869 resultados para Thermal pyrolysis


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De-inking sludge can be converted into useful forms of energy to provide economic and environmental benefits. In this study, pyrolysis oil produced from de-inking sludge through an intermediate pyrolysis technique was blended with biodiesel derived from waste cooking oil, and tested in a multi-cylinder indirect injection type CI engine. The physical and chemical properties of pyrolysis oil and its blends (20 and 30 vol.%) were measured and compared with those of fossil diesel and pure biodiesel (B100). Full engine power was achieved with both blends, and very little difference in engine performance and emission results were observed between 20% and 30% blends. At full engine load, the brake specific fuel consumption on a volume basis was around 6% higher for the blends when compared to fossil diesel. The brake thermal efficiencies were about 3-6% lower than biodiesel and were similar to fossil diesel. Exhaust gas emissions of the blends contained 4% higher CO2 and 6-12% lower NOx, as compared to fossil diesel. At full load, CO emissions of the blends were decreased by 5-10 times. The cylinder gas pressure diagram showed stable engine operation with the 20% blend, but indicated minor knocking with 30% blend. Peak cylinder pressure of the 30% blend was about 5-6% higher compared to fossil diesel. At full load, the peak burn rate of combustion from the 30% blend was about 26% and 12% higher than fossil diesel and biodiesel respectively. In comparison to fossil diesel the combustion duration was decreased for both blends; for 30% blend at full load, the duration was almost 12% lower. The study concludes that up to 20% blend of de-inking sludge pyrolysis oil with biodiesel can be used in an indirect injection CI engine without adding any ignition additives or surfactants.

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Cell-wall components (cellulose, hemicellulose (oat spelt xylan), lignin (Organosolv)), and model compounds (levoglucosan (an intermediate product of cellulose decomposition) and chlorogenic acid (structurally similar to lignin polymer units)) have been investigated to probe in detail the influence of potassium on their pyrolysis behaviours as well as their uncatalysed decomposition reaction. Cellulose and lignin were pretreated to remove salts and metals by hydrochloric acid, and this dematerialized sample was impregnated with 1% of potassium as potassium acetate. Levoglucosan, xylan and chlorogenic acid were mixed with CHCOOK to introduce 1% K. Characterisation was performed using thermogravimetric analysis (TGA) and differential thermal analysis (DTA). In addition to the TGA pyrolysis, pyrolysis-gas chromatography-mass spectrometry (PY-GC-MS) analysis was introduced to examine reaction products. Potassium-catalysed pyrolysis has a huge influence on the char formation stage and increases the char yields considerably (from 7.7% for raw cellulose to 27.7% for potassium impregnated cellulose; from 5.7% for raw levoglucosan to 20.8% for levoglucosan with CHCOOK added). Major changes in the pyrolytic decomposition pathways were observed for cellulose, levoglucosan and chlorogenic acid. The results for cellulose and levoglucosan are consistent with a base catalysed route in the presence of the potassium salt which promotes complete decomposition of glucosidic units by a heterolytic mechanism and favours its direct depolymerization and fragmentation to low molecular weight components (e.g. acetic acid, formic acid, glyoxal, hydroxyacetaldehyde and acetol). Base catalysed polymerization reactions increase the char yield. Potassium-catalysed lignin pyrolysis is very significant: the temperature of maximum conversion in pyrolysis shifts to lower temperature by 70 K and catalysed polymerization reactions increase the char yield from 37% to 51%. A similar trend is observed for the model compound, chlorogenic acid. The addition of potassium does not produce a dramatic change in the tar product distribution, although its addition to chlorogenic acid promoted the generation of cyclohexane and phenol derivatives. Postulated thermal decomposition schemes for chlorogenic acid are presented. © 2008 Elsevier B.V. All rights reserved.

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Phosphorus is a key plant nutrient and as such, is incorporated into growing biomass in small amounts. This paper examines the influence of phosphorus, present in either acid (HPO) or salt ((NH)PO) form, on the pyrolysis behaviour of both Miscanthus × giganteus, and its cell wall components, cellulose, hemicellulose (xylan) and lignin (Organosolv). Pyrolysis-gas chromatography-mass spectrometry (PY-GC-MS) is used to examine the pyrolysis products during thermal degradation, and thermogravimetric analysis (TGA) is used to examine the distribution of char and volatiles. Phosphorus salts are seen to catalyse the pyrolysis and modify the yields of products, resulting in a large increase in char yield for all samples, but particularly for cellulose and Miscanthus. The thermal degradation processes of cellulose, xylan and Miscanthus samples occur in one step and the main pyrolysis step is shifted to lower temperature in the presence of phosphorus. A small impact of phosphorus was observed in the case of lignin char yields and the types of pyrolysis decomposition products produced. Levoglucosan is a major component produced in fast pyrolysis of cellulose. Furfural and levoglucosenone become more dominant products upon P-impregnation pointing to new rearrangement and dehydration routes. The P-catalysed xylan decomposition route leads to a much simpler mixture of products, which are dominated by furfural, 3-methyl-2-cyclopenten-1-one and one other unconfirmed product, possibly 3,4-dihydro-2-methoxy-2H-pyran or 4-hydroxy-5,6-dihydro-(2H)-pyran-2-one. Phosphorus-catalysed lignin decomposition also leads to a modified mixture of tar components and desaspidinol as well as other higher molecular weight component become more dominant relative to the methoxyphenyl phenols, dimethoxy phenols and triethoxy benzene. Comparison of the results for Miscanthus lead to the conclusion that the understanding of the fast pyrolysis of biomass can, for the most part, be gained through the study of the individual cell wall components, provided consideration is given to the presence of catalytic components such as phosphorus.

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The simultaneous use of willow as a vegetation filter and an energy crop can respond both to the increasing energy demand and to the problem of the soil and water contamination. Its characteristics guarantee that the resources are used economically. As a vegetation filter, willow uptakes organic and inorganic contaminants. As a fast growing energy crop it meets the requirements of rural areas without the exploitation of existing forestry. The aim of the research was to gather knowledge on the thermal behaviour of willow, uptaking contaminants and then used as an energy crop. For this reason pyrolysis experiments were performed in two different scales. In analytical scale metal-contaminated wood was investigated and bench scale pyrolysis experiments were performed with nitrogen-enriched willow, originated from a wastewater treatment plant. Results of the pyrolysis showed that 51-81 % of the wastewater derived nitrogen of willow was captured in the char product. Char had low surface area (1.4 to 5.4 m2/g), low bulk density (0.15–0.18 g/cm3), high pH values (7.8–9.4) and high water-holding capacity (1.8 to 4.3 cm3/g) while the bioavailability of char nutrients was low. Links were also established between the pyrolysis temperature and the product properties for maximising the biochar provided benefits for soil applications. Results also showed that the metal binding capacity of wood varied from one metal ion to another, char yield increased and levoglucosan yield decreased in their presence. While char yield was mainly affected by the concentration of the metal ions, levoglucosan yield was more dependent on the type of the ionic species. Combustion experiments were also carried out with metal-enriched char. The burnout temperatures, estimated ignition indices and the conversion indicate that the metal ions type and not the amount were the determining factors during the combustion. Results presented in the Thesis provide better understanding on the thermal behaviour of nitrogen-enriched and metal contaminated biomass which is crucial to design effective pyrolysis units and combustors. These findings are relevant for pyrolysis experiments, where the goal is to yield char for energetic or soil applications.

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Aquatic biomass is seen as one of the major feedstocks to overcome difficulties associated with 1st generation biofuels, such as competition with food production, change of land use and further environmental issues. Although, this finding is widely accepted only little work has been carried out to investigate thermo-chemical conversion of algal specimen to produce biofuels, power and heat. This work aims at contributing fundamental knowledge for thermo-chemical processing of aquatic biomass via intermediate pyrolysis. Therefore, it was necessary to install and commission an analytical pyrolysis apparatus which facilitates intermediate pyrolysis process conditions as well as subsequent separation and detection of pyrolysates (Py- GC/MS). In addition, a methodology was established to analyse aquatic biomass under intermediate conditions by Thermo-Gravimetric Analysis (TGA). Several microalgae (e.g. Chlamydomonas reinhardtii, Chlorella vulgaris) and macroalgae specimen (e.g. Fucus vesiculosus) from main algal divisions and various natural habitats (fresh and saline water, temperate and polar climates) were chosen and their thermal degradation under intermediate pyrolysis conditions was studied. In addition, it was of interest to examine the contribution of biochemical constituents of algal biomass onto the chemical compounds contained in pyrolysates. Therefore, lipid and protein fractions were extracted from microalgae biomass and analysed separately. Furthermore, investigations of residual algal materials obtained by extraction of high valuable compounds (e.g. lipids, proteins, enzymes) were included to evaluate their potential for intermediate pyrolysis processing. On basis of these thermal degradation studies, possible applications of algal biomass and from there derived materials in the Bio-thermal Valorisation of Biomass-process (BtVB-process) are presented. It was of interest to evaluate the combination of the production of high valuable products and bioenergy generation derived by micro- and macro algal biomass.

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This research was carried for an EC supported project that aimed to produce ethyl levulinate as a diesel miscible biofuel from biomass by acid hydrolysis. The objective of this research was to explore thermal conversion technologies to recover further diesel miscible biofuels and/or other valuable products from the remaining solid acid hydrolysis residues (AHR). AHR consists of mainly lignin and humins and contains up to 80% of the original energy in the biomass. Fast pyrolysis and pyrolytic gasification of this low volatile content AHR was unsuccessful. However, successful air gasification of AHR gave a low heating value gas for use in engines for power or heat with the aim of producing all the utility requirements in any commercial implementation of the ethyl levulinate production process. In addition, successful fast pyrolysis of the original biomass gave organic liquid yields of up to 63.9 wt.% (dry feed basis) comparable to results achieved using a standard hardwood. The fast pyrolysis liquid can be used as a fuel or upgraded to biofuels. A novel molybdenum carbide catalyst was tested in fast pyrolysis to explore the potential for upgrading. Although there was no deoxygenation, some bio-oil properties were improved including viscosity, pH and homogeneity through decreasing sugars and increasing furanics and phenolics. AHR gasification was explored in a batch gasifier with a comparison with the original biomass. Refractory and low volatile content AHR gave relatively low gas yields (74.21 wt.%), low tar yields (5.27 wt.%) and high solid yields (20.52 wt.%). Air gasification gave gas heating values of around 5MJ/NM3, which is a typical value, but limitations of the equipment available restricted the extent of process and product analysis. In order to improve robustness of AHR powder for screw feeding into gasifiers, a new densification technique was developed based on mixing powder with bio-oil and curing the mixture at 150°C to polymerise the bio-oil.

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The projected decline in fossil fuel availability, environmental concerns, and security of supply attract increased interest in renewable energy derived from biomass. Fast pyrolysis is a possible thermochemical conversion route for the production of bio-oil, with promising advantages. The purpose of the experiments reported in this thesis was to extend our understanding of the fast pyrolysis process for straw, perennial grasses and hardwoods, and the implications of selective pyrolysis, crop harvest and storage on the thermal decomposition products. To this end, characterisation and laboratory-scale fast pyrolysis were conducted on the available feedstocks, and their products were compared. The variation in light and medium volatile decomposition products was investigated at different pyrolysis temperatures and heating rates, and a comparison of fast and slow pyrolysis products was conducted. Feedstocks from different harvests, storage durations and locations were characterised and compared in terms of their fuel and chemical properties. A range of analytical (e.g. Py-GC-MS and TGA) and processing equipment (0.3 kg/h and 1.0 kg/h fast pyrolysis reactors and 0.15 kg slow pyrolysis reactor) was used. Findings show that the high bio-oil and char heating value, and low water content of willow short rotation coppice (SRC) make this crop attractive for fast pyrolysis processing compared to the other investigated feedstocks in this project. From the analytical sequential investigation of willow SRC, it was found that the volatile product distribution can be tailored to achieve a better final product, by a variation of the heating rate and temperature. Time of harvest was most influential on the fuel properties of miscanthus; overall the late harvest produced the best fuel properties (high HHV, low moisture content, high volatile content, low ash content), and storage of the feedstock reduced the moisture and acid content.

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Digestate from the anaerobic digestion conversion process is widely used as a farm land fertiliser. This study proposes an alternative use as a source of energy. Dried digestate was pyrolysed and the resulting oil was blended with waste cooking oil and butanol (10, 20 and 30 vol.%). The physical and chemical properties of the pyrolysis oil blends were measured and compared with pure fossil diesel and waste cooking oil. The blends were tested in a multi-cylinder indirect injection compression ignition engine.Engine combustion, exhaust gas emissions and performance parameters were measured and compared with pure fossil diesel operation. The ASTM copper corrosion values for 20% and 30% pyrolysis blends were 2c, compared to 1b for fossil diesel. The kinematic viscosities of the blends at 40 C were 5–7 times higher than that of fossil diesel. Digested pyrolysis oil blends produced lower in-cylinder peak pressures than fossil diesel and waste cooking oil operation. The maximum heat release rates of the blends were approximately 8% higher than with fossil diesel. The ignition delay periods of the blends were higher; pyrolysis oil blends started to combust late and once combustion started burnt quicker than fossil diesel. The total burning duration of the 20% and 30% blends were decreased by 12% and 3% compared to fossil diesel. At full engine load, the brake thermal efficiencies of the blends were decreased by about 3–7% when compared to fossil diesel. The pyrolysis blends gave lower smoke levels; at full engine load, smoke level of the 20% blend was 44% lower than fossil diesel. In comparison to fossil diesel and at full load, the brake specific fuel consumption (wt.) of the 30% and 20% blends were approximately 32% and 15% higher. At full engine load, the CO emission of the 20% and 30% blends were decreased by 39% and 66% with respect to the fossil diesel. Blends CO2 emissions were similar to that of fossil diesel; at full engine load, 30% blend produced approximately 5% higher CO2 emission than fossil diesel. The study concludes that on the basis of short term engine experiment up to 30% blend of pyrolysis oil from digestate of arable crops can be used in a compression ignition engine.

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The thermal decomposition behavior of 1,2-bis-(2,4,6-tribromophenoxy)ethane (BTBPE) widely used as flame retardant plastics additive was studied by HRTG and differential scanning calorimetries. It was pyrolysed in inert atmosphere at 240 and 340 °C in isothermal conditions, the decomposition products were collected and investigated by means of IR and GC-MS, most of them are identified. It was found that BTBPE mostly evaporates at 240 °C. The decomposition products at 340°C depend on rate of their removal from the hot reaction zone. Main primary decomposition products found in case of rapid removal are tribromophenol and vinyl tribromophenyl ether. Whereas, prolonged contact with heating zone also produces hydrogen bromide, ethylene bromide, polybrominated vinyl phenyl ethers and diphenyl ethers, and dibenzodioxins. The nature of the identified compounds are in accordance with a molecular and radical pyrolysis reaction pathway. © 2002 Elsevier Science B.V. All rights reserved.

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Halogen-containing aromatics, mainly bromine-containing phenols, are harmful compounds contaminating pyrolysis oil from electronic boards containing halogenated flame retardants. In addition, theirformation increases the potential for evolution of polybrominated dibenzo-p-dioxins (PBDDs) and dibenzofurans (PBDFs) at relatively low temperature (up to 500 °C). As a model compound, 2,4-dibromophenol (DBP) was pyrolyzed at 290-450 °C. While its pyrolysis in a nitrogen flow reactor or in encapsulated ampules yields bromine-containing phenols, phenoxyphenols, PBDDs, and PBDFs, pyrolysis of DBP in a hydrogen-donating medium of polypropylene (PP) at 290-350 °C mainly results in the formation of phenol and HBr, indicating the occurrence of a facile hydrodebromination of DBP. The hydrodebromination efficiency depends on temperature, pressure, and the ratio of the initial components. This thermal behavior of DBP is compared to that of 2,4-dichlorophenol and decabromodiphenyl ether. A treatment of halogen-containing aromatics with PP offers a new perspective on the development of low-environmental-impact disposal processes for electronic scrap. © 2005 American Chemical Society.

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The diglycidyl ether of tetrabromobisphenol A, the diglycidyl ether of bisphenol A and their mixture was cured by 4,4'-diaminodiphenyl methane. The pyrolysis of the obtained epoxy resins was studied by TG, DSC, TG/FTIR as well as FTIR characterization of pyrolysis residues. The gaseous and high boiling pyrolysis products were collected, characterized by GC/MS and their formation is discussed. The brominated epoxy resins are thermally less stable than the non-brominated ones. This effect is caused by the amine-containing hardener. The degradation initiation reaction is associated with the formation of hydrogen bromide which further destabilizes the epoxy network. The effect of the curing agent can be used in recycling of epoxy resins to separate brominated pyrolysis products from non-brominated ones.

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The thermal degradation of 2,6,2',6'-tetrabromo-4,4-pm-isoproylidene-di phenol (tetrabromobisphenol A) (TBBPA) has been investigated and a mechanism for its thermal degradation is suggested. TBBPA is a comonomer widely used in epoxy and in unsaturated polyester resins to impart fire retardance. These resins find a common use in electric and electronic equipment. The presence of bromine atoms is the key factor in fire retardant activity, while on the other hand it represents an ecological problem when pyrolytic recycling is programmed at the end of the useful life of such items. However, pyrolysis is the more advantageous recycling system for thermosetting resins and thus efforts should be made to control the pyrolysis in order to avoid or minimize the development of toxics. Homolytic scission of the aromatic bromine and condensation of aromatic bromine with phenolic hydroxyl are the main processes occuring in the range 270-340°C. A large amount of charred residue is left as a consequence of condensation reactions. HBr and brominated phenols and bisphenols are the main volatile products formed. Brominated dibenzodioxins structures are included in the charred residue and not evolved in the volatile phases.

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This paper presents an assessment of the technical and economic performance of thermal processes to generate electricity from a wood chip feedstock by combustion, gasification and fast pyrolysis. The scope of the work begins with the delivery of a wood chip feedstock at a conversion plant and ends with the supply of electricity to the grid, incorporating wood chip preparation, thermal conversion, and electricity generation in dual fuel diesel engines. Net generating capacities of 1–20 MWe are evaluated. The techno-economic assessment is achieved through the development of a suite of models that are combined to give cost and performance data for the integrated system. The models include feed pretreatment, combustion, atmospheric and pressure gasification, fast pyrolysis with pyrolysis liquid storage and transport (an optional step in de-coupled systems) and diesel engine or turbine power generation. The models calculate system efficiencies, capital costs and production costs. An identical methodology is applied in the development of all the models so that all of the results are directly comparable. The electricity production costs have been calculated for 10th plant systems, indicating the costs that are achievable in the medium term after the high initial costs associated with novel technologies have reduced. The costs converge at the larger scale with the mean electricity price paid in the EU by a large consumer, and there is therefore potential for fast pyrolysis and diesel engine systems to sell electricity directly to large consumers or for on-site generation. However, competition will be fierce at all capacities since electricity production costs vary only slightly between the four biomass to electricity systems that are evaluated. Systems de-coupling is one way that the fast pyrolysis and diesel engine system can distinguish itself from the other conversion technologies. Evaluations in this work show that situations requiring several remote generators are much better served by a large fast pyrolysis plant that supplies fuel to de-coupled diesel engines than by constructing an entire close-coupled system at each generating site. Another advantage of de-coupling is that the fast pyrolysis conversion step and the diesel engine generation step can operate independently, with intermediate storage of the fast pyrolysis liquid fuel, increasing overall reliability. Peak load or seasonal power requirements would also benefit from de-coupling since a small fast pyrolysis plant could operate continuously to produce fuel that is stored for use in the engine on demand. Current electricity production costs for a fast pyrolysis and diesel engine system are 0.091/kWh at 1 MWe when learning effects are included. These systems are handicapped by the typical characteristics of a novel technology: high capital cost, high labour, and low reliability. As such the more established combustion and steam cycle produces lower cost electricity under current conditions. The fast pyrolysis and diesel engine system is a low capital cost option but it also suffers from relatively low system efficiency particularly at high capacities. This low efficiency is the result of a low conversion efficiency of feed energy into the pyrolysis liquid, because of the energy in the char by-product. A sensitivity analysis has highlighted the high impact on electricity production costs of the fast pyrolysis liquids yield. The liquids yield should be set realistically during design, and it should be maintained in practice by careful attention to plant operation and feed quality. Another problem is the high power consumption during feedstock grinding. Efficiencies may be enhanced in ablative fast pyrolysis which can tolerate a chipped feedstock. This has yet to be demonstrated at commercial scale. In summary, the fast pyrolysis and diesel engine system has great potential to generate electricity at a profit in the long term, and at a lower cost than any other biomass to electricity system at small scale. This future viability can only be achieved through the construction of early plant that could, in the short term, be more expensive than the combustion alternative. Profitability in the short term can best be achieved by exploiting niches in the market place and specific features of fast pyrolysis. These include: •countries or regions with fiscal incentives for renewable energy such as premium electricity prices or capital grants; •locations with high electricity prices so that electricity can be sold direct to large consumers or generated on-site by companies who wish to reduce their consumption from the grid; •waste disposal opportunities where feedstocks can attract a gate fee rather than incur a cost; •the ability to store fast pyrolysis liquids as a buffer against shutdowns or as a fuel for peak-load generating plant; •de-coupling opportunities where a large, single pyrolysis plant supplies fuel to several small and remote generators; •small-scale combined heat and power opportunities; •sales of the excess char, although a market has yet to be established for this by-product; and •potential co-production of speciality chemicals and fuel for power generation in fast pyrolysis systems.

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ε-caprolactam is a monomer of high value. Therefore, the chemical reutilization of polyamide 6 containing carpets for ε-caprolactam recovery offers some economic benefit and is performed on a technical scale with the help of the Zimmer-process. By this process polyamide 6 is depolymerized with steam and phosphoric acid. An alternative to this process is the thermal depolymerization - catalyzed or non-catalyzed. To investigate this alternative in more detail, the formal kinetic parameters of (i) the thermal depolymerization of polyamide 6, (ii) the thermal depolymerization in presence of sodium/potassium hydoxide, and (iii) the thermal depolymerization in presence of phosphoric acid are determined in this work. Based on the kinetics of the catalyzed or non-catalyzed depolymerization a stepwise pyrolysis procedure is designed by which the formation of ε-caprolactam from polyamide 6 can be separated from the formation of other pyrolysis products. © 2001 Elsevier Science B.V.

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The research presented in this thesis was developed as part of DIBANET, an EC funded project aiming to develop an energetically self-sustainable process for the production of diesel miscible biofuels (i.e. ethyl levulinate) via acid hydrolysis of selected biomass feedstocks. Three thermal conversion technologies, pyrolysis, gasification and combustion, were evaluated in the present work with the aim of recovering the energy stored in the acid hydrolysis solid residue (AHR). Mainly consisting of lignin and humins, the AHR can contain up to 80% of the energy in the original feedstock. Pyrolysis of AHR proved unsatisfactory, so attention focussed on gasification and combustion with the aim of producing heat and/or power to supply the energy demanded by the ethyl levulinate production process. A thermal processing rig consisting on a Laminar Entrained Flow Reactor (LEFR) equipped with solid and liquid collection and online gas analysis systems was designed and built to explore pyrolysis, gasification and air-blown combustion of AHR. Maximum liquid yield for pyrolysis of AHR was 30wt% with volatile conversion of 80%. Gas yield for AHR gasification was 78wt%, with 8wt% tar yields and conversion of volatiles close to 100%. 90wt% of the AHR was transformed into gas by combustion, with volatile conversions above 90%. 5volO2%-95vol%N2 gasification resulted in a nitrogen diluted, low heating value gas (2MJ/m3). Steam and oxygen-blown gasification of AHR were additionally investigated in a batch gasifier at KTH in Sweden. Steam promoted the formation of hydrogen (25vol%) and methane (14vol%) improving the gas heating value to 10MJ/m3, below the typical for steam gasification due to equipment limitations. Arrhenius kinetic parameters were calculated using data collected with the LEFR to provide reaction rate information for process design and optimisation. Activation energy (EA) and pre-exponential factor (ko in s-1) for pyrolysis (EA=80kJ/mol, lnko=14), gasification (EA=69kJ/mol, lnko=13) and combustion (EA=42kJ/mol, lnko=8) were calculated after linearly fitting the data using the random pore model. Kinetic parameters for pyrolysis and combustion were also determined by dynamic thermogravimetric analysis (TGA), including studies of the original biomass feedstocks for comparison. Results obtained by differential and integral isoconversional methods for activation energy determination were compared. Activation energy calculated by the Vyazovkin method was 103-204kJ/mol for pyrolysis of untreated feedstocks and 185-387kJ/mol for AHRs. Combustion activation energy was 138-163kJ/mol for biomass and 119-158 for AHRs. The non-linear least squares method was used to determine reaction model and pre-exponential factor. Pyrolysis and combustion of biomass were best modelled by a combination of third order reaction and 3 dimensional diffusion models, while AHR decomposed following the third order reaction for pyrolysis and the 3 dimensional diffusion for combustion.