sciences of the United States of America, 105(2), pp.464-9. Available at:
http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=2206559&tool=pmcentrez&rendertype=abstra
ct.
[2]
5. Thomason, W.E. et al., 2004. Switchgrass Response to Harvest Frequency and Time and Rate of
Applied Nitrogen. Journal of Plant Nutrition, 27(7), pp.1199-1226. Available at:
http://www.informaworld.com/openurl?genre=article&doi=10.1081/PLN120038544&magic=crossref||D404A21C5BB053405B1A640AFFD44AE3 [Accessed February 13, 2011].
= (112 kg Nitrogen/ha)(k5,1 ha/mt) = kg Nitrogen/mt Biomass
= (50 kg Phosphate/ha)(k5,1 ha/mt) = kg Phosphate/mt Biomass
= (112 kg Potassium/ha)(k5,1 ha/mt) = kg Potassium/mt Biomass
= (1.75 kg pesticides/ha)(k5,1 ha/mt) = kg Pesticides/mt Biomass
27
Process 2 – Switchgrass Grinding
Flow Labels and Units
Y0,2 – Harvested Switchgrass, mt/yr
Y1,2 – Hammer Milled Switchgrass, mt/yr
Technology Coefficients
k1,2 = mt harvested switchgrass =
mt harvested switchgrass
References
0.9
Assume 10% of switchgrass is lost during grinding.
28
Process 3 – Switchgrass Storage
Flow Labels and Units
Y1,3 – Hammer Milled Switchgrass, mt/yr
Y2,3 – Stored Hammer Milled Switchgrass, mt/yr
Technology Coefficients
References
k2,3 = mt stored hammermilled switchgrass per yr = see below*
mt hammermilled switchgrass per yr
1. Bals, B. et al., 2010. Evaluation of ammonia fibre expansion (AFEX)
pretreatment for enzymatic hydrolysis of switchgrass harvested in different
seasons and locations. Biotechnology for biofuels, 3(1), pp.1-11. Available at:
http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=2823726&tool=pm
centrez&rendertype=abstract.
2. Sanderson, M.A., Egg, R.P. & Wiselogel, A.E., 1997. Biomass Losses
During Harvest and Storage of Switchgrass. Biomass and Bioenergy, 12(2),
pp.107-114.
3. Sokhansanj, S., Kumar, A. & Turhollow, A.F., 2006. Development and
Implementation of Integrated Biomass Supply Analysis and Logistsics Model
(IBSAL). Biomass and Bioenergy, 30(10), pp.838-847. Available at:
http://linkinghub.elsevier.com/retrieve/pii/S0961953406000912.
*K
2,3
= Moisture Content = ~U(0.1,0.25) [1, 2]
k2,3max = (0.3793)*( K2,3)+0.0368 [3]
k2,3 = mt stored hammermilled SG/mt hammermilled SG = 1-[k2,3max*(1-e(-t/180))] [3]
29
Process 6 – Switchgrass Storage
Flow Labels and Units
Y1,6 – Delivered switchgrass, mt/yr
Y2,6 – Stored Delivered switchgrass, mt/yr
Technology Coefficients
k1,6 = mt stored delivered switchgrass per yr =
mt delivered switchgrass per yr
References
1
Assume no switchgrass is lost during this stage of storage.
30
Process 7 – Size Reduction
Flow Labels and Units
Y0,7 – Reduced switchgrass, mt/yr
Y1,7 – Delivered switchgrass, mt/yr
Technology Coefficients
k1,7 = mt reduced switchgrass per yr =
mt delivered switchgrass per yr
References
0.95
Assume 5% of switchgrass is lost during size reduction.
31
Process 8 – Pretreatment
Flow Labels and Units
Y0,8 – pretreated biomass (dry weight), mt/yr
Y1,8 – reduced switchgrass, mt/yr
Y2,8– liquid ammonia, liters/yr
Y3,8– recycled ammonia, liters/yr
Y4,8 – H2O, mt/yr
Technology Coefficients
References
k1,8 = mt pretreated switchgrass per yr = 1 [2]
mt reduced biomass per yr
k2,8 = kg of liquid ammonia per yr = 1000 [1, 3, 5]
mt pretreated biomass per yr
k3,8= Liters recycled ammonia per yr = 990 [4]
mt pretreated biomass per yr
k4,8 =
mt of H2O per yr
= 0.11 [5]
mt pretreated biomass per yr
1. Alizadeh, H. et al., 2005. Pretreatment of Switchgrass by Ammonia Fiber Explosion
(AFEX). Applied Biochemistry And Biotechnology, 121-124, pp.1133-1141.
2. Bals, B. et al., 2010. Evaluation of ammonia fibre expansion (AFEX) pretreatment
for enzymatic hydrolysis of switchgrass harvested in different seasons and locations.
Biotechnology for biofuels, 3(1), pp.1-11.
3. Dale, B. et al., 1996. Hydrolysis of lignocellulosics at low enzyme levels:
Application of the AFEX process. Bioresource Technology, 56(1), pp.111-116.
Available at: http://linkinghub.elsevier.com/retrieve/pii/0960852495001832.
4. Ferrer, A. et al., 2002. Optimizing ammonia processing conditions to enhance
susceptibility of legumes to fiber hydrolysis: Florigraze rhizoma peanut. Applied
Biochemistry and Biotechnology, 98-100, pp.135-46. Available at:
http://www.ncbi.nlm.nih.gov/pubmed/12018243.
5. Holtzapple, M.T. et al., 1991. The Ammonia Freeze Explosion (AFEX) Process: A
Practical Lignocellulose Pretreatment. Applied Biochemistry And Biotechnology, 28/29,
pp.59-74.
32
Process 9 – Cellulose Hydrolysis
Flow Labels and Units
Y0,9 –hydrolyzed biomass, mt/yr
Y1,9 – pretreated biomass, mt/yr
Y2,9 – enzymes, FPU/yr
Y3,9 – buffer (citrate), L/yr
Technology Coefficients
References
k1,9 = mt hydrolyzed biomass per yr =
mt pretreated biomass per yr
k2,9 =
FPU of enzymes per yr =
mt hydrolyzed biomass per yr
k3,9 = Liters buffer (citrate) per yr =
mt hydrolyzed biomass per yr
1
[1]
5.00E+06
2.00E+04
[2, 4]
[3]
1. Bals, B. et al., 2010. Evaluation of ammonia fibre expansion (AFEX) pretreatment
for enzymatic hydrolysis of switchgrass harvested in different seasons and locations.
Biotechnology for biofuels, 3(1), pp.1-11. Available at:
http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=2823726&tool=pmcentrez
&rendertype=abstract.
2. Ferrer, A. et al., 2002. Optimizing ammonia processing conditions to enhance
susceptibility of legumes to fiber hydrolysis: Florigraze rhizoma peanut. Applied
Biochemistry and Biotechnology, 98-100, pp.135-46. Available at:
http://www.ncbi.nlm.nih.gov/pubmed/12018243.
3. Holtzapple, M.T. et al., 1991. The Ammonia Freeze Explosion (AFEX) Process: A
Practical Lignocellulose Pretreatment. Applied Biochemistry And Biotechnology, 28/29,
pp.59-74.
4. Mosier, N. et al., 2005. Features of promising technologies for pretreatment of
lignocellulosic biomass. Bioresource technology, 96(6), pp.673-86. Available at:
http://www.ncbi.nlm.nih.gov/pubmed/15588770.
33
Process 10 – Lignin Recovery/Filtration of Sugar Stream
Flow Labels and Units
Y0,10 – sugar solution, mt/yr
Y1,10 – hydrolyzed biomass, mt/yr
Y2,10 – spent solids, mt/yr
Y3,10 – wash H2O, liters/yr
Y4,10 – excess H2O, liters/yr
Technology Coefficients
mt sugar solution per yr = ~U(0.550,0.600)*
mt hydrolyzed biomass per yr
k2,10 =
mt spent solids per yr
= 0.629 [3]
mt hydrolyzed biomass per yr
k3,10 =
Liters H2O per yr
= (4900)(k1,10)†
mt hydrolyzed biomass per yr
k4,10 =
mt excess H2O per yr
= (7.258)(k1,10)‡
mt hydrolyzed biomass per yr
k1,10 =
*k
1,10 =
†k
3,1 =
References
[2]
1. Chang, S.V., W.E. Kaar, B. Burr, and M.T. Holtzapple. 2001. Simultaneous
saccharification and fermentation of lime-treated biomass. Biotechnology Letters, 23:
1327-1333.
2. Dale, B.E., C.K. Long, T.K. Pham, V.M. Esquivel, I. Rios, and V.M. Latimer. 1996.
Hydrolysis of Lignocellulosics at Low Enzyme Levels: Appication of the AFEX
Process. Bioresource Technology, 56: 111-116.
3. Ferrer, A., F.M. Byers, B. Sulbaran-de-Ferrer, B.E. Dale, and C. Aiello. 2002.
Optimizing Ammonia Processing Conditions to Enhance Susceptibility of Legumes to
Fiber Hydrolysis. Applied Biochemistry and Biotechnology, 98-100: 123-134.
Continuous Uniform Distribution from 550-600 mg sugar/g BM
(4900 liters H20/mt sugar solution)(k1,10) = liters H20/mt hydrolyzed
biomass
= (7.258 mt excess H20/mt sugar solution)(k1,10) = mt excess H20/mt
hydrolyzed biomass
‡k
4,1
34
Process 11 – Fermentation of Glucose & Xylose to Ethanol
Flow Labels and Units
Y0,11 = Broth (3g/L cell mass & 12.5g/L ethanol), L/yr
Y1,11 = Sugar Soln.(10g/L xylose, 20g/L glucose), mt/yr
Y2,11 = Bactopeptone, kg/yr
Y3,11 = Yeast Extract, kg/yr
Y4,11 = Mutant Yeast, kg/yr
Y5,11 = Carbon dioxide, kg/yr
Technology Coefficients
References
L Ferm Broth = see below*
mt Sugar Solution
k2,11 = kg Bactopepetone = (0.02)(k1,11)†
[2]
mt Sugar Solution
k3,11 = kg Yeast Extract = (0.01)(k1,11)‡
[2]
mt Sugar Solution
k4,11 = kg Mutant Yeast = (0.0006)(k1,11)§
mt Sugar Solution
k5,11 = kg Carbon dioxide = (0.489)(k1,11)** [3]
mt Sugar Solution
k1,11 =
*k
-1
6
1,11 = [(12.5 g/L ethanol)/((90-94%)(0.51 g ethanol/g glucose))] *10 =
†k
2,11 = (0.02 kg Bactopepetone/liters Broth)(k1,11) = kg Bactopepetone/mt
‡k
3,11 = (0.01 kg Yeast/liters Broth)(k1,11) = kg Yeast/mt
§k
4,11 = (0.0006 kg Yeast/liters Broth)(k1,11) = mg Mutant Yeast/mt
**k5
,11 = (0.489 kg CO2/kg sugar)(k1,11) = kg CO2/mt
1. Krishnan, M.S. et al., 1997. Fuel Ethanol Production from Lignocellulosic Sugars:
Studies Using a Genetically Engineered Saccharomyces Yeast. In ACS Symposium
Series. pp. 74-92.
2. Krishnan, M.S., Ho, N.W.Y. & Tsao, G.T., 1999. Fermentation Kinetics of Ethanol
Production from Glucose and Xylose by Recombinant Saccharomyces. Applied
Biochemistry And Biotechnology, 77-79, pp.373-388.
3. Xu, Y., Isom, L. & Hanna, M. a, 2010. Adding Value to Carbon Dioxide from
Ethanol Fermentations. Bioresource technology, 101(10), pp.3311-9. Available at:
http://www.ncbi.nlm.nih.gov/pubmed/20110166.
liter/mt
35
Process 12 – Separation of single-cell protein from broth
Flow Labels and Units
Y0,12 = Dilute Ethanol (12.5g/L ethanol), L/yr
Y1,12 = Broth (3g/L cell mass & 12.5g/L ethanol), L/yr
Y2,12 = Yeast Cell Mass, kg/yr
Technology Coefficients
k1,12 = L Dilute Ethanol =
L Broth
k2,12 = kg Yeast Cell Mass =
L Broth
References
1. Shuler, M.L. and F. Kargi, 2002. Bioprocess Engineering: Basic Concepts 2 nd ed.
Prentice Hall.
1
0.003*
*
k2,12 = (0.003 kg yeast cell mass/l dilute ethanol)(k1,12) = .003 kg/l broth
36
Process 13 – Ethanol Recovery and Purification
Flow Labels and Units
Y0,13 = Concentrated Ethanol (95% mass), L/yr
Y1,13 = Dilute Ethanol (12.5g/L or 1.25% mass ethanol), L/yr
Y2,13 = Waste Water, L/yr
Technology Coefficients
References
k1,13 = L Concentrated Ethanol = 0.00125
L Dilute Ethanol
1. Seader, J.D. and Ernest J. Henley, 1990. Separation Process Principles.
k2,13 = L Waste Water
L Dilute Ethanol
=
1*
*
k2,13 = (800 l waste water/l conc eth)*(0.00125 l conc eth) = 1 l waste
water/l dilute eth
37
Process 14 – Ethanol Storage
Flow Labels and Units
Y1,14 = Ethanol influx, L/yr
Y2,14 = Ethanol efflux, L/yr
Technology Coefficients
k2,14 = liter stored 95% ethanol per yr =
liter 95% ethanol per yr
References
1
Assume no switchgrass is lost during this stage of storage.
38
Process 16 – Switchgrass Boiler
Flow Labels and Units
Y0,16
Y1,16
Y2,16
Y3,16
Y4,16
Technology Coefficients
k1,16 =
k1,16 =
k2,16 =
k3,16 =
k3,16 =
k4,16 =
mt ash
mt switchgrass
mt ash
mt switchgrass
mt H2O
mt switchgrass
mt steam
mt switchgrass
mt steam
mt switchgrass
mt CO2
mt switchgrass
=
=
=
=
=
Spent (dry) switchgrass, mt/yr
Ash, mt/yr
H2O, mt/yr
Steam, mt/yr
Carbon Dioxide, mt/yr
References
=
0.05 [1-3]
=
0.273
[4]
=
5.64
[1-3]
=
=
5.64
[1-3]
=
11.3
[4]
11.3
[1-3]
1. Introduction to Chemical Engineering Thermodynamics, 6th ed., J.M. Smith, H.C.
Van Ness and M.M. Abbott, McGraw-Hill, 2001.
2. Elementary Principles of Chemical Processes, 3rd ed., R. Felder and R. Rousseau, J.
Wiley, 2000.
3. McLaughlin, S., J. Bouton, D. Bransby, B. Conger, W. Ocumpaugh, D. Parrish, C.
Taliaferro, K. Vogel, and S. Wullschleger. 1999. Developing switchgrass as a
bioenergy crop. p. 282-299. In: J. Janick (ed.), Perspectives on new crops and new
uses. ASHS Press, Alexandria, VA.
4. Chang, S.V., W.E. Kaar, B. Burr, and M.T. Holtzapple. 2001. Simultaneous
saccharification and fermentation of lime-treated biomass. Biotechnology Letters, 23:
1327-1333.
39
Process 17 – Steam Turbine & Generator
Flow Labels and Units
Y0,17 = Steam, mt/yr
Y1,17 = Spent steam, mt/yr
Technology Coefficients
k1,17 = mt spent steam =
mt steam
References
1
Assume steam entering this process is equal to spent steam.
40
Appendix C: Matlab Code
%______________________________________________________
%______________________________________________________
%
% FILE NAME:
Switch_ModelV5.m
%
% DATE:
July 2011
%
% NAME:
Mariel Eisenberg
%
Department of Biological and Environmental Engineering
%
Cornell University
%
Ithaca, NY 14853
%
% PURPOSE:
Function in which the main parameters of interest
%
in Processes 1, 3, 10 and 11 are all varied to
%
calculate all material flows for switchgrass conversion
%
to ethanol.
%
% REFERENCE:
Masters of Engineering Project: "Assessing the Impact of
%
Uncertainty on Ethanol Production Outcomes"
%______________________________________________________
function [y] = Switch_ModelV5(k1_1, k2_1, k3_1, k4_1, k5_1, k2_3, k1_10, k3_10, k4_10,
k1_11, k2_11, k3_11, k4_11, k5_11, Y2_14)
clc;
%
P2 - Switchgrass Grinding
k1_2 = .9;
%mt harvested SG/mt harvested SG
%
P3 - Switchgrass Storage
%k2_3 = 1;
%mt stored hammermilled SG/mt hamermilled SG
%
P6 - Swithgrass Storage
k2_6 = 1;
%mt stored delivered SG/mt delivered SG
%
P7 - Switchgrass Grinding
k1_7 = .95;
%mt reduced SG/mt delivered SG
%
P8
k1_8 =
k2_8 =
k3_8 =
k4_8 =
- Switchgrass Pretreatment
1;
%mt pretreated SG/mt reduced BM
1000;
%kg liquid ammonia/mt reduced BM
990; %l recycled ammonia/mt reduced BM
0.110;
%mt H20/mt reduced BM
%
P9
k1_9 =
k2_9 =
k3_9 =
- Cellulose Hydrolysis
1.0;
%mt hydrolyzed BM/mt pretreated BM
5.0*10^6; %FPU enzymes/mt pretreated BM
2*10^4;
%l buffer (citrate)/mt pretreated BM
41
k2_10 = 0.629;
%mt spent solids/mt hydrolyzed BM
%
P12 - Cellulose Hydrolysis
k1_12 = 1.0;
%l dilute ethanol/l borth
k2_12 = .003;
%kg/l borth
%
P13 - Separation of single-cell protein from broth
k1_13 = 0.00125; %l concentrated ethanol/l dilute ethanol
k2_13 = 1.0;
%l waste water/l dilute ethanol
%
P14 - Ethanol Storage
k2_14 = 1;
%l ethanol efflux/l ethanol influx
%
P16
k1_16 =
k2_16 =
k3_16 =
k4_16 =
- Switchgrass Boiler
.05;
%mt ash/mt switchgrass
5.64;
%mt water/mt switchgrass
5.64;
%mt steam/mt switchgrass
3.80;
%mt carbon dioxide/mt switchgrass
%
P17 - Steam Condensation
k1_17 = 1.0;
%mt spent steam/mt steam
%
Retrieve Known Stimulus Variables
% fprintf(' \r');
% Y2_14 = input('Enter Value for 95% Ethanol Produced liters/yr, Y2,14: ');
% fprintf(' \r');
%
% SET-UP A MATRIX
%
%
Mapping of Solution Vector to Material Flows
% Y0,1 Y1,1 Y2,1 Y3,1 Y4,1 Y5,1 Y0,2 Y1,2 Y1,3 Y2,3 Y0,4 Y1,6 Y2,6 Y0,7 Y1,7 Y0,8
Y1,8 Y2,8 Y3,8 Y4,8 Y0,9 Y1,9 Y2,9 Y3,9 Y0,10 Y1,10 Y2,10 Y3,10 Y4,10 Y0,11 Y1,11
Y2,11 Y3,11 Y4,11 Y5,11 Y0,12 Y1,12 Y2,12 Y0,13 Y1,13 Y2,13 Y1,14 Y0,16 Y1,16 Y2,16
Y3,16 Y4,16 Y0,17 Y1,17 Y1,20 Y1,21
% y1
y2
y3
y4
y5
y6
y7
y8
y9 y10 y11 y12 y13 y14 y15 y16 y17
y18 y19 y20 y21 y22 y23 y24
y25
y26
y27
y28
y29
y30
y31
y32
y33
y34
y35
y36
y37
y38
y39
y40
y41
y42
y43
y44
y45
y46
y47
y48
y49
y50
y51
42
A=[-k1_1
-k2_1
-k3_1
-k4_1
-k5_1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
-k1_2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
-1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
-k2_3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
-1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
-1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
k2_6 -1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
-1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
-1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
-1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
k1_7 0
0
-1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
-1
0
0
0
0
0
0
-1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
k1_8 0
k2_8 -1
k3_8 0
k4_8 0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
43
0
0
0
0
0
0
0
0
0
0
0
-1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
-1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
-1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
-1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
-1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
k1_9 0
k2_9 -1
k3_9 0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
-1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
-1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
-1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
k1_10
k2_10
k3_10
k4_10
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
-1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
-1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
-1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
-1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
-1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
-1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
k1_11
k2_11
k3_11
k4_11
k5_11
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
-1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
-1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
-1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
-1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
-1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
-1
0
%
% Check the size of the matrix
% %
% fprintf('________________________________________________\r');
% fprintf('________________________________________________\r');
% fprintf(' \r');
% fprintf('C. Properties of A matrix: \r');
% fprintf(' \r');
% [n,m] = size(A);
% fprintf(' \r');
% fprintf('
1. Number of row = %3.0f and Number of Column = %3.0f\r',n,m);
% fprintf(' \r');
% %
% % Check Whether the System of Equations has a Determinant
% %
% d=det(A);
% fprintf('
2. The Determinant of A is %8.1f 1\r',d);
% fprintf(' \r');
% fprintf('________________________________________________\r');
% fprintf(' \r');
% fprintf('
Press any key to continue!\r');
% fprintf(' \r');
% pause;
%
% Set-up b vector
%
b= [0; 0;
0;
0;
0;
0;
0;
0;
0;
0;
0;
0;
0;
0;
0;
0;
0;
0;
0;
0;
0;
0; 0;
0;
0;
0;
0;
0;
0; Y2_14;
0;
0;
0;
0;
0;
0;
0;
0;
0;
0;
0;
0;
0;
0;
0;
0;
0;
0;
0;
0;
0;];
%
% Solve Linear System of Equations
%
y=A\b;
Y0_1 = y(1); % Harvested Switchgrass mt/yr
Y1_1 = y(2); % Nitrogen kg/yr
Y2_1 = y(3); % Phosphate kg/yr
Y3_1 = y(4); % Potassium kg/yr
Y4_1 = y(5); % Pesticides kg/yr
Y5_1 = y(6); % Land ha/yr
Y0_2 = y(7); % Harvested Switchgrass mt/yr
Y1_2 = y(8); % Hammer Milled Switchgrass mt/yr
Y1_3 = y(9); % Hammer Milled Switchgrass mt/yr
Y2_3 = y(10); % Switchgrass mt/yr
Y0_4 = y(11); % Switchgrass transport to plan mt/yr
Y1_6 = y(12); % Delivered Switchgrass mt/yr
Y2_6 = y(13); % Delivered Switchgrass mt/yr
Y0_7 = y(14); % Size Reduced Switchgrass mt/yr
Y1_7 = y(15); % Delivered Switchgrass mt/yr
Y0_8 = y(16); % Pretreated Biomass mt/yr
Y1_8 = y(17); % Size Reduced mt/yr
Y2_8 = y(18); % Liquid Ammonia l/yr
Y3_8 = y(19); % Recycled Ammonia l/yr
Y4_8 = y(20); % H20 mt/yr
Y0_9 = y(21); % Hydrolyzed Biomass mt/yr
Y1_9 = y(22); % Pretreated Biomass mt/yr
Y2_9 = y(23); % Enzymes FPU/yr
Y3_9 = y(24); % Citrate Buffer l/yr
Y0_10 = y(25); % Sugar Solution mt/yr
Y1_10 = y(26); % Hydrolyzed Biomass mt/yr
Y2_10 = y(27); % Spent Solids mt/yr
Y3_10 = y(28); % H20 l/yr
44
Y4_10
Y0_11
Y1_11
Y2_11
Y3_11
Y4_11
Y5_11
Y0_12
Y1_12
Y2_12
Y0_13
Y1_13
Y2_13
Y1_14
Y0_16
Y1_16
Y2_16
Y3_16
Y4_16
Y0_17
Y1_17
Y1_20
Y1_21
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
y(29);
y(30);
y(31);
y(32);
y(33);
y(34);
y(35);
y(36);
y(37);
y(38);
y(39);
y(40);
y(41);
y(42);
y(43);
y(44);
y(45);
y(46);
y(47);
y(48);
y(49);
y(50);
y(51);
% Excess H20 l/yr
% Ferm. Broth (3g/L cell mass & 12.5 g/l ethanol) l/yr
% Sugar Solution (10g/L xylose & 20.0 g/l glucose) mt/yr
% Bactopepton kg/yr
% Yeast Extract kg/yr
% Yeast kg/yr
% CO2 kg/yr
% Dilute Ethanol l/yr
% Ferm. Broth (3g/L cell mass & 12.5 g/l ethanol) l/yr
% High Protein Bioprod kg/yr
% 95 Ethanol l/yr
% Dilute Ethanol l/yr
%Waste Water l/yr
%95 Ethanol l/yr
%Spent Solids mt/yr
%Ash mt/yr
%H20 mt/yr
%Steam mt/yr
%CO2 mt/yr
%Steam mt/yr
%H20 mt/yr
%Make-up Ammonia l/yr
%Make-up H20 mt/yr
%______________________________________________________
%______________________________________________________
45
%______________________________________________________
%
% FILE NAME:
Vary_Parameters.m
%
% DATE:
July 2011
%
% NAME:
Mariel Eisenberg
%
Department of Biological and Environmental Engineering
%
Cornell University
%
Ithaca, NY 14853
%
% PURPOSE:
To call function Switch_ModelV5 in which the main
%
parameters of interest in Processes 1, 3, 10 and 11
%
are all varied to calculate all material flows for
%
switchgrass conversion to ethanol.
%
% REFERENCE:
Masters of Engineering Project: "Assessing the Impact of
%
Uncertainty on Ethanol Production Outcomes"
%______________________________________________________
clear all;
%Clear All
clc;
%Clear Command Window Display
s = input('Enter the number of simulations, s: ');
Y2_14 = input('Enter Value for 95% Ethanol Produced liters/yr, Y2,14: ');
for n=1:s
%
P1 - Switchgrass Production
%
%Select Crop Yield from Normal Distribution ~N(12.5, 2.8) (mt Biomass/ha)
k5_1(n) = (normrnd(12.5,2.8))^-1;
%ha/mt Biomass
%Fixed application rate of Nitrogen
K1_1= 112; %kg N/ha
k1_1(n)= (K1_1)*k5_1(n);
%kg N/mt
%Fixed application rate of Phosphate
K2_1 = 50; % kg Phosphate/ha
k2_1(n)= (K2_1)*k5_1(n);
%kg P/mt
%Fixed application rate of Potassium
K3_1 = 112; % kg Potassium/ha
k3_1(n)= (K3_1)*k5_1(n);
%kg K/mt
%Fixed application rate of Pesticides
K4_1 = 1.75; % kg Pesticides/ha
k4_1(n)= (K4_1)*k5_1(n);
%kg Pesticides/mt
%
P3 - Switchgrass Storage
K2_3(n) = unifrnd(0.1,0.25);
%(continuous uniform distribution) %moisture
content
k2_3_max(n) = 0.3793*K2_3(n)+0.0368;
%max dry matter loss
t_stor= 200;
%time in days
k2_3(n)= 1-((k2_3_max(n))*(1-exp(-t_stor/180)));
%mt stored hammermilled SG/mt
hamermilled SG at time of storage
46
%
P10 - Lignin recovery/filtration of sugar stream
k1_10(n) = unifrnd(0.550,0.600);
%(continuous uniform distribution)
solution/mt hydrolyzed BM
K3_10 = 4900;
%l water/mt sugar solution
k3_10(n) = (K3_10)*(k1_10(n));
%mt spent solids/mt hydrolyzed BM
K4_10 = 7.258;
%mt excess water/mt sugar solution
k4_10(n) = (K4_10)*(k1_10(n));
%mt excess water/mt hydrolyzed BM
mt sugar
%
P11 - Fermentation of sugar stream
%
K1_11(n) = unifrnd(0.9,0.94);
%(continuous uniform distribution), theoretical
yield = 0.51 g ethanol/g glucose)
k1_11(n) = (((12.5)/(0.51*K1_11(n)))^-1)*(10^6);
%liters Broth/ mt sugar
solution
K2_11 = 0.02;
%kg Bactopepetone/liters Broth
k2_11(n) = (K2_11)*(k1_11(n));
%kg Bactopepetone/mt sugar solution
K3_11 = 0.01;
%kg Yeast/liters Broth
k3_11(n) = (K3_11)*(k1_11(n));
%kg Yeast/mt sugar solution
K4_11 = 0.0006;
%kg Yeast/liters Broth
k4_11(n) = (K4_11)*(k1_11(n));
%kg Yeast/mt sugar solution
K5_11 = 0.489;
%kg CO2/kg sugar solution
k5_11(n) = (K5_11)*(k1_11(n));
%kg CO2/mt sugar solution
[y(:,n)] = Switch_ModelV5(k1_1(n), k2_1(n), k3_1(n), k4_1(n), k5_1(n), k2_3(n),
k1_10(n), k3_10(n), k4_10(n),k1_11(n), k2_11(n), k3_11(n), k4_11(n), k5_11(n), Y2_14);
M=[transpose(k5_1) transpose(k2_3) transpose(k1_10) transpose(k1_11)
transpose(y(1,:))]; %creates matrix for linear regression
end
%
%
%
%
%Send Results to Excel Spreadsheet titled 'SGResults'
Run=[1:s];
xlswrite('SGResults',Run, 'Results', 'D1')
xlswrite('SGResults',y, 'Results', 'D2');
fprintf(' \r');
fprintf('________________________________________________\r');
fprintf('________________________________________________\r');
fprintf(' \r');
fprintf('RESULTS\r');
fprintf(' \r');
y5_1= y(6,:);
%land area (ha)
max(y5_1);
min(y5_1);
mean(y5_1);
std(y5_1);
fprintf('y(6) = Y5,1 - Average Land Area = %8.2f ha/yr \n',mean(y5_1));
fprintf('y(6) = Y5,1 - Standard Deviation Land Area = %8.2f ha/yr \n',std(y5_1));
y0_1= y(1,:);
max(y0_1);
min(y0_1);
mean(y0_1);
std(y0_1);
%harvested switchgrass (mt/yr)
47
fprintf('y(1) = Y0,1
fprintf('y(1) = Y0,1
\n',std(y0_1));
fprintf('k5,1
fprintf('k5,1
- Average Harvested switchgrass = %8.2f mt/yr \n',mean(y0_1));
- Standard Deviation Harvested switchgrass = %8.2f mt/yr
- Average Crop Yield = %8.2f ha/mt \n',mean(k5_1));
- Standard Deviation Crop Yield = %8.2f ha/mt \n',std(k5_1));
fprintf('k2,3 - Average Switchgrass Storage Loss = %8.2f mt/mt \n',mean(k2_3));
fprintf('k2,3 - Standard Deviation Switchgrass Storage Loss = %8.2f mt/mt
\n',std(k2_3));
fprintf('k1,10
fprintf('k1,10
- Average Sugar Yield = %8.2f mt/mt \n',mean(k1_10));
- Standard Deviation Sugar Yield = %8.2f mt/mt \n',std(k1_10));
fprintf('k1,11
fprintf('k1,11
- Average Fermentation Yield = %8.2f l/mt \n',mean(k1_11));
- Standard Deviation Fermentation Yield = %8.2f l/mt \n',std(k1_11));
% %Dispay results from single simulation
%
fprintf('_________________________________________________\r');
fprintf(' \r');
fprintf('RESULTS FROM SINGLE RUN\r');
fprintf(' \r');
fprintf('y(1) = Y0,1 - Harvested switchgrass = %8.1f mt/yr \n',y(1));
fprintf('y(2) = Y1,1 - Nitrogen = %8.1f kg/yr\n',y(2));
fprintf('y(3) = Y2,1 - P2O5 - Phosphate = %8.1f kg/yr\n',y(3));
fprintf('y(4) = Y3,1 - K2O - Potassium = %8.1f kg/yr\n',y(4));
fprintf('y(5) = Y4,1 - Pesticides = %8.1f kg/yr\n',y(5));
fprintf('y(6) = Y5,1 - Land = %8.1f ha/yr\n',y(6));
fprintf('y(7) = Y0,2 - Harvested switchgrass = %8.1f mt/yr\n',y(7));
fprintf('y(8) = Y1,2 - Hammer Milled switchgrass = %8.1f mt/yr\n',y(8));
fprintf('y(9) = Y1,3 - Hammer Milled switchgrass = %8.1f mt\n',y(9));
fprintf('y(10) = Y2,3 - Switchgrass =%8.1f mt/yr\n',y(10));
fprintf('y(11) = Y0,4 - Switchgrass transport to plant =%8.1f mt/yr\n',y(11));
fprintf('y(12) = Y1,6 - Delivered switchgrass = %8.1f mt/yr\n',y(12));
fprintf('y(13) = Y2,6 - Delivered switchgrass = %8.1f mt/yr\n',y(13));
fprintf('y(14) = Y0,7 - Size reduced switchgrass = %8.1f mt/yr\n',y(14));
fprintf('y(15) = Y1,7 - Delivered switchgrass = %8.1f mt/yr\n',y(15));
fprintf('y(16) = Y0,8 - Pretreated biomass = %8.1f mt/yr\n',y(16));
fprintf('y(17) = Y1,8 - Size reduced = %8.1f mt/yr\n',y(17));
fprintf('y(18) = Y2,8 - Liquid ammonia = %8.1f kg/yr\n',y(18));
fprintf('y(19) = Y3,8 - Recycled ammonia = %8.1f 1/yr\n',y(19));
fprintf('y(20) = Y4,8 - H2O = %8.1f mt/yr\n',y(20));
fprintf('y(21) = Y0,9 - Hydrolyzed biomass = %8.1f mt/yr\n',y(21));
fprintf('y(22) = Y1,9 - Pretreated biomass = %8.1f mt/yr\n',y(22));
fprintf('y(23) = Y2,9 - Enzymes = %8.3g FPU/yr\n',y(23));
fprintf('y(24) = Y3,9 - Citrate buffer = %8.1f l/yr\n',y(24));
fprintf('y(25) = Y0,10 - Sugar solution = %8.1f mt/yr\n',y(25));
fprintf('y(26) = Y1,10 - Hydrolyzed biomass = %8.1f mt/yr\n',y(26));
fprintf('y(27) = Y2,10 - Spent solids = %8.1f mt/yr\n',y(27));
fprintf('y(28) = Y3,10 - H20 = %8.1f l/yr\n',y(28));
fprintf('y(29) = Y4,10 - Excess H20 = %8.1f l/yr\n',y(29));
fprintf('y(30) = Y0,11 - Ferm. broth (3g/L cell mass & 12.5 g/l ethanol) = %8.1f
1/yr\n',y(30));
fprintf('y(31) = Y1,11 - Sugar solution (10g/L xylose & 20.0 g/l glucose) = %8.1f
mt/yr\n',y(31));
fprintf('y(32) = Y2,11 - Bactopeptone = %8.1f kg/yr\n',y(32));
fprintf('y(33) = Y3,11 - Yeast extract = %8.1f kg/yr\n',y(33));
fprintf('y(34) = Y4,11 - Yeast = %8.1f kg/yr\n',y(34));
fprintf('y(35) = Y5,11 - CO2 = %8.1f kg/yr\n',y(35));
fprintf('y(36) = Y0,12 - Dilute ethanol = %8.1f 1/yr\n',y(36));
48
fprintf('y(37) = Y1,12 - Ferm. broth (3g/L cell mass & 12.5 g/l ethanol) = %8.1f
1/yr\n',y(37));
fprintf('y(38) = Y2,12 - High Protein Bioprod = %8.1f kg/yr\n',y(38));
fprintf('y(39) = Y0,13 - 95 ethanol = %8.1f 1/yr\n',y(39));
fprintf('y(40) = Y1,13 - Dilute ethanol = %8.1f 1/yr\n',y(40));
fprintf('y(41) = Y2,13 - Waste Water = %8.1f 1/yr\n',y(41));
fprintf('y(42) = Y1,14 - 95 ethanol = %8.1f 1/yr\n',y(42));
fprintf('y(43) = Y0,16 - Spent solids = %8.1f mt/yr\n',y(43));
fprintf('y(44) = Y1,16 - Ash = %8.1f mt/yr\n',y(44));
fprintf('y(45) = Y2,16 - H2O = %8.1f mt/yr\n',y(45));
fprintf('y(46) = Y3,16 - Steam = %8.1f mt/yr\n',y(46));
fprintf('y(47) = Y4,16 - CO2 = %8.1f mt/yr\n',y(47));
fprintf('y(48) = Y0,17 - Steam = %8.1f mt/yr\n',y(48));
fprintf('y(49) = Y1,17 - H2O = %8.1f mt/yr\n',y(49));
fprintf('y(50) = Y1,20 - Make-up Ammonia = %8.1f l/yr\n',y(50));
fprintf('y(51) = Y1,21 - Make-up H2O = %8.1f mt/yr\n',y(51));
fprintf('________________________________________________\r');
fprintf('________________________________________________\r');
fprintf(' \r');
figure(1)
hist(y(1,:));
title('Harvested Switchgrass Y_0_,_1 (mt/yr)');
% figure(2)
% hist(y(2,:));
% title('Nitrogen Y_1_,_1 (kg/yr)');
%
% figure(3)
% hist(y(3,:));
% title('Phosphate Y_2_,_1 (kg/yr)');
%
% figure(4)
% hist(y(5,:));
% title('Potassium Y_3_,_1 (kg/yr)');
%
% figure(5)
% hist(y(5,:));
% title('Pesticides Y_4_,_1 (kg/yr)');
%
figure(6)
hist(y(6,:));
title('Land Area Y_5_,_1 (ha/yr)');
%
% figure(7)
% hist(k2_3);
% title('Switchgrass Storage Loss k_2_,_3 (mt/mt)');
%
% figure(7)
% hist(y(8,:));
% title('Hammermilled Switchgrass Y_1_,_2 (mt/yr)');
%
% figure(8)
% hist(y(14,:));
% title('Reduced Switchgrass Y_0_,_7 (mt/yr)');
%
% figure(9)
% hist(y(21,:));
% title('Hydrolyzed Biomass Y_0_,_9 (mt/yr)');
%
% figure(10)
% hist(y(25,:));
49
%
%
%
%
%
title('Sugar Solution Y_0_,_10 (mt/yr)');
figure(11)
hist(y(30,:));
title('Ferm Broth Y_0_,_11 (l/yr)');
50
51