Carbon dioxide stratum leakage monitoring device and method based on distributed optical fiber sensing

Abstract

The invention discloses a carbon dioxide formation leakage monitoring device and method based on distributed optical fiber sensing. The device comprises a simulated formation, an injection system and a DTS system. A thermal insulation device, a thermometer and a production well system are mounted on the simulated stratum; the injection system is used for injecting carbon dioxide and liquid into the simulated stratum; the DTS system comprises a light source assembly, an optical fiber group, a detection assembly and a data acquisition and processing unit which are connected in sequence; a plurality of monitoring points of the optical fiber group are arranged, and the plurality of monitoring points are arranged in the simulated stratum at intervals; the detection assembly is used for detecting Rayleigh scattering frequency shift and Rayleigh backscattering light intensity and phase in the optical fiber group, and the data acquisition and processing unit is used for acquiring signals output by the detection assembly and performing data processing and analysis. According to the invention, fine monitoring and continuous monitoring of carbon dioxide stratum leakage can be realized, the environmental interference resistance is high, and the installation and maintenance cost is low.

Description

Technical Field

[0001] The present invention relates to the technical field of carbon dioxide formation leakage monitoring, and particularly to a carbon dioxide formation leakage monitoring device and method based on distributed optical fiber sensing. Background Art

[0002] Carbon dioxide capture and storage and enhanced oil and gas recovery are key technologies for reducing the concentration of carbon dioxide in the atmosphere and alleviating the rise of global temperature. When injecting carbon dioxide into the formation, carbon dioxide may accidentally escape from the storage layer to other layers or the surface, resulting in carbon dioxide formation leakage. This will not only reduce the storage efficiency, but also may have a negative impact on the environment and ecosystem. Therefore, monitoring carbon dioxide formation leakage is of great importance. Traditional monitoring technologies have limited monitoring range, low resolution, difficult to detect small-scale fractures, vulnerable to environmental interference, high cost, and poor sustainability.

[0003] For this reason, a carbon dioxide formation leakage monitoring device and method based on distributed optical fiber sensing are proposed. Summary of the Invention

[0004] The purpose of the present invention is to provide a carbon dioxide formation leakage monitoring device and method based on distributed optical fiber sensing, aiming to solve or improve at least one of the above technical problems.

[0005] To achieve the above purpose, the present invention provides the following solution: The present invention provides a carbon dioxide formation leakage monitoring device based on distributed optical fiber sensing, including: An artificial formation, on which a heat preservation device, a thermometer and a production well system are installed; An injection system, which is used to inject carbon dioxide and liquid into the artificial formation; A DTS system, which includes a light source component, an optical fiber group, a detection component and a data acquisition and processing unit connected in sequence; a plurality of monitoring points are provided on the optical fiber group, and the plurality of monitoring points are installed in the artificial formation at intervals; the detection component is used to detect the Rayleigh scattering frequency shift, the Rayleigh backscattered light intensity and phase in the optical fiber group, and the data acquisition and processing unit is used to collect the signals output by the detection component and perform data processing and analysis.

[0006] According to the carbon dioxide formation leakage monitoring device based on distributed optical fiber sensing provided by the present invention, the optical fiber group includes a first optical fiber, a second optical fiber and a third optical fiber, and the first optical fiber, the second optical fiber and the third optical fiber are installed in the artificial formation at intervals; One ends of the first optical fiber, the second optical fiber and the third optical fiber are all connected to the light source component, and the other ends are all connected to the detection component.

[0007] According to the carbon dioxide formation leakage monitoring device based on distributed optical fiber sensing provided by the present invention, the light source assembly includes an optical fiber power supply and a first optical fiber coupler, and one ends of the first optical fiber, the second optical fiber, and the third optical fiber are all connected to the optical fiber power supply through the first optical fiber coupler.

[0008] According to the carbon dioxide formation leakage monitoring device based on distributed optical fiber sensing provided by the present invention, the detection assembly includes a first optical fiber detector, a second optical fiber detector, and a second optical fiber coupler; one ends of the first optical fiber, the second optical fiber, and the third optical fiber are all connected to the second optical fiber coupler; The first optical fiber detector is used to detect the Rayleigh scattering frequency shift, and the second optical fiber detector is used to detect the Rayleigh backscattered light intensity and phase; The input ends of the first optical fiber detector and the second optical fiber detector are both connected to the second optical fiber coupler, and the output ends are both connected to the data acquisition and processing unit.

[0009] According to the carbon dioxide formation leakage monitoring device based on distributed optical fiber sensing provided by the present invention, the injection system includes an injection well, an injection pipeline, a carbon dioxide injection assembly, and a liquid injection assembly; The carbon dioxide injection assembly and the liquid injection assembly are communicated with the injection pipeline through a double-rod constant pressure pump, the injection pipeline is communicated with the injection well, the injection well is installed in the simulated formation, and a first pressure gauge and a first valve are installed on the injection pipeline.

[0010] According to the carbon dioxide formation leakage monitoring device based on distributed optical fiber sensing provided by the present invention, the carbon dioxide injection assembly includes a carbon dioxide gas cylinder, a first branch pipe is installed on the carbon dioxide gas cylinder, and a carbon dioxide intermediate container is installed on the first branch pipe; The liquid injection assembly includes a liquid bottle, a second branch pipe is installed on the liquid bottle, and a liquid intermediate container is installed on the second branch pipe; The first branch pipe and the second branch pipe are communicated with the injection pipeline through the double-rod constant pressure pump; regulating valves are installed on both the first branch pipe and the second branch pipe.

[0011] According to the carbon dioxide formation leakage monitoring device based on distributed optical fiber sensing provided by the present invention, the production well system includes a first production well and a second production well, and both the first production well and the second production well are installed in the simulated formation; The first production well is communicated with a first fluid collection device through a third branch pipe, the second production well is communicated with a second fluid collection device through a fourth branch pipe, a second valve, a second pressure gauge, and a second flow meter are installed on the third branch pipe, and a third valve, a third pressure gauge, and a first flow meter are installed on the fourth branch pipe.

[0012] The present invention also provides a method for monitoring carbon dioxide formation leakage based on distributed optical fiber sensing, comprising the following steps: Step 1: Inject carbon dioxide and liquid into the simulated formation. Step 2: Turn on the heat preservation device and install a thermometer. Step 3: The production well system collects the produced simulated formation fluid. Step 4: Turn on the light source assembly and make the emitted optical signal propagate along the optical fiber group. Step 5: Use the detection assembly to detect the Rayleigh scattering frequency shift, the intensity and phase of the Rayleigh backscattered light in the optical fiber group. Step 6: Use the data acquisition and processing unit to calculate the strain according to the signals received in the detection assembly, and determine whether carbon dioxide leaks. When the judgment result is a leak, an alarm is issued; the calculation formula for the strain is: , where is the average wavelength, is the wavelength offset, is the average optical frequency, is the optical frequency shift, is the strain sensitivity coefficient, is the optical fiber strain, is the temperature sensitivity coefficient, is the temperature change.

[0013] The present invention discloses the following technical effects: The present invention injects carbon dioxide and liquid into the simulated formation through the injection system. As the injection of carbon dioxide proceeds, carbon dioxide continuously enters the simulated formation, resulting in a change in the stress field of the simulated formation; a laser pulse is injected into the optical fiber group through the light source assembly. Due to the microscopic inhomogeneity inside the optical fiber group (such as refractive index fluctuations at the molecular level), part of the light will be scattered back, and this phenomenon is called Rayleigh backscattering; the leakage of carbon dioxide will cause changes in the formation temperature, and these temperature changes will propagate to the formation where the optical fiber group is located, causing small deformations of the optical fiber group, thereby changing the intensity and phase of the Rayleigh backscattered light. The DTS system can determine the location and amplitude of the temperature change by detecting these changes, thereby realizing the effective monitoring of small-size fractures; The DTS system of the present invention has a high spatial distribution rate, can achieve fine monitoring and continuous monitoring, can cover a large range and perform distributed monitoring, provides a more comprehensive monitoring network, and has strong anti-environmental interference ability and stable chemical properties and is not easily corroded; it can realize real-time data acquisition and analysis, provide immediate monitoring results, and the continuous data stream can provide detailed information on dynamic changes, and also has low installation and low maintenance costs; The present invention measures the strain caused by acoustic waves and vibrations based on the phase difference of backward Rayleigh scattering signals (scattered light transmitted in different directions in the optical fiber, where the light transmitted in the direction opposite to the incident light). When the optical fiber to be measured is affected by strain, the refractive index distribution inside the optical fiber changes, and Rayleigh frequency shift occurs in the optical fiber to be measured. By calculating the Rayleigh frequency shift between the measured signal (with interference) and the reference signal (without interference), strain measurement at a specific position of the optical fiber and distributed measurement of the entire optical fiber are realized, thereby achieving effective monitoring of carbon dioxide leakage. Brief Description of the Drawings

[0014] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for use in the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can be obtained based on these drawings.

[0015] Figure 1 It is a schematic structural diagram of the present invention.

[0016] Among them, 1. Carbon dioxide gas cylinder; 2. Liquid bottle; 3. Carbon dioxide intermediate container; 4. Liquid intermediate container; 5. Double-rod constant-pressure pump; 6. First pressure gauge; 7. First valve; 8. Heat preservation device; 9. Injection well; 10. First production well; 11. Second production well; 12. Second valve; 13. Third valve; 14. Second pressure gauge; 15. Third pressure gauge; 16. First flowmeter; 17. Second flowmeter; 18. Second fluid collection device; 19. First fluid collection device; 20. First optical fiber detector; 21. Second optical fiber detector; 22. Data acquisition and processing unit; 23. First optical fiber coupler; 24. First optical fiber; 25. Second optical fiber; 26. Third optical fiber; 27. Simulated formation; 28. Thermometer; 29. Second optical fiber coupler; 30. Optical fiber power supply. Detailed Embodiments

[0017] The following will clearly and completely describe the technical solutions in the embodiments of the present invention with reference to the drawings in the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, rather than all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts belong to the protection scope of the present invention.

[0018] To make the above objects, features, and advantages of the present invention more obvious and understandable, the present invention will be further described in detail below with reference to the drawings and specific embodiments.

[0019] Refer to Figure 1, the present invention provides a carbon dioxide formation leakage monitoring device based on distributed optical fiber sensing, including: An analog formation 27, on which a heat preservation device 8, a thermometer 28 and a production well system are installed; An injection system for injecting carbon dioxide and liquid into the analog formation 27; A DTS system, which includes a light source assembly, an optical fiber group, a detection assembly and a data acquisition and processing unit 22 connected in sequence; several monitoring points are provided on the optical fiber group, and the several monitoring points are installed in the analog formation 27 at intervals; the detection assembly is used to detect the Rayleigh scattering frequency shift, the intensity and phase of the Rayleigh backscattered light in the optical fiber group, and the data acquisition and processing unit 22 is used to collect the signals output by the detection assembly and perform data processing and analysis; With such a setting, the present invention injects carbon dioxide and liquid into the analog formation 27 through the injection system. As the injection of carbon dioxide proceeds, carbon dioxide continuously enters the analog formation 27, resulting in a change in the stress field of the analog formation 27; a laser pulse is injected into the optical fiber group through the light source assembly. Due to the microscopic inhomogeneity inside the optical fiber group (such as refractive index fluctuations at the molecular level), part of the light will be scattered back, and this phenomenon is called Rayleigh backscattering; the leakage of carbon dioxide will cause changes in the formation temperature, and these temperature changes will propagate to the formation where the optical fiber group is located, causing slight deformation of the optical fiber group, thereby changing the intensity and phase of the Rayleigh backscattered light. The DTS system can determine the position and amplitude of the temperature change by detecting these changes, so as to realize the effective monitoring of small-size fractures; The DTS system of the present invention has a high spatial distribution rate, can achieve fine monitoring and continuous monitoring, can cover a large range and perform distributed monitoring, provides a more comprehensive monitoring network, and has strong anti-environmental interference ability and stable chemical properties and is not easily corroded; it can realize real-time data acquisition and analysis, provide immediate monitoring results, and the continuous data stream can provide detailed information on dynamic changes, and also has low installation and low maintenance costs; The present invention measures the strain caused by sound waves and vibrations according to the phase difference of the backward Rayleigh scattering (the light scattered in the optical fiber travels in different directions, and the light traveling in the direction opposite to the incident light) signal. When the optical fiber to be measured is affected by strain, the refractive index distribution inside the optical fiber changes, and the optical fiber to be measured generates a Rayleigh scattering frequency shift. Calculate the Rayleigh scattering frequency shift between the measured signal (with interference) and the reference signal (without interference) to realize the strain measurement at a specific position of the optical fiber and the distributed measurement of the entire optical fiber, so as to realize the effective monitoring of carbon dioxide leakage.

[0020] In a further optimized solution, the optical fiber group includes a first optical fiber 24, a second optical fiber 25 and a third optical fiber 26, and the first optical fiber 24, the second optical fiber 25 and the third optical fiber 26 are installed in the analog formation 27 at intervals; One end of the first optical fiber 24, the second optical fiber 25, and the third optical fiber 26 is connected to the light source assembly, and the other end is connected to the detection assembly.

[0021] In a further optimized solution, the light source assembly includes an optical fiber power supply 30 and a first optical fiber coupler 23. One end of the first optical fiber 24, the second optical fiber 25, and the third optical fiber 26 is connected to the optical fiber power supply 30 through the first optical fiber coupler 23.

[0022] In a further optimized solution, the detection assembly includes a first optical fiber detector 20, a second optical fiber detector 21, and a second optical fiber coupler 29; one end of the first optical fiber 24, the second optical fiber 25, and the third optical fiber 26 is connected to the second optical fiber coupler 29; The first optical fiber detector 20 is used to detect the Rayleigh scattering frequency shift, and the second optical fiber detector 21 is used to detect the intensity and phase of the Rayleigh backscattered light; The input ends of the first optical fiber detector 20 and the second optical fiber detector 21 are both connected to the second optical fiber coupler 29, and the output ends are both connected to the data acquisition and processing unit 22; With such a setting, the first optical fiber 24, the second optical fiber 25, and the third optical fiber 26 are installed at intervals in the simulated formation 27 to form a distributed monitoring network; the optical fiber power supply 30 provides high-power and narrow-linewidth laser pulses to ensure that the optical signal has sufficient intensity and stability when propagating in the optical fiber; the first optical fiber coupler 23 evenly distributes the optical signal output by the optical fiber power supply 30 to the first optical fiber 24, the second optical fiber 25, and the third optical fiber 26 to achieve multi-channel synchronous monitoring; the second optical fiber coupler 29 combines the scattered optical signals in the three optical fibers and then transports them to the first optical fiber detector 20 and the second optical fiber detector 21 respectively to achieve multi-parameter synchronous detection; The first optical fiber detector 20 is used to detect the Rayleigh scattering frequency shift in the optical fiber group. When the optical fiber is affected by strain, the refractive index distribution inside the optical fiber changes, resulting in a shift in the frequency of the Rayleigh scattered light. The first optical fiber detector 20 calculates the strain condition of the optical fiber by measuring this frequency shift; the second optical fiber detector 21 is used to detect the intensity and phase of the Rayleigh backscattered light in the optical fiber group. The formation temperature change caused by carbon dioxide leakage will propagate to the location of the optical fiber, causing a slight deformation of the optical fiber, thereby changing the intensity and phase of the Rayleigh backscattered light. The second optical fiber detector 21 monitors the changes in these parameters in real time to provide a basis for leakage judgment.

[0023] In a further optimized solution, the injection system includes an injection well 9, an injection pipeline, a carbon dioxide injection assembly, and a liquid injection assembly; The carbon dioxide injection assembly and the liquid injection assembly are connected to the injection pipeline through a double-rod constant pressure pump 5. The injection pipeline is connected to the injection well 9. The injection well 9 is installed in the simulated formation 27, and a first pressure gauge 6 and a first valve 7 are installed on the injection pipeline.

[0024] For a further optimized solution, the carbon dioxide injection assembly includes a carbon dioxide gas cylinder 1, on which a first branch pipe is installed, and a carbon dioxide intermediate container 3 is installed on the first branch pipe; The liquid injection assembly includes a liquid bottle 2, on which a second branch pipe is installed, and a liquid intermediate container 4 is installed on the second branch pipe; The first branch pipe and the second branch pipe are connected to the injection pipeline through a double-rod constant pressure pump 5; regulating valves are installed on both the first branch pipe and the second branch pipe; The carbon dioxide intermediate container 3 is used to regulate and stabilize the injection pressure of carbon dioxide, the liquid intermediate container 4 is used to regulate and stabilize the injection pressure of the liquid, and the double-rod constant pressure pump 5 ensures that carbon dioxide and the liquid are injected into the simulated formation at a constant pressure.

[0025] For a further optimized solution, the production well system includes a first production well 10 and a second production well 11, both of which are installed in the simulated formation 27; The first production well 10 is connected to a first fluid collection device 19 through a third branch pipe, the second production well 11 is connected to a second fluid collection device 18 through a fourth branch pipe, a second valve 12, a second pressure gauge 14 and a second flowmeter 17 are installed on the third branch pipe, and a third valve 13, a third pressure gauge 15 and a first flowmeter 16 are installed on the fourth branch pipe; The first production well 10 and the second production well 11 are installed in the simulated formation 27 for collecting the produced fluid. The first fluid collection device 19 is connected to the first production well 10 through the third branch pipe to collect the produced fluid; the second fluid collection device 18 is connected to the second production well 11 through the fourth branch pipe to collect the produced fluid; the second pressure gauge 14 and the third pressure gauge 15 monitor the pressure of the produced fluid, and the first flowmeter 16 and the second flowmeter 17 measure the flow rate of the produced fluid.

[0026] The present invention also provides a method for monitoring carbon dioxide formation leakage based on distributed optical fiber sensing, including the following steps: Step 1: Inject carbon dioxide and liquid into the simulated formation 27; Step 2: Turn on the heat preservation device 8 and install the thermometer 28; Step 3: The production well system collects the fluid produced from the simulated formation 27; Step 4: Turn on the light source assembly to make the emitted optical signal propagate along the optical fiber group; Step 5: Use the detection assembly to detect the Rayleigh scattering frequency shift, the intensity and phase of the Rayleigh backscattered light in the optical fiber group; Step 6: Use the data acquisition and processing unit 22 to calculate the strain according to the signals received in the detection assembly, and judge whether carbon dioxide leaks. When the judgment result is leakage, an alarm is issued; the calculation formula for the strain is: , wherein, is the average wavelength, is the wavelength offset, is the average optical frequency, is the optical frequency shift, is the strain sensitivity coefficient, is the fiber strain, is the temperature sensitivity coefficient, is the temperature change.

[0027] In the description of the present invention, it should be understood that the orientation or positional relationship indicated by the terms "longitudinal", "transverse", "upper", "lower", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", etc. is based on the orientation or positional relationship shown in the drawings, and is only for the convenience of describing the present invention, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore should not be construed as a limitation of the present invention.

[0028] Obviously, the above embodiments of the present invention are only examples for clearly illustrating the present invention, rather than limitations on the implementation manners of the present invention. For those of ordinary skill in the art, other different forms of changes or modifications can be made based on the above description. It is not necessary and impossible to enumerate all the implementation manners here. Any modifications, equivalent replacements, and improvements made within the spirit and principle of the present invention shall be included in the protection scope of the claims of the present invention.

Claims

1. A carbon dioxide formation leakage monitoring device based on distributed optical fiber sensing, characterized in that Comprising: A simulated formation (27) on which a heat preservation device (8), a thermometer (28) and a production well system are installed; An injection system for injecting carbon dioxide and liquid into the simulated formation (27); A DTS system, which includes a light source assembly, an optical fiber group, a detection assembly and a data acquisition and processing unit (22) connected in sequence; a number of monitoring points are provided on the optical fiber group, and the number of monitoring points are installed in the simulated formation (27) at intervals; the detection assembly is used to detect the Rayleigh scattering frequency shift, the Rayleigh backscattered light intensity and phase in the optical fiber group, and the data acquisition and processing unit (22) is used to collect the signals output by the detection assembly and perform data processing and analysis.

2. The carbon dioxide formation leakage monitoring device based on distributed optical fiber sensing according to claim 1, wherein: The optical fiber group includes a first optical fiber (24), a second optical fiber (25) and a third optical fiber (26), and the first optical fiber (24), the second optical fiber (25) and the third optical fiber (26) are installed in the simulated formation (27) at intervals; One ends of the first optical fiber (24), the second optical fiber (25) and the third optical fiber (26) are all connected to the light source assembly, and the other ends are all connected to the detection assembly.

3. The carbon dioxide formation leakage monitoring device based on distributed optical fiber sensing according to claim 2, characterized in that: The light source assembly includes an optical fiber power supply (30) and a first optical fiber coupler (23), and one ends of the first optical fiber (24), the second optical fiber (25) and the third optical fiber (26) are all connected to the optical fiber power supply (30) through the first optical fiber coupler (23).

4. The carbon dioxide formation leakage monitoring device based on distributed optical fiber sensing according to claim 2, wherein: The detection assembly includes a first optical fiber detector (20), a second optical fiber detector (21) and a second optical fiber coupler (29); one ends of the first optical fiber (24), the second optical fiber (25) and the third optical fiber (26) are all connected to the second optical fiber coupler (29); The first optical fiber detector (20) is used to detect the Rayleigh scattering frequency shift, and the second optical fiber detector (21) is used to detect the Rayleigh backscattered light intensity and phase; The input ends of the first optical fiber detector (20) and the second optical fiber detector (21) are both connected to the second optical fiber coupler (29), and the output ends are both connected to the data acquisition and processing unit (22).

5. The carbon dioxide formation leakage monitoring device based on distributed optical fiber sensing according to claim 1, characterized in that: The injection system includes an injection well (9), an injection pipeline, a carbon dioxide injection assembly and a liquid injection assembly; The carbon dioxide injection assembly and the liquid injection assembly are communicated with the injection pipeline through a double-rod constant pressure pump (5), the injection pipeline is communicated with the injection well (9), the injection well (9) is installed in the simulated formation (27), and a first pressure gauge (6) and a first valve (7) are installed on the injection pipeline.

6. The carbon dioxide formation leakage monitoring device based on distributed optical fiber sensing according to claim 5, characterized in that: The carbon dioxide injection assembly includes a carbon dioxide gas cylinder (1), a first branch pipe is installed on the carbon dioxide gas cylinder (1), and a carbon dioxide intermediate container (3) is installed on the first branch pipe; The liquid injection assembly includes a liquid bottle (2), a second branch pipe is installed on the liquid bottle (2), and a liquid intermediate container (4) is installed on the second branch pipe; The first branch pipe and the second branch pipe are communicated with the injection pipeline through the double-rod constant-pressure pump (5); regulating valves are installed on both the first branch pipe and the second branch pipe.

7. The carbon dioxide formation leakage monitoring device based on distributed optical fiber sensing according to claim 1, wherein: The production well system includes a first production well (10) and a second production well (11), and both the first production well (10) and the second production well (11) are installed in the simulated formation (27); The first production well (10) is communicated with a first fluid collection device (19) through a third branch pipe, the second production well (11) is communicated with a second fluid collection device (18) through a fourth branch pipe, a second valve (12), a second pressure gauge (14) and a second flowmeter (17) are installed on the third branch pipe, and a third valve (13), a third pressure gauge (15) and a first flowmeter (16) are installed on the fourth branch pipe.

8. A method for monitoring carbon dioxide formation leakage based on distributed optical fiber sensing, and a device for monitoring carbon dioxide formation leakage based on distributed optical fiber sensing according to any one of claims 1-7, characterized in that, It includes the following steps: Step 1: Inject carbon dioxide and liquid into the simulated formation (27); Step 2: Turn on the heat preservation device (8) and install a thermometer (28); Step 3: The production well system collects the fluid produced from the simulated formation (27); Step 4: Turn on the light source assembly to make the emitted optical signal propagate along the optical fiber group; Step 5: Use the detection assembly to detect the Rayleigh scattering frequency shift, the intensity and phase of the Rayleigh backscattered light in the optical fiber group; Step 6: Use the data acquisition and processing unit (22) to calculate the strain according to the signals received in the detection assembly, and judge whether carbon dioxide leaks. When the judgment result is leakage, an alarm is issued; the calculation formula of the strain is: ， wherein, is the average wavelength, is the wavelength offset, is the average optical frequency, is the optical frequency shift, is the strain sensitivity coefficient, is the fiber optic strain, is the temperature sensitivity coefficient, is the temperature change.

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