Volume 96, №2

ANALYSIS OF THE COLLECTOR CHARACTERISTICS OF THE BOTTOMHOLE ZONE OF A STRATUM SUBJECTED TO A HYDRAULIC FRACTURING BY THE NATURAL VIBRATIONS OF THE LIQUID COLUMN IN A WELL
The problem on the natural vibrations of the liquid column in the production string of a vertical oil well in a stratum, arising as a result of a sudden opening-out or a sudden closing-in of the well, was considered. A mathematical model of the dynamics of the liquid column in such a well communicating with the stratum through the permeable walls of the open section of the well and through a hydraulic fracture made in the stratum, has been constructed. On the basis of this model, the analytical solutions, defi ning the damped natural oscillations of the pressure and the velocity of a liquid fl ow in an oil well sank in a stratum subjected to a hydraulic fracturing, caused by the viscous forces acting near the walls of the well as well as by the fi ltration processes occurring in the bottomhole zone of the stratum, have been obtained. A comparative analysis of the results of calculations of the dynamics of the liquid column in such a well and the corresponding fi eld data has shown that the frequency characteristics of the liquid fl ow in a well in a stratum subjected to a hydraulic fracturing and the rate of damping of the natural oscillations of the velocity of this fl ow furnish the intensional information on the collector characteristics of the bottomhole zone of the stratum and on the quality of its hydraulic fracturing  
Author:  V. Sh. Shagapov, G. R. Rafikova, R. A. Bashmakov, Z. Z. Mamaeva
Keywords:  oil well, stratum, liquid column, natural vibrations and oscillations, hydraulic fracture, characteristic equation
Page:  281

DYNAMICS OF PRESSURE IN A WELL DURING TREATMENT OF ITS FACE ZONE BY A THERMAL GAS GENERATOR
An analysis of the pressure wave fi eld that appears in a well as a result of combustion of a powder charge of a thermal gas generator is presented. Based on the solution of the problem obtained by the spectral method, it is shown that in the case under consideration the well represents a resonator that implements wave perturbations of discrete spectrum. Four types of possible pressure fl uctuations in the well are determined, which correspond to the implementation of various combinations of periodic, aperiodic, and resonant modes. For the case of realizing only periodic modes, a comparison with experiment was made, which indicates the predominant contribution of the zero mode. From this it also follows that approximation of oscillations only by the zero mode is possible at both small and large amplitudes. The value of the apparent damping coeffi cient is approximately twice higher for high-amplitude processes, while the circular frequency remains unchanged. It has been established that the attenuation of pressure waves occurs mainly due to elastic losses into the medium surrounding the well. The contribution of dissipative processes caused by the viscous friction of the fl uid in the well is relatively small.  
Author:  A. I. Filippov, O. V. Akhmetova, M. A. Zelenova, A. A. Koval′skii, F. A. Vepritskii
Keywords:  fi ltration waves, resonant mode, periodic mode, aperiodic mode, thermal gas generator, spectral method
Page:  290

INFLUENCE OF THE POSITION OF A HORIZONTAL HYDRAULIC FRACTURE ON THE PRESSURE FIELD IN THE STRATUM
The authors have proposed an analytical-numerical model of fi ltration in a producing stratum with a horizontal fracture, that is based on the solution of a quasi-stationary problem on the fi ltration pressure fi eld in a dominantvertical-permeability anisotropic porous medium divided by a disk hydrofracturing region. On the boundaries separating the fracture from the surrounding rocks, piezoconductivity equations were supplemented with conjugation conditions. The problem has been solved in a zero asymptotic approximation in the Laplace–Carson transform space. Inversion of the formulas was performed with the Iseger numerical algorithm. Results of the computational experiment have been given. It has been shown that the greatest infl uence of the location of the fracture on the pressure fi eld is observed in the case where it is on one boundary of the producing bed, and from an instant of time, the location of the fi ssure ceases to exert an infl uence on the pressure fi eld in the fracture. On the calculated pressure curves, stabilization is observed which is analogous to the existing logarithmic model for the case of a homogeneous stratum. The authors have investigated the space-time dependence of the pressure perturbation across the thickness of the bed in which hydraulic fracturing was implemented. It has been shown that the pressure diff erence between each point of the vertical cross section and the bottom (top) grows at small values of time. Subsequently, the pressure diff erence peaks and the growth is replaced by a drop. A regularity has been noted that implies that the rate of growth in the pressure diff erence between the fracture and the stratum′s bottom is much higher than that of drop  
Author:  A. I. Filippov, O. V. Akhmetova, M. A. Zelenova
Keywords:  hydraulic fracturing, fracture, pressure fi eld.
Page:  301

REPLACEMENT OF METHANE AS PART OF THE GAS HYDRATE BY CARBON DIOXIDE IN THE STRATUM WITH NEGATIVE TEMPERATURE
The authors have constructed a mathematical model of replacement of methane as part of the hydrate in a stratum saturated with methane and its hydrate under the conditions of negative temperatures upon the injection of carbon dioxide. An analysis has been made of the infl uence of the permeability, porosity, and length of the stratum, the initial saturation of the methane hydrate, and the coeffi cient of diff usion through the layer of CO₂ hydrate on the mass of the extracted mixture of methane and carbon dioxide. Basic possible variants of extraction of methane from the stratum depending on the relation of the characteristic times of fi lling of the stratum with carbon dioxide and on the kinetics of phase transitions have been shown.  
Author:  G. R. Rafikova, M. K. Khasanova
Keywords:  gas hydrate, replacement of methane by carbon dioxide, diff usion, gas-hydrate stratum, negative temperatures
Page:  312

MODELING THE MOVEMENT OF A LIQUID IN CAPILLARIES AND NOZZLES OF PRINTERS
The author has obtained the isotherms of wedging pressure of β fi lms from the data on the velocities of fl ow in an inhomogeneous electric fi eld of fi lms of model liquids on the surface of quartz capillaries of diff erent radii. Increase in the fi eld gradients leads to a deviation of the fi lms from the equilibrium state toward a growth in their thickness.  
Author:  inkjet printing, cylindrical channel, ink, liquid column, wetting angle, inhomogeneous electric fi eld, mass transfer
Keywords:  I. N. Karpovich
Page:  322

COLLISIONS OF LIQUID DROPLETS IN A FLOW OF FLUE GASES
Results of experimental investigations on the collision of water droplets and droplets of solutions with a lower surface tension (0.0361 N/m) and a higher dynamic viscosity (0.0108 Pa·s), as compared to those of water, in a fl ow of typical fl ue gases, e.g., the combustion products of kerosene, are presented. To meet the advanced industrial applications, the parameters of the collision of liquid droplets were varied within wide ranges: 0.1–0.7 mm for the radii of droplets, 0.1–7 m/s for the velocities of their movement, and 0–90^o for the angles of attack of the droplets. Video frames of realization of the four regimes of collision of liquid droplets: their coagulation, fl ying-off , breakage, and rebound, were analyzed. Signifi cant diff erences between the characteristics of the surface transformation of water droplets and droplets of solutions as a result of their collision were revealed. A comparison of the collisions of liquid droplets in the fl ue gases and in the air at room temperature has shown that these gases infl uence the characteristics of the liquid droplets colliding in them. The positions of the boundaries between the regimes of collision of liquid droplets on the charts of their interaction regimes were determined with regard for the dynamic viscosity and surface tension of the liquid in the droplets, the dimensionless parameter of their interaction, and the Weber number of the droplets. The main diff erences between the liquids in number and size of the secondary droplets formed as a result of the collision of their primary droplets were ascertained.  
Author:  S. S. Kropotova, N. E. Shlegel′, P. A. Strizhak
Keywords:  colliding droplets, high-temperature gases, combustion products, interaction regimes, chart of interaction regimes, secondary liquid fragments
Page:  328

HEAT TRANSFER INTENSIFICATION DURING CONDENSATION ON A HORIZONTAL PIPE BY MEANS OF COMBINED HYDROPHOBIC COATING
Heat emission during water vapor condensation on a horizontal pipe with a structured hydrophobic coating and without it in the presence of noncondensable gases has been studied. A method has been developed for hydrophobizing a metal heat-exchange surface using a combination of microstructure and nanoparticles, which makes it possible to achieve a contact angle of 158 deg. The infl uence of noncondensable gases and temperature diff erence on the heat emission coeffi cient during water vapor condensation on a horizontal pipe without coating and with a coating consisting of carbon nanoparticles has been studied.  
Author:  Yu. A. Kuzma-Kichta, D. V. Chugunkov, A. V. Lavrikov, N. S. Ivanov
Keywords:  condensation, hydrophobicity, wetting, contact angle, dropwise condensation
Page:  338

INTENSIFICATION OF HEAT TRANSFER DURING BOILING AND CONDENSATION BY MEANS OF MICROAND NANOPARTICLE COATINGS
The intensifi cation of boiling and condensation heat transfer by using coatings of micro- and nanoparticles has been studied. A hydrophilic coating of nanoparticles deposited on the boiling surface reduces the thermal resistance of the thermosyphon and increases the critical thermal load in the microchannel. Dropwise condensation on a horizontal pipe is stabilized by applying a combined hydrophobic coating. A method for obtaining aluminum oxide nanoparticles and a technology of forming a nanorelief have been developed.  
Author:  Yu. A. Kuzma-Kichta, N. S. Ivanov, A. V. Lavrikov, D. V. Chugunkov
Keywords:  boiling, condensation, hydrophilicity, hydrophobicity, wetting, contact angle, dropwise condensation
Page:  345

COMPUTATIONAL MODELING OF PARTIAL PHASE CHANGE IN THE HYPOEUTECTIC BINARY ALLOY Al–7Si MELT OVER A COOLED TILTED PLATE
A computational model has been developed to study the eff ect of the tilt angle (15, 30, 45, and 60^o ) and pouring temperature (893, 903, 913, and 923 K ) on the phase change behavior of the hypoeutectic binary alloy Al–7Si. The analysis has been done with the help of the obtained temperature fi eld, solid fraction evolution, as well as the Si distribution and macrosegregation. The two-dimensional multiphase volume-averaging transient model is used for computational modeling, incorporating phase diagram information, enthalpy-updating scheme, composition–solid fraction coupling, and variation in the thermophysical properties inside a mushy zone. It is observed that the eff ect of the tilt angle on the cooling rate is much superior to the pouring temperature eff ect. Moreover, the formation of eutectic plateau and negative macrosegregation are observed near the surface of the tilted plate in the eutectic temperature zone. Negative macrosegregation becomes high near the exit of the tilted surface.  
Author:  Rishitosh Ranjan, P. Ghose, B. Surekha
Keywords:  hypoeutectic binary alloy, phase change, cooled tilted plate, semisolid metal processing
Page:  350

SPECIFIC FEATURES OF TEMPERATURE DISTRIBUTION DURING SPARK PLASMA SINTERING OF TWO OR MORE MATERIALS SIMULTANEOUSLY
To determine the temperature distribution both on contact boundaries and directly in each of two materials during their simultaneous spark plasma sintering, the solution of the thermal problem has been used and a computational program has been developed. The heating of an alumina sample with tungsten, nickel, and graphite baffl es is considered. It is found that electrical heating of materials with high electrical conductivity occurs with small temperature gradients in both the axial and radial directions, which has made it possible to develop an additive method for obtaining large-size blanks of such materials.  
Author:  V. V. Krizhanovskii, V. I. Mali
Keywords:  alumina, nickel, tungsten, graphite, temperature, electric current, additive SPS
Page:  362

SIMULATION OF THE NONSTATIONARY GASDYNAMIC PROCESSES AND CONJUGATE HEAT TRANSFER IN THE WORKING CAVITIES OF PULSE-PERIODIC SYSTEMS
On the basis of analysis of the results of the numerical simulation of a nonstationary gasdynamic processes and conjugate heat transfer in laser cavities of diff erent geometries, the possibility of organization of a pulse-periodic process with defi nite frequency characteristics in such a cavity was determined depending on the initial pressure of the gas in the cavity, the density of the energy supplied to it, the composition of the gas mixture in the cavity, and the thickness of its walls. The state of the system comprising a gas cavity and its shell under the action of a single laser pulse and a series of laser pulses was simulated.  
Author:  N. A. Brykov, K. N. Volkov, V. N. Emel'yanov
Keywords:  pulse-periodic process, conjugate heat transfer, numerical simulation, power supply, pulse
Page:  368

EFFECT OF DEPOSITION OF MECHANICAL IMPURITIES ON TEMPERATURE DISTRIBUTION OVER THE BORE OF PRODUCING WELL
The work is devoted to studying heat exchange processes of an ascending fl uid fl ow in a producing well during the deposition of mechanical impurities on its walls, for example, of asphalt–paraffi n deposits. A mathematical model and the results of numerical solutions of the formation of a temperature fi eld along the wellbore are considered. It is shown that due to a change in the heat transfer coeffi cient in the areas of deposition of mechanical impurities, a change in the temperature gradient in a nonstationary thermal fi eld is observed. The results obtained can be used in interpreting the data of thermodynamic studies of producing wells.  
Author:  M. F. Zakirov, R. A. Valiullin, R. F. Sharafutdinov, A. Sh. Ramazanov
Keywords:  thermometry, fl ow rate metering, mechanical impurity, deposition, heat exchange, well, discharge, multibed system
Page:  374

EXPERIMENTAL STUDY OF FREE-CONVECTIVE HEAT TRANSFER OF SINGLE-ROW BUNDLES OF TUBES WITH SPIRAL ALUMINUM FINS OF DIFFERENT HEIGHTS IN AN AIR FLOW INTENSIFIED BY AN EXHAUST SHAFT
Experimental studies of free-convective heat exchange between single-row bundles of bimetallic tubes with spiral rolled aluminum fi ns of diff erent heights (2–14.6 mm) and a vertical air fl ow created by an exhaust shaft with adjustable height H = 0.52, 1.16, and 2.12 m are presented. The tubes were layed out with a constant relative transverse spacing σ1 = 1.14 (6 pipes). The data of measurements were used to calculate the average reduced heat transfer coeffi cient, which ranged from 0.78 to 17.30 W/(m² ∙ ^oC) at Rayleigh numbers (19–360)·10³ . A similarity equation is obtained for describing the dependence of heat emission of single-row bundles with diff erent fi n heights in a free convection regime on the relative height of the bundle–shaft system. It is found that intensifi cation of free convection of air by installing an exhaust shaft above the bundle of tubes allows one to increase the heat emission intensity by 2.3 times. Expressions are obtained for determining the energy and aerodynamic effi ciencies of the bundle–shaft system. The optimal height of fi nning (about 8 mm) for bundles of studied tubes with an exhaust shaft was determined.  
Author:  A. B. Sukhotskiia, E. S. Danil′chik
Keywords:  fi nned tube, single-row bundle, exhaust shaft, free air convection
Page:  385

SOLUTION OF GEOCRYOLOGY PROBLEMS ON THE BASIS OF FORMULAS FOR DECAYING HARMONIC WAVES OF HEAT AND MASS TRANSFER IN A HOMOGENEOUS HALFSPACE
An initial boundary value problem has been formulated within the A. V. Luikov theory for calculating temperature and moisture content fi elds in a homogeneous halfspace whose boundary is in a state of heat and mass exchange with an air medium. The halfspace material is made up of a hard substrate (a capillary-porous body) and water, the heat transfer between the halfspace boundary and the air medium occurs according to the Newton law, and the mass transfer occurs according to the Dalton law. In the initial state, the air medium and the material have an identical temperature, and the densities of the heat and moisture fl ows on the boundary separating them are equal to zero. At the instant of time assumed as the computing origin, the air temperature begins to make minor harmonic oscillations near its original value. It has been shown that with the passage of time, a heat and mass transfer regime will set in inside the material, under which temperature and moisture content fi elds have the form of decaying harmonic waves. For a mathematical model of partial-type heat and mass transfer (the movement of moisture of the surface only occurs due to a moisture content diff erential, and the transformation of water into steam only occurs on the surface), a dependence of the penetration depth and phase velocity of these waves on the values assigned under the problem conditions and determining the process has been obtained. The constructed solution and the resulting conclusions are the extension of Fourier′s investigations described in the literature, that refer to a situation when the halfspace material does not contain moisture and, according to a harmonic law, there is variation in the temperature of the material′s surface rather than in the air temperature. The results of the investigation can be used in geocryology as a theoretical tool in simulating daily and annual oscillations in the soil′s thermophysical state, which is an important task for planning economic activity in the frozen rock areas  
Author:  A. M. Afanasiev, Yu. S. Bakhracheva
Keywords:  Luikov equations, problem for halfspace, asymptotic solution, complex amplitude method, decaying harmonic waves, depth of penetration, delay time, geocryology
Page:  394

INFRARED RADIATION PENETRATION INTO VEGETABLE MATERIALS EXPOSED TO THERMAL RADIATION
The results of experimental investigations and numerical simulations of temperature distribution in specimens of vegetable materials exposed to infrared radiation are presented. Based on these investigations, an analysis has been made of the depth of penetration by infrared radiation into wet materials (potatoes, apples, and celery root) in using ceramic and quarts halogen thermal radiators. The research data can be useful in creating energy-effi cient technologies for thermoradiation treatment and drying of vegetable materials.  
Author:  P. V. Akulich, D. S. Slizhuk, A. V. Akulichb
Keywords:  depth of penetration by infrared radiation, thermoradiation treatment of vegetable materials, infrared drying
Page:  403

CAVITATION AND COLLAPSE OF A BUBBLE IN A LIQUID IN A HEAT PIPE
Investigations were carried out to study the mechanisms of heat transfer in heat pipes using the developed experimental stand consisting of a heat pipe, temperature measurement circuit, and a sensor for measuring the integral intensity of ultraviolet radiation. The temperature dependences of the intensities of electromagnetic and acoustic radiations of the liquid heated in a heat pipe have been obtained. It is shown that the acoustic and electromagnetic radiations of the liquid in a heat pipe depend mainly on the surface tension coeffi cient of the liquid and the size of the bubbles in it. It has been established that in order to reduce the destructive eff ect of cavitation and of the collapse of bubbles in the liquid in a heat pipe on its inner surface, it is necessary to minimize its surface tension coeffi cient, for example, by adding a small amount of organic oil to the water. Based on the analysis of the data on the energy liberated on collapse of a bubble in a liquid, a construction of a noiseless jet engine is suggested  
Author:  G. A. Krivonosov
Keywords:  heat pipe, liquid, surface tension, cavitation, bubble collapse, noiseless jet engine
Page:  410

INTENSIFICATION OF HEAT TRANSFER IN THE REFRIGERATION ZONE OF ABSORPTION COLUMNS
The intensifi cation of heat transfer in the refrigeration zone of absorption columns has been studied. It is shown that for the absorption of CO₂ by ammoniated brine it is possible to signifi cantly intensify the process of removing the heat of exothermal reaction. It has been established that the hydraulic resistance of spirally rolled pipes is 1.5 times less than that of pipes with discrete arrangement of annular diaphragms. Data are obtained on K/Ksm and F/Fsm depending on the spacing between spirally rolled turbilizers S/D, and the optimal regions were determined in the range of values S/D = 1.0–1.4. The effi ciency of pipes with spirally rolled turbilizers has been demonstrated.  
Author:  M. M. Abdullaev, S. Kh. Nishanova, É. T. Mavlonov
Keywords:  absorber, tube–grid packing, hydraulic resistance, turbilizer, heat transfer, intensifi cation, heatexchanging surface, water flow rate
Page:  417

HYDROELASTIC BURSTING WAVES IN CHANNEL-SLOT STRUCTURES OF SOLID FUEL
The paper deals with questions related to a description of the propagation of nonlinear waves in homogeneous channels with elastic walls from solid fuel fi lled with solid fuel combustion products, a medium moving at a constant or space-variable velocity determined by the fuel combustion. For ease of reference, hereinafter these waves will be referred to as hydroelastic waves in a solid fuel combustion chamber. Within the framework of a long-wave approximation, a system of equations is proposed for a description of these waves. It is shown that this system is quasi-linear and hyperbolic. It is shown that the propagation velocity of hydroelastic waves is lower than the velocity of waves′ propagation across the compressible fl uid medium fi lling a channel with elastic walls. Riemann invariants have been found. Conditions on strong discontinuities have been obtained and discontinuous solutions, an analog of shock waves in a gas, have been described. It is shown that discontinuous solutions are possible with increase and decrease of pressure after the discontinuity. A Riemann equation describing the propagation of weak discontinuities of hydroelastic waves through the channel has been obtained. The Riemann equation makes it possible to determine the time and place of the occurrence of gradient catastrophes of hydroelastic waves. Numerical-analytical investigations have been conducted into the formation and propagation of strong discontinuities with a rise and drop of pressure after such discontinuities. The proposed theory of propagation of hydroelastic waves can be used for determining the location of leaks in pipeline systems and for predicting the destruction of solid-propellant rocket engines by a hydroelastic wave. An analysis has been made of the nonlinear stability of the fl ows of combustion products in a homogeneous channel with elastic walls.  
Author:  S. V. Sukhinin, A. V. Trilis, V. S. Yurkovskii, A. A. Cheremisin
Keywords:  hydroelastic wave, quasi-linear hyperbolic systems of equations, strong discontinuity, Riccati equation, gradient catastrophe, solid-propellant rocket engine
Page:  423

FEATURES OF THE SURFACE HEATING OF A HEAT-INSULATED BLUNT PLATE IN THE STRONG-INTERACTION REGIME
Results of an experimental investigation of the heating of the surface of a blunt plate, made of a material having a low heat conductivity, in a wind tunnel in the regime of strong viscous-nonviscous interaction of the boundary layer on the surface of the plate with the incident fl uid fl ow are presented. It is shown that the installation of a wedge on this plate in the vicinity of its trailing edge changes the disturbed fl ow region and the temperature distribution over the surface of the plate upstream of the wedge as far as the leading edge of the plate.  
Author:  N. I. Batura, G. N. Dudin, N. G. Zhurkin, N. M. Kolushov
Keywords:  blunt plate, unsteady boundary layer, strong interaction. shock wave, infrared imager
Page:  430

POLYNOMIAL APPROXIMATION OF THE LAMINAR BOUNDARY LAYER ON A FLAT PLATE ON THE BASIS OF THE KARMAN MOMENTUM INTEGRAL
A new approach to the polynomial approximation of the laminar boundary layer on the surface of a fl at plate on the basis of the Karman momentum integral with the use of additional optimum constraints is proposed. The polynomial coeffi cients of a solution of the problem on this layer were determined for the fi rst time with the use of the system of zero boundary conditions for the surface of the plate and defi nite boundary conditions for the outer side of the boundary layer on it. Optimum polynomial solutions of the problem in the zero to twentieth approximations have been obtained. A solution of the problem obtained in the seventeenth approximation is almost identical to the high-accuracy numerical solution of the Blasius equation, obtained by B. D. Ganapol, with a maximum deviation of 6∙10^–7.  
Author:  V. A. Kot
Keywords:  boundary layer, Blasius equation, integral methods, Karman momentum integral, Karman–Pohlhausen method
Page:  438

LBM SIMULATION OF MIXED CONVECTION IN A TILTED LID-DRIVEN CAVITY COOLED WITH A NONUNIFORM TEMPERATURE DISTRIBUTION IN THE PRESENCE OF RADIATION
The laminar mixed heat convection coupled with the surface radiation in an inclined lid-driven square cavity was investigated numerically using the lattice Boltzmann method. The moving wall of the cavity was heated to a constant temperature, and the opposite cavity wall was cooled to a spatially varying temperature. The results of the study show that the combined eff ect of the Richardson number and the inclination of the cavity on the structure of the fl uid fl ow and the heat transfer in it is signifi cant. The changes in the structure of the fl uid fl ow in the cavity with change in the inclination of the cavity are notably aff ected by the radiation of its surface.  
Author:  Youssef Dahani, Mohammed Hasnaoui, Abdelkhalek Amahmid, Safae Hasnaoui
Keywords:  mixed convection, lid-driven square cavity, nonuniform cooling, surface radiation, lattice Boltzmann method
Page:  468

FILM-COOLING PERFORMANCE OF CYLINDRICAL AND CRATERED HOLES FED BY A PERPENDICULAR CROSSFLOW
Recent studies have proven that a coolant crossfl ow infl uences the cooling performance of fi lm-cooling gas turbine holes. The present paper evaluates the cooling performance for several innovative cratered fi lm-cooling holes fed by a perpendicular crossfl ow channel. The fl ow fi elds, discharge coeffi cients, and the cooling eff ectiveness are analyzed and compared based on the results predicted by the methods of computational fl uid dynamics (CFD) for cylindrical, concentric cratered, and contoured cratered holes. The investigated blowing ratio varies from 0.5 to 2.0. The ratio of the velocity at the crossfl ow channel inlet to the mainstream fl ow velocity is equal to 0.6. The study indicates that the character of the vortex pair and the velocity distribution depend on the specifi c hole shape and blowing ratio. A contoured cratered hole is shown to provide a higher cooling eff ectiveness than cylindrical and concentric cratered holes. In addition, it exhibits the highest discharge coeffi cients everywhere over the range of the blowing ratios studied.  
Author:  Y. C. Shi, C. Zhang, Z. Sun, Y. X. He
Keywords:  fi lm cooling, cylindrical hole, cratered hole, cooling eff ectiveness, discharge coeffi cient, numerical computation
Page:  482

THE TWO-STAGE PROCESS OF THERMOCHEMICAL PROCESSING OF LIGNIN IN A FIXED BED. 1. TECHNOLOGICAL SCHEME OF THE INSTALLATION. METHODS FOR CALCULATING PYROLYSIS GAS COMPOSITION
A method is proposed for the thermochemical processing of biomass (lignin) meant for the use of one reactor for the production of two synthetic gases dissimilar in composition and calorifi c value: low-calorie (1800–2000 kcal/nm³ ) and medium-calorie (~4000 kcal/nm³ ) with a low resin content. Two methods for calculating the composition of pyrolysis gas have been developed. Various variants of the operation of installation in cyclic and quasi-stationary modes are considered, taking into account unique technical solutions for supplying coke–ash residue from the pyrolyzer to the gasifi er  
Author:  B. B. Rokhman, V. G. Vyfatnyuk
Keywords:  synthetic gas, pyrolysis, gasifi cation, coke–ash particles, biomass, coke-ash particles, retort, volatile substances
Page:  492

THE TWO-STAGE PROCESS OF THERMOCHEMICAL PROCESSING OF LIGNIN IN A FIXED BED. 2. SIMULATION OF THE WORKING PROCESS IN THE REACTOR AND NUMERICAL ANALYSIS OF GASIFICATION OF COKE–ASH BIOMASS RESIDUE
Mathematical simulation of the process of thermochemical processing of biomass in a reactor is presented. A numerical study of the gasifi cation of coke–ash residue in this reactor was carried out.  
Author:  B. B. Rokhman, V. G. Vyfatnyuk
Keywords:  fi xed bed, biomass, thermal conductivity, heat exchange, steam–air gasifi cation, conductive, radiant, temperature, chemical reactions
Page:  498

THE TWO-STAGE PROCESS OF THERMOCHEMICAL PROCESSING OF LIGNIN IN A FIXED BED. 3. SIMULATION AND NUMERICAL ANALYSIS OF THE NONSTATIONARY PROCESS OF PYROLYSIS IN A RETORT
Using the calculation results given in [1, 2], the dynamics of the exit of volatile substances from a close-packed bed of lignin particles in a retort was studied numerically. A nonstationary model of thermal decomposition of lignin pellets into thermolysis products is constructed taking into account the rates of primary and secondary decomposition reactions. The rates of the production of resin and of its dissipation during transition to light gas and coke were studied.  
Author:  B. B. Rokhman, V. G. Vyfatnyuk
Keywords:  resin, gas, coke, pellets, primary and secondary reactions, volatile substances, fi xed bed, thermolysis products, pyrolysis, particles
Page:  506

POLYACRYLAMIDE HYDROGELS WITH A DISPERSED FILLER: SPECIFICS OF RHEOLOGY AND FILTRATION IN FRACTURES
In using fl ow diversion and water shutoff technologies, the most widely used sealing compounds are polyacrylamide solutions crosslinked with Cr³⁺ ions. To achieve high technological effi ciency, it is necessary to retain structural and mechanical properties of a sealing compound. Earlier, we proposed a hydrogel made up of sodium silicate and polyacrylamide crosslinked by chromium acetate which has good rheological characteristics and high residual resistance factors during fi ltration in fractures. It is noted that the addition of a dispersed fi ller increases substantially the composition effi ciency. In this investigation, a study has been made of the rheology of hydrogels on the basis of sodium silicate, polyacrylamide, and chromium acetate with a dispersed fi ller (rice husk) in fi ltration through a model of an ideal fracture of various degree of openness. It has been established that the addition of a dispersed fi ller increases substantially the strength of water shutoff screen after fi ltration in fractures. In this case, there is almost no mechanical destruction of hydrogel with a fi ller in large fractures. For comparison investigations with hydrogel on the basis of polyacrylamide, resorcinol, and paraform were conducted. It is shown that after fi ltration in fractures, hydrogels on the basis of polyacrylamide, resorcinol, and paraform do not experience, in practice, any mechanochemical destruction. The experimental results indicate that the introduction of dispersed materials into hydrogels for water shutoff of fractured reservoirs increase signifi cantly the technological effi ciency of processes by decreasing the mechanical destruction and increasing the residual resistance factor.  
Author:  A. G. Telin, V. A. Strizhnev, A. V. Fakhreeva, R. R. Asadullin, L. E. Lenchenkova, A. A. Ratner, V. S. Chepenko
Keywords:  water shutoff in fractured reservoirs, polyacrylamide hydrogels, rheological investigations, ideal fracture model, fi ltration, mechanochemical destruction, composite sealing compounds
Page:  515

SOME THERMODYNAMIC PROPERTIES OF PROPICONAZOLE USED AS FUNGICIDE AND ITS MIXTURE WITH CARBON DIOXIDE INVOLVED IN THE PROCESS OF WOOD IMPREGNATION
The paper presents the results of impregnation of dried common pine (Pinus sylvestris) specimens with propiconazole using a supercritical fl uid CO₂ impregnation process carried out at a temperature of 338 K in the pressure range of 10–30 MPa. Within the framework of the formation of a database on the properties of the impregnation material required for the stages of modeling, optimization, and scaling of the impregnation process, an investigation was conducted of some thermodynamic properties of a propiconazole–carbon dioxide mixture in the supercritical fl uid region of the state. The isomeric composition of propiconazole has been investigated, and it has been established that it represents a mixture of two isomers. The methods of thermogravimetric analysis and diff erential scanning calorimetry have been used to study the thermal characteristics of propiconazole. The paper presents the results of an experimental investigation of propiconazole solubility in supercritical carbon dioxide on the isotherms T = 338, 358, and 378 K in the pressure range of 10–30 MPa. The experimental data on solubility have been described using the Peng–Robinson equation of state and providing the pressure of saturated propiconazole vapors with the status of the second adjustable parameter in the calculation algorithm. The paper presents the results of an experimental investigation of the isobaric heat capacity of propiconazole at atmospheric pressure in the temperature interval of 313–573 K and of propiconazole–carbon dioxide mixture in the timperature interval of 313–473 K and the pressure range of 0.098–25.0 MPa.  
Author:  R. F. Gabitov, V. F. Khairutdinov, F. M. Gumerov, Z. I. Zaripov, T. R. Bilalov, Jean-Marie Kuagu, F. R. Gabitov, S. V. Mazanov, V. A. Petrov, V. K. Mingazova
Keywords:  common pine (Pinus sylvestris), impregnation, propiconazole, supercritical carbon dioxide, impregnation process, thermal properties, solubility, isobaric heat capacity.
Page:  520

THERMODYNAMIC ENTROPY BALANCES IN PERFECT MIXING APPARATUSES
The equations of thermodynamic balances are written and relations are obtained for calculating the production of entropy in the stationary regime of ideal mixing apparatuses in which heat transfer processes, chemical reactions, and segregated processes (crystallization, biosynthesis) occur.  
Author:  A. M. Tsirlin, A. M. Vasil′ev
Keywords:  ideal heat transfer, heat transfer coeffi cient, entropy, thermal loads, Newtonian kinetics
Page:  534

ON ACHIEVING THE ENTROPY MAXIMUM IN MECHANICAL SYSTEMS
Consideration has been given to the well-known argument that in a conservative mechanical system existing in an equilibrium state, entropy reaches a maximum. First, using the example of a system of material points modeling a rarefi ed gas, it has been shown that a maximum of entropy defi ned through the number of microstates is achieved on a solution that cannot be approximated by an exponential distribution corresponding to the Maxwell–Boltzmann distribution. There are many such solutions and each of them satisfi es both the condition of invariability of the number of points and the condition of constancy of the system′s total energy. Next, consideration has been given to an alternative defi nition of entropy through the density of distribution of the probability of a mechanical system being in an assigned volume of phase space. It has been shown that a conservative mechanical system of general type assigned by its Hamiltonian, in selecting various sets in the phase space for seeking an extremum, has an entropy maximum on various distributions in the case of one and the same energy. A conclusion has been drawn on the occurrence of a Maxwell–Boltzmann distribution in conservative systems of classical mechanics for reasons unrelated to entropy maximization.  
Author:  A. M. Shmatkov
Keywords:  entropy maximum, statistical weight, Maxwell–Boltzmann distribution
Page:  542

THE EFFICIENCY OF USING DOUBLE CASCADES WITH A CARRIER GAS FOR ENRICHING REPROCESSED URANIUM UNDER THE CONDITIONS OF A MULTIPLE RECYCLE
An estimate has been made of the potential of a double cascade with a carrier gas for enriching reprocessed uranium under the conditions of a multiple recycle. This scheme makes it possible to obtain low-enriched uranium with simultaneous fulfi llment of limitations on concentrations of even-numbered isotopes, fi rst of all, ²³²U, but is unable to prevent ²³⁶U concentration, which entails the need for increasing ²³⁵U enrichment. Hence, since ²³⁶U isotope is responsible for accumulating ²³²U as its daughter isotope, this results in accumulation of ²³²U with a rise in the number of processing cycles and reuse.  
Author:  A. Yu. Smirnov, V. A. Nevinitsa, G. A. Sulaberidze, V. E. Gusev
Keywords:  enrichment, reprocessed uranium, double cascade, carrier gas, multiple recycle
Page:  547

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