JP2000233409A - Apparatus for processing waste plastic metal composite material - Google Patents

Abstract

PROBLEM TO BE SOLVED: To improve energy efficiency and to improve quality of recovered plastics. SOLUTION: An apparatus for processing a waste plastic metal composite material is provided with a melting oven main body 1 with a melting tank 2 heated at a specified temp. and a metal net basket 4 made to come in and out of the melting tank 2. A heating means for the melting tank 2 is a heat exchanger 3 which uses an oil with a little higher condensing temp. than the temp. where a plastic of a composite material A flows as a heat transfer medium and utilizes its latent heat. By immersing and heating the waste plastic metal composite material A in a melting tank 2 filled with a melted plastic P, the waste plastic metal composite material A is separated into the melted plastic P and metals remaining in the metal net basket 4 and is recovered.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a waste plastic / metal composite material treating apparatus for recovering valuable resources from waste of a composite material composed of a thermoplastic and a metal.

[0002]

2. Description of the Related Art Thermoplastics such as polyethylene, polystyrene, and vinyl chloride are widely used as molded products in which metals are embedded. For example, a nichrome wire, brass or brass is used inside a polyethylene pipe joint body. 2. Description of the Related Art Seismic pipe fittings in which a heating element composed of a coil or the like and a power connection terminal are embedded are known. In the case of such a molded product, a defective molded product is generated at a certain rate, and it is necessary to collect and reuse the molded product. Even if a composite material of a thermoplastic such as polyethylene or polypropylene and a metal is directly incinerated in a normal incinerator and the remaining valuable metal is to be recovered, the metal surface is deteriorated by oxidation, and the metal is re-used as it is. It is difficult to use. Moreover, since thermoplastics are easily plastically deformed as they are, it is difficult to crush or crush them. In order to solve such a problem, a spiral heat source conduit (4) is used as shown in FIG.
A melting furnace (41) around which 2) is wound, a wire mesh basket (43) that is moved into and out of the melting furnace (41), and a boiler (44) that generates steam supplied to a heat source conduit (42). A combustion furnace (45) for generating a combustion gas for heating the heat source conduit (42), and a waste plastic metal composite in the melting furnace (41) using superheated steam (47) blown out from the heat source conduit (42) as a heat source. The material (A) is heated in the absence of oxygen, and the plastic (P) that melts and falls from the wire mesh basket (43) is guided to the cooling water tank (46) for recovery, and remains in the wire mesh basket (43). There has been proposed an apparatus for treating a waste plastic-metal composite material that also collects waste metal.

According to the waste plastic metal composite material treating apparatus, a wire mesh basket (43) containing a waste plastic metal composite material (A) is put into a melting furnace (41) (initial charging), and a heat source conduit ( By spraying the superheated steam (47) from (42) onto the waste plastic metal composite (A), the plastic is melted and collected in the cooling water tank (46). Further, the waste plastic metal composite (A) is additionally charged from the additional inlet (48) provided in the melting furnace (41), and when a predetermined amount of the waste plastic metal composite (A) has been treated, the wire mesh is finished. Melting basket (43)
The metal in the non-oxidized state is recovered from (41). By heating the composite material of the thermoplastic and the metal in this manner, the valuable metal and the thermoplastic which constitute the composite material can be separated and recovered in a reusable form.

[0004]

The above-mentioned conventional waste plastic / metal composite material treating apparatus has the following problems.

Along with the progress of the process, the waste plastic metal composite is deformed and the heat transfer area is reduced, and the distribution of the melting rate occurs in the object layer, and the previously melted plastic flows down. A steam blow-through phenomenon occurs, or a drift occurs in which the steam passes only through a portion having low resistance. Therefore, the heat transfer to the processing object layer becomes extremely poor, and the heat transfer speed decreases. If the temperature of the steam is increased to maintain a constant heat transfer rate, a part of the plastic is decomposed to generate flammable gas, and the quality of the recovered plastic is deteriorated.

When melting plastic having a flow temperature of 300 ° C. or more, such as polyethylene, the superheated steam of the heating source is not advantageous as a heat transfer medium because latent heat cannot be used because only the sensible heat is used. Further, when the waste plastic metal composite at room temperature is additionally charged, the steam is cooled and condensed on the surface thereof, so that an energy loss of re-evaporating the condensed water with superheated steam also occurs.

[0007] Since the metals separated from the composite material remain in the wire mesh basket, a large amount of metal deposits on the bottom of the wire mesh basket when the processing amount increases, and it becomes difficult for the molten plastic to pass through the wire mesh basket.

The present invention provides a waste plastic metal composite processing apparatus for separating valuable metals and thermoplastics constituting a composite material and recovering them in a form that can be reused. An object of the present invention is to improve the quality of plastics to be used and to significantly improve operability.

[0009]

SUMMARY OF THE INVENTION An apparatus for treating a waste plastic metal composite according to the present invention includes a melting furnace body having a melting tank heated to a predetermined temperature, and a wire mesh basket moved into and out of the melting tank. The waste plastic metal composite is immersed in a melting tank filled with molten plastic and heated, so that the waste plastic metal composite is separated and recovered into molten plastic and metals remaining in the wire mesh basket. Things.

According to the waste plastic metal composite processing apparatus, as an initial stage, a wire mesh basket containing the waste plastic metal composite is placed in a melting tank, and the melting tank is heated to a predetermined temperature. Thereby, the plastic of the composite material is melted, and a molten plastic layer is formed in the melting tank. In this state, when the waste plastic metal composite is put into the melting tank, the waste plastic metal composite is immersed in the molten plastic and heated by the heat transfer from now on.

It is preferable that the melting tank is provided with an overflow port through which the molten plastic overflows. In this way, the molten plastic can be taken out without passing through the gaps of the metals remaining in the wire mesh basket.

[0012] It is preferable that the apparatus further comprises a heat retention tank which is in communication with the melting tank via a conduit and temporarily stores the molten plastic in the melting tank when taking out the metals in the wire mesh basket. In this way, when it is necessary to open the melting furnace body, for example, when collecting metals, the molten plastic is temporarily stored in a heat retaining tank to prevent generation of plastic decomposition gas in the melting furnace body. Can be kept.

[0013] The heating means of the melting tank is preferably a heat exchanger that uses the latent heat of an oil having a condensation temperature slightly higher than the temperature at which the plastic of the composite material flows as a heat medium. By doing so, the energy given to the melting tank from the heat medium can be increased.

The heating means for the heat retaining tank is a heat exchanger using the same heat medium oil as the heat exchanger for heating the melting tank, and is one of the heat exchanger for heating the melting tank and the heat exchanger for heating the heat retaining tank. It is preferable to provide a heat medium oil switching pipe for sending the heat medium oil to the pipe. In this case, the heat medium oil can be supplied to the two heat exchangers by one heat medium oil boiler.

It is preferable that a heating means different from the heat exchanger is provided as a heating means for the heat retaining tank. As another heating means for the heat retaining tank, for example, an electric heater is used.

The apparatus further comprises a heating tank pressurizing means,
It is preferable that the molten plastic in the heat retaining tank can flow back to the melting tank via a conduit by pressurizing the heat retaining tank. As the heating tank pressurizing means,
For example, a compressor is used. By using the heating tank pressurizing means, the molten plastic stored in the heating tank is quickly and easily returned to the melting tank.

It is preferable that the apparatus further comprises explosion-proof gas introducing means for introducing the explosion-proof gas into the melting furnace body. As the explosion-proof gas, an inert gas or water vapor supplied from a gas cylinder is used. By doing so, the oxygen content of the atmospheric gas in the melting furnace body is reduced, and safety is improved.

In order to operate the waste plastic metal composite material treating apparatus, it is preferable that when the operation is stopped for a long time, the plastic cooled and solidified in the heat retaining tank is melted again to restart the operation. Holding the temperature in the heat retaining tank at a temperature 30 to 50 ° C. lower than the temperature in the melting tank,
It is preferable to suppress generation of plastic decomposition gas in the heat retaining tank.

[0019]

Embodiments of the present invention will be described below with reference to the drawings.

FIG. 1 shows a first embodiment of an apparatus for treating a waste plastic metal composite according to the present invention.

As shown in FIG. 1, a waste plastic metal composite processing apparatus includes a melting furnace body (1) having a melting tank (2).
And a heating device (3) for heating the melting tank (2), and a hoist
A wire mesh basket (4) which is moved up and down by (5) to be moved into and out of the melting tank (2).

The melting furnace body (1) has an openable / closable upper lid (6).
Is provided, and by opening this upper lid (6),
Metals remaining in the wire mesh basket (4) can be taken out. In addition, the melting furnace body (1) has an inlet with an air shutoff mechanism for adding waste plastic metal composite (A).
(7) is provided. An explosion-proof inert gas is supplied into the melting furnace body (1) from an inert gas cylinder (8), and the gas in the melting furnace body (1) is exhausted from a nozzle (9).

The melting tank (2) is of the overflow type, and the overflowed molten plastic is guided from the overflow port (2a) to the cooling tank (10) and collected.

The melting tank heating device (3) is an indirect heat exchanger, in which oil is used as a heat medium. The heat medium oil has a condensation temperature slightly higher than the temperature at which the plastic flows, and the heat exchanger for heating the melting tank (3) uses the latent heat of the heat medium oil. When the plastic is polyethylene, the heating condition is 380 to 420 ° C., and as the heat medium oil, one having a condensing temperature slightly lower than this temperature, for example, Nippon Steel Chemical “Therms 300” is used. Oil vapor is obtained by heating the heat medium oil in a liquid phase in a heat medium oil boiler (11), and the heating source is generated by the combustion of a burner (13) provided in a combustion furnace (12). Combustion gas is used. The combustion furnace (12) is provided with a chimney (14) for discharging flue gas.

A heat-retaining heat exchanger (15) is provided at the outlet of the melting tank (2) so that the overflowed molten plastic does not solidify before being guided to the cooling tank (10).
The heat medium oil vapor obtained in the heat medium oil boiler (11) passes through the heat insulation heat exchanger (15) and is introduced into the melting tank heating heat exchanger (3). It is condensed in (3) and returned to the heat medium oil boiler (11).

According to the waste plastic metal composite processing apparatus of the first embodiment, the waste plastic metal composite
The wire mesh basket (4) containing (A) is initially filled into the melting tank (2) and heated by the heating device (3) to a temperature higher than the flowing temperature of the plastic, whereby the plastic is melted. After all the plastic components of the initially filled composite material (A) have melted, additional waste plastic metal composite material (A) is added from the additional inlet (7) of the melting furnace body (1). It is immersed in the already melted plastic (P) and is heated and melted by the heat transfer from the melted plastic (P).
When the amount of the molten plastic (P) increases and exceeds a predetermined value, the molten plastic (P) overflows from the overflow port (2a) and is guided to the cooling tank (10) where it is cooled and solidified and collected as a product. The inside of the melting furnace body (1) is maintained in a low oxygen concentration atmosphere by an inert gas supplied from an inert gas cylinder (8). In this way, the waste plastic metal composite (A) is heated substantially in the absence of oxygen, the plastic whose hardness has been increased by partial pyrolysis is recovered, and the non-oxidized metals separated from the plastic are removed. After a certain period of time or a certain amount of treatment is completed, the wire mesh basket (4) containing the metals is lifted up above the melting tank (2),
Heating is stopped. Then, after the temperature of the molten plastic (P) becomes lower than a predetermined temperature, the upper lid (6) is opened to collect metals. Cooling the molten plastic (P) to a predetermined temperature is because if the plastic is heated to 300 ° C or more, the plastic partially decomposes and flammable gas is generated, and opening the melting furnace body (1) in this state is dangerous. Because there is. In the next operation, the solidified plastic filled in the melting tank (2) is heated and melted, and then the waste plastic metal composite (A) is added.

FIG. 2 shows a second embodiment of the waste plastic metal composite material treating apparatus according to the present invention. In the following description, the same components as those of the first embodiment are denoted by the same reference numerals, and description thereof is omitted.

The waste plastic metal composite processing apparatus according to the second embodiment is different from the waste plastic metal composite processing apparatus according to the first embodiment in that the tank is kept in communication with the melting tank (2) via a vertical conduit (22). (21) and a heat retaining tank pressurizing means (23). The heat retaining tank (21) is for temporarily storing the molten plastic (P) in the melting tank (2) when removing the metals in the wire mesh basket (4). Heating tank pressurizing means
(23) is for pressurizing the heat retaining tank (21) to cause the molten plastic (P) stored in the heat retaining tank (21) to flow back to the melting tank (2).

The heat retaining tank (21) contains molten plastic.
An air vent valve (24) is provided which is opened when (P) is introduced. The lower end of the vertical conduit (22) is
It is located slightly above the bottom of 1), and a conduit opening / closing valve (22a) is provided at the upper end thereof. By opening the air vent valve (24) and opening the conduit opening / closing valve (22a), the molten plastic (P) in the melting tank (2) can be introduced into the heat retaining tank (21).

The heat retaining tank (21) further includes a heat retaining tank.
(21) A heat exchanger (heating means) (25) for heating the whole is provided. This heat exchanger (25) is a heat exchanger for heating the melting tank.
Uses the same heat medium oil as (3), and switches the heat medium oil to send the heat medium oil to either the heat exchanger for heating the melting tank (3) or the heat exchanger for heating the holding tank (25). Piping (2
6) is provided.

The heat medium oil switching pipe (26) includes an extraction pipe (27) for extracting heat medium oil vapor from the heat medium oil boiler (11),
A heat medium introduction pipe (28) for heating the melting tank which branches from the discharge pipe (27) to the heat exchanger (15) for heat retention, and a heat exchanger (25) for heating the heat retention tank which branches off from the discharge pipe (27). ), And a return pipe (30) for returning the heat medium oil discharged from the melting tank heating heat exchanger (3) to the heat medium oil boiler (11), Heat medium discharge pipe (31) for joining the heat medium oil discharged from the heat tank heat exchanger (25) to the return pipe (30), and heat medium introduction pipe (28) for heating the melting tank It comprises a first valve (31) provided in the middle and a second valve (32) provided in the middle of the heating medium introducing pipe (29) for heating the heat retaining tank. By opening the first valve (31) and closing the second valve (32), the heat medium oil vapor from the heat medium oil boiler (11) is supplied to the extraction pipe (27) and the heat medium for heating the melting tank. After passing through the pipe (28), the heat exchanger (15) for keeping heat and the heat exchanger (3) for heating the melting tank, it is returned to the heat medium oil boiler (11) by the return pipe (30). Further, by closing the first valve (31) and opening the second valve (32), the heat medium oil vapor from the heat medium oil boiler (11)
The liquid is returned to the heat medium oil boiler (11) by the return pipe (30) through the take-out pipe (27), the heat medium heating pipe for heat retaining tank heating (29), and the heat exchanger for heat retaining tank heating (25).

The heating tank pressurizing means (23) includes a compressor
(33) or a cylinder (34), a gas conduit (35) for sending compressed air from the compressor (33) or inert gas from the cylinder (34) to the heat retaining tank (21), and a gas conduit. (3
5) Consists of a third valve (36) provided on the way. To return the molten plastic (P) stored in the heat retaining tank (21) to the melting tank (2), use the conduit opening / closing valve of the vertical conduit (22).
Open (22a), close air release valve (24), third valve (36)
Compressed air or inert gas can be sent from the pressure source into the heat retaining tank (21) by applying pressure to the surface of the molten plastic (P). Melting tank (2) through vertical conduit (22)
Will be returned within.

Although not shown, a heating means other than a heat exchanger such as an electric heater can be appropriately provided as a heating means for the heat retaining tank.

According to the waste plastic metal composite processing apparatus of the second embodiment, the waste plastic metal composite
The wire mesh basket (4) containing (A) is initially filled into the melting tank (2) and heated by the heating device (3) to a temperature higher than the flowing temperature of the plastic, whereby the plastic is melted. After all the plastic components of the initially filled composite material (A) have melted, additional waste plastic metal composite material (A) is added from the additional inlet (7) of the melting furnace body (1). It is immersed in the already melted plastic (P) and is heated and melted by the heat transfer from the melted plastic (P).
When the amount of the molten plastic (P) increases and exceeds a predetermined value, the molten plastic (P) overflows from the overflow port (2a) and is guided to the cooling tank (10) where it is cooled and solidified and collected as a product. The inside of the melting furnace body (1) is maintained in a low oxygen concentration atmosphere by an inert gas supplied from an inert gas cylinder (8). In this way, the waste plastic metal composite (A) is heated substantially in the absence of oxygen, the plastic whose hardness has been increased by partial pyrolysis is recovered, and the non-oxidized metals separated from the plastic are removed. After a certain period of time or a certain amount of collection is completed, both the air bleed valve (24) and the conduit opening / closing valve (22a) are opened, and the molten plastic (P) in the melting tank (2) is removed from the vertical conduit. It flows down into the heat retention tank (21) through (22). Then
Conduit opening / closing valve (22a) and heat medium introduction pipe for melting tank heating
(28) The first valve (31) provided on the way is closed together,
As a result, the heating of the melting tank (2) is stopped and the melting tank (2) is stopped.
Is cooled. At this time, since there is no molten plastic (P) in the melting tank (2), no dangerous gas is generated in the melting furnace body (1). At the same time, the second valve (32) provided in the middle of the heat retaining tank heating heat medium introduction pipe (29) is opened, whereby the heat retaining tank (21) is heated. After the melting tank (2) has cooled down to some extent, the metal mesh basket (4) containing the metals is lifted above the melting tank (2), and the upper lid (6) is opened to collect the metals. The molten plastic (P) in the heat retaining tank (21) is supplied with heat corresponding to the heat loss from the heat exchanger for heating the heat retaining tank (25), and is maintained in a liquid state. When the next operation is started, the air release valve (24) is closed, and the conduit opening / closing valve (22a) and the third valve (36) in the middle of the gas conduit (35) are both opened. The molten plastic (P) flows back into the melting vessel (2) through the vertical conduit (22). As a result, the inside of the melting tank (2) is filled with the molten plastic (P), and thereafter, the melting tank (2)
The required treatment proceeds only by adding the waste plastic metal composite (A) while heating the wastewater.

When the operation is restarted from the state where the molten plastic (P) in the heat retaining tank (21) is solidified due to the stoppage of the heat medium oil boiler (11), the solidified plastic in the heat insulating tank (21) is re-started. You can start by heating. First
In the embodiment, the heat exchanger (3) for heating the melting tank has a heat transfer section provided at a lower portion or a side wall of the melting tank (2) in order to secure a space for the wire mesh basket (4). ,
When melting the solidified plastic in the melting tank (2),
Although it takes time to completely melt the melting tank (2) because it cannot be heated as a whole, in the second embodiment, it is not necessary to secure such a space in the heat retaining tank (21), (21) The whole can be heated, and the time until complete melting can be shortened.

[0036]

According to the waste plastic metal composite processing apparatus of the present invention, the waste plastic metal composite is not heated by superheated steam but is immersed in the molten plastic and heated by the heat transfer from now on. Therefore, even if the object to be processed is deformed by heating, blow-through and drift are not generated as in the case of steam heating, so that heat transfer conditions do not decrease during processing.

In the case where the molten plastic overflows, the molten plastic is taken out of the melting tank through a path which does not come into contact with the metals which have already been separated, so that even if the processing amount is increased, there is no adverse effect on the removal of the molten plastic.

[0038] In the case where the heating tank is provided for temporarily storing the molten plastic in the melting tank when removing the metals in the wire mesh basket, the solidified plastic is heated when the operation is stopped and then restarted. Energy does not need to be melted. In addition, since there is no flammable gas generated by eliminating the molten plastic inside the melting furnace body, there is no need to wait for the melting furnace body to open until the melting plastic temperature drops, from the end of heating to the removal of metals. Time is greatly reduced.

In the case where the heating means of the melting tank is a heat exchanger using oil having a condensation temperature slightly higher than the temperature at which the plastic flows as a heat medium and utilizing the latent heat thereof, the latent heat of condensation can be utilized. Energy efficiency is better than that using sensible heat when steam goes from high temperature to low temperature. Moreover, since the upper limit of the heat source temperature is set, generation of decomposition gas is suppressed, and the quality of the recovered plastic is improved.

[Brief description of the drawings]

FIG. 1 is a view showing a first embodiment of a waste plastic metal composite material treating apparatus according to the present invention.

FIG. 2 is a view showing a second embodiment of the waste plastic metal composite material treating apparatus according to the present invention.

FIG. 3 is a view showing a conventional waste plastic metal composite material processing apparatus.

[Explanation of symbols]

 (1) Melting furnace body (2) Melting tank (2a) Overflow port (3) Heat exchanger (melting tank heating means) (4) Wire mesh basket (8) Explosion-proof gas introducing means (21) Heat insulation tank (22) Pipe (23) Heating tank pressurizing means (25) Heat exchanger (heating tank heating means) (26) Heat medium oil switching pipe (A) Waste plastic metal composite (P) Molten plastic

 ──────────────────────────────────────────────────続 き Continuing on the front page (72) Yoshio Fujimoto, Inventor 1-7-89, Minamikohoku, Suminoe-ku, Osaka-shi Inside Tachibashi Shipbuilding Co., Ltd. (72) Inventor Michitaka Kobayashi 1-7-89, Minamikohoku, Suminoe-ku, Osaka-shi No. Date T-Shipbuilding Co., Ltd. F-term (reference) 4D004 AA07 AA21 BA05 BA07 CA22 CA29 CB32 CB50 CC01 CC03 DA02 DA03 DA06 4F301 AA13 AA14 AC08 AC12 AD02 BA01 BA02 BA21 BA29 BF10 BF15 BF31

Claims (14)

[Claims] A melting furnace body (1) having a melting tank (2) heated to a predetermined temperature, and a wire mesh basket (4) to be moved into and out of the melting tank (2). The waste plastic metal composite (A) is placed in the melting tank (2) filled with
The waste plastic metal composite (A) is separated and recovered by melting and heating the waste plastic metal composite (A) into the molten plastic (P) and the metals remaining in the wire mesh basket (4). Processing equipment. 2. The waste plastic metal composite treating apparatus according to claim 1, wherein an overflow port (2a) for overflowing the molten plastic (P) is provided in the melting tank (2). waste 3. The molten plastic (P) in the melting tank (2), which is in communication with the melting tank (2) through a conduit (22) and removes metals in the wire mesh basket (4). 3. The apparatus according to claim 1, further comprising a heat storage tank for temporarily storing the heat.
An apparatus for treating a waste plastic metal composite according to the above. The heating means for the melting tank (2) is a heat exchanger (3) utilizing an oil having a condensation temperature slightly higher than a temperature at which the plastic of the composite material (A) flows as a heat medium and utilizing its latent heat.
The waste plastic metal composite treating apparatus according to claim 1, wherein: 5. The heating means of the heat retaining tank (21) is a heat exchanger (2) using the same heat medium oil as the heat exchanger (3) for heating the melting tank.
5), and a heat medium oil switching pipe (26) for feeding the heat medium oil is provided to one of the heat exchanger for heating the melting tank (3) and the heat exchanger for heating the heat retaining tank (25). The waste plastic metal composite treating apparatus according to claim 4. 6. An apparatus for treating a waste plastic metal composite according to claim 5, wherein a heating means different from the heat exchanger is provided as a heating means for the heat retaining tank. 7. The apparatus for treating a waste plastic metal composite according to claim 6, wherein another heating means for the heat retaining tank is an electric heater. 8. A heating tank pressurizing means (23) is further provided. By pressurizing the inside of the heating tank (21), the molten plastic (P) in the heating tank (21) is connected via a conduit (22). The apparatus for treating a waste plastic metal composite according to any one of claims 3 to 7, wherein the apparatus is capable of flowing back to the melting tank (2). 9. The apparatus for treating a waste plastic metal composite according to claim 8, wherein the heat retaining tank pressurizing means (23) is a compressor. 10. The apparatus for treating a waste plastic metal composite according to claim 1, further comprising an explosion-proof gas introducing means (8) for introducing an explosion-proof gas into the melting furnace body (1). 11. The processing apparatus for waste plastic metal composite according to claim 10, wherein the explosion-proof gas is an inert gas supplied from a gas cylinder. 12. The explosion-proof gas is water vapor.
An apparatus for treating a waste plastic metal composite according to the above. 13. A method for operating a waste plastic metal composite material treating apparatus according to claim 3, wherein when the operation is stopped for a long time, the plastic cooled and solidified in the heat retaining tank (21) is removed. An operation method characterized by re-melting and restarting operation. 14. A method for operating a waste plastic metal composite material treating apparatus according to claim 3, wherein the temperature in the heat retaining tank (21) is 30 to 50 ° C. lower than the temperature in the melting tank (2).
An operation method comprising maintaining a low temperature to suppress generation of plastic decomposition gas in a heat retaining tank (21).