Borehole Gravity Survey
Planning
Planning a BHGM survey involves a consideration of the
expected signal from the target and the survey parameters
required to resolve the target signal under the well
conditions.
Planning Example
It is desirable to measure changes in
carbonate porosity in an oil reservoir to an accuracy of 1%.
The change in formation bulk density due to a change in
porosity, Df, is expressed by:
Dr_{B} = Df (r_{o}
 r_{m} + S_{w}(r_{w} r_{o}))
Equation 1
for:
an oil density, r_{o} of 0.85 g/cc
water density, r_{w} of 1.04 g/cc
water saturation, S_{w},
of 0.1
grain density, r_{m} of 2.71 g/cc
.01 p.u. the change in bulk
density
Dr_{B} is
0.018 g/cc.
We can use Equation 3 below to
calculate the BHGM density error using reasonable survey
parameters:
Depth interval : 5 meters
Gravity difference error : 0.005
milligals
Depth interval error : 1 cm.
Formation density : 2.71 g/cc
Number of gravity difference
readings (passes) : 1
The resultant BHGM density error is 0.012
g/cc., so a 1 p.u. porosity change could be detected using a
5 meter station interval. It is recommended that more than 1
pass be made through the formation for two reasons.
1. The gravity meter readings drift with
time and repeat readings should be made to enable drift
corrections to be made.
2. More than one pass will allow
calculation of density measurement accuracy estimates and
decrease the error as shown by Equation 3.
In the above example if 3 passes were made
the BHGM density error would drop to 0.007 g/cc.
BHGM Apparent Density
The BHGM tool measures gravity, g, while the
tool is held stationary in the well. The BHGM apparent
density is obtained from the vertical gradient of gravity
calculated between two adjacent gravity readings:
r_{A} = 3.68237 
0.005247 sin^{2}q  0.00000172
 11.92601Dg/Dz
Equation 2
where:
r_{A}
is the BHGM apparent density
Dg is
the gravity difference in milligals
Dz is
the depth difference in meters
q is
the well latitude
is the average reading depth
This density is an apparent density because
it yields the density which a fictitious uniform density
earth must have to produce the measured gravity gradient. In
cases where the geology is flat for large distances around
the well, the apparent BHGM density will equal the formation
density between the two gravity measurements. In conditions
where there is a need for high absolute density accuracy and
the structure is not uniformly flat lying, the apparent BHGM
density can be structurally corrected to yield the formation
bulk density, r_{B}.
BHGM Density Measurement Error
The error in BHGM density due to errors in Dg and Dz is
found by taking the square root of the sum of the squares of
the partial derivatives of Equation 2 with respect
to Dg and Dz.
The result is divided by the square root of the number of
times the interval measurements are performed, N.
^{
}Equation 3
where:
 dDg is the error in
the gravity differential
 dDz is the error in
the depth differential
The errors in the density measurement can be controlled in
field surveys, by varying Dg, Dz and N.
The error in Dg is dependent on
noise conditions at the time of the measurement. The
resolution of the recording electronics is better than 0.001
milligals. Under ideal conditions the repeatability of the
gravity measurements is about 0.002 milligals. A conservative
value for survey planning purposes is 0.005 milligals. Under
some circumstances, for example in storms offshore, this
error will be larger due to noise.
The relative depth error, dDz,
is normally below 1 cm for depth intervals below 10 meters.
For intervals less than 2.8 meters, the shuttle system
eliminates the relative depth errors.
Ambient noises cause accelerations of the sensor and vary
with the logging environment. At shallow depths, noise is
generally weather related and transmitted to the tool via the
cable or through the earth. Weather related noise transmitted
through the cable decreases with increasing depth due to the
damping action of the wireline cable and the well fluid. This
noise can be minimized by clamping the cable to the well head
or clamping the tool to the inside of the hole. Noise from
offshore platform motion in bad weather must be minimized
with a downhole clamp. Some noise is also generated downhole
by movement of fluids in open hole. Again a down hole clamp
can minimize these noises. After a record is obtained noise
can be minimized by editing and / or filtering the data
recordings.
Structural Corrections
Structural corrections are not always needed, particularly
in flat lying terrain and geology. The need for a structural
correction will be apparent when the BHGM density is compared
to other porosity logs in tight or water saturated zones.
Structural corrections are performed in two stages:
 The first stage involves a downhole calibration
of the BHGM density across rocks where the
density is accurately known, for example the
shale cap rock and below the oil water contact.
Corrections are then known at two points bounding
the reservoir. Often the correction is constant
or varies linearly between these two points and
can be extrapolated.
 A second stage is sometimes incorporated whereby
a structural model is constructed using data from
seismic surveys or a field structural map. This
information is used to extrapolate the correction
over the zone of interest.
The formation bulk density, r_{B
}is related to the BHGM apparent density, r_{A}, by:
r_{B = }r_{A}G_{f + }Corr_{S}
where:
Corr_{S }is the
structural correction and may vary slowly with
depth.
G_{f} is a geometric
factor due to the non finite extent of the
reservoir. For large reservoirs, G_{f} is
close to 1.0.
