In recent years, the suspended (boiling, fluidized) bed technique has been widely used in industrial practice as one of the existing means of intensifying a number of processes. The main processes in which fluidization of solid particles of granular materials is used include:

1. Chemical processes: catalytic cracking of petroleum products, numerous heterogeneous catalytic reactions, gasification of fuels, roasting of sulfide ores, etc.

2. Physical and physico-chemical processes: drying of fine-grained, pasty and liquid materials, dissolution and crystallization of salts, adsorption purification of gases, heat treatment of metals, heating and cooling of gases, etc.

3. Mechanical processes: beneficiation, classification, granulation, mixing and transportation of granular materials.

The fluidized layer received its name due to its external similarity to the behavior of an ordinary droplet liquid: the fluidized layer takes the shape of the containing vessel, the surface of the fluidized layer is horizontal without taking into account splashes, it is fluid and has viscosity. Bodies with a specific gravity less than the fluidized layer float in it, and bodies that have a greater specific gravity sink.

The widespread introduction of fluidization technology into industrial practice is due to a number of its advantages. Solid granular material in a fluidized state, due to fluidity, can be moved through pipes, which allows many batch processes to be carried out continuously. Thanks to the intensive mixing of solid particles in the fluidized bed, the temperature field is practically leveled, the possibility of local overheating and associated disruptions in the course of a number of technological processes is eliminated.

Along with great advantages, the fluidized bed also has some disadvantages. Thus, due to the intense mixing of solid particles, temperatures and concentrations in the layer are equalized, which reduces the driving force of the process, wear of the solid particles themselves, erosion of equipment, and the formation of large charges of static electricity occur; Fluidized bed plants require powerful dust removal devices.

Hydrodynamics of the fluidization process

The hydrodynamic essence of fluidization is as follows. If an ascending flow of a fluidizing agent (gas or liquid) passes through a layer of granular material located on a supporting gas distribution grid, then the state of the layer is different depending on the speed of this flow (Fig. 1).

Rice. 1.

a) the process of filtering gas through a layer of granular material (the particles are immobile),

b) homogeneous fluidized layer,

c) heterogeneous fluidized layer (presence of gas bubbles in the layer, significant splashes of granular material),

d) removal of granular material from the working volume of the apparatus.

The behavior of a granular material when an ascending flow of gas (liquid) passes through it is clearly illustrated by a graph of the change in pressure drop in a layer of granular material depending on the speed of the fluidizing agent (fictitious gas speed related to the cross-sectional area of ​​the apparatus), presented in Fig. 2.

Rice. 2.

On the graph of the fluidization process (Fig. 2), the filtration process corresponds to the ascending branch OA. In the case of small particle sizes and low filtration rates of the fluidizing agent, its mode of movement in the layer is laminar and the OA branch is straight. In a layer of large particles at sufficiently high speeds of the fluidizing agent, the pressure drop can increase nonlinearly with increasing speed (transition and turbulent modes).

The transition from the filtration mode to the fluidization state corresponds to the critical speed of the fluidized agent Wcr on the fluidization curve. (point A), called the onset velocity of fluidization. At the moment fluidization begins, the weight of the granular material per unit cross-sectional area of ​​the apparatus (cylindrical or rectangular in shape) is balanced by the hydraulic resistance force of the layer.

DPSl = Gsl. /F(1)

where Gsl. - weight of material in the layer, kg (N); F is the cross-sectional area of ​​the apparatus, m2.

Since the weight of the layer Gcl. = h0 (1 - e0) F (c - c0), then

DPSl. = (c -c0) (1 - e0) h0(2)

where с, с0 - density of solid particles and fluidizing agent, kg/m3;

e0 is the porosity of the fixed layer, i.e. relative void volume of the layer (for spherical particles e0 = 0.4); h0 is the height of the fixed layer, m.

Starting from the speed of the onset of fluidization and above the resistance of the layer DRsl. maintains an almost constant value and dependence of DPsl. = f (W) is expressed by straight line AB (Fig. 2), parallel to the abscissa axis, so we can write:

DPSl. = (c - c0) (1 - e0) h0 = (c - c0) (1 - e) h,

h = (1 - e0)/ 1 - e? h0(3)

where h is the height of the fluidized layer, m; e - porosity of the fluidized layer.

Depending on the properties of the fluidizing agent and its speed, several stages of fluidization can be observed.

At gas velocities slightly exceeding Wcr., i.e. at W?Wcr. so-called homogeneous fluidization is observed (Fig. 1 b). As the gas velocity increases, compact masses of gas (“bubbles”, “cavities”) appear in the layer, intensely turbulizing solid particles and forming splashes of granular material on the surface. In this case, significant pulsations of the static and dynamic pressure of the fluidized agent are observed. This type of layer hydrodynamics is called inhomogeneous fluidization (Fig. 1c). Finally, upon reaching a certain second critical value of the speed Wу, called the entrainment speed, solid particles begin to be removed from the layer (Fig. 1d) and their number in the apparatus decreases. The porosity of such a layer tends to 1, and the resistance of the layer to the right of point B (Fig. 2) also decreases.

In engineering calculations, it is very important to determine the limits of the existence of a fluidized layer (Wcr. - Wу), i.e. determine Wcr. and Wу.

To determine the value of Wcr. there are a large number of empirical, semi-empirical and theoretical dependencies proposed by various authors.

A convenient relationship for determining the critical fluidization velocity (valid for all flow regimes) is the interpolation formula of Todes, Goroshko, Rosenbaum (for spherical particles):

Recr. = Ar / 1400 + 5.22vAr(4)

where Recr. = Wcr. d /n, Ar = gd3 (c - c0)/ n2 ?c0.

The upper limit of the fluidized state corresponds to the speed of free floating of single particles (e? 1). At a flow speed exceeding the soaring speed, i.e. at Wу > Wvit. particles will be removed from the layer of granular material.

The soaring speed can also be approximately estimated using formula (4):

Revit. = Ar / 18 + 0.61 vAr,(5)

where Revit. = Wvit. d/n.

As noted above, with an increase in flow velocity, the suspended layer expands (an increase in the porosity of the layer and its height). The porosity of the suspended layer can be calculated using the formula

e = (18 Re + 0.36 Re2/Ar)0.21(6)

In formulas (4), (5), (6), the following dimensions of the main physical quantities are adopted:

d is the diameter of spherical particles, m;

n - kinematic viscosity of the fluidizing agent, m2/s;

c is the density of the particle material, kg/m3;

с0 - density of the fluidizing agent, kg/m3;

g - gravity acceleration, m/s2.

If the suspended layer is formed from a polydisperse material, then we substitute the equivalent diameter into the formulas, which is calculated using the formula

de = 1/У xi/di(7)

where xi is the mass content of the i-th fraction in fractions of a unit;

di is the average sieve size of the i-th fraction.

To calculate the values ​​of w and e from the known properties of the system (solid particles - gas), the graphical dependence is convenient

Ly = f (Ar, e), (8)

where Ly = Re3/Ar = w3с02/м0(с - с0)g - Lyashchenko criterion;

Ar = gd3с0(с - с0)/m02 - Archimedes' criterion;

Re = wdс/m0 - Reynolds criterion.

The convenience of dependence (8) lies in the fact that the Ly criterion does not contain the particle diameter, and the Ar criterion does not contain the gas velocity.

The appendix presents in logarithmic coordinates the dependence of the Ly criterion on the Ar criterion for different values ​​of e (dependence 8).

GOAL OF THE WORK

1. Obtaining the Drsl dependency. on gas speed.

2. Experimental determination of the critical fluidization rate (according to the fluidization curve) and comparing it with the calculated values ​​using formula (4) and graphical dependence (8).

3. Determination of the weight of the layer Gsl. according to formula (1) and the height of the fluidized layer according to formula (6).

4. Determination of the limits of existence of a fluidized bed for a given material (wcr. - wу.).

INSTALLATION DESCRIPTION (Fig. 3)

The installation consists of a metal column 1 mounted on a panel, having an internal diameter of 150 mm. The column has a fitting 2 for loading granular material, a device 3 for unloading material from the chamber and a gas distribution cap grille 4, having a free cross-section of 10%. For visual observation of the behavior of the fluidized layer of particles, the column is equipped with viewing windows 5 of rectangular shape. The air supplied by two fans passes through a flow meter (flat diaphragm) 6 and enters under the column grille. Air flow is regulated by valve 7. Valve 8 is used to discharge part of the air into the atmosphere. The resistance of the column without a layer of granular material on the gas distribution grid and with a layer on it is measured using a differential pressure gauge 9.

Rice. 3.

1 - vertical column, 2 - fitting for loading granular material, 3 - fitting for unloading granular material, 4 - gas distribution grille, 5 - inspection windows, 6 - flat diaphragm, 7 - valve for regulating air flow, 8 - valve for air discharge into the atmosphere, 9,10 - differential pressure gauges, 11 - battery cyclone (4-element), 12 - bag filter.

The air flow rate passing through the column is determined from the readings of a differential pressure gauge 10 attached to a flat diaphragm 6 and is calculated using the formula

E = 2.5 v?h/st, m3/h(9)

where Dh is the difference in static pressure in the throttle device, measured before and after the diaphragm (mm water column) using a differential pressure gauge 10; сt - air density at the diaphragm, kgf/m3.

Air density ct at operating conditions, i.e. temperature and barometric pressure B, calculated by the formula:

сt = с0 273 (B + P)/(273+t) 760, kg/m3 (10)

where c0 is the air density at initial conditions (t = 00C, B = 760 mm water column), kg/m3; B - barometric pressure, mm water column; P - pressure (vacuum) in the column, mm water column.

WORK PROCEDURE

When starting work, completely close valve 7 and open valve 8 to allow air to escape into the atmosphere. After this, the blowers are put into operation. The first series of experiments is carried out in the absence of a layer of granular material on the gas distribution grid.

By opening valve 7, set the initial air flow such that the reading of differential pressure gauge 10 at the flow meter is 20 mm water column. According to the readings of differential pressure gauge 9, the resistance of the entire column is measured at this flow rate. Having recorded the measurement results in the reporting table, measurements are carried out in the same sequence at the second air flow, then at the third, etc. to the maximum, each time increasing the air flow by such an amount that the reading of differential pressure gauge 10 increases by 20 mm water column. When valve 7 is fully open, a further increase in the flow rate in the column is obtained by reducing the release of air into the atmosphere, closing valve 8. At the end of this series of experiments, the air temperature in the column and barometric pressure are measured using a potentiometer and a barometer. At the end of the work, valve 8 is fully opened and valve 7 is closed.

The second series of experiments is carried out in the same sequence, but with a layer of granular material loaded onto the gas distribution grid (the quantity and name of the material are determined by the teacher’s instructions).

In this series of experiments, the resistance of the layer is measured both when the air flow rate increases and when it decreases from the maximum value to the minimum by closing valve 8. The reading of differential pressure gauge 10 should change by 20 mm water column.

Experience table

Student______________________Teacher___________

PROCESSING OF EXPERIMENTAL DATA

Based on the table data, a graph of the dependence of Drsl is constructed. from the air speed W and find from it the experimental value of the critical fluidization speed Wcr. Then the calculated values ​​of the critical fluidization speed are calculated using formula (4) and dependence (8). The values ​​of Wcr. found by experiment and calculation are compared.

Using formula (5) and dependence (8) at e = 1, the entrainment rate for a given size of granular material and the corresponding air flow rate are determined by calculation.

Using formula (6) for one of the gas flow rates (as instructed by the teacher), the porosity of the suspended layer is determined.

According to formula (3), using the found layer porosity value, the height of the fluidized bed is determined for a given weight load.

Using formula (1), the weight of the layer is determined and compared with the experiment.

Note: the bulk density of the material and the diameter of the particles are determined experimentally.

COMPILATION OF A REPORT

The report on laboratory work is drawn up on sheets of format II (297x210). The title page must correspond to the title page of the methodological instructions for the work, indicating the department, the title of the work, its number, surname, and affiliation. student, group, specialty and surname, acting teacher who accepted the job.

The report must present:

Description of the purpose of the work,

Laboratory setup diagram,

Description of the installation operation,

Methodology of work,

The experimental data obtained,

Results of processing experimental data,

SAFETY WHEN PERFORMING LABORATORY WORK

1. Before starting work you must:

Make sure that there is no obvious damage to the laboratory installation;

Check the presence of rubber mats in front of the control panel;

Check the presence of dust collectors at the battery cyclone and bag filter.

2. During operation:

Follow these instructions strictly;

To avoid the release of liquid from the differential pressure gauge 10, turn on the second blower with valve 8 fully open, which serves to discharge part of the air into the atmosphere.

CHECK QUESTIONS FOR ADMISSION TO PERFORM ABORATORY WORK

1. What is the purpose of the upcoming work?

2. What elements does the laboratory setup consist of and what is the purpose of each of them?

3. Explain the design and operating principle of the battery cyclone and bag filter.

4. What is the procedure for performing laboratory work?

5. What experimental data are recorded while performing the work?

SAMPLE LIST OF QUESTIONS FOR PROTECTING THE RESULTS OF ABORATORY WORK

1. What causes the widespread use of fluidized beds in technology?

2. What possible states of a layer of solid particles can be observed depending on the speed of the upward flow of gas passing through the layer?

3. What is the fluidization rate, how to determine it?

4. What is pneumatic transport and at what speeds is this phenomenon observed?

5. Under what conditions and the equality of what forces is the onset of fluidization observed?

6. What is the speed of free floating of particles and why can this speed be determined in the same way as the speed of free settling of a single particle?

7. Why is the phenomenon of hysteresis observed when the flow rate decreases after fluidization of the bed?

8. What are the limits of the existence of a fluidized bed?

9. What is the fluidization number and what does it characterize?

10. What is homogeneous and inhomogeneous fluidization?

11. Do and how do the properties of granular material affect the nature of fluidization?

12. Name the main hydrodynamic characteristics of fluidized beds.

13. Under what conditions is piston fluidization observed?

BIBLIOGRAPHICAL LIST

1. Pavlov K.F., Romankov P.G., Noskov P.G. Examples and tasks for the course “Processes and apparatus of chemical technology”. - L.: Chemistry, 1987.

2. Zabrodsky S.S. Hydrodynamics and heat transfer in a fluidized bed. - M.: Gosenergoizdat, 1963.

3. Romankov P.G., Noskov A.A. Collection of calculation diagrams for the course of processes and apparatus of chemical technology. - L.: Chemistry, 1977.

Mixed hydrodynamics problem

In technological processes for the production of building materials, the movement of flows through a layer of granular or lump materials is quite common. Almost no aerodynamic calculation in ceramic or binder technology can be carried out without knowledge of the laws of fluid movement through granular layers.

The granular layer may consist of particles of the same size or of particles of different sizes (i.e., it can be monodisperse or polydisperse).

The mode of flow through such layers depends on many factors. The distribution of velocities over the cross section of the layer is primarily affected by physical properties of the flow and structure of the granular layer.

The granular layer is characterized by:

· layer porosity- (V – total volume of the layer; V 0 – volume occupied by the particles of the layer);

· specific surface s;

· equivalent channel diameter d e and their tortuosity;

· particle soaring speed.

Pressure loss when fluid moves through a granular layer, they can be determined similarly to the calculation of pressure losses due to friction in pipelines:

, (6.10)

where l is a coefficient reflecting the influence of not only friction resistance, but also additional local resistance of intergranular channels, i.e. l is total resistance coefficient.

Significant difficulties in calculating pressure losses are caused by determining the equivalent diameter of tortuous intergranular channels. It has been established that the calculation of the equivalent diameter can be determined by the formula:

It is quite difficult to determine the actual soaring speed included in equation (10). Therefore, in practice they calculate the so-called fictitious speed w 0 , which is equal to the ratio of the volumetric flow rate of liquid to the entire cross-sectional area of ​​the granular layer. When determining it, the curvature of the channels is neglected (curvature coefficient a=1), i.e. It is assumed that the length of the channels is equal to the height of the layer h. In this case, the fictitious speed is determined by the formula:

Then the pressure loss when the fluid moves through the granular layer:

(6.13)

As with the movement of liquid in a pipeline, l depends on the mode of movement of the liquid. It has been experimentally established that the generalized equation for calculating the drag coefficient is applicable for all flow regimes:

(6.14)

When a fluid moves through granular layers, turbulence in the flow develops much earlier than when flowing through pipes, without a sharp transition from one regime to another. An almost laminar regime exists at Re £ 50. At Re > 7000, a self-similar (with respect to the Reynolds criterion) region of turbulent flow is observed. Then l = 2.34 = const.

Pressure loss largely depends on the porosity of the layer, which, in turn, largely depends on the method of loading the layer into the apparatus and on the ratio of the diameters of the grain and the apparatus. In practice, with a free backfill of the free volume layer, e = 0.35...0.5.

The density of the layer adjacent to the walls of the apparatus is less than in the center. It's connected with wall effect. The larger the ratio of the diameter of the apparatus and the grain (D/d), the smaller the near-wall effect and the less uneven the distribution of flow velocities in the center and in the peripheral zone of the apparatus.

When a liquid moves from bottom to top through a layer of loosely poured granular material, particles of the solid phase experience drag, which depends on changes in flow speed. This leads to a certain mobile state of the grains.

The different mobile states of the granular layer are widely used in the processes of drying powder materials in a fluidized bed, when transporting powders, mixing them, etc.

At low speeds the flow of liquid passing through the granular layer from below, the latter remains motionless, because flow passing through intergranular channels, filtered through layer.

As the flow speed increases, the gaps between the particles increase - the flow seems to lift them. The particles move and mix with the liquid. The resulting mixture is called suspended or fluidized bed, because As a result of continuous mixing in an upward flow, the mass of solid particles comes into a highly mobile state, similar to a boiling liquid.

The state and conditions of existence of the suspended layer depend on:

· upstream speed;

· physical properties of the system: density, viscosity, particle size, etc.

Depending on the speed of fluid movement, there are three modes that characterize the interaction of the flow and the individual grain of the material:

1) the layer will remain motionless in the upward flow if the flow speed is less than the speed of particles hovering ( filtration);

2) the layer will be in a state of equilibrium (hovering) if the flow speed is equal to the speed of hovering particles ( suspended layer);

3) solid particles will move in the direction of the flow if the flow speed is higher than the particle soaring speed ( entrainment).

In Fig. 6.3 shows graphs of changes in the height of the granular layer and the pressure drop in it depending on the value of the fictitious speed.

The speed at which the immobility of the layer is broken and it begins to enter a fluidized state is called fluidization speed w ps .

Rice. 6.3 Dependence of layer height and its hydraulic resistance on flow speed

When the fictitious flow speed increases to the fluidization speed, the layer height remains practically unchanged, but the hydraulic resistance increases. The pressure drop in the layer corresponding to point B (Fig. 6.3b), immediately before the start of fluidization (point C), is slightly greater than that required to maintain the layer in suspension, which is due to the action of adhesion forces between the particles of the layer. When the flow reaches fluidization speed, the adhesion forces between the particles are overcome, and the pressure drop becomes equal to the weight of the particles. This condition is satisfied for the entire region of existence of the fluidized layer (line CE). With a further increase in the flow speed, the layer is destroyed and mass entrainment of particles begins, corresponding to the soaring speed.

Consequently, the limits of the existence of a fluidized layer are limited by the speeds w ps and w vit. The ratio of the operating flow rate to the speed at which fluidization begins is called fluidization number K w .

In the building materials industry, fluidization processes are most often used in the gas-solid phase system. For this system, fluidization is usually non-uniform: part of the gas moves through the layer in the form of bubbles or through one or more channels through which a significant amount of gas escapes.

At large values ​​of K w, the movement of gas in the form of bubbles leads to heterogeneity of the fluidized layer and fluctuations in its height (lines CE and CE 1 B in Fig. 6.3, a), while the bubbles can increase to the size of the entire cross-section of the apparatus. This mode of operation is called piston fluidization. It is extremely undesirable, just like gushing, which is the limiting case of the merging of gas flows moving through several channels into one, usually near the axis of the apparatus.

In various technological processes, one often has to deal with the movement of flow through layers of granular or lump materials, as well as packing elements of various sizes and shapes. In this case, the layer can be monodisperse (consist of particles of the same size). Such movement is typical for hydromechanical processes carried out in scrubbers, filters, centrifuges, dryers, adsorbers, extractors, chemical reactors and other devices.

When the free space between the particles of the layer is filled with liquid or gas, the flow simultaneously flows around individual particles or elements of the layer and moves inside the pores and voids, forming a system of tortuous channels of variable cross-section. Depending on the flow speed, the following cases are possible:

– liquid or gas at a low flow rate passes through the layer, like through a filter. In this case, the solid particles forming the layer are at rest and the pressure drop or resistance of the layer also increases as the flow speed increases;

– a layer of particles of solid material, upon reaching a certain flow rate, begins to noticeably increase in volume, its individual particles acquire the ability to move and mix, and the pressure drop, i.e. the layer resistance becomes constant;

– particles of the layer material with a further increase in the speed of liquid or gas flow are carried away by the flow and form a suspension. This state occurs when the resistance to motion of an individual particle suspended in a liquid or gas becomes equal to the weight of the particle in this medium. This state of a layer of solid material is called fluidized, and the layer – boiling. The speed of particles of solid material suspended in a flow is called speedwithania;

– when the flow speed increases to a value greater than the soaring speed, i.e.
, solid particles are carried out by flow from the apparatus;

– if the flow speed is less than the soaring speed, i.e.
,Suspended solids settle under the influence of gravity.

The main characteristics of a layer of granular or lumpy material are porosity , particle size , their geometric shape and specific surface area .

Porosity represents the fraction of free volume in the total volume of the layer

(1.97)

Where
– layer volume, free volume and solid phase volume, respectively;
– bulk density of the granular material and the density of the material itself.

Specific surface areaf(m 2 / m 3) is the surface of solid particles per unit volume of the layer. In a monodisperse layer of spherical particles with a diameter The specific surface area can be determined through the porosity of the layer and the particle size:

. (1.98)

The equivalent diameter of the channels formed by the voids between particles of solid material can also be calculated using bed porosity and particle size:

. (1.99)

Movement of fluid through a fixed layer

The resistance law for a stationary layer of granular materials, by analogy with equation (1.60), can be written in the form

, (1.100)

Where
– loss of pressure when a liquid or gas flow moves through the layer; – layer height;
– flow speed;
– equivalent diameter of channels between solid particles;
– coefficient of hydraulic resistance of the layer.

Equation (1.100) includes the difficult-to-determine actual flow velocity. It is usually expressed in terms of speed, conventionally related to the total cross-section of the layer or apparatus. This speed, equal to the ratio of the volumetric flow rate of the liquid to the entire cross-sectional area of ​​the layer, is called fictitious speed and is denoted by . The relationship between real and fictitious speed is expressed by the relation

. (1.101)

In reality the speed
less than what follows from relation (1.101) due to the curvature of the channels. However, this difference does not have a significant impact on the type of calculated relationship for determining hydraulic resistance.

If we correct for the tortuosity of the channels
, substitute values
And
, we get

(1.102)

, (1.103)

Where – density of the liquid moving through the layer.

Magnitude
is a function of the flow regime through the layer. The critical value of the Reynolds criterion, corresponding to the end of the laminar regime, is taken equal to
. In the case of laminar mode, to determine
you can use the expression obtained earlier for the flow in a straight pipe, according to which

. (1.104)

(1.105)

. (1.106)

In turbulent mode, determination
is associated with additional difficulties due to the influence of surface roughness of solid particles. Therefore, in practice, they use a universal semi-empirical formula that allows one to determine the pressure drop p in an unlimited range of Re values:

. (1.107)

When fluid moves through stationary granular layers, the flow flows around individual elements of the layer and moves inside channels of complex shape. The analysis of such motion represents a mixed problem of hydrodynamics. To simplify the calculation of such processes, they are considered as an internal problem. Then we can write

Here the friction coefficient is total resistance coefficient, depends on the geometric characteristics of the granular material and is determined by empirical equations.

The difficulty when calculating using the above equation is the determination of the equivalent diameter, which is expressed through the main characteristics of the granular material - specific surface And free volume.

Specific surface area- - surface of particles of material located in a unit of volume occupied by this material.

Free volume (layer porosity)- - the ratio of voids between particles to the volume occupied by this material.

Where is the total volume occupied by the granular layer;

Free layer volume;

The volume occupied by the particles forming a layer (i.e., a dense monolithic material of particles).

A dimensionless quantity, expressed in fractions or percentages.

If is the density of the material; - bulk density of the material and taking into account that, we get

Porosity depends on the method of loading the material. With free filling of spherical particles, porosity can be from 0.35 to 0.45, and also depends on the ratio of the diameter of the apparatus and the diameter of the particles. At<10 проявляется wall effect - an increase in the porosity of the layer near the wall compared to the porosity in the central part of the apparatus. This leads to an uneven distribution of velocities across the cross section of the apparatus (near the wall the velocity can be much higher). As a result, flow particles slip through without prolonged contact with the layer particles. This phenomenon is called bypassing .

The equivalent diameter of the granular layer can be determined as

where is the cross-sectional area of ​​the channel, is the wetted perimeter of the channel formed by granular material or nozzle.

The volume of the granular layer in the apparatus, where is the cross-section of the apparatus filled with a granular layer to a height. Then. The surface of particles, equal to the surface of the channels they form, can be defined as:

Let us denote >1, where is the length of the channels.

Then the free volume of the granular layer is hence, where is the number of channels in the layer of granular material or packing. Considering that

You can express it like this.

End of work -

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Subject and objectives of the discipline
Chemical technology considers processes in which starting materials change their physical and chemical properties. Chemical technology studies the production processes of various

Basic processes of chemical technology
Classification of the main processes of chemical technology. Stationary and non-stationary processes. Continuous and batch processes. Medium continuity hypothesis. Modes of movement of the environment. Classification

Medium continuity hypothesis
The liquid medium fills the volume without any free spaces, in a continuous manner. The liquid medium, due to a change in the distance between particles, changes the external configuration, i.e. deform

Modes of movement of liquid media
When a liquid medium (liquid) flows, two modes are realized: laminar and turbulent Laminar mode - the liquid flows at low speed, in separate jets

Equilibrium conditions
The state of an isolated system at equilibrium is determined only by internal conditions. Therefore, the differentials of intensive parameters must be equal to zero: - condition

Molecular mechanism
The molecular mechanism of substance transfer is due to the thermal movement of molecules. The interaction between molecules can be represented as “hard” repulsion at small distances between their centers

Condition for the manifestation and direction of transfer processes
If the system is in equilibrium, then macroscopic transfer of substance does not occur. Thermal motion of molecules in all directions is equally probable. Equilibrium in one phase

Mass transfer. Molecular mechanism of mass transfer
Molecular mass transfer in a homogeneous mixture is called molecular diffusion. Directed movement of the i-th component occurs only if there is a gradient in the medium

Turbulent mass transfer mechanism
Turbulent mass transfer can be considered by analogy with molecular transfer, as a consequence of the chaotic movement of vortices. Instead of the molecular diffusion coefficient Dm in

Local form of conservation of mass
z jmx jmx+dx x &nb

Integral form of the law of conservation of energy (first law of thermodynamics)
The change in energy in the system is caused by the difference in energy inflow and outflow. Considering that energy can be transferred in the form of heat and work, we can write: E¢ = (Q¢Tpr

Local form of the law of conservation of energy
The local energy conservation equation can be obtained for a unit volume as follows: The transferred substance is the energy of a unit volume rE¢. T

Local form of the law of conservation of momentum
Similar to the laws of conservation of mass and energy, one can obtain a local (for a point) form of the law of conservation of momentum. The difference will be only in the vector nature of the transfer

Uniqueness conditions
The general solution of a differential equation describes a whole class of processes. To obtain a particular solution, it is necessary to specify uniqueness conditions. They include: 1) geometric shape and

Analogy of transfer processes
The analogy of the transfer equations of the corresponding substances and the conservation laws is determined by the identity of the mechanisms of transfer of substances. Complete analogy, i.e. field match C

Local form of equations
Let us consider an elementary section of the interphase surface dF, coinciding with the XOY plane. The flow of substances is directed along the Z axis, the phase movement is along the X axis. Z

Local form of equations
Let us consider the transfer of a substance from phase 1 through the interphase surface to phase 2 due to molecular and turbulent mechanisms. Let us assume that the resistance to substance transfer from the interphase p

Integral form of equations
By averaging the local equations of interphase transfer of substances over a section of surface F, one can obtain the integral form of the equations: , (2.85) , (2.86) . (2.8

Hydrodynamic similarity
Let's write the H-C equation for the z axis. If the motion is steady, then we replace the differentials with finite values, - the defining size

The problem of large-scale transition for industrial devices
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Model identification
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Flow Structure Models
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Hydromechanical processes and devices
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Bernoulli's equation
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Calculation of complex pipelines
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Main line calculation
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Basics of gas pipeline calculations
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Fluidized beds
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Pneumatic and hydraulic transport
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Calculation of hydraulic resistance of devices and optimization of movement in them
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Advocacy
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Granular and porous layers

In many chemical technology processes, droplet liquids or gases move through stationary layers of materials consisting of individual elements.

The shape and size of the elements of granular layers are very diverse: the smallest particles of filter cake layers, granules, tablets and pieces of catalysts or adsorbents, large packed bodies (in the form of rings, saddles, etc.) used in absorption and distillation columns. In this case, granular layers can be monodisperse or polydisperse depending on whether the particles of the same layer are the same or different in size.

When a liquid moves through a granular layer, when the flow completely fills the free space between the particles of the layer, we can assume that the liquid simultaneously flows around the individual elements of the layer and moves inside channels of irregular shape formed by voids and pores between the elements. The study of such motion, as indicated, constitutes a mixed problem of hydrodynamics.

When calculating the hydraulic resistance of a granular layer, a dependence similar in form to equation (II.67a) can be used to determine the pressure loss due to friction in pipelines:

However, the coefficient l in equation (II.75) only formally corresponds to the friction coefficient in equation (II.67a). It reflects not only the influence of friction resistance, but also additional local resistances that arise when the fluid moves along curved channels in the layer and flows around individual elements of the layer. Thus, l in equation (II.72) is the overall resistance coefficient.

Equivalent diameter d e corresponding to the total cross-section of the channels in the granular layer can be determined as follows.

The granular layer is characterized by the size of its particles, as well as the specific surface area and the proportion of free volume.

Specific surface a(m 2 / m 3) represents the surface of elements, or particles of material located in a unit volume occupied by a layer,

Free volume fraction, or porosity e, expresses the volume of free space between particles per unit volume occupied by the layer.

If V− the total volume occupied by the granular layer, and V 0 is the volume occupied by the elements themselves, or particles forming the layer, then e = ( V− V 0)/V, i.e. is a dimensionless quantity.

Let the cross section of the apparatus filled with a granular layer be S (m 2), and the layer height is N (m). Then the volume of the layer V=SH and volume V 0 = SH(1 − e). Accordingly, the free volume of the layer V St. =SH e, and the surface of the particles, equal to the surface of the channels they form, is Sha.

In order to determine the total cross-section of the channels of the layer, or the free cross-section of the layer, necessary for calculating d uh, we need to divide the free volume of the layer V sv for the length of the channels. However, their lengths are not the same and must be averaged. If the average length of the channels exceeds the total height of the layer by a times, then the average length of the channels is equal to a H, and the free cross section of the layer is SH e/a to H = S e/a k, where a k is the channel curvature coefficient.

The wetted perimeter of the free section of the layer can be calculated by dividing the total surface of the channels by their average length, i.e. SH a/a to H = S a/a k.

Consequently, the equivalent diameter of the channels in the granular layer, according to equation (II.27a), will be expressed by the ratio

(II,76)

Thus, the equivalent diameter for a granular layer is determined by dividing the quadruple share of the free volume of the layer by its specific surface area.

Equivalent diameter d e can also be expressed in terms of the size of the particles that make up the layer. Let at 1 m 3 occupied by the layer, there is P particles. The volume of the particles themselves is equal to (1 - e), and their surface area is a,

Average volume of one particle

and its surface

Where d- the diameter of an equivalent sphere having the same volume as the particle; F- shape factor determined by equation (II.76); for spherical particles F = 1.

Then the ratio of the particle surface to its volume

Substituting the value a into equation (II.76), we get

For polydisperse granular layers, the calculated diameter d calculated from the ratio

Where x i- volumetric or, at the same density, mass fraction of particles with a diameter d i. When determining the dispersed composition by sieve analysis, the values di represent the average sieve sizes of the corresponding fractions, i.e. average values ​​between the sizes of pass and non-pass sieves.

Equation (II.72) includes the actual fluid velocity in the channels of the layer, which is difficult to find. Therefore, it is advisable to express it in terms of speed, conventionally related to the total cross-section of the layer or apparatus. This speed, equal to the ratio of the volumetric flow rate of the liquid to the entire cross-sectional area of ​​the layer, is called fictitious speed and is designated by the symbol w 0 .

In this case, to calculate the actual speed, the curvature of the channels through which the liquid moves in the layer is conventionally neglected, i.e. consider the average length of the channels to be equal to the height H layer (a k = 1). At l = N the total cross-section of the channels is SH e/ H = S e; the product of this cross section and the speed w in the channels is equal to the volumetric flow rate, which can also be determined by the product Sw 0 . From here S e w = Sw 0 . Accordingly, the relationship between the actual speed w and fictitious speed w 0 is expressed by the relation

Actually the value w the fluid velocity in real channels is lower, and to a greater extent, the greater the curvature coefficient w j. However, this difference does not have a significant impact on the form of the design equation for hydraulic resistance. Therefore, into equation (II.72) we substitute w, according to expression (II.73), and instead of the channel length l- overall height H layer. Moreover, instead of d e into equation (II.74) we substitute its expression in accordance with dependence (II.77), Then we get

(II,81)

Resistance coefficient H, as with the movement of liquid in pipes and the movement of bodies in liquids, depends on the hydrodynamic regime, determined by the value of the Reynolds criterion. In this case, after substituting w from expression (II.81) and d e, according to dependence (II.75), the expression of the Reynolds criterion takes the form

Where W- mass velocity of the liquid, divided by 1 m 2 apparatus cross-section, kg/ m 2 sec).

When replacing the specific surface area in expression (II.82) a its value from dependence (II.81) or by direct substitution into Re of the quantity d e, according to equation (II.77), we obtain the relation:

(II.83)

The dimensionless complex Re 0 is a modified Reynolds criterion, expressed in terms of fictitious fluid velocity and layer particle size ( d- the diameter of a ball having the same volume as the particle).

A number of dependencies have been proposed for calculating the resistance coefficient R, under different modes of fluid movement through the layer. All these equations were obtained by summarizing the experimental data of various researchers and give results that are more or less consistent with each other. For all driving modes, in particular, the generalized equation is applicable

In this equation, the Re 0 criterion is expressed by dependence (II.82) or (II.83).

It should be noted that when a liquid (gas) moves through a granular layer, turbulence develops in it much earlier than when flowing through pipes, and there is no sharp transition between laminar and turbulent regimes. The laminar regime practically exists at approximately Re< 50. В данном режиме для зернистого слоя l = A/Re [ср. с урав­нениями (II,53) и (II,62)].

At Re< 1 вторым слагаемым в правой части уравнения (II,85) можно пренебречь и определять l по уравнению

At Re > 7000, a self-similar region of turbulent motion in the granular layer occurs, when the first term on the right side of equation (II.134) can be neglected. In this case

[cf. with expressions (II.60) and (II.62) for the flow of liquid through pipes and for the movement of bodies in liquids].

Equation (II.85) is applicable for granular layers with a relatively uniform distribution of voids (layers of balls, granules, grains, particles of irregular shape). At the same time, for ring-shaped nozzles, the values ​​of l according to this equation in turbulent mode are underestimated due to the fact that the internal cavities of the rings disrupt the uniformity of the distribution of voids.

Let us consider in more detail the laminar movement of liquid through a granular layer. This regime of liquid flow is often observed in one of the common processes for separating inhomogeneous systems - filtration through a porous medium (a layer of sediment and holes in the filter partition). With a small pore diameter and a correspondingly low Re value (less than critical), the movement of liquid during filtration is laminar. Substituting l from equation (II.85a) and expression (II.72) for Re into equation (II.81), after elementary transformations we obtain

where j Ф is the shape factor related to the shape factor by the relation

j Ф = 1/Ф 2 (II.86a)

Equation (II.86) can be used to calculate the resistivity of the sediment when its particle size is large enough.

From equation (II.86) it is clear that the hydraulic resistance of the granular layer during laminar fluid movement is proportional to its speed to the first power.

As turbulence increases, the effect of fluid velocity on hydraulic resistance increases. In the limit - for the self-similar region - substituting the value l from expression (II.74) into equation (II.70) leads to a quadratic dependence D R from speed.

The values ​​of e, a, Ф (or j Ф) for various materials with different methods of loading them are, as a rule, found experimentally and are given in reference literature.

Experimentally, F (or j f) is often determined by measuring the hydraulic resistance of a layer consisting of particles of a given material of the appropriate size, with a known fraction of free volume. Having measured D R at a certain value W 0, corresponding to the laminar regime, and a fixed temperature (and therefore viscosity) of the liquid, calculate Ф (or j f) using equation (II.75).

Porosity e largely depends on the method of loading the layer. Thus, with a free filling of a layer of spherical particles, the fraction of the free volume of the granular layer can be taken on average as e » 0.4. However, in practice e in this case can vary from 0.35 to 0.45 or more. In addition, the value of e may depend on the relationship between the diameter d particles and diameter D apparatus in which the layer is located. This is due to the so-called wall effect: the packing density of particles adjacent to the walls of the apparatus is always lower, and the porosity of the layer near the walls is always higher than in the central part of the apparatus. The indicated difference in porosity is the more significant, the greater the ratio d/D. Yes, when d/D= 0.25, i.e. when the diameter of the apparatus is only four times the diameter of the layer particles, the porosity of the layer can be approximately 10% greater than in an apparatus in which the influence of the walls is negligible. As a result, when modeling industrial devices with a granular layer, the diameter of the model must exceed the diameter of the layer particles by at least 8-10 times.

The wall effect not only changes the porosity of the layer, but also leads to uneven porosity across the cross section of the apparatus. This, in turn, causes an uneven distribution of flow velocities: the velocities near the walls, where the fraction of the free volume of the layer is greater and the resistance to movement is lower, exceed the velocities in the central part of the apparatus. Thus, in the near-wall layers, breakthrough (“bypass”) of a larger or smaller part of the flow can occur without sufficiently long contact with the granular layer.

Some devices work with a moving granular layer, the movement of gases (less often liquids) occurs through dense granular layers slowly moving from top to bottom (under the influence of gravity). For example, adsorbers with a moving layer of granular sorbent operate on this principle. The hydraulic resistance of a moving granular layer differs from the resistance of a stationary layer due to an increase in the proportion of free volume of the layer during its movement, as well as some entrainment of gas (or liquid) by the moving layer. Data for calculating the hydraulic resistance of moving granular layers are given in specialized literature.