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# Borehole gravimetry

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Borehole gravity was pioneered by Smith[1] and then applied to problems of reservoir evaluation by McCulloh et al.[2] The borehole gravity meter or gravimeter responds to variations in density. Modern instruments sense a rock volume that is approximately the same as that investigated by deep resistivity tools. Unlike the shallower-sensing density log, the borehole gravimeter is insensitive to wellbore conditions such as rugosity and the presence of casing. Its principal applications are:

• Through-casing time-lapse monitoring of saturations/fluid contacts in gas reservoirs
• Downhole calibration of surface geophysical mapping of geological structures

## Theory

Any two masses, mi and mj, separated by a distance, r, experience a gravitational force of attraction, f, which is expressed as

....................(1)

where G is the universal gravitational constant (6.6726 × 10 –8 cgs units). More specifically, a mass, m, on the surface of the Earth would experience a gravitational force given by

....................(2)

where M is the mass of the Earth, R is its radius, and an acceleration due to gravity, g, is given by

....................(3)

Because the Earth is a rotating oblate spheroid, the quantity g at mean sea level varies with latitude, and it must be corrected for tidal effects. The unit of g is the Gal [1 cm/s2]. Surface gravity surveys use the milliGal as the preferred unit. Borehole gravity surveys often use the microGal. The acceleration due to gravity, or just "gravity," is measured with a gravimeter.

## Measurement

A borehole gravimeter follows the same principles of operation as a surface gravity meter. It is essentially a very sensitive spring balance. The weight of a horizontal hinged beam with a small mass attached to its free end is balanced by a combination of the tension in a compensating spring and an electrostatic force (Fig.1). When the acceleration due to gravity increases, the weight of the beam increases, and there is a greater tension in the spring. The spring tension is directly related to the acceleration due to gravity. It is controlled by an adjusting screw for which the number of turns is calibrated in gravitational units. The electrostatic force brings the beam to a horizontal position for reading purposes. It, too, is calibrated in gravitational units. The gravity reading is the difference between the spring tension and the electrostatic force: a tidal gravity correction has to be applied. In this way, differences in gravity can be measured between two places (e.g., between two depth locations in a borehole). Downhole measurements are made by occupying selected gravity stations. They are not continuous measurements with depth.

It can be shown[3] that the difference in gravity, Δg (mGal), between two locations at the top and bottom of an infinite horizontal reservoir layer penetrated by a vertical well is related to the density, ρ (g/cm3), and thickness, hm (m), of that layer by the expression:

....................(4)

where F is the vertical gradient of gravity (mGal/m), and G is in cgs units. Eq.4 can be solved for the layer density so that

....................(5)

The gradient, F (mGal/m), is a function of latitude, λ (degrees), and elevation, h (m), as per the Intl. Gravity Formula of 1967, as follows:

....................(6)

By substituting for F in Eq.5, we have

....................(7)

where h¯ is the mean elevation of the layer (m), and Δg/hm is in mGal/m. Eq.7 is that most commonly used for deriving density from borehole gravity measurements. If the borehole is deviated at an angle, α, the measured depth interval has to be converted to a true stratigraphic thickness using a specific form of Eq.5 for zero dip. Corrections are needed where the model of an infinite layer breaks down because of the presence of structural discontinuities away from the wellbore. Modern borehole gravimeters can detect gravity differences of a few microGals.

The borehole gravity meter delivers an interval density. It is the only tool that can furnish through-casing density. Where the layer is heterogeneous, the computed density is an average or apparent density. The error in density is a function of the layer thickness. With a LaCoste-Romberg borehole gravimeter, a single measurement of gravity above and below a layer of thickness 6.6 ft [2 m] should result in an error in apparent density of approximately ± 0.025 g/cm3. This expected error can be reduced through repeat measurements and by selecting a larger depth interval. Turning this around, the spatial resolution of a borehole gravimeter is governed by the accuracy to which density is required. For example, an accuracy of ±0.01 g/cm3 would be achieved through three measurements of gravity at the top and at the base of the target layer, provided that the latter is at least 9 ft [2.7 m] thick.

Borehole gravity tools have different sizes for different hole conditions. For example, the EDCON tools range in diameter from 3.875 in. [98 mm] for low-temperature (110°C), low-pressure (8,000 psi) applications to 5.25 in. [133 mm] for high-temperature (204°C), high-pressure (20,000 psi) applications. The temperature range can be extended to 260°C with special ring seals. Because of the tool size, there are limits on the deviation of boreholes in which it can be deployed. The measurement stations are located relative to other logging runs by using the gamma log and the casing collar locator(CCL). The depth of investigation within a homogeneous layer is governed by the contrast between the mud filtrate and formation fluids. It is typically more than 23 ft [7 m]. A larger station spacing, hm, will not increase this range. It will merely reduce the ability of the tool to see near-well density anomalies. Like surface gravity meters, the tool suffers from drift (of the spring tension), which makes accurate calibration difficult.

## Application

Key thrusts in reservoir evaluation have been the sensing of vuggy, fractured, and heterogeneous reservoirs, in which a deep-sensing porosity measurement is needed to complement the volumetric-sensing capability of deep resistivity logs.[4][5] More recent applications have been directed at through-casing monitoring of gas saturations.[6][7] In this respect, it is noteworthy that the larger volumes sensed by the borehole gravity meter, relative to conventional density logs, are more closely associated with the simulator grid scale. Moreover, time-lapse gravity measurements are not degraded by structural anomalies.

As an example, time-lapse borehole gravimetry has been used to determine the residual oil saturation to gas within the oil rim of the onshore Rabi field in Gabon.[3] The reservoir comprises clean, coarse-grained sands with high-salinity formation water. The required accuracy for residual oil saturation was ± 10 saturation units. A baseline gravity survey was run over an undepleted oil-bearing interval near the gas/oil contact (GOC) (Run 1). As the reservoir is depleted, the GOC moves down and the oil saturation decreases toward its residual value. A second gravity survey (Run 2) allowed the change in gas saturation, ΔSg, to be calculated from the change in measured density, Δρb, porosity, ϕ, and the densities of oil, ρo, and gas, ρg.

....................(8)

Once ΔSg was known, the oil saturation could be calculated, assuming no change in connate-water saturation.

Three surveys were undertaken twelve months apart (Fig.2). All measurements were made in a data-dedicated borehole. Gravity was measured four to six times at each station, with station intervals as low as 3.3 ft [1 m]. Stations were reoccupied with a shuttle-based system for enhanced depth control. The overall accuracy of the density difference in Eq.8 was 0.015 g/cm3. This accuracy corresponds to an accuracy of 0.7 μGal on the station-specific readings and an accuracy of 1.0 μGal on the gravity difference. The residual oil saturation was determined as 15±10 saturation units. Of this uncertainty, eight saturation units could be ascribed to the borehole-gravity measurements and two saturation units to uncertainties in porosity and connate-water saturation. This study set new objectives and standards for borehole gravimetry.

## Nomenclature

 c = gravimeter design constant, L, m d = gravimeter design constant, L, m f = gravitational force of attraction, mL/t2, N Fr = ratio factor for the minimum curvature method F = vertical gradient of gravity, 1/t2, mGal/m g = acceleration due to gravity, L/t2, mGal G = universal gravitational constant, L3/mt2, dyne cm2/g2 h = elevation, L, m hm = measured bed thickness, L, m mi, mj = any two gravitationally attracting masses, m, kg m = mass, m, kg M = mass of the Earth, m, kg r = distance between two gravitationally attracting masses, L, m R = Earth’s radius, L, km = mean elevation of layer, L, m T = tension, mL/t2, N φ = dip, –, degrees Δg = difference in gravity between two locations at the top and bottom of an infinite horizontal reservoir layer penetrated by a vertical well, L/t2, Gal Δρb = change in measured density, m/L3, g/cm3 λ = latitude, –, degrees ρ = density, m/L3, g/cm3 ρg = gas density, m/L3, g/cm3 ρo = oil density, m/L3, g/cm3 ϕ = porosity χ = magnetic susceptibility of the rock

## References

1. Smith, N.L. 1950. The Case for Gravity Data From Boreholes. Geophysics 15 (4): 605-636. http://dx.doi.org/ 10.1190/1.1437623.
2. McCulloh, T.H., Kandle, G.R., and Schoellhamer, J.E. 1968. Application of Gravity Measurements in Wells to Problems of Reservoir Evaluation. Trans., Soc. of Professional Well Log Analysts 9th Annual Logging Symposium, New Orleans, paper O.
3. Alixant, J.-L. and Mann, E. 1995. In-Situ Residual Oil Saturation to Gas from Time-Lapse Borehole Gravity. Presented at the SPE Annual Technical Conference and Exhibition, Dallas, Texas, 22-25 October 1995. SPE-30609-MS. http://dx.doi.org/10.2118/30609-MS.
4. Jageler, A.H. 1976. Improved Hydrocarbon Reservoir Evaluation Through Use of Borehole-Gravimeter Data. J Pet Technol 28 (6): 709-718. SPE-5511-PA. http://dx.doi.org/10.2118/5511-PA.
5. Gournay, L.S. and Lyle, W.D. 1984. Determination of Hydrocarbon Saturation and Porosity Using a Combination Borehole Gravimeter (BHGM) and Deep Investigating Electric Log. Presented at the SPWLA 25th Annual Logging Symposium, 1984. SPWLA-1984-WW.
6. Popta, J.V., Heywood, J.M.T., Adams, S.J. et al. 1990. Use of Borehole Gravimetry for Reservoir Characterisation and Fluid Saturation Monitoring. Presented at the European Petroleum Conference, The Hague, Netherlands, 21-24 October 1990. SPE-20896-MS. http://dx.doi.org/10.2118/20896-MS.
7. Brady, J.L., Wolcott, D.S., and Aiken, C.L.V. 1993. Gravity Methods: Useful Techniques for Reservoir Surveillanc. Presented at the SPE Western Regional Meeting, Anchorage, Alaska, 26-28 May 1993. SPE-26095-MS. http://dx.doi.org/10.2118/26095-MS.