17.1 Error Models and Instrument Performance Models

Historically four error models have been commonly used in the industry (including one special model developed by Shell for internal use only). These error models define how various error sources affect the observations in the well and thus the positional uncertainty along the wellbore. The mathematical relationship between for example, a bias error on the y axis accelerometer and the positional error at a given survey point is a complicated formula but easily established by these error models. The key to their ability to successfully represent the positional uncertainty is not usually the mathematics but rather the coefficients used to define the numerical accuracies for various tools and how they improve with corrections such as sag, IFR, stretch, interference corrections and so on.

The error models are:

The Cone of Uncertainty Model
The Wolff and De Wardt Error Model
The SESTEM Error Model
The ISCWSA Error Model

A brief explanation of each follows.

The Cone of Uncertainty was a simple model applied in the early versions of COMPASS introduced by Angus Jamieson in the early 1980s. It consisted of a simple ratio with measured depth that applied over a range of inclinations. For example, an MWD survey might provide uncertainty of 7ft/1000ft at up to 15° of inclination, then 10ft/1000ft at up to 30° degrees of inclination and so on. This model was widely used but is very conservative and probably not suitable for close drilling situations.

The Wolff and De Wardt Error Model was published in 1981 and used 5 separate sources of error. These are: a compass reference error; a drillstring magnetization error; an inclination error; a misalignment error; and a relative depth error. All tools were classified as either “gyro” or “magnetic” and either “good” or “poor” quality. A set of values (coefficients) were chosen for each tool and the mathematical model produced an ellipse of uncertainty around the wellbore that could be used for anti-collision calculations. These coefficients were only meant to be used for North Sea operations and were reference to the quality of tools available at the time.

In 1987 the Shell Extended Systematic Tool Error Model (SESTEM) was developed in The Hague by Robin Hartman. It provided a significant improvement on the earlier models. This model considers the equipment running conditions, the location of the well, the background magnetic field accuracy, and considers the measurement error sources at their individual component levels.

Around the same time, a group of industry wellbore surveying experts formed the Industry Steering Committee for Wellbore Survey Accuracy or ISCWSA under the leadership of Hugh Williamson. Under the auspices of ISCWSA a sophisticated model recognized as the industry standard has been developed.

An ‘IPM’ is an ‘Instrument Performance Model’ and describes the error sources, their magnitudes and how they propagate. It is these IPMs that determine how big the uncertainty envelope will be. The temptation is often to use IPMs that are overly optimistic. That is not a best practice. A good guideline is that the IPM values should be a realistic representation of the errors in the entire system and be able to be demonstrated by good quality control in the field or in the calibration process. In all cases the error models and IPMs should be agreed with the client during the well planning stage in order that subsequent changes do not render a planned well undrillable.