1. Hubbert oil peak and Hotelling rent revisited by a simulation model
OTAE 2009
July 7th, 2009, at Mines-ParisTech
Pierre-Noël GIRAUD (CERNA, Mines ParisTech)
Aline SUTTER – Timothée DENIS (EDF R&D)

2. Outline Questions addressed Model principles Results
Single agent exploring 1 global area
Single agent exploring 2 areas
Stackelberg oligopoly 2

3. At stakes: the oil price trajectory on the long term Peak oil: why and when? Scarcity rent: when and how much? Gb
$/bl
At peak oil:
oil price = substitute price
demand for fuel
late asymmetrical peak with sharp dropping
Marginal extraction cost
Hubbert symmetrical peak
year
2010 ?
2050 ? 3

4. Hubbert oil peak Starting point
Hubbert forecasted the 48-US oil production peak 15 years in advance (with a 1 year error!) 4
1956 4

5. Hubbert oil peak
Total production of a multi-deposit region is supposed to show a peak
when half of total reserves is depleted
At a global scale, the symmetry of the total production profile is subjected to strong hypothesis related to the exploration strategy
production path of several oil wells through time
What happens with more realistic exploration dynamics
 exploration responding to price signals? 5 5

6. Hotelling rent Assumptions Hotelling scarcity rent
no arbitrage opportunity
production of resource is optimal any time
constant discounted scarcity rent over time
random
Hotelling scarcity rent
What happens if T0 is a random variable with a decreasing variance along time? 6 6

7. Model 7

8. 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

9. The explorer-producer The marginal oilfield owner
Model Structure
Exploration-Production heuristics
Learning process about reserves
Hotelling scarcity rent calculation
The explorer-producer
explores and produces to meet the (exogenous) demand at minimal cost
assess the risk of holding oil as an asset
The marginal oilfield owner
improves the common knowledge on the remaining reserves
marginal production cost
Hotelling scarcity rent
Oil Price 9

10. 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 10 10

11. 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:
it proceeds with exploration, which randomly returns the size and production cost of the discovered oilfields
E[Cost exploration] + E[marginal Cost production(new port.)]
be less or equal than
E[marginal Cost production(old port.)] 11

12. Exploration heuristics
The expected total cost curve shows minimum 12

13. 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
Profile of a producing oilfield 13

14. 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
buying an oilfield and keeping the oil in the ground till depletion date
Le Modèle d'Evaluation des Actifs Financiers ou Capital Assets Pricing Model (CAPM) est utilisé pour évaluer des actions dans un marché en équilibre. Il est basé sur le fait que seul le risque de marché, ou risque non diversifiable, est rémunéré par les investisseurs dans un tel marché. La rentabilité exigée par un investisseur est alors égale au taux de l'argent sans risque majoré d'une prime de risque uniquement liée au risque de marché de l'actif : R = rf + beta x (rm - rf)
buying a financial asset with the same risk 14

15. 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 $/bl
Volume (Gb) / Extraction cost ($/b) 15 25 35 45 55 2 77 76 12 32 30 58 4 15

16. Results
Single agent exploring one global area 16

17. Results: single actor / mono zone
1 scenario – exploration non caped

18. Results: single actor / mono zone
1 scenario – exploration caped

19. Results: single actor / mono zone
100 scenarii exploration caped 19

20. Comments
No symmetric peak oil at the world level, unless exploration is caped

21. Results
Single agent exploring 2 areas 21

22. Simulation data Area 1: larger and more competitive reserves
Area 2: smaller and more expensive reserves
oilfields
oilfields
oilfields
oilfields
oilfield 22

23. Allocating exploration between the two regions

24. Results: single actor / 2 areas
1 scénario exploration non caped 24

25. Results: single actor / 2 areas
1 scénario exploration caped in area 1 ( most favourable zone)

26. 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 ?

27. Stackelberg oligopoly
OPEC as the heart of an oligopoly with a competitive fringe
(preliminary) 27

28. 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

29. OPEC – competitive fringe
Modelling of interaction 29

30. Results Stackelberg oligopoly
1 scénario 30

31. Comments An intriguing result:
Optimal oligopoly behaviour leads to price instability….

32. 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

33. Thanks for your attention33