Kinetics of heterogeneous reactions of carbon and oxygen during combustion of porous carbon particles in oxygen

A model of combustion of a high-porosity carbon particle in oxygen is considered, which takes into account heterogeneous and homogeneous chemical reactions inside the particles and radiative heat transfer. The boundaries of the domain where the burning rate depends on the particle temperature are determined. The possibility of two combustion regimes is demonstrated: regime with a high burning rate, where the carbon-oxygen reaction proceeds in a layer adjacent to the particle surface, and regime with a low burning rate, where the reaction proceeds in the entire particle volume. In the regime with a high burning rate, the main product of the reaction between carbon and oxygen is carbon monoxide, whereas both carbon monoxide and carbon dioxide can be formed in the regime with a low burning rate. The kinetic equations of heterogeneous reactions C + O₂ = CO₂ and 2C + O₂ = 2CO are determined, which reveal the retarding effect of carbon monoxide and dioxide on the rates of these reactions. __________ Translated from Fizika Goreniya i Vzryva, Vol. 42, No. 3, pp. 11–22, May–June, 2006.     

Ignition, extinction, and thermal hysteresis of a heterogeneous exothermic reaction

Critical conditions of ignition and extinction are studied theoretically for the case of a heterogeneous exothermic reaction proceeding on the uniformly accessible surface of a channel or a pore. Particular emphasis is placed on the thermal-hysteresis effect of the reaction (an ignition temperature in excess of the extinction temperature), which ensures stability of the reaction against changes in the external conditions. A model for the process is proposed and substantiated. It permits one to analyze the main regularities of the thermal reaction regime with allowance for the distribution of heat flows from the reaction zone to the reaction medium and the channel wall. The dependence of the critical conditions of ignition and extinction on the rate constants of heat release, the reaction order, and the thermal and geometric characteristics of the system is established. A rule is proposed that permits evaluating the effect of heat losses on the critical phenomena and the thermal hysteresis of a reaction on a cooled surface in the case where the critical conditions for the reaction on an adiabatic surface are known. Translated fromFizika Goreniya i Vzryva, Vol. 34, No. 2, pp. 51–58, March–April, 1998.     

Thermophoresis of a particle in a concentric cavity with thermal stress slip

The thermophoretic motion of a spherical particle situated at the center of a spherical cavity filled with a gaseous medium under a prescribed temperature gradient is studied analytically. The Knudsen number is small for the gas motion in the slip-flow regime, and the temperature jump, thermal creep, frictional slip, and particularly, thermal stress slip are allowed on the solid surfaces. After solving the equations of heat conduction and fluid motion, an explicit formula for the migration velocity of the confined particle is obtained for different temperature conditions of the cavity with arbitrary values of the particle-to-cavity radius ratio and other parameters. Contributions from the thermoosmotic flow along the cavity wall and from the wall-corrected thermophoretic force to the particle velocity are equivalently important and can be linearly superimposed. With either or both of these contributions, the particle velocity in general is a decreasing function of the particle-to-cavity radius ratio and vanishes in the limit. The effects of the thermal stress slip at the solid surfaces to the migration velocity of the confined particle can be significant and interesting, dependent on the thermal and interfacial properties of the particle and surrounding gas. The wall effect on the thermophoretic migration of the particle in a cavity is qualitatively different from that on the motion of the particle in a circular tube.

Copyright © 2018 American Association for Aerosol Research     

Transient three-dimensional heat transfer from rotating spheres with surface blowing

Transient heat transfer and thermal patterns around a rotating spherical particle with surface blowing are studied numerically for Reynolds numbers in the range 10?Re?300 and non-dimensional angular velocities up to Ω=1. This range of Reynolds number includes three distinct wake regimes: steady and axisymmetrical, steady but non-symmetrical, and unsteady with vortex shedding. The Navier-Stokes and energy equations for an incompressible viscous flow are solved numerically by a finite-volume method in a three-dimensional and time-accurate manner. The transient aspects of the thermal wakes associated with the aforementioned wake regimes have been explored. An interesting feature associated with particle rotation and surface blowing is that they can affect the near wake structure in such a way that an unsteady three-dimensional flow with vortex shedding develops at lower Reynolds numbers as compared to flow over a solid sphere in the absence of these effects, and thus, the temperature distributions around the particle are significantly affected. Despite the fact that particle rotation brings about major changes locally, the surface-averaged heat transfer rates are not influenced appreciably even at high rotational speeds; consequently, it is shown that the total heat transfer rates associated with rotating spheres with surface blowing can be calculated from heat transfer correlations developed for flow over evaporating droplets.     

De- and rehydration of Ca(OH)2 in a reactor with direct heat transfer for thermo-chemical heat storage. Part A: Experimental results

Heat storage technologies are used to improve energy efficiency of power plants and recovery of process heat. Storing thermal energy by reversible thermo-chemical reactions offers a promising option for high storage capacities especially at high temperatures. Due to its low material cost the use of the reversible reaction Ca(OH)₂ ? CaO + H₂O has been suggested. This paper reports on the thermal behavior of a reactor with direct heat transfer between the gaseous reactant and the solid material. Cycling stability is confirmed and the impact of the most significant parameters such as the maximum possible enthalpy difference of the heat transfer fluid between inlet and outlet, the heat transfer, the particle reaction rate and the mass transport is derived. In the test system the particle reaction rate could be identified as the main limiting parameter.     

Transient thermal behaviour of a cylindrical wood particle during devolatilization in a bubbling fluidized bed

This work proposes a transient heat transfer model to predict the thermal behaviour of wood in a heated bed of sand fluidized with nitrogen. The 2-D model in cylindrical coordinates considers wood anisotropy, variable fuel properties, fuel particle shrinkage, and heat generation due to drying and devolatilization. The influence of initial fuel moisture content, thermal diffusivity, particle geometry, shrinkage, external heat transfer coefficient, chemical reaction kinetics and heats of reaction on temperature rise is presented. The cylindrical wood particles chosen for the study have length (l) = 20 mm, diameter (d) = 4 mm and l = 50 mm and d = 10 mm, both having an aspect ratio (l/d) of 5. The bed temperature is 1123 K. The model prediction is validated using measurements obtained from literature. The temperature rise in the wood particle is found to be sensitive to changes in the moisture content and thermal diffusivity and heat of reaction (in larger particles) while it is less sensitive to the external heat transfer coefficient and chemical kinetics. Also shrinkage is found to have a compensating effect and it does not have any significant influence on the temperature rise. Beyond an aspect ratio of three, the wood particle behaves as a 1-D cylinder.     

Thermal decomposition of pyrite in the nitrogen atmosphere

The effects of gas flow rate, reaction temperature, particle size, and time on thermal decomposition of pyrite have been investigated between 673 and 1073 K in a nitrogen gas environment in which the gas–solid contact is effective. The decomposition reaction is well represented by the “shrinking core” model and can be divided into two regions with different rate controlling step. The rate-controlling step was found to be the heat transfer through the gas film for low conversion, but the mass transfer through product ash layer for high conversion. The activation energies for the heat transfer through the gas film and mass transfer through product ash layer-controlled cases were calculated as 113 and 96 kJ mol⁻¹, respectively.     

Thermophoretic Motion of a Cylindrical Particle with Chemical Reactions

The thermophoresis of a circular cylindrical particle bearing a chemical reaction in a gas prescribed with a uniform temperature gradient in the direction perpendicular to its axis is analyzed. The Knudsen number is assumed to be moderately small so that the fluid motion is in the slip-flow regime with effects of temperature jump, thermal creep, frictional slip, and thermal stress slip at the particle-gas interface. The appropriate governing equations of heat conduction/generation and fluid motion are solved analytically and the thermophoretic velocity of the particle is obtained in closed forms. The thermophoretic velocity is a linear function of the thermal stress slip coefficient whose effect increases with an increase in the Knudsen number. When the composition-dependent factor of the chemical reaction within the particle does not depend on position, the thermophoretic velocity is diminished as the reaction is endothermic and augmented as the reaction is exothermic. When this factor is a function of position, the particle velocity can deflect from the direction of the imposed temperature gradient. For specified system characteristics, the effect of the chemical reaction on the thermophoretic velocity of a circular cylindrical particle is significantly greater than that of a spherical particle due to its smaller specific surface area.

Copyright 2014 American Association for Aerosol Research     

The kinetics of combustion of chars derived from sewage sludge

Experiments have been conducted to determine the combustion characteristics of sewage sludge chars in electrically heated beds of silica sand fluidised by air. The effects of the initial size of the char particles, the temperature of the bed and [O₂] in the fluidising gas were investigated. Also, the temperatures of burning particles were measured with embedded thermocouples. The kinetics of combustion were measured at temperatures low enough for the CO formed by initial reaction between the carbon and oxygen to burn at some distance away from the particle. Accordingly, the particle is only heated by the enthalpy of the reaction C+0.5O₂→CO. The activation energy for the intrinsic kinetics of combustion of the char was estimated to be 130–144 kJ/mol. The former value makes allowance for the fact that the particles are at a temperature in excess of that of the bed (determined by a heat balance on a reacting particle), whilst the latter value assumes that the particles are at the same temperature of the bed. It is probable that the lower value is closer to the actual value, thought to be 135±15 kJ/mol, reflecting the catalytic nature of the ash skeleton on which the carbon is supported. It was possible to obtain good agreement between measured burnout times and those predicted using the grain model of Szekely J, Evans JW, Sohn HY. Gas–solid reactions. New York: Academic Press; 1976, for the case where the kinetics are controlled by a combination of: (i) external mass transfer of oxygen from the particulate phase to the external surface of the burning char particle, (ii) diffusion of oxygen from the external surface into the porous matrix to the surfaces of grains, of which the solid is composed, and (iii) diffusion of oxygen into the microporous grains, where reaction occurs with the carbon. It was found that, for particles with diameters of 2 mm or larger, the initial rates of reaction, for bed temperatures in excess of 750 °C, are dominated by external mass transfer. This explains the dependence of the rate of oxidation of unit mass of char on 1/d_p, and the relatively small influence of temperature on these rates. Particles of char from sewage sludge are so reactive that it is essential to make allowance for a difference in temperature between the particle and the bed. Thus, experimental determinations on particles with d_p∼6.5 mm, suggested a difference in temperature of ∼150 K, in line with calculations using a steady-state heat balance.     

Analysis of the Critical Conditions for Ignition of Gas–Particle Mixtures by a Heated Body with Pulsed Energy Supply

The critical conditions for the ignition of solid particles suspended in a gas by a heated body with pulsed energy supply are determined using numerical and approximate methods. It is shownthat in the kinetic (onetemperature) ignition regime, the critical duration of the thermal pulse is equal to the time of establishment of a zero gradient on the interface between the heaterand the gas–particle mixture. In the diffusive (twotemperature) ignition regime (small coefficients of heat transfer between the particles and the gas), the critical duration of the thermal pulse is much shorter than the time of establishment of a zero gradient. It is established that the critical duration of the thermal pulse is determined from the condition that the time of complete particle burnout on the interface between the heater and the gas–particle mixture is equal to the time of repeated heating of the gas to the temperature of the transition of the particle oxidation reaction tothe diffusive reaction regime. An approximate method for calculating the critical duration of the thermal pulse for the diffusive ignition regime is proposed. Numerical calculations show that the minimum time of establishment of the hightemperature combustion regime is reached when the thermal pulse duration is equal to the time of attainment of a zero pressure gradient on the interface between the heater and the gas–particle mixture.     

Stable and critical heat- and mass-transfer regimes of a traveling carbon particle

We consider the effect of the relative velocity of a carbon particle on the specific features of the time dependences of the temperature and dimater of the particle at given temperatures of air and the wall of a reaction device and at a specified oxygen concentration in the medium. The stable and critical values of the temperature and combustion rate of the particle versus the initial particle diameter at its given velocity and the relative velocity of a particle of given size are studied. The effect of the diameter and velocity of the particle on the critical values of its initial temperature, which determine ignition inside hysteresis loops, is analyzed. The dependences of the critical particle diameter at which the thermal regime changes (ignition and extinction) on the relative particle velocity are derived. Translated fromFizika Goreniya i Vzryva, Vol. 34, No. 1, pp. 25–30, January–February, 1998.     

Surface-to-bed heat transfer in fluidised beds of fine particles

This work reports experimental results on the heat transfer between a fluidised bed of fine particles and a submerged surface. Experiments have been carried out using different bed materials (polymers, ballotini, corundum, carborundum and quartz sand) with Archimedes number between 2 and 50. Dry air at ambient pressure and temperature has been used as fluidising gas. Three different exchange surfaces, namely a sphere and two cylinders with different base diameter and same height, have been used.Experimental results show that the heat transfer coefficient increases with particle Archimedes number and is almost independent from particle thermal conductivity for K_p/K_g > 30. Finally, the comparison of heat transfer coefficient for the different surfaces shows that the effect of the surface geometry may account for a 30% variation in the heat transfer coefficient, with higher differences occurring for coarser particles.     

Model for devolatilization of coal particles in fluidized beds

A model for the devolatilization of coal in a non-combusting fluidized bed is proposed. Previous studies have either considered devolatilization as a non-rate process or assumed the devolatilization coal particle as isothermal. The assumption of an isothermal particle requires the heat transfer Biot number ?0.02. In view of the larger Biot numbers predicted using existing fluidized bed gas-solid heat exchange correlations and reported values for thermophysical properties, the present model considers the devolatilizing particle to be, in general, non-isothermal. The temperature profiles are computed from the analytical solution of the one-dimensional spherical coordinate unsteady heat transport equation with a convective boundary condition. The temperatures are then used in the non-isothermal coal decomposition kinetic expression proposed by Anthony et al., integrated over the particle to obtain the fractional volume average devolatilization at any given time. Parametric studies show a chemical kinetics controlled regime for small particles, a heat transfer controlled regime for larger particles and a mixed regime for intermediate particle sizes. The extent of the mixed regime depends on the type of coal as well as the operating conditions. The model results are also compared with the fluidized CH₄ and CO evolution data reported in the literature for various particle sizes and different temperatures.     

A 1-D non-isothermal dynamic model for the thermal decomposition of a gibbsite particle

A 1-D mathematical model describing the thermal decomposition, or calcination, of a single gibbsite particle to alumina has been developed and validated against literature data. A dynamic, spatially distributed, mass and energy balance model enables the prediction of the evolution of chemical composition and temperature as a function of radial position inside a particle. In the thermal decomposition of gibbsite, water vapour is formed and the internal water vapour pressure plays a significant role in determining the rate of gibbsite dehydration. A thermal decomposition rate equation, developed by closely matching experimental data reported previously in the literature, assumes a reaction order of 1 with respect to gibbsite concentration, and an order of −1 with respect to water vapour pressure. Estimated values of the transformation kinetic parameters were k₀ = 2.5 × 10¹³ mol/(m³ s) for the pre-exponential factor, and E_a = 131 kJ/mol for the activation energy. Using these kinetic parameters, the gibbsite particle model is solved numerically to predict the evolution of the internal water vapour pressure, temperature and gibbsite concentration. The model prediction was shown to be very sensitive to the values of heat transfer coefficient, effective diffusivity, particle size and external pressure, but relatively less sensitive to the mass transfer coefficient and particle thermal conductivity. The predicted profile of the water vapour pressure inside the particle helps explain some phenomena observed in practice, including particle breakage and formation of a boehmite phase.     

Design and simulation of a solar chemical reactor for the thermal reduction of metal oxides: Case study of zinc oxide dissociation

A laboratory-scale solar reactor was designed and simulated for the thermal reduction of metal oxides involved in water-splitting thermochemical cycles for hydrogen production. This reactor features a cavity-receiver directly heated by concentrated solar energy, in which solid particles are continuously injected. A computational model was developed by coupling the fluid flow, heat and mass transfer, and the chemical reaction. The reactive particle-laden flow was simulated, accounting for a multiphase model (solid-gas flow). A discrete phase model based on a Lagrangian approach was developed. The kinetics of the chemical reaction was considered in the specific case of zinc oxide dissociation for which reliable data are available. The complete model predicts temperature and gas velocity distributions, species concentration profiles inside the reactor, particle trajectories and fates, and conversion rate assessing the reaction degree of completion. The reaction extent is highly dependent on temperature of the radiation-absorbing particles. Initial diameter of injected particles is also a key parameter because it determines the available surface area for a given particle mass feed rate. The higher the particle surface area, the higher the conversion rate. As a result, reaction completion can be achieved when particle temperature exceeds 2200 K for a initial particle diameter.     

Methanol synthesis in a three‐phase catalytic bed under nonwetted condition

To overcome the heat removal problem encountered in methanol synthesis at high syngas concentrations in the gas phase, a three‐phase nonwetted catalytic system was established by introducing an inert liquid medium into a fixed‐bed reactor. To form a repellent interface between the liquid and the catalyst, the catalyst was modified into hydrophobic, while the liquid medium was chosen as a room temperature ionic liquid with hydroxyl groups. The liquid‐solid contact angle was measured to be 115°, and only 20% of the catalyst external surface was wetted by the liquid. Under three‐phase condition, the reaction rate was measured to be 60%–70% of gas‐phase reaction, while it was merely 10%–20% for the fully wetted catalyst. From the resistance analysis on the mass transfer and reaction steps, the overall reaction rate is expected to increase further if the surface could be more wet proofed. © 2016 American Institute of Chemical Engineers AIChE J, 63: 226–237, 2017     

Natural convection and flow simulation in differentially heated isosceles triangular enclosures filled with porous medium

A finite element analysis is performed to investigate the effects of uniform and non-uniform heating of bottom wall on natural convection flows within isosceles triangular enclosures filled with porous medium. The detailed analysis is carried out in two cases depending on various thermal boundary conditions:

(I)

two inclined walls are maintained at constant cold temperature while the bottom wall is uniformly heated;

(II)

two inclined walls are maintained at constant cold temperature while the bottom wall is non-uniformly heated.

The present numerical procedure adopted in this investigation yields consistent performance over a wide range of parameters of Darcy number, Da (10^-5?Da?10^-3), Rayleigh number, Ra (10³?Ra?10⁶) and Prandtl number, Pr (0.026?Pr?1000) in all the cases mentioned above. Numerical results are presented in terms of stream functions, temperature profiles and Nusselt numbers. It is observed that at small Darcy numbers, the heat transfer is primarily due to conduction irrespective of Pr. As the Darcy number increases, there is a change from conduction dominant regime to convection dominant regime. Flow circulations are also found to be strong functions of Pr at large Da (Da=10^-3) and multiple circulation cells occur at small Pr with Ra=10⁶. Non-uniform heating of the bottom wall produces greater heat transfer rate at the center of the bottom wall than uniform heating case, but average Nusselt number shows overall lower heat transfer rate for non-uniform heating case. As average Nusselt number is same on both the inclined walls, the average Nusselt number for bottom wall is times that of the inclined wall which is well matched in two cases considered for verifying the thermal equilibrium of the system. The correlations are proposed for average Nusselt number as functions of Ra for various Darcy and Prandtl numbers.     

Temperature differences between phases in a moving bed reactor

Pseudo-homogeneous models of packed bed reactors assume equal temperatures and concentrations (or chemical potentials) for the solid and the fluid phases and are simpler than heterogeneous models. An analysis is presented for the degree of temperature departure between these two models under plug flow conditions with no axial dispersion. Fixed bed, cocurrent and countercurrent flow reactors are considered. The analysis yields two important parameters: α, the ratio of solid to gas thermal capacitances, and β, which is closely related to the number of interphase heat transferase units. In most industrial reactors, where β is greater than 50, the average temperature difference between phases is small, except for countercurrent reactors where gas and solid heat capacitances are nearly equal. Within this range of α, temperature differences can persist through the reactor, even with large values of β. The maximum temperature difference between phases is attained when the reaction heat effect is released in the worst case of a localized pulse in the reactor stream with the smaller thermal capacitance. These temperature difference measures can be used to estimate the validity of a pseudo-homogeneous model. This analysis is easily extended to concentration differences between phases.     

Heterogeneous thermochemical decomposition of a semi-transparent particle under direct irradiation

Transient heat and mass transfer in a non-uniform emitting, absorbing and anisotropically scattering medium inside a semi-transparent, optically large and chemically reacting particle directly exposed to an external source of high-flux radiation is analyzed numerically. Thermal decomposition of calcium carbonate is selected as the model chemical reaction. The unsteady mass and energy equations are solved numerically using the finite volume technique and the explicit Euler time-integration scheme. Radiative transport is modeled using the Rosseland diffusion approximation and the Monte Carlo ray tracing method. Direct irradiation and internal radiative transfer in the particle are highly favorable for particle heating and the decomposition reaction, decreasing the total reaction time by a factor of 15, as compared to the case with external and internal radiation neglected in the analysis. In the latter case, the temperatures at the particle center and the particle surface increase monotonically to 1406 and 1417 K for the reacting particle, and 1428 and 1432 K for the non-reacting particle, respectively, after 179 s—the total reaction time of the reacting particle. With radiation included in the analysis, the surface temperatures of both reacting and non-reacting particle increase from the initial 300 to 1300 K in less than 2 s, and at the same rate until the onset of the endothermic chemical reaction at t=1.1 s. The surface temperature of the reacting particle increases further up to 2000 K after 12 s, when the whole particle is calcined. Weak dependence of the temperature, the overall reaction extent, and the total reaction time on the CaO grain size is observed in spite of strong dependence of the radiative properties of porous CaO on the CaO grain size.     

Coagulation of highly concentrated aerosols

A number of material synthesis processes such as flame, plasma and laser ablation have been developed for production of films and powders at low pressure and high temperature. At these conditions particle growth typically takes place by coagulation in the free molecule and transition regimes. As economic manufacturing of these materials favors operation at high particle concentrations, classic coagulation theory may not be sufficient to describe the ensuing aerosol dynamics, especially if fractal-like particles are formed. The coagulation rate of highly concentrated, polydisperse aerosols is investigated here from the free molecule to the continuum regime by solving the corresponding Langevin dynamics (LD) equations. The LD simulations are validated by monitoring the attainment of the self-preserving size distribution (SPSD) for dilute particle volume fractions, φ_s, below 0.1%. High particle concentrations in the free molecule regime lead to deviations of the aerosol dynamics from the kinetic theory of gases especially during instantaneous coalescence (completely inelastic particle–particle collisions) resulting in slower coagulation rates and slightly narrower SPSDs than in conventional dilute aerosols. In the transition regime, the coagulation rate of highly concentrated aerosols is progressively higher than that for dilute aerosols as growing particles enter the continuum regime where coagulation rates are 2–30 times higher than that of classic Smoluchowski theory. At high particle concentrations (φ_s>1%), a SPSD is approached (σ_g,n=1.42) that does not exhibit the characteristic minimum at the transition regime of dilute aerosols. A relationship is developed for the aerosol coagulation rate of highly concentrated aerosols from the free molecule to continuum regime.