JP2019183261A - Device for determining condition of blast furnace, method for operating blast furnace and method for determining condition of blast furnace - Google Patents

Abstract

To provide: a device for determining conditions of a blast furnace, capable of appropriately determining deviation and disorder in raw material insertion and reaction in the circumferential direction of the blast furnace; a method for operating the blast furnace; and a method for determining the conditions of the blast furnace.SOLUTION: The device for determining conditions of a blast furnace comprises: temperature distribution measurement means for measuring temperature distribution right above a raw material insertion surface in the blast furnace; high temperature portion position detecting means for detecting a position of a high temperature portion having a temperature more than a predetermined temperature on the basis of information on the temperature distribution measured by the temperature distribution measurement means; and determining means for determining whether the conditions of the furnace are abnormal on the basis of the position of the high temperature portion detected by the high temperature portion position detecting means.SELECTED DRAWING: Figure 1

Description

  The present invention relates to a blast furnace state determination apparatus, a blast furnace operating method, and a blast furnace state determination method for determining a furnace state of a blast furnace.

  Conventionally, it has been known to monitor the in-furnace state of a blast furnace (hereinafter referred to as the furnace state), and to operate the blast furnace by changing to an appropriate operating condition (Patent Document 1, etc.). For this reason, it is important to quickly and accurately grasp abnormalities in the blast furnace state. Since the blast furnace is a cylindrical furnace, if the raw material is charged or the reaction is biased or disturbed in the circumferential direction of the blast furnace, the operating condition may deteriorate due to variations in the circumferential direction of the tapping state. is there. Therefore, early detection of raw material charging in the blast furnace circumferential direction and reaction bias and disturbance is one of the important abnormality detection targets.

  Conventionally, as a method of detecting material charging and reaction bias and disturbance in the blast furnace circumferential direction, a method of measuring the temperature distribution immediately above the raw material charging surface in the blast furnace is known. When there is a bias or disorder in the raw material charging or reaction, it appears as a bias or disorder in the temperature distribution just above the raw material charging surface.

JP 2005-272880 A

Arai, Yamamoto, Kajiya, Chemical Engineering Journal, 1989, Vol. 15, No. 6, p.1073-1075

  However, since the abnormality can be detected only from the temperature information at the measurement position directly above the raw material charging surface in the blast furnace, the operator can determine the raw material charging in the circumferential direction of the blast furnace and the determination of reaction bias and disturbance. If this is done, the determination criteria will be personal, and the determination results will vary, and there is a risk that appropriate determination will not be possible at all times.

  The present invention has been made in view of the above-mentioned problems, and the purpose thereof is a blast furnace state determination apparatus, a blast furnace, which can appropriately determine raw material charging and reaction bias and disturbance in the blast furnace circumferential direction. It is to provide an operation method and a blast furnace state condition determination method.

  In order to solve the above-described problems and achieve the object, a blast furnace state determination apparatus according to the present invention is a blast furnace state determination apparatus for determining a furnace state of a blast furnace, in which raw material charging in the blast furnace is performed. A temperature distribution measuring means for measuring a temperature distribution immediately above the surface, and a high temperature part position detecting means for detecting a position of a high temperature part exceeding a predetermined temperature based on the information of the temperature distribution measured by the temperature distribution measuring means; And determining means for determining whether or not the furnace state is abnormal based on the position of the high temperature portion detected by the high temperature portion position detecting means.

  Further, in the blast furnace state condition determining apparatus according to the present invention, in the above invention, the temperature distribution measuring means transmits sound waves from one sound wave transmitting / receiving means among a plurality of sound wave transmitting / receiving means provided at the top of the blast furnace furnace. The sound wave transmission time in each sound wave propagation path from the time when the sound wave is received by the different sound wave transmission / reception means until the sound wave transmission / reception means receives each sound wave is measured by all the sound wave transmission / reception means. And the temperature distribution at the top of the blast furnace is measured based on the sound wave propagation time.

  Moreover, the operating method of the blast furnace which concerns on this invention changes an operating condition according to the furnace state state of the blast furnace determined by the blast furnace state state determination apparatus of said invention.

  Further, the blast furnace state state determining method according to the present invention is a blast furnace state state determining method for determining a furnace state state of the blast furnace, and a temperature distribution measuring step for measuring a temperature distribution immediately above the raw material charging surface in the blast furnace. And a high temperature part position detecting step for detecting a position of a high temperature part exceeding a predetermined temperature based on the information of the temperature distribution measured in the temperature distribution measuring step, and the high temperature detected in the high temperature part position detecting step. A furnace condition abnormality determining step for determining whether or not the furnace condition is abnormal based on the position of the section.

  In the blast furnace state state determination method according to the present invention, in the above invention, in the temperature distribution measurement step, a sound wave is transmitted from one sound wave transmitting / receiving means among a plurality of sound wave transmitting / receiving means provided at the top of the blast furnace furnace. The sound wave transmission time in each sound wave propagation path from the time when the sound wave is received by the different sound wave transmission / reception means until the sound wave transmission / reception means receives each sound wave is measured by all the sound wave transmission / reception means. And the temperature distribution at the top of the blast furnace is measured based on the sound wave propagation time.

  In the blast furnace state determination method according to the present invention, in the above invention, the charge in which the position of the high-temperature part is detected is continued a plurality of times, with the repetition unit in which the raw material is charged into the blast furnace as one charge. In this case, it is determined that the furnace state is abnormal.

  The blast furnace operation method according to the present invention is a blast furnace operation method using the blast furnace state determination method according to the present invention, wherein the blast furnace state is within a predetermined time from the time when the operation specifications are changed. When the state of the furnace is determined to be abnormal by the state determination method, the operation specifications before the change time of the operation specifications are returned to the operation specifications.

  Moreover, the operating method of the blast furnace which concerns on this invention is the above-mentioned invention. WHEREIN: The said operation item is a charge distribution, It is characterized by the above-mentioned.

  The blast furnace state determination apparatus, the blast furnace operation method, and the blast furnace state determination method according to the present invention have the effect that it is possible to appropriately determine raw material charging and reaction bias and disturbance in the blast furnace circumferential direction. Play.

FIG. 1 is a diagram illustrating a schematic configuration of a blast furnace state state determining apparatus according to an embodiment. FIG. 2 is a flowchart showing an example of a blast furnace state state determination method according to the embodiment. FIG. 3 is a diagram showing a case where ten microphone / speaker elements are installed along the circumferential direction toward the inside of the blast furnace top as a temperature distribution measuring apparatus using sound waves. FIG. 4 is a diagram used for explaining how to obtain the temperature based on the sound velocity distribution. FIG. 5 is a diagram illustrating a range in which the temperature measurement data is used in the embodiment. FIG. 6 is a diagram in which the blast furnace top is divided into a plurality of regions. FIG. 7 is a graph showing the relationship between the number of regions where the average temperature exceeds the temperature threshold in the second region and the third region and the ventilation resistance index with the same charge. FIG. 8 is a graph showing a change in the number of regions in which the average temperature of the second region and the third region after the charge distribution is changed exceeds the temperature threshold.

  Hereinafter, an embodiment of a blast furnace state determination apparatus, a blast furnace operation method, and a blast furnace state determination method for determining a furnace state of a blast furnace to which the present invention is applied will be described. In addition, this invention is not limited by this embodiment.

  FIG. 1 is a diagram showing a schematic configuration of a blast furnace state state determination apparatus 1 according to the embodiment. As shown in FIG. 1, the blast furnace state state determination device 1 according to the embodiment includes a temperature distribution measurement sensor 2, a data collection device 3, a high temperature part position detection device 4, a determination device 5, and a notification device 6. It is constituted by.

  The temperature distribution measuring sensor 2 is a temperature distribution in a space immediately above a raw material charging surface which is the uppermost surface of a layer made of raw material charged from the top of the blast furnace inside a blast furnace that produces pig iron using iron ore as a raw material. (Here, for example, it is a gas temperature distribution, and hereinafter, simply referred to as a temperature distribution immediately above the raw material charging surface) is measured. The temperature distribution measuring sensor 2 may be a thermocouple so that the temperature at a plurality of positions can be measured in the furnace radial direction embedded in a sonde installed at the top of the furnace, but in order to obtain a more detailed temperature distribution, It is preferable to use a temperature distribution measuring device (temperature distribution measuring device using acoustic tomography).

  The data collection device 3 collects and accumulates temperature distribution data (temperature distribution information) that is a measurement value from the temperature distribution measurement sensor 2.

  If the time until the temperature distribution measurement over the entire area immediately above the raw material charging surface is completed by the temperature distribution measuring sensor 2 is too late with respect to the raw material charging timing interval in the blast furnace, the measured temperature distribution There is a possibility that there is a high possibility that the abnormality determination is biased or disturbed. Therefore, the temperature distribution measurement sensor 2 completes the measurement of the temperature distribution over the entire region immediately above the raw material charging surface within 30 [s], and the data distribution device collects the real-time temperature distribution data from the temperature distribution measurement sensor 2. Collect and accumulate in step 3.

  Based on the temperature distribution data accumulated in the data collection device 3, the high temperature part position detection device 4 determines the position at which a temperature equal to or higher than a preset temperature threshold appears immediately above the raw material charging surface in the blast furnace, that is, the position of the high temperature part. To detect. For example, the high temperature part position detection device 4 can calculate the average temperature in the region by mapping the temperature distribution data accumulated in the data collection device 3 to the coordinate system set at the top of the furnace. . Moreover, what is necessary is just to implement | achieve as a high temperature part position detection apparatus 4 as a computer program. In the high temperature portion position detection device 7, the position of the high temperature portion is not directly from the temperature distribution data accumulated in the data collection device 3 but directly from the temperature distribution data (temperature distribution information) measured by the temperature distribution measurement sensor 2. May be detected.

  The determination device 5 determines the furnace state based on the position of the high temperature portion detected by the high temperature portion position detection device 4, and the case where the average temperature in the designated area at the top of the furnace is higher than a certain period. Judged as abnormal furnace conditions.

  The notification device 6 presents the determination result of the determination device 5 to the operator by an alarm or the like. An operator who knows that an alarm from the notification device 6 has caused an abnormal furnace condition, that is, raw material charging in the blast furnace circumferential direction or reaction bias or disturbance has occurred, for example, how to load the raw material in the blast furnace circumferential direction. Change the operating conditions of the blast furnace to suppress raw material charging and reaction bias and disturbance in the blast furnace circumferential direction, such as by changing the charge control pattern that has been set in advance. .

  In addition, raw material charging is performed by alternately charging different raw materials, and the repeating unit is referred to as one charge.

  Here, in the blast furnace, when the raw material falls into the furnace, the quality of the furnace condition greatly depends on the distribution state of the charged raw material. Therefore, in order to accurately control the distribution of the inserted raw material (charge distribution), depending on the raw material type and raw material particle size, etc., the tilt angle of the turning chute in the furnace, the number of turns and the direction of charging (in the radial direction) From inside to outside or from outside to inside in the radial direction) is determined in advance and charged. However, since the raw materials vary in particle size and shape, even if the raw material is charged to the target location with the target distribution, a part of the raw material may collapse and the distribution may be disturbed (flow of the raw material). In particular, in order to create a distribution in a portion slightly inside the outer periphery of the blast furnace, complicated charging may be performed. In such a case, the present inventors have discovered that the raw material may collapse inside the furnace, and the high-temperature gas rises from the portion where the raw material remains broken. It was also found that if this situation continues, the furnace condition deteriorates. Such a phenomenon often occurs in the middle part in the radial direction in the furnace, and monitoring the appearance of the high temperature part at such a position is effective for determining the furnace condition abnormality.

  Next, a blast furnace state state determination method according to the embodiment will be described. FIG. 2 is a flowchart showing an example of a blast furnace state state determination method according to the embodiment. The blast furnace state determination method according to the embodiment shown in FIG. 2 includes a temperature distribution measurement step (step S1), a temperature distribution data accumulation step (step S2), a high temperature part position detection step (step S3), a furnace A situation abnormality determination step (step S4).

  In the blast furnace state condition determination method according to the embodiment shown in FIG. 2, first, in the blast furnace that produces pig iron using iron ore as a raw material, the heat from the tuyeres at the lower part of the furnace is blown into the furnace. A temperature distribution immediately above the raw material charging surface of hot air blown up through the exchange is measured (step S1). Next, the temperature distribution data obtained in the temperature distribution measurement step (step S1) is accumulated (step S2). Next, the position of the high temperature part is detected based on the temperature distribution data (temperature distribution information) accumulated in the temperature distribution data accumulation step (step S2) (step S3). Then, it is determined whether the furnace state is abnormal based on the position of the high temperature part detected in the high temperature part position detection step (step S3) (step S4).

  In the operation of the blast furnace, mainly when there is a misrecognition of the raw material properties (particle size distribution, components, etc.), or an error occurs in the weighing machine such as a charging bunker at the top of the furnace, and the result of rolling the raw material with a tilting chute When there is a deviation in the furnace diameter direction, the charge distribution, which is one of the operation specifications, is not performed as designed, and the furnace condition may be deteriorated. It is known that the raw material charged in the blast furnace is discharged out of the furnace as molten iron in about 8 hours.

  Normally, when the raw material falls from the middle to the lower part of the shaft part of the furnace body, and the raw material falls to the height at which melting starts (to reach the cohesive zone), it is thought that the furnace condition will be affected. . This is presumably because the assumed gas flow is disturbed by an unexpected charge distribution and the shape of the cohesive zone is deformed. It is known that it takes about 8 hours for the charged raw material to be discharged from the blast furnace as molten iron, but the shaft is roughly at a position intermediate from the charging surface, and is generally in the radial direction of the blast furnace. In the outermost part, it is considered that the cohesive zone is located near the lower part of the shaft portion, and the cohesive zone is located at the upper side as it proceeds inward in the radial direction of the blast furnace. And in the core part which is the center of the diameter direction of a blast furnace, it is thought that the cohesive zone has reached the upper part of the shaft. Therefore, after the charge distribution is changed, the furnace state starts to be affected after 2 to 4 hours when the raw material descends to the vicinity of the cohesive zone. That is, when the changed charge distribution is not appropriate, the gas blown into the furnace from the tuyere rises to the furnace top without sufficiently exchanging heat with the raw material. Therefore, it can be seen that when the high temperature portion appears in the temperature distribution at the top of the furnace after 2 to 4 hours after the charge distribution change, the charge distribution is not appropriate. If abnormalities appear in such furnace conditions, it may be possible to avoid abnormalities in furnace conditions by performing an operation to return to the charge distribution before the charge distribution change time. It is done.

  If the charge distribution is not appropriate, the shaft pressure often becomes abnormal. On the other hand, if there is an improper part of the charge distribution in the middle part of the blast furnace in the radial direction, the gas flow in the part near the core will be disturbed, so the shaft pressure gauge installed on the surface of the furnace body Influence is hard to appear. Therefore, the present invention is effective particularly for a reactor state abnormality in which a high temperature portion appears at a position close to the core portion.

[Example]
Next, an embodiment of the present invention using temperature distribution measurement data immediately above the actual raw material charging surface will be described. In the present embodiment, a temperature distribution measuring device (a temperature distribution measuring device using acoustic tomography) using sound waves is used as the temperature distribution measuring sensor 2 for measuring the temperature distribution immediately above the raw material charging surface.

  FIG. 3 is a diagram showing a case where ten microphone / speaker elements 20a to 20j are installed along the circumferential direction toward the inside of the blast furnace top 10 as a temperature distribution measuring apparatus using sound waves. In the embodiment, as shown in FIG. 3, 10 microphone / speaker elements 20 a to 20 j (microphone / speaker elements 20 a to 20 j) that serve as microphones and speakers serving as sound wave transmitting and receiving means are directed toward the inside of the blast furnace top 10. Are not specifically distinguished, they are referred to as microphone / speaker elements 20) along the circumferential direction. Then, a sound wave is transmitted from one of the microphone / speaker elements 20a to 20j, for example, a speaker of the microphone / speaker element 20a, and the sound wave is received by each of the remaining microphones / speaker elements 20b to 20j. The sound wave propagation time in each sound wave propagation path of the sound wave from when the sound wave is transmitted until it is received by each microphone is measured. Then, sound waves are sequentially transmitted from the speakers of all the microphone / speaker elements 20a to 20j, the sound wave propagation times are measured for all the microphone / speaker elements 20a to 20j as described above, and based on the measured sound wave propagation times. Then, measure the temperature distribution just above the raw material charging surface.

  Here, the sound wave emitted from the speaker of the microphone / speaker element 20 propagates through the space in the blast furnace top 10, and the speed of sound is expressed by the following equation (1) between the temperature of the gas serving as a medium. There is a relationship.

  In the above equation (1), T is the average temperature on the sound wave propagation path, C is the speed of sound, R is the gas constant, γ is the specific heat ratio, and M is the molecular weight of the gas.

  Note that the speed of sound C in the above equation (1) is such that the distance from the speaker of the microphone / speaker element 20 that transmitted the sound wave to each microphone of the remaining microphone / speaker element 20 is known, so the sound wave is transmitted from the speaker. Then, it can be obtained by measuring the time until the sound wave is received by the microphone. Accordingly, the average temperature on the sound wave propagation path from the speaker of the microphone / speaker element 20 that has transmitted the sound wave to each microphone of the remaining microphone / speaker element 20 is calculated from the relationship shown in the above formula (1). Can do.

  Next, how to obtain the temperature will be described. The temperature distribution is calculated based on the sound speed distribution, for example, by the following method.

  As shown in FIG. 4, a pair of a microphone and a speaker of a pair of microphone / speaker elements 20 whose sound wave propagation paths are parallel to each other is considered. A sound wave signal is transmitted and received from the speaker in the s-axis direction perpendicular to the r-axis. Further, if the angle formed by the x axis of the xy axis set at the blast furnace top 10 (the origin coincides with the core) and the r axis is θ, the polar coordinate of a certain point of the blast furnace top 10 is (R, θ). Can be represented. If the sound velocity distribution is f (x, y), the projection data g (r, θ) acquired by the speaker is a sound wave propagation time distribution and is expressed by the following equation (2).

  Here, in the above equation (2), the following equation (3) can be expressed as the following equation (4).

  The above equation (4) has the same form as X-ray CT, and the sound speed distribution can be reconstructed by the CT algorithm.

  The accuracy is improved by calculating θ (g, r) by changing θ for another pair of the speaker / microphone of the pair of microphone / speaker elements 20 whose sound wave propagation paths are parallel to each other. As a specific method, for example, a two-dimensional Fourier transform method described in Non-Patent Document 1 can be applied.

  FIG. 5 is a diagram illustrating a range in which the temperature measurement data is used in the embodiment. As shown in FIG. 5, by detecting the position of the high temperature portion with respect to the temperature distribution data in the region inside the outer peripheral side in the radial direction of the blast furnace top 10, the flow of the charge distribution is detected, and the furnace It is possible to grasp the situation. The state in which the raw material is fluidized is a range in the radial direction of the blast furnace top 10 from the center O to a distance of 3/4 of the radius r and from the center O to a distance of 1/4 of the radius r. This is conspicuous in the intermediate portion MA indicated by hatching in the figure. And this inventor discovered that when a high temperature part appeared in the intermediate part MA, a furnace condition will become unstable in many cases.

  Therefore, in this embodiment, as shown in FIG. 6, the blast furnace top 10 is divided into four equal parts in the radial direction, and the first region, the second region, the third region, and the fourth region are formed in order from the inside. Further, the blast furnace top 10 was divided into eight equal parts in the circumferential direction, and the A region, B region, C region, D region, E region, F region, G region, and H region were sequentially arranged in the clockwise direction in the figure. And the area | region divided into the radial direction and the circumferential direction of the blast furnace top part 10 in this way is area | region 1-A, area | region 1-B, ..., area | region 2-A, ..., respectively. .., Region 4-A,..., Region 4-A,.

  In the present embodiment, the second region and the third region which are regions corresponding to the middle portion MA of the blast furnace top 10 in particular, that is, the region 2-A, ..., the region 2-H, the region 3-A, ... When focusing on region 3-H and the furnace condition is considered to be unstable, it is detected whether a high-temperature part having an average temperature of 300 [° C.] or more, which is the temperature threshold, has appeared in these focused regions did. In this example, the furnace condition abnormality was determined when a high temperature portion appeared in three consecutive charges in the same region, or when a high temperature portion appeared in six or more regions with the same charge.

  FIG. 7 is a graph showing the relationship between the number of regions where the average temperature exceeds the temperature threshold in the second region and the third region and the ventilation resistance index with the same charge. In the blast furnace of this example, it is considered that the furnace condition is unstable when the ventilation resistance index representing the furnace condition of the blast furnace exceeds 1.1. Therefore, in this embodiment, as shown in FIG. 3, the number of regions in which the average temperature exceeds the temperature threshold in the second region and the third region with the same charge, in other words, the second region and the third region with the same charge. It can be seen that when the number of regions where the high temperature portion appears in the region is 6 regions or more exceeding the ventilation resistance index of 1.1, the furnace condition may be regarded as abnormal.

  As another blast furnace state determination method, counting the number of times that exceeds a predetermined average temperature during one charge (the number of times a high temperature portion has appeared during one charge) is also considered to be an effective determination method. .

  FIG. 8 is a graph showing a change in the number of regions in which the average temperature of the second region and the third region after the charge distribution is changed exceeds the temperature threshold. As shown in FIG. 8, the number of regions where the average temperature of the second region and the third region exceeded the temperature threshold gradually increased from about 2 hours after the charge distribution change. And, as shown in FIG. 8, since the number of regions exceeded 6 after 4 hours after the charge distribution change, when the charge distribution was returned to the original, the area gradually increased from 6 hours. The number of areas decreased.

DESCRIPTION OF SYMBOLS 1 Blast furnace state state determination apparatus 2 Temperature distribution measurement sensor 3 Data collection apparatus 4 High temperature part position detection apparatus 5 Determination apparatus 6 Notification apparatus 10 Blast furnace top 20 Microphone / speaker element

Claims (8)

A blast furnace state determination device for determining the state of a blast furnace,
Temperature distribution measuring means for measuring the temperature distribution immediately above the raw material charging surface in the blast furnace;
Based on the temperature distribution information measured by the temperature distribution measuring means, a high temperature part position detecting means for detecting a position of a high temperature part exceeding a predetermined temperature;
Determination means for determining whether or not the furnace state is abnormal based on the position of the high temperature part detected by the high temperature part position detection means;
A blast furnace state determination device characterized by comprising: In the blast furnace state determination apparatus according to claim 1,
The temperature distribution measuring means transmits sound waves from one sound wave transmitting / receiving means among a plurality of sound wave transmitting / receiving means provided at the top of the blast furnace furnace, receives the sound waves by different sound wave transmitting / receiving means, and transmits the sound waves. Measurement of the sound wave propagation time in each sound wave propagation path from the time point until reception by each sound wave transmission / reception means is carried out by all sound wave transmission / reception means, and the temperature distribution at the top of the blast furnace is measured based on the sound wave propagation time. A blast furnace state determination apparatus characterized by:   A method for operating a blast furnace, wherein the operating conditions are changed according to the furnace state of the blast furnace determined by the blast furnace state determining apparatus according to claim 1. A blast furnace state determination method for determining a blast furnace state,
A temperature distribution measuring step for measuring the temperature distribution immediately above the raw material charging surface in the blast furnace;
Based on the temperature distribution information measured in the temperature distribution measurement step, a high temperature part position detection step for detecting a position of a high temperature part exceeding a predetermined temperature;
A furnace condition abnormality determining step for determining whether the furnace condition state is abnormal based on the position of the high temperature part detected in the high temperature part position detecting step;
A method for determining the state of a blast furnace state, comprising: In the blast furnace state determination method according to claim 4,
In the temperature distribution measuring step, a sound wave is transmitted from one sound wave transmitting / receiving means among a plurality of sound wave transmitting / receiving means provided at the top of the blast furnace, and the sound waves are received by different sound wave transmitting / receiving means, and the sound waves are transmitted. Measurement of the sound wave propagation time in each sound wave propagation path from the time point until reception by each sound wave transmission / reception means is carried out by all sound wave transmission / reception means, and the temperature distribution at the top of the blast furnace is measured based on the sound wave propagation time. A method for determining a state of a blast furnace state characterized by: In the blast furnace state determination method according to claim 4 or 5,
The repeating unit in which the raw material is charged into the blast furnace is defined as one charge, and when the charge in which the position of the high temperature portion is detected continues several times, it is determined that the furnace state is abnormal. Blast furnace state condition judgment method. A blast furnace operating method using the blast furnace state condition determining method according to any one of claims 4 to 6,
If the furnace state is determined to be abnormal by the blast furnace state determination method within a predetermined time from the time when the operation item is changed, the operation items before the change of the operation item are determined. Blast furnace operation method characterized by returning to the original. In the operating method of the blast furnace of Claim 7,
The operating method of a blast furnace, wherein the operating specifications are a distribution of charges.

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