19.1 Introduction

Like all measurements, borehole surveys are subject to errors and uncertainties which mean that a downhole survey result is not 100% accurate. For many applications, such as anti-collision and target sizing, it is very important to be able to quantify the position uncertainty around a wellbore trajectory. However, since many different factors contribute to the final position uncertainty it is not a trivial matter to determine these bounds.

The Industry Steering Committee for Wellbore Survey Accuracy (ISCWSA) has produced an error model in an attempt to quantify the accuracy or uncertainly of downhole surveys. The error model is a body of mathematics for evaluating the uncertainty envelope around a particular survey.

Originally the error model dealt with only MWD surveys, but it has later been extended to also cover gyro surveys. This document sets out to provide an overview and understanding of these models. The full details can be found in two SPE papers; SPE-67616 and SPE-90408 (see references below). There have also been successive revisions to both models, details of which can be obtained from the ISCWSA website iscwsa.org

The error model identifies a number of physical phenomena which contribute to borehole survey errors and provides a mathematical framework for determining in numeric terms the uncertainty region around a particular survey. Typically this error model will be implemented in directional drilling software. The user will select the appropriate tool model for the survey tool that has been run and the error results will be used in anti-collision or target sizing calculations.

In simple terms, the error model is a means to start from a gyro drift specification in deg/hr or a tool misalignment in degrees and evaluate how that error effects the borehole survey measurements of inclination, azimuth and measured depth at a particular survey station. The model then propagates and combines these error contributions, taking into account all of the important physical errors, at all of the survey stations from all of the survey runs within a well. The final results are error ellipse dimensions, in metres or feet, within which the actual wellbore is expected to be found to a specified level of confidence.

It is common to talk about the MWD model and the gyro model, but in fact these both of these models share a common framework for describing and propagating the errors. This document will present some of the background information on the ISCWSA models before presenting this basic mathematical framework on which they are based. The MWD model is described in some detail, followed by a discussion of the gyro error model. There follows a section which is concerned with implementation details, which will mainly be of interest to software developers. The last section discusses standardisation of the model.

There is some maths in these early sections but it should still be possible to follow the thread of the discussion without worrying too much about the details of the equations. For those with a thirst for more, three appendices present in detail the mathematics of the framework and all of the weighting function equations.

To follow the discussion, the reader should at least be familiar with the basic concepts of borehole surveying. A good starting point would be an understanding of chapters 5 and 10 of this book which describe the principles of MWD and gyro tools and also chapters 18 and 20 which present an introduction to error modelling and error propagation.