Energy Policy and Economics 021
“ Dynamics of the Oil Transition:
Modeling Capacity, Costs, and Emissions”
Adam R. Brandt and Alexander E. Farrell
Energy and Resources Group, University of California, Berkeley
January 2008
This paper is part of the University of California Energy Institute's ( UCEI) Energy
Development and Technology Working Paper Series. UCEI is a multi- campus research
unit of the University of California located on the Berkeley campus.
UC Energy Institute
2547 Channing Way
Berkeley, California 94720- 5180
www. ucei. org
This report is issued in order to disseminate results of and information about energy
research at the University of California campuses. Any conclusions or opinions
expressed are those of the authors and not necessarily those of the Regents of the
University of California, the University of California Energy Institute or the sponsors of
the research. Readers with further interest in or questions about the subject matter of the
report are encouraged to contact the authors directly.
Dynamics of the oil transition: modeling capacity,
costs, and emissions 
Adam R. Brandt† and Alexander E. Farrell‡
Energy and Resources Group, University of California, Berkeley
January 15th, 2008
Abstract
The global petroleum system is undergoing an “ oil transition,”
shifting from conventionally produced petroleum to a suite of sub-stitutes
for conventional petroleum ( SCPs). This paper describes the
Regional Optimization Model for Emissions from Oil Substitutes, or
ROMEO, which models this oil transition. ROMEO models the dy-namics
of the transition to substitutes for oil and the environmental
impacts ( greenhouse gas ( GHG) intensity) of such a transition. It
models the global liquid fuel market in an optimization framework.
The ROMEO market mechanism operates differently than “ perfect
foresight” models: it solves each year sequentially, with each year op-timized
under uncertainty about future prevailing prices or resource
quantities.
ROMEO includes more fuel types than models designed for in-tegrated
assessments of climate change. ROMEO also includes the
differing carbon intensities and costs of production of these fuel types.
We use ROMEO to calculate the uncertainty of future costs, emissions,
and total fuel production under a number scenarios. We first explore
the effects of altering three key input parameters. We then use this
flexibility to more formally explore two uncertainties simultaneously:
the endowment of conventional petroleum, and future carbon taxes.
Results indicate that emissions penalties from production of oil sub-stitutes
are on the order of 5- 20 GtC over the next 50 years, and that
these results are highly sensitive to the endowment of conventional oil
and less sensitive to the values of a carbon tax.
 Preparation of this report was supported in part by a competitive grant from UCEI.
† Contact: abrandt@ berkeley. edu
‡ Contact: aef@ berkeley. edu
1
1 Introduction: vast uncertainties, few guideposts
Liquid fuels are incredibly useful for powering automobiles, airplanes and
other forms of transport. Where will we get these fuels in twenty years? In
fifty years? What affect will production, refining, and consumption of these
fuels have on the future environment? Or, perhaps more fundamentally, will
we need liquid fuels at all? And, if there is to be a transition to replacements
for conventional petroleum, will it be a benign transition induced by the
development of a superior technology such as advanced biofuels? Or, will it
be a unfavorable and panicked response to high oil prices and geopolitical
threats to conventional oil supply?
The answer to the first of these questions is likely as follows: approxi-mately
where we get them today. The time required for capacity expansion
in such an enormous and inertial industrial system suggests that twenty
years is not sufficient time for large changes to occur. The answers to the
other questions are not nearly so certain. All that can be said, whether
qualitatively ( e. g. via informed discussion or scenario planning), or quanti-tatively
( e. g. through models) is at least somewhat speculative. In short,
these questions are important and their answers are clouded by uncertain-ties.
It is useful to outline some of these uncertainties. First, the future
of global petroleum supply is uncertain. This uncertainty is due to poor
knowledge of petroleum resources, data that are unavailable for political
or economic reasons, and varying definitions of resources. There is also
uncertainty about the potential to produce oil- like hydrocarbon fuels from
non- conventional petroleum resources or other fossil fuels. Just as impor-tantly,
future hydrocarbon demand is uncertain: some predict a transition
to non- hydrocarbon fuels, such as biofuels, hydrogen, or electricity, while
others see steadily increasing demand for hydrocarbons. Because the en-vironmental
impacts of fuels differ, all of these uncertainties translate into
significant uncertainty about future environmental impacts from liquid fuel
production and consumption.
Despite this uncertainty, one aspect of the problem is clear: a transition
to substitutes for oil is underway. Petroleum producers currently exploit a
variety of hydrocarbon deposits of differing composition and quality, with
a trend over time toward increased exploitation of high- cost, low- quality,
non- conventional petroleum. In addition, synthetic liquid fuels from non-petroleum
feedstocks ( coal and natural gas) are currently produced in small
quantities, plug- in hybrid electric cars are nearing commercial production,
and biofuels production is increasing rapidly.
2
For simplicity, this paper focuses on the transition to hydrocarbon- based
substitutes for conventional petroleum. As stated above, this transition is
already underway and these fuels are already produced in significant quanti-ties.
Enhanced oil recovery represented about 10% of total US oil production
in 2004, almost entirely from steam- induced heavy oil production in Cali-fornia
[ 30]. Production of oil from Canada’s tar sands passed 1 Mbbl/ d in
2004 [ 31]. Production from Venezuela’s extra- heavy oil reached about 0.6
Mbbl/ d in 2000 [ 39]. In addition, approximately 150,000 bbl/ d of synthetic
fuels are produced, primarily from coal [ 16]. Oil shale is only produced in
minor quantities around the world in small facilities, with total world output
estimated at 10,000 to 15,000 bbl/ d [ 2]. Total SCP production, as defined
above, is somewhere above 2 Mbbl per day, depending on the definition
used, and is growing rapidly.
These resources have two properties that cause them to differ from con-ventional
oil and result in necessarily higher GHG emissions: 1) they tend
to be more difficult to extract than conventional oil, and 2) they tend to be
hydrogen deficient compared to the approximately 2: 1 H to C ratio present
in liquid fuels. Heavy and extra- heavy oil are very viscous and require the
injection of thermal energy to allow flow out of the reservoir. Tar sands
are currently produced by either mining or steam stimulation, with the for-mer
being more common [ 31]. Both of these types of fuels must also be
chemically upgraded ( H must be added or C rejected) and often cleaned of
impurities such as heavy metals and sulfur before use.
Oil shale is sedimentary rock that contains a significant percentage of
organic matter. It is thought be the same material from which oil is naturally
created [ 13]. Oil shale must be heated in the absence of oxygen to 300 to
500  C in order to produce usable hydrocarbons. This requires energy and
therefore adds cost and carbon emissions. Retorting of oil shale can also
release inorganic CO2 from carbonate minerals present in the shale, possibly
resulting in very high emissions [ 35, 37].
In contrast to synthetic crude oils produced from the above processes,
finished synthetic liquid fuels can also be produced, typically either from
natural gas or coal. These fuels are currently manufactured in two steps:
a syngas comprised mainly of CO and H2 is created from the hydrocarbon
feedstock, then the syngas is converted into liquid fuel using the Fischer-
Tropsch ( FT) process, a catalytic process that “ chains together” the carbon
atoms from the CO to produce a variety of hydrocarbon products. The
much higher C to H ratio of coal causes more emissions of carbon from CTL
production than GTL production.
3
Previous modeling efforts Because of this uncertainty about oil re-sources,
many modelers have attempted to forecast the future of liquid fuel
production. Current models come from three communities: petroleum ge-ologists,
energy and climate modelers, and resource economists. Petroleum
geologists’ predictions of conventional petroleum production often assume
that production follows a Gaussian curve ( the Hubbert methodology) and
therefore that production increases until resources are half consumed, at
which point production decreases [ 3, 9, 11, 12]. Some assessments are sim-ilar
but different models for depletion, such as exponential models [ 5, 41].
These predictions are typically based on bottom- up assessments of global
oil endowment and have historically tended to be conservative with respect
to available resources and future technologies.
Energy modelers and climate analysts are also interested in petroleum
production because of carbon dioxide ( CO2) emissions from oil use. These
models typically employ a “ top- down” perspective. They simulate the ex-traction
of oil by calling upon a simplified non- specific petroleum resource
base. Examples of these types of models include the six modeling efforts rep-resented
in the Intergovernmental Panel on Climate Change ( IPCC) Special
Report on Emissions Scenarios ( SRES) [ 23, 24]. These top- down models
generally assume larger amounts of petroleum resources than do the typ-ical
Hubbert- type projections. They also allow for a variety of petroleum
resources of varying quality [ 6, 34]. 1 Unfortunately, these top down mod-els
typically do not include detailed characteristics of individual SCPs: in
some SRES models all oil types have identical emissions, while in others
the emissions are modeled using only two resource categorizations. This is
problematic because of the fundamental differences between resource types
described above. For a detailed analysis of this problem, see Brandt and
Farrell [ 6].
In contrast to energy/ climate modeling efforts, economists have pro-duced
models of depletable resources for decades. These models are typ-ically
termed “ optimal depletion” models, and they attempt to determine
the level of production, and therefore speed of depletion, of a resource that
results in the maximum net present value of the resource [ 15, 22]. Often-times
these models describe a transition to “ backstop” resources, such as
Nordhaus’ classic model of long- term transitions to nuclear power and syn-thetic
fuels [ 32]. Economic optimal depletion models typically do not have
1 The justification for inclusion of a wide spectrum of resources is valid: there is little
hope of guessing today the technologies that might be developed over the coming century
to exploit low- quality resources, and resources that seem uneconomic today will likely
become economic in the future.
4
detailed characterization of different resources and lack detail with regard to
production techniques [ 40]. 2 These models also generally lack phenomena
such as exogenous increasing energy efficiency or technological learning ( see
Slade [ 36] for an exception), features that are common in energy- climate
models.
The important model of Green et al. [ 20, 21] models much the same
phenomenon as ROMEO. This model looks at many of the same questions
as ROMEO, but with less of a focus on greenhouse gas ( GHG) emissions
consequences of the transition. One ROMEO module ( the depletion module)
was directly inspired by this model, and other inspiration was found in their
work as well.
A role for ROMEO ROMEO fills a gap in the current literature - it ex-plores
the emissions consequences of depletion of conventional oil by mod-eling
the transition to substitutes for conventional petroleum. ROMEO
models the transition from conventionally produced petroleum to fossil- fuel-based
petroleum substitutes and forecasts the greenhouse gas emissions ( as
carbon equivalent, or Ceq.) consequences of this transition. The four sub-stitutes
for petroleum included in ROMEO are tar sands and extra- heavy
oil, gas- to- liquid synfuels ( GTL synfuels), coal- to- liquid synfuels ( CTL syn-fuels),
and oil shale.
For the purposes of this documentation, this suite of four liquid fuels
produced from low- quality petroleum resources or non- petroleum fossil- fuel
feedstocks will be called substitutes for conventional petroleum ( SCPs). We
omit biofuels and electricity from this definition, and from the current in-carnation
of ROMEO, simply to limit problem scope.
2 Methods: ROMEO in brief
2.1 ROMEO’s goals and scope
ROMEO works from a set of exogenous demand functions for liquid hy-drocarbons
from the IPCC SRES. The SRES documents the results of 6
international modeling teams who forecast future energy use under a vari-ety
of scenarios. Specifically, the demand functions come from the IMAGE
implementation of the SRES scenarios [ 23]. The IMAGE ( Integrated model
2 Withagen discusses this problem in detail, stating that “ considerable further work
is needed to understand the micro- foundations of the industry cost function” [ 40]. A
lack of available data on the oil industry is the culprit, with no public data available for
specification or design of improved production cost models.
5
to assess the global environment) model is produced by the Netherlands
Institute for Public Health and the Environment ( RIVM). 3 These projec-tions,
as extracted from the IMAGE model, already account for biofuels
production and non- liquid fuels penetration into the transportation market,
allowing our model to focus on the supply of crude oil and crude- oil- like
hydrocarbon fuels.
ROMEO compares these demand projections to forecasts of conventional
oil resource availability. Estimates of ultimate recovery of conventional oil
( estimated ultimate recovery, or EUR), are between 1800 to 4000 gigabar-rels
( Gbbl) [ 1], while consumption to date is approximately 1000 Gbbl. This
suggests that roughly 1000 to 3000 Gbbl of conventional oil remain. How-ever,
consumption of oil in the SRES scenarios is as high as 5200 Gbbl over
the next century. This means that unconventional oil must be produced if
these demand projections are to be fulfilled [ 6].
Thus, ROMEO can answer a two- part question: 1) “ given modeled de-mand
for petroleum products, and a range of estimates of conventional pet-roleum
supply, what is the difference between supply and demand, and how
is it optimally filled with substitutes for conventional oil?” and 2) “ what
are the emissions consequences of filling this gap with the modeled suite of
oil substitutes?” ROMEO is therefore not a full featured emissions model:
it models a specific portion of the energy system in more detail than was in-cluded
in the IPCC SRES models, and should be considered complementary
to those efforts. The system boundaries of ROMEO, including the features
that are implicitly and explicitly included in ROMEO, are shown in Figure
1.
2.2 A brief outline of ROMEO model structure
What follows is a brief outline of the structure of ROMEO. For more details,
see Appendix A and the full ROMEO model documentation [ 7]. Within
this working paper, names of model elements ( functions, parameters, data
inputs) are presented in sans serif font. Indexed elements are presented as
coded in the model. For example, fuel production, an element indexed over
regions ( r), fuels ( f) and years ( y), is written FuelProduction[ r, f, y].
ROMEO is a nonlinear optimization model, coded in the AMPL mathe-matical
programming language [ 17] and solved using the SNOPT solver [ 19].
It models the adoption of substitutes for conventional petroleum ( SCPs) over
3 IMAGE has undergone a number of model versions. ROMEO is based on output from
IMAGE version 2.2 and the current model version is 2.4 ( as of November 2007).
6
Figure 1: ROMEO model scope. Elements in light gray are included implic-itly
through IMAGE input data, but are not explicitly included in ROMEO.
Supply Demand
Conventional oil
Tar sands production
GTL production
CTL production
Oil shale production
Biofuels production
Hydrogen production
Natural gas for transport
Fuel trade
Petroleum
product
demand
Alt. liquid fuel demand
Alt. transport fuel demand
Included in ROMEO optimization
Included through input data, not modeled in ROMEO
the years 2000 to 2050 based on the demand for liquid hydrocarbons, avail-ability
of conventional oil, the prices of SCPs, and the SCP resource base in
each of 17 model regions. ROMEO does not solve for all fifty years of pro-duction
simultaneously, but instead solves each year sequentially, ensuring
that supply equals demand in each year. A “ run script” is used to load the
model in each year, save results, and transfer information between model
years.
Objective function The objective function of ROMEO, which is mini-mized
by the solver, is equal to the total cost of capital investment in fuel
production infrastructure, fuel production, and fuel trade:
( 1) min X y
T o t a l C a p a c i t y C o s t [ y ] + X y
T o t a l P r o d u c t i o n C o s t [ y ]
+ X y
T o t a l S h i p p i n g C o s t [ y ].
By constructing ROMEO in a cost- minimization framework, we are assum-ing
that the global fuels market seeks to supply fuels at the lowest cost ( or,
equivalently, that at a given market price, producers will act to maximize
profits).
7
Decision variables The solver minimizes the objective function by choos-ing
optimal values of the decision variables. These decision variables include:
NewCapacity[ r, f, y], the amount of new production capacity added in a given
region r and year y for each fuel f; FuelProduction[ r, f, y], the amount of a given
fuel f produced in each region r in a given year y; and FuelShipped[ r1, r2, f, y],
the amount of fuel f traded from a given region r1 to another region r2 in
year y. There are  75,000 decision variables over all years, mostly in the
fuel trading module.
Constraints The values of decision variables chosen by the solver are
subject to a number of constraints. Some constraints prevent non- physical
solutions, such as limiting the solver to positive values of FuelProduction so
that “ negative fuel” is not be produced. Also, the cumulative extraction of
a resource over time cannot be larger than the original resource base in each
region. A second type of constraint guarantees that the fuel market func-tions.
For example, supply of all fuels in each region must be greater than or
equal to the adjusted demand ( the demand that remains after accounting for
the effect of the oil price through the price elasticity of petroleum demand).
Still other constraints attempt to reproduce more subtle aspects of the global
oil market. One such constraint limits the rate at which production capacity
can be built in each region:
( 2) N e w C a p a c i t y [ r , f , y ]  M a x C a p a c i t y G r o w t h .
Another constraint is important enough to deserve description here. Pro-duction
of fuels is not dictated by externally generated functional forms ( e. g.
Gaussian- based Hubbert curves). Instead the shape of production is gov-erned
by a constraint that limits production in a given year to a defined
fraction of the remaining resource base. This assumes that production can
increase freely until the reserve- to- production ratio ( or, more accurately, a
“ resource- to- production ratio”) hits a specified level:
( 3) F u e l P r o d u c t i o n [ r , f , y ] 
M a x A n n u a l P e r c e n t a g e × ( A v a i l a b l e R e s o u r c e [ r , f ]
− C u m u l a t i v e F u e l P r o d u c t i o n R e s o u r c e C o n s u m p t i o n [ r , f , y ]).
Each of these terms is defined in detail in the full ROMEO documentation
[ 7]. The result of this constraint is exponential decay of production once the
minimum reserve- to- production ratio is met. A similar model was used by
Wood et al. in projecting future production and an equivalent exponential
8
formulation was found to fit historical oil production profiles slightly better
than a Gaussian model in a comprehensive study of 139 historical oil pro-duction
curves [ 5, 41]. All constraints are defined mathematically below in
Appendix A.
Three important modules ROMEO has a three important modules that
govern model functioning in significant ways: the short- and long- term price
elasticity of fuel demand, technological learning which lowers production
costs, and resource depletion, which increases production costs. Each of
these modules are described briefly below and in more detail in Appendix
A.
First, ROMEO accounts for the price elasticity of fuel demand. Along
with demand projections, corresponding oil price series are extracted from
IMAGE and input to ROMEO. This provides a baseline price and level of
fuel demand for each year. If the cost of production of the most expensive
barrel of fuel ( the marginal cost, equal to the oil price in a competitive mar-ket)
rises above the price of oil from the IMAGE model, then the demand
for fuels is reduced. This is performed on a yearly basis, using the marginal
cost of the current year’s production ( short- term elasticity of demand, mod-eled
with elasticities found by Krichene and Cooper [ 27, 10]). Additionally,
a weighted average of historical marginal production costs is compared to
the IMAGE input oil price to account for the long- term elasticity in demand
allowed by changes in fuel consuming capital ( e. g. automobile efficiency),
consumption patterns, and long- term economic growth. This long- term elas-ticity
module is adapted from Gately and Huntington’s econometric model,
which weights previous years’ prices with decaying importance. We also use
their elasticities as found for OECD and non- OECD nations [ 18]. These
modules are somewhat complex, especially the calculation of the marginal
cost, which involves a non- linear threshold value that prevents very small
quantities of fuel from affecting the marginal cost. See Appendix A for a
full specification.
ROMEO also models the declining cost of production that occurs due
to experience gained over time, commonly called “ learning by doing” [ 29]:
Y = aX− b, where Y represents cost of production, a is the cost of the first
unit of output, X represents cumulated output, and b represents the learning
elasticity [ 29]. Because of poor data availability, each fuel in ROMEO is
subject to the same learning rate. Also, the learning module affects capital
costs only. As an example of this effect, see Figure 9 for tar sands capacity
costs in the baseline scenario.
9
Lastly, ROMEO accounts for the fact that the last barrel of fuel produced
from a given resource base is invariably more costly to produce than the
first barrel produced. To do this, ROMEO utilizes the depletion module
developed by Greene et al. for their model of oil depletion and transition
[ 20]. This module is adapted somewhat from Greene et al.’ s formulation
and is parameterized using ROMEO- specific data. It is defined as follows:
( 4) D e p M u l t i p l i e r [ r , f , y ] =
ln  1
D e p l e t i o n R a t i o [ r , f , y ] − 1  − A l p h a [ r , f ]
I n i t i a l C o s t D e p l e t i o n [ r , f ] × B e t a [ r ]
,
where DepMultiplier is a multiplicative factor that increases the cost of pro-duction
as depletion progresses. An example of this module is shown in
Figure 10 which plots DepMultiplier for tar sands resources by region. This
module aids smooth model functioning because regions with a small resource
base experience production cost increases as they deplete their meager re-sources,
providing a “ soft” constraint that gradually makes their resources
uneconomic.
Of these modules, only the price elasticity of demand modules are imple-mented
in a truly non- linear, current- year fashion. The other two modules
act “ between years.” That is, they utilize the previous year’s data within
the run script to calculate new, static factors for input as fixed data into
the current year’s solution of the model. Thus, to the solver these modules
are seen as linear, while across years they act in a pseudo- nonlinear fashion.
This choice was made to minimize the non- linearity of the model, improving
model stability and solvability.
3 Results: the baseline scenario, and its sensitiv-ity
to model parameters
The results of ROMEO, and the sensitivity of those results to parameter
inputs, are easiest to illustrate by first showing a suite of results from a
“ baseline” scenario and then showing summary figures resulting from per-turbations
to the model parameters.
3.1 Baseline results - scenario s2
The standard ROMEO model runs include 8 scenarios, s1- s8, as described
below in Appendix A ( See Table 3) and further described in the full ROMEO
model documentation [ 7]. Of these scenarios, scenario s2 is chosen as the
baseline scenario for this report. It is a very “ central” or “ normal” scenario,
10
with demand and conventional oil endowment set to their medium ( med) lev-els,
and technological learning, price elasticity of demand, fuel input prices,
and depletion impacts all set to moderate levels. To illustrate the suite of
graphical outputs from the model, a number of plots from scenario s2 are
presented below.
First, overall fuel supply over time is shown in Figure 2. We see that as
conventional oil production is forced down by resource constraints, uncon-ventional
production increases, but fitfully and with some lag, creating an
“ undulating plateau” of the kind described by Yergin and others ( a good
summary of differing views of peak oil, including Yergin’s, is provided by
Kerr [ 26]). We see that tar sands production increases first, followed quickly
by GTL synfuels and small amounts of CTL synfuels. The magnitude of
total fuel production can be compared to the original exogenous demand
projection from IMAGE, as shown in figure 3. Note that ROMEO modeled
demand is lower than the IMAGE input demand data because the prices
modeled in ROMEO are higher than the prices modeled in IMAGE. These
relative price levels are shown in Figure 4. The top curve is the modeled
oil price path from ROMEO, while the bottom curve is the exogenous oil
price path associated with the IMAGE demand projection utilized in the
model run. In this figure the result of the peak and decline in conventional
oil production is clear: the price rises consistently to levels that will support
production of substitutes for conventional petroleum so as to meet demand.
The production profiles for the various modeled fuels are also of interest.
Figure 5 shows oil production by region and year, Figure 6 shows tar sands
production, Figure 7 shows GTL production, and Figure 8 shows CTL pro-duction,
all in units of Gbbl/ y. This fuel production over the model run
results in a decline in capacity costs through the learning- by- doing module,
as shown in Figure 9 for tar sands and heavy oil. But, because of the deple-tion
module, this fuel production also results in a depletion- induced increase
in variable costs. DepMultiplier, defined above, is plotted by model region
for the tar sands and heavy oil resource in Figure 10. Note that regions with
small tar sands and heavy oil endowment use their resources up quickly, in-creasing
their depletion multiplier and making further production of their
resources uneconomic.
The end result of the modeled fuel production on carbon emissions is
plotted in Figure 11 as an “ emissions penalty.” This is the difference in
emissions between the model results and what emissions would have been
had the same modeled demand been met with conventional oil. Since the
alternatives to oil included in the model are all more carbon intensive than
conventional oil, the emissions penalty is positive. The results shown here
11
Figure 2: FuelProduction[ r, f, y] - supply of fuels over time, scenario s2. Values
summed over all regions for each fuel.
suggest that emissions penalties from SCPs may approach 1 GtC per year
by mid- century. This result is of a consistent order of magnitude across all
scenarios.
These results from scenario s2 are indicative of the overall results from
the eight ROMEO scenarios. In general, altering the parameters produces
straightforward and predictable changes: tightening constraints results in
a less smooth transition, a generally higher oil price and generally higher
emissions. This is because there is a correlation between fuel price and fuel
carbon emissions across the fuels studied here.
12
Figure 3: Global fuel supply, exogenous input demand from IMAGE, and
adjusted demand, summed over all regions.
Figure 4: IMAGE input oil price, ImageOilPrice[ y], bottom curve, and mod-eled
oil price from ROMEO, MarginalCost[ y], top curve.
13
Figure 5: FuelProduction[ r, oil, y] - oil production by region and year.
Figure 6: FuelProduction[ r, tar, y] - tar sands production by region and year.
14
Figure 7: FuelProduction[ r, gtl, y] - GTL production by region and year.
Figure 8: FuelProduction[ r, ctl, y] - CTL production by region and year.
15
Figure 9: Tar sands capacity costs by year, InitialCapactiyCost[ tar] × Learn-ingMultiplier[
r, y].
Figure 10: DepletionMultiplier[ r, tar, y] - tar sands/ extra heavy oil depletion
multipliers by year.
16
Figure 11: Emissions increment from the adoption of SCPs.
17
3.2 Effects of varying model parameters
What happens when ROMEO model parameters are varied? This depends
on the sensitivity of the model to the input parameter. For data inputs, this
sensitivity varies depending on how fundamental the varied data are ( e. g. a
change in total global oil endowment is more important than a change in the
initial regional cumulated production used to calibrate the learning module).
When altering constraint parameters, such as the maximum amount of ca-pacity
that can be added in a given year, the impact depends on whether
or not the constraint is binding. And lastly, some model parameters have
effects of greater importance than might be expected because of non- linear
model behavior. These non- linearities cause minor variations of certain pa-rameters
to affect the overall functioning of the model. We will illustrate
the impacts of these three types of parameter changes with three examples
below.
Altering key data inputs First, we can plot the results of altering a
key data input: the conventional oil endowment. As discussed elsewhere
[ 6, 14], the endowment of conventional oil is quite uncertain, with USGS
uncertainty bounds ( 95% to 5%) ranging from about 2000 to 4000 Gbbl of
conventional oil [ 38]. The amount of conventional oil available will affect
the speed and extent of a transition to substitutes for conventional oil.
In scenario s2, the global oil endowment parameter is set to its med level.
We can alter this to the low and high values and plot the results. The results
of altering the global oil endowment are shown in Figure 12. The impact
on the overall fuel production ( corresponding to Figure 2 above) is shown in
the left- hand figures and on the modeled oil price ( corresponding to Figure
4) in the right- hand figures. The middle results correspond to scenario s2
as shown above and their captions are highlighted in bold.
From these results we can see that lower conventional crude oil availabil-ity
has the following results: less overall fuel consumption, the transition
to substitutes for oil occurs sooner, and more SCPs are produced overall.
We also see that the highest price achieved (>$ 100/ bbl) is seen in the low
conventional oil endowment scenario These results are congruent with what
one would expect.
18
( a) Low oil endowment - production ( b) Low oil endowment - price
( c) Med oil endowment - production ( d) Med oil endowment - price
( e) High oil endowment - production ( f) High oil endowment - price
Figure 12: Change in total fuel production ( left) and modeled oil price
( right) with variations in assumed conventional oil endowment.
19
Altering a binding constraint A key binding constraint in the model is
the maximum level of capacity expansion per fuel per region per year. This
is an important model parameter because it strongly governs the adoption
of particular fuels and overall model behavior. Unfortunately, this model
parameter is uncertain.
Historical data on production capacity additions are difficult to obtain,
so production data from BP Statistical Review are used instead [ 4]. We
sort and aggregate national production data from 1965 to 2004 into the 17
IMAGE regions. We then find the largest year- to- year production growth
across the 17 model regions, excluding Russian Federation and Middle East
data because of politically- induced swings in production. The largest in-crease
over the time period for the remaining regions was 1.084 Mbbl/ d
between 1976 and 1977 for region 9, OECD Europe, a result of increased
production from significant discoveries in the North Sea.
Can SCP technologies expand at this rate of 1 mbbl/ d over a one year
period? Could this rate of expansion go on across multiple regions at the
same time? Arguments could be made in either direction regarding this
historical analogue. One could argue that production from SCPs will not be
able to grow this fast, because they are more capital intensive, are difficult to
extract, and do not exist in high- flow deposits. As an example, Canadian tar
sands production grew to 1 Mbbl/ d over three decades, not one year. One
could also argue that the urgency created by oil price increases that could
accompany a peak in conventional oil production would spur development
of SCPs as fast as has been seen historically for crude oil.
To account for this uncertainty, we choose values for maximum capacity
growth of 0.5, 0.75, and 1 Mbbl/ d capacity increase ( maxgrowth = low, med,
high, respectively). The default value for baseline scenario s2 is maxgrowth
= med. We discuss potential improvements to this constraint below in Con-clusions.
The impact of changing this model value is shown below in Figure
13. In this figure, the captions are bold for the settings corresponding to the
baseline s2 scenario. Note that the low capacity expansion setting results
in more erratic expansion of SCPs and a higher oil price. This, again, is
consistent with expectations.
20
( a) Low cap expansion - production ( b) Low cap expansion - price
( c) Med cap expansion - production ( d) Med cap expansion - price
( e) High cap expansion - production ( f) High cap expansion - price
Figure 13: Change in total fuel production ( left) and modeled oil price
( right) with variations in maximum capacity expansion. MaxGrowth = low,
med, high in top, middle and bottom figures respectively.
21
Altering a non- linear model feature It is most difficult to predict the
impact of varying a parameter related to non- linear aspects of the model.
The key non- linearities in the current version of ROMEO involve the opera-tion
of the oil market. As an example, here we explore the impact of altering
the parameter EconomicLimit from its baseline value ( see Appendix A and
the ROMEO documentation for how EconomicLimit is defined in terms of
the model equations [ 7]).
The oil market in ROMEO does not include in its oil- price- setting mech-anism
the production cost of all fuels that could be produced, but only those
that are produced. This is because the model sets the price to the cost of the
marginal ( most expensive) barrel produced. Unfortunately, if the oil market
mechanism is set to include all fuels with values of FuelProduction[ r, f, y]  0, all fuels effectively end up being included in the oil market calculation.
This is because the precision of the numerical solver is set such that small
quantities ( below 1×10− 6) are “ ignored” for the purposes of determining
model feasibility. ( If the feasibility tolerance is decreased, errors occur, such
as tiny amounts of negative production, e. g. - 1×10− 19 bbl of fuel, causing
the violation of positivity constraints.)
To solve this problem, fuels only “ enter the market,” or are included in
the calculation of the marginal cost of production, if they are produced in
quantities greater than the parameter EconomicLimit. If fuels are produced
in quantities less than EconomicLimit it is assumed that these are experimen-tal
fuels that producers do not expect to be economic under current market
conditions. In the baseline settings that produced all of the above results,
EconomicLimit is set to 0.0001825 Gbbl, or 500 barrels of fuel produced per
day. Although this is a highly uncertain number, there is some justification
for the order of magnitude used. For example, OSEC Inc., an oil shale de-velopment
company, is planning a 3- phase scale- up process for testing their
above- ground shale oil retorting technology. Phase 2 of their plan is still
clearly experimental, with 6000 bbl to be produced over the course of one
year, or roughly 20 bbl/ d [ 33, pp. 28- 29]. Phase 3 of their operation will
involve a 250 ton/ hr retort and will produce on average 2500 bbl/ d over
the two year time period [ 33, pp. 33- 36]. While the Phase 2 operation is
clearly still experimental, and is likely not expected to be economic, Phase
3 is clearly of the scale that should be approaching economic viability ( pro-ducing
2500 bbl/ d, with each barrel produced at an economic loss, seems
unrealistic for long periods of time).
To study the impact of varying this aspect of the ROMEO fuel market,
we adjust the EconomicLimit parameter from its baseline setting by one
order of magnitude in each direction. The resulting range clearly includes
22
projects that any industry would consider experimental ( 50 bbl/ d), as well
as projects that seem likely to be of economic scale ( 5000 bbl/ d). The results
of varying this value are shown in Figure 14, with the baseline result ( from
scenario s2 above) presented with a bold caption. These results show that
altering this parameter significantly changes the dynamics of the transition:
if EconomicLimit is set to a low value, the transition happens suddenly, while
if it is set to a higher value the market is less responsive and takes more
time to transition to SCPs.
23
( a) Low economic limit - production ( b) Low economic limit - price
( c) Med economic limit - production ( d) Med economic limit - price
( e) High economic limit - production ( f) High economic limit - price
Figure 14: Change in fuel production and oil price with variations in the
parameter EconomicLimit from 50 bbl/ d ( top) to 500 bbl/ d ( middle, as mod-eled
in baseline s2 scenario) to 5000 bbl/ d ( bottom).
24
3.3 A more formal uncertainty analysis: the case of conven-tional
oil endowment and a carbon tax
The ROMEO run script allows for simple specification of group scenario
runs for uncertainty analysis. To illustrate the possibilities therein, we show
an example where we vary two parameters simultaneously and tabulate the
results of this two- dimensional exploration. In this example we vary the con-ventional
oil endowment and the carbon tax. 4 We first set the conventional
oil endowment to four values: VeryLow, Low, Med, and High. The actual
input values and sources for these conventional oil estimates are given in Ta-ble
1. In addition, we vary the time path of the carbon tax to four different
settings. In the off setting, there is no carbon tax. In the low setting the
tax increases to $ 7 per metric tonne of carbon in 2010 and remains constant
thereafter. In the med and high settings the tax starts at $ 7 as above, but
increases linearly to $ 20 and $ 50 per tonne, respectively, by 2050. These two
parameters with four settings each produce a matrix of sixteen scenarios.
Four summary statistics from each of the sixteen scenarios are presented
in Table 2. Also, these summary statistics are plotted in Figure 15 as func-tions
of the two variables. The summary statistics include: the total cumu-lative
cost of meeting fuel demand plus the carbon tax paid ( in trillions of
2000$), the total cumulative amount of fuel consumed ( in trillions of bbl of
crude- oil- equivalent fuels), the “ emissions penalty” ( in gigatonnes of carbon
equivalent), and the total emissions from fuel production and consumption
( in gigatonnes of carbon equivalent). Recall that the “ emissions penalty” is
the difference between the total emissions as modeled and the total emissions
as they would be if demand were the same, but conventional oil was able
the meet all demand ( see Figure 11). The results from this two- dimensional
uncertainty analysis are congruent with what intuition would suggest:
1. Total cost of fuel consumption increases as the carbon tax increases
and as the endowment of conventional oil decreases, simply because our
assumed “ backstop” resources are more expensive than conventional
oil;
2. The total amount of fuel consumed increases with increasing conven-tional
oil endowment and decreases with an increasing carbon tax;
3. The “ emissions penalty” increases with decreasing conventional fuel
availability, since all backstop resources considered are more carbon
4 The carbon tax is an optional setting in ROMEO and is set to zero for the purposes
of the baseline scenario s2 described above.
25
intensive than conventional oil;
4. Total emissions increase with increasing conventional oil availability
and with decreasing carbon tax, because the price elasticity impact of
the more expensive fuels outweighs the increased carbon intensity of
the fuels produced.
Two phenomena of interest are illustrated by Figure 15. First, in Fig-ure
15( c) we see that the emissions penalty increases as the conventional
oil endowment decreases. This is because we have to produce more carbon-intensive
fuels to fill the gap between conventional oil supply and demand.
But, interestingly, Figure 15( d) shows that the total emissions decline with
less conventional oil availability. This, as stated above, is due to the price
elasticity of demand, which causes overall demand to drop by a sufficient
amount to counteract the impact of using more carbon intensive fuels. Thus,
whether or not this transition to oil substitutes is seen as more carbon inten-sive
depends on one’s perspective ( i. e. the baseline against which emissions
are being compared).
Also of interest is the generally weak response, across all four plots in
Figure 15, of the oil market to the magnitude of the applied carbon tax. The
potential for this type of behavior has been noted in numerous places, and
the reason is straightforward: a carbon tax affects the price of liquid fuels
less than other energy types because liquid fuels are already more expensive
when measured by energy or embodied carbon content as compared to other
fuels ( e. g. applying a carbon tax to coal- fired electric power will raise the
price proportionately much more than applying the same tax to oil, because
coal is very carbon intensive and its conversion to electricity is inefficient,
resulting in greater embodied carbon content per unit of electricity).
The potential for a more complete, multidimensional uncertainty analy-sis
is described below in Conclusions.
26
Table 1: Resource[ r,‘ oil’] - Conventional oil resource endowments as set by
supply parameter ( Gbbl) a
Regional total VeryLowb Lowc Medc Highc
Canada 50.0d 42.5 44.5 48.2
USA 67.2e 345.0 362.0 383.0
Central America 31.5 80.1 94.6 121.9
South America 64.6 196.2 274.1 419.2
Northern Africa 70.2 113.9 127.8 153.3
Western Africa 46.7 88.0 123.5 169.5
Eastern Africa 3.6 0.6 1.6 2.8
Southern Africa 6.2 14.4 24.6 40.4
OECD Europe 44.5 88.4 155.1 249.3
Eastern Europe 4.3 14.8 15.7 17.3
Former USSR 200.7 433.2 512.3 648.2
Middle East 549.2 969.2 1108.9 1323.5
South Asia 7.7 17.7 19.7 22.6
East Asia 31.9 76.3 84.9 100.8
South East Asia 34.4 63.5 73.2 89.2
Oceania 7.4 13.7 17.2 23.3
Japan 1×10− 3 1×10− 3 1×10− 3 1×10− 3
Total 1220 2557 3039 3812
a - Values of 1×10− 3 are entered for regions with no appreciable resources so as to
prevent errors from dividing by zero in the depletion module.
b - Campbell’s estimates [ 8]. To achieve congruence with USGS estimates, natural
gas liquids are added using the USGS low estimates ( highest likelihood of being
found). See full ROMEO documentation for more details [ 7].
c - US Geological Survey estimates used [ 38]. For low setting their 95% likely to
be found estimate is used, for med their mean or 50% probability estimate is used,
and for high the 5% probability estimate is used. In each case, already consumed
oil and known oil reserves [ 38, Table AR- 9] are added to the appropriate estimate
of undiscovered oil. Natural gas liquids are added as well in the same fashion. See
full ROMEO documentation for more details [ 7].
d - Campbell includes 40 Gbbl to be found in “ unforseen” location. We add this to
Canada because Campbell has a skeptical view of Canadian low- quality oil, thus,
this brings his estimate somewhat closer to other resource assessments.
e - 50 Gbbl is added to the US endowment because Campbell’s US endowment is
sufficiently low that the ROMEO runs into immediate infeasiblities if his endowment
is used.
27
Table 2: Two- dimensional analysis results. Each value results from a
ROMEO model run with the carbon tax setting specified by the top leg-end
and the conventional oil endowment specified by the left legend.
Total Cost ( T$)
Carbon tax
Conv. oil Off Low Med High
Very low 50 56 54 65
Low 45 46 51 61
Med 43 47 50 62
High 39 44 52 58
Total fuel production ( Tbbl)
Carbon tax
Conv. oil Off Low Med High
Very low 2.7 2.7 2.6 2.6
Low 2.8 2.8 2.8 2.7
Med 3.0 2.9 2.9 2.9
High 3.0 3.1 3.1 3.0
Carbon emissions penalty ( Gtonne C)
Carbon tax
Conv. oil Off Low Med High
Very low 20 21 18 17
Low 14 12 12 12
Med 10 9 8 9
High 4 4 4 3
Total emissions ( Gtonne C)
Carbon tax
Conv. oil Off Low Med High
Very low 286 293 269 269
Low 299 285 286 282
Med 311 307 300 303
High 317 318 328 305
28
( a) Total cost
( b) Fuel production
29
( c) Emissions penalty
( d) Total emissions
Figure 15: Variation in summary parameters with variation in endowment
of conventional oil and carbon tax. These plot use the data of Table 2.
30
4 Conclusions
4.1 Concluding thoughts and preliminary numerical conclu-sions
ROMEO allows increased understanding of the transition to oil substitutes
and illustrates a number of important phenomena:
1. The rate of capacity addition possible in a given region or fuel may be
a critical determinant for the fuels we produce in the future ( indeed,
such constraints are currently limiting production of conventional pet-roleum);
2. The environmental impacts of a transition to substitutes for conven-tional
petroleum are somewhat uncertain because of the impact of the
demand elasticity on total fuel consumption; and
3. The transition to substitutes for petroleum may be relatively smooth
or may be jarring, depending on the responsiveness and functioning of
the world oil market.
Additionally, some tentative quantitative results are suggested by ROMEO.
First, consistent price behavior is seen across all scenarios modeled: a “ floor”
appears under the oil price, varying by scenario, generally from $ 60 to $ 80
year- 2000 dollars per barrel of crude oil or synthetic- crude- oil. This floor
is required to support the production of fuels that replace conventional oil,
and if the price were to drop below this floor, production capacity would
be taken offline until the price rises again. This sort of behavior has been
long predicted by energy economists, and may be beginning in the current
oil market as tar sands and other marginal, expensive fuels become increas-ingly
important. As modeled in ROMEO, if the oil price were to drop below
the level at which these fuels are profitable, they would not be produced
and the price would then increase.
Secondly, the impact of a carbon tax can be seen to be fairly muted in this
model. The change in cumulated total emissions with year- 2050 carbon tax
rate ranges from 0.15 to 0.3 GtC per dollar of carbon tax applied in the year
( see Table 2). The drop by 2050, in cumulated emissions, due to the carbon
tax ranges from 8 to 17 GtC depending on the conventional oil endowment.
This is not an insignificant quantity of avoided emissions ( current global
emissions are  7 GtC per year), but it does not seem as large when compared
to cumulated total emissions from the sector ( on order 300 GtC). As noted
31
above, this effect can be compared to the electricity generation sector, where
carbon taxes of $ 50 per tonne are predicted to result in significant mitigation
efforts, including carbon capture and sequestration [ 25].
These conclusions, although preliminary, illustrate the potential for fu-ture
understanding that could be gained from an expanded version of this
model.
4.2 Possible improvements to ROMEO
There seem to be a number of ways to improve ROMEO, and some of these
improvements may be implemented in a future version of ROMEO.
A number of “ small” changes will likely be implemented in ROMEO be-fore
final publication of these results. One such change would be to improve
the capacity addition constraints in a number of ways. First, each region
could have an individual capacity addition constraint, based on historical
production capacity increases. This would account for the historical fact,
and likely continuing reality, of slower possible capacity additions in under-developed
regions of the world, such as East Africa. Alternatively, capacity
constraints could be represented in terms of capital flow, such that total
capacity investment could not increase above a given level. This, of course
would be more realistic, as it is easier to add cheap capacity than expen-sive
capacity. Another change might be to disaggregate the learning rate by
fuel: because the SCPs modeled by ROMEO are quite different ( tar sands
are much like heavy oil production, while GTL synfuel processes are more
akin to refining), there may be benefit to disaggregating the learning mod-ule
by fuel. See the full ROMEO documentation for the sources of learning
rates across the range of applicable industries [ 7].
Furthermore, a number of additions call out for inclusion in a longer-term
ROMEO project. First, the capacity addition process is not modeled
realistically in ROMEO. Because ROMEO is myopic, each model year is
solved separately, and the model cannot add capacity for future years be-cause
it does not know that those future years exist. ROMEO avoids this
problem by assuming that capacity addition can occur within one year ( that
is, production can occur in the same year that capacity construction begins).
Given that large capital projects commonly take 3 to 7 years to construct,
this assumption needs to be reworked. The solution to this problem will
likely require modeling a more sophisticated “ agency” for the model equa-tions
that govern capacity addition. This would require equations that add
capacity based on projections of future prices and future demand. Thus,
the model would look at previous years’ demand and prices, commit to
32
adding capacity based on the projected profitability of that capacity, and
wait multiple years for the capacity to become available.
Another future improvement would be to treat uncertainty in a much
more sophisticated and comprehensive manner. One potential way to do
this would be to model a large number of scenarios with ROMEO, possibly
using the “ robustness” framework of Lempert et al. [ 28]. This framework is
based on exploring a wide subset of the parameter space and by varying mul-tiple
parameters over wide ranges. A summary statistic from each run ( e. g.
total carbon emissions) can then be compared to a target value, illustrating
potential “ danger” regions, or could be plotted as surfaces such as in Figure
15. This method would require partitioning the input parameter space into
a number finely graduated segments, and running the model many times
( hundreds to thousands), varying the input parameters and recording the
output. Each outcome can then be evaluated and rated based on defined
criteria.
A third possible extension to ROMEO would be to model more than just
the liquid hydrocarbon/ petroleum system. The input data extracted from
IMAGE and used in the current version of ROMEO represent petroleum
demand after accounting for increased efficiency, fuel substitution ( biofuels,
hydrogen, etc.), and economic growth. By using these input data we assume
that the IMAGE projections for alternative fuels penetration are correct. A
more broad and interesting version of ROMEO would model some or all parts
of the broader fuel substitution question. This problem is of indeterminate
size: adding biofuels to the current model could be seen as a relatively minor
addition, while modeling systemic changes ( e. g. large- scale electrification of
transport) would require substantial reworking of the model structure.
33
5 Appendix A: Simplified ROMEO documenta-tion
This appendix is a shortened version of the complete ROMEO documen-tation,
which is available at http:// abrandt. berkeley. edu. The full model
documentation includes a glossary of model terms and additional support-ing
information ( e. g. all data inputs and data sources in tabular or graphical
form).
5.1 Modeling methodology
ROMEO is a nonlinear optimization model, coded in the AMPL mathemat-ical
programming language [ 17] and solved using the SNOPT solver [ 19]. It
models the adoption of substitutes for conventional petroleum ( SCPs) over
the years 2000 to 2050 based on the demand for liquid hydrocarbons, avail-ability
of conventional oil, the prices of SCPs, and the SCP resource base in
each of 17 model regions.
ROMEO does not solve for all fifty years of production simultaneously,
but instead solves each year sequentially, ensuring that supply equals de-mand
in each year. A “ run script” is used to call the model each year, save
results, and transfer information between model years. Some complex model
elements are included explicitly in the model, while others are implemented
through the run script ( more on this in Important model features).
Within this documentation, names of model elements ( functions, pa-rameters,
data inputs) are presented in sans serif font. Indexed elements
are presented as coded in AMPL. For example, fuel production, an element
indexed over regions ( r), synfuels ( s) and years ( y), is written FuelProduc-tion[
r, s, y]. File names are presented in typewriter font.
5.2 Objective function and constraints
Objective function
The objective function ( the function minimized by the solver) is the cost
of filling the conventional petroleum shortfall in each region by either trade
or production of SCPs. By constructing ROMEO within an optimization
framework, we assume that the world petroleum market supplies fuels at the
lowest cost ( or equivalently, at the highest profit for producers at a given
34
price). The objective function is defined as follows:
( 5) min X y
T o t a l C a p a c i t y C o s t [ y ] + X y
T o t a l P r o d u c t i o n C o s t [ y ]
+ X y
T o t a l S h i p p i n g C o s t [ y ].
The objective function is minimized in each year y. These terms can be
expanded:
( 6) T o t a l C a p a c i t y C o s t [ y ] = X r, f
N e w C a p a c i t y [ r , f , y ]
× I n i t i a l C a p a c i t y C o s t [ f ] × L e a r n i n g M u l t i p l i e r [ f , y ];
( 7) T o t a l P r o d u c t i o n C o s t [ y ] = X r, f
F u e l P r o d u c t i o n [ r , f , y ]
× [ O t h e r V a r i a b l e C o s t [ f ] + R e s o u r c e C o s t [ r , f ]] × D e p M u l t i p l i e r [ r , f , y ];
and
( 8) T o t a l S h i p p i n g C o s t [ y ] =
X r1, r2, f
F u e l S h i p p e d [ r 1 , r 2 , f , y ] × D i s t a n c e [ r 1 , r 2 ] × S h i p p i n g C o s t .
In these equations NewCapacity, FuelProduction, and FuelShipped are the
decision variables. LearningMultiplier and DepMultiplier are described below
in Important model features.
Decision variables
Decision variables are variables whose values are chosen by the solver so as to
minimize the objective function. In ROMEO, the decision variables include:
NewCapacity[ r, f, y], the amount of new production capacity added in a given
region and year for each fuel f; FuelProduction[ r, f, y], the amount of a given
fuel f produced in each region r in a given year y; and FuelShipped[ r1, r2, f, y],
the amount of fuel f shipped from a given region r1 to another region r2 in
year y.
Constraints
Constraints limit the ranges of values chosen for decision variables, ensuring
that the values are logically consistent and realistic. The constraints are:
35
1. Positivity Decision variables must be positive ( e. g. negative fuel can-not
be created):
( 9) F u e l P r o d u c t i o n [ r , s , y ]  0,
( 10) N e w C a p a c i t y [ r , s , y ]  0,
( 11) F u e l S h i p p e d [ r 1 , r 2 , f , y ]  0.
2. Demand constraint Demand must be met. Thus in each region r1
the supply of all liquid fuels5 ( conventional oil, SCPs and net imports of all
liquid fuels) must be greater than or equal to demand for liquid fuels in that
region:
( 12) X f
F u e l P r o d u c t i o n [ r 1 , f , y ] + X r1, r2, f
F u e l S h i p p e d [ r 2 , r 1 , f , y ]
− X r1, r2, f
F u e l S h i p p e d [ r 1 , r 2 , f , y ]  A d j u s t e d D e m a n d [ r 1 , y ].
for each time period y and region r1. AdjustedDemand is the demand for
crude- oil- equivalent fuels, adjusted using the price elasticity of petroleum
demand. It is described in detail in Important model features.
3. Availability of resources More resources cannot be extracted from
any region than exist in that region. For each region r, fuel f, and year y:
( 13)
y X
t= 2000
F u e l P r o d u c t i o n [ r , f , y ]  A v a i l a b l e R e s o u r c e [ r , f ],
where AvailableResource[ r, f] equals TotalResourceNotConsumedByImage[ r, f]
multiplied by ConversionFactor[ f]. ConversionFactor[ f] accounts for losses in
converting fuels from their primary energy type to modeled fuel production
( it is equal to 1 except for CTL and GTL, as other resources are measured
in units of crude oil volume). TotalResourceNotConsumedByImage[ r, f] is the
total available resource from which ROMEO draws. See Appendix A for
more details.
5 Although omitted here for simplicity, the model equation multiplies each fuel by a
factor called CrudeOilEquivalence[ f]. This corrects for the fact that the model accounts for
volumes of crude oils produced, but CTL and GTL produced finished fuels, thus displacing
more than 1 unit of crude for each unit produced. See discussion in Appendix A.
36
4. Speed of resource extraction This constraint limits the percentage
of remaining resource that can be extracted in a given year:
( 14) F u e l P r o d u c t i o n [ r , f , y ] 
M a x A n n u a l P e r c e n t a g e × ( A v a i l a b l e R e s o u r c e [ r , f ]
− C u m u l a t i v e F u e l P r o d u c t i o n R e s o u r c e C o n s u m p t i o n [ r , f , y ]).
In this constraint MaxAnnualPercentage is the percentage of the total re-source
that can be extracted in each year ( See full ROMEO documentation
for values [ 7]). This constraint stabilizes model output. Without this con-straint,
regions can increase production sharply and deplete their resources
in only a few years. Also, this constraint governs the overall shape of increas-ing
and decreasing production of a resource, being, in effect, an exponential
model of resource extinction. 6 CumulativeFuelProductionResourceConsump-tion
is the amount of resource consumed producing fuel since the model
began. See equation in Appendix A.
5. Production is constrained by capacity This constraint limits the
production of fuels in each region to less than or equal to the fuel production
capacity. For all regions r, fuels f, and years y:
( 15) F u e l P r o d u c t i o n [ r , f , y ] 
N e w C a p a c i t y [ r , f , y ] + F u n c t i o n a l C a p a c i t y [ r , f , y ].
Note that because NewCapacity[ r, f, y] is included in the constraint, we as-sume
that new capacity can come online within a one year time period
( This does not cohere with actual practice, but significantly improves model
functioning. See discussion below in Potential for future improvements to
ROMEO).
6. Trade is constrained by production The amount of fuel f shipped
out of a region r1 must be less or equal to production of that fuel in that
region. So, for all regions r1, fuels f, and years y:
( 16) X r2
F u e l S h i p p e d [ r 1 , r 2 , f , y ]  F u e l P r o d u c t i o n [ r 1 , f , y ].
6 Exponential models of oil depletion have been explored by Wood et al. [ 41], and were
found to be as good as or superior to the Hubbert ( Gaussian) model in a systematic
comparison of 139 oil producing regions [ 6].
37
7. Capacity does not grow too quickly Capacity additions in each
year y and region r for fuel f are limited. This constraint models the limita-tions
on the ability of the market to access capital and construct production
capacity. Without this constraint, unrealistic solutions are found by the
solver ( e. g. replicating one- third of the existing global oil infrastructure in a
single region in a single year). Thus:
( 17) N e w C a p a c i t y [ r , f , y ]  M a x C a p a c i t y G r o w t h .
5.3 Important model features
There are three complex model functions that are key to model functioning.
These include adjusting demand given the price of fuels prevalent in a given
year, the effect of resource depletion on the cost of production, and the
technical learning associated with growth of industries.
These features are implemented in two ways. First, the effect of price on
demand is explicitly written into the model structure. Therefore it affects
the model as seen by the solver and makes the model non- linear. The other
two features of the model described above are defined “ outside” the model.
They operate within the run script that carries the model from year to year,
saves results, and updates cumulated parameters. Therefore, these features
of the model are seen as linear from the point of view of the solver ( they
are dependent on unvarying parameters), although they are dynamic across
years. This layered model structure is illustrated in Figure 16. Ideally all
model features would be included explicitly in the model structure. Unfor-tunately,
this would make the model significantly more non- linear and thus
more difficult to solve.
Price elasticity of petroleum demand
The elasticity of petroleum demand with respect to price is modeled in
ROMEO. As the price of the marginal barrel of liquid fuel in ROMEO
increases above the price at which the IMAGE demand was modeled, de-mand
is reduced below the level modeled in IMAGE. This is implemented
as follows:
( 18) A d j u s t e d D e m a n d [ r , y ] = D e m a n d [ r , y ]
× ( 1 + [( P r i c e R a t i o [ y ] − 1) × D e m a n d E l a s t i c i t y ])
× ( 1 + [( L o n g P r i c e R a t i o [ y ] − 1) × R e g i o n a l L o n g D e m a n d E l a s t i c i t y [ r ]]),
38
Figure 16: ROMEO model structure, interaction between run script and
model.
where DemandElasticity is the short- run price elasticity of liquid fuel de-mand,
and RegionalLongDemandElasticity[ r] is the region- specific long- run
price elasticity of petroleum demand. Demand[ r, y] is the exogenous base-line
demand from IMAGE ( again, see full ROMEO documentation for more
details [ 7]).
The parameter PriceRatio[ y] is the ratio of the current year’s cost of pro-duction
for the marginal barrel of fuel produced ( or the price in a competitive
market) to the current year’s input oil price from IMAGE. LongPriceRatio[ y]
is the ratio of a long- run weighted price to the current year’s price from
IMAGE. Since the IMAGE oil prices are the prices at which our exogenous
input demand was forecast, these ratios show how much higher our modeled
prices are than the prices that generated the input demand. These ratios
are defined as follows:
( 19) P r i c e R a t i o [ y ] = M a r g i n a l C o s t [ y ]
I m a g e O i l P r i c e [ y ]
,
39
and
( 20) L o n g P r i c e R a t i o [ y ] = A v e r a g e M a r g i n a l C o s t X Y e a r H i s t o r i c a l [ y ]
I m a g e O i l P r i c e [ y ]
.
In the LongPriceRatio equation “ X” represents the string ‘ five’, ‘ ten’, or
‘ twenty’ depending on the number of years over which the long- run price is
averaged ( i. e. the long- run price is computed over the last 5, 10 or 20 years).
This parameter is controlled through the LongElastTime parameter, and the
default value is twenty years. As an example, AverageMarginalCostThree-
YearHistorical[ y], if it were to be used, would be defined as follows:
( 21) A v e r a g e M a r g i n a l C o s t T h r e e Y e a r H i s t o r i c a l [ y ] =
( M a r g i n a l C o s t [ y ] +  · M a r g i n a l C o s t [ y − 1 ] +  2 · M a r g i n a l C o s t [ y − 2 ])
1 +  +  2 .
In this equation, MarginalCost[ y] is the current year’s marginal cost of
production, MarginalCost[ y- 1] 7 is the marginal cost from the previous year’s
model run, etc. The parameter  , named ThetaElasticity in the model, is
the decay rate of the influence of prior year’s prices. This formulation is
adapted from Gately and Huntington [ 18, Table 6], and we use their value
of  , 0.84 derived from non- OECD regions. 8
The effect of this equation is to have previous years’ prices affect demand
in the current model year, with decaying impact over time. Gately and
Huntington, when calculating their estimates for long- run demand elasticity,
did not truncate the effect of any year’s price, but included all of their data
( there is little effect from including more data: given the decay implied by
 , prices occurring 20 years previous to the modeled year are multiplied by
 19 ( 0.8419, or 0.0002), and so have little effect on model results).
In these equations, MarginalCost[ y] is defined as the cost of production
of the highest- priced barrel of fuel produced in the model. It is calculated
as follows:
( 22) M a r g i n a l C o s t [ y ] =
if max
r, f
B r e a k E v e n P r i c e [ r , f , y ]  I m a g e O i l P r i c e [ y ],
then max
r, f
B r e a k E v e n P r i c e [ r , f , y ], else I m a g e O i l P r i c e [ y ].
7 The model actually uses AnnualMarginalCost[ y- 1] etc. in this equation, because
MarginalCost[ y] does not store previous year’s model results.
8 It is unclear whether this non- OECD value of  or the OECD value would be more
accurate to use over the time period of the model, so this value is chosen because of the
likely future increase in non- OECD demand.
40
Where BreakEvenPrice is defined as follows:
( 23) B r e a k E v e n P r i c e [ r , f , y ] = if F u e l P r o d u c t i o n [ r , f ]  E c o n o m i c L i m i t then
L e a r n i n g M u l t i p l i e r [ f ] × ( C a p i t a l R e c o v e r y F a c t o r × I n i t i a l C a p a c i t y C o s t [ f ])
+ D e p M u l t i p l i e r [ r , f ] × ( O t h e r V a r i a b l e C o s t [ f ] + R e s o u r c e C o s t [ r , f ]).
BreakEvenPrice is only defined for fuels that meet a minimum economic level
of production, which helps to eliminate the “ knife- edge” behavior that oc-curs
when tiny amounts of an expensive fuel are produced and drive up the
cost of the marginal barrel of fuel. EconomicLimit is the minimum amount
of production above which we can assume that fuels will need to be eco-nomic.
That is, if fuels are produced in less than this quantity, they can be
seen as “ experimental” or in the scale- up stage, and not be expected to be
traditionally profitable. Therefore the cost of producing these fuels does not
affect the going price of fuels.
The learning effect
ROMEO models the declining cost of production that occurs due to experi-ence
gained over time. This effect is commonly called “ learning by doing.”
This effect is calculated using the Wright learning model [ 29]:
( 24) Y = aX− b
where Y represents cost of production, a is the cost of the first unit of out-put,
X represents cumulated output, and b represents the learning elasticity
[ 29].
Since the initial cost of production for the first unit is not available, we re-quire
X in multiples of the initial cumulative production ( InitialCumulativeProduction).
We call parameter b the LearningRate[ f] and a the InitialCapicityCost. Thus,
InitialCapacityCost[ f] is multiplied by a learning multiplier:
( 25) L e a r n i n g M u l t i p l i e r [ f , y ] =  C u m u l a t i v e G l o b a l P r o d u c t i o n [ f , y ]
I n i t i a l C u m u l a t i v e G l o b a l P r o d u c t i o n [ f ]  L e a r n i n g R a t e [ f ]
.
We use cumulative output rather than cumulative capacity additions be-cause
“ cumulated industry output is the best single proxy for learning” [ 29].
Because of poor data availability, each fuel in ROMEO is subject to the same
learning rate. As a further simplification, learning affects capital costs only.
The full ROMEO documentation includes more discussion of the learning
rate [ 7].
41
Resource depletion
The depletion cost multiplier, DepMultiplier[ r, s, y], increases the cost of pro-duction
as a resource is depleted. Our model is based on the oil depletion
model of Greene et al. [ 20]. DepMultiplier[ r, s, y] affects the variable cost of
production of synfuels. Thus it acts in opposition to the learning effect:
as production increases, learning lowers the capital costs, but depletion in-creases
the variable costs. 9 The depletion multiplier is equal to:
( 26) D e p M u l t i p l i e r [ r , f , y ] =
ln  1
D e p l e t i o n R a t i o [ r , f , y ] − 1  − A l p h a [ r , f ]
I n i t i a l C o s t D e p l e t i o n [ r , f ] × B e t a [ r ]
,
where DepletionRatio[ r, f, y] is the fraction of total resource endowment de-pleted
( See Appendix A). InitialCostDepletion[ r, f] is the total variable cost
of resource f at time y = 2000. This functional form results in variable
costs that rise rapidly at first, then level off, and begin to finally rise rapidly
again once depletion reaches a significant level. The parameters Alpha[ r, f]
are tuning parameters that fit the curve to each region. Due to lack of data
we assume a value of 0.15 for Beta[ r] for all regions, as did Greene et al. [ 20].
Alpha[ r, f] are obtained using the initial state of depletion and initial cost.
Because the depletion multiplier is nonlinear ( logarithmic), we simplify
its implementation. First, it is evaluated between years, not within each
model year. That is, the depletion multiplier is calculated using the deple-tion
level from the previous year ( CumulativeResourceConsumption [ r, f, y] is
defined as the cumulative consumption up to that year, not including the
consumption in the year currently being modeled). This makes depletion lin-ear
from the viewpoint of the solver, allowing more reliable solutions. 10 Sec-ond,
each region needs an endowment of each resource because the depletion
multiplier is undefined if there is zero resource. Small amounts of each re-source
( 1×10− 3) are added to each region where data on the resource endow-ment
could not be found. Third, when the depletion ratio is zero, i. e., when
none of the resource has been exploited, the function is also undefined. Thus,
all regions with no production to date ( InitialCumulativeResourceConsumption
[ r, f]) are given a nominal production- to- date of 1×10− 4. Lastly, the function
9 In the case of tar and shale, DepMultiplier modifies only the OtherVariableCost term in
the objective function ( because tar sands/ extra- heavy oil and shale have zero Resource-
Cost), while in GTL and CTL production, it modifies OtherVariableCost as well as Resource-
Cost, the cost of feedstock natural gas and coal.
10 For reliable solutions, nonlinear aspects of large models such as ROMEO should be
linearized as much as possible [ 17].
42
approaches 1 as depletion approaches 100%. Thus, the depletion multiplier
is only defined for DepletionRatio[ r, s, y] between 0.001 and 0.999.
There are shortcomings with this implementation. It is not clear that the
effects of depletion will be solely to increase the variable cost of production.
Indeed, it is easy to argue that depletion could affect the capital costs of
production as well as the variable costs. But, in order to simplify the model,
depletion only acts on the variable costs of production in this version of
ROMEO.
5.4 Scenarios in ROMEO
ROMEO is run over a number of base- case scenarios. Possibilities for op-tional
exploratory scenarios are also described.
Base- case scenarios
Base- case scenarios provide an illustration of model functioning. These base-case
scenarios are “ economic” scenarios. In them the supply and trade of
fuels is governed only by cost, and restrictions due to non- economic factors
are not included. The settings for the baseline scenarios are shown in Table
3.
There are eight base- case scenarios modeled. Scenarios 1- 6 are grouped
into two categories: low cost ( scenarios 1- 3) and high cost ( scenarios 4- 6).
In scenarios 1- 3, demand is set to medium, while supply of conventional oil
varies from low ( scenario 1), to medium ( scenario 2), to high ( scenario 3).
In all of these scenarios the cost of fuels is low ( e. g. oilcost = low). The cost
parameter adjusts the variable costs, capital costs, conversion efficiencies,
and emissions in unison ( i. e. “ cost” is broadly defined), so this set of scenar-ios
can be seen representing a smoother, easier transition to low- polluting
fuels. In scenarios 4- 6, the settings are the same as scenarios 1- 3, except
all fuel cost parameters are set to high ( e. g. tarcost = high) and the maxi-mum
rate at which capacity can be added is set to low ( maxgrowth = low).
These scenarios therefore represent a more difficult transition to more costly,
environmentally damaging fuels.
Scenario 7 is a “ best case” scenario: supply of conventional oil is high,
while demand remains low. Costs are low, emissions are low, and the limit
on capacity growth is high, ensuring a more smooth transition. Scenario
8 is a “ worst case” scenario: supply of conventional oil is low, demand is
high, costs and emissions of substitutes are high, and the rate of capacity
addition is slow. In addition, the short- and long- run elasticities of petrol-
43
Table 3: Parameter settings for studied baseline scenariosa, b
Scenario Demand Supply Fuel
Costsc
Conv.
Eff.
Emiss. Demand
Elast. d
Max.
growth
1 M L L H L H M
2 M M L H L H M
3 M H L H L H M
4 M L H L H H M
5 M M H L H H M
6 M H H L H H M
7 L H L H L H H
8 H L L H L L L
a - L = low, M = medium, H = high
b - A number of the parameters remain constant across all eight baseline scenarios:
deplete = yes, longelasttime = twenty, maxperc = med, disrupt = no, import = no,
and expensivegas = no.
c - SCP costs are varied in unison with efficiency and emissions. That is, high cost
is always paired with low efficiency and high emissions, while low cost is paired
with high efficiency and low emissions. There remains the possibility to study the
effects of increasing one of the costs individually to ascertain the possible effects of
an optimistic viewpoint for costs of a certain SCP.
d - In no scenarios do we turn off the price elasticity of petroleum demand.
eum demand are low, such that very high price spikes are needed to induce
demand reductions.
Exploratory scenarios
A number of exploratory scenarios will be implemented in future versions of
ROMEO. These include policy- relevant scenarios such as a carbon tax sce-nario,
or import limitation scenarios. These also might include geopolitical
scenarios that involve oil production disruption due to conflict.
5.5 Post- optimization calculation of emissions
After production is modeled, the resulting emissions are calculated. The
total volume of crude fuels produced is multiplied by production emissions.
Only a portion of hydrocarbon output is refined, and the rest is used in
chemical feedstocks or in an unrefined state ( such as in power production or
industrial boiler applications). The fraction refined is multiplied by produc-
44
tion, and this quantity for each fuel is multiplied by refining emissions. 11 We
use the fraction of crude production refined as given by IMAGE: Fraction-
Refined[ y] [ 23]. For simplicity, refining emissions are assumed to be equal
for all fuels that require refining. Combustion of the finished, refined fuel
is assumed to result in equal emissions for all fuel types. Three primary
equations calculate emissions in each year: 12
( 27) M o d e l e d P r o d u c t i o n E m i s s i o n s [ y ] =
X r X f
( F u e l P r o d u c t i o n [ r , f , y ] × P r o d u c t i o n E m i s s i o n s [ f ]),
( 28) M o d e l e d R e  n i n g E m i s s i o n s [ y ] =
X r X f
F u e l P r o d u c t i o n [ r , f , y ] × F r a c t i o n R e  n e d [ y ] × R e  n i n g E m i s s i o n s [ f ],
and
( 29) M o d e l e d C o m b u s t i o n E m i s s i o n s [ y ] =
X r X f
F u e l P r o d u c t i o n [ r , f , y ] × C o m b u s t i o n E m i s s i o n s [ f ].
And, summing these emissions components we arrive at total emissions.
( 30) M o d e l e d T o t a l E m i s s i o n s [ y ] = M o d e l e d P r o d u c t i o n E m i s s i o n s [ y ]
+ M o d e l e d R e  n i n g E m i s s i o n s [ y ] + M o d e l e d C o m b u s t i o n E m i s s i o n s [ y ].
These emissions can be compared to “ baseline” emissions that would
occur if fuel production were the same as our modeled cases, but demand
until 2050 was filled with conventional oil with constant emissions per unit
of energy:
( 31) B a s e l i n e P r o d u c t i o n E m i s s i o n s [ y ] =
X r X f
( F u e l P r o d u c t i o n [ r , f , y ] × P r o d u c t i o n E m i s s i o n s [ o i l ]),
11 CTL and GTL synfuels produce synthetic finished fuels as modeled in this analysis,
not synthetic crude oil.
12 In the actual model code AnnualFuelProduction[ r, f, y] is used, as this stores the values
of FuelProduction[ r, f, y] from each year.
45
( 32) B a s e l i n e R e  n i n g E m i s s i o n s [ y ] = X r X f
F u e l P r o d u c t i o n [ r , f , y ]
× F r a c t i o n R e  n e d [ y ] × R e  n i n g E m i s s i o n s [ o i l ],
and
( 33) B a s e l i n e C o m b u s t i o n E m i s s i o n s [ y ] =
X r X f
( F u e l P r o d u c t i o n [ r , f , y ] × C o m b u s t i o n E m i s s o n s [ o i l ]).
Again, we can sum these emissions to arrive at total baseline emissions:
( 34) B a s e l i n e T o t a l E m i s s o n s [ y ] = B a s e l i n e P r o d u c t i o n E m i s s i o n s [ y ]
+ B a s e l i n e R e  n i n g E m i s s i o n s [ y ] + B a s e l i n e C o m b u s t i o n E m i s s i o n s [ y ].
The parameter IncrementalSynfuelEmissions[ y] is the key diagnostic pa-rameter
used to understand the emissions consequences over the model run.
It is plotted over time in Figure 11 and is defined as follows:
( 35) I n c r e m e n t a l S y n f u e l E m i s s i o n s [ y ] =
M o d e l e d T o t a l E m i s s i o n s [ y ] − B a s e l i n e T o t a l E m i s s i o n s [ y ].
Even more concisely, CumulativeIncrementalSynfuelEmissions presents the
total emissions impacts over the 50- year modeling period in a single value:
( 36) C u m u l a t i v e I n c r e m e n t a l S y n f u e l E m i s s i o n s =
2050 X y= 2000
I n c r e m e n t a l S y n f u e l E m i s s i o n s [ y ].
This value is used in tabular comparison of the results from different sce-narios.
46
6 Acknowledgements
Preparation of this report was supported by a competitive grant from the
University of California Energy Institute. Support was provided for an ear-lier
incarnation of this research by the Climate Decision Making Center.
This Center is supported by a cooperative agreement between the National
Science Foundation ( SES- 034578) and Carnegie Mellon University. Richard
Plevin provided the original translation of ROMEO from Excel to AMPL
code, and offered much assistance along the way. Helpful comments were
provided by members of the University of California Energy Institute, espe-cially
Jim Bushnell. Helpful comments were also provided by attendees of
the DOE/ EPA Modeling the oil transition workshop in April of 2006.
References
[ 1] Andrews, S. and Udall, R. Oil Prophets: Looking at World Oil Studies Over
Time. In Campbell, C. J., editor, International Workshop on Oil Depletion
2003, Paris, France, 2003. ASPO. Available from: http:// www. peakoil. net/
iwood2003/ iwood2003. html.
[ 2] Bartis, J. T., LaTourrette, T., Dixon, L., Peterson, D. J. and Cecchine, G. Oil
shale development in the United States: Prospects and policy issues. Technical
report, RAND, 2005.
[ 3] Bentley, R. W. Global oil & gas depletion: an overview. Energy Policy,
30( 3): 189– 205, 2002.
[ 4] BP. BP Statistical Review of World Energy. Technical report, British Petrol-eum,
June 2005.
[ 5] Brandt, A. R. Testing Hubbert. Energy Policy, 35( May): 3074– 3088, 2007.
[ 6] Brandt, A. R. and Farrell, A. E. Scraping the bottom of the barrel: CO2
emission consequences of a transition to low- quality and synthetic petroleum
resources. Climatic Change, 84( 3- 4): 241– 263, 2007.
[ 7] Brandt, A. R., Plevin, R. J. and Farrell, A. E. Documentation for ROMEO:
the regional optimization model for emissions from oil substitutes. Techni-cal
report, Energy and Resources Group, University of California Berkeley,
January 15 2008.
[ 8] Campbell, C. J. Regular conventional oil production to 2100 and resource
based production forecast, August 15th 2006. Available from: http:// www.
oilcrisis. com/ campbell/.
[ 9] Campbell, C. J. and Laherrere, J. The end of cheap oil. Scientific American,
278( 6), 1998.
47
[ 10] Cooper, J. C. B. Price elasticity of demand for crude oil: estimates for 23
countries. OPEC Review, 2003( March): 8, 2003.
[ 11] Deffeyes, K. S. Hubbert’s Peak: The Impending World Oil Shortage. Princeton
University Press, Princeton, Oxford, 2001.
[ 12] Deffeyes, K. S. Beyond oil: the view from Hubbert’s peak. Hill and Wang, New
York, 1st paperback edition, 2005.
[ 13] Dyni, J. R. Geology and resources of some world oil- shale deposits. Technical
Report 2005- 5294, US Geological Survey, US Department of the Interior, 2006.
[ 14] Farrell, A. E. and Brandt, A. R. Risks of the oil transition. Environmental
Research Letters, 1( 1), 2006.
[ 15] Fisher, A. C. Resource and Environmental Economics. Cambridge Surveys
of Economic Literature. Cambridge University Press, Cambridge, New York,
1981.
[ 16] Fleisch, T. H., Sills, R. A. and Briscoe, M. D. 2002 - Emergence of the Gas- to-
Liquids Industry: a Review of Global GTL Developments. Journal of Natural
Gas Chemistry, 2002( 11): 1– 14, 2002.
[ 17] Fourer, R., Gay, D. M. and Kernighan, B. W. AMPL: A modeling language
for mathematical programing. Brooks/ Cole Thomson Learning, Pacific Grove,
CA, Second Edition edition, 2003.
[ 18] Gately, D. and Huntington, H. G. The asymmetric effects of changes in price
and income on energy and oil demand. Energy Journal, 23( 1): 19– 55, 2002.
[ 19] Gill, P., Murray, W. and Saunders, M. SNOPT, 2007. Available from: http:
// www. sbsi- sol- optimize. com/ asp/ sol product snopt. htm.
[ 20] Greene, D. L., Hopson, J. L. and Li, J. Running out of and into oil: Analyzing
global oil depletion and transition through 2050. Technical Report ORNL/ TM-
2003/ 259, Oak Ridge National Laboratory, October 2003.
[ 21] Greene, D. L., Hopson, J. L. and Li, J. Have we run out of oil yet? Oil peaking
analysis from an optimists perspective. Energy Policy, 34: 515– 531, 2006.
[ 22] Hanley, N., Shogren, J. F. and White, B. Environmental Economics: in theory
and practice. Oxford University Press, New York, 1996.
[ 23] IMAGE. The IMAGE 2.2 Implementation of the SRES Scenarios: a compre-hensive
analysis of emissions, climate change, and impacts in the 21st century,
July 2001.
[ 24] IPCC. Special Report on Emissions Scenarios. Cambridge University Press,
Cambridge, UK, 2000.
[ 25] IPCC. Special Report on Carbon Dioxide Capture and Storage. Cambridge
University Press, Cambridge, UK, 2005.
48
[ 26] Kerr, R. A. ENERGY SUPPLIES: Bumpy Road Ahead for World’s Oil. Sci-ence,
310( 5751): 1106– 1108, 2005. Available from: http:// www. sciencemag. org.
[ 27] Krichene, N. World crude oil and natural gas: a demand and supply model.
Energy Economics, 24(( 2002)): 557– 576, 2002.
[ 28] Lempert, R. J., Popper, S. W. and Bankes, S. C. Shaping the next one hundred
years: new methods for quantitiative, long- term policy analysis. RAND, Santa
Monica, CA, 2003.
[ 29] Liberman, M. B. The learning curve and pricing in the chemical processing
industries. RAND Journal of Economics, 15( 2): 213– 228, 1984.
[ 30] Moritis, G. EOR continues to unlock oil resources. Oil & Gas Journal,
102( 14): 45–+, 2004.
[ 31] NEB. Canada’s oil sands: opportunities and challenges to 2015. Technical
report, National Energy Board, Canada, May 2004.
[ 32] Nordhaus, W. D. Allocation of Energy Resources. Brookings Papers on Eco-nomic
Activity, 3: 529– 570, 1973.
[ 33] OSEC. Oil shale research, development, and demonstration project: White
River mine, Uintah County, Utah. Technical report, Oil Sands Exploration
Company and U. S. Department of the Interior, Bureau of Land Management,
Vernal field office, September 18 2006.
[ 34] Rogner, H. H. An assessment of world hydrocarbon resources. Annual Review
of Energy and the Environment, 22: 217– 262, 1997.
[ 35] Sato, S. and Enomoto, M. Development of new estimation method for CO2
evolved from oil shale. Fuel Processing Technology, 53( 1997): 41– 47, 1997.
[ 36] Slade, M. E. Trends in Natural- Resource Commodity Prices: An Analysis of
the Time Domain. Journal of Environmental Economics and Management,
9( June): 122– 137, 1982.
[ 37] Sundquist, E. T. and Miller, G. A. Oil shales and carbon dioxide. Science,
208( 4445): 740– 741, 1980.
[ 38] U. S. Geological Survey World Energy Assessment Team, U. U. S. Geological
Survey World Petroleum Assessment 2000. Technical report, USGS, 2000.
[ 39] Williams, B. Heavy hydrocarbons playing key role in peak- oil debate, future
energy supply. Oil & Gas Journal., 101( 29): 20, 2003.
[ 40] Withagen, C. Untested hypotheses in non- renewable resource economics. En-vironmental
& Resource Economics, 11( 3- 4): 623– 634, 1998.
[ 41] Wood, J. H., Long, G. and Morehouse, D. F. Long term oil supply scenarios:
the future is neither as rosy or as bleak as some assert. Technical report,
Energy Information Administration, 2000.
49