Density of softwood bark and softwood char: procedural calibration and measurement by water soaking and kerosene immersion method

Particle density plays an important role in the design and operation of thermoconversion reactors fed with bed of particles such as softwood bark (SB). Little information is available on the single particle density of SB and charcoal derived. As SB and softwood char (SC) particles are highly irregular in shape and size, conventional methods of particle density measurement cannot be applied. A method known as the water soaking and kerosene immersion procedure, used for density measurement of sugarcane bagasse, has been tested and adapted to the density measurement of individual particles of softwood (SW), SB and SC. The particle density has been determined to be 360, 482 and 299 kg m⁻³ for SW, SB and SC, respectively. The average particle density of a typical SB feedstock sample comprised of ca. 30% SW and 70% SB was calculated to be 438 kg m⁻³.     

Specific heat and thermal conductivity of softwood bark and softwood char particles

Very few data exist regarding the thermal properties of softwood bark and therein derived softwood chars. This work describes the measurement of specific heat and particle thermal conductivity of softwood (SW), softwood bark (SB) and therein derived softwood char (SC). Differential scanning calorimetery (DSC) was used to measure the specific heat. At 313 K, the measured specific heat was found to be 1172, 1364 and 768 J kg⁻¹ K⁻¹ for SW, SB and SC, respectively. The specific heat of SW and SB increased linearly from 1172 to 1726 and 1364 to 1777 J kg⁻¹ K⁻¹, respectively, with an increase in temperature from 313 to 413 K. With an increase in temperature from 313 to 713 K, the specific heat of SC doubled from 768 to 1506 J kg⁻¹ K⁻¹ and followed a polynomial relationship with temperature. A modified Fitch apparatus was constructed, calibrated and used for measurement of particle conductivity of SW, SB and SC. The particle thermal conductivity of SB was found to be twice that of SC, i.e. 0.2050 and 0.0946 W m⁻¹ K⁻¹, respectively, at 310 K. The particle thermal conductivity of SW, SB and SC followed a linear increase with temperature.     

Modelling the Effective Thermal Conductivity in Polydispersed Bed Systems: A Unified Approach using the Linear Packing Theory and Unit Cell Model

A comprehensive, unified approach, using the Linear Packing Theory and Unit Cell Model, is proposed for calculating of the effective thermal conductivity of polydispersed packed beds. In this new approach, the effect of packing density is incorporated by the use of (i) an initial porosity to take into account the packing of mono‐sized particles, and (ii) the packing size ratio as a measure of the particle‐particle interaction. The proposed approach was validated with the experimental measurements of binary and ternary beds. This new approach demonstrates that the effective thermal conductivity of beds composed of polydispersed particles can be simulated for any composition without the need to measure the in situ porosity.     

Settling of particles in liquids: Effects of material properties

This article presents a numerical study on the settling of uniform spheres in liquids by means of the discrete element method. The effects of particle and liquid properties, such as particle size, Hamaker constant, liquid density, and viscosity, on the formation of packed beds or cakes were studied in terms of packing fraction, radial distribution function (RDF), and coordination number (CN). The results showed that the packing fraction of a cake increases with increasing particle size but decreases with increasing the Hamaker constant, liquid density, and viscosity. RDF and CN also change correspondingly: packings with lower packing fraction generally have RDFs with fewer peaks and smaller mean CNs. A good correlation between packing fraction and other structural properties was identified. The analysis of the particle‐particle and liquid‐particle interactions showed that the packing properties are mainly affected by the ratio of the interparticle cohesion to the effective gravity of particles. The previously proposed equation linking packing fraction with the interparticle forces has been extended to incorporate the impact‐induced pressure force in a settling process. Based on the modified equation, the effects of key variables on the relationship between packing fraction and particle size were re‐examined for general application. © 2011 American Institute of Chemical Engineers AIChE J, 2012.     

Near-wall porosity characteristics of fixed beds packed with wood chips

Packed beds of fuel wood chips are commonly found in thermal conversion processes such as combustion or gasification. Wood chips in particular are mostly used as fuel for small-scale domestic heating boilers but also for commercial-scale combustion units. The characterization of spatial voidage distribution inside the wood chip beds is of great importance for flow and reactor modelling. This study focuses on the radial porosity variations of cylindrical beds of three different types of commercially available wood chips including chips classified as G30 size class. The conventional technique of consolidating packed beds with a resin was chosen as the experimental procedure. The radial voidage distribution in different cylindrical beds is determined by image analysis of sections of the solidified packings. Additionally, a packing of monosized spheres was investigated in order to assess the selected procedure in comparison with widely available literature data for spheres. The results are discussed and summarized in a mathematical expression correlating the radial voidage distribution depending on average wood chip size, packing core porosity and dimensionless distance from the tube wall.     

Studies of the Effects of Particle Size Distribution on the Packing Efficiency of Particles

In the studies of pigment volume effects in paint films, particle packing has been shown to be very important. The effects of particle size distribution on this packing has been known but has received little quantitative consideration. In this paper we consider the packing of real and model continuous distributions of particle sizes. An extension of an algorithm for the calculation of random densest packing is given which applies to continuous distributions. Using a log-normal distribution as a model, the effect of the width of a single distribution on packing is considered. Mixtures of distributions are also considered with the calculation of packing efficiency as a function of mean size ratio and distribution widths. Maxima are shown to occur in the packing efficiency of mixtures of distributions as a function of the volume fractions of the individual distributions. The implications of these packing variations in real systems are then discussed.     

Hydropyrolysis of kraft hardwood and softwood black liquor

The hydropyrolysis of hardwood and softwood derived black liquor was studied to develop material balance data and to investigate the potential yield of phenolic oils that might be obtained as chemical by-products of a kraft pulp mill. Hydropyrolysis reactions on softwood liquors were found to be more efficient in char formation than those on hardwood liquors. The yield of extractible phenolic oils was low, around 20–30 percent of black liquor organics, but the yields of simple phenols determined by gas chromatography were found to be even lower at 1–5 percent on black liquor organics.     

Wall Loss Rate of Polydispersed Aerosols

Wall loss rates of polydispersed aerosols in a stirred vessel were studied theoretically and experimentally. A formula for the poly- dispersity factor of the wall loss rate was derived using the moment method of log-normal size distribution and compared with numerical calculations. The representative theory of Crump and Seinfeld (1981) was used as the wall loss rate of monodispersed aerosols in which the Brownian diffusion, the turbulent eddy diffusion, and the gravitational settling are included as wall loss mechanisms. The results of the analysis show that the wall loss rate of a polydispersed aerosol is substantially higher than that based on a monodispersed size distribution model if the particle size distribution can be represented reasonably well by a log-normal function. The existing diagram showing the loss rate as a function only of the particle size was expanded to include the polydispersity effects. Experimental measurements of particle wall loss rate were performed by observing the time-dependent changes in particle number concentration for various stirring intensities in a cylindrical stirred chamber. It was shown that by correcting for the polydispersity effect, the dependence of the wall loss rate on particle size and stirring intensity agreed with the theory of Crump and Seinfeld (1981).     

Analysis of particle porosity distribution in fixed beds using the discrete element method

This report discusses the use of the discrete element method (DEM) to the porosity distribution of spherical particles in narrow pipes as a function of the pipe-to-particle diameter ratio. It was found that the packing structure depends mainly on the pipe-to-particle ratio and the particle friction. The numerical results with respect to the radial porosity distribution are in agreement with experimental data from the literature. Radial porosity distributions were calculated using algorithms developed by Mueller. The packing structure of the particles shows channeling for small pipe to particle diameter ratios. The simulated height averaged porosity distribution agrees with models from the literature. Moreover, DEM provides the possibility to include particle properties which reflect on the porosity distribution.     

Analytic solution for polydispersed aerosol dynamics by a wet removal process

An analytic solution for polydispersed aerosol dynamics by wet deposition of droplets was obtained. The collection efficiency used was based on the results of Jung and Lee (Aerosol Sci. Technol. 29 (1998) 389). The derived efficiency was compared with the existing formula of Slinn (Atmospheric Science and Power Production—1979, Division of Biomedical Environmental Research, U.S. Department of Energy, Washington DC, USA, 1983 (Chapter 11)) and showed good agreement. The particle size distribution was assumed to have a log-normal function, and the Cunningham slip correction factor was simplified to introduce the moment relationship. Both analytic and numerical solutions were obtained and compared with each other. The results show that the analytic solution can simulate the scavenging of polydispersed aerosol by wet deposition for the diffusion-dominant range well. The particle diameter of minimum collection efficiency was obtained analytically. It was found that the minimum collection efficiency diameter increases with decreasing velocity and decreasing packing density.     

A new computational method for studying heat transfer in fluid bed reactors

Effective thermal conductivity (ETC) is an important parameter describing the thermal behaviour of packed beds with a stagnant or dynamic fluid, and has been extensively examined in the past decades. Recently, an approach of coupled discrete particle simulation (DPS) and computational fluid dynamics (CFD) has been extended to predict the ETC, allowing the elucidation of the underlying heat transfer mechanisms at a particle scale. However, because of the sensitivity of heat transfer to particle–particle contact, a large Young's modulus and small time step have to be employed in the DPS to generate accurate results, resulting in a high computational cost. This paper proposed a method to overcome this problem. It is done by introducing a correction coefficient in the calculation of the particle–particle contact radius between colliding particles. The treatment is first implemented in our recent DPS-CFD modeling of the heat transfer in gas fluidization, and is validated by comparing the predicted ETC with literature data. The effects of model parameters, particle size, and bed average temperature on ETC are also analyzed.     

A polydispersed particle system representation of the porosity for non-saturated cementitious materials

In this paper, the porosity of cementitious materials is described in terms of pore size distribution by means of a 3-dimensional overlapping sphere system with polydispersivity in size. On the basis of results established by Lu and Torquato [B. Lu, S. Torquato, Nearest-surface distribution functions for polydispersed particle systems, Phys. Rev. A 45(8) (1992) 5530-5544] and Torquato [S. Torquato, Random Heterogeneous Media: Microstructure and Macroscopic Properties. Springer-Verlag: New York, 2001] providing relations for nearest-neighbor distribution functions, the volume fraction of pores having a radius larger than a prescribed value is explicitly expressed. By adopting an appropriate size distribution function for the sphere system, it is shown that the pore size distribution of cementitious materials as detected for instance by mercury intrusion porosimetry (MIP), which generally points out several pore classes, can be well approached. On the basis of this porosity representation, the evaluation of the capillary pressure in function of the saturation degree is provided. The model is then applied to the simulation of the saturation degree versus relative humidity adsorption curves. The impact of the pore size distribution, the temperature and the thickness of the adsorbed water layer on these parameters are assessed and analyzed for three model materials having different pore characteristics.     

Packing of multi-sized mixtures of wet coarse spheres

The effect of water addition on the packing of multi-sized coarse spheres has been experimentally investigated under standard poured packing conditions. The results indicate that porosity is strongly affected by particle characteristics such as particle sizes and their distribution, in addition to water content. The packing features in the relationship between porosity and moisture content for wet multi-sized spheres are found to be similar to those for wet mono-sized spheres, implying that the same governing mechanisms apply. The comparison between the dry and wet packing systems confirms that there is a similarity between them, suggesting that the packing of wet particles can be predicted within the framework of a packing model developed for dry coarse particles. Future work in this direction is also discussed.     

A numerical investigation of the void structure of fibrous materials

The void structure of particulate solids has been studied with the aid of a numerical packing algorithm based on the minimisation of an energy potential. This algorithm has been used to form densely packed assemblies of spherical and fibrous particles. The void space within these materials has been characterised using an algorithm that finds chains of voids that pass through the assemblies. The tortuosity (as defined by Carman [P.C. Carman, Fluid flow through granular beds, Trans. Instn. Chem. Engrs., v15 pp 150-166, 1937.]) and mean diameter of these chains have been determined and examined as important parameters that are relevant to the permeability of these materials. Tortuosity was approximately constant in the spherical particle assemblies, while the void size varied with the particle size. In general, the spherical particle assemblies showed much smaller void sizes (relative to the particle diameter) and lower tortuosity than the fibrous materials. The tortuosity of the fibrous materials was found to be a function of both the aspect ratio of the fibres, and the packing efficiency of the assembly.     

Counter-current flow of dispersed and continuous phase—I: Discrete polydispersed model

A discrete mathematical model has been proposed of the counter-current gravitational flow of a continuous and a polydispersed phase in vertical column contactors. Allowances have been made for particle entrainment, newly defined back flow of particles in relation to the back flow of the continuous phase, particle dispersion and coalescence. Appropriate solutions enable profiles to be obtained of local hold-up of the dispersed phase as well as those of particle size distribution along the contactor's length. The model with the parameters distributed with respect to particle size has served to derive in turn a lumped parameter modification whose limits of applicability have been shown.     

The Dependence of Pore Size Distribution on Porosity in Hot Isostatically Pressed Porous Alumina

Pore size distributions in porous alumina bodies produced by the capsule-free hot isostatic pressing technique have been determined experimentally. The distribution of pore diameter has been found to be dependent on the size of the pre-sintered powders and the amount of open porosity in the sintered body. An empirical model has been developed to predict the modal pore size as a function of median particle size and open porosity. The pore size distributions were found to widen with reduced porosity. They were also shown to be positively skewed. The skew reduced with decreasing porosity. The pore size variation with porosity for specimens produced with a sintering aid could not be described by the same mathematical functions developed for specimens produced by solid-state sintering.     

Improved Equation of the Continuous Particle Size Distribution for Dense Packing

The Furnas model describes the discrete particle size distribution for densest packing. Using a model that considers a continuous particle size distribution for the densest packing to be a mixture of infinite Furnas discrete particle size groups, an equation for the cumulative particle size distribution providing the densest packing was derived. Monosize particles with different shapes have a different packing pore fraction. One parameter in the equation is the pore fraction of packed monosize particles; the particle size distribution for achieving densest packing is a function of this pore fraction. A reduced form of this equation is also presented as a working equation. The equation derived here is compared to the modified Andreasen equation for dense packing. An equation and the correlated graph for calculating theoretically the geometric mean particle size and an equation for calculating the specific surface area of the particle size distribution of the improved equation are also derived.     

Cyclic cold isostatic pressing and improved particle packing of coarse grained oxide ceramics for refractory applications

This study investigated the cold isostatic pressing of coarse grained alumina refractories applying either a cyclic pressure increase or a cycling at maximum pressure. Additionally the effects of the maximum pressure and the particle size distribution on physical, mechanical and thermomechanical properties were analyzed. The cyclic pressure increase resulted in a slightly higher apparent density and lower apparent porosity. A cycling at maximum pressure decreased the median pore size to some extent. Remarkably, an optimized particle size distribution resulted in a lower apparent porosity, lower median pore size and in a higher Young's modulus before and after thermal shock together with a slightly lower relative decrease of the Young's modulus. A higher pressing pressure which decreased the apparent porosity did not affect the Young's modulus. Thus, apparently the optimized particle size distribution improved the particle packing which was associated with a smaller median pore size. This smaller pore size increased the number of pores relative to the total porosity, which then acted as points of crack initiation and crack deflection limiting the length of propagating cracks in case of thermal shock. Thus, tailoring the pore size distribution is a promising starting point to improve the thermomechanical properties of refractories.     

Phenolic compounds from vacuum pyrolysis of wood wastes

Various softwood and hardwood bark residues, primary sludges and softwood sawdust residues were processed by vacuum pyrolysis in a laboratory scale batch reactor. The pyrolysis oil, water, charcoal, and gas were recovered and analyzed. The pyrolysis oils were analyzed in details for their content in phenolic compounds after derivatization to their acetyl derivatives. The influence of temperature, heating rate, feedstock bed thickness, particle size and feedstock water pretreatment on the yield of phenols was investigated. The highest yield of phenols was obtained when hardwood bark was soaked in water for 48 hours and pyrolyzed at a temperature of 450°C and a heating rate of 10°C/min. Pyrolysis performance was evaluated in terms of total phenolic yield and composition.     

Analysis of solar‐driven gasification of biochar trickling through an interconnected porous structure

The efficient transfer of high‐temperature solar heat to the reaction site is crucial for the yield and selectivity of the solar‐driven gasification of biomass. The performance of a gas‐solid trickle‐bed reactor constructed from a high thermal conductivity porous ceramic packing has been investigated. Beech char particles were used as the model feedstock. A two‐dimensional finite‐volume model coupling chemical reaction with conduction, convection, and radiation of heat within the packing was developed and tested against measured temperatures and gasification rates. The sensitivity of the gasification rate and reactor temperatures to variations of the packing's pore diameter, porosity, thermal conductivity, and particle loading was numerically studied. A numerical comparison with a moving bed projected a more uniform temperature distribution and higher gasification rates due to the increased heat transfer via combined radiation and conduction through the trickle bed. © 2014 American Institute of Chemical Engineers AIChE J, 61: 867–879, 2015