BUOG
Earth’s Field Measurements
Gravitational Forces-Part-1
Prepared by
Najah Saeed Abdulridha
PETE414 , 2nd Semester
29th _January_2021
n.saeed@buog.edu.iq
Objectives
1. Describe the gravitational force measured by the tool
2. List the causes of variation in the gravitational force
3. Describe the theory and operating principles of accelerometer packages
4. Explain the calculation of the total gravitational vector GFH
5. Define g and its relationship to tool G
6. Define an orthogonal set and state the axis convention used in D&I
2
Introduction
To determine the inclination of a survey point, the MWD tool measures its orientation to the
gravitational force.
• This measurement is part of the raw data that the tool transmits to the surface system software. The
software calculates inclination from the raw data.
• In this section, you will learn how the MWD tool measures its orientation to the gravitational force.
• In a later section, you will learn how the software calculates inclination.
3
The Earth's Gravitational Force
• The Earth's gravitational force is referred to as "g.“
• "g" describes the force of attraction exerted by the Earth's mass onto each particle of matter.
• According to Newton's Law of Gravitation, every particle of matter in the universe attracts every other
particle with a force that is directly proportional to the product of the masses and inversely
proportional to the square of the distance between them.
Newton's Law of Gravitation
4
Variations in Earth's Gravitational Force (g)
"g" is primarily a function of latitude, depth/altitude (reference to sea level) and regional fluctuations in the density of the Earth's crust.Variations
in the Earth's gravitational force are so small that measured g should remain constant at every survey point in a wellbore. If you do see a
variation in measured g from a downhole survey, it is an indication of tool error or an incorrect survey procedure.
1. Variations due to latitude
The Earth's rotation gives it a slightly flattened shape. As a result, g varies from 0.997 at 0º latitude (Equator) to approximately 1.003 at
90º latitude.
2. Variations due to depth
“g” varies as wellbore depth increases. The rate of change is approximately 0.0005 per 10,000 feet. Such variations are too small to affect
the MWD tool.
3. Variations due to regional fluctuations
Regional fluctuations are caused by varying density and mass of the Earth's crust in regional areas.
1.003 at 90º latitude(Pole)
0.997 at 0º latitude (Equator)
5
• Accelerometer Sensor
A hinged pendulum suspended inside a case attempts to continue to hang in
alignment with the Gravity vector even if the case is tilted used to measure the
intensity and direction of the earth’s gravitational field.
Determines position of tool relative to earth’s gravitational field.
Gtool 
Gx2  G y2  Gz2
Inclination
Gravity Vector
 We have 3 of these devices in Measuring tool
 They are arranged at 90 degrees to each other in a
mutually orthogonal set
 Each of the 3 accelerometer sensors reads some value
of the Vector G.
 Together, they are called the orthogonal set.
 The sum of the 3 measurements equals total Vector g
(GFH).
TG
Accelerometers Output
 The measurement for each accelerometer ranges from 1.0g to -1.0g.
 The accelerometer reads 1g when its reference axis is aligned with
the gravitational force in the same direction and is not moving.
 It reads 0g when its reference axis is perpendicular to the force.
 the accelerometer's measurement is negative when its in opposite
direction to gravity direction
 These measurements are converted to Tool G by the software, Tool
G is a measure of g in counts. For example, 1g = 1000 counts.
Note The Definition Of The Axes. This Is A Different Arrangement Than Most
Companies And You Must Be Careful If Reading Industry Papers.
Accelerometers Output
– An accelerometer lined up with the Gravity Vector gives +/- 1000 counts or +/- 1 volt
– An accelerometer perpendicular to the Gravity Vector gives zero counts
WHAT IS THE RESPONSE OF A, B & C?
Gravity
Inc = 0, tool is vertical
Top of the DAS
Note:
Yellow cap in C pointing towards center
Yellow cap in A,B pointing outwards (opposite direction)
Top of tool
Accelerometer Output vs. Orientation
0 deg
+1G= +1 V
45 deg
90 deg
135 deg
AS THE SENSOR IS
ROTATED, THE OUTPUT
DESCRIBES A COSINE WAVE.
180 deg
225 deg
270 deg
315 deg
OUTPUT VALUES ARE NOT
UNIQUE. ANGULAR DISPLACEMENT
CANNOT BE MEASURED
WITH ONE SENSOR.
0
-1G=-1 V
GRAVITY
360 deg
MWD TOOL INCLINATION AND GRAVITY
TOOL IS VERTICAL
Inc = 180
TOOL IS HORIZONTAL
G
Inc = 90
Inc = 45
Inc = 135
Inc = 0
What do you think about this ?
https://youtu.be/1HiBeLRsJoM?si=_m_E8Qm1znVpyL1U
How Inclination is Measured
 Angle between the X axis of the tool and the Gravity vector
GX
GFH
I
Tg
Gtool  G  G  G
2
x
2
y
Tg  Gy  Gz
2
2
z
2
 Gx 
Inc  Cos 
 GFH 

1
Inc  Tan
1
 Gx 
 Tg 


14
How Inclination is Measured- GFH - Total Vector
• No matter what the tool orientation, GFH is stable
• GFH as calculated from tool should be close to Geomag value
• An accelerometer lined up with the Gravity Vector gives a larger reading.
• Units of measurement are “counts”, 1000 “counts” = 1g
• This can therefore be used as a Quality Control Measurement
Quality Checks -GFH
• GFH remains stable at each survey point in a wellbore.
• As a result, it can be used to identify failed sensors and to determine the quality of the
MWD tool measurements.
• Quality checks are necessary because of possible instrumentation errors that can be
attributed to the following:
Temperature sensitivity of the accelerometers, which must be taken into consideration
Electronic circuitry problems
Movement of the tool during a survey procedure
How Inclination is Measured-Tg Vector
• The Vector Tg is actually the projection of GFH onto the Y-Z plane
• No matter what the tool orientation, Tg is stable (Roll Test)
• This can therefore be used as a Quality Control Measurement
Inc  Tan
1
 Gx 
 Tg 


Gravity Vector
Gtool  Gx2  Gy2  Gz2
Gx
1  Gx 
Inc  Cos 
Cos( Inc) 

GFH


Gtool
Inclination
TG
17
CHECK:
When the MWD tool is in a vertical wellbore, which reference axis is
parallel to vector g?"
CHECK :
Calculate the value of Inclination from the data below:
• Gx = 765
• Gy = 234
• Gz = 600
GX
GFH
I
Tg
CHECK:
"At which survey point will the current output from the X-axis accelerometer be
the greatest?“
The options provided are:
A
C
B