US20080034855A1

US20080034855A1 - Sliding weight borehole gravimeter

Info

Publication number: US20080034855A1
Application number: US11/759,030
Authority: US
Inventors: Maximiliaan Peeters; Roelof K. Snieder
Original assignee: Individual
Current assignee: Colorado School of Mines
Priority date: 2006-08-11
Filing date: 2007-06-06
Publication date: 2008-02-14
Also published as: WO2008021643A3; WO2008021643A2

Abstract

A borehole tool including an interferometer, a light source, a chamber containing a sliding weight having a first optical prism, a second optical prism located within the chamber, a tilt measuring device, and a timing device operatively associated with the interferometer. The light source, the interferometer, and the first and second optical prisms are configured to cause light emitted by the light source to form a first beam and a second beam that interfere with each other. The interferometer measures distances traveled by the sliding weight in the upward and downward direction by counting the fringes caused by the interference between the first beam and the second beam. The tilt measuring device measures the angle of the chamber relative to vertical. The influence of friction on the sliding weight's motion is eliminated by comparing the distances traveled by it in its upward and downward path over an equal time interval.

Description

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims under 35 U.S.C. §119(e) the benefit of U.S. Provisional Application No. 60/822,188, entitled “Sliding Weight Borehole Gravimeter” and filed on Aug. 11, 2006, which is incorporated herein by reference in its entirety.

FIELD OF THE INVENTION

The present invention relates generally to instruments for measuring a rock layer's density, and more particularly to a borehole gravimeter.

BACKGROUND OF THE INVENTION

Rock density is an important parameter for assessing underground oil and gas reservoirs because it can provide an indication of the storage capacity (porosity) and the fluid type (gas/oil/water) in a rock's pores. Density measuring instruments such as induced gamma-gamma probes and gravimeters may be run at the end of a wireline in a well to measure the density of rock layers around the hole. Conventional density measuring instruments can typically measure rock density up to about 30 cm from the hole. In contrast, gravimeters can potentially measure rock density up to 100 m from the hole and can provide information on the behavior of a much larger volume of a hydrocarbon reservoir (Gournay, Luke S. and Maute, Robert E., Detection of Bypassed Gas Using Borehole Gravimeter and Pulsed Neutron Logs, The Log Analyst, v. 23, No. 3, pp. 27-32, 1982; Van Popta, J. et al., Use of Borehole Gravimetry for Reservoir Characterization and Fluid Saturation Monitoring, SPE 20896, 1990).
Gravimeters are routinely used on the earth's surface. Surface gravimeters typically use either a Lacoste-Romberg spring sensor, quartz or a falling weight sensor. For measuring rock densities underground, gravimeters using Lacoste-Romberg sensors are used in boreholes. Such gravimeters generally have diameters greater than 4 inches (10.2 cm). These relatively large diameters severely limit their use in oil well boreholes since oil well production tubing typically has an inside diameter of 2 to 4 inches (5.1 to 10.2 cm). These gravimeters also require near vertical holes, which further limits their use since many oil well boreholes deviate significantly from the vertical, up to 90°.
Accordingly, what is needed in the art is an improved device and method for measuring rock densities around boreholes.

BRIEF SUMMARY OF THE INVENTION

A borehole tool is disclosed herein. In one embodiment, the borehole tool includes an interferometer, a light source, a chamber containing a sliding weight including a first optical prism, a second optical prism located within the chamber, a tilt measuring device, and a timing device operatively associated with the interferometer. The sliding weight is movable within the chamber. The light source, the interferometer, the first optical prism, and the second optical prism are configured to cause at least a portion of light emitted by the light source to form a first beam and a second beam that interfere with each other. The interferometer measures the interference between the first beam and the second beam. The tilt measuring device measures the angle of the chamber relative to vertical.
A method for determining a gravitational acceleration is disclosed herein. In one embodiment, the method includes providing a borehole tool including a chamber with a sliding weight, propelling the sliding weight upward in the chamber, determining an upward distance and a downward distance traveled by the propelled sliding weight during a select time period, determining an angle of the chamber relative to vertical during the select period of time, and determining the gravitational acceleration using the determined upward and downward distances traveled by the sliding weight, a time length of the select period of time, and the determined angle.
A method for determining a density of an underground rock layer is disclosed herein. In one embodiment, the method includes providing a borehole tool, positioning the borehole tool at a first select depth underground near the underground rock layer, launching a sliding weight upward, determining an upward distance and a downward distance traveled by the launched sliding weight during a select period of time, determining an angle from vertical of the chamber during the select period of time, and determining a gravitational acceleration using the determined upward distance and the determined downward distances traveled by the sliding weight, a time length of the select time period, and the determined angle from vertical of the chamber. In one embodiment, the borehole tool includes an interferometer, a light source operatively associated with the interferometer, the chamber containing the sliding weight, a propulsion device operatively associated with the sliding weight, a second optical prism located within the chamber and operatively associated with the interferometer, a tilt measuring device operatively associated with the chamber, and a timing device operatively associated with the interferometer. The sliding weight includes a first optical prism operatively associated with the interferometer and the second optical prism.
A borehole tool system is disclosed herein. In one embodiment, the system includes a weight in a tube, an incline measuring device, a timer and a processor. The weight is displaceable along the tube an upward distance and a downward distance during a displacement cycle, wherein the upward and downward distances are substantially similar. The incline measuring device is configured to measure a tube incline during the displacement cycle. The timer is configured to measure a displacement cycle time period. The processor calculates a gravitational acceleration from the upward and downward distances, the tube incline and time period.
Yet another method for determining a density of an underground rock layer is disclosed herein. In one embodiment, the method includes providing a borehole tool including a first borehole gravimeter and a second borehole gravimeter positioned a select distance from the first borehole gravimeter, positioning the borehole tool at a first select depth underground near the underground rock layer, determining a first gravitational acceleration using the first borehole gravimeter, determining a second gravitational acceleration using the second borehole gravimeter, and determining a density of the underground rock layer at the first select depth using the first gravitational acceleration and the second gravitational acceleration.
Yet another borehole tool is disclosed herein. In one embodiment, the borehole tool includes a first interferometer, a light source, a chamber containing a first sliding weight including a first optical prism and a second sliding weight including a second optical prism, a third optical prism located within the chamber, a tilt measuring device, and a timing device operatively associated with the interferometer. The first and second sliding weights are movable within the chamber. The light source, the first interferometer, the first optical prism, and the third optical prism are configured to cause at least a portion of light emitted by the first light source to form a first beam and a second beam that interfere with each other. The first interferometer measures the interference between the first beam and the second beam. The tilt measuring device measures an angle of the chamber relative to vertical.
Yet another borehole tool is disclosed herein. The borehole tool includes a means for containing a weight, a means for measuring an incline of the weight containing means during a displacement cycle of the weight, a means for measuring a duration of upward and downward distances of the weight, and a means for calculating a gravitational acceleration from the upward and downward distances, the incline of the weight containing means, and the durations of the upward and downward distances. The weight is displaceable within the weight containing means for the upward and downward distance during the displacement cycle. The upward and downward distances are substantially similar.
Still yet a further borehole tool is disclosed herein. The borehole tool includes a means for determining interferences between at least two light beams, a means for producing a light beam, a means for containing a sliding weight including a first means for at least partially reflecting the light beam, a second means for at least partially reflecting the light beam, a means for measuring an angle, and a means for measuring time. The second light reflecting means is located within the sliding weight containing means. The means for measuring time is operatively associated with interference determining means. The sliding weight is movable within the sliding weight containing means. The light producing means, the interference determining means, the first reflective means and the second reflective means are configured to cause at least a portion of light emitted by the light producing means to form a first beam and a second beam that interfere with each other. The interference determining means measures the interference between the first beam and the second beam. The angle measuring means measures an angle of the sliding weight containing means relative to vertical.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 depicts a schematic view of a first embodiment of a borehole tool with a borehole gravimeter.

FIG. 2 depicts a schematic view of a second embodiment of a borehole tool with two borehole gravimeters.

FIG. 3 depicts a schematic view of a third embodiment of a borehole tool with a borehole gravimeter.

DETAILED DESCRIPTION OF THE INVENTION

Oilfield operators typically want to minimize pulling production tubing from an oil well borehole because it interrupts production and carries the risk that production of the entire well will be lost. Production tubing typically has an inside diameter of 2 to 4 inches (5.1 cm to 10.2 cm). Thus, rock density measuring devices should preferably fit within an instrument with a diameter of 1 11/16 inches (4.28 cm), which is an oil industry standard for production logging tools. Described herein are density measuring devices that take the form of borehole gravimeters. The borehole gravimeters may be fitted in an 1 11/16″ (4.28 cm) diameter logging tool and may be run in wells with deviations from the vertical of up to 80 degrees. Further, these borehole gravimeters may withstand temperatures and pressures of at least 350° F. (177° C.) and 20,000 psi.
FIG. 1 depicts a schematic view of a first embodiment of a borehole tool 100 containing a borehole gravimeter 105. The logging tool 100 may include a housing 110 for containing various components of the borehole gravimeter 105. The borehole gravimeter 105 includes a tilt measuring device 115, a timing device 120, a vacuum chamber or tube 125, an interferometer 130, and a light source 135. The tilt measuring device 115 measures the angle of tilt of the borehole gravimeter 105 relative to vertical. The tilt measuring device 115 may be any commercially available tilt-meter used with borehole technology (such as a Lippmann two-channel borehole tilt-meter), an array of tilt-meters, or any other tilt measuring device or system that can withstand high borehole temperatures and pressures. The timing device 120 may be an atomic clock or other suitable timing device for obtaining required measurement accuracies in the range of 1 in 10⁹.
The vacuum chamber 125 contains a magnetic sliding weight 140, which may slide up and down within the vacuum chamber 125 and may be generally semi-cylindrically shaped or any other suitable shape. The sliding weight 140 may be propelled upward using an induction coil or other suitable device contained within a catcher 145 for catching the sliding weight 140. Launching the sliding weight upwards with a magnetic field generated by the coil, or by other means using another suitable device, starts a movement cycle in which the sliding weight 140 moves upward in the vacuum chamber 125 until it reaches the top of its trajectory and then moves downward in the vacuum chamber 125 until stopped by the catcher 145.
The vacuum chamber 125 may have an internal surface with a Teflon or other suitable coating to reduce friction between the contact surfaces of the sliding weight 140 and the vacuum chamber 125. Further friction reductions between the contact surfaces may be obtained by maintaining the temperature of the vacuum chamber 125 above approximately 80° C., using a sledge design, and/or equipping the sliding weight 140 with ball bearings or other suitable friction reduction devices.
The sliding weight 140 has an optical prism 150 for reflecting a portion of a light beam 155 to a stationary optical prism 160 located near the bottom end of the vacuum chamber 125. The stationary optical prism 160, in turn, reflects light received from the sliding weight's optical prism 150 to a mirror 175 for reflection to an interference area 165 in the interferometer 130, which also receives another portion of the light beam 155 emitted by the light source 135. The light source 135 may be a laser or other suitable light emitting device, which can be located outside the chamber 125 or at any other suitable location relative to the chamber 125. The interferometer 130 may have two or more fully reflective and/or semi-transparent mirrors that cause the portion of the light beam 155 received from the light source 135 to be directed to the sliding weight's prism 150 and the second portion to the interference area 165. The mirrors may be located within the chamber 125, outside the chamber 125, or some combination of inside and outside the chamber 125. In one embodiment, as shown in FIG. 1, the fully reflective mirror 170 is located outside the chamber 125 to reflect light 155 from the light source 135 into the chamber 125 and onto the semi-transparent mirror 175, and the semi-transparent mirror 175 is located within the chamber 125.
With reference to FIG. 1, the light beam 155 exits the light source 135 and travels along a first light path 180 to the fully reflective mirror 170. The fully reflective mirror 170 redirects the light beam 155 towards the semi-transparent mirror 175 along a second light path 185. A first portion of the light beam 155 is transmitted through the semi-transparent mirror 175 and travels along a third light path 190 to the light interference area 165 in the interferometer 130. A second portion of the light beam 155 is redirected by the semi-transparent mirror 175 to travel towards the sliding weight 140 along a fourth light path 195. The optical prism 150 of the sliding weight 140 redirects the second portion of the light beam 155 towards the stationary optical prism 160 along a fifth light path 200. The stationary optical prism 160 redirects the second portion of the light beam 155 back towards the semi-transparent mirror 175 along a sixth light path 205. The semi-transparent mirror 175 then redirects the second portion of the light beam 155 towards the light interference area 165 along a seventh light path 210. The first portion of the light beam 155 interferes with the second portion in the light interference area 165.
The interference of light received directly from the light source 135 (i.e., the first portion of the light beam 155) with light received from the stationary prism 160 (i.e., the second portion of the light beam 155) creates light interference fringes, which provide an indication of the distance that the sliding weight 140 travels during a certain measuring period. The measuring period is determined using the timing device 120 (e.g., an atomic clock). The interferometer 130 may include an optical fringe detector 215 or other suitable device to measure the interference fringes to enable the distance traveled by the sliding weight 140 during the measuring period to be determined. Further, the timing device 120 may be used in conjunction with the optical fringe detector 215 to determine the distance traveled by the sliding weight 140 during any select time period. More particularly, the timing device 120 is utilized in conjunction with the interferometer 130 to establish the number of fringes measured during the select period of time, which is then used to establish the distance traveled by the sliding weight 140 during the select period of time.
For the borehole gravimeter 105 depicted in FIG. 1, the downward distance X_itraveled by the sliding weight 140 over a time period t_iduring the downward motion may be calculated, if second and higher order powers of time multiplied by the gravitational gradient (γ) are ignored, using the equation:
X _i =X _oi +V _oi t _i+½g ₀(cos θ−η sin θ)t _i ² (1)
where X_oiis the initial position of the sliding weight;

- V_oiis the initial velocity of the sliding weight;
- g₀is the gravitational acceleration;
- θ is the tilt angle of the borehole gravimeter relative to vertical; and
- η is the coefficient of friction between the sliding weight and the vacuum chamber;
  and the upward distance X_jtraveled by the sliding weight 140 over a time period t_jduring the upward motion may be calculated using the equation:

X _j =X _oj +V _oj t _j+½g ₀(cos θ+η sin θ)t _j ² (2)
where X_ojis the initial position of the sliding weight; and

- V_ojis the initial velocity of the sliding weight.
  Further, when the sliding weight 140 is propelled upwards by the induction coil, it will momentarily have zero velocity as it stops at the top of its travel trajectory. This point in time can be determined with great accuracy using the interferometer 130 because this is when the first derivative of the phase versus time is zero. By taking this point as the starting point for the time periods of upward and downward travel used in equations 1 and 2, X_oi, X_oj, V_oj, and V_oiare equal to zero. Accordingly, equations 1 and 2 may be rewritten as:

X _i=½g ₀(cos θ−η sin θ)t _i ² (3)
and
X _j=½g ₀(cos θ+η sin θ)t ₂ (4)
Setting X_oi, X_oj, V_oj, and V_oiequal to zero additionally results in the elimination of the terms for the second and third order powers of time multiplied by the gravitational gradient, which were ignored in equations 1 and 2. This leaves only time to the fourth power multiplied by the gravitational constant (i.e., γg₀t⁴/24) as the term ignored when using equations 1 and 2. This fourth power of time term will generally be very small compared to numbers resulting from the terms used in equations 1 and 2, and thus will generally not significantly impact the calculated distances using equations 1 and 2. If the length of the time period of the sliding weight's downward travel is selected equal to the length of the time period of the sliding weight's upward travel (i.e., t_i=t_j=t), then equations 3 and 4 may be added together to obtain the following equation:
X _i +X _j =g ₀(cos θ)t ² (5)
and equation 3 may be subtracted from equation 4 to obtain the following equation:
X _j −X _i =ηg ₀(sin θ)t ² (6)
By combining the downward and upward distances traveled by the sliding weight 140 during a trajectory cycle, the effect of the coefficient of friction is eliminated. By subtracting the downward distance traveled by the sliding weight 140 from its upward distance, the coefficient of friction can be determined using, as described in more detail below, the gravitational acceleration determined from equation 5. Additionally, the fourth order power of time term ignored in equations 1 and 2 will cancel out in equation 6, thus resulting in substantially no difference in coefficient of friction values obtained between using equations that take into account the fourth order power of time terms and using those that ignore this term.
As further described below, in some embodiments, multiple measurements of upward and downward distances traveled by the sliding weight 140 during a period of time at a specific location are taken to enable multiple calculations for the gravitational acceleration and the coefficient of friction to be done. These multiple calculations help to average out the error in the gravitational acceleration calculations, and provide a continuous check for the constancy of the coefficient of friction for the vacuum chamber.
Elimination of the coefficient of friction from the determination of the gravitational acceleration by adding together the upward and downward distances traveled by the sliding weight 140 means that the sliding weight 140 may contact the walls of the vacuum chamber 125 so long as the upward and downward paths of the sliding weight 140 are substantially similar and the angle of the gravimeter 105 relative to vertical remains substantially constant during the upward and downward travel cycle of the sliding weight 140. Further, the effect of any remaining air resistance in the vacuum chamber 125 also cancels out in a manner similar to the canceling out of the coefficient of friction when both upward and downward movement of the sliding weight 140 are combined to determine the gravitational acceleration. Thus, the vacuum requirements in the vacuum chamber 125 may be relaxed. With less strict vacuum requirements, an ion vacuum pump, which is typically used in surface falling weight gravimeters, may be eliminated. Elimination of the ion vacuum pump reduces the required size of the borehole gravimeter 105 since this component tends to be rather large and generally does not fit in a 2″ (5.08 cm) diameter or less wireline borehole logging tool.
Returning to equation 5, the distance traveled upward by the sliding weight 140 for the selected time period length prior to the sliding weight 140 reaching its top trajectory may be determined. Additionally, the distance traveled downward by the sliding weight 140 from its top trajectory over the same time period length may also be determined. Further, since the angle of the borehole gravimeter 105 related to the vertical at any time is known, the angle of the borehole gravimeter relative to vertical during the selected time periods may be determined. Thus, every variable of equation 5 is known except for the gravitational acceleration, which may be determined by inputting the data for the known variables into the equation.
Once the gravitational acceleration is determined, the rock density around the borehole may be determined. Specifically, the density ρ_bof a rock layer with thickness Δz is proportional to the difference in gravitational acceleration Δg measured over the layer:
$\begin{matrix} ρ_{b} \div \frac{Δ g}{Δ z} & (7) \end{matrix}$

Therefore, once the gravitational accelerations are known along the depth of a rock layer, the rock layer's density may be determined using equation 7.

In operation, the tool 100 containing the borehole gravimeter 105 is inserted into a borehole. At a desired depth for measuring the gravitational acceleration, the borehole gravimeter 105 is maintained in a substantially stationary position by clamping the tool 100 to the borehole wall or by using any other suitable mechanism or method to maintain the borehole gravimeter 105 in a substantially stationary position. The sliding weight 140 is propelled upwards using the induction coil or any other suitable means. Measurements using the tilt meter 115, the interferometer 130, and the timing device 120 are taken during the sliding weight's upward and downward path of travel. These measurements are provided to a processor 220, which utilizes the measurements to calculate the gravitational acceleration at the location of the measurements. In one embodiment, the processor 220 is part of the gravimeter 105. In another embodiment; the processor 220 is separate from the gravimeter 105, but electrically coupled to the gravimeter 105 via a hardwire or wireless connection.
If desired, the sliding weight 140 may be launched upwards multiple times to obtain multiple measurements at a desired depth in the borehole. In some embodiments, at least one hundred upward and downward cycles are measured at the desired depth. This allows for the estimation of the uncertainty in the gravitational acceleration measurement and compensates for small movements that could effect one measurement. Similarly, in some embodiments during any one upward and downward cycle, multiple measurements are taken using the tiltmeter 115 and averaged to account for small variations in the angle of the gravimeter 105 relative to vertical that occur due to micro-seismic movements in the rock.
After completion of at least one upward and downward movement cycle of the sliding weight 140, the borehole gravimeter 105 is moved to another depth in the borehole. At the new depth, the steps for measuring the required parameters for determining the gravitational acceleration at the new location are repeated, and the new measurements are also provided to the processor 220 to calculate a second gravitational acceleration. The processor 220 utilizes the two gravitational accelerations to determine a gravitational gradient, which is utilized to determine the mass density of the rock layer.
To take direct underground rock density measurements, two borehole gravimeters 300, 305 may be arranged within a housing 110 of a wireline logging tool 310 to work in tandem as shown in FIG. 2. In such an embodiment, the density of a rock layer is the ratio of the difference between the gravitational accelerations measured by each borehole gravimeter 300, 305 and the distance between the two borehole gravimeters 300, 305. The two borehole gravimeters 300, 305 may be similar to the borehole gravimeter 105 described for the first embodiment of the tool 100. For the embodiment of the tool 310 shown in FIG. 2, like numbers may be used for components that are the same or similar to components for the first embodiment of a logging tool 100.
Each borehole gravimeter 300, 305 may have its own tilt measuring device 115 a,b as shown in FIG. 2, or may share a tilt measuring device. In one embodiment, the vacuum chambers 125 a,b and sets of prisms for the gravimeters 300, 305 are about one meter apart. In other embodiments, the distance between the vacuum chambers 125 a,b and sets of prisms are more or less than one meter apart. The first and second borehole gravimeters 300, 305 may each use the same processor 220 and timing device 120 as shown in FIG. 2, or may use separate processors and timing devices.
The borehole gravimeters 300, 305 may each use the same light source 135 as shown in FIG. 2, or may use different light sources. When using the same light source 135, the light source 135 may emit a light beam 155 that travels along a first pathway 315 to a semi-transparent mirror 320 for the first interferometer 130 a of the first borehole gravimeter 300. At the semi-transparent mirror 320, a first portion of the light beam 155 may be redirected for use in the first borehole gravimeter 300 along a second pathway 325 and a second portion of the light beam 155 may continue to travel along the first pathway 315 towards a fully reflective mirror 330 for the second interferometer 130 b. At the fully reflective mirror 330, the second portion of the light beam 155 may be redirected for use in the second borehole gravimeter 305 along a third pathway. Once redirected into the first and second borehole gravimeters 300, 305, the first and second portions of light beam 155 may travel along light paths substantially similar to the light paths described above with respect to the embodiment of the borehole gravimeter 105 depicted in FIG. 1 to create light interference patterns for determining the distances traveled by the sliding weights in each gravimeter 300, 305 as described in more detail above.
Each borehole gravimeter 300, 305 is operated as described above to obtain measurements for determining a gravitational acceleration. Using equation 7, the determined density represents an average density of the underground rock layer adjacent to the borehole tool 310 between the first borehole gravimeter 300 and the second borehole gravimeter 305. The difference between the gravitational accelerations determined from the measurements made using each borehole gravimeter 300, 305 indicates the gravitational gradient Δg. The distance Δz between the two sensors is known with the required accuracy of 1 mm (0.1%). However, since the exact distance between the tops of the trajectories of the two sliding weights is not known with the required accuracy, calibration on the surface with absolute gravimeters may be necessary.
FIG. 3 depicts a third embodiment of a borehole tool 400 containing a borehole gravimeter 405. Like numbers may be used for the components that are the same as or similar to the components of the first embodiment. The third embodiment is similar to the first embodiment except the induction coil is replaced with a lifting mechanism 410 for returning two sliding weights 140 a,b to a drop position and the tool 400 includes two interferometers 130 a,b. Also, one or more light sources may emit a separate light beam for each sliding weight 140 a,b. For example, a single light source 135 as shown in FIG. 3 may emit a first light beam 415 for the first sliding weight 140 a and a second light beam 420 for the second sliding weight 140 b. Each light beam may be directed by a reflective mirror 425 to first and second semi-transparent mirrors 430, 435 respectively. As described above for the first embodiment, a first portion of each light beam 415, 420 passes through its respective semi-transparent mirror 430, 435 to proceed directly to an interference area in its interferometer 130 a,b and a second portion is redirected along a pathway that includes its respective sliding weight 140 a,b and stationary prism 160 a,b. Also as described above with respect to the first embodiment, the first and second portions for each light beam 415, 420 interfere in an interference area within the beam's respective interferometers 130 a,b. The interference of the portions of each light beam 415, 420 provide an indication of the distance traveled by the sliding weight 140 a,b associated with the light beam 415, 420. Each interferometer 130 a,b may use the same processor 220 and timing device 120 as shown in FIG. 3, or may have its own processor and/or timing device.
In operation, the sliding weights 140 a,b are moved to their drop position using the lift mechanism 410, which can be a moving electromagnetic coil, a magnetic elevator or other suitable device. When the weights 140 a,b are released, they travel downward in the vacuum chamber 125 until their movements are stopped by the catchers 145 a,b. The two weights 140 a,b have approximately an equal mass, but the contact area A₁of the first weight 140 a with the chamber surface of the first weight is approximately twice the contact area A₂of the second weight 140 b. The contact areas can be controlled to a high degree of accuracy by using a sledge or other suitable design. Assuming that the start velocities V_oof the two sliding weights 140 a,b are equal, the equations that describe the incremental movements ΔX_kand ΔX_lof the two weights over the same time interval t are:
ΔX _k =V _o t+½g ₀(cos θ−A ₁η′ sin θ)t ² (8)
and
ΔX _l =V _o t+½g ₀(cos θ−Δ₂η sin θ)t ² (9)
where g_ois gravitational acceleration;

- A₁is the contact area of the first sliding weight;
- A₂is the contact area of the second sliding weight;
- θ is the tilt angle of the borehole gravimeter relative to vertical; and
- η′ is the coefficient of friction per surface unit between the sliding weight and the vacuum chamber.

Taking the difference between ΔX_kand ΔX_lyields:

ΔX _k −ΔX _l=(A ₁ −A ₂)g _oη′(sin θ)t ² (10)
In a manner similar to the one described above for the first embodiment of a borehole gravimeter 100, ΔX_kand ΔX_lare determined by counting fringes using the interferometers 130 a,b and two light beams 415, 420 with different wavelengths. Time t is measured with a timing device 120 (e.g. an atomic clock), the angle θ with a tilt-meter 115, and areas A₁and A₂from calibration at the surface. With this information, the product of g₀η′ may be determined. The gravitational acceleration g₀may then be determined by inserting this calculated product for g₀η′ in either equation 8 or 9.
Although the present invention has been described with reference to example embodiments, persons skilled in the art will recognize that changes may be made in form and detail without departing from the spirit and scope of the invention. The invention is limited only by the scope of the following claims.

Claims

1. A borehole tool comprising:

an interferometer;

a light source;

a chamber containing a sliding weight including a first optical prism;

a second optical prism located within the chamber;

a tilt measuring device; and

a timing device operatively associated with the interferometer; wherein:

the sliding weight is movable within the chamber;

the light source, the interferometer, the first optical prism, and the second optical prism are configured to cause at least a portion of light emitted by the light source to form a first beam and a second beam that interfere with each other;

the interferometer measures the interference between the first beam and the second beam; and

the tilt measuring device measures an angle of the chamber relative to vertical.

2. The borehole tool of claim 1, further comprising a propulsion device configured to propel the sliding weight upward in the chamber.

3. The borehole tool of claim 2, wherein the sliding weight is magnetic and the propulsion device comprises an induction coil.

4. The borehole tool of claim 1, wherein the timing device comprises an atomic clock.

5. The borehole tool of claim 1, wherein the light source comprises a laser.

6. The borehole tool of claim 1, wherein the tilt measuring device comprises a borehole tilt-meter.

7. The borehole tool of claim 1, wherein a distance traveled by the sliding weight during a select period of time is determined using the interferometer and the timing device.

8. The borehole tool of claim 2, wherein a gravitational acceleration is determined by propelling the sliding weight upward in the chamber, determining an upward and a downward distance traveled by the sliding weight during a select time period using the interferometer and the timing device, measuring an angle of tilt of the chamber during the select time period using the tilt measuring device, and using the determined upward and downward distances, a length of time of the select time period, and the angle of tilt to calculate the gravitational acceleration.

9. The borehole tool of claim 1, further comprising:

a second interferometer;

a second sliding weight contained within the chamber and including a third optical prism; and

a fourth optical prism located within the chamber; wherein:

the second sliding weight is movable within the chamber;

the light source, the second interferometer, the third optical prism, and the fourth optical prism are configured to cause at least a portion of light emitted by the light source to form a third beam and a fourth beam that interfere with each other; and

the second interferometer measures the interference between the third beam and the fourth beam.

10. The borehole tool of claim 1, further comprising

a second interferometer;

a second chamber containing a second sliding weight including a third optical prism;

a fourth optical prism located within the second chamber;

a second tilt measuring device; and

the timing device operatively associated with the second interferometer; wherein:

the second sliding weight is movable within the second chamber;

the light source, the second interferometer, the third optical prism, and the fourth optical prism are configured to cause at least a portion of light emitted by the light source to form a third beam and a fourth beam that interfere with each other;

the second interferometer measures the interference between the third beam and the fourth beam; and

the second tilt measuring device measures an angle of the second chamber relative to vertical.

11. A method for determining a gravitational acceleration comprising:

providing a borehole tool comprising a chamber with a sliding weight;

propelling the sliding weight upward in the chamber;

determining an upward distance and a downward distance traveled by the propelled sliding weight during a select time period;

determining an angle of the chamber relative to vertical during the select period of time; and

determining the gravitational acceleration using the determined upward and downward distances traveled by the sliding weight, a time length of the select period of time, and the determined angle.

12. The method of claim 11, wherein the borehole tool further comprises a tilt measuring device to measure the angle of the chamber relative to vertical.

13. The method of claim 11, wherein:

the borehole tool further comprises an interferometer, a timing device, a first optical prism, and a light source;

the sliding weight includes a second optical prism; and

the interferometer, the timing device, the first and second optical prisms, and the light source are operatively associated for determining the upward and downward distance traveled by the sliding weight during the select period of time.

14. The method of claim 11, wherein the select period of time includes a time when the sliding weight reaches a maximum upward position.

15. The method of claim 11, wherein the select period of time includes an upward time period and a downward time period.

16. The method of claim 15, wherein the upward and the downward time period are substantially equal.

17. The method of claim 16, wherein the gravitational acceleration is determined using the following equation:

g ₀=(X _i +X _j)/(cos (θ)·t ²)

where g₀is the gravitational acceleration;

X_iis the downward distance traveled by the sliding weight during the upward time period;

X_jis the upward distance traveled by the sliding weight during downward time period;

θ is the angle of the first chamber relative to vertical; and

t is either the upward time period or the downward time period.

18. A method for determining a density of an underground rock layer comprising:

providing a borehole tool comprising an interferometer, a light source operatively associated with the interferometer, a chamber containing a sliding weight including a first optical prism operatively associated with the interferometer, a propulsion device operatively associated with the sliding weight, a second optical prism located within the chamber and operatively associated with the first optical prism and the interferometer, a tilt measuring device operatively associated with the chamber, and a timing device operatively associated with the interferometer;

positioning the borehole tool at a first select depth underground near the underground rock layer;

launching the sliding weight upward;

determining an upward distance and a downward distance traveled by the launched sliding weight during a select period of time;

determining an angle from vertical of the chamber during the select period of time; and

determining a gravitational acceleration using the determined upward and determined downward distances traveled by the sliding weight, a time length of the select time period, and the determined angle from vertical of the chamber.

19. The method of claim 18, further comprising:

positioning the borehole tool at a second select depth underground near the underground rock layer; and

repeating the steps of launching the sliding weight, determining an upward distance and a downward distance, determining an angle, and determining a gravitational acceleration.

20. The method of claim 19, further comprising determining a density of the underground rock layer using the first and second determined gravitational accelerations, the first select depth, and the second select depth.

21. The method of claim 20, wherein the density of the underground rock layer is determined using the following equation:

ρ_{b} \div \frac{Δ g}{Δ z}

where ρ_bis the density of the underground rock layer;

Δg is the difference between the first and second determined gravitational accelerations; and

Δz is the difference between the first and second select depths.

22. A method of claim 18, further comprising:

the borehole tool further comprising a second interferometer, the light source operatively associated with the second interferometer, a second chamber containing a second sliding weight including a third optical prism operatively associated with the second interferometer, a second propulsion device operatively associated with the second sliding weight, a fourth optical prism located within the second chamber and operatively associated with the third optical prism and the second interferometer, a second tilt measuring device operatively associated with the second chamber, and the timing device operatively associated with the second interferometer;

launching the second sliding weight upward;

determining an upward distance and a downward distance traveled by the launched second sliding weight during a second select period of time;

determining an angle from vertical of the second chamber during the second select period of time; and

determining a second gravitational acceleration using the determined upward and determined downward distances traveled by the second sliding weight, a time length of the second select time period, and the determined second angle from vertical of the second chamber.

23. The method of claim 22, further comprising determining a density of the underground rock layer using the first and second determined gravitational accelerations.

24. The method of claim 23, wherein the first interferometer and the second interferometer are a select distance apart.

25. The method of claim 24, wherein the density of the underground rock layer is determined using the following equation

η_b÷Δg/Δz

where ρ_bis the average density of the underground rock layer proximate the first select depth;

Δz is the select distance between the first and second interferometers.

26. A borehole tool system comprising:

a weight in a tube, wherein the weight is displaceable along the tube an upward distance and a downward distance during a displacement cycle, wherein the upward and downward distances are substantially similar;

an incline measuring device configured to measure a tube incline during the displacement cycle;

a timer configured to measure a duration of the upward and downward distances; and

a processor for calculating a gravitational acceleration from the upward and downward distances, the tube incline and the duration of the upward and downward distances.

27. The system of claim 26, further comprising a second weight in a second tube.

28. The system of claim 26, wherein the tube is a vacuum tube and the system does not include an ion vacuum pump.

29. The system of claim 26, further comprising a light source, a stationary prism, and an interferometer that receives a light beam, that is generated by the light source and reflected from the stationary prism.

30. The system of claim 29, wherein the weight includes a prism that reflects the light beam.

31. A system of claim 26, further comprising a second weight in the tube.

32. A method for determining a density of an underground rock layer comprising:

providing a borehole tool including a first borehole gravimeter and a second borehole gravimeter positioned a select distance from the first borehole gravimeter;

determining a first gravitational acceleration using the first borehole gravimeter and a second gravitational acceleration using the second borehole gravimeter; and

determining a density of the underground rock layer proximate the first select depth using the first gravitational acceleration and the second gravitational acceleration.

33. The method of claim 32, wherein the density of the underground rock layer at the first select depth is determined using the following equation:

ρ_{b} \div \frac{Δ g}{Δ z}

Δz is the select distance between the first and second gravimeters.

34. The method of claim 32, wherein the distance between the first and second gravimeters is calibrated on the surface of the earth using an absolute surface gravimeter.

35. The method of claim 32, wherein the determined density represents an average density of the underground rock layer adjacent to the borehole tool between the first borehole gravimeter and the second borehole gravimeter.

36. A borehole tool comprising:

a first interferometer;

a light source;

a chamber containing a first sliding weight including a first optical prism and a second sliding weight including a second optical prism;

a third optical prism located within the chamber;

a tilt measuring device; and

a timing device operatively associated with the first interferometer; wherein:

the first sliding weight is movable within the chamber;

the second sliding weight is movable within the chamber;

the light source, the first interferometer, the first optical prism, and the third optical prism are configured to cause at least a portion of light emitted by the light source to form a first beam and a second beam that interfere with each other;

the first interferometer measures the interference between the first beam and the second beam; and

37. The borehole tool of claim 36, further comprising:

a second interferometer;

a fourth optical prism located within the chamber;

the light source, the second interferometer, the second optical prism, and the fourth optical prism are configured to cause at least a portion of light emitted by the light source to form a third beam and a fourth beam that interfere with each other; and

38. The borehole tool of claim 37, wherein a product of a gravitational acceleration by a coefficient of friction is determined by dropping the first and second sliding weights in the chamber, determining a downward distance traveled by the first sliding weight during a select time period using the first interferometer and the timing device, determining a downward distance traveled by the second sliding weight during the select time period using the second interferometer and the timing device, measuring an angle of tilt of the chamber during the select time period using the tilt measuring device, and using the determined downward distances of the first and second sliding weights, a length of time of the select time period, and the angle of tilt to calculate the product of the gravitational acceleration by the coefficient of friction.

39. A borehole tool comprising:

a means for containing a weight, the weight displaceable within the weight containing means for an upward and a downward distance during a displacement cycle and the upward and downward distances are substantially similar;

a means for measuring an incline of the weight containing means during the displacement cycle;

a means for measuring a duration of the upward and downward distances; and

a means for calculating a gravitational acceleration from the upward and downward distances, the incline of the weight containing means, and the durations of the upward and downward distances.

40. The borehole tool of claim 39, further comprising a second weight in a second means for containing a weight.

41. The borehole tool of claim 39, further comprising:

a means for producing a light beam;

a means for at least partially redirecting the light beam; and

a means for determining interferences between a first and a second portion of the light beam.

42. The borehole tool of claim 41, wherein the weight includes a second means for at least partially redirecting the light beam.

43. A borehole tool comprising:

a means for determining interferences between at two light beams;

a means for producing a light beam;

a means for containing a sliding weight including a first means for at least partially reflecting the light beam;

a second means for at least partially reflecting the light beam, the second means located within the sliding weight containing means;

a means for measuring an angle; and

a means for measuring time operatively associated with the interference determining means; wherein:

the sliding weight is movable within the sliding weight containing means;

the light producing means, the interference determining means, the first reflective means and the second reflective means are configured to cause at least a portion of light emitted by the light producing means to form a first beam and a second beam that interfere with each other;

the interference determining means measures the interference between the first beam and the second beam; and

the angle measuring means measures an angle of the sliding weight containing means relative to vertical.

44. The borehole tool of claim 43, further comprising a means for propelling the sliding weight upward in the sliding weight containing means.

45. The borehole tool of claim 43, further comprising:

a second means for determining interferences between at least two light beams;

a second sliding weight contained within the sliding weight containing means, the second weight including a third means for at least partially reflecting the light beam;

a fourth means for at least partially reflecting the light beam located within the sliding weight containing means; wherein:

the second sliding weight is movable within the sliding weight containing means;

the light producing means, the second interference determining means, the third and fourth reflective means are configured to cause at least a portion of light emitted by the light producing means to form a third beam and a fourth beam that interfere with each other; and

the second interference determining means measures the interference between the third beam and the fourth beam.

46. The borehole tool of claim 43, further comprising

a second means for determining interferences between at least two light beams;

a second means for containing a second sliding weight including a third means for at least partially reflecting the light beam;

a fourth means for at least partially reflecting the light beam, the fourth reflective means located within the second sliding weight containing means;

a second means for measuring an angle; and

the timing measuring means operatively associated with the second interference determining means; wherein:

the second sliding weight is movable within the second sliding weight containing means;

the light producing means, the second interference determining means, the third and fourth reflective means are configured to cause at least a portion of light emitted by the light producing means to form a third beam and a fourth beam that interfere with each other;

the second interference determining means measures the interference between the third beam and the fourth beam; and

the second angle measuring means measures an angle of the second sliding weight containing means relative to vertical.