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A Quantitative Analysis of the Impact of Production Uncertainty on the Offshore Oil Project Investment
Available online at www.sciencedirect.com
ScienceDirect Energy Procedia 75 (2015) 3007 – 3013
The 7th International Conference on Applied Energy – ICAE2015
A Quantitative Analysis of the Impact of Production Uncertainty on the Offshore Oil Project Investment Cheng Chenga, Zhen Wangb*,Mingming Liua, Yikang Zhaoc a
Academy of Chinese Energy Strategy,China University of Petroleum, 18 Fuxue Road , Changping District, Beijing, 102249 , China b CNPC, 9 Dongzhimen North Street, Dongcheng District, Beijing, 100007, China c CNODC/CNPC International,No. 6-1, Fuchengmen Beidajie, Xicheng District, Beijing, 100034, China, ,
Abstract Investors in the petroleum industry realize offshore oil projects are much more complicated than onshore projects. The offshore projects are characterized by large investment and high uncertainties. A tiny change of the uncertain factor may cause a large fluctuation of total investment. Production uncertainty is an important uncertain factor, which has a great influence on the investment. In our study of FPSO (Floating Production Storage and Offloading) + Wellhead development concept, firstly we check the composition of total investment. Then we classify them into different items. We research on the possible relations between the items and oil production by using ordinary least square method (OLS), and then we use the relations to set up a model to estimate the offshore investment. Based on the model, we then quantitatively analyze the impact of production uncertainty by using Monte Carlo simulations. Finally, we estimate the possible distribution of the investment. © 2015 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license
© 2015 The Authors. Published by Elsevier Ltd. (http://creativecommons.org/licenses/by-nc-nd/4.0/). under responsibility of ICAE Selection peer-review of Peer-reviewand/or under responsibility Applied Energy Innovation Institute
Key words: offshore oil projects, investment esitmation, production uncertainty, quantitative analysis, investment probability curve
1. Introduction Over the last two decades, oil markets have seen changes concerning offshore oil sector. Offshore oil production has increased greatly. According to Infield Systems’ Offshore Energy Database, total offshore oil production accounted for 22% of global production in 2000. In 2010 the figure raised to 33%. In 2012, 32% (146 in total) of the new oil and gas findings were located on oceans. However, the 146 findings accounted for 88% of the world new recoverable reserves. The offshore recoverable reserves were 3.21
* Corresponding author. Tel.: +86-10-8973-1752 ; fax: +86-10-8973-1752. E-mail address: [email protected].
1876-6102 © 2015 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of Applied Energy Innovation Institute doi:10.1016/j.egypro.2015.07.614
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Cheng Cheng et al. / Energy Procedia 75 (2015) 3007 – 3013
billion tons of oil equivalent in 2012. In the future, the offshore oil sector will play an important role in the petroleum industry. Compared with the traditional onshore projects, the offshore oil projects are more complex. The development environments are more severe and inconstant; advanced technologies, equipment and materials are needed in the development process, excellent management skills are also indispensable. To summary, the offshore oil projects involve huge investments, long period and lots of uncertainties (or risks). Therefore, it is necessary to find the possible relationships between the investment and uncertain factors. The motivation for this study is twofold. First, we propose to investigate the relations between the investment and uncertain factors, especially the relations between different investment items and productions. Second, we want to define the possible distribution of the investment based on a certain assumption of production, and explain how it will affect the decisions. The remainder of this paper is organized as follows: Section 2 is about the literature reviews on the application of uncertainty (risk) analysis in petroleum industry. Section 3 summaries the composition of offshore oil project investment and sets up the evaluation model. Section 4 presents the results of Monte Carlo simulation for the total investment. Section 5 talks about main conclusions and some suggestions. 2. Literature Review Allais[1] was the first economist who adopted the probability theory in his research on the economics and risks in the exploration period. In his study on the economic feasibility of exploring the Algerian Sahara, exploration period was divided into several sequential and independent stages, and an explicit modeling was set up. Based on probability theory and Monte Carlo simulations, he analyzed the economic feasibility and risks on the entire exploration stage. Allais’s work demonstrated how Monte Carlo method was used in the complex probability analysis. During the 1960s, risk analysis methods were only applied in the academia and were quit new to petroleum industry. Grayson[2], Arps and Arps[3], Newendorp[4], Negill[5] were the first group of scholars who introduced risk analysis methods into petroleum industry, and made great contribution in the application of risk analysis in petroleum industry. In 1980s and 1990s, some new statistical methods were absorbed into risk analysis such as: (1) lognormal risk resources distribution (Attanasi and Drew[6]), (2) Pareto distribution applied to petroleum field-size data in a play (Crovelli[7]) and (3) fractal normal percentage (Crovelli et al.[8]). In the field appraisal and development period, the most useful way is the recovery factor. Saloma˜o and Grell[9] presented that the simplest way to estimate the recovery factor was through analytical procedures, empirical correlations and simulation runs. Paddock et al.[10] presented an classical work to apply real option into the petroleum industry. In their study of oil development process, they made an analogy between real options and American call options. Galli et al.[11] discussed the application of real options, decision trees and Monte Carlo simulations. Risk analysis methods and technologies have been applied into petroleum industry for more than half a century. Different methods are used to investigate different academic problems in different period of petroleum development. But scholars seldom research on the possible distribution of investment before oil companies bid for the oilfields. This investment is very large and will have a great influence on the project’s benefit, especially for the offshore oil projects. Neglecting the possible change of the investment, managers may be over-optimistic or over-pessimistic about the project. Thus, it is necessary and important to analyze the risk before bidding. 3. Model
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Cheng Cheng et al. / Energy Procedia 75 (2015) 3007 – 3013
ĂĂ
Contingency
ĂĂ
Ins & Cer
ĂĂ
Des & Pro M
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HUC
ĂĂ
Installation
Contingency
Material
ĂĂ
Contingency
Indirect Cost
Fabrication
ĂĂ
Indirect Cost
Installation
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Contingency
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Ins & Cer
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Des & Pro M
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HUC
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Installation
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Fabrication
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Material
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Equipment
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Material
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Installation
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Ins & Cer Des & Pro M ĂĂ
Fabrication
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Material
ĂĂ
Equipment
ĂĂ
Equipment
Direct Cost
Direct Cost
Topside 1
Indirect Cost
Jacket
Contingency
Contingency
Direct Cost
Topside 2
FPSO + Wellhead
Drilling
Tanker
Pipeline Direct Cost
Direct Cost Direct Cost ĂĂ
Material
Indirect Cost
Contingency
Ins & Cer
Contingency
Ins & Cer
ĂĂ
Des & Pro M
ĂĂ
Contingency
ĂĂ
Indirect Cost Des & Pro M ĂĂ
Installation
Equipment
ĂĂ
ĂĂ
Ins & Cer
Material
ĂĂ
ĂĂ
Des & Pro M
Fabrication
ĂĂ
ĂĂ
Contingency
Installation
ĂĂ
HUC
ĂĂ
Contingency
Indirect Cost
Contingency
Fig. 1. The composition of investment of FPSO + Wellhead concept
Notes: 1. HUC represents Hook-up & Commissioning, Ins & Cer. represents Insurance & Certification, Des. & Pro. M represents Design & Project Management; 2. The figure is not an intact one because of the space limitation.
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Cheng Cheng et al. / Energy Procedia 75 (2015) 3007 – 3013
In this Section, we set up a certain evaluation model for a certain development concept – FPSO (Floating Production Storage and Offloading) + Wellhead. Firstly we summary the composition of this concept, divide the total investment into different items. Then, we investigate the relationship between all the items and the production level. Finally, we set up an evaluation model for this development concept by the relations above, and test its precision. We subdivide the offshore investment in our study. As shown in Fig. 1, it is divided into six categories – topside 1 (which is connected with tanker), topside 2 (which is connected with jacket), jacket, tanker, pipelines and drilling. Each one is composited by three parts – direct costs, indirect costs and contingency. For each of the six categories, the indirect costs and contingency includes the same investment items. Indirect costs are divided into two parts, i.e. Design & Project Management and Insurance & Certification. Generally, oil companies estimate the total investment of oil fields by using “gravimetric method”. The method estimates the weights and prices separately, and then calculates the investment by multiplying them. We take the same method to investigate the relations between the items and production. We try to find the relations between the weights of all the items and production. In this study, we have three assumptions: (1) The price for different items are exogenous and fixed; (2) Some other uncertain factors, like the soil quality, tides etc. are neglected. We just focus on the production uncertainty, which influence the investment most; (3) The tanker is new built, not converted. One point that should be emphasized is that we set up the evaluation model under the assumption of fixed water depth and jackets’ legs, although we consider the influence of water depth and the jackets’ legs when we investigate the relations between the items’ weights and different uncertain factors. After the research, we find the quantitative relations between the items and the production .There is a significant linear relationship between some items and production, like secondary steel. Some items have a leap relationship with production, like dehydration equipment. The remainders have no relationship with production, like heating equipment. Their relations are shown in Fig. 2.
Fig. 2. (a) Relationships between weights of secondary steel and production; (b) Relationships between weights of dehydration and production; (c) Relationships between weights of heating and production
With all the regulations we get, an evaluation model is made. We test the model with realistic data, and the error of this model is -26.26%. The error is mainly caused by the fact that we neglect many other uncertain factors. However, in the application area, an error within f 30% is acceptable. So it is reasonable to make a quantitative risk analysis on this evaluation model. In the model, every items has a quantitatively relationship with production. The production is inconstant and uncertain. In order to find the possible distribution of investment, we assume the production follows the triangle distribution, which is consistent with many scholars’ hypothesis. By applying the Monte Carlo simulations in the model, we simulate the possible distribution of investment, which will be shown in the next section. 4. The Monte Carlo simulation and the distribution of investment
Cheng Cheng et al. / Energy Procedia 75 (2015) 3007 – 3013
In this Section, we use Monte Carlo simulations methods to research the possible distribution of investment. We assume that the production follows triangle distribution, which is shown in Fig. 3(a). By Monte Carlo simulations, the distribution of total investment is shown in Fig. 3(b). Most of the possible investments values are less than 433.35 million dollars, which account for 90% of all possible values. In other words, the possibility, of which total investment is less than 433.35 million, is 90%. By using goal seek method, it is easy to know that the production that makes the minimum value of possible investment values exceed 439 million dollars is 19.8 KBPD (thousand barrels per day).
Fig. 3. (a) Distribution of Production; (b) Probability density of total investment
Two methods are used to fit the distribution of the total investment. Firstly, we use absolute fitting methods. The result is shown in Fig. 4 (a) and Fig. 4 (b). Then, we choose relative fitting methods, and we set the Std Deviation as 1. The result is shown in Fig. 4 (c) and Fig. 4 (d).
Fig. 4 (a) Fitting of probability density curve by absolute fit; (b) Fitting of cumulative probability curve by absolute fit; (c) Fitting of probability density curve by relative fit; (b) Fitting of cumulative probability curve by relative fit.
As shown in Fig. 4, the result of absolute fit indicates that the LogLogistic distribution is the most suitable distribution for the probability density curve and cumulative probability curve of the investment, ranked by the Chi-Square Statistic. As Fig. 4(b) shows, the biggest difference appears at the range of
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Cheng Cheng et al. / Energy Procedia 75 (2015) 3007 – 3013
(443.40, 437.45), where the cumulative probability curve of simulated investment increases slightly, while the LogLogistic distribution curve increase steadily. The result of relative fit indicates that a totally different distribution fits best. It recommends that the triangle distribution fits best. As showed in the investment simulation (see Fig.3 (b)), the investments values mainly lies in the range of (431, 433.5). Investment distribution in this range is similar to triangle distribution. This is the main reason why the two different fitting methods indicate different distributions. When the Std Deviation is set as 3, both the two methods recommend the LogLogisitic as the best fitting distribution. 5. Conclusion The paper sets up an evaluation model of FPSO + Wellhead concept. In the model, the total investment is calculated by “gravimetric method”. All the relationships between the weights of different investment items and production are investigated. The prices of different items, which are the real data from an offshore project, are exogenous and fixed. In order to analyze the possible distribution of the investment, we assume that the production follows triangle distribution. By using Monte Carlo simulations, we find the best fitting distribution of investment is the LogLogistic distribution. The distribution provides a way to quantitatively analyze the impact of production uncertainty on the offshore oil project investment. We can get the possible range, in which the probability of that total investment is is the biggest, from the probability density curve and cumulative probability curve of investment. The model can also be used to calculate the probability of a certain range where the total investment may be. Thus, it can provide the decision makers with a concept, which is similar to VaR( value at Risk). When the investment is close to the value, the decision maker should be aware of possible losses. They should try to make sure the investment doesn’t exceed the value; otherwise the benefits of the project will be affected. We can also use goal seek method to estimate the possible production level which will satisfy the eigenvalues of a certain distribution. In our study, we only consider the impact of production uncertainty, and neglect other factors, which will also influence the distribution of investment. In the future, we will carry on further research by considering other uncertain factors. Acknowledgements The authors would thank financial support from National Science and Technology Major Project of the Ministry of Science and Technology of China - “Research on Investment estimation tools and economic appraisal system integration and development” (2011ZX05030-006-04). References [1] Allais, M. E´valuation des Perspectives E´conomiques de la Recherche Minie`re sur de Grands Espaces - application au Sahara Alge´rien. Revue de l’Industrie Mine´rale, Paris, January, 1956;329 - 383. [2] Grayson, Charles Jackson. Decisions under uncertainty: Drilling decisions by oil and gas operators. Arno Press, 1979. [3] Arps J J, Arps J L. Prudent risk-taking. Journal of Petroleum Technology 1974, 26: 711-716. [4] Newendorp P D. Decision analysis for petroleum exploration. 1975. [5] Megill R E. An introduction to risk analysis. 1984. [6] Attanasi E D, Drew L J. Lognormal field size distributions as a consequence of economic truncation. Journal of the International Association for Mathematical Geology 1985, 17: 335-351. [7] Crovelli R A. The generalized 20/80 law using probabilistic fractals applied to petroleum field size. Nonrenewable Resources 1995, 4: 233-241.
Cheng Cheng et al. / Energy Procedia 75 (2015) 3007 – 3013
[8] Crovelli R A, Schmoker J W, Balay R H. US department of the interior US geological survey: Fractal lognormal percentage analysis of the US geological survey’s 1995 national assessment of conventional oil and gas resources. Nonrenewable Resources 1997, 6: 43-51. [9] Salomão M C, Grell A P. Uncertainty in production profiles on the basis of geostatistic characterization and flow simulation. SPE Latin American and Caribbean Petroleum Engineering Conference. Society of Petroleum Engineers, 2001. [10] Paddock J L, Siegel D R, Smith J L. Option valuation of claims on real assets: The case of offshore petroleum leases. The Quarterly Journal of Economics 1988: 479-508. [11] Armstrong M, Jehl B. Comparison of three methods for evaluating oil projects. Journal of petroleum technology 1999, 51: 44-49.
Biography Zhen Wang is a professor from China University of Petroleum, Beijing. He was a Fulbright Visiting Research Scholar at the Darden Graduate School of Business at the University of Virginia, Charlottesville, VA. Wang got his PhD in Finance from Peking University and his areas of interests include M&A and energy finance.
3013
ScienceDirect Energy Procedia 75 (2015) 3007 – 3013
The 7th International Conference on Applied Energy – ICAE2015
A Quantitative Analysis of the Impact of Production Uncertainty on the Offshore Oil Project Investment Cheng Chenga, Zhen Wangb*,Mingming Liua, Yikang Zhaoc a
Academy of Chinese Energy Strategy,China University of Petroleum, 18 Fuxue Road , Changping District, Beijing, 102249 , China b CNPC, 9 Dongzhimen North Street, Dongcheng District, Beijing, 100007, China c CNODC/CNPC International,No. 6-1, Fuchengmen Beidajie, Xicheng District, Beijing, 100034, China, ,
Abstract Investors in the petroleum industry realize offshore oil projects are much more complicated than onshore projects. The offshore projects are characterized by large investment and high uncertainties. A tiny change of the uncertain factor may cause a large fluctuation of total investment. Production uncertainty is an important uncertain factor, which has a great influence on the investment. In our study of FPSO (Floating Production Storage and Offloading) + Wellhead development concept, firstly we check the composition of total investment. Then we classify them into different items. We research on the possible relations between the items and oil production by using ordinary least square method (OLS), and then we use the relations to set up a model to estimate the offshore investment. Based on the model, we then quantitatively analyze the impact of production uncertainty by using Monte Carlo simulations. Finally, we estimate the possible distribution of the investment. © 2015 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license
© 2015 The Authors. Published by Elsevier Ltd. (http://creativecommons.org/licenses/by-nc-nd/4.0/). under responsibility of ICAE Selection peer-review of Peer-reviewand/or under responsibility Applied Energy Innovation Institute
Key words: offshore oil projects, investment esitmation, production uncertainty, quantitative analysis, investment probability curve
1. Introduction Over the last two decades, oil markets have seen changes concerning offshore oil sector. Offshore oil production has increased greatly. According to Infield Systems’ Offshore Energy Database, total offshore oil production accounted for 22% of global production in 2000. In 2010 the figure raised to 33%. In 2012, 32% (146 in total) of the new oil and gas findings were located on oceans. However, the 146 findings accounted for 88% of the world new recoverable reserves. The offshore recoverable reserves were 3.21
* Corresponding author. Tel.: +86-10-8973-1752 ; fax: +86-10-8973-1752. E-mail address: [email protected].
1876-6102 © 2015 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of Applied Energy Innovation Institute doi:10.1016/j.egypro.2015.07.614
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Cheng Cheng et al. / Energy Procedia 75 (2015) 3007 – 3013
billion tons of oil equivalent in 2012. In the future, the offshore oil sector will play an important role in the petroleum industry. Compared with the traditional onshore projects, the offshore oil projects are more complex. The development environments are more severe and inconstant; advanced technologies, equipment and materials are needed in the development process, excellent management skills are also indispensable. To summary, the offshore oil projects involve huge investments, long period and lots of uncertainties (or risks). Therefore, it is necessary to find the possible relationships between the investment and uncertain factors. The motivation for this study is twofold. First, we propose to investigate the relations between the investment and uncertain factors, especially the relations between different investment items and productions. Second, we want to define the possible distribution of the investment based on a certain assumption of production, and explain how it will affect the decisions. The remainder of this paper is organized as follows: Section 2 is about the literature reviews on the application of uncertainty (risk) analysis in petroleum industry. Section 3 summaries the composition of offshore oil project investment and sets up the evaluation model. Section 4 presents the results of Monte Carlo simulation for the total investment. Section 5 talks about main conclusions and some suggestions. 2. Literature Review Allais[1] was the first economist who adopted the probability theory in his research on the economics and risks in the exploration period. In his study on the economic feasibility of exploring the Algerian Sahara, exploration period was divided into several sequential and independent stages, and an explicit modeling was set up. Based on probability theory and Monte Carlo simulations, he analyzed the economic feasibility and risks on the entire exploration stage. Allais’s work demonstrated how Monte Carlo method was used in the complex probability analysis. During the 1960s, risk analysis methods were only applied in the academia and were quit new to petroleum industry. Grayson[2], Arps and Arps[3], Newendorp[4], Negill[5] were the first group of scholars who introduced risk analysis methods into petroleum industry, and made great contribution in the application of risk analysis in petroleum industry. In 1980s and 1990s, some new statistical methods were absorbed into risk analysis such as: (1) lognormal risk resources distribution (Attanasi and Drew[6]), (2) Pareto distribution applied to petroleum field-size data in a play (Crovelli[7]) and (3) fractal normal percentage (Crovelli et al.[8]). In the field appraisal and development period, the most useful way is the recovery factor. Saloma˜o and Grell[9] presented that the simplest way to estimate the recovery factor was through analytical procedures, empirical correlations and simulation runs. Paddock et al.[10] presented an classical work to apply real option into the petroleum industry. In their study of oil development process, they made an analogy between real options and American call options. Galli et al.[11] discussed the application of real options, decision trees and Monte Carlo simulations. Risk analysis methods and technologies have been applied into petroleum industry for more than half a century. Different methods are used to investigate different academic problems in different period of petroleum development. But scholars seldom research on the possible distribution of investment before oil companies bid for the oilfields. This investment is very large and will have a great influence on the project’s benefit, especially for the offshore oil projects. Neglecting the possible change of the investment, managers may be over-optimistic or over-pessimistic about the project. Thus, it is necessary and important to analyze the risk before bidding. 3. Model
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Cheng Cheng et al. / Energy Procedia 75 (2015) 3007 – 3013
ĂĂ
Contingency
ĂĂ
Ins & Cer
ĂĂ
Des & Pro M
ĂĂ
HUC
ĂĂ
Installation
Contingency
Material
ĂĂ
Contingency
Indirect Cost
Fabrication
ĂĂ
Indirect Cost
Installation
ĂĂ
Contingency
ĂĂ
Ins & Cer
ĂĂ
Des & Pro M
ĂĂ
HUC
ĂĂ
Installation
ĂĂ
Fabrication
ĂĂ
Material
ĂĂ
Equipment
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Material
ĂĂ
Installation
ĂĂ
Ins & Cer Des & Pro M ĂĂ
Fabrication
ĂĂ
Material
ĂĂ
Equipment
ĂĂ
Equipment
Direct Cost
Direct Cost
Topside 1
Indirect Cost
Jacket
Contingency
Contingency
Direct Cost
Topside 2
FPSO + Wellhead
Drilling
Tanker
Pipeline Direct Cost
Direct Cost Direct Cost ĂĂ
Material
Indirect Cost
Contingency
Ins & Cer
Contingency
Ins & Cer
ĂĂ
Des & Pro M
ĂĂ
Contingency
ĂĂ
Indirect Cost Des & Pro M ĂĂ
Installation
Equipment
ĂĂ
ĂĂ
Ins & Cer
Material
ĂĂ
ĂĂ
Des & Pro M
Fabrication
ĂĂ
ĂĂ
Contingency
Installation
ĂĂ
HUC
ĂĂ
Contingency
Indirect Cost
Contingency
Fig. 1. The composition of investment of FPSO + Wellhead concept
Notes: 1. HUC represents Hook-up & Commissioning, Ins & Cer. represents Insurance & Certification, Des. & Pro. M represents Design & Project Management; 2. The figure is not an intact one because of the space limitation.
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Cheng Cheng et al. / Energy Procedia 75 (2015) 3007 – 3013
In this Section, we set up a certain evaluation model for a certain development concept – FPSO (Floating Production Storage and Offloading) + Wellhead. Firstly we summary the composition of this concept, divide the total investment into different items. Then, we investigate the relationship between all the items and the production level. Finally, we set up an evaluation model for this development concept by the relations above, and test its precision. We subdivide the offshore investment in our study. As shown in Fig. 1, it is divided into six categories – topside 1 (which is connected with tanker), topside 2 (which is connected with jacket), jacket, tanker, pipelines and drilling. Each one is composited by three parts – direct costs, indirect costs and contingency. For each of the six categories, the indirect costs and contingency includes the same investment items. Indirect costs are divided into two parts, i.e. Design & Project Management and Insurance & Certification. Generally, oil companies estimate the total investment of oil fields by using “gravimetric method”. The method estimates the weights and prices separately, and then calculates the investment by multiplying them. We take the same method to investigate the relations between the items and production. We try to find the relations between the weights of all the items and production. In this study, we have three assumptions: (1) The price for different items are exogenous and fixed; (2) Some other uncertain factors, like the soil quality, tides etc. are neglected. We just focus on the production uncertainty, which influence the investment most; (3) The tanker is new built, not converted. One point that should be emphasized is that we set up the evaluation model under the assumption of fixed water depth and jackets’ legs, although we consider the influence of water depth and the jackets’ legs when we investigate the relations between the items’ weights and different uncertain factors. After the research, we find the quantitative relations between the items and the production .There is a significant linear relationship between some items and production, like secondary steel. Some items have a leap relationship with production, like dehydration equipment. The remainders have no relationship with production, like heating equipment. Their relations are shown in Fig. 2.
Fig. 2. (a) Relationships between weights of secondary steel and production; (b) Relationships between weights of dehydration and production; (c) Relationships between weights of heating and production
With all the regulations we get, an evaluation model is made. We test the model with realistic data, and the error of this model is -26.26%. The error is mainly caused by the fact that we neglect many other uncertain factors. However, in the application area, an error within f 30% is acceptable. So it is reasonable to make a quantitative risk analysis on this evaluation model. In the model, every items has a quantitatively relationship with production. The production is inconstant and uncertain. In order to find the possible distribution of investment, we assume the production follows the triangle distribution, which is consistent with many scholars’ hypothesis. By applying the Monte Carlo simulations in the model, we simulate the possible distribution of investment, which will be shown in the next section. 4. The Monte Carlo simulation and the distribution of investment
Cheng Cheng et al. / Energy Procedia 75 (2015) 3007 – 3013
In this Section, we use Monte Carlo simulations methods to research the possible distribution of investment. We assume that the production follows triangle distribution, which is shown in Fig. 3(a). By Monte Carlo simulations, the distribution of total investment is shown in Fig. 3(b). Most of the possible investments values are less than 433.35 million dollars, which account for 90% of all possible values. In other words, the possibility, of which total investment is less than 433.35 million, is 90%. By using goal seek method, it is easy to know that the production that makes the minimum value of possible investment values exceed 439 million dollars is 19.8 KBPD (thousand barrels per day).
Fig. 3. (a) Distribution of Production; (b) Probability density of total investment
Two methods are used to fit the distribution of the total investment. Firstly, we use absolute fitting methods. The result is shown in Fig. 4 (a) and Fig. 4 (b). Then, we choose relative fitting methods, and we set the Std Deviation as 1. The result is shown in Fig. 4 (c) and Fig. 4 (d).
Fig. 4 (a) Fitting of probability density curve by absolute fit; (b) Fitting of cumulative probability curve by absolute fit; (c) Fitting of probability density curve by relative fit; (b) Fitting of cumulative probability curve by relative fit.
As shown in Fig. 4, the result of absolute fit indicates that the LogLogistic distribution is the most suitable distribution for the probability density curve and cumulative probability curve of the investment, ranked by the Chi-Square Statistic. As Fig. 4(b) shows, the biggest difference appears at the range of
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Cheng Cheng et al. / Energy Procedia 75 (2015) 3007 – 3013
(443.40, 437.45), where the cumulative probability curve of simulated investment increases slightly, while the LogLogistic distribution curve increase steadily. The result of relative fit indicates that a totally different distribution fits best. It recommends that the triangle distribution fits best. As showed in the investment simulation (see Fig.3 (b)), the investments values mainly lies in the range of (431, 433.5). Investment distribution in this range is similar to triangle distribution. This is the main reason why the two different fitting methods indicate different distributions. When the Std Deviation is set as 3, both the two methods recommend the LogLogisitic as the best fitting distribution. 5. Conclusion The paper sets up an evaluation model of FPSO + Wellhead concept. In the model, the total investment is calculated by “gravimetric method”. All the relationships between the weights of different investment items and production are investigated. The prices of different items, which are the real data from an offshore project, are exogenous and fixed. In order to analyze the possible distribution of the investment, we assume that the production follows triangle distribution. By using Monte Carlo simulations, we find the best fitting distribution of investment is the LogLogistic distribution. The distribution provides a way to quantitatively analyze the impact of production uncertainty on the offshore oil project investment. We can get the possible range, in which the probability of that total investment is is the biggest, from the probability density curve and cumulative probability curve of investment. The model can also be used to calculate the probability of a certain range where the total investment may be. Thus, it can provide the decision makers with a concept, which is similar to VaR( value at Risk). When the investment is close to the value, the decision maker should be aware of possible losses. They should try to make sure the investment doesn’t exceed the value; otherwise the benefits of the project will be affected. We can also use goal seek method to estimate the possible production level which will satisfy the eigenvalues of a certain distribution. In our study, we only consider the impact of production uncertainty, and neglect other factors, which will also influence the distribution of investment. In the future, we will carry on further research by considering other uncertain factors. Acknowledgements The authors would thank financial support from National Science and Technology Major Project of the Ministry of Science and Technology of China - “Research on Investment estimation tools and economic appraisal system integration and development” (2011ZX05030-006-04). References [1] Allais, M. E´valuation des Perspectives E´conomiques de la Recherche Minie`re sur de Grands Espaces - application au Sahara Alge´rien. Revue de l’Industrie Mine´rale, Paris, January, 1956;329 - 383. [2] Grayson, Charles Jackson. Decisions under uncertainty: Drilling decisions by oil and gas operators. Arno Press, 1979. [3] Arps J J, Arps J L. Prudent risk-taking. Journal of Petroleum Technology 1974, 26: 711-716. [4] Newendorp P D. Decision analysis for petroleum exploration. 1975. [5] Megill R E. An introduction to risk analysis. 1984. [6] Attanasi E D, Drew L J. Lognormal field size distributions as a consequence of economic truncation. Journal of the International Association for Mathematical Geology 1985, 17: 335-351. [7] Crovelli R A. The generalized 20/80 law using probabilistic fractals applied to petroleum field size. Nonrenewable Resources 1995, 4: 233-241.
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Biography Zhen Wang is a professor from China University of Petroleum, Beijing. He was a Fulbright Visiting Research Scholar at the Darden Graduate School of Business at the University of Virginia, Charlottesville, VA. Wang got his PhD in Finance from Peking University and his areas of interests include M&A and energy finance.
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