Patent Application
20080295594
The present invention relates to gravity measurements and in particular, to a method and apparatus for measurements of gravity in small diameter boreholes.
Measurements of the acceleration “g” due to the Earth's gravitational attraction are of considerable interest for a variety of objectives, such as the basic mapping of subsurface geology, the exploration for and development of mineral and hydrocarbon resources, volcanology, geotechnical investigations and the environment. For mapping purposes, measurements of the value g are commonly made at stations on surface on a systematic grid basis, or at regular intervals down a borehole, but they may also be made at the same stations at different times, in order to monitor changes in the gravitational field that may have occurred. Such time-lapse changes are of significance in the prediction of volcanic eruptions and the probability of earthquake occurrences, and for monitoring changes in the condition of hydrocarbon reservoirs, etc. With the increased value of crude oil and natural gas, there is great incentive to optimize the efficiency in the extraction of hydrocarbon resources from their source deposits. As such, monitoring changes in the condition of hydrocarbon reservoirs and the like is of particular interest.
The value of g is normally expressed in one of two units, namely m/s2 or Gal (after Galileo Galilei, 1564-1642). This second unit for the value of g is commonly employed by geophysicists. One Gal is defined as 10−2 m/s2. The value of g varies over a relatively small range on the Earth, namely only about 0.5% from the equator (about 9.780 m/s2) to the poles (about 9.830 m/s2). The degree of precision (or sensitivity) required for an individual measurement of the value g depends on the application for the measurement. For example, for regional geological mapping on the scale of 1:1,000,000, a sensitivity of 1 mGal (milliGal, or 10−5 m/s2) is adequate. However, when monitoring changes in hydrocarbon reservoirs, or in precise determinations of bulk densities in boreholes, it is necessary to achieve a measurement sensitivity in the order of 1 μGal, namely one part per billion of the value of g.
The paper entitled “On Density Derived from Borehole Gravity”, authored by Xiong Li and Michel Chouteau (The Log Analyst, Vol. 40, No. 1, pages 33-40, 1999), may be used to provide the theoretical basis for the relationship between the vertical gradient of gravity in a borehole and the bulk density of the formations being traversed by the borehole. The normal vertical gradient (increase) of gravity (dg) with increasing depth (dz) in a borehole in mGal/m (or μGal/mm), is given by Equation (1) below:
dg/dz=(0.3086−0.0838d) (1)
where:
d is the bulk density, in g/cm3, of the formation being traversed; and
z is the depth in metres.
Equation (1) can be inverted to derive bulk density d according to Equation (2) as follows:
d=11.93(0.3086−dg/dz) (2)
Thus, by measuring the value of gravity between two stations at different depths in a borehole, one may determine the mean bulk density of the formations lying between the two depths.
There are basically two types of gravimeters in use today for stationary gravity measurements, namely “absolute” and “relative” gravimeters. Absolute gravimeters in use today measure the total field or full value of g, by dropping a corner cube in a vacuum, and measuring the acceleration of the corner cube, using a laser beam which is reflected by the corner cube, and an interferometer. A good example of a modern absolute gravimeter is the FG5 instrument produced by Micro-g-LaCoste of Colorado, U.S.A. as is disclosed in U.S. Pat. No. 5,351,122 to Niebauer et al.
Relative gravimeters do not provide measurements of the full value of g, but only measure differences in g, from place to place, or from time to time. Relative gravimeters in use today commonly operate on the deflection, by changes in gravity, of the position of a proof mass which is supported by an elastic spring member. A good example of a modern relative gravimeter is the CG5 instrument produced by Scintrex Limited of Ontario, Canada. Whereas relative gravimeters enjoy certain advantages, such as size and power requirements relative to a falling body absolute gravimeter, they are subject to drift, which is a concern for long term monitoring of hydrocarbon reservoir changes.
The earliest device that has been employed to measure the total or absolute value of g is the pendulum. Serious attempts to measure the period of an oscillating pendulum in order to determine the value of g were initiated in the early part of the 19th century, and continued, with progressive improvements in sensitivity, until the latter part of the 20th century. Interest waned in pendulum measurements of g with the advent around 1930, of the first relative gravimeters. Interest diminished further around 1980 with the introduction of the direct measurement of g (to the order of 10 μGal), using optical interferometry to observe the time of fall of a falling body. A general review of these and other gravity measuring devices may be found in the publication entitled “Gravimetry”, authored by W. Torge (Walter de Gruyter publishers, 1989). Despite the paucity of interest in recent times, the pendulum is, in principle, a very simple approach to the measurement of the total value of g.
The importance of monitoring the status of hydrocarbon reservoirs during the resource extraction stage is well acknowledged in the industry. It is also acknowledged that essential information on the status of hydrocarbon reservoirs can be derived by monitoring changes in the bulk density of the hydrocarbon reservoir formations. As a result, measuring the value of gravity in boreholes is of great interest. Such boreholes are however, typically small in diameter, reaching diameters as small as 58 mm. This of course makes taking gravity measurements downhole challenging.
U.S. Pat. No. 6,671,057 to Orban discloses a differential gravity sensor and system for monitoring reservoirs. The gravity sensor includes a first mass adapted to free fall when selectively released from an initial position. The first mass has optical elements adapted to change a length of an optical path in response to movement of the first mass. The sensor output is coupled to a beam splitter. One output of the beam splitter is coupled substantially optically directly to an interferometer. Another output of the beam splitter is coupled to the interferometer through an optical delay line. The frequency of the interference pattern is directly related to gravity at the first mass. A second such mass having similar optics, optically coupled in series to the first mass and adapted to change the path length in opposed sign, when selectively dropped to cause time coincident movement of the two masses, generates an interference pattern having frequency related to gravity difference. As will be appreciated, the Orban gravity sensor is an absolute one, based on measurements of a free-falling body. Unfortunately, this gravity sensor is simply far too large and complex for use in the small diameter borehole environment in the hydrocarbon industry.
U.S. Pat. No. 5,892,151 to Niebauer et al. discloses a differential interferometric ballistic gravity measurement apparatus and method for measuring differential gravity between separate points. The apparatus employs at least two separate gravity sensors having respective free-fall masses capable of independent operation, an arrangement mounting the gravity sensors independent of one another in respective self-leveling states and at separate locations, a fiber optic-guided laser light interferometer coupled to the gravity sensors and adapted to produce a light signal indicative of a single measurement of differential gravity between the separate locations where the gravity sensors are situated, and a processing control system coupled to the gravity sensors and the interferometer for activating independent operation of the gravity sensors and the interferometer and for detecting the light signal and producing an electrical signal representing the measurement of differential gravity between the separate locations. Similar to the Orban gravity sensor, this ballistic gravity measurement apparatus is costly and complex, making it unsuitable for use in a small diameter borehole environment in the hydrocarbon industry.
As will be appreciated there is a need for a total field gravimeter that is compatible in sensitivity, size, complexity and cost, with the reservoir monitoring needs of the hydrocarbon industry. The only type of absolute gravity sensor that appears to be suited to this requirement of the hydrocarbon industry is one based on a pendulum. Unfortunately, the high sensitivity pendulums described in the aforementioned Torge publication are much too large (25 cm or longer) to be used in a small diameter borehole for determination of the bulk density of formations traversed by the borehole. However, in the publication entitled “A Pendulum Gravimeter for Precision Detection of Scalar Gravitational Radiation”, authored by David A. Curott (PhD. Thesis, Princeton University, May, 1965), a smaller pendulum sensor having a total length in the order of 2 cm, and a measurement sensitivity in the order of several tens of μGals is disclosed. Although of interest, the sensitivity of this pendulum sensor is still at least one order of magnitude too large to meet the requirements of the hydrocarbon industry.
It is therefore an object of the present invention to provide a novel method and apparatus for measurements of gravity in small diameter boreholes.
Accordingly, in one aspect there is provided an apparatus for measuring gravity in a small diameter borehole comprising:
a pressure tube; and
at least one pendulum gravity sensor accommodated by said pressure tube, said at least one gravity sensor comprising a pendulum and circuitry to monitor generally continuously the swing period and amplitude of said pendulum.
In one embodiment, each pendulum gravity sensor further comprises a sealed enclosure accommodating the pendulum and a leveling mechanism that maintains the enclosure generally in a level condition. The pendulum comprises a mass that moves back and forth between a pair of plates. The plates form part of the circuitry. The circuitry applies an electrostatic pulse between the plates to cause the mass to swing.
The circuitry in one embodiment comprises an AC capacitor bridge. One arm of the capacitor bridge is defined by one of the plates and the mass and another arm of the capacitor bridge is defined by another of the plates and the mass. A measurement circuit communicates with the AC capacitor bridge. The measurement circuit examines output of the AC capacitor bridge to determine times of closest approach of the mass to the plates thereby to determine the swing period and determines the amplitude of the swing at each closest approach. The measurement circuit corrects the swing period using the swing amplitude. If desired, the measurement circuit can average the swing period and amplitude over selected time intervals and transmit the swing period and amplitude to a surface location.
To maintain accuracy, the enclosure is evacuated and the pendulum is formed of material having a low co-efficient of thermal expansion. The pendulum has a swing period of about 0.2 seconds and a maximum swing amplitude of about 10−2 radians.
In another embodiment, the apparatus comprises a plurality of spaced, pendulum gravity sensors accommodated by the pressure tube.
According to another aspect there is provided a method of measuring gravity within a small diameter borehole comprising:
deploying at least one pendulum gravity sensor within a pressure tube downhole;
leveling each said sensor relative to the vertical;
causing a pendulum of each said sensor to swing;
measuring the swing period and amplitude of swing of each pendulum generally continuously; and
determining the value of gravity from said measurements.
According to yet another aspect there is provided an apparatus for measuring gravity in a small diameter borehole comprising:
an outer casing; and
a plurality of spaced, miniature pendulum gravity sensors accommodated by said casing.
Embodiments will now be described more fully with reference to the accompanying drawings in which:
A method and apparatus for measuring gravity in a small diameter borehole is described herein. The apparatus comprises a pressure tube and at least one pendulum gravity sensor accommodated by the pressure tube. During measuring, the apparatus is deployed downhole while maintaining the at least one pendulum gravity sensor in a substantially level condition. The pendulum of each sensor is caused to swing and the swing period and amplitude of the pendulum are measured generally continuously. The value of gravity is accurately determined using the swing period and swing amplitude measurements. Specific embodiments of the apparatus for measuring gravity in a small diameter borehole will be described with reference to
As shown in the publication entitled “The Earth and its Gravity Field”, authored by Heiskanen and Meinesz (McGraw-Hill, 1958, p 87-93), for a simple “mathematical” pendulum, the relationship expressed by Equation (3) below exists between the period of a pendulum T (seconds), its length l (m), and the value of g (m/s2):
]T=2π(l/g)1/2 (3)
From Equation (3), the value of g can be determined according to Equation (4) below:
g=4π2l/T2 (4)
For a real physical pendulum, l is replaced by the term K/Ma, where K is the moment of inertia of the pendulum about the swinging axis, M is the mass of the pendulum, and a is the distance between the centre of mass of the pendulum and its point of suspension. As will be appreciated, Equation (3) is just a first approximation to the solution of the equation of motion of the pendulum, and applies only for infinitesimally small amplitudes of oscillation. A more rigid relationship between the period of the pendulum and the value of g involves an elliptic integral of the first kind, as discussed in the Heiskanen and Meinesz reference referred to above.
A correction to Equation (3) may be made, however, for finite but small angles of oscillation, based on the expansion of the elliptic integral in a power series, provided that these angles of oscillation may be measured with high precision. This correction to include the next term in the full solution for finite but small angles of oscillation φ0 (in radians), is given by Equation (5) below:
T=T
0(1+φ02/16) (5)
where:
T is the observed period; and
T0 is the period for infinitesimally small oscillation amplitudes.
Taking the above into account, Equation (4) becomes:
g=4π2l(1+φ02/16)2/T2 (6)
For small angles of oscillation φ0, Equation (6) above may be written as:
g=4π2l(1+φ02/8)/T2 (7)
To examine the dependence of the determination of the value g on the stability of the maximum oscillation (or swing) amplitude φ0, it can be determined from Equation (5), that for a change dφ0 in oscillation amplitude φ0 the resultant change dg in the value g is given by Equation (8) below:
dg/g=+φ
0
dφ
0/4 (8)
If sensitivity in the order of 1 μgal (1 ppb) in the measurement of the value g by a pendulum is desired, three options are available. As a first option, the term φ02/16 may be reduced to <10−9 requiring that the maximum oscillation amplitude φ0<26 arc seconds, a very small amplitude of oscillation indeed. As a second option, for finite, but still small oscillation amplitudes φ0, the term φ0dφ0 may be reduced to <10−8. For example, if the maximum oscillation amplitude θ0 of 10−2 radians (0.5 degrees), then dφ0 must be maintained <10−6 radians (0.2 arc seconds). This requires an extreme order of stabilization of the amplitude of oscillation of the pendulum. As a third option, the oscillation amplitude φ0 of the pendulum can be generally continually measured with sufficient precision that appropriate corrections for the value g may be applied to each observed period, T, in accordance with Equations (6) or (7). The apparatus for the measurement of absolute gravity discussed herein employs the third option, as will now be described.
Turning now to
Turning now to
A circuit 44 is coupled to the capacitor plates 30 and 32 to establish an AC capacitor bridge circuit. One arm of the capacitor bridge circuit is defined by the capacitor plate 30 and the mass 24 and the other arm of the capacitor bridge circuit is defined by the capacitor plate 32 and the mass 24. Circuit 44 communicates with a measurement circuit 46.
The atmosphere within the enclosure 20 is evacuated to about 3×10−9 torr to reduce damping of the pendulum motion to a very low order. To reduce errors due to thermal expansion of the pendulum 22, the material of the mass 24 and fibre 26 is chosen for its very low intrinsic coefficient of thermal expansion (e.g. fused quartz or invar), and the enclosure 20 is placed within a thermostatically controlled oven, virtually to eliminate any residual thermal effects.
The AC capacitor bridge circuit is used to apply a DC electrostatic pulse between the two capacitor plates 30 and 32 thereby to cause the pendulum 22 to swing, or to increase its amplitude, from time to time. The measurement circuit 46, which communicates with the AC capacitor bridge circuit, measures the swing amplitude and period of the pendulum 22 generally continuously, as will now be described.
In operation, the sonde 10 is lowered down a borehole so that measurements can be made downhole at spaced intervals. When a measurement is to be made, the AC capacitor bridge circuit is conditioned to apply a DC electrostatic pulse between the capacitor plates 30 and 32 causing the pendulum 22 to swing, resulting in the mass 24 moving between the capacitor plates 30 and 32. In this embodiment, the pendulum 22 has a mean swing period of about 0.2 seconds and a maximum swing amplitude of about 10−2 radians.
Ca/Cb=x
2
/x
1 (9)
The output of the AC capacitor bridge circuit is applied to the measurement circuit 46. Measurement circuit 46 uses the output of the AC capacitor bridge circuit for two purposes, firstly to measure the swing period of the pendulum 22, in order to derive the value of absolute gravity, and secondly, to measure the swing amplitude of the pendulum 22. The swing amplitude information is required in order to apply a correction to the swing period to take into account the finite amplitude of the pendulum swing, in accordance with Equations (6) or (7). If the maximum swing amplitude of the mass 24 is very close to the separation of the two capacitor plates 30 and 32, the ratio of Ca/Cb becomes very large at the extremes of the pendulum swing. As a result, this pendulum motion measuring technique is extremely sensitive to small changes in the maximum displacement of the pendulum 22. In fact, the AC capacitor bridge circuit can measure pendulum swing changes as small as an Angstrom (10−10 m). For a pendulum 22 having a length of about 2 cm and a swing oscillation amplitude φo of 10−2 radians, a displacement change of 1 Angstrom in the extreme position of the mass 24 is equivalent to φ0dφ0=10−10, which is well within the degree of precision required to measure total gravity to the order of a few μgals.
In order to determine the swing amplitude of the pendulum 22, the measurement circuit 46 determines the maximum and minimum peak values of the AC capacitor bridge circuit output, which represent the extremes of the swing of the pendulum 22. Due to the non-linearity of the ratio expressed by Equation (9), the ratio is very sensitive to the points of closest approach of the mass 24 to each fixed capacitor plate 30 and 32. The measurement circuit 46 determines the times of closest approach of the mass 24 to the capacitor plates 30 and 32 by detecting the zero crossings of the time derivative of Equation (9), thereby to determine the period of the pendulum 22. The determined pendulum swing amplitude and period are averaged by the measurement circuit 46 over appropriate time intervals to improve the signal-to-noise (SNR) ratio. The average pendulum swing amplitude and period are then transmitted along cable 16 by the measurement circuit 46 for recording and/or further processing as required.
Turning now to
In the above embodiments, although an AC capacitor bridge circuit is used to monitor generally continually the swing amplitude and period of the pendulum 22, those of skill in the art will appreciate that other methods may be employed for making highly sensitive measurements of the pendulum swing period and amplitude, and for imparting energy as required to maintain the motion of the pendulum.
Also, in the above embodiments, the gravity pendulum sensor is described as having a length in the order of about 2 cm. A gravity pendulum sensor with a length less than 3 cm will however permit measurements of the desired sensitivity to be made.
Although embodiments have been described above with reference to the figures, those of skill in the art will appreciate that variations and modifications may be made without departing from the spirit and scope thereof, as defined by the appended claims.
| Number | Date | Country | |
|---|---|---|---|
| 60907151 | Mar 2007 | US |
