Dense flows of grains are commonplace throughout natural and industrial environments, from snow-avalanches down the sides of mountains to flows of cereal down chutes as it is transported from one part of a factory to another. A ubiquitous feature in all of these flows is their ability to separate the different grain types when shaken, stirred, sheared or vibrated. Many flows are sheared through gravity and these flows are particularly efficient at segregating particles based on their size, with small particles percolating to the bottom of the flow and large particles collecting at the top. Within this mechanism, an asymmetry between the large and small particles has been observed, with small particles percolating downwards through many large particles at a faster rate than large particles rise upwards through many small particles. This alternative format thesis presents a revised continuum model for segregation of a bidisperse mixture that can account for this asymmetry. A general class of asymmetric segregation flux functions is introduced that gives rise to asymmetric velocities between the large and small grains. Exact solutions for segregation down an inclined chute, with homogenous and normally graded inflow conditions, show that the asymmetry can significantly enhance the distance for complete segregation. Experiments performed using a classical shear-box with refractive index matched scanning are able to quantify the asymmetry between large and small particles on both bulk and particle scales. The dynamics of a single small particle indicate that it not only falls down faster than a single large particle rises, but that it also exhibits a step-like motion compared to the smooth ascent of the large grain. This points towards an underlying asymmetry between the different sized constituents. The relationship between the segregation-time and the volume fraction of small grains is analysed, and solutions presented for the steady-state balance between segregation and diffusive remixing. These help to show the good agreement between the asymmetric model and experimental data. Segregation at the front of natural avalanches produces a recirculation zone, known as a `breaking size-segregation wave', in which large particles are initially segregated upwards, sheared towards the front of the flow, and overrun before being resegregated again. Solutions for the structure of this recirculation zone are derived using the asymmetric flux model, revealing a novel `lens-tail' structure. Critically, it is seen that a few large particles starting close to the bottom of the flow are swept a long way upstream and take a very long time to recirculate. The breaking size-segregation waves highlight the important interplay between segregation and the bulk velocity field. The properties of flowing monodisperse grains are explored through experiments on a cone that produce a beautiful radial fingering pattern. Equations developed in a conical coordinate system reproduce the measured linear relationship between fingering radius and initial flux, whilst also predicting the slowing and thinning dynamics of the flow. Overall, these results illustrate the complex nature of the granular rheology and provide perspectives for future modelling of segregation in dense granular flows.

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / The main objective of this work was evaluating the possibility of using the Acoustic Doppler Velocimeter (ADV) to quantify the suspended sediment concentration (SSC). For this purpose, a laboratory experiment was developed, where a controlled environment was sought to test the ADV response for tests conducted in samples with known characteristics. Eight concentrations and five particles sizes of five types from soil types of three cities were used in the test. An experimental apparatus was built in order to obtain data in homogeneous water and soil samples utilizing the Sontek Horizon ADV software. Samples were collected in six different positions, 6cm, 12cm and 18cm from the bottom of the vessel, totalizing more than 600 sampling. The software Win ADV was utilized to visualize the data and the post processing, applying the PSTM filter to eliminate data that were affected by noise effects, maintaining a large percentage of data. The collected data showed an increase of SNR compared to the increase of SSC for the different soil types for the five particle sizes, wherein the best correlations between echo and SSC occurred for the tests with soils 2,3 and 4. By the measurements with ADV in laboratory, was possible to investigate the relation signal/noise for different particle sizes and SSC of soil when soil is suspended in water. It was noted that the found SNR values did not follow a pattern in relation to soil particle size. In other words, it cannot be concluded that the increase of particle size results in increase of SNR, whereas the SNR values found were larger for some particle sizes in some concentrations and smaller in others. In relation to SSC, it is easy to note that, in general, the higher the concentration of sediments, higher is the found SNR value. This result meets with what have been seen in the literature. / Este trabalho teve como objetivo principal avaliar a possibilidade do uso do Velocímetro Acústico Doppler (ADV) para quantificar a concentração de sedimento em suspensão (CSS). Para isso foi desenvolvido um experimento em laboratório, onde se buscou em um ambiente controlado, testar a resposta do ADV para testes conduzidos em amostras de características conhecidas. Foram utilizadas oito concentrações e cinco faixas granulométricas de cinco tipos de solo de três cidades nos ensaios. Foi construído um aparato experimental, a fim de obter dados em amostras homogêneas de água e solo utilizando o programa Sontek Horizon ADV. Coletou-se as amostras em diferentes posições a 6 cm, 12 cm e a 18 cm do fundo do recipiente, totalizando mais de 600 ensaios. Para visualização dos dados e pós processamento utilizou-se o programa Win ADV aplicando o filtro (PSTM) a fim de eliminar os dados que foram afetados por algum efeito de ruído, mantendo um grande percentual de dados. Os dados coletados mostraram o aumento do SNR em relação ao aumento da CSS para os diferentes tipos de solos para as cinco granulometrias, sendo que as melhores correlações entre o eco e a CSS ocorreram para os ensaios com os solos 2, 3 e 4. Através das medições com o ADV em laboratório, foi possível investigar a relação sinal/ruído para diferentes faixas granulométricas e CSS de solo quando em suspensão em água. Notou-se que os valores encontrados para o SNR não seguiram uma regra determinada em relação à faixa granulométrica do solo. Ou seja, não se pode concluir que o aumento da faixa granulométrica indica o aumento do SNR, já que os valores de SNR encontrados foram maiores para algumas granulometrias em algumas concentrações e menores em outras concentrações. Já no que diz respeito às diferentes CSS, em geral, quanto maior a concentração de sedimentos, maior é o valor de SNR encontrado. Esse resultado vem ao encontro com o que tem sido visto na literatura.

Abstract Zinc production has been known since 200 BC. Fluidised bed roasting is the first process stage of the electrolytical zinc production process, was developed in the 1940s. The raw material for zinc is usually sphalerite concentrate. This sulphide concentrate is oxidised in a roaster. Oxidation reactions produce energy, which is removed as steam, and sulphur dioxide, which is used as the raw material of sulphuric acid. During recent decades sphalerite concentrates have contained more and more impurities and at the same time they have become more fine-grained. Impurities cause problems during fluidised bed roasting. As a consequence, production capacity decreases, there are breaks in production. Starting up and shutting down a process during production breaks cause the environmental emissions. In order to be able optimise production, the oxidation mechanisms of impure sphalerite and methods for controlling them have to be known. The hypothesis of this work was as follows: In addition to temperature, the impurity content and particle size of the feed and oxygen coefficient also have an effect on the stability of fluidised bed roasting. Diverse concentrates require different oxygen coefficients and temperatures. The basic target of this work was to develop a method to help find the required conditions and to control them in industrial roasters. This study was restricted to considering the effects of the iron, copper and lead contents in sphalerite concentrate. A review was made of earlier roasting studies and experiences. This study also evaluated the thermodynamic background of roasting. The oxidation mechanisms were also studied in the laboratory using a fluidised bed roaster and horizontal tube furnace. The results were validated in an industrial roaster. On the grounds of these studies the different sphalerite concentrates really do require diverse roasting temperatures and oxygen coefficients. Foremore, the same kinds of concentrates require a different roasting temperature and oxygen coefficient, if their particle size distributions are different. Controlling the concentrate feed particle size may help to control the stability of the roasting bed and the temperature of the upper part of the furnace. The impurities increase the forming of direct bond sintering and thus the forming of sulphide liquid phases. Oxides and sulphates may also form liquid phases. These kinds of liquid phases cause problems in the fluidised bed. Continuous control of the oxygen coefficient and bed temperature and the use of a unique oxygen coefficient and temperature range for every concentrate mixture would make it possible to minimise problems in the furnace. Laboratory and industrial scale tests have verified the variables and methods for controlling conditions in the roaster bed. / Tiivistelmä Sinkin valmistus on ollut tunnettua ajalta 200 eKr. Leijukerrospasutus, joka on ensimmäinen prosessivaihe elektrolyyttisessä sinkin valmistusprosessissa, otettiin sekin käyttöön jo 1940-luvulla. Sinkin raaka-aineena käytetään sfaleriittirikastetta, joka hapetetaan pasutuksessa. Hapetusreaktiot tuottavat energiaa, joka otetaan talteen höyrynä, ja rikkidioksidia, josta tuotetaan rikkihappoa. Viime vuosikymmeninä sfaleriittirikasteet ovat tulleet epäpuhtaammiksi ja samalla partikkelikooltaan hienommiksi. Epäpuhtaudet aiheuttavat ongelmia leijupetiin. Tämän seurauksena uunien kapasiteetti laskee, tulee tuotannon seisauksia. Näiden seisauksien yhteydessä tapahtuvat prosessin ylös- ja alasajot aiheuttavat päästöjä. Tuotannon optimoimiseksi täytyy tuntea epäpuhtaiden sfaleriittirikasteiden hapetusmekanismit ja tavat niiden hallitsemiseksi. Tämän työn hypoteesi oli: Leijukerrospasutuksen stabiilisuuteen vaikuttaa lämpötilan lisäksi epäpuhtauksien määrä syötteessä ja syötteen partikkelikokojakauma sekä happikerroin. Erilaiset rikasteet vaativat erilaisen happikerroin- ja lämpötila-alueen. Työn tavoite oli kehittää menetelmä,jolla saadaan vaaditut olosuhteet syntymään ja hallittua. Tutkimuksissa rajoituttiin tarkastelemaan sfaleriittirikasteiden sisältämän raudan, kuparin ja lyijyn vaikutusta. Työssä tutustuttiin epäpuhtaiden sfaleriittirikasteiden pasutuksen alueelta aiemmin tehtyihin tutkimuksiin ja eri pasutoilla saatuihin kokemuksiin sekä selvitettiin pasutuksen termodynaaminen tausta. Laboratoriotutkimuksilla selvitettiin hapettumismekanismeja leijukerrosreaktorissa ja pelleteillä kvartsilaivassa putkiuunissa. Tulosten todentaminen tehtiin koeajoilla teollisessa tuotantolaitoksessa. Johtopäätöksenä näistä tutkimuksista voidaan todeta, että erilaiset sfaleriittirikasteet edellyttävät kullekin rikasteelle ominaista pasutuslämpötilaa ja happikerrointa. Lisäksi samantyyppistenkin rikasteiden vaatima pasutuslämpötila ja happikerroin voivat vaihdella, jos rikasteen partikkelikokojakauma vaihtelee. Syötteen partikkelikokoa säätäen voidaan ohjata pedin stabiilisuutta ja uunin yläosan lämpötilaa. Epäpuhtaudet lisäävät suorasidossintrautumien syntyä ja siten sulfidisulafaasien muodostumista. Sulafaaseja voivat muodostaa myös tietyt oksidit ja sulfaatit. Tästä seuraa ongelmia leijupedissä. Happikertoimen jatkuva seuranta ja säätö kullekin rikasteelle ominaisella alueella, samoin kuin lämpötilan seuranta ja säätö, mahdollistavat ongelmien minimoinnin. Tähän työhön liittyvissä laboratoriotutkimuksissa ja teollisen mittakaavan tutkimuksissa todennettiin muuttujat ja keinot olosuhteiden hallitsemiseksi.

Kyoto University (京都大学) / 0048 / 新制・課程博士 / 博士(工学) / 甲第16887号 / 工博第3608号 / 新制||工||1545(附属図書館) / 29562 / 京都大学大学院工学研究科化学工学専攻 / (主査)教授 松坂 修二, 教授 宮原 稔, 教授 大嶋 正裕 / 学位規則第4条第1項該当

A vast amount and variety of mine tailings are produced around the world each day. In the gold¬mining industry in South Africa the residue of crushed are is disposed of in large tailings or hydraulic fill dams. The outer walls of these dams are built up of layers of material, each of which is allowed to dry before the next layer is placed. In order to study the stability of these walls, the appropriate engineering properties of the tailings must be ascertained. Due to the construction technique used in tailings dam construction, the outer walls are in an unsaturated state, which also means that suctions are generated within the tailings. Various techniques exist to measure suction, most of which are indirect methods. The recent development of the mid-¬plane suction probe at the University of Pretoria created the opportunity of measuring suctions directly on desiccating samples of gold mine tailings. A test method has been developed from which soil mechanics parameters can be derived from suction measurements. The experimental programme consisted of a series of these newly developed tests on fine and coarse samples of gold mine tailings, as well as on different particle size ranges. The experimental results were used in the development of a new method of predicting the air-entry value, with only the grading of the tailings known. A new method of predicting the soil-water characteristic curve up to the air-entry value was also proposed. The results of the research showed that the tailings remain saturated up to the air-entry value. The clay, fine silt and medium silt sized tailings was found to be the controlling particle size ranges in the development of suctions. The vast amount of parameters and information gained through the use of the proposed test method clearly indicates its effectiveness in studying the performance and characteristics of a material drying from saturation. The results also indicated the effectiveness of the mid-plane suction probe for the direct measurement of suction. / Dissertation (M Eng (Geotechnical Engineering))--University of Pretoria, 2006. / Civil Engineering / unrestricted

O objetivo do presente estudo foi avaliar o desempenho, saúde intestinal e metabolizabilidade de dietas para frangos de corte alimentados com o uso contínuo ou mudança brusca de diferentes rações à base de milho e sorgo moído ou inteiro. No Exp. 1 foi estudada a mudança no tipo de grão com as dietas: M100% (ração à base de milho); S100% (ração à base de sorgo); M:S50% (ração à base de 50% milho e 50% sorgo); PS-M (ração à base de sorgo na fase pré-inicial e milho nas demais fases); PM-S (ração à base de milho na fase pré-inicial e sorgo nas demais fases). No Exp. 2 foi estudada a mudança na forma do grão de sorgo: Sm100% (ração à base de sorgo moído); Si100% (ação à base de sorgo inteiro); PSm-Si (ração à base de sorgo moído na fase pré-inicial e inteiro nas demais fases) e PSi- Sm (ração à base de sorgo inteiro na fase pré-inicial e moído nas demais fases). Os experimentos foram conduzidos em um delineamento em blocos casualizados (blocos no tempo) para avaliar o desempenho e epitélio jejunal (r=8), microbiota intestinal (r=4) e metabolizabilidade das dietas (r=10). As mudanças entre milho e sorgo não alteraram o desempenho, epitélio jejunal nem a metabolizabilidade das rações, mas influenciaram a porcentagem de Clostridium, Weissella, Bacillus e Alkaliphilus no intestino delgado e Lactobacillus e Desulfotomaculum nos cecos. O uso de sorgo inteiro piorou o desempenho aos sete dias. Aos 40 dias, Sm100% e PSm-Si apresentaram desempenhos semelhantes, PSi-Sm apresentou menor ganho de peso, mas melhor conversão alimentar e Si100% apresentou o pior desempenho. Si100% e PSm-Si apresentaram aumento no peso relativo da moela e na metabolizabilidade das rações, assim como diminuição de Clostridium e aumento de bactérias das famílias Actinomycetales e Bacillales no intestino delgado, Si100% resultou em menor porcentagem de Alkaliphilus e Enterococcus que Sm100% nos cecos. Conclui-se que a melhor estratégia de uso do sorgo é a substituição total de milho por sorgo moído ao alojamento com posterior mudança para sorgo inteiro, pois não afeta o desempenho e epitélio jejunal das aves, melhora a metabolizabilidade das rações e potencializa a redução de Clostridium no intestino delgado de frangos de corte. / The aim of this study was to evaluate performance, intestinal health and metabolizability of diets in broilers fed different corn- or sorghum (ground or whole)- based diets, continuously or with abrupt change between the diets. Exp. 1 - Change in the type of grain: C100% (corn-based diet); S100% (sorghum-based diet); C:S50% (50% corn and 50% sorghum-based diet); PC-S (corn-based diet in pre-starter phase and sorghum-based diet in other phases); PS-C (sorghum-based diet in pre-starter phase and corn-based diet in other phases). Exp. 2 - Change in the form of sorghum grain: Gs100% (ground sorghum-based diet); Ws100% (whole sorghum-based diet); PGs-Ws (ground sorghum-based diet in pre-starter phase and whole sorghum-based diet in other phases); PWs-Gs (whole sorghum-based diet in pre-starter phase and ground sorghum-based diet in other phases). Experiments were conducted in a randomized block design for to evaluate performance and jejunal epithelium (r=8), intestinal microbiota (r=4) and metabolizabilty of diets (r=10). The changes between corn and sorghum did not affect performance, jejunal epithelium or metabolizability of the diets, but influenced the genera Clostridium, Weissella, Bacillus and Alkaliphilus in the small intestine, and Lactobacillus and Desulfotomaculum in the caecum. Whole sorghum resulted in decreased performance at seven days of age. At 40 days, Gs100% and PGs-Ws showed similar performance, PWs-Gs showed lower weight gain and the best feed conversion rate, and Ws100% showed the worst performance. Ws100% and PGs-Ws resulted in the biggest gizzard relative weight and the highest diet metabolizability values, as well as the lowest level of Clostridium and highest level of Actinomycetales and Bacillales in the small intestine. Ws100% showed lower level of Alkaliphilus and Enterococcus than Gs100% in the caecum. The best strategy to use sorghum in broilers diets is replacing 100% of corn for ground sorghum since the first day followed by change to whole sorghum, because this diet did not affect performance or jejunal epithelium, improved diet metabolizability values, and reduced Clostridium in the small intestine of broilers.

For disperse system drug formulations, meaningful particle size distribution (PSD) comparators are essential in determining pharmaceutical equivalency and predicting biopharmaceutical equivalence in terms of the effect of particle size on the rate and extent of drug input. In formulation development and licensure, particle size characterization has been applied to establish relationships for bioequivalence of generic pharmaceutical drug products. The current approaches recommended by the US-FDA using median and span are not adequate to predict drug product performances or account for multi-modal PSD performance properties. The use of PSD similarity metric and the development and incorporation of drug release predictions based on PSD properties into PBPK models for various drug administration routes may provide a holistic approach for evaluating the effect of PSD differences on in vitro release of disperse systems and the resulting pharmacokinetic impact on drug product performance. The objectives of this study are to provide a rational approach for PSD comparisons by 1) developing similarity computations for PSD comparisons and 2) using PBPK-models to specifically account for PSD effects on drug input rates via a subcutaneous (SQ) administration route. Two techniques for measuring PSDs of reference (reference-listed drug product) and test (generic) drug products were investigated: OVL and PROB, as well as the current standard measurements of median and span. In addition, release rate profiles of each product pair simulated from modified Bikhazi and Higuchi’s model were used to compute release rate comparators such as similarity factor (f2) and fractional time ratios. A subcutaneous input PBPK model was developed and used to simulate blood concentration-time profiles of reference and test drug products. Pharmacokinetic responses such as AUC, Cmax, and Tmax were compared using standard bioequivalence criteria. PSD comparators, release rate comparators, and bioequivalence metrics were related to determine their relationships and identify the appropriate approach for bioequivalence waiver. OVL showed better predictions for bioequivalence compared to PROB, median, and span. For release profile comparisons, the f2 method was the best for bioequivalence prediction. The use of both release rate (e.g., f2) and PSD (e.g., OVL) comparison metrics significantly improved bioequivalence prediction to about 90%.

Practical combustion devices such as gas turbines and diesel engines operate at high pressures to increase their efficiency. Pressure significantly increases the overall soot yield. Morphology of these ultra-fine particles determines their airborne lifetime and their interaction with the human respiratory system. Therefore, investigating soot morphology at high pressure is of practical relevance. In this work, a novel experimental setup has been designed and built to study the soot morphology at elevated pressures. The experimental setup consists of a pressure vessel, which can provide optical access from 10° to 165° for multi-angle light scattering, and a counterflow burner which produces laminar flames at elevated pressures. In the first part of the study, N2-diluted ethylene/air and ethane air counterflow flames are stabilized from 2 to 5 atm. Two-angle light scattering and extinction technique have been used to study the effects of pressure on soot parameters. Path averaged soot volume fraction is found to be very sensitive to pressure and increased significantly from 2 to 5 atm. Primary particle size and aggregate size also increased with pressure. Multi-angle light scattering is also performed and flames are investigated from 3 to 5 atm. Scattering to absorption ratio is calculated from multi-angle light scattering and extinction data. Scattering to absorption ratio increased with pressure whereas the number of primary particles in an aggregate decreased with increasing pressure. In the next part of the study, Thermophoretic Sampling of soot is performed, in counterflow flames from 3 to 10 atm, followed by transmission electron microscopy. Mean primary particle size increased with pressure and these trends are consistent withour light scattering measurements. Fractal properties of soot aggregates are found to be insensitive to pressure. 2D diffused light line of sight attenuation (LOSA) and Laser Induced Incandescence (LII) are used to measure local soot volume fraction from 2 to 10 atm. Local soot volume fraction increased with pressure and soot concentration profiles showed good agreements when measured by both techniques. Experimental data obtained in this work is very helpful for the modelers for validating their codes and predicting the soot formation in pressurized flames.

The structural organization of plant organs and tissues determine the intake potential through the ease of forage particle breakdown, the nature of the particles produced as well as the rate of passage from the rumen. The cell wall content of forages influences the amount of energy required for chewing, and accounts for a considerable proportion of the total energy requirement. In the past, neutral detergent fibre (NDF) has been used as the only feed characteristic to predict the filling effects of forages, but there is substantial evidence that NDF alone is inadequate to make these predictions. Forage fragility is defined as the relative rate at which the particle size of forages are reduced during processes such as chewing or milling, and forage fragility might be related to lignin concentration and digestibility, as well as to anatomical differences among plant species. The physical characteristics of feedstuffs are not measured regularly, and these physical characteristics in relation to their nutritional properties should be taken into account for more precise feed formulation. Through the measurement of grinding energy, the possibility exists to predict forage fragility as related to the chemical composition of forages, which could lead to improved predictions of animal chewing activity and energy usage during the process of chewing. In order to investigate the possibility of developing a model for the prediction of forage fragility, twenty eight different forage samples were collected from 11 different locations. Samples included legumes, C3- and C4- grasses. Dried samples were analysed for various chemical components, as well as 24-hour in vitro NDF digestibility (ivNDFd) and rate of NDF degradation (NDFkd). Dried samples were pre-cut with a knife mill, fitted with a 2 cm screen, after which particle size distribution for each sample was determined using a Retsch Sieve shaker. Ten g duplicate samples were milled with a laboratory hammer mill and an ultra-centrifugal mill, both fitted with a 1 mm screen, for the measurement of grinding energy. During the grinding process, energy usage of the specific mill was measured using a data logger with corresponding computer software and energy transducer. Energy measurements were reported as J/g sample on dry matter (DM) basis. The 2 cm samples were milled with the knife mill again, fitted with a 1 mm screen, after which particle size distribution was determined again to analyse change in particle distribution for each forage sample. The results of this study indicated that dry matter, nitrogen, ivNDFd, NDFkd and initial particle size (IPS) can all be associated with increased forage fragility, as there was a decrease in energy usage during grinding with an increase in any of the aforementioned components. The acid detergent fibre (ADF), NDF, total phenols (TP), non-tannic phenols (NTP), as well as the % change in particle size can all be associated with decreased forage fragility, as there was an increase in energy usage during grinding with an increase in any one of these components. It would be expected that acid detergent lignin (ADL) is also associated with decreased forage fragility; however, this can only be assumed as the results for the effect of lignin on forage fragility are inconclusive in this study. Literature on energy requirement for milling operations of forages is inadequate. Grinding energy is related to the stem mechanical properties (such as maximum cutting force and stem shear strength), and physical properties (such as stem diameter, DM density and moisture content). The use of grinding energy has the potential be a practical and useful measure to predict forage fragility, however, the relative contribution of factors such as original particle size, shape, surface area, morphology and many other factors toward the fragility of forages is difficult to predict. More research is needed on the prediction of forage fragility before it can be incorporated as a meaningful input into nutritional models such as NRC, CNCPS and AMTS. / Dissertation (MScAgric)--University of Pretoria, 2014. / tm2015 / Animal and Wildlife Sciences / MScAgric / Unrestricted

This thesis is a part of a collaboration between Höganäs AB and Luleå University of Technology, aiming at replacing fossil process coal with bio-coal in their sponge iron process. The difference in gasification reactivity, i.e. reaction rate, between fossil coals and bio-coals is the major challenge in the endeavor to decrease the climate impact of the existing process. The goal of this thesis is to develop a model of reaction rate for bio-coals in relation to particle size distribution. Different particle size distributions were combined and tested to see how that affects the effective reaction rate. Within the scope of this work, gasification reactivities of different materials, including coal, cokes, and bio-coals, were determined. Three bio-coals were selected to study the effect of particle size distribution on reactivity. Kinetic parameters were determined by using thermogravimetric analysis in the temperature range of 770-850 °C while varying CO2 partial pressure between 0.1-0.4 atm. The effect of particle size on the reaction rate was investigated by using particles with diameter between 0.18 and 6.3 mm. The effect of particle size distribution on the reactivity of bio-coal in a packed bed was carried out in a macro thermogravimetric reactor with a constant bed volume of 6.5 cm3 at 980 °C and 40% (vol.) of CO2. The experimental investigation in three different rate-limiting steps was done for one bio-coal sample, i.e. Cortus Bark bio-coal. The activation energy of the bio-coal was 187 kJ mol-1, and the reaction order was 0.365. For the internal diffusion control regime, an increase in particle size resulted in low reaction rate. The effective diffusivity calculated from the Thiele modulus model was 1.41*10-5 m2 s-1. For the external diffusion control regime, an increase in particle size increased the reaction rate up to a certain point where it plateaued at >1 mm. By choosing two discrete particle size distributions, where a smaller average distribution can fit into a larger average distribution the reaction rate was lowered by 30% compared to only using a single narrow particle size distribution. This solution decreased the difference of apparent reaction rate in a packed bed between the bio-coal and anthracite from 6.5 times to 4.5 times. At the moment the model is not generalized for all bio-coals. However, the developed methodology can be routinely applied to assess the different bio-coal samples. One possible error can be that pyrolysis influences the gasification rate for bio-coal that is pyrolyzed below the temperature of the gasification test. There is a clear correlation between particle size distributions, bulk density, and apparent reactivity. By mixing two distributions the reaction rate of Cortus Bark was reduced from 6.5 times the reaction rate of anthracite to 4.5.