1 optimal ccs, carbon capture and storage, under risk international seminars in life sciences...
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Optimal CCS, Carbon Capture and Storage, Under Risk
International Seminars in Life Sciences Universidad Politécnica de Valencia
Thursday 2008-10-16Updated 2011-03-22
Peter Lohmander
Professor of Forest Management and Economic OptimizationSLU, Swedish University of Agricultural Sciences
Umea, Sweden
http://www.Lohmander.com
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Optimal CCS, Carbon Capture and Storage, Under Risk
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A presentation within the lectures by Peter Lohmander at UPV, Polytechnical University of Valencia, October 2008.
General theme of the lectures:Optimal forest management with
consideration of risk, CO2 and the forest- and energy industries
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CO2
Permanent storage of CO2
How to reduce the CO2 level in the atmosphere,
not only to decrease the emission of CO2
Energy plant with CO2 capture and separation
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CO2
Permanent storage of CO2
Coal mine
Oil field
Natural gas
CCS has alreadybecome the main emissionreduction method of the fossile fuel energy industry
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Reference to CCS in the energy industry and EU policy
2nd Annual EMISSIONS REDUCTION FORUM: - Establishing Effective CO2, NOx, SOx Mitigation Strategies for the Power Industry, CD, Marcus Evans Ltd, Madrid, Spain, 29th & 30th September 2008
The CD (above) includes presentations where dominating European energy companies show how they develop and use CCS and where the European Commission gives the general European emission and energy policy perspective.
Conference programme:
http://www.lohmander.com/Madrid08/MadridProg08.pdf
Lohmander, P., Tools for optimal coordination of CCS, power industry capacity expansion and bio energy raw material production and harvesting, 2nd Annual EMISSIONS REDUCTION FORUM: - Establishing Effective CO2, NOx, SOx Mitigation Strategies for the Power Industry, CD, Marcus Evans Ltd, Madrid, Spain, 29th & 30th September 2008
http://www.lohmander.com/Madrid08/Madrid_2008_Lohmander.ppt
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References with links:
• Lohmander, P., Adaptive Optimization of Forest Management in a Stochastic World, in Weintraub A. et al (Editors), Handbook of Operations Research in Natural Resources, Springer, Springer Science, International Series in Operations Research and Management Science, New York, USA, pp 525-544, 2007 http://www.amazon.ca/gp/reader/0387718141/ref=sib_dp_pt/701-0734992-1741115#reader-link
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• Lohmander, P., Mohammadi, S., Optimal Continuous Cover Forest Management in an Uneven-Aged Forest in the North of Iran, Journal of Applied Sciences 8(11), 2008 http://ansijournals.com/jas/2008/1995-2007.pdfhttp://www.Lohmander.com/LoMoOCC.pdf
• Mohammadi, L.S., Lohmander, P., A game theory approach to the Iranian forest industry raw material market, Caspian Journal of Environmental Sciences, Vol 6, No1, pp. 59-71, 2008 http://research.guilan.ac.ir/cjes/.papers/969.pdfhttp://www.Lohmander.com/MoLoAGTA.pdf
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• Lohmander, P., Guidelines for Economically Rational and Coordinated Dynamic Development of the Forest and Bio Energy Sectors with CO2 constraints, Proceedings from the 16th European Biomass Conference and Exhibition, Valencia, Spain, 02-06 June, 2008 (In the version in the link, below, an earlier misprint has been corrected. ) http://www.Lohmander.com/Valencia2008.pdf
• Lohmander, P., Economically Optimal Joint Strategy for Sustainable Bioenergy and Forest Sectors with CO2 Constraints, European Biomass Forum, Exploring Future Markets, Financing and Technology for Power Generation, CD, Marcus Evans Ltd, Amsterdam, 16th-17th June, 2008 http://www.Lohmander.com/Amsterdam2008.ppt
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Lohmander, P., Optimal resource control model & General continuous time optimal control model of a forest resource, comparative dynamics and CO2 consideration effects, Seminar at SLU, Umea, Sweden, 2008-09-18
• http://www.Lohmander.com/CM/CMLohmander.ppt• http://www.Lohmander.com/CM/CM.htm
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• Lohmander, P., Tools for optimal coordination of CCS, power industry capacity expansion and bio energy raw material production and harvesting, 2nd Annual EMISSIONS REDUCTION FORUM: - Establishing Effective CO2, NOx, SOx Mitigation Strategies for the Power Industry, CD, Marcus Evans Ltd, Madrid, Spain, 29th & 30th September 2008
http://www.lohmander.com/Madrid08/Madrid_2008_Lohmander.ppt
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Lohmander, P., Optimal CCS, Carbon Capture and Storage, Under Risk, International Seminars in Life Sciences, UPV, Universidad Politécnica de Valencia, Thursday 2008-10-16
• http://www.Lohmander.com/OptCCS/OptCCS.ppt
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Optimal CCS, Carbon Capture and Storage, Under Risk
The objective function is the total present value of CO2 storage minus CCS costs.
Discountingfactor
u = control = CCS level
x = The total storage level of CO2
2 2( )rt
t
e ku pu fx gx dt
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The controlled storage
A stochastic differential equation:
Change of theCO2 storage level. Control =
CCS level.
Expected CO2 leakage.
The CO2 storage level is to some extent affected by stochastic leakage and other stochastic events. Z = standard Wiener process.
( )dx u mx n dt sx dz
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2 2( )rt
t
e ku pu fx gx dt
( )dx u mx n dt sx dz
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The Hamilton-Jacobi-Bellman Equation equation with optimized control:
2 2( )rt
t
e ku pu fx gx dt
( )dx u mx n dt sx dz
2 22 2( ) ( ) 0
2rt xx
x t
J s xe ku pu fx gx J u mx n J
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Optimization with respect to the control, u:
2 22 2( ) ( )
2rt xx
x
J s xH e ku pu fx gx J u mx n
( 2 ) 0rtx
dHe k pu V
du
2
2( 2 ) 0rtd H
e pdu
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( , ) ( )rtJ x t e V x
2( )V x a bx cx
( 2 )rt rtx xJ e V e b cx
(2 )rt rtxx xxJ e V e c
2( ) ( )rt rttJ re V x re a bx cx
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2 22 2( ) ( )
2rt xx
x
V s xH e ku pu fx gx V u mx n
*
*
*
*
*
0 ( 2 ) 0
2 0
2
2
2
2
2
rtx
x
x
x
dHe k pu V
du
k pu V
pu V k
V ku
p
b k cxu
p
b k cu x
p p
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*
2
b k cu x
p p
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The Hamilton-Jacobi-Bellman equation:
Let us input the optimal control in the Hamilton-Jacobi-Bellman equation:
2 22 2( ) ( ) ( ) 0
2xx
x
V s xku pu fx gx V u mx n rV x
2 2* * 2 2 *( ( ) ) ( ) ( ) 0
2xx
x
V s xku p u fx gx V u mx n rV x
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2
2
2 2
2 2
2 2
2( ) 0
2 2xx
x
b k cx b k cxk p fx gx
p p
V s xb k cxV mx n rV x
p
22
2
2
2 22
2 2
2 2
2 (2 )( 2 ) ( ) 0
2 2
b k cx b k cxk p fx gx
p p
b k cx c s xb cx mx n r a bx cx
p
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2 2 2
2 2
4 (2 )1
4 ( ) ( 2 ) 04
4 2 ( 2 )
x c cp m r s gp
x b c mp pr c k np fpp
apr b b k np k
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2 2 2
2 2
4 (2 )1
4 ( ) ( 2 ) 04
4 2 ( 2 )
x c cp m r s gp
x b c mp pr c k np fpp
apr b b k np k
2 2
2 2 2
2 2 2
(2 ) 0
(2 ) (4 (2 ) )
2
(2 ) (4 (2 ) )
2
c cp m r s gp
p m r s p g p m r sc
p m r s p g p m r sc
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2 2 2
2 2
4 (2 )1
4 ( ) ( 2 ) 04
4 2 ( 2 )
x c cp m r s gp
x b c mp pr c k np fpp
apr b b k np k
( ) ( 2 ) 0
( 2 )
( )
b c mp pr c k np fp
c k np fpb
p m r c
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2 2 2
2 2
4 (2 )1
4 ( ) ( 2 ) 04
4 2 ( 2 )
x c cp m r s gp
x b c mp pr c k np fpp
apr b b k np k
2 2
2 2
4 2 ( 2 ) 0
2 ( 2 )
4
apr b b k np k
b b k np ka
pr
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Optimal objective function:
2( , ) rtV x t e a bx cx The parameters should be determined in the following order:
2 2 2(2 ) (4 (2 ) )
2
p m r s p g p m r sc
( 2 )
( )
c k np fpb
p m r c
2 22 ( 2 )
4
b b k np ka
pr
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Optimal control:
*
2
b k cu x
p p
*0 xu u u x
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U*
r = 3% and s = 0
r = 3% and s = 1
32Stock level
Time
ExpectedPresentValue
r = 3%, s = 0 (upper graph) ands = 1 (lower graph)
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U*
r = 5% and s = 0
r = 5% and s = 1
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ExpectedPresent Value
Time
Stock level
r = 5%, s = 0 (upper graph) ands = 1 (lower graph)
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Conclusions:
• A mathematical approach to optimal CCS control has been developed that can handle risk.
• Possible leakage is an important issue that has to be carefully investigated in the future.
• It is important that the future management decisions are based on a decision model consistent with the structure of this model and that the parameter values are carefully estimated before practical management decisions are calculated.
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Thank you for listening!Here you may reach me in the future:
Peter LohmanderProfessor of Forest Management and Economic Optimization,SLU, Swedish University of Agricultural Sciences, Faculty of Forest Sciences, Dept. Of Forest Economics, SE-901 83 Umea, Sweden
http://www.Lohmander.com
Version 2007-02-18