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 mainlysystematic rather than random. The error model, based on systematic errors, compares well withpractical experience. A graph is presented that shows practical experience. A graph is presented that shows typical lateral position uncertainties of deviated wellsfor various kinds of surveys.
During the past 10 years, the uncertainties involvedin determining the true course of a borehole havebecome a cause for concern. The more deviated anddeeper the holes were drilled, the more often were theoperators faced with inexplicable differences betweenvarious surveys made in the same well. As early as 1971, Truex mentioned that possible lateral positionerrors of highly inclined wells could be up to 30 m ata depth of only 2000 m. Two years before that, Walstrom et al. introduced the ellipse-of-uncertainty concept to describe the positionuncertainty, which can be expected with various surveymethods. Experience, however, has shown that theellipse calculated by this random error model isunrealistically small, which is thought to be duemainly to the nature of the statistical error modelused.The essential differences between the existingrandom error model and the model proposed in thisarticle are illustrated by the following simplifiedexample. Consider the straight and inclined part of awell with these directional characteristics: total depthalong hole (AHD or DAH) 2500 m, surveyed at100 stations at 25-m intervals, and all having aninclination of I Delta I = 30 0.5 and an azimuthof 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, andV = D AH cos I = 2165 m.
The position uncertainty of the bottom of thiswell, according to the error model presented in thisarticle, follows straightforwardly from theassumption that the measuring errors at all 100 stations havethe same magnitude (they are correlated fully).Hence, by simple trigonometry, as sketched in Fig. 1,
In the random error model, however, it is assumedthat the measuring errors vary randomly from onestation to another, which gives them a tendency tocompensate one another. This randomness of themeasuring errors causes the position uncertainty tobe smaller than the former values - in our example, by a factor equal to the square root of the number ofmeasuring stations, which is 100 = 10.