Appendix F D&I COMPUTATIONS
M3/M10 6 AXIS SURVEY CALCULATION
The ADC in the M3/M10 is a 12 bit converter. In other words: -5V = 0 Cts 0V = 2048 Cts 5V = 4095 Cts The Advisor/IDEAL uses the following scheme:
-5V = -2048 Cts 0V = 0 Cts 5V = 2048 Cts
This is necessary because the sensors are centered on 0 Volts and therefore, for example, the counts for -5V and 5V should be equal in magnitude. Therefore, the raw data on the Advisor/IDEAL is defined as Counts from the SPM - 2048.
Consequently, the raw data sent by the TCA and decoded on the SPM is different from that displayed on the Advisor/IDEAL.
Ax Mx Ay My Az Mz
SPM DATA 1000 3252 1542 3358 422 2976
RAW DATA -1048 1204 -506 1310 -1626 928
The Advisor algorithms are setup to deal with M1 data. Therefore, the Advisor now needs to convert the M3 Raw data to the equivalent reading the M1 would send. The M3 survey data is a 12 bit word while the M1 survey data is a 10 bit word (11 bits with the sign word). The conversion then is:
(M3 Raw Data) = (M1 Equiv) 2048 1024 The survey calculation would then be as follows:
Ax Mx Ay My Az Mz RAW DATA -1048 1204 -506 1310 -1626 928 M1 Equiv -524 602 -253 655 -813 464 Apply SF -1 -1 -1 Calc. Data Gx Hx Gy Hy Gz Hz 524 602 253 655 813 464
The same principle would apply for the vectors in the toolface frame, except that they are 8 bit words instead of 12 bit words.
Note: The raw data on the Advisor/IDEAL can be negative, but the tool is transmitting
positive values. At this point, the survey calculations are the same as the previous example.
D. Survey Calculations with a Bad Sensor
This section is intended to clarify the procedures to be used when one of the D&I sensors fail. It provides some useful hints on recognizing a failed sensor.
Examination of equations 1 - 9 will lead to the following conclusions: * If a magnetometer fails, then the azimuth will be affected.
* If an accelerometer fails, both azimuth and inclination will be affected.
* If a sensor fails, its sign, as indicated by the Sign Word (SW), may also be in error. Any error here will only affect the bad sensor.
Recognizing a Failed Sensor:
The first indication of a possible D&I failure occurs when the survey is computed and either GFH or HFH is out of range, or the calculated inclination/azimuth does not agree with previous surveys.
Identify the following problems:
1. Was this a valid survey? Could the cause of the problem be: a) Moving the drill pipe while surveying.
b) Signal problems during the D&I frame transmission. 2. Which parameters are wrong?
a) Good GFH, good inclination indicate that the accelerometers are functional. b) Bad HFH, bad azimuth indicate that the magnetometer has failed.
c) Good HFH, bad GFH, bad inclination and bad azimuth indicate an accelerometer failure.
d) Bad GFH, bad HFH, bad inclination and bad azimuth indicate that both an accelerometer and magnetometer have failed.
3. Compare current incorrect data to prior surveys.
a) X-axis data will change very little from survey to survey, so Ax, Mx, Gx, Gx’, Hx or Hx’ should all be similar to previous surveys. If there is a major change, suspect the X-axis sensor.
b) The values for the Y and Z axes will change constantly as the tool rotates downhole. Rotate the drill pipe and take another survey. The new values should change; if one axis sensor remains constant, that is the failed sensor.
Assumptions
1. Assuming an average for GFH or HFH then solving for the sensor value reveals the magnitude of the sensor, but not its sign.
2. The sign of the X-axis sensors will normally be positive. Gx will be positive if the inclination is less than 90 degree. There is not a simple relationship for understanding when Hx is positive or negative. The sign of these sensors can be checked by comparing the latest processed data to previous good survey processed data.
3. The signs of Gy and Gz do not matter when computing the inclination. See equations 3, 4 and 5.
4. The signs of Gy, Gz, Hy and Hz are critical to the calculation of a correct azimuth. Since Y and Z continually change as the drill string rotates, signs from the previous survey cannot be used in the azimuth computations. When a defective accelerometer or magnetometer is isolated and its magnitude computed, this value with both possible signs must be tested.
Sin-1V = Dip Angle ... Equation 10
Since Sin-1V is the dip angle, this is a quick check of whether the correct sign has been used.
5. It is impossible to obtain the sign of the defective sensor from the Sign Word (SW). When a sensor fails, it may have the incorrect sign, as well as an incorrect magnitude. Only the bad sensor will be affected; the signs of the operative sensors will still be correct.
6. The Advisor/IDEAL software (4/5 axis D*I correction) will identify the failed sensor(s) and compute a corrected drift and azimuth. If the 4/5 axis correction is enabled the Master Processor will check the MWD survey for the failed axes. It can detect and correct up to two bad axes, but they must be of different sensor types (i.e. one G and one H).
The correction technique operates by comparing the computed values for drift, azimuth, magnetic dip, G and H with operator entered references. These references are entered manually on the Master Quickstart menu (Advisor) or the survey page (IDEAL). These values are updated whenever a good survey is received or a good correction is made.
The entered MWD Initialization for tool G and H should be that received from the tool prior to the axis failure. This is a very important number as it is used as the
Advisor: If any axes fail during a T/F run, they must be identified from the D&I frame data and manually specified to the computer via "4/5 Axis" option on the MWD INIT page. Axes thus identified will be recomputed before the T/F calculations are made. Refer to Advisor System User’s Guide for D&I Axis Correction and Toolface With A Failed Axis.
Refer to IDEAL FRM for D&I Axis Correction.
FIVE AXIS D&I PROCEDURE GFH = Ã Gx2 + Gy2 + Gz2 HFH = Ã Hx2 + Hy2 + Hz2
{(Gx . Hx) + (Gy . Hy) + (Gz .Hz)} / (GFH . HFH) = SIN DIP
The procedure will also utilize the GFH or HFH from previous good surveys depending upon which type of sensor has failed, that is, accelerometer or magnetometer.
Bad Accelerometer
1. Copy Gx, Gy and Gz; then change signs.
Gx = ________________________ x (-1) = _______________________ Gy = ________________________ x (-1) = _______________________ Gz = ________________________ x (-1) = _______________________ 2. Find the average GFH from previous good surveys.
GFH ave = ____________________
3. Make an estimate of gx. (All estimates will be denoted by a small initial, eg. gx, gy and gz).
4. Try that estimate in the DIP formula.
Temp 1 = Gy.Hy’ + Gz.Hz’ = ____________________ Temp 2 = gx.Hx’ = ____________________
Dip gx (+) = Temp 1 - Temp 2 = ____________________ Dip gx (-) = Temp 1 + Temp 2 = ____________________ Similarly check for gy and gz.
5. gy = GFH ave2 - Gx2 - Gz2 = _____________________ Temp 3 = Gx.Hx’ + Gz.Hz’ = ______________________ Temp 4 = gy.Hy’ = ______________________
Dip gy(+) = Temp 3 - Temp 4 = _______________________ Dip gy(-) = Temp 3 + Temp 4 = _______________________ 6. gz = GFH ave2 - Gx2 - Gy2 = ________________________
Temp 5 = Gx.Hx’ + Gy.Hy’ = _______________________ Temp 6 = gz.Hz’ = _______________________
Dip gz(+) = Temp 5 - Temp 6 = _______________________ Dip gz(-) = Temp 5 + Temp 6 = _______________________
7. Compute the Sin of the actual DIP angle and multiply by the GFH ave. DIP = Sin (magnetic dip angle) x GFH ave = _____________________
8. Compare your estimates of DIP with the actual DIP. DIP - Dip gx(+) = ______________________ DIP - Dip gx(-) = ______________________ DIP - Dip gy(+) = ______________________ DIP - Dip gy(-) = ______________________ DIP - Dip gz(+) = ______________________ DIP - Dip gz(-) = ______________________ Bad Magnetometer 1. Copy Hx, Hy and Hz. Hx = _____________________ Hy = _____________________ Hz = _____________________ 2. Use HFH ave = _______________________ 3. Estimate for hx. hx = HFH ave2 - Hy2 - Hz2 = ______________________ Temp 1 = Gy’.Hy + Gz’.Hz = _______________________ Temp 2 = Gx’.hx = __________________________
Dip hx(+) = Temp 1 + Temp 2 = _______________________ Dip hx(-) = Temp 1 - Temp 2 = _______________________
4. Estimate for hy.
hy = HFH ave2 - Hx2 - Hz2 = _______________________ Temp 3 = Gx’.Hx + Gz’.Hz = _______________________ Temp 4 = Gy’.hy = ______________________
Dip hy(+) = Temp 3 + Temp 4 = _______________________ Dip hy(-) = Temp 3 - Temp 4 = _______________________ 5. Estimate for hz.
hz = HFH ave2 - Hx2 - Hy2 = ________________________ Temp 5 = Gx’.Hx + Gy.Hy’ = _______________________ Temp 6 = Gz’.hz = ______________________
Dip hz(+) = Temp 5 + Temp 6 = _______________________ Dip hz(-) = Temp 5 - Temp 6 = _______________________ 6. Compare your Dip estimates to the real DIP.
7. Calculate the Sin of the actual DIP and multiply by HFH ave. DIP - Dip hx(+) = _____________________
DIP - Dip hx(-) = _____________________ DIP - Dip hy(+) = _____________________ DIP - Dip hy(-) = _____________________ DIP - Dip hz(+) = _____________________ DIP - Dip hz(-) = _____________________