Oxidation blower system

Abstract

The present application relates to the field of flue gas desulfurization energy saving technology, disclose a kind of oxidizing fan system, comprising: frequency conversion centrifugal fan unit is input oxidizing air to slurry pool;Calcium sulfite concentration tester obtains calcium sulfite concentration value from slurry pool;Dissolved oxygen meter obtains dissolved oxygen concentration value from slurry pool;When calcium sulfite concentration value≤0.01mmol / L, dissolved oxygen concentration value>0.6mg / L, reduce output frequency;When calcium sulfite concentration value≤0.01mmol / L, dissolved oxygen concentration value<0.6mg / L, improve output frequency;When calcium sulfite concentration value≤0.01mmol / L, dissolved oxygen concentration value is 0.6mg / L, maintain output frequency.The application combines calcium sulfite concentration value and dissolved oxygen concentration value with frequency conversion centrifugal fan unit, adjusts the output frequency of frequency conversion centrifugal fan unit, realizes air volume regulation, and plays the energy saving effect.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of flue gas desulfurization energy-saving technology, and particularly relates to an oxidation fan system. BACKGROUND

[0002] In a coal-fired power plant, a limestone-gypsum wet desulfurization system is generally used to desulfurize raw flue gas. In the process of desulfurizing raw flue gas, an oxidation fan system is generally used to supply oxygen for the limestone-gypsum wet desulfurization system. The energy consumption of the oxidation fan system accounts for about 15% of the energy consumption in the desulfurization process, and is an important component of the desulfurization energy consumption.

[0003] The oxidation fan system has high energy consumption, which is mainly caused by the following reasons: the oxidation fan in the oxidation fan system has a large design margin, and the air volume of the oxidation fan cannot be adjusted. The oxidation fan is generally designed according to the highest load of the unit and the worst working condition; at present, the load rate of most units is low, and the actual operating condition often deviates from the design condition, resulting in a series of problems such as over-oxidation of the circulating slurry in the slurry pool provided at the bottom of the desulfurization absorption tower and excessive overall power consumption. SUMMARY

[0004] Therefore, the present application provides an oxidation fan system to solve the problem of high energy consumption of the oxidation fan system in the process of desulfurizing raw flue gas by using a limestone-gypsum wet desulfurization system.

[0005] The present application provides an oxidation fan system, comprising:

[0006] The variable frequency centrifugal fan unit inputs oxidation air into the slurry pool provided at the bottom of the desulfurization absorption tower through the oxidation air pipe; first, the oxidation air demand is determined according to the flow of the raw flue gas input into the desulfurization absorption tower, the concentration of sulfur dioxide in the raw flue gas and the oxidation air utilization rate; then the initial output frequency of the variable frequency centrifugal fan unit is determined according to the oxidation air demand;

[0007] The calcium sulfite concentration tester is signal connected with the variable frequency centrifugal fan unit, and is adapted to sample from the first sampling port of the slurry pool to obtain the concentration value of calcium sulfite;

[0008] The dissolved oxygen meter is signal connected with the variable frequency centrifugal fan unit, and is adapted to sample from the second sampling port of the slurry pool to obtain the dissolved oxygen concentration value;

[0009] The oxidation fan system is suitable for reducing the output frequency of the variable frequency centrifugal fan unit to reduce the amount of oxidation air when the concentration value of calcium sulfite is less than or equal to 0.01 mmol / L and the concentration value of dissolved oxygen is greater than 0.6 mg / L; or increasing the output frequency of the variable frequency centrifugal fan unit to increase the amount of oxidation air when the concentration value of calcium sulfite is less than or equal to 0.01 mmol / L and the concentration value of dissolved oxygen is less than 0.6 mg / L; or maintaining the output frequency of the variable frequency centrifugal fan unit when the concentration value of calcium sulfite is less than or equal to 0.01 mmol / L and the concentration value of dissolved oxygen is 0.6 mg / L. The application has the advantages that the adjustable air volume, high efficiency and low energy consumption of the variable frequency centrifugal fan unit are fully utilized, the concentration value of calcium sulfite and the concentration value of dissolved oxygen are measured online, the output frequency of the variable frequency centrifugal fan unit is corrected and adjusted, the air volume of the variable frequency centrifugal fan unit can be accurately adjusted, high efficiency and energy saving are achieved, and good energy saving and environmental protection benefits are obtained.

[0010] Optionally, further comprising:

[0011] A slurry pump, one end of which is connected to the second sampling port;

[0012] A gypsum slurry cyclone, one end of which is connected to the other end of the slurry pump;

[0013] A clarifier, one end of which is connected to the overflow port provided on the gypsum slurry cyclone; the clarifier is also connected to the dissolved oxygen meter. The application has the advantages that the gypsum slurry cyclone is combined with the clarifier to reduce the solid content of the slurry, and the test accuracy of the dissolved oxygen meter is significantly improved.

[0014] Optionally, the first sampling port is located below the oxidation air pipe, and the second sampling port is located above the oxidation air pipe.

[0015] Optionally, the slurry at the bottom of the gypsum slurry cyclone is sent back to the desulfurization absorption tower through a ditch combined with a sump pump. The application has the advantages that the slurry is recycled and the cost is reduced.

[0016] Optionally, further comprising:

[0017] A primary air breaking structure, a plurality of nozzle assemblies are arranged at intervals on the part of the oxidation air pipe located in the slurry pool; the nozzle assemblies are suitable for spraying oxidation air downward; the primary air breaking structure is arranged below each nozzle assembly; the primary air breaking structure is suitable for breaking the oxidation air sprayed by the nozzle assemblies once;

[0018] A secondary air breaking structure is arranged above the part of the oxidizing air pipe located in the slurry pool; the secondary air breaking structure is suitable for breaking the rising oxidizing air again. Beneficial effects: the application uses the above technical scheme, breaks the large bubbles in the oxidizing air into small bubbles through the primary air breaking structure and the secondary air breaking structure, significantly improves the contact area and contact time of the bubbles and the desulfurization slurry, significantly improves the utilization rate of the oxidizing air, and further reduces the energy consumption of the oxidizing fan system.

[0019] Optionally, the primary air breaking structure comprises:

[0020] Two first hole plates arranged at an angle are connected with the oxidizing air pipe through a first connecting piece, and the nozzle assembly is located on the inner side of the angle.

[0021] Optionally, the angle of the angle is 90 degrees.

[0022] Optionally, the secondary air breaking structure comprises:

[0023] A horizontally arranged second hole plate is connected with the oxidizing air pipe through a second connecting piece.

[0024] Optionally, the first connecting piece is two first rib plates, and the two first hole plates are connected with the oxidizing air pipe through the first rib plates respectively; the second connecting piece is three second rib plates arranged at an angle.

[0025] Optionally, the nozzle assembly comprises:

[0026] A first nozzle is arranged downward along the vertical direction;

[0027] A second nozzle is arranged downward along the vertical direction, and the length of the second nozzle is greater than the length of the first nozzle. Beneficial effects: the application uses the above technical scheme, when the first nozzle is blocked, the oxidizing air is sprayed from the second nozzle, avoiding the problem of incomplete oxidation of the slurry caused by the blockage of the first nozzle, effectively preventing the further rise of the pressure of the oxidizing air, thereby significantly improving the safety and energy efficiency of the oxidizing fan system. BRIEF DESCRIPTION OF DRAWINGS

[0028] In order to more clearly illustrate the specific embodiments of the application or the technical solutions in the prior art, the following will briefly introduce the drawings needed to be used in the description of the specific embodiments or the prior art. Obviously, the drawings in the following description are some embodiments of the application, and those skilled in the art can also obtain other drawings according to these drawings without creative labor.

[0029] Figure 1 It is a connection structure diagram of the oxidizing fan system provided in the embodiments of the application.

[0030] Figure 2 Partial cross-sectional structure schematic diagram of the oxidation fan system provided in the embodiment of the present application;

[0031] Figure 3 Partial front view structure schematic diagram of the oxidation fan system provided in the embodiment of the present application.

[0032] Explanation of reference signs:

[0033] 1, first variable frequency centrifugal fan; 2, second variable frequency centrifugal fan; 3, oxidation air pipe; 4, desulfurization absorption tower; 5, slurry pool; 6, raw flue gas; 7, calcium sulfite concentration tester; 8, first sampling port; 9, dissolved oxygen meter; 10, second sampling port; 11, slurry pump; 12, gypsum slurry cyclone; 13, clarifier; 14, primary air breaking structure; 15, secondary air breaking structure; 16, first orifice plate; 17, second orifice plate; 18, first baffle plate; 19, second baffle plate; 20, first nozzle; 21, second nozzle; 22, trench; 23, purified flue gas. DETAILED DESCRIPTION

[0034] In order to make the purpose, technical scheme and advantages of the embodiments of the present application clearer, the technical scheme in the embodiments of the present application will be described clearly and completely below in combination with the drawings in the embodiments of the present application. Obviously, the described embodiments are some of the embodiments of the present application, rather than all the embodiments of the present application. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor fall within the scope of protection of the present application.

[0035] The oxidation fan has low oxygen supply efficiency to the slurry pool through the oxidation air pipe. After the oxidation air enters the slurry, the air bubbles are large, and a large amount of oxidation air cannot be dissolved into the slurry in time, but escapes into the purified flue gas, resulting in low utilization rate of oxidation air. In order to ensure the oxygen supply amount, the operation power of the oxidation fan needs to be increased, resulting in increased energy consumption. The conventional pipe network type oxidation air branch pipe generally uses a 157 mm diameter 2205 material steel pipe, and the air outlet is a small hole with a nominal diameter range of 20 mm to 25 mm. The air bubbles of the above air outlet are large, and most of the oxidation air escapes into the flue gas in the slurry. Due to the above reasons, an improved oxidation fan system is proposed.

[0036] As Figures 1 to 3One specific embodiment of the oxidation fan system shown includes: a variable frequency centrifugal fan unit, a calcium sulfite concentration meter 7, a dissolved oxygen meter 9, a slurry pump 11, a gypsum slurry hydrocyclone 12, a clarifier 13, a primary air-breaking structure 14, and a secondary air-breaking structure 15. Specifically, the variable frequency centrifugal fan unit can be a first variable frequency centrifugal fan 1 and a second variable frequency centrifugal fan 2 arranged in parallel. Both the first variable frequency centrifugal fan 1 and the second variable frequency centrifugal fan 2 are magnetically levitated variable frequency oxidation fans. The oxidation fan system described in this application is applied to a limestone-gypsum wet desulfurization system.

[0037] like Figure 1 As shown, the variable frequency centrifugal fan unit supplies oxidation air to the slurry pool 5 located at the bottom of the desulfurization absorption tower 4 through the oxidation duct 3; the oxidation duct 3 is installed 4.5~5.0m below the liquid level in the slurry pool 5. First, the required amount of oxidation air is determined based on the flow rate of the raw flue gas 6 input to the desulfurization absorption tower 4, the concentration of sulfur dioxide in the raw flue gas 6, and the oxidation air utilization rate; then, the initial output frequency of the variable frequency centrifugal fan unit is determined based on the required amount of oxidation air. Under standard dry conditions, the raw flue gas 6 contains 6% oxygen, and the oxidation air utilization rate can be 30%. The purified flue gas 23 is discharged from the top of the desulfurization absorption tower 4. Figure 1 The arrow on the left indicates the flow direction of the original flue gas 6. Figure 1The arrow in the upper part indicates the flow direction of the purified flue gas 23. The calcium sulfite concentration tester 7 is connected to the variable frequency centrifugal fan unit, and is adapted to sample from the first sampling port 8 of the slurry tank 5 to obtain the concentration value of calcium sulfite in real time. Specifically, the first sampling port 8 is located below the oxidation air pipe 3. One end of the slurry pump 11 is connected to the second sampling port 10, and the other end of the slurry pump 11 is connected to one end of the gypsum slurry cyclone 12. One end of the clarification tank 13 is connected to the overflow port of the gypsum slurry cyclone 12. The solid content of the overflow slurry is less than 3%. The clarification tank 13 is also connected to the dissolved oxygen meter 9. The dissolved oxygen meter 9 is connected to the variable frequency centrifugal fan unit, and can sample from the second sampling port 10 of the slurry tank 5 to obtain the dissolved oxygen concentration value in real time. Alternatively, the dissolved oxygen meter 9 can also sample from the clarification tank 13 to obtain the dissolved oxygen concentration value in real time. The dissolved oxygen meter 9 is commonly used for testing the dissolved oxygen content of water samples in the chemical industry, and has certain requirements for the turbidity of water quality. If the turbidity is too high, it will affect the measurement accuracy. In this application, the slurry with a solid content of about 15% is pumped into the gypsum slurry cyclone 12 through the slurry pump 11, and the overflow slurry after cyclone has a solid content of ≤1%, which meets the use requirements of the dissolved oxygen meter 9 and significantly improves the test accuracy. Specifically, the second sampling port 10 is located above the oxidation air pipe 3, and the second sampling port 10 can be arranged at different typical positions above the oxidation air pipe 3. Further, the slurry at the bottom of the gypsum slurry cyclone 12 is returned to the desulfurization absorption tower 4 through the trench 22 combined with the pit pump. The solid content of the slurry at the bottom of the gypsum slurry cyclone 12 is more than 75%. When the concentration value of calcium sulfite is ≤0.01 mmol / L and the dissolved oxygen concentration value is >0.6 mg / L, the output frequency of the variable frequency centrifugal fan unit is reduced to reduce the amount of oxidation air. Alternatively, when the concentration value of calcium sulfite is ≤0.01 mmol / L and the dissolved oxygen concentration value is <0.6 mg / L, the output frequency of the variable frequency centrifugal fan unit is increased to increase the amount of oxidation air. Alternatively, when the concentration value of calcium sulfite is ≤0.01 mmol / L and the dissolved oxygen concentration value is 0.6 mg / L, the output frequency of the variable frequency centrifugal fan unit is maintained. The concentration value of calcium sulfite and the dissolved oxygen concentration value reflect the operating conditions of the limestone-gypsum wet desulfurization system. The reason for taking 0.01 mmol / L as a special value point of the concentration value of calcium sulfite is that when the oxidation rate of calcium sulfite in the slurry reaches more than 95%, the concentration value of calcium sulfite is ≤0.01 mmol / L, and the quality of gypsum at this time meets the emission standard of coal-fired power plants.The output frequency of the variable frequency centrifugal fan unit can be first adjusted in steps of 1 Hz so that the concentration of calcium sulfite is ≤0.01 mmol / L; then the output frequency of the variable frequency centrifugal fan unit is adjusted in steps of 0.2 Hz so that the dissolved oxygen concentration is maintained at 0.6 mg / L, and the dissolved oxygen concentration can be obtained every 180 seconds. The handheld calcium sulfite concentration tester is modified by adding a remote module to obtain the calcium sulfite concentration tester 7 described in the present application, and the first sampling port 8 can be set at a position 0.5 m below the oxidation air pipe 3. 2- oxidized to SO4 2- After that, the molecular weight of the formed gypsum is greater than that of calcium sulfite, and the gypsum precipitates to the bottom of the slurry tank 5. By setting the first sampling port 8 at the above position, the true oxidation degree of SO3 2- in the slurry can be understood, which is representative.

[0038] As shown in Figure 2 and Figure 3 , a plurality of nozzle assemblies are arranged at intervals in the part of the oxidation air pipe 3 located in the slurry tank 5; the nozzle assemblies are adapted to spray oxidation air downward; the primary air breaking structure 14 is arranged below each nozzle assembly; the primary air breaking structure 14 is adapted to break the oxidation air sprayed by the nozzle assemblies once. The secondary air breaking structure 15 is arranged above the part of the oxidation air pipe 3 located in the slurry tank 5; the secondary air breaking structure 15 is adapted to break the rising oxidation air twice.

[0039] Specifically, the primary air-breaking structure 14 includes two first perforated plates 16 arranged at an included angle, connected to the oxidation duct 3 via a first connector, with the nozzle assembly located inside the included angle. The included angle can be 90 degrees, the two first perforated plates 16 are symmetrically arranged, and the nozzle assembly is approximately located at the center of symmetry of the two first perforated plates 16. The secondary air-breaking structure 15 includes a horizontally arranged second perforated plate 17, connected to the oxidation duct 3 via a second connector. More specifically, the first connector is two first stiffening plates 18, with the two first perforated plates 16 respectively connected to the oxidation duct 3 via the first stiffening plates 18; the second connector is three second stiffening plates 19 arranged at an angle. Both the first perforated plates 16 and the second perforated plates 17 can be made of 2205 stainless steel. After the oxidizing air is ejected from the nozzle assembly, it is first broken up by the primary air breaking structure 14. Most of the large bubbles are broken into small bubbles after passing through the first orifice plate 16. A small portion of the large bubbles are guided by the primary air breaking structure 14 and then, together with the broken small bubbles, are broken up by the secondary air breaking structure 15. The bubbles are further reduced in size, and most of the large bubbles are broken into small bubbles. This significantly increases the contact area between the oxidizing air and the desulfurization slurry, and at the same time increases the residence time of the bubbles in the slurry, thus significantly improving the utilization rate of the oxidizing air.

[0040] Specifically, the nozzle assembly includes a first nozzle 20 and a second nozzle 21. The nominal diameter of both the first nozzle 20 and the second nozzle 21 can be 20 mm. The first nozzle 20 is vertically downward. The second nozzle 21 is also vertically downward, and its length is greater than that of the first nozzle 20. The second nozzle 21 is at least 30 cm longer than the first nozzle 20, when the slurry density is 1200 kg / m³. 3 The outlet pressure of the second nozzle 21 is 3.6 kPa higher than the outlet pressure of the first nozzle 20. When the first nozzle 20 is blocked, the pressure of the oxidation air rises. When the pressure rise is higher than 3.6 kPa, the oxidation air is ejected from the second nozzle 21, avoiding the problem of incomplete slurry oxidation caused by the blockage of the first nozzle 20. Thus, the safety and energy efficiency of the oxidation blower system are significantly improved.

[0041] During the oxidation process of the desulfurization circulating slurry, oxidizing air is introduced. Part of the oxidizing air undergoes gas-liquid two-phase mass transfer with the slurry, and some of the oxidizing air dissolved into the slurry reacts with SO3. 2- Oxidation reaction occurs, but not with SO3 2- The oxidizing air that reacts is to maintain SO3 2- The oxidation reaction is driven by air, but only a small portion of this oxidizing air dissolves in the slurry; most of the oxidizing air eventually overflows from the slurry pool and mixes with the original flue gas. The greater the amount of air bubbles dissolved in the slurry, the better it affects the production of SO3. 2-The higher the reaction driving force of oxidation is, the higher the utilization rate of the oxidation air is, the smaller the bubbles sprayed by the nozzle assembly are, the larger the contact area between the oxidation air and the slurry is, and the higher the dissolution amount in the slurry is. Therefore, breaking the bubbles of the oxidation air and improving the utilization rate of the oxidation air are important measures to improve the economy of the oxidation fan system.

[0042] The existing desulfurization system of a certain 660MW unit is a single tower system, the oxidation air system adopts a Roots blower, two in one, the oxidation air pipe adopts a pipe network structure combined with a pulse suspension pump, the power consumption of a single oxidation fan is 255kWh / h, the power consumption of two oxidation fans is 510kWh / h, the oxidation air pipe is blocked or broken all the year round, the slurry oxidation is insufficient, and the gypsum dehydration is often difficult. The technical scheme of the application is used to reform the above-mentioned oxidation fan system, three Roots blowers are removed and replaced with two variable frequency centrifugal fans, a set of calcium sulfite concentration tester 7 and dissolved oxygen meter 9 are added, the slurry is introduced two meters below the overflow port of the desulfurization absorption tower 4, introduced into a cyclone of the gypsum slurry cyclone 12 through the slurry pump 11, the overflow port of the gypsum slurry cyclone 12 is separately introduced into the newly added clarifier 13 or clarifier tank, the dissolved oxygen meter 9 is installed in the clarifier 13 or clarifier tank, the signals of the flow of the raw flue gas 6, the concentration of sulfur dioxide in the raw flue gas 6 and the oxidation air utilization rate are input into the PLC control system of the variable frequency centrifugal fan, the concentration value of calcium sulfite and the dissolved oxygen concentration value obtained online in real time are combined to determine the output frequency of the variable frequency centrifugal fan. The oxidation air pipe 3 is additionally provided with a primary air breaking structure 14 and a secondary air breaking structure 15. According to the scheme of the application, after the reform is completed, the power consumption of a single variable frequency centrifugal fan is reduced to 165kWh / h, the power consumption of two variable frequency centrifugal fans is 330kWh / h, the power consumption is reduced by more than 35%, the plant power rate is significantly reduced, and the blockage of the oxidation air pipe 3 is also obviously alleviated.

[0043] Although the embodiments of the application are described in conjunction with the drawings, various modifications and changes can be made by those skilled in the art without departing from the spirit and scope of the application, and such modifications and changes fall within the scope defined by the appended claims.

Claims

1. An oxidation fan system, characterized in that, include: The variable frequency centrifugal fan unit inputs oxidation air into the slurry pool (5) at the bottom of the desulfurization absorption tower (4) through the oxidation air duct (3); firstly, the oxidation air demand is determined based on the flow rate of the original flue gas (6) input into the desulfurization absorption tower (4), the concentration of sulfur dioxide in the original flue gas (6), and the oxidation air utilization rate; then, the initial output frequency of the variable frequency centrifugal fan unit is determined based on the oxidation air demand. The calcium sulfite concentration tester (7) is connected to the frequency converter centrifugal fan unit. The calcium sulfite concentration tester (7) is adapted to take a sample from the first sampling port (8) of the slurry tank (5) to obtain the concentration value of calcium sulfite. Dissolved oxygen meter (9) is connected to the variable frequency centrifugal fan unit. The dissolved oxygen meter (9) is adapted to take a sample from the second sampling port (10) of the slurry tank (5) to obtain the dissolved oxygen concentration value. The oxidation fan system is adapted to reduce the output frequency of the variable frequency centrifugal fan unit to decrease the amount of oxidation air when the concentration of calcium sulfite is ≤0.01mmol / L and the dissolved oxygen concentration is >0.6mg / L; or to increase the output frequency of the variable frequency centrifugal fan unit to increase the amount of oxidation air when the concentration of calcium sulfite is ≤0.01mmol / L and the dissolved oxygen concentration is <0.6mg / L; or to maintain the output frequency of the variable frequency centrifugal fan unit when the concentration of calcium sulfite is ≤0.01mmol / L and the dissolved oxygen concentration is 0.6mg / L. Also includes: A slurry pump (11) is connected at one end to the second sampling port (10); A gypsum slurry hydrocyclone (12) is connected at one end to the other end of the slurry pump (11); The clarification tank (13) is connected at one end to the overflow port of the gypsum slurry hydrocyclone (12); the clarification tank (13) is also connected to the dissolved oxygen meter (9); The slurry at the bottom of the gypsum slurry hydrocyclone (12) is returned to the desulfurization absorption tower (4) through the trench (22) and the pit pump; Also includes: A primary air-breaking structure (14) is provided with multiple nozzle assemblies at intervals in the portion of the oxidation air duct (3) located within the slurry pool (5); the nozzle assemblies are adapted to spray oxidation air downwards; the primary air-breaking structure (14) is provided below each nozzle assembly; the primary air-breaking structure (14) is adapted to break up the oxidation air sprayed by the nozzle assembly in one step. A secondary air crushing structure (15) is disposed above the portion of the oxidation air duct (3) located inside the slurry tank (5); the secondary air crushing structure (15) is adapted to crush the rising oxidation air in a secondary manner.

2. The oxidation blower system according to claim 1, characterized in that, The first sampling port (8) is located below the oxidation air duct (3), and the second sampling port (10) is located above the oxidation air duct (3).

3. The oxidation blower system according to claim 1, characterized in that, The primary air-breaking structure (14) includes: Two first perforated plates (16) set at an angle are connected to the oxidation air duct (3) via a first connector, and the nozzle assembly is located inside the angle.

4. The oxidation blower system according to claim 3, characterized in that, The included angle is 90 degrees.

5. The oxidation blower system according to claim 3, characterized in that, The secondary air-breaking structure (15) includes: The horizontally arranged second perforated plate (17) is connected to the oxidation duct (3) via a second connector.

6. The oxidation blower system according to claim 5, characterized in that, The first connector consists of two first stiffening plates (18), and the two first perforated plates (16) are connected to the oxidation duct (3) through the first stiffening plates (18); the second connector consists of three second stiffening plates (19) arranged at an angle.

7. The oxidation blower system according to claim 1, characterized in that, The nozzle assembly includes: The first nozzle (20) is set downward in the vertical direction; The second nozzle (21) is set vertically downward, and the length of the second nozzle (21) is greater than the length of the first nozzle (20).

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