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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.
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,
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.
Abstract Measurement While Drilling (MWD) is a common survey tool used in wellbore positioning. The industry often uses the Industry Steering Committee on Wellbore Survey Accuracy (ISCWSA) error models for estimating the Wellbore Position Uncertainty (WPU). However, the model's sensitivity to direction and nature of trajectory has not been discussed in detail. In this paper, a software model has been developed to better understand the influence of the individual error sources on measurement and position uncertainty in various drilling directions and hole sections. Most operators have classified accurate wellbore positioning and directional design as one of the pillars of safety. It is commonly known that measurement accuracy of frequently used MWD instruments decreases with increasing hole inclination. Survey accuracy is also influenced by North to East direction. This work provides a detailed understanding of the behavior and contribution of each survey error source and screens the error terms contributing most towards WPU. Visualizing the contribution of each error source as a function of well path direction and inclination will support the understanding of position uncertainty of individual wells. The results in this paper are based on analysis of the ISCWSA Non-mag error model. It has been observed that some errors are most dominant in the North/South drilling direction while others are most dominant in the East/West direction. Similarly, some error sources are most effective in the vertical hole section and least effective in the build-up or horizontal sections. This process continues for all different error sources in various hole sections and drilling directions. Therefore, this paper has summarized the most important error sources for the vertical, build-up and horizontal sections of the three wells, i.e North/South (NS), North/East (NE) & East/West (EW). The visualization of error sources will provide a more focused approach towards ultimately reducing the WPU. The work in this paper is a part of a new digital well planning and well construction software tool. The working title of this software is Life Cycle Well Integrity Model – LCWIM.
Abstract As modern drilling projects continue to include increased use of extended-reach wellbores directed to smaller targets, the need for an accurate assessment of uncertainty in bottom-hole location is becoming increasingly critical. Incorrect assessment of the probability of intersecting the target can lead to an equally incorrect assessment of the viability of the project. Most published methods for computing wellbore position uncertainty are based on the analysis of systematic errors in inclination, azimuth and measured depth. The underpinning of such analyses is that these various error terms are uncorrelated constants, but this assumption may not always be justified. The technique has therefore been generalized to make use of more fundamental input error terms. and to take account of the probabilistic nature of such terms, thereby calculating an ellipsoidal probability field for each point along the well. Examples are presented which illustrate the advantages of this method, including the ability to take into account the rotation of an electronic magnetic survey instrument such as an MWD tool. When one survey tool is followed in the hole by another, some error terms may behave in a systematic fashion across the tie-on point while others combine randomly. Since the computed uncertainty in bottom-hole location depends on the degree of correlation between one set of errors and the next, a flexible means is suggested for accommodating such tie-ons. Since a probability can be assigned to the hypothesis that a point in a planned or drilled wellbore occupies a given volume of space, this method can also be used to determine the probability that a particular point in the well might intersect an adjacent wellbore or an arbitrary target volume. This makes possible improved computation of the probabilities of wellbore collision or target penetration. Introduction The calculation of wellbore position uncertainty has been addressed by Walstrom et al and by Wolff and deWardt. It is commonly accepted today that such uncertainty is dominated by systematic errors, thus most popular models are based on the systematic analysis outlined by Wolff and deWardt. With extensive field usage of these models over the years, some limitations have become apparent. These include the deterministic nature of the systematic model as originally described, the definition of most instrument errors in terms of fixed inclination and azimuth uncertainties, failure to include random errors as well as systematic, and the inability to assign a probability to borehole position. A modified treatment of uncertainty which overcomes these limitations is described here. Although several of these improvements have been used for many years by a number of companies, until now there has been little documentation of them in the literature. Calculation of Wellbore Position Uncertainty Wellbore surveys are typically performed at a number of discrete survey stations along the course of the well by measuring components of the earth's gravity field and either the local magnetic field or a rotation vector. An instrument performance model is used to convert these raw measurements to inclination I, and azimuth A, which together with the along-hole depth L, make up a three-component measurement vector p. A wellbore trajectory model is then employed to convert the set of measurement vectors into a position vector r in a north, east, and vertical (N, E, V) coordinate system. An instrument performance model includes potential sources of error or uncertainty in the measurement. P. 411
Figure 1: (a) Map view showing a treatment well and two mornitor wells, and five hypothetical sources (solid circles) along an assumed fracture (dashed line).
Abstract 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.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,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.