The gyro drilling inclinometer is a measurement instrument for drilling trajectory that is not affected by geomagnetic interference and surrounding magnetic fields. It is mainly used for measuring drilling trajectories in magnetic ore areas, including boreholes, casings, and drill rods, and can also be used for trajectory measurement in other non-magnetically disturbed boreholes.

　　 Compared to gyroscopes used in aircraft, the gyroscopes used for logging have the following characteristics influenced by their operating environment. First, there are strict size requirements, especially a small diameter, which must adapt to the casing well diameter after the instrument is formed, and it should even be able to be inserted from the drill rod when opening a window. Second, there is a strong resistance to vibration, ensuring that the gyro body will not be damaged when measuring while opening a window or when inserted at the bottom of the well. Additionally, there are wide temperature requirements, meaning the instrument can operate normally for at least 2 hours in a 125° environment, and the overall accuracy of the instrument meets design requirements within the temperature range of -10 to 125°.

　　 Gyroscopes can be classified into mechanical gyroscopes, optical gyroscopes, and semiconductor gyroscopes based on their structure and manufacturing processes. Among them, mechanical gyroscopes include frame gyroscopes, dynamically tuned gyroscopes, liquid floating rate integrating gyroscopes, and electrostatic gyroscopes. Optical gyroscopes mainly consist of laser and fiber optic gyroscopes. The most common semiconductor gyroscope is the silicon micro-gyroscope.

　　 Among these gyroscopes, the electrostatic gyroscope is extremely difficult to manufacture and expensive, used only in the most advanced weapon systems, with the technology mastered by only a few countries in the world, so it will not be applied in other fields in the short term. Silicon micro-gyroscopes have low precision and significant temperature drift. Although they have good vibration resistance and ideal size, there are discussions about forming instruments, but due to the limitations of their own technological development level, they are currently mostly used in dynamic imaging and other feedback loop detection, and it is unlikely that ideal logging products will appear for a considerable period.

　　 The gyroscopes currently seen for logging almost cover all varieties of mechanical gyroscopes, including frame gyroscopes, dynamically tuned gyroscopes, and liquid floating rate integrating gyroscopes.

 　 Frame Gyroscope

　　 The frame gyroscope is one of the earliest developed and most mature classic types of gyroscopes. It is easy to manufacture, inexpensive, and has good vibration resistance. The theory of frame gyroscopes is very mature in countries like the United States and Russia, and some foreign brands of gyro inclinometers, such as 'Harris', use frame gyroscopes. Its structure is shown in Figure 1.

Figure 1. Structure of Frame Gyroscope

    The main advantage of the frame gyroscope is its strong impact resistance, allowing for continuous measurement. However, it has many factors affecting the anti-torque during operation, and it has the following disadvantages:

　　  1. The measurement process is cumbersome; ground orientation must be performed before downhole measurement, and after measurement, the instrument must be recalibrated on the ground to compensate for error data.

　  　2. The friction between the inner and outer frame structure causes significant gyroscope drift, which cannot be compensated or eliminated, resulting in low precision and a larger outer diameter.

     Due to the above reasons, frame gyroscopes are rarely used in precise navigation fields.

　　  Dynamically Tuned Gyroscope

　　  The rotor support element of the dynamically tuned gyroscope uses flexible support instead of the ball support in the frame gyroscope. The gyroscope body consists of a rotor, flexible joint, sensor, torque generator, and drive circuit. The structure is shown in Figure 2. The flexible joint consists of three rings: upper, middle, and lower, which are key components determining its working quality. Compared to frame gyroscopes, the structure of the rotor part has been improved, using rigid and sensitive flexible joints for support, reducing interference torque. Therefore, this type of gyroscope is small in size, has a short startup time, and has significantly improved precision compared to frame gyroscopes. However, the dynamically tuned gyroscope is expensive and complex to manufacture, especially the flexible joint, which is very fragile and can easily break during vibration, leading to gyroscope damage. If the rigidity of the flexible joint is increased, the precision will greatly decrease. This is a fatal weakness limiting its promotion in petroleum instruments. In China, there are manufacturers using dynamically tuned gyroscopes to develop gyro inclinometers, but the current application results are not ideal, mainly because the issue of gyroscope fragility has not been resolved.

Figure 2. Structure of Dynamically Tuned Gyroscope

   In the liquid floating rate integrating gyroscope, a high-density, high-viscosity suspension liquid is filled between the rotor and the shell, allowing the rotor to be in a suspended state at an appropriate working temperature, with the rotor connected to the shell by elastic hairspring. Its advantages include good vibration resistance and small size, but due to the limitations of the suspension liquid, it has a long working preparation time and significant temperature drift, generally requiring operation in a constant temperature state. Although the liquid floating gyroscope has relatively good vibration performance indicators, strictly speaking, this type of gyroscope is not suitable for use in gyro inclinometers. The presence of suspension liquid means that large temperature differences in the working environment can cause significant changes in the density and viscosity of the suspension liquid, even losing its damping effect, directly leading to unpredictable large changes in gyroscope precision, or even failure. If an accurate temperature control circuit is added, it will increase the size of the instrument and is also not suitable for high-temperature and high-pressure environments underground.

　　 The three types of mechanical gyroscopes mentioned above, when applied to petroleum instruments, have significant defects due to their principles when comprehensively considering the three major selection indicators of precision, vibration resistance, and environmental temperature. Optical gyroscopes can be applied to gyro inclinometers. Common optical gyroscopes include fiber optic gyroscopes and laser gyroscopes. However, laser gyroscopes are currently not considered due to their excessively large size. The following focuses on the application of fiber optic gyroscopes in inclinometers.

   Fiber Optic Gyroscope

   Modern fiber optic gyroscopes are developed based on the Sagnac theory. The key point of the Sagnac theory is that when a light beam travels in a circular path, if the circular path itself has a rotational speed, the time required for the light to travel in the direction of the path's rotation is longer than the time required to travel in the opposite direction. In other words, when the optical loop rotates, the optical path length of the light in different directions changes compared to the path length when the loop is stationary. By utilizing this change in optical path length, if interference is created between light traveling in different directions to measure the rotational speed of the loop, an interferometric fiber optic gyroscope can be manufactured.

　　 The basic optical components of a fiber optic gyroscope include a light source, coupler, polarizer, fiber coil, detector, etc. The fiber optic gyroscope components are mostly semiconductor devices, connected by plug connections, and directly soldered onto a printed circuit board. The fiber optic gyroscope overcomes almost all the disadvantages of mechanical gyroscopes when used in oil instruments, such as poor vibration resistance, magnetic field variations, multiple drift torque factors, and significant environmental temperature effects. The fiber optic gyroscope is very suitable as an orientation sensor for gyroscopic inclinometer. A significant inherent defect of the fiber optic gyroscope is that the cost of the components is high, and it has poor high-temperature resistance. To ensure accuracy, an increasing number of fiber turns are used, resulting in a relatively large size. The solution is to add an efficient thermal insulation bottle, ensuring that the maximum working environment temperature of the fiber optic gyroscope is below 80°C, which can basically meet the measurement needs for well depths within 4000 meters. Corresponding to the limitations of wellbore diameter, by changing the winding method of the fiber, its diameter can be effectively reduced to meet the requirements for placement in the drill pipe.

　　 The AgileLight-IM series fiber optic gyroscope developed by Wuxi Msensor Sensor Technology Co., Ltd. is a fiber optic gyroscope specifically customized for wellbore inclination measurement. This gyroscope has an outer diameter of only 32mm, a range of ±4°, a zero bias of 0.5°/hr (0.2°/hr under thermal equilibrium), a scale factor of 0.000125, and a bandwidth of 10Hz. It can withstand shocks of 100g, operates in a temperature range of -40° to +75°, has a lifespan of 55,000 hours, and has no special environmental requirements during transportation and use, making it very suitable for use in inclinometers.

   Composition and Principle of the Inclinometer

　　 The inclinometer mainly includes a surface part and a downhole part, as shown in Figure 3, with the surface part and downhole part connected by a logging cable.

Figure 3. Structure Diagram of the Inclinometer

   Surface Part

　　 The surface part mainly includes signal reception and decoding circuits, depth display, surface power supply, and computer.

　　 1. The function of the signal reception and decoding circuit is to receive signals sent from downhole to the surface, decode them, and then forward them to the surface computer for processing.

　　 2. The depth display part receives the optical pulse signals from the winch control system, converts them into depth values, and displays them.

　　 3. The function of the surface power supply is to convert the AC power supply into a DC power supply for use by downhole sensors and circuit components, and it is assembled together with the signal reception and decoding circuit and depth display to form the surface control box.

 　 4. The function of the surface computer is to calculate the spatial orientation of the instrument's position in the borehole based on the gyroscope and accelerometer signal values sent from downhole to the surface, namely the inclination angle, azimuth angle, and tool face angle, while also issuing control commands to perform different operations on the downhole instruments.

   Downhole Part

   The downhole part includes an inertial component composed of a fiber optic gyroscope and accelerometer sensors, a motor, downhole secondary power supply, data acquisition and encoding circuits, and secondary circuits for the gyroscope and accelerometer.

　　 The inertial component is the core part of the entire instrument, consisting of 2 quartz flexible accelerometers and 1 single-axis fiber optic gyroscope (a dual-axis gyroscope can also be used, but the cost and price will double; in that case, the motor only needs to rotate 180° once, while using a single-axis gyroscope requires the motor to rotate four times, each time rotating 90°). The gyroscope and accelerometer are arranged in a strapdown configuration, with the gyroscope and accelerometer directly mounted on the inertial component with precise positioning references, forming the inertial component assembly, where the 2 accelerometers are fixed on the 2 orthogonal planes of the inertial component, and the output axes of the accelerometer and gyroscope are perpendicular to the axis of the inertial component.

　　The function of the motor is to make the inertial component perform four measurements with a phase difference of 90° during measurement, obtaining

and

and eliminating the fixed zero bias error of the inertial component.

　　  The secondary circuit of the sensor includes the secondary circuits of the gyroscope system and the accelerometer, etc.

　　  The signal acquisition and encoding circuit completes data acquisition, control, and communication between the downhole system and the surface system for the gyroscope and accelerometer. After receiving commands sent from the surface, it decodes them to complete their respective functions.

　　  The function of the downhole secondary power supply is to convert the high-voltage DC power supply provided from the well into a low-voltage DC power supply, providing working voltage for the downhole system.

     Measurement Principle

     The measurement mode of the fiber optic gyroscope inclinometer is to lower the inclinometer to a predetermined position, keep the inclinometer stable, and the fiber optic gyroscope and accelerometer of the inclinometer sense the gravitational acceleration of the Earth. Based on the output values of the gyroscope and accelerometer, the azimuth angle A, inclination angle I, and tool face angle T of the borehole at that position are calculated, completing the measurement of one point. The inclinometer is then moved to another position, and the above actions are repeated to measure that point.

　　   The calculation process for the inclination angle I, azimuth angle A, and tool face angle T is as follows: taking the coordinate system of the gyroscope inclinometer, i.e., the measurement device coordinate system, as the reference coordinate system, counterclockwise rotation is considered positive, and the latitude of the gyroscope inclinometer is set as

. The coordinate transformation situation is as follows: the geographic coordinate system northeast sky

, first rotate around

in the positive direction to angle A, then rotate around

in the positive direction to reach

正向转动角I到达

Finally, it rotates

The rotation angle T reaches

, which is the coordinate system of the gyroscopic inclinometer. Angle A is the azimuth angle, angle I is the inclination angle, and angle T is the tool face angle, as shown in Figure 4.

   Figure 4. Schematic diagram of inclinometer coordinate transformation

　　The direction cosine matrix between the geographic coordinate system and the instrument coordinate system (coordinate transformation relationship) is:

　　The direction cosine matrix establishes the following relationship:

As long as the Earth's angular velocity along the probe coordinate axis is measured

and the gravitational acceleration

these 4 parameters, and obtained from the local latitude

and

, the azimuth angle, inclination angle, and tool face angle of the probe can be calculated, with the formulas as follows:

　　Inclination angle:

　　Tool face angle:

　　Azimuth angle:

　　It can be seen that the inclination angle I and tool face angle T are only related to the output values of the accelerometer, while the azimuth angle is related to the outputs of both the gyroscope and the accelerometer.

　　Conclusion

　　The gyroscopic inclinometer uses inertial navigation technology for drilling measurements. It leverages the strong autonomy, high navigation accuracy, and good reliability of inertial navigation devices, employing a strapdown north-seeking system composed of fiber optic gyroscopes and accelerometer sensors. It measures the components of the Earth's rotation angular velocity through the gyroscope and the components of the Earth's gravitational acceleration through the accelerometer, and then calculates the drilling inclination angle, azimuth angle, and tool face angle using relevant formulas. The gyroscopic inclinometer has the following characteristics:

　　Small drift, high precision, and no correlation between data at different measurement points, eliminating the cumulative errors of previous gyroscopic inclinometers, effectively improving the accuracy of drilling trajectory measurement results.

　　The working process automatically seeks north, requiring no initial ground orientation, and no need for north calibration before and after measurement, eliminating human error.

　　Not affected by geological and surrounding environmental factors, resistant to magnetic interference, and can be used in drill rods, magnetic casings, and magnetic ore areas.