Generalized Functional Models for Drilling Cost Estimation

Abstract

Summary A new approach to drilling cost estimation is presented that establishes a general framework for cost estimation using a formalized systems perspective. A generalized functional approach is developed that combines regression-based techniques, as used in the Joint Association Survey (JAS), with the multidimensional attributes of drilling, as incorporated in the Mechanical Risk Index (MRI), Directional Difficulty Index (DDI), and Difficulty Index (DFI) models. A generalized methodology for framing the drilling cost estimation problem is presented and illustrated using a stylized example. Introduction The objective of drilling a hydrocarbon well is to make hole as quickly as possible subject to the technological, operational, quality, and safety constraints associated with the process. These objectives are frequently conflicting and depend on factors that interrelate, that vary with respect to time, location, and personnel, and that are subject to significant intrinsic and market uncertainty. Drilling rates are often constrained by factors that the driller does not control and in ways that cannot be documented. In many situations, the causes of dysfunction are complex, occur simultaneously, and lack effective solutions. The evaluation of drilling performance commands a high degree of visibility in oil and gas companies, and over the past few decades, various methods have been proposed to evaluate drilling cost and complexity. To understand the drilling process, it is necessary to isolate the factors affecting drilling and to quantify their interaction (Brett and Millheim 1986; Schreuder and Sharpe 1999; Mannon 2001; Jones and Poupet 2000). There is no way to identify all the characteristics of drilling that might be important, but many characteristics of the process can be observed, and in practice it is necessary to consider only a set of factors that adequately represent drilling conditions. Well characteristics are measured directly, while operator experience and wellbore quality frequently need to be represented by proxy variables. Many unobservable factors also impact drilling performance, such as well planning and preparation, project management skills, communication skills, and training (Rowe et al. 2000; Holland et al. 2003; Cayeux et al. 2001; Kaminski et al. 2002; Ursem et al. 2003; Harris 1999). The premise of a systems approach to cost estimation is that examination of process characteristics from a large collection of wells will allow the factors that influence drilling cost to be discovered. The outline of the paper is as follows. Drilling performance benchmarks and estimation techniques that are commonly used in industry are first summarized. The main factors that characterize the drilling process are then formally defined. The generalized functional approach is specified and calibrated, and an example is used to illustrate the procedure. In the Appendix, a formulation of the JAS and the MRI model is presented. Drilling Performance Benchmarks Two methods are commonly used to benchmark drilling performance. The first method is based on experimental design and controlled field studies. Typically, one or more parameters of the drilling process are varied, and the impact of the variable(s) on output measures such as the rate of penetration (ROP) or cost per foot (CPF) is examined (Bourgoyne et al. 2003). Controlled field studies are often the best way to understand the relationships between drilling factors under a set of conditions that are tightly controlled. The analytic results that are derived are often based on engineering and scientific fundamentals specific to the wellbore conditions, experimental design, equipment, and contractor, and therefore the ability to generalize the results to other wells and locations may be limited. The second method of studying factor effects is based on an aggregate assessment of well data. In this method, data that characterize a set of wells are collected and relationships are established between the variables using empirical modeling techniques (Iyoho et al. 2005; Bond et al. 1996; Saifaldeen et al. 1997; Noerager et al. 1987). The aggregate approach to analysis uses a set of drilling data and seeks to discover relationships between various drilling factors and the cost and complexity of the wellbore. In this approach, wells drilled under a wide variety of conditions provide the raw data to explore the manner in which (measurable) factors contribute to drilling cost. This allows researchers to compare and contrast a variety of factors that impact drilling and to develop models that describe the average behavior of the performance metrics. In the Gulf of Mexico, the JAS and the MRI are popular methods used to evaluate drilling cost and complexity. The JAS estimates drilling cost using survey data and quadratic regression models constructed from four descriptor variables (API 2002). The MRI is a risk index that uses six primary variables and 14 qualitative indicators to characterize wellbore complexity (Dodson and Dodson 2003). In the Appendix, the formulation of these models is provided. A DDI and a DFI have been introduced to characterize the complexity of drilling directional and extended-reach wells (Oag and Williams 2000; Shirley 2003), and recently Mechanical Specific Energy (MSE) surveillance has been used to improve bit efficiency and performance and obtain a more objective assessment of drilling efficiency (Curry et al. 2005; Dupriest and Koederitz 2005; Dupriest 2006).

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