JP3548736B2 - Backwashing method of separation membrane - Google Patents

Description

[0001]
TECHNICAL FIELD OF THE INVENTION
The present invention relates to a method for backwashing a separation membrane for membrane-separating a fluid to be treated.
[0002]
[Prior art]
Filtration treatment by membrane separation is widely used for purification treatment of a fluid to be treated (liquid to be treated, water to be treated) containing solid matter, particulate matter, etc., various solid-liquid separation, liquid-liquid separation, etc. Various separation membranes are applied according to the filtration accuracy (filter size). Examples of the separation membrane include a microfiltration (MF) membrane, an ultrafiltration (UF) membrane, a nanofiltration (NF) membrane, and a reverse osmosis (RO) membrane.
[0003]
In such membrane separation, in order to maintain good membrane separation performance, that is, filtration performance, for a long period of time, solids and the like, which are filtration residues adhered or deposited on the separation membrane surface, are appropriately washed. In recent years, in the purification treatment, further improvement of the water quality of the treated liquid (purified water, etc.) has been desired, and in order to cope with this, the filtration performance of the separation membrane or the entire membrane module is maintained sufficiently low to maintain the filtration performance. The importance of membrane cleaning has been further increased in order to maintain good results.
[0004]
By the way, the properties and shapes of these separation membranes vary widely depending on the application, and in particular, in a purification treatment in which a large amount of a fluid to be treated is continuously separated while biological treatment is performed, for example, a plurality of membrane elements are used. In many cases, collectively arranged membrane modules are provided in multiple stages. In particular, those using a hollow fiber membrane as the form of the separation membrane are various types of solid-liquid separation, liquid-liquid separation, and gas-liquid separation from the viewpoint of simple equipment configuration, high volumetric efficiency, and excellent operability. It is heavily used for
[0005]
Such a hollow fiber membrane is generally used as a hollow fiber membrane module in which a large number of hollow fiber membrane elements are bundled, and as a filtration method, an internal pressure type in which a fluid to be treated is supplied from the inside of the hollow fiber, and There is an external pressure type in which the fluid to be treated is supplied from outside the hollow fiber. As a membrane cleaning method, a backwash with a liquid (cleaning liquid) or gas is generally used.
[0006]
[Problems to be solved by the invention]
However, in the case of membrane cleaning by general backwashing of a membrane separation device or a membrane filter using a hollow fiber membrane module, it may be difficult to achieve a further improvement in the cleaning effect as described above. In particular, when a fine pore having a smaller pore size at the membrane surface is used in accordance with the minimization of the filtration size, blockage of the fine pores by the filtration residue such as solid content becomes remarkable, and therefore, a function having a particularly high filtration accuracy is used. It has been desired to further improve the washing efficiency when the membrane is used as a hollow fiber membrane.
[0007]
Therefore, the present invention has been made in view of such circumstances, and when backwashing the separation membrane of the fluid to be treated, the separation efficiency of the separation membrane can be significantly improved as compared with the related art. It is intended to provide a backwash method.
[0008]
[Means for Solving the Problems]
In order to solve the above-mentioned problem, a method for backwashing a separation membrane according to the present invention is a method for membrane-separating a fluid to be treated, wherein a cleaning liquid is applied to the separation membrane from a permeation side in a flow direction of the fluid to be treated. By supplying and reducing the pressure on the non-permeate side of the separation membrane in the flow direction of the fluid to be treated to a predetermined pressure, the boiling state of the cleaning liquid is caused on the membrane surface of the separation membrane on the non-permeate side. Features.
[0009]
Here, as the “separation membrane” in the present invention, the type, properties, shape, etc. of the membrane are not limited as long as it is a separation membrane to which backwashing can be applied. From the viewpoint of reducing the pressure on the permeation side, it is suitable for those used in a form capable of performing membrane separation (membrane filtration) under a positive pressure or a negative pressure. For example, preferably, a hollow membrane element having a tubular or tubular shape is preferred. And more preferably a hollow fiber membrane.
[0010]
Further, the “non-permeate side” means a side to which the fluid to be treated is supplied to the separation membrane, and the “permeate side” means that the fluid to be treated that has been subjected to membrane separation, that is, the processed fluid is discharged as a permeate. The side that is being done. Specifically, taking a hollow fiber membrane as an example, when the membrane separation is performed by an internal pressure method, the “non-permeate side” is inside the hollow fiber membrane while the “permeate side” is the hollow fiber When the membrane is separated by an external pressure method outside the membrane, the “non-permeate side” is outside the hollow fiber membrane, whereas the “permeate side” is inside the hollow fiber membrane.
[0011]
In such a separation membrane, a filtration residue such as a solid content usually adheres and accumulates on the membrane surface on the non-permeate side (side on which the fluid to be treated is supplied) as the membrane separation proceeds, and the separation membrane The micropores are closed and the filtration resistance increases. When the backwashing method of the present invention is applied to this separation membrane, and the cleaning liquid is supplied from the permeation side (the side from which the treated fluid is discharged) to the separation membrane, the cleaning liquid flows along the membrane separation direction. It flows into the micropores of the separation membrane from the opposite direction, and comes into contact with the deposits closing the micropores or the deposits or deposits on the non-permeation side membrane surface (hereinafter collectively referred to as “deposits”). I do.
[0012]
At this time, when the pressure on the non-permeate side of the separation membrane is reduced so that the pressure on the non-permeate side becomes a predetermined pressure, a boiling state of the cleaning liquid that has reached the non-permeate side membrane surface through the micropores can be generated. Specifically, by setting the predetermined pressure on the non-permeate side to a value equal to or lower than the saturated vapor pressure (hereinafter, simply referred to as “vapor pressure”) at the temperature of the cleaning liquid, the cleaning liquid boils and vaporizes, A type of explosion occurs due to expansion. As a result, the deposit on the film surface is crushed and separated from the film surface so as to be ejected to the non-permeation side.
[0013]
Further, it is preferable to adjust the reduced pressure amount on the non-permeation side so that a boiling state of the cleaning liquid is generated according to the type of the cleaning liquid. As the washing liquid, water, organic solvents such as alcohols, inorganic solvents such as acids and alkalis can be appropriately selected and used at various concentrations and the like, and various additives such as surfactants can be used. Can be added. Different types of cleaning liquids have different vapor pressures even at the same temperature. Therefore, by adjusting the pressure reduction amount on the non-permeate side according to the type (including properties, concentration, etc.) of the cleaning liquid to be used, the non-permeate side is adjusted. Can be appropriately controlled to a required vapor pressure.
[0014]
Further, among the cleaning liquids listed above, it is more preferable to use water or alcohols from the viewpoints of handleability, safety, prevention of cross-contamination of the treated fluid, and in particular, the number of carbon atoms in the molecule. When an alcohol (lower alcohol) having a relatively small amount, such as methanol (CH ₃ OH) or ethanol (C ₂ H ₅ OH), is used, the vapor pressure is higher than that of water at the same temperature, and the reduced pressure is relatively small. Since only a small amount is required, it is useful in that power costs can be reduced.
[0015]
Furthermore, the first space region in which the membrane surface portion on the non-transmission side abuts and the second space region having a second pressure smaller than the first pressure in the first space region communicate with each other. It is preferable to reduce the pressure in the first space region so that the non-transmission side has a predetermined pressure.
[0016]
With this configuration, for example, the second space region is previously reduced in pressure to a second pressure smaller than the first pressure, and when the first space region and the second space region communicate with each other in this state, The first pressure in the first space region drops sharply. At this time, if the volume of the second space region is made sufficiently large as compared with the first space region and / or the second pressure is made a sufficiently low value as compared with the first pressure, The pressure change in the first space region becomes steeper. This makes it possible to instantaneously reduce the pressure around the membrane surface portion in contact with the first space region from the first pressure (for example, normal pressure) to the vapor pressure of the cleaning liquid. Explosion state can be generated strongly in a short time. Therefore, the effect of removing and removing the deposits and the volume on the film surface portion is further enhanced.
[0017]
Here, as an apparatus for effectively performing the separation membrane backwashing method according to the present invention, for example, a separation membrane backwashing apparatus for membrane-separating a fluid to be treated, and the fluid to be treated with respect to the separation membrane is used. The cleaning liquid supply unit connected to the permeation side in the flow direction of the liquid to be filtered is connected to the non-permeation side in the flow direction of the fluid to be treated with respect to the separation membrane, and the non-permeation side is kept at a predetermined pressure. And a pressure reducing unit for reducing the pressure on the side. More specifically, the decompression unit is connected to the first space region where the membrane surface portion of the separation membrane abuts on the non-permeate side, and is smaller than the first pressure in the first space region. Suitably, it comprises a container comprising a second spatial region having a pressure of 2.
[0018]
BEST MODE FOR CARRYING OUT THE INVENTION
Hereinafter, embodiments of the present invention will be described in detail. Note that the same components are denoted by the same reference numerals, and redundant description will be omitted. Unless otherwise specified, the positional relationship such as up, down, left, and right is based on the positional relationship shown in the drawings. The dimensional ratios in the drawings are not limited to the illustrated ratios.
[0019]
FIGS. 1 and 2 are cross-sectional views schematically showing a configuration of a preferred embodiment of an apparatus for carrying out a method for backwashing a separation membrane according to the present invention, and FIG. FIG. 2 shows a state in which a membrane separation process is being performed by the obtained membrane separation apparatus, and FIG. 2 shows a state in which the separation membrane is being backwashed by the backwash apparatus.
[0020]
In the figure, a membrane separation device 10 is an internal pressure type capillary type membrane separation device using a hollow fiber membrane, and a plurality of hollow fiber membrane elements 2 (separation membranes) are arranged in a longitudinal direction in a housing 1. In this case, a membrane module 20 is provided. Above and below the membrane module 20 in the housing 1, the fluid supply section SI and the fluid supply section are respectively connected so as to communicate with the internal space S <b> 1 (first space area, non-permeable side) of the hollow fiber membrane element 2. A processing fluid outlet SO is defined. A supply port N1 to which the fluid to be treated W is supplied is provided on the bottom wall of the housing 1, and the fluid to be treated W is introduced into the fluid supply part SI through the pipe having the pump 3 and the valve V3. On the other hand, the upper wall of the housing 1 is provided with a discharge port N3 through which the fluid W that cannot pass through the membrane wall of the hollow fiber membrane element 2 is discharged as a non-permeable fluid Wh.
[0021]
Further, a supply port N4 to which a cleaning liquid M (see FIG. 2) is supplied is provided on a side wall of the housing 1, and the hollow fiber membrane element 2 in the membrane module 20 is passed through a pipe having a pump 5 and a valve V5. The cleaning liquid M is introduced into the external space S2 (transmission side). Further, a discharge port N2 for discharging the cleaning liquid M is provided on a side wall of the housing 1. This discharge port N2 communicates with the external space S2, and the target fluid W that has passed from the internal space S1 of the hollow fiber membrane element 2 to the external space S2 through the membrane wall into the external space S2 is a permeated fluid Ws (FIG. 1). (See Reference)).
[0022]
The bottom wall of the housing 1 is provided with an outlet N5 that communicates with the internal space S1 of the hollow fiber membrane element 2 via the fluid supply section SI. The discharge port N5 is for discharging the cleaning liquid M or the like that has permeated from the external space S2 of the hollow fiber membrane element 2 through the membrane wall to the internal space S1 to the outside of the housing 1 as a backwash liquid Mm. Further, a pipe having a vacuum tank 6 (container) connected to the vacuum pump 4 and a valve V6 is connected to the discharge port N5. Furthermore, the vacuum chamber 6 has a space part S6 (second space area) that can communicate with the internal space S1 of the hollow fiber membrane element 2 via the pipe and the fluid supply part SI to be treated.
[0023]
As described above, the pump 5, the valve V5, and the supply port N4 constitute a supply section of the cleaning liquid M, and the vacuum pump 4, the valve V6, the vacuum tank 6, and the discharge port N5 constitute a pressure reducing section. Further, a backwashing apparatus for the separation membrane according to the present invention is constituted by the supply section and the pressure reducing section.
[0024]
An example of the membrane separation process using the membrane separation apparatus 10 provided with the separation membrane backwashing apparatus according to the present invention configured as described above, and an example of the separation membrane backwashing method according to the present invention will be described below. First, the pump 3 is operated with the discharge ports N2 and N3 opened and the valves V5 and V6 closed, and the valve V3 is opened at a predetermined opening to supply the fluid W to be processed from the supply port N1. It is introduced into the fluid supply section SI (see FIG. 1). The fluid W to be processed flows into the internal space S1 of the hollow fiber membrane element 2 that communicates with the fluid supply section SI.
[0025]
Here, FIG. 3 is a cross-sectional view schematically showing a main part in a state where the membrane separation is performed by the membrane separation device 10 shown in FIGS. The membrane wall 2a of the hollow fiber membrane element 2 is provided with a large number of micropores P. Of the fluid W to be processed flowing up the internal space S1, the liquid component that has passed through the micropores P is converted into a permeated fluid Ws by the outside. It flows out into the space S2 and is discharged to the outside of the membrane separation device 10 through the discharge port N2. The discharged permeate fluid Ws is subjected to other processing as necessary.
[0026]
On the other hand, the liquid component or solid component of the target fluid W that cannot pass through the micropores P flows up the internal space S1, and finally passes through the target fluid discharge portion SO and the discharge port N3 as a non-permeate fluid Wh. It is discharged outside the separation device 10. As the membrane separation proceeds, a part of the solid content adheres, accumulates, or deposits on the membrane surface portion 2b as a filtration residue, and a part of the solid content accumulates while penetrating into the micropores P. (Hereinafter, solids deposited, deposited, etc. are collectively referred to as “deposit R”). Thus, the filtration resistance of the membrane module 20 increases.
[0027]
Next, when the filtration resistance value reaches a preset limit value, the membrane separation is temporarily interrupted and backwashing is performed. First, the pump 5 is operated with the outlet N3 and the valve V3 closed and the N2 opened. The vacuum pump 4 is operated with the valve V6 closed. At this time, the processing target fluid W in the processing target fluid supply unit SI is discharged to the outside of the housing 1. Next, the pressure in the space portion S6 of the vacuum chamber 6 was reduced to a predetermined pressure (second pressure) sufficiently smaller than the pressure in the internal space S1 and the pressure of the fluid supply portion SI (first pressure). Thereafter, the valve V5 is opened to supply the cleaning liquid M to the external space S2. Next, after the outer space S2 is filled with the cleaning liquid M, the valve V6 is opened.
[0028]
In this way, the space S6 of the vacuum chamber 6 and the internal space S1 of the hollow fiber membrane element 2 are communicated via the fluid supply section SI. Since the pressure in the space S6 is reduced first, the gas in the internal space S1 and the gas in the fluid supply part SI to be processed are immediately diffused to the vacuum tank 6 side, and the internal pressure in the internal space S1 drops rapidly. Here, FIG. 4 is a cross-sectional view schematically showing a main part in a state where back washing is performed in the membrane separation device 10 shown in FIGS. The cleaning liquid M filled in the external space S2 flows into the micropores P of the membrane wall 2a of the hollow fiber membrane element 2, and comes into contact with the deposit R that has closed the micropores P on the membrane surface 2b side. . Further, the cleaning liquid M permeates into the deposit R and flows out or leach to the internal space S1 side.
[0029]
In this state, the internal space S1 is rapidly reduced in pressure as described above. At this time, if the pressure in the internal space S1 is equal to or lower than the vapor pressure of the cleaning liquid M at that temperature, the cleaning liquid M flowing or leaching into the internal space S1 instantaneously boils and evaporates, causing rapid volume expansion. Is generated, and an explosion state of the vaporized cleaning liquid Mg toward the internal space S1 is generated.
[0030]
Then, by the ejection power, the sediment R is crushed and blown off to the inner space S1 side, and becomes a crushed piece (object) Rs, and flows down in the inner space S1 together with the gas-liquid mixture of the cleaning liquid M as the backwash liquid Mm. I do. The backwash liquid Mm flows into the vacuum tank 6 from the discharge port N5 through the fluid supply section SI, and is further discharged outside the system for processing. Then, the backwashing process is continued for a certain period of time to restore the filtration resistance of the membrane module 20 to the original value, and the above-described membrane separation procedure is performed again to restart the membrane separation process for the fluid W to be treated.
[0031]
By the way, as described above, the washing liquid M used in the present invention can be used in various concentrations and the like by appropriately selecting water, an organic solvent such as alcohols, an inorganic solvent such as acids and alkalis, and the like. Further, various additives such as a surfactant may be added. Here, when water is used as the cleaning liquid M, the space S6 of the vacuum chamber 6 is depressurized by opening the valve V6 so that the pressure of the internal space S1 becomes equal to or lower than the vapor pressure of water.
[0032]
The predetermined pressure in the space S6, that is, the second pressure mainly depends on (1) the vapor pressure of the water to be used, and (2) the volume of the internal space S1, the fluid supply section SI to be processed, the pipe, and the vacuum tank 6. In addition, other correction factors, for example, the amount of leaching of water into the internal space S1, the amount of the sediment R (can also be grasped by filtration resistance), the height of the membrane module 20, and the fluid supply part SI , The pressure loss due to the shape factor of the piping and the vacuum tank 6, and the like.
[0033]
FIG. 5 is a graph showing the relationship between the vapor pressure of water and the temperature, and shows, for convenience, those generally known as various physical properties of water. From this drawing, for example, when hot water in which the temperature in the internal space S1 is about 60 ° C. is used as the cleaning liquid M, the pressure in the internal space S1 is about 150 mmHg (20 kPa) with the valve V6 opened. By doing so, the boiling state of the cleaning liquid M on the film surface portion 2b can be caused, and the explosive state of the vaporized cleaning liquid Mg as shown in FIG. 4 can be generated.
[0034]
Also, when another cleaning liquid M is used, the second pressure of the space S6 of the vacuum chamber 6 can be set in the same manner as when water is used. Here, FIG. 6 is a graph showing the relationship between the vapor pressure of methanol as an example of alcohols and the temperature, and shows, for convenience, those generally known as various physical properties of methanol. As shown in this drawing, when methanol is used as the cleaning liquid M, the vapor pressure at the same temperature (60 ° C.) as that of the above-mentioned water is slightly higher than 610 mmHg (81 kPa). Therefore, the amount of reduced pressure in the space S6 can be significantly reduced as compared with the case where water at the same temperature is used. In addition, lower alcohols such as methanol and ethanol are excellent in industrial use, and high-purity alcohols are available. Therefore, they are useful in these respects.
[0035]
In other words, since the vapor pressure of the cleaning liquid M varies depending on the type, concentration, additive content, and the like (liquid properties) of the cleaning liquid M, the vacuum pressure varies depending on the liquid properties of the cleaning liquid M. It is desirable to control the operation of the vacuum pump 4 so as to adjust the amount of reduced pressure in the space S6 of the tank 6 and thus in the internal space S1 of the hollow fiber membrane element 2. Further, if the predetermined pressure in the internal space S1 is set to a pressure lower than the vapor pressure of the cleaning liquid M with a margin, the time required for the cleaning liquid M flowing or leaching into the internal space S1 to boil is further reduced. This is more preferable because the crushing force of the sediment R by the explosion is enhanced.
[0036]
According to the membrane separation device 10 configured as described above and the backwashing method using the same, the cleaning liquid M is supplied to the external space S2 in the hollow fiber membrane element 2 and the pressure in the internal space S1 is reduced for cleaning. The boiling state is generated when the liquid M has a vapor pressure equal to or lower than the vapor pressure at that temperature, and the explosive force crushes the deposit R to separate and remove the deposit R from the film surface portion 2b. Therefore, the sediment R that has entered the micropores P of the membrane wall 2a and deposited can be sufficiently crushed and ejected toward the internal space S1, and the crushing force causes the periphery of the micropores P in the membrane surface portion 2b. Can be removed so as to blow off the deposit R. Therefore, the backwashing efficiency of the membrane module 20 can be significantly improved as compared with the conventional backwashing method.
[0037]
Further, in a state where the vacuum chamber 6 is provided, the external space S2 is filled with the cleaning liquid M and flows into the fine holes P, the space S6 of the vacuum chamber 6 and the internal space S1 which have been previously depressurized are separated. Since the boiling state of the cleaning liquid M in the internal space S1 is instantaneously formed, the explosive force of the vaporized cleaning liquid Mg can be increased. Therefore, the effect of removing the deposit R on the film surface portion 2b is further enhanced, and the backwashing efficiency can be further improved. Further, when the cleaning liquid M is appropriately selected and used, and particularly when a lower alcohol such as methanol is used, the amount of decompression of the space S6 of the vacuum chamber 6 and thus the internal space S1 can be reduced, so that power costs are reduced and economy is reduced. It is advantageous.
[0038]
The present invention is not limited to the above-described embodiment. For example, instead of the internal pressure type membrane separation device 10 shown in FIGS. Is also applicable. The type of the hollow fiber membrane element 2 is not particularly limited. Further, the installation direction (longitudinal direction) of the membrane module 20 is not limited to the vertical direction.
[0039]
Furthermore, the procedure for reducing the pressure in the internal space S1 and the procedure for supplying the cleaning liquid M to the external space S2 are not limited to the above-described procedures. For example, the space S6 of the vacuum chamber 6 is steadily depressurized in advance, and the valve V6 is opened when the membrane separation is completed, or the supply of the cleaning liquid M is started and the valve V6 is opened. Various operations are possible. Furthermore, the number of the membrane modules 20 is not limited to the illustrated one, and according to the present invention, the backwashing of the membrane separation device having the multi-stage number of the membrane modules 20 can be performed with higher efficiency than in the past.
[0040]
【The invention's effect】
As described above, according to the method for backwashing a separation membrane of the present invention, the cleaning liquid is supplied to the separation membrane from the permeation side in the flow direction of the fluid to be treated, and the separation fluid is supplied to the separation membrane. By reducing the pressure on the non-permeate side in the flow direction so as to be a predetermined pressure, a boiling state of the cleaning liquid is generated on the membrane surface of the separation membrane on the non-permeate side, whereby solids and the like deposited on the membrane surface are removed. Crush and peel off. Therefore, the cleaning efficiency at the time of backwashing the separation membrane of the fluid to be treated can be significantly improved as compared with the related art. As a result, the desired membrane separation performance of the separation membrane can be favorably maintained for a long period of time.
[Brief description of the drawings]
FIG. 1 is a cross-sectional view schematically showing a configuration of a preferred embodiment of an apparatus for performing a method for backwashing a separation membrane according to the present invention, wherein the membrane is separated by a membrane separation apparatus provided with the backwash apparatus. This shows a state where the separation process is being performed.
FIG. 2 is a cross-sectional view schematically showing a configuration of a preferred embodiment of an apparatus for performing a method for backwashing a separation membrane according to the present invention. It shows the state where it is.
FIG. 3 is a cross-sectional view schematically showing a main part in a state where membrane separation is performed by the membrane separation apparatus shown in FIGS. 1 and 2.
FIG. 4 is a cross-sectional view schematically showing a main part in a state where back washing is being performed by the membrane separation device shown in FIGS. 1 and 2.
FIG. 5 is a graph showing a relationship between vapor pressure of water and temperature.
FIG. 6 is a graph showing the relationship between the vapor pressure of methanol and temperature.
[Explanation of symbols]
Reference numeral 2: hollow fiber membrane element (separation membrane), 20: membrane module, 2a: membrane wall, 2b: membrane surface portion, 4: vacuum pump, 5: pump, 6: vacuum tank (vessel), 10: membrane separation device, M ... cleaning liquid, Mg ... vaporized cleaning liquid, Mm ... backwashing liquid, N1, N4 ... supply port, N2, N3, N5 ... discharge port, P ... micropore, R ... volume, S1 ... internal space ( 1st space area, non-transmission side), S2 ... external space (transmission side), S6 ... space section (2nd space area), SI ... processed fluid supply section, SO ... processed fluid discharge section, V3 V5, V6: valve, W: fluid to be treated, Wh: non-permeable fluid, Ws: permeable fluid.

Claims (3)

A method for backwashing a separation membrane for membrane-separating a fluid to be treated,
A cleaning liquid is supplied to the separation membrane from a permeation side in a flow direction of the fluid to be processed,
By reducing the pressure on the non-permeate side in the flow direction of the fluid to be treated with respect to the separation membrane so as to be a predetermined pressure, a boiling state of the cleaning liquid is caused on the membrane surface of the separation membrane on the non-permeate side.
A method for backwashing a separation membrane, comprising: The method for backwashing a separation membrane according to claim 1, wherein the amount of reduced pressure on the non-permeate side is adjusted so that a boiling state of the cleaning liquid is generated according to the type of the cleaning liquid. By connecting a first space area where the membrane surface portion abuts on the non-transmission side with a second space area having a second pressure smaller than the first pressure in the first space area. Reducing the pressure in the first space region so that the non-permeate side has the predetermined pressure;
The method for backwashing a separation membrane according to claim 1 or 2, wherein:

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