Pressure-drop predictions in a fixed-bed coal gasifier

In the Sasol Synfuels plant in Secunda, Sasol-Lurgi fixed-bed dry-bottom gasifiers are used for the conversion of low-grade bituminous coals to synthesis gas (syngas). The gasifiers are fed with lump coal having a particle size in the range from 5 to 100 mm. Operating experience shows that the average particle size and particle-size distribution (PSD) of feed coal, char and ash influence the pressure drop across the bed and the gas-flow distribution within the bed. These hydrodynamic phenomena are responsible for stable gasifier operation and for the quality and production rate of the syngas. The counter-current operation produces four characteristic zones in the gasifier, namely, drying, de-volatilization, reduction and combustion. The physical properties of the solids (i.e. average particle size, PSD, sphericity and density) are different in each of these zones. Similarly, the chemical composition of the syngas, its properties (temperature, density and viscosity) and superficial velocity vary along the height of the bed. The most popular equation used to estimate the pressure drop in packed beds is that proposed by Ergun. The Ergun equation gives good predictions for non-reacting, isothermal packed beds made of uniformly sized, spherical or nearly spherical particles. In the case of fixed-bed gasifiers, predictions by the Ergun equation based on the average or inlet values of bed and gas flow parameters are unsatisfactory because the bed structure and gas flow vary significantly in the different reaction zones. In this study, the Ergun equation is applied to each reaction zone separately. The total pressure drop across the bed is then calculated as the sum of pressure drops in all zones. It is shown that the total pressure drop obtained this way agrees better with the measured result.     

Verification of a model for estimating the void fraction in a three-component randomly packed bed

The void fraction in a three-component randomly packed bed was calculated from the authors' model, and the calculated values were compared with published experimental data for spherical and irregularly shaped particles and with results from computer simulations. Results from the model were in good agreement with simulated and published experimental data.     

The use of modified threshold pressure for determining the wettability of packs of equal spheres

An equation relating modified threshold pressure, interfacial tension, contact angle and porosity is developed for packs of uniform spheres. On the basis of this equation a method is developed for determining contact angles or wettability from laboratory data. The method calls for careful discrimination between the strictly drainage and pseudo-drainage cases. It may be extended to more general cases and applied to threshold pressure data obtained using Bartell's cells, mercury penetration data or conventional capillary pressure curves, and yields realistic values of contact angle.     

Experimental investigation of pressure drop in packed beds of irregular shaped wood particles

The knowledge of the pressure drop across a packed bed of irregular shaped wood particles is of great importance for achieving optimal control and maximum efficiency in many applications, such as wood drying, pyrolysis, gasification and combustion. In this work the effect of porosity, average particle size and main particle orientation on the pressure drop in a packed bed is investigated. To this end, particle size distributions and porosities are determined experimentally.Based on the experimental results obtained in this study, the form coefficient C and the permeability K of the Forcheimer equation are calculated for different packed beds. The Ergun equation requires an average equivalent particle diameter that is derived from the measured particle size distribution. This equivalent diameter and the corresponding bed porosity are used in the well known Ergun equation in order to derive adapted shape factors A and B.Since a change in bed porosity and particle size, caused by the degradation of the wood particles and gravity, can be expected in a reacting packed bed, a set of shape factors for use with the Ergun equation is determined that are independent of porosity and particle diameter and fit the experimental data very well.     

OPTIMUM DILUTION PROFILES OF COMPOSITE ZEOLITES IN PACKED BEDS

The paper examines theoretically the conversion of methanol over composite zeolite spherical catalytic particles in a fixed bed reactor. The composite zeolite contains small zeolite particles uniformly distributed in an amorphous silica-alumina matrix. Two problems are considered. The first is concerned with the effect of dilution of the catalyst with amorphous silica-alumina on the concentrations of species and temperature along the bed. Isothermal and nonisothermal pellets are considered. The second is concerned with the calculation of the optimum dilution profile which maximizes the rate of consumption of methanol.     

Flow through packed bed reactors: 1. Single-phase flow

Single-phase pressure drop was studied in a region of flow rates that is of particular interest to trickle bed reactors . Bed packings were made of uniformly sized spherical and non-spherical particles (cylinders, rings, trilobes, and quadralobes). Particles were packed by means of two methods: random close or dense packing (RCP) and random loose packing (RLP) obtaining bed porosities in the range of 0.37–0.52. It is shown that wall effects on pressure drop are negligible as long as the column-to-particle diameter ratio is above 10. Furthermore, the capillary model approach such as the Ergun equation is proven to be a sufficient approximation for typical values of bed porosities encountered in packed bed reactors. However, it is demonstrated that the original Ergun equation is only able to accurately predict the pressure drop of single-phase flow over spherical particles, whereas it systematically under predicts the pressure drop of single-phase flow over non-spherical particles. Special features of differently shaped non-spherical particles have been taken into account through phenomenological and empirical analyses in order to correct/upgrade the original Ergun equation. With the proposed upgraded Ergun equation one is able to predict single-phase pressure drop in a packed bed of arbitrary shaped particles to within ±10% on average. This approach has been shown to be far superior to any other available at this time.     

Attrition of char agglomerates

A 15.2 cm diameter fluidized bed system with single- and multiple-jet distributors was designed and constructed to study the attrition behavior and mechanism of Kentucky No. 9 char from IGT's U-GAS fluidized bed gasifier. The effects of the jet and auxiliary gas velocities, the number of jets, the bed height, and the roughness of the fluidized bed wall on the attrition of char particles were studied. Particle shape variation during attrition was calculated by comparing our experimental data on pressure drop for a packed bed with the Ergun equation prediction. A mathematical procedure was developed to translate the size distribution variation of particles in the fluidized bed to the attrition rate expression.     

The measurement of transport coefficients in gas-solid heterogeneous reactions

If reasonably uniformly sized spherical pellets are packed in a tube only slightly larger in size, so that the tube/pellet dia ratio is from 1·1 to 1·4, and the tube contains 50 or more pellets, then the flow behaviour is very similar to that of a conventional packed bed. Pressure drop results and axial dispersion values obtained for non-porous pellets using pulse techniques can be predicted from existing packed bed correlations. Magnetite pellets of different porosities were used as porous packing, also, and, by Fourier analysis of outlet tracer pulse dispersion, external mass transfer and effective diffusion coefficients were obtained, assuming the validity of the Kubin-Kucera model. The use of this ‘single pellet string reactor’ (SPSR) appears to give a convenient laboratory simulation of a packed bed reactor, which would be particularly useful for larger solid particles such as pelletized ores. It also offers a convenient laboratory method for obtaining average effective diffusion coefficients over a range of temperatures and pressures for a representative sample of large porous particles.     

Theoretical analysis of the tensile strength of a powder bed

The authors have proposed an experimental equation which correlates the tensile strength of a powder bed measured by split cell methods with the porosity of a powder bed. In this report, the authors discuss the relationships between the porosity and the pre-compressive stress and also between the tensile strength and the pre-compressive stress. As the results of this discussion, the physical base of the proposed experimental equation is proved theoretically.Furthermore, it has also been proved that the pre-compression of a powder bed brings not only the decrease of the porosity but also the increase of compressive force at the contact point of particles, and therefore the increase of tensile strength by increasing the-compression force cannot be explained simply by the change of the porosity, and then another factor, such as the compressive force at the contact point, must be considered.     

Porosity Calculation of Binary Mixtures of Nonspherical Particles

An investigation has been made of the packing of binary mixtures of either spherical or nonspherical particles. It is shown that this binary packing system can satisfactorily be described by the Westman equation. By use of the concept of "equivalent packing diameter," nonspherical particle packing may be related to spherical particle packing. The porosity of binary mixtures of nonspherical particles can then be predicted by means of a model developed for spherical particles. This approach is verified by the good agreement between the calculated and experimental results.     

Radial porosity distribution in cylindrical beds packed with spheres

Experimental determinations of radial porosity for cylindrical beds packed with spheres are reported. The data indicate that, for a wide range of bed and sphere sizes, porosity varies significantly and regularly near the container wall. For uniformly sized spheres, the oscillations in porosity can be detected up to a distance of about 5 particle diameters from the wall. For mixtures of spheres of two sizes, regular oscillations are detected only up to 2 or 3 diameters from the wall and for three sizes the effect of the wall is observed only within a distance of 1 particle diameter.     

Probability-based contact algorithm for non-spherical particles in DEM

Discrete element method (DEM) is widely used in studies of particulate matter. Most of these studies are limited in the modeling of spherical particles due to contact algorithm. It is important for DEM to simulate non-spherical particles if wondering more authentic behaviors of granular materials. A probability-based contact algorithm is presented in this paper. Contacts between non-spherical particles are transferred into those between spherical particles with probability. The comprehensive mechanical behavior of granular material with a large number of non-spherical particles can be efficiently modeled because contact detection algorithm for spherical particles remains. To validate the presented algorithm, Hopper experiments for spherical and polyhedral particles are physically and numerically performed. To achieve higher accuracy of the angles of repose and profile of the stable particulate piles, a digital image processing method is adopted. The numerical results are in good agreement with the experimental observation, both in the spherical and polyhedral particles. The probability-based contact algorithm is valid in describing the behavior of polyhedral particles.     

A new model to determine contact angles on swelling polymer particles by the column wicking method

The contact angle determination on swelling polymer particles by the Washburn equation using column wicking measurements may be problematic because swelling occurs during the wicking process. The objective of this research was to develop a new model to more accurately determine contact angles for polymer particles that undergo solvent swelling during the column wicking process. Two phenomena were observed related to the swelling effect during the wicking process: (1) a temperature rise was detected during the wicking process when the swelling polymer particles interacted with polar liquids, and (2) a smaller average capillary radius (r) was obtained when using methanol (polar liquid) compared to using hexane (non-polar liquid). The particle swelling will induce both particle geometry changes and energy loss which will influence the capillary rise rate. The model developed in this study considered the average pore radius change and the energy loss due to the polymer swelling effect. Contact angle comparisons were conducted on wood with formamide, ethylene glycol, and water as test liquids, determined by both the new model and the Washburn equation. It was shown that the contact angles determined by the new model were about 4-37° lower than those determined by the Washburn equation for water, formamide, and ethylene glycol. Todetermine whether the polymer particles are swelling, two low surface tension liquids, one polar (methanol) and the other non-polar (hexane), can be used to determine the average pore radius (r values) using the Washburn equation. If the same r values are obtained for the two liquids, no swelling occurs, and the Washburn equation can be used for the contact angle calculation. Otherwise, the model established in this study should be used for contact angle determination.     

Co-ordination number distribution of spherical particles in a packed cylindrical bed

In modeling transport phenomena of packed particles, it is useful to make an assumption regarding the arrangement of particles and the number of contact points with neighboring particles. In this paper the distribution of co-ordination number (contact points) has been determined for a cylindrical bed packed with uniform-sized spheres. For a randomly poured bed with a porosity of 0.39, the average number of contact points was found to be approximately 8. Except for a sharp reduction in value at the wall, the co-ordination number was found to be nearly constant over the interior of the bed. Since an array of particles configured as body-centered orthorhombic has the same number of contact points and porosity, the study suggests that this regular configuration could be used in modeling effective transport properties of random packed beds, except near a container wall.     

Spherical cellulose–nickel powder composite matrix customized for expanded bed application

Expanded bed adsorption (EBA) is an integrated technology for capturing target biomolecules directly from particle‐containing feedstock. The adsorbents are the key base to achieve the EBA process and should be designed specially. In present work a new type of composite particles for EBA application was prepared with cellulose as the skeleton, and nickel powder as the densifier through the method of water‐in‐oil suspension thermal regeneration. Two fractions of spherical particles with mean sizes of 101–119 μm and 168–217 μm were obtained and the effects of nickel powder addition on the physical properties of composite particles were analyzed. The results indicated that the cellulose–nickel powder composite particles prepared have appropriate wet density of 1.14–1.78 g/mL, water content of 51–75%, porosity of 81–93%, pore radius of 41–59 nm, and specific surface area of 30–42 m²/mL of wet particles. The bed expansion factor at the range of 2–3 was investigated and correlated with Richardson–Zaki equation. In addition, the bed stability with composite particles prepared was demonstrated with the observation of liquid mixing in expanded bed. © 2007 Wiley Periodicals, Inc. J Appl Polym Sci 104: 740–747, 2007     

The flow of non-Newtonian slurries through fixed and fluidised beds

Measurements have been taken of the flow rate, pressure drop and bed height characteristics when non-Newtonian slurries flow through fixed and fluidised beds of uniformly sized spherical particles.In the case of fixed beds, the pressure drop-flow rate data has been interpreted using the capillary model of a porous medium together with rheological data for the slurries obtained from a tubular viscometer. The resulting friction factor-Reynolds number relationship is

This correlation was used to satisfactorily predict the minimum fluidisation velocity for a given solid/liquid system by equating the pressure drop to the net weight per unit area of particles in the bed. However, the correlation was not adequate for the prediction of bed expansion in the fluidised state. For systems which have a Reynolds number at minimum fluidisation, Re′_mf′ less than 40 an effect of particle diameter to bed diameter was observed. For systems having Re′_mf >40 the velocity, υ, and voidage, ?, were related to their values at minimum fluidisation by

It is therefore clear that, in the fluidised state, the capillary model does not present an adequate basis for the prediction of bed expansion.     

Modification of Ergun equation for application in trickle bed reactors randomly packed with trilobe particles using computational fluid dynamics technique

Based on a slit model, a pellet scale model has been developed for calculation of drag force imposed on trilobe catalyst particles in a packed bed reactor. The drag coefficient for single gas phase flow in a porous media has been calculated by CFD simulation and the results compared to the Ergun equation. The results show that the drag coefficient predicted by Ergun equation should be modified for various bed porosities, particle aspect ratio and gas densities. Therefore, a correction factor has been proposed to correct the Ergun equation constants in various conditions for trilobe particles. Comparison between the proposed corrected Ergun equation results and experimental data indicates considerable agreement.     

An Experimental Method for Three-Dimensional Dynamic Contact Angle Analysis

Abstract

Droplet dynamics analysis concerns the measurements of droplet volume, cap and base areas and contact angles, as they change in time to study evaporation, wettability, adhesion and other surface phenomena and properties. In a typical procedure, the two-dimensional measurements are based on a series of images recorded at successive stages of the experiment from a single view. Only a few basic dimensions of sessile droplets are commonly measured from such images, while many other quantities of interest are derived utilizing geometrical relationships. The reliability of these calculations is limited by the necessary assumption that the droplet shape can be approximated as a spherical cap. In reality, the sessile droplet shapes are influenced by gravity, liquid surface tension, local surface anisotropy and microstructure, which often produce non-spherical cap shapes.

This paper describes an experimental methodology for determination of key parameters, such as volume and contact angle for dynamic sessile droplets that can be approximated either by spherical or ellipsoidal cap geometries. In this method, images collected simultaneously from three cameras positioned orthogonally to each other are used to record the dynamic behavior of non-spherical droplets. Droplet shape is approximated as an ellipsoid of arbitrary orientation with respect to the cameras, which allows determination of volume and contact angle along the base perimeter. A major advantage of this method is that the dynamic parameters of droplets on anisotropic surfaces can be determined even when the orientation of the axes changes throughout the droplet lifetime. The method is illustrated with experimental results for a spherical and an ellipsoidal droplet.     

Structural properties of packed beds — A review

Some structural properties of packed bed systems on both the local and overall scales which are available in the literature and of interest in chemical engineering applications are discussed. Regular and random packings of uniformly sized spheres are initially analyzed as a basis for the later examination of the more general case of random packed beds containing particles of various sizes and shapes, with or without restraining surfaces.     

Three-dimensional random resistor-network model for solid oxide fuel cell composite electrodes

A three-dimensional reconstruction of solid oxide fuel cell (SOFC) composite electrodes was developed to evaluate the performance and further investigate the effect of microstructure on the performance of SOFC electrodes. Porosity of the electrode is controlled by adding pore former particles (spheres) to the electrode and ignoring them in analysis step. To enhance connectivity between particles and increase the length of triple-phase boundary (TPB), sintering process is mimicked by enlarging particles to certain degree after settling them inside the packing. Geometrical characteristics such as length of TBP and active contact area as well as porosity can easily be calculated using the current model. Electrochemical process is simulated using resistor-network model and complete Butler-Volmer equation is used to deal with charge transfer process on TBP. The model shows that TPBs are not uniformly distributed across the electrode and location of TPBs as well as amount of electrochemical reaction is not uniform. Effects of electrode thickness, particle size ratio, electron and ion conductor conductivities and rate of electrochemical reaction on overall electrochemical performance of electrode are investigated.