Summary The positional uncertainty about a point on a wellbore is commonly represented as an ellipsoid. The ellipsoid also accounts for the dimensions of the casing or open hole. With the use of this model, at any time the resulting uncertainty about a wellbore along its trajectory is a curved, continuous cone. To a good approximation, the intersection of the plane normal to a reference well with these cones can be represented as ellipses. This simple geometrical model has been adopted by standards organizations to define minimal acceptable separation distances between wellbores (e.g., the Norwegian NORSOK D-10 Standard and Oil and Gas UK Well Integrity Guidelines). Because of mathematical difficulties, the existing methods for calculating the resulting separation factors are only approximations and may be either too optimistic or too conservative, particularly for ellipses with high eccentricities. This paper presents explicit equations for determining the exact condition in which the ellipses touch, expressing the result as an expansion scale factor. Methods are presented for the expansion of either ellipse or both, together with implementation notes and other associated tools. The new algorithms are only marginally less efficient than the existing approximation methods, and they can be used to increase the allowable proximity of two adjacent wells while satisfying the geometrical and probabilistic constraints. The examples included in the paper illustrate this. The proposed calculation method is consistent with existing industry wellbore uncertainty models. Because the determination of the osculating condition is exact, the calculation is neither too optimistic nor too conservative. This paper is a response to discussions held at the SPE Wellbore Positioning Technical Section meeting on 3 November 2011.

Depth is a critical measurement in the economic development of a hydrocarbon asset.Almost all downhole activities, from making petrophysical measurements to setting packers, are performed remotely from surface.The common reference for all such activities is depth.A vertical depth error of less than one meter can have a financial impact counted in millions of dollars.However, despite the Industry's heavy reliance on depth, its accuracy is poorly specified. This paper describes a set of error terms which allows proper quantification of along-hole depth uncertainty for commonly used measurement systems.Additionally, the terms include correlation coefficients that allow quantification of the relative uncertainty between two competing measurements. Although the physical measurement that is made at the rig site is normally along-hole depth, it is vertical depth that defines the relationship between sub-surface features.The quantification of along-hole measured depth uncertainty is therefore only a partial solution; it is also necessary to estimate vertical uncertainty. The directional survey of the wellbore defines vertical depth for any along-hole depth, and directional surveys are routinely accompanied by an estimate of positional uncertainty.A method is described for combining the directional survey's estimate of the wellpath's vertical position uncertainty with the along-hole depth uncertainty associated with another downhole operation, resulting in a valid vertical uncertainty for that operation. Adoption of the techniques described in this paper will result in valid estimates of depth uncertainty, which it is hoped will encourage better depth management practices, and result in more productive wells. Introduction There are frequent calls from the end users of formation evaluation (FE) logs for improved depth accuracy.[1]Zones of interest within the wellbore identified from FE logs (e.g. zones targeted for production, injection, etc.) are subsequently exploited using tools and procedures that are also applied at specified depths.It is therefore desirable that improvements made to the measurement and management of FE depths are applied to all other depth measurements. It has been proposed that rational improvement in depth measurement accuracy is not possible until current performance is better understood and properly quantified, and that the directional survey tool error models, commonly used in the Industry to predict wellbore position uncertainty, offer a useful starting point for modelling the performance of depth measurement systems,[2]Survey tool error models quantify accuracy largely in terms of uncertainty or probability.Their outputs are position bias and position uncertainty, but these values are derived from estimates of the biases and uncertainties associated with the measured values of along-hole depth, inclination and azimuth.Along-hole depth is more commonly referred to as measured depth (MD). Several directional survey tool error models are described in the literature.[3–8]These models include MD terms, which can be extracted, revised and added to, to produce a dedicated MD error model.The most recent papers on the subject[7,8] were written under the auspices of the Industry Steering Committee for Wellbore Survey Accuracy (ISCWSA).The models described in these papers are now being widely adopted within the Industry, and are likely to become de facto standards.In 2004, the ISCWSA was assimilated into the SPE as its Wellbore Positioning Technical Section. The new Technical Section saw the development of a comprehensive depth error model as a natural extension of the earlier error modelling work of the ISCWSA, and as something that might benefit the wider wellbore construction community.This paper is a first step in meeting the Section's objective of providing a standard depth error model.

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The positional uncertainty about a point on a wellbore is commonly represented as an ellipsoid. The ellipsoid also accounts for the dimensions of the casing or open hole. Using this model, at any time the resulting uncertainty about a wellbore along its trajectory is a curved, continuous cone. To a good approximation, the intersection of the plane normal to a reference well with these cones can be represented as ellipses. This simple geometrical model has been adopted by various standards organisations to define minimum acceptable separation distances between well bores, for example the Norwegian NORSOK D-10 standard. Because of mathematical difficulties, the existing methods for calculating the resulting separation factors are only approximations and may be either too optimistic or too conservative, particularly for ellipses with high eccentricities. The paper presents explicit equations for determining the exact condition where the ellipses touch, expressing the result as an expansion scale factor. Methods are presented for the expansion of either one, or both ellipses, together with implementation notes and other associated tools. The new algorithms are only marginally less efficient than the existing approximation methods and they can be used to increase the allowable proximity of two adjacent wells whilst satisfying the geometrical and probabilistic constraints. The examples included in the paper illustrate this. The proposed calculation method is consistent with existing industry wellbore uncertainty models. Since the determination of the osculating condition is exact, the calculation is neither too optimistic nor too conservative. This paper is a response to discussions held at the SPE Wellbore Positioning Technical Section meeting on 3rd November 2011.