JP2016079500A - Measuring device and measuring method for evaluating reduction degradation - Google Patents

Abstract

PROBLEM TO BE SOLVED: To measure AE waves for evaluating the reduction degradation for iron oxide raw material for iron making.SOLUTION: Provided is a measuring device for measuring the total of AE energy from AE waves during the reduction of iron oxide raw material for iron making, comprising: a reduction furnace part; a gas feeding part; and an AE measuring part. The reduction furnace part includes: a reaction tube of storing the iron oxide raw material for iron making; and a heating furnace of involving the reaction tube and heating the same. The gas feeding part feeds a reduction gas at least including one kind of CO and Hto the reaction tube. The AE measuring part includes: an AE waveguide member for conducting the AE waves from the iron oxide raw material for ion making; and an AE measuring apparatus for measuring the conducted AE waves.SELECTED DRAWING: Figure 2

Description

  The present invention relates to a measuring apparatus and a measuring method for evaluating reduction powdering of iron oxide raw materials for iron making such as sintered ore and fired pellets. In particular, the present invention simplifies the method for measuring the reduced powder amount defined in JIS and ISO.

  In the stable operation of a blast furnace, which is a furnace for extracting pig iron from iron ore, securing the ventilation of the shaft part is a very important issue. However, when the sintered ore is reduced to powder in the upper part of the shaft, the generated powder inhibits the ventilation of the shaft part. Therefore, conventionally, the RDI test (ISO4696-2) has been used as an index for managing the reduction powdering of sintered ore.

  The reduction test conditions of the RDI test described above were as follows: sintered ore particle size: 16 to 20 mm, sintered ore weight: 500 g, reduction temperature: 550 ° C., reduction time: 30 minutes, reducing gas composition: CO: N 2 = 30: 70. In the RDI test, after the reduction, the sample was put into a cylinder of a predetermined diameter called a drum test, and a total of 900 rotations were carried out at 30 rpm for 30 minutes, followed by sieving and passing through a 3.15 mm square net. The ratio is measured and the value becomes the RDI value.

On the other hand, there is a direct reduction iron making method as one of the iron making methods. This is because, as a reducing gas, natural gas or a gas obtained by reforming natural gas (CO and H ₂ are the main components), coal gas (gas generated when coal is gasified), etc. This is a direct reduction method (see, for example, Patent Documents 1 and 2). Similar to the blast furnace method, when the sintered ore is reduced to powder at the upper part of the shaft, the generated powder inhibits the ventilation of the shaft part. For this reason, the DR-RDI test (ISO11257) is used as an index for managing reduced powdering, although the test conditions differ from those of the blast furnace method.

  In this way, the test method for measuring the reduced pulverization index of the blast furnace method and the direct reduction iron manufacturing method is because the iron oxide raw material is processed in a heated electric furnace and cooled to room temperature, and then a rotation test is performed. The number of man-hours is limited, and it is difficult to quickly measure the reduced powder index of a plurality of types of iron oxide raw materials. Moreover, the test apparatus and the test method are complicated, and it is indispensable to purchase the apparatus and train the technique of the measurer.

Various researches have been conducted on the reduction powdering phenomenon regarding sintered ore in blast furnaces. According to it, cracking occurs in the iron oxide raw material due to strain energy generated by internal stress generated by volume expansion when reducing from hematite (Fe ₂ O ₃ ) to magnetite (Fe ₃ O ₄ ). This is attributed to the fact that the sintered ore is prominent at temperatures around 550 ° C. (see Non-Patent Document 1). It is known that the strength recovers when reducing from magnetite (Fe ₃ O ₄ ) to wustite (FeO), that is, the reduced powdering index correlates with the magnetite content (see Non-Patent Document 2). ).

  As a method for evaluating cracks and crack fracture, there is an AE method in which an acoustic emission (hereinafter referred to as AE) is measured and the obtained waveform is analyzed. AE is a phenomenon in which AE waves (elastic waves such as vibrations and sound waves) are generated along with fractures such as the occurrence and development of cracks, and the generation of sound in the audible area called “pick” when wood breaks is also AE. . A method of detecting this AE wave with an AE sensor and evaluating it nondestructively is called an AE method.

  The AE method is a passive method for detecting an AE wave emitted by a material itself as it cracks or deforms. That is, the AE method can evaluate the progress of cracks in real time. It is an evaluation method that can continuously monitor large-scale facilities in operation as long as AE waves propagate, and can respond to sudden abnormalities that lead to facility shutdown.

  The AE method is also used as a method for evaluating small materials. For example, a technique for evaluating cracks and crack fractures that occur during a steel material tensile test or a ceramic four-point bending test is known (see Non-Patent Documents 3 and 4).

  As a material for the AE sensor, a zirconate titanate (PZT) type piezoelectric element is generally used. A piezoelectric element is a material that generates a charge on its surface when stress is applied. Since the temperature (Curie point) at which the piezoelectricity disappears is about 300 ° C., the PZT type piezoelectric element has a limited use in a high temperature environment. Therefore, the evaluation by the AE method is often performed under a cold condition regardless of whether the size of the crack generation medium is large or small.

  As a method for use in a high temperature environment, there is a method using a waveguide rod or a cooler. For example, a method of measuring cracks due to thermal expansion at a high temperature of a refractory by using a waveguide rod is known (see Non-Patent Document 5).

  The AE method is applied to crack measurement of various materials such as metals, ceramics, and plastics.

JP 63-213613 A JP 2010-043314 A US Pat. No. 3,617,227 US Pat. No. 3,748,120

Iron and steel, Vol. 68, (1982) 740 Materials and Processes, Vol. 15 (1) (2002) 114 D. Tromans amd J.M. A. Meech: Minerals Engineering, 15 (2002) 1027 M.M. Takeda, T .; Onishi, S .; Nakakubo and S.N. Fujimoto: Materials transaction, 50 (2009) 2242. G. Briche et al. : Journal of the European Ceramic Society, 28 (2008) 2835

  There has been no case where the AE method is applied to the blast furnace method of the iron making process or the evaluation method of the reduced powdering index of the direct reduction iron making method, and it has not been clarified whether AE waves are generated at the time of reducing powdering.

  As described above, in the blast furnace method and the direct reduction iron manufacturing method, when the iron oxide raw material is reduced to powder, the air permeability of the furnace (shaft portion) is hindered by the generated powder, which may cause production failure. Therefore, although there is a management index for reducing powderization for each reduction process, it is difficult to quickly measure the reduced powdering index of a plurality of types of iron oxide raw materials.

  Then, an object of this invention is to measure the AE wave for evaluating the reduction | restoration powdering of an iron oxide raw material. Another object of the present invention is to simplify the measurement of the reduced powdering index, which is an evaluation index of reduced powdering of the iron oxide raw material, while speeding up the measurement.

  The present inventors examined the application of AE as a method for solving the above-described problems. Therefore, not only sintered or fired pellets, but also a large number of AE waves are generated by reduction powdering when reducing iron oxide raw materials, and the total amount of AE energy calculated from the generated AE waves and the amount of reduction powdered index change It was found that there is a correlation between the reduced powdering index and the rotational strength of the iron oxide raw material. Furthermore, it has also been found that this correlation varies depending on the type of iron oxide raw material.

  Here, the sum of AE energies represents the area of the frequency spectrum obtained by Fourier transforming the measured AE waveform. It is known that AE energy correlates with crack area. FIG. 1 shows an example of an AE waveform and a frequency spectrum generated during reduction powdering.

  The present invention has been made on the basis of the above knowledge, and it is possible to measure AE waves in order to evaluate reduction powdering of iron oxide raw materials, and to reduce powdering from the sum of AE energies generated during the reduction of iron oxide raw materials. The main point is to estimate the index. The summary is as follows.

(1) A measuring apparatus that has a reduction furnace section, a gas supply section, and an AE measurement section, and measures the total AE energy from AE waves during the reduction of the iron oxide raw material for iron making,
The reduction furnace section includes a reaction tube that contains the iron oxide raw material for iron making, and a heating furnace that encloses and heats the reaction tube,
The gas supply unit supplies a reducing gas containing at least one of CO and H _{2 to} the reaction tube,
The AE measuring unit includes an AE waveguide member that transmits an AE wave from the iron oxide raw material for iron making, and an AE measuring instrument that measures the transmitted AE wave.

(2) A reduction powder index change amount (ΔRDI = RDI−TI _BR ), which is a difference between the reduced powder index (RDI) and the rotational strength (TI _BR ), and the AE energy generated during the reduction powder. A method for measuring a reduced pulverization index, in which a correlation (EQ1) with the sum (E _total ) is determined and a reduced pulverization index is obtained by the following steps a) to c).
a) A first step of measuring the rotational strength (TI _BR ) of the iron oxide raw material for iron making.
b) AE energy during reduction of the iron oxide raw material for iron making using the measuring device of (1)
A second step of measuring the sum of
c) AE energy measured in the second step based on the correlation (EQ1).
The amount of change in reduced powder index (ΔRDI) is estimated from the sum of
From the amount of crystallization (ΔRDI) and the rotational strength (TI _BR ) measured in the first step, the return
3rd process which calculates | requires original powdering index (RDI) by following formula (I).
RDI = ΔRDI + TI _BR (I)

(3) The method for measuring a reduced powder index according to (2), wherein the correlation (EQ1) is determined for each type of iron oxide raw material for iron making.

(4) When the iron oxide raw material for iron making is a sintered ore, the correlation (EQ1) is represented by the following formula (II).
ΔRDI = 2.59 × 10 ⁻⁸ E _total +7.26 (II)

(5) When the iron oxide raw material for iron making is a calcined pellet, the correlation (EQ1) is represented by the following formula (III).
ΔRDI = 6.28 × 10 ⁻⁹ E _total + 5.22 × 10 ⁻¹ (III)

  According to the measuring apparatus of the present invention, it is possible to measure an AE wave for evaluating reduction powdering of an iron oxide raw material.

  According to the measuring method of the present invention, by using the correlation (EQ1), the amount of reduction powdered index change is estimated from the sum of AE energy, and the reduced powder of iron oxide raw material from the amount of reduced powdered index change and the rotational strength. The chemical index can be measured quickly. Moreover, the measurement of a reduction | restoration powdering index | exponent can be simplified by presetting correlation (EQ1). Furthermore, by determining the correlation (EQ1) for each type of iron oxide raw material, the measurement accuracy of the reduced powder index can be improved.

It is a figure which shows an example of the AE waveform and frequency spectrum which generate | occur | produce at the time of reduction | restoration powdering. It is the schematic of the simple measuring apparatus of a reduction | restoration powdering index | exponent. It is a figure which shows the flowchart of the reduced-powdering index simple measuring method. It is a figure which shows the correlation of the sum total of AE energy and (DELTA) RDI in an Example. It is a figure which shows the relationship between a measured value and a calculated value about RDI in an Example.

(Measurement device for reduced powder index of the present invention)
FIG. 2 shows a schematic diagram of a measuring apparatus for reducing powder index. The reduced-powdering index measuring device has a reducing furnace part, a gas supply part, and an AE measuring part.

  The said reduction furnace part has a reaction tube which accommodates the iron oxide raw material (sample) for iron manufacture which is a measuring object, and a heating furnace which encloses and heats it. Further, the reaction tube includes a reaction tube outer tube 1, a reaction tube inner tube 2, a pair of gas rectifying perforated plates 3 separated from each other in the vertical direction of the reaction tube inner tube 2, a gas inlet 4, A discharge port 5, a sample temperature measuring thermocouple 7, and a reaction tube lid 10 are provided. A sample S indicated by a white circle is inserted between a pair of gas rectifying perforated plates 3. The heating furnace includes a furnace temperature control thermocouple 8 and an electric heating furnace body 9.

The gas supply unit guides a reducing gas containing at least one of CO and H ₂ to the gas inlet 4 and supplies it to the inside of the reaction tube inner pipe 2 in the reduction furnace unit. The reducing gas supplied to the inside of the reaction tube inner tube 2 passes through the upper gas rectifying perforated plate 3 and reaches the sample S. Thereby, the sample S is reduced. The gas supply unit includes a gas cylinder 15, a gas flow meter 16, and a gas mixing container 17, and produces the reducing gas. The gas cylinder 15 is provided only for the type of gas. In this embodiment, a plurality of gas cylinders 15 each containing N ₂ , CO, CO ₂ , and H ₂ are provided. Further, as many gas flow meters 16 as the number of gas cylinders 15 are provided. Only one type of gas (for example, N ₂ gas) may be supplied to the gas mixing container 17 or a plurality of types of gases (for example, CO and H ₂ ) may be supplied.

  The AE measurement unit includes an AE waveguide member that transmits an AE wave from the sample S and an AE measurement device that measures the AE wave transmitted by the AE waveguide member. In the present embodiment, a rod-shaped AE waveguide rod 6 is used as the AE waveguide member. The AE measuring instrument includes an AE sensor 11, a signal line 12, an AE measuring device 13, and an analysis PC (Personal Computer) 14. The AE waveguide rod 6 extends into the sample S inserted between the pair of gas rectifying perforated plates 3 and transmits the AE wave generated from the sample S to the AE sensor 11 during reduction. The AE wave detected by the AE sensor 11 is transmitted to the AE measuring device 13 via the signal line 12, and the AE waveform is specified in the AE measuring device 13. The AE waveform is transmitted from the AE measurement device 13 to the analysis PC 14 via the signal line 12, and the AE waveform is subjected to fast Fourier transform in the analysis PC 14.

The gas discharged from this measuring apparatus contains toxic CO gas, explosive H ₂ gas, and the like. The exhaust gas is sent to the exhaust gas treatment facility 18 through the gas discharge port 5. An appropriate exhaust gas treatment facility 18 can be installed according to the type and amount of gas generated.

This measuring device uses toxic CO gas or explosive H ₂ gas as the reducing gas. Appropriate measures are taken to prevent the reducing gas from leaking outside the measuring device as necessary. For example, an O-ring or the like can be attached to the joint portion of the reaction tube (reaction tube inner tube 2) and the reaction tube lid 10 or the like.

(Outline of the method for measuring reduced powder index of the present invention (in the case of sintered ore))
With reference to the flowchart of FIG. 3, a simple estimation method of the reduced powder index when the iron oxide raw material is sintered ore will be described.

In step S100, the rotational strength (TI _BR ) of the sample S to be measured is measured. A sample of iron oxide raw material weight to be measured: 500 g is put in a cylinder of a predetermined diameter called a drum test, and a total of 900 rotations are performed at 30 rpm for 30 minutes. The ratio (mass%) of what passed is measured, and the value becomes the rotational strength (TI _BR ).

In step S101, the total AE energy (E _total ) during reduction is measured. Specifically, the iron oxide raw material (sample S) to be measured is charged into the reduction furnace section (between a pair of gas rectifying perforated plates 3) of the reduced powder index measuring device and measured in an N ₂ atmosphere. The temperature is raised to a temperature, and the type of gas is switched to a reducing gas (in this case, the experimental conditions such as the charged amount of the iron oxide raw material (sample S), the measurement temperature, the reducing gas composition conform to JIS and ISO standards, Detailed description is omitted). The AE measuring unit of the reduced powder index measuring apparatus measures the AE wave generated from the iron oxide raw material (sample S) during the reduction, and is reducing the AE wave from the frequency spectrum obtained by fast Fourier transform using the analysis PC 14. The total AE energy (E _total ) is measured.

In step S102, to derive a sum of the measured AE energy _{(E total)} substitution were reduction degradation index variation by the following formula (1) (ΔRDI) at step S101. For example, the process of step S102 can be performed using the analysis PC 14.

ΔRDI = 2.59 × 10 ⁻⁸ E _total +7.26 (1)
The above formula (1) represents the correlation between the _total AE energy (E _total ) and the reduction powder index change (ΔRDI) when the iron oxide raw material is sintered ore. In the above formula (1), ΔRDI (mass%) is a reduction powdering index change amount, and E _total (eu) is a total of AE energy during reduction.

In step 103, the rotational strength (TI _BR ) measured in step S100 and the reduced powdering index change amount (ΔRDI) obtained in step S102 are substituted into the following formula (2) to derive the reduced powdering index (RDI). . For example, the process of step S103 can be performed using the analysis PC 14.

RDI = ΔRDI + TI _BR (2)

In the above formula (2), RDI (mass%) is the reduced powder index, TI _BR (mass%) is the rotational strength of the sample S before reduction, and ΔRDI (mass%) is the reduction powder index change amount. (Expressed as the difference between RDI and TI _BR ).

  Even if the measurement method of the reduction powdering index is a measurement method for the same blast furnace method such as ISO4696-1 and ISO4696-2, the reduction powdering index is different if the reduction temperature and the reducing gas composition are different. Although the reduction powdering behavior varies depending on the reduction temperature and reducing gas composition, the generated AE wave has a correlation with the reduction powdering behavior, so the measuring device of the present invention is applicable to any reduction powdering index measurement. it can.

Thus, according to the present invention, it is possible to simply and directly estimate the reduced powder index (RDI) from the _total AE energy (E _total ) of the iron oxide raw material.

(When iron oxide raw material is fired pellets)
With reference to the flowchart of FIG. 3, a simple estimation method of the reduced powder index when the iron oxide raw material is calcined pellets will be described. In step S100, similarly to the case of the sintered ore, the rotational strength (TI _BR ) of the sample S to be measured is measured. A sample of iron oxide raw material weight to be measured: 500 g is put in a cylinder of a predetermined diameter called a drum test, and a total of 900 rotations are performed at 30 rpm for 30 minutes. The ratio (mass%) of what passed is measured, and the value becomes the rotational strength (TI _BR ).

As in the case of the sintered ore, in step S101, the total AE energy (E _total ) during reduction is measured.

In step S102, to derive a sum of the measured AE energy _{(E total)} substitution were reduction degradation index variation by the following formula (3) (ΔRDI) at step S101. For example, the process of step S102 can be performed using the analysis PC 14.

ΔRDI = 6.28 × 10 ⁻⁹ E _total + 5.22 × 10 ⁻¹ (3)
The above formula (3) represents the correlation between the _total AE energy (E _total ) and the reduction powder index change amount (ΔRDI) when the iron oxide raw material is calcined pellets. In the above formula (3), ΔRDI (mass%) is a reduction powder amount change amount, and E _total (eu) is a total of AE energy during reduction.

In step 103, the rotational strength (TI _BR ) measured in step S100 and the reduced powdering index change amount (ΔRDI) obtained in step S102 are substituted into the following equation (4) to derive the reduced powdering index (RDI). .

RDI = ΔRDI + TI _BR (4)

In the above formula (4), RDI (mass%) is a reduction powder index, TI _BR (mass%) is the rotational strength of the sample S before reduction, and ΔRDI (mass%) is the amount of change in reduction powder. (Expressed as the difference between RDI and TI _BR ).

As for the correlation between the reduction powder amount change amount (ΔRDI) and the total AE energy (E _total ), the iron oxide raw materials for blast furnace other than the sintered ore and the calcined pellets also have an inherent correlation. Therefore, depending on the type of iron oxide raw material, there is a correlation between the reduced powdering index change amount (ΔRDI) corresponding to the above formulas (1) and (3) and the total AE energy during reduction (E _total ). By deriving in advance, the reduced powdering index (RDI) can be estimated by implementing the present invention in the same manner as in the case of the above-mentioned sintered ore and calcined pellets.

In the present embodiment, the above formula (1) and the above formula (3) are defined in order to derive the reduced powdering index change amount (ΔRDI), but the present invention is not limited to this. Specifically, a map in which the total AE energy (E _total ) and the reduced powdering index change amount (ΔRDI) are associated with each other can be determined in advance. By using this map, it is possible to specify the reduction powderization index change amount (ΔRDI) from the _total AE energy (E _total ).
(Example)

Using the following examples, a method of determining EQ1 (the above formula (1) and the above formula (3)), which is a correlation between the _total AE energy (E _total ) and the reduced powdered index change amount (ΔRDI), explain. Moreover, the validity of the reduced powder index (RDI) estimation method defined in the present invention is shown. In this example, two types of sintered ore and two types of fired pellets having different qualities were used. The average diameter of the sintered ore and fired pellets was 12.5 mm. Table 1 shows the quality of two types of sintered ore and two types of fired pellets. The test method for reduction powdering was in accordance with the reduction powdering test method of JIS. That is, the sample weight was 500 g, the reduction time was 30 min, the reducing gas flow rate was 15 NL / min, and the measurement was performed under five conditions with different reducing temperatures and reducing gas compositions. The reduced sample is subjected to rotary powdering in a cylinder having a predetermined diameter, followed by sieving, and the ratio of those passing through a 3.15 mm square net is measured to evaluate the reduced powdering index (RDI). Rotational strength TI _BR (mass%) before reduction and test conditions (reduction temperature (° C.) and reducing gas composition (%)), total AE energy during reduction (E _total ) (eu), reduced powdering Table 2 shows the index (RDI) and the reduction powder reduction index change (ΔRDI).

The squares (sintered ore) or rhombuses (fired pellets) filled with black in FIG. 4 are measured values of the reduction powder index change (ΔRDI). Based on this, linear regression (solid line in the figure) was performed by the method of least squares to determine the correlation of EQ1. The obtained regression equation (y = ΔRDI, x = E _total ) is also shown in FIG. The above formula (1) for deriving the reduced powdered index change amount (ΔRDI) of the sintered ore described in the embodiment and the above formula (3) for deriving the reduced powdered index change amount (ΔRDI) of the calcined pellet are The regression equation obtained in the example is shown as an example of the embodiment. FIG. 5 shows the relationship between the measured value of the reduced powder index (RDI) and the calculated value of the reduced powder index (RDI) measured by the measurement method of the present invention. Both were in good agreement, and it was found that the method equivalent to that of the prior art can be obtained by the method for measuring the reduced powder index of the present invention.

  As described above, according to the present invention, it is only necessary to determine the correlation (EQ1) for each type of iron oxide raw material, and it is not necessary to consider the reduction temperature, the composition of the reducing gas, and the like. It is possible to quickly measure (estimate) the reduced powder index of the iron raw material. Thereby, the measurement method can be simplified while speeding up the measurement of the reduced powdering index. Furthermore, as shown in the above-described embodiment, the calculated value of the reduced powder index (RDI) can be made to coincide with the actual measured value of the reduced powder index (RDI), thereby improving the accuracy of the calculated value of the reduced powder index. It can also be made. Therefore, the present invention has high applicability in the steel industry.

1: Outer tube, 2: Inner tube, 3: Perforated plate for gas rectification, 4: Gas inlet,
5: Gas outlet, 6: AE waveguide rod, 7: Thermocouple for measuring sample temperature, 8: Thermocouple for controlling furnace temperature,
9: Electric heating furnace body, 10: Reaction tube lid, 11: AE sensor, 12: Signal line,
13: AE measuring device, 14: PC for analysis

Claims (5)

A measuring apparatus that has a reduction furnace part, a gas supply part, and an AE measurement part, and measures the total AE energy from AE waves during reduction of the iron oxide raw material for iron making,
The reduction furnace section includes a reaction tube that contains the iron oxide raw material for iron making, and a heating furnace that encloses and heats the reaction tube,
The gas supply unit supplies a reducing gas containing at least one of CO and H _{2 to} the reaction tube,
The AE measuring unit includes an AE waveguide member that transmits an AE wave from the iron oxide raw material for iron making, and an AE measuring instrument that measures the transmitted AE wave. The reduction powder index change amount (ΔRDI = RDI−TI _BR ), which is the difference between the reduced powder index (RDI) and the rotational strength (TI _BR ), and the sum of the AE energy generated during the reduced powder (E _total ) and a correlation (EQ1) is determined, and the reduced powdered index is determined by the following procedures a) to c).
a) a first step of measuring the rotational strength (TI _BR ) of the iron oxide raw material for iron making,
b) a second step of measuring the total AE energy during the reduction of the iron oxide raw material for iron making using the measuring device according to claim 1;
c) Based on the correlation (EQ1), the reduced powdered index change amount (ΔRDI) is estimated from the sum of the AE energies measured in the second step, and the reduced powdered index change amount (Δ
RDI) and the rotational strength (TI _BR ) measured in the first step, the reduced powdering index (
RDI) is obtained by the following formula (I). Third step RDI = ΔRDI + TI _BR (I)   3. The method for measuring a reduced powder index according to claim 2, wherein the correlation (EQ1) is determined for each type of iron oxide raw material for iron making. When the said iron oxide raw material for iron manufacture is a sintered ore, the said correlation (EQ1) is represented by following formula (II), The measuring method of the reduced-powdering index | exponent of Claim 3 characterized by the above-mentioned.
ΔRDI = 2.59 × 10 ⁻⁸ E _total +7.26 (II) When the said iron oxide raw material for iron manufacture is a baking pellet, the said correlation (EQ1) is represented by following formula (III), The measuring method of the reduction | restoration powder index of Claim 3 characterized by the above-mentioned.
ΔRDI = 6.28 × 10 ⁻⁹ E _total + 5.22 × 10 ⁻¹ (III)

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