How to know evaluation of PDC bit ROP models and the effect of rock strength on model coefficients?

Abstract

Current low oil price conditions have renewed the emphasis on drilling optimization in order to save time drilling oil and gas wells and reduce operational costs. Rate of penetration (ROP) modeling is a key tool in optimizing drilling parameters, namely bit weight and rotary speed  for faster drilling processes. With a novel, all-automated data visualization and ROP modeling tool developed in Excel VBA, ROPPlotter, this work investigates model performance and the impact of rock strength on model coefficients of two different PDC Bit ROP models: Hareland and Rampersad (1994) and Motahhari et al. (2010). These two PDC bit models are compared against a base case, general ROP relation developed by Bingham (1964) in three different sandstone formations in the vertical section of a Bakken shale horizontal well. For the first time, an attempt has been made to isolate the effect of varying rock strength on ROP model coefficients  by investigating lithologies with otherwise similar drilling parameters. Additionally, a comprehensive discussion on the importance of selecting appropriate model coefficients bounds is conducted. Rock strength, accounted for in Hareland's and Motahhari's models but not in Bingham's, results in higher values of constant multiplier model coefficients for the former models, in addition to an increased RPM term exponent for Motahhari's model. Hareland and Rampersad's model is shown to perform best out of the three models with this particular dataset. The effectiveness and applicability of traditional ROP modeling is brought to question, as such models rely on a set of empirical coefficients that incorporate the effect of many drilling factors not accounted for in the model's formulation and are unique to a particular lithology.

Introduction

PDC (Polycrystalline Diamond Compact) bits are the dominant bit-type utilized in drilling oil and gas wells today. Bit performance is typically measured by the rate of penetration (ROP), an indication of how fast the well is drilled in terms of length of hole drilled per unit time. Drilling optimization has been at the forefront of energy companies’ agendas for decades now, and it gains further importance during the current low oil price environment (Hareland and Rampersad, 1994). The first step in optimizing drilling parameters to produce the best possible ROP is the development of an accurate model relating measurements obtained at the surface to drilling rate.

Several ROP models, including models developed specifically for a certain bit type, have been published in the literature. These ROP models typically contain a number of empirical coefficients that are lithology-dependent and may impair comprehension of the relationship between drilling parameters and rate of penetration. The purpose of this study is to analyze model performance and how model coefficients respond to field data with varying drilling parameters, in particular rock strength, for two PDC bit models (Hareland and Rampersad, 1994, Motahhari et al., 2010). Model coefficients and performance are also compared against a base case ROP model (Bingham, 1964), a simplistic relation that served as the first ROP model widely applied throughout industry and still currently in use. Drilling field data in three sandstone formations with varying rock strengths is investigated, and model coefficients for these three models are computed and compared against one another. It is postulated that coefficients for Hareland's and Motahhari's models in each rock formation will span a wider range than Bingham's model coefficients, as varying rock strength is not accounted for explicitly in the latter formulation. Model performance is also evaluated, leading to the choice of the best ROP model for the Bakken shale region in North Dakota.

The ROP models included in this work consist of inflexible equations that relate a few drilling parameters to drilling rate and contain a set of empirical coefficients which combine the influence of hard-to-model drilling mechanisms, such as hydraulics, cutter-rock interaction, bit design, bottom-hole assembly characteristics, mud type, and hole cleaning. Although these traditional ROP models generally do not perform well when compared against field data, they provide an important stepping stone to newer modeling techniques. Modern, more powerful, statistics-based models with increased flexibility can improve the accuracy of ROP modeling. Gandelman (2012) has reported significant enhancement in ROP modeling by employing artificial neural networks instead of traditional ROP models in oil wells in the pre-salt basins offshore Brazil. Artificial neural networks are also successfully utilized for ROP prediction in the works of Bilgesu et al. (1997), Moran et al. (2010) and Esmaeili et al. (2012). However, such improvement in ROP modeling comes at the expense of model interpretability. Therefore, traditional ROP models are still relevant and provide an effective method to analyze how a specific drilling parameter affects rate of penetration.

ROPPlotter, a field data visualization and ROP modeling software developed in Microsoft Excel VBA (Soares, 2015), is employed in calculating model coefficients and comparing model performance.