1. Tools for optimal coordination of CCS, power industry capacity expansion and bio energy raw material production and harvesting Peter Lohmander Prof. Dr. SLU Sweden Peter@Lohmander.com Peter@Lohmander.com 2nd Annual EMISSIONS REDUCTION FORUM: Establishing Effective CO2, NOx, SOx Mitigation Strategies for the Power Industry, Marcus Evans, 29th & 30th September 2008, Madrid, Spain

2. Abstract (Peter Lohmander, Madrid 2008) If we plan the future carbon capture and storage strategy, the power industry capacity expansion and bio energy raw material production and harvesting separately, we will never reach the best possible solution. Alternative approaches to the optimal coordination problem are presented. A new continuous time optimal control model is described and analyzed. The optimal time path of resource extraction is explicitly determined as a function of time dependent CO2 storage revenues and other relevant parameters, including the time dependent parameters of the energy demand function.

3. e-mail: Peter@Lohmander.com References: http://www.lohmander.com/Information/Ref.htm Software: http://www.lohmander.com/Program/Program.htm Conferences: http://www.lohmander.com/Kurser/Kurser.htm

4. If we plan the future carbon capture and storage strategy, the power industry capacity expansion and bio energy raw material production and harvesting separately, we will never reach the best possible solution.

5. We may, with alternative definitions and methods, investigate the system that includes the three ”sectors” Forestry (F), the Forest Products Industry (FPI) and the Forest Raw Material Based Energy Industry (FRMBEI). The ambition is to find the dynamic strategy for the management of this system that leads to the best possible total economic surplus (present value), when we simultaneously consider the CO2 issue.

6. The ”Small Unit Raw Material Perspective” and Optimization You may instantly calculate the economically optimal decisions, from a ”small unit raw material perspective”, using software available from the Internet: http://www.lohmander.com/program/Faust_Slut/InFaust3.html http://www.lohmander.com/program/Stump02/InStump022.html

7. Figure 1. The Present Value EXP(- 0.03·t)·(20000 + 1000·t + 2000) Present Value (SEK/Hectare) Number of Years from the Present

8. = Stock level = Growth = Net Price = Net Price Growth = Land Value = Interest Rate(%) Optimize! Web Software for Economic Optimization from a Raw Material Perspective

9. Optimal Results Optimal Harvest Year Optimal Present Value

10. Age distribution in the county of Gävleborg (2001-2005). Thousands of hectares in different age classes (years). A large part of the forest is much older than the economically optimal harvest age

11. If we invest in CO2 capture and storage technology (CCS) in the energy industry, it is even more important to rapidly harvest the old forest stands! Then, if we increase the area that is replanted with more rapidly growing trees, we will absorb more CO2 from the atmosphere, separate it and store it permanently.

12. http://www.lohmander.com/co2ill2/co2ill2.htm

13. A growing forest captures and stores CO2 from the atmosphere. However, trees do not grow for ever.

14. Sooner or later, the growth level is reduced, because the age of the trees becomes too high and the competition between neighbour trees too strong for continued growth. Furthermore, at some age, trees die, and once again release the stored CO2 to the atmosphere.

15. The total amount of CO2 that may be captured from the atmosphere and permanently stored is much higher if we, in a repeated sequence, harvest the forest, use some part of the biomass for instant energy production, capture and store the CO2 and replant the area again.

16. With repeated harvesting an CCS, we may, in the long run capture and store any amount of CO2 from the atmosphere! We do not only reduce the new emissions of CO2 but we really make sure that the CO2 level of the atmosphere is reduced! If you just leave the forest for ever, without harvesting, you will never be able to store more than what you find in an old forest stand.

17. General continuous time optimal control model of a forest resource, comparative dynamics and CO2 storage consideration effects

18. The Total Economic Result (Present Value) The Stock Level The ”Control” Level Economic valuation of CO2 storage in the natural resource Economic Valuation of the Production of Energy and Other Industrial Products

19. Initial stock level Terminal stock level The change of the stock level during a marginal time interval

20. 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 Software: http://www.lohmander.com/CM/CM.htm

24. Optimal strategy and dynamic effects of the rate of interest

29. Comparisions with alternatives that are not optimal:

30. Optimal strategy and dynamic effects of the slope of the demand function

35. Comparisions with two alternatives:

36. Optimal strategy and dynamic effects of the terminal condition

42. Optimal strategy and dynamic effects of continuous stock level valuation, for instance because we want to reward the storage of CO2

48. Optimal strategy and dynamic effects of continuous stock level valuation in combination with variations of the the slope of the demand function

54. Optimal strategy and dynamic effects of the growth function

60. Total perspective I

61. V0 Time 0 Stock

62. h0 < g h1 > g h2 = g

65. Derivations and parameters (I) Rate of interestr0,06 Growth (now)g106 Growth (future)g106 t15 Stock (now)v03000 Harvest (before t1)h086 z01 z11 z21

66. http://www.lohmander.com/EF2008/EF2008.htm Web software for Total Perspective I Report (in Swedish) with appendix (in English) describing Total Perspective I and II http://www.lohmander.com/EF2008/EF2008Lohmander.pdf

69. vfutureh1t2totval 3000106 inf1680 3000108551703 3000110301718 300011221,61727 300011417,51732 3000116151735

70. Observations Even if we do not accept to decrease the stock level below the very high level of today, we should strongly increase harvesting during a considerable time interval. In this first derivation, the improved growth rate in new plantations has not been considered.

71. vfutureh1t2totval 2500106 inf1680 2500116651800 2500126351886 2500136251939 2500146201973 2500156171997

72. Observations If we are prepared to adjust the stock level to the stock level of the year 1985, (approximately 2 500 Mm3sk), we should increase harvesting very much during a long time period. Then, the total economic value strongly improves. In this derivation, the improved growth rate in new plantations has not been considered.

73. Total perspective II

74. If harvested areas are replanted with more rapidly growing seedlings, the stock path becomes strictly convex (during time periods with constant harvesting)

76. Derivations and parameters (II) Rate of interestr0,06 Growth (now)g0106 Growth (new seedlings)g1126 t15 Stock (now)v03000 Harvest (before t1)h086 z01 z11 z21 ATKvot80

77. http://www.lohmander.com/EF2008/EFchange2008.htm Web software for Total Perspective II

80. h1t2totvalvfuture 1166518063055 1263519062666 1362519662586 1462020042556 1561720292541

81. Conclusions If we plan the future carbon capture and storage strategy, the power industry capacity expansion and bio energy raw material production and harvesting separately, we will never reach the best possible solution. The presented tools may be used to determine what should be done. Peter Lohmander is organizing the conference stream “Optimal Forest Management with Increasing Bioenergy Demand” within The 23rd European Conference on Operational Research (EURO XXIII), July 5-8, 2009, Bonn, Germany. http://www.lohmander.com/Bonn2009/Bonn2009.pdf http://www.lohmander.com/Bonn2009/Bonn2009.pdf Let us continue our discussions and meet there!

82. My warmest ”Thanks” to E.ON Sweden for economic support to the project ”Economic forest production with consideration of the forest- and energy- industries”! Peter Lohmander Professor of Forest Management and Economic Optimization, Swedish University of Agricultural Sciences http://www.Lohmander.com Peter@Lohmander.com