Page | 164
B2 - Historic Terms: No Longer Used in the MWD Model After Revisions 1 and 3 See section Ap1.3.4 for a discussion of the revisions to the MWD model. The following weighting functions have been replaced by new methods introduced in revision 1 (misalignment terms MX and MY replaced) and revision 3 (toolface dependant terms – i.e. all the remaining terms below).
Error Code
Description
Weighting Function
MD
Inc
Azimuth
−𝑐𝑜𝑠𝛼 𝑠𝑖𝑛𝐼
𝑠𝑖𝑛𝛼
0
1
MX
Tool axial misalignment – x-axis
S
𝑠𝑖𝑛𝛼 𝑠𝑖𝑛𝐼
𝑐𝑜𝑠𝛼
0
2
MY
Tool axial misalignment – y-axis
S
−𝑐𝑜𝑠𝐼. 𝑠𝑖𝑛𝛼 𝐺
(𝑐𝑜𝑠𝐼. 𝑠𝑖𝑛𝐴 𝑚 . 𝑠𝑖𝑛𝛼 − 𝑐𝑜𝑠𝐴 𝑚 . 𝑐𝑜𝑠𝛼). 𝑡𝑎𝑛𝛩 − 𝑐𝑜𝑡𝐼. 𝑐𝑜𝑠𝛼 𝐺 (𝑐𝑜𝑠𝐼. 𝑠𝑖𝑛𝐴𝑚. 𝑐𝑜𝑠𝛼 + 𝑐𝑜𝑠𝐴 𝑚 . 𝑠𝑖𝑛𝛼). 𝑡𝑎𝑛𝛩 − 𝑐𝑜𝑡𝐼. 𝑠𝑖𝑛𝛼 𝐺
0
3
ABX
Accelerometer bias x-axis
S
𝑐𝑜𝑠𝐼. 𝑐𝑜𝑠𝛼 𝐺
0
4
ABY
Accelerometer bias y-axis
S
−
𝑠𝑖𝑛𝐼. 𝑐𝑜𝑠𝐼. 𝑠𝑖𝑛 2 𝛼 𝑠𝑖𝑛𝐼. 𝑐𝑜𝑠𝐼. 𝑐𝑜𝑠 2 𝛼
−{𝑡𝑎𝑛𝛩. 𝑠𝑖𝑛𝐼(𝑐𝑜𝑠𝐼. 𝑠𝑖𝑛𝐴 −{𝑡𝑎𝑛𝛩. 𝑠𝑖𝑛𝐼(𝑐𝑜𝑠𝐼. 𝑠𝑖𝑛𝐴
𝑚 . 𝑠𝑖𝑛𝛼 − 𝑐𝑜𝑠𝐴 𝑚 . 𝑐𝑜𝑠𝛼) + 𝑐𝑜𝑠𝐼. 𝑐𝑜𝑠𝛼}. 𝑠𝑖𝑛𝛼 𝑚 . 𝑐𝑜𝑠𝛼 + 𝑐𝑜𝑠𝐴 𝑚 . 𝑠𝑖𝑛𝛼) − 𝑐𝑜𝑠𝐼. 𝑠𝑖𝑛𝛼}. 𝑐𝑜𝑠𝛼
0 0 0
5 6 7
ASX ASY
Accelerometer scalefactor x-axis Accelerometer scalefactor y-axis
S S S
𝑐𝑜𝑠𝐴 𝑚 . 𝑐𝑜𝑠𝛼 − 𝑐𝑜𝑠𝐼. 𝑠𝑖𝑛𝐴 𝑚 . 𝑠𝑖𝑛𝛼 𝐵. 𝑐𝑜𝑠𝛩 −𝑐𝑜𝑠𝐴 𝑚 . 𝑠𝑖𝑛𝛼 + 𝑐𝑜𝑠𝐼. 𝑠𝑖𝑛𝐴 𝑚 𝑐𝑜𝑠𝛼 𝐵. 𝑐𝑜𝑠𝛩
0
MBX Magnetometer bias x-axis
0
0
8
MBY Magnetometer bias y-axis
S
(𝑐𝑜𝑠𝐼. 𝑐𝑜𝑠𝐴 𝑚. 𝑠𝑖𝑛𝛼 − 𝑡𝑎𝑛𝛩. 𝑠𝑖𝑛𝐼. 𝑠𝑖𝑛𝛼 + 𝑠𝑖𝑛𝐴 𝑚 . 𝑐𝑜𝑠𝛼). (𝑐𝑜𝑠𝐴 𝑚 . 𝑐𝑜𝑠𝛼 − 𝑐𝑜𝑠𝐼. 𝑠𝑖𝑛𝐴 𝑚 . 𝑠𝑖𝑛𝛼) −(𝑐𝑜𝑠𝐼. 𝑐𝑜𝑠𝐴 𝑚. 𝑐𝑜𝑠𝛼 − 𝑡𝑎𝑛𝛩. 𝑠𝑖𝑛𝐼. 𝑐𝑜𝑠𝛼 − 𝑠𝑖𝑛𝐴 𝑚 . 𝑠𝑖𝑛𝛼). (𝑐𝑜𝑠𝐴 𝑚 . 𝑠𝑖𝑛𝛼 + 𝑐𝑜𝑠𝐼. 𝑠𝑖𝑛𝐴 𝑚 . 𝑐𝑜𝑠𝛼)
0
0
9
MSX Magnetometer scalefactor x-axis
S
0
0
10
MSY
Magnetometer scalefactor y-axis
S
𝑐𝑜𝑠 2 𝐼. 𝑠𝑖𝑛𝐴
𝑚 . 𝑠𝑖𝑛𝛼(𝑡𝑎𝑛𝛩. 𝑐𝑜𝑠𝐼 + 𝑠𝑖𝑛𝐼. 𝑐𝑜𝑠𝐴 𝑚 ) − 𝑐𝑜𝑠𝛼(𝑡𝑎𝑛𝛩. 𝑐𝑜𝑠𝐴 𝑚 − 𝑐𝑜𝑡𝐼) 𝐺. (1 − 𝑠𝑖𝑛 2 𝐼. 𝑠𝑖𝑛 2 𝐴 𝑚 )
−𝑐𝑜𝑠𝐼. 𝑠𝑖𝑛𝛼
0
11
ABIX Accelerometer bias x-axis when axial interference correction applied. ABIY Accelerometer bias y-axis when axial interference correction applied. ASIX Accelerometer scalefactor x-axis when axial interference correction applied.
S
𝑐𝑜𝑠 2 𝐼. 𝑠𝑖𝑛𝐴
𝑚 . 𝑐𝑜𝑠𝛼(𝑡𝑎𝑛𝛩. 𝑐𝑜𝑠𝐼 + 𝑠𝑖𝑛𝐼. 𝑐𝑜𝑠𝐴 𝑚 ) + 𝑠𝑖𝑛𝛼(𝑡𝑎𝑛𝛩. 𝑐𝑜𝑠𝐴 𝑚 − 𝑐𝑜𝑡𝐼) 𝐺. (1 − 𝑠𝑖𝑛 2 𝐼. 𝑠𝑖𝑛 2 𝐴 𝑚 )
−𝑐𝑜𝑠𝐼. 𝑐𝑜𝑠𝛼
0
12
S
−𝑠𝑖𝑛𝛼[𝑠𝑖𝑛𝐼. 𝑐𝑜𝑠 2 𝐼. 𝑠𝑖𝑛𝐴
𝑠𝑖𝑛𝐼. 𝑐𝑜𝑠𝐼. 𝑠𝑖𝑛 2 𝛼
𝑚 . 𝑠𝑖𝑛𝛼(𝑡𝑎𝑛𝛩. 𝑐𝑜𝑠𝐼 + 𝑠𝑖𝑛𝐼. 𝑐𝑜𝑠𝐴 𝑚 ) − 𝑐𝑜𝑠𝛼(𝑡𝑎𝑛𝛩. 𝑠𝑖𝑛𝐼. 𝑐𝑜𝑠𝐴 𝑚 −𝑐𝑜𝑠𝐼 (1−𝑠𝑖𝑛 2 𝐼. 𝑠𝑖𝑛 2 𝐴 𝑚 )
0
13
S
−𝑐𝑜𝑠𝛼[𝑠𝑖𝑛𝐼. 𝑐𝑜𝑠 2 𝐼. 𝑠𝑖𝑛𝐴
𝑠𝑖𝑛𝐼. 𝑐𝑜𝑠𝐼. 𝑐𝑜𝑠 2 𝛼
𝑚 . 𝑐𝑜𝑠𝛼(𝑡𝑎𝑛𝛩. 𝑐𝑜𝑠𝐼 + 𝑠𝑖𝑛𝐼. 𝑐𝑜𝑠𝐴 𝑚 ) + 𝑠𝑖𝑛𝛼(𝑡𝑎𝑛𝛩. 𝑠𝑖𝑛𝐼. 𝑐𝑜𝑠𝐴 𝑚 −𝑐𝑜𝑠 (1−𝑠𝑖𝑛 2 𝐼. 𝑠𝑖𝑛 2 𝐴 𝑚 )
0
14
ASIY
Accelerometer scalefactor y-axis when axial interference correction applied.
S
− 𝑐𝑜𝑠𝐼. 𝑠𝑖𝑛𝐴 𝑚 𝑠𝑖𝑛𝛼 − 𝑐𝑜𝑠𝐴 𝑚 𝑐𝑜𝑠𝛼 𝐵𝑐𝑜𝑠𝛩. (1 − 𝑠𝑖𝑛 2 𝐼. 𝑠𝑖𝑛 2 𝐴 𝑚 )
0
0
15
MBIX Magnetometer bias x-axis when axial interference correction applied.
S
Made with FlippingBook flipbook maker