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 sin²q - 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_AG_{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.

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