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

Pierre-Noël GIRAUD (CERNA, Mines ParisTech)Aline SUTTER – Timothée DENIS (EDF R&D)

Hubbert oil peak and Hotelling rent revisited by a simulation modelOTAE 2009

July 7th, 2009, at Mines-ParisTech

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Outline

Questions addressed

Model principles

Results

• Single agent exploring 1 global area

• Single agent exploring 2 areas

• Stackelberg oligopoly

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At stakes: the oil price trajectory on the long termPeak oil: why and when?Scarcity rent: when and how much?

Gb

year

demand for fuel

Hubbert symmetrical peak

late asymmetrical peak with sharp dropping

2010 ? 2050 ?

At peak oil:

oil price = substitute price

Marginal extraction cost

$/bl

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Hubbert oil peak

Starting point

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

1956

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production path of several oil wells through time

Hubbert oil peak

Total production of a multi-deposit region is supposed to show a peakwhen 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

What happens with more realistic exploration dynamics

exploration responding to price signals?

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Hotelling rent

Assumptions

))(exp()( 0TTrPPPP ese

Hotelling scarcity rent

random

no arbitrage opportunity

production of resource is optimal any time

constant discounted scarcity rent over time

What happens if T0 is a random variable with a decreasing variance along time?

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Model

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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

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Model Structure

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

Oil Price

marginal production cost Hotelling scarcity rent

improves the common

knowledge on the remaining

reserves

Exploration-Production heuristics

Hotelling scarcity rent calculation

Learning process about reserves

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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

The learning process on reservesThe learning process on reserves

Total oil left estimated by agent (Gb)

0

500

1 000

1 500

2 000

2 500

3 000

1 21 41 61 81 101 121 141 161 181 201 221 241 261 281 301 321

Explorations

(Gb

)

Coefficient of variation (mean over 100 scenarios)

0%

20%

40%

60%

80%

100%

120%

140%

160%

1 21 41 61 81 101 121 141 161 181 201 221 241 261 281 301 321

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Exploration heuristicsExploration 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.)]

E[marginal Cost production(old port.)]

be less or equal than

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Exploration heuristicsExploration heuristics

The expected total cost curve shows minimum

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Production constraintProduction 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

Profile of a producing oilfield

more realistic shape

Production

Time

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0%

5%

10%

15%

20%

25%

30%

35%

40%

45%

0% 20% 40% 60% 80% 100% 120%V(r)

E(r

)

CAPM

Inferring Hotelling rentInferring Hotelling rentHotelling 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

buying a financial asset with the same

risk

))(exp()( 0TTrPPPP ese

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Current Model calibrationCurrent 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 0 0 77 77 76

12 0 32 30 30 0

58 4 4 0 0 0

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Results

Single agent exploring one global area

Results: single actor / mono zoneResults: single actor / mono zone

1 scenario – exploration non caped

Results: single actor / mono zoneResults: single actor / mono zone

1 scenario – exploration caped

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Results: single actor / mono zoneResults: single actor / mono zone

100 scenarii exploration caped

Comments

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

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Results

Single agent exploring 2 areas

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Simulation dataSimulation data

Area 1: larger and more competitive reserves

Area 2: smaller and more expensive reserves

oilfields

oilfields

oilfields

oilfields

oilfield

Allocating exploration between the two regions

2max,1max,

1max,2,1,1 22

1

GG

Geee optopt

2max,1max,

2max,2,1,2 22

1

GG

Geee optopt

With:

ie , the exploration level in region i

iopte , , the exploration level which would optimally meet total demand in region i

iGmax, , the maximum earning in region i coming from meeting total demand in region i

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Results: single actor / 2 areasResults: single actor / 2 areas

1 scénario exploration non caped

Results: single actor / 2 areasResults: 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 ?

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Stackelberg oligopoly

OPEC as the heart of an oligopoly with a competitive fringe

(preliminary)

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Introducing OPECIntroducing 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

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OPEC – competitive fringeOPEC – competitive fringe

Modelling of interaction

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Results Stackelberg oligopolyResults Stackelberg oligopoly

1 scénario

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

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Thanks for your attention