SPE67616 Phil.Dickson@PDGM.com SPE 6716 ISCWSA draft D Along hole depth. I Wellbore inclination Am Wellbore azimuth referenced to magnetic north At Wellbore azimuth referenced to true north Tf Toolface angle B Magnetic field strength Dip Magnetic dip angle Decl Magnetic field dip azimuth Z Vertical depth cos Cosine of angle sin Cosine of angle tan Tangent of angle arctan Inverse tangent cot Cotangent MDI magnetic plane angle Magnetic Dip Some more words here -sin(I) * sin(Am) * (cos(I) - tan(Dip) * sin(I) * cos(Am)) / (1 - sin(I)**2 * sin(Am)**2) MFI magnetic magnetic field strength Magnetic Field Some more words here -sin(I) * sin(Am) * (tan(Dip) * cos(I) + sin(I) * cos(Am)) / (B * (1 - sin(I)**2 * sin(Am)**2)) DBH magnetic magnetic field strength Declination DBH Some more words here 1 / (B * cos(Dip)) DECL magnetic magnetic field strength Declination AZ Some more words here 1 ABX sensor acceleration linear X Accelerometer Bias Some more words here (cos(I) * sin(Am) * sin(Tf) - cos(Am) * cos(Tf)) * tan(Dip) + cot(I) * cos(Tf) -cos(I) * sin(Tf) ABY sensor acceleration linear Y Accelerometer Bias Some more words here (cos(I) * sin(Am) * cos(Tf) + cos(Am) * sin(Tf)) * tan(Dip) - cot(I) * sin(Tf) -cos(I) * cos(Tf) ABZ sensor acceleration linear Z Accelerometer Bias Some more words here tan(Dip) * sin(I) * sin(Am) / G -sin(I) / G ASX sensor X Accelerometer Scale Some more words here -(tan(Dip) * sin(I) * (cos(I) * sin(Am) * sin(Tf) - cos(Am) * cos(Tf)) + cos(I) * cos(Tf)) * sin(Tf) cos(I) * sin(I) * sin(Tf) ** 2 ASY sensor Y Accelerometer Scale Some more words here -(tan(Dip) * sin(I) * (cos(I) * sin(Am) * cos(Tf) + cos(Am) * sin(Tf)) - cos(I) * sin(Tf)) * cos(Tf) cos(I) * sin(I) * cos(Tf) * cos(Tf) ASZ sensor Z Accelerometer Scale Some more words here tan(Dip) * sin(I) * cos(I) * sin(Am) -sin(I) * cos(I) ABIX sensor acceleration linear X Accelerometer Bias - Axial Interference Corrected Some more words here (sin(I) * cos(I) ** 2 * sin(Am) * sin(Tf) * (tan(Dip) * cos(I) + sin(I) * cos(Am)) - cos(Tf) * (tan(Dip) * cos(Am) - cot(I)) ) / (G * (1 - sin(I)**2 * sin(Am)**2)) -cos(I) * sin(Tf) / G ABIY sensor acceleration linear Y Accelerometer Bias - Axial Interference Corrected Some more words here (sin(I) * cos(I) * cos(I) * sin(Am) * cos(Tf) * (tan(Dip) * cos(I) + sin(I) * cos(Am)) + sin(Tf) * (tan(Dip) * cos(Am) - cot(I)) ) / (G * (1 - sin(I)**2 * sin(Am)**2)) -cos(I) * cos(Tf) / G ABIZ sensor acceleration linear Z Accelerometer Bias - Axial Interference Corrected Some more words here (sin(I) * cos(I) * sin(Am) * (tan(Dip) * cos(I) + sin(I) * cos(Am))) / (G * (1 - sin(I)**2 * sin(Am)**2)) -sin(I) / G ASIX sensor X Accelerometer Scale - Axial Interference Corrected Some more words here -sin(Tf) * (sin(I) * cos(I) * cos(I) * sin(Am) * sin(Tf) * (tan(Dip) * cos(I) + sin(I) * cos(Am)) - cos(Tf) * (tan(Dip) * sin(I) * cos(Am) - cos(I))) / (1 - sin(I)**2 * sin(Am)**2) sin(I) * cos(I) * sin(Tf) * sin(Tf) ASIY sensor Y Accelerometer Scale - Axial Interference Corrected Some more words here -sin(Tf) * (sin(I) * cos(I) * cos(I) * sin(Am) * sin(Tf) * (tan(Dip) * cos(I) + sin(I) * cos(Am)) - cos(Tf) * (tan(Dip) * sin(I) * cos(Am) - cos(I)) / (1 - sin(I)**2 * sin(Am)**2) sin(I) * cos(I) * cos(Tf) * cos(Tf) ASIZ sensor Z Accelerometer Scale - Axial Interference Corrected Some more words here cos(I) * (sin(I) * cos(I) * sin(Am) * (tan(Dip) * cos(I) + sin(I) * cos(Am))) / (1 - sin(I)**2 * sin(Am)**2) -sin(I) * cos(I) MBX sensor magnetic field strength X Magnetometer Bias Some more words here (cos(Am) * cos(Tf) - cos(I) * sin(Am) * sin(Tf)) / (B * cos(Dip)) MBY sensor magnetic field strength Y Magnetometer Bias Some more words here -(cos(Am) * sin(Tf) + cos(I) * sin(Am) * cos(Tf)) / (B * cos(Dip)) MBZ sensor magnetic field strength Z Magnetometer Bias Some more words here -sin(I) * sin(Am) / (B * cos(Dip)) MSX sensor X Magnetometer Scale Some more words here (cos(I) * cos(Am) * sin(Tf) - tan(Dip) * sin(I) * sin(Tf) + sin(Am) * cos(Tf)) * (cos(Am) * cos(Tf) - cos(I) * sin(Am) * sin(Tf)) MSY sensor Y Magnetometer Scale Some more words here -(cos(I) * cos(Am) * cos(Tf) - tan(Dip) * sin(I) * cos(Tf) - sin(Am) * sin(Tf)) * (cos(Am) * sin(Tf) + cos(I) * sin(Am) * cos(Tf)) MSZ sensor Z Magnetometer Scale Some more words here -(cos(I) * cos(Am) * cos(Tf) - tan(Dip) * sin(I) * cos(Tf) - sin(Am) * sin(Tf)) * (cos(Am) * sin(Tf) + cos(I) * sin(Am) * cos(Tf)) MBIX sensor magnetic field strength X Magnetometer Bias - Axial Interference Corrected Some more words here -(cos(I) * sin(Am) * sin(Tf) - cos(Am) * cos(Tf)) / (B * cos(Dip) * (1 - sin(I)**2 * sin(Am)**2)) MBIY sensor magnetic field strength Y Magnetometer Bias - Axial Interference Corrected Some more words here -(cos(I) * sin(Am) * cos(Tf) + cos(Am) * sin(Tf)) / (B * cos(Dip) * (1 - sin(I)**2 * sin(Am)**2)) MSIX sensor X Magnetometer Scale - Axial Interference Corrected Some more words here -(cos(I) * cos(Am) * sin(Tf) - tan(Dip) * sin(I) * sin(Tf) + sin(Am) * cos(Tf)) * (cos(I) * sin(Am) * sin(Tf) - cos(Am) * cos(Tf)) / (1 - sin(I)**2 * sin(Am)**2) MSIY sensor Y Magnetometer Scale - Axial Interference Corrected Some more words here -(cos(I) * cos(Am) * cos(Tf) - tan(Dip) * sin(I) * cos(Tf) - sin(Am) * sin(Tf)) * (cos(I) * sin(Am) * cos(Tf) + cos(Am) * sin(Tf)) / (1 - sin(I)**2 * sin(Am)**2) SAG misalignment plane angle BHA Sag Some more words here sin(I) MX misalignment plane angle Misalignment (Lateral error) Some more words here -cos(Tf) / sin(I) sin(Tf) MY misalignment plane angle Misalignment (Highside effect) Some more words here sin(Tf) / sin(I) cos(Tf) AXINT magnetic plane angle Axial Magnetic Interferenc (AZ) Some more words here 1 AMID magnetic plane angle Axial Magnetic Interferenc (AMID) Some more words here sin(I) * sin(Am) DREF depth length Depth Reference Some more words here 1 DSF depth Depth Scale Factor Some more words here D DST depth length Depth Stretch Some more words here D * Z SPE90408 Phil.Dickson@PDGM.com SPE 90408 ISCWSA draft 1.0 Part of the nomenclature was copied from SPE 67616. D Along hole depth. I Wellbore inclination Am Wellbore azimuth referenced to magnetic north At Wellbore azimuth referenced to true north Tf Toolface angle B Magnetic field strength Dip Magnetic dip angle Decl Magnetic field dip azimuth Z Vertical depth K Switching factor for some tools. Then K = 1 when I greater-than-or-equal-to 90, K = -1 when I greater-than 90 This behaviour is determined from the errorModel "switching" value. NRF Noise reduction factor at initialization. This is the errorModel "noiseReductionFactor" value Cant Cant angle of tool. This is the errorModel "cantAngle" value Lat Latitude W12 Misalignment weight for XYMIS1 and XYMIS2 Derived from errorModel "misalignmentMode" W12 = 1 when mode = 1, W12 = 0 when mode = 2 and W12 = sin(I) when mode = 3 W34 Misalignment weight for XYMIS3 and XYMIS4 Derived from errorModel "misalignmentMode" W34 = 0 when mode = 1, W34 = 1 when mode = 2 and W34 = cos(I) when mode = 3. L Interval length Ip Inclination at previous station Tp Computed value of error coefficient at previous station C Running speed of continuous survey cos Cosine of angle sin Cosine of angle tan Tangent of angle arctan Inverse tangent cot Cotangent Erot 0.000072921158156 rad/s Earth rotation rate XYZACCBIASXY sensor plane angle XYZ Accelerometers XY Bias cos(I) / G XYZACCBIASZ sensor plane angle XYZ Accelerometer Z Bias sin(I) / G XYZACCSF sensor plane angle XYZ Accelerometer Scale Factor 1.3 * sin(I) * cos(I) XYZACCMIS sensor plane angle XYZ Accelerometer Misalignment 1.3 * sin(I) * cos(I) XYACCBIAS sensor plane angle XY Accelerometer Bias 1 / (G * cos(1 - K * Cant)) XYACCSF sensor XY Accelerometer Scale 1 XYACCMIS sensor plane angle XY Accelerometer Gravity Bias tan(1 - K * Cant) XYACCGBIAS sensor plane angle XY Accelerometer Gravity Bias tan(1 - K * Cant) / G XYACCBIAS sensor plane angle XY Accelerometer Bias 1 / (G * tan(1 - K * Cant) XYACCSF sensor plane angle XY Accelerometer Scale Factor tan(1 - k * Cant) XYGYROBIAS1 sensor plane angle XY Gyro Bias 1 sin(At) / (Erot * cos(Lat) * cos(I)) stationary XYGYROBIAS2 sensor plane angle XY Gyro Bias 2 cos(At) / (Erot * cos(Lat)) stationary XYGYRONOISE sensor plane angle XY Gyro Random Noise f * (sqrt(1 - cos(At)**2 * sin(I) ** 2) / (Erot * cos(Lat) * cos(I))) stationary XYGYROGDEP1 sensor plane angle XY Gyro g-dept error 1 (cos(At) * sin(I)) / (Erot * cos(Lat))) stationary XYGYROGDEP2 sensor plane angle XY Gyro g-dept error 2 (cos(At) * cos(I)) / (Erot * cos(Lat))) stationary XYGYROGDEP3 sensor plane angle XY Gyro g-dept error 3 sin(At) / (Erot * cos(Lat))) stationary XYGYROGDEP4 sensor plane angle XY Gyro g-dept error 4 (sin(At) * tan(I)) / (Erot * cos(Lat))) stationary XYGYROSF sensor XY Gyro Scale Factor tan(Lat) * sin(At) * tan(I) stationary XYGYROMIS sensor plane angle XY Gyro Scale Factor 1 / (cos(Lat) * cos(I)) stationary XYGYRODRIFT sensor angle per time XY Gyro Drift Tp + (1 / sin((Ip + I) / 2)) * (L / C) continuous XY EXTREF reference plane angle External reference error Azimuth reference by fore-sighting or tie-on to an existing survey. For the latter case, the external reference error has to be propagated systematically across the existing and new surveys. 1 RDMTIE reference plane angle Unmodelled random azimuth in tie-on tool 1 TIEMIS reference plane angle Misalignment effect at tie-on 1 / sin(I) DRAND depth length Depth Random Error 1 DSYST depth length Depth Systematic Reference 1 DSCALE depth length Depth Scale L DSTRETCH depth length Depth Scale (Z + D * cos(I)) * L XYMIS1 misalignment plane angle XY Misalignment 1 W12 XYMIS2 misalignment plane angle XY Misalignment 2 -W12 / sin(I) XYMIS3 misalignment plane angle XY Misalignment 3 -W34 * sin(At) / sin(I) W34 * cos(At) XYMIS4 misalignment plane angle XY Misalignment 4 W34 * cos(At) / sin(I) W34 * sin(At) VSAG misalignment plane angle XY Misalignment 4 sin(I) Large Oil Co Rev 1 Dr Ed O'Research Large Oil Co Internal ISCWSA authorized 1.1 Am Wellbore azimuth referenced to magnetic north cos Cosine of angle FUD magnetic plane angle Fear, Uncertainty and Doubt Some additional peril arising from a sense of generalparanoia cos(Am) stationary continuous Z