Technological modeling of the filtration process. Filtration
1.4.1 Technological simulation of the filtration process
Modeling of technological processes is based on the assumption that when the process changes within certain limits, the physical essence of the phenomena reproduced in production does not change and the forces acting on the development object do not change their nature, but only their magnitude. Technological modeling is especially effective when a purely mathematical description of the process is difficult and experiment is the only means of studying it. In these cases, the use of simulation methods eliminates the need for experimenting with a large number of possible options for choosing process parameters, reduces the duration and volume of experimental studies, and makes it possible to find the optimal technological regime by simple calculations.
Application methods technological modeling in the field of water purification is of great importance as a scientific basis for the intensification and improvement of the operation of existing treatment facilities. These methods point to a system of relatively simple experiments, the processing of the results of which makes it possible to discover hidden reserves of productivity and establish the optimal technological regime for the operation of structures. The use of technological modeling also makes it possible to generalize and systematize experimental and operational data for various types of water sources. And this makes it possible to significantly reduce the amount of experimental research related to the design of new and intensification of existing structures.
To carry out a filtration process analysis, it is necessary to have an installation, the scheme of which is shown in Figure 3. The main element of the installation is a filter column equipped with samplers. To reduce the influence of the near-wall effect, and also to ensure that the flow rate of water taken by samplers is not more than the value allowed for practical experiments, the filter column should have a diameter of at least 150...200 mm. The height of the column is assumed to be 2.5...3.0 m, which ensures the location of a sufficient layer of filter material in it and the formation of sufficient space above the load to increase the water level with an increase in pressure loss in the filter material.
Samplers are installed evenly along the height of the filter column loading at a distance of 15...20 cm from each other. The sampler, located before the water enters the load, serves to control the concentration of suspended matter in the source water. The sampler, located behind the loading, serves to control the quality of the filtrate. The remaining samplers are designed to determine the change in the concentration of suspension in the thickness of the granular load. To obtain reliable results, the filter column must have at least 6 samplers. During the experiment, a continuous outflow of water from the samplers is ensured. The total flow of water from the samplers should not exceed 5% of the total flow of water passing through the column. The column is also equipped with two piezometric sensors to determine total loss pressure in the thickness of the filtering load.
The filter column is loaded with as homogeneous a granular material as possible. It is desirable that the average grain diameter of the load is between 0.7 and 1.1 mm. The thickness of the sand layer must be at least 1.0 ... 1.2 m. The required amount of loading is calculated by the formula
m = r (1 - n) V ,
where m is the mass of the washed and sorted filter material, kg; r - loading density, kg / m 3; n - intergranular porosity of the filter media; V - required loading volume, m 3 .
After filling the filter column, the filter material is compacted by tapping on the column wall until the upper surface of the material reaches the mark corresponding to the specified load volume, when the porosity of the load is equal to the porosity of this material in a real large-scale filter. (5...10 m/h)
2 Settlement and technological part
2.1 Use of filter media in water treatment
2.1.1 Basic parameters of the filter media
Filter loading is the main working element of filtering facilities, therefore right choice its parameters is of paramount importance for their normal operation. When choosing a filter material, the fundamental factors are its cost, the possibility of obtaining this filter complex in the construction area and compliance with certain technical requirements, which include: proper fractional composition of the load; a certain degree of uniformity in the size of its grains; mechanical strength; chemical resistance of materials in relation to filtered water.
The degree of homogeneity of the size of the grains of the filter load and its fractional composition significantly affect the operation of the filter. The use of coarser filter material entails a reduction in the quality of the filtrate. The use of a finer filter material causes a reduction in the filter cycle, excessive consumption of wash water and an increase in the operating cost of water treatment.
An important indicator The quality of the filter material is its mechanical strength. The mechanical strength of filter materials is evaluated by two indicators: abrasion (i.e., the percentage of material wear due to grain friction during washings - up to 0.5) and grindability (wear percentage due to grain cracking - up to 4.0).
An important requirement for the quality of filter materials is their chemical resistance to filtered water, that is, that it is not enriched with substances that are harmful to human health (in drinking water pipes) or to the technology of the production where it is used.
In addition to the above technical requirements, filter materials used in domestic and drinking water supply undergo a sanitary and hygienic assessment for trace elements passing from the material into the water (beryllium, molybdenum, arsenic, aluminum, chromium, cobalt, lead, silver, manganese, copper, zinc, iron, strontium).
The most common filter material is quartz sand - river or quarry. Along with sand, anthracite, expanded clay, burnt rocks, shungizite, volcanic and blast-furnace slags, granodiorite, expanded polystyrene, etc. are used (table 2).
Expanded clay is a granular porous material obtained by firing clay raw materials in special furnaces (Figure 4).
Burnt rocks are metamorphosed coal-bearing rocks that have been burned during underground fires.
Volcanic slag - materials formed as a result of the accumulation of gases in a liquid cooling lava.
Shungizite is obtained by roasting a natural low-carbon material - shungite, which is close to crushed expanded clay in its properties.
Waste can also be used as filter media. industrial productions, blast-furnace slags and slags of copper-nickel production.
Expanded polystyrene is also used as a filter material on the filters. This granular material is obtained by swelling as a result of heat treatment of the starting material - polystyrene beads produced by the chemical industry.
Table 3. Main characteristics of filter materials
| materials | size, | Bulk bulk density | Density, | Porosity, | mechanical strength, | Coefficient |
|
| abrasion | grindability | ||||||
| Quartz sand | 0.6¸1.8 | 2.6 | 42 | 1.17 | |||
| Expanded clay crushed | 0.9 | 400 | 1.73 | 74 | 3.31 | 0.63 | - |
| Expanded clay not crushed | 1.18 | 780 | 1.91 | 48 | 0.17 | 0.36 | 1.29 |
| Anthracite crushed | 0.8¸1.8 | 1.7 | 45 | 1.5 | |||
| Burnt rocks | 1.0 | 1250 | 2.5 | 52¸60 | 0.46 | 3.12 | 2.0 |
| shungizite crushed | 1.2 | 650 | 2.08 | 60 | 0.9 | 4.9 | 1.7 |
| Volcanic slag | 1.1 | - | 2.45 | 64 | 0.07 | 1.05 | 2.0 |
| Agloporite | 0.9 | 1030 | 2.29 | 54.5 | 0.2 | 1.5 | - |
| granodiorite | 1.1 | 1320 | 2.65 | 50.0 | 0.32 | 2.8 | 1.7 |
| clinoptilolite | 1.15 | 750 | 2.2 | 51.0 | 0.4 | 3.4 | 2.2 |
| granite sand | 0.8 | 1660 | 2.72 | 46.0 | 0.11 | 1.4 | - |
| blast furnace slag | 1.8 | 2.6 | 44.0 | - | |||
| Styrofoam | 1.0¸4.0 | 0.2 | 41.0 | 1.1 | |||
| Gabbro diabase | 1.0 | 1580 | 3.1 | 48.0 | 0.15 | 1.54 | 1.75 |
These filter materials do not cover the entire variety of local filter materials offered in recent years. There are data on the use of agloporite, porcelain chips, granodiorite, and so on.
Active filter materials are used, which, due to their properties, can extract from water not only suspended and colloidal impurities, but also truly dissolved impurities. Everyone widely uses activated carbons to extract substances from water that cause tastes and odors. The natural ion-exchange material zeolite is used to remove various dissolved compounds from water. Availability and cheapness of this material allow more and more widely to use it as a load of filtering apparatuses.
Modeling chemical processes in the zone of penetration of process liquid filtrates
In the process of mass-transfer interactions of the flushing fluid filtrate with the substances that make up the collector, the total mineralization of the dispersion medium changes, and due to the hydration of the hydrophilic rock, the current water saturation, effective permeability and porosity change. At the interfaces between the liquid and solid phases, adsorption and sticking forces appear, free energy surfaces appear, and surface tension changes.
The process of hydration leads to the attachment of water to the clay component of the skeleton of the reservoir rock and its swelling, the sorption of ions on the surface of the rock leads to depletion, and desorption leads to enrichment of the leachate filtrate with certain salts.
Let us consider the processes occurring during filtration in the rock and describe them mathematically.
1. Formation of sparingly soluble precipitates in pores and cracks
Let a mole of type ions and moles of type ions participate in the reaction, and in this case a new compound is formed. Then the reaction of precipitate formation in general form can be represented by the following equation:
The condition for the possibility of precipitate formation at any given ion concentrations is as follows:
The reaction product precipitates at a ratio according to which the product of ion concentrations in powers equal to their stoichiometric coefficients is greater than the solubility product of the product.
2. Swelling of clay rocks
The magnitude of the swelling of rocks in various media can be established experimentally on the Zhigach-Yarov device. Knowing this value, it is possible to calculate the final porosity of the rock.
3. Adsorption of reagents on the rock surface
The higher the electron affinity of an element that is part of the rock and the lower the proton affinity, the better it sorbs organic matter. Thus, sorption on minerals of clays, cements, chalk, sands mainly goes through centers containing elements such as .
To determine the amount of adsorption of organic reagents, a dimensionless temperature index is calculated (at temperatures from 20 to 100 C) .
To calculate the adsorption coefficient at temperatures above 100C, it is necessary to additionally take into account the constant of the molar excess of the boiling point of the solution.
4. Formation of boundary layers of water
As a result of adsorption at the interface solid- liquid, boundary layers of liquid are formed, the properties of which are different from those in the volume. The nature of the influence of ions on the structure of such adsorbed film water depends on their radius, charge, configuration, and structure of the electron shell. Two cases of exposure to ions have been established. They either bind the nearest water molecules, while the film structure is strengthened, or increase the mobility of water molecules, while the structure of film water is destroyed.
Such electrolytes, as, reduce the depth of penetration of the drilling fluid filtrate into the formation. Electrolytes of the type, on the contrary, help to reduce the viscosity of the filtrate and increase its mobility, thereby increasing the depth of penetration of the liquid.
The greater the concentration of electrolyte in the pore, the smaller the thickness of the electrical double layer (EDL). The relationship between the DEL thickness and its other parameters, without taking into account the real sizes of the ions, is expressed by the formula:
If the free solution contains several salts, the expression is substituted into formula (5) - ionic strength solution in which the products are summed molar concentration on the valency of each ion present in the solution.
In pore channels of finite size, the actual value will differ significantly from the theoretical one. For a slit-like section, the following formula is proposed for calculating the real value:
Formula (6) can be used to estimate the value () in a cylindrical capillary by substituting the doubled radius instead of the slot width.
The most significant significant controlled factors include the chemical composition of the drilling fluid, its pH and the value of the wetting angle at the oil-filtrate boundary. Uncontrollable factors: the chemical composition of oil and residual water in the reservoir, the chemical composition of the rock and clay cement, as well as its colloidality.
In order to correctly take into account the influence of each factor on the reservoir rock during filtration, a special algorithm was developed based on the difference in the rates of ongoing processes.
So, during the instantaneous filtration, the filtrate is presumably first of all interacting with reservoir fluids, and then with the hydrophilic rock. Under certain conditions, insoluble precipitation can occur in the channels of the formation and their narrowing.
When the drilling fluid filtrate and the rock come into contact, adsorption processes occur, which lead to the accumulation of a polymer film on the surface of the channel walls.
If clayey cement is present in the composition of the reservoir rock, then it may additionally swell.
Simultaneously with sedimentation, the process of formation of water films on the surface of the rock takes place. Their thickness can vary significantly due to swelling of clay cement and adsorption of reagents. For reservoirs with permeability k pr > 0.5 × 10 -12 m 2, the formation of boundary layers of water has little effect.
Based on the above, the calculation algorithm can be represented as follows:
a) According to formula (2), the possibility of insoluble sediments falling out during the interaction of the drilling fluid filtrate and formation water is checked, then their possible amount is calculated. This phenomenon strongly affects the effective radius of the pore channels.
b) Based on the data on the composition of the rocks, the coefficient of swelling of the rocks is determined, and the final porosity is calculated using formula (3).
c) According to formula (4), the amount of reagents adsorbed on the rock surface is calculated. This will allow you to know the change in the concentration of reagents in the drilling fluid filtrate.
d) Taking into account the data obtained in paragraphs a - c, according to formulas (5) - (6), the thickness of the formed boundary layers of water is calculated and, consequently, the final radius of the pore channels.
This algorithm was applied to assess the deterioration of the reservoir properties of the reservoir Ach 3 of the Verkhnenadymskoye field for fresh drilling mud. As a result of rock swelling, the permeability of the formation decreases by 18%, porosity by 48%. The loss of polymers as a result of adsorption on the sludge is 0.4% of their initial quantity. The thickness of surface water films increases by 21%. As a result of all these phenomena, the permeability of the reservoir is reduced by almost 96%.
The developed model satisfies the following requirements:
2) has a set of established petrophysical characteristics;
3) allows to carry out engineering generalization of the established facts and to predict the necessary technological parameters in a convenient form.
List of used literature
mineralization dispersion filtrate
1. Mavlyutov M.R. Physical and chemical clogging with true solutions in drilling. - M.: Obzor/VNII ekon. miner. raw materials and geol.-exploration. works. (VIEMS), 1990.
2.Mikhailov N.N. Change in physical properties rocks in near-wellbore zones. - M.: Nedra, 1987.
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Consider the principle of the filtration process on the example of the operation of the simplest filter for separating suspensions. It is a vessel divided into two parts by a filter partition. If the filter material is free-flowing, then a supporting structure, such as a support grid, can be used to hold it in the form of a layer. The suspension is fed into one part of the vessel, passes through the filtering partition, on which the complete or partial separation of the dispersed phase takes place, and then is removed from the vessel. For forcing fluid through a baffle along different sides a pressure difference is created from it, while the suspension is forced from the part of the vessel with a high pressure into the part of the vessel with a lower pressure. The pressure difference is the driving force behind the filtration process.
If we designate the volume of the obtained filtrate, obtained during the time dτ, as dV f, then the differential equation of the filtration rate can be represented as:
C f = dV f /(F f ∙dτ)
where:
C f - filtering speed;
F f - filtering area.
The filtration area is the main design geometric characteristic (ORH) of filters.
The filter partition is a porous structure, the pore size of which directly affects its filtering ability. The liquid penetrates through the pores as through channels through the partition, and the dispersed phase lingers on it. The process of holding the solid particles can be carried out in several ways. The simplest option is when the pore size is smaller than the size of the particle, and the latter simply settles on the surface of the partition, forming a sediment layer. If the particle size is commensurate with the pore size, then it penetrates into the channels and is already retained inside in narrow areas. And even if the particle size is smaller than the narrowest section of the pore, it can still be retained due to adsorption or settling on the pore wall in a place where the channel geometry is highly curved. If the solid particle was not detained by any of the above methods, then it leaves the filter along with the filtrate flow.
Those particles that are retained inside the pores actually increase the filtering capacity of the entire partition, therefore, when filtering, one can observe such a picture when, in initial period After some time, the resulting filtrate turns out to be turbid due to the presence of “leaked” particles of the dispersed phase, and only after a while the filtrate becomes clear when the retention capacity of the partition reaches the required value. In light of this, there are two types of filtering process:
- with the formation of a precipitate;
- with clogged pores.
In the first case, the accumulation of solid particles occurs on the surface of the partition, and in the second - inside the pores. However, it should be noted that the real process of filtering is usually accompanied by these two phenomena, expressed in different degrees. Filtration with sedimentation is more common.
The filtration rate is proportional to the driving force and inversely proportional to the filtration resistance. Resistance is created by both the partition itself and the resulting precipitate. The filtration rate can be expressed by the following formula:
C f = ΔP / [μ∙(R fp +r o ∙l)]
where:
C f - filtration speed, m/s;
ΔP - pressure drop across the filter (driving force), Pa;
R fp - resistance of the filtering partition, m -1 ;
r o - resistivity draft, m -2;
l is the height of the sediment layer, m.
It is important to note that in the general case R fp and r o are not constant. The resistance of the filter partition may increase due to partial clogging of the pores or swelling of the fibers of the partition itself in the case of the use of fibrous materials. The value of r about is specific, that is, it shows the resistance that will fall per unit height of the sediment. The ability of resistivity to change its value depends on the physical and mechanical properties draft. If, within the framework of the filtration process, the particles forming the precipitate can be assumed to be indeformable, then such a precipitate is called incompressible, and its resistivity does not increase with increasing pressure. If the solid particles are deformed and compacted with increasing pressure, as a result of which the pore sizes in the sediment decrease, then such a precipitate is called compressible.
Filtration to form a precipitate is preferred. In this case, there is almost no clogging of the pores of the baffle due to the formation of domes of solid particles over the entrances to the pore channels, serving as an additional retardation factor for dispersed solids. There is almost no increase in the resistance of the partition R pr, and it is quite easy to control the resistance of the sediment layer by timely removal of part of it. In addition, cleaning the pores of the filter partition is usually very difficult, and in some cases may be completely useless, which means that the filtering ability of the partition is lost, so this type of contamination should be avoided if possible. To prevent clogging of the pores, the suspension to be filtered may be pre-thickened, for example by settling. The mass formation of arches begins when the volume concentration of the solid phase in the suspension reaches about 1%.
Shipilova E. A., Zotov A. P., Ryazhskikh V. I., Shcheglova L. I.
As a result of the analysis of the process of filtering fine aerosols (HPA) by granular layers and the existing approaches to the mathematical modeling of technological processes and apparatuses, we have developed and studied a mathematical model that is a system of nonlinear differential equations in partial derivatives that describes the process of separation of fine aerosols in stationary granular layers at a constant filtration rate, clogging of pores and taking into account the diffusion mechanism of deposition. An analytical solution of the system of equations of the model is obtained, which makes it possible to describe the kinetic regularities and determine the parameters of the filtration process in various moments time .
The linear nature of the relationship between diffusive settling and suffusion is one of the many regularities that take place in real filtration conditions. We also studied the most probable dependencies of a more complex nature (Fig. 1).
The systems of differential equations describing the process of WDA filtration in granular layers, expressed in dimensionless quantities, will take the form:
− E)2To solve the system of equations by the traveling wave method, the following are accepted:
|
layer until saturation of its initial 1
showed experimental
E(-∞) = Epr, N(-∞) = N0. At the same time, the working time of the site turned out to be very large. However, as research, the time of formation of the front, according to
compared with the duration of the filtration process, insignificantly. This can be explained-
thread by the fact that at H = 0 coefficient of the frontal layer it is most efficient to modify the initial and
mass transfer β has great importance, and the engagement mechanism acts on. This allows boundary conditions.
|
The initial and boundary conditions for (1) and (2) will be written as: N (0, θ) 1,
E (0, θ) E pr;
Rice. Fig. 1. Dependence of the entrainment coefficient K on the change
N (X ,0) 0,
E (X ,0) E 0 .
– current
porosity E:
dimensionless aerosol concentration; E-
current value of porosity; E 0 -
|
|
variables, and
E pr ≤ E ≤ E 0 ,
0 ≤ θ ≤ τVph H .
The complexity of the analytical solution of relations (1) and (2) has led to the need to use the numerical method of finite differences. Replacing the partial derivatives in (1), (2) with finite difference relations and using the initial and boundary conditions in the finite difference form:
|
|
N j N j 1K j Z
E j 1 − E j
|
|
system (2), where
K j ∆θ 1 ,
|
|
|
|
|
|
One of the main issues in solving difference schemes is the choice of the grid spacing. Taking into account the computer time required for the calculations, as well as taking into account the required accuracy, it is advisable to divide the grid along the layer height into 20 sections, i.e.
∆x = H/20 or ∆X = ∆x/H.
To select the time step, let us consider the physical meaning of the process of filtering the VDA through a granular layer. Since the gas flow moves in the apparatus at a speed Vf, then the path traveled by the gas flow is x = Vfτ. Therefore, ∆τ ∆x Vf
and, based on the relation θ τVf
H , to determine the dimensionless time step we have: ∆θ ∆X .
For systems (3) and (4), programs for calculating the profiles of changes in the aerosol concentration and layer porosity from the longitudinal coordinate at various fixed points in time were compiled. The calculation results are shown in Figs. 2.
0 0,25 0,5 0,75 1
t=0 h t=12 h t=24 h t=36 h t=48 h t=0 h t=12 h t=24 h t=36 h t=48 h
t=0 h t=12 h t=24 h t=36 h t=48 h t=0 h t=12 h t=24 h
|
0 0,25 0,5 0,75 1
Rice. Fig. 2. Profiles of changes in the porosity of the granular layer (a) and aerosol concentration (b):
– system (3); – – – – system (4)
From fig. 2 shows that in the frontal section of the filter, the porosity of the granular layer and the aerosol concentration reach their limiting value, and the zone of change in porosity and concentration moves to the regions following the frontal section. Such an interpretation of the obtained results is fully consistent with modern ideas about the mechanism of the filtration process with gradual clogging of the pores of the granular layer.
The analysis of the adequacy of the proposed mathematical models was carried out on the basis of comparison with the results of experimental studies. The studies were carried out on granular layers of polyethylene granules with equivalent diameters dz = 3.0⋅10-3 and dz = 4.5⋅10-3 m at a height of 0.1 m. A mixture with air of ceramic pigment VK-112 was used as an aerosol (dh = 1.0⋅10-6 m logσ = 1.2). The volume concentration varied from n0 = 1.27⋅10-7 m3/m3 to n0 =
3.12⋅10-7 m3/m3. The filtration rate was Vf = 1.5 m/s and Vf = 2.0 m/s. As output parameters, we studied
change in hydraulic resistance ∆P and slippage coefficient K during the filtration process. On fig. 3
presents comparative results of the dependences ∆P = f(τ) and K = f(τ), obtained experimentally and calculated by the proposed method. When comparing the obtained results for the calculated data, a correction was introduced for the time of front formation.
Analysis of the graphs in fig. 3 allows us to conclude that the nature of the obtained curves is similar, the initial and
the final values of the resistance of the granular layer for the corresponding conditions differ slightly. The maximum discrepancy between the obtained values is 9%. The experimental and calculated values of the velocity of the WDA deposition front coincide with a sufficient degree of accuracy, where maximum value discrepancies amounted to 9%.
80 0 1
0 1 00 00 2 000 0 3 0 0 0 0 40 00 0 5 00 00
|
|
Rice. Fig. 3. Dependence of the hydraulic resistance of the granular layer (a) and the breakthrough coefficient (b) on the duration of the filtration process for
n0 = 1.27⋅10-7 m3/m3, dz = 3⋅10-3 m, Vph = 1.5 m/s:
– calculations according to (3); ● – calculations according to (4); ▪ – results of the experiment
The obtained results qualitatively and quantitatively confirm the adequacy of the developed mathematical models of the filtration process of WDA with granular layers with a nonlinear law of porosity change, and also substantiate the possibility of assumptions and the chosen method adopted by us to solve the system of equations of the mathematical model.
1. Shipilova E. A. On the calculation of the separation process ... // Technique and technology of environmentally friendly production: Proceedings. report sympos.
young scientists ... M., 2000.
2. Romankov P. G. Hydrodynamic processes of chemical technology. L.: Chemistry, 1974.
ENGINEERING NOMOGRAMS FOR ANALYSIS OF THE PROCESS OF FILTERING AEROSOLS WITH GRAIN LAYERS
Shipilova E. A., Shcheglova L. I., Entin S. V., Krasovitsky Yu. V.
Voronezh State Technological Academy
For analysis and technical calculations of the process of filtering dust and gas flows by granular layers, it is advisable to use nomograms. The nomograms proposed by us turned out to be very convenient for determining the flow regime in the channels of the granular layer (Fig. 1, a) and the hydraulic resistance of the granular layer (Fig. 1, b).
a) b)
Rice. 1. Nomograms for determining the modes of flow in the channels of the granular layer (a) and its hydraulic resistance (b)
On fig. 1, a shows the progress of the solution for the following example: the porosity of the granular layer is εav = 0.286 m3/m3; filtration speed – Vf = 2.0 m/s; equivalent layer grain diameter – dz = 4⋅10-3 m; aerosol density – ρg = 0.98 kg/m3. According to the nomogram, the determined value is Re ≈ 418, according to the formula
(1 − ε)ε 0.5
Re = 412. The relative error is 0.9 \%. In formula (1); ν is the coefficient of kinematic viscosity of the flow;
f is the coefficient of the minimum free section of the channels.
On fig. 1, b shows the solution for the following initial data: εav = 0.278 m3/m3; Re = 10; dz = 1⋅10-3 m; ρg = 1.02 kg/m3;
Vph = 1.9 m/s; granular layer height – H = 2.3 m; The resistance of the granular layer, found from the nomogram, was:
∆P ≈ 6.2⋅105 Pa calculated from the formula
∆P kλ′H ρ V 2
value ∆P ≈ 6.6⋅105 Pa. In this formula: k is the coefficient taking into account the non-sphericity of the layer grains; λ is the coefficient of hydraulic friction.
Of particular interest are nomograms for assessing total and fractional breakthrough coefficients. These
the coefficients are most representative in assessing the separating ability of granular filter partitions, since they show which fractions of the dispersed phase and to what extent are retained by granular
layer. To solve this problem, we used interpolation models in natural variables and
engineering nomograms for them obtained by Yu. V. Krasovitsky and his collaborators (Fig. 2):
|
|
log K 2−5⋅10−6 m
-0.312 - 0.273x1 169x2 - 35.84x3 -
IN FIG. 2, A PRESENTED A NOMOGRAM FOR EQUATION (1). EXAMPLE OF USING THE NOMOGRAM: PARAMETERS OF THE DUST AND GAS FLOW AND FILTER - W = 0.4 M/S; DE = 9 10-4 M; H = 83 10-3 M; τ = 0.9 103 С. IT IS NECESSARY TO DETERMINE THE SLIP OF PARTICLES WITH A SIZE LESS THAN 2⋅10-6 M. THE PROCESS OF THE SOLUTION IS SHOWN ON THE NOMOGRAM FOR WHICH K = 0.194. ON– 276 0.4 9 10-4 + 26.1 103 9 10-4 83 10-3 = –1.647, THEREFORE,
K = 0.192. RELATIVE ERROR 1\%.
IN THE EXAMPLE IN FIG. 2, B THE FOLLOWING PARAMETERS OF THE DUST AND GAS FLOW AND FILTER ARE ACCEPTED: W = 0.4 M/S; DE = 9⋅10-4 M; H = 83⋅10-3 M; τ = 0.9⋅103 M.< (2 – 5)⋅10-6 М, ОПРЕДЕЛЕННЫЙ ПО НОМОГРАММЕ, K = 0,194, ПО УРАВНЕНИЮ (2) – K = 0,192.
EQUATIONS (1) AND (2) AND NOMOGRAMS CONSTRUCTED FOR THEM ARE USED IN PREDICTION OF THE EFFICIENCY OF A GRAIN FILTER INTENDED FOR INSTALLATION BEHIND THE DRYER DRUM d597a.
TO ANALYZE THE FILTRATION PROCESS USING THE NOMOGRAM PRESENTED IN FIG. 2, B ON THE SCALE W FIND A SET VALUE AND BY THE KNOWN VALUES H, DE AND H/D POINT B; BY SCALE DE AND VALUE H - POINT A. FOR DETERMINING THE INTERCEPTION
M AND THEN K CONNECT B TO C AND DRAW AE PARALLELLY TO BC.
|
|
AS an EXAMPLE ON THE NOMOGRAM PRESENTED IN FIG. 2, D, THE PROCESS OF SOLUTION OF EQUATION (4) IS SHOWN WITH THE FOLLOWING INITIAL DATA: W = 0.1 M/S; DE = 1.1⋅10-4 M; H = 83⋅10-3
M. BY NOMOGRAM
0.5350. BY EQUATION (4)
-7 = 0,2586 – 8,416⋅0,1 –
– 2244⋅1.1⋅10-4 – 69.6⋅5⋅10-3 + 49392⋅0.1⋅1.1⋅10-4 = –0.6345. HENCE,
K = 0.5299. RELATIVE
C) D)RICE. 2. NOMOGRAMS FOR EVALUATION OF TOTAL AND FRACTIONAL COEFFICIENTS
FLASH FOR EQUATIONS: A - (1); B - (3); IN 2); G - (4)
THE DESCRIBED INTERPOLATION MODELS AND NOMOGRAMS ARE USED FOR ESTIMATION AND PREDICTION OF FRACTIONAL BREAKTHROUGH COEFFICIENTS BY COUNTING CONCENTRATION DURING THE DEVELOPMENT OF A GRAIN FILTER FROM POROUS METALS FOR THE FINE CLEANING OF COMPRESSED GASES FROM MECHANICAL IMPURITIES.
Educational work to order
Simulation of the process of filtration by granular layers of gas heterogeneous systems with a solid dispersed phase
Type of work: Dissertation Subject: Physical and mathematical sciences Pages: 175original work
Excerpt from work
The performed work is devoted to solving an important problem - the development of a new mathematical model, calculation method and instrumentation for the process of filtering weakly concentrated highly dispersed aerosols (HPA) with granular layers to ensure reliable protection environment from toxic and deficient dust emissions.
Relevance of the topic. High-performance systems, intensification of technological processes and concentration of equipment cause high dust emissions into production facilities and the environment. The concentration of aerosols emitted into the atmosphere is many times higher than the maximum allowable limits. With dust, not only expensive raw materials are lost, but also conditions are created for toxicological damage to humans. Especially dangerous for the respiratory system are aerosols with dust particle sizes from 0.01 to 1.0 microns. Dusts containing free or bound silicic acid have a detrimental effect on the lungs. Of particular danger are radioactive aerosols generated in the nuclear industry. Many processes in the food industry are characterized by high dust emission. In the production of mineral fertilizers, pyrite roasting in the production of sulfuric acid, technological processes in the construction industry, the production of powdered milk, semi-finished products in the confectionery industry, and the processing of sunflower with dust, a large amount of raw materials and final products are lost. Every year these factors exacerbate ecological situation and lead to significant losses of a valuable product.
The cleaning equipment used is not up to the task modern conditions production and human safety. In this regard, much attention is paid to the processes of separation of gas heterogeneous systems with a solid dispersed phase, the development and study of new dust collection systems.
The most common way to remove particles from dusty gas streams is filtration. A special place among gas cleaning equipment is occupied by granular filtering baffles, which combine the possibility of highly efficient sanitary and technological cleaning of dusty gas streams.
Granular layers allow trapping fine dust particles, provide a high degree of separation, have strength and heat resistance in combination with good permeability, corrosion resistance, and the possibility of regeneration. different ways, the ability to withstand sudden pressure changes, the absence of electrocapillary phenomena, make it possible to ensure not only the maximum permissible emissions (MAE) into the atmosphere, but also to utilize the trapped dust. Currently, the following types of granular layers are used for cleaning aerosols: 1) fixed, freely poured or granular materials laid in a certain way; 2) periodically or continuously moving materials;
3) granular materials with a bonded layer structure (sintered or pressed metal powders, glasses, porous ceramics, plastics, etc.) -
4) fluidized granules or powders.
The only method capable of capturing submicron particles with >99.9% efficiency is deep bed filtration, where fine gravel, sand, coke or other granular material is used as a filter membrane. Installations with a deep granular layer have found practical use for trapping radioactive aerosols, air sterilization.
However, the regularities of the HDA filtration process have not been studied enough. The current level of development of computer technology makes it possible to widely use information technologies based on the use of mathematical apparatus and automated systems, which can significantly increase the efficiency of equipment operation, reduce the time of stages preceding operation.
Of particular interest is the analysis of the hydrodynamic features and kinetics of WDA filtration by granular layers, the mathematical description of such a process and the creation of a calculation method based on it to determine the rational mode of operation of existing treatment equipment, the production time and frequency of regeneration of the granular layer, the possibility of automated control of the filtration process.
Thus, the wide distribution, as well as the high level of development of computer technology and automated control systems, on the one hand and specific features equipment and processes for filtering gas heterogeneous systems with a solid dispersed phase, on the other hand, determine the relevance of the problem of creating and improving mathematical description such processes.
The aim of the work is the mathematical modeling of the process and the development on this basis of a calculation method and improvement of the hardware design for the separation of dusty gas flows by granular layers. The means of achieving the set goals is the analysis of the process of filtering the WDA with granular layers, the synthesis of a mathematical model and its variant modifications, the analytical, numerical and experimental study of the obtained dependencies, the development of a method for calculating industrial filters and a software package for its implementation, the creation of unified laboratory stands and pilot plants , development of specific hardware solutions for the process of cleaning gas emissions.
The scientific novelty of the work is as follows:
— a mathematical model and its variant modifications have been developed to analyze the process of HDA separation in stationary granular layers at a constant filtration rate with clogging of pores and taking into account the diffusion mechanism of precipitation;
– an analytical solution of the system of equations of the mathematical model was obtained and experimentally tested with a linear law of change in the porosity of the granular layer;
— on the basis of the developed model, a complex of mathematical models for various laws of change in the porosity of the granular layer is proposed and numerically implemented;
– for the first time the physical and mechanical properties of a number of industrial dusts and technological powders were studied, an equation was proposed for calculating the value of the limiting porosity of the granular layer for the corresponding dusts.
– models for constructing engineering nomograms are proposed for estimating and predicting the pressure drop in a granular layer, determining the modes of movement of a dust and gas flow in the channels of a granular layer and predicting the total and fractional slip coefficients;
— on the basis of the developed model, a method for calculating the filtration process and a software package that implements it is proposed, which makes it possible to determine the rational modes of operation of deep granular filters and their design dimensions.
The following are submitted for defense:
- a mathematical model and its variant modifications for the analysis, calculation and prediction of the process of filtering the VDA with granular layers -
- methods and results of experimental determination of the parameters of the mathematical model of the process of filtering VDA with granular layers -
- a method for calculating depth filters for VDA and a package of original programs for the implementation of this method -
— a new constructive solution of the apparatus for highly efficient cleaning of dusty gases by sedimentation in a centrifugal field with subsequent filtration through a granular layer based on the results of process simulation.
The practical value of the dissertation. A new method for calculating granular filters and a software package that implements it have been developed. The algorithm of the proposed calculation method is used in industry when designing structures of granular filters and to determine the rational modes of operation of operating devices. The use of a filter cyclone in industry (RF patent No. 2 150 988) made it possible to carry out highly efficient purification of industrial dust and gas flows. Accepted industrial enterprises recommendations for improving the process of filtering gas heterogeneous systems with a solid dispersed phase by granular layers. Separate results of the work are used in the educational process (lectures, practical classes, course design) in the presentation of the courses "Processes and apparatuses of chemical technology", "Processes and apparatuses food technology» in VGTA.
Approbation of work.
Dissertation materials reported and discussed:
- at the International Conference (XIV Scientific Readings) "Industry of building materials and the construction industry, energy and resource saving in the conditions of market relations", Belgorod, October 6-9, 1997;
- at the International Scientific and Technical Conference "Theory and Practice of Filtration", Ivanovo, September 21-24, 1998;
— at the II and IV International symposiums of students, graduate students and young scientists "Technique and technology of environmentally friendly production" (UNESCO), Moscow, May 13-14, 1998, May 16-17, 2000
- at the International Scientific and Technical Conference "Gas Cleaning 98: Ecology and Technology", Hurghada (Egypt), November 12-21, 1998-
— at the International scientific and practical conference"Atmospheric air protection: monitoring and protection systems", Penza, May 28-30, 2000-
- at the Sixth Academic Readings " Contemporary Issues building materials science" (RAASA), Ivanovo, June 7-9, 2000-
— at the Scientific Readings "White Nights-2000" of the International Ecological Symposium "Perspective Information Technologies and Problems of Risk Management on the Threshold of the New Millennium", St. Petersburg, June 1-3, 2000.
- at the Russian-Chinese Scientific and Practical Seminar "Modern equipment and technologies of the machine-building complex: equipment, ma
- at the XXXVI, XXXVII and XXXVIII reporting scientific conferences of the VGTA for 1997, 1998 and 1999, Voronezh, March 1998, 1999, 2000
Structure and scope of work. The dissertation consists of an introduction, four chapters, main conclusions, a list of references from 156 titles and applications. The work is presented on 175 typewritten pages and contains 38 figures, 15 tables, 4 block diagrams and 9 appendices.
MAIN CONCLUSIONS
Summarizing the performed studies in combination with the experimental results obtained in laboratory and production conditions on real highly dispersed dust and gas flows, we can conclude:
1. A new mathematical model has been developed and analyzed, which is a system of nonlinear differential equations in partial derivatives, which describes the process of separation of fine aerosols in stationary granular layers at a constant filtration rate, clogging of pores, and taking into account the diffusion mechanism of deposition. An analytical solution of the system of equations of the model is obtained, which makes it possible to describe the kinetic patterns and determine the parameters of the filtration process at various points in time.
2. An algorithm for calculating the mass transfer coefficients has been developed, taking into account the modes of movement of the dust and gas flow in the channels of the granular layer.
3. On the basis of the developed model, a model with modified boundary conditions is proposed, numerically implemented and analyzed.
4. Developed, numerically implemented and analyzed original modifications of the main mathematical model of the process of filtering the WDA with granular layers under different laws of change in porosity.
5. On real dust and gas flows in laboratory and production conditions, the process of separation of gas heterogeneous systems with a solid dispersed phase by bulk granular layers was experimentally studied. On the basis of experiments, a regression equation was proposed for calculating the value of the limiting porosity of a granular layer when filtering a number of industrial dusts.
6. Engineering nomograms are proposed to determine the modes of movement of the dust and gas flow in the channels of the granular layer, its hydraulic resistance, the assessment and prediction of the total and fractional breakthrough coefficients.
7. On the basis of the developed mathematical model, a calculation method is proposed that makes it possible to determine the rational modes of operation of deep granular filters and their design dimensions. A package of applied programs for the calculation of industrial filters has been created.
8. A complex method has been developed for the dispersed analysis of dust, which includes the use of a quasi-virtual cascade impactor NIIOGAZ and scanning electron microscopy, which made it possible for the first time to obtain sufficiently representative data on the dispersed composition of the dust of ceramic pigments and to evaluate the shape of the particles of the dispersed phase in the dust-gas flow.
9. Developed, protected by a RF patent (Appendix 3) and tested a new design solution for a device for highly efficient purification of gas heterogeneous systems with a solid dispersed phase, combining inertial settling and filtration through a rotating metal-ceramic element.
The results obtained are implemented:
— at OJSC Semiluk Refractory Plant (Appendix 4) when upgrading existing and creating new systems and apparatus for dust capture from process waste gases and aspiration emissions (pneumatic transport of alumina from silos to bunkers, aspiration emissions from bulking devices, dispensers, mixers, ball and pipe mills, process gases after drying drums, rotary and shaft furnaces, etc.), for calculating and predicting the efficiency of filtering devices and choosing the optimal area for their operation, for organizing representative sampling of dust and gas samples and introducing the latest methods of express analysis of dispersed composition of dusts and powders of industrial origin -
- in the workshops of CJSC PKF "Voronezh Ceramic Plant" (Appendix 5) when calculating high-performance systems and apparatus for dust collection, as well as when using original, protected by patents of the Russian Federation, const
141 practical solutions for combined dust collectors in the "dry" method of production of ceramic pigments and paints -
- when presenting lecture courses, conducting practical exercises, doing homework, course projects and settlement and graphic works, performing research work in the field of SNO and in the preparation scientific personnel in graduate school, educational practice departments "Processes and apparatus of chemical and food production", "Industrial energy", "Machines and apparatus of food production" of the Voronezh State Technological Academy (Appendix 6).
LIST OF MAIN DESIGNATIONS.
1. FEATURES OF MATHEMATICAL MODELING OF FILTRATION OF GAS HETEROGENEOUS SYSTEMS WITH A SOLID DISPERSIVE PHASE BY GRAIN LAYERS.
1.1. Analysis of modern methods of filtering dust and gas flows and their hardware.
1.2. Basic properties modeled object.
1.2.1 Models of structures of real granular layers.
1.2.2. Modeling of the mechanisms of deposition of particles of the dispersed phase in granular layers.
1.3. Mathematical models of deep filtration of heterogeneous technological media by granular layers.
1.4. Conclusions and formulation of the research problem.
2. MATHEMATICAL MODELS OF DEEP FILTRATION OF WEAKLY CONCENTRATED HIGHLY DISPERSED AEROSOLS
WITH SOLID DISPERSIVE PHASE WITH GRAIN LAYERS.
2.1. Mathematical model of filtration of highly dispersed aerosols by granular layers with a linear change in the entrainment coefficient.
2.1.1. Synthesis of a mathematical model.
2.1.2. Analysis of the mathematical model.
2.1.2.1. Analytical solution of a system of equations with constant coefficients.
2.1.2.2. Model adequacy analysis.
2.1.3. Synthesis of a mathematical model with modified boundary conditions.
2.1.4. Analysis of the mathematical model.
2.1.4.1. Building a model of a difference scheme and solving a system of equations.
2.1.4.2. Model adequacy analysis.
2.2. Mathematical models of deep filtration of weakly concentrated highly dispersed aerosols with non-linear laws of variation of the entrainment coefficient.
2.2.1. Synthesis of mathematical models.
2.2.2. Building models of difference schemes and solving systems of equations.
2.2.3. Model adequacy analysis.
2.3. Findings.
3. EXPERIMENTAL RESEARCH MODELS.
3.1. Planning and conducting experiments.
3.2. Experimental model for the analysis of the physical and mechanical properties of the investigated dusts.
3.3. Analysis of experimental data.
3.3.1. Mathematical model for determining the limit value of the porosity of the filtering granular layer for aerosols from ceramic pigment VK-112.
3.4. Findings.
4. PACKAGE OF APPLIED PROGRAMS AND PRACTICAL IMPLEMENTATION OF RESEARCH.
4.1. Features and specifics of the calculation.
4.2. Description of software.
4.3. Working with application software package.
4.4. Industrial experiment on the calculation of granular filters.
4.5. Models for constructing engineering nomograms for mathematical models of filtering.
4.6. Promising filter solutions based on the results obtained.
4.7. Reliability and durability assessment constructive solutions and recommended devices.
4.8. Prospects for the implementation of the results obtained.
Bibliography
1. Adler Yu. P. Planning an experiment in the search for optimal conditions / Yu. P. Adler, E. V. Markova, Yu. V. Granovsky. M.: Nauka, 1971. - 283 p.
2. Andrianov E. I., Zimon A. D., Yankovsky S. S. Device for determining the adhesion of finely dispersed materials // Factory laboratory. 1972. - No. 3. - S. 375 - 376.
3. Aerov M.E., OM Todes. L.: Chemistry, 1968. - 512 p.
4. Aerov M. E. Apparatus with a stationary granular layer / M. E. Aerov, O. M. Todes, D. A. Narinsky. L .: Chemistry, 1979. - 176 p.
5. Baltrenas P. Methods and devices for controlling the dust content of the technosphere / P. Baltrenas, J. Kaunalis. Vilnius: Technique, 1994. - 207 p.
6. Baltrenas P. Granular filters for air purification from fast-clotting dust / P. Baltrenas, A. Prokhorov. Vilnius: Technique, 1991. - 44 p.
7. Baltrenas P. Air-cleaning granular filters / P. Baltrenas, A. Spruogis, Yu. V. Krasovitsky. Vilnius: Technique, 1998. - 240 p.
8. Bakhvalov H.C. Numerical methods. M.: Nauka, 1975. - 368 p.
9. Byrd R. Transfer Phenomena / R. Byrd, V. Stewart, E. Lightfoot / Per. from English - H.H. Kulakova, B.C. Kruglova - Ed. acad. Academy of Sciences of the USSR N. M. Zhavoronkova and corresponding member. USSR Academy of Sciences V. A. Malyusova. M.: Chemistry, 1974. - 688 p.
10. Bloch JI.C. Practical nomography. M.: graduate School, 1971. - 328 p.
11. V. M. Borishansky, Resistance to air movement through a layer of balls. In: Issues of Aerodynamics and Heat Transfer in Boiler and Furnace Processes / Ed. G. F. Knorre. - M.-JL: State Energy Publishing House, 1958. - S. 290−298.
12. Bretschnaider B. Protection of the air basin from pollution / B. Bretschnaider, I. Kurfurst. JL: Chemistry, 1989. - 288 p.
13. Brownian motion. JL: ONTI, 1936.
14. Waldberg A. Yu. Theoretical foundations for the protection of atmospheric air from pollution by industrial aerosols: Textbook / A. Yu. Valdberg, J1.M. Isyanov, Yu. I. Yalamov. St. Petersburg: SpbTI TsBP, 1993. - 235 p.
15. Viktorov M. M. Methods for calculating physical and chemical quantities and applied calculations. JL: Chemistry, 1977. - 360 p.
16. Vitkov G. A. Hydraulic resistance and heat and mass transfer / G. A. Vitkov, L. P. Kholpanov, S. N. Sherstnev M .: Nauka, 1994. - 280 p.
17. Highly efficient air purification / Ed. P. White, S. Smith. -M.: Atomizdat, 1967. 312 p.
18. Gas cleaning equipment: Catalogue. M.: TSINTIKHIMNEFTEMASH, 1988.- 120 p.
19. Godunov S.K., Difference schemes / S.K. Godunov, V.C. Ryabenky. M.: Nauka, 1977. - 440 p.
20. Gordon G. M. Control of dust collecting installations / G. M. Gordon, I. L. Peysakhov. M.: Metallurgizdat, 1951. - 171 p.
21. GOST 17.2.4.01-84. Protection of Nature. Atmosphere. Terms and definitions of pollution control. M.: Publishing house of standards, 1984. 28 p.
22. GOST 17.2.4.02-81. Protection of Nature. Atmosphere. General requirements to methods for the determination of pollutants. M.: Publishing house of standards, 1982. 56 p.
23. GOST 17.2.4.06-90. Protection of Nature. Atmosphere. Methods for determining the speed and flow rate of gas and dust flows outgoing from stationary sources pollution. M.: Publishing house of standards, 1991. - 18 p.
24. GOST 17.2.4.07-90. Protection of Nature. Atmosphere. Methods for determining the pressure and temperature of gas and dust flows from stationary sources of pollution. M.: Publishing house of standards, 1991. - 45 p.
25. GOST 17.2.4.08-90. Protection of Nature. Atmosphere. Methods for determining the moisture content of gas and dust flows from stationary sources of pollution. M.: Publishing house of standards, 1991. - 36 p.
26. GOST 21 119 .5−75. Organic dyes and inorganic pigments. Density determination method. M.: Publishing house of standards, 1976. - 14 p.
27. GOST 21 119 .6-92. General Methods testing of pigments and fillers. Determination of compacted volume, apparent dust density, compaction and bulk volume. M.: Publishing house of standards, 1993. - 12 p.
28. GOST R 50 820-95. Gas-cleaning and dust-collecting equipment. Methods for determining the dust content of gas and dust flows. M.: Publishing house of standards, 1996. - 34 p.
29. Gouldstein J. Scanning electron microscopy and X-ray microanalysis: In 2 volumes / J. Gouldstein, D. Newbery, P. Echlin and others - Per. from English. M.: Mir, 1984. - 246 p.
30. Gradus L. Ya. Guidelines for disperse analysis by microscopy. M.: Chemistry, 1979. - 232 p.
31. Green X. Aerosols Dusts, smokes and fogs / X. Green, V. Lane-Per. from English. - M.: Chemistry, 1969. - 428 p.
32. Durov B.B. The problem of reliability of dust-collecting equipment // Cement. 1985. - No. 9. - S. 4−5.16.
33. Durov V.V., A.A. Durov, A.A. Dotsenko, P.V. Charty // Tr. NIPIOTSTROM. Novorossiysk, 1987. - S. 3−7.
34. Durov V.V., A.A. Dotsenko, P.V. Charty // Abstracts of reports. VI All-Union Conference. Technical diagnostics. - Rostov n / D, 1987. S. 185.
35. Zhavoronkov N. M. Hydraulic fundamentals of the scrubber process and heat transfer in scrubbers. M.: Soviet Science, 1944. - 224 p.
36. Zhukhovitsky A.A. // A.A. Zhukhovitsky, Ya.JI. Zabezhinsky, A.N. Tikhonov // Zhurn. physical chemistry. -1964. T. 28, no. ten.
37. Zimon A. D. Adhesion of dust and powders. M.: Chemistry, 1976. - 432 p.
38. Zimon A. D. Autohesion of bulk materials / A. D. Zimon, E. I. Andrianov. M.: Metallurgy, 1978. - 288 p.
39. A. P. Zotov, Investigation of mass transfer in stationary granular layers at high diffusion Prandtl numbers, Cand. cand. tech. Sciences. - Voronezh, 1981. 139 p.
40. A. P. Zotov, A. P. Zotov, T. S. Kornienko, and M. Kh. 1980. - V. 53, No. 6. - S. 1307−1310.
41. Idelchik I. E. Handbook of hydraulic resistance. M.: Mashinostroenie, 1975. - 560 p.
42. News of universities. Chemistry and chemical technology. 1981. - T. 14, No. 4. - S. 509.
43. Catalog of gas cleaning equipment: Methodological guide. SPb., 1997.-231 p.
44. Catalog of completed and prospective developments. Novorossiysk: NIPIOTSTROM, 1987. - 67 p.
45. Kafarov V. V. Mathematical modeling of the main processes chemical industries/V.V. Kafarov, M. B. Glebov. M.: Higher school, 1991. - 400 p.
46. Case D. Convective heat and mass transfer. M.: Energy, 1971. - 354 p.
47. Kirsanova N. S. New research in the field of centrifugal separation of dust // Review information. Ser. XM-14 "Industrial and sanitary gas cleaning". M.: TSINTIKHIMNEFTEMASH, 1989. - 40 p.
48. Kishinevskii, M. Kh., Kornienko, TS, and Golikov, AM, Deposition of highly dispersed aerosol particles from a turbulent medium, ZhPKh. 1988. - No. 5. - S. 1164 - 1166.
49. Kishinevskii M. Kh., Kornienko TS, Zotov AP Influence of the initial section on mass transfer under laminar motion and high Schmidt numbers // Bibliographic index "Deposited Manuscripts". VINITI, 1979. - No. 6, b / o 240.
50. Kishinevskii M. Kh. Transfer Phenomena. Voronezh: VTI, 1975. - 114 p.
51. Klimenko A.P. Methods and devices for measuring the concentration of dust. -M.: Chemistry, 1978.-208 p.
52. Panov S. Yu., Goremykin V. A., Krasovitsky Yu. V., M.K. Al-Kudah, E. V. Arkhangelskaya // Engineering protection environment: Sat. scientific tr. intl. conf. M.: MGUIE, 1999. — S. 97−98.
53. Kornienko T. S. Mass transfer in granular layers at turbulent mode movement and 8s “1 / T. S. Kornienko, M. Kh. Kishinevskiy, A. P. Zotov // Bibliographic index “Deposited Manuscripts”. VINITI, 1979. - No. 6, no. 250.
54. Kornienko T. S., Kishinevskii M. Kh. Mass transfer in immobile granular layers at high Prandtl numbers. 1978. -T. 51, no. 7. - S. 1602−1605.
55. Kouzov P. A. Fundamentals of the analysis of the dispersed composition of industrial dusts and crushed materials. L .: Chemistry, 1987. - 264 p.
56. Kouzov P. A. Methods for determining the physical and chemical properties of industrial dusts / P. A. Kouzov, L. Ya. Scriabin. L .: Chemistry, 1983. - 143 p.
57. Krasovitsky Yu. V., Baltrenas P. B., Entin V. I., Anzheurov N. M., Babkin V. F. Dedusting of industrial gases in refractory production. Vilnius: Technique, 1996. - 364 p.
58. Krasovitsky Yu. V. Dedusting of gases by granular layers / Yu. V. Krasovitsky, V. V. Durov. M.: Chemistry, 1991. - 192 p.
59. Krasovitsky Yu. V. Separation of aerosols by filtration at a constant speed of the process and gradual clogging of the pores of the partition // Yu. V. Krasovitsky, V. A. Zhuzhikov, K. A. Krasovitskaya, V. Ya. Lygina // Chemical industry. 1974. - No. 4.
60. V. A. Uspenskii, O. Kh. Vivdenko, A. N. Podolyanko, and V. A. Sharapov, On the Theory and Calculation of a Layered Filter, Inzh.-Fiz. magazine 1974. - T. XXVII, No. 4. - S. 740-742.
61. Kurochkina M.I. Specific surface of dispersed materials: Theory and calculation / M.I. Kurochkina, V.D. Lunev - Ed. Corresponding Member Academy of Sciences of the USSR P. G. Romankov. L .: Publishing house Leningrad. un-ta, 1980. - 140 p.
62. Lev E. S. Filtration of gas through a layer bulk material/ in book. Questions of aerodynamics and heat transfer in boiler-furnace processes - Ed. G. F. Knorre. M.-L.: Gosenergoizdat, 1958. - S. 241−251.
63. V. G. Levich, Physical and Chemical Hydrodynamics. M.: Nauka, 1952. - 537 p.
64. Lygina V. Ya. Study of some patterns of separation of gas heterogeneous systems with a solid dispersed phase by granular filtering partitions: Dis. cand. tech. Sciences. Volgograd polytechnics, in-t, 1975.- 175 p.
65. Mazus M. G. Filters for catching industrial dusts / M. G. Mazus, A. D. Malgin, M. J1. Morgulis. M.: Mashinostroenie, 1985. - 240 p.
66. Mazus M. G. Fabric filters. M.: TSINTIKHIMNEFTEMASH, 1974. 68 p. (Series XM-14 Industrial and sanitary gas cleaning. Review information.)
67. Mednikov E. P. Vortex dust collectors. M.: TSINTIKHIMNEFTEMASH, 1975. 44 p. (Series XM-14 Industrial and sanitary gas cleaning. Review information.)
68. E. P. Mednikov, Turbulent transfer and precipitation of aerosols. M.: Nauka, 1981. - 176 p.
69. Meleshkin M. T. Economics and environment interaction and management / M. T. Meleshkin, A. P. Zaitsev, K. A. Marinov. - M.: Economics, 1979. - 96 p.
70. Method for determining the disperse composition of dust using a cascade impactor with flat steps. M.: NIIOGAZ, 1997. - 18 p.
71. Method for determining the disperse composition of dust using a quasi-virtual cascade impactor. M.: NIIOGAZ, 1997. - 18 p.
72. Mints D. M. Theoretical foundations of water purification technology. M.: Energy, 1964. - 238 p.
73. Mints D. M. Hydraulics of granular materials / D. M. Mints, S. A. Shubert. M.: Ministry of Public Utilities of the RSFSR, 1955. - 174 p.
74. R. N. Mullokandov, “Hydraulic resistance of a layer of spherical particles under isothermal and non-isothermal air flow,” Zh. physical chemistry. 1948. - Vol. 21, issue. 8. - S. 1051−1062.
75. Description of the invention to the patent Russian Federation RU 2 150 988 C1, MKI 7 V 01D 50/00, V 04 C 9/00. Zotov A. P., Krasovitsky Yu. V., Ryazhskikh V. I., Shipilova E. A. Cyclone filter for cleaning dusty gases. Published 06/20/2000, Bull. No. 17.
76. Goremykin V. A., Krasovitsky Yu. V., Agapov B. L. Determination of the fineness of ceramic pigment dust in a dust-gas flow,
77. S. Yu. Panov, M.K. Al-Kudakh, E. A. Shnpnlova // Chemical and oil and gas engineering. 1999. - No. 5. - S. 28 - 30.
78. Panov S. Yu. Development of a method for dry fine cleaning of aspiration emissions from dust in the production of ceramic pigments using energy-saving technology: Dis. cand. tech. Sciences. Ivan, chemical technologist. Academy, 1999. - 198 p.
79. V. M. Paskonov, Numerical modeling of heat and mass transfer processes. M.: Chemistry, 1984. - 237 p.
80. Pirumov A. I. Air dedusting. M.: Stroyizdat, 1981. - 294 p.
81. Primak A.B. Environmental protection at the enterprises of the construction industry / A.B. Primak, P. B. Baltrenas. Kyiv: Budivelnik, 1991. - 153 p.
82. Radushkevich L. V. // Actaphys. chim. U.R.S.S. 1937. - V. 6. - P. 161.
83. Rachinsky B.B. Introduction to the general theory of sorption dynamics and chromatography. M.: Chemistry, 1964. - 458 p.
84. Romankov P. G. Hydrodynamic processes of chemical technology / P. G. Romankov, M. I. Kurochkina. L .: Chemistry, 1974. - 288 p.
85. Handbook of dust and ash collection / Ed. A.A. Rusanov. -M.: Energy, 1975. - 296 p.
86. Handbook of polymer chemistry. Kyiv: Naukova Dumka, 1991. - 536 p.
87. Sugarman's Handbook. M.: Pishch. prom., 1965. - 779 p.
88. Straus V. Industrial gas cleaning. M.: Chemistry, 1981. - 616 p.
89. Dry methods of purification of exhaust gases from dust and harmful emissions. M.: VNIIESM, 1988. - No. 3. - 48 p. (Overview information. Series 11 Use of waste, by-products in the production of building materials and products. Environmental protection.)
90. PK aerosol particle counter. GTA-0.3-002. Passport No. 86 350.
91. Tikhonov A.N. Equations of mathematical physics / A.N. Tikhonov, A.A. Samara. M.: Nauka, 1966. - 724 p.
92. Trushchenko N. G. Filtration of gases by a granular medium / N. G. Trushchenko, K. F. Konovalchuk // Tr. NIPIOTSTROM. Novorossiysk, 1972. Issue. VI. — S. 54−57.
93. Trushchenko N. G. Purification of gases by granular filters / N. G. Trushchenko, A. B. Lapshin // Tr. NIPIOTSTROM. Novorossiysk, 1970. Issue. III. — S. 75−86.
94. Uzhov V. N. Purification of industrial gases from dust / V. N. Uzhov, A. Yu. Valdberg, B. I. Myagkov, I. K. Reshidov. M.: Chemistry., 1981. - 390 p.
95. Uzhov V. N. Purification of industrial gases by filters / V. N. Uzhov, B. I. Myagkov. M.: Chemistry, 1970. - 319 p.
96. Fedotkin I. M., Vorobyov E. I., Vyun V. I. Hydrodynamic theory of suspension filtration. Kyiv: Vishcha school, 1986.- 166 p.
97. Frank-Kamenetsky D. A. Diffusion and heat transfer in chemical kinetics. M.: Nauka, 1987. - 487 p.
98. Fuchs H.A. Aerosol mechanics. M.: Publishing House of the Academy of Sciences of the USSR, 1955. - 352 p.
99. Khovansky G. S. Fundamentals of nomography. M.: Nauka, 1976. - 352 p.
100. Kholpanov L. P. Mathematical modeling of nonlinear thermohydrogasdynamic processes / L. P. Kholpanov, V. P. Zaporozhets, P. K. Zibert, Yu. A. Kashchitsky. M.: Nauka, 1998. - 320 p.
101. Kholpanov L.P. New method calculation of mass transfer in two-phase multicomponent media / L. P. Kholpanov, E. Ya. Kenig, V. A. Malyusov, N. M. Zhavoronkov // Dokl. ANSSSR. 1985. - T. 28, No. 3. - S. 684 - 687.
102. Kholpanov L.P., Malyusov V.A., Zhavoronkov N.M. Investigation of hydrodynamics and mass transfer in a turbulent flow of a liquid film, taking into account the inlet section, Teoret. basics of chem. technology. 1978. - V. 12, No. 3. - S. 438 - 452.
103. L. P. Kholpanov, “Methods for Calculating Hydrodynamics and Heat and Mass Transfer in Systems with a Movable Interface,” Teoret. basics of chem. technology. 1993. - T. 27, No. 1. - S. 18 - 28.
104. Kholpanov L. P. Some mathematical principles chemistry and chemical technology // Khim. prom. 1995. - No. 3. - S. 24 (160) - 35 (171).
105. L. P. Kholpanov, Physicochemical and Hydrodynamic Foundations of Nonlinear Processes in Chemistry and Chemical Technology, Izv. RAN. Ser. chem. -1996.-No. 5.-S. 1065-1090.
106. Kholpanov L. P. Hydrodynamics and heat and mass transfer with the interface / L. P. Kholpanov, V. Ya. Shkadov. M.: Nauka, 1990. - 280 p.
107. Khuzhaerov B. Influence of clogging and suffusion on filtration of suspensions. 1990. - V. 58, No. 2. - S. 244−250.
108. Khuzhaerov B. Suspension filtration model taking into account clogging and suffusion. -1992. T. 63, No. 1. - S. 72−79.
109. Shekhtman Yu. M. Filtration of low-concentration suspensions. -M.: Chemistry, 1961.-246 p.
110. Entin, V.I., Krasovitsky, Yu.V., Anzheurov, N.M., and A.M. Boldyrev, F. Schrage. Voronezh: Origins, 1998.-362 p.
111. Epshtein, S.I., On Similarity Conditions for the Filtration Process Through a Granular Load, ZhPKh. 1995. - T. 68, no. 11. - S. 1849−1853.
112. Epshtein S.I., Muzykina Z.S. On the issue of modeling the process of filtering a suspension through a granular load / S.I. Epshtein, Z.S. Muzykina // Tez. report International conf. Theory and practice of filtering. Ivanovo, 1998. — S. 68−69.
113. Bakas A. Mazqju elektrostatinı oro valymo i'iltrij tyrimal ir panaudojimas. Daktaro disertacijos santrauka. Lietuvos Respublika. VTU. -1996. 27 c.
114. Brattacharya S.N. Mass Transfer to Ziquid in Fixed Beds / S.N. Brattacharya, M. Rija-Roa // Indian Chem. Eng. 1967. - V. 9, No. 4. - P. 65 - 74.
115. Calvert S. Scrubber Handbook. Prepared for EPA, A.P.T. Inc., California, 1972.
116. Carman P. Fluid Flow through Granular Beds, Trans. Inst. Chem. Eng.- 1937.-V. 15, No. 1.-P. 150-166.
117 Chen C.Y. // Chem. Rev. -1955. V. 55. - P. 595.
118. Chilton T.H. Particle-to-Fluid Head and Mass Transfer in Dense Systems of Fine Particles / T.H. Chilton, A.P. Colburn // Ind. Eng. Chem. fundamentals. 1966. - V. 5, No. 1. - P. 9−13.
119. Coulson J.M., Richardson K. // Chemical Engineering. -1968. V. 2. - P. 632.
120 Davies J.T. Local eddy diffusivities related to "bursts" of fluid near solid walls // Chem. Eng. Sei. 1975. - V. 30, No. 8. - P. 996 - 997.
121. Davies C.N. //Proc. Roy. soc. A, 1950. - P. 200.
122. Determining Ceramic Pigment Dust Particle Size in a Flowing Dusty Gas / V.A. Goremykin, B.L. Agapov, Yu.V. Krasovitskii, S.Yu. Panov, M.K. AT-Kaudakh, E.A. Shipilova // Chemical and Petrolium Engineering. 2000. - V. 35, No. 5−6. - P. 266-270.
123. Dullien F.A.L. New Network Permeability Model of Porous Media // AIChE Journal. 1975. - V. 21, No. 2. - P. 299-305.
124. Dwivedi P.N. Particle-Fluid Mass Transfer in Fixed and Fluidized Beds / P.N. Dwivedi, S.N. Upadhyay // Ind. Eng. Chem., Process. Des. dev. 1977. - V. 16, No. 2. - P. 157−165.
125. Fedkin P. Etrance Region (Zevequelike) Mass Transfer Coefficients in Packed Bed Reactors / P. Fedkin, J. Newman // AIChE Journal. 1979. - V. 25, No. 6.- P. 1077−1080.
126 Friedlander S.K. // A.I.Ch.E. Journal. 1957. - V. 3. - P. 43.
127 Friedlander S.K. Theory of Aerosol Filtration // Ind. and Eng. Chemistry. 1958. - V. 50, No. 8. - P. 1161 - 1164.
128. Gaffeney B.J. Mass Transfer from Packing to Organic Solvents in Single Phase Flow through a Column / B.J. Gaffeney, T.B. Drew // Ind. Eng. Chem. 1950.-V. 42, No. 6. P. 1120-1127.
129. Graetz Z. Uber die Warmeleitungsfahigkeit von Flu? igkeiten // Annalen der Physik und Chemie. Neue Folge Band. 1885. - T. XXV, No. 7. - S. 337-357.
130. Herzig J. P. Le calkul previsionnel de la filtration a travers un lit epais. lre part. Proprietes generales et cinetique du colmatage. Chim. et Ind / J. P. Herzig, P. Le Goff // Gen. chim. 1971. - T. 104, No. 18. - P. 2337−2346.
131. Kozeny J. Uber capillare Zeitung des Wassere im Boden // Sitzungs Serinchte Akad. Wiss. wien. Nat. Kl. -1927. Bd 136 (Abt. IIa). S. 271-306.
132. Krasovitzkij Ju.W. Zur Frage der mathematische Modelirung der Filtration heterogener Systeme mit fester disperser Phase // Kurzreferate "Mekhanische Flusskeitsabtrenunge", 10. Diskussionstagung, 11−12 Oktober, 1972, Magdeburg, DDR. — S. 12−13.
133. Langmuir, I., Blodgett, K.B. General Electric Research Laboratory, Rep. RL-225.
134. Marktubersicht uber Filterapparate // Chemie-Ingenieur-Technik. -1995. T. 67, No. 6. S. 678−705.
135. Mass Transfer in Packed Bed Elektrochemical Cells Having Both Uniform Mixed Particle Sizes / R. Alkaire, B. Gracon, T. Grueter, J.P. Marek, A. Blackburn // Journal of Electrochemical Science and Technology. 1980. - V. 127, No. 5. - P. 1086 - 1091.
136. MATHCAD 2000 PROFESSIONAL. Financial, engineering and scientific calculations in the Windows 98 environment. M .: Filin, 2000. - 856 p.
137. McKune Z.K. Mass and Momentum Transfer in Solid-Ziquid System. Fixed and Fluidized Beds / Z.K. McKune, R.H. Wilhelm // Ind. Eng. Chem. 1949.-V. 41, No. 6.-P. 1124-1134.
138. Pajatakes A.S. Model of the Constructed Unit cell Type for Isotropic Granular Porous Media / A.S. Pajatakes, M.A. Neira // AIChE Journal. 1977. - V. 23, No. 6. - P. 922-930.
139. Pasceri R.E., Friedlander S.K., Can. J. // Chem. Eng. -1960. V. 38. - P. 212.
140. Richardson J.F., Wooding E.R. // Chem. Eng. Sei. 1957. - V. 7. - P. 51.
141. Rosin P., Rammler E., Intelmann N. // W., Z.V.D.I. 1932. - V. 76. -P. 433.
142. Seilars J.R. Heat Transfer to Laminar Flow in a Round Tube or Flat Conduit The Greatz Problem Extended / J.R. Sellars, Tribus Myron, J.S. Klein // Trans. ASME. - 1956. - V. 78, No. 2. - P. 441-448.
143. Silverman L. Performance of Industrial aerosol filter // Chem. Eng. Prog. -1951. V. 47, No. 9. - P. 462.
144 Slichter C.S. Theoretical Investigation of the Motion of Ground Water // U.S. Geol. Surv. 1897. - V. 98, part. 2. - P. 295−302.
145. Spruogis A. Mazo nasumo grudetq filtrq kurimas oro valymui statybinii^ medziagij pramoneje. Daktaro disertacijos santrauka. Lietuvos Respublika. VTU, 1996. 26 p.
146. Towsend J.S. Electricity in Gases. Oxford, 1915.
147. Towsend J.S. // Trans. Roy. soc. 1900. V. 193A. — P. 129.
148. Upadhyay S.N. Mass Transfer in fixed and Fluidized Beds / S.N. Upadhyay, G. Tripathi // J. Scient. Ind. Res. 1975. - V. 34, No. 1. - P. 10−35.
149. Upadhyay S.N. Studies on Particle-Fluid Mass Transfer. Part II - Multiparticle System. Fixed and Fluidised Beds / S.N. Upadhyay, G. Tripathi // Indian Journal of Technology. 1972. - V. 2, No. 10. - P. 361 - 366.
150. Wells A.C. Transport of small particles to vertical surfaces / A.C. Wells, A.C. Chamberlain // Brit. J. Appl. Phys. 1967. - V. 18, No. 12. - P. 1793 - 1799.
151. Williamson J.F. Ziquid-Phase Mass Transfer at Zow Reynolds Numbers / J.F. Williamson, K.E. Bazaraire, C.J. Geankoplis // Ind. Eng. Chem. fundamentals. -1963. V. 2, No. 2. - P. 126 - 129.
152. Wilson J. Ziquid Mass Transfer at Zow Reynolds Number in Packed Beds / J. Wilson, C.J. Geankoplis // Ind. Eng. Chem. fundamentals. 1966. - V. 5, No. 1. - P. 9 -14.
153. The program for calculating the process // of filtering VDA with granular layers
154. FILE *in,*outl,*out2,*out3,*out4,*out5,*out6,*p-1. start of main programvoid main(void)(textcolor(1) - textbackground(7) - clrscr() -
155. Displaying the header message printf ("nt g "nt" nt "ntnt") getch () -
156. Program for calculating the parameters of the process of filtering VDA with granular layers
157. Beginning of the main loop for data entrydo
158. Determination of the service life of the granular layer.1
159. Calculation of auxiliary quantities =pow (e0,2.) - a9=1+epr- al0=pow (enp, 2.) - f1=a1*a2*a3- f2=a4*a5*al- f3=2*e0*a2*a5 - f4=2*еО*аЗ*а4-
160. Calculation of intermediate terms and Q values K=(-a9*al*log (al)+a3*a2*log (a2)+а5*а4/2.+2*a5-al*log (al) -a2*log (а2))/(fl*a6) —
161. M=(-a5*a4*log (a5)-al0+enp*e0+a5*a4/2.-a5*log (а5)+а5)/ (f2*а6) —
162. TT=(a5*a4*log (a5)+e0*enp-a8-a5*a4/2.+a5*log (a5)-a5)/ (f3*a6) —
163. H=(a5*a4*log (a5)+e0*enp-al0+a4*log (a4)-2*e0*log (2*e0)+a5)/f4*a6) - Q=K+ M-TT-H-
164. Calculation of the speed of the front U=2*vf*e0*n0/(a4*a5) - if (zz=="2") (xk=U*tau-printf ("n Required height of the granular layer H=%lf m", xk)->printf ("nn Front speed U=%e m/s", U) -//getch () - z=2*vf*eO/U-
165. Calculation of hydrodynamic characteristics *1.013e5) - h=m/pg-
166. Begin cycle by layer height do (e0.=e0- // Assign initial value to e1. Begin cycle by time for (t=l., i=l-t<=900 000.-t=t+900., i=i+l) {
167. Calculation and comparison of the value of the mass transfer coefficient b \u003d beta () - // Calling the subroutine for calculating betaif (b \u003d=0.) (printf ("n Value of the dimensionless relaxation time> 0.22 ") -getch () -return-1. B=6*b/dz-
168. Calculation of the value of P P=-U*z*a5/B-
169. Calculation of the current value of e
170. Subroutine for writing results to a file and accumulating arrays // to display graphsvoid vyv (void) (
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