Numerical Simulation of Combustion and Gasification of Biomass Particles

DOCTORAL DISSERTATION

Hesameddin Fatehi

Division of Fluid Mechanics, Department of Energy Sciences Faculty of Engineering LTH, Lund University

Lund, Sweden, 2014

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© Hesameddin Fatehi

Division of Fluid Mechanics Department of Energy Sciences Faculty of Engineering Lund University Box 118 SE-221 00 Lund University Sweden ISBN 978-91-7473-977-0 (printed) ISBN 978-91-7473-978-7 (pdf) ISSN 0282-1990 ISRN LUTMDN/TMHP-14/1102-SE Printed in Sweden by Media-Tryck, Lund University Lund 2014

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Abstract

In this thesis, a numerical approach is adopted to study biomass thermochemical conversion. Detailed physical and chemical processes involved in the thermochemical conversion of biomass are considered. The aims are to improve the understanding of the physical and chemical processes involved and to develop and validate mathematical models for numerical simulation of the biomass conversion process. The main focus of the thesis work has been on large biomass particles under fixed bed conditions. The thermochemical conversion of single particle is first considered. A comprehensive detailed model is developed and evaluated; the results provide valuable insight into the underlying physics of thermochemical conversion of biomass. Based on the comprehensive model a simplified model is proposed which takes into account some of the detailed reaction and transport process inside the particle at high computational efficiency. A two-dimensional model for the fuel bed of biomass furnace is developed and validated.

Mathematical description of various sub-processes involved in the conversion process is presented taking into account the main features of biomass conversion. Various approaches and assumptions for modeling the different sub-processes are assessed by comparing the numerical results with experimental measurements. Specifically, the different moisture evaporation models and assumptions regarding moisture diffusion and vapor re-condensation are investigated. The kinetic scheme and rate constants of devolatilization process are studied. A systematical approach is presented for the evaluation of the heat of pyrolysis which ensures elemental mass and energy balance. The effects of shrinkage on the particle and the change of porosity and biomass density are considered in the mathematical modeling. The formation of ash around the particle, the ash melting at high temperature and the consequences on the particle conversion are investigated.

By means of a joint numerical study and advanced experimental measurements, a mechanism is proposed for the release of alkali metals from low chlorine biomass and the corresponding kinetic rate constants during devolatilization and char reaction stages are obtained. It is shown that the proposed model is able to predict the release behavior of the alkali metal during biomass gasification at various stages of the biomass conversion.

The heterogeneous char reactions at the regime II reaction is affected by both the intra-particle mass transfer and the chemical kinetic rates. The evolution of

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char porous structure can affect the conversion rate of the char. A model based on the classical capillary pores is developed taking into account different conversion rates for pores having different radii. This model is used to examine the contribution of each group of pores (micro, meso and macro-pores) in the conversion of biomass char.

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Popular Science Description

Most of us are familiar with using plant-derived material such as wood for producing heat for warming the cottages or cooking food when we are camping. Apart from that, plant-derived materials such as trees, forest residues, grasses, agricultural crops, agricultural residues and straw have great potential in producing energy in a larger scale. This group of material is referred to as biomass. Sweden has a great source of biomass as more than half of its area is covered with forest. Among the European countries, Sweden has the top share of using renewable energy sources which provide around 40% of the total energy of the country. The main reasons of recent attraction towards using renewable energy sources are the impact of fossil fuels in climate changes and concerns about permanency of the fossil fuels sources. In contrast to fossil fuels, biomass is renewable and can be CO2-natural if produced in a sustainable manner. The CO2 produced from combustion of biomass will be absorbed by the plants that will replace biomass in a shorter term. In this sense, there is much less increase in CO2 compared with the fossil fuels. As one of the green-house gases, CO2 is believed to have a great impact on climate changes and global warming and therefore it raises concerns about its environmental impacts. Although the replacement of fossil fuel such as coal with renewable sources like biomass can help in producing green energy, there are challenges and problems that should be addressed. Emission of harmful pollutants, deposition of remaining ash in the biomass combustion systems, and corrosion of these systems need to be understood in order to improve the efficiency and decrease the cost of energy production.

The aim of this thesis is to improve the understanding of the underlying physics of conversion of biomass to thermal energy in order to provide suggestions and solutions to improve the energy production system. The questions we are trying to answer are (a) how a biomass particle evolves during the conversion to thermal energy, (b) how various forms of pollutant are formed and released during biomass conversion, and (c) how to mathematically model the process with a balance between the computational time and accuracy of the results. Mathematical equations representing the physical phenomena are solved using numerical methods with the help of advanced computational programs. A biomass conversion model is developed which is comprehensive and can take into account the processes such as evaporation of moisture, decomposition of biomass, combustion of gases extracts from biomass decomposition, surface reactions of char and changes in the thermo-physical properties of the particle. The

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contributions of this thesis are (1) development of a comprehensive biomass conversion model with a reduced number of assumptions, (2) assessment of various modeling approaches and assumptions of different sub-models by comparison with several experimental measurements, such as the different moisture evaporation models and assumptions regarding moisture diffusion and vapor re-condensation, the kinetic scheme and rate constants of biomass decomposition process and the amount of heat required in this process, (3) development of chemical kinetic mechanism for the release of alkali metals, potassium and sodium, from biomass during combustion in high CO2 environment, (4) development of a multi pore structure for gasification of biomass char, and (5) development of a semi-empirical model for fixed-bed combustion.

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List of Publications

I. H. Fatehi, X.S. Bai “A Comprehensive Mathematical Model for Biomass Combustion”, Combustion Science and Technology, 2014, In Press. DOI:10.1080/00102202.2014.883255

II. H. Fatehi, X.S. Bai “Gasification and Combustion of Biomass: Physical Description and Mathematical Modeling”, Book chapter, HANDBOOK OF CLEAN ENERGY SYSTEMS, John Wiley Press, In Press.

III. H. Fatehi, Y. He, Z. Wang, Z.S. Li, X.S. Bai, M. Alden, K.F. Cen “LIBS Measurements and Numerical Studies of Potassium Release during Biomass Gasification”, Accepted for Oral Presentation in Symposium of the Combustion Institute, 2014, San Francisco, USA.

IV. H. Fatehi, X.S. Bai, “A simplified model for char combustion at fixed bed environment”, Manuscript to be submitted.

V. H. Fatehi, X.S. Bai, “Effect of pore size distribution on the gasification of biomass char”, Manuscript to be submitted.

VI. H. Fatehi, X.S. Bai, “Modeling of coarse fuel (biomass) combustion in fixed bed grate system”, 9th European Conference on Industrial Furnaces and Boilers, Portugal, 26-29 April 2011.

Other publications

H. Fatehi, X.S. Bai, “Thermodynamic data and heat of pyrolysis of biomass”, 4th international Conference of Applied Energy , 5-8 July 2012, China

X.S. Bai, H. Fatehi, “CFD Analysis of a high moisture biomass combustion processes in a 10MW grate fired furnace”, 9th European Conference on Industrial Furnaces and Boilers, Portugal, 26-29 April 2011.

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Contents

Abstract iii

Popular Science Description v

List of Publications vii

Nomenclature x

INTRODUCTION 1 Motivations 1 Biomass: from source to bio-energy 1 Thermochemical conversion 2 Challenges and approaches 3 Thesis contribution 4 Thesis outline 5

FUNDAMENTALS OF BIOMASS THERMOCHEMICAL CONVERSION 7

PHYSICAL PROCESSES AND MATHEMATICAL MODELING 11 Modeling approach 11 Basic assumptions 15 Kinetic rates 18 Fluxes 20

Fick’s law and Darcy flow 20 Porosity 22 Specific surface area 25 Multi pore structure 28 Ash layer around the particle 30 Physical and thermochemical properties of biomass 31 Boundary and initial conditions 32 Derivation of Energy Equation 34

RESULTS AND DISCUSSION 37 Model parameters 37 Drying, pyrolysis and char combustion 37

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Heat of pyrolysis 43 Release of alkali metals from biomass 46

Experimental measurements 47 Numerical analysis 50 Alkali metal release sub-model 51

Formation of ash around the particle 56 Gasification of biomass 58 A semi-empirical model for fixed-bed combustion 60

CONCLUSION AND FUTURE PERSPECTIVES 61

SUMMARY OF THE PAPERS 65

ACKNOWLEDGMENTS 69

REFERENCES 71

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Nomenclature

퐴 Pre exponential factor 1/푠 or 푚/푠퐾 퐵푖 Biot number 푐 Heat capacity 퐽/푘푔퐾

퐷푎 Damköhler number 퐽/푘푔퐾 퐷 Effective diffusion coefficient 푚 /푠 푑 Characteristic particle length 푚 퐸 Activation energy 푘퐽/푚표푙푒 퐹 Flux of detached char fragments 푘푔/푚 푠 퐺(푟) Surface area of the particle at radius 푟 푚 ℎ Convective heat transfer coefficient 푊/푚퐾 ℎ Mass transfer coefficient 푚/푠 ℎ° Enthalpy of formation 퐽/푘푔

퐻퐻푉 Higher heating value 퐽/푘푔 퐽 Diffusion flux of species 푖 푘푔/푚 푠 푘 Kinetic rate constant 1/푠 퐾 Permeability 푚 푘 Effective thermal conductivity 푊/푚퐾

퐿퐻푉 Lower heating value 퐽/푘푔 푀 Molecular weight 푘푔/푚표푙푒 푁푢 Nusselt number 푁 Total convective flux 푘푔/푚 푠 푝 Pressure 푃푎 푞 Pore growth rate 푚/푠 ℜ Moisture evaporation rate 푘푔/푚 푠 ℜ Volatile release rate 푘푔/푚 푠 ℜ Char formation rate 푘푔/푚 푠

ℜ Char reaction rate 푘푔/푚 푠 ℜ Source term in energy equation 퐽/푚 푠 푟 Radial position 푚 푟 Pore radius 푚 푅 Particle radius 푚

푆ℎ Sherwood number

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푆 Char specific surface area 푚 /푚 푇 Temperature 퐾 푢 Gas velocity 푚/푠

푣푎푠ℎ Ash volume fraction 푚/푠

푌 Gaseous species mass fraction 푋 Conversion ∆ℎ Heat of reaction 퐽/푘푔

훿 Ash thickness 휀 Void fraction 휂 Effectiveness factor 휃 Shrinkage factor 휇 Viscosity 푘푔/푚푠 휌 Density 푘푔/푚 휗 Stoichiometric coefficient 휏 Tortuosity Υ Ash melting rate 1/푠 Φ Thiele module 휓 Structural parameter in random pore model

Subscripts 푏푚 Biomass 푐 Char 푐표푛푑 Conduction 푐표푛푣 Convection 푓푐 Formation of char 푓푐 − 푡 Char produced by tar secondary reaction 푔 Gas 푔 − 푡 Gas produced by tar secondary reaction 푖 Gas species/Pore size/Numerical cell 푖푛푡 Intrinsic 푗 Species 푘 Reaction index 퐾푛 Knudsen diffusion coefficient 푚 Moisture 푛 Reaction order 푟푎푑 Radiation 푡 Tar 푇푟푢푒 Non-porous density 푣 Volatile 0 Initial state

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Abbreviations ASA Active Site Area CELL Cellulose DAF Dry Ash Free HCL Hemicellulose LIG Lignin RPM Random Pore Model

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INTRODUCTION

Motivations

Increased demands for energy sustainability and concerns over global warming have led to a growing interest in sustainable and renewable sources of energy. The EU’s Renewable Energy Road Map proposes creating a new legislative framework to enhance the promotion and use of renewable energy and sets a mandatory target of 20% energy consumption through renewable energy and a mandatory minimum target of 10% for biofuels by 2020 [1]. As a sustainable and renewable source of energy, biomass has a great potential in generating heat and power. In 2005, the breakdown of renewable energy produced in the EU was as follows: 66.1% from biomass, 22.2% from hydropower, 5.5% from wind power, 5.5% from geothermal energy and 0.7% from solar power (thermal and photovoltaic) [1]. Sweden is the leading country in using renewable energy among EU countries, having achieved over a 40% share of renewable energy in their total energy consumption [2].

The energy from biomass can be utilized either in direct heat production or via conversion to biogas, bio-oil and char as storable and portable fuels. The current breakdown of Sweden’s use of bioenergy indicates that approximately 88% of bioenergy sources are used to produce heat through combustion in combined heat and power (CHP) plants and industry units, while 8% is used to produce electricity in CHP plants and 4% is used in the transport sector [2]. This indicates the importance of biomass combustion in bioenergy production. Although anaerobic digestion in wastewater treatment plants, co-digestion plants, farm plants and landfill plants are the major approaches in Swedish biogas production, there is a trend towards using gasification for the production of biogas, bio-oil and char [3].

Biomass: from source to bio-energy

Biomass is referred to plant-derived materials such as trees, forest residues, grasses, agricultural crops, agricultural residues and straw. In a broader view,

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municipal solid waste (MSW) and waste from food factories can also be included in the biomass category. The composition and thermo-physical characteristics of biomass may vary significantly depending on the source.

To produce bioenergy from biomass, whether through direct heat production or conversion to biofuels, two main routes can be considered: biochemical and thermochemical conversion. In biochemical conversion, biomass is converted to biofuels by using microorganism and catalysts. In thermochemical conversion which is the focus of this study, conversion may take place through torrefaction, pyrolysis, gasification or combustion. Torrefaction results in high-energy-density solid fuels. Bio-oil is the main product of pyrolysis and gasification results in syngas production. In the following Section, the thermochemical conversion of biomass is described briefly.

Thermochemical conversion

Thermochemical conversion of biomass is a complex, multi-phase and multi-scale process. This process is a result of strong interaction between the heat and mass transport phenomena and chemical reactions. Figure 1 shows a schematic diagram of thermochemical conversion of biomass. Depending on the heating rate and the ambient gas composition the desired path from biomass to the product can be selected.

Figure 1. Thermochemical conversion of biomass

The sub-processes involved in thermochemical conversion of a biomass

particle start with transient heat conduction to the particle which results in elevated temperatures. Depending on the presence of moisture, the evaporation of moisture starts soon after the particle temperature reaches the evaporation

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temperature. Free water convection by capillary flow through the void spaces may be important in low-temperature drying [4, 5]. The dried portion of the particle, typically initiating from the surface, starts a thermal decomposition process known as devolatilization. If this process takes place in the absence of oxygen, it is referred to as pyrolysis. The pyrolysis products are lumped in three groups: gas, tar (volatile) and char [6]. Low temperature pyrolysis is in favor of char production whereas the tar reaches its maximum yield in intermediate temperature and gas production increases with increasing temperature [7]. As a result of devolatilization, a layer of char is formed which may further react with oxygen (oxidation process), carbon monoxide and water vapor (gasification process). The volatile passing through the char layer can undergo secondary reactions namely tar cracking and polymerization, at high temperatures and high residence times due to the catalytic effect of char. Pressure induced by formation of volatiles results in a convective flow towards the particle surface. Temperature gradient and pressure buildup induced by formation of volatiles may result in formation of cracks in the particle structure or, in some cases, primary fragmentation [8]. Particle size can undergo shrinkage/swelling due to loss of mass and structural reordering. The transport of mass into the porous structure of char can play an important role during the char gasification and oxidation. Char structure can drastically change by the heterogeneous reactions which lead to peripheral fragmentation.

Challenges and approaches

Different aspects of biomass conversion systems have been extensively studied [9, 10]. However, there are still challenges such as efficiency, pollutant emissions, ash deposition and corrosion that need to be understood and improved. Regarding biomass conversion systems, two approaches can be considered. The first approach is to substitute the coal with biomass either partially (co-firing) or completely in the coal-fired plants in a way that the existing infra-structure can be used with minimum modifications. The challenge arises as thermo-chemical properties of biomass are different from those of coal. Biomass has a lower energy density, a higher volatile content and much higher oxygen content. Moreover, biomass contains higher amounts of alkali metals such as potassium and sodium and deposits from co-firing with biomass are highly adherent to surfaces [11] which can cause serious damage to a combustion system. The second approach is to originally design and develop the conversion system for biomass.

A thorough understanding of the processes occurring during the thermochemical conversion of biomass is essential for the design and optimization of biomass conversion systems in both approaches. Mathematical modeling of thermochemical conversion of biomass can provide a useful tool for addressing

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these challenges where the full scale experimentation is expensive and difficult due to the harsh environment of such systems.

Important parameters on a large-scale reactor level, such as distribution of temperature and species and overall conversion rate of biomass, are strongly dependent on the processes involved in the particle scale. A detailed spatially and temporally resolved numerical simulation of a single particle is helpful for understanding the interaction between transport, chemical kinetic and morphological transformation at particle scale. Moreover, a detailed numerical model of particle conversion can further be used to develop simplified models for CFD calculations of the combustion systems where due to the computational limitations, global modeling are often desired.

Thesis contribution

In this thesis, a numerical approach is chosen to study the thermochemical process of biomass. To this end, biomass conversion is divided into several sub-processes where mathematical description and numerical modeling of each sub-process is explained. Because of the complexity of the problem and the limited computational resources, it is inevitable to make certain assumptions and simplifications or to neglect certain physical effects. Therefore this thesis is aimed at assessment and improvement of these assumptions and simplifications in order to gain a better understanding of the underlying physics of biomass thermochemical conversion. The main contribution of this thesis is listed below.

Development of a comprehensive biomass conversion model

A comprehensive biomass model is developed and evaluated. The model takes into account the main features of biomass conversion. Various modeling approaches and assumptions of different sub-models were assessed by comparison with several experimental measurements. Specifically, different moisture evaporation models and assumptions regarding moisture diffusion and vapor re-condensation, the kinetic scheme and rate constants of devolatilization process and the heat of pyrolysis were studied. In addition, the effect of shrinkage on the particle porosity and biomass density was considered in the mathematical modeling. This model can be used for predictive studies of different controlling parameters on biomass conversion and also can work as a benchmark reference for evaluating model simplifications.

Mechanism and kinetic rate constants of release of alkali metals from biomass during oxy-fuel combustion

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A joint numerical and experimental study is carried out, in which, a mechanism for release of alkali metals from low chlorine biomass was proposed and corresponding kinetic rate constants during devolatilization and char reaction stages were obtained.

Development of a multi pore structure for gasification of biomass char

The heterogeneous char reactions occur at the surface of porous structure of the char. For regime II where the intra-particle mass transfer and chemical kinetic rates have comparable time scales, the evolution of porous structure proved to be important. A model based on the classical capillary tubes was developed taking into account different conversion rates for pores having different radius. This model improves the understanding of the contribution of each group of pores (micro, meso and macro-pores) in the conversion of biomass char.

Development of a semi-empirical model for fixed-bed combustion

Tradeoff was made in favor of computational time by simplifying the processes in a fixed bed combustor and a semi-empirical model was developed. This model can provide acceptable boundary conditions for the CFD simulation at a very low computational cost and is most suitable for the studies where the focus is on the gas phase combustion of free board in a fixed-bed combustor rather than the processes inside the bed.

Thesis outline

The thesis is organized as a collection of papers that have been written during this project. The introductory overview of the topic is presented in the thesis followed by the Papers. An overview of the physical processes involved in the thermochemical conversion of biomass is presented in Chapter 2. Mathematical modeling of each process is discussed in Chapter 3. In Chapter 4, summary of the results and discussions is presented. The detailed results are given in the Papers appended at the end of the thesis. Recommendation for the future work and main conclusions of this work are presented in Chapter 5, followed by summary of the Papers as presented in Chapter 6.

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FUNDAMENTALS OF BIOMASS THERMOCHEMICAL CONVERSION

Various processes involved in thermochemical conversion of biomass are described briefly in this Chapter. The conversion process starts with evaporation of moisture. Moisture evaporation process involves simultaneous heat and mass transfer. Heat is conducted and radiated towards the particle center. The moisture starts to evaporate when the temperature reaches the evaporation temperature at the surface of the particle. By diffusion and capillary movement, the bound and free water move towards the dried surface of the particle. The vapor moves out of the particle by convection and diffusion. Some parts of the vapor may diffuse to the colder inner part of the particle where condensation may occur. It can be shown that for initial moisture contents below the free water continuity point (around 45% on dry bases) and high-temperature drying, the free water movement is negligible [4].

After the moisture leaves the particle, the dry portion of the particle starts to decompose due to external heating. This process is referred to as pyrolysis. Different approaches for modeling the kinetics of pyrolysis have been adapted in the literature. Di Blasi [6] provided a comprehensive review on the kinetics of pyrolysis of biomass. In general, four categories of reaction mechanisms can be identified for biomass pyrolysis: global mechanisms with single-step chemistry, e.g., [12], global mechanisms with three parallel reactions [13]; Functional Group-Depolymerization, Vaporization Crosslinking (FG-DVC) models [14, 15] and multi-component semi-detailed mechanisms [16, 17]. Figure 2 shows a schematic view of the different pyrolysis mechanisms.

The pyrolysis products are usually lumped in three main groups: gas, tar and char. Among others, a review by Neves et al. [7] suggests that depending on the heating rate and reactor temperature, the yield of pyrolysis products may vary significantly. Low temperature pyrolysis can lead to more fixed carbon residue (char), while a high heating rate promotes the formation of gas and tar. The compositions of tar, char and gas are a complex function of various factors, including the elemental mass fractions of carbon, hydrogen and oxygen in the fuel, the particle size, the reactor temperature and the structure of the fuel. The primary

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gas species produced from pyrolysis are CO2, CO, H2, CH4, C2H4 and H2O. Tar is composed of several high molecular weight molecules such as aliphatic hydrocarbons and aromatic and phenolic compounds, which at room temperature are in liquid form.

Figure 2. Schematic view of different pyrolysis schemes; (a) single-step, (b) three parallel with secondary reactions; (c) FG-DVC, and (d) multi-component semi-detailed

The heterogeneous reactions of char are the rate controlling processes in the

overall conversion of biomass. The overall reaction rates of char depend on the following chemical and physical processes: the transport of reaction agents through the external boundary of particle or film diffusion, diffusion through the ash layer, the transport of reaction agents inside the pore structure of char and intrinsic kinetic rates. The intrinsic kinetics rates are referred to those rates that are not influenced by transport processes.

Depending on which of the above processes is controlling the reaction rates, three different burning regimes or zones are distinguished for char combustion and gasification. The Zone I reaction is a regime where the chemical reactions are limiting the reaction rate. In the Zone III reaction regime, the mass loss rate is limited by the rates of oxygen and gasification agents’ diffusion to the outer surfaces of the particle. In the Zone II regime, the characteristic rates for pore

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diffusion and chemical reactions are of similar magnitudes, and both effects are important in determining the mass loss rate.

The changes in the char structure, the distribution of active sites and the catalytic effect of minerals have strong influence on the char reactivity, which introduces great challenges in the modeling of char conversion. To deal with this problem, the reaction rates of char are usually expressed considering two separate effects: the effect of temperature and partial pressure of the gasifying/oxidizing agents and the effect of the specific surface area of the particle,

ℜ = ℜ (푇, 푝 )푓(푋 ),

where 푋 is the char conversion and 푓(푋 ) takes into account the changes in the particle specific surface area as the conversion proceeds. In the expression above, it is assumed that the intrinsic kinetic rates are independent of conversion, which holds only for homogeneous distribution of active sites and minerals inside the char structure. However, in the empirical formulation of 푓(푋 ) these effects are included as it is obtained by fitting the char reactivity to a certain experimental data.

In addition to the chemical and transport phenomena, changes in the structure of biomass during conversion are very important. During its thermochemical conversion, a biomass particle may undergo fracturing and fragmentation at any stages of conversion, i.e., pyrolysis and gasification. Fragmentation process can be divided into two main stages; primary fragmentation and peripheral fragmentation. Primary fragmentation is referred to breakage of particle during the pyrolysis process by forming fractures and smaller particles. Peripheral fragmentation is disintegration of the char particle from its surface. As fragmentation results in producing smaller particles, it can change the overall combustion behavior of the solid particles. Furthermore, the emission of aerosol and flying ash increases due to fragmentation. This indicates the importance of understanding the fragmentation process. The extent and the source of fragmentation depend on several factors such as the particle size and porosity, the biomass type, the volatile content and the furnace temperature. Several studies, mainly focused on coal particles, have been carried out to clarify this process. Several mechanisms have been proposed regarding the source of the particle fracturing and fragmentation such as:

Fractures caused by pressure build-up during the pyrolysis stage Thermal stress induced fractures Compressive stress due to particle shrinkage Attrition due to particle collision or packed bed height pressure Loss of structural integrity due to heterogeneous reactions One or several of the mechanisms mentioned above can cause fragmentation.

The possibility of fragmentation, the time and location of the fractures and the distribution of the smaller particles produced from the fragmentation were subject

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of many numerical and experimental studies. Here, a brief overview of different numerical approaches will be presented.

As coal was one of the major energy sources for a long time, various studies have been carried out on coal primary fragmentation in different combustion systems such as pulverized coal furnaces [18, 19] and fluidized bed furnaces [20, 21]. For the early stage or primary fragmentation, thermal stress and pressure induced fragmentation are introduced as the main mechanisms. The thermal stress due to temperature gradient inside the particle was reported as the main mechanism for fragmentation [22-24]. The volatile pressure built up was also considered as the fragmentation source [21, 23]. During coal particle pyrolysis, an internal pressure as high as 150 bar can be built up inside the particle. For biomass particles, on the other hand, in spite of the high volatile content, the higher permeability of wood structure prevents high volatile pressure built up as compared with coal. As discussed by Sreekanth et al. [8], it is not clear whether this low volatile pressure (2-3 bar) for biomass can cause primary fragmentation. Consequently, Sreekanth et al. [8] proposed that the high shrinkage of biomass particle, up to 50%, can be one of the sources of primary fragmentation in the later stages of pyrolysis.

Peripheral fragmentation, in contrast to primary fragmentation, is mainly due to the loss of structural integrity during the char heterogeneous reactions, i.e., char oxidation and gasification. When the particle porosity reaches a critical value, namely the percolation threshold, the remaining structure may loss its macroscopic connectivity and the particle can break into hundreds or even thousands of smaller particles at the surface and the particle radius shrinks. This phenomenon is called percolative fragmentation. Depending on the regime in which the char particle is reacting, the particle porosity and density may change. For a particle burning in the chemical kinetic control regime, the particle porosity reduces throughout the entire particle and uniform percolation may disintegrate the whole particle structure. When a particle is in the diffusion control regime, i.e., high temperature oxidation of char, the peripheral percolation up to the penetration depth of oxygen may occur [25]. The peripheral fragmentation is studied, among others, by Feng and Bhatia [26], Miccio [27], Hurt and Davis [28], Golfier et al. [29].

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PHYSICAL PROCESSES AND MATHEMATICAL MODELING

Modeling approach

Different types of models have been developed to study thermochemical conversion of biomass with certain simplifying assumptions depending on the model purpose. When modeling the biomass and char conversion, there are different issues that need to be considered. In general, models concerning thermal degradation of biomass assume a uniform porosity while distribution of the pore structure is one of the main concerns in char conversion modeling. The level of complexity of the model depends on the specific case of interest. Non-dimensional analysis can provide useful information on the assumptions and simplifications that can be made for modeling of a given case.

In some special cases the heat and mass transfer or the chemical kinetic rate is the controlling phenomenon. In these cases some simplifications can be made regarding the calculation of certain conversion parameters. To define non-dimensional numbers, first the characteristic rates of reactions as well as the rates of internal and external heat transfer should be defined. Note that here the term “reaction” is used liberally to include drying, pyrolysis and char reactions. The characteristic pyrolysis reaction rate can be expressed as a first order Arrhenius rate. For char on the other hand, the reaction rate may be expressed as per unit of the reacting surface. Then a total reacting surface per unit of mass can be used to express the reaction rate in per second unit. The external heat transfer depends on the convection heat transfer coefficient (ℎ ), the particle density (휌 ), specific heat (푐 ) and the characteristic particle size 푙 = 푉 /퐴 . The internal heat transfer depends on the effective thermal conductivity (푘 , ) of the particle. The following equations describe the characteristic rates of pyrolysis (푅 ), external heat transfer (푅 , ) and internal heat transfer (푅 , ),

푅 = 퐴 exp −퐸ℛ푇 , (1)

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푅 , =ℎ휌 푐 푙 , (2)

푅 , =푘 ,

휌 푐 푙. (3)

The corresponding dimensionless numbers for these specific rates are listed in Table 1 [10]. Thermal and mass Biot number, 퐵푖, quantifies the relation between the internal and external heat and mass transfer. Damköhler number, 퐷푎, for solid particle compares the rate of reactions and the internal or external heat or mass transfer to the particle. For instance, a thermal Biot number that is smaller than unity indicates that the external heat transfer rate is smaller than the internal heat transfer rate. Hence the temperature can be assumed uniform in the entire particle and the particle heating is controlled by the external heat transfer rate. Similarly, a pyrolysis Damköhler number that is larger than unity implies that the pyrolysis process is limited by the heat transfer rate rather than the kinetic rate.

Based on this non-dimensional analysis, expressions to estimate the time of drying and pyrolysis for asymptotic cases can be extracted. Gómez-Barea and Leckner [10] provided these expressions for a variety of asymptotic situations a particle may encounter. Classifications of combustion regimes in a packed bed, based on these non-dimensional numbers is provided in [30]. Table 1. Definition of dimensionless numbers

Thermal 퐵푖 External/Internal heat transfer rate 퐵푖 = ,

,=

Mass 퐵푖 External/Internal mass transfer rate 퐵푖 = ,

,=

Thermal 퐷푎 Reaction/Heat transfer rate; Internal 퐷푎 , =,

External 퐷푎 , =,

Mass 퐷푎 Reaction/Mass transfer rate; Internal 퐷푎 , =

External 퐷푎 , =

As discussed earlier using the non-dimensional numbers provided above,

some simplifications can be made when modeling the biomass conversion under certain conditions. The simplest model developed for conversion of biomass [31, 32] and char [33] is the unreacted shrinking core model as presented in Figure 3. This model assumes that pyrolysis or char conversion takes place at an

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infinitesimally thin surface propagating from the surface of the particle towards the center. When the reaction front passes through any given point in the particle, the conversion is completed and a char layer, in the case of pyrolysis, or an ash layer, in the case of char conversion, will remain.

This means that across the reaction front there is a sudden change in the properties of the solid medium. In the case of pyrolysis the properties of the solid medium change from biomass properties to char properties and in the case of char conversion, from char properties to ash properties. For pyrolysis modeling, both finite rate chemistry in the form of Arrhenius and infinite rate chemistry in the form of constant temperature for pyrolysis have been used within the framework of this model [34]. For char conversion, the rate of diffusion of oxygen through the gas film at the particle boundary, the rate of diffusion of oxygen through the ash layer and the chemical kinetic rates can be taken into account when calculating the conversion rate [35]. This model is also modified to include the moisture evaporation process by assuming constant-temperature evaporation [32, 34].

An estimation of the thickness of the reaction front as 푘 , ∆푇/푞 is given in [31] where ∆푇 is the temperature difference across the reaction front and 푞 is the heating rate. For the assumption of infinitely thin reaction front to be valid, the heat flux to the particle should be sufficiently high. This assumption is more suitable for reaction of char with oxygen at high temperatures or pyrolysis under high heating rates. In case of a slow reaction (kinetic control regime), the model assumption is not valid.

For particle with low ash content or in the case of a fluidized bed where the particle dynamics does not allow for any ash layer to be formed around the particle, an unreacted shrinking particle model may be used. The assumptions are similar to the ones for the unreacted shrinking core model, except that the external radius of the particle will shrink according to the mass loss. These models assume a non-porous structure for the particle. The particle density remains constant and the particle or the core radius decreases in proportion to the particle conversion to the power of 1/3 [36, 37].

A uniform conversion model is another approach valid for 퐵푖 ≪ 1, where the internal field of gas species and temperature are uniform throughout the entire particle. In this model the particle size remains constant and the density decreases in proportion to the particle conversion.

14

Figure 3. Schematic view of unreacted shrinking core model for char reaction and pyrolysis

For slow reactions or a high porosity char where neither the infinitesimal reaction front nor uniform-temperature field assumption is valid, progressive models are developed. Depending on the behavior of the ash, two types of progressive models have been proposed, shrinking particle progressive model and shrinking core progressive model [10, 35]. The solution of the differential equations for species gas profile inside the particle is required for this type of models. The difference between these models and models with the assumption of infinitesimal reaction front is the presence of a broader reaction zone that can grow inwards from the surface to the center of the particle. In this situation, both the particle size and density will change with the particle conversion. The power-law relations [38] may be used to provide the relation between changes in the particle density and the particle size in case of char reaction.

In addition to the simplified models mentioned above, a spatially resolved model for particle conversion has been developed for pyrolysis [39-43], for the entire biomass conversion [44-47] or char conversion [48]. The main features of these spatially resolved models suggested in the literature are the same. These models consider transient partial differential equations for the mass and the energy equations and use the momentum equation in the form of the Darcy law. Although they differ in some details, the basic assumption for these studies is the assumption of continuum.

In continuum models the macroscopic properties such as temperature and species concentrations are smooth functions of time and space. These types of

15

models denote the classical engineering approach which employs the concept of volume averaging to describe a system which is characterized by several length scales. The volume in which the macroscopic properties are represented by average values should be small enough compared with the characteristic length scale of the system such as scalar gradients and large enough compared with the length scale of the porous structure, e.g., pore radius, so that the transport equations would be valid in this volume. The concept of volume averaging introduces some restrictions on employing the continuum models. For instance, in a system with large, disconnected voids or drastic changes in the connectivity of the media, the continuum models are not well suited.

Another approach which is free from the limitations and assumptions of the continuum approach is to use discrete models. Discrete models are based on the percolation theory which deals with the concept of a spread of a hypothetical fluid through a random medium [49]. In these models, the particle is represented by two or three-dimensional random networks of large number of interconnected pore bodies and pore throats. The transport and reaction phenomena in this system can then be studied in a more realistic way by employing the ideas of statistical physics of disordered media. The main disadvantages of these models are the required previous knowledge of the microstructure of the porous system and their high computational costs. These models will not be elaborated here. Readers are referred to [49] for a comprehensive review on these models.

Although due to convenience and the lack of practical alternatives, the continuum approach has been used widely in coal/biomass combustion modeling, one should bear in mind the limitations of this approach, i.e., the porous system should be connected while the pores are small enough to allow for a meaningful volume averaging.

The model developed in this study lies within the category of the continuum approach and the governing equations in the continuum model framework will be presented. The particle is represented by a one-dimensional system consisting of a solid structure with void spaces filled with liquid and gas.

Basic assumptions

As discussed in previous Chapter, thermochemical conversion of biomass is a complex process. At the moment, a comprehensive mathematical description of the process still requires substantial simplifications for various processes involved. The model presented in this study is based on the following assumptions:

The biomass particle consists of multiple components, including solid, gas and liquid

All these components are in thermal equilibrium

16

The particle geometry can be spherical, cylindrical or slab (parallelepiped plate) and it is represented in a one dimensional frame work

Gases inside the porous structure of the particle obey the ideal gas law The momentum transport in the particle is governed by the Darcy law Homogeneous gas reactions inside the particle are neglected For a system of solid, liquid and gas, under the model assumptions stated

above, the conservation of mass for solid and liquid phases are governed by the following equations:

휕휌휕푡 = ℜ , (4)

휕휌휕푡 =

1푟 ∇ ∙ 푟 퐷 ∇휌 + ℜ , (5)

where 휌 is the density, 퐷 is the diffusion coefficient, and ℜ is the mass release rate source term. This system of equations is valid for an arbitrarily shaped particle within a one dimensional framework. Therefore, 푟 is the distance from the particle center and 푛 is the Lamé coefficient accounting for a non-Cartesian coordinates system: 푛 = 2 for spherical, 푛 = 1 for cylindrical and 푛 = 0 for large slab plate shaped particles. The right-hand side terms are the source terms, which are described for each process in the following Section. The conservation of gaseous species and mass and energy are as follows:

휕휕푡 휀휌 푌 +

1푟 ∇ ∙ (푟 푁 푌 ) = −

1푟 ∇. (푟 퐽 ) + 휗 , ℜ , (6)

휕휕푡 휀휌 +

1푟 ∇ ∙ (푟 푁 ) = 휗 , ℜ , (7)

휌 푐 + 휌 푐 + 휌 푐 + 휀휌 푌푐휕푇휕푡 + 푁 푌푐 ∇푇

=1푟 ∇ ∙ 푟 푘 ∇푇 +ℜ ,

(8)

where 푁 is the total convective flux, 퐽 is the diffusion flux of species 푖 and 휀 is the void fraction. 푌 and 휗 , are the mass frction of species 푖 and the stoichiometric coefficient of species 푖 in reaction 푘, repectively. The energy equation as presented in Eq. (8), is derived from the enthalpy form of the energy

17

conservation and ℜ is the heat source term appearing when writing the equation in the temperature form. The source term include the heat of reaction of different processes and the changes in sensible enthalpy as presented in the following equation,

ℜ = ℜ ℎ° − ℎ° + ℜ∈

ℎ° − ℎ°

∆

+ ℜ ℎ° − ℎ°

∆

+ ℜ ℎ° − ℎ°

∆

+ℜ ℎ° − 푌ℎ°

∈ →

∆

+ ℜ ℎ° − ℎ°

∆

+ ℜ ℎ° − 푌ℎ°

∈

∆

+ ℜ 푐 − 푐 푑푇

+ ℜ 푐 − 푌푐 푑푇 + ℜ 푐 − 푐 푑푇

+ ℜ 푐 − 푐 푑푇

+ ℜ 푐 − 푌푐 푑푇

+ ℜ 푐 − 푐 푑푇

+ ℜ 푐 − 푌푐 푑푇 ,

(9)

where ℎ° is the enthalpy of formation and ∆ℎ is the heat of reaction. The derivation of energy equation is presented at the end of this Chapter. The enthalpy of formation of biomass, char and tar are related to their lower heating values

18

(LHV) upon their complete reaction with oxygen. If the 퐶푥퐻푦푂푧 represents either biomass, char or tar, the enthalpy of formation is as follows,

퐶 퐻 푂 + 푥 +푦4 −

푧2 푂 → 푥퐶푂 +

푦2퐻 푂, (10)

ℎ° = 퐿퐻푉 +1

푀 휗 푀 ℎ ,° , (11)

where 푀 is the molecular weight and 휗 is stoichiometric coefficient, e.g., 푥 for 퐶푂 . If the lower heating values are not known, the correlation of Channiwala and Parikh [50] for biomass and char and correlation of Mason and Gandhi [51] for tar provides the heating values with good approximation,

퐻퐻푉 / = 34.9푌 + 117.8푌 + 10.05푌 − 10.3푌 − 1.5푌 − 2.1푌 푀퐽푘푔 , (12)

퐻퐻푉 = 34.1푌 , + 132.3푌 , − 12푌 , 푀퐽푘푔 , (13)

where 퐻퐻푉 is the higher heating value. The reaction rates are presented in the following Section.

Kinetic rates

There are three stages of mass loss during the thermochemical conversion of biomass describing the reaction source terms in the governing equations, drying, pyrolysis and char reaction. The liquid mass conservation is governed by the Eq. (5) where the moisture diffusivity (퐷 , ) inside the particle porous structure depends on the moisture mass fraction and temperature [5],

퐷 , = 푒푥 푝 −9.9−4300푇 + 9.8푌 . (14)

The evaporation source term is based on the equilibrium model that is shown to perform well at different conditions [43]. The model can be mathematically presented as,

ℜ = ℎ , 푆 휌 , − 휌 , , (15)

19

where 휌 , is the saturation vapor density calculated based on the Clausius–Clapeyron relation for the saturation pressure and 휌 , is the partial density of water vapor in the pores of the particle. 푆 is the specific surface area of the particle available for moisture and vapor diffusion. ℎ , is the mass transfer coefficient of vapor in the pores of the particle, which can be determined using the following equation [45],

ℎ , =3.66퐷 ,

푑 , (16)

where 푑 is avarage pore diameter. The dry solid particle (or biomass) mass degradation is governed by Eq. (4), where the source term is calculated according to a pyrolysis mechanism. In general, the pyrolysis reaction is presented as follows,

휕휌휕푡 = −휌 푘 = ℜ , (17)

where 푘 is the rate of reaction 푘 in Arheneous form. If any intermediate solid species are considered by the mechanism, the mass conservation yields,

휕휌휕푡 = 휌 푘 − 휌 푘 . (18)

Two secondary reactions are assumed, converting tar to char and gas,

휕휌휕푡 = −휌 푘 + 푘 = ℜ +ℜ . (19)

Three heterogeneous reactions are considered for char;

퐶 + 휗 푂 → 2 1− 휗 퐶푂 + 2휗 − 1 퐶푂 , (푅 )

퐶 + 퐶푂 → 2퐶푂, (푅 )

퐶 + 퐻 푂 → 퐶푂 +퐻 , (푅 )

where 휗 is the stoichiometric coefficient which depends on the reaction temperature and is evaluated by empirical correlations. The first reaction is the oxidation of char, whereas the second and third are the main reactions in char

20

gasification. The heterogeneous char reaction rates are presented in the following form,

ℜ = 푀 휗 , 푆 푘 , 퐶 , (20)

where 푘 , is the intrinsic rate of conversion per unit area of the carbon in reaction 푘 (푅퐶1 −푅퐶3) and 푖 = O , CO , H O. 푀 is the carbon molecular weight, 푆 is the specific internal surface area of the char pores structure, 휗 , is the stoichiometric coefficient of carbon in reaction 푘, 퐶 is concentration of species 푖 and 푛 is the reaction order.

Fluxes

The diffusion and convection fluxes play an important role during the heterogeneous char reactions. During devolatilization and drying, these fluxes have a direct impact on the pressure built up inside the particle which may or may not cause fractures and fragmentation.

There are different approaches for modeling the transport inside a porous media [52]. In general, two main approaches used extensively in biomass conversion models are extension of the Fick’s law and the Dusty Gas Model (DGM). In both of these models the Knudsen diffusion, molecular diffusion and effect of pressure gradient can be taken into account. DGM is based on the Stefan-Maxwell equation for diffusion and the convection due to pressure gradient. It is not possible to derive an explicit equation from DGM to compute fluxes and therefore a numerical solution is required to solve the nonlinear system of equations. On the other hand, the Fick’s law model has the advantage that explicit analytical expressions can be derived for fluxes. In addition, the deviation between the two models in calculating the fluxes in porous structure have been reported to be negligible [53].

Fick’s law and Darcy flow

When there is a pressure gradient contributing to the total flux of species, a Darcy law equation can be added to the classical Fick’s law resulting in an extension of the Fick’s law model,

21

푚̇ = −휌 퐷 ,휕푌휕푟 +

퐾휌 푌휇

휕푃휕푟 , (21)

where 푚̇ is the total mass flux of species 푖 in gas phase, 퐾 is the permeability, 푃 is the pressure and 휇 is the gas viscosity. Permeability is a measure of mass transfer resistance inside the pores structure of biomass [54].

The diffusion and convection fluxes in Eqs. (6)-(8) can be expressed as follows,

퐽 = −휀휌 퐷 ,휕푌휕푟 , (22)

푁 =퐾휀휌휇

휕푃휕푟 . (23)

Using Eq. (23) the gas velocity can be obtained,

푢 =퐾휇휕푃휕푟 . (24)

In Eq. (11), 퐷 , is the effective diffusion coefficient. 퐷 , takes into account the molecule-wall interaction in small pores (Knudsen diffusion) and molecular diffusion as well as the effect of porosity and tortuous structure of capillaries based on the following equations,

퐷 , =휀퐷휏 ,

1퐷 =

1퐷 +

1퐷 ,

,

(25)

where 퐷 is the Knudsen diffusion coefficient, 퐷 , is a the diffusion coefficient of species 푖 into a mixture of other species 푚, and 휏 is tortuosity, which can be estimated by 휏 = 1/휀 [55]. The Knudsen diffusion coefficient is dependent on the pore radius and is calculated based on the following expression,

퐷 =2푟3

8ℛ푇휋푀 , (26)

where 푀 is the molecular weight of species 푖. Note that Eq. (26) is independent of mixture composition as it depends on the molecular weight of each species

22

individually. 퐷 , depends on the gas composition and temperature which can be calculated based on the binary diffusion coefficient of each species in the mixture,

퐷 , =1 − 푌

∑ 푥퐷

(27)

where 푁 is the total number of gas species. The temperature effect is included in the binary diffusion coefficients, 퐷 . For simplification, the mixture diffusion coefficient can be expressed as a function of temperature which provides sufficient accuracy [56],

퐷 , = 퐷 = 퐷 ,푇푇

. 푃P (28)

where 퐷 , is the diffusion coefficient at reference temperature 298.15퐾 which is equal to 2 × 10 푚 /푠. Figure 4 shows the diffusion coefficients for individual species in the mixture together with the mixture diffusion coefficient as a function of temperature obtained based on Eq. (28). Except for highly diffusive hydrogen, the correlation for the mixture diffusion coefficient is close to the diffusion coefficient of each individual species in the mixture.

Figure 4 Mixture diffusion coefficient as a function of temperature

Porosity

Biomass conversion can be studied as a process in a porous medium in which the physicochemical interaction of a fluid with a porous structure leads to continuous evolution of the solid structure. This process involves several length scales which

23

depending on the shape, size and morphology of the structure can play a fundamental role in transport and reactions in the system. The simplest quantity that can characterize the state of a porous system is the volume fraction. The volume fraction can be defined for as many phases as exist in the system. For phase 휂, gas, liquid or solid, one can write,

휀 =푉푉 , (29)

where 푉 is the total volume of the system. The total porosity in the framework of this study is the sum of the gas and liquid porosities,

휀 = 휀 + 휀 . (30)

It worth noting that the moisture content of the particle is treated as liquid when existing in excess to the free water continuity point (around 45% on dry basis).

The time evolution of porosity is represented by the following equation,

휕휀휕푡 =

1휌 휗 , ℜ (31)

where 휌 is the non-porous solid density. To obtain Eq. (31) it is assumed that the true solid density is constant. During drying and pyrolysis stages, as the remaining solid has a different structure from the original one, this assumption is not valid. The change in the solid structure may cause particle shrinkage. The effect of the particle shrinkage should be included in Eq. (31). As changes in the porosity and particle shrinkage are linked together, an empirical correlation is used for the particle shrinkage.

Figure 5. The relation between mass loss and changes in volume during particle shrinkage

Two different types of shrinkage are distinguished in this study: volumetric shrinkage and peripheral shrinkage. While the volumetric shrinkage is caused due

24

to the structural reordering of the solid, the peripheral shrinkage is a result of the structural disconnection from the outer radius of the particle.

For the volumetric shrinkage, a linear change in the particle volume is assumed with respect to the mass loss during each process. The shrinkage factor 휃 relates the volume change to the release of the biomass components namely moisture, volatiles and char. The slopes of these linear functions are empirically determined,

휃 = 1 + (1− 휃 )휌휌 ,

− 1 + 휃 (1− 휃 )휌휌 ,

− 1 + 휃 휃 (1− 휃 )(휌휌 ,

− 1), (32)

where 휃 is defined as the ratio between the current volume of the particle to its initial volume.휃 , 휃 and 휃 are empirical parameters with values between a minimum value and 1, representing the extent of shrinkage due to moisture evaporation, volatiles release and char reactions, respectively. A minimum value represents a constant density and a value of one represents a constant volume during thermochemical conversion. The minimum value for 휃 is the mass fraction of moisture in as received basis of the particle and minimum value for the volatile release is the mass fraction of final char. The ash mass fraction is the minimum value for 휃 . The subscript 0 denotes the initial state of the particle.

The effect of shrinkage on the porosity is taken into account by adding a pseudo-convective term to Eq. (31), where the corresponding “velocity” for this convective term is the rate of particle volume change,

휕휀휕푡 = −

휀휃휕휃휕푡 +

1휌 휗 , ℜ . (33)

Peripheral fragmentation occurs when the porosity of the particle exceeds a critical value, 휀 . The particle radius (푅 ) then decreases according to the following equation,

=

⎣⎢⎢⎢⎡

⎦⎥⎥⎥⎤

푤ℎ푒푛휀 > 휀 . (34)

The flux of detached char fragments (퐹 ) that leaves the particle is given by [57],

25

퐹 = 휌∗ . (35)

where 휌∗ is the apparent char density at the onset of fragmentation.

Specific surface area

Although porosity provides some information regarding the state of the system, it cannot provide any knowledge on the morphology of the system such as the amount of surface of the porous structure accessible by other phases or the distribution of the pores radius in the structure. For situations that transport or reaction phenomena take place at the surface of the system, such as in char conversion, the interfacial surface density is an important parameter which can be defined as [49]:

푆 =퐴푟푒푎표푓푐표푛푡푎푐푡푏푒푡푤푒푒푛푝ℎ푎푠푒휂푎푛푑휎

푉표푙푢푚푒표푓푡ℎ푒푠푦푠푡푒푚푉 . (36)

This variable is referred to as the specific surface area and as it only appears in the equations during the char conversion, the following discussion only concerns the char particle.

There are different theories developed for representing a porous medium. Capillary models are by far the most commonly used models in this field [49]. One of the well-known theories in capillary models is the random pore model (RPM) developed by Bhatia and Perlmutter [58, 59] and Gavalas [60]. The RPM assumes cylindrical capillaries randomly located and oriented with any distribution of pore radii. The surface area of the structure may increase due to the surface reactions or decrease due to different capillaries overlapping. The specific surface area is related to the conversion degree of carbon structure based on the following equation,

푆 = 푆 , (1− 푋) 1− 휓 ln(1 −푋). (37)

where 푆 , is the initial specific surface area, 푋 is the carbon conversion and 휓 is the structural parameter depending on the carbon structure which can be determined using the original pore size distribution. However, it is usually estimated by fitting to measured experimental data.

For coal, RPM predicts a maximum in the specific surface area as the conversion proceeds. The specific surface area first increases as the pore radius is enlarged due to the ongoing reactions and at a certain point, starts to decrease as the pores merge and coalesce. For biomass, on the other hand, some experimental

26

evidence shows a constant or a continuously increasing trend for the specific area during the conversion. Dasappa et al. [61] measured the specific surface area of different biomass chars at various conversion degrees, up to 80% conversion, using the BET technique. The specific surface area varied weakly as the conversion proceeded. In another experiment, Lussier et al. [62] reported a constant adsorbed hydrogen concentration between 0.5% and 40% conversion of Saran char. A continuous increase in the “reactive” surface area was reported in [63] for the beech wood char.

The reason for these different behaviors can be the different origin of coal and the biomass char. Coal is formed under pressure and heat which cause the structural order of the original source to be destroyed during the process of formation. Biomass char usually has two orders of magnitude greater specific surface areas than coal. Hence wood chars present a remarkably regular structure similar to a beehive network, whereas the coal chars are characterized by highly random structures due to their origin [61]. Because of these differences, the theories originally developed for evolution of a pore structure of coal during the conversion may fail for biomass [64].

Because of the insufficient experimental data and the contradictory results, it is hard to draw a conclusion on the evolution of the surface area. In addition, other complexities such as formation of cracks and presence of ash bring more difficulties to the problem. Some simple models have been used in the literature, one of which assumes a constant specific surface area during the conversion [44, 45]. This model produces good results for high-temperature oxidation, where the boundary diffusion plays a more important role and the evolution of the internal surface area is of less importance. Mermoud et al. [64] developed a simple model based on the assumption that the surface area increases in a way that the conversion rate of a gasifying char remains constant. This model showed good agreement with the few experimental data that were obtained for up to 60% conversion, c.f. Figure 6. In another study, Dasappa et al. [61] argued that assuming a monotonous increasing pore size without any merging and coalescing is more relevant for the ordered structure of wood than using the RPM that was originally developed for coal. This assumption implies that the specific surface area increases continuously. This model is based on the classical capillary tubes model which relates the specific surface area to the porosity and pore radius 푟 by the following equation,

푆 =2휀푟 . (38)

By some mathematical manipulations and the assumption that the pores grow due to the radial expansion, one can relate the specific surface area to the carbon conversion,

27

푆 = 푆 , 1− 푋(1−1휀 ). (39)

In Figure 6 a comparison between the RPM, capillary model and constant reaction rate model is presented together with some experimental data. As discussed previously, there is not enough data to draw a firm conclusion about which model is the most suitable for biomass conversion. However, the RPM can be ruled out, as none of the experiments suggest a remarkable decrease in the specific surface area as the conversion proceeds.

It should be noted that not the entire available surface area participates in the reactions. The concentration of active sites on the char surface is an important parameter in char conversion kinetics and it is expected that the reactions take place only on the surfaces where the oxygen-complexes are formed [35]. Despite many attempts at measuring the active site area (ASA), e.g., [65], there are difficulties in correlating the ASA with the carbon gasification reactivity [66]. As a result, the reason for increasing specific surface area versus conversion may be due to the increase in concentration of the active sites.

The model based on the classical capillary tubes shows acceptable behavior compared with the experimental data and therefore it is used in this study. Based on this model, the volume fraction and pore radius increase with the rate of char conversion. Based on Eq. (38), the rate of increase in surface area yields,

휕푆휕푡 = ℜ /푟 . (40)

Figure 6. Evolution of specific surface area of some biomass driven char at different conversion degree

28

Multi pore structure

There are three distinct groups of pores in the particle structure; Macro-pores (> 50 푛푚 diameter) Meso-pores (2-50 푛푚 diameter) Micro-pores (< 2 푛푚 diameter) The reactions are taking place mainly in macro and meso pores. Although the

contribution of micro-pores in the void fraction is high, their contribution to the conversion is limited due to the limited accessibility to the reactants. Therefore, the entire initial surface may not contribute to the reactions. On the other hand, the accessibility of the micro-pores may increase as the conversion proceeds due to the increase in the pore radius.

Char can undergo different reactions with CO2, H2O and O2. It was observed that different reactants behave differently in micro-pores. Hurt et al. [67] reported that the char reaction with CO2 primarily takes place outside the micro-porous network and according to Ballal and Zygourakis [68] micro-pores are not accessible to O2. On the other hand, H2O can penetrate in small pores that are not accessible to oxygen [69]. The above discussion suggests that during the char conversion different pores may evolve with different rates and their accessibility to certain reactants may change during the conversion.

To take into account the various pore sizes, a pore size distribution is assumed for the char particle. The pore sizes are divided into discrete bins of initial porosity 휀 (푟 ) corresponding to the pore radius, 푟 , distribution. Similar to the work of Singer and Ghoniem [48, 70], a variable 푞 is assumed which indicates the radial expansion of pore 푖 at each time caused by the char conversion. By assuming that the reactions take place on the pore surface, the solid-phase conversion can be rewritten in terms of time variation of 푞 ,

푑푞푑푡 =

1휌 휈 , ℜ , , , (41)

where ℜ , is the intrinsic reaction rate of the char reactions. The pore radius at each time is given by,

푟 = 푟,

+ 푞 . (42)

To identify the degree of participation of each pore in the reactions, the concept of pore scale Thiele module for individual capillary was developed by Gavalas [60]. The effectiveness factor based on the Thiele module is employed here. The effectiveness factor can verify whether or not a pore with a radius of 푟 is in the kinetic control regime. For a first order reaction with an intrinsic rate

29

constant of 푘 , and an effective diffusion of 퐷 , , the Thiele module Φ is given by,

Φ , =푙2

2휈푘 ,

푟 퐷 ,, (43)

where 푙 is the length of the pore 푖. Note that the Thiele module is different for each reaction and each pore radius. The effectiveness factor is given by,

휂 , =tanh(Φ , )

Φ ,. (44)

The effectiveness factor quantifies the participation of each reaction for each pore size, which can be used to modify the pore growth rate,

푑푞푑푡 =

1휌 휂 , 휈 , ℜ , , . (45)

Equation (31) can now be employed for each porosity bin 휀 ,

푑휀푑푡 =

푆휌 휂 , 휈 , ℜ , , , (46)

where 푆 is the specific surface area corresponding to 휀 and 푟 . The effective diffusion for each pore 푖 can be obtained based on the

combined Knudsen, Eq. (26), and bulk diffusion, Eq. (27). Contribution of each pore size in the total effective diffusion coefficient then should be considered. In a slightly different context, Wakao and Smith [71, 72] presented a relation for the diffusion coefficient in a porous catalyst. By assuming that the micro-pores are distributed in the solid structure between the macro and meso pores, the contribution of each group of pores in diffusion can be calculated based on the following equation [73],

퐷 = 휀 퐷 , + 2휀 휀1

1퐷 ,

+ 1퐷 ,

, (47)

where effective diffusion coefficient for each pore radius is,

퐷 , =1

퐷 ,+

1퐷 ,

. (48)

30

Ash layer around the particle

The ash liberated from the particle during the char conversion can form a layer around the particle. This layer affects the char conversion by restricting the oxygen diffusion to the particle. Moreover, the particle radius changes due to the ash layer which has an impact on the heat transfer rate to or from the particle. Two important parameter of ash should be considered, the ash thickness and ash porosity, the first one affects the heat balance and the second one affects the species concentration.

It is assumed that the ash evaporation or reaction has no effect on the temperature of the particle. In other words, in the particle model the ash is assumed inert. Moreover, it is assumed that the ash is distributed uniformly inside the particle and is liberated as the char reaction proceeds. If 휌 denotes the ash density inside the particle structure and 휌 , represents the density of liberated ash in the particle surface,

푑휌 ,

푑푡 = 휌 푌푎,0 ℜ , − 휌 , ℜ , , (49)

where 푌 , is the initial ash mass fraction inside the particle and ℜ , is the rate of ash evaporation.

The thickness of ash is defined as the char (core) radius minus particle radius and depends on the ash porosity. By assuming a uniform distribution of ash inside the particle, the ash thickness can be obtained according to the following equation [57],

푅 푣 = 푅 푣 + 3 푟 (1− 휀 )푑푟, (50)

where 푣푎푠ℎ is the ash volume fraction and it depends on the initial ash mass fraction, initial particle apparent density (휌 , ) and true density of ash (휌 , ),

푣 =푌푎,0휌 ,

휌 ,휃 , , (51)

where 휃푐,0 is the extent of particle shrinkage at the start of char reactions, as it is assumed that ash is liberated by char reactions. In Eq. (50), 푅0 is the radius of particle at the instant of char reaction initiation.

Hurt et al. [74] assumed that before the ash layer reaches a critical thickness (100 휇푚), it is in the form of detached grains. They proposed a relation for the ash porosity of these detached grains. When the thickness of ash layer is above the

31

critical value, the porosity remains constant. The correlation is developed base on the observation for pulverized coal particles. The correlation is suitable for a particle in the pulverized regime. Here it is assumed that the ash is formed with the same porosity as char. The ash porosity, on the other hand, can change with time due to ash melting. With the assumption that the ash porosity is uniform in space, Eq. (50) yields,

푑푅푑푡 =

푅 (1− 휀 )− 푣푑푅푑푡 + 3 푅 − 푅 푑휀

푑푡푅 (1− 휀 ) , (52)

where 푑휀푎푠ℎ/푑푡 represents the variations in the ash porosity due to the ash melting. By assuming that the ash porosity is linearly decreasing in time when the ash is exposed to a temperature higher than melting temperature, the following equation yields the ash porosity [48],

휀 = 휀 , − Υ푑푡

1 + 푒푥푝 −10(푇 − 푇 ), (53)

where Υ is the ash melting rate and 푡 is the time that the ash is exposed to temperature higher than the melting temperature (푇푚푒푙푡).

The effective diffusion coefficient through the ash layer is related to the ash porosity according to the following equation [74],

퐷 , = 퐷 , 휀 . . (54)

The effect of Knudsen diffusion through the ash layer is neglected.

Physical and thermochemical properties of biomass

Heat conductivity is a function of temperature, density, porosity, heat flow direction with respect to the grain and the moisture content [12]. The effective thermal conduction coefficient (푘 ) is a sum of the radiative (푘 ) and conductive (푘 ) heat transfer coefficients. The conductive heat transfer coefficient is a mass weighted sum of moisture (푘 ), char (푘 ), biomass (푘 ) and the gas (푘 ) coefficients,

32

푘 = 푘 + 푘 ,

푘 = 휀푘 + (1 − 휀)[(휌 푘 + 휌 푘 + 휌 푘 )/(휌 +휌 + 휌 )],

푘 =2휀휎푇 푟

휖 .

(55)

where 휎 is the Stefan-Boltzmann constant and 휖 is the emissivity. Permeability is a measure of the mass transfer resistance inside the pore

structures of the biomass. The following expression is often used to predict the permeability [54],

퐾 =푟 휀

45(1− 휀) . (56)

The specific heat of biomass, char [75] and tar [76] are calculated based on the following equations,

푐 = 2400− 2500푒푥푝(−0.004푇), (57)

푐 = 1430 + 0.355푇 −7.32 × 10

푇 , (58)

푐 = 506 + 1.158푇 − 1.158 × 10 푇 −3.33 × 10

푇 . (59)

Boundary and initial conditions

The boundary layer around the particle can affect the heat transfer because of the combustion of volatiles and the formation of flames; this can have a drastic effect during the pyrolysis if oxygen is present. However, due to the high importance of the radiation heat transfer to the particle surface, the boundary layer effect is often negligible. In the set of equations outlined in the previous sections, the boundary layer effect is considered through the heat and mass transfer coefficients by using a Stefan correction. At the particle’s outer surface, the heat and mass transfer fluxes, along with ambient pressure, determine the boundary condition:

33

휀퐷휕퐶휕푟 = ℎ 퐶 , − 퐶 ,

푘휕푇휕푟 = ℎ (푇 − 푇) + 휎휖 푇 − 푇 ,

(60)

where 푇 and 푇 are the gas temperatures at the particle boundary and the wall temperature, respectively. The mass transfer coefficient, ℎ , and the heat transfer coefficient, ℎ , can be calculated according to the following equations:

ℎ =푚̇ 푐

exp푚̇ 푐ℎ − 1

,ℎ =푁푢푘푑 ,

(61)

ℎ =푚̇ /휌

exp푚̇

휌 ℎ − 1,ℎ =

푆ℎ퐷푑 , (62)

where 푑 is a characteristic particle length, e.g., the diameter of a spherical particle, 푐 is the specific heat of the gas, 휌 is the gas density and 푘 and 퐷 are the gas conductivity and diffusivity, respectively. The gas outflow from a particle can influence the convective heat transfer and mass transfer coefficients. The Stefan correlation [52] accounts for the outflow of volatiles and steam (푚̇ ). Nusselt (푁푢) and the Sherwood (푆ℎ) number, which are functions of Prandtl (푃푟) and Reynolds (푅푒) numbers were obtained based on the Ranz-Marshall correlation [77],

푁푢 = 푎 + 푐푅푒 푃푟 , (63)

where 푎, 푐,푚 and 푛 are constants determined by the fluid and particle geometry. At the center of the particle, the gradient of pressure, temperature and all

species are zero due to particle symmetry:

휕푝휕푟 = 0,

휕푇휕푟 = 0, 푢 = 0,

휕퐶휕푟 = 0. (64)

For initial condition, one may assume that the particle is in equilibrium with surrounding gas at ambient pressure and temperature:

푝 = 푝 ,푇 = 푇 ,푢 = 0,퐶 = 퐶 , . (65)

34

Derivation of Energy Equation

The energy equation in the form of the total enthalpy of the system consisting gas, liquid and solid can be written as follows,

휌 퐻 + 휌 퐻 + 휌 퐻 + 휀휌 ∑ 푌퐻 + 휀휌 퐻 + 휀휌 퐻 +

( ) 퐺(푟)푢 휀휌 ∑ 푌퐻 + 휀휌 퐻 + 휀휌 퐻 = ( ) 퐺(푟)푘 +

( ) 퐺(푟) 휀휌 ∑ 퐷 , 퐻 .

where 퐻 is the specific enthalpy and 퐻 = ℎ ,° + ∫ 푐 , 푑푇.By simple

mathematics, one can write,

= ℎ ,° + ∫ 푐 , 푑푇 = ∫ 푐 , 푑푇 = 푐 , ,

= 푐 , .

The energy equation can further be expanded. The first term becomes,

휌 퐻 + 휌 퐻 + 휌 퐻 + 휀휌 ∑ 푌퐻 + 휀휌 퐻 + 휀휌 퐻 =

휌 + 휌 + 휌 + 휀휌 ∑ + 휀휌 + 휀휌 +

퐻 + 퐻 + 퐻 +∑ 푌퐻 + 퐻 +퐻 .

The convection term in the energy equation can be expanded to

( ) 퐺(푟)푢 휀휌 ∑ 푌퐻 + 휀휌 퐻 + 휀휌 퐻 =

휀휌 푢 ∑ + 휀휌 + 휀휌 +

( )∑ 푌퐻

( )+퐻

( )+ 퐻

( )

Two terms in the following equation require further expansion

휀휌 ∑ = 휀휌 ∑ 푌 + 휀휌 ∑ 퐻

35

휀휌 푢 ∑ = 휀휌 푢 ∑ 푌 + 휀휌 푢 ∑ 퐻 .

By substituting = 푐 , and = 푐 , and moving the term in the bracket to the right side of the energy conservation equation, the equation becomes,

휌 푐 + 휌 푐 + 휌 푐 + 휀휌 ∑ 푌푐 + 휀휌 푐 + 휀휌 푐 +

휀휌 푢 ∑ 푌푐 + 휀휌 푐 + 휀휌 푐 =

( ) 퐺(푟)푘 + ( ) 퐺(푟) 휀휌 ∑ 퐷 , 퐻 − ∑ 퐻 −

휀휌 푢 ∑ 퐻 − 퐻 +퐻 + 퐻 + ∑ 푌퐻 +퐻 +

퐻 − ( )∑ 푌퐻

( )+ 퐻 ( ) +퐻

( ).

Here, the terms that appear after the conduction term are examined. By mathematical manipulation and substitution by the conservation of species, one can write,

( ) 퐺(푟) 휀휌 ∑ 퐷 , 퐻 − 휀휌 ∑ 퐻 − 휀휌 푢 ∑ 퐻 =

∑ 퐻 ∑ 휗 , ℜ − 푌 ∑ ∑ 휗 , ℜ + ( ) 퐺(푟) 휀휌 ∑ 퐷 , . .

∑ 퐻 ∑ 휗 , ℜ − 푌 ∑ ∑ 휗 , ℜ is equal to zero if no homogeneous or heterogeneous reaction occurs in the system, e.g., if the case only considers pyrolysis. Otherwise, this term represents the enthalpy changes by the changes in the gas composition due to heterogeneous reactions, e.g., 푘 ∈ 푐ℎ푎푟푟푒푎푐푡푖표푛푠. The second term in the equation is due to the Dufour effect, but its contribution to the overall energy balance is negligible.

The last two terms in the brackets can be simplified further by substituting the mass conservation equations into the source term on the right side of the energy equation. Hence,

퐻 + 퐻 + 퐻 +∑ 푌퐻∈ +퐻 +퐻 +

( )∑ 푌퐻

( )+퐻 ( ) + 퐻

( )= 퐻 +퐻 +

퐻 +∑ 푌퐻 + ( )

( )+ 퐻 + ( )

( ) +퐻 +

( )

( )= 퐻 −ℜ − ℜ −ℜ + 퐻 ℜ +ℜ + 퐻 (−ℜ ) +

∑ 푌퐻 ℜ +ℜ + 퐻 ℜ −ℜ −ℜ +퐻 (ℜ ) +∑ 퐻 ∑ 휗 , ℜ −푌 ∑ ∑ 휗 , ℜ −퐻 ∑ 휗 , ℜ .

The energy equation now can be written in the following form

36

휌 푐 + 휌 푐 + 휌 푐 + 휀휌 ∑ 푌푐 + 휀휌 푐 + 휀휌 푐 +

휀휌 푢∑ 푌푐 + 휀휌 푐 + 휀휌 푐 = ( ) 퐺(푟)푘 + ℜ 퐻 −∑ 푌퐻 + ℜ 퐻 −퐻 + ℜ 퐻 −퐻 + ℜ 퐻 − ∑ 푌퐻 +ℜ 퐻 −

퐻 + ℜ 퐻 − 퐻 + ∑ ℜ ∑ 휗 , 퐻 −퐻

37

RESULTS AND DISCUSSION

Model parameters

The model parameters, including the physical and thermodynamic characteristics of the biomass, are taken from the reported values in each experimental set-up. If a value is not reported, then standard values are used. Particle density, thermal conductivity, diffusivity, emissivity, void fraction, pore size, permeability and specific heats for all components are required for each simulation. Apart from these parameters, the kinetic constants for pyrolysis and char reactions are also assigned based on existing literature. The apparent density of the biomass particle is usually reported and the values range between 330 to 1000 푘푔푚 . The thermal conductivity is calculated based on Eq. (55). The biomass thermal conductivity is set to 0.2 푊푚 퐾 ; as for the moisture inside the biomass, 푘 is set to 0.65 푊푚 퐾 . The thermal conductivity of the char is a function of temperature and is calculated based on the expression from [78] as presented in Eq. (66):

푘 = (1− 휀 )(1.47 + 1.11 × 10 푇), (66)

where 휀 is the char porosity. The ash conductivity is 1.2 푊푚 퐾 and the gas conductivity is 0.026 푊푚 퐾 . The particle emissivity is given as a function of temperature. For temperatures below 450퐾, the emissivity is set to 0.7, and for temperature above 550퐾, the emissivity is set to 0.85. For temperatures in between these values, a linear interpolation between the two values is used [79].

In this Chapter, the main results of the model discussed in the previous Chapter are presented followed by a summary of the papers and additional discussions.

Drying, pyrolysis and char combustion

In Paper I, a comprehensive model for the combustion of biomass was presented. The set of equations for the thermochemical conversion of a biomass particle described in the previous Chapter was used to study physical and chemical

38

processes that occur during biomass conversion. Various sub-processes involved in thermochemical conversion of biomass are described and mathematical modeling of these processes is presented. To validate the model, the experimental data of Lu et al. [45] was examined where temperature and mass loss were examined for a cylindrical particle with a diameter 9.5푚푚 and an aspect ratio (length to diameter) of 4 in a reactor filled with nitrogen with a gas temperature of 1050퐾 and an average wall temperature of 1276퐾, c.f., Figures 1 and 2 in the Paper. To investigate the evaporation behavior, the case with a high moisture particle with 40% moisture based on the dry fuel mass was chosen.

The reaction fronts of different chemical processes involved in the particle conversion for the case discussed in Paper I are illustrated in Figure 7. The changes in the particle radius due to shrinkage are noticeable in this figure. Drying starts immediately after that the particle is exposed to the hot furnace environment. As the drying front propagates inwards to the center of the particle, dry fuel is left behind. The pyrolysis front separates the dry fuel and the newly formed char layer. It takes 40 s for the moisture to evaporate and the devolatilization is completed after 70 s. The char oxidation front is very thin and it does not spread inside the particle as the process is controlled by mass transfer.

Figure 7. Propagation of reaction front during biomass conversion

Release of mass from the particle influences both the particle porosity and

radius. The changes in porosity for a particle during the evaporation and devolatilization stages are presented in Figure 8 for four different time instants. The effect of particle shrinkage can be observed by comparing the solid lines and dashed lines in this figure. If the particle shrinkage was not included in the model, the final char porosity is calculated to be around 95%, whereas by including the particle shrinkage, this value is reduced to 82%, which is a reasonable value for this char particle as the final char yield is around 10% of its initial mass. The

39

distinct effects of drying and devolatilization can be distinguished in this figure as there is a time lag between the reaction fronts passing by each point along the particle radius.

Biomass particles usually have high moisture content. In Paper I, a sensitivity study on different drying models is performed to evaluate the models for prediction of the drying behavior of biomass. Three different evaporation models were considered in this Paper: the heat flux model, the equilibrium model and the chemical kinetic model. The heat flux model is based on the assumption that evaporation takes place in an infinitely thin region and at normal boiling point of water. The equilibrium model is based on the assumption of equilibrium between water vapor and liquid water. In the chemical kinetic model, evaporation rate is expressed using the temperature dependent Arrhenius expression. These three models were compared with experimental measurements, c.f. Figure 5 in Paper I. The results of a detailed model developed by Di Blasi [5] was also included in the comparison. The Di Blasi model takes into account the water vapor convection and diffusion, capillary water convection due to pressure gradient and the bound water diffusion in the pores of the particle, c.f. Figures 6 and 7 in Paper I. The equilibrium model was found to be the best option for evaporation modeling both in comparison with the experimental data and the detailed model. In addition to reproducing the experimental measurements, the equilibrium model is numerically stable and capable of taking into account the moisture diffusion and re-condensation process.

Two assumptions associated with moisture evaporation modeling, moisture diffusion and vapor condensation were further studied in this Paper. It was shown that the diffusion of moisture towards the drying front speeds up the moisture evaporation and hence decreases the drying time. Vapor condensation increases the interior particle temperature and decreases the surface temperature, c.f., Figures 8 and 9 in Paper I. However, these effects are found to be relatively small especially at high-temperature drying conditions.

In Paper II, fundamental processes involved in the gasification and combustion of biomass are discussed in details. The main focus of this Paper is on the devolatilization process. There are major concerns that should be addressed regarding modeling of the devolatilization process; chemical kinetic scheme, kinetic rate constants, secondary reactions and pyrolysis products. In this Paper these topics are discussed extensively.

Three different kinetic schemes for pyrolysis of biomass, as presented in Figure 2, are discussed in this Paper. A single-step global pyrolysis model where biomass is converted to its products, volatiles and char through a one-step reaction, a three-step global scheme where conversion is achieved through three competitive reactions, and a multicomponent semi-detailed pyrolysis kinetic model were studied. The latter assumes that the cellulose, hemicellulos and lignin as the main components of biomass are independently pyrolyzed, forming intermediate products. The intermediates are further decomposed into gas, tar and

40

char. Each of these pyrolysis schemes has advantages and disadvantages, that was discussed in this Paper.

Figure 8. Evolution of particle porosity and effect of particle shrinkage

Different kinetic rate constants were employed when using the single-step

global pyrolysis scheme to reproduce the experimental data of Park et al. [79], as presented in Figure 10 in Paper II. It was shown that none of the reported values for kinetic rates was able to predict the mass loss of the particle in this experimental set-up. It was possible to “tune” the kinetic rates to match the numerical results and the experimental measurements. However, these kinetic constants are considered case-dependent and cannot necessarily predict other experimental results.

The assumption associated with the single-step pyrolysis scheme is that the particle has a uniform temperature. However, for large particles, there is a considerable temperature gradient inside the particle. Figure 9 shows the final char yield and the particle temperature along its radius at the end of pyrolysis. The temperature between the center and surface of the particle differs by 100 K and the final char yield production changes between 0.14 and 0.18 on dry mass basis. The reason for the different final char yield along the particle radius is that the pyrolysis is undergone at different temperatures and heating rates inside the particle. The single-step pyrolysis scheme is hence not suitable for large particles associated with large temperature gradient.

41

Figure 9. Effect of internal particle temperature on the final char yield

The three-step global scheme for biomass pyrolysis is well established and

proved to be a useful tool for prediction of particle mass loss and the major products of pyrolysis. There are plenty of kinetic rate constants associated with this pyrolysis scheme as reviewed in Ref. [6]. As presented in Figures 12 and 13 in Paper II, the kinetic rate constants of Di Blasi and Branca [80] can predict the mass loss behavior of the particle within acceptable tolerances, while the kinetic data of Thurner and Mann [81] under-predicts the mass loss and suggests a higher solid residue after pyrolysis. These results concur with the findings of other studies [82, 83]. The kinetic data of Thurner and Mann [81] for low-temperature pyrolysis and of Di Blasi and Branca [80] for high-temperature pyrolysis can provide accurate predictions of the process.

The shortcoming of the three-step global scheme is that the pyrolysis products are presented as three main groups and detailed information about the gaseous species and tar composition is not provided by this scheme. The kinetic mechanism of Ranzi et al. [17], on the other hand, provides detailed information on gas and tar species produced during biomass pyrolysis. In this semi-detailed mechanism, 20 gaseous species have been carefully chosen to represent the gas and tar yields of the pyrolysis [16, 17]. According to this pyrolysis mechanism, cellulose, hemicellulose and lignin decompose independently. Although they may have interactions during decomposition and also extractives may play a role in the biomass pyrolysis, this is a state-of-art method of simplifying a very complex process. This pyrolysis scheme was considered in the particle model discussed previously and the results were compared with different experimental measurements. The results showed that the multi-component scheme performed well when compared with experiments at low heating rate conditions, c.f., Figures 12 to 14 in Paper II, while the results deviated at high heating rates, Figures 15 and 16 in the Paper.

42

In the multi-component scheme, to have a correct estimation of cellulose, hemicellulose and lignin contents of the particle, biochemical analysis of biomass is required. It is possible to estimate the biochemical analysis based on the ultimate analysis; however, this estimation brings more uncertainty into the calculations. Due to this reason, to have an estimation of biomass pyrolysis products, it is possible to link the three-step global scheme with empirical correlations. In Paper II, a method based on the empirical data of Neves et al. [7] and solving a set of algebraic equations to satisfy elemental mass and energy balance was investigated. It was shown that the prediction of the empirical correlations concurred with the measurements, Figure 17 in Paper II.

The advantage of using empirical correlations over the detailed kinetic mechanism is simplicity. The results and comparison with different experimental setups show that there are a lot of uncertainties on the final products of the pyrolysis. The yield and composition of gas, char and tar produced in the pyrolysis process depend on several parameters, such as the heating rate, temperature, particle size, composition of biomass, residence time of the particle, sweeping gas flow rate and composition. A mechanism including all the details will be computationally heavy and will not be suitable for CFD applications of real furnaces with many particles.

For a typical hardwood particle in millimeter size and in a temperature range of 500퐾 to 1000퐾 the model based on the detailed kinetic mechanism of Ranzi et al. [17] is used to predict the main products of the pyrolysis. The algebraic set of equations along with the empirical correlations proposed by Neves et al. [7] were also used to predict the yield of typical hardwood pyrolysis products in this temperature range. The comparison between the results of these two models is presented in Figure 10. Despite the simplicity of the empirical model, the results are in a good agreement. The model can predict the main products yield very well according to the detailed kinetic model.

43

Figure 10. Behavior of empirical model compared with detailed kinetic mechanism behavior for typical hardwood; symbols: detail kinetic model prediction, solid lines: empirical model prediction

Heat of pyrolysis

The heat of pyrolysis depends on pyrolysis products yield and composition. In a previous publication [84] the heat of biomass pyrolysis was investigated. Empirical correlations and thermodynamic data of biomass and the main pyrolysis products were provided to offer a systematic way for computing the heat of pyrolysis. The heat of pyrolysis can be defined as,

푄 = 푌 , ℎ° − ℎ° = 퐿퐻푉푏푚 − 푌푗,퐹퐿퐻푉푗 퐽푘푔 ,

푗 (67)

where 푌 , is the final yield of the pyrolysis products on a DAF basis of the original fuel (biomass) and the subscript 푗 denotes char, tar and all of the gaseous species in the system. The correlation presented in Eqs. (12) and (13) can be used to compute the heat of pyrolysis. The pyrolysis products yield and composition are strongly dependent on the fuel source, temperature and heating rate to the particle. This results in a huge variation in the heat of pyrolysis of different biomass sources under different reactor conditions. Table 2 presents values and correlations for heat of pyrolysis of different biomass sources reported in different experimental setups.

44

Table 2. Heat of pyrolysis of different biomass sources at different experimental setups

Sample Heat of pyrolysis KJ/Kg Ref

Spruce 342 [85] Eucalyptus 400 [85] Poplar 207 [85] Sawdust 434 [85] Corn 267 [85] Sunflower 292 [85] Straw 375 [85] Sewage sludge 385 [85] Straw 500 [86] Cellulose 538− 2000푌 , [87] Cellulose 400-450 [88, 89] Pine 200 [90] Oak 110 [90] Spruce wood −3827푌 , + 1277(1−푌 , ) [91] Beech wood −3525푌 , + 936(1− 푌 , ) [91] Maple, low heating rate 610 [92] Maple, High heating rate -105 to -395 [92]

By means of Eq. (67) and correlations (12) and (13) and using a detailed

mechanism [14], the effect of heating rate and maximum temperature on the heat of pyrolysis was investigated. The correlation between the heat of pyrolysis and the final char yield at different heating rates is presented in Figure 11.

The heat of pyrolysis decreases monotonically as the final char yield increases; the slope of the change in the heat of pyrolysis depends on the heating rate. A very high final char yield indicates a very short residence time of the particle or a very low reactor temperature. In such cases, the solid residual is not primarily a carbon structure but is an intermediate composition between biomass and char. These data are discarded from Figure 11.

Although there is a clear correlation between the final char yield and the heat of pyrolysis, the increase in the char yield does not cause the exothermicity of the pyrolysis process. This is because the char has higher carbon content and hence a higher heating value compared to the original biomass. Higher char production indicates higher heating value of the products, which results in a higher endothermicity of the pyrolysis process. The variations in the heat of pyrolysis are due to the quality of the produced char and tar at different heating rates or temperatures. Figure 12 shows the changes in the lower heating value of the main

45

pyrolysis products as a function of the heating rate to the particle. As the char yield increases, the resulting char has a lower LHV. In addition, for conditions that favor a higher char yield, less energetic tar and gas components are produced. The effect of heating rate on the LHV of the pyrolysis products can explain the behavior of the pyrolysis heat with respect to the final char yield. This behavior can be explained by considering the changes in the LHV of products at different heating rates. As the heating rate increases, the LHV of char and gas increases, which results in higher heating values of the pyrolysis products. The decrease in the LHV of tar as the heating rate increases is smaller than the increase in the LHV of the gas and char at high char yields.

Figure 11. Relationship between the heat of pyrolysis and char yield (wt% of DAF) at different heating rates

This study showed that higher heating values of the biomass, tar and char can

be correlated with the elemental mass fractions of their components with an uncertainty of 20%. In spite of these uncertainties, the calculation of heat of pyrolysis based on this method can guaranty a strict elemental and energy conservation between the biomass and the pyrolysis products. The model results are consistent with the trends of the experimental data.

46

Figure 12. Changes in the lower heating values of char, tar and gas at different heating rates; the thick line in each group represents the highest heating rate.

Release of alkali metals from biomass

Release of alkali metals during biomass pyrolysis and gasification can cause serious damage to the combustion system due to fouling, slagging and agglomeration [93-96]. Previous investigations show that fouling is mainly due to the sticky deposition layer of alkali metals released from biomass combustion [97]. High-temperature corrosion in furnaces and in the turbine blades in combined cycle technology or reduced heat transfer in boilers due to deposits in convective surfaces are examples of these damages. The deposition of potassium and sodium on the active sites of vanadium and tungsten NOx reduction catalysts in power plants reduce the catalysts’ efficiencies and lead to more emissions [98]. To prevent damages caused by these species it is thus important to understand the release of alkali metals during thermochemical conversion of biomass.

In Paper III, a joint numerical and experimental investigation of the release of potassium from biomass during gasification stage was presented. In this Section the method is further expanded to investigate the release of sodium and potassium during the devolatilization stage.

47

Experimental measurements

A laser-induced breakdown spectroscopy (LIBS) was adopted to measure quantitatively the concentration of alkali metals from gasifying biomass. The effect of temperature on the potassium and sodium release was investigated in hot gas mixture of CO2 and H2O with different concentrations of O2. Experiments were carried out to measure the elemental mass of potassium and sodium of a biomass particle placed in a hot flue gas from combustion of methane/oxygen/carbon-dioxide under fuel-lean and fuel-rich conditions. The experimental results and the numerical results were used to delineate the various stages of potassium and sodium release.

To measure the release of potassium and sodium from gasifying biomass, a cylindrical wood particle is placed on top of a laminar flame burner. The details of the experimental set-up and measurement technique can be found in Paper III. The experimental conditions are presented in Table 3. Two equivalence ratios and four different temperatures are studied. At an equivalence ratio of 0.9, there will be oxygen available in the flue gas at the particle boundary layer, while at an equivalence ratio of 1.2, biomass undergoes only gasification with water and carbon dioxide. Table 3. Temperature profile along radius of the burner exit plane for various test cases

Equivalence ratio Temperature profile along radius [K]a Label r=0 r=10mm r=20mm r=30mm r=33mm

0.9 1596 1584 1515 817 577 F1 1483 1463 1272 749 562 F2 1408 1338 1100 671 567 F3

1.2 1518 1540 1491 1070 718 F4 a measured by an R-type thermocouple

Figure 13 shows direct images from the experimental study providing

qualitative information of different stages of conversion and correspondent release behavior of the particle. At the onset of this figure, the devolatilization stage is presented. The peak of the potassium release corresponds to the highest particle mass loss rate. Towards the end of the devolatilization stage, the potassium concentration decays to a very low level. When the char reactions start, the concentrations of potassium and sodium increase continuously and reach their peak values almost at the end of the char reaction stage. The concentrations monotonically decay during the ash-cooking stage. The yellow light emitted during the ash-cooking stage is due to the presence of sodium.

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Figure 13. Direct images from experimental setup; a particle at three stages of conversion

The measured concentrations of K and Na for four cases, F1-F4, are

presented in Figure 14. The experimental data for each flame condition are marked with symbols and the solid lines show the filtered data. Each measurement point is an average of data from three different biomass samples. The measured data presented in Figure 14 are divided into two parts: the data obtained during the devolatilization stage and the data obtained during the char reaction and ash-cooking stages as they show different behavior. Note that the process of heating, melting, shrinking and splitting of the ash particle in a high temperature environment is referred to as “ash-cooking”.

The Na concentration is considerably lower during the char reaction and ash-cooking stages. The Na concentration for the F3 case was below the sensitivity of the measurement technique. Moreover, for the F4 case, the signal to noise ratio of the sodium concentration is very high due to the low values of sodium release in this case. On the other hand, the sodium concentration during the devolatilization stage is higher than that of potassium. Considering the ultimate analysis of the particle, as presented in Table 1 in Paper III, the initial sodium mass fraction in the particle is lower than the potassium mass fraction, which indicates that a higher percentage of the sodium is released during the devolatilization stage.

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Figure 14. Measured mass concentration of potassium and sodium at four different flame conditions

From Figure 14, the concentrations of K and Na show two distinct peaks

associated with the devolatilization and char combustion. After devolatilization finishes, the concentration of K and Na first decreases significantly and then starts to increase as the char reactions proceed. This phenomenon indicates that two different mechanisms are involved in the release of K and Na during the devolatilization and char reaction stages. During devolatilization, the release of K and Na is mostly due to evaporation of inorganic species inside the particle, whereas during char reaction the main source for K in the gas phase is the decomposition of carboxylic acid groups formed during the devolatilization and reaction of carbonate and sulfate groups. The mechanism for release of alkali metals is elaborated in Paper III.

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Numerical analysis

In case F4 the ambient gases around the particle are the products of a rich methane flame, meaning that no oxygen is available in the vicinity of the particle. For the other cases, F1-F3, the oxygen left from the lean combustion of methane can affect the burning behavior of the particle, which can be the reason for the longer burnout time in F4 compared with the other three cases. To understand the role of oxygen, possibility of air entertainment and accurate boundary conditions of the particle model, a CFD calculation of the flow and transport and reactions of chemical species around the particle was performed. Boundary conditions for the CFD simulation were extracted from the particle model described earlier. The temporal evolution of the mass fractions of the gaseous products as well as the velocity of the gaseous mixture at the surface of the particle was used as the boundary conditions for the CFD simulations. The burner out-flow condition was calculated by a CHEMKIN type solver and the GRI 3.0.2 mechanism [99]. Figure 15 shows the heat release rate, temperature and mass fractions of O2 and CO around the particle at an instance of time during the char combustion stage for the F3 case. The hollow region in the middle of the CFD domain represents the particle boundary. The CFD domain at the top is restricted by the presence of a cap. The reason for placing the cap was to stabilize the flame formed around the particle especially during the devolatilization stage.

Figure 15. Heat release rate, temperature, oxygen and carbon monoxide concentration in gas phase around the particle

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The heat release rate on the particle boundary is due to combustion of the main products of the char reactions, CO and H2, with the oxygen left from the lean combustion of methane. The oxygen concentration between the reaction front and the particle surface is zero, which suggests that the only difference between the F4 and the other cases is the temperature at the boundary of the particle. In another word, in this setup, the behavior of potassium and sodium is independent of the difference between the oxygen concentration in the cases F1-F3 and F4.

Alkali metal release sub-model

The particle model explained in the previous Chapter was used to interpret the experimental data. A sub-model was developed to calculate the release rate of the alkali metals based on the measured concentrations. This sub-model is explained in this Section.

The mass fraction of any species at the particle surface depends on three factors, the formation/consumption rates of that species in the particle, the diffusion of that species from inside to the surface of the particle and the mass transfer rate from ambient to the particle surface. For large particles where the intra-particle mass transfer is important, 퐵푖 larger than unity, the gradient of species inside the particle should be taken into account when calculating the formation/consumption rates of each species. This means that the formation/consumption rates are the sums of the corresponding rates inside the entire particle volume. The rates of formation/consumption of each species due to various processes inside the particle are presented as follows:

ℜ = ℜ + 휗 ℜ −푀푀 ℜ

ℜ = 휗 ℜ −푀푀 ℜ

ℜ = 휗 ℜ +푀푀 ℜ + 2ℜ +ℜ

ℜ = 휗 ℜ

ℜ = 휗 ℜ +푀푀 ℜ

ℜ = −2푀푀 ℜ ,

(68)

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where 휗 acounts for the mass fraction of species 푗 on the basis of the total gas produced due to devolatilization.

The mass transfer rate from ambient to the particle surface is calculated using Eq. (69) where subscripts 푗 denotes each species; 푗 is O2, CO2, H2O, CH4, H2, Tar, Kg and Nag.

퐽 | = 휌 퐴 ℎ 푌 − 푌 . (69)

In Eq. (69) the subscript 푠 and ∞ represent the conditions at the particle surface and in the ambient gas, respectively. 퐴 is the outer surface of the particle which changes with time due to the particle shrinkage and ℎ is the mass transfer coefficient.

By neglecting the diffusion through the ash layer due to the low ash content of the particle, the mass flux of each species at the particle surface can be calculated as the sum of the formation/consumption rate of that species, ℜ , in the entire particle volume, the convective mass flux and the rate of mass transfer from the external boundary layer [52],

푚̇ = 푌 ℜ 푉 + 퐴 ℎ 휌 (푌 − 푌 ) , (70)

where index 푖 represents each numerical cell inside the particle and 푉 is the volume of that cell. The mass fraction of each species at the particle surface is obtained according to the following equation,

푌 =∑ ℜ 푉 + 퐴 ℎ 휌 푌∑ ∑ ℜ 푉 +퐴 ℎ 휌 . (71)

The first term in the numerator is the total mass formation/consumption rates of species 푗 in the entire particle volume due to moisture evaporation, devolatilization and heterogeneous reactions. The second term in the numerator is the mass transfer of species 푗 from/to the ambient gas. The two terms in the denominator are the sum of all the species mass fluxes at the particle surface.

Equation (71) provides the connection between the rate of release of potassium and sodium from the particle and the measured potassium concentration at the particle surface. In the experiments the elemental concentrations of potassium, 퐶 , were measured. The mass fraction of Kg is equal to the concentration divided by the gas density, 푌 = 퐶 /휌 . A CFD calculation of the flow and transport of chemical species around the particle showed that due to the short distance between the particle surface and the measurement point and the quasi-steady behavior of the release process, i.e. the time scale for the transport of potassium from the particle surface to the measurement point is several orders of magnitude lower than the time of the potassium release process

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itself, the mass fraction of Kg at the measurement point is approximately equal to the mass fraction at the particle surface, 푌 ≅ 푌 and similarly for Nag, 푌 ≅ 푌 . In the following sub-sections a method for extracting the kinetic data using the particle model and the experimental data will be explained.

Devolatilization stage For all the species in the system, except for Kg and Nag, the formation and consumption rates are known. By rearranging Eq. (71) and assuming that the concentrations of the gaseous potassium and sodium in the ambient gas are zero, the rate of release of potassium and sodium are,

푟̇ =푌 ∑ 푟̇+퐴 ℎ 휌

1 − 푌 ,푘 = 퐾 and푁푎 , (72)

where 푟̇ = ∑ ℜ 푉 is the sum of formation/consumption rate of species 푗 in the entire particle domain.

The rates of formation of Kg and Nag are equal to the rates of consumption of corresponding species in solid form inside the particle. If 푚 and 푚 represent the mass of K and Na that remain inside the particle at each time, by assuming a first order kinetic rate for evaporation of solid K and Na, one can write,

푑푚푑푡 = 푚 퐴 exp −

퐸ℛ푇 = 푟̇

푑푚푑푡 = 푚 퐴 푒푥푝 −

퐸ℛ푇 = 푟̇ ,

(73)

where 퐴 and 퐸 are pre-exponential factor and activation energy for each reaction mechanism, respectively. The kinetic data of release of K and Na can be expressed as follows,

퐴 exp −퐸ℛ푇 = 푟̇ /푚

퐴 푒푥푝(−퐸ℛ푇 ) = 푟̇ /푚 .

(74)

The natural logarithm of the left hand side of equation (74), is a linear function of 1/푇;

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ln(퐴 )−퐸ℛ푇 = ln

푟̇푚 ; 푘 = 퐾 and푁푎 . (75)

As the release rates of K and Na (푟̇ ) are calculated by using the experimental data and equation (72), by knowing the particle temperature one can compute the kinetic data of K and Na release rates. During the devolatilization stage, the temperature inside the particle shows a huge spatial variation due to the large Biot number and importance of the intra particle heat transfer. The simulation showed that this variation can be up to several hundred Kelvin and therefore it is not suitable to assign an average temperature to the particle. From the particle model the temperature distribution inside the particle at each time is known. Since 푟̇ = ∑ ℜ 푉 , the distribution of the ℜ inside the particle is required to find the kinetic data using Eq. (75) to each data point in the particle domain. To find a spatial distribution for ℜ , it is assumed that, first, the K and Na release start from the particle surface, similar to the drying and devolatilization processes. Second, the spatial distribution of the K and Na release rate inside the particle is similar to the devolatilization rate. Figure 16 shows the devolatilization rate versus particle radius at different times, 푡 = 10, 30 and 50푠. At the beginning of the process, the distribution is more spread along the particle radius due to the relatively low particle temperature. When the particle temperature increases, the distribution becomes sharper, representing a narrower devolatilization front. The same spatial distribution as presented in Figure 16 is assigned to release of K and Na. By knowing the distribution at each time, it is possible to solve Eq. (75) at each numerical cell.

Figure 16. Spatial distribution of devolatilization rate inside the particle at three different times

Figure 17 shows the scatter plots of the inverse temperature and the natural

logarithm of release rate for both K and Na during the devolatilization stage. By plotting ln(푟̇ /푚 ) versus 1000/푇, as presented in Figure 17, and fitting a linear regression function to the data points,퐸 /ℛ푇 and ln(퐴 ) can be found. Each data point in this figure represents a numerical cell with nonzero release rate

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at each time step for all four cases, F1-F4. The linear fit to each set of data, F1 to F4, is presented with a solid line in the same figure. The activation energy is equal to the slope of the linear regression times the universal gas constant, ℛ. For sodium release the activation energy spans from 218to 248푘퐽/푚표푙푒 and for potassium release it changes between 168 and 198푘퐽/푚표푙푒. The frequency factor is equivalent to the exponent of 푦 intercept and shows values between 10 ~10 1/푠 for sodium and 4 × 10 ~9 × 10 1/푠 for potassium. By fitting a line to all data sets, the average values of activation energies and frequency factors in Eq. (73) for sodium and potassium release during the devolatilization stage can be found,

퐴 = 5.3 × 10 1/푠; 퐸 = 185푘퐽/푚표푙푒

퐴 = 3 × 10 1/푠; 퐸 = 223푘퐽/푚표푙푒. (76)

During calculation of the activation energy and frequency factors for the release rate of sodium and potassium during the devolatilization stage, the data corresponding to a very low temperature (less than 750 퐾) were excluded, as they showed very low activation energy. The release of potassium and sodium at low temperature is due to the release of water solvable compounds during the moisture evaporation.

Figure 18 shows the mass loss of sodium and potassium during the devolatilization stage. The mass is normalized with the initial mass of each of these species inside the solid structure, as reported in ultimate analysis of the particle. Sodium mass loss curves show that up to 55% of the sodium is evaporated during the devolatilization stage. This value for potassium is much lower, showing that potassium release mostly occurs during the char burning and ash-cooking stages.

Although the experiments were not conducted in a kinetically controlled regime and the values presented for kinetic rates of sodium and potassium release are associated with some uncertainties, these sets of kinetic rates can provide a good estimation of release of these species in similar conditions.

The kinetic data for potassium during the char combustion and ash-cooking stages along with a proposed mechanism are presented in Paper III.

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Figure 17. Scatter plot of natural logarithm of 푟̇ /푚 versus inverse of temperature for sodium and potassium during the devolatilization stage

Figure 18. Normalized mass of sodium and potassium in the particle during devolatilization stage

Formation of ash around the particle

In Paper IV, by assessment of the different terms in the governing equations of the thermochemical conversion of biomass, a simplified model was developed for high ash content particle at high temperature oxidation conditions. The model was compared with the comprehensive model discussed previously in this thesis. It

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was shown the model can capture the main features of biomass conversion while maintaining low computational cost.

As the model is developed as a sub-model for numerical investigation of fixed bed combustors, formation of ash around the particle as well as effect of ash melting was taken into account. The effect of the ash layer on temperature and oxygen mass fraction at the particle surface for a cylindrical particle with 2% (low) and 10% (high) ash content is presented in Figure 19. By increasing the ash content of the particle the maximum temperature decreases and the total conversion time increases. The oxygen mass fraction at the particle surface is considerably higher indicating a lower reaction rate. The sudden decrease in the oxygen mass fraction is attributed to the start of the char reaction. For the high ash content case, the reason for the char reaction to start earlier, or for the devolatilization to finish earlier, is the lower amount of biomass available for devolatilization.

Figure 19. Effect of ash layer thickness on the particle temperature and oxygen mass fraction at the particle surface

In the above calculations ash porosity was assumed constant and it was set

equal to the char porosity, around 0.8. For a pulverized coal particle, Hurt et al. [74] suggested a value of 0.21 for ash porosity as an estimation for model parameters. However, as the particle radius was much larger in the present case, the higher value of ash porosity presented better results compared with the experimental data.

At high temperature conditions, especially for high potassium ash content, the ash layer around the particle may melt. Melting reduces the ash porosity and if the ash porosity reaches very low values, it may stop the reaction and the char

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particle will be trapped inside the ash layer. For the same particle as presented above and a reactor temperature of 1400 퐾, two scenarios were considered: one with an ash melting temperature higher than 1400 퐾, which results in no ash melting during the particle conversion, and the other with an ash melting temperature of 1300 퐾. Figure 20 shows the effect of melting temperature on the particle conversion. The melted ash prevents oxygen from reaching the char layer and slows down the reaction rate and consequently leads to a lower particle temperature. In the case where the melting temperature of ash was set above the reactor temperature, the porosity remained constant. For the case where the ash started melting due to the high temperature heating from the reactor, the porosity of ash decreased and eventually it stopped the reaction. In this case approximately 5% of the char was trapped in the ash layer.

Figure 20. Effect of ash melting on particle temperature and char conversion, particle conversion and ash porosity

Gasification of biomass

The multi pore model presented in Paper V provides a useful tool to predict and study the conversion of char particle by gasification process. The heterogeneous char reactions at the regime II conditions are substantially affected by the intra-particle mass transfer and chemical kinetic rates. The evolution of char porous structure can affect the conversion rate of the char. A model based on the classical capillary tubes is developed in Paper V taking into account different conversion

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rates for pores having different radius. By means of this model, the contribution of different capillaries with different radius is taken into account using an effectiveness factor presented for each pore radius. As the char conversion proceeds, the pore enlargement increase the contribution of micro-pores, consequently the effective surface area will increase. The increase in the effective surface area leads to an increasing reactivity of char during the entire conversion process. This model improves the understanding of the contribution of each group of pores in the conversion of biomass char and can be a useful tool for providing intrinsic kinetic rates from experimental data.

Gasification of a 10 푚푚 biomass char particle at temperatures of 1200 퐾 and 1300 퐾 and steam partial pressures of 0.1 and 0.2푎푡푚 is presented in Figure 21. The solid line, which presents a good agreement with the experimental data for all three cases, was calculated based on the multi pore model while the dashed-line (only for one case) was obtained by assuming a single pore size. At the beginning of the reaction, the surface area of the micro-pores is not accessible to the reactants, e.g., steam. As the reaction proceeds, the micro-pores enlarge and become partly accessible to the reactants. A portion of these pores will also overlap with the growing macro and meso pores. If the whole surface area measured by the adsorption/desorption method is used in the calculations, the conversion is highly over-predicted, as shown by the dashed-line in Figure 21.

Figure 21. Comparison between model prediction and experiment for conversion of a biomass char particle under various reactor temperature and partial pressure of steam

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A semi-empirical model for fixed-bed combustion

A two dimensional semi-empirical bed model was developed to study the combustion of solid biomass fuel in a fixed bed. Mass and energy conservations along with species transport equations for eight species were solved in a heat transfer environment. The receiving radiation from free board showed a significant effect on the temperature distribution as well as mass conversion rate. The first part of the bed is heated up because of the radiation which eventually leads to the ignition of the bed at the top surface. The sensitivity of the model to the rate constants was investigated showing a low sensitivity of the temperature to these parameters. The model can be used to simulate the temperature profile and species distribution in existing fixed bed grates when certain information of the real bed operations is known. Moreover, the model suggested in this work can be used as a tool to provide boundary conditions for the CFD analysis of the free room combustion.

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CONCLUSION AND FUTURE PERSPECTIVES

There is significant scattering in the thermodynamic properties of biomass, its pyrolysis products and its physical characteristics. There is also a significant scatter of experimental data from experiments conducted in different facilities. These variations are the result of the great diversity of biomass sources and the sensitivity of the thermochemical process to experimental conditions. Due to this wide range of thermochemical properties and physical characteristics, numerical modeling accounting for different physical and chemical processes is a challenging task. In this thesis a comprehensive numerical approach is developed to study the complex, multi-phase and multi-scale thermochemical conversion of biomass.

Various sub-processes involved in the thermochemical conversion of biomass are investigated, and mathematical modeling of these processes is presented. Biomass sources are usually high in moisture content. Sensitivity study on different drying models is performed to find the optimal model that is able to predict the drying behavior of biomass. The equilibrium model is found to be the best option for evaporation modeling. Two assumptions associated with moisture evaporation modeling, moisture diffusion and vapor condensation, are evaluated. Diffusion of moisture toward the drying front will speed up the moisture evaporation and decrease the drying time. Vapor condensation will increase the interior particle temperature and decrease the surface temperature. However, these effects are relatively small, especially at high-temperature drying conditions. The comprehensive model is evaluated by comparing the model predictions with experimental data under different conditions.

Models for the pyrolysis process with chemical kinetic data reported in existing literature show significant differences in the simulation results. This is likely caused by the use of kinetic data that were calibrated on experimental data with large uncertainties and at relatively low heating rate. It has been shown that the multicomponent pyrolysis model exhibited advantages in capturing the details in the pyrolysis process. However, certain adjustments of the model parameters are required to fit to the experimental data especially at high heating rate conditions. In general, the phenomenological models can capture the overall biomass devolatilization process.

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By means of a joint numerical study and advanced experimental measurements a mechanism for the release of alkali metals from low chlorine biomass is proposed. The in-situ time-resolved measurement of alkali metal concentration was used to calculate the kinetics constants of alkali metal release rate based on a particle model. A reaction mechanism was proposed that suggests that the alkali metal release during the devolatilization stage is in the form of KCl and NaCl. The organic and inorganic potassium and sodium will be transformed to char-K and char-Na during this stage. The potassium and sodium release during the char reaction and ash-cooking stages will be in the form of KOH and NaOH. This is because of that a considerable amount of Cl is released during the devolatilization stage and high concentration of H2O is available in the surrounding gas. The rate of release of potassium during char reaction and ash-cooking stages follows a first order Arrhenius expression as 2.5 × 10 ± . exp(−266 × 10 /ℛ푇). The kinetic rate constants for Na release are found to be 4.2 × 10 1/푠 for the pre-exponential factor and 218푘퐽/푚표푙푒 for the activation energy. The kinetics constants along with the reaction path were able to predict the release of these species with an acceptable accuracy. Although the experiments were not conducted in a kinetically controlled regime and the values presented for kinetic rates of sodium and potassium release are associated with some uncertainties, these sets of kinetic rates can provide a good estimation of release of these species in similar conditions.

The heterogeneous char reactions at the regime II conditions are substantially affected by both the intra-particle mass transfer and the chemical kinetic rates. The evolution of char porous structure can affect the conversion rate of the char. A model based on the classical capillary pores is developed taking into account different conversion rates for pores having different radius. This model improves the understanding of the contribution of each group of pores (micro, meso and macro-pores) in the conversion of biomass char and can be useful tool for calibrating intrinsic kinetic rates from experimental data.

For CFD simulations of furnaces and boilers, a representative boundary condition of the biomass bed is crucial for the accuracy of the results of free board combustion. Tradeoff is made in favor of computational time by simplifying the processes in a fixed bed combustor and an empirical model is developed. This model can provide acceptable boundary conditions for the CFD simulation at a very low computational cost.

Future improvements can be suggested for particle scale and reactor scale modeling. The comprehensive model presented in this study can be further extended to include primary fragmentation and formation of aerosol from the particle. Moreover, by extending the multi-pore model to include the evolution of different pores during the pyrolysis, it can provide a valuable tool to predict the char reactivity. For instance, at high heating rate pyrolysis, the pressure build up during the pyrolysis stage can produce a much larger pore structure and more distorted arrangements due to the collapse of pore walls. In addition, the effect of

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parent biomass on the pore structure can be studied in such extended model. Softwood usually has a more uniform pore structure while hardwood has a wide range of pore radius. The evolution of the pore structure originated from the parent wood can provide a more accurate initial condition for the char gasification and combustion.

By combining the simplified particle model with a CFD model for the gas through a fixed bed, a more realistic model can be obtained. This allows for more accurate studies of the reactor by taking into account different processes in the particle scale.

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SUMMARY OF THE PAPERS

This thesis is based on the results of the following papers;

I. H. Fatehi, X.S. Bai “A Comprehensive Mathematical Model For Biomass Combustion”, Combustion Science and Technology, 2014, In Press

In this Paper, a comprehensive model for the combustion of biomass is developed. Various sub-processes involved in thermochemical conversion of biomass are described and mathematical modeling of these processes is presented. Biomass sources are usually high in moisture content. A sensitivity study on different drying models is performed to find the optimal model that is able to predict the drying behavior of biomass. The equilibrium model is found to be the best option for evaporation modeling. Two assumptions associated with moisture evaporation modeling, moisture diffusion and vapor condensation, are evaluated. Diffusion of moisture towards the drying front speeds up the moisture evaporation and hence decreases the drying time. Vapor condensation increases the interior particle temperature and decreases the surface temperature. However, these effects are found to be relatively small especially at high temperature drying conditions. The comprehensive model is evaluated by comparing the model predictions with different experimental data under three different conditions.

I. H. Fatehi, X.S. Bai “Gasification and Combustion of Biomass: Physical Description and Mathematical Modeling”, Book chapter, HANDBOOK OF CLEAN ENERGY SYSTEMS, John Wiley Press, In Press.

In this Paper, the fundamental processes involved in the gasification and combustion of biomass are discussed. The focus is on the mathematical description of the various sub-processes encountered in these thermochemical conversion processes, including drying, devolatilization or pyrolysis, char oxidation and gasification, shrinking of biomass, and heat and mass transfer inside the biomass particles. Phenomenological models for the various sub-processes are reviewed for numerical simulations of the thermochemical conversion of biomass particles. The optimum sub-models and necessary developments are discussed. The models are evaluated by comparing the model results with experimental data

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under various experimental conditions. The basic thermodynamic properties of biomass, char, tar and volatile gases are examined. The performance of various sub-models and suggested model parameters are demonstrated for different test cases.

II. H. Fatehi, Y. He, Z. Wang, Z.S. Li, X.S. Bai, M. Alden, K.F. Cen “LIBS Measurements and Numerical Studies of Potassium Release during Biomass Gasification”, Accepted for Presentation in Proceedings of the Combustion Institute 2014, San Francisco, USA.

In this Paper, a joint numerical and experimental investigation of the release of potassium and sodium from biomass during gasification process is investigated. In this work, laser-induced breakdown spectroscopy (LIBS) was adopted to measure quantitatively the concentration of potassium and sodium from gasifying biomass. The effect of temperature on the potassium and sodium release is investigated in hot gas mixture of CO2, H2O with different concentrations of O2. A biomass thermochemical conversion model is employed to study the physical and chemical processes inside the particle. A sub-model is developed to simulate the various stages of potassium release during biomass conversion and to improve the chemical kinetic mechanism and chemical kinetic constants of the release rate. Two stages of the potassium release associated to devolatilization and char reaction and ash-cooking stages are proposed. A reaction mechanism is proposed suggesting that the potassium release during the devolatilization stage is in the form of KCl. The organic and inorganic potassium is transformed to char-K during this stage. The potassium release during the char reaction and ash-cooking stages is in the form of KOH. This is due to that a considerable amount of Cl is released during the devolatilization stage and high concentration of H2O is available in the surrounding gas. The rate of release of potassium during char reaction and ash-cooking stages follows a first order Arrhenius expression as 2.5 × 10 ± . exp(−266 × 10 /ℛ푇). The kinetics rate constants along with the reaction path appear to be able to predict the potassium release with an acceptable accuracy.

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III. H. Fatehi, X.S. Bai, “A simplified model for combustion of large biomass particle at fixed bed environment”, Manuscript to be submitted.

To obtain a tractable solution for the numerical simulation of the fixed bed, some simplifications to the governing equations as well as using efficient numerical approaches to solve these simplified equations are essential. In this paper, first by means of a detailed model developed for thermochemical conversion of a single particle, the budget of different terms in the fixed bed environment was assessed. Based on this assessment, some simplifications were introduced to the governing equations. It was observed that the high-temperature char combustion was the time limiting process in the overall model calculations. The char combustion was simplified by employing the shrinking core and reacting core model formulations. The ash layer around the particle, and the effect of ash melting were included in the model as the particle in fixed bed usually have high amount of ash. The model was compared with the detailed model both in terms of results and in terms of the calculation time.

IV. H. Fatehi, X.S. Bai, “Effect of pore size distribution on the gasification of biomass char”, Manuscript to be submitted.

In this Paper, the structural evolution of biomass char under regime II conditions is investigated. There are different theories representing porous medium, among which the random pore model (RPM) shows promising results for coal conversion. RPM predicts a maximum in specific surface area during the conversion of char. The specific surface area first increases as the pore radius is enlarged by the reaction and at a certain point starts to decrease as the pores merge and coalesce. For biomass, on the other hand, some experimental evidences show constant or continuously increasing specific area during the conversion. This suggests that using RPM is not suitable for biomass char. In this work, a model based on classical capillary tubes is employed to investigate char conversion during gasification. The results show good agreement with experimental data.

V. H. Fatehi, X.S. Bai, “Modeling of coarse fuel (biomass) combustion in fixed bed grate system”, 9th European Conference on Industrial Furnaces and Boilers, Portugal, 26-29 April 2011.

In this Paper, a steady state two dimensional semi-empirical model for fixed bed combustion is presented. Mass and energy conservations along with species transport equations for eight species (N2, O2, CO, H2, CO2, H2O, CH4 and Tar) are solved in a fixed bed environment. The receiving radiation from free board shows significant effect on the temperature distribution as well as mass conversion rate. Chemical kinetic rates of conversion of fresh wet fuel play an important role in

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modeling of fixed bed combustion. By reviewing existing literature, one can find different approaches and a variety of constants regarding chemical kinetic rates. These dissimilarities arise from different fuel properties and particle size and shape. As this uncertainty is higher for waste incinerators, in this Paper a semi-empirical model is used in which the kinetic rates are calculated based on experimental observation of industrial fixed bed waste incinerators. Eddy dissipation concept is employed to model volatile oxidation rates. The effects of the amount of radiation to the bed and sensitivity to the model parameters are studied. The model is validated and in spite of the simplicity and low computational cost, the results showing a good agreement comparing with available experimental data. My contribution: I am the main author of the papers contributing by carrying out the simulations, planning the cases, analyzing the results and writing the papers. My academic supervisor, Professor Xue-Song Bai, contributed to the problem formulation, discussing the results and helping with the writing of the manuscripts. In Paper III, the experimental measurements were carried out at Department of Combustion Physics, Lund University by the co-authors from Lund University and Zhejiang University, China. My contribution to the Paper is by post-processing the experimental data, developing a sub-model for release of alkali metal and writing the Paper.

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ACKNOWLEDGMENTS

This work was supported by the Swedish Energy Agency (STEM) through CeCOST, and partly sponsored by the Swedish Foundation for Strategic Research (SSF).

I would like to express my gratitude to my supervisor, professor Xue-Song Bai, whose constant support, encouragement and guidance made this work possible. Thank you for your motivation, enthusiasm, and immense knowledge and for giving me the opportunity to find my way in the research world.

I would like to acknowledge my co-authors from the Department of Combustion Physics, Lund University and from Zhejiang University, China, especially Professor Zhongshan Li and Yong He, for providing the experimental data and interesting discussions.

Special thanks go to my friends and colleagues in the Division of Fluid Mechanics and Department of Energy Sciences for providing a nice and friendly environment. Professor Johan Revstedt, Dr. Robert Szász and Dr. Rixin Yu, thank you for your help and support. Dr. Mehdi Jangi, thanks for all the coffee breaks at study centrum talking about combustion, politics, movies and life. Holger, Thanks for closing up Ariman together several times. We will go to “Kilimanjaro” one day! Eric and Piero, thanks for all the happy times during the ping pong tournaments and preparing “shows” for dissertation parties. Aurelia, I’m glad that you decided to move to “my” office! Thank you for your support whenever I needed it. I had a good time having your company especially when running outside. Henning, thanks for always being “up” for discussing work and also for hanging out and revising some funny quotas from “Friends”. Rickard, thanks for always having a good mood with some Family Guy jokes. Mohammad, I never forget your help especially during the first days when I moved to Lund. Tobias, Alper, Jiangfei, Fan, Yagin, Christian, Ali, Naser, Erdzan, Cheng, Vivian, Henrik and everyone who I made friends with during my time in the Department, thanks for creating a nice workplace and joyful after-work events.

During my time in Lund, I have made friends with many wonderful people from all around the world. I would like to thank Alessandro, Kostas, Ali, Björn and Carina for all the exciting and enjoyable experiences we had together. Special thanks to my friends Akram and Naser. I will always remember our “Fringe” marathon and our movie list; we will finish the list one day! The time that we

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shared together in Lund, showed me how great you are. I am thankful for having you guys in my life.

I would like to thank my parents for their faith in me and unconditional love and support. Thank you for acceptance for all these years that I was far from home. I will always be grateful for what you have done for me. I also want to thank my brothers, Saeed and Hamid, and my little sister, Farzan, for their spiritual support.

Last, but by no means least, I would like to thanks my wife, Parisa. Words cannot express my deepest gratitude and love towards you. Without your love and support this work would never have been done. Thanks for your patience and understanding for all the nights that I stayed late at work and thanks for being a wonderful colleague during the past four years and also thanks for reading the whole thesis.

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