Downhole flow tubular conductivity sensor

Abstract

The embodiment of the invention discloses an underground flow pipe type conductivity sensor. The underground flow pipe type conductivity sensor comprises a sensor body and a circuit module, the sensor body comprises a transmitting magnetic ring, a receiving magnetic ring, a zirconia ceramic tube, a sealing ring and a sensor shell; the formation fluid provides electromotive force for the transmitting magnetic ring and the receiving magnetic ring when flowing through the zirconia ceramic tube; the sealing ring is arranged between the zirconia ceramic tube and the sensor shell; a signal generator in the circuit module generates sine wave signals; the power amplifier module amplifies the power of the sine wave signal and excites the transmitting magnetic ring; the signal conversion circuit is used for converting a signal of the receiving magnetic ring into a PWM wave; and the single-chip microcomputer module collects the frequency of the PWM wave as a to-be-processed engineering value so as to calculate the conductivity of the formation fluid according to the calibration formula and the to-be-processed engineering value. The installation mode of the sensor is simpler and more convenient, the sensor does not need to be installed in a test cavity of a formation tester, the influence of sediments and attached pollutants is avoided, and the accuracy of a measurement result is effectively ensured.

Description

Technical Field

[0001] The embodiments of the present application relate to the field of geophysical well logging technology, and in particular to a downhole flow tube conductivity sensor. Background Art

[0002] In the field of geophysical logging, it is necessary to identify the formation fluid. Usually, after the formation tester is lowered to the target depth in the well, the formation fluid is extracted into the internal pipeline. While the fluid is being extracted, the other end of the pipeline discharges the extracted fluid into the annulus. In the process of fluid extraction, the fluid extracted at the beginning is mainly mud filtrate. As the extraction volume increases, the composition of the mud filtrate gradually decreases, and the composition of the original formation fluid gradually increases. Since the conductivity of brine, mud filtrate and oil in the formation fluid is quite different, the difference in conductivity can be used for fluid identification. In the prior art, invasive sensors are usually used to achieve conductivity measurement and determine the composition characteristics of the formation fluid. However, invasive sensors need to be installed in the test cavity, which requires the test cavity to have a large pipeline space, and invasive sensors are easily affected by sediments and attached contaminants in the test cavity, affecting the accuracy of the measurement results. Summary of the invention

[0003] In view of the above problems, the present application is proposed to provide a downhole flow tube conductivity sensor that overcomes the above problems or at least partially solves the above problems.

[0004] According to one aspect of an embodiment of the present application, there is provided a downhole flow tube conductivity sensor, comprising: a sensor body and a circuit module;

[0005] The sensor body includes: a transmitting magnetic ring, a receiving magnetic ring, a zirconia ceramic tube, a sealing ring and a sensor housing;

[0006] When the formation fluid flows through the zirconia ceramic tube, it provides electromotive force for the transmitting magnetic ring and the receiving magnetic ring; the sealing ring is installed between the zirconia ceramic tube and the sensor housing to isolate the high pressure in the pipeline;

[0007] The circuit module includes: a signal generator, a power amplifier module, a signal conversion circuit, a single chip computer module and a power supply module;

[0008] The signal generator is used to generate a sine wave signal;

[0009] The power amplifier module is connected to the signal generator and the transmitting magnetic ring, and is used to amplify the power of the sine wave signal and excite the transmitting magnetic ring;

[0010] The signal conversion circuit is connected to the receiving magnetic ring and is used to convert the signal of the receiving magnetic ring into a PWM wave;

[0011] The single chip microcomputer module is connected to the signal conversion circuit and is used to collect the frequency of the PWM wave as the engineering value to be processed, so as to calculate the conductivity of the formation fluid according to the calibration formula between the conductivity and the engineering value and the engineering value to be processed.

[0012] Optionally, the transmitting magnetic ring and the receiving magnetic ring are coils wound around an amorphous nanocrystalline magnetic core.

[0013] Optionally, the zirconia ceramic tube is an insulated flow tube and can withstand a pressure difference between the inside and outside of the pipeline of up to 140 MPa.

[0014] Optionally, a downhole flow tube conductivity sensor is suitable for use in a formation tester.

[0015] Optionally, the sealing ring is an O-ring.

[0016] Optionally, the signal conversion circuit includes: a signal amplification circuit, an effective value conversion circuit and a voltage-frequency conversion circuit;

[0017] The signal amplification circuit is used to amplify the signal received from the magnetic ring;

[0018] The effective value conversion circuit is connected to the signal amplification circuit and is used to convert the amplified signal into a DC signal;

[0019] The voltage-frequency conversion circuit is connected to the effective value conversion circuit and is used for converting the DC signal into a PWM wave.

[0020] Optionally, the frequency of the PWM wave is proportional to the amplitude of the DC signal.

[0021] Optionally, the signal generator, the power amplifier module, the signal conversion circuit and the single-chip microcomputer module are thick-film integrated circuits.

[0022] Optionally, the circuit module also includes: an RS485 circuit.

[0023] Optionally, the calibration formula is:

[0024]

[0025] Wherein, y is the conductivity; x is the engineering value; A, B, C and D are the parameters obtained in advance.

[0026] According to the technical solution provided in the embodiment of the present application, compared with the invasive sensor in the prior art, the downhole flow tube type conductivity sensor is smaller in size and can be well applied to the formation tester. The installation method is simpler and there is no need to install it in the test chamber of the formation tester. The formation fluid only flows through the zirconia ceramic tube, and there is almost no sediment and attachment contamination, thus avoiding the influence of sediment and attached pollutants and effectively ensuring the accuracy of the measurement results. Moreover, the zirconia ceramic tube is used as a pressure-bearing component with insulation and high-voltage resistance characteristics. The signal generator, power amplifier module, signal conversion circuit and single-chip microcomputer module in the circuit module use thick-film integrated circuits with high-temperature resistance, which can be well applied to high-temperature and high-pressure measurement environments, such as in the field of oil drilling. In addition, a nonlinear scale can be used in the downhole flow tube type conductivity sensor, thereby effectively avoiding the nonlinear problem of the sensor, realizing accurate measurement of conductivity, and being able to accurately identify oil, gas and water.

[0027] The above description is only an overview of the technical solution of the embodiment of the present application. In order to more clearly understand the technical means of the embodiment of the present application, it can be implemented in accordance with the contents of the specification. In order to make the above and other purposes, features and advantages of the embodiment of the present application more obvious and easy to understand, the specific implementation method of the embodiment of the present application is listed below. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] Various other advantages and benefits will become apparent to those of ordinary skill in the art by reading the detailed description of the preferred embodiments below. The accompanying drawings are only used for the purpose of illustrating the preferred embodiments and are not to be considered as limiting the embodiments of the present application. Moreover, the same reference symbols are used throughout the accompanying drawings to represent the same components. In the accompanying drawings:

[0029] Figure 1 A schematic structural diagram of a downhole flow tube conductivity sensor according to an embodiment of the present application is shown;

[0030] Figure 2 shows a schematic structural diagram of the sensor body;

[0031] Figure 3 shows a schematic diagram of a signal generator;

[0032] Figure 4 shows a schematic diagram of a signal amplification circuit;

[0033] Figure 5 A schematic diagram of an effective value conversion circuit is shown;

[0034] Figure 6 A schematic diagram of a single chip microcomputer module is shown;

[0035] Figure 7A curve fitting schematic diagram of the calibration formula is shown. DETAILED DESCRIPTION

[0036] The exemplary embodiments of the present disclosure will be described in more detail below with reference to the accompanying drawings. Although the exemplary embodiments of the present disclosure are shown in the accompanying drawings, it should be understood that the present disclosure can be implemented in various forms and should not be limited by the embodiments set forth herein. On the contrary, these embodiments are provided to enable a more thorough understanding of the present disclosure and to fully convey the scope of the present disclosure to those skilled in the art.

[0037] Compared to the invasive sensors in the prior art, the downhole flow tube type conductivity sensor provided by the present application is smaller in size and can be well suited for use in formation testers. The installation method is simpler and does not need to be installed as a whole in a larger test chamber specially designed for the formation tester. It can be installed at any position of the formation tester as long as the fluid is introduced into and out of the inlet and outlet of the sensor through a connecting pipe. Among them, the formation tester may specifically include a cable formation tester and a drilling formation tester, etc. In addition, the downhole flow tube type conductivity sensor provided by the present application adopts an anti-deposition and anti-pollutant adhesion design. This is because the downhole flow tube type conductivity sensor does not need to be installed in a test chamber, and the formation fluid only flows from the flow tube (i.e. Figure 1 The zirconia ceramic tube 113) in the chamber flows through, and there is almost no contamination by sediments and attached matter, thus avoiding the influence of sediments and attached pollutants and effectively ensuring the accuracy of the measurement results.

[0038] Figure 1 FIG. 4 shows a schematic diagram of a downhole flow tube conductivity sensor according to an embodiment of the present application. Figure 1 As shown, the downhole flow tube conductivity sensor includes a sensor body 110 and a circuit module 120 .

[0039] The sensor body 110 includes: a transmitting magnetic ring 111, a receiving magnetic ring 112, a zirconia ceramic tube 113, a sealing ring 114 and a sensor housing 115. The structural diagram of the sensor body 110 can be shown as follows: Figure 2 shown.

[0040] In a specific application, the geometric dimensions of the transmitting magnetic ring 111 and the receiving magnetic ring 112 can be 17mm*22mm*6.5mm. The inner diameter of the zirconia ceramic tube 113 is 5mm and the outer diameter is 12mm. The sealing ring 114 can be a fluororubber sealing ring. During installation, the zirconia ceramic tube 113 is inserted from the inside of the transmitting magnetic ring 111 and the receiving magnetic ring 112, fixed by epoxy resin glue, and then installed as a whole in the sensor housing 115. Among them, Figure 1 The light yellow portion located outside the transmitting magnetic ring 111 and the receiving magnetic ring 112 corresponds to the epoxy resin glue.

[0041] The transmitting magnetic ring 111 and the receiving magnetic ring 112 are coils wound with amorphous nanocrystalline magnetic cores. The zirconia ceramic tube 113 is an insulated flow tube as a pressure-bearing component, and can withstand a pressure difference of 140 MPa inside and outside the pipeline. Specifically, in a downhole flow tube conductivity sensor, the maximum internal pressure of the zirconia ceramic tube 113 is as high as 140 MPa, and the external pressure is normal pressure. The maximum pressure difference between the two is as high as 140 MPa. The zirconia ceramic tube 113 can withstand a maximum pressure difference of 140 MPa inside and outside the pipeline.

[0042] When the formation fluid flows through the zirconia ceramic tube 113, it provides an electromotive force to the transmitting magnetic ring 111 and the receiving magnetic ring 112. The formation fluid flowing in the zirconia ceramic tube 113 will produce electromagnetic induction. The circuit module 120 measures the change of the signal after electromagnetic induction, and determines the conductivity of the formation fluid through analysis, and then determines the composition characteristics of the formation fluid.

[0043] The sealing ring 114 is installed between the zirconia ceramic tube 113 and the sensor housing 115 to isolate the high pressure in the pipeline. Specifically, the sealing ring 114 can be an O-ring, and two O-rings can be installed between the zirconia ceramic tube 113 and the sensor housing 115. The sensor housing 115 is encapsulated outside the transmitting magnetic ring 111, the receiving magnetic ring 112, the zirconia ceramic tube 113 and the sealing ring 114, so that the transmitting magnetic ring 111, the receiving magnetic ring 112, the zirconia ceramic tube 113 and the sealing ring 114 are not directly in contact with the external environment of the measurement, which helps to ensure stable measurement.

[0044] The circuit module 120 includes: a signal generator 121, a power amplifier module 122, a signal conversion circuit 123, a single chip computer module 124 and a power supply module 125. The power supply module 125 provides power to each component of the circuit module 120. The circuit module 120 also includes: an RS485 circuit 126, which is used to communicate with the main control circuit of the formation tester and transmit the conductivity data and the like to the main control circuit of the formation tester.

[0045] The signal generator 121 is used to generate a sine wave signal, for example, a 40KHz sine wave signal. The power amplifier module 122 is connected to the signal generator 121 and the transmitting magnetic ring 111, and is used to amplify the power of the sine wave signal and excite the transmitting magnetic ring 111. When the formation fluid flows through the zirconia ceramic tube 113, electromagnetic induction is generated between the transmitting magnetic ring 111 and the receiving magnetic ring 112.

[0046] Figure 3The schematic diagram of the signal generator is shown. The single chip microcomputer module 124 generates a 40KHz PWM square wave signal, and after entering the signal generator 121, the signal passes through a second-order active low-pass filter and a common-phase proportional amplifier circuit to generate a 40KHz sine wave signal. The model of the power amplifier module 122 can be QQ11130.

[0047] The signal conversion circuit 123 is connected to the receiving magnetic ring 112 and is used to convert the signal of the receiving magnetic ring 112 into a PWM wave. Figure 1 As shown, the signal conversion circuit 123 includes: a signal amplifying circuit 1231, an effective value conversion circuit 1232 and a voltage-frequency conversion circuit 1233; the signal amplifying circuit 1231 is used to amplify the signal of the receiving magnetic ring 112; the effective value conversion circuit 1232 is connected to the signal amplifying circuit 1231, and is used to convert the signal after signal amplification into a DC signal, wherein the magnitude of the DC signal is the effective value of the input signal (i.e., the signal after signal amplification); the voltage-frequency conversion circuit 1233 is connected to the effective value conversion circuit 1232, and is used to convert the DC signal into a PWM (Pulse Width Modulation) wave, wherein the frequency of the PWM wave is proportional to the amplitude of the DC signal.

[0048] The signal amplifier circuit 1231 is a signal amplifier circuit composed of an instrument amplifier AD620, and the gain is adjusted by a gain adjustment resistor R60. Figure 4 The effective value conversion circuit 1232 is composed of a precision rectifier circuit and an RC resistor-capacitor filter circuit. The sine wave signal is converted into a half-wave signal by the precision rectifier circuit, and then a DC signal is obtained by RC resistor-capacitor filter processing, thereby realizing the effective value conversion function. Figure 5 The schematic diagram of the effective value conversion circuit is shown. The voltage-frequency conversion circuit 1233 is a single-chip solution of AD537, which converts the DC signal into a PWM wave frequency signal and provides it to the single-chip microcomputer module 124. The single-chip microcomputer module 124 is composed of a crystal oscillator, a programming interface, and a reset chip TPS3836. Figure 6 A schematic diagram of the microcontroller module is shown.

[0049] The single chip computer module 124 is connected to the signal conversion circuit 123, and is used to collect the frequency of the PWM wave as the engineering value to be processed, so as to calculate the conductivity of the formation fluid according to the calibration formula between the conductivity and the engineering value and the engineering value to be processed. In practical applications, the conductivity of the current formation fluid can be obtained by substituting the engineering value to be processed into the calibration formula for calculation. Among them, the calibration formula is:

[0050]

[0051] Where y is the conductivity in S / m; x is the engineering value and is dimensionless; A, B, C and D are pre-calculated parameters in S / m.

[0052] In practical applications, A, B, C, and D are calculated through calibration tests to obtain flow rates. The specific calibration examples are shown in Table 1:

[0053] Table 1 Correspondence between conductivity engineering value and conductivity true value

[0054] Conductivity Engineering Value Conductivity actual value (S / m) 0.05306 1 0.05801 1.635 0.08339 2.75 0.12074 4.09 0.15935 5.58 0.22295 7.76 0.37237 13.1 0.51313 18.2 0.65778 23.1 0.87105 30.9

[0055] The engineering value of conductivity is the circuit measurement value and is dimensionless. The true value of conductivity is the conductivity value measured by other conductivity instruments. It is the true conductivity value and is expressed in S / m. Substituting the above data into the calibration formula and using the least squares method to calculate, a set of optimal values ​​for A, B, C, and D are obtained. A, B, C, and D are -0.46404, 35.87241, 0.07957, and -0.00511, respectively, and the goodness of fit is 0.99986. A, B, C, and D are related to the individual heterogeneity of the conductivity sensor. Each sensor has different values. Similarly, a sensor has different values ​​at different times after calibration. Therefore, each sensor should be recalibrated at regular intervals (for example, every year).

[0056] Specifically, the signal generator 121, the power amplifier module 122, the signal conversion circuit 123 and the single-chip computer module 124 are thick film integrated circuits, which have high temperature resistance characteristics, and the circuit temperature resistance is as high as 175°C. Among them, thick film integrated circuits refer to hybrid integrated circuits formed by using thick film processes such as screen printing and sintering to make passive networks on the same substrate, assembling discrete semiconductor device chips or monolithic integrated circuits or micro components on them, and then packaging them. It is generally believed that films with a thickness of several microns to tens of microns are thick films.

[0057] Figure 7 A curve fitting diagram of the calibration formula is shown, such as Figure 7 As shown, the X-axis represents the engineering value of conductivity (i.e., engineering value) measured by the downhole flow tube conductivity sensor during the calibration stage, which is dimensionless; the Y-axis represents the actual conductivity of the fluid measured by the downhole flow tube conductivity sensor during the calibration stage, in units of S / m. During the calibration stage, it was found that when the conductivity was less than 5S / m, the sensor exhibited nonlinear characteristics. In order to cope with nonlinearity, the present application uses the above-mentioned calibration formula to calibrate the sensor, which is consistent with the sensor characteristics, and the goodness of fit can reach 99%. A nonlinear scale can be used in the downhole flow tube conductivity sensor, thereby effectively avoiding the nonlinear problem of the sensor.

[0058] According to the technical solution provided in the embodiment of the present application, compared with the invasive sensor in the prior art, the downhole flow tube type conductivity sensor is smaller in size and can be well applied to the formation tester. The installation method is simpler and there is no need to install it in the test chamber of the formation tester. The formation fluid only flows through the zirconia ceramic tube, and there is almost no sediment and attachment contamination, thus avoiding the influence of sediment and attached pollutants and effectively ensuring the accuracy of the measurement results. Moreover, the zirconia ceramic tube is used as a pressure-bearing component with insulation and high-voltage resistance characteristics. The signal generator, power amplifier module, signal conversion circuit and single-chip microcomputer module in the circuit module use thick-film integrated circuits with high-temperature resistance, which can be well applied to high-temperature and high-pressure measurement environments, such as in the field of oil drilling. In addition, a nonlinear scale can be used in the downhole flow tube type conductivity sensor, thereby effectively avoiding the nonlinear problem of the sensor, realizing accurate measurement of conductivity, and being able to accurately identify oil, gas and water.

[0059] The algorithm and display provided herein are not inherently related to any specific computer, virtual system or other equipment. Various general purpose systems can also be used together with the teachings based on this. According to the above description, it is obvious to construct the structure required for this type of system. In addition, the present application embodiment is not directed to any specific programming language yet. It should be understood that various programming languages ​​can be utilized to realize the content of the present application embodiment described herein, and the above description of specific languages ​​is to disclose the best mode of implementation of the present application embodiment.

[0060] In the description provided herein, a large number of specific details are described. However, it is understood that the embodiments of the present application can be practiced without these specific details. In some instances, well-known methods, structures and techniques are not shown in detail so as not to obscure the understanding of this description.

[0061] Similarly, it should be understood that in order to streamline the present disclosure and help understand one or more of the various inventive aspects, in the above description of the exemplary embodiments of the present application, the various features of the embodiments of the present application are sometimes grouped together into a single embodiment, figure, or description thereof. However, the disclosed method should not be interpreted as reflecting the following intention: the claimed embodiments of the present application require more features than the features clearly stated in each claim. More specifically, as reflected in the claims below, the inventive aspects are less than all the features of the single embodiment disclosed above. Therefore, the claims following the specific embodiment are hereby explicitly incorporated into the specific embodiment, wherein each claim itself serves as a separate embodiment of the embodiment of the present application.

[0062] Those skilled in the art will appreciate that the modules in the devices in the embodiments may be adaptively changed and arranged in one or more devices different from the embodiments. The modules or units or components in the embodiments may be combined into one module or unit or component, and in addition they may be divided into a plurality of submodules or subunits or subcomponents. Except that at least some of such features and / or processes or units are mutually exclusive, all features disclosed in this specification (including the accompanying claims, abstracts and drawings) and all processes or units of any method or device disclosed in this manner may be combined in any combination. Unless otherwise expressly stated, each feature disclosed in this specification (including the accompanying claims, abstracts and drawings) may be replaced by an alternative feature providing the same, equivalent or similar purpose.

[0063] In addition, those skilled in the art will appreciate that, although some embodiments described herein include certain features included in other embodiments but not other features, the combination of features of different embodiments is meant to be within the scope of the embodiments of the present application and to form different embodiments. For example, in the claims below, any one of the claimed embodiments may be used in any combination.

[0064] The various component embodiments of the embodiments of the present application can be implemented in hardware, or in software modules running on one or more processors, or in a combination thereof. It should be understood by those skilled in the art that a microprocessor or digital signal processor (DSP) can be used in practice to implement some or all functions of some or all components according to the embodiments of the present application. The embodiments of the present application can also be implemented as a device or apparatus program (e.g., computer program and computer program product) for executing part or all of the methods described herein. Such a program implementing the embodiments of the present application can be stored on a computer-readable medium, or can have the form of one or more signals. Such a signal can be downloaded from an Internet website, or provided on a carrier signal, or provided in any other form.

[0065] It should be noted that the above embodiments illustrate rather than limit the embodiments of the present application, and that those skilled in the art may design alternative embodiments without departing from the scope of the appended claims. In the claims, any reference symbol between brackets should not be constructed as a limitation to the claims. The word "comprising" does not exclude the presence of elements or steps not listed in the claims. The word "one" or "an" preceding an element does not exclude the presence of multiple such elements. The embodiments of the present application may be implemented by means of hardware including several different elements and by means of appropriately programmed computers. In a unit claim that lists several devices, several of these devices may be embodied by the same hardware item. The use of the words first, second, and third, etc. does not indicate any order. These words may be interpreted as names.

Claims

1. A downhole flow tube conductivity sensor, characterized in that: include: Sensor body and circuit module; The sensor body includes: a transmitting magnetic ring, a receiving magnetic ring, a zirconia ceramic tube, a sealing ring and a sensor housing; When the formation fluid flows through the zirconia ceramic tube, it provides electromotive force for the transmitting magnetic ring and the receiving magnetic ring; the sealing ring is installed between the zirconia ceramic tube and the sensor housing to isolate the high pressure in the pipeline; The circuit module includes: a signal generator, a power amplifier module, a signal conversion circuit, a single chip microcomputer module and a power supply module; The signal generator is used to generate a sine wave signal; The power amplifier module is connected to the signal generator and the transmitting magnetic ring, and is used to amplify the power of the sinusoidal wave signal and excite the transmitting magnetic ring; The signal conversion circuit is connected to the receiving magnetic ring and is used to convert the signal of the receiving magnetic ring into a PWM wave; The single chip microcomputer module is connected to the signal conversion circuit and is used to collect the frequency of the PWM wave as the engineering value to be processed, so as to calculate the conductivity of the formation fluid according to the calibration formula between conductivity and engineering value and the engineering value to be processed.

2. The downhole flow tube conductivity sensor according to claim 1, characterized in that: The transmitting magnetic ring and the receiving magnetic ring are coils wound around amorphous nanocrystalline magnetic cores.

3. The downhole flow tube conductivity sensor according to claim 1, characterized in that: The zirconia ceramic tube is an insulating flow tube and can withstand a pressure difference of 140 MPa between the inside and outside of the pipeline.

4. The downhole flow tube conductivity sensor according to claim 1, characterized in that: The downhole flow tube type conductivity sensor is suitable for use in a formation tester.

5. The downhole flow tube conductivity sensor according to claim 1, characterized in that: The sealing ring is an O-type sealing ring.

6. The downhole flow tube conductivity sensor according to any one of claims 1 to 5, characterized in that: The signal conversion circuit comprises: a signal amplification circuit, an effective value conversion circuit and a voltage-frequency conversion circuit; The signal amplification circuit is used to perform signal amplification processing on the signal of the receiving magnetic ring; The effective value conversion circuit is connected to the signal amplification circuit and is used to convert the amplified signal into a DC signal; The voltage-frequency conversion circuit is connected to the effective value conversion circuit and is used to convert the DC signal into the PWM wave.

7. The downhole flow tube conductivity sensor according to claim 6, characterized in that: The frequency of the PWM wave is proportional to the amplitude of the DC signal.

8. The downhole flow tube conductivity sensor according to any one of claims 1 to 5, characterized in that: The signal generator, the power amplifier module, the signal conversion circuit and the single-chip computer module are thick film integrated circuits.

9. The downhole flow tube conductivity sensor according to any one of claims 1 to 5, characterized in that: The circuit module also includes: an RS485 circuit.

10. The downhole flow tube conductivity sensor according to any one of claims 1 to 5, characterized in that: The calibration formula is: Wherein, y is the conductivity; x is the engineering value; A, B, C and D are the parameters obtained in advance.

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