Appliance for the adjustment of the stoichiometric combustion ratio in burners of an industrial combustion plant

Abstract

The appliance for the adjustment of the stoichiometric combustion ratio in burners of an industrial combustion plant, comprising a first supply line of a combustible fluid connected a burner, and a second supply line of a comburent fluid connected the burner, wherein the appliance comprises: a first pressure sensor operationally connected to the first supply line and configured to measure in real time the pressure of the combustible fluid delivered through the first supply line; a second pressure sensor operationally connected to the second supply line and configured to measure in real time the pressure of the comburent fluid; a control valve of the comburent fluid configured to regulate the flow of the comburent fluid; a regulating unit of the stoichiometric combustion ratio configured to command in real time the control valve to vary the flow of the comburent fluid depending on the measured pressure of the comburent fluid and on the measured pressure of the combustible fluid, to keep the stoichiometric combustion ratio between the comburent fluid and the combustible fluid constant and equal to a predefined value.

Description

[0001] APPLIANCE FOR THE ADJUSTMENT OF THE STOICHIOMETRIC COMBUSTION RATIO IN BURNERS OF AN INDUSTRIAL COMBUSTION PLANT

[0002] Technical Field

[0003] The present invention relates to an appliance for the adjustment of the stoichiometric combustion ratio in burners of an industrial combustion plant.

[0004] Background Art

[0005] The use is well known of industrial gas combustion plants provided with a plurality of burners, generally grouped in zones, wherein the supply of combustion gas (combustible fluid) is adjusted by means of special valves.

[0006] Generally, such valves are controlled by a control system of the plant and they adjust the gas flow rate depending on predefined and programmed values.

[0007] However, in order to reduce the costs of the plant, such valves are usually connected to a group of burners, making the control of the firing process ineffective or otherwise inaccurate in many cases.

[0008] Alternatively, in order to overcome this drawback, the use is known of control systems capable of adjusting the gas flow rate for valves dedicated to individual burners.

[0009] However, such systems are very complex and expensive because the plant control system (usually consisting of a PLC) must be connected to multiple electronic control boards for the individual valves.

[0010] In addition, for both systems described above, the flow rate of the combustion air (comburent fluid) is preset and programmed and does not take into account any real-time changes in the comburent / combustible fluid (air / gas) ratio due to changes in the amount of combustible fluid (gas) delivered to the burners and to any change in the density of the comburent fluid due to changes in the temperature thereof during the process.

[0011] This necessarily results in suboptimal management of the firing process. Description of the Invention

[0012] The main aim of the present invention is to devise an appliance for the adjustment of the stoichiometric combustion ratio in burners of an industrial combustion plant, which allows the adjustment of the stoichiometric combustion ratio regulating the inflow of a comburent fluid (air) to one or more burners of an industrial combustion plant, while keeping the selected comburent / combustible fluid (air / gas) ratio constant as the amount of combustible fluid (gas) delivered to the burners changes and as the density of the comburent fluid changes, if any, due to the change in the temperature thereof during the process.

[0013] Another object of the present invention is to devise an appliance for the adjustment of the stoichiometric combustion ratio in burners of an industrial combustion plant which allows the aforementioned drawbacks of the prior art to be overcome within the framework of a simple, rational, easy and effective to use as well as inexpensive solution.

[0014] The aforementioned objects are achieved by this appliance for the adjustment of the stoichiometric combustion ratio in burners of an industrial combustion plant, according to claim 1.

[0015] Brief Description of the Drawings

[0016] Other characteristics and advantages of the present invention will become more apparent from the description of four preferred, but not exclusive embodiments of an appliance for the adjustment of the stoichiometric combustion ratio in burners of an industrial combustion plant, illustrated by way of an indicative, yet non-limiting example, in the accompanying tables of drawings in which:

[0017] Figure 1 schematically shows a first possible embodiment of the appliance according to the invention;

[0018] Figure 2 schematically shows a second possible embodiment of the appliance according to the invention;

[0019] Figure 3 schematically shows a third possible embodiment of the appliance according to the invention;

[0020] Figure 4 schematically shows a fourth possible embodiment of the appliance according to the invention;

[0021] Figure 5 schematically shows a fifth possible embodiment of the appliance according to the invention;

[0022] Figure 6 schematically shows a sixth possible embodiment of the appliance according to the invention.

[0023] Embodiments of the Invention

[0024] With particular reference to these figures, reference numeral 1 globally denotes an appliance for the adjustment of the stoichiometric combustion ratio in burners of an industrial combustion plant.

[0025] Specifically, the appliance 1 according to the invention allows for the adjustment of the stoichiometric combustion ratio which adjusts the inflow of a comburent fluid (air), to one or more burners of an industrial combustion plant, thus keeping the selected comburent / combustible fluid (air / gas) ratio constant as the amount of the combustible fluid (gas) delivered to the burners changes.

[0026] The appliance 1 can be used on a combustion system comprising at least a first supply line 2 of a combustible fluid (gas) connected to at least one burner, and at least a second supply line 3 of a comburent fluid (air) connected to the burner. The appliance 1 comprises: at least one first pressure sensor 4 operationally connected to the first supply line 2 and configured to measure in real time the pressure of the combustible fluid delivered through the first supply line 2; at least a second pressure sensor 5 operationally connected to the second supply line 3 and configured to measure in real time the pressure of the comburent fluid delivered through the second supply line 3; at least one control valve 6 of the comburent fluid operationally connected to the second supply line 3 and configured to regulate the flow of the comburent fluid within the second supply line 3.

[0027] In addition, the appliance 1 comprises at least one regulating unit 7 of the stoichiometric combustion ratio, operationally connected to the first pressure sensor 4, to the second pressure sensor 5 and to the control valve 6.

[0028] The regulating unit 7 is configured to command in real time the control valve 6 to vary the flow of the comburent fluid depending on the measured pressure of the comburent fluid and on the measured pressure of the combustible fluid to keep the stoichiometric combustion ratio between the comburent fluid and the combustible fluid constant and equal to a predefined value.

[0029] This adjustment allows automatic compensation for the density change in relation to the temperature of the comburent fluid and of the combustible fluid while keeping the set stoichiometric combustion ratio constant, effectively performing a self-adaptive adjustment of the flow of the comburent fluid.

[0030] The appliance 1 according to the invention can be used both considering the pressures and flow rates of the two fluids (and / or fluid mixtures) delivered to the burners.

[0031] Preferably, the pressure and / or flow rate of the combustible fluid occurs by means of sensors 4, external to the appliance, certified for the fluid to be measured.

[0032] The pressure and / or flow rate of the comburent fluid occurs by means of sensors 5, internal to the appliance, certified for the fluid to be measured.

[0033] According to a first possible embodiment, shown in Figure 1, the appliance 1 performs real-time adjustment of the stoichiometric combustion ratio only depending on the pressures of the comburent fluid and combustible fluid.

[0034] Specifically, according to this first embodiment, the appliance 1 comprises: a first pressure sensor 4 operationally connected to the first supply line 2 and configured to measure the pressure of the combustible fluid in real time; a second pressure sensor 5 operationally connected to the second supply line 3 and configured to measure the pressure of the comburent fluid in real time. According to this first embodiment, the regulating unit 7 is operationally connected to the first pressure sensor 4, to the second pressure sensor 5 and to the control valve 6, and is configured to command the control valve 6 in real time to vary the flow of comburent fluid depending on the measured pressure of the comburent fluid and on the measured pressure of the combustible fluid to keep the stoichiometric combustion ratio between the comburent fluid and the combustible fluid constant and equal to a predefined value.

[0035] With reference to a second possible embodiment, shown in Figure 2, the appliance 1 performs the stoichiometric combustion ratio adjustment depending on the pressure of the combustible fluid and on the flow rate of the comburent fluid, compensated with the operating temperature of the comburent fluid.

[0036] Specifically, with reference to this second embodiment, the appliance 1 comprises: a first pressure sensor 4 operationally connected to the first supply line 2 and configured to measure the pressure of the combustible fluid in real time; a pair of second pressure sensors 5 operationally connected to respective stretches of the second supply line 3 and configured to measure a differential pressure of the comburent fluid in real time; a temperature sensor 8 operationally connected to the second supply line 3 and configured to measure the temperature of the comburent fluid.

[0037] With reference to this second embodiment, the regulating unit 7 is operationally connected to the first pressure sensor 4, to the pair of second pressure sensors 5, to the temperature sensor 8 and to the control valve 6, and is configured to command the control valve 6 in real time to vary the flow of the comburent fluid depending on the measured differential pressure and temperature of the comburent fluid and on the measured pressure of the combustible fluid, to keep the stoichiometric combustion ratio between the comburent fluid and the combustible fluid constant and equal to a predefined value. Specifically, in such a case, the regulating unit 7 is configured to command the control valve 6 in real time to vary the flow of the comburent fluid depending on the measured pressure of the combustible fluid and on the flow rate of the comburent fluid, determined from the measured differential pressure and temperature.

[0038] Preferably, with reference to the second embodiment, the appliance 1 comprises at least one calibrated flange 9 arranged between the respective stretches of the second supply line 3 operationally connected to the pair of second pressure sensors 5.

[0039] Specifically, the flow rate of the comburent fluid QA across the calibrated flange 9 depending on the temperature and on the pressure differential is calculated according to the following formula: wherein:

[0040] C is the discharge coefficient of the calibrated flange 9;

[0041] A is the cross-sectional area of the flange (m2),

[0042] AP is the pressure differential across the flange (Pa), p is the density of air (kg / m3).

[0043] Specifically, the air density p varies with temperature and can be calculated using the following formula (law of ideal gases): p = p x ( / ? x T) wherein:

[0044] P is the absolute air pressure (Pa),

[0045] R is the specific air constant (R ~ 287.05 J / (kg x K)),

[0046] T is the absolute temperature in Kelvin (K).

[0047] With reference to a third and a fourth possible embodiments, shown in Figures 3 and 4, the appliance 1 performs the adjustment of the stoichiometric combustion ratio depending on the flow rate of the combustible fluid, compensated with the operating temperature of the combustible fluid, and of the pressure of the comburent fluid.

[0048] Specifically, with reference to this third and fourth embodiments, the appliance 1 comprises: a pair of first pressure sensors 4 operationally connected to respective stretches of the first supply line 2 and configured to measure the differential pressure of the combustible fluid in real time; a second pressure sensor 5 operationally connected to the second supply line 3 and configured to measure the pressure of the comburent fluid in real time; a temperature sensor 10 operationally connected to the first supply line and configured to measure the temperature of the combustible fluid.

[0049] Specifically, according to the third embodiment, schematically shown in Figure

[0050] 3, the pair of first pressure sensors 4 is built within a differential pressure transducer.

[0051] In a different but functionally similar way, there are two separate pressure sensors

[0052] 4, 5 in the fourth embodiment in Figure 4.

[0053] According to such third and fourth embodiments, the regulating unit 7 is operationally connected to the pair of first pressure sensor 4, to the second pressure sensor 5, to the temperature sensor 10 and to the control valve 6, and is configured to command the control valve 6 in real time so as to vary the flow of the comburent fluid depending on the measured pressure of the comburent fluid and on the measured differential pressure and temperature of the combustible fluid, to keep the stoichiometric combustion ratio between the comburent fluid and the combustible fluid constant and equal to a predefined value.

[0054] Specifically, the regulating unit 7 is configured to command the control valve 6 in real time to vary the flow of the comburent fluid depending on the measured pressure of the comburent fluid and on the flow rate of the combustible fluid determined from the measured differential pressure and temperature.

[0055] Preferably, the appliance 1 comprises at least one calibrated flange 11 arranged between the respective stretches of the first supply line 2 operationally connected to the pair of first pressure sensors 4.

[0056] Specifically, the flow rate of the combustible fluid QG across the calibrated flange 11 depending on the temperature and on the pressure differential is calculated according to the following formula: wherein:

[0057] C is the discharge coefficient of the calibrated flange 11;

[0058] A is the cross-sectional area of the flange (m2),

[0059] AP is the pressure differential across the flange (Pa), p is the density of the gas (kg / m3).

[0060] Specifically, the air density p varies with temperature and can be calculated using the following formula (law of ideal gases): p = p x (R X T) wherein:

[0061] P is the absolute gas pressure (Pa),

[0062] R is the specific gas constant,

[0063] T is the absolute temperature in Kelvin (K).

[0064] In addition, with reference to a fifth and sixth possible embodiments, shown in Figures 5 and 6, the appliance 1 performs the adjustment of the combustion stoichiometric ratio depending on the flow rate of the combustible fluid and on the flow rate of the comburent fluid, both of which being compensated with the operating temperatures of the combustible fluid and of the comburent fluid. Specifically, with reference to this fourth and fifth embodiments, the appliance 1 comprises: a pair of first pressure sensors 4 operationally connected to respective stretches of the first supply line 2 and configured to measure the differential pressure of the combustible fluid in real time; a pair of second pressure sensors 5 operationally connected to respective stretches of the second supply line 3 and configured to measure the differential pressure of the comburent fluid in real time; a first temperature sensor 10 operationally connected to the first supply line 2 and configured to measure the temperature of the combustible fluid; a second temperature sensor 8 operationally connected to the second supply line 3 and configured to measure the temperature of the comburent fluid.

[0065] Specifically, according to the fifth embodiment, schematically shown in Figure 5, the pair of first pressure sensors 4 is built within a differential pressure transducer.

[0066] In a different but functionally similar way, there are two separate pressure sensors 4, 5 in the sixth embodiment in Figure 6.

[0067] With reference to this fourth possible embodiment, the regulating unit 7 is operationally connected to the pair of first pressure sensors 4, to the pair of second pressure sensors 5, to the first temperature sensor 10, to the second temperature sensor 8 and to the control valve 6.

[0068] The regulating unit 7 is configured to command the control valve 6 in real time so as to vary the flow of the comburent fluid depending on the measured differential pressure and temperature of the comburent fluid and on the measured differential pressure and temperature of the combustible fluid, so as to keep the stoichiometric combustion ratio between the comburent fluid and the combustible fluid constant and equal to a predefined value.

[0069] Specifically, the regulating unit 7 is configured to command the control valve 6 in real time so as to vary the flow of the comburent fluid depending on:

[0070] - the flow rate of the comburent fluid determined from the measured differential pressure and temperature of the comburent fluid;

[0071] - the flow rate of the combustible fluid determined from the measured differential pressure and temperature of the combustible fluid.

[0072] Referring again to the fifth and sixth possible embodiments, the appliance 1 comprises a first calibrated flange 11 between the respective stretches of the first supply line 2 operationally connected to the pair of first pressure sensors 4, and a second calibrated flange 9 between the respective stretches of the second supply line 3 operationally connected to the pair of second pressure sensors 5.

[0073] Similarly to what has been described above with reference to the second, third and fourth embodiments, the flow rate of comburent fluid QA across the calibrated flange 9 depending on the temperature and on the pressure differential is calculated according to the following formula: wherein:

[0074] C is the discharge coefficient of the calibrated flange 9;

[0075] A is the cross-sectional area of the flange (m2),

[0076] AP is the differential pressure across the flange (Pa), p is the density of air (kg / m3).

[0077] The flow rate of the combustible fluid QG across the calibrated flange 11 depending on the temperature and pressure differential is calculated according to the following formula: wherein: C is the discharge coefficient of the calibrated flange 11;

[0078] A is the cross-sectional area of the flange (m2),

[0079] AP is the pressure differential across the flange (Pa), p is the density of the gas (kg / m3).

[0080] Preferably, the control valve 6 used for all possible embodiments of the appliance 1 is of the type of an electrically-operated control valve.

[0081] In addition, the appliance 1 comprises at least one communication unit 12 configured to communicate with at least one supervisory system of the industrial combustion plant.

[0082] In particular, through the communication with the supervisory system, it is possible to continuously monitor the correct adjustment and to change the stoichiometric combustion ratio according to specific requirements.

[0083] A supervisory system according to the invention comprises a plurality of appliance 1 and at least one control unit operationally connected to the appliance 1.

[0084] With the kind of appliance 1 illustrated, it is possible, through digital communication, to exchange data.

[0085] These data can be read to know the status of the industrial combustion plant and written to change the adjustment and heating environment pattern in real time, which may be reducing, neutral or oxidizing, in order to best optimize the firing of the different materials to be produced.

[0086] Having the ability to read and change the combustion settings in real time allows the production curve to be changed in relation to different types of materials as they move forward through the firing system, without production interruptions.

[0087] These features can be used to avoid production gaps between one product and another, implying that there is no major reduction in harmful gases, pollutants, CO2 and Nox generation.

[0088] Optimization of the stoichiometric combustion ratio also leads to energy savings which, in some cases and for large volumes, can be considerable.

[0089] It has in practice been ascertained that the described invention achieves the intended objects.

[0090] In particular, the fact is emphasized that the appliance according to the invention allows for the adjustment of the stoichiometric combustion ratio that adjusts the inflow of a comburent fluid (air), to one or more burners of an industrial combustion plant, while keeping the selected comburent / combustible fluid (air / gas) ratio constant as the amount of the combustible fluid (gas) delivered to the burners changes and any change in the density of the comburent fluid due to the change in the temperature thereof during the process.

Claims

CLAIMS1) Appliance (1) for the adjustment of the stoichiometric combustion ratio in burners of an industrial combustion plant, wherein said combustion plant comprises at least a first supply line (2) of a combustible fluid connected to at least one burner, and at least a second supply line (3) of a comburent fluid connected to said at least one burner, said appliance (1) being characterized by the fact that it comprises:- at least a first pressure sensor (4) operationally connected to said first supply line (2) and configured to measure in real time the pressure of said combustible fluid delivered through the first supply line (2);- at least a second pressure sensor (5) operationally connected to said second supply line (3) and configured to measure in real time the pressure of said comburent fluid delivered through the second supply line (3);- at least one control valve (6) of the comburent fluid, operationally connected to said second supply line (3) and configured to regulate the flow of the comburent fluid within said second supply line (3);- at least one regulating unit (7) of the stoichiometric combustion ratio, operationally connected to said first pressure sensor (4), to said second pressure sensor (5) and to said control valve (6);- wherein said regulating unit (7) is configured to command in real time said control valve (6) to vary the flow of said comburent fluid depending on the measured pressure of the comburent fluid and on the measured pressure of the combustible fluid, to keep the stoichiometric combustion ratio between the comburent fluid and the combustible fluid constant and equal to a predefined value.2) Appliance (1) according to claim 1, characterized by the fact that it comprises:- a first pressure sensor (4) operationally connected to said first supply line(2) and configured to measure the pressure of said combustible fluid in real time;- a second pressure sensor (5) operationally connected to said second supply line (3) and configured to measure the pressure of said comburent fluid in real time; wherein said regulating unit (7) is operationally connected to said first pressure sensor (4), to said second pressure sensor (5) and to said control valve (6), and is configured to command in real time said control valve (6) to vary the flow of said comburent fluid depending on said measured pressure of the comburent fluid and said measured pressure of the combustible fluid, to keep the stoichiometric combustion ratio between the comburent fluid and the combustible fluid constant and equal to a predefined value.3) Appliance (1) according to claim 1, characterized by the fact that it comprises:- a first pressure sensor (4) operationally connected to said first supply line(2) and configured to measure the pressure of said combustible fluid in real time;- a pair of second pressure sensors (5) operationally connected to respective stretches of said second supply line (3) and configured to measure in real time a differential pressure of said comburent fluid;- a temperature sensor (8) operationally connected to said second supply line(3) and configured to measure the temperature of said comburent fluid; wherein said regulating unit (7) is operationally connected to said first pressure sensor (4), to said pair of second pressure sensors (5), to said temperature sensor (8) and to said control valve (6), and is configured to command in real time said control valve (6) to vary the flow of said comburent fluid depending on said measured differential pressure and on said measured temperature of the comburent fluid and on said measured pressure of the combustible fluid, to keepthe stoichiometric combustion ratio between the comburent fluid and the combustible fluid constant and equal to a predefined value.4) Appliance (1) according to claim 3, characterized by the fact that said regulating unit (7) is configured to command in real time said control valve (6) to vary the flow of said comburent fluid depending on said measured pressure of the combustible fluid and on the flow rate of the comburent fluid, determined from said measured differential pressure and temperature.5) Appliance (1) according to any one of claims 3 and 4, characterized by the fact that it comprises at least one calibrated flange (9) between said respective stretches of the second supply line (3) operationally connected to said pair of second pressure sensors (5).6) Appliance (1) according to claim 1, characterized by the fact that it comprises:- a pair of first pressure sensors (4) operationally connected to respective stretches of said first supply line (2) and configured to measure the differential pressure of said combustible fluid in real time;- a second pressure sensor (5) operationally connected to said second supply line (3) and configured to measure the pressure of said comburent fluid in real time;- a temperature sensor (10) operationally connected to said first supply line and configured to measure the temperature of said combustible fluid; wherein said regulating unit (7) is operationally connected to said pair of first pressure sensors (4), to said second pressure sensor (5), to said temperature sensor (10) and to said control valve (6), and is configured to command in real time said control valve (6) so as to vary the flow of said comburent fluid depending on said measured pressure of the comburent fluid and on said measured differential pressure and temperature of the combustible fluid, to keep the stoichiometric combustion ratio between the comburent fluid and the combustible fluid constantand equal to a predefined value.7) Appliance (1) according to claim 6, characterized by the fact that said regulating unit (7) is configured to command in real time said control valve (6) to vary the flow of said comburent fluid depending on said measured pressure of the comburent fluid and on the flow rate of the combustible fluid determined from said measured differential pressure and temperature.8) Appliance (1) according to any one of claims 6 and 7, characterized by the fact that it comprises at least one calibrated flange (11) between said respective stretches of the first supply line (2) operationally connected to said pair of first pressure sensors (4).9) Appliance (1) according to one or more of claims 6 to 8, characterized by the fact that said pair of first pressure sensors (4) is built within a differential pressure transducer.10) Appliance (1) according to claim 1, characterized by the fact that it comprises:- a pair of first pressure sensors (4) operationally connected to respective stretches of said first supply line (2) and configured to measure the differential pressure of said combustible fluid in real time (delivered through the first supply line);- a pair of second pressure sensors (5) operationally connected to respective stretches of said second supply line (3) and configured to measure the differential pressure of said comburent fluid in real time (delivered through the second supply line);- a first temperature sensor (10) operationally connected to said first supply line (2) and configured to measure the temperature of said combustible fluid;- a second temperature sensor (8) operationally connected to said second supply line (3) and configured to measure the temperature of saidcomburent fluid; wherein said regulating unit (7) is operationally connected to said pair of first pressure sensors (4), to said pair of second pressure sensors (5), to said first temperature sensor (10), to said second temperature sensor (8) and to said control valve (6), and is configured to command said control valve (6) in real time so as to vary the flow of said comburent fluid depending on said measured differential pressure and temperature of the comburent fluid and on said measured differential pressure and temperature of the combustible fluid, so as to keep the stoichiometric combustion ratio between the comburent fluid and the combustible fluid constant and equal to a predefined value.11) Appliance according to claim 10, characterized by the fact that said regulating unit (7) is configured to command said control valve (6) in real time so as to vary the flow of said comburent fluid depending on:- the flow rate of the comburent fluid determined from said measured differential pressure and temperature of the comburent fluid- the flow rate of the combustible fluid determined from said measured differential pressure and temperature of the combustible fluid.12) Appliance (1) according to any one of claims 10 and 11, characterized by the fact that it comprises a first calibrated flange (11) between said respective stretches of the first supply line (2) operationally connected to said pair of first pressure sensors (4), and a second calibrated flange (9) between said respective stretches of the second supply line (3) operationally connected to said pair of second pressure sensors (5).13) Appliance (1) according to one or more of the preceding claims, characterized by the fact that said flow rate of the comburent fluid (QA) through said calibrated flange (9) depending on the temperature and on the differential pressure is calculated according to the following formula:wherein:C is the discharge coefficient of the calibrated flange (9);A is the cross-sectional area of the calibrated flange (9),AP is the differential pressure across the calibrated flange (9), p is the density of the comburent fluid.14) Appliance (1) according to one or more of the preceding claims, characterized by the fact that said flow rate of the combustible fluid (QG) through the calibrated flange (11) depending on the temperature and on the differential pressure is calculated according to the following formula:wherein:C is the discharge coefficient of the calibrated flange (11);A is the cross-sectional area of the calibrated flange (11),AP is the differential pressure across the calibrated flange (11), p is the density of the combustible fluid.15) Appliance (1) according to one or more of the preceding claims, characterized by the fact that said control valve (6) is of the type of an electrically-operated control valve.16) Appliance (1) according to one or more of the preceding claims, characterized by the fact that it comprises at least one communication unit (12) configured to communicate with at least one supervisory system of said industrial combustion plant.17) Supervisory system of an industrial combustion plant, characterized by the fact that it comprises a plurality of appliances (1) according to one or more of thepreceding claims and at least one control unit operationally connected to said appliances (1).

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