Flue gas sampling device for coal-fired power plant

Abstract

The coal-fired power plant flue gas sampling device comprises a shell, a baffle is arranged at an opening in the top of the shell, a filtering mechanism is installed at the upper end of the baffle, a sampling barrel is rotationally arranged at the lower end of the baffle, and a suction pump and a storage tank are fixedly arranged in the shell; the upper end of the sampling barrel is communicated with an inlet of the filtering mechanism through a through hole in the baffle, an outlet of the filtering mechanism is communicated with an inlet of the suction pump through a metal hose, an outlet of the suction pump is communicated with the storage tank, and the device can avoid the problem of smoke moisture condensation.

Description

Technical Field

[0001] The invention belongs to the technical field of flue gas sampling, and in particular relates to a flue gas sampling device for a coal-fired power plant. Background Art

[0002] Electricity is used everywhere in our daily lives. In thermal power plants, boilers are typically used to convert the chemical energy of fuel into heat. This heat is then converted back into electricity by steam turbine generators, which are then transmitted to users via the power system. The fuel and air in the boilers are mixed and burned, producing high-temperature flue gas. This flue gas releases heat in the boiler and is ultimately discharged into the atmosphere. Flue gas emitted into the atmosphere includes nitrogen, oxygen, nitrogen oxides, carbon monoxide, carbon dioxide, sulfur dioxide, and sulfur trioxide. Except for nitrogen and oxygen, any of these flue gases released into the air pollutes the air quality and poses a threat to human health. Therefore, various countries have established standards for flue gas emissions. In thermal power plants, flue gas analyzers are typically used to measure the content of each gas in the flue gas from boiler combustion. To do this, a flue gas sampling device is used to sample the flue gas from the boiler.

[0003] Publication No. CN112362416A discloses an airbag sampling intermittent flue gas measurement system, comprising a gas storage device, a shell, a flue gas sampling tube, a first check valve, a second check valve, a flue gas analyzer, a computer, a first solenoid valve, an air pump and an air duct; the gas storage device is located in the shell, the bottom of the gas storage device is fixedly connected to the inner wall of the shell, one end of the flue gas sampling tube is inserted into the flue, the other end of the flue gas sampling tube is connected to the inlet of the gas storage device through the first check valve, the outlet of the gas storage device is connected to the inlet of the flue gas analyzer through the second check valve, and the output end of the flue gas analyzer is connected to the input end of the computer; the air vent of the shell is connected to the inlet of the air pump through the first solenoid valve, the air duct is connected to the inlet of the air pump, a second solenoid valve is provided on the air duct, and the outlet of the air pump is divided into two paths, one of which is connected to the air vent on the shell through the third solenoid valve, and the other is connected to the fourth solenoid valve. When flue gas sampling is to be carried out, the control system opens the vacuum pump and the first and fourth solenoid valves, closes the second and third solenoid valves, and the vacuum pump draws air to generate negative pressure in the shell. The gas storage device draws flue gas from the flue through the flue gas sampling tube, the filter, and the first check valve. When the sampling of the gas storage device reaches the set volume, the controller closes the first and fourth solenoid valves, opens the second and third solenoid valves, and at the same time inflates the shell through the vacuum pump to generate positive pressure in the shell and compress the gas storage device. The flue gas is counted into the flue gas analyzer through the second check valve and the flue gas pretreatment device for component analysis, and the analysis results are input into the computer. When the measurement is completed, the fifth solenoid valve is opened to discharge the remaining gas in the gas storage device. The vacuum pump draws air to generate negative pressure in the shell, and the gas storage device draws the flue gas through the flue gas sampling tube, the filter, and the first check valve to realize the sampling of the flue gas in the flue; the vacuum pump inflates the shell to generate positive pressure in the shell, compressing the gas storage device, so that the flue gas enters the flue gas analyzer for component analysis, so as to realize continuous measurement of the flue gas. At the same time, the cost is low and the adaptability is strong, which greatly reduces the cost of the multi-point measurement system.

[0004] However, the flue gas sampling devices in the prior art mostly use stainless steel tubes to directly sample the flue gas. The part of the stainless steel tube exposed to the flue quickly cools down in the atmospheric environment, causing condensation in the flue gas inside the tube, resulting in excessive accumulation of internal soot. At the same time, dust will be inhaled, affecting storage.

[0005] Therefore, a flue gas sampling device for a coal-fired power plant is needed to improve the above problems. Summary of the Invention

[0006] The purpose of the present invention is to overcome the shortcomings of the above-mentioned prior art and provide a flue gas sampling device for a coal-fired power plant, which can avoid the problem of flue gas condensation.

[0007] To achieve the above-mentioned purpose, the present invention discloses a flue gas sampling device for a coal-fired power plant, comprising a shell, a baffle being provided at the top opening of the shell, a filtering mechanism being installed at the upper end of the baffle, a sampling cylinder being rotatably provided at the lower end of the baffle, a suction pump and a storage tank being fixedly provided inside the shell, the upper end of the sampling cylinder being connected to the inlet of the filtering mechanism through a through hole on the baffle, the outlet of the filtering mechanism being connected to the inlet of the suction pump through a metal hose, and the outlet of the suction pump being connected to the storage tank.

[0008] The further improvement of the coal-fired power plant flue gas sampling device of the present invention is:

[0009] Furthermore, a handle is installed on the upper end of the filtering mechanism.

[0010] Furthermore, a pulley is fixedly provided at the lower end of the shell.

[0011] Furthermore, the filtering mechanism includes a filtering tank, which is fixed on the baffle, a cover plate is connected to the surface of the filtering tank, and a filter screen is provided inside the filtering tank.

[0012] Furthermore, the sampling cylinder includes a heat-conducting metal cylinder, which is connected to the baffle through a bearing.

[0013] Furthermore, a plurality of heat sinks are fixedly provided on the surface of the heat-conducting metal cylinder.

[0014] Furthermore, the sampling tube also includes a scraper, and the scraper is fixedly arranged on the inner side of the heat-conducting metal tube.

[0015] Furthermore, a motor is provided inside the shell, an output shaft of the motor is connected to a take-up roller, and part of the metal hose is wound around the take-up roller.

[0016] Furthermore, the cover plate is threadedly connected to the filter tank.

[0017] Furthermore, the heat sinks are distributed in sequence along the circumferential direction.

[0018] The present invention discloses a flue gas sampling device for a coal-fired power plant, comprising a housing, a baffle being provided at a top opening of the housing, a filter mechanism being mounted on the upper end of the baffle, a sampling cylinder being rotatably provided on the lower end of the baffle, a suction pump and a storage tank being fixedly provided inside the housing, the upper end of the sampling cylinder being connected to the inlet of the filter mechanism via a through hole in the baffle, the outlet of the filter mechanism being connected to the inlet of the suction pump via a metal hose, and the outlet of the suction pump being connected to the storage tank;

[0019] The filter mechanism comprises a filter tank, which is fixed on the baffle, a cover plate is connected to the surface of the filter tank, and a filter screen is provided inside the filter tank;

[0020] The sampling cylinder comprises a heat-conducting metal cylinder, which is connected to the baffle through a bearing.

[0021] The present invention has the following beneficial effects:

[0022] During specific operation, the flue gas sampling device for a coal-fired power plant described in the present invention starts the suction pump, extracts the flue gas through the sampling cylinder, and then enters the storage tank after being filtered by a filtering mechanism. It should be noted that the sampling cylinder and the storage tank are both arranged in a shell to avoid exposure to the external environment, thereby avoiding the problem of flue gas condensation. The structure is simple and the practicability is extremely strong.

[0023] Furthermore, when working, by holding the handle, the metal hose is driven by the motor to take samples through the sampling tube. The flue gas enters through the heat-conducting metal tube and is filtered by the filter mesh plate in the filter mechanism to prevent dust from entering the storage tank. The suction pump draws the flue gas into the storage tank for storage. The cover can be opened to clean the cover, and the heat-conducting metal tube is rotated. The internal scraper will clean the dust inside the heat-conducting metal tube to prevent the inner wall of the heat-conducting metal tube from being blocked, and the heat sink will dissipate heat from the heat-conducting metal tube. BRIEF DESCRIPTION OF THE DRAWINGS

[0024] The accompanying drawings, which constitute part of the present invention, are intended to provide a further understanding of the present invention. The exemplary embodiments of the present invention and their descriptions are intended to explain the present invention and do not constitute an undue limitation of the present invention. In the accompanying drawings:

[0025] Figure 1 It is a schematic diagram of the overall three-dimensional structure of the present invention;

[0026] Figure 2 It is a schematic diagram of the overall internal structure of the present invention;

[0027] Figure 3 Schematic diagram of the internal structure of the sampling tube 4 of the present invention;

[0028] Figure 4 It is a structural schematic diagram of the filtering mechanism 2 of the present invention.

[0029] Among them, 1 is a handle, 2 is a filtering mechanism, 3 is a baffle, 4 is a sampling tube, 5 is a suction pump, 6 is a storage tank, 7 is a shell, 8 is a pulley, 9 is a take-up roller, 10 is a motor, 11 is a heat sink, 12 is a heat-conducting metal tube, 13 is a scraper, 14 is a through hole, 15 is a filter tank, 16 is a cover plate, and 17 is a filter mesh plate. DETAILED DESCRIPTION

[0030] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of them. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without making any creative efforts shall fall within the scope of protection of the present invention.

[0031] In the description of the present invention, it is to be understood that the terms “include” and “comprise” indicate the presence of the described features, wholes, steps, operations, elements and / or components, but do not exclude the presence or addition of one or more other features, wholes, steps, operations, elements, components and / or collections thereof.

[0032] It should also be understood that the terms used in the present specification are only for the purpose of describing particular embodiments and are not intended to limit the present invention. As used in the present specification and the appended claims, the singular forms "a", "an", and "the" are intended to include the plural forms unless the context clearly indicates otherwise.

[0033] It should be further understood that the term "and / or" as used in the present specification and the appended claims refers to and includes any and all possible combinations of one or more of the associated listed items. For example, A and / or B may represent: A exists alone, A and B exist simultaneously, and B exists alone. In addition, the character " / " in the present invention generally indicates that the associated objects are in an "or" relationship.

[0034] It should be understood that although the terms "first," "second," and "third" may be used to describe preset ranges in embodiments of the present invention, these preset ranges should not be limited to these terms. These terms are merely used to distinguish one preset range from another. For example, without departing from the scope of embodiments of the present invention, the first preset range may also be referred to as the second preset range, and similarly, the second preset range may also be referred to as the first preset range.

[0035] The word "if," as used herein, may be interpreted as "at the time of" or "when" or "in response to determining" or "in response to detecting," depending on the context. Similarly, the phrases "if it is determined" or "if (stated condition or event) is detected" may be interpreted as "when it is determined" or "in response to the determination" or "when detecting (stated condition or event)" or "in response to detecting (stated condition or event)," depending on the context.

[0036] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Generally, the components of the embodiments of the present invention described and shown in the drawings herein can be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the present invention provided in the drawings is not intended to limit the scope of the claimed invention, but merely represents selected embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0037] The accompanying drawings illustrate various schematic diagrams of structures according to embodiments disclosed herein. These figures are not drawn to scale; for clarity, some details are exaggerated and some details may be omitted. The shapes of the various regions and layers shown in the figures, as well as their relative sizes and positional relationships, are merely exemplary and may deviate in practice due to manufacturing tolerances or technical limitations. Those skilled in the art may design regions / layers with different shapes, sizes, and relative positions as needed.

[0038] As we all know, flue gas sampling in coal-fired power plants is a key link in environmental monitoring and emission control. The following is an introduction from three aspects: sampling method, device composition, and precautions:

[0039] Sampling method

[0040] Dilution sampling: The sampling gun is equipped with a cyclone separator at the front, which removes large particles larger than PM and droplets from the flue gas. A jet nozzle is connected after the cyclone separator. The high flow of dilution air in the dilution gas inlet pipe draws in the flue gas based on the jet principle. The flue gas and clean air are diluted and mixed in the primary dilution mixing section. The mixed and diluted flue gas enters the secondary dilution mixing section for further mixing and dilution, ensuring sufficient residence time in the sampling device. Finally, the flue gas enters the analysis and sampling equipment through the secondary mixed gas sampling port.

[0041] Direct extraction sampling: The sampling probe is equipped with a heating and filtering device to filter out most dust in the flue gas. The heating device can also slow down dust caking. During the negative pressure extraction sampling process, the flue gas is drawn into the condenser in the analyzer cabinet by the probe and heated piping. The water vapor in the flue gas rapidly cools to approximately 4 degrees Celsius, forming condensate. This condensate is then deposited at the bottom of the condenser and discharged by a peristaltic pump to a water collection tank outside the system. After the water vapor in the flue gas is completely filtered out, it passes through a final fine filter before entering the spectrum analyzer for spectral analysis.

[0042] Device composition

[0043] Sampling gun unit: The main function is to extract flue gas from the flue and simulate the dilution and condensation process of flue gas entering the atmospheric environment.

[0044] Dilution unit: includes air compressor, filter, dryer, etc. The air compressor generates a large flow of air, which passes through the dryer to remove moisture from the air, passes through the HEPA filter to remove more than 99.97% of particulate matter in the air, and finally passes through the activated carbon adsorber to remove more than 99.9% of gaseous substances in the air. The resulting clean air enters the sampling gun.

[0045] Sampling and Analysis Unit: This unit further analyzes the diluted sample. Flue gas enters the PM2.5 analysis and sampling equipment from the secondary mixed gas sampling port. This equipment includes a filter with a sampling membrane and an impactor, a laser particle counting system (SMPS), and an electric charge-based particle counting (ELPI). Following the sampling equipment are a flow meter and a sampling pump.

[0046] Precautions

[0047] Sampling probe is clogged: The sampling probe is in direct contact with the flue gas and is prone to clogging. If the flue gas flow rate decreases, check the sampling probe for blockage.

[0048] Sampling pump: Ensure that the sampling pump operates normally to ensure the continuity and stability of sampling.

[0049] Sampling process control: When using the predicted flow rate method to collect high-concentration smoke samples, the pre-meter pressure and indicated flow rate increase rapidly due to the resistance at the filter cartridge. When the flow meter is manually adjusted to maintain a constant speed, the flow meter reading should be corrected at any time according to the changes in the pre-meter pressure and temperature, and the pre-meter pressure must accurately reflect the actual value.

[0050] Sampling point arrangement: According to the monitoring standards, the measuring points should be arranged on a section of the straight pipe that is more than 6 times the equivalent diameter away from the upstream elbow or reducer, and more than 3 times the equivalent diameter away from the downstream elbow or reducer, and the vertical pipe section should be given priority. If this condition cannot be met on site, both vertical and straight pipe sections should be taken into account, and the number of measuring points arranged should greatly exceed the standard requirements to increase the accuracy of the measurement. Unless absolutely necessary, the measuring holes should not be opened at the top of the flue to avoid the filter cartridge opening facing downward when the smoke is sampled. If the measuring holes must be opened at the top of the flue, a filter cartridge can be used for each measuring hole, and sampling should be carried out from far to near, and finally at the sampling point close to the measuring hole, so that the sampling tube can be quickly removed in the vacuum state to minimize the loss of smoke samples and errors in the sampling volume.

[0051] Example 1

[0052] refer to Figure 1 、 Figure 2 、 Figure 3 and Figure 4 The present invention discloses a flue gas sampling device for a coal-fired power plant. The device comprises a housing 7, a baffle 3 provided at the top opening of the housing 7, a filter mechanism 2 mounted on the upper end of the baffle 3, a sampling barrel 4 rotatably provided at the lower end of the baffle 3, a suction pump 5 and a storage tank 6 fixedly provided inside the housing 7, the upper end of the sampling barrel 4 communicating with the inlet of the filter mechanism 2 via a through hole in the baffle 3, the outlet of the filter mechanism 2 communicating with the inlet of the suction pump 5 via a metal hose, and the outlet of the suction pump 5 communicating with the storage tank 6. The sampling barrel 4 comprises a heat-conducting metal barrel 12 connected to the baffle 3 via a bearing; the filtering mechanism 2 comprises a filter tank 15 fixedly provided on the baffle 3, a cover plate 16 connected to the surface of the filter tank 15, and a filter mesh plate 17 provided inside the filter tank 15.

[0053] Example 2

[0054] refer to Figure 1 、 Figure 2 、 Figure 3 and Figure 4 To further complete this application, the coal-fired power plant flue gas sampling device described in the present invention includes a handle 1, a filter mechanism 2, a baffle 3, a sampling cylinder 4, a suction pump 5, a storage tank 6, a shell 7, a pulley 8, a take-up roller 9, a motor 10, a heat sink 11, a heat-conducting metal cylinder 12, a scraper 13, a through hole 14, a filter tank 15, a cover plate 16 and a filter mesh plate 17. The upper end of the shell 7 is provided with a baffle 3, the upper end of the baffle 3 is provided with a filter mechanism 2, the upper end of the filter mechanism 2 is installed with a handle 1, and the lower end of the baffle 3 is rotatably provided with a sampling cylinder 4. The inside of the shell 7 is fixed with a suction pump 5 and a storage tank 6, and the bottom of the shell 7 is fixed with a pulley 8. Hold the handle 1 and drive the metal hose through the motor 10 to take samples through the sampling cylinder 4. The flue gas enters through the heat-conducting metal cylinder 12 and is filtered by the filter mesh plate 17 in the filter mechanism 2. The suction pump 5 draws the flue gas into the storage tank 6 for storage.

[0055] The cover 16 can be opened to clean the cover 16 , and the heat-conducting metal cylinder 12 can be rotated. The internal scraper 13 can clean the dust inside the heat-conducting metal cylinder 12 , and the heat sink 11 can dissipate heat from the heat-conducting metal cylinder 12 .

[0056] As an embodiment of the present invention, the filtering mechanism 2 includes:

[0057] The filter tank 15 is fixedly arranged on the baffle 3 , a cover plate 16 is threadedly connected to the surface of the filter tank 15 , and a filter screen plate 17 is arranged inside the filter tank 15 .

[0058] As an embodiment of the present invention, the sampling tube 4 includes:

[0059] The heat-conducting metal cylinder 12 has a plurality of heat sinks 11 fixedly disposed on its surface. The heat-conducting metal cylinder 12 is connected to the baffle 3 via a bearing.

[0060] As an embodiment of the present invention, the sampling tube 4 further includes:

[0061] The scraper 13 is fixedly arranged on the inner side of the heat-conducting metal cylinder 12 , and a plurality of through holes 14 are provided on the surface of the baffle 3 , and the through holes 14 face the inner side of the heat-conducting metal cylinder 12 .

[0062] As an embodiment of the present invention, a take-up roller 9 is provided inside the housing 7 and driven by a motor 10. A metal hose is wrapped around the surface of the take-up roller 9. The storage tank 6, the suction pump 5 and the cover plate 16 are connected in sequence through the metal hose.

[0063] Example 3

[0064] This embodiment discloses a coal-fired power plant flue gas sampling method, which is implemented based on a coal-fired power plant flue gas sampling system. The coal-fired power plant flue gas sampling system includes a handle 1, a filter mechanism 2, a baffle 3, a sampling cylinder 4, a suction pump 5, a storage tank 6, a shell 7, a pulley 8, a take-up roller 9, a motor 10, a heat sink 11, a heat-conducting metal cylinder 12, a scraper 13, a through hole 14, a filter tank 15, a cover plate 16 and a filter mesh plate 17; the specific connection relationship is shown in Example 2.

[0065] Specifically, the coal-fired power plant flue gas sampling method includes the following steps:

[0066] The working principle of the present invention is: when in use, hold the handle 1, drive the metal hose through the motor 10, sample through the sampling tube 4, the smoke enters through the heat-conducting metal tube 12, is filtered by the filter plate 17 in the filter mechanism 2, and the suction pump 5 draws the smoke into the storage tank 6 for storage.

[0067] The cover 16 can be opened to clean the cover 16 , and the heat-conducting metal cylinder 12 can be rotated. The internal scraper 13 can clean the dust inside the heat-conducting metal cylinder 12 , and the heat sink 11 can dissipate heat from the heat-conducting metal cylinder 12 .

[0068] Those skilled in the art will readily identify other embodiments of the present invention after considering the specification and disclosure of the invention. This application is intended to cover any variations, uses, or adaptations of the present invention that follow the general principles of the invention and include common knowledge or customary techniques in the art not disclosed herein. The description and examples are to be considered as exemplary only, with the true scope and spirit of the invention being indicated by the following claims.

[0069] It should be understood that the present invention is not limited to the exact construction described above and shown in the drawings, and that various modifications and changes may be made without departing from the scope thereof. The scope of the present invention is limited only by the appended claims.

[0070] The above description is only a preferred embodiment of the present invention and does not limit the present invention in any way. Any simple modification, change and equivalent structural change made to the above embodiment based on the technical essence of the present invention shall still fall within the scope of protection of the technical solution of the present invention.

Claims

1. A flue gas sampling device for a coal-fired power plant, characterized in that: The invention comprises a shell (7), a baffle (3) is provided at the top opening of the shell (7), a filter mechanism (2) is installed on the upper end of the baffle (3), a sampling cylinder (4) is rotatably provided on the lower end of the baffle (3), a suction pump (5) and a storage tank (6) are fixedly provided inside the shell (7), the upper end of the sampling cylinder (4) is connected to the inlet of the filter mechanism (2) through the through hole on the baffle (3), the outlet of the filter mechanism (2) is connected to the inlet of the suction pump (5) through a metal hose, and the outlet of the suction pump (5) is connected to the storage tank (6).

2. The flue gas sampling device of a coal-fired power plant according to claim 1, characterized in that: A handle (1) is installed on the upper end of the filtering mechanism (2).

3. The flue gas sampling device of a coal-fired power plant according to claim 1, characterized in that: A pulley (8) is fixedly provided at the lower end of the housing (7).

4. The flue gas sampling device of a coal-fired power plant according to claim 1, characterized in that: The filtering mechanism (2) comprises a filtering tank (15), which is fixedly arranged on the baffle (3), a cover plate (16) is connected to the surface of the filtering tank (15), and a filtering screen plate (17) is provided inside the filtering tank (15).

5. The flue gas sampling device of a coal-fired power plant according to claim 1, characterized in that: The sampling cylinder (4) comprises a heat-conducting metal cylinder (12), and the heat-conducting metal cylinder (12) is connected to the baffle (3) via a bearing.

6. The flue gas sampling device of a coal-fired power plant according to claim 5, characterized in that: A plurality of heat sinks (11) are fixedly provided on the surface of the heat-conducting metal cylinder (12).

7. The flue gas sampling device of a coal-fired power plant according to claim 6, characterized in that: The sampling cylinder (4) further comprises a scraper (13), and the scraper (13) is fixedly arranged on the inner side of the heat-conducting metal cylinder (12).

8. The flue gas sampling device of a coal-fired power plant according to claim 1, characterized in that: A motor (10) is provided inside the housing (7), and an output shaft of the motor (10) is connected to a take-up roller (9), on which part of the metal hose is wound.

9. The flue gas sampling device of a coal-fired power plant according to claim 4, characterized in that: The cover plate (16) is threadedly connected to the filter tank (15).

10. A flue gas sampling device for a coal-fired power plant, characterized in that: The invention comprises a housing (7), a baffle (3) is provided at the top opening of the housing (7), a filter mechanism (2) is installed on the upper end of the baffle (3), a sampling cylinder (4) is rotatably provided on the lower end of the baffle (3), a suction pump (5) and a storage tank (6) are fixedly provided inside the housing (7), the upper end of the sampling cylinder (4) is connected to the inlet of the filter mechanism (2) through the through hole on the baffle (3), the outlet of the filter mechanism (2) is connected to the inlet of the suction pump (5) through a metal hose, and the outlet of the suction pump (5) is connected to the storage tank (6); The sampling cylinder (4) comprises a heat-conducting metal cylinder (12), and the heat-conducting metal cylinder (12) is connected to the baffle (3) via a bearing; The filtering mechanism (2) comprises a filtering tank (15), which is fixedly arranged on the baffle (3), a cover plate (16) is connected to the surface of the filtering tank (15), and a filtering screen plate (17) is provided inside the filtering tank (15).

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