Mathematical modeling of the heat treatment and combustion of a coal particle. V. Burn-up stage

The present material is a sequel of the previous publications of the authors in this journal under a common title in which by means of mathematical modeling the sequential stages of the process of combustion of coal fuels have been obtained: heating, drying, escape of volatiles, and ignition. Mathematical models of the final stage of combustion of an individual particle — the burn-up stage — have been formulated. On the basis of the solution methods for nonlinear boundary-value problems developed by us, approximate-analytic formulas for two characteristic regimes, burn-up simultaneously with the evaporation of the remaining moisture and burn-up of the completely dried coke residue, have been obtained. The previous history of the physical and chemical phenomena in the general burning pattern is taken into account. The influence of the ash shell on the duration of combustion has been extimated. Comparison of calculations by the obtained dependences with the results of other authors has been made. It showed an accuracy sufficient for engineering applications.     

Mathematical modeling of the heat treatment and combustion of a coal particle. I. Heating stage

Mathematical modeling of the heat treatment and subsequent combustion of a coal particle as a multistage process has been carried out. The basic parameters of the following sequential stages of this process have been calculated by approximate-analytic dependences: heating of particles; their drying; yield of volatiles, their ignition and combustion; and burning out of the coke residues. A detailed parametric analysis of the influence of the physical and regime characteristics of the process on the burning mechanism of a coal particle (with the example of coal from the Shivee-Ovoo deposit in Mongolia) has been performed. The conditions for effective burning of a single coal particle as the main element of the whole process in the furnace have been determined.     

Mathematical modeling of the heat treatment and combustion of a coal particle. II. drying stage

This article is a continuation of the previous article in which, with the aid of mathematical modeling, the regime of radiative-convective heating of a coal particle was studied in detail and which was devoted to an analysis of the stage of coal drying, very important in the general picture of coal combustion. The process of coal drying is formulated as the nonlinear Stefan problem with a moving liquid-vapor phase change interface. The rate and time of coal particle drying, the temperature distribution inside a particle, and other parameters of the process have been found approximately analytically depending on the regime of heat supply. A parametric analysis of the influence of physical and regime factors on the dynamics of drying as an integral part of heat treatment of a fuel for its ignition and combustion has been carried out.     

Mathematical modeling of thermal processing of individual solid-fuel particles

A mathematical model, an algorithm, and a program for calculating the thermal processing of individual solid-fuel particles are developed with account for moisture evaporation, escape of volatiles, and burn-out of the carbon residue. Numerical calculations of the influence of regime conditions on the gasification-combustion of individual particles of Chelyabinsk brown coal are performed. A comparison with experiment is made.Institute for Problems of Energy Conservation, Academy of Sciences of Ukraine, Branch of High-Temperature Energy Conversion, Kiev. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 68, No. 1, pp. 96–109, January–February, 1995.     

ISOTHERMAL PREDICTION OF PARTICLE AND GAS FLOW IN A COAL-FIRED REACTOR

The steady, turbulent gas flow with entrained coal particles in a laboratory-scale axisymmetric coal gasification reactor is numerically analyzed. The reactor is designed to provide rapid mixing and heatup of the coal in a configuration which results in a nearly isothermal and uniform flow in the main reaction chamber so as to allow controlled study of coal gasification. A detailed knowledge of the reactor dynamics is required in order to interpret experimental results. The nonreacting, isothermal flow pattern is first presented as a base case. Calculations are performed with an iterative, implicit scheme suitable to the elliptic nature of the gas flow equations in an Eulerian frame-work. The turbulent motion is resolved using the eddy-viscosity concept with the standard k-ε turbulence model. Coal particle trajectories are then calculated using the Lagrangian form of the momentum equations. The influence of solid particles on the gas phase is neglected. Particle trajectories and residence time distributions are presented for a variety of particle sizes and particle inlet locations. The influence of the inlet conditions, turbulent diffusion, and gravity on the particle motion, are investigated. Implications of the predictions, with respect to the design of the reactor, are discussed.     

Mathematical modeling of the heat treatment and combustion of a coal particle. IV. Ignition stage

The present paper is the continuation of the previous publications of the present authors in the Journal of Engineering Physics under the general title in which three sequential stages of the thermal preparation of a carbon particle for combustion are considered: heating, drying, and the yield of volatiles. The present paper is devoted to a detailed investigation of the stage of ignition of a carbon particle under the conditions of external radiative-convective supply that most adequately reflects the furnace medium. The characteristics of thermal ignition of a carbon matrix were studied with the aid of the adiabatic method. Such parameters as time and the heating temperature, the time of induction, the total time and the temperature of ignition of a carbon particle, the scale temperature, etc. have been found. The degree of dependence of the time of ignition on the initial temperature of the particle, the temperature of the external medium, heat transfer coefficient, and other inlet data has been analyzed.     

粒径对煤粉云最低着火温度特性的影响

为了研究粒径对煤粉云最低着火温度特性的影响,采用粉尘云最低着火温度测试装置测试了不同粒径下煤粉云的最低着火温度,并结合ReaxFF分子动力学对其反应机理进行了微观层面的探讨。结果表明:当煤粉中位径在34 μm时,煤粉云的最佳着火质量浓度为750 g/m³,最低着火温度为550 ℃;随着煤粉粒径的增加,煤粉云最低着火温度逐渐增大,当煤粉中位径达到124 μm,煤粉云最低着火温度上升至650 ℃。通过ReaxFF分子动力学对煤粉热解过程的计算结果表明:随着反应的进行,大分子煤结构逐步分解,芳香环、C—C键、C—O键和C—H键等断裂,产生更小的分子结构,其中,H₂、H₂O、CO₂和CH₂O等小分子产生的数量逐渐增多;H·自由基和OH·自由基在反应初期有明显的数量变化,且其含量对于最终稳定产物有重要影响。     

Eulerian–Lagrangian method for three-dimensional simulation of fluidized bed coal gasification

A comprehensive three-dimensional numerical model has been developed to simulate the coal gasification in a fluidized bed gasifier. The methodology is based on the multiphase particle-in-cell (MP-PIC) model, which uses an Eulerian method for fluid phase and a discrete particle method for particle phase. Dense particulate flow, mass and heat transfer, homogeneous and heterogeneous chemistry between phases and within the fluid mixture are considered. The dynamics of the particle phase is calculated by solving a transport equation for the particle distribution function (PDF) f. Particle collisions and chemical reactions are solved on a grid cell with particle properties mapped from discrete particles to the grid. Solid mass consumed or produced in reactions changes the size of particles. Simulations were carried out in a coal gasifier with a height of 2.0 m and a diameter of 0.22 m at atmosphere. The calculated product gas compositions compare well with the experimental data. The formation of flow patterns, profiles of particle species and gas compositions, distributions of reaction rates and consumption of carbon mass were investigated under different operating conditions.     

Influence of model particle size and spatial resolution in coarse-graining DEM-CFD simulation

The discrete element method (DEM) coupled with computational fluid dynamics (CFD) is a powerful tool for exploring the detailed behaviors of dense particle–fluid interaction problems such as fluidized beds. Coarse-graining models have been proposed to decrease the computational cost by increasing the model particle size. In this study, we examine the influence of the model particle size and the spatial resolution on the average size and number of bubbles in coarse-graining DEM-CFD calculations of bubbling fluidized beds. Calculation results indicate that the bubble size is scaled by the model particle size if parameters are following similarity laws defined in a particle scale, as well as the geometric similarity of the whole system is maintained. The usage of coarse spatial resolution increases the bubble size and decreases the number of bubbles. The countervailing influence of the model particle size and the spatial resolution in a practical coarse-graining scenario results in nearly the same bubble size.     

Experimental study on spontaneous imbibition characteristics of coal based on fractal theory

Coal seam water injection is a widely used dust reduction technology in Chinese coal mines. During the process of coal seam water injection, a large amount of broken coal particles will accumulate in the pore, which will affect the flow characteristics of water. It's very important for improving the on-site coal seam water injection and dust reduction technology to study the influence of coal particles on the water migration law. In this paper, a spontaneous upward imbibition experiment was used to study the effect of coal particles stacked in front fractures on water migration in coal seam water infusion. Then, a mathematical model was established to express imbibition speed and stable imbibition height. The results show when the largest particle size is selected, theoretical calculation results of stable imbibition height is closest to the experimental data; coal particles with a size of 564–1589 μm have the greatest influence on the wetting phase of coal seam water infusion; the metamorphic grade and particle size of the samples mainly affect the initial stage of water migration, and the initial imbibition speed of each coal sample is quite different. However, with increasing imbibition height, the imbibition speed difference of each coal sample gradually decreases.     

Chemical properties of superfine pulverized coal particles. Part 1. Electron paramagnetic resonance analysis of free radical characteristics

Superfine pulverized coal combustion is a new pulverized coal combustion technology with lots of advantages. A mechanochemical effect exists during the comminution process, which changes the chemical properties of coal significantly. Free radical concentrations and certain functional groups would increase with the decrease of particle sizes. In this paper, we combined electron paramagnetic resonance (EPR) and ¹³C solid-state nuclear magnetic resonance (NMR) techniques to study the free radical characteristics of superfine pulverized coal thoroughly. The final results indicate that the EPR spectra of coal are the superimpositions of several lines induced by different paramagnetic centers, which can be fitted by 1 Gaussian and 3 Lorentzian lines. The influences of coal maturities and particle sizes on EPR parameters, such as g-values, linewidths, and spin concentrations, are analyzed in detail. It is shown that with the decrease of particle sizes, more free radicals are induced through bond cleavages. Mechanical forces initiate the accumulation of free radicals in the fractures and inner pore surfaces of coal. Furthermore, the influence of particle sizes on oxygen-containing radicals (i.e., Lorentzian 1 types) is the greatest. This work provides a primary picture of the occurrence modes and spatial distributions of free radicals in superfine pulverized coal. The findings will help form the basis and provide guidance for further studies on revealing the correlations between the free radical reaction pathways and NO_x formation mechanisms.     

Modeling the dynamics of several particles behind a propagating shock wave

The interaction of a shock wave in a gas phase with a system of particles moving in this gas has been numerically simulated. The wave pattern of the nonstationary interaction of the propagating shock wave with these particles is described in detail. The mathematical model and computational technology employed is compared with experimental data on the dynamics of particles behind the shock wave. It is established that the approximate model of separate particles used to calculate relaxation of their velocities unsatisfactorily operates in the presence of a mutual influence of particles, whereby one particle can occur in the aerodynamic shadow of an adjacent particle.     

Experimental study on geometric parameters of pore structure and quantitative evaluation of complexity of pulverized coal with different metamorphic degrees

In order to quantify pore structure complexity of coal, the low pressure argon adsorption method (LP-ArGA) was used to study geometric parameters of pore structure and quantitative evaluation of complexity of pulverized coal. The results showed that the geometric parameters of pore structure of most single-particle coals showed an obvious downward trend with the decrease of particle size, indicating that the pore structure became simpler in the pulverization process. The weight value of equivalent matrix scale is the largest, which is 0.4871, indicating that it has the greatest influence on pore structure complexity. With the decrease of particle size, the composite evaluation index of complexity of 1#, 2#, 3#, 4#, 5# and 6# samples decreased by 52.4%, 61.1%, 86.3%, 42.1%, 74.6% and 39.9%, respectively. It indicated that particle size has an extremely influence on pore complexity characteristics of single-particle coal. With the decrease of particle size, the pore complexity characteristics of coal samples tended to be simple, on the contrary, they showed medium or complex characteristics. The model has important guiding significance for evaluating the same coal sample with different particle sizes, but there are still some deficiencies for different coal samples.     

A discrete element method-based approach to predict the breakage of coal

Pulverization is an essential pre-combustion technique employed for solid fuels, such as coal, to reduce particle sizes. Smaller particles ensure rapid and complete combustion, leading to low carbon emissions. Traditionally, the resulting particle size distributions from pulverizers have been determined by empirical or semi-empirical approaches that rely on extensive data gathered over several decades during operations or experiments, with limited predictive capabilities for new coals and processes. This work presents a Discrete Element Method (DEM)-based computational approach to model coal particle breakage with experimentally characterized coal physical properties. The effect of select operating parameters on the breakage behavior of coal particles is also examined.     

Modeling electrowinning process in an expanded bed electrode

A theoretical model has been developed to describe the flow behavior of conducting particles in a fluidized bed electrode for electro winning of metal ions present in the dilute solution. Model equations have been developed for potential and current distributions and mass transfer rates. The influence of operating parameters on particle growth has been critically examined. It has been observed from the present investigation that the particle size increased with electrolysis time. The present model simulations have been compared with the experimental data reported in the literature and observed that the model predictions satisfactorily match with the reported experimental findings.     

Theoretical Investigations on Sprayed Particle-Plasma Interactions to Optimize Processing Parameters in D.C. Thermal Plasma Spraying

A numerical model is proposed to simulate the behavior of particles injected into a dc spraying plasma in conjunction with the code that calculates the plasma jet characteristics. The sprayed particle-plasma interaction, particle loading effect and the particle internal heat transfer including phase transformations are considered together in the model to present a realistic prediction for the characteristic features of plasma spraying.

The temperature and velocity fields in a plasma jet expanding region outside the nozzle are found by a pre-developed code based on the arc-gas interactions inside the nozzle depending on the operating conditions of the torch. The influence of particle injection on the plasma jet characteristics is treated as the source in the fluid equations governing the plasma jet in semi-three dimensional calculations caused by non-axisymmetric injection of powders. The calculated velocity profiles of powder particles along the axial distance are compared with those obtained from experiments, and the determination of optimal spraying conditions are discussed from the results calculated from the present model.

This model gives more realistic information for plasma spraying than earlier works which have not included the loading effects and non-axisymmetric injection of powders in dc thermal plasma spraying. The theoretical predictions of the sprayed particle characteristics using this model can be helpful for determining preliminary range and optimal values of operating parameters for plasma spray processes.     

Explosibility boundaries for fly ash/pulverized fuel mixtures

Incomplete combustion and subsequent fuel contamination of a waste stream can pose a serious explosion hazard. An example of this type of incident is the contamination of fly ash with unburned pulverized coal. The coal, if present in sufficient quantities in the mixture, can act as a fuel source for a potential explosion. Experiments were conducted in a 20l Siwek explosibility test chamber to determine the minimum fuel contamination of fly ash required to form an explosible mixture. A sample of fly ash from Ontario Power Generation (OPG) (Ont., Canada) was artificially contaminated with Pittsburgh pulverized coal dust (the surrogate used to represent unburned fuel dust). Additionally, the influence of fly ash particle size on the amount of fuel contaminant required to form an explosible mixture was examined. Fine and coarse size fractions of fly ash were obtained by screening the original sample of OPG fly ash.The results show that at least 21% Pittsburgh pulverized coal (or 10% volatile matter) was required to form an explosible mixture of the original fly ash sample and coal dust. The results also illustrate that fly ash particle size is important when examining the explosibility of the mixture. The fine size fraction of fly ash required a minimum of 25% coal dust (12% volatile matter) in the mixture for explosibility, whereas the coarse fly ash required only 10% coal dust (7% volatile matter). Thus, the larger the particle size of the inert fly ash component in the mixture, the greater the hazard.     

矿井煤与瓦斯突出数学模型的建立

为研究煤与瓦斯突出的特点及危害,同时为进一步研究其诱发瓦斯爆炸继发性灾害发生规律提供基础,运用气体动力学和瓦斯在煤层中流动的基本理论,建立了煤与瓦斯突出的数学模型。同时,为考察模型的准确性,在不同工况下,将模拟计算结果与文献中的实验室实验数据进行了对比。结果表明：模型计算与实验结果符合良好,可预报煤与瓦斯突出整个发生、发展和衰减过程中的突出压力及瓦斯量等参数变化趋势。     

褐煤煤尘爆炸火焰传播特性及燃烧热分解机理研究

煤尘爆炸是矿井安全开采的主要危险源之一。以褐煤煤尘为研究对象,探究煤尘粒径对煤尘火焰传播过程的影响。用高速摄影装置记录火焰的传播过程,进而分析不同粒径下煤尘爆炸火焰传播的高度和速度。为进一步分析煤尘燃烧过程中的化学反应机理,借助反应分子动力学方法对煤分子燃烧中的初始热分解过程进行了模拟。研究结果表明:爆炸火焰传播高度呈先增加、后稳定的趋势,传播速度呈先增大、后减小的趋势;随着煤尘粒径的减小,火焰传播高度和传播速度均呈增大的趋势;当煤尘粒径为10.5 μm时,火焰传播高度和传播速度的峰值分别为623 mm和4.3 m/s;煤尘热分解主要产物为H₂、H₂O、CO₂和CH₂O,这些产物进一步与氧气的结合会促进煤尘燃烧和火焰传播过程,使得整个体系燃速加快。为煤尘热分解和燃烧提供了较为充分的数据基础。