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Mathematical Problems in Engineering
Volume 2015, Article ID 631290, 9 pages
Research Article

Mathematical Modeling Applied to Drilling Engineering: An Application of Bourgoyne and Young ROP Model to a Presalt Case Study

1Universidade Estadual Paulista (UNESP), Faculdade de Engenharia, Câmpus de Guaratinguetá (FEG), Departamento de Mecânica (DME)/PRH48-ANP, Avenida Ariberto Pereira da Cunha 333, Portal das Colinas, 12.516-410 Guaratinguetá, SP, Brazil
2Montanuniversität Leoben (MUL), Department of Petroleum Engineering (DPE), Chair of Drilling and Completion Engineering (CDC), Erzherzog-Johann-Straße 3, 8700 Leoben, Austria

Received 25 June 2015; Revised 18 August 2015; Accepted 20 August 2015

Academic Editor: Reza Jazar

Copyright © 2015 Andreas Nascimento et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Several mathematical ROP models were developed in the last five decades in the petroleum industry, departing from rather simple but less reliable R-W-N (drilling rate, weight on bit, and rotary speed) formulations until the arrival to more comprehensive and complete approaches such as the Bourgoyne and Young ROP model (BYM) widely used in the petroleum industry. The paper emphasizes the BYM formulation, how it is applied in terms of ROP modeling, identifies the main drilling parameters driving each subfunction, and introduces how they were developed; the paper is also addressing the normalization factors and modeling coefficients which have significant influence on the model. The present work details three simulations aiming to understand the approach by applying the formulation in a presalt layer and how some modification of the main method may impact the modeling of the fitting process. The simulation runs show that the relative error measures can be seen as the most reliable fitting verification on top of R-squared. Applying normalization factors and by allowing a more wide range of applicable drillability coefficients, the regression could allow better fitting of the simulation to real data from 54% to 73%, which is an improvement of about 20%.