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Ap1.2.2 Error Sources An error source is any physical phenomenon which contributes to the overall positional measurement error.
Examples of error sources include residual sensor errors after calibration, misalignment of the survey tool with the bo hol xs,unc n s n h E h’sm gn cf ld,whch s h f nc g ns whchMW m su m ns are made, deflection of the survey tool under gravity, stretch of drillpipe or wireline under the weight of the BHA or survey tool etc. Between all versions of the MWD and gyro models, some ninety-eight individual error sources are identified. These are not all applicable to each survey tool, but are dependent on the type of tool in operation and how it works. A typical tool model (or IPM file) defines which of these error sources are invoked to model that tool. Ap1.2.3 Error Magnitudes For a particular tool model, each error source has an error magnitude. The error magnitude is essentially the standard deviation of the range of values which the error source might be expected to take over a statistical sample of survey data under normal field operating procedures. For example, if you consider a large number of MWD runs, what are the statistics for the range of tool misalignments to the borehole? The values may change depending on what survey techniques or corrections are being applied to the job in hand. So as previously mentioned, using an IFR survey to measure the declination value in the field reduces the magnitude of the declination error term. There is still a declination error source, and the weighting functions remain the same, but compared to the MWD tool model, the MWD+IFR tool model will have a smaller magnitude for the declination term. h MW p p g s lu sfo h s fo ‘nom l’MW su yng.How b yond h n ls o m gn ud s are not set by the ISCWSA.
For the gyro error model, it is expected that error magnitudes will be supplied by the gyro contractor. Test cases are defined in the gyro paper but these are not considered to model any particular survey tools.
The error magnitudes defined in the MWD paper are all at one standard deviation (1-sigma). If the user requires final error ellipses at two standard deviations (or three) then the 1-sigma ellipses can simply be multiplied up and typically drilling software has a user control to define at what level error ellipses are to be output. There are two provisos to this – some drilling software packages allow the user to enter error magnitudes at different defined confidence levels (e.g. 1-sigma or 2-sigma etc.) Also, changes to the MWD at revision 4 may require the user to define the required output confidence level first so that certain magnetic field reference terms can be correctly calculated (for further details see section Ap1.3.4 below.) Weighting Functions Each error source has a set of weighting functions which define how that error source effects the actual survey measurements of measured depth, inclination and azimuth. These weighting functions are simply the equations that link the error source to the survey measurements, e.g. the weighting functions enable us to take a z-magnetometer bias uncertainty in nano-Teslas and calculate a survey azimuth uncertainty in degrees at a particular survey station in a particular wellbore. Ap1.2.4
The actual survey inclination and azimuths are obtained from the sensor data via a set of survey equations. So for example for a standard MWD tool the inclination and azimuth are determined from the following equations:
𝑮 𝒛
𝑰 = 𝒄𝒐𝒔 −𝟏
𝟐 +𝑮
𝒚 𝟐 +𝑮
𝒛 𝟐
√𝑮 𝒙
(
)
𝟐 +𝑮
𝒚 𝟐 +𝑮
𝒛 𝟐
(𝑮 𝒙 𝑩 𝒚 −𝑮 𝒚 𝑩 𝒙 )√𝑮 𝒙
−𝟏
𝑨 𝒕𝒓𝒖𝒆 = 𝒕𝒂𝒏
+𝜹
𝟐 +𝑮
𝒚 𝟐 )−𝑮
𝑩 𝒛 (𝑮 𝒙
𝒛 (𝑮 𝒙 𝑩 𝒙 −𝑮 𝒚 𝑩 𝒚 )
(
)
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