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A random pore model with application to char gasification at chemically controlled rates
... On this basis elegant mathematical models have been published giving theoretical deductions for the change of the reaction surface as the burn-off proceeds. [1][2][3][4] However, subsequent char gasification studies revealed more and more difficulties. Hurt et al. 5 proved the special role of microporous surface area in carbon gasification processes. ...
... The maximumcurve character of these functions is much more pronounced than that of the theoretical surface models deduced from pore distribution hypotheses. [1][2][3][4] As an explanation, we assume that the burn-off of the samples started with an activation of the char surface. The prolonged heating at 950°C during the preparation of the samples probably stabilized the surfaces. ...
... The scattering resulted from the following sources: (i) coal char particles always show some heterogeneity; (ii) due to this heterogeneity, the mineral matter in the small samples of this study varied by 1 -2 % from experiment to experiment; (iii) the kinetic evaluation of the Gardanne lignite char curves was disturbed by the presence of a prominent carbonate decomposition peak; (iv) iii) distort the cj coefficients and affect the kinetic parameters. The gas composition errors can formally be compensated by small log Aj changes in models based on equation(2). The variation of log Aj can formally describe temperature errors, too, as outlined in the Discussion of the Results. ...
The kinetics of the coal char + O2 reaction was studied by thermogravimetry. Low sample masses were employed to ensure an approximate kinetic regime. Special emphasis was placed on clarifying how the recirculation of the flue gases (i.e. the presence of a high amount of CO2 at low O2 concentrations) affects the reactivity. The ambient gas concentrations varied from 100% O2 to 5% O2 in CO2 or Ar. A semiempirical model is presented that can approximate the reactivity changes during the conversion and takes into account the heterogeneity of the samples. A least-squares evaluation procedure resulted in a good fit to the experimental data over a wide variety of temperature programs and ambient gas concentrations. The overall burn-off time of the samples varied from 8 min to 3 h depending on the experimental conditions. The reaction rate was found to be proportional to the O2 concentration of the ambient gas and was not influenced by the presence of high amounts of CO2. The reaction started with a sharp acceleration period, indicating an initial activation of the char surface.
... Previous mathematical models based on parallel-pore representations (e.g., Ramachandran and Smith, 1977;C!+tman and Edgar, 1983) provide a good description of the process at the local (pore) level, but are inherently inadequate for the accurate prediction of the time rate of change of accessible surface area and volume, effective diffusivity, and ultimately conversion efficiency and pore blockage time. Subsequent investigations by Gavalas (1980), and Bhatia and Perlmutter (1980), among others, imparted considerable insight into the effects of the topology of the porous medium by utilizing random pores. ...
... Several studies conducted in the context of gasification of solids allow a more elaborate statistical representation of the pore structure (e.g., Gavalas, 1980;Bhatia and Perlmutter, 1980). Havever, a concrete elucidation of the important role of topology and connectivity in determining transport properties in porous media was only recently obtained in fluid flow in porous media studies associated with the enhanced recovery of oil. ...
... This comparison was made for the purpose of illustrating the effects of topology on the reaction performance. No comparison was attempted with the distributed pore size model of Christman and Edgar (1983), or the random pore models of Gavalas (1980) and Batia and Perlmutter (1980). However, since the latter works do not address the question of network accessibility, we anticipate a discrepancy that would be larger as the coordination number decreases. ...
This paper utilizes network representations and percolation theory to develop expressions for pore closure time and the evolution of accessible volume, effective diffusivity, and conversion rates. By using population balances and elements from percolation theory, we develop a general theory that rigorously accounts for the effect of geometrical (e. g. , pore size distribution) and topological (e. g. , connectivity, accessibility) aspects of the porous structure on the evolution in time of the above quantities. It is shown that a proper accounting of the nonaccessible fraction of open pores leads to higher estimates of pore closure time and lower estimates of conversion as compared to parallel-pore models. This discrepancy is found to increase with an increase in process time.
... An unreacted shrinking core model considering intraparticle diffusion was developed to satisfy the regime zone of II, where the reaction rate was mainly limited by the layer of ash or solid fuel impurity leftovers. 6,7 RPM was proposed by Gavalas (1980) 8 was also derived and proved to be the most suitable model. These two studies conclude that the reaction rates are functions of the carbon conversion state, which can be described using Eq.3 in Table 1. ...
... An unreacted shrinking core model considering intraparticle diffusion was developed to satisfy the regime zone of II, where the reaction rate was mainly limited by the layer of ash or solid fuel impurity leftovers. 6,7 RPM was proposed by Gavalas (1980) 8 was also derived and proved to be the most suitable model. These two studies conclude that the reaction rates are functions of the carbon conversion state, which can be described using Eq.3 in Table 1. ...
Combustion of carbonaceous solid fuels was modeled using a number of methods, and the employed models were further improved by thoroughly studying the physical and chemical interactions between carbonaceous solid fuels and oxidizers. Simulation accuracy was improved by using special techniques to reduce the fitting errors of earlier models, e.g., errors in the isothermal coal char combustion rate model were reduced by modifying the well-established random pore model, with increased model flexibility generally considered vital for improvement. Thermogravimetric analyses were performed for four categories of carbonaceous fuels: semi-anthracite coals, bituminous coals, sub-bituminous coals, and biomass. Scanning electron microscopy imaging was employed to understand correlations between fuel structure and model parameters. The obtained results were used to confirm the hypotheses of the used models, and a general model of carbonaceous solid fuel combustion, termed “flexibility-enhanced random pore model,” was established, improving correlation coefficients from 0.7 to 0.98 and decreasing deviations from 20 to 3%.
... Neste modelo, a reação ocorre inicialmente nos grãos da superfície externa da partícula e então a zona global de reação vai se movendo para o seu interior [4,5]. O MPR, por sua vez, assume que os poros se sobrepõem conforme a reação ocorre e inclui parâmetros relacionados com a estrutura porosa inicial do char [6,7]. Devido às especificidades das reações de gaseificação com biomassa, os modelos nem sempre conseguem descrever o aumento da taxa da reatividade em altas conversões de carbono [8]. ...
... Definições: é um parâmetro relacionado com a estrutura porosa inicial do char 3 , c e p são parâmetros adimensionais 4 . Fonte: 1 [3], 2 [5], 3 [6,7], 4 [9]. ...
A gaseificação é uma tecnologia promissora para a produção de energia a partir de resíduos, porém, o mecanismo desta reação para biomassas ainda não é completamente entendido. Assim, o objetivo deste trabalho foi avaliar a cinética da gaseificação com vapor de água da serragem de madeira, utilizando três modelos cinéticos teóricos e um modelo semiempírico. Primeiramente, a serragem foi pirolisada em um reator de leito fixo. O sólido bruto e o biochar foram caracterizados por análises físico-químicas. Os ensaios de gaseificação foram feitos em uma termobalança, com 100 mg de biochar, entre 750 e 850 °C e concentração de 30 vol.%H2O. Verificou-se que um aumento na temperatura eleva a taxa de gaseificação, sendo esta aproximadamente constante para conversões entre 10-90% nas maiores temperaturas. Nas menores temperaturas, um pico acentuado foi verificado em 10%, com declínio até o final da curva de conversão. O modelo melhor ajustado foi o semiempírico, que leva em conta a influência catalítica dos metais presentes na serragem. Com os parâmetros ajustados foi possível verificar a troca do regime controlador e encontrar os parâmetros cinéticos, os quais se aproximaram aos valores de literatura para biomassas, indicando o potencial da serragem para aproveitamento energético.
... Models based on the capillary theory are by far the most commonly used models in this field [ 5 ] . One of the well-known models in capillary models is the random pore model (RPM) developed by Bhatia et al. [ 6 , 7 ] and Gavalas [8] . The RPM assumes cylindrical capillaries randomly located and oriented with any distribution of pore radii. ...
... To identify the degree of participation of each pore in the reactions, the concept of pore scale Thiele module for individual capillary developed by Gavalas [8] is adapted. Thiele Module provides a comparison between the diffusion and reaction rates in a porous structure, here a cylindrical pore. ...
The evolution of char porous structure can affect the conversion rate of the char by affecting the intra-particle transport, especially in the zone II conversion regime. A multi-pore model based on the capillary pore theory is developed to take into account different conversion rates for pores with different radii. The model is valid for biomass chars produced under relatively low heating rates, when the original beehive structure of the biomass is not destroyed during the pyrolysis stage. The contribution of different pores with different radius is taken into account using an effectiveness factor presented for each pore radius with respect to different reactions. As the char conversion proceeds, the pore enlargement increases the contribution of micro-pores; consequently the effective surface area will increase. The increase in the effective surface area leads to an increased reactivity of char during the entire conversion process. This model is used to analyze the steam gasification process of biomass char of centimeter sizes. The results from the present multi-pore model are in better agreement with experimental data than those from a corresponding single pore model. Since the multi-pore model accommodates the detailed intra-particle transport, it is a useful basis toward developing a more predictive model for biomass char gasification.
... randomly overlapping pores (37)(38)(39) and randomly intersecting nonoverlapping pores (40,41). ...
... Gavalas (37)(38)(39), regards the solid particle as composed of overlapping pores with random distribution, i.e., the position and orientation of pores are independent of each other. Pores are usually treated as capillary, cylinder or slit for simplification in calculation. ...
... Models based on the Capillary Theory are by far the most commonly used models in this field [1]. One of the well-known models in capillary theory is the random pore model (RPM) developed by Bhatia and Perlmutter [2,3] and Gavalas [4]. The RPM assumes cylindrical capillaries randomly located and oriented with any distribution of pore radii. ...
... To identify the degree of participation of each pore in the reactions, the concept of pore scale Thiele module for individual capillary developed by Gavalas [4] is adapted. An effectiveness factor based on the Thiele module is employed here. ...
The evolution of char porous structure can affect the gasification rate of biomass char. A model based on the classical capillary pores is developed taking into account different conversion rates for pores having different radii. The contribution of different pores with different radii is taken into account using an effectiveness factor presented for each pore radius. As the char conversion proceeds, the pore enlargement increases 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 is used to examine the contribution of each group of pores in the conversion of biomass char and can be a useful tool for developing and calibrating intrinsic kinetic rates from experimental data.
... Ces modèles considèrent la phase solide comme continue ou ne la considèrent que comme le complément volumique de l'ensemble des pores et décrivent l'évolution géométrique des pores due à la réaction. A l'instar des modèles de grains, les modèles de pores se sont sophistiqués depuis les premières publications (Ramachandran et Smith, 1977 ;Bhatia et Perlmutter, 1980, 1981Gavalas, 1980Gavalas, , 1981. Sahimi et coll. ...
... Dans ce dernier, le réseau poreux est initialement constitué d'un ensemble de capillaires cylindriques de diamètres variés, aléatoirement distribués dans l'espace et qui peuvent se chevaucher. Les propriétés structurales d'un tel réseau ont été étudiées par Gavalas (1980), qui a montré qu'il pouvait être complètement décrit par une seule fonction de répartition de longueur l(R0), où l(R0)dR0 représente la longueur totale des pores de rayon compris entre [R0, R0+dR0] par unité de volume de particule. En particulier, la porosité et l'aire volumique initiales du solide poreux sont données par : ...
Gas-solid reactions control a great number of major industrial processes involving matter transformation. This dissertation aims at showing that mathematical modelling is a useful tool for both understanding phenomena and optimising processes. First, the physical processes associated with a gas-solid reaction are presented in detail for a single particle, together with the corresponding available kinetic grain models. A second part is devoted to the modelling of multiparticle reactors. Different approaches, notably for coupling grain models and reactor models, are illustrated through various case studies: coal pyrolysis in a rotary kiln, production of uranium tetrafluoride in a moving bed furnace, on-grate incineration of municipal solid wastes, thermogravimetric apparatus, nuclear fuel making, steelmaking electric arc furnace.
... specially prepared, pure model carbons) the reaction rate is proportional to the surface area, and the change of the surface area during the reaction can be described by theoretical models. [19][20][21][22] In case of real chars, however, complicating factors arise: (i) the accessibility of the internal pores, including the opening of closed pores; (ii) the role of the inorganic catalysts; (iii) the chemical/physical inhomogeneity of the carbon phase. Accordingly, the dependence of the reaction rate on the burn-off cannot be interpreted as the change of an active surface alone. ...
... Both f2(2) and f3(3) of the partially demineralized charcoal and the f2(2) of the curves are markedly concave. The f3(3) functions of the untreated charcoals in panel b are similarto the ones deduced from the random pore models[19][20][21][22] reflecting that the growth of the internal pores increases the available reaction surface area and its accessibility during the burn-off. After reaching a maximum, this effect is counterbalanced by the consumption of the sample. ...
Charcoals produced by a modern, efficient method were studied in the kinetic regime, at oxygen partial pressures of 0.2 and 1 bar by thermogravimetric experiments and their reaction kinetic modeling. The charcoals were ground to an average particle size of 5−13 μm. A partial removal of minerals from the feedstock (corncobs) by an acid-washing procedure resulted in ca. 6 times higher specific surface area in the charcoal. Despite the increased surface area, this sample evidenced a much lower reactivity. A model based on three reactions gave an adequate description over a wide range of experimental conditions. Thirty-eight experiments on four charcoal samples were evaluated. The experiments differed in their temperature programs, in the ambient gas composition, and in the grinding of the samples. Characteristics of the combustion process were determined including activation energy values characteristic for the temperature dependence of the burnoff, formal reaction orders characterizing the dependence on the oxygen content of the ambient, and functions describing the conversion dependence of the partial processes.
... There are theoretical models for the f() function in eq 1 which describes the change of the reactive surface area as the reaction proceeds. 13,14 The simple shrinking core model, f()=(1-) 2/3 , also falls into this category. 15 The theoretical f() models were deduced for pure, homogeneous carbons. ...
... (ii) We cannot exclude the possibilities of growing internal surfaces as predicted by the models deduced for ideal carbons. 13,14 To check this possibility we carried out the evaluation with an empirical f() function that can mimic a wide variety of shapes: 12,20,21,24 d3/dt = A3 exp(-E3/RT) f3(3) CCO 2 ...
The CO2 gasification of pine and birch charcoals was studied by thermogravimetric analysis (TGA) at CO2 partial pressures of 51 and 101 kPa. Linear and stepwise heating programs were employed to increase the information content of the experimental data sets. Low sample masses were used because of the high enthalpy change. Seven experiments with different experimental conditions were evaluated simultaneously for each sample. The method of least-squares was employed. Three reactions appeared in the temperature domain evaluated (600−1000 °C). The first and second reactions were due to the devolatilization and did not show a significant dependence upon the CO2 concentration. They were approximated by first-order kinetics. The third reaction corresponded to the gasification. Its modeling was based on an empirical approximation of the change of the reaction surface during the gasification and by a formal reaction order with respect to the CO2 concentration. Very close results were obtained for the two charcoals. The dependence upon the conversion could be well-approximated by power law kinetics. In the next step of the evaluation, the experiments of the two samples (14 experiments combined) were evaluated together, assuming common activation energy values and a common reaction order with respect to the CO2 concentration. This process led to nearly the same fit as the separate evaluation of the two samples. The activation energy of the gasification step was 262 kJ/mol. The reaction order of CO2 was 0.40.
... Many of such model have been proposed, see e.g. [116,64,58,167,45,14,203,149,152]. Three of the most popular approaches are sketched in the following. ...
The design and optimization of entrained flow gasifiers is conducted more and more via computational fluid dynamics (CFD). A detailed resolution of single coal particles within such simulations is nowadays not possible due to computational limitations. Therefore the coal particle conversion is often represented by simple 0-D models. For an optimization of such 0-D models a precise understanding of the physical processes at the boundary layer and within the particle is necessary. In real gasifiers the particles experience Reynolds numbers up to 10000. However in the literature the conversion of coal particles is mainly regarded under quiescent conditions. Therefore an analysis of the conversion of single particles is needed. Thereto the computational fluid dynamics can be used. For the detailed analysis of single reacting particles under flow conditions a CFD model is presented. Practice-oriented parameters as well as features of the CFD model result from CFD simulations of a Siemens 200MWentrained flow gasifier. The CFD model is validated against an analytical model as well as two experimental data-sets taken from the literature. In all cases good agreement between the CFD and the analytics/experiments is shown. The numerical model is used to study single moving solid particles under combustion conditions. The analyzed parameters are namely the Reynolds number, the ambient temperature, the particle size, the operating pressure, the particle shape, the coal type and the composition of the gas. It is shown that for a wide range of the analyzed parameter range no complete flame exists around moving particles. This is in contrast to observations made by other authors for particles in quiescent atmospheres. For high operating pressures, low Reynolds numbers, large particle diameters and high ambient temperatures a flame exists in the wake of the particle. The impact of such a flame on the conversion of the particle is low. For high steam concentrations in the gas a flame appears, which interacts with the particle and influences its conversion. Furthermore the impact of the Stefan-flow on the boundary layer of the particle is studied. It is demonstrated that the Stefan-flow can reduce the drag coefficient and the Nusselt number for several orders of magnitude. On basis of the CFD results two new correlations are presented for the drag coefficient and the Nusselt number. The comparison between the correlations and the CFD shows a significant improvement of the new correlations in comparison to archived correlations. The CFD-model is further used to study moving single porous particles under gasifying conditions. Therefore a 2-D axis-symmetric system of non-touching tori as well as a complex 3-D geometry based on the an inverted settlement of monodisperse spheres is utilized. With these geometries the influence of the Reynolds number, the ambient temperature, the porosity, the intrinsic surface and the size of the radiating surface is analyzed. The studies show, that the influence of the flow on the particle conversion is moderate. In particular the impact of the flow on the intrinsic transport and conversion processes is mainly negligible. The size of the radiating surface has a similar impact on the conversion as the flow in the regarded parameter range. On basis of the CFD calculations two 0-D models for the combustion and gasification of moving particles are presented. These models can reproduce the results predicted by the CFD sufficiently for a wide parameter range.
... The internal surface area of a char will change as char conversion proceeds. Two common models describing this change are the grain model [81,82] and the random pore model [81,[83][84][85]. In the grain model, which presumes the porous carbon particle to be a collection of grains of various shapes and sizes, the volume specific internal surface area (in m 2 /m 3 ) is given by ...
This paper gives a review of the current state of the art for numerical simulations of char conversion. In particular, it presents models that have been developed to describe the physical and chemical phenomena that characterize thermochemical char conversion. All particle sizes are covered, ranging from pulverized particles to wood logs. The aim of the paper is to give the reader the required starting point in order to develop his own simulation tool. Two fundamentally different approaches are studied in detail, namely the resolved particle approach and the point particle approach. In the resolved approach, both the char particle itself and the surrounding boundary layer is resolved. This means that heat, mass and momentum transfer are accurately handled. For the point particle approach, which is computationally much cheaper, one has to rely on suitable models to estimate for example the heat, mass and momentum transfer. Finally, the paper also gives detailed descriptions of how to handle ash inclusions in the char in addition to particle fragmentation and thermal annealing.
... As the reaction proceeds, pores begin to overlap, reaching a maximum specific surface area followed by a monotonic decrease until the end of the reaction. In the scientific literature, there are several works on pore overlap models, among which the works of Gavalas, 36 and Bhatia and Perlmutter 37,38 stand out. However, these models assume that pores growth is radial. ...
This work proposes a novel population‐balance based model for a bubbling fluidized bed reactor. This model considers two continuum phases: bubble and emulsion. The evolution of the bubble size distribution was modeled using a population balance, considering both axial and radial motion. This sub‐model involves a new mathematical form for the aggregation frequency, which predicts the migration of bubbles from the reactor wall toward the reactor center. Additionally, reacting particles were considered as a Lagrangian phase, which exchanges mass with emulsion phases. For each particle, the variation of the pore size distribution was also considered. The model presented here accurately predicted the experimental data for biochar gasification in a lab‐scale bubbling fluidized bed reactor. Finally, the aggregation frequency is shown to serve as a scaling parameter.
... The slight variation in pore volume signifies the heterogeneity of charification occurred at the surface of the porous structure due to the blending effects (Fig. 4fen). Also, during the carbon conversion, the surface area of the pore structures may increase due to the external reactions, or decrease due to the different capillary overlapping [74]. However, a significant difference is noticed between pore volumes of 100% press mud and bottom ash of the blending ratio 6:4. ...
The reactivity of coal and biomass has been evaluated by comparing the optical and chemical changes in feed material prior and after the co-gasification. The proximate, ultimate, GCV, low-pressure N2 sorption isotherm, micropetrography, SEM and EDX spectroscopy analyses are carried out to assess the reactivity of blends of high ash Indian coal and biomass. The relative changes in parameters like surface area, pore size, and pore volume have been correlated with reacted percentage area of coal macerals and cellulose-lignin cellular structures of biomass. The Optimas image processing software is being used to mark the reacted portion of organic constituents and calculated the reactivity percentage. The bottom ash of pure coal has shown the least reacted organic matters, indicating inefficiency of high ash coal due to a large amount of inorganic and inertinite contents that is resisting the oxidation. The reactivity percentage is determined by the petrographic and SEM images, and varies from 36.34 to 99.64% and 6.61–96.22%, respectively. It is summarised that the estimation of percentage alteration of macerals and other micro-organic constituents can be used as one of the practical approaches for the assessment of the reactivity of coal and biomass. The blending ratio 6:4 of coal and press mud has shown the highest reactivity (>99.64%). The values of petrographic and SEM reactivity have shown good correlations with the carbon contents, unreacted vitrinites, mineral matters and biomass remnants. These relations have been taken into account to formulate the proposed petrographic empirically calculated reactivity (RPEC). The focus has also been made to investigate the influence of feed composition on carbon conversion and heating value of the product gas.
... The kinetic parameters (EA and k0) were determined using three theoretical models (Table I) under the conversion range between 0 and 95 % using MS Excel software. In this study, the volumetric model (VM) [32,33], shrinking model (SCM) [34,35] and the random pore model (RPM) [36][37][38][39] were used to fit the experimental data, and each model covers a different form of the function f(X), which describes the changes in the physical and chemical properties of the sample during the gasification process. The agreement between the experimental data and the values calculated by the kinetic models were expressed by the coefficient of determination (R 2 ) where 0 <R 2 <1. ...
The objective of this study was to evaluate the kinetic parameters of a gasification process, under CO2 atmosphere, of biochars produced from the agroindustrial wastes: castor bean presscake (CBP) and mesquite pod bagasse (MPB). The biochars were produced by pyrolysis under atmospheric pressure with N2 gas flow of 400 mL min-1 at two conditions, the first at 700 ºC (heating rate of 160 °C min-1) and the second at 900 ºC (heating rate of 224 °C min-1), both with a 5 min residence time at the final temperature. The biochars showed a potential to be used in energy production systems due to their HHV compared with some fossil fuels. The isothermal gasification of the biochar runs were performed in a thermogravimetric analyzer at atmospheric pressure. The theoretical kinetic models used to adjust the experimental data were volumetric model (VM), shrinking model (SCM) and random pore model (RPM). In terms of CO2 reactivity, the biochars from MPB were more reactive than biochars from the CBP, in the temperature range of 760-920 °C. The EA values related to the biochars gasification were around 187-238 kJ mol-1 , and the theoretical kinetic model of RPM proved more appropriate for representing the experimental data.
... There are theoretical models to describe the roles of the internal pores which have been deduced for ideal cases, assuming pure carbon particles of regular shape. 30, 31 The gasification of a real char, however, differs from the ideal behavior by several complicating factors, including the presence of the mineral matter and the irregular geometry. ...
The CO2 gasification of chars was investigated by thermogravimetry (TGA). The chars were prepared from spruce and its forest residue. Prior to the gasification the raw materials were pelletized and pulverized. Part of the samples was directly gasified in the TGA when the char was formed at low heating rates before the gasification. Another sort of char was prepared in a drop tube reactor (DTR) at a heating rate of around 1×10⁴ °C/s and a residence time of 0.2 s at 1200°C. The kinetic evaluation was based on TGA experiments with linear, modulated, and constant-reaction rate (CRR) temperature programs. The gasification of the DTR chars took place at temperatures 80–100°C lower than the chars formed at low heating rates. The chars formed at low heating rates exhibited a side reaction that occurred 80–100 °C below the main peak of the mass-loss rate curves during the gasification. Accordingly the gasification kinetics of these chars was described by assuming two pseudo-components. The thermal annealing (thermal deactivation) of the chars during the gasification experiments was taken into account by the pre-exponential factors which were allowed to have different values at different temperature programs. A strong compensation effect was observed between the activation energy (E) and the rest of the kinetic parameters. Nevertheless, the obtained E values varied in a narrow interval (from 219 till 227 kJ/mol) and were very close to the ones obtained for other chars with similar kinetic evaluation procedures (Wang et al., Energy & Fuels 2013, 27, 6098-6107 and 2014, 28, 7582-7590.)
... The random pore model (RPM) developed by Bhatia and Perlmutter [16] as well as Gavalas [17] is supported as being appropriate for application. This model accounting for the effects of pore growth and coalescence has often shown satisfactory agreement between theory and experiment. ...
... Obviously normfactor is not an independent parameter, it is a simple function of n and z. 13 There are theoretical models to describe the roles of the internal pores which have been deduced for ideal cases, assuming pure carbon particles of regular shape. 26,27 The burn-off of a real char, however, differs from the ideal behavior by several complicating factors, including the presence of the mineral matter and the irregular geometry. ...
The combustion properties of spruce chars and spruce forest residue chars were studied in the kinetic regime by a series of thermogravimetric analysis (TGA) experiments. The work aimed at establishing how the pressure of the char preparation affects the reactivity with oxygen. Parts of the chars were prepared from a thin layer of biomass in inert gas flow at atmospheric pressure and 0.8 MPa. Other chars were formed in a pressurized reactor by a flash carbonization method [Antal, M. J., Jr., Mochidzuki, K., and Paredes, L. S.Flash carbonization of biomass. Ind. Eng. Chem. Res.2003, 42 (16), 3690−3699, DOI: 10.1021/ie0301839]. Despite the differences in the preparation, remarkable similarities were observed in the combustion behavior of the samples. The kinetics of the char burnoff was described by assuming three partial reactions. A total of 18 experiments at three different temperature programs were evaluated by the method of least squares to obtain dependable kinetic model variants. A common activation energy of 150 kJ/mol gave a reasonable description for the three partial reactions in all experiments.
... Numerous studies have dealt with the gasification of chars from the pyrolysis of coal, synthetic polymers or biomass (Diblasi, 2008;Hurt and Mitchell, 1992;Laurendeau, 1978;Mermoud et al., 2006;Miura et al., 1989;Smith, 1982; Van de steene et al., 2011;). The char conversion rate can be modelled by empirical laws fitted on the mass loss of the solid (Diblasi, 2008;Laurendeau, 1978;Teixeira et al., 2014) but the most advanced models are rather based on the fundamental parameters which control the reactivity of char, namely: the carbon active sites and surface chemistry of char (Bar-Ziv and Kantorovich, 2001;Campbell and Mitchell, 2008;Davis et al., 1995;Geier et al., 2013;Gupta and Bhatia, 2000;Hurt and Calo, 2001;Hurt and Haynes, 2005;Klose and Wölki, 2005;Leistner et al., 2012;Lizzio et al., 1990;Radović et al., 1983), the accessible surface area and porous structure of the particle (Ballal and Zygourakis,Extensive models have emphasized the importance of structural effects on the conversion rate especially for microporous char (Ballal and Zygourakis, 1987;Bhatia and Perlmutter, 1980;Bhatia and Vartak, 1996;Gavalas, 1980;Kantorovich and Bar-Ziv, 1994). It has been shown that the surface chemistry is also a very important parameter and should be considered with the porous structure for a proper modelling of char oxidation (Bar-Ziv and Kantorovich, 2001;Gupta and Bhatia, 2000;Kantorovich and Bar-Ziv, 1994;Leistner et al., 2012;Ma and Mitchell, 2009;Miura et al., 1989;Yaşyerli ̇ et al., 1996). ...
In combustion and gasification reactors, solid fuels such as coal or biomass undergo a pyrolysis step to form volatiles and a char. Pyrolysis is combined with an oxidation by O2, H2O and/or CO2 of the resultant char. Here we propose an original approach to model the oxidation of a single char particle. The intrinsic chemical reactivity of the char surface is assessed by the reactive surface area (RSA). The evolution of the RSA upon the conversion of the particle (burn-off) is modelled by a specific kinetic law similar to the law used to model the evolution of active sites in catalysis. This approach is applied on experimental results taken from the literature for coal and wood chars for O2, H2O or CO2 gasification. The evolution of the total surface area (TSA) is modelled by the random pore model. Diffusional limitations are also accounted for.
... Uniform or peripheral percolative fragmentation of carbon particles during combustion or gasification has been modeled by a number of authors using either a continuum approach (Gavalas, 1980;Mohanty et al., 1982;Salatino andMassimilla, 1985, 1989;Jensen, 1986a, 1986b;Srinivasachar et al., 1988;Fuertes and Marban, 1994;Marban and Fuertes, 1997), a discrete approach (Sahimi and tsotsis, 1987;Kerstein and edwards, 1987;Salatino andMassimilla, 1988, 1991;Miccio and Salatino, 1992) or a coupled approach . Salatino and Massimilla (1988) likely to be negligible with respect to attrition by abrasion. ...
The different modes and sources of attrition relevant to fluidized bed combustion and gasification are surveyed. The broad spectrum of attrition mechanisms and phenomenologies is comprehensively described. The survey addresses attrition of the different types of solids employed in fluidized bed combustion and gasification: solid fuels, sorbent materials, inert bed solids (ash and ballast materials, e.g. sand). Moreover, the survey considers attrition of bed solids that are currently employed in modern solids looping processes aimed at CCS-ready conversion of solid fuels, e.g. sorbents in carbonate looping and oxygen carriers in chemical looping combustion and gasification. The analysis specifically addresses the important topic of the mutual interaction between attrition and the progress of chemical reactions. The current status of modeling of attrition phenomena and the available tools to account for attrition in comprehensive population balance models of fluidized bed combustors and gasifiers are presented.
... If the reaction takes place on the external surface of homogeneous, isotropic spherical particles of equal size, then the contracting sphere (shrinking sphere) model can be employed, while the presence of internal reaction surfaces leads to self-acceleration which can be described by random-pore models. [28][29][30] The biomass chars, however, are usually too complex for these theories because they are chemically inhomogeneous, geometrically irregular, and contain mineral matter with more or less catalytic activity. Accordingly, only empirical f(?) functions can be employed. ...
The CO2 gasification of torrefied wood samples was examined by thermogravimetric analysis (TGA) at linear, modulated, and constant reaction rate (CRR) temperature programs. The untreated raw materials and chars prepared at 750 °C were also included in the study. The gasification temperature range separated sufficiently from the pyrolysis in the experiments for its separate analysis. Characteristic gasification reactivity differences were observed between the samples that were due to the differences of the char-forming reactions at different conditions. Various groups of experiments were evaluated together by the method of least squares, under various hypotheses on the dependence of the reaction rate upon the reacted fractions. The differences between the samples were described by different pre-exponential factors, while the rest of the kinetic parameters were kept identical during an evaluation. The effect of thermal annealing on the gasification kinetics was also expressed by the values of the pre-exponential factors. When the experiments of the samples prepared from birch were evaluated together, self-accelerating kinetics was obtained with E = 225 kJ/mol. The experiments belonging to the samples prepared from spruce resulted in n-order kinetics with E = 223 kJ/mol.
... Bhatia and Perlmutter (1983) and Sotirchos and Yu (1988) have presented a general overlapping model for gas-solid systems that exhibit first-order kinetics with respect to the gaseous reactant concentration. This model is derived from random pore structure models, developed for the case where the system is initially formed of an unreacted solid matrix with randomly distributed overlapping cylindrical pores Perlmutter, 1980, 1981;Gavalas, 1980;Sotirchos and Yu, 1985). They considered that the initial porous structure can be represented by a population of particles of a given geometry in a certain size range, randomly distributed in space. ...
... A promising model of predicting the evolution of internal surface area of the pores with burn-off has been developed independently by Gavalas 31 and Bathia and Perlmutter. 32 It assumes a solid porosity consisting of infinitely-long overlapping random cylinders, and accounts for the widening and the random overlap of reacting surfaces (or coalescence) of the pores. ...
A massive air or steam ingress in High Temperature Reactors (HTRs) nominally operating at 600-950 o C is a design-basis accident requiring the development and validation of graphite oxidation and erosion models to examine the impact on the potential fission products release and the integrity of the graphite core and reflector blocks. Nuclear graphite is of many types with similarities but also differences in the microstructure, volume porosity, impurities, type and size of filler coke particles, graphitization and heat treatment temperatures, and the thermal and physical properties. These as well as the temperature, types and partial pressures of oxidants affects the prevailing oxidation mode and kinetics of the oxidation processes of graphite in HTRs. This paper reviews the graphite crystalline structure, the fabrication procedures, characteristics, chemical kinetics and modes of oxidation of nuclear graphite for future model developments.
... It has an abundance of submicropores, of which the surface areas have been thought to be predominant in the char reactions. Some researchers put forward different reaction models [10][11][12][13][14] to depict them, while the random pore model (RPM) developed by Bhatia and Perlmutter [15] as well as Gavalas [16] is supported as being appropriate for application. ...
The gasification of straw stalk in CO2 environment was studied by isothermal thermogravimetric analysis. The characteristics of rice straw and maize stalk gasification at different temperatures were examined under CO2 atmosphere. The relationship between reaction time and carbon conversion of two biomass chars was analyzed by the random pore model (RPM), and compared with the simulation of the shrinking core reaction model (SCRM). The results show that the random pore model is better to predict the experimental data at different temperatures. This means that the characteristics of pore structure for the influence of biomass chars gasification is well reflected by parameter ψ used in RPM. It indicates that the RPM can be applied to the comprehensive simulation of biomass chars gasification in CO2 environment.
... Another approach employing population balance equations to describe the change in the pore structure during gasification process was proposed by Hashimoto and Silveston (1973). Gavalas (1980) used a random capillary model to model char gasification. A random pore model for interpreting of fluid-solid reaction was developed by Bhatia and Perlmutter (1980). ...
... There are theoretical models for that situation in the literature that have been deduced for ideal cases with pure carbon particles of regular shape. 32,33 The gasification of a real char, however, can be altered from the ideal behavior by several complicating factors, including the presence of the mineral matter and the irregular geometry. Hence, a simple empirical formula can be used instead of a theoretical one that can mimic a wide varieties of shapes 34 ...
The CO2 gasification of chars prepared from Norway spruce and its forest residue was investigated in a thermogravimetric analyzer (TGA) at slow heating rates. The volatile content of the samples was negligible; hence the gasification reaction step could be studied alone, without the disturbance of the devolatilization reactions. Six TGA experiments were carried out for each sample with three different temperature programs in 60 and 100% CO2. Linear, modulated, and constant-reaction rate (CRR) temperature programs were employed to increase the information content available for the modeling. The temperatures at half of the mass loss were lower in the CRR experiments than in the other experiments by around 120 °C. A relatively simple, well-known reaction kinetic equation described the experiments. The dependence on the reacted fraction as well as the dependence on the CO2 concentration were described by power functions (n-order reactions). The evaluations were also carried out by assuming a function of the reacted fraction that can mimic the various random pore/random capillary models. These attempts, however, did not result in an improved fit quality. Nearly identical activation energy values were obtained for the chars made from wood and forest residues (221 and 218 kJ/mol, respectively). Nevertheless, the forest residue char was more reactive; the temperatures at half of the mass loss showed 20–34 °C differences between the two chars at 10 °C/min heating rates. The assumption of a common activation energy, E, and a common reaction order, ν, on the CO2 concentration for the two chars had only a negligible effect on the fit quality.
... Both features are known to be important in adsorption processes. Prediction of porosity development during combustion and gasification involves a significant effort in and of itself [105,106]. This effort is in addition to that needed to describe the formation of bubble and void structures in softening coals [107,108], or the fragmentation of particles during combustion [84,109]. ...
The control of mercury in the air emissions from coal-fired power plants is an ongoing challenge. The native unburned carbons in fly ash can capture varying amounts of Hg depending upon the temperature and composition of the flue gas at the air pollution control device, with Hg capture increasing with a decrease in temperature; the amount of carbon in the fly ash, with Hg capture increasing with an increase in carbon; and the form of the carbon and the consequent surface area of the carbon, with Hg capture increasing with an increase in surface area. The latter is influenced by the rank of the feed coal, with carbons derived from the combustion of low-rank coals having a greater surface area than carbons from bituminous- and anthracite-rank coals.The chemistry of the feed coal and the resulting composition of the flue gas enhances Hg capture by fly ash carbons. This is particularly evident in the correlation of feed coal Cl content to Hg oxidation to HgCl2, enhancing Hg capture. Acid gases, including HCl and H2SO4 (at small concentrations) and the combination of HC1 and NO2, in the flue gas can enhance the oxidation of Hg.In this presentation, we discuss the transport of Hg through the boiler and pollution-control systems, the mechanisms of Hg oxidation, and the parameters controlling Hg capture by coal-derived fly ash carbons.
... With the solution of this closure problem may appear to be excessively complex, it is comparable in difficulty to a random capillary model [43] and indeed that particular geometrical model can be solved within the framework of Equations 207-212. One must keep in mind, however, that random capillary tube models are generally used to predict mass transport and in that case the detailed structure of the K-phase is not particularly important. ...
This chapter begins with a detailed description of the axioms for mass, momenum and energy for multicomponent systems. A precise derivation of the thermal energy equation is given, and this is followed by a development of the local volume averaged equations for the species molar concentration and the temperature in porous catalysts. Results for the effective thermal conductivity are presented. The local volume averaged form of the thermal energy equation for the fluid phase is then developed, and we illustrate how this result is connected to the thermal energy equation for the porous solid phase
... Two independent mechanisms are responsible for surface area evolution during gasification. One is caused by reaction alone, which can be represented by the random pore model [48][49][50]. The other one is due to annealing. ...
This paper surveys the database on char gasification at elevated pressures, first, to identify the tendencies that are essential to rational design of coal utilization technology, and second, to validate a gasification mechanism for quantitative design calculations. Four hundred and fifty-three independent tests with 28 different coals characterized pressures from 0.02 to 3.0 MPa, CO2 and steam mole percentages from 0 to 100%, CO and H2 levels to 50%, gas temperatures from 800 to 1500 °C, and most of coal rank spectrum. Only a handful of cases characterized inhibition by CO and H2, and only a single dataset represented the complex mixtures of H2O, CO2, CO, and H2 that arise in practical applications. With uniform gas composition, gasification rates increase for progressively higher pressures, especially at lower pressures. Whereas the pressure effect saturates at the higher pressures with bituminous chars, no saturation is evident with low-rank chars. With fixed partial pressures of the gasification agents, the pressure effect is much weaker. Gasification rates increase for progressively higher gas temperatures. In general, gasification rates diminish for coals of progressively higher rank, but the data exhibit this tendency only for ranks of hv bituminous and higher.
... Since the structure of a porous medium is often characterized by a pore-size distribution (Dullien, 1979;Conner et al., 1983), there is a natural tendency to investigate random arrays of capillary tubes in an effort to model transport processes in heterogeneous media, Although the random array of spheres seems to be a plausible representation of unconsolidated porous media, one can put forth reasonable arguments in favour of random arrays of capillary tubes as a model to be used with consolidated media. Examples of this approach are given by Gavalas (1980), Bhatia and Perlmutter (1983) and Greenkorn (1983). In addition, the random nature of many heterogeneous media has motivated numerous studies of the diffusion and reaction process using percolation theory, An example of this type of analysis is given by Mohanty et al. (1982). ...
This paper presents a general theoretical analysis of the problem of diffusion and chemical reaction in heterogeneous two-phase media in which membrane or interfacial resistances can be important. Volume-averaged transport equations are derived for both phases with a first-order, irreversible reaction occurring in the dispersed phase. From these equations, a one-equation model is derived and the constraints that the one-equation model must satisfy are identified. A method of closure is developed in order to determine effective diffusivities, and the influence of the membrane permeability on the effective diffusivity is illustrated for a wide range of the parameters that describe the system. Experimental data for the effective diffusivity in a cellular system are used in conjunction with our theoretical results to determine the membrane permeability of a biological system.
... The above solutions conform to solutions for the kinetics-controlled regime (& Q 1) given by Del Borghi er al. (1976), Gavalas (1980), Simons (1983) and Tseng and Edgar (1984). ...
In Part I, analytical solutions were given for the non-linear isothermal heterogeneous conversion of a porous solid particle. Account was taken of a reaction rate of general order with respect to the gas reactant, intrinsic reaction surface area and effective pore diffusion, which change with solid conversion and external film transport. In this part, the analytical solutions are extended to non-isothermal conversion. Analytical solutions for the particle overshoot temperature due to heat of reaction are derived from the governing differential equation pertaining to conservation of energy, considering the limiting cases of small and large Thiele moduli. The solutions are used to assess the effect of interaction between chemical reaction rate and particle overshoot temperature on particle conversion. The analytical solutions are shown to compare favourably with numerical simulation results.
... The pore volume distribution corresponding to these distribution functions is similar to that utilized in the random pore model (Gavalas, 1980(Gavalas, & 1981. However, the pore tree model and the random pore model differ dramatically in their choice of the pore aspect ratio (length to diameter) and its implications with respect to pore branching. ...
The 'pore tree' model of pore structure was developed for catalysts and sorbents to allow diffusion within a porous media in the absence of convection through the media. The pore tree model is extended herein to describe the permeable pore structure which characterizes the subsurface flow of water in soil, the dispersion of contaminants and the in-situ remediation of contaminated sites. Permeability requires a statistical determination of the 'branches' that are common to several trees to allow percolation through the large scale (mobile) structure in addition to diffusion through the smaller scale (immobile) structure. While permeability is dominated by the largest pores, it is important to determine the level of convection that is occurring at the intermediate scales in order to accurately describe transport. (AN)
... In the case of ideal chars (specially prepared, pure model carbons), the reaction rate is proportional to the surface area, and the change of the surface area during the reaction can be described by theoretical models. [26][27][28][29] In the case of a tobacco or a biomass fuel, however, ...
Two blends of tobacco (Virginia and Burley) were studied by thermogravimetry at linear and nonlinear heating programs in gas flows containing 2, 4, and 9% oxygen. A kinetic scheme of successive devolatilization and char-burnoff reactions was assumed. A distributed activation energy model was assumed for devolatilization with a Gaussian distribution and a constant preexponential factor. The evaluations were also carried out using nonconstant preexponential factors that depended on the activation energy. The char burnoff was described by first-order kinetics and by an empirical model that took into account the change of the reactivity with conversion of the sample. The dependence of the rate of combustion on the oxygen concentration was approximated by a power function. Series of 15 and 30 experiments were used for the determination of the model parameters by simultaneous least-squares evaluation of the experiments. The considerations, methods, and results can also be used in the fields of biomass gasification and combustion.
... In ideal cases the corresponding change of the surface area during the reaction can be described by theoretical models. 32,33 In the case of a biomass fuel, however, complicating factors arise that are connected to the accessibility of the internal pores, the role of the inorganic catalysts, and the chemical/physical inhomogeneity of the solid phase. Among others, the char formation is not separated from the char burn-off; the formed char particles may burn before developing a bulk with internal pores. ...
Wheat straw, willow from an energy plantation, and municipal sewage sludge were studied by thermogravimetry at linear and nonlinear heating programs in gas flows containing 4 and 20% oxygen. A kinetic scheme of successive devolatilization and char burnoff reactions was assumed. A distributed activation energy model (DAEM) was assumed for the devolatilization with a Gaussian distribution and a constant pre-exponential factor. The burnoff of the forming char was approximated by first-order kinetics with respect to the amount of char. The dependence of the reactions upon the oxygen concentration was described by power functions. This model gave a suitable description for the wheat straw and sewage sludge. An additional partial reaction with accelerating kinetics was needed for describing the oxidative cellulose pyrolysis in the willow sample. The evaluations were carried out by the method of least squares. 9–17 model parameters were determined from ten experiments for each sample. Good fit quality and reasonable kinetic parameters were obtained. Test evaluations revealed that the first-order kinetics with respect to the amount of char is an adequate model; the assumptions of more complex char burnoff submodels did not led to notable improvements. The replacement of the DAEM devolatilization by simpler n-order kinetics gave inadequate performance. Earlier works with simpler models and linear temperature programs showed that the successive mechanism can be well-approximated by parallel reactions. Such approximations proved to be viable in the present case, too.
... The structured-type model explicitly consider the structural solid changes during reaction by modeling the variation of the internal solid matrix (grain models: Szekely et al. 15 ; Heesink et al. 16 ) or the internal pore structure (pore development models: Bhatia and Perlmutter 17,18 ; Gavalas. 19,20 ) In the volumetric-type approach, in contrast, the changes in pore structure during conversion are considered by using experimental correlations. ...
Chemical Looping Combustion technology involves circulating a metal oxide between a fuel zone where methane reacts under anaerobic conditions to produce a concentrated stream of CO2 and water and an oxygen rich environment where the metal is reoxidized. Although the needs for electrical power generation drive the process to high temperatures, lower temperatures (600–800°C) are sufficient for industrial processes such as refineries. In this paper, we investigate the transient kinetics of NiO carriers in the temperature range of 600 to 900°C in both a fixed bed microreactor (WHSV = 2-4 g CH4/h/g oxygen carrier) and a fluid bed reactor (WHSV = 0.014-0.14 g CH4/h per g oxygen carrier). Complete methane conversion is achieved in the fluid bed for several minutes. In the microreactor, the methane conversion reaches a maximum after an initial induction period of less than 10 s. Both CO2 and H2O yields are highest during this induction period. As the oxygen is consumed, methane conversion drops and both CO and H2 yields increase, whereas the CO2 and H2O concentrations decrease. The kinetics parameter of the gas–solids reactions (reduction of NiO with CH4, H2, and CO) together with catalytic reactions (methane reforming, methanation, shift, and gasification) were estimated using experimental data obtained on the fixed bed microreactor. Then, the kinetic expressions were combined with a detailed hydrodynamic model to successfully simulate the comportment of the fluidized bed reactor. © 2010 American Institute of Chemical Engineers AIChE J, 2010
... This article aims to develop a generalised dynamic model that integrates research results in various areas of concern discussed above. It consists of ÿve sub-models: (1) multi-component mass transfer with chemical reactions in porous media using the dusty-gas model, and in the ue gas ÿlm using the Maxwell-Stefan analysis (Jackson, 1977;Krishna & Wesselingh, 1997), (2) heat transfer between ue gas and char particle, (3) microstructure evolution using the classical random pore model (Bhatia & Perlmutter, 1980;Gavalas, 1980), (4) peripheral fragmentation, and (5) computations of physical properties under the simulated operational conditions. These ÿve sub-models are inter-connected and solved simultaneously by using a uniÿed computational algorithm. ...
A generalised model for the prediction of single char particle gasification dynamics, accounting for multi-component mass transfer with chemical reaction, heat transfer, as well as structure evolution and peripheral fragmentation is developed in this paper. Maxwell–Stefan analysis is uniquely applied to both micro and macropores within the framework of the dusty-gas model to account for the bidisperse nature of the char, which differs significantly from the conventional models that are based on a single pore type. The peripheral fragmentation and random-pore correlation incorporated into the model enable prediction of structure/reactivity relationships. The occurrence of chemical reaction within the boundary layer reported by Biggs and Agarwal (Chem. Eng. Sci. 52 (1997) 941) has been confirmed through an analysis of CO/CO2 product ratio obtained from model simulations. However, it is also quantitatively observed that the significance of boundary layer reaction reduces notably with the reduction of oxygen concentration in the flue gas, operational pressure and film thickness. Computations have also shown that in the presence of diffusional gradients peripheral fragmentation occurs in the early stages on the surface, after which conversion quickens significantly due to small particle size. Results of the early commencement of peripheral fragmentation at relatively low overall conversion obtained from large a number of simulations agree well with experimental observations reported by Feng and Bhatia (Energy & Fuels 14 (2000) 297). Comprehensive analysis of simulation results is carried out based on well accepted physical principles to rationalise model prediction.
Coking during the hydrocarbon fuel pyrolysis is a key problem that needs to be considered. To get more insights into coke, this work explored deposit formation of hydrocarbon fuels from the coke characteristics. Pyrolytic deposition experiments of n-decane and HF-01 were experimentally performed by using electric heating stainless steel and TiN-coated tubes to investigate the different growth pathway of coke. The morphology, graphitization degree and mass of coke produced under different experimental conditions were analyzed by means of scanning electron microscopy, Raman spectroscopy and carbon burn-off method, respectively. Results reveal that the differences in physical properties and reactivity of coke between different tubes are due to the different growth mechanism. The graphitization degree of coke can distinguish the main growth mechanism. It is also found that the low reactive filamentous carbon with ID/IG value below 2.7 produced by metal catalytic coking is the primary cause of pipeline blockage. TiN coating effectively inhibits the production of filamentous carbon, meanwhile, the coking inhibition efficiency can reach above 70%. The simplified coking kinetic models and semi-empirical coke combustion models are established to explore the coke formation and oxidation process. The models are performed to investigate the coke characteristics, for further exploring and understanding intrinsic hydrocarbon fuel pyrolysis coking mechanism.
The gasification kinetics of charcoals and biomass chars is complicated by several factors, including chemical and physical inhomogeneities, the presence of mineral matter, and the irregular geometry of the pore structure. Even the theoretically deduced gasification models can only provide empirical or semiempirical descriptions. In this study, an empirical kinetic model from the earlier works of the authors was adapted for the CO2 gasification of biomass chars. It is based on a versatile polynomial approximation that helps to describe the dependence of the reaction rate on the progress of the conversion. The applicability of the model was tested by the reevaluation of 24 thermogravimetric analysis (TGA) experiments from earlier publications. The adjustable parameters of the model were determined by the method of least squares by evaluating groups of experiments together. Two evaluation strategies were tested. In the regular evaluations, the same kinetic parameters were employed for all the experiments with a given sample. The use of experiments with modulated and constant reaction rate (CRR) temperature programs made it possible to employ another approach too, when the preexponential factor was allowed to vary from experiment to experiment. The latter approach allows a formal kinetic description of the differences in the thermal deactivation of the samples caused by different thermal histories as well as of some inevitable systematic errors of the TGA experiments. The evaluations were carried out by both approaches, and the results were compared. The evaluations were based on 12 experiments. As a test, each evaluation of the study was repeated with only 8 experiments. The results of the latter test calculations indicated that the information content of the employed experiments is sufficient for the evaluation approaches of this work.
With the transition to renewable energies and, above all, strongly fluctuating electricity from wind and solar energy, there will be a need for energy storage in the future. For central grid-scale storages, underground geological storage, similar to those already used for fossil fuels, is in the first place under review. Compressed Air Energy Storages have already been successfully used to provide minutes to hours reserve. For storage capacities in the day to week range, storage is required on a chemical rather than a mechanical basis, through either the conversion of electricity into pure hydrogen (H2) or the generation of mixtures of natural gas and synthetic methane. The latter – the so-called power-to-gas option – allows the use of the existing gas infrastructure. A likely first choice for the storage of H2 or H2-SNG mixtures are man-made salt caverns. The suitability of porous rock storage (depleted hydrocarbon reservoirs or water-bearing reservoirs – aquifers) is still under investigation. Interest in porous rock storage options arises, inter alia, from the fact that many regions of Europe lack suitable salt deposits. Favorable salt deposits exist in the UK, notably in the Cheshire Basin to the west and in eastern England, with six salt cavern-hosted facilities operated as natural gas storages. In any case, underground gas storages are characterized by high safety and low environmental impact.
The total worldwide resources of oil sands, heavy oil, oil shale and coal far exceed those of conventional light oil. In situ combustion and gasification are techniques that can potentially recover the energy from these unconventional hydrocarbon resources. In situ combustion can be used to produce oil, especially viscous and immobile crudes, by heating the oil and reducing the viscosity of the hydrocarbon liquids allowing them to flow to production wells. In situ gasification can be used to convert deep carbonaceous materials into synthesis gas which can be used at surface for power generation and petrochemical applications. While both in situ combustion for oil recovery and in situ gasification of coal have been developed and demonstrated over many decades, the commercial applications of these techniques have been limited to date. There are many physical processes occurring during in situ combustion, including multi-phase flow, heat and mass transfer, chemical reactions in porous media and geomechanics. A key tool in analysing and optimising the technologies involves using numerical models to simulate the processes. This paper presents a brief review of mathematical modelling of in situ combustion and gasification with an emphasis on developing a generalised framework and describing some of the key challenges and opportunities.
Anthropogenic carbon dioxide (CO2) emissions, major contributors to the greenhouse effect, are considered as the main cause of global warming. So, decrease of CO2 emitted by large industrial combustion sources or power plants, is an important scientific goal. One of the approaches is based on CO2 separation and capture from flue gas, followed by sequestration in a wide range of geological formations. In this aim, CO2 is captured by sorbents like calcium oxide (CaO) in multi-cycle process of carbonation/decarbonation. However, it was shown that the most important limitations of such process are related to the reversibility of reaction. CaO rapidly loses activity towards CO2, so the maximum extent of carbonation decreases as long as the number of cycles increases. In order to well understand the processes and parameters influencing the capture capacity of CaO-based sorbents, it appears important to get details on the kinetic law governing the reaction, which have not been really studied up to now. To investigate this reaction, CaO carbonation kinetics was followed by means of thermogravimetric analysis (TGA) on divided materials. Special care was given to the validation of the usual kinetic assumptions such as steady state and rate-determining step assumptions. The aim was to obtain a model describing the reaction in order to explain the influence of intensive variables such as carbonation temperature and CO2 partial pressure. TGA curves obtained under isothermal and isobaric conditions showed an induction period linked to the nucleation process and a strong slowing down of the reaction rate once a given fractional conversion was reached. Both phenomena were observed to depend on carbonation temperature and CO2 partial pressure. To explain these results, the evolution of texture and microstructure of the solid during the reaction was regarded as essential. Reaction at the grain scale induces a volume increase from CaO to CaCO3 which causes a change in the porosity characteristics at the aggregates scale, which could block the access of the gas to the core of aggregates. Temperature jumps during TGA experiments have put in evidence a complex kinetic behavior since three distinct domains must be distinguished, over all the conversion range, whatever the temperature and CO2 pressure could be. The discussion of the results emphasizes the role of the porosity on the kinetic anti-Arrhenius behavior observed in the second domain. So carbonation reaction can be described by a two scales model: at a nonporous grain scale for the chemical reaction and at the aggregate scale, for the CO2 intergranular diffusion. The kinetic modeling, thanks to the software CIN4 (developed in collaboration with Astek), is able to couple both modeling scales in order to explain the kinetic slowing down and the influence of temperature and CO2 partial pressure on the reaction rate.
Three bituminous coal chars (Illinois #6, Utah Skyline, & Pittsburgh #8) were gasified separately at total pressures of 10 and 15 atm in an entrained-flow reactor using gas temperatures up to 1830 K and particle residence times < 240 ms. Most of the experiments were performed at conditions where the majority of particle mass release was due to H2O gasification, although select experiments were performed at conditions where significant mass release was due to gasification by both H2O and CO2. The measured coal data were fit to 3 char gasification models including a simple first-order global model, as well as the CCKN and CCK models that stem from the CBK model. The optimal kinetic parameters for each of the 3 models are reported, and the steam reactivity of the coal chars at the studied conditions is as follows: Pittsburgh #8 > Utah Skyline > Illinois #6.
We investigated the effects of the concentration of carbon dioxide on the char- gasification reaction under isothermal conditions of using the Drayton coal. Potassium carbonate was used to improve the low-temperature gasification reactivity. The enhancement of carbon dioxide concentration increased the gasification rate of char, while gasification rate reached a saturated value at the concentration of 70%. The best concentration for gasification is determined to be 70%. We compared the shrinking core model (SCM), volumetric reaction model (VRM) and modified volumetric reaction model (MVRM) of the gas-solid reaction models. The correlation coefficient values, by linear regression, of SCM are higher than that of VRM at low concentration. While the correlation coefficients values of VRM are higher than that of SCM at high concentration. The correlation coefficient values of MVRM are the highest than other models at all concentration.
A mathematical model is constructed to describe the dynamics of the pore structure of cokes of high-ash coals with allowance for the fact that the different parts of the internal volume of the structure are not equally accessible to the gaseous reactant. The model accounts for the increase in the area of the pore structure due to the removal of organic material, coalescence of pores, and opening of the interior volumes of the sample in the course of conversion. In the examination of heat- and mass-transfer processes inside the particles, attention is given to the thermal effect of the reaction along with diffusion resistance in the mineral component and the layer of reaction products — which decreases the cross section of the transport pores. The results of the calculations are compared with experimental data on the gasification of culm in gaseous carbon dioxide.
A Bethe network description of porous solids is used to model pore structure changes, including pore plugging, in the sulphation of calcined limestone. This model accounts for diffusion of SO2 in the shrinking pore space as well as in the product layer. The model predictions clearly demonstrate the increasing diffusion resistance and isolation of partially reacted pores causing incomplete conversion of the solid. The importance of an accurate description of pore space topology both in the interpretation of Hg porosimetry data and in transport calculations is illustrated. The model simulations show excellent agreement with published experimental observations.
The influence of structural heterogeneity, in the form of a non-uniform pore size distribution, on the isotherms and surface diffusion coefficients for monolayer physical adsorption is studied. A pore size dependent langmuirian isotherm is used along with consideration of equality of chemical potentials at the pore mouths at an intersection. The diffusion is modelled by a recently developed random walk formulation. It is found that the surface diffusion coefficients are strongly influenced by the heterogeneity and have a stronger increase with overall coverage than that predicted by the Darken equation. The results are found to match the experimental data of P. C. Carman and F. A. Raal on the diffusion of carbon dioxide in carbon black without the use of a fitting parameter.
A kinetic characterization of the CO2 gasification of chars from Argentinean low-rank coals, subbituminous (SB) and high volatile bituminous (HVB), is performed by isothermal thermogravimetry. Temperatures in the range 1173–1433 K and CO2 concentrations among 50% and 70% v/v are employed. Experimental data obtained for both chars for the whole range of experimental conditions explored were satisfactorily described by a single master curve. Reactivity differences between chars are discussed in terms of carbon content, microporosity and crystallinity of the char carbonaceous part. In addition, potential catalytic effects of inherent minerals on chars gasification reactivity are examined by demineralizing the chars. For the subbituminous char, catalytic effects due to mineral matter content are detected up to 1333 K, whereas at higher temperatures they become considerably less pronounced. For the bituminous char, reactivity seems to depend more on structural and textural features than on catalysis over the whole range of operating conditions. Intrinsic gasification rates for both chars are properly represented by the well-known random capillary and random pore models (RPM). Recent models based on modifications introduced to the latter are also applied and kinetic data description is discussed.
When a gasification reaction occurs within a porous solid the pore structure of the reacting solid changes with conversion. Such changes are especially important for the production of a solid product (e. g. , activated carbon) whose adsorption performance is closely associated with the pore structure that is developed. To quantify such changes, a general equation is derived that predicts the evolution of pore volume distribution during isothermal gasification in the regime of kinetic control, starting from a given initial condition. The development takes into account pore enlargement as well as pore intersections. Equations are also derived for the special cases of (1) uniform pore size and (2) bimodal distribution. The results are used to interpret the experimental data of previous researchers.
A review is made of the role of mathematics in the field of chemical engineering in the latter half of the twentieth century. The beginning of this era was marked by the concerted effort of a few to raise the mathematical consciousness of the profession to think fundamentally about processes. We have accomplished this review by providing a rough structure of the areas of mathematics, deliberating on how each area has matured through growing applications, to conclude that mathematics is the main medium to meditate not only about processes, but even about materials and products. As we are clearly entering another era where the domain of chemical engineering is expanding into new areas with a focus on discovery oriented high throughput technology, modeling and rapid computation must provide the guidelines for rational interpretation of multitudes of observations. © 2004 American Institute of Chemical Engineers AIChE J, 50: 7–23, 2004
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