Application of decision theory to the procurement of a
geothermal power plant
April 2nd 2008
Viktor Þórisson
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Presentation Overview
1. Company overview & background
2. What is geothermal energy?
3. Definition of the project
4. Application of @risk and precision tree in this
project
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Company Overview
Export of Icelandic Geothermal Know-how
What we do
Development of geothermal potential for
electrical generation and
direct use.
Feasibility Studies & Business Plans
Reliance on
comprehensive know-how and
operational experience.
Engineering
Founded in 1969 by the main geothermal consultancies
in Iceland to export the Icelandic geothermal consulting.
Project Management
Construction & Commissioning
Operation
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What is geothermal energy?
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What is geothermal?
The thermal energy stored within the
earth's crust is collectively called
geothermal energy.
Faults and fractures develop where
the earth crust is unstable or is
moving, most commonly in areas of
active volcanism.
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What is geothermal?
In areas of active volcanism, the upper
crust is frequently intruded by hot
magmatic intrusions.
These intrusions move heat from the inner
parts of the earth towards the outer crust.
They are the prime force that usually
drives geothermal systems.
In some parts of the world hot rock
formations within the crust contain water,
which is the ideal medium for carrying this
energy up to the earth's surface in a
useful form.
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Simplified geothermal power plant cycle
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Waste water bathing
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Main factors affecting the profitability
•
•
•
•
Temperature of reservoir (or enthalpy)
Flow from well (or production index)
Depth of well
Chemical conditions of the brine
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Definition of the project
Decision tree to answer the question:
In a geothermal project.
When to procure the critical components with the longest lead
time for a power plant, after last drilling, before first drilling or
somewhere in between?
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The project chart if components are ordered after
drilling
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Main trade offs in the model are
Benefit:
•Shorter time until plant is
operational.
Trade-off:
•More information available when
components are ordered and thus optimizing
the efficiency of the plant
•The risk of higher investment cost than
necessary due to over dimensioning of the
turbine.
•Potential higher costs if project results in no
go after drilling and thus order cancellation
fees of components are incurred.
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Overview
of the
Overview
oftree
the tree
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Probabilities, methodology
(1-cummulative distribution)
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Fitted distributions
Normal(1,21184; 0,66555)
Normal(160,289; 18,687)
1,0
1,0
0,8
0,8
0,6
0,6
0,4
0,4
0,2
0,2
< 5,0%
129,55
90,0%
5,0% >
191,03
<
-Infinity
100,0%
2,5
2,0
1,5
1,0
0,5
0,0
0,0
200
190
180
170
160
150
140
130
120
0,0
>
+Infinity
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Definition of failure
Insurance line
148
146
Temperature [°C]
144
142
140
Insurance line
138
136
134
132
0
0,2
0,4
0,6
0,8
1
1,2
Production Index [l/sek/m]
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Probability of failure first drilling
• Probability of failure due to
reasons other than geological
is defined as 5%.
• Probability of success first
drilling is therefore:
89,26% * 95% = 84,9%
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Probability of success second drilling
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Given success first drilling
BetaGeneral(3,6130; 1,2859; 109,492; 177,157)
Uniform(0,13379; 2,4238)
BetaGeneral(3,6130; 1,2859;
109,492; 177,157)
1,0
1,0
4,0
0,8
0,8
3,5
PI
5,0%
2,309
5,0%
90,0%
135,81
180
90,0%
135,81
<
170
180
170
160
150
140
Temperature
90,0%
0,248
130
120
110
2,5
2,0
1,5
1,0
0,5
0,0
0,0
160
0,0
0,5
150
0,0
1,0
140
0,2
1,5
130
0,2
2,0
120
0,4
0,4
2,5
110
0,6
100
0,6
Values x 10^-2
3,0
175,12
175,12
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Results from simulation, probability of failure of the
project, given success/given failure first drilling.
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Potential plant size
Distribution for peak plant cut of belove insurance function
X <=-2,5
.032%
0,12
X <=7,36
10.74%
0,1
0,08
0,06
0,04
0,02
0
-5
0
5
10
15
20
25
Mean plant size 13,8 MW given
success first drilling. Example of
Possible values:
T
PI
165
1,5
160
2,1
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30
The newsboy problem
CO * PO = CU * PU
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Sensitivity of production to flow
20%
10%
-40%
-30%
-20%
power
Sensitivity
0%
-10%
0%
-10%
flow to turbine
10%
20%
30%
40%
-20%
-30%
-40%
-50%
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Other costs
• Cost of over sizing (CO)
500.000 EUR/MW unnecessary investment cost.
• Cost of under sizing (CU)
Expected cancellation fee of turbine.
Cost of lost production
Cost per MW lost production
thousends of Euros
4500
4000
3500
3000
2500
Cost of lost
production
2000
1500
1000
500
0
8
8,5
9
9,5
10
10,5
MW
11
11,5
12
12,5
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The optimal path
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Sensitivity of costs
Spider graph of NPV
13500
13000
12500
1. Expected lost
revenues due to
efficiency reduction
NPV
12000
11500
2. Expected value of
lost production
explained above
3. Expected value of
extra investment cost if
pre ordered
11000
10500
10000
9500
9000
0%
200%
400%
600%
% change from base value
800%
1000%
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Sensitivity of costs
Decisions, drilling vs. ordering turbine before first drilling
14000
1. Drill first
well without
ordering
components
13000
12000
NPV
11000
10000
2. Order
genset
before first
drilling
9000
8000
7000
6000
0%
200%
400%
600%
800%
1000%
% Change from base value of expected extra investm ent cost if pre ordered
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2 way decision analyze of costs
% change from base value of
expected extra investment cost
2 way decision analys
1000%
900%
800%
700%
600%
500%
400%
300%
200%
100%
0%
1. Drill first well
without ordering
components"
2. Order genset
before first drilling"
0%
200%
400%
600%
800%
1000%
% change from base value of lost efficiency
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Sensitivity of probabilities
Sensitivity of probabillities
NPV
20000
15000
P(success|success)
10000
P(success|failure)
5000
P(success)
0
-60%
-50%
-40%
-30%
-20%
-10%
0%
-5000
10%
20%
P(nongeological
success)
-10000
% change of probabillities from base value
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2 way decision analyze of probabilities
% Change from base value
of P(nongeological success)
2 way decision analys
70%
60%
50%
1. Drill first well
without ordering
components
40%
30%
2. Order genset
before first drilling
20%
10%
0%
0%
10%
20%
30%
40%
50%
60%
70%
% Decrease from base value P(success)
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Thank you
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