The Economics of Engine Replacement/Repair for Biodiesel Fuels

Transcription

The Economics of Engine
Replacement/Repair
for Biodiesel Fuels
Final Report *’
Nicolas B. C. Ahouissoussi
and
Michael E. Wetzstein
University of Georgia
Department of Agricultural and Applied Economics
March 1995
This research was partially funded by the Office of Technology,
USDA and the National Biodiesel Board
EXECUTIVE SUMMARY
TITLE:
The Economics of Engine Replacement/Repair for Biodiesel Fuels
CONTRACTOR:
National Biodiesel Board, Jefferson City, MO.
USDA, Office of Energy
PRINCIPAL
INVESTIGATORS
Michael E. Wetzstein, Professor
Nicolas B. C. Ahouissoussi. Research Assistant
OBJECTIVE:
The over-all objective of this study was to develop a dynamic
control model for determining the present value of operating costs
of biodiesel buses and its competitors, diesel, methanol, and
compressed natural gas. Accordingly, this analysis aimed at
comparing the expected life cycle costs of operating a transit bus
fleet fueled with these alternative fuels.
RESULTS:
A nested fixed point algorithm model was used for estimating
marginal operating cost for four fleets fueled with alternative fuels,
biodiesel, diesel, methanol, and compressed natural gas. The
method assumes that transit authorities have developed a procedure
for optimally determining when a bus engine should be rebuilt or
replaced. Given this optimal timing, the model estimates what the
marginal cost per month should be to obtain this optimal timing.
Knowledge of this marginal cost along with information on
infrastructure, refueling, and any incremental bus capital costs,
allows the comparison of net present value for alternative fueled
buses with diesel buses. Such a comparison accounts for not only
the explicit cost such as maintenance but also the opportunity cost.
including loss of goodwill, associated with bus failure.
Assuming a 35 percent blend biodiesel fuel can comply with
regulatory emission standards. biodiesel buses at prices at high as
$3.00 per gallon are competitive with the other alternative fuels.
A constraint on the robustness of these results is the limited data on
both number of buses and months of bus operations. Currently,
CIFER is collecting additional data, in the form of increased bus
numbers and operation length. Analysis of these data will result in
a more definitive comparison of these alternative fuels.
IMPLICATIONS:
This analysis reveals that biodiesel is competitive with CNG/Diesel
and methanol fuels. However. it is less competitive compared with
petroleum diesel fuel. In the present situation of liquid fuel supply
and at current crude oil prices, there is no incentive to find
replacements for liquid fossil fuels. There would therefore need to
be compelling environmental and socio-economic benefits from
conversion of vegetable oil to biodiesel to warrant incentives for
promoting biodiesel fuel. These incentives will be necessary to
allow the industry to further develop to meet expected demand. as
well as to meet the challenge of reducing the cost of producing
biodiesel, thus making the fuel more competitive in the commercial
marketplace.
Biodiesel represents one of the best alternatives as renewable fuel
for diesel engines from both the energy and environmental
protection aspect. Nevertheless, in the current state, for biodiesel
to have a likelihood of controlling a major portion of fuels markets,
on-going test program should develop a biodiesel-fueled engine that
achieves PM and NOx reductions beyond those attainable from
using low-sulfur diesel and catalytic converters in new engines.
and/or low sulfur diesel and standard rebuild kits in existing
engines.
TABLE OF CONTENTS
I
INTRODUCTION, RESEARCH ISSUES AND ORGANIZATION
Historical Perspectives of Alternative Fuel Development . . . . . . . . . . . . . 4
Research Issues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6
Research Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
12
Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
13
Organization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
14
II
OVERVIEW OF MAJOR ALTERNATIVE FUELS IN USE IN
THE UNITED STATES
Fundamental Characteristics of Alternative Fuels . . . . . . . . . . . . . . . . .
Gaseous Fuels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Alcohol Fuels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Biofuels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Biodiesel Fuel: Background and Characteristics . . . . . . . . . . . . . . . . .
An Evaluation of the Environmental Benefits of Biodiesel . . . . . . . . . .
III
LITERATURE REVIEW
A General Model of Replacement Principles . . . . . . . . . . . . . . . . . . .
Operating Cost Estimation Models and Replacement Analysis . . . . . . .
Replacement Cost Minimization Principles . . . . . . . . . . . . . . . . . . . .
Operating Cost as a Function of Age . . . . . . . . . . . . . . . . . . . . . . . .
Operating Cost as a Function of Cumulative Usage . . . . . . . . . . . . . .
Operating Cost as Function of Cumulative Usage and
Mechanical Condition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Other Economic Replacement Model . . . . . . . . . . . . . . . . . . . . . . . .
IV
42
47
47
50
53
53
55
THEORETICAL FRAMEWORK
An Optimal Replacement Model for Bus Engine . . . . . . . . . . . . . . . .
Application of the Nested Fixed Point Algorithm to Bus
Engine Replacement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
V
16
16
21
28
30
35
SOURCE, ASSUMPTIONS, DATA TRANSFORMATION, AND
PRELIMINARY RESULTS
Data Source . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
General Assumntions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
59
66
1
69
70
Data Transformation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Preliminary Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
VI
78
80
MODEL RESULTS AND ANALYSIS
87
Model Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
90
Discounted Operating Cost Analysis . . . . . . . . . . . . . . . . . . . . . . . . .
.
.
.
.
.
.
.
.
.
99
Estimated Versus Actual Present Value of Operating Costs
VII SUMMARY, CONCLUSIONS, AND POLICY IMPLICATION
Summary and Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Implications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
102
103
VIII REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
LIST OF TABLES
Table 1.1
Clean Air Act Amendments of 1990 U.S. Heavy Duty
Urban Bus Engine Emissions Standards G/HP-HR . . . . . . . _. . . . . . . 7
Table 2.1
Advantages and Disadvantages of Compressed Natural Gas . . . . . . . . 18
Table 2.2
Advantages and Disadvantages of Liquefied Petroleum Gas . . . . . . . . 20
Table 2.3
Advantages and Disadvantages of Hydrogen . . . . . . . . . . . . . . . . . . 22
Table 2.4
Fundamental Advantages and Disadvantages of M-l 00 . . . . . . . . . . . 25
Table 2.5
Fundamental Advantages and Disadvantages of EthanolGasoline Blends . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
Table 2.6
Advantages and Disadvantages of Electricity . . . . . . . . . . . . . . . . . . 29
Table 2.7
Exhaust Emissions of Biodiesel Compared to Conventional
Diesel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
Table 5.1
Characteristics of Buses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
Table 5.2
Diesel Bus Cost Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
Table 5.3
Methanol Bus Cost Summary . . . . . . . . . . . . . . . . . . . , . . . . . . . . 75
Table 5.4
CNG Dual Bus Cost Summary . . . . . . . . . . . . . . . . . . . . . . . . _. 76
Table 5.5
Startup Costs and Incremental Fixed Costs for Methanol and
Dual CNG/Diesel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
Table 5.6
Summary Statistics of Rebuilds . . . . . . . . . . . . _ _ . . . _ . . . . . . 81
Table 5.7
Biodiesel Fuel Price for Percentage Blend of 20, 35, 60, and 100
Table 5.8
Fuel Efficiency of Biodiesel Blend Fuels Compared with Diesel
Table 5.9
. . . 82
. . . . 83
Monthly Travelled Mileage and Rebuild Cycle . . . _. . . . . . . . . . . 84
J
Table 5.10 Actual Average Operating Costs for Diesel, Methanol, CNG/Diesel,
and Biodiesel Buses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ‘86
Table 6.1
Marginal Cost Estimation Results for Diesel, Methanol,
and CNG/Diesel Buses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
Table 6.2
Monthly Estimated Diesel Bus Cost for a Replacement Cycle . . . . . . 91
Table 6.3
Monthly Estimated Biodiesel Bus Cost for a Replacement
Cycle with Biodiesel Fuel Price of $1.75 per gallon . . . . . . . . . . . . . 92
Table 6.4
Monthly Estimated Biodiesei Bus Cost for a Replacement
Table 6.5
Monthly Estimated Biodiesel Bus Cost for a Replacement
Table 6.6
Monthly Estimated Methanol Bus for a Replacement Cycle . . . . . . . . 95
Table 6.7
Monthly Estimated CNG/Diesel Operating Cost for a
Replacement Cycle with Fuel Prices of $0.352. $0.3975,
and 0.443 per gallon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
Table 6.8
Present Value per Mile of Estimated Operating Costs Over
a 30 Year Life Cycle With Discount Rates of Zero, Five,
and Seven Percent . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
Table 6.9
Present Value of Actual and Estimated Total Operating Costs
Over a 30 Year Life Cycle With Discount Rate of Five
Percent . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
LIST OF FIGURES
Figure 1
The Self-Replacement Solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
Figure 2. The Self-Replacement Solution for a Machine . . . . . . . . . . . . . . . . . . 46
INIRoDucIIm, REsE4RcHIssuE;s
AND
ORGANIzAmm
As the world chugged toward the 20th century, nations measured progress in terms
of smokestacks. Smoke-belching steam engines powered weaving looms, ships at sea,
trains. even automobiles. People accepted air pollution as the price of progress (Biodiesel
information
Kit).
But times have changed There is a new understanding of the impact airborne
pollutants have on human health and the environment. Though new laws are mandating
cleaner air through reduced vehicle emissions and cleaner burning tiels.
As America
rises to meet the clean air challenge, a new fuel for diesel engines is emerging.
Also, at present, known reserves of crude oil sum to 1,006.8 billion barrels.
portioned out into MiddIe Eusl661.8; Lain America 123.8; Aftica 61.9; Former USSR
59.2; Asia and Australia 44.6; North America 39.7; and Europe 15.8.
Crude oil
production is currently 23.6 billion barrels per year, thus known reserves assuming the
same rate of usage will last 42.6 years. New fmds of oil continue to occur in the world
and without doubt major new discoveries will be obtained in the future.
However,
exploration is progressively moving to more geqraphically hostile environments such as
Siberia and the Falkands (Walker and Korbitz). In addition, as lmown reserves are
progressively realized
the financial cost of achieving higher recovery rates from these
sources increases steadily.
The resource cost of obtaining oil from these diffic$
environments is also likely to increase. An energy balance of 5: 1 for mineral oil
1
I
2
production was quoted in 1981 figures, but this is likely to progessively decline. &ainst
this however, is the continued advance of technology and better depletion levels.
Nevertheless it is without doubt that world reserves are &rite and that unless there
is a major change in the assessment of world reserves the M&Ye Eust will occupy a
progressively important and dominant role in the supply of world energy.
The current world recession has seen oil prices fall to historically low levels in
real terms. It is difficult to foresee that this will not change. Consequently, there is a
progressively important requisite to develop technologies which not only reduce the KS
dependence on these finite politically sensitive resources, but also contribute significantly
to air pollution reduction. Two main factors are driving demand for alternative fuels.
Necessily
for a - hi~ti0f~~
Six major types of air pollutants in American metropolitan areas comprise carbon
monoxide, volatile opnic compou~ (reactive hydrocarbons), nitrogen oxides, sulfur
oxides, led andparticulate
contribute [email protected]
mater. Emissions from gasoline and diesel powered vehicles
to five of the six sources of poIlution,
causing on average
approximately 90% of the carbon monoxide pollution, 30% of the lead, 50% of the
volatile organic compound and 50% of nitrogen oxides, which in turn combine to form
roughly 50% of the photochemical oxidants, including harmful ozone (MVIv& 1988).
Diesel powered vehicles are also a substantial contributor to particulate pollution.
Carbon monoxide (CO) is a by-product of incomplete fuel combustion. Colorless,
odorless and tasteless, it is asphyxiant and displaces oxygen in the respiratory system
The air qua&y monitoring data (1987-89) identified 41 metropolitan areas where CO
exceeded National Ambient Air Qua&v StanaL&
(h!AAQS)
(Ritchey et al., 1990).
Vehicles contribute on average 90% of the CO in the atmosphere.
Reactive kyzhzbon
/
and nitrogen oxides are corrosive gases which react in the
atmosphere with other substances to form photochemical oxidants including the most
3
popular ozone. Photochemical oxidants are the major component of smog; they cause
respiratory and eye irritation and lachrymation,
contribute to many respiratory
malignancies and cause damage to important crops and other vegetation. The air quality
monitoring data (1987-89) identified 96 urban areas where ozone exceeded NAAQS, and
nine other areas were designed “extreme.”
Lea2 is a cumulative toxin which afEcts
children. Lead pollution Tom
introdnction
the nervous system especially in
the atmosphere has declined significantly since the
of lead-&x gasoline; however, automobiles still contribute over 30% of the
atmospheric lead pollution (m 1988).
Purticulate matter is suspended particles which float or drift in the atmosphere
similar to dust and pollen. Several types of particulate are poisonous to human health.
Vehicles, primarily diesel engines are thought to contribute 16% or more of the particulate
pollution in metropolitan areas (MVMA, 1988).
The 1990 Clean Air Act and amendments require both mobile (principally
automotive) and stationary sources of pollutants to progessively reduce emissions over
the next decade. Emissions from alternative fuel powered en_@nes consistently show
lower emissions of reactive hydrocarbons. carbon monoxide and particulate matter than
gasoline or diesel eqties. For example, NSDB reported that biodiesel used in a IO/80
blend with petroleum diesel? along with a catalytic converter, reduces diesel e@ne air
pollution.
!g&3carbon
Reductions include purticulate mater 3 I%-cwbon monoxide 2.1% and total
47%.
Concern -for Reliable Sowre of Bergy Supp&
The United States and Canada hold only 4% of the world’s proven crude oil
reserves; the Middle East controls 70%. The United States imports a large portion of the
crude oil it consumes from OPEC nations. Sudden and siktificant disruptions of
availability have occurred three times in the past two decades.
4
Since 1973. the nations of the Orgmization
for Economic Cooperation and
Development (OECD) have reduced oil’s share of total energy consumption by 10
percentage points from 55% to 45Y4 however, the United States, clue to its oil dependent
transportation industry, has reduced oil’s share of total energy consumption by only 2%
from 44% to 42% (Anderson).
Transportation activities accounted for 28% of all KY. enerGgy supply use in 1987;
more than 97% of this energy was in petroleum products.
Moreover, 63% of all
petroleum is used directly for transportation. Thus, the development of alternative fuels
will help to reduce significantly the dependency and help secure energy supply in the
United States.
l!Estitical Petspedives of Altemative Fuel Developmnt
“Alternative
fuel” is a generic term commonly used to describe a fuel that is not
made from crude oil. Alternative. nonpetroleum motor fuels have been known and
occasionally used since the introduction of motor vehicles more than a century To.
However. they have not benefited Corn the intensive research and development efforts that
have produced the highly evolved, petroleum-fueled modern motor vehicle. Scientific
investigation of alternative motor fuels was rekindled in the late 1960’s by concern in
academia and government over the growing problem of urban air quality. This interest
declined as provisional solutions were found through technical modifications to
conventional vehicles that lessened new vehicle emissions levels.
Although the Clean Air Act Amendments (CAAA) of 1970 established a federal
requirement for elimkting urban air pollution on an expedited agenda, over twenty years
later it is generally recognized
that air pollution remains a persistent problem in many
areas and that emissions from gasoline-fueled motor vehicles contribute significantly to
violations of the National Ambient Air @a&y Stanuhd~ (NAAQS).
5
In recent years, the concern of reducing air
pollution
in many areas of the KS.
was the main reason that regulators and environmentalists advocated the replacement of
gasoline and diesel fuel with alternative fuels. The energy supply and price shocks of the
1970’s added another stimulus for alternative fuels, stemming fkom a desire of diminishing
dependence on imported petroleum Also, with the conflict in the Persiun Gz& there is
a renewed sense of urgency in using alternative fkels for reducing LW. dependency on
oil. Research initiated by the Environmental Protection Agency @?A) and continued by
the Enew Resemch and Development Adninistralion
(and subsequently the Department
ofEnew) aimed at establishing the foundation of technical information for development
of the options for displacing petroleum fuels (Exxon Research, 1974; Institute of Gas
TechnoloB, 1974). Repeatedly, however, the major policy implemented in reducing
dependence on the foreign oil cakd for [email protected]
improvements to light-duty vehicle
fuel economy, rather than alternative fuels.
However, refinements to conventional petroleum-fueled vehicles have been
incapable of eliminating air-quality and oil-dependency problems. In spite of significant
reductions in emissions Corn conventionally fueled vehicles, achieved mainly by technical
advances in fuel injection. computerized er@ne control, and the three-way catalytic
converter. several areas of the Nation failed to achieve National Ambient Air Qua/in/
Stmhd~ (U.S. DOE 1992). Moreover. in the absence of new policy initiatives, US. oil
consumption is expected to increase by 20% over the next 20 years, reaching 20.1 million
barrels per day in 2010 (EIq 1992). With twc&irds of the world’s confirmed reserves
and an increasingly large share of world oil production concentrated in the Pemian Gulf
region, the economic. environmental. and energy security implications of this scenario
deserve thorough attention.
Generally, various models of policies are useful in dealing with conassociated with these overlapped trends in oil use. For instance, energy security can be
xklressed
through the procurement of strategic petroleum reserves,
enhanced
policy
6
coordination with other reserve-holding nations, a reduction in the geographic
concentration of world oil production, increased domestic oil production, reduced
domestic oil consumption, and prominent flexibility in domestic energy markets, each of
which can serve in reducing both the likelihood and the repercussions of future oil price
shocks.
A counterbalanced approach will necessarily consist of a combination of these
different policies. However, the important role of reductions in oil use and the fact that
the transportation sector accounts for twc4irds of US. consumption suggest the necessity
of giving chiefly regard to measures with the potential of cost-effectively reducing the use
of petroleum-based motor fuels.
Alternative motor fuels can make a major contribution
toward reducing petroleum use in the transportation sector. Some alternative fuels can
be produced domestically; their use represents, to a considerable extent, a substitution of
domestic fuel for imported petroleum
Reseamh Issues
Despite the demonstrated and anticipated reductions in emissions from gasolinefieled
vehicles. motor vehicle emissions are projected to remain a significant contributor
to air pollution (Gordon and Austin). This is one of the reasons that there has been
considerable interest in reducing emissions through the use of alternative fuels.
Subjugated to the Clean Air Act of 1970, the Environmental Protection Agency
(EPA) established Nadond Arnhem Air Quality St&ds for six pollutants; carbon
monoxide, inhddde particuhes,
nitrogen dioxide, ozone, suIfirr oxides, ad lead These
standards reported in Table 1.2 for heavy duty urban buses in grams per horsepower hour
resulted in progams designed for lessening emissions of these pollutants.
J
Because ozone is the product of complex chemical reactions involving volatile
organic compounds (VK’), nitrogen oxides (A%), and sunlight, programs also were
7
T’e 1.1. Clean Air Act Amendments of 1990 U.S. Heavy Duty Urban Bus En-&e
Emission Standards G/HP-HR
1.3
1.3
1.3
1.3
Carbon Monoxide
15.5
15.5
15.5
15.5
Oxides of Nitrogen
5.0
5.0
5.0
4.0
Particulate Matter
0.25
0.10
0.05’
0.05l
Hydrocarbon
’ Administration may relax particulate standard to 0.07 if 0.05 is determined not to be
technologically achievable.
8
initiated for reducing VK. Since 1970, no nattainment of certain national ambient air
quality standards has led to different alternative vehicle and fuel proposals during the
debate on Clean Air Act Amenakzents.
This resulted in a phased-in adoption of clean tieI
vehicles under the 1990 Clean Air Act Amenakzents
and the National Enepp Sttategy.
Clean fuel vehicles are defined by their capability to meet non-fuel specific emission
,standards that are more stringent than the basic Federal emission standards.
Although extensive interest during the last past decade of research centered upon
ethanol and methanol processing technologies and policies, more recent research
emphasized the potential of plant oils as diesel tie1 extenders or replacements (Gavett:
McIntosh et ~2.). Alternative fuel vehicles including biodiesel fLels may offer emission
benefits over conventional vehicles, and thus, partially supplant current vehicle fuels in
obtaining emission standards.
Federal reG&atory policies resulting from implementation of the Clean Air Act
Amendments of 1990 and the N&o& Enerp Policy Act WEPA) will encourqe the
adoption and use of alternative fuel vehicles and associated technologies.
This is
particularly true for the urban bus market where recent Environmental Protection Agency
regulatory activities are aimed at reducing emissions of volatile organic compounds,
(VOC), nitrogen oxide (NOX), and particulate matter (PM) as a means of controlling
urban ozone. Recently, there has been a strong view that biodiesel is one alternative tieI
with a great promise.
Nevertheless. a number of other alternative fuels. including
compressed natural gas (CNG) and methanol, will be competing with biodiesel fuel.
Biodiesel is a clean-burning, renewable. non-toxic, biodegradable and
environmentally friendly
transportation fuel that can be used neat or in blend with
petroleum-derived diesel (Holmberg et u/.). Interest in biodiesel has increased because
advanced agricultural practices and changing dietary habits in the United States haye
reduced the price received for biodiesel feedstocks. Increased dietary use of lighter, more
unsaturated vegetable oil is leading to lower demand for saturated oils and fats in human
9
and animal feeds, enhancing the availability of a range of animal fats and vegetable oils
for conversion into biodiesel. Biodiesei blended with diesel is positioned to reduce
signific.antIy
emissions of particukttes, carbon monoxide and unburned
hydrocarbons.
With a slight engine timing modification, emissions of oxides of nitrogen (fVa> can also
be reduced One promising crop for biodiesel fuel is soybean; because soybeans are
legumes and their production and use are part of the natural carbon cycle, biodiesel is one
of the best fi.te1.s at stabilizing greenhouse gas emissions. When soybean farmer.5 practice
sustainable agriculture such as no till/minimum till, the soil becomes a carbon “sink” (it
builds up organic matter) which puts biodiesel at the top of the fuels list in terms of
stabilizing the build-up of carbon dioxide in the atmosphere (Merrill, 1993).
Compressed natum? gar (CNG) is one of the fuels viewed as potentially meeting
tighter vehicle emission requirements designed to bring many areas into attainment of
national ambient air quality standards. Extracted f?om underground reservoirs, natural gas
is a fossil fuel composed primarily of methane, along with other hydrocarbons such as
ethane, propane. butane. and inert gas such as carbon dioxide. nitrogen and helium
(Development and Communication
O&e). Interest in using natural gas as a
transportation fuel has increased in recent years, particularly in urban areas because it
offers the potentkl for reducing exhaust emissions and the US. has large resources of
natural gas. so that this fuel can help to reduce dependence on fore&n oil at a competitive
cost.
Ahethanol is another alternative fuel that can be produced from domestic resources,
both fossil and renewable. It can be used in neat ( 100%) form as a gasoline substitute
or in a blend with gasoline, commonly as A485 (85% methanol, 15% gasoline). The
majority of the methanol prochced in the United Sides is from natural gas resources.
Other feeds for methanol production include coal. residual oil, and biomass.
/
Regulatory policies place the biodiesel fuel industry at a critical junction. Fti
and government agencies promoting biodiesel fuel have the opportunity to initiate
10
programs, which can significantly influence the adoption of biodiesel fuel. ConventionaI
economic theory states that the rate and degee of alternative fire1 adoption, by transit
system will depend on their comparative competitiveness.
With the competitive markets, the fuel which is most economically feasible will
dominate its competitors. However, in general this is not how economic systems work.
For example, the VCR market started out with two competing formats selling at about the
same price, VHS and Beta. Similar to alternative
fuels each VCR format could realize
increasing retums to size. Large numbers of VHS recorders would encourage video
outlets to stock more prerecorded tapes in VHS format thereby enhancing the value of
owning a VHS recorder and leading more consumers to buy the VHS format. lhe same
would be true for the Beta format. Thus, a small gain in the market share would improve
the competitive position of one system and help it further increase its lead.
Such a
market, including alternative fuels, is initially unstable. It would be impossible at the
outset to predict which one system or fuel would survive. However. by some small event
one system will experience a relative greater increase in sales. Increased production
results in more experience in the processing of the commodity which lowers the costs of
production. Thus. depending on some event. alternative equilibrium solutions are
possible.
A new line of economic theory called positive feedback economics is designed to
explain this type of new technology adoption. Positive feedback economics finds its
parallels in modem nonlinear physics. Ferromagnetic materials, spin glasses, solid state
l==s and 0th~~ physical systems that consist of mutually reinforcing elements show the
same properties as the VCR example, and the potential market for alternative fuels. They
phased lock into one of many possible configurations. Small perturbations at critical
times influence which outcome is selected, and the chosen outcome may be less thaw
optimal.
,
The current state of biodiesel fuel is at such a critical time. A small policy change
11
by government or product promotion by industry may determine which alternative
fkels
will be adopted to a large extent. Assuming all alternative fuels have the potential of
improving air quality as regulated by EPA, firms and govemmental agencies promoting
biodiesel tie1
have an opportunity for initiating the small perturbation, and thus,
significantly influencing the adoption of biodiesel fuel. However: such promotion requires
tiormation on the performance of alternative fuels. Such information
can then be used
for determining the expected operating costs, and accordingly the expected
replacementkpair programs for these alternative fkels.
For example, evidence suggests
that alcohol fuels may be more corrosive than current fkels, and thus, lead to more
tiequent
overhauls and replacements. Unfortunately, data necessary for such an analysis
are fkqynented
and dispersed- Primary information on alternative fuel technologies in
urban buses was collected as part of various demonstration projects sponsored by the
Federal Trait Adninistmtion
as authorized by the Alternative Motor Fuels Act of 1988.
Nevertheless, a data set based on this information for analysis of life-cycle operating costs
and conceivably optimal engine replacementkpair has not been constructed.
This data set cannot solely consist of information on either initial start-up costs
of an alternative tie1 or the expected cost per unit of a fuel.
Instead, for urban mass
transit systems, information on safety, emissions. maintenance costs, and fuel economy
of a fleet of vehicles using a particular alternative fuel is required throughout their life.
An estimation of life-cycle operating costs and possibly an optimal schedule for
maintenance, rebuilding, and replacement of an engine can then be determined, by
dyamic COII~IO~
techniques, for a
particular
Abel under
&x-native possible EPA
re_@ations and other governmental policies. The comparative advantage of one fkei over
another is then determined by calculating the discounted net present value of benefits and
costs for the optimal schedule associated with each alternative fuel and policy option.
1
12
Reseamh Objectives
Biodiesel has a promising future in the united States. Recent environmental and
energy legislation has opened the market for this clean burning, non-toxic, biodegradable
fuel. However, this same le@slation controls access to that market, requiring extensive
testing and demonstrations for verifying pe15ormance and emission reductions compared
to clean diesel. The Abtional SoyDiesel Development Bawd (NSDB) is funding the
engine and fuel testing necessary to achieve WA recognition as a cleaner-burning fuel.
This study is a subset of a much broader economic and technical comparative analysis
being carried out on biodiesel fi.rel for its promotion.
The over-all purpose of this study is to develop a dynamic control model for
determining the net present value of operating costs of biodiesel he1 and its competitors,
diesel, CNG, and methmol,
based on a particular set of policy options. Consequently,
this analysis aims at comparing the expected total life-cycle costs of operating a transit
bus fleet fueled with the different alternative fuels. The costs considered are all
applicable capital and operating costs. These costs are normally borne by the transit
property, i.e., the entity facing the bus purchase decision.
The diesel en&tie has played a significant role in powering urban buses for the last
50 years and these diesel eqgine powered urban buses have provided service to every
major municipality in the United Stales.
Because these buses smoked and emitted an
odor. they came under regulatory attention in the 1960s and had their emissions hrst
re_dated by the US. EPA in 1974. The Clean Air Act Ame&ents
of 199() further
regulated urban buses--specifically differentiated fiorn inter-city coaches and heavy-duty
trucks. It is anticipated that by the year 2002, all buses operating in large metropolitan
areas would use alternative fuels. Therefore, urban buses are the focus of this study.,
Specific objectives include:
1. Assembly and construction of a data set detailing the safety, emissions, and
,
13
tie1 economy based upon traveled mileages and associated costs of a fleet of transit buses
using each alternative fuel This data set will contain the current level of knowledge
existing on engine rep1 acement and repair for alternative fkel technologies.
2. Based on this current knowledge an optimal control model for engine
replacement, repair, and operating costs for diesel, biodiesel,
CNG, and methanol will be
developed.
3. This model will reveal potential competitiveness of diesel, biodiesel carpred
with CNG, and methunol under alternative policies. Mbrmation f?om this analysis will
aid in the development of policy and programs which can significantly influence the
adoption of bioa!iesel
fkel.
The first task in this analysis will be accomplished using primary data collected
by the Colormlo Imtitute for Fuels aud High Altitude Engine Research (CIm).
CSER
as part of its commitment in this project is collecting data on the performance of fleets
of buses tieled with biodiesel, CNG, methunol and diesel. With respect to the second
specific objective. a stochastic dynamic progr amming model of bus engine rebuilding will
be developed assuming that CIFER’s decisions of bus engine rebuilding coincide with a
strategy which indicates whether or not to rebuild the current engine each period as a
function of observed and unobserved state variables. This model will formalize the tradeoff
between the cordlkting objectives of r&irking maintenance costs versus minimizing
unexpected engine failures.
Finally, based upon results from the econometric estimation of operating costs, the
competitiveness of these different alternative fkels will be determined by calculating tJe
net present value of total life-cycle operating costs. Different sets of policy alternatives
including re&atory or tax incentives will be discussed in combination with the relative
14
air pollution benefits of each altemative fuel.
Currently, only methanol and CNG have
benefited some incentives from the U.S. government
for their promotion.
Sensitivity of
the results to changes in technological parameters will also be discussed
The remainder of this dissertation is organized into five chapters. Chapter II
presents an overview of the main different altemative fuels along with their fundamental
and air pollution characteristics.
The literature review comprises chapter III.
Methodology is examined in chapter IV, including a discussion of operating costs
estimation, along with the mechanics of data collection. Chapter V includes results,
analysis and implications for bus transit systems. Topics for fkrther research, limitations,
and conclusions will be presented in the final chapter.
OLWWIEWOFMAJoRAL~A~FUELS
lNUSEINlHEUNITWSTATf!S
The Alternative Motor Fuels Act of 1988 (WA) was created to help achieve
energy security, improve air quality, and foster the production of methanol, ethanol, and
natural gas powered motor vehicles by encouraging, the development and widespread
consumer use of methanol, ethanol, and natural gas as transportation fuels (U.S. DO&
1992). AMFA seeks to help transportation f%els to carry over the threshold level of
commercial application and consumer acceptability at which they can successfully
compete with petroleum-based transportation fLels.
Initiatives that emerged include
increased Federal support to States and localities for advancing the use of alternative
fuels. increased research and development on electric vehicles and advanced biofLels
technology.
In concert with the support of research and development programs for developing
en&ties that can use alternative tieis. Federal support can help to improve the
understanding of the fuels, reduce the cost of producing the f%els, and address legitimate
market barriers that hamper the penetration of cost-competitive fuels into the marketplace.
The hMmu/ Energy Smegy (Ii%S,, is expected to accelerate the introduction of
alternative fuels between 1995 and 2010 (U.S. DOE 1992).
This chapter reassesses the status of several important alternative-fuel technologies.
The review covers the status of gaseous fuels (including natural gas. liquefied petroleum
/
gases and hydrogen), alcohol fuels including (methanol and ethanol), and electricity
15
16
(including battery-electric vehicles). Biofhels
and biodiesel production issues cut across
fuel types and are treated separately.
FU&UHX&I
charactetitics of Alternative Fwls
Despite environmental and energy supply shortcomings, petroleum-meled
internal
combustion engines have given alternative fuels stringent competition at every turn.
Because the technology of conventional petroleum fuels and vehicles is so highly
developed and continues to improve, research and development efforts to ameliorate
alternative fuels and alternative-fuel
vehicles (AIT) is acute to developing alternative
technologies that meet both the needs of society and the consurner. Every alternative fuel
has advantages and disadvantages in comparison with existing vehicles.
Some
disadvantages, such as higher costs. may be worked out by achieving economies to size
via the mass production of alternative vehicles and fuels.
Some weaknesses of alternative
mels will necessitate technological solutions, while others. such as lower energy densities,
will remain shortcomings that must be counterbalanced by others unique benefits.
The principal gaseous fuels under consideration as motor fuels are natural gas;
liquefied petroleum gas; and hydrogen.
Because petroleum fuels are under normal
ambient conditions. there are greater differences between the technology required for
gaseous motor fuels and conventional technology than there are for other liquid alternative
fhels. These differences include mainly refireling
the combustion chamber.
on-board storage, and fuel delivery to
1
17
Niztwd Gus
Natural gas composed essenti~y of methane, is virtually
United St&es.
omnipresent in the
Natural gas must be compressed to 140 to 220 atmospheres (atrn) or stored
cryogenicdy to achieve suf%icient
energy density for practical on-board storage as a
motor-vehicle tie1 (Owen and Coley, 1990). Even with compression to 220 atm
compressed natural gas (CNG) has an energy density only one-fifth that of gasoline on
a volumetric basis. Vehicle refueling with CNG is entirely different from retieling with
gasoline or diesel fuel.
Retieling is extremely important to CNG vehicles because the
low energy density limits vehicle range to 80 to 200 miles, depending on the number of
storage cylinders and the storage pressure.
Natural gas is an excellent fuel for spark-ignition engines but cannot be used in
unmodified compression-ignition engines because of its very low Wane number. The
conversion of gasoline to dual-tie1 CNGlgasoline
operation is a proven technoloo, and
dual-fuel CNG vehicles have been proven to operate properly with fewer overall
maintenance problems. Their weaknesses include mainly reduced pe15oxmance due the
fact that natural gas displaces air in the cylinder; limited driving range because of their
lower energy density; and loss of storage space. owing to the need for separate fuel
systems and the bulkiness of the cylindrical tanks presently used in conversion
technolo~q.
Natural gas is a relatively clean transportation fuel as compared with gasoline, and
diesel. The possible exception is nitrous oxide (NO), emissions which are believed
manageable with known emission control technology.
It has possible reduced
maintenance costs. Although not yet well established. most reports indicate lower
maintenance costs with CNG. This is attributed to the cleaner and more complete burning
that occurs due to its chemical nature and relatively simple composition compared wii
gasoline or diesel. Characteristics of CNG are summa&ed in Table 2.1.
,
18
TaMe 2.1. Advantages and Disadvantages of Compressed Natural Gas (CNG)
Advantages
Lhadvantages
(1) Relatively low cost compared with other fuels.
(1)~bestoredintankathighpressureor
under cryogenic conditions. When stored as high
pressure gas. the tank takes space in the vehicle and
has low energy density of storage relative to
diesel
(2) CNG vehicles do not require the fuel/air ratio
to be enriched during warming because as
a gas it mixes very well witb air at low
temperatures.
(2) Relatively high volumetric fuel-air ratio reduces
engine air consumption by about loo/, thereby
reducing peak power unless there are
compenming changes in compression ratio or
boost.
(3) Evaporative emissions am no problem with
CNG because as a high pressure gas: all
connections are very tight.
(3) Relatively high cost of converting existing
vehicles.
(4) Unburned fuel emissions have verv low
photochemical
reactivity.
(4) Added weight of tankage reduces vehicle
caqing capacity.
(5) Very high octane number and high lean flame
ignition limit.
19
LiqwJ%d P~hn GaY
Liquefied petroleum gases (LPG) are mixtures of propane and butane in which
propane usually predominates. For example, when used as a motor tieI, LB3 contains
at least 97.5 percent propane (Owen and Coley, 1990). Propane is mainly produced as
a byproduct of natural gas processing. Unlike natural gas, it can be stored as a liquid
under modest pressure.
For use as a transportation fuel, it is stored in liquid form
offkring a volumetric energy density of 75 to 80 percent of that of gasoline. Ekcause of
its handling propane refueling and on-board storage are less difficult than for natural gas.
It has a higher octane number; excellent cold-starting characteristics; it burns cleaner than
gasoline, and is very low in sulfk
Like natural gas, propane faces several comparable challenges, but its differences
with gasoline are moderate. The technology for converting diesel engine to dual-fuel
operation on propane compromises some of the superior characteristics of propane fuel.
The need for dual-fuel systems adds complexity and costs and sacrifices storage space.
Improvements in tank design and cost reductions would benefit the economics of propane
vehicles.
About 70% of LEG supply is fi-om natural gas operations and the remainder
fkom crude oil operations. Its use will displace crude oil to some extent. However, it has
limited
availability. As CNG use increases. the availability of LE will increase.
LE is a cleaner fkel than gasoline or diesel. However, relatively little emissions
testing has been done with LFG conversions, and significant variations can result Tom
improper installations or adjustments. LK has some capability for ozone reduction due
to lower volatile organic compounds (Yoc) and possible reductions of nitrogen oxide
(N(k) (Radian, 1989). There is a significant reduction in carbon monoxide and, when
used to replace diesel fuel,
LPI; has significant particulate matter (PM) emissions
reductions (Radian 1989). The advantages and disadvantages of LE are listed in Tab&
2.2.
20
Table 2.2. Advantages and Disadvm~es
Advantages
of Liquefied Petroleum Gas (L&J
Disadvantages
(1) Unburned fuel emissions are low in
photochemical
reactivity.
(1) Availability. Propane is recovered from natural
gas (about 70%) and the remainder from crude oil.
‘Ihe availability may be the limiting f&tor for its
use. As nahual gas use increases, the availabili~
of JTG will also increase.
(2) Evapoxative emissions are eliminated
by pressurized fuel system
(2) Added fuel tanks. LPG fuel tanks are needed
for dual operations.
(3) Liquid over ambient tempemture
range in pressurized container.
(3) Relatively high cost of converting existing
vehicles and conversion equipment.
(4) Like methane. it does not have to be
driven hei rich during warmup.
(5) High octane (over 100).
Hydrogen is a gas rarely found by itself in nature, but ofkn occurrhg in
combination with other elements. There has been considerable interest in the past in a
hydrogen economy. L&e natural gas, hydrogen is gaseous under the full range of ambient
temperatures. With the same pressure, volume and temperature, hydrogen has only l/3
the energy density of CNG. It is the cleanest burning fuel along with electricity (Gordon
and Austin). The products of hydrogen combustion are only water, hydrogen and nitrogen
oxide. If the combustion chamber is rich burning the nitrogen oxide may be reduced to
meet exhaust standards, although mileage would be lost. Aside from its relatively low
energy density, hydrogen is expensive.
Hydrogen is the fuel which powered the L?S. space vehicles and is attractive
because of its high energy conversion efficiency, low emission characteristics, and the fact
that it can be produced f?om water. Unfortunately, the high cost combined with the low
energy density and storage problem have resulted in little interest in hydrogen as a
replacement for conventional fuel in the foreseeable fkture.
Its advantages and
disadvantages are listed in Table 2.3.
Alcohol F&T
Alcohol fkels, which are liquids at ambient temperatures and atmospheric pressure,
also have energy densities one-half (methanol) to twc&irds (ethanol) that of diesel. Their
higher octane ratings and higher heats of vaporization allow engines designed for alcohol
fLels to produce. more power than engines of equal size optimized for gasoline. Alcohol
tiels also have superior emissions properties. Their evaporative emissions contribute less
to smog formation and because they contain oxygen they tend to reduce the formation
of carbon monoxide in exhaust emissions. The relatively low vapor pressures and hi@
latent heats of vaporization of neat alcohol fuels lead to poor volatility and thus coldstarting and warm-up problems.
22
Table 2.3. Advantages and Disadvantages of Hydrogen
Advantages
Disadvantages
(1) Unburned fuel emissions do not contribute to
ozone formation.
(1) Present processes for making hydrogen arc
(a) producing carbon monoside and using later gas
shift with a catalyst. The process is expensive and
it uses fossil fuels as reactants.
(b) Electrolyis. f%pensive. Depends on fkel for
production of electricity.
(2) High octane (over 100)
(2) One third the energy den&y at the same
pressure, volume and tempexature as methane.
(3) Excellent lean limit ignition permitting high
compression and excess air in chamber.
(3) Any developments of hydrogen technology from
electrolysis. especially by thin film solar cells are
farinthe fkturc.
23
However, these problems are avoided by the addition of a volatile primer usually gasoline
in amounts of about 15 percent.
I?xperiene in designing and mass producing neat and near-neat alcohol vehicles.
together with technological advances in systems, lead to the development of flexible fuel
vehicles (Fn’), which permits the use of either methyl or ethyl alcohol fuels or gasoline
in any mixture (J.E. Sinor, 1992).
A major advantage of KV’s over dual-fuel vehicles
is that in F3;y the fuels share the same fuel systerq elirni&ng the complexity, weight,
and space requirements of dual systems. However, a drawback of the FF’V is that the
emissions advantages of neat methanol and ethanol are seriously compromised by the
addition of even 15 percent gasoline. The two major alcohol fuels in use in the United
States are methanol and ethanol.
Methanol commonly called wood alcohol, because it was or&ally
made by
pyrolysis of wood is a colorless liquid. It bums in air with an almost colorless flame.
It forms practically no soot when substituted for diesel fire1 in a modified bus engine.
Required modifications for ensurin g materials compatibility and higher fuel delivery rates
include methanol-tolerant, higher volume fuel injectors and some form of ignition
assistance.
Disadvantages include poor cold starting. The vapor space in a container of pure
methanol (M-100) is explosive in the ambient temperature range. Therefore, vehicles’ fuel
tanks of A4ZOO would have to be inerted to prevent an external ignition source from
propagating a flame into the fuel tank. A large spill of M-IO0 or M-85 could contaminate
an aquifer, making the water non-potable until it is thoroughly flushed.
The use of 15 percent gasoline in the methanol increases the vapor pressure of the
/
fuel which eliminates the cold start problem and the fuel tank vapor is no longer in the
explosive range at normal ambient temperatures. However, the addition of gasoline
24
presents some disadvantages. The exhaust contains not only methanol and formaldehyde.
but unburned carbon and hydrogen.
The evaporative and running losses are not
significantly reduced and include both methanol and gasoline vapor.
Methanol is toxic in relatively smaIl doses and can be absorbed by skin contact.
Since it has little taste or odor, methanol as M-100 presents a health and safety concern
for use by the general public.
Ekcause, MI00 burns with no visible flame. it is
considered a moderate safety risk, but still less than that of gasoline (Radian,
1989).
There is an increased danger of accidents with methanol since twice the volume would
need to be transported as compared with gasoline.
OveraIl, methanol is a less polluting fuel than gasoline or diesel. For controlled
emissions, findings are mixed, with US General Accounting office (GAO) reporting NOX
emissions similar to gasoline and KS. Depamnent
of Eneqp @OEJ reporting lowered
NOX levels. It is believed that reduced hydrocarbon (HZ) emissions from alcohol fuel
coupled with reduced NOX emissions (possibly from cooler combustion temperatures) will
reduce ozone formation (Sperhng). In diesel applications. methanol eliminates most of
the particulate emission problem of diesel fuel and substantiahy
reduces N0x emissions.
Methanol is currently made from natural gas and it is probable to be made from
this same raw materiaI in the foreseeable future. The worlds proven reserves of natural
gas ax-e very large approaching those of crude oil. Unfortunately, the United Stale.7 only
has 5% of the world proven natural gas reserves, while the former Soviet Union and Irm7
have the primary proven reserves, 38% and 12.5%respectively
(Gordon and Austin). The
essential advantages and disadvantages of M-100 are summarized in Table 2.4.
Ethanol from biomass, a liquid fuel Ii-om renewable, virtuahy inexhaustib$
domestic resources is a nonfossil transportation fuel contributing no net carbon dioxide
to the atmosphere. It is a potentiahy
clean-burning fuel that reduces air pollution
25
Table 2.4. Fundamental Advantages and Disadvantages of MI00
Disadvantages
(1) Produces no soot: mainly advantageous in
compression ignition engines.
(1) Infinitely soluble in water demands that
underground storage tanks be n-ee of wxer
contamination from internal or eszernal source
(2) High octane rating
(2) Attacks many gasket materials as well as some
metal and alloys such as protective inner layer of
gasoline fuel tank.
(3) lkellent lean ignition
(3) Bums with colorless flame in daylight.
increasing risk for occupants during vehicle fires
(4) Low vapor pressure relative to gasoline should (4) Potentially hard cold starting due to low fuel
reduce evaporative and running loss emissions.
volatiliq.
(5) Unburned fuel emissions are low
photochemical
reactivity.
(6) Can be produced from U.S. natural
(5) Incomplete combustion produces formaldehyde.
which has higher photochemical reactivity than
unburned gasoline.
gas or coal. (6) Methanol-air mixtures arc explosive over some
of the ambient temperature range.
(7) Low emission levels.
(7) Extimelp toxic compound by either skin
absorption or by ingestion. Large spills can
contaminate aquifers.
(8) Can be used as additive or fuel to reduce
dependency on imported petroleum products.
(8) Only has half the energy density of gasoline
thereby reducing vehicle range per gailon of fuel
tank capacity.
26
problems such as
smog
and carbon
monoxide,
and can be used as a blend or as a pure
with good efficiency.
In the United States ethanol is prodnced mainly fiorn corn which is also valuable
as food and feed crop. Efforts have been made to develop an ethanol feedstock from
celhrlosic
biomass, herbaceous and woody plants agricultural and forest residues, and
municipal solid waste.
These cellulosic
materials can provide an abundant and
inexpensive source for ethanol.
Materials compatibility is less of a concern than for methanol. The United States
corn ethanol industry is a subsidized, high cost, trade protected, limited scale industry;
unable to compete in fi-ee markets or to efficiently supply new fuel demands of clean air
leg&rtion
(Rask et a%). Significant advantages and disadvantages of ethanol-gasoline
blends are summarized in Table 2.5.
l3ectricity
Electric vehicles (Ws) are powered by electric motors operated from rechargeable
batteries carried on the vehicles. Ws are quiet and easy to operate. Depending upon the
source of fuel for electricity for recharging the batteries, Ws can produce less emissions
than other fuels. Electricity is mostly generated f?om non-crude oil fuels. As a result
there will be a substantial BTU displacement of crude oil by electric vehicles. The only
common emissions that are directly from electric vehicles (EVs) are low levels of
hydrogen emitted during pack recharging. Emissions estimates for Ws o&n include
estimates of the original power source emissions. Improved batteries are the key to more
general axeptance of electric vehicles. The drawbacks of the present lead acid batteries
include relatively smaIl number of duty cycles of charge-discharge before needing to be
replaced: and relatively small energy density.
The major limitations are relatively low travel mileage distance with the present
battery pack before recharge is necessary; low energy density; long recharging time; and
27
Table 2.5. Fundamental Advantages and Disadva~~tages
of Ethanol-Gasoline Blends
(1) Ethanol has an octane rating over 100, so the
octane mting of the blend is increased over
that of unleaded straight nm gasoline.
(1) To encourage the use of grain ethanol. both
state and federal taxes on the fuel are xkved.
(2) Because ethanol is partially oxidized for
any given fuel-air rnixhne there will be less
carbon monoxide in the exhaust.
(2) Ethanol has a much smaller BTU/gallon than
gasoline.
(3) Ethanol addition to gasoline increases fuel
vapor, which may lead to higher evaporative
emissions.
(4) Like methanol. ethanol-air mixtures form
explosive mixtures in the ambient temperarure
range.
28
the need of replacing the expensive battery pack. Energy on a volumetric basis ranges
from about 1 percent of that of gasoline for lead-acid batteries up to 2 percent for
advanced sodium-sulfur batteries.
Mer 20 years of federally sponsored research and significant advanced battery
technology, marketable W technology is still dependent on the lead-battery. Because
limited range and long recharging time are the chiefs obstacles to marketability of batterypowered W, fuel cells (electrochemical devices that combine oxygen and hydrogen and
convert the chemical into electricity) or fuel cell-battery hybrids provide an attractive
possibility (U.S. DOE, 1992). The chief attraction of fuel cells are their potential for zero
emissions and their theoretically higher energy conversion efficiency, nearly twice of that
of internal combustion engines. The advantages and disadvantages of electricity are noted
in Table 2.6.
BiofueZs
Biofirels
commonly
are considered to be all solid liquid and gaseous fuels
obtained from plant materials and wastes from biological systems, including municipal
wastes. Biofirels
for transportation usually include ethanol, methanol, and ethyl and
methyl ternary butyl esters derived from them; synthetic gasoline and distillate; methane;
and distillatelike vegetable oils (U.S. DO& 1992).
Generally, the primary advantages of
biofirels are that they are renewable; can be produced using domestic resources, thereby
displacing imported petroleum; and produce no net addition of greenhouse gases
(depending on the energy source).
Nonpetroleum diesel fire1 substitutes can be obtained from oil-seed crops such as
soybean sunflower, and rapeseed. Methyl and ethyl esters made Corn soybean and
industrial rapeseed oils have been found to have properties much closer to
/
29
Table 2.6. Advantages and Disadvm~es
of Ekctricity
Disadvantages
Amantages
(1) Non-polluting except for very small
emissions of hydrocarbons from lubricants.
However. depending on fuel. there is pollution
at utility station to generate electrici~.
(1) Need for battey pack:
(a) Extra weight and space
(b) Very low energy density compared to liquid
fildS.
(c) Limited number of charge-discharge cycles
requires battery replacement.
(d) Limited driving range.
(2) A portion of braking energy tirn the vehicle
can be captuted as electrical energy and fed back
to battery pack and overall efficiency is
potentially superior to gasoline fueled vehicle
of comparable weight.
(2) E&awe the battery pack can be recharged with
household cut-rem road tax collection may be
difficult.
(3) If the battery pack can be recharged &XII
household current, recharging may be more
convenient
(3) High capital cost and replacement batteries
30
conventional diesel fuel (Ziejewski ef al., 1983; Clark et al. 1983). These fuels, pr&&
via chemical or thermal processes, ref&red to as biodiesel fuel, constitute the focus of the
present study.
Biodiesel Fuel: Bac@d
and Chamc&titics
The term “biodiesel” is used to cover a large group of chemicals called “esters”
which can be used as a diesel tie1 replacement. These esters can be economically derived
Corn many vegetable oils and animal fats.
Ori@y introduced in South Africa before World War II, biodiesel is gaining
acceptance worldwide. There are significant biodiesel industries in Europe and there is
a developing biodiesel in- in the United States. Biodiesel production is a relatively
simple process. It is made by esterifjing
a vegetable oil such as soybean or rapeseed oil
and/or animal fat. This esterification process involves mixing the oil or fat with an
alcohol in the presence of a catalyst (potassium or sodium hydroxide) and allowing them
to react. If methanol is used the process produces a methyl ester such as methyl soyate
f?om soybean oil or methyl tallowate from animal fat and glycerin. As the methyl soyate
is formed valuable glycerine separates out and sinks, thereby removing the gumming
factor. The methyl soyate is decanted off, and can beused in most diesel engines with
no modilication.
In the United States, promotion of biodi
use is =ppofidbytJle oils&
and other biodiesel feedstock producers and pro
because of the availability of a wide range of
fats and vegetable oils for their
conversion into biodiesel fuel at a competiti
This wide variety of potential
feedstocks
including used vegetable oils (
) means &af SOme type of
biodiesel can be produced eveqwhere in the
try. In addition, international
agreements afExting
Agreement
agriculture, such as the Gene
on Tar@ and Tnxk
31
(GATT) or the North American Free Trade Agreement (NAFTA), and the European
pursuit of biodiesel have also stimulated
interest in biodiesel in the United States.
Fin&y, stricter EPA emissions requirements for heavy-duty engines, both on and off-road,
including urban buses have generated interest in biodiesel. Its performance similarities
to conventional fossil fuel-based diesel have propelled biodiesel into strong consideration
as one clean-burning alternative fuel that may be required in fleets and other applications.
?he National SoyDiesel Development Bomd (NS’DB) now the Nationa/ Biodiesel
Board (NBB) and the American BiofueIs Association (ABA) are two principal structures
supporting the advancement of biodiesel in the United States. Their intent is to advance
biodiesel in a manner benefiting farmers, rural America and the environment.
The NSDB is managed by a executive director, and is directed by an Executive
Committee headed by farmers. It is mostly funded by “check-off’ dollars administrated
by the United States Soybean Boa-d (c/SB) and the Qualified Stae Soybean Boa&~
(QSSB). The QSSB fhds directly the NSDB, while the USB hds the American
Sqvbean Association (ASA) that manages the contract with NSDB for the USB.
The ABA is managed by its president, and directed by a board of directors who
are members of the association. ABA has performed contract work for the NSDB in
areas pertaining to public policy such as research, project management, cost sharing for
research and testing.
Potential CL!2 Biodiesel h&ion Gpzbiiity
The United States consumes over 25 billion gallons of diesel fuel for
transportation annually. The current US. production of all vegetable oils and animal f&t
is nearly 23 billion pounds per year. At a conversion rate of seven and a half pounds of
oil/fat per gallon of biodiesel, the current US. production of oils and animal fats is only
32
sdicient
to produce some 3.1 billion gallons of bided, about 12 percent of the
transportation diesel market.
These figures are sonmdmt deluding both becase most of this oil already has
a food or feed market and because it does not represent the full production potential.
Over a billion pounds of soybean oil is in excess, capable of producing about 133 million
gallons of biodiesel. Using land idled by the LLY. commodity programs (about 50 million
acres) would permit additional production of about 3 billion gallons per year of biodiesel
and not interrupt any current use of oils. Furthermore, aggregate crop yields in the LB.
are increasing at the rate of 1 to 2 percent per year, so cropland availability is not a major
coIlstraiTlt.
Approximately 2.5 billion pounds of waste cooking fats are collected annually
f?om restaurants in the UnitedStates
(Gaur and Graboski, 1992). In addition, 500 million
pounds of fatty material are removed at municipal waste faciities
nationwide. This is a
large amount of material, approximately 3.7 percent of all municipal solid waste recycled
in the United Stutes.
LandfU restrictions specify that none of this waste may be
landf?lled and municipal wastewater treatment plants are unable to treat the material since
it obstructs f3ter.s. Thus, the only option for the material is to be recycled for reuse.
Currently, the spent greases are collected by various companies who process the waste
into yellow grease used for a feed supplement for cattle, hogs, and poultry.
However,
another interesting market for the waste grease is to convert it into biodiesel.
Given these factors, it is reasonable to assume the LG. plausible capability of
producing biodiesel tie1 is enormous. and economics will largely determine the size of
biodiesel market. The NSDB has identified potential niche markets for biodiesel. Should
soughx&er incentives become available. these markets will expand considerably.
33
FiuzdamerdaI C3um&&ics of Biodiesel
Methyl soyate as a fitel or blended into diesel fuel as a component
offers
several
advantages as an energy resource. It is a renewable resoure f?om agricultural products,
relatively easily processed, is a liquid with physical properties in the same range as diesel
fuel, and due to its oqgen content, offers advantage from an exhaust emission standpoint.
The fuel chemical and physical property characterization and impact on engine are as
follow.
The major fuel characteristics include ignition quality commonly expressed by the
cetane number; fire1 stability, indicated by carbon residue and accelerated
stability; low
temperature flow performance, indicated by fuel cloud point; and fuel energy content from
lower heating value in BTUlgallon.
1. Ignition quality
One of the primary advantages of diesel is its high cetane rating which allows the
fuel to autoignite when sufkiently compressed. The cetane rating is a number indicating
a fuel’s ability to self ignite, the higher the number, the easier it self-ignites. Currently
reported cetane numbers for biodiesel range between 46 and 5 1. depending on the
feedstock used to make the ester. Whereas. a typical cetane number for No. 2 diesel is
40-45, and for No. 1 diesel, 48-52. Experimental data fi-om Southwest Resemh Institute
(SwEu) indicates that blends of biodiesel and No. 2 diesel may have cetane numbers that
are higher than either of the original neat fuels. This indicates methyl esters may have
a blending cetane number that is greater than the value for the neat fuel.
34
2. Fuel Stability
The stability of the meI is described by carbon residue and accelerated stability:
blends up to 30 percent are still within the satisfactory range expressed by the Detmit
Diesel Corpomtion
Specification
3. Low Temperatunz Pefommrce
Biodiesel is somewhat more viscous than petrodiesel. This is not of major concern
for biodiesel as long as routine measures used to ensure the flow of petrodiesel are
employed, but cold weather additives are being explored.
4. Fuel Energy Content
Neat methyl soyate has a significantly lower heating value (BTU/gallon) than
diesel fuel (12.5% lower). Because this is essentially a straight line blending function
the heating value of the blend is proportional to the methyl soyate concentration.
However- the density of methyl soyate is greater than diesel fuel, so the effect on enerrgy
density (BTU/gallon)
is not as great. Therefore, because diesel engines inject me1 by
volume, not mass. the impact of the lower heating value of methyl soyate will not be as
great. It is highly probable that any change in the chemical characteristics of BD20 or
BLI-30 (in this study BD2O means a 20% biodiesel and 80% petrodiesel blend; BD30
a 30% biodiesel and 70% petrodiesel blend etc.) compared to the base petrodiesel will
be (with the exception of the oxygen content) within the chemical range of petrodiesel
(Merrill, 1994).
Impctonhgines
1. Materials Comp&bili&
There has been no evidence of any problems with materials compatibility using
BD20 or BD30. However, in neat form, biodiesel may cause problems when coming
35
in contact with certain elastomers. Comprehensive testings to address remaining materials
compatibility issues are underway.
2. Dun&i&y and Impact on Lubricants
As reported by&&en-ill ( 1994), most studies have shown no appreciable difference
between biodiesel and petrodiesel. Based on wear metal analysis of the [email protected] lubricating
oil. engine wear rates were well within the specified range for the ergties tested althouc@
some lube oil dilution occurred.
3. khintenauce
Recommendation
Studies and evidence being collected by the iVSDB suggests that
tiequent
engine
oil change will not be necessary for BD2U and BD-30.
ln summary, from these characteristics it appears biodiesel fuel and neat diesel
behave in a similar manner. The only exception is the cetane result with methyl soyate
which in itself supports the substantially similar argument for biodiesel since the blends
were not different fi-om diesel. Loss of energy due to reduction of heating value is not
an important issue at the blend levels anticipated. Performance areas needing attention
are stability, and low temperature performance.
An Evaluation of the Einimmntal
Benefits of Biodiesel
There are three key areas of environmental gain from the use of biodiesel fuel:
Biodiesel has nil acute oral and dermal toxity, and is rapidly
biodegradable.
. Biodiesel use results in a reduction in greenhouse gas production.
Biodiesel produces significantly lower levels of most exhaust emissions,
36
1. Biodegradabiliry
Biodiesel is biodegradable and non-toxic. Over 98 percent of biodiesel degrades
biologically in three weeks whereas in the same time only approximately 50% of fossil
diesel degrades, after which degradation is much slower (Walker
and Korbitz 1994).
Risks of ground water pollution would be significantly reduced if biodiesel were
introduced Large scale spillage
of biodiesel would cause temporary deoxygenation of
water, but this is still significantly less damaging than an equivalent fossil diesel spill.
These characteristics make it a valuable
fuel, particuharly
in environmentaIly
sensitive areas. It is thought that biodiesel wiIl improve the biodegradability and reduce
the toxity of petrodiesel. The effect on biodegradability when biodiesel is blended with
petrodiesel in varying percentages is being studied
2. Greenhouse ties
A recent study by Muschalek
and Scharmer. converted all greenhouse gas
emissions horn biodiesel into carbon dioxide (CO?) equivalents. This is of major
importance in providing a clearer view of the overall benefits of biodiesel production in
terms of benefit to the environment. The study involves not only gaseous emissions from
the combustion of biodiesel, but took into account carbon dioxide and other gaseous
emissions for each step of production transformation and final use. The conclusion was
that each kilogram (1 kg = 2.2 lb.) of biodiesel produced avoids the emission of
greenhouse gases equivalent to 2.88 kg CO,.
Biodiesel is often claimed to be carbon dioxide neutral, on the basis that CO,
during burning is equivalent to that taken up by the growing crop, and as such should not
contribute to the greenhouse effect.
3. Exhaust Emission
According to Whitelegg et al. the incidence of asthma, particularly in the young
has increased dramatically in the last thirty years. While the link between or&nal onset
of the problem and vehicle exhaust pollution has yet to be absolutely determined. there
is no doubt that this pollution can exacerbate and increase the frequency of the attacks.
Diesel emission particulates are strongly linked to infant mortality in urban areas.
and are probable carcinogens. Carbon monoxide reduces the absorption of oxygen and
is associated with restricted f&al growth and tissue development in young children,
lower worker productivity and has a synergistic action with other pollutants to increase
respiratory and circulatory problems. Sulfbr dioxide causes impaired lung function, and
is the major constituent of acid rain. Hydrocarbons cause eye irritation, coughing and are
linked to particulates in causing lung disease and cancer. Nitrogen oxides increase
susceptibility to viral infections, increase sensitivity in asthmatics, and have significantly
greater effects in the presence of other pollutants. Biodiesel gives significant reductions
in the levels of most emissions.
In an unmodified engine, EPA-regulated emissions f?om BD20 and ED-30 are
lower than those for petrodiesel. except for nitrogen oxide (NOX) emissions. which can
be slightly above the baseline emissions. The NSDB is determined to ensure that NOX
emissions are also reduced below the baseline petrodiesel and is exploring a number of
approaches to reduce Na emissions without adversely affecting biodiesel’s ability to
reduce particulate matter (PM)‘. Biodiesel is also essentially f?ee of sulfi.u- and aromatics.
It could, therefore, be used to dilute the sulfur and aromatic content of petrodiesel to meet
federal low-sulk
regulations. Emissions data from various sources are presented in
Table 2.7.
In summary, it appears that biodiesel offers several advantages over 0th~
alternative fuels. While biodiesel emissions profile is radically lower than traditional
fuels. biodiesel functions in the engine the same way as petroleum diesel, and
38
Table 2.7. J3dmst Emissions of Biodiesel Compared to Conventional Diesel.
Reference’
Sulfix Carbon
dioxide monoxide
ZIlItlOSt
za-0
F.O.P.
U
Koch
90%
lower
Wade
90%
lower
Polvcvclic
- EUOITUliC
Nitrous Particulate
oxides matter
Smoke
>lO%
lower
50%
lower
hydrocabon
60% loxr
>lO%
lower
Long
Pachter
Unburned
hydrocarbon
lower or
higher
50% lower
slightl>
higher
65%
lower
12% lower
16%
lower
10%
lower
lower
lower
40% lower
higher
57%
lower
lower
lower
lo-12%
lower
“Esters from Vegetable Oil as Diesel Fuels.” Fedemrion Fmpse des Productem d’Ol&peu (TOP).
AFPPAGPO. 12 Avenue George V. 75008 Paris.
Koch D. Personal Gnnnumi cation, Novamont. Milan Italy, 1992
Long. E. “Spring Rape Rise.” Farmem WeeI+. March 1992
Pachter. H and G. Hohl. “Rapeseed Oil Methyl Ester (RME) as an Alternative Diesel Fuel: &et Trials
in the Austrian Army.” AVL Conference. Engine Environment (1991):279-292.
Wade. R and R Irving. “Biodiesel - Technical Note.”
MAFF. unpublished.
39
does not require new refkeling
modifications.
stations, new parts inventories, or expensive en&&e
While it may seem hard to believe that diesel engines can mn on modified
vegetable oil, it is worthwhile to note that & Diesel, inventor of the diesel engine was
using 100 percent vegetable oil in diesel engines long before a petroleum-based diesel fuel
was ever re6ned (NSDB).
As we move into the 21st century, today’s knowledge and technological skills
mean biodiesel may be the least cost alternative fuel option for meeting stringent clean
air guidelines. The switch to biodiesel makes for cleaner emissions without having to
commit huge sums to convert fleets. However, this assertion remains to be determined
in terms of overall operating costs which is the purpose of the present study. The next
chapter reviews relevant literature related to equipment replacementirepair
subsequent operating cost estimation.
and their
Notes
I. There is an inverse correlation between emissions of NOX and PM As an engine is
optimized to reduce Nchc exnissions, each unit of NOX reduction will routinely result in
a co~esponding increase of PM Similarly, a reduction in PMwill result in increased
NOX emissions. Altho~~& this correlation holds true for biodiesel as well, the severity
of the trade-off is not as significant as it is in petrodiesel (Marshall).
CHAPTER III
LITERATURE REVIEW
Replacement theory analyzes the optimal life of capital equipment. Optimal life
may be defined as the period between the time the equipment enters service and the time
when it should be replaced for economic reasons. Optimal life and replacement policy
are important topics in the management of capital equipment and have been extensively
studied.
Economic reasons leading to equipment replacement are based upon operating
costs. Generally, the operating cost of a piece of capital equipment rises as its condition
deteriorates over time. When the cost reaches a certain level, the long-run cost associated
with investing in a new piece of equipment becomes less than that of keeping the old
equipment. At that point, replacement is called for. Thus. a basic replacement analysis
usually consists of studies of both the trend in operating cost and the net cost of
replacement, defined as the difference between the cost of the new equipment and the
salvage value.
The underlying methodology for analyzing the repair-replacement problem is
based on the asset replacement theory first developed by Faustmann and subsequently
refined by Samuelson and others.
This methodology has previously been applied in
agriculture to problems including determining the optimal replacement of farm machinery
assets and culling replacement decisions in livestock management.
Applications and
extensions of net present value analysis have also been made in deterrking bus engise
replacement.
41
42
A General Model of Replacement Principles
Research on the optimal replacement problem has emphasized specification of
the theoretically appropriate criterion. The fundamental principles of asset replacement
decisions as presented by Hirschleifer, Samuelson, Perrin, Burt, and Jorgenson. are
grounded on the broad notion that assets are retained in the production until the net
present value of future income streams associated with that asset and sequence of
replacement assets is maximized.
A decision policy is a sequence of replacement
decisions, and an optimal policy denotes a decision policy which maximizes net present
value of future income streams from a replacement sequence (McClelland et al.).
The principles of optimal asset replacement are stated by Perrin (1972): “A
machine should be kept another period if the marginal costs of retaining for another
period are less than the average costs of a replacement machine.” Assume initially there
is no defender’ in use and the challenger’, if acquired. will be replaced by a series of
identical
challengers
(self-replacement).
The present value of the stream of returns
associated with the first asset alone is
C(bJ,l) = jJ!(t)e -pW& + M(s)e -p(s-b) - M(b)
(3-U
b
where C(b,s,m) is the present value of the stream of residual earnings from a challenger
to be purchased at age b and replaced at age s by a series of m identical challengers. and
M(s), M(b) and R(s) represent respectively the market (or salvage) value of the asset at
age s. acquisition value, and the flow residual earnings from the process when the asset
age is s; p=lnfl fry is the interest rate which, when compounded continuously, results in
an annual growth rate of r. i.e, fl=e@=(l+r)‘,and t an integer of number of years.
’ The term defender is used for an asset already in use.
’ The term challenger is used for an asset which can be purchased to replace a
defender.
Taking
I
43
the first derivative of C(b,s,I) with respect to replacement age s and setting it equal to
zero, the replacement age which maximizes the present net value of the returns for this
first asset is obtained as
(3.2)
R(s) + M’(s) = pM(s).
The value-maximizing replacement age s is the age at which marginal revenue (residual
earnings plus changes in asset value) equals marginal opportunity costs.
Figure 1
illustrates a possible path of R(s)+M’(s) through time and the replacement which satisfies
equation (3.2). For the case of a series of identical cycles of an asset the replacement
problem is to find the date (s) which maximizes the value of the entire income stream.
Then the present value of the entire stream is
W&-J)
= C(Os,l) + e -p”C(Os,l) + e -pzrC(O~,l) + . . . .
(3.3)
This series reduces to
wJ,ml = ~C(Os,l).
(3.4)
1 -e -Ps
The first order condition for maximizing (3.4) with respect to replacement age s is
WJJ)
R(s)
+
M’(s)
=
p
M(s)
+
1
!
-e
-Ps
I
(3.5)
The difference between (3.5) and (3.2) reflects the opportunity cost of postponing the
earnings which will be realized from the next and subsequent assets. The alternative on
the right-hand side of (3.5) indicates that to maximize present value, the asset should be
replaced when the net flow of benefits equals the flow which could be realized by
immediate
replacement.
Substituting from (3.1) and collecting terms, a principlmf
I
replacement can be derived as:
44
/time
p V(s)
1 -p
PM(S)
0
Replacement Age
Figure 1. The Self-Replacement Solution
sz
%
45
s
R(s) +
M’(s) =
--P/
(X6.1)
R(t)e -P’dt + M(s) - M(0)
1 -e -ps I a
I
R(s) + M’(s) = -P- V(s)
1 -e -Ps
(3.62)
where V(s) represents the second term on the right-hand side of (3.6.1). V(s) can be
interpreted as the present value of an upcoming replacement; the amount V(s) is received
as a perpetual annuity every s years. The replacement principle in (3.6.2) specifies the
asset be held to the age in which marginal revenue equals marginal opportunity costs, with
the latter being interpreted as the flow of earnings which would be realized from an s-year
replacement policy. This criterion is shown on Figure 1 to yield an optimum replacement
age s:. Thus, considering the solution of earnings from the second and subsequent assets
leads to an earlier replacement age than the one-cycle solution s,.
The replacement of durable equipment such as a bus is a special case of the
replacement theory developed above. In considering such an asset, current costs can be
defined to include any deterioration in the flow of services with age. Assuming the flow
of services is by definition constant, the total value of the services rendered by the
machine is irrelevant to the replacement problem.
Maximizing the present value of
residual earnings is then equivalent to minimizing the present value of the costs of the
machine. Figure 2 illustrates a typical path of repair, depreciation. and deterioration
(-Rhj-M’(l)) as a machine ages. along with a curve defining the appropriate opportunity
costs against which these costs must be compared. Figure 2 is just merely Figure 1
reversed given costs are negative returns. The identical-challenger model presented abave
is theoretically valid and, given relatively accurate empirical estimates of its parameters,
it can be used to make replacement decisions. However, this implies realistically
46
Cost in $ per
time period
0
Age of Machine, s
Figure 2. The Seif-Replacement Solution for a Machine
47
estimating the cost of machine maintenance and repairs over time, and accurately
estimating the salvage value and determining opportunity costs of untimely breakdowns.
Operating Cost Estimation Models and Replacement Analysis
The problem of replacing equipment can encompass anything from vehicles to
farm machinery. The characteristic pattern of expense for a machine consists of a large
initial purchase price that is followed by low maintenance costs which gradually grow
with increasing use of the machine until further repair becomes uneconomic. As
machinery grows older, the increasing costs of operation and maintenance are
accompanied by a fall in its productivity. The maximum physical life of a capital good
ends when its repair is physically impossible. Similarly, the maximum economic life of
a bus may be defined as ending when its marginal repair costs will exceed its marginal
replacement cost. The problem, however, is finding the optimum economic life of the
equipment.
The unit operating cost,of a capital equipment can be modeled in a number of
ways. It can be specified as a function of age. as a function of cumulative usage such as
mileage. or as a function of age. cumulative usage and mechanical condition.
The
underlying methodology of these different techniques is grounded upon cost minimization
principles.
Replacement Cost Minimization Principles
A general theory of a machine replacement cost minimization principles is
provided by Bertsekm (1976). Assume a certain component of a machine is in any one
of a continuum of states. represented by the interval [0, I]. At the beginning of ea2h
period
the
component
is
inspected.
its
current
state
x
E
[O,
determined, and a decision made whether or not to replace it at a cost R > 0 by a new one
I]
48
at state x = 0. The expected cost of having the component at state x for a single period
is C(x), where
C( . ) is a nonnegative bounded increasing function of x on [0, 11. The conditional
cumulative probability distribution F(z 1 x) of the component being at a state less than or
equal to z at the end of the period given that it was at state x at the beginning of the
period is known. In addition, for each y E [0, I], the following inequality holds
This inequality assumption implies that the machine tends to turn worse gradually with
usage, i.e, for each YE [0, l] there is a greater chance that the component will go to a final
state in the interval [y, l] when at a worse initial state.
Assuming a discount factor fl E (0. 1) and infinite horizon, the problem is
determining the optimal replacement policy which minimizes the total expected valuediscounted replacement cost. The optimal value function J* is the unique solution of the
functional
equation
J’ = mi.n R+C(O)+PjJ*(z)d(:,O),
0
I
1
C(x)+/3sJ’(z)dF(z~x) .
0
J
(3.8)
Thus. an optimal replacement policy is given by:
Replace if
R + C(0) + P jJ*(z)d(r ,O) I C(x) + pjj*dF(z/x).
0
0
Do not replace otherwise.
Assuming J,(x) = 0,
and
(3.9)
49
(3.10)
1
TqJ(x)
= nlin[R + C(0) + p~Tk-‘(JJ(z)dF(z
IO),
0
(3.11)
C(x) + p/TyJJ(z)dF(z lx)], k=1,2,...
0
Since C(x) is increasing in x, T(Ja)(x) is nondecreasing in x. It follows that r’(JJ(x) is
nondecreasing in x and so is the limit of
J’ = lim T’(J&x).
k-m
(3.12)
CC@ + P/-J * (z)Wz 1x1
(3.13)
It follows that
0
is also nondecreasing in x, and the optimal cost cannot decrease as the initial state
increases. Thus, an optimal policy takes the form
Replace
if x 2 x*
Do not replace
if x < x* where x* is the smallest scalar for
which
R + C(0) + p)j(z)dflz ,O) = C(x
0
l
) + $J*(z)dF(z,x *).
(3.14)
0
There are many possible ways to classify the works in maintainability. One
could establish a multidimensional grid whose coordinates would be (i) states of the
1
system. such as deterioration level, age, or number of state variables etc.. (ii) actions
available as repair, replacement, or opportunistic replacement, (iii) the time horizon
50
involved, such as finite or infinite and discrete or continuous, (iv) knowledge of the
system, such as complete knowledge or partial knowledge involving such things as noisy
observation of the states, unknown cost, or unknown failure distribution, (v) stochastic or
deterministic models, (vi) objectives of the system, such as minimize long-run expected
average costs per-unit time, or minimize total costs, and (vii) methods of solution, such
as linear programming, dynamic programming, etc.
Although this classification is useful for establishing an underlying general
theory on maintainability, the current survey specifically deals with models relevant to
operating
estimation
models. Thus, there are four major sections. The first section
surveys age-dependent cost models. The second presents an operating cost as a function
of cumulative usage model, and the third section provides a model of operating cost as
a function of both cumulative usage and mechanical condition. Finally, the last section
presents an economic replacement model based upon the theory of repair limit.
Operating Cost as a Function of Age
Terborgh
(1949) was the first to develop a theory for equipment replacement
based on explicitly expressed assumptions of a linear operating cost function that is timedependent with known parameters. He developed procedures for comparing current
equipments with challengers and descendants by extrapolating the historical rate of
obsolescence into the future on the principle of a uniform rate of technology innovation.
The combined cost per year E is a sum of two terms: the first increases with
equipment age (operating inferiority) and the second decreases with increasing age (capital
cost).
E = cn-‘k +
A-S
- + I(A+S)
n
2
(3.15)
J
,
where. c is the inferiority gradient. or the constant rate of cost accumulation due to
2
!
operating inferiority; A is the acquisition cost: S represents the salvage value; r is the rate
51
of return on capital investment within the firm; and n is the age of the equipment.
The
first term is the average operating cost increase per year. and the second term is the
average capital cost per year.
The adverse -urn, n,, is the age that minimizes E, and thus
264 -3
no =
(3.16)
c
or
nOc
-
2
-
A-S
(3.17)
nO
Therefore. the average increase in costs due to operating inferiority is equal to the average
annual depreciation in capital at the optimum. Terborgh neglected the salvage value S
and assumed that future challengers will have the same adverse minimum as the present
one.
Makomson (1979) criticizing Terborgh pioneer work stated that the ruie oniy
applies under certain conditions, and even under those conditions it is an approximate rule
and the magnitude of the error of approximation is not clear. Moreover, the rule requires
that the optimal replacement age of equipment is constant through time and hence it is not
directly generalizabie to situations in which this is not the case.
For specific assumptions about future costs an iterative process was developed
by Maicomson for determining optimal replacement ages to any desired accuracy whether
or not the optimal replacement age is constant through time. This technique makes use
of the first-order necessary conditions for an optimal solution and uses them for
expressing the optimal age at which to scrap currently installed equipment in terms of the
operating cost function. the capital cost of new equipment. and the optimal replacement
,
age of that new equipment.
Following Terborgh. Maicomson assumed the operating cost at time t of
52
producing a unit of output on a given equipment installed at time v is given by E, - at
+ pft - v), where E, cr. and /3 are positive constants, and that the capital cost per unit of
output on new equipment remains constant through time at a value q. It is also assumed
that operating costs on a given piece of equipment increase at a constant exponential rate
through time, that new equipment becomes more productive at a constant rate. and that
equipment has no scrap value and that its utilization rate remains constant throughout its
life. Note that these assumptions can be relaxed without great difficulty. Under these
assumptions, Malcomson demonstrated that the optimal policy is to replace at time t all
equipment of age T(t) or greater where
T(t> = -L
i (a + P)
(3.18)
in which r is the discount rate and L(t) is the optimal age at which to replace new
equipment installed at time t. Inverting equation (3.18) gives
L(t) = -iloge 1 - rT(t) + AZr
(a + PI
i
(3.19)
which may be abbreviated as
L(t) = -%og,F(T(r))
r
(3.20)
where F(T(t)) is implicitly defined. For any given value of T(t), this can be used to
calculate L(t) and this value of L(t) can be inserted into the right-hand side of equation
(3.20) to calculate LCt+L(t)), and so on. For any such path to be considered as optimal
path F( I must lie between zero and one.
I
This iterative procedure is not limited to the specific assumptions about costs
used in deriving it; it can readily be adapted to others. Moreover, this analytic framework
53
can also be used to derive the correct economic depreciation to apply to a piece of
equipment when the optimal replacement policy is used.
Operating Cost as a Function of Cumulative Usage
Rust (1987) formulated a regenerative optimal stopping model of bus engine
replacement to test the hypothesis that a bus company manager decisions on bus engine
replacement coincide with an optimal stopping rule, i. e, a strategy which specifies whether
or not to replace the current engine each period as a function of observed and unobserved
state variables. The model depends on unknown “primitive parameters” which specify the
manager’s expectations of the future values of the state variables, the expected costs of
regular maintenance, and his perceptions of the customer goodwill costs of unexpected
failures.
The model illustrates an estimation technique. a nested fixed point maximum
likelihood algorithm, that allows to compute maximum likelihood estimates of the
primitive parameters even though there is no analytic formula for the associated likelihood
function. This maximum likelihood estimation algorithm for a class of dynamic discrete
choice models treats unobservable E, in an internally consistent fashion by explicitly
incorporating them into the formulation and solution of the model. It mainly consists of
deriving a regenerative stochastic process (i, x,> with an associated likelihood function
/ci,, ...I i, x,,..., x7.,4) where i, = I if replacement occurs at time t and i, = 0 otherwise and
xt is the state variable, and 0 is parameters of a specified cost function.
Operating Cost as a Function of Cumulative Usage and Mechanical Condition
Ahmed (1973) stated that the main economic factors affecting the decision to
replace a given vehicle are age. mileage. and mechanical condition which constitute the
components of a state vector of a system. However. because the mechanical condition
is generally reflected in the trade-in value of a vehicle. the age and mileage factors are
54
considered to be of primary importance in determining replacement policies. Thus. he
developed a model based on a physical life of a vehicle represented by age and mileage.
The system is divided into states, each state representing the age and mileage travelled
during a given fixed period (six months in this case).
At any moment of time the vehicle may exist in any of the defined states, and
the system is allowed to make transitions from one state to another. The movement from
state to state is associated with a transition probability, P, which may be termed a
survival probability for a vehicle that is in a given state of the system.
The planner makes a decision at each planning stage of the system. It is in his
best interest to choose the policy, among all possible policies, that will minimize the
expected operating cost. The basic equations governing the system are:
qi = -Ei
qi =
T~-C~-E~
(3.21)
(3.22)
where. q, is the immediate expected operating cost for a vehicle in a state i for the fixed
period: E, is the immediate operating cost for a vehicle in state i for the fixed period; 7,
represents the trade-in value of the vehicle in state i: C, is the purchase price of the
vehicle in state j for the fixed period: j represents the possible alternatives.
Equation (3.21) refers to the policy of keeping the same vehicle in operation
until the next planning stage. If the decision is to keep the same vehicle, the decision
variable is only its operating cost. However. if the policy is to trade with a vehicle in any
of the other possible states. then. equation (3.22) is applicable, where the variables are the
trade-in value of the vehicle in that state. purchase price of the vehicle being acquired and
its operating cost for the fixed period
1
The policy iteration starts with the selection of an initial policy, which computes
the test quantities 4, for all alternatives in each state of the system. Then the program
would select the largest test quantity and the corresponding policy for each state of the
system.
This process will generate the initial policy vector which can be used
conveniently to generate successive new values and the policies of the system. The
optimal policy is independent of the starting policy.
Other Economic Replacement Model
Another economic replacement is based on the theory of repair limit. The
repair limit is a ceiling on the amount of money which can be spent on the repair of a
vehicle at any particular job (Drinkwater and Hastings, 1967). The values of the repair
limits are dependent on the type, age and in some cases on the location of vehicle. A
vehicle which needs repair work in excess of the appropriate repair limit is not repaired
but is scrapped, and thus the repair limit provides an economic replacement policy which
ensures that vehicles are continuously wasted out of service.
Drinkwater and Hastings developed a method for determining the upper limit
for any repair cost on a machine in a fleet of similar equipment. The limit decreases with
the age of the machine. The model consists of two random variables, the cost of any
future repair and the number of repairs in the future period of use.
Consider a fleet of vehicles which is subject to a replacement policy of some
type. for example, replacement of vehicles at a predetermined age or replacement by an
arbitrary chosen set of repairs limits. Assume this initial replacement system give rise to
an overall average cost per vehicle-year denoted 19~. Consider a vehicle at age I which
requires repair.
If the vehicle is repaired. the future cost per vehicle-year will be:
3 The average cost per vehicle year up to age t is given by
6 = y/t, where y is the cumulative cost of the vehicle when the
age is t.
56
(3.23)
where, r is the cost of this repair, m(r) is the expected total cost of future repair; and g(r)
is the expected remaining life of the vehicle.
If the vehicle is scrapped, the expected future cost per vehicle-year will 8.
Ignoring resale value, the vehicle should be repaired provided .$ < 8. Otherwise the
decision should go in favor of scrapping the vehicle. The critical or limiting value of r
occurs when
where r,(l) represents the repair limit at time t. Hence the repair limit r,,(t) is given by
r,(t) = Oxg(t) -m(t)
(3.25)
Subsequent work by Hastings (1969) applied dynamic programming to the
model to improve the method for determining the repair limits. Although this method
detects a machine having a very high cost for an individual repair. it does not necessarily
detect a machine having consistently more frequent or higher repair costs than the average
machine of its class.
Lambe (1974) established a repair limit formula using data on past repairs for
the machine under study, and all available knowledge on the general repair characteristic
of its class of machine. The random nature of the costs and the intervals between these
costs present difficulties in deciding whether to repair or replace a machine when a
component fails. The problem is greatest with equipment having infrequent. but costly
repairs. The basic rule for deciding when to replace a machine is to continue using it
until the cost for a prospective repair exceeds the expected net benefits from future tie
of the machine if it were repaired. Thus, the limit to the amount to be spent for a repair
is equal to the implicit value of the vehicle after repair, less the value of salvage if it is
57
not repaired.
Assume the average cost per mile, L, for purchase and repair of a series of
machines is a constant that equals the current rate of depreciation in the value of any
specific machine, plus its expected cost of repair or loss due to scrapping during the
interval AA (A is the age of the machine). Because the repair Emit W equals the implicit
value V less a constant value for salvage. it also decreases at the same rate and is given
by
Fff = (l/y)
1 +Wexp(F(A) -yLA] J exp(-F(x) +yLr)dx
(3.26)
r=A
where, y is the characteristic of the repair cost for any particular machine. and equals to
the reciprocal of the expected cost of a repair if y is known precisely; and F(A) represents
the
number of expected repairs for a machine at age A.
In the special case where the expected frequency of repair is proportional to
age, fL4] = A.4. and the repair limit formula becomes
W = (l/y)
1 + 3[exph(A -y~L/h)~/2]
1
exp( -x 2/2)~
0
x=&4-y41)
(3.27)
The final step in using this model is to determine the repair characteristics y and
X for any particular machine. &ryes’ formuia provides the mathematical method for
making the necessary adjustments. For example, the algebraic structure of Baves’ formula
is simplified if a gamma function is used to describe a person’s uncertainty about the cost
characteristic y and a repair frequency X. This is a flexible class of functions that can
have any positive average value and variance. and therefore should be adequate for
capturing the essential form of a person’s uncertainty.
/
In summary, maintenance involves planned and unplanned actions carried out
to retain a system in or to restore it to an acceptable condition. Optimal maintenance
58
policies aim to minimize downtime while providing for the most effective use of systems
in order to secure the desired results at the lowest possible costs. Works on operating cost
estimation and replacement analysis have focused on the age, cumulative usage, and
mechanical conditions. Given that mechanical condition is generally embodied in the
trade-in value of a vehicle and critically depends on its cumulative usage. the key factor
for operating cost estimation model specification would be cumulative usage. Thus,
Rust‘s model will be of primary importance for developing an optimal control model for
determining the net present value of total operating costs of the alternative fuels under
consideration.
CHAF’TER IV
THEORETICAL FRAMEWORK
The models in the previous chapter provide a theoretical underpinning for
developing a dynamic model for estimating total operating costs. The specific model will
be based on Rust’s optimal replacement approach. His model will be extended to include
more than two replacements. The purpose of this chapter will be to develop a conceptual
framework and apply the model for estimating operating costs of a transit bus fleet on
dual compressed natural gas/diesel (CNG/Diesel), methanol, biodiesel, and diesel fuels.
An Optimal Replacement Model for Bus Engine
The optimal timing for bus engine repairs, rebuilding, or replacement will be
determined for each alternative fuel technology given a particular policy using dynamic
control theory.
Determining
optimal
repair/rebuild/replacement
strategies
for
each
alternative fuel provides a common basis for computing comparable net present values.
The decision to adopt a particular fuel will be based on the economic performance of a
sequence of assets utilizing either CNG,
methanol, diesel, or biodiesel fuel. Economic
performance is measured by the net present value of total operating costs of the sequence
of assets. As the equipment-replacement problem incorporates that of timing, operating
costs can be expressed as functions of age or cumulative usage. Typical costs rise with
usage.
Thus. operating cost can serve as a measure of economic performance 2f
equipment.
59
60
The bus engine replacement problem is to determine how long one should
continue to operate and maintain a bus before it is optimal to “discard” the engine and
replace it with either a new or rebuilt engine.
The idea is that a bus engine can be
regarded as a portfolio of individual components each of which has its own stochastic
failure as a function of accumulated use (Rust, 1987). If a particular component fails
when a bus has relatively low mileage, then it may be optimal to just replace or repair
this failed component. In contrast. for a bus with relatively high mileage. the optimal
solution may be to replace the entire engine. Specifically, the distribution of time failure
exhibits wearout as the failure rate increases with age. Given an objective of minimizing
unexpected failures. if a particular component fails when a bus has relatively high mileage
the probability of other parts failing increases. so it might be optimal to replace the entire
engine.
Bus failures on the road are expensive both in terms of explicit costs such as
towing costs and opportunity costs including lost bus driver and passenger time.
Thus.
a rebuild after failure costs more than a rebuild before failure. An unplanned rebuild or
repair occurs suddenly possibly resulting in long periods waiting for service.
Whereas,
by definition a planned rebuild or repair reduces this waiting time. Also, the value per
unit time of the output (service) foregone during an unscheduled action often exceeds the
same measure for a scheduled action. As a consequence an in-service failure should be
more costly than a planned rebuild. Thus. a policy of preventive periodical repair or
rebuilding is cost effective, and the optimal preventive maintenance will primarily depend
upon the tradeoff between the value of unused life and the cost of failure. Assuming that
such a preventive replacement strategy is optimal. a model that determines the time and
mileage at which engine rebuilding occurs is required.
Ideally, the model would consist of determining an optimal stopping strategy
which is the solution to a stochastic dynamic programming problem. Such a model woufp
formalize the trade-off between minimizing maintenance costs versus minimizing
unexpected engine failures. The optimal strategy would specify whether or not to rebuild
61
a current engine each time period as a function of observed and unobserved state
variables.
A nested fixed point algorithm developed by Rust (1987). may for such a
stochastic process {i, x,> with an associated likelihood function
L(i,, . . . . i, x1 ,..., x7;
e),
where i, = I if replacement occurs at time
t
and i, = 0 otherwise, x, is the state variable
which explains the time series data collected on a fleet of buses, and 8 is a parameter to
be estimated,
t
= I,.., T. This nested fixed point algorithm is a maximum likelihood
estimation algorithm that computes maximum likelihood estimates of structural parameters
of a wide class of discrete control processes. These stochastic processes are solutions to
infinite horizon Markovian decision problems with discrete choice or control variables.
The stochastic control problem is solved numerically by computing the associated
functional fixed point as a subroutine or nested within a standard nonlinear maximum
likelihood
optimization
algorithm.
Let the state variable be the accumulated mileage (since last replacement) on
the bus engine at time
t,
the expected per period operating costs C(x, 03 can be
decomposed as follows:
where m(x, e,,) is the conditional expectation of normal maintenance and operating
expenses, pfx, I~,J is the conditional probability of an unexpected engine failure, and
b(x, f3,J is the conditional expectation of towing costs, repair costs, and the perceived
dollar cost of lost transit company goodwill in the event of an unexpected engine failure.
Given actual maintenance and operating cost data. m may be estimated by nonlinear
regression. Note that operating costs include maintenance, fuel, insurance costs (which
are potentially observable), plus an estimate of the costs of ridership and goodwill due t,o
unexpected breakdowns. The latter costs are generally not directly observable due to the
62
lack of appropriate data especially on the occurrence of unexpected breakdowns, but can
be estimated from the total cost C(x, t?J and the maintenance cost m(x, 0,J.
Consider the mileage traveled each month by a given bus is exponentially
distributed with parameter e2, independently of mileage driven in previous periods. Each
month the discrete decision is to perform regular maintenance on the current bus engine
and incur operating costs Cfx,, 03 or “cannibalize” the old bus engine for scrap value p,
install a new (or rebuilt) bus engine at cost p, and incur operating costs C(0, 0,).
Assuming an optimal replacement policy to minimize the expected discounted costs of
maintaining the fleet of buses, it follows that the stochastic process governing {i, x,} is
the solution to a “regenerative optimal stopping problem:”
(4.2)
r/e('1>
= "P ' C ly-r '('Jo,',)
x
1 j=r
(x,
i
where p is the discount factor and the utility function u is given by
where
~(x$,,~J =
-dx,k$>
-[F-E+c(O,B,)]
if i, = 0,
if i, = 1.
(4.3)
with 7r an infinite sequence of decision rules x = @, A+,, . ...’ and each Jr; specifies
replacement decision at time t as a function of the entire record of the process,
i, = Ah, i,-,, x,-,, i,-,, x ,-2, . ..). The utility function u depends on an unknown parameter
vector 8,. The behavioral hypothesis is that the agent chooses a decision rule
i, = f(x, e,, 0) to maximize his expected discounted utility over an infinite horizon where
the discount factor fi is a real number between 0 and 1. The utility function reveals why
the model is called a regenerative optimal stopping model of engine replacement: once
the bus is replaced the system “regenerates” to state x, = 0.
This
regenerative
characteristic is conventionally specified by the stochastic mechanism governing t&
,
evolution of { x, > given by the transition probability p(x!+, 1 x, i, 0,).
63
The function V&J is the value function which equals the maximum expected
discounted utility obtainable by the agent when the state variable is (x, E) i.e, the unique
solution to Bellman’s equation given by
(4.4)
where C(xJ = {O, 1,’ and the expected value function EV,(x, is is defined by
(4.5)
Using Bellman’s equation and following Rust (1986) the Markovian optimal
stationary replacement policy rc is given by
4 = -fbe) =
1
1 if
0
xt’Y(epeJ’
i f X, 5 y(e,,e,).
(4.6)
where the constant y represents a threshold value of mileage such that whenever current
mileage on the bus x, exceeds *J it is optimal to replace the old bus engine with a new
one. Using the regenerative property and assuming that monthly mileage and replacement
decisions are independently distributed across buses. the precise functional form of the
likelihood function L(8) for the full sample of data may be derived. However, there are
some reservations about using this model because the solution for the likelihood function
depends critically on exact choice of functional form. Furthermore, the basic formulation
of the model which assumes that the physical state of a bus is completely described by
a single variable, accumulated mileage x, is limiting. In addition, if looking at the data
the variation of mileage at replacement is large the fixed optimal stopping rule might be
inconsistent. It might be assumed that the odometer value x, might be only one indicagr
and that the replacement decisions are based upon other information E,.
,
64
To circumvent these limitations the maximum likelihood estimation technique
for a class of dynamic discrete choice models can be used. This technique does not
require closed-form solutions for the agent’s stochastic control problem and associated
likelihood
function.
It treats unobservable e, in an internally compatible fashion by
explicitly affiliating them into the frame and solution of the model will be used.
Provided the stochastic change of the state variables (x, E,) represented by the
transition probability p, the agent must choose a sequence of decision rules or controls
A@, E, 0) to maximize expected discounted utility over an infinite horizon. Define the
value function VB by
where r = &, A+,, J;+?, . ..I. J; E C(xJ for all t and the expectation is taken with respect to
the controlled stochastic process (x, e,> whose probability density is defined from x and
the transition probability p by
dP { Xl+I’Et+l’
N-l
(4.8)
The optimal value function V8 is the unique solution to Bellman’s equation
given by
(4.9)
where
(4.W
and the optimal control f is defined by
(4.11)
Econometric implementation of the model i ,= fcx, E, 8) may be difficult
because (i) commonly chosen distributions for the unobservable E, will be continuously
distributed with unbounded support, raising dimensionality problems since the optimal
stationary policy f will be computed by solving for the fixed point Ye from the Bellman’s
equation; (ii) since E, appears nonlinearly in the unknown function EV,,
there is an
additional problem of integrating out over the E, distribution to obtain choice probabilities.
However, the conditional independence assumption (Cr> developed by Rust (1987)
facilitates
in
circumventing
these
problems.
The (Cr> assumption involves two
restrictions; (i) T+~ is a sufficient statistic for Et+,, which implies that any statistical
dependence between E, and E,,, is carried entirely through the vector x,,, ; (ii) the
probability density relies only on x, and not on E,. The consequence of the assumption
is twofold. First, (Cr) implies that EP’, is not a function of E, so that the required choice
probabilities will not require integration over the unknown function EV,. Second, (KY)
avoids the numerical integration required to obtain EVO from V,.
Given time series observations {(i, xd, (i,, x J, . . . , (i7, XT)} for a single
individual the likelihood function f(i,, x,, . . . . i,, x7 1 i, xti 0) can be formed and the
unknown parameters 19 can be estimated by the method of maximum likelihood. Rust
indicates that under assumption (Cr> the likelihood function // is given by
where P(i 1 x, 0) denotes the conditional probability of choosing action i E C(x) given
state x. It can be established that as the number of individuals in the cross-section tends
to infinity, the corresponding sequence of maximum likelihood estimators are consistent
and asymptotically normally distributed. The worth of this approach is that it releases the
66
researcher from using restrictive and contrived functional forms just because they yield
closed-form solutions. However, the weakness is the computational hardship of numerical
solution of the contraction fixed point EVe needed to solve the stochastic control problem.
The conditional independence assumption and the relationship (4.12) suggest the
following nested fixed point algorithm: an “internal” fixed point algorithm computes the
unknown function EV, for each of value of 8. and an “external” hill climbing algorithm
searches for the value of 8 which maximizes the likelihood function.
The Newton-
Kantorovich algorithm can be used to compute EV,, and as a by-product, yields analytic
solutions for the 8 derivatives of EV, necessary to compute the derivatives of the
likelihood
function.
Application of the Nested Fired Point Algorithm to Bus Engine Replacement
The regenerative optimal stopping model presented above is used, eliminating
restrictive assumptions about functional form and incorporating unobserved state variables.
The choice set is binary, CcxJ = {O, I] and unobserved state variables are incorporated
by assuming unobserved costs {e(O),
e,(I)) follow a specific stochastic process. Let Y
denote the expected cost of a rebuild bus engine, r = p - e and C(x, OJ the expected per
period operating costs. the implied utility function is as follows:
u(x,,i,8,) + El(i) =
1
-r - c(O,t3,) + E&l)
-c(x,,Q + E,(O)
if i = 1,
if i = 0.
(4.13)
Letting monthly mileage (x,,, - XJ have a subjective parametric density function
g implies a transition density of the form
67
P(X,+, I xpip 0,) =
g(x,+l -x,9 0,)
g(x
r+l-O9Q
if i, = 0,
if i, = 1.
(4.14)
Suppose that the data consist of {i,“‘, x,“‘> (t = I ,..., T,,,; m = I ,... M) where i,“, is the
engine replacement decision in month f for bus m and x , “ ’ is the mileage since the last
replacement of bus m in month t. The approach is to estimate the unknown parameters
f3 = (0, 01, r, OJ by maximum likelihood using the nested fixed point algorithm. Thus.
the state variable x, (mileage) should be discretized into a certain number of intervals say
n of a specified length which implies that the fixed point EV, will be an element of the
Banach space B = R”.
Using the discretized mileage data, the distribution g reduces to a multinomial
distribution in the set corresponding to the monthly mileage in the concurrent intervals.
For simplicity and based upon arguments developed by Rust, a linear functional form for
C is specified. The specification does not include a constant term because subtracting a
constant term from the utility function (4.13) will not affect the choice probabilities. The
most that can be identified is the value of change in operating costs as a function of
mileage, so C can be normalized by setting C(0, 0,) = 0. It is hypothesized that the
unobservable state variables {E,(O), e,(I)) obey an independently and identically
distributed bivariate process: with normalized mean and variance because neither the
location nor the scale of these observed costs are identifiable without further information.
Notice that E,(O) should be interpreted as an unobserved component of maintenance and
operating costs for the bus in period t and e,(I) can be interpreted as an unobserved
component of cost associated with rebuilding the bus engine.
Also, it is implicitly
assumed that the stochastic process (x:, E/} is independently distributed across buses.
The estimation procedure consists of the three stages corresponding to each,of
the likelihood functions I’, 1’ and /‘, where I/ is the full likelihood
68
and 1’ and l’ are partial likelihood functions
(4.16)
12(x, ,....) i,, . . . . . i, 1e) =fi fyi, Ix,,e),
t=1
(4.17)
The first stage is to estimate the parameters 8, of the transition probability
P(x,+~
1 x, i, 03 using the likelihood function I’. In stage 2 the remaining structural
parameters (0, 13,, r) are calculated using t and the estimates of 19~ as initial starting
values. The final stage 3 estimation will use the initial consistent estimate of 8 computed
in stage 1 and 2 to produce efficient maximum estimates of 0 using z Notice that the
estimation results for fl = 0 can be interpreted as a “myopic model” of bus engine
replacement under which a replacement occurs only when current operating costs
Cfx, S,) exceed the current cost of replacement r -+ C(U, 0,). On the other hand, the
estimation results for /3 greater than 0 can be interpreted as a “dynamic model” of bus
replacement which recognizes that replacing a bus engine is an investment which not only
reduces costs, but future costs as well. Abel’s Theorem also known as the final value of
Z-transforms suggests that if minimizing long run average costs, @ can be driven to 1.
The structural parameters of the cost function are used along with observed engine rebuild
cost to identify the scale of the unobserved {e,(0), e,(1) } .
CHAPTER V
SOURCE, ASSUMPTIONS, DATA TRANSFORMATION,
AND PRELIMINARY ANALYSIS
In this chapter, data source, data transformation, and preliminary analysis will
be discussed. First, the data source is described; then a discussion is presented about how
key variables in the model are transformed. Finally. a preliminary analysis of actual
operating cost is provided.
Data Source
Data
on
refueling
infrastructure, fuel system. engine performance, fuel
efficiency, monthly mileage, and rebuild were collected from an experiment involving
diesel. methanol, and dual CNG by the Colorado Institute for Fuels and High Altitude
Engine Research (CIFER).
As part of its commitment to Clean Air, the Regional
Transportation District (RTD) is conducting an alternative fuels research program using
neat methanol as fuel for operating regular transit buses.
For the purpose of the test
program. five methanol buses were purchased from Transportation Manufacturing
Corporation (‘TMC) and were put in revenue service in June 1989. Five diesel buses were
also converted into dual compressed natural gas/diesel (CNG/Diesel) buses and put into
service in 199 1.
For comparison, five diesel buses were selected as control buses. Since RTJD
does not operate any TMC diesel buses. the 1987 Model AN440 Neoplan diesel buses
69
70
were selected. These Neopian buses were the newest ones in the diesel fleet and have
similar specifications as the methanol buses. The five methanol buses had 900 to 6.100
miles of service, the five CNGIDiesel
buses had 146,000 to 228,600 miles of service, and
the five diesel control buses had 95,000 to 114,000 miles at the beginning of the program.
The physical characteristics of the competing technologies are presented in Table 5.1. The
characteristics for biodiesel buses are the same as for diesel buses.
No engine
modifications are required, only the fuel is modified by blending diesel fuel with biodiesel
which does affect fuel efficiency.
The three fleets of buses are exposed to similar service factors such as schedule
speeds, stops per mile, traffic conditions, and passenger loading. They are operated five
days a week and run on the same route and block number during the route assignment.
A route assignment lasts approximately four months. The same driver operates a
methanol. CNG/Diesel, or diesel control bus for the four months. The buses are operated
from the Platte Maintenance Facility and are maintained under the same preventive
maintenance program (PM).
The buses are fueled on site.
General Assumptions
Refueling Infrastructure
The refueling infrastructure costs are based on the Colorado Institute,fir FueI
and High Altitude Engine Research following assumptions. The refueling infrastructure
includes facility building assumed to be 1,000 square feet per lane at $92,000 per square
feet: refueling equipment estimated $25.000; and underground tank installation with a
capacity of 20,000 gallons per tank. The service life for the refueling infrastructure is
assumed to be 30 years.
1
Table 5.1. Characteristics of Buses
Characteristic
Year
Engine
Transmission
Seats
Purchase Price
(model 1991)
Converter Ratio
Retarder
Axle Ratio
Curb Weight
Gross Weight
Fuel Tank
Diesel
Methanol
CNGIDiesel
1989
6V-92 TA DDEC I
Allison
HTB- 748 ATEC
43 (37 standing)
1989
6V-92 TAM DDEC II
Allison
V-731 ATEC
43 (37 standing)
1986
6V-92 TA DDECII
AIIison
HTB- 748 A TEC
43 (37 standing)
$217,400
2.2 1: 1 TC495
Yes
4.67: 1
28,680 lbs
35,130 Ibs
125 gallons
$188,500
3.43:1 TC470
No
5.13:1
28,560 Ibs
34,970 lbs
285 gallons
$252,400
4.67: 1
38,000 lbs
8,084 CNG
(cubic feet)
62.5 diesel
(gallons)
Source: Colorado Institute for Fuel and High Altitude Engine Research
Refueiing Labor and Materials
The RTD fleet is approximately 1,000 buses. The RTD currently refuels the entire
operating fleet on the third shift. Each bus requires four minutes to refuel. In one
refueling center, RTD
refuels approximately 280 buses per night in a three fuel lane
system. The three lanes can service 360 buses at full capacity.
Refueling labor includes one supervisor per three lanes and three laborers per one
lane. Two laborers drive the buses to the lane and the third laborer refuels the buses.
Methanol (IV&H) contains only about 40% of BTU/gallon of diesel. Refueling
methanol
buses requires 2.5 times as many lanes as diesel refueling because of the increase fuel
usage. and therefore more laborers.
Labor cost assumption for a supervisor includes hourly rate of $16.00 plus benefits
of 29%; five day work week. eight hours per day yielding 2,080 hours per year; fifteen
days of paid vacation (120 hours), nine paid holidays (72 hours). and eight paid sick leave
days (64 hours) yield a loss of 256 hours. Actual hourly rate is then $16.00[(2080/1824)
+ 0.291 = $22.89. Hourly rate for a laborer is $13.95 which results in $19.95 actual labor
cost based on the same formula used for the supervisor’s rate.
Diesel Bus Assumptions
The diesel tankage is assumed to be $40,600 per 20,000 gallon tank (based on
$10.600 for the tank plus 1.5 times the tank size for accessories). A tank capacity of
26.666 gallons is required per lane. Diesel tank is a FTP-3 20,000 gallon tank with
dimensions of eleven foot diameter and 28 feet tall. The diesel engine and fuel system
are the base for this study. Therefore, total startup cost of the diesel engine and fuel
system is zero. Infrastructure costs. refueling costs, and bus capital costs for diesel,
methanol, and CNGldiesel are listed in Tables 5.2-5.4.
J
73
Methanol Bus Assumptions
The methanol tankage is based on 2.5 times diesel tankage given MeOH buses
require on average 2.5 times as much as fuel, and thus requires higher refueling costs.
Lubrizol is added at 6.25 gallons per 10,000 gallons of MeOH at $15.69 per gallon. Total
incremental startup costs for methanol buses are assumed to be $38,296. They include
incremental refueling infrastructure and bus capital costs. Incremental fixed cost of the
fuel system is $12,900, and accrued every ten years. These costs are summarized in Table
5.3.
CNGLDiesel Bus Assumptions
The CNGIDiesel
refueling station for fast filling 50 equivalent gallons into 300
buses in a single shift is assumed to cost for installation $1,700,000 plus 10% for
contractor’s markup, 10% for engineering, 5% for development and permitting, and 10%
of installed cost for engineering plus development and permitting contingency.
CNG/Diesel technology requires eight lanes instead of three for diesel and methanol.
Total startup costs are assumed to be $43.727. They comprise incremental
refueling infrastructure, fuel system and engine conversion costs. Incremental fixed cost
of the CNG/Diesel dual fuel engine conversion and fuel system is $35,000, accrued every
ten years. These costs are reported in Table 5.5.
Engine Rebuild Assumptions
The basic idea behind a rebuild is to make the engine as good as new. It consists
of saving parts from the old engines by reconditioning and reusing the rods and
crankshaft. The engine block is inspected and reused. For the engine rebuild. all new
Table 5.2. Diesel Bus Cost Summary
Units
unit cost
Annual miles driven
Infrastructure cost per lane
Building cost, $0000 sq ft per lane
Tankage, 20,000 gallon size
Total infrastructure cost
Total infrastructure cost per bus
Total Cost
36,578 (per bus)
$92.000
40.600
Refueling cost
Labor costs per lane per day
Supervisor
22.89 per hour
Labor
19.95 per hour
Labor costs per day for three lanes
539.84
Overhead multiplier
Total labor costs per bus per year (365 days)
Fuel usage ($/gal, gal/ma)
0.67
Annual refueling cost per bus
Cost per mile
Bus capital data
Incremental first cost, bus engine plus fuel systema
3
300
$276.000
162,400
438.400
1,461
l/8
61.04
24
3
2
478.80
1,620
3.240
3.942
6,963
4
866
10.905
0.298
0.000
a The diesel engine and fuel system are the base, so there is no incremental cost for a
diesel bus system.
75
Table 5.3. Methanol Bus Cost Summary
unit cost
Annual miles driven
Building cost, WOO0 sq ft per lane
Tankage, 20,000 gallon size
Total infrastructure cost per bus
units
Total Cost
29,801 (per bus)
$92.000
268,148
Refueling cost
Supervisor
22.89 per hour
Labor
19.95 per hour
Labor costs per day for three lanes
1.258.24
Overhead multiplier
Fuel usage ($/gal, gal/year)
0.59
Lubrizol ($/gal,gal/year)
15.69
Cost per mile
Bus capital data
Incremental first cost. bus engine plus fuel system”
3
8
300
318
60
3
2
19,867
12.42
$276.000
2.68 1,480
2,957.480
9.858
61.04
1,197.20
3,775
7,550
9.185
11.722
195
21,102
0.708
29,900
’ The diesel engine and fuel system are the base, so the incremental cost is the
additional cost of methanol fuel engine and fuel system.
76
Table 5.4. CNG Dual Bus Cost Summary
Units
unit cost
Annual miles driven
Building cost, $/lo00 sq ft per lane
Fueling facility
Total cost infrastructure cost per bus
Total Cost
34,691 (per bus)
$92,000
Refueling cost
Supervisor
22.89 per hour
Labor
19.95 per hour
Labor costs per day for eight lanes
501.77
Overhead multiplier
Fuel usage per bus per year
0.40
( $/gal, gal/year)
Maintenance costs per bus per year
Energy cost of compressors
per bus per year
1.28
Cost per mile
Bus capital data
Incremental first cost. bus engine plus fuel system”
8
300
$736,000
2.320.500
3,056,500
10,188
1
24
8
2
22.89
478.80
4,014
8,028
9,767
10,764
4,306
400
365
467
14,940
0.43 1
35,000
’ CNG/diesel bus engine is the same as the diesel bus. so the incremental cost is the
conversion cost of a diesel bus to CNG and additional cost of the fuel system.
77
Tabie 5.5. Startup Costs and Incremental Fixed Costs for Methanol and Dual CNG/Diesel
Buses
Alternative Fuel
startup cost”
Methanol
$38.296
$12,900
CNGDual
43,727
35,000
Incremental Fixed Costb
a Startup costs are initial incremental infrastructure and bus capital costs.
b Incremental fixed costs are fuel system and engine conversion costs. They are accrued
every ten years.
78
pistons, piston rings, and bearings are used. The cyiinder heads. blowers. injectors. and
the turbochargers are generally rebuilt and reused. Sometimes. however, everything has
to be scrapped; it all depends on the condition of the engine. In general, a rebuilt engine
is up to the specifications of a completely new engine.
The cost for the rebuild is an average of all rebuilds performed at the Colorado
Institute for FueI and High Altitude Engine Research. Rebuild cost for diesel and
CNGIDiesel engine are $6,500 including $3,070 for parts and $3,430 for labor. Methanol
engine rebuild costs $9,500 including $6,070 for parts and $3,430 for labor.
Data Transformation
The data for the nested fixed point algorithm technique consists of monthly
observations on the odometer readings for each bus of the fleets, and data on the date and
odometer readings at which rebuild was performed. An engine rebuild or replacement is
defined as an actual physical replacement of the existing engine with either a new or a
used engine involving replacing or rebuilding a majority of the components as previously
described.
Because the observed state variable x, (mileage) is a continuous variable. the
required fixed point EV, in equation 4.4 is actually an infinite dimensional object lying
in the Banach space B of all measurable functions of x (Rust). Computing EVe requires
discretization of the state space so that the state variable x, takes on only finite values.
Then the function EV, becomes a finite dimensional vector in R”, with dimension equal
to the number of possible values the discretized state variable x, can assume. In essence,
the discretization procedure amounts to approximating the infinite dimensional Banach
space B by a high dimensional Euclidian space R” (Rust).
J
An appropriate way for discrerizing the state space in the bus engine rebuild
problem is to divide mileage into equally sized ranges. Following Rust, a length of 5,000
79
and an upper bound of 450,000 miles on mileage are selected. This is consistent with the
data because no bus ever got more than 400,000 miles between engine rebuilds. Then the
Banach space dimension is n = 90, and EV, is a vector in R9’, and the state variable is
assumed to have only discrete integer values in the set ( 1, . ..) n> which can be interpreted
as mileage ranges in the underlying continuous state space. Using the discretized state
variable, the transition probability function p(x,+, 1 x, i, 63 becomes an n x n Markov
transition matrix. In this particular case, the monthly mileage distribution
p(x,+,
/ x, i, 03 equals the density probability g(x,+, - x, 6’3 when i, = 0, as defined in
4.14 which reduces to a multinomial
distribution in the discretized space. With n = 90,
this reduces to a trinomial distribution on the set (0, 1, 2) corresponding to [0, 5,000),
[5,000,
lO,OOO),
and [lO,OOO,
0), respectively.
Putting an upper bound on mileage x, requires to place an absorbing state at
x, = n. Thus if at time t a bus is in state x, = n and no rebuild occurs, then at time
t-k I it will also be in state x, = n with probability 1.
Letting pj = ProbJx,,, = x,+J,
j = 0, I, 2, and f o11 owing Rust, the discrete transition probability can be represented as
an n x n Markov transition matrix.
PO
PI
Pz
0
0
*
.
*
*
OP,P,P,OO*.
0
0
PO
0
0
0
PO
.
.
.
.
.
.
.
.
.
.
.
*
0
*
0
*
0
*
0
.
-000
PI
P?
PI
.
0
.
*
0
P?
0
0
.
0
.
.
.
.
.
.
*
*
PO
PI
P?
.
.
.
0
PO
PI
.
p.
.
.
.
.
0
0
*
.
0
.
.
.
.
0
Pz
l-p,
.
1
80
This is the transition probability matrix for the uncontrolled Markov process assuming
rebuild never occurs. Summary statistics of the raw rebuild data is provided in Table 5.6
Preliminary Analysis
Biodiesel Fuel Costs
Three prices, $1.75, $2.50, and $3.00 per gallon are assumed for biodiesel fuel
costs. Assume x percent of biodiesel and y percent of diesel o/ = 100 - x), pn and pd the
price of biodiesel and diesel fuel per gallon, respectively. Then the blended fuel price
p is calculated by the formulap = ph * x% + pd * y%. Using this formula and assuming
$0.67 per gallon for diesel fuel, the biodiesel fuel price per gallon is listed in Table 5.7.
Biodiesel Fuel Consumption
Biodiesel fuel consumption data were obtained from engine ceil test runs at the
Colorado Institute for Fuel and High Altitude Engine Research. using #2 diesel (D) and
biodiesel (B). Regression of the data through zero was used for the fuel consumption
calculations. Then. the regression value is divided into the fuel consumption of the diesel
to obtain the fuel consumption for biodiesel (for different percent biodiesel). The fuel
consumption data is presented in Table 5.8.
Rebuild Cycle
A rebuild cycle is defined as the time elapsed between two consecutive engine
rebuilds. Using the mileage data. monthly average travelled mileage, rebuild cycle, and
rebuild cost are summarized in Table 5.9.
81
Table 5.6. Summary Statistics of Rebuilds
summary
Diesel
Methanol
CNGIDiesel
5
5
5
89,600
12,150
55,271
28.861
110.100
14,590
53,432
27,016
34.500
20,200
26,833
5.901
28
34
5
17.33
8.79
10
6
8.33
1.63
Statistics
Number of Buses
Mileage at Rebuild
Maximum
Minimum
Mean
Standard Deviation
Elapsed Time between Rebuilds
(months)
Maximum
Minimum
Mean
Standard Deviation
82
Table 5.7.
Biodiesel Fuel Price for Percentage Blend o f 20, 35, 6 0 and 100.
Biodiesel Fuel Price per Gallon
Percent
Blend
$1.75
20
$2.50
$3.00
$0.886
$1.036
$1.136
35
1.048
1.310
1.485
60
1.318
1.768
2.068
100
1.75
2.50
3.00
Table 5.8. Fuel Effkiency of Biodiesel Blend Fuels Compared with Diesel
Percent Blend
Biodiesel
0%
Ratio of Brake Specific Fuel
Consumption (Fuel Efficiency)
1
20
0.9916
35
0.9766
60
0.9297
100
0.8887
Tabie 5.9. Monthly Travelled Mileage and Rebuild Cycle
Alternative
Fuel
Monthly Travelled
Mileage
Rebuild Cycle”
(months)
Engine Rebuild
cost
Diesel
and
Biodiesei
2,900
20
$6,500
Methanol
2,600
21
9.500
CNGIDiesel
2,700
10
6,500
a Rebuild cycle is average mileage at rebuild divided by monthly travelled mileage.
Actual Operating Costs
Actual total operating costs are real costs borne by running the fleet of buses, and
obtained as an average form of operating costs data. They are maintenance and fuel costs,
and are summarized in Table 5.10. Three prices are considered for CNGIDiesel. The
monthly maintenance costs are the highest for methanol buses followed by considerably
lower costs for CNGIDiesel. The lowest monthly maintenance cost is for diesel and
biodiesel buses. Diesel and biodiesel buses are assumed to have the same maintenance
cost. Fuel costs and associated monthly costs vary by type of fuel and price. A high
blend of biodiesel and methanol are the high cost fuels and diesel is the lowest cost. Note
biodiesel is competitive with CNGIDiesel
in terms of total monthly costs at low blend
levels. In the next chapter actual monthly costs are used to calculate the present value of
total operating costs per mile over the life-cycle of 30 years.
86
Table 5.10. Actual Average Operating Costs for Diesel, Methanol, CNGIDiesel. and
Biodiesel Buses.
Monthly
Engine
Maintenance
cost
Fuel Cost
Total Cost
Diesel
$41.90
$864.47
$906
Methanol
419.38
1,841.03
2.260
CNGIDiesel
$.352/gallon
$.3975/gallon
$.4430/gallon
71.59
71.59
71.59
1,122.49
1,160.62
1,198.72
1,194
1,232
1.270
Biodiesel
$1,75/gallon
Percent Blend
20
35
60
100
41.90
41.90
41.90
41.90
1,048.71
1,196.69
1,480.56
1,934.95
1,091
1.239
1,522
1,977
$2SO/gallon
Percent Blend
20
35
60
100
41.90
41.90
41.90
41.90
1,173.46
1,418.14
1,879.36
2.630.28
1.215
1,460
1.921
2.672
$3 .OO/gallon
Percent Blend
20
35
60
100
41.90
41.90
41.90
41.90
l-256.43
1,565.78
2,145.22
3,093.38
1,298
1.608
2.187
3,135
CHAPTER VI
MODEL RESULTS AND ANALYSIS
As hypothesized in the theoretical model, the analysis of rebuild data suggests that
an optimal timing for engine rebuild is inconsistent with the data given a large variation
of mileage at rebuilds. Thus, taking observed engine rebuilds as optimal, the main task
of the theoretical model is to infer the total operating costs leading to these rebuilds. This
chapter presents empirical results based on the theoretical model and the derivation of the
present value of total operating costs. Also. an analysis of these results is provided in
terms of the relative competitiveness of the different alternative fuels.
Model Results
The parameters of the theoretical model include the rebuild or replacement cost
r and the parameter 8, associated with the linear cost function C(x, 6J = 0.001 *x*8,.
Table 6.1 presents the structural unknown parameters (I; 19,) estimates computed by
maximizing the full likelihood function l/ using the nested fixed point algorithm. A
discount factor p = 0.999, corresponding to a very low annual real rate of 0.1 per cent
was considered. With this discount factor, the model can be considered as a dynamic
model of bus engine rebuild which recognizes that rebuilding or replacing a bus engine
is an investment which not only reduces current costs. but future costs as well. Note that
changing slightly fl produced negligible changes in the parameters (r, 0,). This
87
~
88
Table 6.1. Marginal Cost Estimation Results for Diesel. Methanol, and CNG/Diesel
Buses
summary
Diesei
Methanol
3.38
5.06
15.55
4.64
0.89
3.21
Rebuild Costs, RCb
6,500
9,500
6,500
Scale Parameter, fs
1,284
2,047
2.025
Marginal Cost (per 5,000 miles)’
$4.34
$31.84
$1.80
CNG/Diesel
Statistics
Structural Coefficients
Operating Costs, 8,”
Rebuild Costs, r
a Operating costs include maintenance costs, insurance costs, and loss of ridership and
goodwill costs due to unexpected breakdowns.
b Scale parameter is the actual rebuild cost. RC. divided by the rebuild cost coefficient.
Y.
’ Marginal cost is obtained by multiplying the constant scaling CT times the estimated value
of 8, to obtain a dollar estimate of 19,.
89
insensitivity may be explained by the highly collinearity of fi with the rebuild cost Y
because both parameters have similar effects on replacement behavior. For example,
raising I- tends to retard engine replacement, an effect which can also be achieved by
lowering the discount factor p. Furthermore, a high value of 0 may also be explained by
Abel’s theorem suggesting that if minimizing long run average costs. /3 can be driven to
1 (Howard, 1971).
The value of the cost function parameter 8, for dual CNGIDiesel bus is relatively
small. This small value may be explained by the low standard deviation of elapsed time
between rebuilds. As C is normalized C(O, 03 = 0, the most that is identified is the value
of the change in operating costs. Thus. using observed engine rebuild cost. the scale of
the coefficients (r, 0,) can be determined.
The average observed rebuild costs were
$6.500 and $9,500, for diesel and dual CNGIDiesel, and methanol, respectively.
Computing the ratio of actual to estimated rebuild cost, a scale of (T is obtained.
Multiplying this scaling constant times 8, gives a dollar estimate of 8,. These estimates
of $4.34, $3 1.84. and $1.80 for diesel. methanol and dual CNGIDiesei. respectively
indicate that the Regional Transportation District perceives average monthly maintenance
costs to increase by these amounts for every 5.000 accumulated miles on the buses. Note
that the mileage range in the discretization of the data was 5,000, then the estimated
marginal cost is over this range.
The large variation in marginal cost can be explained by the relatively large
rebuild cost and variation in mileage at rebuild of methanol compared with CNGIDiesel.
This wide variation in mileage at rebuild implies higher marginal cost associated with
determining optimal preventive maintenance (Table 5.5). For example, considering
methanol rebuild data. there was one bus which was rebuilt only one time at a relatively
very high mileage of 110,100. This iarge accumulated mileage before rebuild might
increase the probability of failure. and consequently insinuate a higher marginal cost. ’
90
Given monthly travelled mileage. and considering maintenance cost changes eve?
5,000 miles, estimated changes in operating costs are used to calculate average monthly
maintenance costs over a rebuild cycle, which are then used to calculate the present value
of total operating cost over the refueling infrastructure life-cycle, 30 years.
after a rebuild or replacement the system starts new.
Note
Thus. rebuild cycles are repeated
through the life-cycle. Tables 6.2-6.7 present the monthly total operating costs for a
replacement cycle. Total operating costs include monthly maintenance cost and fuel cost.
There is an additional rebuild cost at the end of each replacement cycle.
Discounted Operating Cost Analysis
For a full comparison of the operating costs among the alternative fuels. all
applicable capital costs including startup costs, engine conversion, refueling system. and
operating costs are considered. Then, the discounted cash flow technique is used to
calculate the present value of total operating costs over a 30 year life-cycle.
Total startup costs are $38,296 and $43,727 for methanol and dual CNG/Diesel
buses. respectively (Table 5.5). These costs comprise incremental refueling infrastructure
costs and incremental bus capital cost. As hypothesized in the data section, it is assumed
that the Regional Transportation District already has diesel bus refueling and maintenance
facilities. Therefore, fixed costs of maintenance and refueling facilities are incremental
to diesel bus fixed costs. This assumption may favor diesel and biodiesel economics, but
it is realistic because all existing transit properties do in fact have diesel facilities.
Table 6.2.
Month
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
Monthly Estimated Diesel Bus Cost for a Replacement Cycle
Cumulative
Mileage
2,900
5,800
8,700
11,600
14,500
17,400
20,300
23,200
26,100
29,000
3 1,900
34,800
37,700
40,600
43,500
46,400
49,300
52.200
55,100
58.000
Estimated Operating
Cost9
$4.34
13.02
21.70
34.72
47.74
65.10
86.80
108.50
134.54
160.58
190.96
225.68
260.40
299.46
338.52
381.92
425.32
473.06
525.14
577.22
Total
Costb
$869
877
886
899
912
930
951
973
999
1,025
1,055
1,090
1,125
1,164
1.203
1,246
1,290
1.338
1,390
7.942’
a Estimated operating costs are obtained from Table 6.1. Given monthly average travelled
mileage, and considering operating cost increases by the same amount every 5,000 miles,
monthly operating costs are calculated accordingly to accumulated mileage.
b Total estimated cost includes fuel cost and maintenance cost.
’ Rebuild cost in month 20 is $6,500
92
~~COw~~m-N\C
-O~r4WUW&
~mNuwm--ar-~uoo-wOb-iO~
-q U” rn” ‘“” rn” m” wc w” w I F -” -” Do, 00” 0‘” Q” 0” m
~---------,---c---~&
b4
~oocoo20cooooooooo
oooooc
=oooooooooco
o\cL)m-Tmr4
-* 0” a* 00” F” W” ‘“” U” I--” N - 0
& v; a” P- 0” m- w o\ - u r- 0 m w a r.rv;ca”
--r4r4Nr4mmmuuuu~b-lm
93
oooooooooooooooooooo
oooooooocoooocoooooo
a OQ w ” ?. 7 ? c-4 - C m 00, I---- Wn me u m w - 0
u r- 0 m” ti & L u r-- 0 m w” 6 t-i m” CQ”
Pi b-i- a7 m-v ~4~~4mmmmauuummm
75
.-8
-c
C
.22
OOOOCooOoooooCooOooo
oco300cocGoooooooooo
0. 00 r- ‘9 ? -.. m m - 0 0s 09 y Wn m, u m r4 - 0
0 m d & 6 vf w”
4 6 w- - u w
m’ 6 0; - u F
-cc 0
r4r4r4r4mmmuuuummm
‘=0
z
-r4mumwr-w240 -r4mu~w~wmo
-----c-----N
Table 6.6. Monthly Estimated Methanol Bus Cost for a Replacement Cycle
Month
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
Cumulative
Mileage
2,600
5,200
7,800
10,400
13,000
15,600
18,200
20,800
23,400
26,000
28,600
31.200
33.800
36,400
39,000
41,600
44,200
46,800
49,400
52,000
54,600
Estimated Maintenance
cost”
$31.84
95.52
159.20
254.72
350.24
477.60
604.96
764.16
923.36
1,114.40
1,305.44
1.528.32
1,75 1.20
2.005.92
2.260.64
2.547.20
2,833.76
3,152.16
3.470.56
3,820.80
4.202.88
Total Estimated
Costb
$1.873
1.937
2.000
2.096
2.191
2,319
2.446
2.605
2,764
2.955
3,146
3.369
3,592
3,847
4.102
4,388
4,675
4,993
5,312
5,662
16,814’
mileage, and considering operating cost increases by the same amount every 5.000 miles.
monthly operating costs are calculated accordingly to accumulated mileage.
b Total estimated cost include estimated operating cost and fuel cost.
’ Rebuild cost in month 21 is $9,500.
96
Table 6.7. Monthly Estimated CNGIDiesel Operating Cost for a Repiacement Cycle
with Fuel Prices of $0.3520, $0.3975, and $0.443 per gallon
Total Estimated Cost
Month
1
2
3
4
2
7
8
9
10
Cumulative
Mileage
2,700
5,400
8,100
10,800
13,500
16,200
18,900
21,600
24,300
27,000
Operating
cost”
$1.80
5.40
9.00
14.40
19.80
27.00
34.20
43.20
52.20
63.08
$0.352
$0.3975
1,124
1.128
1,131
1,137
1,142
1,149
1,157
1,166
1,175
7,685b
$1,162
1,166
1,170
1,175
1,180
1,188
1,195
1,204
1.213
7,724b
$0.443
$1.201
1.204
1,208
1,213
1,219
1,226
1,233
1,242
1,251
7,762b
mileage, and considering operating cost increases by the same amount every 5,000 miles,
b Rebuild cost in month 10 is $6.500.
97
The present value of total operating cost is calculated as follow
360 Moc’+Fc
M MOC
PVC = IC+C-+ c i=l (1 +r)’ j=M+l (1 +ry’
1
(6.1)
+ (1 +r)24a I
where, PVC is present value of total operating cost, IC is all initial fixed costs. MoC is
monthly operating cost, r is monthly discount rate, ~Moc’ monthly operating costs without
an additional rebuild cost at the end of the last replacement cycle, and FC is incremental
fixed cost. The variable Mtakes values of 336, 340, and 350, respectively for methanol,
diesel and biodiesel, and dual CNGIDiesel
buses. Note, M+I is the start of the last
rebuild cycle. Initial fixed costs (KY) are startup costs for methanol and dual CNGIDiesel
(Table 5.5). Incremental fixed costs (FC) are fuel system cost, and fuel system and
engine conversion costs for methanol and dual CNGIDiesel
buses, respectively
(Table 5.5). These latter costs are additional costs accrued every ten years, represented
by 120, and 240 in equation (6.1). Monthly discount rate r is obtained by dividing annual
rate by twelve. Note for diesel and biodiesel buses IC and FC are assumed to be zero.
The life cycle of the refueling infrastructure is 30 years or 360 months. At the end
of these 30 years, the salvage value of the refueiing facilities is assumed to be zero.
However, the salvage value of the bus is incorporated into the model as described in the
theoretical
framework.
In fact, the replacement parameter r in equation (4.13) was
assumed to be the difference between the scrap value and the cost of installing a new
engine or rebuilding the old one.
Present value per mile of total operating costs are
presented in Table 6.8.
Present value is calculated over a 30 year life cycle which is the estimated life of
the refueling infrastructure. Three annual discount rates. zero, five, and seven percent are
used for comparison.
The present value of biodiesel is calculated under three price
scenarios, $1.75, $2.50. and $3.00 per gallon and at 20, 35, 60, and 100 percent bl&d.
98
Table 6.8. Present Value per Mile of Estimated Operating Costs Over a 30 Year Life
Cycle With Discount Rates of Zero, Five, and Seven Percent
Discount Rate
Zero
Alternative
Fuel
Diesel
Methanol
cost
$0.479
Five
Ratio”
1
cost
$0.246
Seven
Ratio”
1
cost
$0.198
Ratio”
1
1.392
2.90
0.736
2.99
0.599
3.02
CNG/Diesel
$.3520/gallon 0.740
$.3975/gallon 0.754
$.4430/gallon 0.769
1.54
1.57
1.60
0.407
0.415
0.422
1.65
1.68
1.71
0.337
0.343
0.349
1.70
1.73
1.76
Biodiesel
S 1.75/gallon
Percent Blend
20
0.542
35
0.593
60
0.691
100
0.848
1.13
1.24
1.44
1.77
0.279
0.306
0.357
0.438
1.13
1.24
1.44
1.77
0.225
0.246
0.287
0.353
1.13
1.24
1.44
1.77
$2.5O/gallon
Percent Blend
20
0.585
35
0.670
60
0.829
100
1.088
1.137
1.39
1.73
7 37
-.-
0.302
0.346
0.428
0.563
1.22
1.39
1.73
2.27
0.243
0.278
0.344
0.452
1.22
1.39
1.73
2.27
$3 .OO/gailon
Percent Blend
20
0.614
35
0.721
60
0.921
100
1.247
1.28
1 so
1.92
2.60
0.316
0.372
0.475
0.645
1.28
1.50
1.92
2.60
0.255
0.299
0.382
0.519
1.28
1.50
1.92
2.60
a Ratio denotes alternative fuel relative to diesel, alternative fuel cost divided by cost of
1
diesel.
99
Also, three price scenarios, $0.3520, $0.3975, and $0.4430 per gallon are considered for
dual CNG/Diesel.
Results indicated that methanol buses and 100 percent biodiesel buses priced at
$3.00 per gallon are comparable in relative percentage mark-up above diesel buses. A
methanol bus cost per mile is approximately three times more expensive to operate than
diesel buses and a 100 percent biodiesel bus at $3.00 per gallon is approximately 2.6
times more expensive than diesel. Methanol blended with diesel would reduce this cost
similar to the per mile cost savings associated with blending biodiesel. This may result
in methanol being as competitive with CNGldiesel and a 35 percent biodiesel blend at
$3.00 per gallon.
In terms of biodiesel, the threshold at which biodiesel is competitive with
CNGIDiesel
on a cost per mile basis is between a 35 to 60 percent blend priced at $1.75
and $2.50 per gallon. and around a 35 percent blend priced at $3.00 per gallon.
Estimated Versus Actual Present Value of Operating Costs
For comparison the present value per mile of actual total operating costs is
calculated and contrasted with the present value of estimated operating costs. Actual
operating costs are the sum of actual maintenance costs and fuel costs.
Actual
maintenance costs are obtained as an average of real costs borne by running the fleets of
buses. Results are reported in Table 6.9. As expected, estimated operating costs per mile
are higher than actual costs. except for dual CNGIDiesel
because the former costs account
not only for the explicit costs such as maintenance. but also and most importantly the
opportunity costs of such loss of ridership and goodwill due to unexpected breakdowns.
Actual costs account only for explicit operating costs.
1
Considering the present value of actual operating costs, results with a five discount
rate indicate that methanol buses ($.521/mile) and between 60 to 100 percent blend of
100
Tabie 6.9. Present Value of Actual and Estimated Total Operating Costs over a 30 Year
Life Cycle With Discount Rate of Five Percent
Estimated
Actual
Alternative Fuel
cost
Diesel
$0.216
Ratio”
cost
$0.247
Ratio”
1
Methanol
0.521
2.41
0.736
2.98
C’NGlDiesel
$0.3520/gallon
$0.3975/gallon
$0.443O/gallon
0.416
0.424
0.43 1
1.92
1.96
1.99
0.408
0.415
0.422
1.65
1.68
1.70
Biodiesel
S 1.7Ygallon
Percent Blend
20
35
60
100
0.249
0.275
0.326
0.407
1.15
1.27
1.50
1.88
0.280
0.306
0.357
0.438
1.13
1.24
1.44
I .77
$2SO/gallon
Percent Blend
20
35
60
100
0.271
0.315
0.397
0.53 1
1.25
1.45
1.82
2.45
0.302
0.346
0.428
0.561
1.22
1.40
1.73
2.27
$3 .OO/gallon
Percent Blend
20
35
60
100
0.286
0.341
0.444
0.614
1.32
1.58
2.05
2.84
0.317
0.372
0.475
0.644
1.28
1.50
1.92
2.60
a Ratio denotes alternative fuel relative to diesel, alternative fuel cost divided by cost of
diesel
1
101
biodiesel priced at $2.50 ($.397/mile and $0.531/mile), and a 60 percent blend of
biodiesei priced at price $3 .OO per gallon ($.444/mile) are comparable in relative mark-up
percentage above diesel buses. A methanol bus cost per mile is approximately 2.41 times
more expensive to operate than diesel buses and a 60 percent blend biodiesel priced at
$2.50 and $3.00 per gallon are 1.82 and 2.05 times, respectively, more expensive than
diesel.
With respect to CNGIDiesel
buses. results indicate that 100 percent biodiesel
priced at $1.75 per gallon, 20-60 percent blend at $2.50 per gallon and 20-35 percent
blend at $3.00 per gallon are comparable on a cost per mile basis. The CNG/Diesel
technology is in process of being replaced by neat CNG engines. However. at the present
time there are too few CNG engines being used and these have insufficient operating
hours to determine the total cost per bus mile. Therefore, the CNGIDiesel costs are the
best proxy for total cost per bus mile for CNG. Results are similar with discount rates
of zero and seven percent.
In summary, assuming a 35 percent blend biodiesel fuel can comply with
regulatory emission standards, biodiesel buses at prices as high as $3.00 per gallon are
competitive with the other alternative fuels. The nested fixed point algorithm provides
a consistent method for determining the marginal operating cost. while the actual cost
estimation only gives a fixed average cost over a rebuild cycle. A fixed monthly average
operating cost is inconsistent with rising operating cost as developed in the literature
review chapter.
CHAPTER VII
SUMMARY, CONCLUSIONS, AND POLICY IMPLICATIONS
Summary and Conclusion
At the beginning of this study, two major problems driving demand for alternative
fuels in the United States were identified and discussed. The first relates to the necessity
of cleaner emissions. This problem is apparent considering emissions from gasoline and
diesel powered vehicles which contribute significantly to five of six major sources of
pollution. The second problem relates to the concern for reliable source of energy. The
United States is a repository of only a small portion of the world’s proven crude oil
reserves imports a large portion of the crude oil it consumes from OPEC nations.
These
sources of imports are subject to sudden and significant disruptions. The motivation of
this research was to provide economic information on the comparison of four alternative
fuels -- compressed natural gas, methanol. diesel. and biodiesel. In fact, as the market for
cleaner burning renewable fuels is becoming increasingly important there is a significant
gap in the literature comparing these alternative fuels because most of the current works
on the comparison of these alternative fuels are technical.
The main objective of this study was to develop a dynamic model for estimating
and comparing present value of total operating costs for four alternative fuels. This model
was applied to transit buses because transit bus authorities are under mandate of adopting
alternative fuels for reducing air pollution. Attempts were made to analyze a typic+
102
103
transit fleet with typical costs based on data obtained from the Colorado Institute for Fuel
and High Altitude Engine Research (CIFER).
The model was developed based on Rust’s nested fixed point algorithm which
provides a consistent method for determining marginal cost for alternative fuels. Basically
the method assumes that transit authorities have developed a procedure for optimally
determining when a bus engine should be rebuilt or replaced. Given this optimal timing,
the model estimates what the marginal cost per month should be to obtain this optimal
timing. Knowledge of this marginal cost along with information on infrastructure,
refueling, and any incremental bus capital costs, allows the comparison of net present
value for alternative fueled buses with diesel buses. Such a comparison accounts for not
only the explicit cost such as maintenance but also the opportunity cost, including loss of
goodwill, associated with bus failure.
Assuming a 35 percent blend biodiesel fuel can
comply with regulatory emission standards, biodiesel buses at prices at high as $3.00 per
gallon are competitive with the other alternative fuels.
A constraint on the robustness of these results is the limited data on both number
of buses and months of bus operations. Currently, CIFER is collecting additional data,
in the form of increased bus numbers and operation length. Analysis of these data will
result in a more definitive comparison of these alternative fuels.
Implications
This analysis reveals that biodiesel is competitive with CNG/Diesel and methanol
fuels. However, it is less competitive compared with petroleum diesel fuel. In the
present situation of liquid fuel supply and at current crude oil prices. there is no greater
incentive to find replacements for liquid fossil fuels than for solid ones. There would
therefore need to be compelling environmental and socio-economic benefits from
conversion of vegetable oil to biodiesel to warrant incentives for promoting biodiesel fuel.
104
These incentives will be necessary to allow the industry to further develop to meet
expected demand, as well as to meet the challenge of reducing the cost of producing
biodiesel, thus making the fuel more competitive in the commercial marketplace.
The driving force behind the biodiesel industry is the recognition that soil, water,
sun. and wind (coupled with the greatest agricultural practices and production in the
world) are to the United States as oil and gas are to the Middle East.
With advanced
technology and farming practices. the U.S. will. in a few generations, greatly enhance in
its ability to produce transportation fuels and chemical feedstocks, whereas the Middle
East and other oil-producing parts of the world will have depleted much of their natural
resources. It would seem in the best interest of the global economy and the environment
to coordinate these forces in a way that respects the needs of future generations in all
parts of the world.
Biodiesel represents one of the best alternatives as a renewable fuel for diesel
engines from economic, energy and environmental protection aspects.
Due to its
structural nature, biodiesel is a fuel that does not influence the greenhouse effect as
regards emissions of CO,. Note substitution of biodiesel reduces the greenhouse effect
as it recycles carbon rather than pumping it from oil well. Nevertheless. in the current
state. for biodiesel to have a likelihood of controlling a major portion of the on-road fuels
markets. on-going research should develop a biodiesel-fueled engine that achieves PM and
NOX
reductions beyond those attainable from using low-sulfur diesel and catalytic
converters in new engines. and/or low sulfur diesel and standard rebuild kits in existing
engines (Booz-Allen and Hamilton Inc).
In general, research and development projects regarding viable alternatives to
petroleum energy sources can and must be encouraged on the one hand for economic and
environmental reasons and on the other hand to sustain a different model of developme,nt
that not only ensures the growth of developed countries, but also satisfies the increasing
demand for a better quality of life.
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The Economics of Engine Replacement/Repair for Biodiesel Fuels

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