JP2008180704A - Method and device for estimating pressure loss, and system for transporting particle - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To execute designs and operations of transporting lines with high-precision by precisely calculating and estimating pressure losses. <P>SOLUTION: A system for calculating a pressure loss estimates a pressure loss ΔP/L in a pipe length L by the formula ΔP/L=150(1+2dp/(3D(1-ε)))<SP>2</SP>η(1-ε)<SP>2</SP>/(ε<SP>3</SP>((1-0.645ϕs)dp)<SP>2</SP>)Ua+1.75ρa(1-ε)/(ε<SP>3</SP>(1-0.645ϕs)dp)Ua<SP>2</SP>, using a rate of straight line ϕs, a sphere-equivalent diameter dp, a void ration ε, a fluid velocity Ua, a fluid density ρa, a fluid viscosity η, and a pipe inner diameter D. <P>COPYRIGHT: (C)2008,JPO&INPIT

Description

  The present invention relates to a pressure loss estimation method and a pressure loss detection device for estimating and detecting a pressure loss when a fluid flows through a particle layer in a pipe, and a particle mixed with a fluid flowing in the pipe. The present invention relates to a particle transportation system for transportation.

The phenomenon of fluid passing through a stationary particle packed bed, which is an aggregate of many stationary particles, is called a packed bed permeation flow phenomenon. The application range of the packed bed permeation flow phenomenon is from the chemical industry such as dust collection and treatment in exhaust gas, adsorption removal of dioxins and odor treatment in sewer facilities, natural soil flow and natural gas flow such as natural gas flow, etc. It is extremely wide, even in the scientific field.
For this reason, it is extremely important to know the relationship between the flow velocity and the pressure loss when a fluid flows in the particle packed bed, and a conventional technique for estimating the pressure loss of the packed bed filled with particles. Have been proposed (see, for example, Patent Documents 1 and 2).
Furthermore, one of the pressure loss calculation formulas is the Ergun formula proposed by Ergun. The Ergun formula is a formula with a wide range of application including the laminar flow region to the turbulent flow region.
JP 2006-266824 A JP 2006-272192 A

The Ergun equation is an effective equation for calculating the pressure loss. However, it is known that there is an error between the calculated value and the experimental value depending on conditions such as the kind of particles in the packed bed and the flow velocity of the fluid. Therefore, if the Ergun equation is used as it is, the calculated (estimated) pressure loss is inaccurate, so the transportation line that transports particles is designed using the calculated pressure loss. And even if you drive, it will not be done with high accuracy.
An object of the present invention is to perform design and operation of a transportation line and the like with high accuracy by calculating and estimating pressure loss with high accuracy.

In order to solve the above-mentioned problem, a pressure loss estimation method according to claim 1 is a pressure loss estimation method for estimating a pressure loss when a fluid flows through a particle layer in a pipe line. The total linear length of the projected particles is divided by the perimeter of the particles projected onto a two-dimensional plane to calculate the linear rate φs, and the calculated linear rate φs is stored in the storage means. Sphere equivalent diameter dp, void ratio ε, fluid velocity Ua, fluid density ρa and fluid viscosity η in the pipe line are acquired, the acquired values are stored in a storage means, and the straight line stored in the storage means Using the ratio φs, sphere equivalent diameter dp, porosity ε, fluid velocity Ua, fluid density ρa and fluid viscosity η,
ΔP / L = 150 · (η · (1-ε) ² / (ε ³ · ((1−0.645 · φs) · dp) ² )) · Ua + 1.75 · (ρa · (1-ε) / (Ε ³ · (1−0.645 · φs) · dp)) · Ua ²
Thus, the pressure loss ΔP / L at the pipe length L is estimated.

A pressure loss estimation method according to a second aspect of the present invention is the pressure loss estimation method according to the first aspect of the present invention, wherein the acquired pipe inner diameter D is stored in the storage means and stored in the storage means. Using the pipeline inner diameter D, the following formula was corrected:
ΔP / L = 150 · (1 + 2 · dp / (3 · D · (1-ε))) ² · η · (1-ε) ² / (ε ³ · ((1−0.645 · φs) · dp ² ) · Ua + 1.75 · ρa · (1-ε) / (ε ³ · (1−0.645 · φs) · dp) · Ua ²
Thus, the pressure loss ΔP / L is estimated.

A pressure loss estimation method according to a third aspect of the invention is characterized in that in the pressure loss estimation method according to the first or second aspect of the invention, the pipe is a bent pipe.
According to a fourth aspect of the present invention, there is provided a pressure loss detection device for detecting a pressure loss when a fluid flows through a particle layer in a pipe line. dp, and void ratio ε, fluid velocity Ua, fluid density ρa, and fluid viscosity η in the pipe line,
ΔP / L = 150 · (η · (1-ε) ² / (ε ³ · ((1−0.645 · φs) · dp) ² )) · Ua + 1.75 · (ρa · (1-ε) / (Ε ³ · (1−0.645 · φs) · dp)) · Ua ²
Is used to calculate the pressure loss ΔP / L at the pipe length L.
A value acquisition unit that acquires a value for calculating the pressure loss ΔP / L, a two-dimensional projection image acquisition unit that acquires a two-dimensional projection image of the particle, and a particle acquired by the two-dimensional projection image acquisition unit In the two-dimensional projection image, the particle state detecting means for detecting the length and the peripheral length of the linear portion of the particle, and the total length of the straight portion detected by the particle state detecting means is divided by the peripheral length. A linear rate calculating means for calculating the linear rate φs; a linear rate φs calculated by the linear rate calculating means; a sphere equivalent diameter dp which is a value acquired by the value acquiring means; a void ratio ε; a fluid velocity Ua; pressure loss calculating means for calculating pressure loss ΔP / L by the above formula using ρa and fluid viscosity η.

According to a fifth aspect of the present invention, in the pressure loss detection device according to the fourth aspect of the present invention, the value acquisition means acquires a pipe inner diameter D, and the pressure loss calculation means. Is the following formula, which is obtained by correcting the formula using the pipe inner diameter D acquired by the value acquisition means,
ΔP / L = 150 · (1 + 2 · dp / (3 · D · (1-ε))) ² · η · (1-ε) ² / (ε ³ · ((1−0.645 · φs) · dp ² ) · Ua + 1.75 · ρa · (1-ε) / (ε ³ · (1−0.645 · φs) · dp) · Ua ²
To calculate the pressure loss ΔP / L.

According to a sixth aspect of the present invention, in the pressure loss detection apparatus according to the fourth or fifth aspect of the present invention, the pipe is a bent pipe.
The particle transport system according to the invention of claim 7 is a particle transport system for transporting particles by mixing particles with a fluid flowing in a pipe line, wherein the linear rate φs, the spherical equivalent diameter dp of the particles, Using the particle velocity us and the porosity ε, fluid velocity Ua, fluid density ρa, and fluid viscosity η in the pipeline,
ΔP / L = 150 · (η · (1-ε) ² / (ε ³ · ((1−0.645 · φs) · dp) ² )) · (Ua−us) + 1.75 · (ρa · ( 1−ε) / (ε ³ · (1−0.645 · φs) · dp)) · (Ua-us) ²
Is used to calculate the pressure loss ΔP / L at the pipe length L.
Supply pressure control means for controlling the supply pressure on the upstream side for pumping in the pipeline, value acquisition means for acquiring a value for calculating the pressure loss ΔP / L, and a two-dimensional projection image of the particles Two-dimensional projection image acquisition means for acquiring, particle state detection means for detecting the length and peripheral length of the linear portion of the particles in the two-dimensional projection image of the particles acquired by the two-dimensional projection image acquisition means, and the particles A linear rate calculating means for calculating the linear rate φs by dividing the total length of the straight line portions detected by the state detecting means by the peripheral length; a particle transport amount detecting means for detecting the transport amount of the particles; The control means includes a linear rate φs calculated by the linear rate calculation means and a value acquired by the value acquisition means when the transport amount of particles detected by the particle transport amount detection means is different from a target value. Sphere equivalent diameter dp, particle The upstream supply pressure is changed based on the pressure loss ΔP / L given by the above equation using the velocity us, the porosity ε, the fluid velocity Ua, the fluid density ρa, and the fluid viscosity η. .

The particle transport system according to an eighth aspect of the present invention is the particle transport system according to the seventh aspect of the present invention, wherein the control means is configured to target the transport amount of particles detected by the particle transport amount detection means. When the supply pressure Pt is different from the value, the following formula, where Ms is the target value of the transport amount of particles, A is the cross-sectional area in the pipeline, ρ _B is the bulk density, and us is the particle velocity,
Pt = ∫ (Ms / (A · ρ _B · us) · ΔP / L · dL
It is characterized by controlling to become.

The particle transport system according to the invention described in claim 9 is the particle transport system according to claim 7 or 8, wherein the value acquisition means acquires the pipe inner diameter D, and the control means includes: Using the pipe inner diameter D acquired by the value acquisition means,
ΔP / L = 150 · (1 + 2 · dp / (3 · D · (1-ε))) ² · η · (1-ε) ² / (ε ³ · ((1−0.645 · φs) · dp ^{) 2) · (Ua-us} ) +1.75 · ρa · (1-ε) / (ε 3 · (1-0.645 · φs) · dp) · (Ua-us) 2
The supply pressure on the upstream side is changed based on the pressure loss ΔP / L given by.

The particle transport system according to the invention described in claim 10 is the particle transport system according to any one of claims 7 to 9, wherein the pipe is of a bent pipe. And
Here, the following equation for calculating the pressure loss ΔP / L:
ΔP / L = 150 · (η · (1-ε) ² / (ε ³ · ((1−0.645 · φs) · dp) ² )) · Ua + 1.75 · (ρa · (1-ε) / (Ε ³ · (1−0.645 · φs) · dp)) · Ua ²
Is the following Ergun equation:
ΔP / L = 150 · (η · (1-ε) ² / (ε ³ · dp ² )) · Ua + 1.75 · (ρa · (1-ε) / (ε ³ · dp)) · Ua ²
Is obtained by correcting by placing dp = (1−0.645 · φs) · dp. That is, the equation obtained by correcting the particle linearity φs.

  According to the present invention, it is possible to calculate and estimate the pressure loss with high accuracy by correcting the Ergun equation using the linearity rate φs of the particles. Thereby, design of a transportation line etc. and also operation can be performed with high accuracy.

The best mode for carrying out the present invention (hereinafter referred to as an embodiment) will be described in detail with reference to the drawings.
(1) Technology as a premise of the embodiment First, a technology as a premise of the present embodiment will be described.
(1-1) Ergun equation The Ergun equation is a typical equation for calculating the pressure loss in the stationary particle packed bed. This Ergun equation is an effective equation for calculating the pressure loss. In the present invention, the pressure loss is calculated by using the Ergun equation as a basis and modifying the Ergun equation. The Ergun equation (Ergun equation before correction) is expressed as the following equation (1).
ΔP / L = k ₁ · (η · (1−ε) ² / (ε ³ · dp ² )) · Ua + k ₂ · (ρa · (1−ε) / (ε ³ · dp)) · Ua ² ··・ (1)

Where ΔP is the pressure difference (pressure loss), L is the length of the packed bed in the pipeline, ε is the porosity in the pipeline, η is the air viscosity in the pipeline, Ua is the air velocity in the pipeline, and dp is the particle The diameter and ρa are the air density in the pipeline, and k ₁ and k ₂ are eigenvalues in the laminar flow region and the turbulent flow region, respectively. In the formula (1), the first term on the right side represents the pressure loss for laminar flow, and the second term represents the pressure loss for turbulent flow.
Ergun derives k ₁ = 150 and k ₂ = 1.75 from many experimental data using spherical particles, and the following equation (2) is obtained.
ΔP / L = 150 · (η · (1-ε) ² / (ε ³ · dp ² )) · Ua + 1.75 · (ρa · (1-ε) / (ε ³ · dp)) · Ua ² ··・ (2)

That is, Ergun considers that the gap in the packed bed is replaced with a state where the capillaries are gathered in the process of deriving the equation (1), and from the condition that the hydraulic radii in the capillary and the packed bed are equal, Led.
((Π / 4) · de ² · Le) / (π · de · Le) = ε / (Sv · (1-ε)) (3)
Here, de is the diameter of the capillary, and Le is the length of the capillary. For spherical particles, the following equation (4) can be derived.
Sv = 6 / dp (4)
Ergun uses the equations (3) and (4) to derive the equation (2).
(1-2) Modified Ergun Formula By the way, in many cases, the shape of the particles filled in the particle packed bed is non-spherical. However, when the particles are non-spherical, an error occurs in the Ergun equation.

On the other hand, when the particles are non-spherical, the inventors of the present invention reduce the area where the particle surface and the fluid are in contact with each other by the surface contact between the particles in the flat portion of the particles, thereby filling the particles. It was considered that the hydraulic radius in the packed bed changed, the above equation (3) was not established, and an error occurred in the Ergun equation. For this reason, the present inventor applied such a sphere diameter representing the particle surface area that is actually in contact with the fluid, that is, the effective particle diameter dp ′ to the above formulas (1) and (2). I thought that (error) could be corrected.
Here, as a particle property value, a linear rate φs is defined as in the following equation (5).
φs = ΣL _i / Ls (5)

As shown in the equation (5), the linear rate φs is obtained by taking the particle two-dimensionally as shown in FIG. 1 and calculating the length L _i of the linear part of the two-dimensional (two-dimensional projection plane) particle. The total (L ₁ + L ₂ + L ₃ + L ₄ + L _{5 in} FIG. 1) is the outer peripheral length Ls of the particles (in FIG. 1, L ₁ + L ₂ + L ₃ + L ₄ + L ₅ + L _c1 + L _c2 + L _c3 + L _c4 + L _c5 +) The value obtained by dividing. It can be said that as the linear ratio φs increases, the number of linear portions of the particles increases. In such a case, it is considered that the proportion of particles in surface contact increases and the error in pressure loss increases.
Then, the particle diameter dp ′ was defined as the following equation (6) using the linear rate φs as an equation considering the shape.
dp ′ = (1−As · φs) · dp (6)
Here, As is a correction coefficient related to φs.

By substituting the equation (6) into the particle diameter dp of the equation (2), the following equation (7) is obtained as a modified equation of the Ergun equation considering the linear rate. Here, about correction coefficient As, 0.645 was obtained by experiment.
ΔP / L = 150 · (η · (1-ε) ² / (ε ³ · ((1-As · φs) · dp) ² )) · Ua + 1.75 · (ρa · (1-ε) / (ε ³ (1-As / φs) / dp)) / Ua ² (7)
By setting As = 0.645 to this equation (7), the porosity ε, the air viscosity η, the air velocity Ua, the particle diameter dp and the air density ρa are given, and further obtained by measurement or the like. By giving the linear rate φs, the pressure loss ΔP / L can be obtained.

(1-3) Experimental apparatus and experimental method By the following experimental apparatus and experimental method, the correction coefficient As was obtained as 0.645.
(1-3-1) Experimental Device FIG. 2 shows a schematic diagram of the experimental device.
As shown in FIG. 2, an air compressor 1 is used as an air source, an air chamber 2 is used to store compressed air from the air compressor 1, and a downstream stage of the air chamber 2 is used to depressurize the compressed air. The pressure reducing valve 3 is installed. A flow meter 4, a flow rate adjusting valve 5, and a check valve 6 are installed downstream of the pressure reducing valve 3 for measuring and adjusting the air flow rate.

  Then, a pipe line 8 is formed at a predetermined distance L1 (for example, 500 [mm]) from the hose outlet 7 positioned downstream of the check valve 6 to form a stationary particle packed layer packed with particles used for measurement. Yes. In the experiment, a straight pipe is used for the pipe line 8. And, as the pipe line 8, a pipe having a different inner diameter D and length L2 is used. When the inner diameter D = 26, 38, 50 [mm], the pipe line 8 having a length L2 = 550 [mm] is used. When the inner diameter D = 70 [mm], the pipe line 8 having a length L2 = 150 [mm] is used.

The front and rear ends of the plug model are fixed with a net to maintain the plug state and attached to the experimental device, and the pressure loss before and after the plug model is calculated. For this purpose, pressure taps 9 and 10 are installed one by one on the surface of the acrylic pipe upstream and downstream of the plug model, and the average pressure in the pipe is measured by the measuring devices 11 and 12.
(1-3-2) Experimental conditions As particles, polyethylene pellets (PEP), polystyrene pellets (PSP), plastic pellets (PTP), red beans (SMB), Nipolon hard (Nipolon hard: registered trademark, NLH), Petrocene (Petrocene: (Registered trademark, PTS) and hard capsule (CPS) are used. Table 1 below mainly shows physical property values of these used particles. Table 2 below shows experimental conditions for this time.

(1-3-3) Experimental results and discussion The experimental results are as follows.
FIG. 3 shows theoretical values (calculation formulas, values on the vertical axis) of pressure loss according to the Ergun equation (formula (2)) and experimental values (horizontal values) for polystyrene pellets (PSP) and plastic pellets (PTP). A comparison result with the axis value) is shown.
As shown in FIG. 3, there is an error between the theoretical value and the experimental value depending on the particles (toward the polystyrene pellets). On the other hand, there is almost no difference in the tendency of matching between the theoretical value and the experimental value due to the difference in the pipe diameter of the pipe 8.
As described above, a difference in error is observed depending on the difference in particles. From this, it is considered that the main cause of the error is due to the physical properties (shape) of the particles. FIG. 4 shows the relationship between the linear ratio φs and the pressure loss error (the ratio between the theoretical value and the experimental value (theoretical value / experimental value)) for all particles.

  As shown in FIG. 4, the error increases as the linear ratio φs increases for all the particles (a great difference from 1). This is because, in the case of spherical particles, the particles are in point contact with each other, whereas in the case of particles having a linear portion (particles having a certain linear rate φs), the particles are in surface contact with each other, and the packed bed It is considered that the hydrodynamic radius in the inside becomes different, and by adjusting the particle diameter dp using the linear rate φs from the above formulas (3) and (4), the consistency between the theoretical value and the experimental value can be improved. I thought.

Here, FIG. 5 shows the relationship between the particle diameter ratio dp ′ / dp between the effective particle diameter dp ′ and the particle diameter dp and the linear rate φs for all particles.
From the results shown in FIG. 5, it was possible to obtain the slope, that is, the particle size ratio dp ′ / dp was 0.645. Thereby, the correction coefficient As can be obtained as 0.645 (As = 0.645). When As = 0.645, the equation (7) becomes the following equation (8).
ΔP / L = 150 · (η · (1-ε) ² / (ε ³ · ((1−0.645 · φs) · dp) ² )) · Ua + 1.75 · (ρa · (1-ε) / (Ε ³ · (1−0.645 · φs) · dp)) · Ua ² (8)

FIG. 6 shows the theoretical value calculated by the above equation (8) when the condition is D = 26 [mm] for polyethylene pellets (PEP) and D = 70 [mm] for polystyrene pellets (PSP). The comparison result of ((ΔP / L) th) and the experimental value ((ΔP / L) e) is shown. In the same figure, the theoretical value ((ΔP / L) th) calculated by the equation (8) is shown as a modified value (Modified) value, and the theoretical value calculated by the equation (2) ( (ΔP / L) th) is shown as an uncorrected value (Not modified).
As shown in FIG. 6, the error is greatly improved compared to the theoretical value by the Ergun equation before correction (see FIG. 3), and a value close to the experimental value is obtained by taking the linear rate into consideration. I can see that. That is, the calculation accuracy of the pressure loss by the equation (8) is high. Similarly, the error could be reduced within ± 10% for all particles and all conditions (see FIGS. 12 to 18 described later).

(2) Embodiment of the Invention An embodiment based on the above-described technique will be described below.
(2-1) First Embodiment The first embodiment is a pressure loss calculation system to which the present invention is applied.
(2-1-1) Configuration FIG. 7 shows a configuration of the pressure loss calculation system.
As shown in FIG. 7, the pressure loss calculation system includes a particle image acquisition unit 21, a linear rate calculation unit 22, a data acquisition unit 23, a condition setting unit 24, a pressure loss calculation unit 25, a pressure loss determination unit 26, and an output unit 27. It has.
FIG. 8 shows a processing procedure by the pressure loss calculation system. With this process, the pressure loss under a predetermined condition is calculated. The processing content of each component 21-26 which comprises a pressure loss calculation system is demonstrated along the process sequence of FIG.

As shown in FIG. 8, when the process is started, first, in step S1 to step S6, the particle image acquisition unit 21, the linear rate calculation unit 22, and the data acquisition unit 23 acquire various data.
That is, in step S1, particles for pressure loss calculation or transportation are selected.
Subsequently, in step S2, the data acquisition unit 23 measures the particle density ρs of the particles selected in step S1. For example, the particle density ρs selected in step S1 is acquired with reference to a table or database comprising particle property values.

Subsequently, in step S3, the data acquisition unit 23 measures the particle mass M of the particles selected in step S1.
Subsequently, in step S3, the data acquisition unit 23 calculates the sphere equivalent diameter dp of the particle based on the particle density ρs and the particle mass M obtained by the measurement in the step S2 and step S3. Then, the process proceeds to step S7.
On the other hand, in step S5, the particle image acquisition unit 21 acquires a two-dimensional image of the particles selected in step S1 using an imaging device (camera or the like). Here, a considerable number (for example, 10 0 grains) is randomly photographed from 10 directions to obtain a two-dimensional projection image (for example, a 100 × 10 pattern two-dimensional projection image).

  Subsequently, in step S6, the linear rate calculation unit 22 calculates the linear rate φs. Specifically, the linear rate calculation unit 22 measures the outer peripheral length Ls of the particle and the length Li of the linear part from the two-dimensional projection image for the considerable number of particles acquired in step S5, and measures them. Using the outer circumferential length Ls and the length Li of the straight line portion, the linear rate φs is calculated by the above equation (5). Then, the process proceeds to step S7. Note that the linear rate calculation unit 22 measures the outer peripheral length Ls of the particle and the length Li of the linear part by, for example, an image analysis system or software, or by manual work.

For example, the values obtained in steps S1 to S6 are stored in a storage unit such as a memory.
In step S7, the condition setting unit 24 sets conditions for the packed bed (pipe) filled with the particles selected in step S1. Specifically, the condition setting unit 24 sets the porosity ε.
Subsequently, in step S8, the condition setting unit 24 sets fluid conditions. Specifically, the condition setting unit 24 sets the fluid velocity Ua, the fluid density ρa, and the fluid viscosity η. For example, with respect to the fluid density ρa and the fluid viscosity η, the fluid density ρa and the fluid viscosity η corresponding to the fluid to be used are set with reference to a table or database including the physical property values of the fluid.

  Subsequently, in step S9, the pressure loss calculator 25 calculates the equivalent spherical diameter dp of the particles calculated in step S4, the linear rate φs calculated in step S6, and the porosity ε set in steps S7 and S8. The pressure loss ΔP / L is calculated using the fluid velocity Ua, the fluid density ρa, and the fluid viscosity η. That is, here, the pressure loss ΔP / L is calculated by the equation (8).

Subsequently, in step S10, the pressure loss determination unit 26 determines whether or not the pressure loss ΔP / L calculated in step S9 is a predetermined pressure loss. For example, it is determined whether or not the calculated pressure loss ΔP / L is within a predetermined range of allowable values. Here, if the pressure loss ΔP / L calculated in step S9 is a predetermined pressure loss, the pressure loss determination unit 26 proceeds to step S11, and otherwise proceeds to step S12.
In step S11, the output unit 27 performs output processing. For example, together with the pressure loss ΔP / L calculated in step S9, the value used for the calculation is output to a monitor or other system.

  In step S12, the condition setting unit 24 determines whether or not the fluid condition can be changed. For example, it is determined whether or not the fluid speed Ua, the fluid density ρa, and the fluid viscosity η, which are fluid conditions, have values that are allowed to be changed. Here, when the fluid condition can be changed, the condition setting unit 24 proceeds to step S8, sets the condition of the fluid again (for example, changes the fluid condition within the change allowable range), and after step S9. Perform the process. If the fluid condition cannot be changed, the condition setting unit 24 proceeds to step S13.

  In step S13, the condition setting unit 24 determines whether or not the packed bed condition can be changed. For example, it is determined whether or not a change in the porosity ε, which is a packed bed condition, is allowed. Here, when the packed bed condition can be changed, the process proceeds to step S7, the packed bed condition is set again (for example, the packed bed condition is changed within the change allowable range), and the processing after step S8 is performed. Do. If the packed bed condition cannot be changed, the process proceeds to step S1, another particle is selected, and the processes after step S2 are performed.

(2-1-2) Operation, action, and effect are as follows.
Particles to be calculated or transported for pressure loss are selected (step S1), and the particle density ρs and particle mass M of the selected particles are measured (steps S2 and S3). Then, based on the particle density ρs and the particle mass M obtained by the measurement, the sphere equivalent diameter dp of the particle is calculated (step S4). Further, a two-dimensional image is acquired for a considerable number of particles, and the linear rate φs is calculated from the acquired two-dimensional image (steps S5 and S6). Further, the condition setting of the packed bed (setting of the void ratio ε) and the condition setting of the fluid (setting of the fluid velocity Ua, the fluid density ρa and the fluid viscosity η) are performed (steps S7 and S8).

  Then, the pressure loss ΔP / L is calculated using the sphere equivalent diameter dp, the linear ratio φs, the void ratio ε, the fluid velocity Ua, the fluid density ρa, and the fluid viscosity η (step S9). Here, when the calculated pressure loss ΔP / L is a predetermined pressure loss, output processing is performed, while when the calculated pressure loss ΔP / L is not a predetermined pressure loss, The pressure loss ΔP / L is calculated again by changing the packed bed condition and the fluid condition (steps S10 to S13).

  Through the processing as described above, the pressure loss ΔP / L under a certain condition can be calculated as a predetermined value (within a predetermined range). And since the calculation precision of said Formula (8) used for calculation of pressure loss is high, the pressure loss calculated in this process will also have high precision. Thus, based on the pressure loss ΔP / L calculated in this way, and further on the conditions for obtaining the pressure loss ΔP / L, the transportation line and the like are designed and operated, so that such a transportation line etc. The design and further operation can be performed with high accuracy.

(2-2) Second Embodiment The second embodiment is an air transportation plant to which the present invention is applied. In an air transportation plant, particles are transported by air.
(2-2-1) Configuration FIG. 9 mainly illustrates the configuration of the control system of the pneumatic transportation plant.
As shown in FIG. 9, the pneumatic transportation plant includes a particle image acquisition unit 21, a linear rate calculation unit 22, and a data acquisition unit 23, as in the first embodiment. The pneumatic transport plant includes a particle transport amount measurement unit 31, a line specification acquisition unit 32, an operation state determination unit 33, a control unit (calculation unit) 34, and a transport line system 35.

FIG. 10 shows a processing procedure in the pneumatic transportation plant. The processing content of each component 21-23, 31-35 which comprises an air transportation plant is demonstrated along the process sequence of FIG.
As shown in FIG. 10, when the process is started, as in the first embodiment, first, in step S21 to step S26, the particle image acquisition unit 21, the linear rate calculation unit 22, and the data acquisition unit 23 acquire various data. To do.
That is, in step S21, particles to be transported in the pneumatic transportation plant are acquired.

Subsequently, in step S22 and step S23, the data acquisition unit 23 measures the particle density ρs and particle mass M of the particles acquired in step S21, and in step S24, the particle density ρs and particle mass M obtained by the measurement. Based on the above, the sphere equivalent diameter dp of the particle is calculated. Then, the process proceeds to step S27.
On the other hand, in step S25, the particle image acquisition unit 21 acquires a two-dimensional image of the particles acquired in step S21 using an imaging device (camera or the like).

  Subsequently, in step S26, the linear rate calculation unit 22 calculates the linear rate φs. Specifically, the linear rate calculation unit 22 measures the outer peripheral length Ls of the particle and the length Li of the linear part from the two-dimensional projection image for the considerable number of particles acquired in step S25, and measures them. Using the outer circumferential length Ls and the length Li of the straight line portion, the linear rate φs is calculated by the above equation (5). Then, the process proceeds to step S27.

In step S27, the data acquisition unit 23 confirms the physical properties. Specifically, the data acquisition unit 23 confirms (acquires) the porosity ε and the bulk density ρ _B of the packed bed (pipe). The porosity ε and the bulk density ρ _B of the packed bed (pipe) are detected values or values stored in a database.
Subsequently, in step S28, the particle transport amount etc. measuring unit 31 measures the particle transport amount Msm and the air mass flow rate Mam. For example, the particle transport amount Msm and the air mass flow rate Mam are measured within a predetermined time, and the average value is obtained.

For example, the values obtained in steps S21 to S28 are stored in storage means such as a memory.
Subsequently, in step S29, the line specification acquisition unit 32 confirms (acquires) the line specification. Specifically, the line specification acquisition unit 32 confirms the particle transport amount Ms and the air mass flow rate Ma as the line specification. For example, the particle transport amount Ms and the air mass flow rate Ma are confirmed with reference to a table or database consisting of line specifications.

Subsequently, in step S30, the operation state determination unit 33 matches the particle transport amount Msm obtained by the measurement in step S28 with the particle transport amount Ms of the line specification (target value) confirmed in step S29 (predetermined value). Whether it is within the error range). Here, when the particle transport amount Msm obtained by the measurement matches the particle transport amount Ms of the line specification, the operation state determination unit 33 proceeds to step S31, and otherwise proceeds to step S32.
In step S31, the control unit 34 continues the operation. That is, the transport line system 35 is controlled under the current control conditions (supply pressure Pt and air mass flow rate Ma).

On the other hand, in step S32, the data acquisition unit 23 measures the particle velocity us.
Subsequently, in step S33, the data acquisition unit 23 or the control unit 34 selects the air mass flow rate Ma. Here, the air mass flow rate Ma is selected with reference to the air mass flow rate Mam measured in step S28 and the air mass flow rate Ma of the line specification confirmed in step S29. For example, an air mass flow rate Ma that does not differ from the air mass flow rate Ma measured in step S28 and the air mass flow rate Ma of the line specification confirmed in step S29 is selected.

Subsequently, in step S34, the control unit 34 calculates the necessary supply pressure Pt by the following equation (9). Here, the expression (9) is an expression that is generally used to calculate a supply pressure necessary for transporting particles in plug transportation.
Pt = ∫ (Ms / (A · ρ _B · us)) · ΔP / L · dL (9)
Here, ρ _B is the value confirmed (acquired) in step S27, Ms is the particle transport amount Ms (target value) of the line specification acquired in step S29, and A is the cross-sectional area in the pipeline. is there.

  Then, the equation (8) is used as the value of ΔP / L in the equation (9). In addition, due to the plug transport, the velocity of the particles is also taken into consideration, and the air velocity Ua in the equation (8) is replaced with the relative velocity (Ua-us) between the air and the particles. Thereby, ΔP / L in the equation (9) is calculated using the particle velocity us measured in step S32 in addition to the air mass flow rate Ma selected in step S33, and the calculated ΔP / L is Using this, the required supply pressure Pt is calculated.

Subsequently, in step S35, the control unit 34 becomes the air mass flow rate Ma selected in step S33 (used for calculating the pressure loss ΔP / L in step S34) and the required supply pressure Pt calculated in step S34. To control. For example, the actual supply pressure Pt is measured, and control is performed so that the difference between the measured actual supply pressure Pt and the necessary supply pressure Pt calculated in step S34 becomes zero.
And under such control, the process after said step S28 is performed again. That is, the particle transport amount Msm and the air mass flow rate Mam are measured (step S28), the particle transport amount Ms and the air mass flow rate Ma of the line specifications are confirmed (step S29), and the particle transport amount obtained by measurement is measured. It is determined whether or not Msm matches the line specification particle transport amount Ms (step S30).

(2-2-2) Operation, action, and effect are as follows.
Particles to be transported are acquired in the pneumatic transport plant (step S21), and the particle density ρs and particle mass M of the acquired particles are measured (steps S22 and S23). Then, based on the particle density ρs and the particle mass M obtained by the measurement, the sphere equivalent diameter dp of the particle is calculated (step S24). Further, a two-dimensional image is acquired for a considerable number of particles, and the linear rate φs is calculated from the acquired two-dimensional image (steps S25 and S26). Further, the porosity ε and bulk density ρ _B of the packed bed (pipe) are confirmed (obtained) (step S27).
Then, the particle transport amount Msm and the air mass flow rate Mam are measured, the particle transport amount Ms and the air mass flow rate Ma of the line specification are confirmed (acquired), and the particle transport amount Msm obtained by the measurement is the particle of the line specification. It is determined whether or not it matches the transport amount Ms (steps S28 to S30).

  Here, when the particle transport amount Msm obtained by the measurement coincides with the particle transport amount Ms of the line specification, the operation is continued (step S31). On the other hand, when the particle transport amount Msm obtained by measurement does not coincide with the particle transport amount Ms of the line specification, control is performed so as to become the particle transport amount Ms of the line specification. That is, the particle velocity us is measured and the air mass flow rate Ma is selected (steps S32 and S33). Then, the required supply pressure Pt is calculated using the particle velocity us and the air mass flow rate Ma, and control is performed based on the calculated required supply pressure Pt and the air mass flow rate Ma (steps S34 and S35). And under such control, the process after said step S28 is performed again.

By the above processing, the transport line system 35 for transporting particles is controlled so as to achieve the particle transport amount Ms of the line specification. Since the calculation accuracy of the equation (8) used for calculating the pressure loss is high, the pressure loss calculated in this process shows an accurate value. As a result, the control of the particle transport amount Ms is accurate. Will be made.
In the second embodiment, the control is performed so that the particle transport amount Ms of the line specification is achieved, but the control may be performed so that the air mass flow rate Ma of the line specification is achieved. In this case, the control is performed so that the air mass flow rate Ma of the line specification is obtained by changing the particle transport amount.

In addition, the said embodiment can also be implement | achieved by the following structures.
That is, the pressure loss ΔP / L can also be calculated from an equation obtained by adding a correction term to the equation (8).
Here, the following equation (10) is known as a modified equation of the Ergun equation that considers the influence of the wall surface (tube diameter) on the pressure loss.
ΔP / L = 150 · (1 + 2 · dp / (3 · D · (1-ε))) ² · η · (1-ε) ² / (ε ³ · dp ² ) · Ua + Cw · ρa · (1-ε ) / (Ε ³ · dp) · Ua ² (10)
Here, Cw is a coefficient (= k ₂ = 1.75), and D is a tube diameter.

Then, the equation (10) is corrected to the following equation (11) in consideration of the particle diameter, that is, the particle diameter dp ′ using the linear rate φs of the expression (6) is substituted for the particle diameter dp. The pressure loss ΔP / L is calculated by the following equation (11).
ΔP / L = 150 · (1 + 2 · dp / (3 · D · (1-ε))) ² · η · (1-ε) ² / (ε ³ · ((1−0.645 · φs) · dp ² ) · Ua + Cw · ρa · (1-ε) / (ε ³ · (1−0.645 · φs) · dp) · Ua ² (11)
Here, Cw is the same value as the characteristic value _{k 2,} for example, 1.75.

For example, in the first embodiment, in step S7, in addition to the porosity ε, the tube inner diameter D is set as the condition setting of the packed bed. In step S9, the equation (11) is set. Thus, the pressure loss ΔP / L is calculated.
In the second embodiment, in step S27, as a physical property confirmation, in addition to the porosity ε and the bulk density ρ _B , the pipe inner diameter D is confirmed (acquired). In the step S34, The pressure loss ΔP / L is calculated by the equation (11).

FIG. 11 shows the eigenvalue calculated by the above equation (1), that is, the Ergun equation that does not consider the influence of the wall surface (tube diameter) on the pressure loss when the tube diameter ratio D / dp is changed. k ₁ and k ₂ are shown.
Although must become _{k 1 = 150, k 2 =} 1.75 would otherwise, in the region tube diameter ratio D / dp is small, as shown in FIG. 11 (a), in particular eigenvalue _{k 1,} 0.99 Greatly deviate from. Thus, in the region where the pipe diameter ratio D / dp is small, the eigenvalue k ₁ does not show a correct value, that is, an error occurs in the pressure loss ΔP / L calculated by the above equation (1). The pressure loss is calculated by the equation (11) considering the influence.

  12 to 18 show changes in the ratio α between the theoretical value and the experimental value when the air velocity Ua is changed using the tube diameter D as a parameter (D = 26, 38, 50, 70). Here, the result using a straight pipe is shown. When the theoretical value is the value of the equation (11), it is a modified (Modified) α, and the theoretical value is the value of the equation (8) (the equation not considering the tube diameter D). Is not modified α.

FIG. 12 shows the results using plastic pellets (PTP), FIG. 13 shows the results using red beans (SMB), FIG. 14 shows the results using Nipolon Hard (NLH), and FIG. FIG. 16 shows the results using petrocene (PTS), FIG. 17 shows the results using hard capsules (CPS), and FIG. 18 shows the results using polystyrene pellets (PEP). The result using (PSP) is shown.
As shown in FIGS. 12 to 18, α is close to 1, that is, the theoretical value (the value of the equation (11)) in a wide range of the air velocity Ua for any particle and even for any tube diameter D. A value close to the experimental value is shown. That is, the calculation accuracy of the pressure loss ΔP / L according to the equation (11) is high.

  19 to 22 show the results obtained for a curved pipe (bend pipe). Here, the radius of curvature (1 / R) of the curved pipe is set to 10 times the pipe diameter D (R = D · 10). 19 to 22 show changes in the ratio α between the theoretical value and the experimental value when the air velocity Ua is changed with the tube diameter D as a parameter (D = 38, 50). When the theoretical value is the value of the equation (11), it is a modified (Modified) α, and the theoretical value is the value of the equation (8) (the equation not considering the tube diameter D). Is not modified α.

19 shows the results using plastic pellets (PTP), FIG. 20 shows the results using red beans (SMB), FIG. 21 shows the results using polyethylene pellets (PEP), and FIG. The result using a polystyrene pellet (PSP) is shown.
As shown in FIGS. 19 to 22, α is close to 1, that is, the theoretical value (the value of the above equation (11)) in a wide range of the air velocity Ua for any particle and even for any tube diameter D. A value close to the experimental value is shown. That is, the calculation accuracy of the pressure loss ΔP / L according to the equation (11) is high. Furthermore, it can be seen from this result that the accuracy of calculating the pressure loss ΔP / L according to the equation (11) is increased even in the case of a curved pipe.
Further, the particles filled in the packed bed or transported particles are not limited to those specifically shown in the description of the present embodiment, and may be other particles, and the fluid flowing in the pipe line Is not limited to air and may be other fluids.

  In the description of the first embodiment, the data acquisition unit 23 realizes a value acquisition unit that acquires a value for calculating the pressure loss ΔP / L, and the particle image acquisition unit 21 A two-dimensional projection image acquisition unit that acquires a two-dimensional projection image of a particle is realized, and the straight line ratio calculation unit 22 performs straight line of the particle in the two-dimensional projection image of the particle acquired by the two-dimensional projection image acquisition unit. Particle state detecting means for detecting the length of the part and the peripheral length, and a linear rate calculating means for calculating the linear ratio φs by dividing the total length of the straight line portions detected by the particle state detecting means by the peripheral length The pressure loss calculation unit 25 is configured such that the linear rate φs calculated by the linear rate calculation unit, the sphere equivalent diameter dp that is the value acquired by the value acquisition unit, the porosity ε, the fluid velocity Ua, and the fluid density. ρa and fluid viscosity η There are realizes a pressure loss calculating means for calculating the pressure loss [Delta] P / L.

  In the description of the second embodiment, the control unit 34 realizes supply pressure control means for controlling the supply pressure on the upstream side for pumping in the pipe line, and the data acquisition unit 23 A value acquisition unit that acquires a value for calculating the pressure loss ΔP / L is realized, and the particle image acquisition unit 21 realizes a two-dimensional projection image acquisition unit that acquires a two-dimensional projection image of the particle. In addition, the linear rate calculation unit 22 includes a particle state detection unit that detects a length and a peripheral length of the linear part of the particle in the two-dimensional projection image of the particle acquired by the two-dimensional projection image acquisition unit, and the particle state detection A linear rate calculating means for calculating the linear rate φs by dividing the total length of the linear portions detected by the means by dividing the circumference is realized, and the particle transport amount measuring unit 31 is provided in the pipeline. Fluid flow rate and particle transport volume The particle transport amount detection means to be output is realized, and the processing of step S34 of the control unit 34 is performed when the fluid flow rate and the particle transport amount detected by the detection means are different from the target values. The pressure loss ΔP / Based on L, the processing of the control means for changing the upstream supply pressure is realized.

It is a figure used for description of calculation of linear rate φs. It is a figure which shows an experimental apparatus outline. It is a characteristic view which shows the comparison result of the theoretical value calculated by Ergun type | formula (Formula (2)), and an experimental value. It is a characteristic view used for verification of an error between the theoretical value calculated by the Ergun equation (equation (2)) and the experimental value. It is a characteristic view showing the relationship between the particle size ratio dp ′ / dp between the effective particle size dp ′ and the particle size dp, and the linear rate φs. It is a characteristic view which shows the comparison result of the theoretical value calculated by the correction formula (Equation (8)) of the Ergun equation and the experimental value. It is a block diagram which shows the structure of the pressure loss calculation system of the 1st Embodiment of this invention. It is a flowchart which shows the process sequence of a pressure loss calculation system. It is a block diagram which shows the structure of the pneumatic transportation plant of the 2nd Embodiment of this invention. It is a flowchart which shows the process sequence of control in an air transportation plant. It is a characteristic view which shows the relationship between the pipe diameter ratio D / dp and the eigenvalues k ₁ and k ₂ calculated by the Ergun equation (Equation (1)). It shows the relationship between the air velocity Ua and the corrected equation of the Ergun equation (Equation (11)), and is a characteristic showing the results using straight pipes and plastic pellets (PTP). It shows the relationship between the air velocity Ua and the corrected equation of the Ergun equation (Equation (11)), and is a characteristic showing the results using straight pipes and red beans (SMB). It shows the relationship between the air velocity Ua and the corrected equation of the Ergun equation (Equation (11)), and is a characteristic showing the result of using a straight pipe and Nipolon hard (NLH). It shows the relationship between the air velocity Ua and the corrected equation of the Ergun equation (Equation (11)), and is a characteristic that shows the results using straight pipes and polyethylene pellets (PEP). It shows the relationship between the air velocity Ua and the corrected equation of the Ergun equation (Equation (11)), and is a characteristic that shows the results using straight pipe and petrocene (PTS). It shows the relationship between the air velocity Ua and the corrected equation (Equation (11)) of the Ergun equation, and is a characteristic showing the result using a straight pipe and a hard capsule (CPS). It shows the relationship between the air velocity Ua and the corrected equation of the Ergun equation (Equation (11)), and is a characteristic showing the results using straight pipes and polystyrene pellets (PSP). It shows the relationship between the air velocity Ua and the corrected equation of the Ergun equation (Equation (11)), and is a characteristic showing the result using a curved pipe and a plastic pellet (PTP). It shows the relationship between the air velocity Ua and the corrected equation (Equation (11)) of the Ergun equation, and is a characteristic that shows the result using a curved pipe and red beans (SMB). It shows the relationship between the air velocity Ua and the corrected equation of the Ergun equation (Equation (11)), and is a characteristic that shows the result of using a curved pipe and polyethylene pellets (PEP). It shows the relationship between the air velocity Ua and the corrected equation of the Ergun equation (Equation (11)), and is a characteristic that shows the result of using a bent tube and a polystyrene pellet (PSP).

Explanation of symbols

  21 Particle image acquisition unit, 22 Linear rate calculation unit, 23 Data acquisition unit, 24 Condition setting unit, 25 Pressure loss calculation unit, 26 Pressure loss determination unit, 27 Output unit, 31 Particle transport amount measurement unit, 32 line specification acquisition Part, 33 operation state judgment part, 34 control part, 35 transport line system

Claims (10)

In a pressure loss estimation method for estimating a pressure loss when a fluid flows through a particle layer in a pipeline,
The total linear length of the particle projected onto the two-dimensional plane is divided by the circumference of the particle projected onto the two-dimensional plane to calculate the linear rate φs, and the calculated linear rate φs is stored in the storage means. And
The sphere equivalent diameter dp of the particles, the void ratio ε, the fluid velocity Ua, the fluid density ρa and the fluid viscosity η in the pipe line are acquired, and the acquired values are stored in the storage means.
Using the linear rate φs, sphere equivalent diameter dp, porosity ε, fluid velocity Ua, fluid density ρa and fluid viscosity η stored in the storage means,
ΔP / L = 150 · (η · (1-ε) ² / (ε ³ · ((1−0.645 · φs) · dp) ² )) · Ua + 1.75 · (ρa · (1-ε) / (Ε ³ · (1−0.645 · φs) · dp)) · Ua ²
A pressure loss estimation method characterized by estimating a pressure loss ΔP / L in the pipe length L by The pipeline inner diameter D is acquired, the acquired pipeline inner diameter D is stored in the storage means, and the pipeline inner diameter D stored in the storage means is used.
ΔP / L = 150 · (1 + 2 · dp / (3 · D · (1-ε))) ² · η · (1-ε) ² / (ε ³ · ((1−0.645 · φs) · dp ² ) · Ua + 1.75 · ρa · (1-ε) / (ε ³ · (1−0.645 · φs) · dp) · Ua ²
The pressure loss estimation method according to claim 1, wherein the pressure loss ΔP / L is estimated by the following.   The pressure loss estimation method according to claim 1 or 2, wherein the pipe is a bent pipe. In the pressure loss detection device for detecting the pressure loss when the fluid flows through the particle layer in the pipeline,
Using the linear ratio φs, the sphere equivalent diameter dp of the particles, the void ratio ε, the fluid velocity Ua, the fluid density ρa, and the fluid viscosity η in the pipe,
ΔP / L = 150 · (η · (1-ε) ² / (ε ³ · ((1−0.645 · φs) · dp) ² )) · Ua + 1.75 · (ρa · (1-ε) / (Ε ³ · (1−0.645 · φs) · dp)) · Ua ²
Is used to calculate the pressure loss ΔP / L at the pipe length L.
Value acquisition means for acquiring a value for calculating the pressure loss ΔP / L;
Two-dimensional projection image acquisition means for acquiring a two-dimensional projection image of the particles;
Particle state detection means for detecting the length and circumference of the linear portion of the particle in the two-dimensional projection image of the particle acquired by the two-dimensional projection image acquisition means;
A linear rate calculating means for calculating the linear rate φs by dividing the total length of the straight line portions detected by the particle state detecting means by the peripheral length;
Using the linear rate φs calculated by the linear rate calculating unit and the sphere equivalent diameter dp, the void ratio ε, the fluid velocity Ua, the fluid density ρa, and the fluid viscosity η, which are values acquired by the value acquiring unit, Pressure loss calculating means for calculating the loss ΔP / L;
A pressure loss detection device comprising: The value acquisition means acquires a pipe inner diameter D, and the pressure loss calculation means uses the pipe inner diameter D acquired by the value acquisition means, and corrects the above formula,
ΔP / L = 150 · (1 + 2 · dp / (3 · D · (1-ε))) ² · η · (1-ε) ² / (ε ³ · ((1−0.645 · φs) · dp ² ) · Ua + 1.75 · ρa · (1-ε) / (ε ³ · (1−0.645 · φs) · dp) · Ua ²
The pressure loss detection device according to claim 4, wherein the pressure loss ΔP / L is calculated by:   The pressure loss detection device according to claim 4 or 5, wherein the pipe is a bent pipe. In a particle transport system for transporting particles by mixing particles with a fluid flowing in a pipeline,
Using the linear ratio φs, the sphere equivalent diameter dp of the particles, the velocity us of the particles, the porosity ε, the fluid velocity Ua, the fluid density ρa, and the fluid viscosity η in the pipe,
ΔP / L = 150 · (η · (1-ε) ² / (ε ³ · ((1−0.645 · φs) · dp) ² )) · (Ua−us) + 1.75 · (ρa · ( 1−ε) / (ε ³ · (1−0.645 · φs) · dp)) · (Ua-us) ²
Is used to calculate the pressure loss ΔP / L at the pipe length L.
Supply pressure control means for controlling the supply pressure on the upstream side for pumping in the pipeline;
Value acquisition means for acquiring a value for calculating the pressure loss ΔP / L;
Two-dimensional projection image acquisition means for acquiring a two-dimensional projection image of the particles;
Particle state detection means for detecting the length and circumference of the linear portion of the particle in the two-dimensional projection image of the particle acquired by the two-dimensional projection image acquisition means;
A linear rate calculating means for calculating the linear rate φs by dividing the total length of the straight line portions detected by the particle state detecting means by the peripheral length;
Particle transport amount detecting means for detecting the transport amount of the particles;
With
When the particle transport amount detected by the particle transport amount detection unit is different from a target value, the control unit corresponds to a sphere that is the linear rate φs calculated by the linear rate calculation unit and the value acquired by the value acquisition unit. Using the diameter dp, particle velocity us, porosity ε, fluid velocity Ua, fluid density ρa, and fluid viscosity η, the upstream supply pressure is changed based on the pressure loss ΔP / L given by the above equation. A particle transport system characterized by that. When the particle transportation amount detected by the particle transportation amount detection means is different from the target value, the control means is configured such that the supply pressure Pt is such that Ms is the target value of the particle transportation amount and A is the cross-sectional area in the pipeline. , Ρ _B is the bulk density and us is the particle velocity,
Pt = ∫ (Ms / (A · ρ _B · us)) · ΔP / L · dL
The particle transport system according to claim 7, wherein control is performed so that The value acquisition means acquires the pipe inner diameter D, and the control means uses the pipe inner diameter D acquired by the value acquisition means,
ΔP / L = 150 · (1 + 2 · dp / (3 · D · (1-ε))) ² · η · (1-ε) ² / (ε ³ · ((1−0.645 · φs) · dp ^{) 2) · (Ua-us} ) +1.75 · ρa · (1-ε) / (ε 3 · (1-0.645 · φs) · dp) · (Ua-us) 2
The particle transport system according to claim 7 or 8, wherein the supply pressure on the upstream side is changed based on the pressure loss ΔP / L given by.   The particle transportation system according to any one of claims 7 to 9, wherein the pipe is of a bent pipe.

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