Modeling of chemical processes in the zone of penetration of process liquid filtrates

In the process of mass transfer interactions of the washing fluid filtrate with the substances that make up the reservoir, the overall 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 of the liquid and solid phases, adsorption and adhesion forces appear, free energy surfaces appear, and surface tension changes.

The hydration process leads to the addition of water to the clay component of the reservoir rock skeleton and its swelling, the sorption of ions on the rock surface leads to depletion, and desorption leads to the enrichment of certain salts in the filtrate of the washing liquid.

Let us consider the processes occurring during filtration in the rock and describe them mathematically.

1. Formation of sparingly soluble sediments in pores and cracks

Let moles of type ions and moles of type ions participate in the reaction, and 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 the ratio according to which the product of ion concentrations in powers equal to their stoichiometric coefficients is greater than the product of the solubility of the product.

2. Swelling of clayey rocks

The amount of swelling of rocks in various environments can be determined experimentally using the Zhigach-Yarov device. Knowing this value, the final porosity of the rock can be calculated.

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 substances. Thus, sorption on minerals of clays, cements, chalk, and sands mainly occurs at 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 solid-liquid interface, boundary layers of liquid are formed, the properties of which are different from those in the bulk. The nature of the influence of ions on the structure of such film adsorbed water depends on their radius, charge, configuration and structure of the electronic shell. Two cases of ion exposure have been identified. They either bind nearby water molecules, and the structure of the film is strengthened, or they increase the mobility of water molecules, and the structure of film water is destroyed.

Electrolytes such as reduce the depth of penetration of drilling fluid filtrate into the formation. Electrolytes, on the contrary, help reduce the viscosity of the filtrate and increase its mobility, thereby increasing the depth of penetration of the liquid.

The higher the electrolyte concentration in the pore becomes, the smaller the thickness of the electrical double layer (EDL). The relationship between the thickness of the EDL and its other parameters without taking into account the actual sizes of the ions is expressed by the formula:

If a free solution contains several salts, the expression is substituted into formula (5) - the ionic strength of the solution, in which the products of the molar concentration and the valence of each ion present in the solution are summed up.

In pore channels of finite size, the actual value will differ significantly from the theoretical value. For the slot-shaped section, the following formula is proposed to calculate the real value:

Formula (6) can be used to estimate the value () in a cylindrical capillary by substituting twice the radius instead of the slit width.

The most significant controllable factors include the chemical composition of the drilling fluid, its pH and the value of the contact angle at the oil-filtrate interface. 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 the processes occurring.

Thus, during instantaneous filtration, the filtrate presumably interacts first with formation fluids, and then with hydrophilic rock. Under certain conditions, precipitation of insoluble sediments in the formation channels and their narrowing may occur.

When the drilling fluid filtrate comes into contact with the rock, adsorption processes occur, which lead to the accumulation of a polymer film on the surface of the channel walls.

If clay cement is present in the reservoir rock, then additional swelling is possible.

Simultaneously with sedimentation, the process of formation of water films on the surface of the rock occurs. Their thickness can vary significantly due to the swelling of clay cement and the adsorption of reagents. For reservoirs with permeability k pr > 0.5 H10 -12 m 2, the formation of boundary layers of water has an insignificant effect.

Based on the above, the calculation algorithm can be presented as follows:

a) Using formula (2), the possibility of precipitation of insoluble sediments during the interaction of drilling fluid filtrate and formation water is checked, then their possible amount is calculated. This phenomenon greatly affects the effective radius of the pore throats.

b) Based on the rock composition data, the rock swelling coefficient is determined, and the final porosity is calculated using formula (3).

c) Using formula (4), the amount of reagents adsorbed on the surface of the rock is calculated. This will allow you to find out the change in the concentration of reagents in the drilling fluid filtrate.

d) Taking into account the data obtained in paragraphs a - c, formulas (5) - (6) calculate the thickness of the formed boundary layers of water and, consequently, the final radius of the pore channels.

This algorithm was used to assess the deterioration of the reservoir properties of the Ach 3 formation of the Verkhnenadymskoye field for fresh drilling mud. As a result of rock swelling, the formation permeability decreases by 18% and porosity by 48%. The loss of polymers as a result of adsorption on sludge is 0.4% of their initial amount. The thickness of surface water films increases by 21%. As a result of all these phenomena, the permeability of the formation is reduced by almost 96%.

The developed model satisfies the following requirements:

2) has a set of established petrophysical characteristics;

3) allows for an engineering generalization of established facts and prediction of the necessary technological parameters in a convenient form.

List of used literature

filtrate mineralization dispersive

1. Mavlyutov M.R. Physico-chemical colmatation with true solutions in drilling. - M.: Obzor/VNII econ. miner raw materials and geological exploration works (VIEMS), 1990.

2. Mikhailov N.N. Changes in the physical properties of rocks in near-well zones. - M.: Nedra, 1987.

Modeling 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: 175

Original work

Excerpt from work

The work performed is devoted to solving an important problem - the development of a new mathematical model, calculation method and hardware design of the process of filtering low-concentrated highly dispersed aerosols (HDA) with granular layers to ensure reliable protection of the environment from toxic and scarce 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 many times exceeds the maximum permissible standards. With dust, not only expensive raw materials are lost, but also conditions are created for toxicological damage to humans. Aerosols with dust particle sizes from 0.01 to 1.0 microns are especially dangerous for the respiratory system. Dusts containing free or bound silicic acid have a detrimental effect on the lungs. Radioactive aerosols generated in the nuclear industry pose a particular danger. Many food industry processes produce high levels of dust. During the production of mineral fertilizers, roasting pyrite to produce sulfuric acid, during 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 the final product are lost. Every year, these factors aggravate the environmental situation and lead to significant losses of valuable products.

The treatment equipment used does not meet the requirements of modern production conditions 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 method of removing particles from dusty gas streams is filtration. A special place among gas cleaning equipment is occupied by granular filter baffles, which combine the possibility of highly effective sanitary and technological cleaning of dusty gas flows.

Granular layers make it possible to capture fine dust particles, provide a high degree of separation, have strength and heat resistance combined with good permeability, corrosion resistance, the ability to be regenerated in various ways, the ability to withstand sudden changes in pressure, the absence of electrocapillary phenomena, and allow to ensure not only maximum permissible emissions (MPE) into the atmosphere, but also to dispose of captured dust. Currently, the following types of granular layers are used to clean aerosols: 1) stationary, freely poured or laid in a certain way granular materials; 2) periodically or continuously moving materials;

3) granular materials with a coherent layer structure (sintered or pressed metal powders, glass, porous ceramics, plastics, etc.) -

4) fluidized granules or powders.

The only method that can capture submicron particles with >99.9% efficiency is deep bed filtration, where fine crushed stone, sand, coke or other granular material is used as a filter wall. Installations with a deep granular layer have found practical application for capturing radioactive aerosols and air sterilization.

However, the regularities of the VDA filtration process have not been sufficiently studied. 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 and reduce the time required for the stages preceding operation.

Of particular interest is the analysis of the hydrodynamic features and kinetics of the filtration of AMA by granular layers, the mathematical description of such a process and the creation on its basis of a calculation method for determining the rational operating mode of existing treatment equipment, the production time and frequency of regeneration of the granular layer, and the possibility of automated control of the filtration process.

Thus, the widespread use, as well as the high level of development of computer technology and automated control systems, on the one hand, and the specific features of equipment and processes for filtering gas heterogeneous systems with a solid dispersed phase, on the other, determine the relevance of the problem of creating and improving a mathematical description of such processes.

The goal of the work is mathematical modeling of the process and, on this basis, the development of a calculation method and improvement of the hardware design for the separation of dusty gas flows into granular layers. The means of achieving the set objectives is the analysis of the process of filtering VDA by granular layers, the synthesis of a mathematical model and its variant modifications, 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 industrial installations , 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 separation of VDA in stationary granular layers at a constant filtration rate with clogging of pores and taking into account the diffusion mechanism of deposition -

— an analytical solution to the system of equations of the mathematical model under the linear law of changes in the porosity of the granular layer was obtained and experimentally tested;

— based on the developed model, a set of mathematical models for various laws of changes 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 maximum porosity of the granular layer for the corresponding dusts.-

— models have been proposed for constructing engineering nomograms for assessing and predicting the pressure drop in the granular layer, determining the modes of movement of the dust and gas flow in the channels of the granular layer and predicting the general and fractional breakthrough coefficients;

— based on the developed model, a method for calculating the filtration process and a software package that implements it is proposed, making it possible to determine the rational operating modes of deep granular filters and their design dimensions.

The following are submitted for defense:

— mathematical model and its variant modifications for analysis, calculation and prediction of the process of filtering VDA by 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 implementing this method -

— a new design solution for a device for highly efficient purification of dusty gases by sedimentation in a centrifugal field followed by filtering through a granular layer based on the results of process modeling.

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 rational operating modes of operating devices. The use of a filter cyclone in industry (RF patent No. 2 150 988) made it possible to carry out highly effective purification of industrial dust and gas flows. Recommendations for improving the process of filtering gas heterogeneous systems with a solid dispersed phase into granular layers have been developed, accepted by industrial enterprises. Some results of the work are used in the educational process (lectures, practical exercises, course design) when presenting the courses “Processes and apparatus of chemical technology”, “Processes and apparatus of food technology” at VGTA.

Approbation of work.

The dissertation materials were reported and discussed:

- at the International Conference (XIV Scientific Readings) “Building materials industry and construction industry, energy and resource conservation in market conditions”, 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, Postgraduate Students and Young Scientists “Engineering and Technology of Environmentally Clean Production” (UNESCO), Moscow, May 13−14, 1998, May 16−17, 2000.

- at the International Scientific and Technical Conference “Gas Purification 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 “Modern Problems of Construction Materials Science” (RAASA), Ivanovo, June 7−9, 2000-

- at the Scientific Readings “White Nights-2000” of the International Environmental Symposium “Advanced Information Technologies and Risk Management Problems 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 mechanical engineering 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 used sources of 156 titles and appendices. The work is presented on 175 pages of typewritten text and contains 38 figures, 15 tables, 4 block diagrams and 9 appendices.

MAIN CONCLUSIONS

Summarizing the research performed in combination with 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 partial differential equations that describes the process of separation of highly dispersed 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 to the system of model equations has been obtained, which makes it possible to describe the kinetic patterns and determine the parameters of the filtration process at different times.

2. An algorithm has been developed for calculating mass transfer coefficients, taking into account the modes of movement of the dust and gas flow in the channels of the granular layer.

3. Based on the developed model, a model with modified boundary conditions is proposed, numerically implemented and analyzed.

4. Original modifications of the basic mathematical model of the process of filtering VDA by granular layers under various laws of porosity changes have been developed, numerically implemented and analyzed.

5. The process of separation of gas heterogeneous systems with a solid dispersed phase by bulk granular layers was experimentally studied using real dust and gas flows in laboratory and production conditions. Based on experiments, a regression equation has been proposed to calculate the value of the maximum porosity of the granular layer when filtering a number of industrial dusts.

6. Engineering nomograms have been proposed to determine the modes of movement of dust and gas flow in the channels of the granular layer, its hydraulic resistance, assessment and prediction of general and fractional breakthrough coefficients.

7. Based on the developed mathematical model, a calculation method is proposed that allows one to determine rational operating modes of deep granular filters and their design dimensions. A package of application programs for calculating industrial filters has been created.

8. A comprehensive method of dispersed analysis of dust has been developed, including the use of a quasi-virtual cascade impactor NIIOGAZ and scanning electron microscopy, which for the first time made it possible to obtain fairly representative data on the dispersed composition of dust of ceramic pigments and to evaluate the shape of particles of the dispersed phase in a dust-gas flow.

9. A new design solution for an apparatus for highly efficient purification of gas heterogeneous systems with a solid dispersed phase, combining inertial sedimentation and filtration through a rotating metal-ceramic element, has been developed, protected by a patent of the Russian Federation (Appendix 3) and tested.

The results obtained are implemented:

- at JSC Semiluksky Refractory Plant (Appendix 4) when upgrading existing and creating new systems and devices for collecting dust from waste process gases and aspiration emissions (pneumatic transport of alumina from silos to bunkers, aspiration emissions from pouring devices, dispensers, mixers, ball and pipe mills, process gases after drying drums, rotary and shaft kilns, etc.), for calculating and predicting the efficiency of filter devices and for choosing the optimal area of their operation, for organizing representative sampling of dust and gas samples and introducing the latest methods for express analysis of dispersed composition of dusts and powders of industrial origin -

- in the workshops of JSC PKF "Voronezh Ceramic Plant" (Appendix 5) when calculating highly efficient systems and devices for dust collection, as well as when using original, protected by patents of the Russian Federation, const.

141 manual solutions for combined dust collectors for the “dry” method of production of ceramic pigments and paints -

— when presenting lecture courses, conducting practical classes, doing homework, course projects and computational and graphic works, performing research work through the SSS and in training scientific personnel through graduate school, in the educational practice of the departments of “Processes and apparatus of chemical and food production”, “Industrial Energy”, “Machines and apparatus for food production” of the Voronezh State Technological Academy (Appendix 6).

LIST OF MAIN NOTATIONS.

1. FEATURES OF MATHEMATICAL MODELING OF FILTERING GAS HETEROGENEOUS SYSTEMS WITH A SOLID DISPERSED PHASE BY GRANULAR LAYERS.

1.1.Analysis of modern methods of filtering dust and gas flows and their hardware.

1.2. Basic properties of the modeled object.

1.2.1. Models of the structures of real granular layers.

1.2.2. Modeling of mechanisms of sedimentation of dispersed phase particles in granular layers.

1.3. Mathematical models of deep filtration of heterogeneous technological media by granular layers.

1.4. Conclusions and statement of the research problem.

2. MATHEMATICAL MODELS FOR DEPTH FILTERING WEAKLY CONCENTRATED HIGHLY DISPERSED AEROSOLS

WITH SOLID DISPERSED PHASE IN GRANULAR LAYERS.

2.1. Mathematical model of filtering 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. Construction of a difference scheme model and solution of a system of equations.

2.1.4.2. Model adequacy analysis.

2.2. Mathematical models of deep filtration of weakly concentrated highly dispersed aerosols under nonlinear laws of change in the entrainment coefficient.

2.2.1. Synthesis of mathematical models.

2.2.2. Construction of difference scheme models and solution of systems of equations.

2.2.3. Model adequacy analysis.

2.3. Conclusions.

3. EXPERIMENTAL RESEARCH MODELS.

3.1. Planning and conducting experiments.

3.2. Experimental model for analyzing the physical and mechanical properties of the dusts under study.

3.3. Analysis of experimental data.

3.3.1. Mathematical model for determining the limiting porosity value of the filter granular layer for aerosols from the ceramic pigment VK-112.

3.4. Conclusions.

4. APPLIED PROGRAM PACKAGE AND PRACTICAL IMPLEMENTATION OF RESEARCH.

4.1. Features and specifics of calculation.

4.2. Description of the 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 filtration.

4.6. Promising filter solutions based on the results obtained.

4.7. Assessment of the reliability and durability of design solutions and recommended devices.

4.8. Prospects for implementing the results obtained.

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153. Program for calculating the process // of filtering VDA with granular layers

154. FILE *in,*outl,*out2,*out3,*out4,*out5,*out6,*p-1. Start of the main program void 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 cycle for data entry

158. Determination of the service life of the granular layer.1

159. Calculation of auxiliary quantities al=l-enp- a2=1-e0- a3=1+eO- a4=e0+epr- a5=e0-epr-ab=p0+e0-epr- a7=e0/epr- a8 =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*eO*a3*a4-

160. Calculation of intermediate terms and values Q K=(-a9*al*log (al)+a3*a2*log (a2)+a5*a4/2.+2*a5-al*log (al) -a2*log (a2))/(fl*a6) —

161. M=(-a5*a4*log (a5)-al0+enp*e0+a5*a4/2.-a5*log (a5)+a5)/ (f2*a6) —

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 front speed U=2*vf*e0*n0/(a4*a5) - if (zz=="2") (xk=U*tau-printf ("n Required height of 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 m=(17.Ze-6*397/(T+124))*pow (T/273.3./2.) - рд=(29.0/22.4)*273*Рд/(Т *1.013e5) - h=m/pg-

166. Beginning of the cycle by layer height do (е0.=е0- // Assigning an initial value to e1. Beginning of the 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=beta () - // Call the subroutine for calculating betaif (b==0.) (printf (“n Value of the dimensionless relaxation time > 0.22 “)-getch ()-return-1. B=6*b/dz-

168. Calculation of P value P=-U*z*a5/B-

169. Calculation of the current value e e1.=epsilon (ei-1.) - eср=(е+е[i])/2.-

170. Subroutine for writing results to a file and accumulating arrays // for outputting graphsvoid vyv (void) (

Let's consider the principle of the filtration process using the example of the operation of a simple filter for separating suspensions. It is a vessel divided into two parts by a filter partition. If the filter material is free-flowing, a support 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 a filter partition, where complete or partial separation of the dispersed phase occurs, and then is removed from the vessel. To force the liquid through the partition, a pressure difference is created on opposite sides of it, and the suspension is forced from a part of the vessel with high pressure to a part of the vessel with lower pressure. The pressure difference is the driving force behind the filtration process.

If we designate the volume of the resulting filtrate obtained during the time dτ as dV f, then the differential equation for the filtration rate can be presented as:

C f = dV f /(F f ∙dτ)

Where:
C f - filtration speed;
F f - filtering area.

The filtration area is the main calculated geometric characteristic (CGG) of filters.

The filter membrane is a porous structure, the pore size of which directly affects its filtering ability. The liquid penetrates through the pores as if through channels through a partition, and the dispersed phase is retained on it. The solid particle retention process can be accomplished in several ways. The simplest option is when the pore size is smaller than the particle size, and the latter simply settles on the surface of the partition, forming a layer of sediment. If the particle size is commensurate with the pore size, then it penetrates inside the channels and is retained inside in narrow areas. And even if the particle size is smaller than the narrowest cross section of the pore, it can still be retained due to adsorption or sedimentation on the pore wall in a place where the channel geometry is strongly curved. If the solid particle was not retained 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, during filtration, one can observe the following picture: in the initial period of time, the resulting filtrate turns out to be cloudy due to the presence of “slipped” particles of the dispersed phase, and only after a while the filtrate becomes clear, when the stopping capacity of the partition reaches the required value. In light of this, two types of filtration process are distinguished:

with the formation of sediment;
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 actual filtration process is usually accompanied by these two phenomena, expressed to varying degrees. Filtration to form a precipitate is more common.

The filtration speed is proportional to the driving force and inversely proportional to the filtration resistance. Resistance is created both by the partition itself and by the resulting sediment. 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 filter partition, m -1;
r o - sediment resistivity, m -2;
l is the height of the sediment layer, m.

It is important to note that in the general case R fn 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 if fibrous materials are used. The value r o is specific, that is, it shows the resistance that will be per unit height of the sediment. The ability of resistivity to change its value depends on the physical and mechanical properties of the sediment. If, within the framework of the filtration process, the particles forming the sediment can be assumed to be non-deformable, then such a sediment is called incompressible, and its resistivity does not increase with increasing pressure. If, with increasing pressure, solid particles undergo deformation and become compacted, as a result of which the pore sizes in the sediment decrease, then such a sediment is called compressible.

Preferred is filtration to form a precipitate. In this case, almost no clogging of the pores of the partition occurs due to the formation of arches of solid particles above the entrances to the pore channels, serving as an additional retention factor for dispersed solid particles. There is almost no increase in the resistance of the partition Rpr, and it is quite easy to control the resistance of the sediment layer by timely removing part of it. In addition, cleaning the pores of the filter partition is usually associated with great difficulties, and in some cases it may turn out to be completely useless, which means the loss of the filtering ability of the partition, therefore, if possible, this type of contamination should be avoided. To prevent clogging of the pores, the filtered suspension can be subjected to preliminary thickening, for example, by settling. Mass formation of vaults begins when the volumetric concentration of the solid phase in the suspension reaches about 1%.

1.4.1 Technological modeling 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 modeling methods eliminates the need to experiment with a large number of possible options for selecting process parameters, reduces the duration and volume of experimental studies and allows one to find the optimal technological regime using simple calculations.

The application of technological modeling methods in the field of water treatment is important as a scientific basis for intensifying and improving 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 productivity reserves and establish the optimal technological operating mode of structures. The use of technological modeling also makes it possible to generalize and systematize experimental and operational data on various types of water sources. And this makes it possible to significantly reduce the volume of experimental research related to the design of new and intensification of existing structures.

To carry out filtration technological analysis, it is necessary to have an installation, the diagram 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 wall effect, as well as to ensure that the flow rate of water taken by samplers does not exceed the value acceptable for practical experiments, the filter column must have a diameter of at least 150...200 mm. The height of the column is taken to be 2.5...3.0 m, which ensures the placement of a sufficient layer of filter material in it and the formation of sufficient space above the load to increase the water level with increasing pressure loss in the filter material.

The samplers are installed evenly along the loading height of the filter column at a distance of 15...20 cm from each other. The sampler, located before the water enters the load, serves to monitor the concentration of suspended matter in the source water. The sampler located behind the load serves to control the quality of the filtrate. The remaining samplers are designed to determine changes in the concentration of suspended matter in the thickness of the granular load. To obtain reliable results, the filter column must have at least 6 samplers. During the experiment, ensure continuous flow of water from the samplers. 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 the total pressure loss in the thickness of the filter media.

The filter column is loaded with the most uniform granular material possible. It is desirable that the average diameter of the loading grains be from 0.7 to 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 using the formula

m = r(1 - n)V,

where m is the mass of washed and sorted filter material, kg; r - loading density, kg/m3; n is the intergranular porosity of the filter media; V is the required loading volume, m3.

After filling the filter column, the filter material is compacted by tapping the wall of the column until the top 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 Calculation and technological part

2.1 Application of filter materials in water treatment

2.1.1 Basic parameters of filter media

The filter media is the main working element of filter structures, therefore the correct choice of 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 it in the area of construction of the given filter complex and compliance with certain technical requirements, which include: the 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 uniformity of the grain sizes of the filter media and its fractional composition significantly affect the operation of the filter. The use of larger filter material entails a decrease in the quality of the filtrate. The use of finer filter material causes a reduction in the filter cycle, excessive consumption of wash water and an increase in the operating cost of water purification.

An important indicator of the quality of a filter material is its mechanical strength. The mechanical strength of filter materials is assessed by two indicators: abrasion (i.e., the percentage of wear of the material due to friction of grains with each other during washing - up to 0.5) and grindability (percentage of wear due to cracking of grains - up to 4.0).

An important requirement for the quality of filter materials is their chemical resistance to the filtered water, that is, that it is not enriched with substances harmful to human health (in drinking water supplies) or to the production technology where it is used.

In addition to the above technical requirements, filter materials used in domestic drinking water supply undergo a sanitary and hygienic assessment for microelements passing from the material into 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 rock, shungizite, volcanic and blast furnace slag, 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 were burned during underground fires.

Volcanic slag is a material formed as a result of the accumulation of gases in liquid cooling lava.

Shungizite is obtained by firing a natural low-carbon material - shungite, which in its properties is close to crushed expanded clay.

Industrial waste, blast furnace slag and copper-nickel production slag can also be used as filter materials.

Polystyrene foam is also used as a filter material on 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 mass	Density,	Porosity,	Mechanical strength,		Coefficient
	Size,	Bulk bulk mass	Density,	Porosity,	erasability	grindability	Coefficient
Quartz sand	0.6¸1.8		2.6	42			1.17
Crushed expanded clay	0.9	400	1.73	74	3.31	0.63	-
Uncrushed expanded clay	1.18	780	1.91	48	0.17	0.36	1.29
Crushed anthracite	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			-
Expanded polystyrene	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

The specified filter materials do not cover the entire variety of local filter materials proposed in recent years. There is evidence of the use of agloporite, porcelain chips, granodiorite, and so on.

Active filter materials are used, which, due to their properties, can remove from water not only suspended and colloidal impurities, but also truly dissolved contaminants. Activated carbons are widely used to extract substances that cause tastes and odors from water. A natural ion exchange material, zeolite, is used to remove various dissolved compounds from water. The availability and low cost of this material make it possible to increasingly use it as a feed for filtering devices.

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UDC 542.67:544.272

MODELING THE PROCESS OF MEMBRANE FILTRATION OF LIQUID SYSTEMS

Babynyshev Sergey Petrovich

Doctor of Technical Sciences, Professor

Chernov Pavel Sergeevich

Senior Lecturer

Pyatigorsk State Technological University, Pyatigorsk, Russia

Mamai Dmitry Sergeevich

graduate student

Stavropol State Agrarian University, Stavropol, Russia

It has been shown that the use of averaged characteristics in formulas relating the permeability of filtration partitions to the parameters of the porous structure is permissible only for some model membranes

Key words: filtration rate, surface friction, capillary

UDC 542.67:544.272

membrane filtration process modeling applying to liquid systems.

Babenyshev Sergey Petrovich

Dr.Sci.Tech, professor

Chernov Pavel Sergeevich

Pyatigorsk state technological university, Pyatigorsk, Russia

Mamay Dmitry Sergeevich

postgraduate students

Stavropol state agrarian university, Stavropol, Russia

It is shown, that use of average characteristics in the formulas, which interconnect penetrability of filtration barriers with porous structure parameters, is relevant only for several kinds of membranes

Keywords: filtration velocity, surface friction, capillary

The relatively low efficiency of ultrafiltration separation of protein solutions predetermined the conduct of theoretical studies with the aim of developing and justifying a method for intensifying the process. Increasing the productivity of membrane equipment can be achieved by increasing the filtration surface of individual modules and increasing the filtration speed by finding optimal conditions for the separation of liquid polydisperse systems. Currently, in rolled membrane elements, a high density of membrane packing can be achieved by organizing the laminar flow regime of the separated system above the membrane, which is limited by the hydrodynamic flow conditions above and below the membrane, the physical characteristics of semi-permeable partitions and drainage materials. The main reason causing the reduction in separation efficiency is the phenomenon of concentration polarization and membrane fouling. Therefore, an indispensable condition for the effective operation of membrane equipment is the preliminary cleaning of the initial separated system in order to remove micro- and macro-suspensions from it, which complicate the separation process. The lack of a complete understanding of the mechanism of membrane separation and especially the mechanism of ultrafiltration of protein solutions makes it difficult to resolve issues of choosing directions and methods for intensifying the process. This is due to the fact that until now there are no sufficiently substantiated ideas about the molecular interaction in the system: protein solution - membrane partition. It is possible that this is due to the influence of Coulomb forces and the conditions of hydrophilization of the membrane; the physical interaction of molecules of the dispersed phase and the membrane, determined by van der Waals forces, electrostatic interaction or viscous friction, is not excluded. In the practice of using membrane methods to increase salt retention, membranes are sometimes treated with surfactants. Modification of the membrane with a low-molecular-weight surfactant leads to partial blocking of the pores, resulting in a decrease in the effective pore size and an increase in separation selectivity. In this case, the permeability of membranes treated with surfactants stabilizes over time.

Intensification of the process is also achieved by immobilizing proteolytic enzymes on the membrane. Proteases located in the surface layers of the membrane, interacting with the protein, cause its breakdown and thereby prevent the formation of gel structures above the membrane. An effective method for reducing concentration polarization is to increase the speed of the flow circulating over the membrane. Turbulization of the flow can be enhanced by introducing additional dispersed particles into the flow (gas bubbles, solid and colloidal particles, etc.). In this case, the decrease in concentration polarization occurs depending on the density and size of dispersed particles. The increase in permeability with increasing turbulization is explained by a decrease in the thickness of the boundary layer and a decrease in the concentration of the solution in it. Insufficient turbulization of the solution can lead to the formation of boundary layers 100-300 microns thick. This widely used method of turbulizing the separated solution by increasing the speed of the circulating flow leads to excessive heating of the solution and necessitates the use of additional cooling equipment. An increase in the specific productivity of the membrane apparatus can be achieved using a short-term supply of reverse liquid flow during the operating mode of the filtration process. The effect is explained by “alternating” pressure in the working chamber of the apparatus, which ensures the release of blocked pore inlet openings from a certain proportion of particles that have clogged them. The use of such pulsation modes makes it possible to achieve the effect of destruction of the polarization layer, while the membrane permeability and separation efficiency increase with increasing pulsation frequency. When carrying out dead-end ultrafiltration of water for membrane regeneration, it is proposed to use backwashing, carried out during the ultrafiltration process by supplying permeate to the working area. This stabilizes the operation of the active ultrafiltration cycle. It is possible to reduce concentration polarization by using the concentrating effect of the intermembrane flow, which provides sedimentation reverse transport of particles from the membrane surface. A promising direction for increasing the separation efficiency when using nuclear filters is the use of nuclear membrane partitions with an anisotropic structure. When solving issues of process intensification, much attention is paid to the use of external fields, which to a certain extent predetermine the interaction of the components of the solution with the membrane. Methods using ultrasound are being used, but the difficulty of generating sound waves in industrial membrane devices hinders the implementation of these methods. Intensification of the process is achieved by applying an electric field and magnetic treatment of the separated solution, which leads to a decrease in the thickness of the gel film formed on the membrane and a decrease in filtration resistance. Much attention in the industrial use of ultrafiltration in the food industry is paid to the processes of regeneration and washing of contaminated membranes. When ultrafiltrating protein solutions, washing is usually carried out using solutions of surfactants and detergens. Due to the specific nature of food production and taking into account the fact that the separated solutions are a good breeding ground for various microorganisms, membrane washing is combined with sanitary treatment of membrane equipment, which is usually carried out once per shift in accordance with technological instructions. Thus, sanitization has two goals: to restore productivity by removing deposits and to ensure the removal of product residues and the microbiological cleanliness of the working area of the device. The effectiveness of membrane regeneration in this case is determined by the correct choice of detergent and modes of its use. There is a wide variety of solution compositions, methods of regeneration and washing of membrane devices. Typically, industrial operation of membrane equipment requires a washing station, the cost of which is up to 20-25% of the total cost of the installation. It should be added that washing systems, especially those of an enzymatic nature, significantly increase the cost of the regeneration process. It should also be taken into account that chemical and biochemical washing are quite lengthy processes. The composition of the detergent and the processing mode depend on the type of solutions being separated, the type of membrane partition and the degree of membrane contamination. The organization of the washing process, regardless of the nature of the product being separated and the type of membrane, is carried out by supplying a washing solution to the working area of the apparatus and ensuring its circulation under a certain (less than operating) pressure. The permeate zone is treated with a solution passing through the membrane under the influence of a pressure difference. Existing methods and detergents recommended for sanitary treatment of membrane equipment used for separating dairy products provide, depending on the degree of restoreability of the permeability of the installation, after washing, additional treatment of the working area with an acid composition after alkaline washing. It should be noted that the practice of operating ultrafiltration equipment shows that washing with the use of surfactants and detergents provides satisfactory restoration of permeability during a shift cycle of operation, and only after several tens of cycles do signs of incomplete restoration of productivity appear, which indicates the presence of unremoved deposits, apparently , in the pore space.

Despite the fact that at present a fairly large amount of empirical material has been accumulated, the analysis of which allows, in most cases, to predict the kinetic parameters of the process of separation of liquid polydisperse systems, during the technological calculation of ultrafiltration equipment, two main questions arise: how quickly the permeate flow decreases during one separation cycle and how membrane permeability changes over time. Usually, to solve them, one or another method of modeling the processes occurring during baromembrane separation of liquid systems is used. Methods for developing a theoretical description of the process are usually based on modified dependencies from the theory of filtration.

In accordance with the basic principles of Stokes, the filtration rate of liquids Q through a layer of porous material thick h at small values Re under the influence of pressure difference DR is described quite accurately by the Darcy equation:

flow liquid membrane porous

Where h- dynamic viscosity of the liquid, K- coefficient of permeability of the medium, which must take into account all the features of the flow caused by the properties of the porous medium.

All subsequent studies of filtration patterns within the framework of the applicability of Darcy’s law, as a rule, come down to considering the relationship between permeability and the characteristics of the filter medium or the properties of liquids flowing through them, for example, the Kozeny-Karman equation:

or dependency:

Where e - porosity of the medium; WITH- pore shape constant, S- specific surface area of the medium; O- tortuosity. Expressions (2) and (3) are identical if the average pore radius r described by the equation:

If instead r in (3) substitute its integral value:

Where f(r) is the distribution function of pore volumes along radii, then the expression for permeability will take the form:

It should be noted that in addition to the obtained equation (4), which does not explicitly include the factor e, other particular formulas that express k through the parameters of the porous structure, obtained both experimentally and on the basis of various models describing it, are widely used. But at the same time, the whole variety of approaches is united by solutions to the equations of fluid motion, provided that for low flow velocities the inertial terms can be neglected. In the case of a single straight capillary, such a solution, known as the Hagen-Poiseuille equation, can be obtained from the balance of forces acting on the fluid, since in a stationary fluid flow, the pressure drop of the fluid at the inlet and outlet of the capillary is entirely spent on overcoming the viscous forces of internal friction, determined by integration along the capillary radius, equations of the form:

Where Ff - tangential component of the internal friction force, related to the area of contact of the particles; V - local fluid velocity, x - coordinate perpendicular to the direction of fluid velocity

In this case, the so-called Poiseuille parabolic flow velocity profile is realized in the capillary, corresponding to the equation (in relation to the cylindrical model):

The current paradigm for fluid flow through porous media is based on three basic assumptions:

1. The resistance to fluid flow due to changes in the pore cross-section in comparison with viscous friction can be neglected.

2. The permeability of a porous medium is only its geometric characteristic, independent of the properties of the liquid and the pore surface.

3. Only the Poiseuille fluid flow profile extends over the entire cross section of the pores.

This gives reason to assume that for liquid flow at low Reynolds numbers, its transfer potential is spent only on overcoming surface friction forces in the pores. In this case, the average flow velocity in the pores VWed should be times greater than calculated by equation (1):

Taking into account the above assumptions and equations (4), (5), (6) and (7), the total friction force FTp on the surface of the pores can be represented in the following form:

Where F- surface area of a porous medium divided by its volume

Equating FTP to the fluid pressure drop at the boundaries of a porous layer of thickness L, multiplied by the share of the overall surface attributable to pores, we obtain that

those. Darcy's law (1), where K is in accordance with expression (2).

Assessing the possibility of practical use of these formulas for preliminary calculation of the permeability of industrial membranes, we will take into account that, other things being equal, the filtration rate is determined by the parameters of the semi-permeable membrane and the physicochemical properties of the liquid system being separated.

It is generally accepted that the most complete characteristic of a porous medium is the distribution curve of pore sizes over radii. By integrating these curves in accordance with (4), one can obtain the dependence of the values TO on the pore radius, which would make it possible to quantitatively assess the effect of pores with different sizes on the kinetic parameters of filtration. However, a comparison of permeabilities calculated based on (2) and (4) shows that the results almost always have a significant discrepancy even for homogeneous porous structures. Therefore, it is not entirely correct to determine the values of the medium permeability coefficient K using equations (2) and (4) for conventional industrial samples of polymer and inorganic membranes; these formulas are applicable only for model porous media.

Of the variety of liquid systems, the most studied are those in which the dispersion medium is water. At the same time, there is data proving the influence of phenomena occurring directly at the surface of the pores on the speed of water flow in them, caused by the pressure difference. Its decrease, in comparison with the speed of the Poiseuille flow, can be explained by an increase in viscosity caused by the orientation of water molecules near the phase boundary. This is indirectly confirmed by the effect of disruption of the structure of water at temperatures above 65°C, when its viscosity in the capillaries becomes the same as the values in the volume. An increase in flow velocity in the pores of a hydrophobic medium is usually associated with a decrease in the viscosity of the near-wall layer of water, and the boundary condition at which the fluid velocity on the surface is zero is replaced by the condition of flow with slip, introducing a corresponding correction in the form of a slip coefficient into the Hagen-Poiseuille equation. At the same time, the work notes the existence of special slip planes, characterized by a sharp change in viscosity in the volume of liquid at a considerable distance from the surface. The complexity of the physico-chemical composition and, accordingly, the properties of liquid systems actually used, for example, in the dairy industry, casts doubt on the possibility of taking this factor into account by introducing a certain average viscosity value into the Hagen-Poiseuille or Darcy equation. For the case of reverse osmosis baromembrane separation, for example, natural whey, it is quite possible that there is bound water in the membrane pores. In its physical properties it differs from the usual one, that is, free. It can be characterized as a viscous-plastic fluid with appropriate shear strength. When a pressure gradient appears that slightly exceeds a certain initial value determined by this shear strength, a filtration process described by Darcy’s linear law may well occur in nanoporous media. From this point of view, this can be considered the lower limit of applicability of the linear filtration law.

BIBLIOGRAPHY

1. Babenyshev S.P. Determination of pressure in the channel of a baromembrane apparatus [Text] / S.P. Babenyshev, G.A. Vitanov, A.G. Skorokhodov // Mechanization and electrification of agriculture: collection. scientific tr. No. 7 - Stavropol: StGAU 2007. - pp. 9-10.

2. Babenyshev S.P. Calculation of the radial velocity of a dispersed phase particle in the channel of a pressure membrane apparatus with a spiral flow turbulator [Text] / S.P. Babenyshev, G.A. Vitanov, A.G. Skorokhodov // Mechanization and electrification of agriculture: collection. scientific tr. No. 7 - Stavropol: StGAU 2007.- P. 11-12.

3. Babenyshev S.P. Features of formalization of the description of the flow of whey permeate through a nanoporous medium [Text] / S.P. Babenyshev, I.A. Evdokimov // Storage and processing of agricultural raw materials: collection of articles. scientific tr. No. 7 - Stavropol: SevKavGTU 2008.- P. 37-39.

4. Greg S., Singh K. Adsorption, specific surface area, porosity [Text] / S. Greg, K. Singh. M.: Mir, 1970 - 120 p.

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10. Churaev N.V., Sobolev V.D., Zorin Z.M. Measurement of viscosity of liquids in quartz capillaries // Spec. Discuss. Faraday Soc. N.Y.-L.: Acad. Press, 1971.

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