Prediction Of Minimum Fluidization Velocity Research Articles

Artificial Neural Network Prediction of Minimum Fluidization Velocity for Mixtures of Biomass and Inert Solid Particles

The fluidization of certain biomasses used in thermal processes, such as sawdust, is particularly difficult due to their irregular shapes, varied sizes, and low densities, causing high minimum fluidization velocities (Umf). The addition of an inert material causes its Umf to drop significantly. The determination of the Umf of the binary mixture is however hard to obtain. Generally, predictive correlations are based on a small number of specific experiments, and sphericity is seldom included. In the present work, three models, i.e., an empirical correlation and two artificial neural networks (ANN) models were used to predict the Umf of biomass-inert mixtures. An extensive bibliographical survey of more than 200 datasets was conducted with complete data about densities, particle diameters, sphericities, biomass fraction, and Umf. With the combined application of the partial dependence plot (PDP) and the ANN models, the average effect of sphericity on Umf was quantitatively determined (inverse relationship) together with the average impact of the biomass fraction on Umf (direct relationship). In comparison with the empirical correlations, the results showed that both ANN models can accurately predict the Umf of the presented binary mixtures with errors lower than 25%.

Data-Driven Prediction of Minimum Fluidization Velocity in Gas-Fluidized Beds Using Data Extracted by Text Mining

Minimum fluidization velocity (Umf) is of fundamental importance in gas fluidization. Lots of empirical correlations have so far been reported in the literature to calculate Umf. However, Umf is affected by numerous factors, including, among others, the operation conditions and physical properties of both solids and gases. The applicability of empirical correlations relies essentially on the experiments upon which they were developed, and in practice, the choice of Umf is a matter of the knowledge and experience of chemical engineers. In this work, we proposed to establish a database by extracting experimental data of Umf from open literature using the text mining technique. We first presented a pipeline of natural language processing to identify and extract the functional parameters related to Umf with 83% accuracy from ∼40 000 papers. A database of Umf containing eight impacting factors, i.e., particle diameter, particle density, particle sphericity, bed voidage at minimum fluidization, gas density, gas viscosity, operating temperature, and pressure, was created. We then used a data-driven machine learning method with the extracting data to predict Umf, which is shown superior over the empirical correlations by achieving higher accuracy for a much wider range of gas–solid systems. We expect this work illustrates a potential and promising approach to make use of the huge amount of experimental data in the literature and replace the empirical correlations in practical chemical engineering design and operations.

Fluidization of biomass: a correlation to assess the minimum fluidization velocity considering the influence of the sphericity factor

This paper deals with the influence of different definitions for evaluating the sphericity factor on the prediction of minimum fluidization velocity (U mf) of different agro-industrial/forestry biomass residues and sand. Three biowastes (sawdust, grape marc, and grape stalk) and sand were characterized by sieving, and sphericity was calculated using images obtained by scanning electron microscopy (SEM). Two particle size populations (with mean diameters and density corresponding to B and D Geldart groups) were adopted for each biomass. As for sand, particles with a mean diameter of 0.33 mm were used. Tests were carried out in a lab-scale fluidized bed. Bed pressure drop was measured as a function of the superficial velocity of air at two different initial bed heights, for each type of biomass and mixtures with sand. Ratios of 0.50 and 0.75 (v/v) were used for mixtures. For all cases, U mf values were calculated experimentally and were compared against predicted values obtained from Ergun's equation and other correlations. It was found that the methodology adopted for determining sphericity significantly influences the obtained value of U mf. The lowest relative error between predicted and experimental U mf values was obtained using Riley’s sphericity method. Finally, a new correlation for U mf was proposed.

Significance of the particle physical properties and the Geldart group in the use of correlations for the prediction of minimum fluidization velocity of biomass–sand binary mixtures

The present study explores the relevance of the physical properties of biomass particles on the determination of the minimum fluidization velocity (Umf) of binary mixtures. Fluidization experiments were performed in a cold flow unit with diverse biomasses mixed with sand in different mass fractions. Gas velocity and pressure drop across the bed were used to determine Umf. Different correlations reported in the literature were evaluated on their ability to accurately predict Umf of the mixtures. Results showed satisfactory predictions when appropriately identifying correlations according to the corresponding Geldart groups for the biomass particles. This perspective opens new possibilities toward the generalization of correlation factors and helps in improving the accuracy of the prediction for highly heterogeneous mixtures. The methodology also allows the analysis of mixtures for which the experimental approach is difficult, such as those including char particle, with the only requirement of carefully measuring the physical properties of the particles.

Prediction of minimum fluidization velocity in pulsed gas–solid fluidized bed

Fluidized bed technology plays a vital role in petrochemistry and coal separation. To enhance fluidization stability, the flow is periodically introduced into the gas–solid fluidized bed to form a pulsed gas–solid fluidized bed (PGFD). As the main fluidization parameter, the minimum fluidization velocity (umf) can reflect the change of the critical state of particles in the PGFD, directly affecting the study of two-phase distribution in the bed. Due to lack of theoretical study on umf in PGFD, the work proposed a novel method to predict umf combined with soft sphere model. Meanwhile, the spring-damping model (SDM) and the resonance force model (RFM) were developed under the action of pulsating airflow. A theoretical model of umf was then derived for PGFD based on experimental stress analysis of particles. The error of the new model is small, which is in good agreement with the data in the existing literature and present work.

Prediction of minimum fluidization velocity for binary mixtures of biomass and inert particles

Fluidization of biomass particles is an important process in the gasification, pyrolysis and combustion of biomass for the extraction of energy. In this study, experiments were carried out in a 14.5 cm internal diameter cold flow fluidization bed to determine the minimum fluidization velocities with air as fluidizing medium. Studies on the fluidization of biomass particles (corn cobs and walnut shells), inert particles (sand, glass beads, and alumina), and biomass and sand mixtures were performed. Various weight percentages of biomass particles in the biomass and sand mixture were chosen in the range of 0–100%. On the of basis of experimental data from both present work and those found in the literature, new correlations were developed to predict the minimum fluidization velocity for inert particles, biomass particles, and biomass and sand mixtures in terms of biomass weight percentage. It was found that our results for the inert particles and biomass particles are in good agreements with those found in the literature. It was further found that the minimum fluidization velocity based Reynolds number for the mixture of biomass and inert particles depends on the weight percentage of biomass particles other than the Archimedes number. Based on our experiment results, we proposed a new correlation which includes the weight percentage as an additional variable for the mixture of biomass and sand particles. This new correlation can also be applied to inert particles or biomass particles by setting the weight percentage to be 0 or 100% accordingly.

Studies on Minimum Fluidization Velocity and Liquid Hold in an Internal Loop Airlift Fluidized Bed Reactor

The influence of superficial gas and liquid velocities, particle diameter and sphericity, physical and rheological properties of liquids on minimum fluidization velocity and liquid holdup were studied in an internal loop airlift fluidized bed reactor. Spheres, Bearl saddles and Raschig rings were used as solid phases. Water, n-Butanol, two concentrations of Glycerol (60 and 80%) were used as Newtonian liquids and three concentrations (0.25%, 0.6% and 1.0%) of Carboxy Methyl Cellulose (CMC) solutions were used as non-Newtonian liquids. Superficial gas velocity was varied from 0.142 x 10-3 m/s to 5.662 x 10-3 m/s and superficial liquid velocity was varied from 0.001 to 0.12 m/s. The experimental results showed that increase in particle size and sphericity increased minimum fluidization velocity whereas increase in superficial gas velocity decreased minimum fluidization velocity. The liquid holdup increased with increase in particle size and superficial liquid velocity. An increase in superficial gas velocity decreased the liquid holdup for Newtonian and non-Newtonian systems. Based on the experimental results separate correlations were developed for the prediction of minimum fluidization velocity and liquid holdup for both Newtonian and non-Newtonian liquids for a wide range of operating conditions.

Models for prediction of hydrodynamic characteristics of gas–solid tapered and mini-tapered fluidized beds

Prediction of hydrodynamic characteristics is a prerequisite in the design and operation of tapered and mini-tapered fluidized beds. This paper has been focused on the development of generalized models for prediction of minimum fluidization velocity and maximum pressure drop in gas–solid tapered and mini-tapered fluidized beds. The empirical correlations were developed based on dimensionless analysis of empirical data. These correlations have the ability to predict the minimum fluidization velocity and maximum pressure drop in both tapered and cylindrical beds (the beds with tapered angle of zero). The empirical data were collected from tapered beds with different cone angles for various particles. The predicting capability of correlations has been discussed. Predicted values of minimum fluidization velocity and maximum pressure drop by the proposed models compared well with the empirical data. The effects of tapered angle are also discussed.

Correlation for Prediction of Minimum Fluidization Velocity and Riser Liquid Holdup in Three-Phase External Loop Air Lift Fluidized Bed Reactor

The effect of superficial gas and liquid velocities and properties of solids on the minimum fluidization velocity and riser liquid holdup of a three-phase external loop air lift fluidized bed reactor was characterized using Newtonian and non-Newtonian systems. Water, 65% and 85% of glycerol and n-Butanol were used as Newtonian liquids and different concentrations of carboxymethyl cellulose (i.e. 0.2%, 0.5% and 1% CMC) were used as non-Newtonian liquids. Spherical glass beads, bearl saddles and rasching rings of different sizes were used as solid phases. The phase flow rates and properties of solid particles had significant effects on the hydrodynamic characteristics of the external loop air lift fluidized bed reactor, such as minimum fluidization velocity and riser liquid holdup. Unified correlations have been developed to estimate the minimum fluidization velocity and riser liquid holdup as a function of superficial phase velocities, properties of solid particles and physical properties of both Newtonian and non-Newtonian liquid systems. The predicting ability of the correlations were tested with the experimental data and found to be a good fit with an absolute average relative deviation (AARD) of ± 6.5 % and ± 7.8 % for minimum fluidization velocity and riser liquid holdup, respectively.

Prediction of Minimum Fluidization Velocity in Two-Phase and Three-Phase Fluidized Beds: Air/Newtonian and Non-Newtonian Liquids

The present experimental data on minimum fluidization velocity for two-phase and three-phase fluidized beds, involving 459 measurements were used for the analysis. Apart from this, 70 literature data points from different published sources, using 11 different liquids and 11 different particles have been used for the development of minimum fluidization velocity correlation. The developed correlation for the prediction of the minimum fluidization velocity for two-phase and three-phase fluidized beds was found to be satisfactory for the Newtonian and non-Newtonian systems with a wide range of variables covered in the present investigation.

Prediction of minimum fluidization velocity for fine tailings materials

The suitability of several minimum fluidization velocity correlations has been investigated for fine zinc slime, iron ore tailings, both pre and post hydro-cyclone uranium tailings, and a relatively coarse grade of fly ash. It has been found that most of the published correlations significantly underestimate the value of minimum fluidization velocity for the four different tailings materials. Predictions due to Van Heerden et al. (1951) [45], Noda et al. (1986) [76], Coltters and Rivas (2004) [39], and Xu and Zhu (2009) [93], agree reasonably with the experimental data, whereas the fly ash, which belongs to Geldart Group B materials, has shown a large deviation. Thus these correlations could be used for the fine tailings materials that comprise a variety of constituents and possess a degree of cohesiveness. A modification of Coltters and Rivas correlation has also been suggested to assess the combined effect of particle size and density on minimum fluidization velocity.

Hydrodynamics and energy consumption studies in a three-phase liquid circulating three-phase fluid bed contactor

The hydrodynamics and energy consumption have been studied in a cold flow, bubbling and turbulent, pressurized gas–liquid–solid three-phase fluidized bed (0.15 m ID × 1 m height) with concurrent gas–liquid up flow is proposed with the intention of increasing the gas hold up. The hydrodynamic behaviour is described and characterised by some specific gas and liquid velocities. Particles are easily fluidized and can be uniformly distributed over the whole height of the column. The effect of parameters like liquid flow rate, gas flow rate, particle loading, particle size, and solid density on gas hold up and effect of gas flow rate, solid density and particle size on solid hold up, energy consumption and minimum fluidization velocity has been studied. At the elevated pressures a superior method for better prediction of minimum fluidization velocity and terminal settling velocities has been adopted. The results have been interpreted with Bernoulli’s theorem and Richardson–Zaki equation. Based on the assumption of the gas and liquid as a pretend fluid, a simplification has been made to predict the particle terminal settling velocities. The Richardson–Zaki parameter n′ was compared with Renzo’s results. A correlation has been proposed with the experimental results for the three-phase fluidization.

Prediction of minimum fluidization velocity of gas–solid fluidized beds by pressure fluctuation measurements — Analysis of the standard deviation methodology

We analyze here an experimental method for the evaluation of U mf in gas fluidized beds, based on pressure fluctuation measurements in which U mf is determined by the relationship between the standard deviation of pressure measurements and fluid velocity [M. Puncochar, J. Drahos, J. Cermak, K. Selucky, Evaluation of minimum fluidizing velocity in gas fluidized bed from pressure fluctuations, Chem. Eng. Commun. 35 (1985) 81–87]. This was tested in four different particles: Sand, Microcrystalline Cellulose, FCC and Alumina using two circular plexiglass columns with internal diameters of 0.11 m and 0.14 m as the experimental apparatus. Validation of the method was made by comparing our U mf results with those obtained by the fluid-dynamic curve. The experimental data revealed that: (1) the valid range of fluid velocity in the method employed by us is broader than those observed by other authors; (2) the method is suitable for both Geldart A and B solids. Influence of probe location and type of pressure measurement (either absolute or differential) were also analyzed and discussed.

Minimum fluidation velocity correlations in particulate systems

A new relationship for the prediction of minimum fluidization velocity is proposed. It has been made a comprehensive critical review, concluding that in order to apply, some of these correlations additional experimental data is required, such as bed voidage and shape factors. It is found a strong dependency of the physical and chemical properties of the particle surface on the minimum fluidization velocity. This influence of the nature of the particle surface allows that empirical equations are applicable in specific cases, but cannot be generalized. The original equation presented in this paper allows the predicting minimum fluidization velocity in a very simple way without the need of experimental determination of bed voidages and shape factors. The new correlation was tested using 189 measurements reported in the literature on about 90 different materials. The results shown that the new correlation is in very well agreement with the experimental data.

Revisiting the Wen and Yu Equations for Minimum Fluidization Velocity Prediction

Correlating data is a delicate task where the best is among the worse. The present study aims at presenting an improvement of the use of Wen and Yu simplifications for minimum fluidization velocity having presented the scientific awkwardness contained in the usual method of using their or similar relations simultaneously in combination with Ergun's equation. The present study has demonstrated the contradiction deduced from the simultaneous use of these Wen and Yu relations as it is the case for the minimum fluidization velocity. The method of Wen and Yu which consists of simultaneously eliminating the bed voidage at minimum fluidization and particle sphericity from the minimum fluidization velocity calculation remains definitively scientifically wrong and should be avoided. A change in the Wen and Yu's correlations use is then suggested to increase, on the one hand, the prediction accuracy for the minimum fluidization velocity calculation, and on the other hand, the scientific exactness of this generally received engineering method. Performances of the new method significantly improves the prediction of minimum fluidization velocity.

Pressure Effects on Gas-Solid Fluidized Bed Behavior

The purpose of this paper is to review the state of our knowledge of the effects of operating pressure on the hydrodynamic behavior of fluidized beds. With the development of coal combustion and gasification fluidized bed processes in the early 1970s, many academic and industrial researchers have studied the effect of pressure on fluidized bed behaviour. This review covers experimental and theoretical studies of effects of elevated operating pressure on fluidization, published in the literature before August, 2002.The review begins with the discussion of the effect of pressurized conditions on non-bubbling fluidization and several methods for better prediction of minimum fluidization velocity at elevated pressure are presented. The effects of pressure on non-bubbling bed expansion in the region between minimum fluidization and minimum bubbling velocities are considered and areas of uncertainty or disagreement are highlighted. The influence of pressure on the dynamics of gas bubbles and bubbling bed expansion is described next. In addition to fundamental hydrodynamics of fluidization, bed-to-surface heat transfer, jet penetration, solids mixing and particle entrainment are mentioned.

Prediction of Minimum Fluidization Velocity in Two and Three Phase Inverse Fluidized Beds

AbstractGeneralized equations for predicting minimum fluidization velocities in two‐phase L‐S and three‐phase G‐L‐S inverse fluidized bed are developed covering a wide range of variables using the experimental data obtained from the present work and that available in the literature. It is found that the classical Wen and Yu equation for predicting minimum fluidization velocity can satisfactorily be used for two‐phase inverse fluidized bed. A model based on empiricism and another based on the gas perturbed liquid model, which reduce to limiting conditions such as liquid solid and three‐phase batch liquid systems are proposed.

Prediction of minimum fluidization velocity for vibrated fluidized bed

The prediction of minimum fluidization velocity for vibrated fluidized bed was performed. The Geldart group A and C particles were used as the fluidizing particles. The method based on Ergun equation was used to predict the minimum fluidization velocity. The calculated results were compared with the experimental data. The calculated results of minimum fluidization velocity are in good agreement with experimental data for Geldart group A particles. For group C particles, the difference between the calculated results and experimental data is large because of the formation of agglomerates. In this case, the determination of agglomerate diameter is considered to be necessary to predict the minimum fluidization velocity.

Fluidization at vacuum conditions. A generalized equation for the prediction of minimum fluidization velocity

The hydrodynamical behaviour of fluidized beds at reduced pressures is studied. The minimum fluidization velocity is strongly influenced by pressure, decreasing as pressure increases. The well-known equation of Wen and Yu and two equations proposed for the calculation of u mf at reduced pressures are tested; the comparison with experimental data shows that they can be applied only over restricted pressure ranges. The relationship between flow rate, pressure and pressure drop at conditions ranging from high vacuum to high pressure is analysed for the different flow regimes (molecular, slip, laminar, transition and turbulent). A generalized equation is found which predicts fairly well the value of u mf at vacuum conditions, atmospheric pressure and high pressures.

Non-Newtonian fluidization of spherical-particle beds

Fluidization of spherical-particle beds with viscoelastic shear thinning polymer solutions was experimentally investigated in creeping- and transient-flow regions. The results of measurements show that the course of bed expansion depends on the kind and degree of non-Newtonian anomaly, on the flow region, and on the apparatus wall effect. The limited bed expansion observed during fluidization in the creeping-flow region weakened with the increasing Reynolds number and vanished when a critical value of Reynolds number was exceeded. Empirical equations based on the Carreau viscosity model were suggested for the prediction of minimum fluidization velocity and for bed expansion in both creeping- and transient-flow regions.