Field calibration method and system for electrical resistance tomography sensor

Abstract

The invention discloses a field calibration method and system for an electrical resistance tomography sensor. The method comprises the following three steps: under a laboratory condition, establishing a mapping function model between a voltage measurement value and the conductivity by controlling the temperature of a fluid and synchronously measuring the conductivity of the fluid and the voltage response of an ERT sensor; the method comprises the following steps of: migrating a mapping function model established in a laboratory by using a calibration voltage and conductivity of a field to-be-measured fluid as a reference so as to adapt to a field actual condition; and measuring the conductivity in real time and calculating the calibration voltage by using the migrated model. Through detailed calibration under a laboratory condition and introduction of a field calibration point, the method can effectively reduce the influence of a field environment on the measurement accuracy of the ERT sensor, and ensures the accuracy of a measurement result. The method can flexibly cope with changes of different field environments, frequent recalibration is not needed, and the maintenance cost and the operation complexity are reduced.

Description

Technical Field

[0001] The present application belongs to the field of modern industrial detection technology, and is specifically a field calibration method and system for resistance tomography sensors, which are widely used in geological exploration, industrial process monitoring, environmental monitoring, biomedical imaging and other fields. Background Art

[0002] The basic principle of electrical resistance tomography (ERT) sensor technology is to arrange an electrode array outside the object, apply an excitation current, measure the response voltage, and use an inversion algorithm to reconstruct the conductivity distribution image inside the object. The conductivity distribution of the conductive medium can be visualized by measuring the voltage change between the electrode pairs. The principle is that when the distribution of the conductive medium in the channel changes, the distribution of conductivity will change, which will lead to a change in the potential distribution in the channel.

[0003] Due to the advantages of ERT technology such as non-invasiveness, non-radiation, and good real-time performance, it has been widely used in many fields. However, the measurement accuracy and stability of the ERT system are affected by many factors, such as electrode contact resistance, medium distribution changes, edge effects, etc. In order to ensure the accuracy and reliability of the ERT system in practical applications, its sensors need to be calibrated on-site.

[0004] In the oil field environment, the fluid in the oil and gas channel needs to be measured using an RTD sensor. In order to ensure the accuracy of the measurement, the RTD sensor needs to be calibrated. Under laboratory conditions, the key parameter of the RTD sensor - voltage calibration value V ω , which is usually established by filling the test channel with liquid fluid and measuring the voltage value at this state. However, for the complex and changeable oil field production site, the fluid in the oil and gas channel is a gas-water two-phase fluid, and the volume flow of the gas phase often dominates, far exceeding the liquid phase flow, which directly leads to the difficulty of simulating the full water state in the channel for voltage calibration. Therefore, the current oil field site has a lot of problems with V ω The calibration work has to rely on tedious and time-consuming manual operations. This method is not only inefficient, but also easily affected by human factors, making it difficult to ensure the accuracy and consistency of the calibration results.

[0005] In addition, V ω The temperature changes greatly, resulting in the successful acquisition of V under certain conditions. ω Once the ambient temperature changes, the calibration value will lose its reliability as a calibration benchmark, which brings great challenges to the real-time and accurate calibration work at the oil field site, and thus affects the efficiency and stability of the overall production process.

[0006] Because, in view of the particularity and complexity of the voltage calibration of resistance tomography sensors, it is urgent to develop a more efficient, automated calibration technology and system that can adapt to changes in ambient temperature. Summary of the invention

[0007] This application proposes a field calibration method and system for resistive tomography sensors to overcome the limitations of existing methods, thereby improving the real-time and accuracy of field flow detection, especially in oil and gas channels, and thus effectively improving the efficiency and accuracy of field production, especially in oilfields.

[0008] The technical solution of this application is as follows:

[0009] A method for field calibration of a resistance tomography sensor, comprising a resistance tomography sensor, is characterized by comprising the following steps:

[0010] S1: Fill the measurement channel of the RTI sensor with fluid, heat the fluid to the first set temperature, and then slowly cool it down to the second set temperature. During this period, a conductivity meter is used to measure the conductivity σ of the fluid. ω , and record the corresponding voltage measurement value V obtained by the resistance tomography sensor ω ; thereby obtaining the conductivity of the first set temperature and the second set temperature interval and its corresponding voltage measurement value; establishing the voltage measurement value V according to the measurement data ω and conductivity σ ω The mapping function model V ω (σ ω , θ) curve; when constructing the mapping function model, the formula with offset is used for fitting:

[0011] V ω (σ ω ,θ)=θ1 / (σ ω+ θ2)+θ3 (1),

[0012] Among them, θ=(θ1,θ2,θ3) is the parameter to be fitted, σ ω is the measured conductivity;

[0013] S2: By obtaining a calibration voltage f(x) and its conductivity x of the fluid to be tested on site as the calibration point, a mapping function model V is constructed. ω (σ ω , θ) curve to obtain a migrated mapping function model f(x) curve, and the coordinate points that satisfy the calibration voltage f(x) and the conductivity are located on the migrated mapping function model f(x) curve;

[0014] S3: The migrated mapping function model f(x) calculates the calibration voltage f(x) by measuring the conductivity x;

[0015] f(x)=a / (x+b)+c, (2),

[0016] Among them, a, b, c are the parameters to be fitted, and x is the measured conductivity.

[0017] In V w (σ w , θ) are calculated on this basis to obtain the parameters a, b, c to be fitted:

[0018] The a, b, and c mentioned above correspond to θ1, θ2, and θ3 obtained under laboratory conditions, where a = θ1, b and c need to be fixed according to the situation and one of them needs to be fitted to the other (for example, if b = θ2, then c = V ω -θ1 / (σ ω+ θ2 where V ω and σ ω It is the conductivity measurement value and its corresponding voltage value of a calibration point obtained under field conditions).

[0019] The on-site fluid to be tested is the oil and gas channel fluid at the oil field site.

[0020] In step S2, the method for obtaining a calibration voltage and conductivity of the fluid to be tested on site as a calibration point is as follows:

[0021] When the conductivity of the calibration point is small, a and c can be regarded as constants, and b can be solved as a variable;

[0022] When the conductivity of the calibration point is large, a and b can be regarded as constants, and c can be solved as a variable;

[0023] Avoid selecting calibration points where the conductivity x is in the middle range.

[0024] Preferably, when the conductivity at the calibration point is small, it means x<5; when the conductivity at the calibration point is large, it means x>20.

[0025] Preferably, the conductivity of the calibration point is in the middle range, which is 5 <x<20。

[0026] The first set temperature is 80°C, and the second set temperature is 5°C.

[0027] The fluid in step S1 is water.

[0028] The electrical resistance tomography sensor is provided with 8 measuring electrodes.

[0029] A field calibration system for a resistance tomography sensor comprises a memory and a processor, wherein the memory stores a computer program, and wherein the computer program executes the above-mentioned field calibration method for a resistance tomography sensor.

[0030] In the present application, under laboratory conditions, the measurement channel of the resistance tomography sensor is filled with fluid, and the temperature of the fluid is changed to record the conductivity of the fluid at different temperatures and its corresponding voltage measurement value.

[0031] Using these data, a mapping function model curve between voltage measurement values ​​and conductivity is established. This model is fitted by a formula with an offset and can reflect the nonlinear relationship between conductivity and voltage measurement values.

[0032] In the field, by obtaining a calibration voltage and its corresponding conductivity as a calibration point, the mapping function model established in the laboratory is migrated to the field environment. The migrated mapping function model curve ensures that the coordinate points of the calibration voltage and conductivity are on the curve.

[0033] Using the migrated mapping function model, the corresponding voltage is directly calculated by measuring the conductivity of the fluid in the field. This process achieves a fast conversion from conductivity to voltage measurement.

[0034] By performing precise calibration under laboratory conditions and considering the effect of temperature on fluid conductivity, an accurate mapping function model was established. This allows accurate voltage measurements to be obtained through the migrated mapping function model even when environmental conditions change in actual measurements.

[0035] This method is not only applicable to laboratory environments, but can also achieve accurate measurement of on-site fluids by migrating the mapping function model to the on-site environment. This flexibility enables the resistance tomography sensor to be used in a wider range of application scenarios. This greatly simplifies the operation process and improves measurement efficiency.

[0036] Compared with the traditional calibration method, this method does not require complex calibration experiments on site, and only requires laboratory calibration results and a calibration point on site to achieve the migration of the mapping function model, which reduces the calibration cost and time cost.

[0037] In summary, the field calibration method of the resistance tomography sensor achieves accurate measurement of the field fluid conductivity through three stages: laboratory calibration, field migration and actual measurement. It also has the advantages of improving measurement accuracy, enhancing applicability, simplifying operation procedures and reducing costs.

[0038] The field calibration method and system of the resistance tomography sensor proposed in this application overcome the limitations of existing methods, realize the rapid acquisition and dynamic tracking of the ERT full water calibration value at the oil field site, are efficient, automated and adaptable to changes in ambient temperature, have high practical application value for oil and gas channel flow detection, and thus effectively improve the efficiency and accuracy of oil field production. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 This is a flow chart of the working principle of this application.

[0040] Figure 2 Schematic diagram of the measurement channel structure of the electrical resistance tomography sensor.

[0041] Numbers in the figure: 1. temperature sensor, 2. measurement channel, 3. electric discharge valve, 4. resistance tomography sensor.

[0042] Figure 3 This is a schematic diagram of the data acquisition and processing system.

[0043] Figure 4 is the full water measurement value V of the resistance tomography sensor under different conductivity ω .

[0044] Figure 5 V ω The validation data were compared with the fitted curve.

[0045] Figure 6-1 To obtain V under laboratory conditions ω and σ ω The corresponding model function curve M.

[0046] Figure 6-2 To obtain a set of V ω and σ ω The corresponding point Φ.

[0047] Figure 6-3 To transfer the model function curve M through point Φ, we obtain M'. DETAILED DESCRIPTION

[0048] See also Figure 3 The present application proposes a device for an on-site calibration method of a resistance tomography sensor, including a sensing module and a data acquisition and processing system. A signal transmission connection is established between the sensing module and the data acquisition and processing system. The sensing module is mainly used to convert the changes in resistance and temperature of the measured fluid injected into the channel of the resistance tomography sensor into recognizable electrical signals. The data acquisition and processing system amplifies and samples the electrical signal generated on the sensing module and sends it to the main control circuit. The main control circuit digitally quantifies it to obtain the resistance value, and this resistance value is output to the host computer through the communication module.

[0049] The channel in the resistance tomography sensor serves as a fixed body of various components of the sensing module. The temperature sensor is installed on the top of the resistance tomography sensor channel by means of threads, and the electric exhaust valve is installed on the bottom of the resistance tomography sensor channel by means of threads.

[0050] The resistance tomography sensor is used to convert the conductivity change of the measured fluid into a recognizable voltage signal, the temperature sensor is used to measure the temperature change of the measured fluid, and the electric discharge valve is used to discharge the measured fluid.

[0051] The data acquisition and processing system includes a resistance detection circuit, a temperature detection circuit, a main control circuit, a communication module, and a power module. The resistance detection circuit is used to amplify the resistance change signal generated by the sensor module, sample it, and then send it to the main control circuit. The temperature detection circuit is used to amplify the temperature change signal generated by the sensor module, sample it, and then send it to the main control circuit. The main control circuit digitally quantifies the signals on the resistance detection circuit and the temperature detection circuit into specific resistance values ​​and temperature values. Under the control of the main control circuit, the communication module outputs the specific resistance value and temperature value to the host computer. The power module is used to provide power to the resistance detection circuit, the temperature detection circuit, the main control circuit, the communication module, and the electric discharge valve.

[0052] The resistance detection circuit is connected to the main control circuit signal transmission, and is connected to the resistance tomography sensor signal transmission on the sensor module. The temperature detection circuit is connected to the main control circuit and the temperature sensor signal transmission respectively, the communication module is connected to the main control circuit and the host computer signal transmission, and the power supply module is electrically connected to each circuit module and the electric discharge valve to provide them with power.

[0053] During calibration measurement, the measured fluid flows into the channel from the temperature sensor end, and the data acquisition and processing system monitors the voltage change on the resistance tomography sensor in real time, obtains the potential distribution in the device, and thus calculates the conductivity of the fluid. After the measured fluid is measured, the electric discharge valve is opened to discharge the measured fluid from the device.

[0054] Conductivityσ ω To the ERT full water voltage measurement value V ω Theoretically, the conductivity σ ω and the calibration voltage V ω The inverse function relationship is:

[0055]

[0056] However, in practical applications, affected by environmental conditions, σ ω and V ω It does not always conform to the inverse proportional relationship as shown above, so when constructing the mapping function model, a formula with an offset is used for fitting:

[0057] V ω (σ ω , θ)=θ1 / (σ ω+ θ2)+θ3 (2),

[0058] Among them, θ=(θ1,θ2,θ3) is the parameter to be fitted, σ ω is the measured conductivity.

[0059] The measurement channels of the electrical resistance tomography sensor are shown in Figure 2 A temperature sensor 1 is installed at the upper end of the measuring channel 2 of the resistance tomography sensor 4, and an electric discharge valve 3 is installed at the bottom of the measuring channel 2.

[0060] ERT has 20 independent measurements, corresponding to 20 measurement channels, of which 8 channels have adjacent excitation electrode pairs and measurement electrode pairs, 8 channels have one electrode between the excitation electrode pairs and measurement electrode pairs, and 4 channels have two electrodes between the excitation electrode pairs and measurement electrode pairs (opposite). The same type of measurement channels in ERT (i.e., adjacent electrodes, alternate electrodes, and opposite electrodes, denoted as: Adj, Ap1, and Opp, respectively) have the same full water measurement value V ω Therefore, according to the ERT full water measurement values ​​of different categories of channels, the parameters of the function model output value fitting are different.

[0061] Under laboratory conditions, the ERT full water measurement values ​​under different conductivity conditions are obtained by changing the temperature. The experimental data are sampled at a frequency of 1 Hz to obtain data points.

[0062] Figure 4 It is a scatter plot drawn based on experimental data, which contains 303,989 collected data and completely covers the commonly used conductivity range.

[0063] Figure 4 After the data in is randomly divided, about 80% is used for fitting formula (2) and about 20% is used to verify the fitting effect. The data fitting effect verification is shown in the following table:

[0064] Table 1 Verification of the fitting effect of the function model

[0065]

[0066]

[0067] The data in the table show that when the relative error band is set to 5%, the model confidence probabilities of the three electrode channels are 98.54%, 87.95% and 85.15% respectively; when the relative error band is set to 10%, the model confidence probabilities of the three electrode channels are 100.00%, 100.00% and 99.99% respectively. The fitting effect of the model meets the needs of practical applications. The three model functions are as follows:

[0068]

[0069] Figure 5This is the comparison between the mapping function model curve and the verification data. The discrete data points in the figure are the ERT full water measurement values ​​V ω , the curve is the mapping function model curve. It can be seen that the model curve is consistent with V ω There is good consistency, indicating that the model performs well.

[0070] However, it should be noted that the ERT measurement value is related to factors such as the parameters of the sensor device, the size of the external excitation current, and the gain parameters.

[0071] Therefore, for different ERT sensors, the fitting parameters in the model also need to be adjusted accordingly. However, based on the above experiments, it can be seen that the parameter adjustment of the model can be solved by simply collecting a few sets of experimental data without repeating a large number of tedious experiments.

[0072] Field calibration method for electrical resistance tomography sensor

[0073] The conductivity σ under laboratory conditions is obtained above ω To the ERT full water voltage measurement value V ω The mapping function model V ω (σ ω ,θ)=θ1 / (σ ω+ For the resistance tomography sensors with the same structure and configuration, θ1 in their mapping function model is the same. Changes in the application environment will only change the values ​​of θ2 and θ3. That is, when the same type of resistance tomography sensor is used in different environments, the shape of the curve of its mapping function model will not change, only the up, down, left and right positions of the curve will change.

[0074] Therefore, for the ERT model curve at the oil field site, the resistance tomography sensor is used to measure the oil and gas fluid voltage. By obtaining a set of corresponding relationships between the conductivity x and the ERT full fluid voltage measurement value f(x), a point on the curve is determined and the mapping function model V ω (σ ω ,θ)=θ1 / (σ ω+ θ2)+θ3 migration, to obtain a migration mapping function model f(x) curve, and the coordinate point that satisfies the calibration voltage f(x) and the conductivity is located on the migration mapping function model f(x) curve;

[0075] like Figure 1 The specific steps are as follows

[0076] S1: Under laboratory conditions, fill the measurement channel of the RTI sensor with water, heat the water to 80°C, and then slowly cool it down to 5°C. During this time, a conductivity meter is used to measure the conductivity of the fluid σ ω , and record the corresponding voltage measurement value V obtained by the resistance tomography sensorω ; Thus, the conductivity in the range of 5℃-80℃ and its corresponding voltage measurement value are obtained; according to the measurement data, the voltage measurement value V is established ω and conductivity σ ω The mapping function model V ω (σ ω , θ) curve; when constructing the mapping function model, the formula with offset is used for fitting:

[0077] V ω (σ ω , θ)=θ1 / (σ ω+ θ2)+θ3 (1),

[0078] Among them, θ=(θ1,θ2,θ3) is the parameter to be fitted, σ ω is the measured conductivity;

[0079] The correctness of formula (1) has been verified in the laboratory.

[0080] S2: By obtaining a calibration voltage f(x) and its conductivity x of the fluid to be tested on site as the calibration point, a mapping function model V is constructed. ω (σ ω , θ) curve to obtain a migrated mapping function model f(x) curve, and the coordinate points that satisfy the calibration voltage f(x) and the conductivity are located on the migrated mapping function model f(x) curve;

[0081] S3: The migrated mapping function model f(x) calculates the calibration voltage f(x) by measuring the conductivity x;

[0082] f(x)=a / (x+b)+c, (2)

[0083] Among them, a, b, c are the parameters to be fitted, and x is the measured conductivity.

[0084] In V w (σ w , θ) are calculated on this basis to obtain the parameters a, b, c to be fitted:

[0085] The a, b, and c mentioned above correspond to θ1, θ2, and θ3 obtained under laboratory conditions, where a = θ1, b and c need to be fixed according to the situation and one of them needs to be fitted to the other (for example, if b = θ2, then c = V ω -θ1 / (σ ω+ θ2 where V ω and σ ω It is the conductivity measurement value and its corresponding voltage value of a calibration point obtained under field conditions).

[0086] Specific methods such as Figure 6-1 ,6-2 , as shown in 6-3.

[0087] The following uses the error analysis method to determine the calibration point, that is, the impact on the overall error when the parameters a, b, and c to be fitted are disturbed:

[0088] A. For the error caused by the disturbance of parameter a, suppose there is a point (x0, y0) on the curve, y0 = a / (x0+b)+c. Let's assume that there is a disturbance Δa>0 in coefficient a. At this time, the calculated value y0' corresponding to the conductivity x0 on the curve is y0' = (a+Δa) / (x0+b)+c, then the relative error ε generated is:

[0089] ε=|y0-y0'| / y0=|a / (x0+b)-(a+Δa) / (x0+b)| / [a / (x0+b)+c]

[0090] =Δa / [a+c(x0+b)]<Δa / a;

[0091] Combining the existing function model, we know that a>400, so when Δa<4, the relative error generated is less than 1%, so the a value can be regarded as a fixed value when the curve migrates.

[0092] B. For the error caused by the perturbation of parameter b, suppose there is a point (x0, y0) on the curve, y0 = a / (x0+b)+c. Let's assume that there is a perturbation Δb>0 in coefficient b, then y0' = a / (x0+b+Δb)+c, then the relative error ε generated is

[0093] ε=|y0-y0'| / y0=|a / (x0+b)-a / (x0+b+Δb)| / [a / (x0+b)+c]

[0094] <|a / (x0+b)-a / (x0+b+Δb)| / [a / (x0+b)]

[0095] =1-(x0+b) / (x0+b+Δb)=Δb / (x0+b+Δb);

[0096] Therefore, the relative error ε decreases monotonically with x. When the value of x is large, the relative error is <1%, which is within the acceptable range.

[0097] C. For the error caused by the disturbance of parameter c, suppose there is a point (x0, y0) on the curve, y0 = a / (x0+b)+c. Let's assume that there is a disturbance Δc>0 in coefficient c, then y0' = a / (x0+b)+c+Δc, then the relative error ε generated is

[0098] ε=|y0-y0'| / y0=|Δc| / [a / (x0+b)+c];

[0099] Obviously, the relative error ε increases monotonically with the increase of x. When x is relatively small, the relative error is < 1%, which is within the acceptable range.

[0100] In summary, for the fitting parameters a, b, and c in the migrated mapping function model f(x) = a / (x + b) + c, the perturbation of a has a relatively small impact on the overall error deviation, while the perturbation of b has a greater impact when x is small, and the perturbation of c has a greater impact when x is large. Therefore, the following method for selecting the calibration points is obtained:

[0101] When the conductivity of the calibration point is small (such as x < 5), a and c can be regarded as constants, and b can be solved as a variable;

[0102] When the conductivity of the calibration point is large (such as x > 20), a and b can be regarded as constants, and c can be solved as a variable;

[0103] In addition, the situation where the conductivity of the calibration point is selected in the middle range (5 < x < 20) should be avoided as much as possible.

[0104] Verification of the migration effect of the function model

[0105] Table 2 shows the verification results of the migration effect of the function model of adjacent electrode channels of the electrical resistance tomography sensor. That is, when the calibration point is selected as x = 2, a and c are regarded as constants, and b is substituted into the function equation as a variable to solve; when the calibration point is selected as x = 20, a and b are regarded as constants, and c is substituted into the function equation as a variable to solve. It can be seen that the relative error of the migrated model function is well controlled and meets the requirements of practical applications. In addition, when x = 12, the error rate is significantly larger, which also verifies that the selection of the conductivity calibration point should avoid the situation in the middle range as much as possible.

[0106] Table 2 Verification of the migration effect of the function model

[0107]

Claims

1. A method for field calibration of a resistance tomography sensor, comprising a resistance tomography sensor, characterized in that: The following steps are involved: S1: Fill the measurement channel of the RTI sensor with fluid, heat the fluid to the first set temperature, and then slowly cool it down to the second set temperature. During this period, a conductivity meter is used to measure the conductivity σ of the fluid. ω , and record the corresponding voltage measurement value V obtained by the resistance tomography sensor ω ; thereby obtaining the conductivity and the corresponding voltage measurement value of the first set temperature and the second set temperature interval; establishing the voltage measurement value V according to the measurement data ω and conductivity σ ω The mapping function model V ω (σ ω ,θ) curve; when constructing the mapping function model, a formula with an offset is used for fitting; S2: By obtaining a calibration voltage f(x) and its conductivity x of the fluid to be tested on site as the calibration point, a mapping function model V is constructed. ω (σ ω , θ) curve to obtain a migrated mapping function model f(x) curve, and the coordinate points that satisfy the calibration voltage f(x) and the conductivity are located on the migrated mapping function model f(x) curve; S3: The migrated mapping function model f(x) calculates the calibration voltage f(x) by measuring the conductivity x.

2. The on-site calibration method of an electrical resistance tomography sensor according to claim 1, characterized in that: The on-site fluid to be tested is the oil and gas channel fluid at the oil field site.

3. The on-site calibration method of an electrical resistance tomography sensor according to claim 1, characterized in that: In step S2, the method for obtaining a calibration voltage and conductivity of the fluid to be tested on site as a calibration point is as follows: When the conductivity of the calibration point is small, a and c can be regarded as constants, and b can be solved as a variable; When the conductivity of the calibration point is large, a and b can be regarded as constants, and c can be solved as a variable; Avoid selecting calibration points where the conductivity x is in the middle range.

4. The on-site calibration method of an electrical resistance tomography sensor according to claim 3, characterized in that: When the conductivity of the calibration point is small, it means x<5; when the conductivity of the calibration point is large, it means x>20.

5. The on-site calibration method of an electrical resistance tomography sensor according to claim 3, characterized in that: The conductivity of the calibration point is in the middle range, which means 5 <x<20。 6. The on-site calibration method of an electrical resistance tomography sensor according to claim 1, characterized in that: The first set temperature is 80°C, and the second set temperature is 5°C.

7. The on-site calibration method of an electrical resistance tomography sensor according to claim 1, characterized in that: The fluid in step S1 is water.

8. The on-site calibration method of an electrical resistance tomography sensor according to claim 1, characterized in that: The electrical resistance tomography sensor is provided with 8 measuring electrodes.

9. The on-site calibration method of an electrical resistance tomography sensor according to claim 1, characterized in that: In step S1, the formula fitting with an offset is as follows: V ω (s ω ,θ)=θ1 / (σ ω+ θ2)+θ3 (1), Among them, θ=(θ1,θ2,θ3) is the parameter to be fitted, σ ω is the measured conductivity; In step S2, the calibration voltage f(x) is calculated by measuring the conductivity x using the following formula: f(x)=a / (x+b)+c, (2) Among them, a, b, c are the parameters to be fitted, and x is the measured conductivity.

10. A field calibration system for an electrical resistance tomography sensor, comprising a memory and a processor, wherein the memory stores a computer program, characterized in that: The computer program executes the method according to any one of claims 1 to 9.

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