Summary In this paper a new method for predicting wellbore position uncertainty which responds to the current needs of the industry is described. An error model applicable to a basic directional measurement while drilling (MWD) service is presented and used for illustration. As far as possible within the limitations of space, the paper is a self-contained reference work, including all the necessary information to develop and test a software implementation of the method. The paper is the product of a collaboration between the many companies and individuals cited in the text. Introduction As the industry continues to drill in mature oil provinces, the dual challenges of small geological targets and severe well congestion increase the importance of quantifying typical wellbore positional errors. The pioneering work of the 1970's culminated in the paper by Wolff and de Wardt.1 Their approach, albeit extensively modified and added to, has remained the de facto industry standard to this day. At the same time, various shortcomings of the method have been identified,2–4 but are not discussed further here. In recent years, a number of factors have created the opportunity for the industry to develop an alternative method:risk-based approaches to collision avoidance and target hitting require position uncertainties with associated confidence levels, something which Wolff and de Wardt specifically avoided;changing relationships brought about by integrated service contracts have forced directional drilling and survey companies to share information on tool performance;the development of several new directional software products and their integration with subsurface applications has provided the necessity and the opportunity to develop new means of communicating and visualizing positional uncertainty. This paper provides a three-part response to this need. 1. Error Model for Basic MWD. This is based on the current state of knowledge of a group of industry experts. There are several reasons why directional MWD is the most suitable survey service to illustrate a new method of error modeling. The error budget is dominated by environmental effects, so that accuracy differences attributable to tools alone are minimal. It is the survey tool of choice for most directional wells, where position uncertainty is of greatest concern. The physical principles of its operation, including the navigation equations, are in the public domain. 2. Mathematical Basis. This is a rigorous description of the propagation of errors in stationary tools. Fit-for-purpose error models using the same basis are in development for inertial and continuous gyroscopic tools, although some simplification and compromise are inevitable. A rigorous treatment of continuous survey tools would probably have too restricted a cognoscenti to be practical. 3. Standard Examples and Results. Despite the apparent simplicity of the Wolff and de Wardt method, different software implementations generally give subtly different results. While an effort has been made in this paper to provide a comprehensive description of the new method, there will surely remain some areas of ambiguity or confusion. In such cases, reproduction of the numerical results at the end of the paper will act as a powerful criterion for "validation." Genesis of the Work. The content of this paper is the fruit of two collaborative groups. ISCWSA. The Industry Steering Committee on Wellbore Survey Accuracy is an informally constituted group of companies and individuals established following the SPWLA Topical Conference on MWD held in Kerrville, Texas in late 1995. The group's broad objective is "to produce and maintain standards for the industry relating to wellbore survey accuracy." Much of the content of this paper, and specifically the details of the basic MWD error model, had its genesis in the group's meetings, which were distinguished by their open and cooperative discussions. Four Company Working Group. The ISCWSA being too large a forum to undertake the detailed mathematical development of an error propagation model, this was completed by a small working group from Sysdrill Ltd., Statoil, Baker Hughes INTEQ, and BP Exploration. The mathematical model created by the group and described below has been made freely available for use by the industry. Assumptions and Definitions The following assumptions are implicit in the error models and mathematics presented in this paper.Errors in calculated well position are caused exclusively by the presence of measurement errors at wellbore survey stations.Wellbore survey stations are, or can be modeled as, three-element measurement vectors, the elements being along-hole depth, D, inclination, I, and azimuth, A. The propagation mathematics also requires a toolface angle, ?, at each station.Errors from different error sources are statistically independent.There is a linear relationship between the size of each measurement error and the corresponding change in calculated well position.The combined effect on calculated well position of any number of measurement errors at any number of survey stations is equal to the vector sum of their individual effects. No restrictive assumptions are made about the statistical distribution of measurement errors. Error Sources, Terms and Models. An error source is a physical phenomenon which contributes to the error in a survey tool measurement. An error term describes the effect of an error source on a particular survey tool measurement. It is uniquely specified by the following data:a name;a weighting function, which describes the effect of the error ? on the survey tool measurement vector p. Each function is referred to by a mnemonic of up to four letters.A mean value, ?.A magnitude, ?, always quoted as a 1 standard deviation value.A correlation coefficient ?1 between error values at survey stations in the same survey leg. (In a survey listing made up of several concatenated surveys, a survey leg is a set of contiguous survey stations acquired with a single tool or, if appropriate, a single tool type.)A correlation coefficient ?2 between error values at survey stations in different survey legs in the same well. 1. Error Model for Basic MWD. This is based on the current state of knowledge of a group of industry experts. There are several reasons why directional MWD is the most suitable survey service to illustrate a new method of error modeling. The error budget is dominated by environmental effects, so that accuracy differences attributable to tools alone are minimal. It is the survey tool of choice for most directional wells, where position uncertainty is of greatest concern. The physical principles of its operation, including the navigation equations, are in the public domain. 2. Mathematical Basis. This is a rigorous description of the propagation of errors in stationary tools. Fit-for-purpose error models using the same basis are in development for inertial and continuous gyroscopic tools, although some simplification and compromise are inevitable. A rigorous treatment of continuous survey tools would probably have too restricted a cognoscenti to be practical. 3. Standard Examples and Results. Despite the apparent simplicity of the Wolff and de Wardt method, different software implementations generally give subtly different results. While an effort has been made in this paper to provide a comprehensive description of the new method, there will surely remain some areas of ambiguity or confusion. In such cases, reproduction of the numerical results at the end of the paper will act as a powerful criterion for "validation." Genesis of the Work. The content of this paper is the fruit of two collaborative groups. ISCWSA. The Industry Steering Committee on Wellbore Survey Accuracy is an informally constituted group of companies and individuals established following the SPWLA Topical Conference on MWD held in Kerrville, Texas in late 1995. The group's broad objective is "to produce and maintain standards for the industry relating to wellbore survey accuracy." Much of the content of this paper, and specifically the details of the basic MWD error model, had its genesis in the group's meetings, which were distinguished by their open and cooperative discussions. Four Company Working Group. The ISCWSA being too large a forum to undertake the detailed mathematical development of an error propagation model, this was completed by a small working group from Sysdrill Ltd., Statoil, Baker Hughes INTEQ, and BP Exploration. The mathematical model created by the group and described below has been made freely available for use by the industry.

The anticancer prodrug 1,2-bis(methylsulfonyl)-1-(2-chloroethyl)-2-[[1-(4-nitrophenyl)ethoxy]carbonyl]hydrazine (KS119) selectively releases a short-lived cytotoxin following enzymatic reduction in hypoxic environments found in solid tumors. KS119, in addition to two enantiomers, has two stable atropisomers (conformers differing in structure owing to hindered bond rotation) that interconvert at 37 °C in aqueous solution by first order kinetics with t1/2 values of ~50 and ~64 hours. The atropisomers differ in physical properties such as partition coefficients that allow their chromatographic separation on non-chiral columns. A striking difference in the rate of metabolism of the two atropisomers occurs in intact EMT6 murine mammary carcinoma cells under oxygen deficient conditions. A structurally related molecule, 1,2-bis(methylsulfonyl)-1-(2-chloroethyl)-2-[[1-(3-hydroxy-4-nitrophenyl)ethoxy]carbonyl]hydrazine (KS119WOH), was also found to exist in similar stable atropisomers. The ratio of the atropisomers of KS119 and structurally related agents has the potential to impact the bioavailability, activation and therapeutic activity. Thus, thermally stable atropisomers/conformers in small molecules can result in chemically and enantiomerically pure compounds having differences in biological activities.

In previous descriptions of the application of quantitative risk assessment (QRA) to subsurface well collisions, several key parts of the analysis have been missing. In particular, no allowance has been made for human error, the distribution of survey errors has not been adequately investigated, and no distinction has been made between real and modeled risks. This precludes immediate application of the technique in cases where personnel or the environment are at risk.These three problem areas each require a challenging analysis, but their resolution would provide a generally applicable risk-based well separation rule. Moreover, once such a rule were in place, there would be several options for further reducing well separations without relaxing the tolerable risk levels.When neither personnel nor the environment are at risk, the problems with the basic analysis are less acute. The technique is currently being applied operationally in these cases.

Summary Monte Carlo simulation is rapidly superceding deterministic methods as the preferred technique for many well-forecasting applications. This paper contrasts the two techniques and highlights the potential benefits of the former. The main part of the paper is a discussion of the application of Monte Carlo simulation to time and cost estimation of single wells and, in particular, of some common errors that the authors have observed practitioners to make (or have themselves made) within this context. This discussion, together with sections covering multiwell programs, scheduling, and production issues, demonstrates that although Monte Carlo simulation has the potential to enhance the reliability of well forecasts, this potential can be realized only if the technique is applied with great care. Introduction Predictions of the duration and cost of well construction, project schedules, production rates, and cash flows are key inputs into the appraisal, planning, and monitoring of wells projects. These predictions may collectively be termed well forecasts. Some of these forecasts, while of interest in themselves, are also used as the building blocks of other forecasts. Thus, there emerges a hierarchical structure (Fig. 1). The sustained delivery of new production at reasonable cost and the achievement of results signaled to and/or expected by investors are central to an E&P company's profitability and reputation. Errors in well time and cost forecasts will propagate through to production and cash-flow forecasts, potentially putting the company's entire business plan at risk. If the forecasts are basically sound, random variation caused by the inherent unpredictability of well operations ought not to have a significant effect on the final, rolled-up results. In contrast, the effects of systematic errors in forecasting technique are likely to be cumulative, resulting in possible substantial variance between forecast and actual results. It is the identification and elimination of these errors in technique with which this paper is concerned.

Summary Subsurface separation criteria have evolved empirically over the years. They still are based largely on untested assumptions about safety factors, comfort values, and survey tool accuracy. A mathematical analysis of the probability of collision combined with a decision tree describing the consequences provides a method of risk evaluation. The mathematics can be simplified under certain special assumptions, allowing key features of the problem to he illustrated. A flow chart of the directional-drilling tolerance setting procedure shows how the methods described can be used in daily well-planning operations. Introduction Formal methods for planning deviated wells, determining safe interwell separations, and executing drilling programs are poorly described in the literature. Basic geometrical calculations are covered in textbooks, but the more detailed procedures for operating on multiwell platforms have evolved gradually over the years and are largely undocumented. Two approaches commonly are used to establish safe well separations. 1. A set of fixed separation guidelines is defined as a function of depth. This method has the major advantage of simplicity. The rules may be empirical or may have been derived from an analysis of survey errors. The principal difficulty with this method is that there is no way to assess whether the values are conservative. 2. Ellipses of uncertainty can be calculated and separation criteria can be based on a minimum allowable distance between ellipses. While appearing to be more "scientific," many uncertainty models are not formally validated, and the use of confidence intervals appears to be quite arbitrary. Consequently, users are again unable to assess whether the predictions are conservative. In the face of the twin pressures of safety and cost-effectiveness, neither procedure allows the planner to balance the sizes of tolerances, costs of surveying, efficiency of drilling, loss of production, and probability of collision against the consequences of a production, and probability of collision against the consequences of a collision. Therefore, there is good justification for developing Procedures that enable engineers to demonstrate the optimum Procedures that enable engineers to demonstrate the optimum operational plan when the consequences of undetected errors have been minimized. This problem has five solution components:a set of formally validated models of instrument behavior;a mathematical estimate of probability of intersection between two wells at a specified separation for a given level of survey uncertainty;a method establish maximum tolerable probability of intersection between two wells;a procedure for defining subsurface tolerances based on the intersection criteria; anda management structure for plan execution at the wellsite. The purpose of this paper is to describe a risk-analysis-based solution to the well-collision problem embodying three new ideas: a method to derive maximum tolerable intersection criteria, calculation of intersection probability between wells, and a method to integrate these solutions into the directional-well planning process. Risk Analysis The process of risk analysis involves three steps: devising an event/outcome tree, quantifying the consequences of different branches, and assessing whether the resulting risks are tolerable. Inspection of the well-intersection problem indicates that the most important considerations are fluids in the well, the flowing characteristics of the well and its pressure regime; the nature of any barriers to the blowout, such as a blowout preventer (BOP) or subsurface safety valve (SSSV); properties of the drilling well, including mud weight and fracture gradient; and probability of ignition of the blowout. The problem may be analyzed by means of an event/outcome tree (Fig. 1 and Tables 1 and 2).