STANDARD HANDBOOK OF PETROLEUM & NATURAL GAS ...

MWD and LWD 919
Also needed:
Vector well direction located along the well (sonde axis) and is defined by
the coordinates Zx = 0, Zy = 0 and Zz = 1.
Ox is lined up with the mule shoe key and the tool face direction.
For the numerical applications, we shall have:
Accelerometer scale factor 3 mA/g, Ix = -2 mA, Iy = 1 mA, IT = 2 mA at a
given depth,
Magnetometer readings: Hx = -0.1077 G, HY = 0.2 G, Hz = 0.45 G at the
same depth,
Magnitude of the magnetic field: 0.52 G, magnetic field inclination: 30"
with respect to the vertical.
1. Compute the borehole deviation. Show that a check of the accelerometer
readings is possible if we assume that the G vector module is g.
2. Compute the tool face orientation. In the numerical application above, is
the borehole going to turn right, left or go straight if we keep on drilling
with this orientation?
3. Show that we can check the magnitude of the magnetic field vector and
correct for an axial field due to the drill collars.
4. Compute the dip angle of the magnetic field vector after correction for
the drill collar field, it should check with the local magnetic field data.
What do you conclude if it does not?
5. Compute the orientation of the borehole with respect to magnetic north
without axial field correction.
6. Write an interactive computer program for solving the above questions.
Solution
1. i = 48.2"; 3 mA.
2. TF = +26.5"; turning right.
3. Drill collar magnetic field = 0.0178 G; H7 corrected = 0.468 G.
4. h = 30" from vertical.
5. One way of making the calculation is to use the three vectors:
G (Gx, G , GI)
H (Hx, dy? HJ
z (0, 0, 1)
(See Figure 4-233 a and b).
a. Compute the coordinates of vector A normal to vector G and vector H.
Vector A = cross-product of vector G by vector H.
b. Compute the coordinates of vector B normal to vector G and vector Z.
Vector B = cross-product of vector G by vector Z.
c. Compute the angle between vector A and vector B. Being both normal
to vector G, they are in the horizontal plane. The angle represents the
azimuth. In some configurations 180" must be added. The angle is
computed by making the scalar product of vector A by vector B.
A B = (AI IBI cos Az = AxBx + AyBy + AzBz
Care must be exercised since cos(Az) = cos(-Az).
d. Numerical results: Angle between vertical planes, 31.71"; azimuth, 328.29".