The basic purpose of the error model is to combine the effects of the various different physical factors which lead to survey errors in order to determine the 3-dimensional position error ellipse at any particular survey station. The same basic mathematical framework is used for both the MWD and gyro error models.
To do this,
i) the model identifies a number of error sources which effect downhole surveys. These are identifiable physical phenomena which will lead to an error in the final wellbore position; for example, the residual sensor error after calibration.
ii) each error source has an error code string such as ABZ or MSZ. This is simply a shorthand identifier.
iii) each error source has a set of weighting functions, which are the equations which describe how the error source effects the actual survey measurements of measured depth, inclination and azimuth.
iv) Each error source also has a propagation mode which defines how it is correlated from survey to survey; this is used in summing up the errors.
v) for a particular survey tool, each error source has an error magnitude.
Example 1: Declination error
Downhole MWD tools measure magnetic azimuth and in order to calculate the true (or grid) north azimuth values, the declination term has to be added to the downhole data:
Usually, declination is determined from a global magnetic model like the BGGM or IGRF models. However, these work on a macro scale and may not be totally accurate in an oil field. So there is some uncertainty (or error bounds) on the declination value and this is clearly a possible source of survey error.
Therefore, the MWD model identifies an error source with the mnemonic code DEC which can be used to model declination uncertainty. From the above equation we can see that a declination error will lead directly to an error in the true azimuth, but it has no effect on inclination or depth measurements. Hence the DEC weighting functions are [0,0,1] (i.e. md=0, inc=0, az=1).
The standard MWD model gives the DEC error source a* magnitude *of 0.36˚. If an In-Field Reference survey was carried out in the field, then the declination uncertainty would be smaller and there could be a different tool model for MWD+IFR with a smaller magnitude for this error source.
If we assume that, whatever the value, the declination is constant over the whole oil field then all MWD surveys, with all different survey tools and in all BHA used in all the wells in the field will be subject to the same error.
Hence then DEC term has a global propagation mode.
Declination error is a function of the Earth’s magnetic field and has no influence on gyro survey tools, so the gyro model doesn’t need to include a declination error term.
(N.B. In fact to model the variation in declination over the global the MWD model uses both the constant DEC term described here and also a second DBH term which is inversely proportional to the horizontal component of total field, but that complication can be ignored for the sake of this discussion.)
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