Hubbert oil peak and
Hotelling rent revisited
by a simulation model
OTAE 2009
July 7th, 2009, at Mines-ParisTech
Pierre-Noël GIRAUD
Aline SUTTER – Timothée DENIS
(CERNA, Mines ParisTech)
(EDF R&D)
Outline
Questions addressed
Model principles
Results
2
•
Single agent exploring 1 global area
•
Single agent exploring 2 areas
•
Stackelberg oligopoly
At stakes: the oil price trajectory on the long term
Peak oil: why and when?
Scarcity rent: when and how much?
Gb
$/bl
demand for fuel
At peak oil:
oil price = substitute price
late asymmetrical peak with
sharp dropping
Marginal
extraction cost
Hubbert symmetrical peak
year
2010 ?
3
2050 ?
Hubbert oil peak
Starting point
Hubbert forecasted the 48-US oil production peak 15 years in advance (with a 1
year error!)
4
1956
Hubbert oil peak
Total production of a multi-deposit region is supposed to show a peak
when half of total reserves is depleted
What happens with more realistic exploration dynamics
 exploration responding to price signals?
production path of several oil wells through time
At a global scale, the symmetry of the total production profile is
subjected to strong hypothesis related to the exploration strategy
5
Hotelling rent
Assumptions
no arbitrage
opportunity
production of resource is
optimal any time
constant discounted
scarcity rent over time
random
P  Pe  ( Ps  Pe ) exp( r (T  T0 ))
Hotelling scarcity rent
What happens if T0 is a random variable with a decreasing variance along time?
6
Model
7
Model type and objectives
A simulation model with two representative agents:
One explorer-producer representing a set of competing companies: it minimizes the cost
of meeting the demand of the next time step
The owner of the marginal oilfield in production who hedges between holding oil reserves
or financial assets
The model accounts for:
The need to explore before producing oil
Oil production technical constraints
A learning process on the volume and cost of the remaining reserves
The explorer- producer being a myopic cost minimizing agent with imperfect but
improving information
Oilfield owners with imperfect but improving information
8
Model Structure
Exploration-Production
heuristics
Learning process about
reserves
The marginal oilfield
owner
The explorer-producer
explores and
produces to meet
the (exogenous)
demand at
minimal cost
improves the
common
knowledge on
the remaining
reserves
marginal production cost
assess the risk of
holding oil as an
asset
Hotelling scarcity rent
Oil Price
9
Hotelling scarcity rent
calculation
The learning process on reserves
At the beginning
the agent only knows the total number of oilfields: N ( number of sedimentary basins with oilfields)
but it ignores the sizes ( index i) and extraction costs ( index j) of the oilfields to be discovered
It will then use the outcome of its exploration campaigns to progressively update its
knowledge
He simply assume the actual distribution by size and extraction costs of the N deposits is homothetic to the sample already discovered.
He then computes an estimated peak oil date, and knows the standard deviation of this estimate
He also compute the probability of discovering an oilfield of size i and extraction cost j during the next campaign
Coefficient of variation (mean over 100 scenarios)
Total oil left estimated by agent (Gb)
3 000
160%
140%
2 500
120%
2 000
(Gb)
100%
1 500
80%
60%
1 000
40%
500
20%
0%
0
1
10
21
41
61
81 101 121 141 161 181 201 221 241 261 281 301 321
Explorations
1
21
41
61
81 101 121 141 161 181 201 221 241 261 281 301 321
Exploration heuristics
The explorer producer agent explores as to minimize the cost of
meeting the demand only for the following time steps
the agent owns an oilfield portfolio inherited from his
exploration/production decisions in the past
it then computes for each period an exploration level which minimizes the cost of
meeting the demand for the next steps:
E[Cost exploration] + E[marginal Cost production(new port.)]
be less or equal than
E[marginal Cost production(old port.)]
it proceeds with exploration, which randomly returns the size and production
cost of the discovered oilfields
11
Exploration heuristics
The expected total cost curve shows minimum
12
Production constraint
Demand is satisfied by putting new oilfields into production, in the
increasing cost order
Under a technical constraint: an oilfield yields a constant rate of
production during  years
Production
more realistic shape
Time
13
Profile of a producing oilfield
Inferring Hotelling rent
Hotelling rent is computed by considering the oil deposit as a
financial asset
characterized by an expected level of risk and return
The equilibrium rent level is then set through hedging with
financial assets
P  Pe  ( Ps  Pe ) exp( r (T  T0 ))
CAPM
45%
40%
35%
30%
E(r)
buying an oilfield
and keeping the
oil in the ground
till depletion date
25%
20%
15%
10%
5%
0%
buying a financial
asset with the
same risk
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0%
20%
40%
60%
V(r)
80%
100%
120%
Current Model calibration
constant and inelastic demand: D = k t
5 cost-differentiated types of oil available spread into 330 unknown oilfields of 3
different sizes (see below)
constant discovery cost per oilfield
randomness on both size and production cost of discovered oilfields
infinitely and immediately available backstop technology at 100 $/bl
15
Volume (Gb) /
Extraction cost ($/b)
15
25
35
45
55
2
0
0
77
77
76
12
0
32
30
30
0
58
4
4
0
0
0
Results
Single agent exploring
one global area
16
Results: single actor / mono zone
1 scenario – exploration non caped
Results: single actor / mono zone
1 scenario – exploration caped
Results: single actor / mono zone
100 scenarii exploration caped
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Comments
No symmetric peak oil at the world level, unless exploration is
caped
Results
Single agent exploring 2 areas
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Simulation data
Area 1: larger and more competitive reserves
Area 2: smaller and more expensive reserves
oilfields
oilfields
oilfields
oilfields
oilfield
22
Allocating exploration between the two regions
Gmax,1
1 eopt ,1  eopt , 2
e1 
2
2
Gmax,1  Gmax, 2
Gmax, 2
1 eopt ,1  eopt , 2
e2 
2
2
Gmax,1  Gmax, 2
With:

ei , the exploration level in region i

eopt ,i , the exploration level which would optimally meet total demand in region i

Gmax, i , the maximum earning in region i coming from meeting total demand in region i
Results: single actor / 2 areas
1 scénario exploration non caped
24
Results: single actor / 2 areas
1 scénario exploration caped in area 1 ( most favourable zone)
Comments
A peak oil appears in region 2, the region which has
progressively proved to be less favourable
The case of the USA exhibited by Hubbert ?
All the more when exploration is caped in the more favourable
region: the middle East ?
Stackelberg oligopoly
OPEC as the heart of an
oligopoly with a competitive
fringe
(preliminary)
27
Introducing OPEC
OPEC : Stackelberg oligopoly with a competitive fringe
competitive fringe
has to explore to satisfy demand
minimizes its costs
oligopoly
owns most low cost oil reserves and knows them (no need to explore)
maximises its profit
has to forecast the fringe exploration strategy
perfectly anticipates the fringe exploration outcome
work in progress: faces the random result of exploration as the fringe does
28
OPEC – competitive fringe
Modelling of interaction
29
Results Stackelberg oligopoly
1 scénario
30
Comments
An intriguing result:
Optimal oligopoly behaviour leads to price instability….
It’s still a work in progress...
Comments warmly welcome on:
That type of model
Modelling the learning process
Oil fields owners behaviour
Modelling the choice between the two zones
Thanks for your
attention
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