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Abstract
Estimation of drilling budget and duration is a high-level challenge for oil and gas industry. This is due to the many uncertain activities in the drilling procedure such as material prices, overhead cost, inflation, oil prices, well type, and depth of drilling. Therefore, it is essential to consider all these uncertain variables and the nature of relationships between them. This eventually leads into the minimization of the level of uncertainty and yet makes a "good" estimation points for budget and duration given the well type. In this paper, the copula probability theory is used in order to model the dependencies between cost/duration and MRI (mechanical risk index). The MRI is a mathematical computation, which relates various drilling factors such as: water depth, measured depth, true vertical depth in addition to mud weight and horizontal displacement. In general, the value of MRI is utilized as an input for the drilling cost and duration estimations. Therefore, modeling the uncertain dependencies between MRI and both cost and duration using copulas is important. The cost and duration estimates for each well were extracted from the copula dependency model where research study simulate over 10,000 scenarios. These new estimates were later compared to the actual data in order to validate the performance of the procedure. Most of the wells show moderate - weak relationship of MRI dependence, which means that the variation in these wells can be related to MRI but to the extent that it is not the primary source.
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References
- Aas K (2006), Technical report on “Modeling the dependence structure of financial assets: A survey of four copulas”. Norwegian Computing Center, Oslo, Norway.
- Al-Harthy M, Begg S, Bratvold RB (2007), Copulas: A new technique to model dependence in petroleum decision making. Journal of Petroleum Science and Engineering 57(1): 195-208.
- Chiyoshi FY (2004), Modeling dependence with copulas: a useful tool for field development decision process. Journal of Petroleum Science and Engineering 44(1): 83-91.
- Clayton D G (1978), A model for association in bivariate life tables and its application in epidemiological studies of familial tendency in chronic disease incidence. Biometrika 65(1): 141-151.
- Embrechts P, McNeil A, Straumann D (2002), Correlation and dependence in risk management: properties and pitfalls. Risk Management: value at risk and beyond 176- 223.
- Frank MJ (1979), On the simultaneous associativity of F(x,y) and x+y-F(x,y). Aequationes Math, 1: 194-226.
- Genest C, Ghoudi K, Rivest LP (1995), A semiparametric estimation procedure of dependence parameters in multivariate families of distributions. Biometrika 82(3): 543-552.
- Gumbel EJ (1960), Bivariate exponential distributions. Journal of the American Statistical Association 55(292): 698-707.
- Jaworski P, Durante F, Hardle WK, Rychlik T (2010), Copula theory and its applications. New York: Springer.
- Kaiser MJ, Pulsipher AG (2005), Rigs-to-reef programs in the Gulf of Mexico. Ocean Development and International Law, 36(2): 119-134.
- Mahfoud M (2012), Bivariate archimedean copulas: an application to two stock market indices. Vrije Universiteit Amsterdam, BMI Paper, Amsterdam.
- Nelsen RB (1998), An Introduction to Copulas (Lecture Notes in Statistics).
- Noerager JA, Norge E, White JP, Floetra A, Dawson R (1987), Drilling time predictions from statistical analysis. Society of Petroleum Engineers doi:10.2118/16164-MS.
- Patton AJ (2012), A review of copula models for economic time series. Journal of Multivariate Analysis 110: 4-18.
- Pradier E (2011), Copula theory: an application to risk modeling. Technical report, Grenoble INP-Ensimag.
- Valdes A, McVay DA, Noynaert SF (2013), Uncertainty quantification improves well construction cost estimation in unconventional reservoirs. Proceedings of SPE Unconventional Resources Conference Canada. 5-7 November, Calgary, Canada.
- Williams C, Mason JS, Spaar J (2001), Operational efficiency on eight-well sidetrack program saves $7.3 million vs historical offsets in MP 299 / 144 GOM. Society of Petroleum Engineers doi: 10.2118/67826-MS.
- Zoller SL, Graulier JR, Paterson AW (2003), How probabilistic methods were used to generate accurate campaign costs for Enterprise's Bijupira and Salema development. In the proceedings of the SPE/IADC Drilling Conference, Amsterdam, The Netherlands. SPE eLibrary 79902.
References
Aas K (2006), Technical report on “Modeling the dependence structure of financial assets: A survey of four copulas”. Norwegian Computing Center, Oslo, Norway.
Al-Harthy M, Begg S, Bratvold RB (2007), Copulas: A new technique to model dependence in petroleum decision making. Journal of Petroleum Science and Engineering 57(1): 195-208.
Chiyoshi FY (2004), Modeling dependence with copulas: a useful tool for field development decision process. Journal of Petroleum Science and Engineering 44(1): 83-91.
Clayton D G (1978), A model for association in bivariate life tables and its application in epidemiological studies of familial tendency in chronic disease incidence. Biometrika 65(1): 141-151.
Embrechts P, McNeil A, Straumann D (2002), Correlation and dependence in risk management: properties and pitfalls. Risk Management: value at risk and beyond 176- 223.
Frank MJ (1979), On the simultaneous associativity of F(x,y) and x+y-F(x,y). Aequationes Math, 1: 194-226.
Genest C, Ghoudi K, Rivest LP (1995), A semiparametric estimation procedure of dependence parameters in multivariate families of distributions. Biometrika 82(3): 543-552.
Gumbel EJ (1960), Bivariate exponential distributions. Journal of the American Statistical Association 55(292): 698-707.
Jaworski P, Durante F, Hardle WK, Rychlik T (2010), Copula theory and its applications. New York: Springer.
Kaiser MJ, Pulsipher AG (2005), Rigs-to-reef programs in the Gulf of Mexico. Ocean Development and International Law, 36(2): 119-134.
Mahfoud M (2012), Bivariate archimedean copulas: an application to two stock market indices. Vrije Universiteit Amsterdam, BMI Paper, Amsterdam.
Nelsen RB (1998), An Introduction to Copulas (Lecture Notes in Statistics).
Noerager JA, Norge E, White JP, Floetra A, Dawson R (1987), Drilling time predictions from statistical analysis. Society of Petroleum Engineers doi:10.2118/16164-MS.
Patton AJ (2012), A review of copula models for economic time series. Journal of Multivariate Analysis 110: 4-18.
Pradier E (2011), Copula theory: an application to risk modeling. Technical report, Grenoble INP-Ensimag.
Valdes A, McVay DA, Noynaert SF (2013), Uncertainty quantification improves well construction cost estimation in unconventional reservoirs. Proceedings of SPE Unconventional Resources Conference Canada. 5-7 November, Calgary, Canada.
Williams C, Mason JS, Spaar J (2001), Operational efficiency on eight-well sidetrack program saves $7.3 million vs historical offsets in MP 299 / 144 GOM. Society of Petroleum Engineers doi: 10.2118/67826-MS.
Zoller SL, Graulier JR, Paterson AW (2003), How probabilistic methods were used to generate accurate campaign costs for Enterprise's Bijupira and Salema development. In the proceedings of the SPE/IADC Drilling Conference, Amsterdam, The Netherlands. SPE eLibrary 79902.