Prediction of pressure drop and minimum spouting velocity in draft tube conical spouted beds using genetic programming approach

The smart method of genetic programming (GP) is used to predict the operating pressure drop (ΔP_s) and the minimum spouting velocity u_ms for conical spouted beds (CSBs) equipped with nonporous draft tubes. Accordingly, six dimensionless variables have been taken as model inputs, including crucial parameters associated with the bed and tube geometric and operating conditions. Two general correlations comprising almost all constitutive and operating variables have been derived for the first time by the GP approach. Both ΔP_s and u_ms values predicted by the GP technique are in a fair agreement with the values corresponding to the experiments, with average absolute relative errors (AARE) of 18.9 and 19.9 %, respectively. The results of the proposed correlations show that the GP method is a powerful tool to make reasonable estimates.     

Minimum spouting velocity of dense particles in shallow spouted beds

Quantitative method is used to experimentally measure the minimum spouting velocity in shallow conical spouted bed. And a new minimum spouting correlation for shallow conical spouted beds is developed. It is based on spherical ZrO₂ particles whose density is as high as 5890 kg/m³ while the other U_ms correlations published so far are mainly based on relatively deep conical beds composed of lower density particles with density around or lower than 3000 kg/m³. The new U_ms correlation can predict U_ms of heavy particles well within the range of the experimental matrix. © 2011 Canadian Society for Chemical Engineering     

Determination of Minimum Spouting Velocities in Conical Spouted Beds

Minimum spouting velocities in conical spouted beds have been obtained from pressure drops versus the superficial gas velocity curves, based on both increasing and decreasing the superficial gas velocity. It has been shown that the minimum spouting velocity from decreasing the superficial gas velocity is lower than from increasing the superficial gas velocity in most cases. This phenomenon is similar to that in conventional spouted beds and different from the early works. The experimental results also showed that there isn't significant difference in the pressure drop and U_ms under identical operating conditions between semi‐circular and circular conical spouted beds, and the same U_ms can be obtained from absolute pressure drops at any position above the gas inlet. The U_ms is found to increase with increasing the cone angle and static bed height, as well as the gas inlet diameter to a less extent.     

Fluidization Characteristics in Micro‐Fluidized Beds of Various Inner Diameters

The fluidization characteristics of quartz sand and fluid catalytic crack (FCC) catalyst particles in six micro‐fluidized beds with inner diameters of 4.3, 5.5, 10.5, 15.5, 20.5, and 25.5 mm were investigated. The effects of bed diameter (D_t), static bed height (H_s), particles and gas properties on the pressure drop and minimum fluidization velocity (u_mf) were examined. The results show that the theoretical pressure drops of micro‐fluidized beds deviated from the experimental values under different particles and gas properties. The possible reason is due to an increase in bed voidage under smaller bed diameters. The equations for conventional fluidized beds did not fit for micro‐fluidized beds. u_mf increased with decreasing D_t. When the ratio of H_s to D_t ranged from 1:1 to 3:1, u_mf was characterized by a linear equation with H_s, while the slope of the equation u_mf versus H_s decreased with increasing D_t. In this paper, D_t/d_p and H_s/d_p were defined as dimensionless variables and a new equation was developed to predict u_mf in micro‐fluidized beds under the present experimental conditions.     

Hydrodynamic characteristics of activated carbon in air- and water-fluidized beds

The hydrodynamic characteristics of small hydrophobic activated carbon particles were determined in air flowing through both fixed and fluidized bed layers and water flowing through an inverse fluidized bed. Based on experimental data the Ergun-equation was corrected. A new relationship is proposed to predict the pressure drop in a fixed bed with gas flowing by using the minimum fluidizing velocity (u _mf ) and particle terminal velocity (u _t ). Apparent density of oven-dried activated carbon increases with filling the internal pores by water. After the bed density reaches the density of water, the system switches from an inverse fluidized layer into the classical fluidized state. Finally, it has been demonstrated that the Reynolds number (Re _mf ) at u _mf associated with the original Archimedes number (Ar) for gas-solid fluidized system and the modified Ar numbers characterizing the inverse fluidized beds lie on identical curves.     

Fluidization of mixtures of two solids differing in density or size

The complex mechanism by which homogeneous mixtures of two solids achieve fluidization is subjected to theoretical analysis, to elaborate relationships capable to provide their “initial” and “final fluidization velocity” u_if and u_ff, i.e., the limits that encompass the suspension process. The article shows how the equation that describes the force equilibrium of fluidization can be rewritten in forms that account for the distribution of the components of density‐ or size segregating mixtures during the transition to the fluidized state. This approach leads to the theoretical expression of u_if and u_ff of either type of system, whose differences of behavior are correctly reproduced by accounting for the voidage reduction typical of beds of particles of different size. The comparison with experimental results at varying mixture composition demonstrates that the equations give a coherent interpretation of the dependence of the fluidization velocity interval of two‐solid mixtures on the principal variables of interest. © 2010 American Institute of Chemical Engineers AIChE J, 2011     

Liquid-phase mass transfer of magnetic ion exchangers in magnetically influenced fluidized beds: I. DC fields

Fluidized beds of magnetic ion exchangers exhibit special features because of the additional influence of magnetic forces, which cannot be achieved in conventional fluidized or fixed beds. Specific choice of the magnetic parameters, such as particle magnetization, field strength and frequency of the external magnetic field, allows various operating conditions to be attained, the extremes of which may be described by the terms Magnetically Stabilized Fluidized Bed (MSFB) and Magnetically Stirred Reactor (MSR). The experiments conducted in this work show that liquid fluidized MSFBs exhibit a marked decrease in mass transfer compared to conventional fluidized beds operated under the same conditions. We have demonstrated a correlation between the transition from a fluidized bed to a magnetically stabilized fluidized bed and an increase in the value of a newly defined dimensionless number, M^*. Provided that the physical properties (magnetization, density and diameter) of the particles are known, it is then possible to obtain a first estimate with regard to the magnetic field required for attaining an MSFB. The experimental data clearly show that the magnitude of the decrease in liquid-side mass transfer associated with this transition is influenced mainly by the ratio between the flow velocity, u, and the minimum fluidization velocity of the particles, u_mf. Based on this observation, an empirical correlation is presented, which allows an estimation of the Sherwood number, Sh, of an MSFB to be made as a function of the parameters M^* and u/u_mf.     

Homogeneous Fluidization Characteristics of Vibrating Fluidized Beds

The effects of vibration parameters, operating conditions and material properties on fluidization quality were investigated by the measurement and analysis of voidage fluctuation signals in a vibrating fluidized bed with a diameter of 148 mm. The fluctuation deviation of the bed voidage and the enhancement index of the bed derived can describe bed homogeneity and its extension. A new criterion of homogeneity, consisting of the material parameter (Ar), operating parameters (H₀, u/u_mf) and vibration parameters (a, ω), is proposed to predict a suitable range of homogeneous fluidization. Experimental results on eight kinds of solids, five static bed heights and different vibration parameters were used to propose guidelines for the reasonable selection of operating conditions for vibrating fluidization and better operating conditions.     

kL a correlation established on the basis of a neural network model

A k_L a correlation has been developed with the aid of a neural network model. The neural network model has served as a non-linear relationship performer correlating the volumetric mass transfer coefficient k_L a in stirred tank reactors with the operating conditions, reactor geometry and material properties. In order to achieve an optimum correlation, experimental data taken from different sources have been used to train the network. The correlation obtained in this way is able to predict k_L a in stirrer tanks reasonably well, if the operating conditions, reactor geometry and material properties fall into the trained ranges. Although the experimental data were widely spread and could only be fitted to individual correlations, the neural network is in a position to give a general correlation for all the data.     

加压喷动床中细颗粒喷动特性

在内径分别为 186mm和 80mm的加压喷动床中 ,以空气为喷动介质 ,在 10 1～ 70 0kPa的压力范围内考察了几种不同粒度的细颗粒在加压下的喷动特性 .研究结果表明在不同的Re_t 内压力对最小喷动速度的影响不同 .实验还发现 ,随着压力的升高 ,喷动区直径增大 ,稳定操作区域增大 ,加压可明显改善喷动床的操作稳定性     

Application of Magnetic Resonance Imaging (MRI) to Determine the Influence of Fluid Dynamics on Desulfurization in Bench Scale Reactors

The influence of fluid dynamics on the hydrodesulfurization (HDS) reactions of a diesel oil in bench‐scale reactors was evaluated. The porosities and liquid saturations of catalyst beds were quantified by using the MRI technique. The gas‐liquid systems used in the experiments were nitrogen diesel and hydrogen diesel. An apparatus was especially constructed, allowing in situ measurements of gas and liquid distributions in packed beds at elevated pressure and temperature up to 20 bar and 200 °C, respectively. The reactor itself had a length of 500 mm and an internal diameter of 19 mm. The packed beds used in this MRI study consisted of: (1) 2 mm diameter nonporous spherical glass beads and (2) 1.3 mm diameter porous Al₂O₃ trilobes having the same size as the original trilobe catalyst used in HDS bench‐scale experiments. The superficial gas and liquid velocities were set within the range of trickle flow, e.g., u_0G = 20–500 mm/s and u_0L = 0.1–6 mm/s. In parallel with the MRI experiments, the hydrodesulfurization of a gas oil was investigated in a bench‐scale plant. Its reactor had the same dimensions of the trickle‐bed column used in the MRI experiments and was filled with original trilobe catalyst. These catalytic experiments were carried out at a wide range of operating conditions (p = 30–80 bar, T = 300–380 °C, LHSV = 1–4 h^–1). The results of both fluid dynamic and catalytic reaction experiments were then combined for developing a simulation model to predict the HDS performance by accounting for fluid dynamic nonidealities.     

Refinement of the kinetic model for guaiacol hydrodeoxygenation over platinum catalysts

In our prior work (Ind Eng Chem Res, 2015, 54, 10638-10644), hydrodeoxygenation (HDO) kinetics of guaiacol, a well-known model compound of bio-oil, over Pt/AC (activated carbon) catalysts were investigated under integral operating conditions. It was found that the pseudo-homogeneous plug-flow model utilizing these kinetics describes the experimental observations well (with normalized RMS error = 7.6%). In the present work, under differential operating conditions instead, we refine the kinetic model for the same reaction network over the same catalyst. We show that among the five reaction steps in the network, the reaction order of one step differs from our prior work, while the orders remain unchanged for the other four steps. The activation energies of two steps differ from our prior values by 10–15 kJ/mol, and for the other three steps remain essentially consistent with our prior work. The kinetic parameters from the present work are used to predict fixed-bed reactor performance under integral operating conditions as well. The comparison between experimental and predicted values for both the prior and new sets of data is excellent and even better than our prior model (with reduced normalized RMS error = 4.2%). The kinetic analysis additionally proposed that the direct and indirect pathways of phenol formation from guaiacol HDO depend on guaiacol conversion values. The present work demonstrates that kinetic expressions and parameters obtained from a gradientless differential reactor are more reliable and can be used to successfully predict integral reactor performance data.     

Evaluation of heat transfer parameters in packed beds with cocurrent downflow of liquid and gas

The results of an experimental investigation on heat transfer from a packed bed with cocurrent gas–liquid downflow to the wall are presented and analyzed in this contribution. The measurements cover the range of operating variables corresponding to the so-called trickle regime in beds presenting aspect ratios (tube to particle diameter ratio) from 4.67 to 34.26. Water and air were employed as model fluids. The heat transfer process was first analyzed by means of a two-dimensional pseudohomogeneous plug-flow model with two parameters, the effective radial thermal conductivity (k_er) and the wall heat transfer coefficient (h_w). k_er is well correlated with liquid and gas Reynolds numbers and particle diameter, except for the lowest experimental aspect ratio (4.67). Instead, a meaningful correlation of h_w stands only for aspect ratios larger than 15. These results are analyzed and the evidence points out to sustain the hypothesis that the model fails at low aspect ratios because an apparent contact resistance (1/h_w) can no longer accommodate the effects of significant fluid bypassing and finite size of the near-wall region. The experimental set of data were also used to develop a correlation for the overall heat transfer coefficient (h_T), which can be employed satisfactorily to predict heat transfer rates in the whole range of variables here investigated.     

Theoretical and experimental study on hydrodynamic characteristics of fluidization in air-sand conical beds

This work was aimed at modeling hydrodynamic characteristics of fluidization in conical beds using quartz sand as the inert bed material and air as the fluidizing agent. The minimum fluidization velocity, u_mf, and the minimum velocity of full fluidization, u_mff, were determined by Peng and Fan's models modified for conical fluidized bed. Meanwhile, the pressure drop across a bed, Δp (including Δp_max and Δp_mff corresponding to u_mf and u_mff, respectively), was predicted by using modified Ergun's equations for variable superficial air velocity at an air distributor, u₀. The predicted results were validated by experimental data for some operating conditions. Effects of the sand particle size, cone angle and static bed height on the fluidization pattern and hydrodynamic characteristics are discussed. With the proposed models, the Δp-u₀ diagram were obtained with rather high accuracy for the conical air-sand beds of 30-45^° cone angles and 20-30 cm static bed heights, when using 300- sand particles. For the predicted u_mf and u_mff, the relative computational errors were found to be within 20% for wide ranges of operating variables, whereas Δp_max and Δp_mff could be predicted with lower (10-15%) relative errors. With higher cone angles and/or bed heights, the computational accuracy was found to deteriorate.     

Estimation of dispersion coefficients in packed beds

The design and performance of fixed beds are greatly influenced by fluid dispersion. Unfortunately, the existing design data do not provide an accurate picture of this phenomenon. This paper presents an attempt to characterize the dispersive features of packed beds by obtaining reliable estimates of the associated coefficients in the axial (D_L ) and radial (D_R ) directions. Such an objective is achieved by developing a representative two-dimensional pseudo-continuous dispersed flow model which is subsequently employed to compute the desired coefficients using data obtained from a refined experimental approach. The established values have been correlated to allow such coefficients to be reliably predicted under a variety of physical and operating conditions.     

Pressure drop in slotted spouted beds of grains: Comparison of data with models

Data obtained in a rectangular slot spouted bed for two different grains (wheat and oats) have been analyzed to determine the minimum spouting velocity (V_ms) and the minimum spouting pressure drop (ΔP_ms) as a function of the bed height.Three different aerodynamic regimes occur as the bed height is increased.The results are compared with the literature models for the conventional (conical-cylindrical) spouted bed.For shallow beds, the experimental minimum spouting velocity and minimum spouting pressure drop can be well represented by the Littman et al.'s two-dimensional model.     

Development and simulation studies of an unsteady state biofilter model for the treatment of cyclic air emissions of an α‐pinene gas stream

This paper describes the development and simulation of an unsteady state biofilter model used to predict dynamic behaviour of cyclically‐operated biofilters and compares it with experimental results obtained from three, parallel, bench‐scale biofilters treating both periodically fluctuating concentrations and constant concentrations of an α‐pinene‐laden gas stream. The dynamic model, using kinetic parameters estimated from the constant concentration biofilter, was able to predict the performance of cyclic biofilters operating at short cycle periods (ie, in the order of minutes and hours). Steady state kinetic data from a constant concentration biofilter can be used to predict unsteady state biofilter operation. At a 24 h cycle period, the dynamic model compared well with experimental results. For long cycle periods (ie, hours and days), removal efficiency decreased after periods of non‐loading: the longer the period of non‐loading, the poorer the biofilter's performance at the re‐commencement of pollutant loading. At longer time scales the model did not effectively predict transient behaviour, as adsorption and changes in kinetic parameters were not accounted for. Modelling results showed that similar biofiltration performance for the cyclic and constant concentration biofiltration of α‐pinene is expected for biofilters operating solely in the first order kinetics regime. Poorer performance for cyclic biofilters following Monod kinetics spanning the entire kinetics range is expected as the cycle amplitude increases. The most important parameters affecting the performance of a cyclically‐operated biofilter with short cycle periods are: amplitude of cyclic fluctuations, C_{g, max}/C_g, relative value of the half‐saturation constant in the Monod expression, K_s, and effective diffusivity of α‐pinene in the biofilm, D_e. Copyright © 2005 Society of Chemical Industry     

New Predictive Correlations for the Drop Size in a Rotating Disc Contactor Liquid‐Liquid Extraction Column

Sauter mean drop sizes (d₃₂) generated from a hole distributor in liquid extraction RDC columns were studied under various conditions. Experiments were designed to generate data required to determine the main variables that control the drop sizes in RDCs. Two precise correlations were proposed for predicting d₃₂ in a RDC extraction column. The first was based on operating variables, hole‐distributor diameter, disc speed, column geometry, and system physical properties. The second one considered the same variables, except the column geometry. This model can be used for design purposes. The two correlations are the first of their type to consider the distributor hole inlet diameter in a RDC column. This diameter has been neglected by previous investigators. The maximum standard deviation for all data is 0.75 %, with a maximum absolute error of 6.8 %.     

A Generalized Dimensionless Model for Deep Bed Drying of Paddy

A generalized dimensionless model of paddy drying was developed from a validated partial differential equation (PDE) drying model using the dimensional analysis of Buckingham theorem. This generalized dimensionless model considered all drying parameters in an equation to predict the grain moisture content during the drying process. Statistical parameters, namely, coefficient of determination (R ²), chi-square (χ²), mean relative deviation (MRD), and root mean square error (RMSE), were used as criteria to compare the dimensionless model with a validated PDE model. Based on these calculated parameters, it was concluded that the generalized dimensionless model fitted reasonably well with data from the PDE model and good agreement was found between the generalized dimensionless model and experimental drying data.     

WATER ACTIVITY IN SOLUTIONS CONTAINING ORGANIC ACIDS

ABSTRACT

A thermodynamic model for the activity coefficient was used to predict au in some food-related solutions. Water activity values for organic acids solutions (malic, tartaric and citric) were measured experimentally and used to adjust interaction parameters for the UNIFAC model. The partial dissociation phenomenon for weak electrolytes in aqueous systems was considered and concentrations of species were calculated. Predictions of au with mean deviations of 0.26% were obtained.