Backmixing Coefficient Research Articles

Модернизация насадочных ректификационных колонн с применением математической модели разделения многокомпонентной смеси

The scientific and technical problem of mathematical modeling and calculation of separation of hydrocarbon mixtures in industrial columns with chaotic and regular nozzles is solved. Multicomponent transfer is calculated using a matrix of volumetric mass transfer coefficients, and the reverse (longitudinal) mixing of steam and liquid flows by Pekle numbers with back-mixing coefficients. The task of developing options for upgrading the stabilization column of the oil and gas condensate mixture at an oil refinery is considered. Calculated profiles of concentrations of key components in the mixture are presented. The required height of the nozzle layer has been determined. After upgrading the column with a new nozzle, a stable mode of operation of the unit is provided in the specified range of loads and the composition of the mixture. We also solved the problem of designing two industrial columns in the technological scheme for the separation of benzene from stable condensate (gasoline fraction). As a result of calculations based on a mathematical model, the operating and structural characteristics of columns with the use of chaotic metal nozzles "Injekhim-2012"were established.

Modelling of mass transfer in separation of hydrocarbon mixtures and modernization of industrial columns

A system of differential equations of mass transfer with an interfacial mass source for multicomponent distillation in a column with random and structured packings in the film mode is presented. The interfacial source is associated with the matrix of volumetric mass transfer coefficients as well as a driving force for mass transfer. The diffusion fluxes of mass of components are written in the form of Fick’s law with elements of the matrix of coefficients of molecular diffusion in the gas (vapor) phase. To simplify the mathematical model, one dimensional equations for the diffusion model of the structure of flows in the gas and liquid phases with the interfacial sources and coefficients of back (longitudinal) mixing of gas and liquid flows are used. The Dankwerts boundary conditions are applied to the system of equations. To calculate the back mixing coefficients, experimental data obtained for the selected types of packings are used. When modelling mass transfer in hydrocarbon mixtures consisting of several dozen components, the system of equations for the diffusion models is solved for the key components and fractions of the oil and gas condensate (OGC) mixture stabilization column at an industrial enterprise. A brief description of the technological scheme is given. Scientific and technical solutions are developed to replace obsolete sieve trays in the stabilizer column with a new structured corrugated roll packing having a rough surface. It is found that a packing height of eight meters is sufficient for separating OGC in a given composition range. As a result of implementation of the new packing, the content of isopentane in the stable condensate decreases and its concentration in the broad fraction of light hydrocarbons increases from 9 wt.% to 11.7 wt.%. The implementation of packing in the stabilizer column meets the requirements of the technical specifications.

Determining efficiency of removal of dispersed phase from gases and modernization of scrubbers using high-performance packings

A solution to the problem of modeling the removal of a finely dispersed phase from stack gases and process gases at power engineering and petrochemical enterprises using a column apparatus filled with new highly efficient random and structured packings is considered.The use of diffusion and cell models of the flow structure for calculating a concentration profile of particles settling on a liquid fi lm in apparatuses filled with various packings is shown. Accounting for the deposition of finely dispersed particles from gases on the interfacial surface of the liquid fi lm flowing down along the packing is carried out using a bulk source of mass. The model of turbulent-inertial sedimentation of particles is adopted. The main parameters of the model are the coefficient of turbulent migration of particles to the fi lm surface on contact devices, a modified Peclet number with a backmixing coefficient, and the number of complete mixing cells. This approach can be generalized to a wide class of fi lm-type apparatuses for wet gas cleaning with the aim of designing them or choosing modernization options. Expressions are obtained for calculating the efficiency of aerosol separation on packings as well as the required depth of the packed bed for a given efficiency.Results of calculating the efficiency of gas purification from aerosols with the use of various types of packings in scrubbers as well as the required depth of the packed bed for a given efficiency are presented. A graphical dependence of the power spent on gas cleaning in apparatuses with different packings is given. Results of solving the production problem of cleaning pyrogas from coke and tar by circulating water in a modernized scrubber with new highperformance packings are shown.Expressions for calculating the rate of turbulent particle migration for random and structured packings as well as modified Peclet numbers are presented. A distinctive feature of these expressions is the calculation based on the known hydraulic resistance of contact devices.

The profiles of radial liquid velocity and mixing parameters in multi-stage bubble columns

Liquid circulation flow is one of the important hydrodynamic characteristics of the multi-stage bubble column. In this paper, the radial liquid velocity, axial back-mixing coefficient, and liquid exchange velocity were studied in a multi-stage bubble column with 2,000 mm height and 282 mm diameter using a Pavlov tube and the tracer method. The effects of superficial gas velocity and plate structure on the mixing characteristics are presented. With an increase of the superficial gas velocity, the liquid velocity in the centre of the bubble column increases. With a decrease in the percentage of free area, the hole diameter, and tongue angle, the gas hold-ups below the perforated plate increases greatly. Moreover, the addition of a perforated plate enhances the eddy strength in the bubble column, which increased the coalescence and breakup of bubbles.

Backmixing in Karr Reciprocating-Plate Extraction Columns

A study of backmixing in the continuous phase has been presented for a 50 mm diameter Karr reciprocating-plate extraction column using the two-phase system kerosene/tributyl phosphate (continuous)−phenol−water (dispersed). The column was operated in the emulsion region with nylon plates of 45% open area. Backmixing was determined using the unsteady-state tracer injection technique in which tracer concentrations at two distinct locations in the column were measured. Operating parameters, including frequency and amplitude of agitation and solvent and aqueous-phase flow rates, have been studied over a range of values to investigate their influence on the extent of backmixing in the continuous phase. A model based on the “two-zone approach” model used for predicting backmixing performance in a pulsed perforated-plate column (Prvcic, L. M.; Pratt, H. R. C.; Stevens, G. W. AIChE J. 1989, 35, 1845−1855) has been refitted for the current data to predict the effects of continuous-phase backmixing in a Karr reciprocating-plate column. Results indicate that the backmixing coefficient can be predicted within 13% using this model.

The influence of non-ideal phase flow on the extraction efficiency for the case of a linear equilibrium distribution

The influence of the fundamental parameters of non-ideal phase flow and the extraction parameters on the number of equilibrium stages - ND, theoretical stages - NT, as well as the number of stages (ND - NT), the existence of which is a consequence of the backflow in extractors, was investigated. The calculated number of stages (ND - NT) served as a measure of the influence of the denoted parameters on the extraction efficiency. The results of the investigation indicate that the number of stages (ND - NT) considerably increased with increasing backmixing coefficients and that the dependence was linear. It was established that the increase of the ratio of the flow rate of the heavy and light phase and the decrease of the equilibrium distribution coefficient, as well as the increase of the total separation factor, led to an exponential increase of the number of stages in the extractor, which consequently caused a decrease in the extraction efficiency.

A simplified method of obtaining the backmixing coefficient of a solvent extraction column from tracer pulse data

A method based on transfer function matching is used to obtain the backmixing coefficient of a solvent extraction column. The method demonstrates the exploitation of the symbolic manipulation capability of the current generation of scientific computing software. It starts with the dynamic model of Dongaonkar et al. and makes use of a set of tracer pulse data of Dongaonkar for a Kühni column. Compared to the existing methods of evaluating backmixing coefficient, this new method is more direct and simple to implement on computers. It has the potential of being applicable to more elaborate dynamic models of plate columns.

Residence times and mixing of a novel continuous oscillatory flow screening reactor

This paper is concerned with the fluid mechanics and mixing performance of a novel oscillatory flow screening reactor. Using fibre optic probes, a mixing coefficient k m is determined for the system as a function of the applied fluid oscillation frequency and amplitude. In a continuous operation mean residence time and a backmixing coefficient g are estimated as a function of the oscillation conditions. Finally, in order to compare data with numerical simulations steady state flow data are also included. The screening reactor presented an intermediate mixing behaviour throughout all the studied range of oscillation amplitudes (0–3 mm centre-to-peak) and frequencies (0–20 Hz). The backmixing was found to be highly dependent of the oscillation frequency and amplitude. Nevertheless, a stronger effect of the oscillation amplitude over the axial dispersion was detected presumably due to the increase of the mixing length. On the other hand, the increase of the oscillation frequency was concluded to have the increase in the radial mixing rates as the main effect. Thus, it was possible to achieve a decrease in the axial dispersion with the screening reactor using oscillatory flow, when compared to the laminar steady flow in a plain tube with the same mean internal diameter.

Hydrodynamic characteristics of a FCC regenerator

The hydrodynamic and gas mixing characteristics have been determined in a FCC regenerator (0.48 m I.D.x3.4 m high) with FCC particles. Solids holdup in the dense bed decreases with increasing gas velocity, but it increases in the freeboard region. The bubble/void fraction increases with an increase along the bed height at a given gas velocity and increases with increasing gas velocity at a constant bed height. Backmixed tracer gas at the wall region is higher than that at the center region of the bed. The gas backmixing coefficient decreases with increasing gas velocity.

Gas backmixing in the dense region of a circulating fluidized bed

The gas backmLxing characteristics in a circulating fluidized bed (0.1 m-Dx5.3-m high) have been deter- mined. The gas backmixing coefficient (D~.,:) from the axial dispersion model in a low velocity fluidization region increases with increasing gas velocity. The effect of gas velocity on D~,,, in the bubbling bed is more pronounced compared to that in the Circulating Fluidized Bed (CFB). In the dense region of a CFB, the two-phase model is proposed to calculate D~, from the two-phase model and mass transfer coefficient (k) between the crowd phase and dispersed phase. 211e gas baclmaixJng coefficient and the mass transfer coefficient between the two phases increase with increasing the ratio of average particle to gas velocities (UyU,.).

Gas backmixing in a circulating fluidized bed

The gas backmixing characteristics in a circulating fludized bed (0.1 m i.d., 5.3 m high) of fluid catalytic cracking (FCC) particles have been determined. The gas backmixing coefficient has been determined based on the axial dispersion model by using two tracer gases (He and CO 2) in a circulating fluidized bed (CFB). The obtained gas backmixing coefficients by using the absorbed CO 2 gas overestimates the gas backmixing coefficient 60–62% in the dense region, 49–62% in the transition region and 2.4–19% in the dilute regulates compared to the values obtained by the non-adsorbed He tracer gas. The gas backmixing coefficient increases with increasing the ratio of particle to gas velocities ( U p/ U g). In the upper dilute region, the core annulus model is proposed to determine the gas backmixing coefficients and the mass transfer coefficients between the core and the annulus regions. The gas backmixing coefficient and mass transfer coefficient increase with increasing U p/ U g.

A study of fluid dispersion in oscillatory flow through a baffled tube

AbstractPrevious studies show that axial dispersion in steady laminar flow can be substantially reduced by superimposing fluid oscillation in a baffled tube. In this paper, experimental observations on fluid dispersion for oscillatory flow in a baffled tube are obtained in a series of concentration measurements using high spatial resolution local conductivity probes, and two models—the continuous stirred tank (CST) with feedback and the plug flow with axial dispersion—are used to analyse the concentration curves and determine the fluid dispersion for such a system. The CST with feedback model combines the algorithms from Mecklenburgh and Hartland with the evaluations of unbiased moments from Anderssen and White to determine the dimensionless dispersion coefficient, D/uL, and the backmixing coefficient, F. The plug flow with axial dispersion model, on the other hand, utilises the axial diffusion model by replacing the molecular diffusion coefficient to the axial dispersion coefficient. This model uses an upstream concentration measurement together with an imperfect pulse technique to predict a downstream concentration profile, and thereby determine a best fit value for the dispersion coefficient D/uL. The axial dispersion results show that there is generally more dispersion predicted using the plug flow with axial dispersion model than when using the CST with feedback model for all the oscillatory Reynolds numbers and Strouhal numbers tested. The difference in the calculated D/uL between the two models is discussed.

Wave model for longitudinal dispersion: Analysis and applications

AbstractAn analysis and applications of the wave model for longitudinal dispersion are pre‐sented. Asymptotic forms of the wave model are considered and analytical solutions of typical linear stationary and nonstationary problems of chemical reactor engineering interest are obtained and compared to those for the Fickian dispersion model. The wave model leads to efficient analytical solutions for linear problems, which in principle differ from the solutions of the Fickian dispersion model; only for slowly varying concentration fields do the soluctions of both models approach each other. Spatial and time moments of the concentration distribution are obtained for pulse‐dispersion problems; the first three spatial moments of the mean, variance, and skewness have exact, large‐time asymptotic forms in the case of Taylor dispersion. Old experiments that could not be explained with the standard dispersion model are reconsidered and explained: the change with time of the variance of a concentration pulse when the flow direction is reversed and the difference in values of the apparent axial dispersion coefficient and the backmixing coefficient in a rotating disk contactor. The experimental determination of model parameters is discussed.

PERFORMANCE OF JET PLATES IN PULSED LIQUID-LIQUID EXTRACTION COLUMNS.

Abstract Jet plates with elevated rims around their openings are assumed to improve the performance of pulsed extraction columns. A comparison with conventional plates was carried out in a pilot-plant size column with the system of water, toluene and acetone. Hold-up, drop size, backmixing and axial concentration profiles in both phases were measured simultaneously. Mass transfer coefficients were evaluated from measured data by minimising the deviations of measured concentration profiles from model prediction using standard and open-end stagewise backflow models. Equations from the literature for prediction of drop size, hold-up and backmixing coefficients were modified by recalculating the empirical coefficients from recent data to enable quantification of trends and replacement of missing values. The transfer coefficents correlated against actual velocity of the dispersed phase rised to a power between 0.6 and 1, the influences of pulsation velocity, drop size and actual velocity of the continuous phase being by an order of magnitude smaller. The magnitude of the transfer coefficients was comparable to those measured earlier under similar conditions in a reciprocating plate extraction column where, however, the mentioned additional influences were more important. A strong influence of mass transfer direction on hydrodynamic parameters was observed. Transferring acetone from continuous water into dispersed toluene, the jet plates flooded at higher specific loading and the transfer coefficients were above those observed on conventional plates. In the opposite direction no significant differences were found.

Mass transfer and axial dispersion in a Kühni extraction column

AbstractConcentration profiles were determined in both phases for the system methyl isobutyl ketone (MIBK)—water‐acetic acid in a Kühni 72.45‐mm‐dia. Extraction column of 25 stages. Mass transfer and backmixing parameters were estimated numerically from the profiles in terms of the backflow model. The results indicated that backmixing of the continuous phase was appreciable, while that of the dispersed phase was negligible. Independent values of the continuous‐phase backmixing coefficient, αc, were also determined by both unsteady‐state and continuous tracer injection, in the former case both with and without mass transfer. The results indicated that αcis increased by mass transfer, and that the tracer values, both with and without mass transfer, are greater than those obtained from the profile data.

GAS MIXING IN SLUGGING AND TURBULENT FLUIDIZED BEDS

Abstract The gas phase mixing in a fluidized bed of glass beads (dp = 0.362 mm) in the slugging and turbulent flow regimes has been studied in a 0.1 m-ID × 3.0 m high Plexiglas column. The gas dispersion in the downstream of the bed has been described by a diffusion process with the axial and radial dispersion coefficients. The radial dispersion coefficient of the gas phase is nearly constant with the variation of gas velocity in the slugging flow regime, but it increases with an increase in gas velocity in the turbulent flow regime. Appreciable backmixing of the gas phase is pronounced in the slugging flow regime whereas the lower gas backmixing is produced in the turbulent flow regime. The gas backmixing coefficient increases with an increase in gas velocity in the slugging flow regime, but it decreases slightly with an increase in gas velocity in the turbulent flow regime. The radial mixing and backmixing coefficients of the gas in terms of Peclet numbers have been correlated with the relevant dimensio...

Axial dispersion in pulsed‐, perforated‐plate extraction columns

AbstractContinuous‐phase backmixing coefficients have been determined by continuous tracer injection for pulsed‐plate extraction columns of 72‐, 152‐ and 300‐mm‐diameter. Both single‐phase water and two‐phase kerosene‐water were studied in all three columns, together with four other solvent‐water systems in the smallest column; in all cases, water was the continuous phase. Evidence of maldistribution of the phases was obtained in the largest column. The backmixing coefficient was found to increase with column diameter in single‐phase operation, but was diameter‐independent in the two‐phase case. Alternative correlations of the data were based on dimensional analysis and on a physical model, respectively. The influence of different systems was accounted for in the latter in terms of droplet size and terminal velocity, dispersed phase holdup, and density difference. Qualitative color tracer tests on the dispersed phase gave no evidence of backmixing of this phase, although strong forward dispersion was observed in the emulsion regime.

Sensitivity of countercurrent extraction column response to changes in operating parameters

The performance of a typical liquid-liquid extraction column is essentially determined by the throughputs of both phases, the distribution factor, mass transfer rate and magnitude of the axial mixing. Though the actual response to changes in these parameters must be determined experimentally, general guidelines may be obtained by examining the properties of the analytical solution of the dispersion model. This work identifies the major influences and demonstrates the achievable accuracy in simulation of column performance, evaluation of mass transfer and backmixing coefficients, column design and scale-up.

Model‐based analysis of data from countercurrent liquid‐liquid extraction processes

AbstractAn efficient iterative method for solving the equations which describe the steady state of a staged countercurrent extraction process is described. The equations include the effects of backmixing, and apply to an arbitrary number of solutes, to nonlinear equilibrium relations, and to variable net phase flow rates (and thus to partially miscible solvents). The solution procedure, based on partial linearization of the equations, is related to and extends the method of Ricker et al. (1980).This solution procedure has been used, in conjunction with nonlinear regression methods, to investigate problems related to the determination of parameters by analyzing steady state data. The simultaneous determination of several parameters, including mass transfer coefficients, backmixing coefficients, and equilibrium constants, is shown to be possible. The accuracy with which the parameters can be estimated depends, however, on many factors, including the number and location of the sampling points, the intensity of the backmixing, and the extent to which equilibrium is approached in the column.

Prediction of drop diameter, hold‐up and backmixing coefficients in liquid‐liquid spray columns

AbstractThe available literature data for the drop diameter, hold‐up and backmixing coefficients were tested experimentally in a pilot plant size spray column. For all these parameters correlations were found which gave results in agreement with the experimental data so that reasonable prediction is possible. Different equations were compared and the ones giving the best fit are recommended.