JP2006272192A - Pressure-loss estimation method, pressure-loss estimation program and recording medium recording the program - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To accurately estimate a pressure loss of fluid in a particle packed layer which is formed by mixing a plurality of particle groups. <P>SOLUTION: In the first, the particle groups which constitute the particle packed layer are determined and the geometrical standard deviation σ<SB>i</SB>, the geometrical average diameter d<SB>i</SB>and the kinetic shape factor κ<SB>i</SB>are obtained (S10). Secondarily, the viscosity μ and the superficial velocity u of the fluid passing through the particle packed layer are obtained (S11). Then, the height H and the porosity ε in the particle packed layer and the particle number n<SB>i</SB>of each particle group existing per unit volume of the particle packed layer are obtained (S12). Then, the obtained numerical value is substituted for a formula to calculate the pressure loss ΔP (S13). <P>COPYRIGHT: (C)2007,JPO&INPIT

Description

  The present invention relates to a pressure loss estimation method, a pressure loss estimation program for estimating a pressure loss of a fluid flowing through a gap of a particle packed bed formed by mixing a plurality of particle groups, and a recording medium on which the program is recorded.

  The phenomenon of fluid such as liquid and gas permeating through the gaps between the particle packed layers (fixed layers) occurs industrially in various apparatuses. Examples of these devices include a filtration device that separates solid and liquid, a bag filter for collecting dust, a catalytic reaction device that reacts gas through a catalyst particle layer, and a powder drying device that ventilates wet powder. Is mentioned.

  When the above phenomenon occurs, the fluid flow is lost due to resistance from the particle packed bed. This loss is expressed in terms of pressure and is called pressure loss. An apparatus in which the above phenomenon occurs needs to be designed after predicting the pressure loss of the particle packed bed. Otherwise, for example, problems such as a decrease in liquid flow and aeration, and inadequate reaction and drying may occur.

In the present application, the fluid flow around the particles is a laminar flow, that is, the Stokes region (region where the Reynolds number based on particle size is 5 or less) is limited. The simplest Darcy law is known as a relational expression of pressure loss in this case. Darcy's law is expressed by the following equation.
ΔP / H = (μ / k) × u _S.
Here, μ is the viscosity (Pa · s), H is the height (thickness) (m) of the particle packed bed, and u _S is the superficial velocity (apparent velocity) of the fluid (m / s). It is. K is the transmittance of the particle packed layer and is a dimensionless constant determined by the physical properties of the particle packed layer.

Against Darcy's Law, by targeting considers particle packing layer and one tube introduces the concept of a tube resistance, filler other than spherical surface coefficients as phi _c, Kozeni Carman (Kozeny-Carman ) Is obtained. Cozeny Carman's formula is as follows:
ΔP / H = 180 × (μ × u _S / (φ _c ² × d _p ² )) × ((1−ε) ² / ε).
Here, d _p is the diameter (particle diameter) (m) of the particles, and ε is the porosity (dimensionalless). Usually, the pressure loss is theoretically predicted using the Cozeny Kerman equation (see, for example, Non-Patent Documents 1 and 2).
Edited by Chemical Society of Japan, “Handbook of Chemical Engineering”, 6th revised edition, Maruzen Co., Ltd., February 25, 1999, p. 310-312 The Chemical Society of Japan, “Modern Chemical Engineering II”, first edition, Asakura Shoten Co., Ltd., February 20, 1989, p. 39-41 IF Macdonald, et al., Ind. Eng. Chem. Fundamentals, 18 (1979), 199-208 MJ Macdonald, et al., AIChE Journal, 37 (1991), 1583-1588 Y. Li, et al., Ind. Eng. Chem. Res., 37 (1998), 2005-2011 Y. Endo, et al., Filtration & Separation, March 1998, 191-195

  However, there is a problem that the Cozeny-Kerman equation can be applied only to a particle packed layer composed of one kind of particles having a narrow particle size distribution (see, for example, Non-Patent Document 3). In order to solve this problem, various relational expressions of pressure loss and transmittance have been proposed as described in Non-Patent Documents 4 to 6, for example.

  Non-Patent Document 4 discloses that the Blake-Kozeny formula (Kozeny Kerman formula) is generalized to spherical particles of multiple sizes. In Non-Patent Document 4, an experiment is performed to determine the porosity and transmittance of a particle-filled layer of frit glass in which three particle groups having the same spherical particle shape and different particle size distribution are mixed. Non-Patent Document 5 discloses the transmittance of a particle packed bed composed of spherical particles having various particle size distributions.

  As described above, Non-Patent Documents 4 and 5 include relational expressions of pressure loss and transmittance with respect to a particle packed bed composed of particles having a wide particle size distribution and a particle packed layer composed of a plurality of particle groups having different particle size distributions. It is disclosed. However, in Non-Patent Documents 4 and 5, since the particle is limited to a spherical shape, when the particle is a non-spherical shape such as sand, the relationship between the pressure loss and the transmittance may not be satisfied. is there.

  On the other hand, the inventor of the present application has proposed a relational expression of pressure loss regarding a particle packed bed in which two particle groups having different particle size distributions are mixed in Non-Patent Document 6. In Non-Patent Document 6, the shape of the particles may not be a spherical particle. Further, in Non-Patent Document 6, dust-containing air generated by mixing alumina particles (average particle size 0.7 μm) and Arizona road dust (average particle size 2.0 μm) is collected in an air filter and dust. A state in which a cake is formed is disclosed.

  However, Non-Patent Document 6 does not disclose a relational expression of pressure loss related to a particle packed bed in which three or more particle groups are mixed. Further, in Non-Patent Document 6, since the thickness of the dust cake is measured only up to about 450 μm, it is unclear whether or not the relational expression of the pressure loss can be applied to the particle packed layer having a thickness of 1 mm or more. is there.

  The present invention has been made in view of the above problems, and an object of the present invention is related to a particle packed bed formed by mixing a plurality of particle groups having different particle size distributions. Pressure loss that can be estimated well even if the particle shape is non-spherical, the number of particle groups is 3 or more, or the thickness of the particle packed layer is 1 mm or more It is to provide an estimation method and the like.

In order to solve the above problems, a pressure loss estimation method according to the present invention is a pressure loss estimation method for estimating a pressure loss ΔP of a fluid that permeates through a particle packed bed formed by mixing a plurality of particle groups. The particle group is composed of particles having substantially the same particle shape and a particle size distribution according to a lognormal distribution, and a fluid characteristic acquisition step of acquiring the viscosity μ and the apparent velocity u related to the fluid; The particle packing layer characteristic acquisition step for acquiring the height H and the porosity ε of the particle packing layer, and the particle packing for the i-th particle group (where i = 1 to N, N is an integer of 2 or more). Obtain the number n _{i of} particles present in a given volume of the layer, the geometric mean diameter d _i and geometric standard deviation σ _{i of} the particle size distribution, and the dynamic shape factor κ _i and do this for all particle groups. Particle swarm characteristics The acquisition step and the acquired numerical value are expressed by the equation (ΔP / (μ × u × H)) × R = 18 × v (ε) × (1−ε) / ε ² (1) (where v ( ε) is the porosity function and R is

And n _t is the total number of particles present in a predetermined volume of the particle packed layer. ), And a pressure loss calculating step for calculating the pressure loss ΔP.

  The inventor of the present application derived the above formulas (1) and (2), which are further generalized from the relational expression of the pressure loss described in Non-Patent Document 6, and calculated using the formulas (1) and (2). When the calculated value of the pressure loss ΔP is compared with the measured value of the pressure loss ΔP actually measured by the fluid permeation test, the thickness of the particle packed bed is 1 mm or more even when there are three or more particle groups. Even if it exists, it turned out that the said calculated value adapts well to the said measured value.

  Furthermore, the inventor of the present application has made various studies.For example, even when the particle composition is the same and the particle size distribution is a logarithmic distribution, the particle shape is different. It was found that the calculated values can be more accurately matched to the measured values by separating the particles into different particle groups having substantially the same shape.

Therefore, according to the above method, the fluid viscosity μ and superficial velocity u, the particle packed bed height H and porosity ε, the geometric standard deviation σ _i of each particle group, the geometric mean diameter d _i , and the power Obtaining the geometrical shape factor κ _i and the number of particles n _i of each particle group existing per unit volume of the particle packed bed, thereby estimating the pressure loss ΔP of the fluid that permeates the particle packed bed Can do. Furthermore, by making the shape of the particles in the particle group substantially the same, an appropriate dynamic shape factor κ _i can be assigned to the particle group, so that the pressure loss ΔP can be estimated with higher accuracy.

Incidentally, in the particle group characteristic acquisition step, when the shape of the particles in a certain particle group is non-spherical, with respect to the particle group, the geometric mean diameter d _i of the particle size distribution, particle with an equal volume sphere equivalent diameter of It is preferable to use the geometric mean diameter when the diameter distribution is obtained.

  Further, various functions are known from experiments as the porosity function v (ε) in the pressure loss calculation step, and one example is v (ε) = 10 × (1−ε) / ε. .

Further, in the particle group property acquisition step, the number n _i of particles existing in the predetermined volume of the particle packed layer is the particle group existing in the predetermined volume of the particle packed layer with respect to the i-th particle group. The total mass m _i of the particles and the particle density ρ _{i of the} particle group are obtained, and the obtained numerical value is expressed by the equation: n _i = (m _i / ρ _i ) / ((π / 6) × d _i ), Can be obtained by substituting for.

  In addition, before the particle group characteristic acquisition step, when the particle shape is different with respect to a certain particle group, it is preferable to separate the particle group into a plurality of particle groups based on the shape. In this case, since the shape of the particles in the separated particle group can be made substantially the same, the pressure loss ΔP can be obtained with high accuracy.

  In addition, each step in said pressure loss estimation method can be performed on a computer by a pressure loss estimation program. Furthermore, the pressure loss estimation program can be executed on any computer by storing the pressure loss estimation program in a computer-readable recording medium.

As described above, the pressure loss estimation method according to the present invention includes the fluid viscosity μ and superficial velocity u, the particle packed bed height H and porosity ε, the geometric standard deviation σ _i of each particle group, By obtaining the average diameter d _i , the dynamic shape factor κ _i, and the number of particles n _i of each particle group existing per unit volume of the particle packed bed, the pressure loss of the fluid that permeates the particle packed bed ΔP can be estimated satisfactorily, and the pressure loss ΔP can be estimated more accurately by making the shape of the particles in the particle group substantially the same.

  Before describing the embodiment of the present invention, a relational expression of pressure loss ΔP used in the present invention will be described. In deriving this relational expression, the following assumptions are introduced.

  (Assumption 1) The particles constituting the particle packed layer are packed randomly. For this reason, there is no local distribution of particles.

  (Assumption 2) The fluid flow around the particles is limited to the Stokes region (region where the Reynolds number on the basis of particle size is 5 or less) where the fluid flow is laminar.

(Assumption 3) The particle size distribution of each particle group follows a logarithmic normal distribution f _i (lnd _p ) (where i = 1 to N, N is an integer of 2 or more).

Here, d _p is the particle size, σ _i is the geometric standard deviation of the i-th particle group, and d _i is the geometric mean diameter of the i-th particle group.

From these assumptions, a relational expression of the pressure loss ΔP of the fluid that permeates the particle packed bed is derived by the same method as in Non-Patent Document 6 as follows.
(ΔP / (μ × u × H)) × R = 18 × v (ε) × (1-ε) / ε ² (1)
(However, R is represented by the following formula.)

  Here, the symbol μ and the symbol u relate to the fluid that passes through the particle packed bed, and represent the viscosity (viscosity) (Pa · s) and superficial velocity (apparent velocity) (m / s), respectively. . The fluid viscosity μ can be determined by the fluid used. The superficial velocity u of the fluid can be easily measured with a flow meter.

Further, symbol H, symbol ε, and symbol v (ε) relate to the particle packed layer, and the height (m), the porosity (non-dimensional), and the void function (non-dimensional), respectively. Represents. The height H of the particle packed bed can be easily measured by an instrument for measuring the length. Further, the porosity ε can be obtained from the actual volume (m ³ ) and the total volume (m ³ ) of the particle packed bed.

  The porosity function v (ε) corrects the particle proximity effect. The proximity effect of particles means that the viscosity (resistance) of a fluid appears to suddenly increase when the particles gather. Various functions are known as the porosity function v (ε) through experiments. In the present embodiment, v (ε) = 10 × (1−ε) / ε is used. Therefore, the porosity function v (ε) can be obtained from the porosity ε.

Further, as described above, the symbol σ _i and the symbol d _i relate to the particle size distribution (log normal distribution) of the i-th particle group, and represent the geometric standard deviation and the geometric mean diameter (m), respectively. The geometric standard deviation σ _i and the geometric mean diameter d _i of the i-th particle group can be obtained from the particle size distribution of the i-th particle group. When the particle shape of the i-th particle group is non-spherical, the equivalent volume equivalent diameter of the particles may be used as the particle size.

The symbol κ _i represents the dynamic shape factor of the particles in the i-th particle group. The dynamic shape factor κ _i is defined as the ratio of the drag force experienced by the particle in question to the resistance force experienced by a sphere having a volume equivalent diameter of the particle. The dynamic shape factor κ _i is 1 when the particle shape is spherical, and is greater than 1 when the particle shape is non-spherical. The dynamic shape factor κ _i can be determined from the shape of the particles using values described in the literature (for example, CN Davies, J. Aerosol Sci., 10 (1979) 477-513).

Moreover, the symbol n _i represents the number of particles of the i group of particles present per predetermined volume of the particle-filled layer, the symbol n _t is representative of the total number of particles present per predetermined volume of particle packing layer Yes. In the present embodiment, a unit volume is used as the predetermined volume.

The particle number n _i and the total number of particles n _t can be determined from the following equation.

Here, the symbol v _bed represents the total volume of the particles of the i-th particle group existing in the unit volume of the particle packed _bed , the symbol v _{particle_i} represents the volume of one particle of the i-th particle group, and the symbol m _i represents the total mass of the particles of the i-th particle group existing in the unit volume of the particle packed bed, and the symbol ρ _i represents the density of the particles of the i-th particle group. Therefore, by obtaining the total mass m _i of the particles of the i-th particle group existing in the unit volume of the particle packed bed and the density ρ _i of the particles of the i-th particle group, the number n of particles of the i-th particle group is obtained. _i can be obtained, and by obtaining the number of particles of each particle group, the total number of particles n _t can be obtained.

From the above, the viscosity μ and superficial velocity u of the fluid, the height H and the porosity ε of the particle packed bed, the geometric standard deviation σ _i , the geometric mean diameter d _i , and the dynamic shape factor κ of each particle group. _It can be understood that by obtaining _i and the number of particles n _i of each particle group existing per unit volume of the particle packed bed, the pressure loss ΔP of the fluid passing through the particle packed bed can be calculated. Further, instead of the number of particles n _i of each particle group existing per unit volume of the particle packed bed, the density ρ _i of the particles of the i particle group and the i th particle group existing in the unit volume of the particle packed bed It is obtained of the total mass m _i of the particle can be understood that it is possible to calculate the pressure loss ΔP of the fluid passing through the particle packing layer.

Further, in the present invention, the following assumption 4 is added to the above assumptions 1 to 3.
(Assumption 4) The shape of the particles in each particle group may be non-spherical, but is substantially the same shape.
Based on this Assumption 4, in the present embodiment, when the shape of the particles of a certain particle group is different, the particles are separated into different particle groups based on the particle shape. As a result, an appropriate dynamic shape factor κ _i can be assigned to each separated particle group, so that the pressure loss ΔP can be obtained with high accuracy.

Embodiment
Next, an embodiment of the present invention will be described with reference to FIGS. FIG. 1 shows a processing flow in a pressure loss estimation method for estimating a pressure loss when a fluid permeates a certain particle packed bed. As shown in the figure, first, particle groups constituting the particle packed bed are determined, and the geometric standard deviation σ _i , geometric mean diameter d _i , and dynamic shape factor κ _i of each determined particle group are acquired (steps). S10 (hereinafter sometimes abbreviated as “S10”. The same applies to the other steps).

  FIG. 2 shows the detailed processing flow in step S10. As illustrated, first, a particle group to be mixed in the particle packed layer is determined (S20). Next, the following processing is performed for a certain particle group.

  That is, first, it is determined whether or not the particles of the particle group have substantially the same shape (S21). The shape of the particles can be specified by observing many particles with a microscope. If the particles are not substantially the same shape (NO in S21), it is determined whether the particle group can be separated by the shape (S22). If the separation is impossible (NO in S22), the pressure loss ΔP cannot be estimated with high accuracy, and the process is terminated. On the other hand, if the separation is possible (YES in S22), the particles are separated into separate particle groups based on the shape (S23), and the process returns to step S21.

  On the other hand, when the particles have substantially the same shape (YES in S21), it is determined whether or not the particle size distribution of the particles of the particle group follows a logarithmic normal distribution (S24). The particle size distribution of the particles can be measured by, for example, a sieving method, an image analysis method (microscope method), or the like. If the particle size distribution does not follow the logarithmic normal distribution (NO in S24), it is determined whether or not the particle size distribution can be separated (S25). If the separation is impossible (NO in S25), the pressure loss ΔP cannot be estimated with high accuracy, and the process is terminated. On the other hand, if the separation is possible (YES in S25), the particles are separated into separate particle groups based on the particle size distribution (S26), and the process returns to step S21.

On the other hand, if the particle size distribution follows a logarithmic normal distribution (YES in S24), the geometric standard deviation σ _i , geometric mean diameter d _i , and dynamic shape factor κ _i of the particle group are acquired (S27). ). The geometric standard deviation σ _i and the geometric mean diameter d _i can be obtained from the particle size distribution. The dynamic shape factor κ _i can be obtained from the shape of the particles.

  And after repeating the said process S21-S27 about all the particle groups (S28), it returns to the original process routine.

  Referring to FIG. 1 again, after step S10, the viscosity μ and superficial velocity u of the fluid that passes through the particle packed bed are obtained (S11). The viscosity μ of the fluid can be measured by, for example, a capillary viscometer or a conical disk rotational viscometer. Alternatively, when a known fluid such as water or air is used, a value described in the literature may be used as the viscosity μ instead of the measured value. The superficial velocity u can be measured by, for example, a flow meter. Alternatively, instead of the measured value, a value required in the device design may be used as the superficial velocity u.

Next, to obtain the ε height H and porosity of the particle packing layer, and a particle number n _i of each group of particles present per unit volume of particle packing layer (S12). As described above, instead of the number of particles n _i of each particle group, the particle density ρ _{i of} each particle group and the total mass m _i of particles of each particle group existing in the unit volume of the particle packed bed. And may be acquired. The height H of the particle packed bed can be easily measured by an instrument for measuring the length. Alternatively, a value required in the design of the apparatus may be used as the height H instead of the measured value. The porosity ε can be obtained from the actual volume and the total volume of the particle packed bed.

The particle density ρ _i is determined by, for example, an immersion method such as a pycnometer method, a suspension method, a specific gravity method, or a gas volume method such as a constant volume compression method, a constant volume expansion method, an indefinite volume method, or a pressure comparison method. It can be measured. The total mass m _i of each particle group of particles present in a unit volume of the particle packing layer can be determined by measuring the mass (weight) of each particle group into the container isochoric.

  The above steps S10 to S12 may be performed simultaneously or in any order.

  Next, the pressure loss ΔP is obtained by substituting the acquired numerical values into the above formulas (1) and (2) (S13). Then, after the obtained pressure loss ΔP is output (S14), the pressure loss ΔP estimation process is terminated.

〔Example〕
Next, an example in which the pressure loss estimation method of the above embodiment is applied to actual particles will be described with reference to FIGS. In this example, compressed dry air having a viscosity μ = 1.8 × 10 ⁻⁵ (Pa · s) was used as the fluid that permeates the particle packed bed.

FIG. 3 shows the particle groups used in this example and the characteristic values of each particle group in a tabular form. The characteristic values of each particle group are as follows: average particle diameter d _i (μm), porosity ε, particle packed bed height H (mm), total mass m _i (kg) in unit volume, particle density ρ _i (kg) / M ³ ), geometric standard deviation σ _i , and dynamic shape factor κ _i . Moreover, in the same figure, GB_A-C have shown three types of glass beads from which an average particle diameter and a porosity differ, respectively. PP_A to C indicate three types of polypropylene having different average particle diameters.

The average particle diameter d _i and the geometric standard deviation σ _i were measured using a sonic fully automatic sieving measuring instrument (model number: RPS-85C manufactured by Seishin Enterprise Co., Ltd.). This measuring instrument can automatically measure the particle size distribution and can automatically output the average particle size d _i and the geometric standard deviation σ _i . Total mass m _i in a unit volume of each particle group was determined by mass each particle group into the container at constant volume (weight) is measured by an electronic balance.

The particle density ρ _i of each particle group was measured using a dry automatic densimeter (Accupic 1330-03 manufactured by Shimadzu Corporation) using a constant volume expansion method. If there is a literature value such as a catalog value as the particle density ρ _i of each particle group, the literature value may be used. The porosity ε is obtained by substituting the total mass _mi and the particle density ρ _{i in} the unit volume of each particle group measured as described above into the equation ε = 1− (m _i / ρ _i ). Can be sought.

The value described in the literature (CN Davies, J. Aerosol Sci., 10 (1979), 477-513) was used for the dynamic shape factor κ _i . According to the above document, spherical particles have a dynamic shape factor κ _i of 1, and silica particles having a spherical shape with spherical particles have a dynamic shape factor κ _i of 1.57. Therefore, since the glass beads GB_A to C in this example are spherical particles, the dynamic shape factor κ _{i is set} to 1. On the other hand, polypropylene PP_A to C has a particle shape intermediate between spherical particles and silica particles, and is rather a particle shape close to silica particles. Therefore, the dynamic shape factor κ _i was set to 1.4.

  Then, using the characteristic value of each particle group and the characteristic value of the fluid, the pressure loss ΔP in the particle packed layer formed by mixing glass beads GB_A to C and the particle packed layer formed by mixing polypropylene PP_A to C The pressure loss ΔP was calculated. As a comparative example, the particle packed bed was actually generated and a fluid permeation test was performed to measure the pressure loss ΔP. As a result, the table shown in FIG. 4 and the graph shown in FIG. 5 were obtained.

FIG. 4 shows a predetermined empty column formed in various particle heights H with respect to a particle packed layer formed by mixing glass beads GB_A to C and a particle packed layer formed by mixing polypropylene PP_A to C. The pressure loss ΔP when the fluid of the velocity u (= 1.39 × 10 ⁻² m / s) permeates is obtained. Among these, the calculated value of the pressure loss ΔP is calculated using the pressure loss estimation method of the present embodiment, and the measured value of the pressure loss ΔP is actually measured by performing a fluid permeation test. The porosity ε of the particle packed layer formed by mixing the glass beads GB_A to C is 0.34, and the porosity ε of the particle packed layer formed by mixing the polypropylene PP_A to C is 0.40. It was.

  FIG. 5 shows the relationship between the calculated value and the measured value shown in FIG. In the figure, triangles indicate the calculated values and the measured values shown in FIG. Of the three straight lines passing through the origin, the middle straight line indicates a line whose calculated value is equal to the measured value, and the upper straight line indicates a line whose calculated value is 5% smaller than the measured value. The lower straight line shows a line whose calculated value is 5% larger than the measured value. Referring to FIG. 5, it can be understood that the pressure loss ΔP calculated in the present example is within a range of ± 5% with respect to the pressure loss ΔP measured by the fluid permeation test. Therefore, it can be understood that the pressure loss ΔP when the fluid permeates through the particle packed bed can be accurately estimated even when there are three particle groups and the height H of the particle packed bed is on the order of 10 mm.

  For reference, details of the fluid permeation tester 2 that performs the fluid permeation test will be described with reference to FIG. FIG. 6 shows a schematic configuration of the fluid permeation tester 2. As illustrated, the fluid permeation tester 2 includes a packed column 11, a pump 12, a pressure gauge 13, a control device 14, a flow meter 15, and a bag filter 16.

  The packed tower 11 has a cylindrical shape with a square cross section, and stands in a substantially vertical direction. A dispersion plate 20 is provided below the center of the packed tower 11 from the center, and a particle packed bed 21 is disposed on the dispersion plate 20. The dispersion plate 20 prevents the powder from falling downward, and allows the compressed dry air to permeate downward. For the dispersion plate 20, for example, a perforated plate or a net is used.

  Further, pressure-sensitive elements 22 and 23 for detecting air pressure and converting them into electric signals are respectively provided below the dispersion plate 20 and above the particle packed bed 21 in the packed tower 11. The pressure sensitive elements 22 and 23 output the converted electric signal to the external pressure gauge 13.

  The packed tower 11 may be a drying device that passes dry air through the powder to dry the powder, a reaction device that reacts the powder with the catalyst in the gas phase, or a filtration device that separates gas-liquid or solid-liquid. can do.

  The pump 12 supplies dried compressed air (hereinafter abbreviated as “dry compressed air”) to the packed tower 11. Dry compressed air from the pump is supplied to the inside from the upper end of the packed tower 11 via the flow meter 15. The flow meter 15 measures the flow rate of the compressed dry air from the pump. The superficial velocity u of the fluid can be obtained from the flow meter 15.

  The pressure gauge 13 obtains the differential pressure of the air pressure above the dispersion plate 20 with respect to the air pressure below the particle packed bed 21 based on the electrical signal from the pressure sensitive elements 22 and 23 provided in the packed tower 11. is there. That is, this differential pressure is a pressure loss ΔP between the air before passing through the particle packed layer 21 and the air after passing through the particle packed layer 21.

  The control device 14 comprehensively controls various components in the fluid permeation tester 2. The bag filter 16 is provided in the flow path of the air discharged from the packed tower 11, and collects the powder contained in the air discharged from the packed tower 11 by filtration using a filter bag. It prevents the body from leaking outside.

  The present invention is not limited to the above-described embodiments, and various modifications can be made within the scope shown in the claims. That is, embodiments obtained by combining technical means appropriately modified within the scope of the claims are also included in the technical scope of the present invention.

  For example, in the above embodiment, three particle groups are mixed to form the particle packed layer, but two particle groups may be mixed, or four or more particle groups may be mixed.

  1 and 2 may be configured by hardware logic, or may be realized by software on a computer as follows.

  In other words, the computer has a central processing unit (CPU) that executes instructions of a control program that realizes each function, a read only memory (ROM) that stores the program, a random access memory (RAM) that expands the program, and the program And a storage device (recording medium) such as a memory for storing various data. The object of the present invention is to record a program code (execution format program, intermediate code program, source program) of a control program, which is software that realizes the processes shown in FIGS. This can also be achieved by supplying a medium to the computer and reading out and executing the program code recorded on the recording medium by the computer (or CPU or MPU).

  Examples of the recording medium include tape systems such as magnetic tape and cassette tape, disk systems including magnetic disks such as flexible disks / hard disks, and optical disks such as CD-ROM / MO / MD / DVD / CD-R, and IC cards. A card system such as an optical card (including a memory card) or a semiconductor memory system such as a mask ROM / EPROM / EEPROM / flash ROM can be used.

  The computer may be configured to be connectable to a communication network, and the program code may be supplied via the communication network. The communication network is not particularly limited. For example, the Internet, intranet, extranet, LAN, ISDN, VAN, CATV communication network, virtual private network, telephone line network, mobile communication network, satellite communication. A net or the like is available. Also, the transmission medium constituting the communication network is not particularly limited. For example, even in the case of wired such as IEEE 1394, USB, power line carrier, cable TV line, telephone line, ADSL line, etc., infrared rays such as IrDA and remote control, Bluetooth ( (Registered trademark), 802.11 wireless, HDR, mobile phone network, satellite line, terrestrial digital network, and the like can also be used. The present invention can also be realized in the form of a carrier wave or a data signal sequence in which the program code is embodied by electronic transmission.

  As described above, the pressure loss ΔP of the particle packed bed formed by mixing a plurality of particle groups can be accurately estimated. Thus, a filtration device that separates solid and liquid, a bag filter for collecting dust, and a gas through the catalyst particle layer. The present invention can be used for the design of a catalytic reaction device for reaction and a powder drying device for aeration drying wet powder.

It is a flowchart which shows the process of the pressure loss estimation method which is one Embodiment of this invention. In the pressure loss estimation method, it is a flowchart showing details of processing for determining a particle group constituting a particle packed bed and obtaining a geometric standard deviation, a geometric mean diameter, and a dynamic shape factor of each determined particle group. . It is a figure which shows the particle group used in one Example and comparative example of this invention, the average particle diameter of each particle group, the porosity, and the height of a particle | grain packed bed in a tabular form. Regarding the particle packed bed formed by mixing a plurality of the particle groups, the calculated value of the pressure loss obtained by the pressure loss estimation method as the above example and the measured value obtained by the fluid permeation test as the comparative example. It is a figure shown in a table format. It is a graph which shows the relationship between the said calculated value and the said measured value. It is a block diagram which shows schematic structure of the fluid permeability test apparatus which performs the said fluid permeability test.

Explanation of symbols

ΔP Pressure loss μ Fluid viscosity u Fluid apparent velocity H Particle packed bed height ε Particle packed bed porosity n Number of particles in the i-th particle group existing in a predetermined volume of the _i- particle packed bed d _i- th i-th particle All present in a given volume of dynamic shape factor n _t particles packed bed of particles in the geometric standard deviation kappa _i i-th particle group of the particle size distribution in the geometric mean diameter sigma _i i-th particle group of the particle size distribution in the group particle density of the total mass [rho _i i-th particle group of the i particle group of particles present in a given volume of the particle number v (epsilon) porosity function m _i particle packing layer

Claims (7)

A pressure loss estimation method for estimating a pressure loss ΔP of a fluid that permeates the particle packed bed with respect to a particle packed bed formed by mixing a plurality of particle groups,
The particle group is composed of particles having substantially the same particle shape and a particle size distribution according to a lognormal distribution,
A fluid property acquisition step for acquiring a viscosity μ and an apparent velocity u for the fluid;
A particle packed bed property obtaining step for obtaining a height H and a porosity ε of the particle packed bed;
With respect to the i-th particle group (where i = 1 to N, N is an integer of 2 or more), the number of particles n _i existing in a predetermined volume of the particle packed layer and the geometric mean diameter d _i of the particle size distribution A particle swarm characteristic obtaining step of obtaining a geometric standard deviation σ _i and a dynamic shape factor κ _i and performing this for all particle swarms;
The obtained numerical value is expressed by the formula (ΔP / (μ × u × H)) × R = 18 × v (ε) × (1-ε) / ε ²
(Where v (ε) is the porosity function and R is

And n _t is the total number of particles present in a predetermined volume of the particle packed layer. ),
And a pressure loss calculating step of calculating the pressure loss ΔP by substituting into. In said particles characteristic acquisition step, when the shape of the particles in a certain particle group is non-spherical, with respect to the particle group, the geometric mean diameter d _i of the particle size distribution, particle size distribution with an equal volume sphere equivalent diameter of The pressure loss estimation method according to claim 1, wherein the geometrical average diameter is obtained. The porosity function v (ε) in the pressure loss calculation step is
v (ε) = 10 × (1−ε) / ε
The pressure loss estimation method according to claim 1 or 2, wherein: In the particle group property acquisition step, the number of particles n _i existing in the predetermined volume of the particle packed layer is the number of particles of the particle group existing in the predetermined volume of the particle packed layer with respect to the i-th particle group. Of the total mass m _i and the particle density ρ _{i of the} particle group,
n _i = (m _i / ρ _i ) / ((π / 6) × d _i ),
The pressure loss estimation method according to any one of claims 1 to 3, wherein the pressure loss estimation method is obtained by substituting into.   The particle group separation step of separating the particle group into a plurality of particle groups based on the shape when the particle shape is different with respect to a certain particle group before the particle group property acquisition step. The pressure loss estimation method according to any one of claims 1 to 4, wherein:   The pressure loss estimation program for making a computer perform each step in the pressure loss estimation method of any one of Claim 1 thru | or 5.   A computer-readable recording medium on which the pressure loss estimation program according to claim 6 is recorded.

Images