cost evaluation of a novel 5-kw diesel-powered solid...
TRANSCRIPT
COST EVALUATION OF A NOVEL 5-KW DIESEL-POWERED
FUEL CELL AUXILIARY POWER UNIT (APU)
Chakradhar Pillala
Problem Report submitted to the College of Engineering and Mineral Resources
at West Virginia University in partial fulfillment of the requirements
for the degree of
Master of Science in
Industrial Engineering
Approved by
Robert C. Creese, Ph.D., Chair Bhaskaran Gopalakrishnan, Ph.D, Majid Jaraiedi, Ph.D.,
Department of Industrial and Management Systems Engineering
Morgantown, West Virginia 2009
Keywords: Solid Oxide Fuel Cell, Auxiliary Power Unit, Cost Estimation, PRICE software, Cost Estimating Relationships
ABSTRACT
Cost Evaluation of a Novel 5-kW Diesel-Powered Fuel Cell Auxiliary Power Unit (APU)
Idling heavy-duty trucks result in poor fuel consumption and harmful emissions. The Auxiliary
Power Unit (APU) is one of the methods to reduce idling. The Solid Oxide Fuel Cell (SOFC)
APU can provide auxiliary power to the trucks during idling. The cost estimation for mass
manufacturing the APU was performed by two approaches. The PRICE software, a parametric
approach was adopted to obtain a top-down cost estimate. The results obtained from PRICE
software were in accordance with the earlier results available. The Cost Estimating Relationship
(CER) model approach consisted of developing cost estimating relationships with process
parameters like temperature, power density, transfer area, etc. and using the improvement rate
effects obtained from the PRICE cost models, to estimate the cost of the APU. Sensitivity
analysis was performed on the CER model results and the CER model results as well as the
sensitivity analysis conformed to the earlier findings from the available references. A Visual
Basic model has been developed, which is a user interface and allows the user to input the values
for the various parameters and obtain the cost estimate. The VB model was based on the CER’s
developed and also used the improvement rates from the PRICE models.
ACKNOWLEDGEMENTS
Completing this problem report, although was a challenge for me, I would not have
achieved it without the support, inspiration, encouragement and contribution of many people.
First of all, I would like to take this opportunity to express my profound thanks to my advisor Dr.
Robert Creese for his excellent mentorship throughout my stay and studies at West Virginia
University. Without his guidance, I would have never completed this research work.
I would like to express my gratitude to Dr. Bhaskaran Gopalakrishnan and Dr. Majid
Jaraiedi for being my committee members and for their valuable suggestions in directing my
efforts to present my work as a complete report.
I would like to thank NETL, Morgantown, for giving me the opportunity and providing
the grant to work on this research project. Their inputs have been immensely helpful in completing
this research.
I would like to express my profound gratefulness to my parents who have always
supported my vision and have given me timely guidance, support, freedom and inspiration until
now in every aspect of my life. My wife, Vijaya and her family, have been a wonderful source
of inspiration to me in finishing my Masters and I would like to express my gratitude for their
support.
I would also like to express my special thanks to my friends Raja A. Prem Kumar,
Deepak Gupta, Subodh Chaudhari, Ashutosh Nandeshwar, Srinivas Seggum, Praveen Kumar
Kavipurapu and Naveen Kumar Alamanda who have contributed in countless ways, in
completing my studies and thesis.
I would like to mention special thanks to Michelle Moore for editing my document.
Finally, I would like to dedicate my work to my recently expired grandmother.
iii
Table of Contents ABSTRACT.................................................................................................................................... ii
ACKNOWLEDGEMENTS........................................................................................................... iii
Table of Contents........................................................................................................................... iv
List of Figures ................................................................................................................................ vi
List of Tables ............................................................................................................................... viii
List of Nomenclature ...................................................................................................................... x
1. Introduction................................................................................................................................ 1
1.1. Background to the Project................................................................................................... 1
1.1.1. Fuel Cells ..................................................................................................................... 1
1.1.2. Fuel Cells for Heavy-Duty Trucks............................................................................... 5
1.2. US DOE Auxiliary Power Unit (APU)............................................................................... 8
1.3. Problem Statement .............................................................................................................. 9
2. Cost Estimation Methodologies............................................................................................... 10
2.1. Estimating Approaches ..................................................................................................... 10
2.1.1. Bottom-Up Estimating ............................................................................................... 10
2.1.2. Top-Down Estimating................................................................................................ 11
2.2. Estimating Classes and Accuracy ..................................................................................... 13
2.2.1. Three-Level Classification System............................................................................ 13
2.2.2. Five-Level Classification System .............................................................................. 14
2.3. Cost Estimation Methodologies Summary ....................................................................... 17
3. Literature Review of Cost Data for the Solid Oxide Fuel Cell Auxiliary Power Unit ............ 18
4. Cost Model Results .................................................................................................................. 23
4.1. PRICE Models .................................................................................................................. 23
4.1.1. PRICE Results Discussion......................................................................................... 23
4.1.2. PRICE Results For Year 2009 .................................................................................... 29
4.1.3. PRICE Model Assumptions........................................................................................ 33
4.1.4. Key Parameters Used.................................................................................................. 36
4.1.5. PRICE Model Results for 10,000 units....................................................................... 39
4.2 Traditional Cost Models ..................................................................................................... 56
4.2.1. CER Model Results..................................................................................................... 56
iv
4.2.2. CER Results For Year 2009........................................................................................ 59
4.2.3. Cost Estimating Relationships .................................................................................... 62
4.2.4. Discussion of the Cost Estimating Relationships ....................................................... 67
4.2.5. Improvement Rates ..................................................................................................... 68
4.2.6. First Unit Cost Calculations........................................................................................ 78
4.2.7. Sensitivity Analysis .................................................................................................... 80
4.3. Visual Basic Model........................................................................................................... 83
5. Summary and Conclusions ...................................................................................................... 87
5.1. Summary of the Cost Models developed .......................................................................... 87
5.2. Future Research ................................................................................................................ 89
6. Bibliography ............................................................................................................................ 91
7. Appendix - Visual Basic Code.................................................................................................. 94
v
List of Figures Figure 1.1. Operation of a Solid Oxide Fuel Cell [28] .................................................................. 4
Figure 1.2. Tubular Solid Oxide Fuel Cell Design and Stack [29]................................................ 4
Figure 1.3. Planar Solid Oxide Fuel Cell Design [29]................................................................... 5
Figure 1.4. A Class 8 Truck [4] ..................................................................................................... 6
Figure 1.5. Estimated Idle Fuel Usage per Year, Class 8 Truck [5] .............................................. 7
Figure 1.6. Auxiliary Power Unit Fuel Cell System Diagram....................................................... 9
Figure 4.1. Unit Cost Versus Quantity (semi-log scale)............................................................. 27
Figure 4.2. Unit Cost Versus Quantity (log-log scale) ............................................................... 28
Figure 4.3. Cost/kW versus Quantity (semi-log scale) ............................................................... 28
Figure 4.4. Cost/kW versus Quantity (log-log scale) .................................................................. 29
Figure 4.5. PRICE Model Input Format for APU....................................................................... 33
Figure 4.6. PRICE input values for Manufacturing Complexity Parameter versus Platform..... 37
Figure 4.7. PRICE input values for MPI Parameter versus Quantity ......................................... 38
Figure 4.8. Development Category Cost..................................................................................... 52
Figure 4.9. Production Category Cost......................................................................................... 52
Figure 4.10. Total Category Cost................................................................................................ 53
Figure 4.11. Development Component Cost............................................................................... 53
Figure 4.12. Production Component Cost................................................................................... 54
Figure 4.13. Total Component Cost............................................................................................ 54
Figure 4.14. LM Breakout .......................................................................................................... 55
Figure 4.15. Distribution of Effort.............................................................................................. 55
Figure 4.16. Plot of the scroll compressor cost data .................................................................... 64
Figure 4.17. Exergy Heat Exchanger Cost Data [25] .................................................................. 66
Figure 4.18. Depiction of Slope Calculations.............................................................................. 69
Figure 4.19. Combustor Plot to Calculate the Improvement Rates ............................................. 70
Figure 4.20. ZnO Bed Plot to Calculate the Improvement Rates ................................................ 71
Figure 4.21. ATR Plot to Calculate the Improvement Rates ....................................................... 72
Figure 4.22. Air Compressor Plot to Calculate the Improvement Rates ..................................... 73
Figure 4.23. Fuel Cell Stack Plot to Calculate the Improvement Rates ...................................... 74
vi
Figure 4.24. Air Pre-heater Plot to Calculate the Improvement Rates ........................................ 75
Figure 4.25. Steam Generator Plot to Calculate the Improvement Rates .................................... 76
Figure 4.26. Exhaust Condenser Plot to Calculate the Improvement Rates ................................ 77
Figure 4.27. Sensitivity Plot of APU Parameters ........................................................................ 82
Figure 4.28. Visual Basic Input Form for Fuel Cell Stack and Compressor ............................... 83
Figure 4.29. Input Form for Heat Exchangers ............................................................................. 84
Figure 4.30. Input Form for Combustor, ZnO Bed, and ATR..................................................... 85
Figure 4.31. Input Form for the Fuel Pump and the Water Pump ............................................... 86
Figure 4.32. Visual Basic Results Form for the SOFC APU at 500,000-units............................ 86
vii
List of Tables Table 1.1. US Truck Classes.......................................................................................................... 6
Table 1.2. Emissions for a Heavy-duty Truck While Idling and When an APU is Used [6] ........ 7
Table 2.1. Three-Level Classification System............................................................................. 13
Table 2.2. Cost Estimate Classification Matrix for Process Industries (AACE, International)... 15
Table 2.3. Information Required for Specific Estimate Class (AACE International) ................. 16
Table 3.1. Five Cases as Considered by the ADL [17] Report for a 5 kW SOFC APU.............. 19
Table 3.2. Specifications and Costs of the Various Cell Manufacturers [18].............................. 20
Table 3.3. Solid Oxide Fuel Cell Stack Costs with Ceramic and Metallic Interconnect Materials
[19]........................................................................................................................................ 20
Table 3.4. Material costs for Perovskite Production [20] ............................................................ 21
Table 3.5. Unit Prices and Theoretical Densities of Raw Materials [21] .................................... 22
Table 4.1. PRICE I Results .......................................................................................................... 25
Table 4.2. PRICE II Results......................................................................................................... 26
Table 4.3. Unit Cost and Cost per kW Obtained from PRICE I................................................. 27
Table 4.4. PPI Values [29]........................................................................................................... 30
Table 4.5. 2009 PRICE I Results ................................................................................................. 31
Table 4.6. 2009 PRICE II Results................................................................................................ 32
Table 4.7. Specifications for the Components of the Auxiliary Power Unit .............................. 35
Table 4.8. Manufacturing Complexity Factors for Various Battery Types ................................ 36
Table 4.9. Manufacturing Process Index Values in PRICE at the Maximum Quantity for Index
Value ..................................................................................................................................... 37
Table 4.10. Values of MPI Parameter Using the New Relationship .......................................... 38
Table 4.11. Values of MPI Parameter Using the New Relationships......................................... 39
Table 4.12. PRICE Input for 10,000 Unit Base Case .................................................................. 40
Table 4.13. Assembly Cost .......................................................................................................... 41
Table 4.14. Combustor Cost ........................................................................................................ 42
Table 4.15. ZnO Bed Cost .......................................................................................................... 43
Table 4.16. Auto Thermal Reformer Cost ................................................................................... 44
Table 4.17. Air Compressor Cost ................................................................................................ 45
Table 4.18. Fuel Pump Cost......................................................................................................... 46
viii
Table 4.19. Water Pump Cost ...................................................................................................... 47
Table 4.20. Fuel Cell Stack Cost ................................................................................................. 48
Table 4.21. Cathode Air Pre-heater Cost ..................................................................................... 49
Table 4.22. Steam Generator Cost ............................................................................................... 50
Table 4.23. Exhaust Condenser Cost ........................................................................................... 51
Table 4.24. CER Model I Results ................................................................................................ 57
Table 4.25. CER Model II Results............................................................................................... 58
Table 4.26. 2009 CER Model I Results ....................................................................................... 60
Table 4.27. 2009 CER Model II Results...................................................................................... 61
Table 4.28. Manufacturing Cost Data for Combustor [24].......................................................... 62
Table 4.29. Combustor Parameters and Total Cost Data [24] ..................................................... 63
Table 4.30. Air Compressor Cost Data........................................................................................ 64
Table 4.31. ADL Fuel Cell Stack Cost Data [17] ........................................................................ 65
Table 4.32. Steam Generator Cost Data [25]............................................................................... 66
Table 4.33. Summary of the CER’s Developed for SOFC Components and the Improvement
Rates used ............................................................................................................................. 67
Table 4.34. PRICE II Results for Combustor .............................................................................. 69
Table 4.35. PRICE II Results for ZnO Bed ................................................................................. 70
Table 4.36. PRICE II Results for ATR........................................................................................ 71
Table 4.37. PRICE II Results for Air Compressor ...................................................................... 72
Table 4.38. PRICE II Results for Fuel Cell Stack ....................................................................... 73
Table 4.39. PRICE II Results for Air Pre-heater ......................................................................... 74
Table 4.40. PRICE II Results for Steam Generator ..................................................................... 75
Table 4.41. PRICE II Results for Exhaust Condenser ................................................................. 76
Table 4.42. Variation of Parameters for Sensitivity Analysis ...................................................... 81
Table 4.43. Sensitivity Data......................................................................................................... 81
Table 5.1. Manufacturing Cost for 500,000 APU’s Obtained from Various Models (Base Year
2003) ..................................................................................................................................... 90
ix
List of Nomenclature AACE Association for the Advancement of Cost Engineering
ADL Arthur D. Little
AFC Alkali Fule Cell
APU Auxiliary Power Unit
ATR Auto Thermal Reformer
CCHP Combined Cooling, Heating and Power Application
CER Cost Estimating Relationship
DMFC Direct Methanol Fuel Cell
DOE US Department of Energy
DTI UK Department of Trade and Industry
MCFC Molten Carbonate Fuel Cell
NETL National Energy Technology Laboratory
PAFC Phosphoric Acid Fuel Cell
PEMFC Proton Exchange Membrane Fuel Cell
PPI Producer’s Price Index
PRICE Parametric Review of Information for Costing and Evaluation
RFC Regenerative Fuel Cell
SOFC Solid Oxide Fuel Cell
x
1. Introduction 1.1. Background to the Project
Heavy-duty diesel trucks idle for a significant amount of time because of various
restrictions imposed on their period of operation. During idling, the engine is running and diesel
fuel is being wasted. Diesel fuel produces particulate matter and other harmful emissions that
increase greenhouse effects in the earth’s atmosphere. To prevent burning fuel during idling, the
United States Department of Energy (DOE) is promoting the concept of Auxiliary Power Units
(APU’s) to provide power to trucks when idling. These units would generate the electricity
required for all the truck accessories during idling and thus obviate the need for engine usage.
There are different types of fuel cells to provide power to the APU. This project investigated
Solid Oxide Fuel Cells (SOFC) to provide power to the APU. By using the APU, the fuel usage
and the amount of harmful by-products can be reduced. Cost models to estimate the cost to mass
manufacture the APU were investigated in this study.
1.1.1. Fuel Cells
Fuel cells have existed for more than 150 years, but they became the subject of intense
research and development only after World War II. Fuel cells hold promise for a low-cost,
highly efficient method of power generation. They generate electricity in a cleaner fashion,
reducing harmful emissions, and are more environmental friendly. Fuel cells generate electricity
by a chemical reaction. A fuel cell has two electrodes (anode and cathode) and an electrolyte
that carries the electrically charged particles from one electrode to the other. Hydrogen fuel is
supplied to the fuel cell at the anode and oxygen is fed at the cathode. The hydrogen atoms at
the anode separate into protons (positive ions) and electrons in the presence of a catalyst. The
electrolyte conducts the positively charged hydrogen ions through it, while the electrons reach
the cathode through an external load providing electric power. At the cathode, the hydrogen
ions, electrons, and oxygen atoms combine to produce water. The electricity is generated by a
chemical reaction and water is a byproduct. A single fuel cell generates a tiny amount of direct
current (DC), and many fuel cells are usually assembled into a stack to provide sufficient current.
There are different types of fuel cells that generate electricity, but all of them more or less follow
the same principle. Some of the common types of fuel cells are:
1
1. Proton Exchange Membrane Fuel Cells (PEMFC)
2. Alkali Fuel Cells (AFC)
3. Phosphoric Acid Fuel Cells (PAFC)
4. Direct Methanol Fuel Cells (DMFC)
5. Regenerative Fuel Cells (RFC)
6. Molten Carbonate Fuel Cells (MCFC)
7. Solid Oxide Fuel Cells (SOFC)
The type of fuel cell used depends on the particular application. The Proton Exchange
Membrane, the Alkali, the Phosphoric Acid and the Direct Methanol fuel cells operate at low
temperatures. The Solid Oxide and Molten Carbonate fuel cells operate at high temperatures and
are candidates for Combined Cooling, Heating, and Power (CCHP) applications.
Proton Exchange Membrane Fuel Cells work with a polymer membrane as the electrolyte
to allow the flow of positively charged hydrogen ions and stop the electron flow through it.
They operate at a temperature of about 80 degrees centigrade. These fuel cells require an
external reformer to reform fuels like gasoline, methanol, etc., and supply hydrogen to the anode
of the fuel cell because of the low operating temperature. They are suitable for applications
requiring quick start-up times such as in light-duty vehicles.
Alkali Fuel Cells use a solution of potassium hydroxide in water as the electrolyte. The
hydroxide ions from the cathode pass through the electrolyte and reach the anode where they
combine with the hydrogen atoms and produce water and electrons. These electrons reach the
cathode through an external circuit, generating electric power, and combine with water and
oxygen atoms to produce more hydroxide ions. They operate at temperatures of about 200
degrees centigrade. They also need an external reformer to supply pure hydrogen to the anode of
the fuel cell and are mainly used for space applications.
The Phosphoric Acid Fuel Cells were the first type considered commercially viable.
They use phosphoric acid as the electrolyte and have operating temperatures of about 200
degrees centigrade, and they need an external reformer to supply hydrogen to the fuel cell.
Direct Methanol Fuel Cells use a polymer membrane as the electrolyte to allow the flow
of positively charged hydrogen ions through it. They operate between 48 and 88 degrees
centigrade. These fuel cells do not require an external reformer because the catalyst at the anode
2
itself will draw the hydrogen from the liquid methanol being supplied at the anode to the fuel
cell.
Regenerative Fuel Cells are the least developed fuel cells. Water is separated into its
components (hydrogen and oxygen) by a solar-powered electrolyzer and then fed into the fuel
cell anode and cathode respectively. In the fuel cell, these combine to generate electricity and
water. This water is re-circulated to the solar-powered electrolyzer, and the process is repeated.
The Molten Carbonate Fuel Cell uses lithium-potassium carbonate salts heated to 650
degrees centigrade as the electrolyte. The carbonate ions move from cathode to anode and react
with hydrogen there to produce water, carbon dioxide, and electrons. These electrons reach the
cathode through an external circuit, generating electricity. At the cathode these electrons
combine with oxygen and carbon dioxide to form more carbonate ions. These fuel cells do not
need an external reformer for supplying hydrogen to the fuel cell because of their higher
operating temperatures. There is considerable waste heat in the system to be captured and used
for other purposes, and these fuel cells are candidates for combined cooling, heating, and power
applications.
The Solid Oxide Fuel Cells use a solid ceramic electrolyte (a mixture of Zirconium Oxide
and Calcium Oxide) instead of a liquid electrolyte. They operate at high temperatures of about
1000 degrees centigrade. Ni-YSZ (Nickel/Yttria Stabilized Zirconium) is the material used for
the anode whereas the material for the cathode is (La0.8Sr0.2)0.96MnO3 (Lanthanum Strontium
Manganate). Figure 1.1 shows the operation of a solid oxide fuel cell. The negatively charged
oxygen ions formed at the cathode pass through the electrolyte and reach the anode to oxidize the
fuel when a fuel gas containing hydrogen is passed over the anode. The electrons produced at
the anode travel through an external circuit to the cathode, generating electricity. One fuel cell
produces a very small amount of direct current (DC) and for this current to be useful many such
single fuel cells must be assembled together in a stack. The solid oxide fuel cell stacks can be
arranged in the following two ways:
1. Tubular
2. Planar
Figures 1.2 and 1.3 show the solid oxide fuel cells in both these arrangements.
3
Figure 1.1. Operation of a Solid Oxide Fuel Cell [28]
Figure 1.2. Tubular Solid Oxide Fuel Cell Design and Stack [29]
4
Figure 1.3. Planar Solid Oxide Fuel Cell Design [29]
Solid oxide fuel cells can internally reform any fuel into a hydrogen-rich stream and are
suitable for the combined cooling, heating and power applications because of their higher
operating temperatures.
1.1.2. Fuel Cells for Heavy-Duty Trucks
One application for fuel cells is using them to power vehicles running on internal
combustion engines. The internal combustion engines provide the mechanical power to drive the
vehicles by direct combustion of the fuel (gasoline, diesel, etc.), resulting in many harmful
emissions. This problem is severe when heavy-duty diesel trucks are idling.
One of the major problems of heavy-duty trucks is that they idle for significant amounts
of time. Drivers idle engines to power the accessories such as air conditioners, heaters,
refrigerators, microwave ovens and televisions as well as to avoid start-up problems during cold
weather. Trucks are classified based on the weight they carry, and Class 7 or Class 8 trucks are
classified as heavy-duty trucks as indicated in Table 1.1.
5
Table 1.1. US Truck Classes
Weight ClassWeight Carried in
Pounds 1 Up to 6,000 2 6,001 – 10,000 3 10,001 – 14,000 4 14,001 – 16,000 5 16,001 – 19,500 6 19,501 – 26,000 7 26,001 – 33,000 8 More than 33,000
According to the Energy Efficiency and Renewable Energy website [1], a heavy-duty
truck idles six hours per day on average. This average was obtained considering the following
assumptions:
1. A heavy-duty truck runs for 303 days a year.
2. On the 85 winter days, the trucks idle for 10 hours per day.
3. On the 218 non-winter days, they idle for 4.5 hours per day.
Using these assumptions, a truck will idle a total of 1830 hours in a year. Eight hundred
forty million gallons of diesel fuel are consumed annually in U.S. by the idling of heavy-duty
trucks. Figure 1.4 shows one such Class 8 Truck.
Figure 1.4. A Class 8 Truck [4]
6
Figure 1.5 depicts the idle fuel usage per year for a Class 8 Truck (heavy-duty line-haul
diesel trucks) when three different technologies are used to power the vehicle when idling: 1)
existing alternators, 2) advanced alternators, and 3) Solid Oxide Fuel Cells. If a truck travels for
250 days in a year, remains idle for 6 hours per day, and the average fuel consumption per hour
is approximately 5 gallons, the idle engine consumes approximately 7,500 gallons per year.
SOFC
Existing Alternators
Advanced Alternators
0200400600800
10001200140016001800
Gal
lons
per
Yea
r (a
t Idl
e)
Figure 1.5. Estimated Idle Fuel Usage per Year, Class 8 Truck [5]
Figure 1.5 and Table 1.2 show the advantages of using Auxiliary Power Units to reduce
the fuel and emissions from the idling of heavy-duty trucks. APU’s can provide power to
accessories when the vehicle is idling and thereby reduce engine wear and tear, fuel
consumption, and emissions. Initially, the Proton Exchange Membrane fuel cells were
considered the most suitable for transportation applications, but now Solid Oxide Fuel Cells are
much more promising, because they do not need an external reformer and can tolerate small
amounts of sulfur in the fuel.
Table 1.2. Emissions for a Heavy-duty Truck While Idling and When an APU is Used [6]
Product Symbol Emissions in grams/hour Idling Truck Pony Pack
Total Hydrocarbons THC 12.6 0.45 Carbon Monoxide CO 94.6 7.5 Nitrogen Oxides NOX 56.7 11.6
Particulate Matter PM 2.57 0.69 Carbon Dioxide CO2 10,397 1,871
7
1.2. US DOE Auxiliary Power Unit (APU)
The US Government Department of Energy (DOE) is developing an Auxiliary Power
Unit with a net power output of 5 kW powered by a planar Solid Oxide Fuel Cell. The system
design for this APU consists of the following components:
1. Air compressor
2. Fuel pump
3. Water pump
4. Heat exchangers
4.1 Cathode pre-heater
4.2 Steam generator
4.3 Exhaust condenser
5. Auto thermal reformer (ATR)
6. Combustor
7. Desulphurization bed
8. Fuel cell stack
Figure 1.6 shows the outline of the process for the NETL Auxiliary Power Unit system.
In Figure 1.6, air absorbed from the atmosphere is compressed in the air compressor. The
compressed air passes through the air pre-heater, where it exchanges heat with the exhaust gases
coming from the fuel cell stack, and then is split into two streams. One stream goes to the
cathode of the fuel cell stack and the other stream goes to the Auto Thermal Reformer (ATR)
where the oxygen in the air reforms the fuel coming in through the fuel pump along with the
steam coming through the steam generator. In the ATR, the diesel fuel is reformed into
hydrogen and carbon monoxide for the anode side of the fuel cell stack. The hydrogen rich fuel
from the ATR passes through the ZnO desulphurization bed, which removes any sulfur traces
that might spoil the electrodes. Oxygen ions are formed from the air at the cathode and diffuse
through the cell to the anode. Hydrogen and some carbon monoxide react chemically at the
anode with the oxygen ions from the cathode and generate electricity (electrons) as well as water
and very small amounts of carbon dioxide. The exhaust heat produced by the reaction is
circulated to the ATR and the heat is exchanged with cathode air pre-heater to preheat the air
going to the ATR and the cathode side of the fuel cell stack. After losing some heat in the air
8
pre-heater, the exhaust gases pass through the steam generator to generate steam required in the
ATR and, in the process, loses some more heat. Finally, the exhaust goes through to the exhaust
condenser to bring the exhaust gases to room temperatures. The net power generated is 5 kW,
that is, the net output after the parasitic loads (air compressor, fuel, and water pumps) on the
system have been deducted from the total power produced.
+
_
Cathode
Anode
8000C
8000C
Air Compressor
1
Cathode Pre-heater
4.1
Fuel Pump
2 ATR
5
6
Water Pump
3
Steam Generator
4.2
Exhaust Condenser
4.3
Desulphur-ization
Bed (ZnO) 7
Fuel Cell Stack
8
6
air
diesel
Combustor
Pre-heated air Fuel Exhaust Steam Air, Water
6500C
Figure 1.6. Auxiliary Power Unit Fuel Cell System Diagram
1.3. Problem Statement
The objective of the problem report was to estimate the cost to mass manufacture the
NETL proposed 5 kW APU system. The research was focused mainly on developing various
cost models and comparing them with the existing data from literature, to arrive at conclusions
regarding the viability of the fuel cell technology use to prevent heavy-duty truck idling. Also,
the research was aimed at identifying the key process parameters that affected the system cost.
The affect of learning curves at different production quantities was also analyzed and a software
model was developed to simulate the cost estimate by varying the different process parameters.
9
2. Cost Estimation Methodologies
There are several methodologies for classifying estimating systems, and two of the most
important issues are: (A) The Estimating Approach and (B) Estimating Accuracy. The
estimating approach focuses upon whether the methodology is a bottom-up estimate with
specific details of the work breakdown structure or a top-down estimate emphasizing the
performance characteristics. The level of detail indicates the relative accuracy of the estimate
and the estimated cost increases as project details increase.
2.1. Estimating Approaches
2.1.1. Bottom-Up Estimating
The bottom-up cost estimating approach is the standard approach used by most
companies for standard products. A detailed work breakdown structure is required to describe
all the materials used and the labor requirements for design, production, tooling, assembly,
testing, etc to produce the product including the various overheads. Since many products include
components, tooling, etc., from suppliers, the costs of these items must also be included in the
estimate. The bottom-up estimate would be the most accurate since it is based upon actual costs
and detailed processes. But it often is not possible to obtain all the details to perform a complete
estimate, and some items are estimated by other means. In some cases, many of the components
used in a product are also used in other products and these can be obtained quickly. Some of the
specific bottom-up approaches are:
1) Detailed Cost Estimating
2) Standard Cost Estimating
3) Activity Based Estimating
Detailed cost estimating determines all the operations in the work breakdown structure and
determines a cost for each item. All the steps in the procedure are priced in detail, including
material, labor, and overhead. Standard costing uses cost standards that have been determined
by the accounting or industrial engineering departments to determine the costs of the operations.
Activity based costing (ABC) is similar to standard costing, except that it attempts to use several
cost drivers for the many overhead activities rather than using only direct materials or direct
10
labor for the overhead estimates. The overhead costs tend to be major cost items, and ABC is an
attempt to allocate the overhead costs more accurately than standard cost accounting. All of the
bottom-up costing methodologies require that the work breakdown structure be specified in
detail and for many new projects, these details are not known, and thus bottom-up costing cannot
be utilized.
2.1.2. Top-Down Estimating
Top-down estimating is often used for new products where the work breakdown structure
is not known and where considerable development work is required or where the specific
operation details are not known. Some of the top-down estimating procedures are:
1) Target Costing
2) Ratio Cost Estimating
3) Parametric Cost Estimating
Target costing is a procedure starting with the estimated market-selling price and deducts
the desired profit level to obtain the product target cost. The product target cost is then
distributed to the various components of the work breakdown structure, and these costs become
the goal for each of the components. The design, process, materials, or assembly procedures
may be changed to attain the desired cost for each component. The focus will be on those
components whose costs exceed the “target” so the overall target can be met. Sometime this is
also referred to as “Price-to-Win” estimating when the price rather than the cost is the focus.
This forces product designers and manufacturing engineers to focus upon cost during the design
and product planning stages rather than after production has started. It is easier to reduce costs
and make changes before production starts rather than make changes after production has started,
as the tooling costs will have been committed.
Ratio cost estimating is one of the oldest cost estimating procedures and is commonly
known as cost capacity estimating or parametric equipment costing. This methodology assumes
there is an economy of scale, that is, the doubling of capacity does not result in the doubling of
cost. The six-tenths rule is an example of ratio cost estimating, that is
Cd = Ck ( Sd / Sk)b
11
where
Cd = Desired Equipment Cost of Size d
Ck = Known Equipment Cost of Size k
Sd = Size of Equipment Desired
Sk = Size of Equipment of Known Cost
b = Cost Capacity Exponent (0.6 for the six-tenths rule)
Since Ck and Sk are known, the equation can be written as a parametric equation of the
form:
Cd = A [Sd]b
where
A = Equation Constant
b = Equation Exponent
The data for parametric cost curves were obtained from various manufacturers, plotted on
log-log figures, and used to estimate equipment costs for equipment that may not exist in the size
desired. These curves are extremely useful in planning equipment purchases for new plants or
production lines. Additional factors can be applied to the base equipment costs to estimate the
facility costs, and this approach is utilized in AACE 16R-90, the recommended practice [14] for
conducting technical and economic evaluations in the process and utility industries.
Parametric cost estimating is a cost estimating process that uses Cost Estimating
Relationships (CER’s) to estimate costs. The cost estimating relationships relate costs to various
physical product parameters or process performance parameters of the system being estimated.
These systems are used when the design details of the system are not known, only the desired
performance characteristics are known. These systems are used for new military systems, such
as new airplanes, which have new performance standards such as higher speed or more thrust
than existing airplanes. Since the design details are not known, the bottom-up costing approach
cannot be used. There are several existing commercial parametric cost estimating programs,
such as PRICE and FASTE. PRICE [23] is the most common and the acronym represents
Parametric Review of Information for Costing and Evaluation and has been in existence for
nearly 40 years. FASTE is from Friedman Parametric Systems and Mr. Friedman is one of the
originators of parametric cost modeling. The commercial models do not present the details of
12
the relationships used, so they cannot be copied. The traditional models are those in which the
cost estimating relationships are presented, so users can modify them.
2.2. Estimating Classes and Accuracy
The accuracy of the estimate depends upon the information and the type of estimate
desired. There are various estimating accuracy systems, and two of the more common systems
are the three-level and the five-level classification systems. There are also four-level and six-
level classification systems, but the three- and five-level systems are adequate for most
applications.
2.2.1. Three-Level Classification System
The three-level classification system is illustrated by the ANSI-Z94.0 classification
system. The three types of estimates in the three-level system are the Conceptual Estimate, the
Preliminary Estimate, and the Detailed Estimate. Table 2.1 gives the accuracy ranges for the
three level estimate systems.
Table 2.1. Three-Level Classification System
Estimate Class Type of Estimate Description Estimate Range
(Percent of Actual)
Low Conceptual Estimate,
Order-of-Magnitude Estimate
-30 to +50
Medium Preliminary Estimate,
Budget Estimate
-15 to + 30
High Detailed Estimate,
Definitive Estimate
- 5 to + 15
It must be noted that the estimate range is not symmetric; the estimate has a larger
positive error (the estimate is low) than the negative error (the estimate is high). Items are
frequently left out of the estimate, which results in the estimate being low. This indicates the
13
14
condition of whether or not the term has been included in the estimate and not the particular
accuracy of the item being estimated.
2.2.2. Five-Level Classification System
The five-level classification system presented is the system in the AACE International
Recommend Practice 18R-97[23], which is for engineering, procurement, and construction in the
process industries. Table 2.2 gives the estimate class and expected accuracy as well as the level
of project definition, preparation effort required, typical methodology, and end use of estimate.
The primary characteristic for the estimate is the level of project definition, which is the
% of detail of the complete project. For class 5 estimates, the level of project definition is
between 0 and 2 percent, but the accuracy can be 100 percent low or 50 percent high. The class
5 estimate has the greatest error, whereas the class 1 estimate has the smallest error, which can
be as small as plus or minus 3%. The expected accuracy is a range, and the value of –3 to –10
% indicates the error could be as low as -3% or as high as –10%. The smaller error would be
for projects similar to previous projects and the larger term would apply to complex projects or
projects with new processes or concepts.
Table 2.2 gives the expected accuracy range for the different classes of estimates and the
relative estimate costs using the conceptual screening estimate as the base. For example, the
Class 2 estimate has an accuracy range of –15 to –30 on the low side. The estimate would
typically be low 15 to 30% in the worst case. The range exists as some processes have better
estimating parameters and the error would be only –15% whereas for other processes it could be
up to –30%. On the high side, or when the estimate is low, it can be from 20% to 50%,
depending upon the estimating capabilities of the process.
Table 2.3 indicates the information required for the different estimate classes for process
construction projects. The accuracy of the estimate depends largely upon the information
available, and accurate estimates require detailed information. Note that for a Class 5 estimate,
very little information is required, whereas for a Class 1 estimate, nearly all design must be
completed, and the few remaining items are in advanced stages. A table of information
Table 2.2. Cost Estimate Classification Matrix for Process Industries (AACE, International)
ESTIMATE LEVEL OF END USAGE METHODOLOGY EXPECTED PREPARATION CLASS PROJECT (2) (2) ACCURACY EFFORT (2) DEFINITION (1) RANGE (2) Expressed as % Typical purpose Typical estimating Typical variation in Typical degree of
effort of of estimate method low and high range relative to least cost complete (a) index of 1 definition (b)________ Class 5 0% to 2% Concept Screening Capacity Factored, L: -20% to -50% 1 Parametric Models, H:+30% to +100% Judgment or Analogy Class 4 1% to 15% Study or Feasibility Equipment L: -15% to -30% 2 to 4 Factored or H: +20% to + 50% Parametric Models
Class 3 10% to 40% Budget, Semi-Detailed Unit Costs L: - 10% to – 20% 3 to 10 Authorization, or with Assembly Level H: +10% to +30% Control Line Items Class 2 30% to 70% Control or Bid/ Detailed Unit Cost with L: - 5% to - 15% 4 to 20 Tender Forced Detailed Take-Off H: +5% to + 20% Class 1 50% to 100% Check Estimate or Detailed Unit Cost with L: -3% to - 10% 5 to 100 Bid/Tender Detailed Take-Off H: +3% to + 15% Notes: (1) This is the primary characteristic (2) This is a secondary characteristic (a) The state of process technology and availability of applicable reference cost data affect the range markedly. The +/- value represents typical percentage variation of actual costs from the cost estimate after application of contingency (typically at a 50% level of confidence) for given scope. (b) If the range index value of “1” represents 0.005% of project costs, then an index value of 100 represents 0.5%. Estimate preparation effort is highly dependent upon the size of the project and the quality of estimating data and tools.
15
16
Table 2.3. Information Required for Specific Estimate Class (AACE International) ESTIMATE CLASSIFICATION General Project Data: Class 5 Class 4 Class 3 Class 2 Class 1 Project Scope Description General Preliminary Defined Defined Defined Plant Production/Facility Capacity Assumed Preliminary Defined Defined Defined Plant Location General Approximate Specific Specific Specific Soils & Hydrology None Preliminary Defined Defined Defined Integrated Project Plan None Preliminary Defined Defined Defined Project Master Schedule None Preliminary Defined Defined Defined Escalation Strategy None Preliminary Defined Defined Defined Work Breakdown Structure None Preliminary Defined Defined Defined Project Code of Accounts None Preliminary Defined Defined Defined Contracting Strategy Assumed Assumed Preliminary Defined Defined
Engineering Deliverables:
Block Flow Diagrams S/P P/C C C C Plot Plans S P/C C C Process Flow Diagrams (PFDs) S/P P/C C C Utility Flow Diagrams (UFDs) S/P P/C C C Piping & Instrument Diagrams (P&IDs) S P/C C C Heat & Material Balances S P/C C C Process Equipment List S/P P/C C C Utility Equipment List S/P P/C C C Electrical One-Line Drawings S/P P/C C C Specifications & Datasheets S P/C C C General Equipment Arrangement Drawings S P/C C C Spare Parts Listings S/P P C
Mechanical Discipline Drawings S P P/C Electrical Discipline Drawings S P P/C Instrumentation/Control System Discipline Drawings S P P/C Civil/Structural/Site Discipline Drawings S P P/C
S=work has started on the engineering deliverable P=work on the deliverable is advanced C=work on the deliverable is complete AACE International Recommended Practice No.17R-97, Cost Estimate Classification System.
similar to that in Table 2.3 could be prepared for new product development. This would be very
valuable to manufacturing engineers and product designers.
2.3. Cost Estimation Methodologies Summary
Most new projects, such as the development of APU units would be Class 5 estimates, as
little details are known about the equipment. Both estimating processes have their advantages
and limitations, and estimates will be prepared using both methodologies. The elemental costs
for the system are assumed to be the total costs including overhead and assembly of the elements
into the system. The design parameters, such as the temperature, pressure, etc., are considered as
the input parameters in the bottom-up costing but are included in the complexity factors for the
top-down costing. Data for both models were difficult to obtain. Better data would be necessary
for more accurate estimates.
17
3. Literature Review of Cost Data for the Solid Oxide Fuel Cell Auxiliary Power Unit
For a traditional bottom-up cost model to be developed, the system was first broken down
into subsystems, and the subsystems were divided into individual elements. The 3 subsystems
considered by Arthur D. Little Inc. for the US Department of Energy [17] were:
1. Fuel Processor Subsystem
2. Fuel Cell Subsystem
3. Balance of Plant
Further, each subsystem was broken down into its individual components. The Fuel
Processor subsystem was split into:
1. Reformate Generator, which consists of the Auto Thermal Reformer, Desulphurization
Bed, Steam Generator, and Cathode Air Pre-heater
2. Fuel Supply, which consists of Fuel Pump
3. Water Supply, which consists of Water Pump and Exhaust Condenser
Similarly, the Fuel Cell subsystem was divided into:
1. Fuel Cell Stack, which consists of many individual fuel cell units
2. Stack Hardware
3. Air Compressor
Finally, the Balance of Plant subsystem was subdivided into:
1. System Controller
2. Safety
3. System Packaging
4. Electrical Instrumentation
5. Piping
The ADL cost report submitted to the US Department Of Energy (DOE) [17] evaluated a
planar solid oxide fuel cell auxiliary power unit (APU), operating at a power density of 0.3
W/cm2 and cell voltage of 0.7 V. The operating temperature was between 6500C and 8000C and
the volume of production was assumed to be 500,000-units per year. The ADL report considered
5 different cases varying the power density and the operating temperature of the fuel cell stack.
The results are in Table 3.1.
18
Table 3.1. Five Cases as Considered by the ADL [17] Report for a 5 kW SOFC APU
Base Case Improved Stack Design
Poorer Stack Design
Higher Power Density
Sulfur-free Fuel
Cathode Air Inlet Temperature (0C)
650 500 750 650 650
Power Density (W/cm2)
0.3 0.6 0.3 0.6 0.3
Cost ($) 2,636 1,754 3,332 2,076 2,461 Cost / kW ($/kW) 527 351 666 415 492
The cost of an APU obtained at this production volume was around $2,636 for cathode
air inlet temperature of 6500C and results in 37% efficiency. They used RAPIDTM methodology
to develop the SOFC for APU applications. The fuel cell stack and the reformer costs were
identified as critical costs. The costs for the SOFC APU were lower for the high power density
cases. The fuel cell stack cost was the major cost item of the APU, which constituted 27 – 44%
of the total system costs. This cost model excluded the profit and general and administrative
expenses. The cost of the fuel cell stack consisted of the raw material costs, the processing costs,
and the capital recovery costs, whereas for all other items, the cost was the sum of the raw
material costs and the processing costs. The raw material costs for all the components were
industry inputs during the time of preparation of the estimate. The fuel cell stack thermal
management was also identified as a critical factor affecting the overall cost of the system. If the
amount of heat to be removed from the system is high, higher cost material heat exchangers are
required. The system contained few purchased items, such as the compressor and the fuel and
water pumps.
The Rolls-Royce Advanced Engineering Center carried out a study for the United
Kingdom Department of Trade and Industry (DTI) [18] on fuel cell-based power plants from 1
kW to 20 MW. Some of the selected cell manufacturers include the Westinghouse tubular SOFC
manufacturer, Siemens Planar SOFC, and Rolls-Royce Integrated Planar SOFC. Table 3.2 gives
the specifications and costs of the companies manufacturing the SOFC’s, which were identified
after contacting the respective companies and also after consulting many customer organizations.
19
Table 3.2. Specifications and Costs of the Various Cell Manufacturers [18]
SOFC Stack Manufacturer Westinghouse Siemens Rolls-Royce
Operating Voltage (V) 0.7 0.7 0.7
Current Density (mA/cm2) 240 270 400
Cell Operating Temperature (0C) 1,000 850 900
Stack Inlet Temperature (0C) 600 650 600
Cost/kW ($/kW) 673.73 809.78 323.90
The major cost drivers for the SOFC stacks were the raw materials, which consist of rare
earth oxides for the electrode and electrolyte materials, the expensive manufacturing procedures
adopted, and the thermal management of the stack. The heat exchanger cost data was plotted
against the heat exchanger size, and the appropriate heat exchanger was selected depending upon
the temperature at which it operates. The study was done for Combined Cooling Heat and Power
(CHP) applications, and all the equations derived are valid for the CHP scenario.
Joseph P. Strakey [19] estimates the raw material costs associated with the fuel cell stack
interconnects in a report done for the Strategic Center for Natural Gas (SCNG). The solid oxide
fuel cell stack hardware cost data for ceramic and metallic interconnects is presented in Table
3.3.
Table 3.3. Solid Oxide Fuel Cell Stack Costs with Ceramic and Metallic Interconnect Materials [19]
SOFC Component Material Cost ($/kW) Ceramic Interconnect Metallic Interconnect
Ni/ZrO2 anode (500 microns) 11.67 11.67
ZrO2/Y2O3 electrolyte (10 microns) 0.4 0.4
LaMnO3 cathode (50 microns) 2.3 2.3 End Plates (1.25 centimeters) 0.7 0.7
Ceramic Interconnect (2.5 millimeters) 137.5 6.67 Subtotal 152.57 21.74
50 % Contingency 76.28 10.87 Total Material Costs 228.85 32.61
20
The evaluation of the cost performance of the SOFC [20] investigated the manufacturing
cost of a single cell. They evaluated 6 different types of SOFC, out of which 4 are tubular and 2
are planar, and are produced by different manufacturing techniques. They identified power
density and yield as the cost drivers. Also, if power densities greater than 0.3 W/cm2 are
achieved, the SOFC systems can be manufactured at lower costs. The costs of rare earth oxides
used as raw material (perovskites) for electrodes and electrolyte are shown in Table 3.4. The
costs for the raw materials for various processes like Electrochemical Vapor Deposition (EVD),
Laser Ablation, Plasma Spray (PS), and Sintering are calculated for the electrodes, the
electrolyte, and the interconnectors. All the above processes yielded approximately the same
manufacturing cost when 1 million cells are manufactured per plant per year.
Table 3.4. Material costs for Perovskite Production [20]
Raw Material Quality (%) Price (U.S. $/kg)
La2O3 99.9 20
SrCO3 99.5 12
MnO2 > 99 2.6
Cr2O3 > 99 10
Hibiki Itoh, etc. [21] studied the production costs of the planar and tubular solid oxide
fuel cells from the Japanese manufacturing companies. The planar cells were fabricated using
the Tape Casting, Screen Printing, and Co-firing (TSC) processes, and the quantity manufactured
was 5,000 units/month. Power per stack was 400 W. The tubular cells were manufactured by
using the EVD process or the PS process and the quantity manufactured was 2,000 units/month,
and power per stack was 1,000 W. The cost of raw materials per unit weight was the cost driver
for both cases, and the yield of the raw material affects the processing cost. The production cost
of the planar SOFC was $ 1,021 per kW, and the materials cost constitutes 60 % of this cost. For
the tubular cells, EVD process resulted in $5,338 per kW, and PS process resulted in $ 2,535.
The production costs were more for the tubular type because the labor costs increased and
material utilization was lower. If the power density is improved up to 0.5 W/cm2, the
components in the planar type will become thinner resulting in lower costs, thus making them
21
viable for commercial application. Table 3.5 shows the unit prices and densities of raw materials
used in SOFC production.
Table 3.5. Unit Prices and Theoretical Densities of Raw Materials [21]
Stack Components of
SOFC
Raw Materials Price per unit
($/kg)
Theoretical Density
(g/cm3)
Electrolyte 8 mol% yttria stabilized
zirconia (YSZ)
60.56 5.90
Fuel Electrode 40 vol.% Ni-YSZ 51.91 6.32
Air Electrode (La0.8Sr0.2)0.96MnO3 54.50 6.27
The literature review section dealt with the various approaches used to estimate the cost
of the solid oxide fuel cell systems. All the approaches, except the ADL report [17] and the DTI
study [18], estimated the cost from the raw materials details and the processes used for
production. The different manufacturing processes for the production of the solid oxide fuel
cells were discussed and the costs obtained from the different methods were analyzed. Further
improvements in manufacturing technology can cut down the costs of production. The ADL
report [17] and the DTI study [18] have not only discussed the cost of production, but also
estimated the cost of the solid oxide fuel cell systems using detailed cost estimating approaches.
No literature was found in which the cost of the fuel cell system was estimated by developing
cost estimating relationships from the existing industrial input for various components in the
system. The focus of the work done was to develop a cost model, which would estimate the cost
of manufacturing the solid oxide fuel cell auxiliary power unit using the available industrial data
and not going into the details about the raw materials and the manufacturing processes used.
22
4. Cost Model Results Two estimating approaches were used to estimate the cost of the Auxiliary Power Unit
(APU). The first approach was the use of PRICE software to estimate the cost. This software
used the physical characteristics of the components in APU. The weight, volume, and the
manufacturing complexity are critical data items used by PRICE to estimate the cost. The
second approach was the traditional approach, which used the Cost Estimating Relationships
(CERs) developed from industrial data or existing literature data to estimate the cost. The
improvement rates obtained from the PRICE model were used to adjust the costs for various
production levels in the CER Models.
4.1. PRICE Models 4.1.1. PRICE Results Discussion
PRICE, which is an acronym for Parametric Review of Information for Costing and Evaluation,
is a parametric cost-estimating program initially developed in the 1960s and has been continually
updated and improved. The PRICE estimating suite has four individual applications, which are
as follows:
1. PRICE H, the Hardware Estimating Model
2. PRICE HL, the Hardware Life Cycle Estimating Model
3. PRICE S, the Software Development and Support Cost Estimating Model
4. PRICE M, the Electronic Module and Microcircuit Estimating Model
The model used to estimate the cost of the Auxiliary Power Unit was the PRICE H, the
Hardware Estimating Model. PRICE H is used to estimate costs and schedules for electro-
mechanical and structural assemblies. The parametric approach uses variables that can be
quantified easily such as weight, volume, etc., to estimate the variables that are difficult to
quantify such as cost and schedule. The parametric approach is based on a number of cost
estimating relationships between the quantifiable and the non-quantifiable variables. PRICE H
uses industry-average values generated internally by the software for those parameters about
which the input data is not available to develop an estimate. The PRICE models were initially
23
24
developed because the data for the traditional models were difficult to obtain and the PRICE
results gave an indication of the magnitude of the costs for the various components.
A major difficulty in using the PRICE models was the determination of the complexity
values and the manufacturing process index parameters. The PRICE support staff was very
helpful in developing estimates for the complexity values, especially for the fuel cell. The
manufacturing process index parameter varied for different production quantities and a
relationship was developed so consistent results would be obtained as the production quantity
was varied. The PRICE model was used to develop the improvement rates for the traditional
models developed later. The manufacturing process index had a major impact upon the cost and
two different models were developed. In the PRICE I model a single relationship of
manufacturing process index versus the production quantity was used, and in the PRICE II
model, the production quantity was divided into two ranges and a relationship was developed for
each range.
The results for PRICE I model for production levels from 10 units to 1 million units are
presented in Table 4.1, and the focus was on the 500,000-unit level for comparisons with the
NETL [24] and the ADL (Arthur D. Little) results [17]. The results from PRICE I model were $
2,015 for the 5 kW APU at the 500,000-unit production level or a cost of $ 403/kW. The costs
for the Fuel Cell Stack were lower than expected and this led to the use of the two ranges for the
manufacturing process index. Small differences in the index at high production levels led to
large differences in the component costs, and a better fit was obtained when the data was divided
into two ranges.
The results for PRICE II model are presented in Table 4.2 and the major cost increases
are at high production levels from 100,000 to 1,000,000 units. The costs for PRICE II were
lower than the PRICE I for production quantities less than 100,000-units. The results from
PRICE II were $ 2,621 for the 5 kW APU at 500,000-units production level with a cost of $
524/kW. These results were in better agreement with the ADL results.
Although the models included the costs of the major components, it is estimated that an
additional cost increase of 10 percent would be required for the assembly container. It is
estimated that the total estimate range would be from –15 to +30% of the total estimate as the
fuel cell stack cost data was approximate, and this was a major cost component in the estimate.
Table 4.1. PRICE I Results
Component Cost
(USD) Cost
(USD) Cost
(USD) Cost
(USD) Cost
(USD) Cost
(USD) Cost
(USD) Cost
(USD) Cost
(USD) Cost
(USD) Cost
(USD) Units 10 100 1,000 5,000 10,000 20,000 50,000 100,000 200,000 500,000 1,000,000
Combustor 1,310.00 719.00 345.50 250.62 220.44 182.48 144.08 121.56 96.92 66.06 35.40 ZnO Bed 1,650.00 613.00 276.60 197.54 173.35 133.50 113.09 95.27 75.90 51.65 27.64
ATR 910 490 238.5 173.16 152.34 126.43 99.76 84.05 66.98 45.6 24.44 Air Compressor 3,110.00 1,802.00 870.70 623.26 545.61 442.62 350.09 296.63 236.86 162.14 86.93
Fuel Pump 110 99 97.2 97.18 97.19 97.19 97.19 97.19 97.19 97.19 97.19 Water Pump 110 99 97.2 97.18 97.19 97.19 97.19 97.19 97.19 97.19 97.19
Fuel Cell Stack 27,210.00 9,601.00 4,305.20 2,964.94 2,604.22 2,247.07 1,881.72 1,480.68 1,182.37 806.42 452.73 Air Pre-heater #1 4,800.00 2,818.00 1,372.80 975.06 852.19 683.91 541.09 460.92 367.09 251.11 134.65 Steam Generator 6,600.00 3,925.00 1,933.90 1,361.72 1,188.17 950.39 752.06 641.19 510.79 349.86 186.57
Exhaust Condenser 1,720.00 963.00 462.80 333.28 292.73 241.56 190.90 161.36 128.75 87.92 47.12
Unit Cost 47,530 21,129 10,000 7,074 6,223 5,202 4,267 3,536 2,860 2,015 1,190 Cost/kW 9,506.00 4,225.80 2,000.08 1,414.79 1,244.69 1,040.47 853.43 707.21 572.01 403.03 237.97
Total Cost*
(Thousand Dollars) 475.3 2,112.9 10,000.4 35,369.7 62,234.3 104,046.8 213,358 353,604 572,008 1,007,570 1,189,860
*Total Cost is in thousands of dollars.
25
Component Cost
(USD) Cost
(USD) Cost
(USD) Cost
(USD) Cost
(USD) Cost
(USD) Cost
(USD) Cost
(USD) Cost
(USD) Cost
(USD) Cost
(USD) Units 10 100 1,000 5,000 10,000 20,000 50,000 100,000 200,000 500,000 1,000,000
Combustor 1,290.00 586.00 297.20 222.92 198.88 169.88 139.47 125.24 109.59 88.31 68.82 ZnO Bed 1,630.00 505.00 238.70 175.80 156.41 133.59 109.44 98.15 85.85 69.12 53.91
ATR 900 399 205.1 153.98 137.41 117.68 96.56 86.6 75.76 61 47.62 Air Compressor 3,070.00 1,474.00 750.40 554.94 492.64 412.23 338.95 305.53 267.55 216.09 167.61
Fuel Pump 110 98 97.2 97.18 97.19 97.19 97.19 97.19 97.19 97.19 97.19 Water Pump 110 98 97.2 97.18 97.19 97.19 97.19 97.19 97.19 97.19 97.19
Fuel Cell Stack 27,000.00 8,434.00 3,717.20 2,641.26 2,352.18 2,094.06 1,822.22 1,525.11 1,335.76 1,075.31 867.66 Air Pre-heater #1 4,730.00 2,310.00 1,184.80 868.68 769.80 637.09 523.92 474.70 414.45 334.14 258.55 Steam Generator 6,500.00 3,223.00 1,671.50 1,213.80 1,073.72 885.49 728.26 660.29 576.45 464.96 357.04
Exhaust Condenser 1,690.00 787.00 398.40 296.56 264.18 224.91 184.79 166.23 145.52 117.39 91.32
Unit Cost 47,030 17,914 8,658 6,322 5,640 4,869 4,138 3,636 3,205 2,621 2,107 Cost/kW 9,406.00 3,582.80 1,731.54 1,264.46 1,127.92 973.86 827.60 727.25 641.06 524.14 421.38
Total Cost*
(Thousand Dollars) 470.3 1,791.4 8,657.7 31,611.5 56,396 97,386.1 206,899.5 363,623 641,062 1,310,350 2,106,910
Table 4.2. PRICE II Results
26
*Total Cost is in thousands of dollars.
The total cost to manufacture increases as the quantity manufactured increases, but the
unit cost of an Auxiliary Power Unit and the cost per kW decreases. Table 4.3 summarizes the
unit cost and cost per kW obtained for the different cases considered using the PRICE I model.
Table 4.3. Unit Cost and Cost per kW Obtained from PRICE I
Quantity Unit Cost ($) Cost/kW ($)10 47,530.00 9,506.00 100 21,129.00 4,225.80
1000 10,000.00 2,000.08 5000 7,074.00 1,414.79
10000 6,223.00 1,244.69 20000 5,202.00 1,040.47 50000 4,267.00 853.43 100000 3,536.00 707.21 200000 2,860.00 572.01 500000 2,015.00 403.03
1000000 1,190.00 237.97
The unit cost and cost per kW data in Table 4.3 are plotted versus quantity, and the
results are illustrated graphically in Figures 4.1 through 4.4. Figure 4.1 is a plot of the unit cost
of Auxiliary Power Unit versus the quantity manufactured when cost is on a linear scale and
quantity on a logarithmic (log) scale. Figure 4.2 depicts the relationship when the data is plotted
on a log-log scale.
Unit Cost (vs) Quantity
0.00
10,000.00
20,000.00
30,000.00
40,000.00
50,000.00
1 10 100 1000 10000 100000 1000000
Quantity
Uni
t Cos
t ($)
Figure 4.1. Unit Cost Versus Quantity (semi-log scale)
27
The equation for the log-log relationship obtained was:
Unit Cost ($/unit) = 86,513 (Quantity)-0.2893
The linear equation developed from above is:
log (Unit Cost) = 4.937081 – 0.2893 * log (Quantity)
Unit Cost (vs) Quantityy = 86513x-0.2893
1.00
10.00
100.00
1,000.00
10,000.00
100,000.00
1 10 100 1000 10000 100000 1000000
Quantity
Uni
t Cos
t ($)
Figure 4.2. Unit Cost Versus Quantity (log-log scale)
Figure 4.3 indicates how the cost/kW for the Auxiliary Power Unit was reduced as the
number of units manufactured increases. Since the design was for a 5kW unit, the expression for
the cost/unit is the equivalent of the unit cost relationship divided by 5.
Cost/kW (vs) Quantity
0.00
2,000.00
4,000.00
6,000.00
8,000.00
10,000.00
1 10 100 1000 10000 100000 1000000
Quantity
Cos
t/kW
($/k
W)
Figure 4.3. Cost/kW versus Quantity (semi-log scale)
Figure 4.4 depicts the relationship between the cost/kW and quantity on a log-log scale.
28
Cost/kW (vs) Quantityy = 17303x-0.2893
1.00
10.00
100.00
1,000.00
10,000.00
1 10 100 1000 10000 100000 1000000
Quantity
Cos
t/kW
($/k
W)
Figure 4.4. Cost/kW versus Quantity (log-log scale)
4.1.2. PRICE Results For Year 2009
The PRICE results obtained above have been from the data collected in 2003 (time of reference).
To adjust the prices to year 2009 (time of interest), equation 1 [10] was used:
C(t) = C(r) * I(t) / I(r) Eq. 4.1
Where C(t) = Cost at time of interest
C(r) = Cost at time of reference
I(t) = Cost index at the time of interest
I(r) = Cost index at the time of reference.
The Marshall and Swift cost indices data for the year 2003 and 2009 was unavailable. The
Producers Price Index values published by the US government every month were used instead.
The PPI values obtained for various components of the APU are listed in Table 4.4.
29
30
Table 4.4. PPI Values [29]
Component 2009 Cost Index 2003 Cost Index Description Combustor 139.3 100 Steel foundries, except investment ZnO Bed 221.7 100 Other basic inorganic chemical mfg.
ATR 139.3 100 Steel foundries, except investment
Air Compressor 130.4 100 Compressors and compressor units, all
refrigerants, except automotive Fuel Pump 127.8 100 Pump and compressor manufacturing.
Water Pump 127.8 100 Pump and compressor manufacturing.Fuel Cell Stack 113.7 100 primary batteries, dry and wet
Air Pre-heater #1 137.8 100 Power boiler and heat exchanger
manufacturing.
Steam Generator 137.8 100 Power boiler and heat exchanger
manufacturing.
Exhaust Condenser 137.8 100 Power boiler and heat exchanger
manufacturing.
The 2003 costs (cost at the time of reference) for each component at various quantities,
and the cost indices from the PPI values were substituted in Eq. 1 to obtain the 2009 costs (cost
at the time of interest). PRICE I and PRICE II results obtained for the year 2009 are listed in
Tables 4.5 and 4.6.
Table 4.5. 2009 PRICE I Results
Component Cost
(USD) Cost
(USD) Cost
(USD) Cost
(USD) Cost
(USD) Cost
(USD) Cost
(USD) Cost
(USD) Cost
(USD) Cost
(USD) Cost
(USD) Units 10 100 1,000 5,000 10,000 20,000 50,000 100,000 200,000 500,000 1,000,000
Combustor 1,824.83 1,001.57 481.28 349.11 307.07 254.19 200.70 169.33 135.01 92.02 49.31 ZnO Bed 3,658.05 1,359.02 613.22 437.95 384.32 295.97 250.72 211.21 168.27 114.51 61.28
ATR 1,267.63 682.57 332.23 241.21 212.21 176.12 138.97 117.08 93.30 63.52 34.04 Air Compressor 4,055.44 2,349.81 1,135.39 812.73 711.48 577.18 456.52 386.81 308.87 211.43 113.36
Fuel Pump 140.58 126.52 124.22 124.20 124.21 124.21 124.21 124.21 124.21 124.21 124.21 Water Pump 140.58 126.52 124.22 124.20 124.21 124.21 124.21 124.21 124.21 124.21 124.21
Fuel Cell Stack 30,937.77 10,916.34 4,895.01 3,371.14 2,961.00 2,554.92 2,139.52 1,683.53 1,344.35 916.90 514.75 Air Pre-heater #1 6,614.40 3,883.20 1,891.72 1,343.63 1,174.32 942.43 745.62 635.15 505.85 346.03 185.55 Steam Generator 9,094.80 5,408.65 2,664.91 1,876.45 1,637.30 1,309.64 1,036.34 883.56 703.87 482.11 257.09
Exhaust Condenser 2,370.16 1,327.01 637.74 459.26 403.38 332.87 263.06 222.35 177.42 121.15 64.93
Unit Cost 60,104 27,181 12,900 9,140 8,039 6,692 5,480 4,557 3,685 2,596 1,529 Cost/kW 12,020.85 5,436.24 2,579.99 1,827.97 1,607.90 1,338.35 1,095.97 911.49 737.07 519.22 305.75
Total Cost* (Thousand Dollars) 601.04 2,718.1 12,899.95 45,699.37 80,394.89 133,834.58 273,993.06 455,744.63 737,071.38 1,298,044.295 1,528,735.89
*Total Cost is in thousands of dollars.
31
Component Cost
(USD) Cost
(USD) Cost
(USD) Cost
(USD) Cost
(USD) Cost
(USD) Cost
(USD) Cost
(USD) Cost
(USD) Cost
(USD) Cost
(USD) Units 10 100 1,000 5,000 10,000 20,000 50,000 100,000 200,000 500,000 1,000,000
Combustor 1,796.97 816.30 414.00 310.53 277.04 236.64 194.28 174.46 152.66 123.02 95.87 ZnO Bed 3,613.71 1,119.59 529.20 389.75 346.76 296.17 242.63 217.60 190.33 153.24 119.52
ATR 1,253.70 555.81 285.70 214.49 191.41 163.93 134.51 120.63 105.53 84.97 66.33 Air Compressor 4,003.28 1,922.10 978.52 723.64 642.40 537.55 441.99 398.41 348.89 281.78 218.56
Fuel Pump 140.58 125.24 124.22 124.20 124.21 124.21 124.21 124.21 124.21 124.21 124.21 Water Pump 140.58 125.24 124.22 124.20 124.21 124.21 124.21 124.21 124.21 124.21 124.21
Fuel Cell Stack 30,699.00 9,589.46 4,226.46 3,003.11 2,674.43 2,380.95 2,071.86 1,734.05 1,518.76 1,222.63 986.53 Air Pre-heater #1 6,517.94 3,183.18 1,632.65 1,197.04 1,060.78 877.91 721.96 654.14 571.11 460.44 356.28 Steam Generator 8,957.00 4,441.29 2,303.33 1,672.62 1,479.59 1,220.20 1,003.54 909.88 794.35 640.71 492.00
Exhaust Condenser 2,328.82 1,084.49 549.00 408.66 364.04 309.93 254.64 229.06 200.53 161.76 125.84
Unit Cost 59,452 22,963 11,167 8,168 7,285 6,272 5,314 4,687 4,131 3,377 2,709 Cost/kW 11,890.32 4,592.54 2,233.46 1,633.65 1,456.97 1,254.34 1,062.77 937.33 826.11 675.40 541.87
Total Cost* (Thousand Dollars) 594.52 2,296.27 11,167.3 40,841.17 72,848.72 125,433.72 265,691.78 468,665.17 826,114.14 1,688,488.78 2,709,351.87
Table 4.6. 2009 PRICE II Results
32
*Total Cost is in thousands of dollars.
4.1.3. PRICE Model Assumptions
The PRICE model assumptions and results are explained in detail below, giving all the data used
in the model and the expressions developed for the manufacturing process index. The
Combustor, ZnO Bed, Auto Thermal Reformer, Air Compressor (of required specifications), the
Fuel Cell Stack and the particular tube-in-tube heat exchangers were assumed not to be standard
manufactured products. Also all of these elements were considered to be structural elements.
The Fuel Pump and the Water Pump were assumed to be purchased from the existing equipment
in the market. A sample PRICE file for the APU design is shown in Figure 4.5.
Figure 4.5. PRICE Model Input Format for APU
Since many of the components had not been manufactured, some assumptions were made
to estimate the parameters required for the PRICE model. The Combustor, ZnO Bed, Auto
Thermal Reformer (ATR), and Scroll Air Compressor were assumed to be made from carbon
steel. The Air Pre-heater #1, Steam Generator, and Exhaust Condenser were assumed to be
made from stainless steel. The weight of the fuel stack cell of 3 Kg/kW was obtained from a
33
34
SAE paper [26]. The losses of the fuel cell were estimated to be 0.8 kW to give a net power
output of 5.0kW. This resulted in a weight of 17.4 Kg using a total power of 5.8 kW generated
by the fuel stack cell. The fuel pump and water pump weights were 0.51 kg as reported by the
reference used [24]. The air compressor data was obtained from a website [30]. The PRICE
software used this equipment data to estimate the cost of making the Auxiliary Power Unit.
Table 4.7 shows the specifications for the components of the APU and an asterisk (*) indicates
the values required by the PRICE model.
Auxiliary Power Unit Components Parameter Combustor ZnO Bed ATR Scroll
CompressorFuel
Pump Water Pump
Fuel Cell Stack
Air Pre-heater
Steam Generator
Exhaust Condenser
Length (m) 0.3 0.206 0.3 0.3 0.07 0.07 0.3 3.954 6.122 0.957
Outer Tube Diameter (m) 0.1286 0.116 0.082 0.15 0.052 0.052 0.052
Outer Tube Inner Diameter (m) 0.032 0.032 0.032
Inner Tube Outer Diameter (m) 0.0254 0.0254 0.0254
Inner Tube Inner Diameter (m) 0.0054 0.0054 0.0054
Width (m) 0.07 0.07 0.101
Height (m) 0.06 0.06 0.101
Wall thickness (m) 0.01 0.01 0.01
*Density (kg/ m3) 7801 7801 7801 7801 8027 8027 8027
*Weight (kg) 11.48 7.49 6.865 31.75 0.5103 0.5103 17.4 57.2 88.62 13.85
*Volume (m3) 0.003896 0.002177 0.00158 0.000294 0.000294 0.000294 0.00306 0.00713 0.01104 0.001725
Power (kW) 0.75 5.8
Speed (rpm) 7000
*Cost ($) 109 109
Table 4.7. Specifications for the Components of the Auxiliary Power Unit
35
4.1.4. Key Parameters Used
The key parameters used for the PRICE Model were based upon discussions with the
PRICE help desk [18] and an analysis of the parameters in the PRICE Model. The key items
were the number of prototypes, the manufacturing complexity, and the manufacturing process
index. The number of prototypes at the 10-unit level was considered to be two; at the 100-unit
level the number of prototypes was assumed to be 10, and at levels of 1,000 or above the process
was assumed to be mature, and there would be no need to manufacture prototypes.
The manufacturing complexity is a measure of the difficulty in manufacturing a particular
component. A new product needing new technology would have a high manufacturing
complexity value compared to a standard product of current technology. The complexity values
for the fuel cell stack were estimated from analyzing the data from various batteries. The
manufacturing complexity factors for the lead acid, nickel hydrogen and nickel cadmium
batteries are listed in Table 4.8, and a plot of the values is presented in Figure 4.6. The expected
platform for the fuel cell was selected to be 0.9, and the manufacturing complexity was estimated
to be 5.8, slightly higher than the expected manufacturing complexity of the nickel hydrogen
batteries at a platform of 0.9.
Table 4.8. Manufacturing Complexity Factors for Various Battery Types
Platform Complexity Factor
Lead Acid, Auto Type Lead Acid, Sealed Nickel Hydrogen Nickel Cadmium 0.6 2.83 4.74 0.8 3.1 5.19 0.9 3.22 5.4 1 3.33 5.58
1.2 2.65 3.53 5.91 1.4 2.79 3.71 6.21 1.6 2.91 3.87 6.49 1.7 3.97 6.73 6.61 1.8 4.02 6.85 6.73 2 7.51 7.38
2.5 8.07 7.92
36
0
1
2
3
4
5
6
7
8
9
0 0.5 1 1.5 2 2.5 3
Platform
Com
plex
ity
Lead Acid Auto Lead Acid Sealed Nickel Hydrogen Nickel Cadmium
Figure 4.6. PRICE input values for Manufacturing Complexity Parameter versus
Platform
Table 4.9. Manufacturing Process Index Values in PRICE at the Maximum Quantity for
Index Value
Quantity
Manufacturing Process Index Value
6 1.75 56 1.3
301 1 10251 0.7
510001 0.25
37
The manufacturing process index is dependant upon the quantity being manufactured. As
indicated in Table 4.9, the Manufacturing Process Index decreases as the production quantity
increases. A relationship was developed from data in the PRICE software and was plotted in
Figure 4.7.
Quantity (vs) MPIy = -0.1257Ln(x) + 1.8526
00.20.40.60.8
11.21.41.61.8
2
1 10 100 1000 10000 100000 1000000
Quantity
Man
ufac
turin
g Pr
oces
s In
dex
Figure 4.7. PRICE input values for MPI Parameter versus Quantity
The relationship developed for the Manufacturing Process Index (MPI) was:
MPI = 2.000 – 0.316 Log (Quantity) Eq. 4.2
The MPI values obtained using the relationship for the various production quantities is
presented in Table 4.10. These values were used in the PRICE model for the MPI values for the
different production levels.
Table 4.10. Values of MPI Parameter Using the New Relationship
Quantity Manufacturing Process Index10 1.68
100 1.37 1,000 1.05 5,000 0.83
10,000 0.74 20,000 0.64 500,00 0.52
100,000 0.42 200,000 0.32 500,000 0.20 1000,000 0.10
38
The manufacturing process index parameter values from the PRICE indicated that there
were two ranges – one when the production quantity was between 6 and 301 units, and, two,
when the production quantity was between 301 and 510,001 units. This difference resulted in
two separate equations for the MPI parameter. The equations were:
MPI = 2.0879 - 0.4424 * Log (Quantity) Eq. 4.3
when the production quantity was less than 301 units and
MPI = 1.5967 – 0.2328 * Log (Quantity) Eq. 4.4
when the production quantity was greater than 301 units or greater
From the above equations, new MPI values were developed for PRICE II. Table 4.11
shows the new MPI values obtained.
Table 4.11. Values of MPI Parameter Using the New Relationships
Quantity MPI 10 1.646 100 1.203
1,000 0.898 5,000 0.736 10,000 0.666 20,000 0.595 50,000 0.503
100,000 0.433 200,000 0.363 500,000 0.27
1,000,000 0.2
4.1.5. PRICE Model Results for 10,000 units
The detailed results for the 10,000-unit base case model are summarized here. The input
values for the base case are in Table 4.12, and the detailed component costs are in Tables 4.13
through 4.23.
39
Table 4.12. PRICE Input for 10,000 Unit Base Case Input Combustor ATR ZnO Bed Air Fuel
Pump Water Pump
Fuel Cell Stack
Air Pre-heater
Steam Generator
Exhaust Condenser Compressor
Quantity 10,000 10,000 10,000 10,000 10,000 10,000 10,000 10,000 10,000 10,000 Number of Prototypes 0 0 0 0 0 0 0 0 0 0
Weight (kg) 11.48 6.86488 7.488 31.75 0.5103 0.5103 17.4 57.233 88.62 13.8534 Volume (m3) 0.00147 0.00088 0.00096 0.0053 0.00029 0.00029 0.00306 0.00713 0.01104 0.00173
Quantity Next Higher Assembly 1 1 1 1 1 1 1 1 1 1 Mechanical Integration Factor 0.15 0.15 0.15 0.15 0.15 0.15 0.35 0.15 0.15 0.15
Platform 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 Year of Technology 2003 2003 2003 2003 2003 2003 2003 2003 2003 2003
Structure Weight (kg) 11.48 6.86488 7.488 31.75 0.5103 0.5103 17.4 57.233 88.62 13.8534 Manufacturing Complexity 3.655 3.655 3.655 3.8 2.65 2.65 5.8 3.8 3.8 3.8
New Structure 0.2 0.2 0.5 0.2 0.85 0.2 0.2 0.2 Design Repeat 0.552 0.552 0.552 0.552 0.552 0.552 0.552 0.552
Mechanical Reliability 0 0 0 0.3 0 0 0 0 Development Start Date 104 104 104 104 104 104 104 104
Development First Prototype 0 0 0 0 0 0 0 0 Development Last Prototype 504 504 504 504 505 504 504 504
Engineering Complexity 0.2 0.2 0.51 0.2 1.25 0.2 0.2 0.2 Development Tooling & Test
Equipment 0 0 0 0 0 0 0 0
Prototype Support 1 1 1 1 1 1 1 1 Production Start Date 504 504 504 504 505 504 504 504
Production First Article Delivery Date
Production End Date 105 105 105 105 105 105 105 Price Improvement Factor Production Tooling & Test
Equipment 0 0 0 0 0 0 0 0
Rate Tooling 0 0 0 0 0 0 0 0 Purchased Item Cost ($) 109 109
Manufacturing Process Index 0.74 0.74 0.74 0.74 0.74 0.74 0.74 0.74
40
Table 4.13. Assembly Cost
Program Cost Development Production Total CostEngineering
Draft 25.6 0.7 26.3 Design 84.6 1.9 86.5 System 15.2 - 15.2
Project Management 24.7 3848.5 3873.2 Data 8.3 908.6 916.9
Subtotal (ENG) 158.4 4759.7 4918.1 Manufacturing
Production - 53742.4 53742.4 Prototype 0 - 0
Tool Test Equipment. 16.8 1613.2 1630 Purchased 0 1943.7 1943.7
Subtotal (MFG) 16.8 57299.3 57316.1 G & A / CoM 0 0 0
Fee / Profit 0 0 0 Total Cost 175.2 62059.0 62234.2
System Total 175.2 62059.0 62234.2
Schedule Start Jan 04 [7] May 04 [19]
First Item Jul 04 [10] Nov 05 [11] Finish May 05 [17] Oct 06 [30]
Assy Weight 235.71 Assy WS 235.71
Assy Series MTBF Hrs 72072 Assy Quantity 10000 Avg Assy Cost 6.3
From Table 4.13, it can be seen that the total weight of the assembly is 235.71 kilograms.
All the costs are in thousands of dollars, i.e., the total cost to manufacture the 10,000 Auxiliary
Power Units is $ 62,234,200, which yields a cost of $ 6,223.42 for each unit. Tables 4.14
through 4.23 indicate the cost to manufacture each individual element, and the total system cost
adds up to the assembly cost shown in Table 4.13 and Table 4.1.
41
Table 4.14. Combustor Cost
Program Cost Development Production Total Cost Engineering
Draft 0.3 0 0.4 Design 0.7 0 0.7 System 0 - 0
Proj. Mgmt. 0.7 163.5 164.2 Data 0.2 38.9 39.1
SubTotal(ENG) 1.9 202.4 204.3 Manufacturing
Production - 1957.1 1957.1 Prototype 0 - 0
Tool Test Eq. 0.6 42.5 43.1 SubTotal(MFG) 0.6 1999.6 2000.1
G & A / CoM 0 0 0 Fee / Profit 0 0 0 Total Cost 2.4 2202.0 2204.4
Schedule Start Jan 04 [1] May 04 [3]
First Item Jan 04*[4] Jul 04*[6] Finish May 04 [5] Jan 05 [9]
Unit Production Cost 0.2 Monthly Prod Rate 1587.69
Production Quantity 10000
Unit Weight 11.48 Unit Volume 0.001 Quantity/Next Higher Assy 1
Design Factors MECHANICAL Product Descriptors
Weight 11.48 Eng. Complexity 0.2 Density 7809.524* Prototype Support 1
MFG. Complexity 3.655 Proto Schedule Factor 0.250* New Design 0.2
Design Repeat 0 Platform 0.9 Engineering Changes 0.002* Year of Technology 2003
Reliability Factor 1 Integration Level 0.15 MTBF (Field) 1054941.518*
Supplemental Information Tooling & Process Factors Development Tooling 1.0*
Amortized Unit Cost 0.22* Production Tooling 1.0* T-1 Cost 0.418* Rate Tooling 0
Dev Cost Multiplier 1.000* Prod Cost Multiplier 1.000* MPI 0.74 Matl Learning Curve 93.82*
Labor Learning Curve 93.82*
42
Table 4.15. ZnO Bed Cost
Program Cost Development Production Total Cost Engineering
Draft 1.5 0 1.5 Design 3.6 0 3.6 System 0.3 - 0.3
Proj. Mgmt. 1.5 126.4 128.0 Data 0.5 30.2 30.7
SubTotal(ENG) 7.5 156.7 164.2 Manufacturing
Production - 1539.6 1539.6 Prototype 0 - 0
Tool Test Eq. 1.2 28.5 29.7 SubTotal(MFG) 1.2 1568.1 1569.3
G & A / CoM 0 0 0 Fee / Profit 0 0 0 Total Cost 8.7 1724.8 1733.5
Schedule Start Jan 04 [2] May 04 [3]
First Item Feb 04*[3] Jul 04*[6] Finish May 04 [5] Jan 05 [9]
Unit Production Cost 0.16 Monthly Prod Rate 1542.01
Production Quantity 10000
Unit Weight 7.488 Unit Volume 0.001 Quantity/Next Higher Assy 1
Design Factors MECHANICAL Product Descriptors
Weight 7.488 Eng. Complexity 0.51 Density 7800* Prototype Support 1
MFG. Complexity 3.655 Proto Schedule Factor 0.250* New Design 0.5
Design Repeat 0 Platform 0.9 Engineering Changes 0.004* Year of Technology 2003
Reliability Factor 1 Integration Level 0.15 MTBF (Field) 1199226.455*
Supplemental Information Tooling & Process Factors Development Tooling 1.0*
Amortized Unit Cost 0.17* Production Tooling 1.0* T-1 Cost 0.330* Rate Tooling 0
Dev Cost Multiplier 1.000* Prod Cost Multiplier 1.000* MPI 0.74 Matl Learning Curve 93.80*
Labor Learning Curve 93.80*
43
Table 4.16. Auto Thermal Reformer Cost
Program Cost Development Production Total Cost Engineering
Draft 0.3 0 0.3 Design 0.5 0 0.5 System 0 - 0
Proj. Mgmt. 0.5 120 120.5 Data 0.2 28.7 28.9
SubTotal(ENG) 1.4 148.7 150.1 Manufacturing
Production - 1346.6 1346.6 Prototype 0 - 0
Tool Test Eq. 0.4 26.2 26.7 SubTotal(MFG) 0.4 1372.8 1373.3
G & A / CoM 0 0 0 Fee / Profit 0 0 0 Total Cost 1.8 1521.6 1523.4
Schedule Start Jan 04 [1] May 04 [2]
First Item Jan 04*[4] Jun 04*[7] Finish May 04 [5] Jan 05 [9]
Unit Production Cost 0.14 Monthly Prod Rate 1533.41
Production Quantity 10000
Unit Weight 6.865 Unit Volume 0.001 Quantity/Next Higher Assy 1
Design Factors MECHANICAL Product Descriptors
Weight 6.865 Eng. Complexity 0.2 Density 7801* Prototype Support 1
MFG. Complexity 3.655 Proto Schedule Factor 0.250* New Design 0.2
Design Repeat 0 Platform 0.9 Engineering Changes 0.002* Year of Technology 2003
Reliability Factor 1 Integration Level 0.15 MTBF (Field) 1230895.166*
Supplemental Information Tooling & Process Factors Development Tooling 1.0*
Amortized Unit Cost 0.15* Production Tooling 1.0* T-1 Cost 0.289* Rate Tooling 0
Dev Cost Multiplier 1.000* Prod Cost Multiplier 1.000* MPI 0.74 Matl Learning Curve 93.79*
Labor Learning Curve 93.79*
44
Table 4.17. Air Compressor Cost
Program Cost Development Production Total Cost Engineering
Draft 0.6 0 0.6 Design 1.2 0.1 1.3 System 0 - 0
Proj. Mgmt. 1.1 367 368.2 Data 0.3 86.7 87.1
SubTotal(ENG) 3.3 453.9 457.2 Manufacturing
Production - 4854.2 4854.2 Prototype 0 - 0
Tool Test Eq. 1.1 143.7 144.8 SubTotal(MFG) 1.1 4997.9 4999
G & A / CoM 0 0 0 Fee / Profit 0 0 0 Total Cost 4.4 5451.8 5456.1
Schedule Start Jan 04 [1] May 04 [3]
First Item Jan 04*[4] Jul 04*[6] Finish May 04 [5] Jan 05 [9]
Unit Production Cost 0.49 Monthly Prod Rate 1793.56
Production Quantity 10000
Unit Weight 31.75 Unit Volume 0.005 Quantity/Next Higher Assy 1
Design Factors MECHANICAL Product Descriptors
Weight 31.75 Eng. Complexity 0.2 Density 5990.566* Prototype Support 1
MFG. Complexity 3.8 Proto Schedule Factor 0.250* New Design 0.2
Design Repeat 0 Platform 0.9 Engineering Changes 0.002* Year of Technology 2003
Reliability Factor 1 Integration Level 0.15 MTBF (Field) 686467.440*
Supplemental Information Tooling & Process Factors Development Tooling 1.0*
Amortized Unit Cost 0.55* Production Tooling 1.0* T-1 Cost 1.023* Rate Tooling 0
Dev Cost Multiplier 1.000* Prod Cost Multiplier 1.000* MPI 0.74 Matl Learning Curve 93.94*
Labor Learning Curve 93.94*
45
Table 4.18. Fuel Pump Cost
Program Cost Production Purchased Item Cost 971.9
G & A / CoM 0 Fee / Profit 0 Total Cost 971.9
Unit Production Cost 0.1 Input Cost 109.00 (Single Units) Base Year 2003
Production Quantity 10000
Unit Weight 0.51 Unit Volume 0 Quantity/Next Higher Assy 1
Design Factors MECHANICAL Product Descriptors
Weight 0.51 Density 1759.655* Platform 0.9
MFG. Complexity 2.65 Year of Technology 2003 Int Design Level 0.15 Reliability Factor 1
MTBF (Field) 7652770.379* Integration Level 0.15
Supplemental Information Prod Cost Multiplier 1.000* Matl Learning Curve 95.64* Labor Learning Curve 95.64*
46
Table 4.19. Water Pump Cost
Program Cost Production Purchased Item Cost 971.9
G & A / CoM 0 Fee / Profit 0 Total Cost 971.9
Unit Production Cost 0.1 Input Cost 109.00 (Single Units) Base Year 2003
Production Quantity 10000
Unit Weight 0.51 Unit Volume 0 Quantity/Next Higher Assy 1
Design Factors MECHANICAL Product Descriptors
Weight 0.51 Density 1759.655* Platform 0.9
MFG. Complexity 2.65 Year of Technology 2003 Int Design Level 0.15 Reliability Factor 1
MTBF (Field) 7652770.379* Integration Level 0.15
Supplemental Information Prod Cost Multiplier 1.000* Matl Learning Curve 95.64* Labor Learning Curve 95.64*
47
Table 4.20. Fuel Cell Stack Cost
Program Cost Development Production Total Cost Engineering
Draft 20.6 0.5 21.1 Design 74.2 1.4 75.6 System 14.7 - 14.7
Proj. Mgmt. 16.4 1501.1 1517.4 Data 5.7 353.1 358.8
Subtotal (ENG) 131.5 1856.0 1987.5 Manufacturing
Production - 23393.4 23393.4 Prototype 0 - 0
Tool Test Eq. 9.4 651.9 661.2 Subtotal (MFG) 9.4 24045.3 24054.7
G & A / CoM 0 0 0 Fee / Profit 0 0 0 Total Cost 140.9 25901.3 26042.2
Schedule Start Jan 04 [7] May 05 [7]
First Item Jul 04*[10] Nov 05*[12] Finish May 05 [17] Oct 06*[18]
Unit Production Cost 2.4 Monthly Prod Rate 858.85
Production Quantity 10000
Unit Weight 17.4 Unit Volume 0.003 Quantity/Next Higher Assy 1
Design Factors MECHANICAL Product Descriptors
Weight 17.4 Eng. Complexity 1.25 Density 5686.275* Prototype Support 1
MFG. Complexity 5.8 Proto Schedule Factor 0.250* New Design 0.85
Design Repeat 0 Platform 0.9 Engineering Changes 0.011* Year of Technology 2003
Reliability Factor 1 Integration Level 0.35 MTBF (Field) 212479.100*
Supplemental Information Tooling & Process Factors Development Tooling 1.0*
Amortized Unit Cost 2.66* Production Tooling 1.0* T-1 Cost 5.464* Rate Tooling 0
Dev Cost Multiplier 1.000* Prod Cost Multiplier 1.000* MPI 0.74 Matl Learning Curve 93.25*
Labor Learning Curve 93.25*
48
Table 4.21. Cathode Air Pre-heater Cost
Program Cost Development Production Total Cost Engineering
Draft 0.9 0.1 0.9 Design 1.7 0.1 1.8 System 0 - 0
Proj. Mgmt. 1.6 572.8 574.4 Data 0.5 135.3 135.8
Subtotal (ENG) 4.7 708.3 713 Manufacturing
Production - 7550.3 7550.3 Prototype 0 - 0
Tool Test Eq. 1.5 257.2 258.7 Subtotal (MFG) 1.5 7807.4 7809
G & A / CoM 0 0 0 Fee / Profit 0 0 0 Total Cost 6.2 8515.7 8521.9
Schedule Start Jan 04 [1] May 04 [4]
First Item Jan 04*[4] Aug 04*[5] Finish May 04 [5] Jan 05 [9]
Unit Production Cost 0.76 Monthly Prod Rate 1914.63
Production Quantity 10000
Unit Weight 57.233 Unit Volume 0.007 Quantity/Next Higher Assy 1
Design Factors MECHANICAL Product Descriptors
Weight 57.233 Eng. Complexity 0.2 Density 8027.069* Prototype Support 1
MFG. Complexity 3.8 Proto Schedule Factor 0.250* New Design 0.2
Design Repeat 0 Platform 0.9 Engineering Changes 0.002* Year of Technology 2003
Reliability Factor 1 Integration Level 0.15 MTBF (Field) 575240.041*
Supplemental Information Tooling & Process Factors Development Tooling 1.0*
Amortized Unit Cost 0.86* Production Tooling 1.0* T-1 Cost 1.580* Rate Tooling 0
Dev Cost Multiplier 1.000* Prod Cost Multiplier 1.000* MPI 0.74 Matl Learning Curve 94.00*
Labor Learning Curve 94.00*
49
Table 4.22. Steam Generator Cost
Program Cost Development Production Total Cost Engineering
Draft 1.1 0.1 1.2 Design 2.1 0.1 2.2 System 0.1 - 0.1
Proj. Mgmt. 2.1 798 800 Data 0.6 188.5 189.2
Subtotal (ENG) 6 986.7 992.7 Manufacturing
Production - 10488.1 10488.1 Prototype 0 - 0
Tool Test Eq. 2 398.9 400.9 Subtotal (MFG) 2 10887 10889
G & A / CoM 0 0 0 Fee / Profit 0 0 0 Total Cost 7.9 11873.8 11881.7
Schedule Start Jan 04 [1] May 04 [4]
First Item Jan 04*[4] Aug 04*[5] Finish May 04 [5] Jan 05 [9]
Unit Production Cost 1.06 Monthly Prod Rate 2024.88
Production Quantity 10000
Unit Weight 88.62 Unit Volume 0.011 Quantity/Next Higher Assy 1
Design Factors MECHANICAL Product Descriptors
Weight 88.62 Eng. Complexity 0.2 Density 8027.174* Prototype Support 1
MFG. Complexity 3.8 Proto Schedule Factor 0.250* New Design 0.2
Design Repeat 0 Platform 0.9 Engineering Changes 0.002* Year of Technology 2003
Reliability Factor 1 Integration Level 0.15 MTBF (Field) 504525.984*
Supplemental Information Tooling & Process Factors Development Tooling 1.0*
Amortized Unit Cost 1.20* Production Tooling 1.0* T-1 Cost 2.180* Rate Tooling 0
Dev Cost Multiplier 1.000* Prod Cost Multiplier 1.000* MPI 0.74 Matl Learning Curve 94.05*
Labor Learning Curve 94.05*
50
Table 4.23. Exhaust Condenser Cost
Program Cost Development Production Total Cost Engineering
Draft 0.4 0 0.4 Design 0.8 0.1 0.8 System 0 - 0
Proj. Mgmt. 0.8 199.7 200.5 Data 0.2 47.2 47.5
Subtotal (ENG) 2.2 247 249.2 Manufacturing
Production - 2613.1 2613.1 Prototype 0 - 0
Tool Test Eq. 0.7 64.3 65 Subtotal (MFG) 0.7 2677.4 2678.1
G & A / CoM 0 0 0 Fee / Profit 0 0 0 Total Cost 2.9 2924.4 2927.3
Schedule Start Jan 04 [1] May 04 [3]
First Item Jan 04*[4] Jul 04*[6] Finish May 04 [5] Jan 05 [9]
Unit Production Cost 0.26 Monthly Prod Rate 1661.76
Production Quantity 10000
Unit Weight 13.853 Unit Volume 0.002 Quantity/Next Higher Assy 1
Design Factors MECHANICAL Product Descriptors
Weight 13.853 Eng. Complexity 0.2 Density 8007.746* Prototype Support 1
MFG. Complexity 3.8 Proto Schedule Factor 0.250* New Design 0.2
Design Repeat 0 Platform 0.9 Engineering Changes 0.002* Year of Technology 2003
Reliability Factor 1 Integration Level 0.15 MTBF (Field) 880392.126*
Supplemental Information Tooling & Process Factors Development Tooling 1.0*
Amortized Unit Cost 0.30* Production Tooling 1.0* T-1 Cost 0.556* Rate Tooling 0
Dev Cost Multiplier 1.000* Prod Cost Multiplier 1.000* MPI 0.74 Matl Learning Curve 93.87*
Labor Learning Curve 93.87*
51
The various development, production total costs, labor and material costs, and distribution of
effort are presented in Figures 4.8 through 4.15 for the auxiliary power unit. Figure 4.8 indicates
that design cost is the major cost component of the development category cost.
Figure 4.8. Development Category Cost
Figures 4.9 and 4.10 indicate that production is the major cost component of the production
category cost and of the total category cost.
Figure 4.9. Production Category Cost
52
Figure 4.10. Total Category Cost
Figures 4.11, 4.12 and 4.13 indicate that the solid oxide fuel cell stack is the most expensive
component of the auxiliary power unit because of its complexity and because it is not yet fully
developed. The steam generator, cathode air pre-heater, and the air compressor, in that order, are
the next most expensive components after the fuel cell stack.
Figure 4.11. Development Component Cost
53
Figure 4.12. Production Component Cost
Figure 4.13. Total Component Cost
The LM (labor and materials) break-out graph, Figure 4.14, indicates that materials have the
maximum share in the total cost. The materials to labor cost share ratio is almost 6.
54
LM Breakout
Labor % ofTotal
Material % ofTotal
%
Auxiliary Power Unit
15.5
84.5
Figure 4.14. LM Breakout
Figure 4.15 indicates that the production stage requires most of the effort.
Distribution of Effort
Draft
Design
System
Proj. Mgmt.
Data
Production
Prototype
Tool Test Eq.
Costsin
Hours
Auxiliary Power Unit
0
50000
100000
150000
Figure 4.15. Distribution of Effort
One major advantage of the PRICE models is the ease with which various outputs can be
obtained. The PRICE models were extremely useful in estimating the improvement rates to use
in the traditional cost models developed in the next section.
55
56
4.2 Traditional Cost Models
4.2.1. CER Model Results
The traditional cost models used the cost estimating relationships developed from
industrial data and data from the literature. The data to develop CERs was sparse, and the
relationships developed for the components could have considerable error. The need for the
traditional models was to include the effects of the process variables such as temperature, power
density, fuel utilization, transfer area, volume, and horsepower. Some of the relationships had to
be adjusted for improvement rates obtained from the first unit cost, and this was done utilizing
the improvement rates obtained from the PRICE models developed. Two different models were
developed using the improvement rates from the PRICE models.
The CER Model I used the improvement rates for both ranges for all components. The
CER Model I results are presented in Table 4.24 for the production quantities from 10 units to 1
million units. The results were $2,055 for the 5 kW APU at the 500,000-production level with a
cost of $411/kW. The costs for the fuel cell stack were approximately $300 higher using the
CER model than the PRICE models, but the total cost was lower than PRICE II results. The
costs for the fuel pump and water pump were considered as purchased parts and the
improvement rate was considered as 2% over the first 1,000 units.
The CER Model II used the lower improvement rates (that is, the improvement rates at
the higher production quantities) for the air compressor, air pre-heater #1, steam generator, and
the exhaust condenser. The lower rates were used as the CERs for these components were
developed from industrial or published data and the higher initial improvement rates most likely
would have been obtained previously. The results for the CER Model II are in Table 4.25 for
production levels from 10 units to 1 million units. The estimate at the 500,000-unit level was
$2,378 for the 5 kW APU with a cost of $476/kW. The results of Model II are closer to the
results expected as the improvement rate effects have been reduced on the equations developed
from the existing equipment rather than equipment being developed. These estimates from the
CER Model II were in better agreement with the PRICE models, NETL model, and ADL model
than the CER Model I estimates.
Table 4.24. CER Model I Results
Element A Cost
(USD) Cost
(USD) Cost
(USD) Cost
(USD) Cost
(USD) Cost
(USD) Cost
(USD) Cost
(USD) Units 10 100 1,000 10,000 100,000 200,000 500,000 1,000,000
Combustor 2,629.22 1,673.93 867.49 424.00 238.95 149.35 130.25 108.81 95.01 ZnO Bed 2,472.83 1,385.73 593.25 233.97 114.85 69.33 60.16 50.00 43.51
ATR 2,696.37 1,709.89 880.91 427.74 239.66 149.64 130.49 109.00 95.17 Air Compressor 3,073.00 1,993.11 1,061.83 535.20 301.19 186.03 161.59 134.26 116.75
Fuel Pump 109.00 104.37 98.13 91.86 91.86 91.86 91.86 91.86 91.86 Water Pump 109.00 104.37 98.13 91.86 91.86 91.86 91.86 91.86 91.86
Fuel Cell Stack 68,286.39 37,695.42 15,777.18 6,065.17 2,936.93 1,767.51 1,533.51 1,274.25 1,108.81 Air Pre-heater #1 1,822.33 1,189.83 640.19 326.25 183.98 113.03 97.98 81.20 70.46 Steam Generator 2,020.82 1,328.26 721.79 371.91 210.42 128.84 111.55 92.28 79.97
Exhaust Condenser 521.61 334.29 174.96 86.46 48.39 30.09 26.20 21.85 19.05
Unit Cost 47,519.21 20,913.84 8,654.43 4,458.11 2,777.55 2,435.47 2,055.37 1,812.47 Cost/kW 9,503.84 4,182.77 1,730.89 891.62 555.51 487.09 411.07 362.49
Total Cost* (Thousand Dollars) 475.1921 2,091.3844 8,654.434 44,581.117 277,754.542 487,093.911 1,027,686.569 1,812,472.318
*Total Cost is in thousands of dollars.
57
Element A Cost
(USD) Cost
(USD) Cost
(USD) Cost
(USD) Cost
(USD) Cost
(USD) Cost
(USD) Cost
(USD) Units 10 100 1,000 10,000 100,000 200,000 500,000 1,000,000
Combustor 2,629.22 1,673.93 867.49 424.00 238.95 149.35 130.25 108.81 95.01 ZnO Bed 2,472.83 1,385.73 593.25 233.97 114.85 69.33 60.16 50.00 43.51
ATR 2,696.37 1,709.89 880.91 427.74 239.66 149.64 130.49 109.00 95.17 Air Compressor 3,073.00 2,296.31 1,508.09 957.61 603.77 380.18 330.75 275.12 239.34
Fuel Pump 109.00 104.37 98.13 91.86 91.86 91.86 91.86 91.86 91.86 Water Pump 109.00 104.37 98.13 91.86 91.86 91.86 91.86 91.86 91.86
Fuel Cell Stack 68,286.39 37,695.42 15,777.18 6,065.17 2,936.93 1,767.51 1,533.51 1,274.25 1,108.81 Air Pre-heater #1 1,822.33 1,356.07 885.15 558.29 349.60 218.62 189.80 157.44 136.68 Steam Generator 2,020.82 1,499.60 974.85 612.12 381.56 237.51 205.91 170.50 147.81
Exhaust Condenser 521.61 391.95 259.53 166.28 105.80 67.24 58.66 48.97 42.72
Unit Cost 48,217.65 21,942.69 9,628.91 5,154.86 3,223.10 2,823.25 2,377.81 2,092.79 Cost/kW 9,643.53 4,388.54 1,925.78 1,030.97 644.62 564.65 475.56 418.56
Total Cost* (Thousand Dollars) 482.175 2,194.269 9,628.910 51,548.589 322,310.313 564,650.639 1,188,904.414 2,092,786.757
Table 4.25. CER Model II Results
58
*Total Cost is in thousands of dollars.
59
4.2.2. CER Results For Year 2009
The CER results obtained above have been from the data collected in 2003 (time of reference).
To adjust the prices to year 2009 (time of interest), Equation 1 was used:
C(t) = C(r) * I(t) / I(r) Eq. 4.1
Where C(t) = Cost at time of interest
C(r) = Cost at time of reference
I(t) = Cost index at the time of interest
I(r) = Cost index at the time of reference
The Marshall and Swift cost indices data for the year 2003 and 2009 was unavailable.
The Producers Price Index values published by the US government every month were used
instead. The PPI values obtained for various components of the APU are listed in Table 4.4.
Table 4.4. PPI Values [29] Component 2009 Cost Index 2003 Cost Index Description
Combustor 139.3 100 Steel foundries, except investment ZnO Bed 221.7 100 Other basic inorganic chemical mfg.
ATR 139.3 100 Steel foundries, except investment
Air Compressor 130.4 100 Compressors and compressor units, all
refrigerants, except automotive Fuel Pump 127.8 100 Pump and compressor manufacturing.
Water Pump 127.8 100 Pump and compressor manufacturing. Fuel Cell Stack 113.7 100 Primary batteries, dry and wet
Air Pre-heater #1 137.8 100 Power boiler and heat exchanger
manufacturing.
Steam Generator 137.8 100 Power boiler and heat exchanger
manufacturing.
Exhaust Condenser 137.8 100 Power boiler and heat exchanger
manufacturing.
The 2003 costs (cost at the time of reference) for each component at various quantities and the
cost indices from the PPI values were substituted in Eq. 1 to obtain the 2009 costs (cost at the
time of interest). CER Model I and CER Model II results obtained for the year 2009 are listed in
Tables 4.26 and 4.27.
Table 4.26. 2009 CER Model I Results
Element A Cost
(USD) Cost
(USD) Cost
(USD) Cost
(USD) Cost
(USD) Cost
(USD) Cost
(USD) Cost
(USD) Units 10 100 1,000 10,000 100,000 200,000 500,000 1,000,000
Combustor 2,629.22 2,331.78 1,208.41 590.63 332.86 208.05 181.44 151.57 132.35 ZnO Bed 2,472.83 3,072.16 1,315.23 518.71 254.63 153.69 133.38 110.85 96.46
ATR 2,696.37 2,381.88 1,227.11 595.84 333.85 208.44 181.77 151.84 132.58 Air Compressor 3,073.00 2,599.01 1,384.62 697.90 392.75 242.59 210.71 175.08 152.25
Fuel Pump 109.00 133.39 125.40 117.40 117.40 117.40 117.40 117.40 117.40 Water Pump 109.00 133.39 125.40 117.40 117.40 117.40 117.40 117.40 117.40
Fuel Cell Stack 68,286.39 42,859.69 17,938.65 6,896.09 3,339.29 2,009.66 1,743.61 1,448.82 1,260.72 Air Pre-heater #1 1,822.33 1,639.59 882.18 449.57 253.53 155.75 135.02 111.89 97.10 Steam Generator 2,020.82 1,830.35 994.63 512.50 289.96 177.55 153.72 127.16 110.20
Exhaust Condenser 521.61 460.66 241.09 119.14 66.68 41.46 36.11 30.11 26.25
Unit Cost 57,441.89 25,442.74 10,615.20 5,498.36 3,432.00 3,010.56 2,542.12 2,242.71 Cost/kW 11,488.38 5,088.55 2,123.04 1,099.67 686.40 602.11 508.42 448.54
Total Cost* (Thousand Dollars) 574.419 2,544.274 10,615.204 54,983.581 343,199.653 602,111.366 1,271,059.459 2,242,708.769
*Total Cost is in thousands of dollars.
60
Element A Cost
(USD) Cost
(USD) Cost
(USD) Cost
(USD) Cost
(USD) Cost
(USD) Cost
(USD) Cost
(USD) Units 10 100 1,000 10,000 100,000 200,000 500,000 1,000,000
Combustor 2,629.22 2,331.78 1,208.41 590.63 332.86 208.05 181.44 151.57 132.35 ZnO Bed 2,472.83 3,072.16 1,315.23 518.71 254.63 153.69 133.38 110.85 96.46
ATR 2,696.37 2,381.88 1,227.11 595.84 333.85 208.44 181.77 151.84 132.58 Air Compressor 3,073.00 2,994.39 1,966.55 1,248.72 787.32 495.76 431.29 358.75 312.10
Fuel Pump 109.00 133.39 125.40 117.40 117.40 117.40 117.40 117.40 117.40 Water Pump 109.00 133.39 125.40 117.40 117.40 117.40 117.40 117.40 117.40
Fuel Cell Stack 68,286.39 42,859.69 17,938.65 6,896.09 3,339.29 2,009.66 1,743.61 1,448.82 1,260.72 Air Pre-heater #1 1,822.33 1,868.66 1,219.74 769.33 481.74 301.26 261.54 216.95 188.35 Steam Generator 2,020.82 2,066.45 1,343.34 843.51 525.78 327.29 283.75 234.94 203.68
Exhaust Condenser 521.61 540.11 357.63 229.13 145.80 92.65 80.83 67.48 58.87
Unit Cost 58,381.90 26,827.47 11,926.77 6,436.08 4,031.61 3,532.41 2,976.01 2,619.91 Cost/kW 11,676.38 5,365.49 2,385.35 1,287.22 806.32 706.48 595.20 523.98
Total Cost* (Thousand Dollars) 583.819 2,682.747 11,926.775 64,360.846 403,160.805 706,481.03 1,488,006.13 2,619,910.755
Table 4.27. 2009 CER Model II Results
61
*Total Cost is in thousands of dollars.
4.2.3. Cost Estimating Relationships
The cost of each component of the APU was estimated using cost estimating
relationships, and then all the component costs were summed to obtain the total cost of the APU.
These CERs were developed from various reference sources for the different components. When
CER’s could not be developed, data from the NETL [1] model was used. CER’s were not
developed for the ZnO bed, Auto Thermal Reformer (ATR), Fuel pump, and Water pump. Data
for each component of the APU and the equation developed for that component are presented
with the appropriate figures.
1. Combustor: The data was given by NETL [24]. Table 4.28. presents the manufacturing cost
data for the combustor.
Table 4.28. Manufacturing Cost Data for Combustor [24]
Sheet Metal Work Number Quantity Cost per Cost ($) Shearing 2 1 0.2 $/cut 0.40 Stamping 1 122.97 in2 0.05 $/in2 6.15
2 33.44 in2 0.05 $/in2 3.34 Welding 1 12.00 in2 0.35 $/in 4.20
2 10.25 in2 0.35$/in 7.18 Total Cost 21.27
Table 4.29 gives the other specifications for the combustor and the total cost obtained.
62
Table 4.29. Combustor Parameters and Total Cost Data [24]
Residence Time 0.05 sec Fuel Eq. Ratio, phi 0.3
Actual phi 0.03777 Inlet temp 800 oC
Outlet temp 863.1 oC Operation Adiabatic Flow Rate 118.4 m3/hr
0.03289 m3/secVolume of Reactor 0.002 m3
1.644 Liter Length 12 in
0.305 m Diameter 0.083 m
Wall Thickness 0.01 m Volume of Steel 0.0009 m3
Unit Weight 7801 kg/m3
Cost/kg 5.512 $/kg Material Cost ($) 38.759 Vessel Cost ($) 38.76
Manufacture Cost ($) 21.27 Total Cost ($) 60.03
The equation developed from the above data was:
Cost ($/unit) = 42 * (Volume) 0.7 Eq. 4.5
where Volume is in Liters.
The combustor equation was based on the volume of 1.644 liters from the NETL data and
is valid when the production quantity is 500,000. The default value for the volume here is
taken as 3.896 liters, which the NETL is planning to use in the APU.
2. ZnO Bed: The ZnO bed purifies the fuel, input to the stack anode, by removing any sulfur
impurities. The data for the ZnO bed is given in the ADL report [17] and according to the
study, the cost of one unit of ZnO bed was $50 per unit when the production quantity is
500,000-units.
3. ATR: The Auto Thermal Reformer partially oxidizes the fuel input to the stack anode. The
data for the ATR was given in the ADL report [17] and the cost of one unit of ATR was $109
per unit when the production quantity is 500,000-units. The cost of $109 included the cost of
the pre-heaters according to ADL.
63
4. Air Compressor: The air compressor compresses the air to the stack cathode and increases
the temperature of the air. The compressor data collected from three different scroll air
compressor company manufacturers is in Table 4.30.
Table 4.30. Air Compressor Cost Data
Power (HP) Quoted Cost ($) Company 3.00 5730.00 Atlas Copco 5.00 6605.00 Atlas Copco 0.028 500.000 Air Squared 0.33 2500.00 Air Squared 0.50 5000.00 Air Squared 3.00 4205.00 Compressorworld.com 5.00 4920.63 Compressorworld.com 10.00 11125.00 Compressorworld.com 15.00 15250.00 Compressorworld.com 20.00 19250.00 Compressorworld.com
The equation developed from the data was:
Cost ($/unit) = 2218 + 855 * Horsepower Eq. 4.6
The default value to calculate the cost of the first compressor was 1 Hp. NETL is using
the 1 Hp unit in the APU. Figure 4.16 shows the plot between the cost and horsepower data.
Cost (vs) Hp y = 855.35x + 2217.5R2 = 0.9602
0.00
5000.00
10000.00
15000.00
20000.00
25000.00
0.00 5.00 10.00 15.00 20.00 25.00
Horsepower
Cos
t ($)
Figure 4.16. Plot of the scroll compressor cost data
5. Fuel Pump: The fuel pump was a purchased component and the price quoted both by NETL
[24] and ADL [17] was $109 per unit.
64
6. Water Pump: The fuel pump was a purchased component, and the price quoted both by
NETL [24] and ADL [17] was $109 per unit.
7. Fuel Cell Stack: The solid oxide fuel cell stack is the primary component to provide power in
the APU. The cost data for the stack was very limited, and the only data available was from
the ADL report [17]. This ADL data for 500,000-units of production is presented in Table
4.31 [17]. The gross power of the stack is 5.8 kW, but the net power output of the NETL unit
was 5 kW because of the parasitic loads of the compressor and the pumps, which consumed
about 0.8 kW.
Table 4.31. ADL Fuel Cell Stack Cost Data [17]
Power Density (W/cm2) Temperature (degree Celsius) Fuel Utilization (%) Cost ($) 0.3 650 90 1184 0.6 500 90 595 0.3 700 70 1369 0.6 650 90 643
Regression analysis of the data in Table 4.32 resulted in the following equation:
Cost($/unit) = 2277.5 – 1803.33*PD + 0.32*T – 8.45*FU Eq. 4.7
where PD = Power Density is in W/cm2
T = Temperature is in degrees Centigrade
FU = Fuel Utilization is in percent.
This equation is for a net 5 kW APU unit and the default values used were: 0.3 W/cm2,
800 0C, and 85 % for the power density, temperature, and fuel utilization, respectively, as the
stack in the NETL APU would be operating at these specifications.
8. Air Pre-heater: The cathode air pre-heater takes heat from the exhaust stream of the stack to
heat the air, input to the stack cathode. The data for this heat exchanger was from [18] and
the equation developed from this data was:
Cost ($/unit) = 1/1.6 * [(18 * T – 9500)* (TA) 0.45] Eq. 4.8
where T = Temperature is in degrees Centigrade
TA = Transfer Area is in square meters (m2).
The factor of 1/1.6 is used to convert the cost to US dollars, as the costs in the original
report were in GB pounds. The default temperature was 800 0C, and the transfer area was
calculated by the formula π * D * L, where D is the diameter of the inner tube of the heat
65
exchanger, and L is the length of the heat exchanger. The default values were 0.0254m and
3.954m, which are the NETL specifications for the APU and result in a transfer area of 0.315
square meters.
9. Steam Generator: The steam generator takes heat from the exhaust stream of the stack to
form steam required for the partial oxidation of the fuel. The cost data for the steam
generator is from the Exergy [25] company catalog. Table 4.32 gives the cost data for the
steam generator.
Table 4.32. Steam Generator Cost Data [25]
Transfer Area (m2) Cost ($) Cost ($/m2)0.11 670 6090.91 0.16 920 5750 0.26 1260 4846.15
The equation developed from the above data was:
Cost ($) = 3409.9 * (Transfer Area) 0.73 Eq. 4.9
where Transfer Area is in square meters (m2).
The transfer area was calculated by the formula π * D * L, where D is the diameter of the
inner tube of the heat exchanger, and L is the length of the heat exchanger. The default
values were 0.0254m and 6.12m and result in a transfer area of 0.488 square meters, which
the NETL is using for the APU. Figure 4.17 shows the plot between the specific costs of the
heat exchangers against the transfer area.
Heat Exchanger Costsy = 3409.9x-0.2699
R2 = 0.9587
0
2000
4000
6000
8000
0 0.1 0.2
Transfer Area (m2)
Cos
t ($/
m2)
0.3
Figure 4.17. Exergy Heat Exchanger Cost Data [25]
66
10. Exhaust Condenser: The exhaust condenser cost data is the same as for the steam generator,
and the equation developed for the steam generator was also used for the exhaust condenser.
The equation used was:
Cost ($) = 3409.9 * (Transfer Area) 0.73 Eq. 4.10
where Transfer Area is in square meters (m2).
The transfer area was calculated by the formula π * D * L, where D is the diameter of the
inner tube of the heat exchanger, and L is the length of the heat exchanger. The default
values were 0.0254m and 0.957m and resulted in a transfer area of 0.076 square meters,
which were the values used by NETL for the APU.
Table 4.33 summarizes the equations developed and the improvement rates used to calculate
the costs.
Table 4.33. Summary of the CER’s Developed for SOFC Components and the
Improvement Rates used
Component Cost Estimating Relationship Variables Improvement
Rates < 1,000 > 1,000
Combustor C = 42 * (V) 0.7C = Cost ($/unit)
V = Volume (Liters) 20 % 13 % ZnO Bed $50 (Estimated Cost) 25 % 13 %
ATR $109 (Estimated Cost) 20 % 13 %
Air Compressor C = 2218 + 855 * (Hp) C = Cost ($/unit) Hp = Horsepower 19 % 13 %
Fuel Pump $109 (Purchased Component) 2 % 0% Water Pump $109 (Purchased Component) 2 % 0%
Fuel Cell Stack C = 2277.5 – 1803.33 * PD + 0.32 * T –
8.45 * FU
C = Cost ($/unit) PD = Power Density (W/cm2)
T = Temperature (0C) FU = Fuel Utilization (%) 26 % 13 %
Air Pre-heater #1 C = 1/1.6 * (18 * T – 9500) * (TA) 0.45
C = Cost ($/unit) T = Temperature (0C)
TA = Transfer Area (m2) 19 % 13 %
Steam Generator C = 3409.9 * (TA) 0.73C = Cost ($/unit)
TA = Transfer Area (m2) 19 % 13 %
Exhaust Condenser C = 3409.9 * (TA) 0.73C = Cost ($/unit)
TA = Transfer Area (m2) 20 % 13 %
4.2.4. Discussion of the Cost Estimating Relationships
The data for the SOFC components was limited and led to serious concerns on the specific
values for the model. Some of the specific issues were:
67
1. The combustor equation was developed from the NETL [24] data and the use of 0.7 as
the cost capacity exponent.
2. The expression for the scroll air compressor was developed from three sources whose
data was above or below the desired range. The combined data was used, and it did
cover the desired range, but errors could be large.
3. For the fuel cell stack, the NETL temperature (800 0C) was outside the ADL data points
(500 0C – 700 0C), but this was the only data available. Moreover the data was for
gasoline powered fuel cells.
4. For the air pre-heater, the data was from “market orientated design studies for SOFC
based systems” [18], which were of the size of more than 2 square meters, whereas the
proposed design was 0.315 square meters.
5. For the steam generator, the data ranged from 0.11 to 0.26 square meters, whereas the
proposed design was 0.488 square meters.
6. For the exhaust condenser, the data ranged from 0.11 to 0.26 square meters, whereas the
proposed design was 0.076 square meters.
7. Appropriate data could not be found for the ZnO Bed, Auto Thermal Reformer (ATR),
Fuel Pump, and Water Pump. The data used for these items was from previous reports.
4.2.5. Improvement Rates
The PRICE II results were used to estimate the improvement rates to be used in the
traditional cost models. Each component’s costs at the different production quantities were
plotted on a log-log graph and the improvement rates were derived from the slopes (adjusted for
the scale differences). Figure 4.18 indicates the slopes on the graph. From Figure 4.18 there are
two improvement ranges – one for production quantities 1 through 1,000 and the second for
production quantities 1,000 through 500,000. The slopes were taken for both the ranges using
the formulae:
BB1 = (log C 10 – log C 1,000) / (log 10 – log 1,000) Eq. 4.11
BB2 = (log C 1,000 – log C 500,000) / (log 1,000 – log 500,000) Eq. 4.12
where C 10, C 1,000 and C 500,000 are the costs at 10, 1,000 and 500,000-units of production
respectively. B1 and B2 are the slopes of the curve.
68
The improvement rates were calculated by using the formulae:
I1 = 100 * (1 – 2 B1) Eq. 12
I2 = 100 * (1 – 2 B2) Eq. 13
where I1 and I2 are the improvement rates and b1 and b2 are the slopes of the curve.
All the component plots have the same improvement ranges as in Figure 4.18 and the
formulae used to calculate improvement rates for all the components were the same.
Unit Cost (vs) Quantity
1
10
100
1,000
10,000
1 10 100
1,00
0
10,0
00
100,
000
1,00
0,00
0
Quantity
Uni
t Cos
t ($)
b1
b2
Figure 4.18. Depiction of Slope Calculations
The combustor results from PRICE II are shown in Table 4.34 and Figure 4.19 is a plot of the
results.
Table 4.34. PRICE II Results for Combustor
Quantity Cost 10 1,290.00
100 586.00 1,000 297.20 5,000 222.92
10,000 198.88 20,000 169.88 50,000 139.47
100,000 125.24 200,000 109.59 500,000 88.31
1,000,000 68.82
69
From Figure 4.19, the improvement rates for the combustor were 20%, when the
production quantity was less than 1,000 units and 13% when the production quantity was above
1,000 units. These improvement rates were used in Models I and II.
Unit Cost (vs) Quantity for Combustor
1
10
100
1,000
10,000
1 10 100 1000 10000 100000 1000000
Quantity
Uni
t Cos
t ($)
Figure 4.19. Combustor Plot to Calculate the Improvement Rates
The ZnO bed results from PRICE II are shown in Table 4.35 and Figure 4.20 is a plot of the
results.
Table 4.35. PRICE II Results for ZnO Bed
Quantity Cost 10 1,630.00
100 505.00 1,000 238.70 5,000 175.80
10,000 156.41 20,000 133.59 50,000 109.44
100,000 98.15 200,000 85.85 500,000 69.12
1,000,000 53.91
70
From Figure 4.20, the improvement rates for the ZnO bed were 25% when the production
quantity was less than 1,000 units and 13% when the production quantity was above 1,000 units.
These improvement rates were used in Models I and II.
Unit Cost (vs) Quantity for ZnO Bed
1.00
10.00
100.00
1,000.00
10,000.00
1 10 100 1000 10000 100000 1000000
Quantity
Uni
t Cos
t ($)
Figure 4.20. ZnO Bed Plot to Calculate the Improvement Rates
The ATR results from PRICE II are shown in Table 4.36 and Figure 4.21 is a plot of the
results.
Table 4.36. PRICE II Results for ATR
Quantity Cost 10 900
100 399 1,000 205.1 5,000 153.98
10,000 137.41 20,000 117.68 50,000 96.56
100,000 86.6 200,000 75.76 500,000 61
1,000,000 47.62
71
From Figure 4.21, the improvement rates for the ATR were 20% when the production
quantity was less than 1,000 units and 13% when the production quantity was above 1,000 units.
These improvement rates were used in Models I and II.
Unit Cost (vs) Quantity forATR
1
10
100
1000
1 10 100 1000 10000 100000 1000000
Quantity
Uni
t Cos
t ($)
Figure 4.21. ATR Plot to Calculate the Improvement Rates
The air compressor results from PRICE II are shown in Table 4.37 and Figure 4.22 is the
plot of the results.
Table 4.37. PRICE II Results for Air Compressor
Quantity Cost 10 3,070.00
100 1,474.00 1,000 750.40 5,000 554.94
10,000 492.64 20,000 412.23 50,000 338.95
100,000 305.53 200,000 267.55 500,000 216.09
1,000,000 167.61
72
From Figure 4.22, the improvement rates for the air compressor were 19% when the
production quantity was less than 1,000 units and 13% when the production quantity was above
1,000 units. These were the improvement rates used in Model I whereas in Model II, the
improvement rate was 13% for all the production quantities.
Unit Cost (vs) Quantity for Air Compressor
1.00
10.00
100.00
1,000.00
10,000.00
1 10 100 1000 10000 100000 1000000
Quantity
Uni
t Cos
t ($)
Figure 4.22. Air Compressor Plot to Calculate the Improvement Rates
For the fuel and water pumps, the improvement rate was 2% when the production quantity was
less than 1,000 units, and there was no improvement when the production quantity was above
1,000 units. The fuel cell stack results from PRICE II are shown in Table 4.38 and Figure 4.23 is
the plot of the results.
Table 4.38. PRICE II Results for Fuel Cell Stack
Quantity Cost 10 27,000.00
100 8,434.00 1,000 3,717.20 5,000 2,641.26
10,000 2,352.18 20,000 2,094.06 50,000 1,822.22
100,000 1,525.11 200,000 1,335.76 500,000 1,075.31
1,000,000 867.66
73
From Figure 4.23, the improvement rates for the fuel cell stack were 26% when the
production quantity was less than 1,000 units and 13% for production quantities above 1,000
units. These improvement rates were used in Models I and II.
Unit Cost (vs) Quantity for Fuel Cell Stack
1.00
10.00
100.00
1,000.00
10,000.00
100,000.00
1 10 100 1000 10000 100000 1000000
Quantity
Uni
t Cos
t ($)
Figure 4.23. Fuel Cell Stack Plot to Calculate the Improvement Rates
The air pre-heater results from PRICE II are shown in Table 4.39 and Figure 4.24 is the
plot of the results.
Table 4.39. PRICE II Results for Air Pre-heater
Quantity Cost 10 4,730.00
100 2,310.00 1,000 1,184.80 5,000 868.68
10,000 769.80 20,000 637.09 50,000 523.92
100,000 474.70 200,000 414.45 500,000 334.14
1,000,000 258.55
From Figure 4.24, the improvement rates for the air pre-heater #1 were 19% when the
production quantity was less than 1,000 units and 13% for production quantities above 1,000
74
units. These were the improvement rates used in Model I whereas in Model II, the improvement
rate was 13% for all the production quantities.
Unit Cost (vs) Quantity for Air Pre-heater
1.00
10.00
100.00
1,000.00
10,000.00
1 10 100 1000 10000 100000 1000000
Quantity
Uni
t Cos
t ($)
Figure 4.24. Air Pre-heater Plot to Calculate the Improvement Rates
The steam generator results from PRICE II are shown in Table 4.40 and Figure 4.25 is a
plot of the results.
Table 4.40. PRICE II Results for Steam Generator
Quantity Cost 10 6,500.00
100 3,223.00 1,000 1,671.50 5,000 1,213.80
10,000 1,073.72 20,000 885.49 50,000 728.26
100,000 660.29 200,000 576.45 500,000 464.96
1,000,000 357.04
From Figure 4.25, the improvement rates for the steam generator were 19% when the
production quantity was less than 1,000 units and 13% for production quantities above 1,000
75
units. These were the improvement rates used in Model I whereas in Model II, the improvement
rate was 13% for all the production quantities.
Unit Cost (vs) Quantity for Steam Generator
1.00
10.00
100.00
1,000.00
10,000.00
1 10 100 1000 10000 100000 1000000
Quantity
Uni
t Cos
t ($)
Figure 4.25. Steam Generator Plot to Calculate the Improvement Rates
The exhaust condenser results from PRICE II are shown in Table 4.41 and Figure 4.26 is
a plot of the results.
Table 4.41. PRICE II Results for Exhaust Condenser
Quantity Cost 10 1,690.00
100 787.00 1,000 398.40 5,000 296.56
10,000 264.18 20,000 224.91 50,000 184.79
100,000 166.23 200,000 145.52 500,000 117.39
1,000,000 91.32
From Figure 4.26, the improvement rates for the exhaust condenser were 20% when the
production quantity was less than 1,000 units and 13% for production quantities above 1,000
76
units. These improvement rates were used in Model I whereas in Model II, the improvement rate
was 13% for all the production quantities.
Unit Cost (vs) Quantity for Exhaust Condensor
1.00
10.00
100.00
1,000.00
10,000.00
1 10 100 1000 10000 100000 1000000
Quantity
Uni
t Cos
t ($)
Figure 4.26. Exhaust Condenser Plot to Calculate the Improvement Rates
CER Model I used both the improvement rates obtained from the plots for all the
components, whereas CER Model II used only one improvement rate for the air compressor, air
pre-heater #1, steam generator, and exhaust condenser. The improvement rates obtained from
the second range of the plots were used for all the production quantities to calculate the costs for
these four components. This was done because these items were developed from existing
identical equipment, and the initial increased improvement effects have been realized. Otherwise
the unit costs at the 500,000-units would be lower than expected. The Darnell Group Inc., in its
report to the U.S. Fuel Cell Council [32], tested the fuel cell technology adoption forecasts based
on a complex business model, which included five parameters. The five parameters were the
learning curve associated with fuel cell production, start quantity, the first premium price, the
majority premium price, and the adoption rate for the fuel cell powered devices. They performed
sensitivity analysis on this model and found that it was most sensitive to the learning rates. The
study stated that the improvement rate for the Proton Exchange Membrane fuel cells was 20%.
This improvement rate was for small fuel cells used in mobile phones, battery chargers, notebook
77
computers, etc., for which the power requirement was less than 1 kW. The improvement rates
obtained for all the components from PRICE II were in that range.
4.2.6. First Unit Cost Calculations
The value of A (first unit cost) for combustor, ZnO bed, ATR, and fuel cell stack were
derived using the Crawford model equations for the improvement rates. The equation for total
cumulative cost to produce N units was [10]:
TC (N) = [A1 / (B1 + 1)] * [(N1 + 0.5) (B1 + 1) – (0.5) (B1
+ 1)] +
[A2 / (B2 + 1)] * [(N2 + 0.5) (B2 + 1) – (N1 + 0.5) (B2
+ 1)] Eq. 4.14
where TC (N) is total cumulative cost.
A1 was the cost of the first unit, in the first range of the production quantity.
A2 was the cost of the first unit, in the second range of the production quantity.
B1 was the exponent for first improvement curve.
B2 was the exponent for second improvement curve.
N1 was the quantity for which the first improvement rate was valid.
N2 was the quantity for which the second improvement rate was valid.
The following equation [10] holds good at the point where both the improvement rates
are the same:
A1 * N1 B1 = A2 * N1 B2 Eq. 4.15
where N1 was the quantity at which both the improvement rates are the same.
From the above two equations,
TC (N) = [A1 / (B1 + 1)] * [(N1 + 0.5) (B1 + 1) – (0.5) (B1
+ 1)] +
[A1 * N1 (B
1 – B
2) / (B2 + 1)] * [(N2 + 0.5) (B2
+ 1) – (N1 + 0.5) (B2 + 1)] Eq. 4.16
So, the equation for A1 is:
A1 = TC (N) / [[{(N1 + 0.5) (B1 + 1) – (0.5) (B
1 + 1)} / (B1 + 1)] + [{(N2 + 0.5) (B2
+ 1) – (N1
+ 0.5) (B2 + 1)} * N1
(B1
– B2
) / (B2 + 1)]] Eq. 4.17
1. Combustor: The value of A for the combustor was calculated by substituting the B1, B2, N1
and N2 values in the above equation. The improvement rate for the combustor when the
production quantity was less than 1,000 units was 20% (I1) and the improvement rate for the
78
combustor when the production quantity was more than 1,000 units was 13% (I2). From
these improvement rates, the values of B1 and B2 were calculated using the formulae:
BB1 = log [(100 – I1) / 100] / log 2 and
BB2 = log [(100 – I2) / 100] / log 2
The values of B1 and B2 obtained from the above equations were -0.319 and -0.195.
The cost of combustor at 500,000-units was obtained using the equation:
Cost = 42 * (Volume) 0.7 Eq. 4.5
The default value used for volume was 3.896 liters, which resulted in a cost of $108.81.
The value of A1 obtained was $2629.22. This value of A1 was used as A for further cost
calculations in the cost models.
2. ZnO Bed: The value of A for the ZnO bed was calculated by substituting the B1, B2, N1 and
N2 values in the equation for A1. The improvement rate for the ZnO bed when the
production quantity was less than 1,000 units was 25% (I1) and the improvement rate for the
combustor when the production quantity was more than 1,000 units was 13% (I2). From
these improvement rates, the values of B1 and B2 were calculated using the formulae:
BB1 = log [(100 – I1) / 100] / log 2 and
BB2 = log [(100 – I2) / 100] / log 2
The values of B1 and B2 obtained from the above equations were -0.418 and -0.199.
The cost of ZnO bed at 500,000-units was given as $50 in the ADL report [17]. The
value of A1 obtained was $2472.83. This value of A1 was used as A for further cost calculations
in the cost models.
3. ATR: The value of A for the ATR was calculated by substituting the B1, B2, N1 and N2 values
in the equation for A1. The improvement rate for the ATR when the production quantity was
less than 1,000 units was 20 percent (I1) and the improvement rate for the combustor when
the production quantity was more than 1,000 units was 13% (I2). From these improvement
rates, the values of B1 and B2 were calculated using the formulae:
BB1 = log [(100 – I1) / 100] / log 2 and
BB2 = log [(100 – I2) / 100] / log 2
The values of B1 and B2 obtained from the above equations were -0.322 and -0.195.
79
The cost of ATR at 500,000-units was given as $109 in the ADL report [17]. The value
of A1 obtained was $2696.37. This value of A1 was used as A for further cost calculations in
the cost models.
4. Fuel Cell Stack: The value of A for the fuel cell stack was calculated by substituting the B1,
BB2, N1, and N2 values in the equation for A1. The improvement rate for the fuel cell stack
when the production quantity was less than 1,000 units was 26% (I1) and the improvement
rate for the combustor when the production quantity was more than 1,000 units was 13 %
(I2). From these improvement rates, the values of B1 and B2 were calculated using the
formulae:
BB1 = log [(100 – I1) / 100] / log 2 and
BB2 = log [(100 – I2) / 100] / log 2
The values of B1 and B2 obtained from the above equations were -0.430 and -0.199.
The cost of fuel cell stack at 500,000-units was obtained using the equation:
Cost =2277.5 – 1803.33*PD + 0.32 *T – 8.45 *FU. Eq. 4.7
The default values used were 0.3 W/cm2 for power density, 800 0C for temperature and
85% for fuel utilization, which resulted in a cost of $1274.25.
The value of A1 obtained was $68286.39. This value of A1 was used as A for further cost
calculations in the cost models. The value of A for the pumps was from market price quotes.
The value of A for air compressor, air pre-heater #1, steam generator, and the exhaust
condenser also were obtained from the equations developed by substituting the default
values.
4.2.7. Sensitivity Analysis
A sensitivity analysis was performed on CER Model II at the production level of
500,000-units. The unit change was different for each variable, for example a unit temperature
change was 25 oC, whereas a unit change in power density was 0.1 W/cm2. The sensitivity of the
CER Model II when the production quantity was 500,000-units, was obtained by varying the
following parameters:
1. Temperature was varied by + 25 0C from the base value of 800 0C.
2. Volume was varied by + 0.1 liter from the base value of 3.896 liters.
80
3. Power Density was varied by + 0.1 W/cm2 from the base value of 0.3 W/cm2.
4. Fuel Utilization was varied by + 5 % from the base value of 85%.
5. Transfer Area was varied by + 0.05 m2 from the base value of the transfer area of the
respective heat exchangers.
6. Horsepower was varied by + 0.1 Hp from the base value of 1 Hp.
7. Improvement Rate was varied by + 1 % from the base values of the respective components.
Table 4.42. Variation of Parameters for Sensitivity Analysis
Parameters Low Base High
Temperature (0C) 775 800 825 Volume (liters) 2.896 3.896 4.896
Power Density (W/cm2) 0.2 0.3 0.4 Fuel Utilization (%) 80 85 90
Transfer Area (m2), Air Pre-heater #1 0.265 0.315 0.365 Transfer Area (m2), Steam Generator 0.438 0.488 0.538
Transfer Area (m2), Exhaust Condenser 0.026 0.076 0.126 Horsepower (hp) 0.9 1.0 1.1
Table 4.42 shows the variation of the parameters. The base values are the default values.
The sensitivity plots show the variation of unit cost to the changes in one of the above
parameters. The plots are obtained by varying a parameter, while the remaining parameters
remain unchanged. Table 4.43 and Figure 4.27 show the effect of varying each parameter on the
unit cost of the Auxiliary Power Unit (APU), when the production quantity is 500,000-units.
Table 4.43. Sensitivity Data
Variable Base Change Cost ($/Unit) (-1 Unit) Base (+1 Unit)
Temperature 800 25 0C 2,354.44 2,377.81 2,399.34 Power Density 0.3 0.1 W/cm2 2,558.14 2,377.81 2,197.48 Fuel Utilization 85 5% 2,420.06 2,377.81 2,335.56
Combustor Volume 3.896 1 liter 2,357.41 2,377.81 2,396.69 Air Compressor Power 1 0.1 Hp 2,370.15 2,377.81 2,385.46 Heat Exchanger Area 0.488 0.05 m2 2,326.23 2,377.81 2,422.56
Improvement Rate * 1% 2,556.53 2,377.81 2,254.59 * All the components had different improvement rates and they were all changed
from their respective base levels
81
Sensitivity Plot
2150
2200
2250
2300
2350
2400
2450
2500
2550
2600
-1.5 -1 -0.5 0 0.5 1 1.5
Change in Parameters
Uni
t Cos
t ($)
Temperature Power DensityFuel Utilization Combustor VolumeAir Compressor Horsepower Heat Exchangers Transfer AreaImprovement Rate
Figure 4.27. Sensitivity Plot of APU Parameters
From Figure 4.27, the unit cost of the APU was most sensitive to the power density, the
improvement rate and the fuel utilization in that order. A small change (0.1 W/cm2) in the
power density resulted in a large change in the cost, indicating that the power density is the main
factor, which can reduce the cost/kW and make the APU’s competitive. The improvement rate
affected the costs significantly, which implies that as the skill of the laborers increases, the
manufacturing costs are reduced. If the fuel utilization is high, the cost/kW comes down. The
transfer area had the next largest effect on the cost apart from the above three parameters. The
temperature was considered a main factor, which would reduce the costs, but it did not affect the
cost as expected as a small coefficient in the equation used, which was developed from the ADL
[17] data. The model was insensitive to the combustor volume and the air compressor power.
82
4.3. Visual Basic Model
A Visual Basic Model was developed for CER Model II. The default values are the base
case values used and the user can change the values of variables to any desired value. The model
permits investigation of different scenarios for CER Model II. Figure 4.28 shows the user input
form for the Stack and the Air Compressor.
Figure 4.28. Visual Basic Input Form for Fuel Cell Stack and Compressor
83
The stack input parameters were the operating temperature, power density, and fuel utilization.
These were the cost drivers according to the ADL report [17]. The CER developed from the
ADL data was used to calculate the cost of the stack. The improvement rates were derived from
the PRICE II models and the equations from the Crawford model [10] were used to estimate the
cost. The horsepower was the cost driver for the air compressor and the CER developed from
the industry data was used along with the Crawford model [10] equations to estimate the cost of
the air compressor.
Figure 4.29 presents the input form for the Cathode Air Pre-heater #1, Steam Generator,
and the Exhaust Condenser. The parameters for the cathode air pre-heater #1 were the operating
temperature and the transfer area. The CER for this was developed from the DTI report [18].
The parameter for the steam generator and the exhaust condenser was the transfer area, and the
CER for these was developed from the Exergy catalog [25]. The improvement rates for all these
elements were obtained from the PRICE II results, and the Crawford model equations were used
to estimate the cost.
Figure 4.29. Input Form for Heat Exchangers
84
The input form for the Combustor, ZnO bed, and the ATR is shown in Figure 4.30. The CER for
the combustor was developed from the NETL data [24]. The parameter for the combustor was
volume. The unit costs for the ZnO bed and the ATR were taken from the ADL data [17]
directly. The improvement rates for all these were derived from the PRICE II results and the
Crawford model equations were used to estimate the cost.
Figure 4.30. Input Form for Combustor, ZnO Bed, and ATR
The input form for the pumps is shown in Figure 4.31. The unit cost for the fuel pump as
well as the water pump was $109. This input was taken from the NETL [24] and ADL [17] data.
The improvement rates were obtained from the PRICE II results, and the Crawford model
equations were used to estimate the cost.
85
Figure 4.31. Input Form for the Fuel Pump and the Water Pump
Figure 4.32 shows the results form. All the elemental costs were obtained and the final cost was
calculated by adding the elemental costs. The unit cost obtained was $2280, which was the same
as obtained from CER Model II.
Figure 4.32. Visual Basic Results Form for the SOFC APU at 500,000-units.
86
5. Summary and Conclusions 5.1. Summary of the Cost Models developed Two approaches and four models were developed to estimate the cost of the novel 5 kW
diesel-powered APU. The approaches were the top-down parametric approach using PRICE and
an approach using the cost estimating relationships derived from the industrial/commercial data
and data from the literature review. Two models of each approach were developed with the
difference in the PRICE models being the manufacturing process index parameter and the
improvement rates for the CER models.
The PRICE models were developed first while the search for the data for the CER’s was
performed. The PRICE manufacturing complexity factor and manufacturing process index
parameters were two key values that had to be determined. An expression for the manufacturing
process index had to be developed as the model default values resulted in some inconsistencies
when the production quantities were varied. The manufacturing complexity factor had to be
estimated for other energy sources (batteries), as no values were available for the fuel cells. The
results for the PRICE models were in agreement with those previously estimated by ADL [17]
and NETL [24] at the 500,000-unit production quantity. The results were graphed for production
levels from 10 units to 1 million units, and it appeared that the improvement rates were changing
and lower improvement rates occurred at production levels greater than 1,000 units. The
improvement rates were modified to the lower rates for the entire production level in the PRICE
II model for the air compressor, air pre-heater #1, steam generator, and exhaust condenser. The
improvement rates for the pumps were set at 2% for levels up to 1,000 units and then no further
improvement was expected. The PRICE models assume that automation is increased as the
production levels increase and thus the unit labor costs decrease. The difficulty with the PRICE
models was that there was no easy approach to examine the changes in the process parameters,
such as temperature or power density, as these were embedded in the manufacturing complexity
index.
The CER models were more difficult to develop since data was extremely difficult to
obtain to develop the Cost Estimating Relationships. The industrial/commercial data and
literature data were extremely sparse and the CERs developed are approximate expressions. It
was important to develop some expressions to be able to estimate the sensitivity to the input
87
parameters. The improvement rates used were those obtained form the PRICE II model. These
improvement rates were in agreement with the value (20 %) estimated for the small fuel cells.
The difference between the two CER models was in the improvement rates. CER Model I used
both the improvement rates for all the components. CER Model II used only one improvement
rate for the air compressor, air pre-heater #1, steam generator, and the exhaust condenser. This
was done because these items were developed from the existing identical equipment and the
higher initial improvement effects would have been reflected in the costs. Otherwise, the unit
costs at the 500,000-unit level would have been lower than expected if the higher improvement
rates were used.
Sensitivity analysis was carried out on the traditional Cost Model II. The results obtained
from the sensitivity analysis indicated that the power density and improvement rates were the
most sensitive parameters. A study done by the Darnell group [32] also indicated that the
improvement rate was one of the most sensitive variables in estimating the cost of the fuel cell
systems.
The NETL and the ADL results of the two PRICE and two CER models at 500,000-units
are presented in Table 5.1. The total costs of all the models are comparable although the
individual components have large variations between the high and low values. The high and low
estimates from the six models for the common components are also presented. The average of
the high and low values of the common elements give an estimate of $460/kW and a total cost of
$2,298 for the 5 kW APU. An additional cost of approximately 10 percent would be required for
the assembly container. The ZnO bed would need to be replaced after one year of operation and
the replacement costs were not included in the model.
The fuel cell stack is the major cost item in the auxiliary power unit, and its cost depends
mainly upon the power density. The fuel cell stack cost ranges from 40 to 60 percent of the total
cost of the APU. If the power density is increased, the fuel cell stack cost can be significantly
lowered. The fuel cell unit would require the most development of all the components, and thus,
it has the highest improvement rates. Therefore, unit costs would increase significantly if the
production quantities were decreased or would decrease significantly if production quantities
were increased.
The unit cost and the cost/kW values from the traditional cost models and the PRICE
models when the production quantity was 500,000-units were compared with the NETL [24] and
88
89
the ADL [17] data in Table 5.1. The costs obtained from the traditional cost models were
approximately in the same range given in [24] and [17]. The high and the low values for each
component were identified from all the models and the unit cost, and cost/kW were calculated.
The high value was $621.50 and the low value was $292.11, which resulted in an average cost of
$456.81/kW. Although the various models give somewhat consistent results, there is a need for
a more detailed investigation of the fuel cell stack costs as it is the critical component. The
expressions for the development of the cost estimates of the fuel cells were based upon the
similarities with batteries in the PRICE models and upon reported costs of ADL for the CER
models and not upon actual cost data of existing fuel cells. Production processes for high
production quantities have not been developed, and new technologies for fuel cells may lead to
further cost reductions of this component.
5.2. Future Research The data available to develop the cost models were very sparse and so the errors could be
significant in the cost estimates. Further research into the current technology and more relevant
data needs to be collected. DOE has successfully tested a SOFC APU powering a heavy-duty
truck by simulating the idling conditions [33]. GE and Delphi Automotive systems are
continuously working towards reducing the fuel cell stack costs [34]. With more advanced
technology in the fuel cell APU systems, more detailed data becomes available, and better cost
models can be developed, which will estimate the cost more accurately. Also, the VB software
model code can be changed very easily to incorporate the newly developed CER’s and thus can
be reused to simulate the new costs.
Component NETL [24] ADL [17] PRICE I PRICE II MODEL I MODEL II High Low Combustor 60.03 66.06 88.31 108.81 108.81 108.81 60.03 ZnO Bed 35.17 50.00 51.65 69.12 50.00 50.00 69.12 35.17
ATR 88.69 109.00 45.6 61 109.00 109.00 109.00 45.6 Air Compressor 331.46 272.00 162.14 216.09 134.26 275.12 331.46 134.26
Fuel Pump 109.00 109.00 97.19 97.19 91.86 91.86 109.00 91.86 Water Pump 109.00 97.19 97.19 91.86 91.86 109.00 91.86
Fuel Cell Stack 954.02 1,184.00 806.42 1075.31 1,274.25 1,274.25 1,274.25 806.42 Air Pre-heater #1 414.52 158.00 251.11 334.14 81.20 157.44 414.52 81.20 Steam Generator 98.04 349.86 464.96 92.28 170.50 464.96 92.28
Exhaust Condenser 53.44 87.92 117.39 21.85 48.97 117.39 21.85 Anode Gas Recuperator 62.00
Tail gas burner 42.00 Balance of System 420.00
Eductor 12.00 Labor, indirect & depreciation 215.00
Unit Cost 2,253.37 2,633.00 2,046.36 2,661.96 2,055.37 2,377.81 3,107.51 1,460.53 Cost/kW 450.67 526.60 409.27 532.39 411.07 475.56 621.50 292.11
Total Cost (Thousand Dollars) 1,126,685 1,316,500 1,023,180 1,330,980 1,027,685 1,188,905 1,553,755 730,265
Table 5.1. Manufacturing Cost for 500,000 APU’s Obtained from Various Models (Base Year 2003)
90
6. Bibliography
1. http://www1.eere.energy.gov/vehiclesandfuels/avta/pdfs/heavy/2006_idle_reduction_
rpt.pdf (as on 07/30/2009)
2. http://fuelcells.si.edu (as on 07/30/2009)
3. http://www.class8truck.com/ (as on 07/30/2009)
4. “Transportation Applications for Solid Oxide Fuel Cells – Auxiliary Power,”
Department of Energy, Pacific Northwest National Laboratory presentation, June 1,
2000.
5. http://www.transportation.anl.gov/pdfs/TA/15.pdf (as on 07/30/2009)
6. “Evaluation of Fuel Cell Auxiliary Power Units for Heavy-duty Diesel Trucks,”
Christie Joy Brodrick, Timothy E. Lipman, Mohammad Farshchi, Nicholas P. Lutsey,
Harry A. Dwyer, Daniel Sperling, S. William Gouse, III, D. Bruce Harris, Foy G.
King Jr, Transportation Research Part D 7, pp. 303-315, 2002.
7. “Fuel Cell Systems Explained,” James Larminie, Andrew Dicks, John Wiley & Sons,
first edition, 2000.
8. www.chemistry.nus.edu.sg/ (as on 07/30/2009)
9. “Estimating and Costing for the Metal Manufacturing Industries,” Robert C. Creese,
M. Adithan and B.S. Pabla, Marcel Dekker, Inc., 1992.
10. “Cost Estimating,” Phillip F. Ostwald, second edition, Prentice Hall, Inc., pp. 206 –
217, 1984.
11. “Plant Design and Economics for Chemical Engineers,” Peters, M. S. and
Timmerhaus, K. D., McGraw Hill, fourth edition, 1991.
12. “Encyclopedia of Chemical Processing and Design,” John J. McKetta and William A.
Cunningham, Vol.12, Marcel Dekker, Inc., pp. 135 – 144, 1981.
13. “Conducting Technical and Economic Evaluation in the Process and Utility
Industries, AACE Recommended Practice No. 16R-90,” American Association of
Cost Engineers, Morgantown, WV, pp. 1 – 84, 1990.
14. www.pdhonline.org/courses (as of 07/30/2009)
91
15. “Fuel Cells for Transportation, Annual Progress Report,” US Department Of Energy,
Office of Transportation Technologies, Energy Efficiency and Renewable Energy, pp.
40 – 50, 2001.
16. “Conceptual Design of POX/SOFC 5Kw-Net System, Final Report,” Arthur D. Little,
Inc., Department of Energy, NETL, Reference 71316, January 8, 2001.
http://www.netl.doe.gov/scng/enduse/refshelf/Adlcost.pdf
17. “Market Orientated Design Studies for SOFC based systems,” prepared by T Nietsch
and J Clark, ETSU f/01/00129/Rep, Contractor Rolls-Royce Advanced Engineering
Center, © Crown copyright 1999.
18. “Status of Solid State Energy Conservation Alliance Program,” Joseph P. Strakey,
DOE – OHVT, Essential Power Systems Workshop, December 12, 2001.
19. “Evaluation of the cost performance of the SOFC cell in the market,” M.
Ippommatsu, H. Sasaki and S. Otoshi, Fundamental Research Laboratories, Osaka
Gas Co., Ltd, Science Center Building, Kyoto, Japan, Int. J. Hydrogen Energy, Vol.
21, No. 2, pp. 129-135, 1996.
20. “Production cost estimation of solid oxide fuel cells,” Hibiki Itoh, Masashi Mori,
Noriyuki Mori and Toshio Abe, Chemical Energy Engineering Department, Chemical
Power Generation Group, Central Research Institute of Electric Power Industry,
Kanagawa, Japan, Journal of Power Sources, 49, pp. 315-332, 1994.
21. “Your Guide to PRICE H” PRICE Systems, L.L.C., Mt. Laurel, New Jersey, U.S.A.,
1998, reprinted 1999.
22. AACE International Recommended Practice No. 18R-97, “Cost Estimate
Classification System – As Applied in Engineering, Procurement, and Construction
for the Process Industries,” American Association of Cost Engineers, Morgantown,
WV, 1997, pp.1-8.
23. Private Communication, NETL Excel Spreadsheet for 800 oC Solid Oxide fuel cell
systems – Model, Equipment, Design and Cost Summary Sheets, given by NETL
Morgantown.
24. Exergy Inc., company price catalog. (as on 07/30/2009)
92
25. James Zizelman, Steven Shaffer and Subharish Mukerjee, Delphi Automotive
Systems, Solid Oxide Fuel Cell Auxiliary Power Unit – A Development Update; SAE
2002 World Congress, Detroit, Michigan, March 4-7, 2002.
26. http://www.csa.com/discoveryguides/fuecel/overview.php (as on 07/30/2009).
27. [Singhal] S. C. Singhal, "Science and Technology of Solid-Oxide Fuel Cells," MRS
Bull.Vol.25, No.3, 2000, p.16-21.
28. http://www.bls.gov/ppi/ppi_dr.pdf (as of 07/30/09)
29. http://www.airsystems.cc/product_pages/compressors/portable_ambient_air_compres
sors.htm (as of 07/30/09)
30. PRICE Help (1-800-43-PRICE), www.pricesystems.com
31. Fuel Cells for Portable Power: Markets, Manufacture and Cost, revised final report
for Breakthrough Technologies & U.S. Fuel Cell Council, by Darnell Group Inc.,
January 13, 2003.
32. NETL: News Release from March 2009. SOFC successfully powers truck cab and
sleeper. FE Office of Communications, 202-586-0507
33. http://netl.doe.gov/technologies/coalpower/fuelcells (as of 07/30/09)
93
7. Appendix - Visual Basic Code
Visual Basic Code for the Introduction Form
Private Sub Form_Load ()
Timer1.Enabled = True
Timer1.Interval = 2000
End Sub
Private Sub Timer1_Timer ()
Unload Me
frmStackInput.Show
End Sub
Visual Basic Code for the Stack and Compressor Input
Dim No As Double
Private Sub Cmdnext_Click ()
'Variable Declaration for Stack
Dim OPT As Double, PD As Double, FU As Double, IRS1 As Double, IRS2 As Double
Dim Scost As Double, bS1 As Double, bS2 As Double, CStack As Double, CStack1 As
Double
'Variable Declaration for Scroll Compressor
Dim HP As Double, IRSC As Double
Dim SCcost As Double, bSC As Double, CScroll As Double, CScroll1 As Double
'Assignment of variables to TEXTBOX
No = Val (txtNOU.Text)
OPT = Val (txtOPT.Text)
PD = Val (txtPD.Text)
FU = Val (txtFU.Text)
IRS1 = Val (txtIRS1.Text)
IRS2 = Val (txtIRS2.Text)
HP = Val (txtHP.Text)
94
IRSC = Val (txtIRSC.Text)
'Constraint Declaration for Stack
If OPT < 500 Or OPT > 900 Then
MsgBox "enter a value between 500 and 900 for temperature"
GoTo 10
End If
If PD < 0.1 Or PD > 1 Then
MsgBox "enter a value between 0.1 and 1 for power density"
GoTo 10
End If
If FU < 65 Or FU > 100 Then
MsgBox "enter a value between 65 and 100 for fuel utilization"
GoTo 10
End If
If IRS1 < 0 Or IRS1 > 49 Then
MsgBox "enter a value between 0 and 49 for improvement rate 1"
GoTo 10
End If
If IRS2 < 0 Or IRS2 > IRS1 Then
MsgBox "enter a value between 0 and IRS1 for improvement rate 2"
GoTo 10
End If
'Constraint Declaration for Scroll
If HP < 0.028 Or HP > 15 Then
MsgBox "enter a value between 0.028 and 15 for the horsepower"
GoTo 10
End If
If IRSC < 0 Or IRSC > 49 Then
MsgBox "enter a value between 0 and 49 for air compressor improvement rate"
GoTo 10
End If
95
'Calculations for stack cost
bS1 = ((Log ((100 - IRS1) / 100)) / 2.303) / ((Log (2)) / 2.303)
bS2 = ((Log ((100 - IRS2) / 100)) / 2.303) / ((Log (2)) / 2.303)
Scost = 2277.5 - 1803.33 * PD + 0.32 * OPT - 8.45 * FU
FScost = ((Scost * 500000) / (((((1000.5) ^ (bS1 + 1)) - ((0.5) ^ (bS1 + 1))) / (bS1 + 1)) +
((((1000) ^ (bS1 - bS2)) * (((500000.5) ^ (bS2 + 1)) - ((1000.5) ^ (bS2 + 1)))) / (bS2 +
1))))
If No <= 1000 Then
CStack = ((FScost * (((No + 0.5) ^ (bS1 + 1)) - ((0.5) ^ (bS1 + 1)))) / ((bS1 + 1) * No))
CStack1 = Round (CStack, 2)
End If
If No > 1000 Then
CStack = ((FScost * (((((1000.5) ^ (bS1 + 1)) - ((0.5) ^ (bS1 + 1))) / (bS1 + 1)) +
((((1000) ^ (bS1 - bS2)) * (((No + 0.5) ^ (bS2 + 1)) - ((1000.5) ^ (bS2 + 1)))) / (bS2 +
1)))) / No)
CStack1 = Round (CStack, 2)
End If
'Calculations for scroll cost
bSC = ((Log ((100 - IRSC) / 100)) / 2.303) / ((Log (2)) / 2.303)
SCcost = (2218 + (855 * HP))
CScroll = ((SCcost * (((No + 0.5) ^ (bSC + 1)) - ((0.5) ^ (bSC + 1)))) / ((bSC + 1) * No))
CScroll1 = Round (CScroll, 2)
frmStackInput.Visible = False
frmHeatExchangersInput.Visible = True
frmResults.txtSC = CStack1
frmResults.txtSCC = CScroll1
10 End Sub
Private Sub Cmdexit_Click ()
End
End Sub
96
Visual Basic Code for the Heat Exchangers Input
Dim NOU As Double
Private Sub Cmdnext_Click ()
'Variable declaration for air pre-heater
Dim OPT As Double, TAAP As Double, IRAP As Double
Dim APcost As Double, bAP As Double, CAirpreheater, CAirpreheater1 As Double
'Variable declaration for steam generator
Dim TASG As Double, IRSG As Double
Dim SGcost As Double, bSG As Double, CSteamgenerator, CSteamgenerator1 As
Double
'Variable declaration for exhaust condenser
Dim TAEC As Double, IREC As Double
Dim ECcost As Double, bEC As Double, CExhaustcondenser, CExhaustcondenser1 As
Double
'Assignment of variables to TEXTBOX
NOU = frmStackInput.txtNOU
OPT = Val (txtOPT.Text)
TAAP = Val (txtTAAP.Text)
IRAP = Val (txtIRAP.Text)
TASG = Val (txtTASG.Text)
IRSG = Val (txtIRSG.Text)
TAEC = Val (txtTAEC.Text)
IREC = Val (txtIREC.Text)
'Constraint Declaration for Air Pre-heater
If OPT < 500 Or OPT > 900 Then
MsgBox "enter a value between 500 and 900 for temperature"
GoTo 10
End If
If TAAP < 0.2 Or TAAP > 100 Then
MsgBox "enter a value between 0.2 and 100 for the air pre-heater transfer area"
97
GoTo 10
End If
If IRAP < 0 Or IRAP > 49 Then
MsgBox "enter a value between 0 and 49 for the air pre-heater improvement rate"
GoTo 10
End If
'Constraint Declaration for Steam Generator
If TASG < 0.1 Or TASG > 0.5 Then
MsgBox "enter a value between 0.1 and 0.5 for the steam generator transfer area"
GoTo 10
End If
If IRSG < 0 Or IRSG > 49 Then
MsgBox "enter a value between 0 and 49 for the steam generator improvement rate"
GoTo 10
End If
'Constraint Declaration for Exhaust Condenser
If TAEC < 0.05 Or TAEC > 0.2 Then
MsgBox "enter a value between 0.05 and 0.2 for the exhaust condenser transfer area"
GoTo 10
End If
If IREC < 0 Or IREC > 49 Then
MsgBox "enter a value between 0 and 49 for the exhaust condenser improvement rate"
GoTo 10
End If
'Calculations for air pre-heater cost
bAP = ((Log ((100 - IRAP) / 100)) / 2.303) / ((Log (2)) / 2.303)
APcost = ((((18 * OPT) - 9500) * ((TAAP) ^ (0.45))) / (1.6))
CAirpreheater = ((APcost * (((NOU + 0.5) ^ (bAP + 1)) - ((0.5) ^ (bAP + 1)))) / ((bAP +
1) * NOU))
CAirpreheater1 = Round (CAirpreheater, 2)
98
'Calculations for steam generator cost
bSG = ((Log((100 - IRSG) / 100)) / 2.303) / ((Log(2)) / 2.303)
SGcost = 3409.9 * (TASG) ^ 0.73
CSteamgenerator = ((SGcost * (((NOU + 0.5) ^ (bSG + 1)) - ((0.5) ^ (bSG + 1)))) / ((bSG
+ 1) * NOU))
CSteamgenerator1 = Round (CSteamgenerator, 2)
'Calculations for exhaust condenser cost
bEC = ((Log ((100 - IREC) / 100)) / 2.303) / ((Log (2)) / 2.303)
ECcost = 3409.9 * (TAEC) ^ 0.73
CExhaustcondenser = ((ECcost * (((NOU + 0.5) ^ (bEC + 1)) - ((0.5) ^ (bEC + 1)))) /
((bEC + 1) * NOU))
CExhaustcondenser1 = Round (CExhaustcondenser, 2)
frmHeatExchangersInput.Visible = False
frmCombustorInput.Visible = True
frmResults.txtAPC = CAirpreheater1
frmResults.txtSGC = CSteamgenerator1
frmResults.txtECC = CExhaustcondenser1
10 End Sub
Private Sub Cmdexit_Click ()
End
End Sub
Private Sub Cmdprv_Click ()
Unload Me
frmStackInput.Show
End Sub
Visual Basic Code for the Combustor, ZnO Bed and ATR Input Dim NOU As Double
Private Sub Cmdnext_Click ()
'Variable declaration for combustor
Dim VOL As Double, IRC1 As Double, IRC2 As Double
99
Dim Ccost As Double, bC1 As Double, bC2 As Double, CCombustor As Double,
CCombustor1 As Double
'Variable declaration for znO bed
Dim IRZnO1 As Double, IRZnO2 As Double
Dim ZnOcost As Double, bZnO1 As Double, bZnO2 As Double, CZnObed As Double,
CZnObed1 As Double
'Variable declaration for atr
Dim IRATR1 As Double, IRATR2 As Double
Dim Atrcost As Double, bATR1 As Double, bATR2 As Double, CAtr As Double, CAtr1
As Double
'Assignment of variables to TEXTBOX
NOU = frmStackInput.txtNOU
VOL = Val (txtVOL.Text)
IRC1 = Val (txtIRC1.Text)
IRC2 = Val (txtIRC2.Text)
UCZnO = Val (txtUCZnO.Text)
IRZnO1 = Val (txtIRZnO1.Text)
IRZnO2 = Val (txtIRZnO2.Text)
UCATR = Val (txtUCATR.Text)
IRATR1 = Val (txtIRATR1.Text)
IRATR2 = Val (txtIRATR2.Text)
'Constraint Declaration for Combustor
If VOL < 1.5 Or OPT > 5 Then
MsgBox "enter a value between 1.5 and 5 for volume"
GoTo 10
End If
If IRC1 < 0 Or IRC1 > 49 Then
MsgBox "enter a value between 0 and 49 for the combustor improvement rate 1"
GoTo 10
End If
If IRC2 < 0 Or IRC2 > IRC1 Then
100
MsgBox "enter a value between 0 and IRC1 for combustor improvement rate 2"
GoTo 10
End If
'Constraint Declaration for ZnO Bed
If UCZnO <= 0 Then
MsgBox "enter a value greater than 0 for the cost of the ZnO Bed"
GoTo 10
End If
If IRZnO1 < 0 Or IRZnO1 > 49 Then
MsgBox "enter a value between 0 and 49 for the ZnO Bed improvement rate 1"
GoTo 10
End If
If IRZnO2 < 0 Or IRZnO2 > IRZnO1 Then
MsgBox "enter a value between 0 and IRZnO1 for ZnO bed improvement rate 2"
GoTo 10
End If
'Constraint Declaration for ATR
If UCATR <= 0 Then
MsgBox "enter a value greater than 0 for the cost of the ATR"
GoTo 10
End If
If IRATR < 0 Or IRATR > 49 Then
MsgBox "enter a value between 0 and 49 for the ATR improvement rate 1"
GoTo 10
End If
If IRATR2 < 0 Or IRATR2 > IRATR1 Then
MsgBox "enter a value between 0 and IRATR1 for ATR improvement rate 2"
GoTo 10
End If
'Calculations for combustor cost
bC1 = ((Log ((100 - IRC1) / 100)) / 2.303) / ((Log (2)) / 2.303)
101
bC2 = ((Log ((100 - IRC2) / 100)) / 2.303) / ((Log (2)) / 2.303)
Ccost = 42 * ((VOL) ^ 0.7)
FCcost = ((Ccost * 500000) / (((((1000.5) ^ (bC1 + 1)) - ((0.5) ^ (bC1 + 1))) / (bC1 + 1))
+ ((((1000) ^ (bC1 - bC2)) * (((500000.5) ^ (bC2 + 1)) - ((1000.5) ^ (bC2 + 1)))) / (bC2 +
1))))
If NOU <= 1000 Then
CCombustor = ((FCcost * (((NOU + 0.5) ^ (bC1 + 1)) - ((0.5) ^ (bC1 + 1)))) / ((bC1 + 1)
* NOU))
CCombustor1 = Round (CCombustor, 2)
End If
If NOU > 1000 Then
CCombustor = ((FCcost * (((((1000.5) ^ (bC1 + 1)) - ((0.5) ^ (bC1 + 1))) / (bC1 + 1)) +
((((1000) ^ (bC1 - bC2)) * (((NOU + 0.5) ^ (bC2 + 1)) - ((1000.5) ^ (bC2 + 1)))) / (bC2 +
1)))) / NOU)
CCombustor1 = Round (CCombustor, 2)
End If
'Calculations for ZnO bed cost
bZnO1 = ((Log ((100 - IRZnO1) / 100)) / 2.303) / ((Log (2)) / 2.303)
bZnO2 = ((Log ((100 - IRZnO2) / 100)) / 2.303) / ((Log (2)) / 2.303)
FZnOcost = ((UCZnO * 500000) / (((((1000.5) ^ (bZnO1 + 1)) - ((0.5) ^ (bZnO1 + 1))) /
(bZnO1 + 1)) + ((((1000) ^ (bZnO1 - bZnO2)) * (((500000.5) ^ (bZnO2 + 1)) - ((1000.5)
^ (bZnO2 + 1)))) / (bZnO2 + 1))))
If NOU <= 1000 Then
CZnObed = ((FZnOcost * (((NOU + 0.5) ^ (bZnO1 + 1)) - ((0.5) ^ (bZnO1 + 1)))) /
((bZnO1 + 1) * NOU))
CZnObed1 = Round (CZnObed, 2)
End If
If NOU > 1000 Then
CZnObed = ((FZnOcost * (((((1000.5) ^ (bZnO1 + 1)) - ((0.5) ^ (bZnO1 + 1))) / (bZnO1
+ 1)) + ((((1000) ^ (bZnO1 - bZnO2)) * (((NOU + 0.5) ^ (bZnO2 + 1)) - ((1000.5) ^
(bZnO2 + 1)))) / (bZnO2 + 1)))) / NOU)
102
CZnObed1 = Round (CZnObed, 2)
End If
'Calculations for ATR
bATR1 = ((Log ((100 - IRATR1) / 100)) / 2.303) / ((Log (2)) / 2.303)
bATR2 = ((Log ((100 - IRATR2) / 100)) / 2.303) / ((Log (2)) / 2.303)
FATRcost = ((UCATR * 500000) / (((((1000.5) ^ (bATR1 + 1)) - ((0.5) ^ (bATR1 + 1)))
/ (bATR1 + 1)) + ((((1000) ^ (bATR1 - bATR2)) * (((500000.5) ^ (bATR2 + 1)) -
((1000.5) ^ (bATR2 + 1)))) / (bATR2 + 1))))
If NOU <= 1000 Then
CAtr = ((FATRcost * (((NOU + 0.5) ^ (bATR1 + 1)) - ((0.5) ^ (bATR1 + 1)))) / ((bATR1
+ 1) * NOU))
CAtr1 = Round (CAtr, 2)
End If
If NOU > 1000 Then
CAtr = ((FATRcost * (((((1000.5) ^ (bATR1 + 1)) - ((0.5) ^ (bATR1 + 1))) / (bATR1 +
1)) + ((((1000) ^ (bATR1 - bATR2)) * (((NOU + 0.5) ^ (bATR2 + 1)) - ((1000.5) ^
(bATR2 + 1)))) / (bATR2 + 1)))) / NOU)
CAtr1 = Round (CAtr, 2)
End If
frmCombustorInput.Visible = False
frmPumpsInput.Visible = True
frmResults.txtCC = CCombustor1
frmResults.txtZnOC = CZnObed1
frmResults.txtATRC = CAtr1
10 End Sub
Private Sub Cmdexit_Click ()
End
End Sub
Private Sub Cmdprv_Click ()
Unload Me
frmHeatExchangersInput.Show
103
End Sub
Visual Basic Code for the Pumps Input
Dim NOU As Double
Private Sub Cmdnext_Click ()
'Variable declaration for fuel pump
Dim IRFP As Double
Dim bFP As Double, CFuelpump As Double, CFuelpump1 As Double
'Variable declaration for water pump
Dim IRWP As Double
Dim bWP As Double, CWaterpump As Double, CWaterpump1 As Double
'Assignment of variables to TEXTBOX
NOU = frmStackInput.txtNOU
UCFP = Val (txtUCFP.Text)
IRFP = Val (txtIRFP.Text)
UCWP = Val (txtUCWP.Text)
IRWP = Val (txtIRWP.Text)
'Constraint Declaration for fuel pump
If UCFP <= 0 Then
MsgBox "enter a value greater than 0 for the cost of the fuel pump"
GoTo 10
End If
If IRFP < 0 Or IRFP > 49 Then
MsgBox "enter a value between 0 and 49 for the Fuel Pump improvement rate"
GoTo 10
End If
'Constraint Declaration for water pump
If UCWP <= 0 Then
MsgBox "enter a value greater than 0 for the cost of the water pump"
GoTo 10
End If
If IRWP < 0 Or IRWP > 49 Then
104
MsgBox "enter a value between 0 and 49 for the Water Pump improvement rate"
GoTo 10
End If
'Calculations for Fuel pump cost
bFP = ((Log ((100 - IRFP) / 100)) / 2.303) / ((Log (2)) / 2.303)
If NOU <= 1000 Then
CFuelpump = ((UCFP * (((NOU + 0.5) ^ (bFP + 1)) - ((0.5) ^ (bFP + 1)))) / ((bFP + 1) *
NOU))
CFuelpump1 = Round (CFuelpump, 2)
End If
If NOU > 1000 Then
CFuelpump = ((UCFP * (((1000 + 0.5) ^ (bFP + 1)) - ((0.5) ^ (bFP + 1)))) / ((bFP + 1) *
1000))
CFuelpump1 = Round (CFuelpump, 2)
End If
'Calculations for Water pump cost
bWP = ((Log ((100 - IRWP) / 100)) / 2.303) / ((Log (2)) / 2.303)
If NOU <= 1000 Then
CWaterpump = ((UCWP * (((NOU + 0.5) ^ (bWP + 1)) - ((0.5) ^ (bWP + 1)))) / ((bWP +
1) * NOU))
CWaterpump1 = Round (CWaterpump, 2)
End If
If NOU > 1000 Then
CWaterpump = ((UCWP * (((1000 + 0.5) ^ (bWP + 1)) - ((0.5) ^ (bWP + 1)))) / ((bWP +
1) * 1000))
CWaterpump1 = Round (CWaterpump, 2)
End If
frmPumpsInput.Visible = False
frmResults.txtFPC = CFuelpump1
frmResults.txtWPC = CWaterpump1
frmResults.Show
105
10 End Sub
Private Sub Cmdprev_Click ()
Unload Me
frmCombustorInput.Show
End Sub
Private Sub Cmdexit_Click ()
End
End Sub
Visual Basic Code for the Results
Private Sub Cmdback_Click(ByVal eventSender As System.Object, ByVal eventArgs As
System.EventArgs) Handles Cmdback.Click
Me.Close()
frmStackInput.Show()
End Sub
Private Sub Cmdexit_Click(ByVal eventSender As System.Object, ByVal eventArgs As
System.EventArgs) Handles Cmdexit.Click
End
End Sub
Private Sub Cmdcalcu_Click(ByVal eventSender As System.Object, ByVal eventArgs
As System.EventArgs) Handles Cmdcalcu.Click
txtFC.Text = CStr(Val(txtCC.Text) + Val(txtZnOC.Text) + Val(txtATRC.Text) +
Val(txtSCC.Text) + Val(txtFPC.Text) + Val(txtWPC.Text) + Val(txtSC.Text) +
Val(txtAPC.Text) + Val(txtSGC.Text) + Val(txtECC.Text))
txtCPKW.Text = CStr(Val(txtFC.Text) / 5)
End Sub
Private Sub cmdAdjustCost_Click(ByVal sender As System.Object, ByVal e As
System.EventArgs) Handles cmdAdjustCost.Click
If txtCIATR.Text <> String.Empty And txtCIZnO.Text <> String.Empty And
txtCIAirCompressor.Text <> String.Empty And _
106
txtCIPumps.Text <> String.Empty And txtCIFuelCellStack.Text <> String.Empty And
txtCIHeatExchanger.Text <> String.Empty Then
'txtCC
'txtATRC
txtCC.Text = CStr((Val(txtCC.Text) * Val(txtCIATR.Text)) / 100)
txtATRC.Text = CStr((Val(txtATRC.Text) * Val(txtCIATR.Text)) / 100)
'txtZnOC
txtZnOC.Text = CStr((Val(txtZnOC.Text) * Val(txtCIZnO.Text)) / 100)
'txtSCC
txtSCC.Text = CStr((Val(txtSCC.Text) * Val(txtCIAirCompressor.Text)) / 100)
'txtFPC
'txtWPC
txtWPC.Text = CStr((Val(txtWPC.Text) * Val(txtCIPumps.Text)) / 100)
txtFPC.Text = CStr((Val(txtFPC.Text) * Val(txtCIPumps.Text)) / 100)
'txtSC
txtSC.Text = CStr((Val(txtSC.Text) * Val(txtCIFuelCellStack.Text)) / 100)
'txtAPC
'txtSGC
'txtECC
txtAPC.Text = CStr((Val(txtAPC.Text) * Val(txtCIHeatExchanger.Text)) / 100)
txtSGC.Text = CStr((Val(txtSGC.Text) * Val(txtCIHeatExchanger.Text)) / 100)
txtECC.Text = CStr((Val(txtECC.Text) * Val(txtCIHeatExchanger.Text)) / 100)
txtCIATR.Text = String.Empty
txtCIZnO.Text = String.Empty
txtCIAirCompressor.Text = String.Empty
txtCIPumps.Text = String.Empty
txtCIFuelCellStack.Text = String.Empty
txtCIHeatExchanger.Text = String.Empty
Else
MsgBox("Please enter Cost Indices for all components to adjust costs for time.",
MsgBoxStyle.Information)
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End If
End Sub
Private Sub LinkLabel1_LinkClicked(ByVal sender As System.Object, ByVal e As
System.Windows.Forms.LinkLabelLinkClickedEventArgs) Handles
LinkLabel1.LinkClicked
LinkLabel1.LinkVisited = True
System.Diagnostics.Process.Start("http://www.bls.gov/ppi/#tables")
End Sub
End Class
Private Sub Cmdback_Click ()
Unload Me
frmStackInput.Show
End Sub
Private Sub Cmdexit_Click ()
End
End Sub
'Final cost calculations
Private Sub Cmdcalcu_Click ()
txtFC.Text = Val (txtCC.Text) + Val (txtZnOC.Text) + Val (txtATRC.Text) + Val
(txtSCC.Text) + Val (txtFPC.Text) + Val (txtWPC.Text) + Val (txtSC.Text) + Val
(txtAPC.Text) + Val (txtSGC.Text) + Val (txtECC.Text)
txtCPKW.Text = Val (txtFC.Text) / 5
End Sub
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