19.3.6 Revisions to the MWD Error Model

The reprinted MWD paper [1] by Hugh Williamson covers three distinct areas. It lays out the framework of the ISCWSA error model as discussed in the previous section, it defines the error sources applicable to MWD tools and it provides error magnitudes for these values, complete with a technical justification.

However, work on the ISCWSA error models is on-going and to date several revisions have been made to the basic model as defined in [1]. A summary of the revisions is presented here. More details can be found in [4,5,6].

The revisions to the MWD Error Model are:

Revisions 0 and 2 make some relatively minor corrections and changes to the original paper. However, revisions 1 and 3 are more major and replace all if the toolface dependant terms misalignments. Combined these constitute a large change to the model. Between them these two revisions replace 18 of the original 33 weighting functions, including the misalignment terms, the x and y axis sensor biases and scale factors. 24 new sources are added to model these.

Revision 0 consists of some relatively minor typographical and parameters corrections.

Revision 1 introduces a new method of calculating the effect of tool misalignment to the borehole axis. This avoids the complication of toolface dependency in the misalignments and is considered to handle certain
geometries, such helix-shaped, vertical boreholes better than the original MWD terms. This replaces the two existing misalignment terms MX and MY and introduces four new terms and three possible calculation options which are handled via two weight parameters.

The calculation options are:

Alternatives 1 and 2 have their own strengths and weaknesses, whereas Alternative 3 is designed to combine the best of both options and is the preferred calculation option. This is discussed in detail in Appendix B of [2] and in [4].

Revision 2 makes some corrections to the depth error magnitudes.
Revision 3 replaced the remaining 16 tool face dependant weighting functions with 20 new ones, following a method developed for the gyro error model. This removes the need to either include survey tool faces, or use methods to evaluate at the planning stage which tool faces might be observed, a process which can give rise to unexpected results. The new terms replace all the existing x and y accelerometer and x and y magnetometer bias and scale factor terms, for both the standard MWD and MWD with Axial correction cases. The new terms lump together the x and y effects, and the propagation mode varies from either random, where the tool face varies between survey stations and systematic for sliding between survey stations with constant tool face. In practice for MWD the random propagation would normally be considered at the planning stage. The details of revision 3 are dealt with in [5].

Revision 4 brings in lookup tables for the uncertainty in the BGGM model which will change how the error magnitudes are determined for the reference field terms. This revision does not may any changes to the
weighting functions.

As discussed in section 19.2.3, the error model assumes that all the errors are Gaussian. However, as detailed in [6] it has come to light that the errors in the global geomagnetic models are in fact, non-Gaussian and are best modelled with a Laplacian distribution which has greater likelihood in the tails of the distribution. This presents some problems in the implementation, especially when varying the number of standard deviations at which to report the output results.

The current recommendation is to define in advance the number of standard deviations required for output and then determine the uncertainty in the magnetic model at that confidence level. Divide this value by the number of standard deviation required to get an ‘equivalent Gaussian standard deviation’ (valid only at the confidence level in question) and then use that value as normal in the subsequent calculations.

Although revision 4 has been approved by the ISCWSA, there is still on-going discussion on this point. The appearance of new global magnetic models may lead to further changes in this part of the model.