A model for the pressure balance of a low density circulating fluidized bed

The pressure balance along the solid circulation loop of a circulating fluidized bed equipped with a solid flux regulating device has been modelled and the influence of the pressure balance on the riser behaviour has been predicted.The solid circulation loop has been divided into many sections, where the pressure drop was calculated independently: riser, cyclone, standpipe, control device and return duct. A new theoretical model, that is able to predict the pressure losses in the return path of the solid from the standpipe to the riser, has been built. A new correlation for cyclone pressure loss with very high solid loads has been found on the basis of experimental data.The pressure loss in the riser has been calculated by imposing the closure of the pressure balance, ΣΔP = 0. Once the riser pressure drop had been calculated, the holdup distribution along the riser was obtained by imposing a particular shape of the profile, according to the different fluid-dynamics regimes (fast fluidization or pneumatic transport). In the first case, an exponential decay was imposed and the bottom holdup was adjusted to fit the total pressure drop, in the second case, the height of the dense zone was instead varied.The experimental data was used to develop the sub-models for the various loop sections have been obtained in a 100 mm i.d. riser, 6 m high, CFB. The solid was made of Geldart B group alumina particles. The tests were carried out with a gas velocity that ranged between 2 and 4 m/s and a solid flux that ranged between 20 and 170 kg/m²s. A good agreement was found between the model and experimental data.     

Magnesite products of increased density

Conclusions A system of preparing magnesite powders has been introduced in the section of chrome-magnesite products, which includes a pneumatic classifier and ensures the separation of the powder into narrow grain-size fractions without dust being emitted into the production rooms. Trials showed that the performance of the pneumatic classifier is stable at loads of 1.5–10 tons/h.The system makes it possible to divide the powder not only in terms of grain sizes but also in terms of density; it can be recommended also for the processing of other refractory materials.Translated from Ogneupory, No. 5, pp. 9–12, May, 1978.     

Dispersion of an Impurity in Flow Apparatuses and the Effect of Its Concentration on the Transfer Velocity

The dispersion of a material in a flow apparatus is analyzed for the case in which the transfer velocity of a desired material depends on its concentration, i.e., in which, contrary to traditional theoretical concepts, the transferred material is not dynamically passive. The presence of circulation zones and the dependence of the diffusion coefficient on the impurity concentration, coordinates, and time are taken into account (if required). The nonlinear dispersion equation derived is used to obtain nonlinear equations of the cell models. Some examples of calculations are given. A hierarchy of the mass-transfer models describing flow structure in apparatuses is considered.__________Translated from Teoreticheskie Osnovy Khimicheskoi Tekhnologii, Vol. 39, No. 4, 2005, pp. 379–389.Original Russian Text Copyright © 2005 by Moshinskii.     

Mathematical Modeling of Electrodialysis Demineralization Using a Stochastic Model

A stochastic model is proposed to calculate efficiency indices for the treatment of liquid mixtures by electrodialysis using methods of queuing theory. Electrodialysis demineralization of an ammonium sulfate solution is experimentally studied. Comparison between the experimental and theoretical data confirms the validity of the model.__________Translated from Teoreticheskie Osnovy Khimicheskoi Tekhnologii, Vol. 39, No. 3, 2005, pp. 278–281.Original Russian Text Copyright © 2005 by Yustratov, Pavskii, Krasnova, Ivanova.     

An experimental study of energy-saving pneumatic conveying system in a horizontal pipeline with dune model

In order to reduce power consumption and conveying velocity, a pneumatic conveying system where a dune model is mounted in a pipeline is proposed in this paper. The experimental study focuses on the effect of the mounted dune model in the horizontal pneumatic conveying system in terms of pressure drop, power consumption and conveying velocity. The test pipeline consisted of a horizontal smooth acrylic tube with an inside diameter of 80 mm and a length of about 5 m. Polyethylene spherical particles with a density of 952 kg/m³ and diameters of 2.3 and 3.3 mm are used as conveying materials. The mean air velocity is varied from 9 to 16 m/s, and the solid mass flow rate is from 0.25 to 0.45 kg/s. Firstly, the effect of the dune model location on pneumatic conveying is experimentally studied. It is found that in the lower air velocity range, the pressure drop of the pneumatic conveying with a mounted dune model is lower than that of a conventional pneumatic conveying system. A lower conveying velocity and energy-saving conveying can be realized by installing a dune model in the conveying pipe. Especially the case of fixing the dune model on the bottom of the pipe at the inlet of particle feed is more effective. The particle flow patterns also show that the dune model reduces the deposition of particles. Then, the effect of different surface materials of the dune model is examined. By using a surface material of the dune model with a large coefficient of restitution, the pressure drop of conveying large particles is the lowest. When conveying relatively small particles, however, the pressure drop becomes the lowest by a small coefficient of restitution. The maximum reduction rates of the minimum velocity and power consumption by the dune model are about 19% and 34%, respectively.     

Increasing urea-N efficiency for transplanted lowland rice by pneumatic injection: Yield and economics at the farm level

To increase the fertilizer-N efficiency in lowland rice (Oryza sativa L.) cultivation, new management practices are needed. Main cause of the present low efficiency is the low N recovery by plants, as a considerable part of the N applied is lost; deep placement techniques improve the recovery. A pneumatic injector, with which urea prills can be point-placed at a depth of 5–10 cm in paddy soils, was tested in 38 on-farm trials in 1989/90, mostly during the wet season. The experiments, located in Africa and Asia, focussed on differences in grain yield between conventional methods of broadcasting urea and injection by the pneumatic injector, at recommended N-rates. The study shows that the pneumatic injector is effective as a tool to improve the N fertilizer efficiency. The average yield increases per region, resulting from the use of the injector, ranged from about 250 to 1300 kg grain ha^–1. The value of the yield increase would allow most farmers to recover the costs of the injector within one season, even if labour was hired to carry out the injections. The average labour requirement of the injector was 40 hours ha^–1. In Indonesia, injection of prilled urea gave yields similar to those obtained with urea briquettes.     

A new model for estimation of the critical properties of alkanes

A simple model is proposed to estimate the critical properties of alkanes—temperature, pressure, and volume. This model is dependent on normal boiling and molecular weight of hydrocarbons. The model has been expanded based on a Taylor series in the form of a polynomial function of normal boiling. Because methane has the simplest structure among hydrocarbons, this model has been calculated around methane. The coefficients of this model were assumed in the form of a linear function of molecular weight. These parameters can be obtained from regression between experimental results and results from this model. By a comparison of this model and previous models, it is shown that this model is suitable to use for estimation of the critical properties of alkanes.From Teoreticheskie Osnovy Khimicheskoi Tekhnologii, Vol. 39, No. 1, 2005, pp. 80–82. Original English Text Copyright © 2005 by Pazuki, Mokhatab, Jahanshahi.This article was submitted by the authors in English.     

Development of a Mathematical Model of the Synthesis of SKDK Rubber in the Presence of Ethylene and Toluene

A mathematical model is proposed to describe butadiene rubber polymerization in the petroleum solvent Nefras on a cobalt catalyst in the presence of ethylene and toluene in batch and continuous reactors. The main elementary steps are determined, and a kinetic scheme of the process under investigation is developed. Using the proposed model, the molecular-weight characteristics of the process at different ethylene and toluene concentrations are studied. An original method is proposed to solve the set of equations describing the process in a cascade of continuous reactors with allowance for the reaction of polyaddition of macromolecules.__________Translated from Teoreticheskie Osnovy Khimicheskoi Tekhnologii, Vol. 39, No. 4, 2005, pp. 466–475.Original Russian Text Copyright © 2005 by Aminova, Manuiko, Litvinenko, Bronskaya, Bronskii, D’yakonov, Bronshtein.     

Mathematical Modeling of Heat and Mass Transfer in Gas Absorption on a Drop of a Volatile Absorbent

A model of simultaneous heat and mass transfer in absorption of component A from a gas mixture in a drop of a volatile absorbent at commensurable phase resistances is constructed based on the known model of heat and mass transfer inside a drop. Heat and mass transfers in the gas phase are described in terms of the heat and mass transfer coefficients. The relation between the dimensionless mole fraction of component A and temperature averaged over the drop volume and the mole fraction and temperature at the drop surface is found using Duhamel’s principle and the balance of the heat and mass flows at the interface. The solutions of the resulting integro-differential equations are presented as a series of exponential functions with constant coefficients, as is the solution of the internal problem. For the process of absorption of ammonia in a water drop, the dimensionless average temperature in the drop as a function of time are given at different concentrations of vapor in the bulk of the dispersion medium.__________Translated from Teoreticheskie Osnovy Khimicheskoi Tekhnologii, Vol. 39, No. 4, 2005, pp. 401–406.Original Russian Text Copyright © 2005 by Murav’ev.     

Heat Transfer Complicated by Phase Transitions in a Moving Layer

A mathematical model of heat transfer that is complicated by phase transitions in a moving layer is proposed. An analytical solution is obtained using fractional differential-integral calculus. An expression for the temperature in the front as a function of the phase-transition boundary velocity is derived, from which an expression for the front velocity is found. The theoretical expression of the front velocity fits experimental data. A method for estimating the activation energy is proposed.__________Translated from Teoreticheskie Osnovy Khimicheskoi Tekhnologii, Vol. 39, No. 3, 2005, pp. 243–250.Original Russian Text Copyright © 2005 by Kholpanov, Zakiev, Pomogailo.     

Predicting axial pressure profile of a CFB

The numerical simulation of CFBs is an important tool in the prediction of its flow behavior. Predicting the axial pressure profile is one of the major difficulties in modeling a CFB. A model using a Particle Based Approach (PBA) is developed to accurately predict the axial pressure profile in CFBs. The simulation model accounts for the axial and radial distribution of voidage and velocity of the gas and solid phases, and for the solids volume fraction and particle size distribution of the solid phase. The model results are compared with and validated against atmospheric cold CFB experimental literature data. Ranges of experimental data used in comparisons are as follows: bed diameter from 0.05 to 0.305 m, bed height between 5 and 15.45 m, mean particle diameter from 76 to 812 μm, particle density from 189 to 2600 kg/m³, solid circulation fluxes from 10.03 to 489 kg/m² s and gas superficial velocities from 2.71 to 10.68 m/s. The computational results agreed reasonably well with the experimental data. Moreover, both experimental data and model predictions show that the pressure drop profile is affected by the solid circulation flux and superficial velocity values in the riser. The pressure drop increases along the acceleration region as solid circulation flux increases and superficial velocity decreases.     

Combustion of sprayed liquid fuel in a swirling flow

A physicomathematical model and results of numerical studies of aerodynamics and combustion of liquid fuel in a coaxial swirling flow of a gaseous oxidizer are presented. The characteristics of liquid-fuel spraying by a centrifugal injector were determined on the basis of experimental data obtained under isothermal conditions. The influence of flow swirling on the burner characteristics is analyzed.__________Translated from Fizika Goreniya i Vzryva, Vol. 41, No. 2, pp. 26–37, March–April, 2005.     

Application of high-speed PIV and image processing to measuring particle velocity and concentration in a horizontal pneumatic conveying with dune model

The purpose of this study focuses on analyzing the particle velocity and concentration characteristics in a horizontal pneumatic conveying with dune model, so as to reveal the mechanism of the low conveying velocity and saving-energy conveying. The test pipeline consisted of a horizontal smooth acrylic tube with an inside diameter of 80 mm and a length of about 5 m. The polyethylene particles of density 978 kg/m³ and 952 kg/m³ with diameters of 2.3 and 3.3 mm are used as conveying materials. High-speed PIV was first applied to measure the time-averaged particle velocity and was proven to be an efficient measurement technique in the pneumatic conveying. Then the particle velocity and concentration distributions of three locations were measured at mean air velocities of 12 m/s and 13 m/s and the solid mass flow rates of 0.45 kg/s and 0.43 kg/s. A comparison of the particle velocity and concentration profiles between dune model and non-dune model was performed. It is found that the particle concentration of using dune model becomes higher in the upper part of pipeline and becomes lower near the bottom of pipeline in the acceleration region. The particle velocities of using dune model are clearly higher than that of the conventional pneumatic conveying along pipeline and display a uniform profile at the downstream. It is also clear that the particles can be effectively accelerated by increasing air velocity and impacting the surface of dune model. The effect of dune model on the velocity profile of relatively small particles is larger than that of the larger particles and maintains to the downstream.     

Mass-Transfer Equation in Multicomponent Mixtures

A multicomponent mass-transfer equation for the distillation of multicomponent mixtures is derived in terms of the thermodynamics of irreversible processes.__________Translated from Teoreticheskie Osnovy Khimicheskoi Tekhnologii, Vol. 39, No. 3, 2005, pp. 337–344.Original Russian Text Copyright © 2005 by Serafimov, Timoshenko.     

Radial Reactor-Heat Exchanger for Natural Gas Combustion in a Structured Porous Metal Catalyst Bed

A compact (0.01 m³ in volume) radial reactor for deep oxidation of methane (with a heat output of 16–30 kW) that is combined with an internal water heat exchanger is designed. The reactor contains the structured porous metal catalyst 5% (0.5% Pt/γ-Al₂O₃) + 65% Ni + 5% Al. The reactor performance at different heat outputs is experimentally studied. It is demonstrated that, if catalytic methane combustion is virtually complete, the fraction of heat transferred to the internal heat exchanger (to the water) is large (31–53%) and allows the reactor to reach a specific heat output up to 130 kW/m² (on the outer surface of the catalytic heating element). The coefficients of heat transfer to the internal heat exchanger and the radial thermal conductivity of the catalyst bed are shown to theoretically strongly affect the thermal conditions in the catalyst bed. It is concluded that the proposed mathematical model fits the experimental data well.__________Translated from Teoreticheskie Osnovy Khimicheskoi Tekhnologii, Vol. 39, No. 4, 2005, pp. 432–439.Original Russian Text Copyright © 2005 by Kirillov, Kuzin, Kuz’min, Skomorokhov, Shigarov.     

Statistical simulation of aluminum agglomeration during combustion of heterogeneous condensed mixtures

A statistical model of aluminum agglomeration during combustion of solid composite rocket propellants is considered; the model describes the process dynamics, beginning from propellant heating in the combustion wave and ending by separation of agglomerates from the burning surface. An algorithm of computing the agglomeration process by the Monte Carlo method is proposed. A series of computations of aluminum agglomeration is performed; the density distribution functions for agglomerate sizes are derived; the dependence of the mean-mass size of agglomerates on the mean-mass size of ammonium-perchlorate particles is determined. The model proposed predicts power dependences of the mean-mass size of agglomerates on pressure and burning rate, which agrees with available experimental data.__________Translated from Fizika Goreniya i Vzryva, Vol. 41, No. 2, pp. 62–74, March–April, 2005.     

Calculation of binodal lines for a multicomponent mixture by the homotopy method

Equations are proposed for binodal lines of a multicomponent mixture in the T-P and P-V planes. A numerical method for solving the equations of the thermodynamics model is described, which is based on the homotopy method and uses the physical parameters of the system, in particular, temperature and pressure, as parameters of continuation of solution. Calculation results illustrating the features of the phase states of binary and multicomponent mixtures are presented.Translated from Teoreticheskie Osnovy Khimicheskoi Tekhnologii, Vol. 39, No. 1, 2005, pp. 88–94.Original Russian Text Copyright © 2005 by Yermakova, Sazhina, Anikeev.     

Effect of Longitudinal Dispersion Parameters on the Gas Cleaning Efficiency in a Membrane Cell with Retentate Recycle

Computational experiments using a mathematical model of the gas separation process have determined the conditions under which retentate recycle is expediently used for fine gas cleaning. The results of the theoretical calculations agree quite well with experimental data on fine argon cleaning to remove propane and water impurities.__________Translated from Teoreticheskie Osnovy Khimicheskoi Tekhnologii, Vol. 39, No. 4, 2005, pp. 420–425.Original Russian Text Copyright © 2005 by Vorotyntsev, Kirillov, Drozdov.     

Mathematical Description of the Electrostatic State of Chemical Fibres with Consideration of the Forms of Intermolecular and Interfibre Interactions

A method for determining the electrostatic state of chemical fibres is developed. Mathematical dependences that allow determining the electrical capacitance of chemical fibres with different structural features and packages with longitudinal and transverse arrangement of the fibres are obtained. The inverse problem — finding the functional dependence of the dielectric constant of the investigated material on the initial capacitance — is solved.__________Translated from Khimicheskie Volokna, No. 1, pp. 56–58, January–February, 2005.