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Following some work done for the gyro error model, the misalignment of the survey tool to the wellbore is now modelled with four misalignment terms. A further term is used to account for sag – the deflection of the BHA under gravity, which leads to an inclination error since the centreline of the survey tool will not be orientated parallel to the borehole axis 5) Depth errors (4 error sources) A total of four error sources are used to model the errors in measured depth, due to both random and systematic errors, scale factor errors on the depths and drillpipe stretch under tension from the weight of the BHA. In this modelling some physical error sources may be lumped together into one error source if in practise it is difficult or unnecessary to separate them. So for example, the misalignment error sources that are identified are for the misalignment of the tool itself to the borehole, not the sensors to the tool. The misalignment of the sensors themselves to the tool axes are accommodated within the sensor bias and scalefactors and are not explicitly separated out. MWD Weighting Functions As described in the example in section Ap1.2.4 the MWD weighting functions are determine by taking the partial derivatives of the survey equations with respect to the error sources. All of the MWD weighting functions are detailed in Appendix B. Ap1.3.3 Even a quick glance shows that many of the weighting functions are zero. Of the total list of error sources, only the four depth terms have any influence on measured depth. Some of the functions such as the effect of the declination errors on azimuth or sag error on inclination are relatively simple equations. However, other sources such as the accelerometer error sources may influence both the inclination and azimuth measurements and, particularly in the azimuth case, lead to relatively complex equations to be evaluated at each survey station. MWD Error Magnitudes The MWD model is the only case for which the ISCWSA defines error magnitudes and provides complete tool models, if only for a limited number of situations. This is because it is considered that the performance of most modern MWD tools is quite similar and a generic model is valid. Ap1.3.4 Much of the MWD paper [1] is given over to a justification of error magnitudes for the MWD error sources and a complete tool models are given both standard MWD surveys and for surveys which are corrected for axial-interference for the combinations situation where the tools are run from a fixed land rig with fixed depths and for an offshore floating platform.
So effectively there are four defined tool models: i.
MWD-Fixed Rig
ii.
MWD-Floating Platform
iii. iv.
MWD + Axial Correction – Fixed Rig
MWD + Axial Correction – Floating Platform
The application of survey correction techniques to improve the accuracy of MWD surveys will generally change the magnitudes of one or two error sources. So for example, running sag-correction software will reduce the magnitude of the sag error term; conduc ng n F su y w ll mp o h knowl dg of h E h’s m gn c f ld nd l d o reduced magnitudes for the four reference field error terms. The use of the error model as implemented in directional- drilling software is the appropriate way to evaluate the effect of these techniques and to determine an appropriate survey program for a well. However, the ISCWSA has not defined or standardised values to be used to model these.
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