Time Series Model for the Rate of Penetration in a Reference Oil Well: Puerto Boyacá - Colombia Case

Main Article Content

Henry Daniel Hernández Martínez http://orcid.org/0000-0001-6239-9764
Diego Fernando Lemus Polanía http://orcid.org/0000-0002-6336-9636


penetration rate, long memory process, ARFIMA model, optimization


In this work, a time series control model was identified to describe the rate of penetration in a reference oil drilling well named V∗∗∗. The oil field development plan was named VEL (located in the Magdalena Medio Valley, municipality of Puerto Boyacá - Colombia). The fitted values of the identified model and its 95% confidence interval can be used to guide the wells drilling process for the same field in order to reduce uncertainty in operation times. It is necessary to make a comparative analysis between different ROP drilling processes to verify that the presented methodology can be used in the entire field.

MSC: 62F86, 62L12, 62M10, 62P30, 80M50


Download data is not yet available.
Abstract 4460 | PDF (Español) Downloads 1830 HTML (Español) Downloads 731


[1] M. M. Moradi, V. Alvarado, and S. Huzurbazar, “Effect of salinity on waterin-crude oil emulsion: Evaluation through drop-size distribution proxy,” Energy and Fuels, vol. 25, no. 1, pp. 260–268, 2011.

[2] R. Caenn, H. C. H. Darley, and G. R. Gray, Composition and Properties of Drilling and Completion Fluids, 6th ed. 225 Wyman Street, Waltham, MA 02451, USA: Elsevier, 2011.

[3] I. D. R. Bradford, W. A. Aldred, J. M. Cook, E. F. M. Elewaut, J. A. Fuller, T. G. Kristiansen, and T. R. Walsgrove, “When rock mechanics met drilling: Effective implementation of real-time wellbore stability control.” Society of Petroleum Engineers.

[4] G. E. Box, G. M. Jenkins, and G. C. Reinsel, Time Series Analysis: Forecasting and Control, 4th ed. 111 River Street, Hoboken, NJ 07030, USA: John Wiley and Sons, 2008.

[5] E. Castaño, K. Gómez, and S. Gallón, “Una nueva prueba para el parámetro de diferenciación fraccional,” Revista Colombiana de
Estadística, vol. 31, no. 1, pp. 67–84, 2008. [Online]. Available: http://www.bdigital.unal.edu.co/30708/

[6] D. F. Lemus and E. Castaño, “Prueba de hipótesis sobre la existencia de una raíz fraccional en una serie de tiempo no estacionaria,” Lecturas de economía, vol. 78, no. 1, pp. 151–184, 2013.

[7] J. Beran, Statistics for long-memory processes, 1st ed. One Penn Plaza New York, NY 10119: Chapman & Hall, 1994.

[8] V. M. Guerrero, Análisis estadístico de series de tiempo económicas, 2nd ed. International Thomson Editores, S. A. de C. V., 2003. 155
[9] W. W. S. Wei, Time Series Analysis : Univariate and Multivariate Methods, 2nd ed. Addison Wesley Pub Co Inc, 2005.

[10] P. J. Brockwell and R. A. Davis, Time Series: Theory and Methods, 2nd ed. 233 Spring Street, New York, NY 10013, USA: Springer Science + Business Media, 2006.

[11] J. a. Beran, “Maximum likelihood estimation of the differencing parameter for invertible short and long memory autoregressive integrated moving average models,” Journal of the Royal Statistical Society, vol. 57, no. 4, pp. 659–672, 1995.

[12] J. R. M. Hosking, “Fractional differencing,” Biometrika, vol. 68, no. 1, pp. 165–176, 1981.

[13] W. Palma, Long-Memory Time Series. Theory and Methods, 1st ed. 111 River Street, Hoboken, NJ 07030, USA: Jhon Wiley and Sons, Inc., 2007.

[14] D. A. Dickey and W. A. Fuller, “Distribution of the estimators for autoregressive time series with a unit root,” Journal of the American Statistical Association, vol. 74, no. 1, pp. 427–431, 1979.

[15] J. G. MacKinnon, “Critical values for cointegration tests,” 2010. 157 [16] J. G. a. MacKinnon, “Approximate asymptotic distribution functions for unit root and cointegration tests,” Journal of Business and Economic Statistics, vol. 12, no. 2, pp. 167–176, 1994.

[17] P. C. B. Phillips and P. Perron, “Testing for a unit root in time series regression,” Biometrika, vol. 75, no. 2, pp. 335–346, 1988. 157
[18] J. Geweke and S. Porter-Hudak, “The estimation and application of longmemory time series models,” Journal of Time Series Analysis, vol. 4, no. 4, pp. 221–238, 1983.

[19] P. M. Robinson, “Log-periodogram regression of time series with long range dependence,” The Annals of Statistics, vol. 23, no. 3, pp. 1048–1072, 1995.

[20] C. S. Kim and P. C. B. Phillips, “Log periodogram regression: The nonstationary case,” University of Yale, Tech. Rep., 2006. 159
[21] C. S. Kim, “Log periodogram estimation with nonstationary process,” Journal of Economic Theory and Econometrics, vol. 19, no. 3, pp. 1–23, 2008.

[22] P. C. B. Phillips and K. Shimotsu, “Pooled log-periodogram regression,” Journal of Time Series Analysis, vol. 23, no. 1, pp. 57–93, 2002.

[23] D. W. K. Andrews and P. Guggenberger, “A bias-reduced log-periodogram regression estimator for the long-memory parameter,” Econometrica, vol. 71, no. 2, pp. 675–712, 2003.

[24] C. Velasco, “Non-gaussian log-periodogram regression,” Econometric Theory, vol. 16, no. 1, pp. 44–79, 2000.

[25] M. S. Raymond and W. L. Leffler, Oil and Gas Production in Nontechnical Language, 1st ed. 1421 S Sheridan Rd, Tulsa, Oklahoma, Estados Unidos: PennWell Corporation, 2005.

[26] C. J. Wright and R. A. Gallun, Fundamentals of Oil and Gas Accounting, 5th ed. 1421 S Sheridan Rd, Tulsa, Oklahoma, Estados Unidos: PennWell Corporation, 2008.

[27] F. X. Diebold and G. Rudebusch, “On the power of dickey-fuller tests against fractional alternatives,” Economics Letters, vol. 35, no. 2, pp. 155–160, 1991.

[28] U. Hassler and J. Wolters, “On the power of unit root tests against fractional alternatives,” Economics Letters, vol. 45, no. 1, pp. 1–5, 1994.