Borehole Position Uncertainty - Analysis of Measuring Methods and Derivation of Systematic Error Model

Summary

This article presents a new model for describing well- position uncertainties. An analysis for surveying position uncertainties. An analysis for surveying errors is given that demonstrates that they are mainly systematic rather than random. The error model, based on systematic errors, compares well with practical experience. A graph is presented that shows practical experience. A graph is presented that shows typical lateral position uncertainties of deviated wells for various kinds of surveys.

Introduction

During the past 10 years, the uncertainties involved in determining the true course of a borehole have become a cause for concern. The more deviated and deeper the holes were drilled, the more often were the operators faced with inexplicable differences between various surveys made in the same well. As early as 1971, Truex mentioned that possible lateral position errors of highly inclined wells could be up to 30 m at a depth of only 2000 m. Two years before that, Walstrom et al. introduced the ellipse-of- uncertainty concept to describe the position uncertainty, which can be expected with various survey methods. Experience, however, has shown that the ellipse calculated by this random error model is unrealistically small, which is thought to be due mainly to the nature of the statistical error model used. The essential differences between the existing random error model and the model proposed in this article are illustrated by the following simplified example. Consider the straight and inclined part of a well with these directional characteristics: total depth along hole (AHD or DAH) 2500 m, surveyed at 100 stations at 25-m intervals, and all having an inclination of I Delta I = 30 0.5 and an azimuth of A Delta A 90 1. The bottomhole position of this well in north, east, and vertical coordinates easily is found as

N = D AH sin I cos A = 0, E = D AH sin I sin A = 1250 m, and V = D AH cos I = 2165 m.

The position uncertainty of the bottom of this well, according to the error model presented in this article, follows straightforwardly from the assumption that the measuring errors at all 100 stations have the same magnitude (they are correlated fully). Hence, by simple trigonometry, as sketched in Fig. 1,

and

In the random error model, however, it is assumed that the measuring errors vary randomly from one station to another, which gives them a tendency to compensate one another. This randomness of the measuring errors causes the position uncertainty to be smaller than the former values - in our example, by a factor equal to the square root of the number of measuring stations, which is 100 = 10.

JPT

P. 2339