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ArticleMay 15, 2008

Comprehensive Study of Biomass Particle Combustion
生物质颗粒燃烧的综合研究
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Energy & Fuels

Cite this: Energy Fuels 2008, 22, 4, 2826–2839

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https://doi.org/10.1021/ef800006z

Published May 15, 2008

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Abstract 摘要

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This investigation provides a comprehensive analysis of entrained-flow biomass particle combustion processes. A single-particle reactor provided drying, pyrolysis, and reaction rate data from poplar particle samples with sizes ranging from 3 to 15 mm.
本研究对悬浮流生物质颗粒燃烧过程进行了全面分析。通过单颗粒反应器，获得了杨木颗粒（尺寸范围为 3 至 15 毫米）的干燥、热解及反应速率数据。
A one-dimensional particle model simulates the drying, rapid pyrolysis, gasification, and char oxidation processes of particles with different shapes. The model characterizes particles in three basic shapes (sphere, cylinder, and flat plate).
一个一维颗粒模型模拟了不同形状颗粒的干燥、快速热解、气化和焦炭氧化过程。该模型将颗粒特征化为三种基本形状（球体、圆柱体和平板）。
With the particle geometric information (particle aspect ratio, volume, and surface area) included, this model can be modified to simulate the combustion process of biomass particles of any shape.
包含颗粒几何信息（颗粒长宽比、体积和表面积）后，该模型可进行修改，以模拟任意形状生物质颗粒的燃烧过程。
The model also predicts the surrounding flame combustion behaviors of a single particle. Model simulations of the three shapes agree nearly within experimental uncertainty with the data.
该模型还能预测单个颗粒周围的火焰燃烧行为。三种形状的模型模拟结果与实验数据几乎一致，误差在实验不确定性范围内。
Investigations show that spherical mathematical approximations for fuels that either originate in or form aspherical shapes during combustion poorly represent combustion behavior when particle size exceeds a few hundred microns.
研究表明，对于起始或燃烧过程中形成非球形形状的燃料，当颗粒尺寸超过几百微米时，球形数学近似无法准确反映其燃烧行为。
This includes a large fraction of the particles in both biomass and black liquor combustion.
这涵盖了生物质和黑液燃烧中大量颗粒的部分。
In particular, composition and temperature gradients in particles strongly influence the predicted and measured rates of temperature rise and combustion, with large particles reacting more slowly than is predicted from isothermal models.
特别是颗粒中的成分和温度梯度对预测和测量的升温速率及燃烧速率有显著影响，大颗粒的反应速度比等温模型预测的要慢。

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Subjects

1 Introduction 1 引言

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During the past two decades, interest in renewable energy sources has increased due to at least two driving forces: (1) the increasing concern about the environmental impact of fossil and nuclear energy; and (2) the increasing anxiety regarding the security and longevity of fossil fuel.
在过去二十年间，由于至少两个驱动因素，人们对可再生能源的兴趣日益增长：（1）对化石能源和核能环境影响的日益关注；以及（2）对化石燃料安全性和持久性的日益担忧。

The threat of regional and global climate change (global warming) may require significant reduction in the emissions of greenhouse gases—most notably CO ₂. One potential strategy for reducing such emissions is the replacement of fossil fuels with renewable biomass fuels. Renewable fuels can be essentially CO ₂-neutral if derived from sustainable cultivation practices with minimal fossil fuel usage. Unlike fossil fuels, biomass fuels can be renewable and CO ₂-neutral in the sense that the CO ₂ generated by biomass utilization recycles from the atmosphere to the plants that replace the fuel, closing the carbon loop on a short time scale. If the biomass is renewably produced (as is generally the case in developed nations), there is little net increase in atmospheric CO ₂ content. Since most biomass, including essentially all biomass residue, decays in any case, sometimes producing methane and other decomposition products that greatly exceed the potency of CO ₂ as greenhouse gases, use of biomass residues as fuel has the potential of actually decreasing greenhouse gas impacts, not just being neutral. (1)
区域性和全球性气候变化（全球变暖）的威胁可能需要大幅减少温室气体排放，尤其是二氧化碳（CO₂）。减少此类排放的一个潜在策略是用可再生生物质燃料替代化石燃料。如果采用可持续的种植实践并尽量减少化石燃料的使用，可再生燃料基本上可以实现二氧化碳中性。与化石燃料不同，生物质燃料可以实现可再生和二氧化碳中性，因为生物质利用产生的二氧化碳会从大气中循环到替代燃料的植物中，在短时间内闭合碳循环。如果生物质是可持续生产的（这在发达国家通常是如此），大气中二氧化碳的净增量很小。由于大多数生物质，包括几乎所有生物质残留物，无论如何都会腐烂，有时会产生甲烷和其他分解产物，这些气体的温室效应远超二氧化碳，因此将生物质残留物用作燃料，实际上有可能减少温室气体的影响，而不仅仅是保持中性。(1)

Di Blasi (2) investigated the influences of physical properties on biomass devolatilization. A detailed particle energy and mass transport model predicted the effects of density, thermal conductivity, permeability to gas flow, and specific heat capacity.
Di Blasi (2) 研究了物理性质对生物质热解的影响。一个详细的颗粒能量和质量传输模型预测了密度、导热性、气体流动渗透性以及比热容的影响。
The author concluded that variations in physical properties mainly affect reactivities of secondary reactions of tar vapors and the conversion time for conversion in a thermally thick regime (intraparticle heat transfer control).
作者得出结论，物理性质的差异主要影响焦油蒸气的二次反应活性以及在热厚状态下（颗粒内传热控制）的转化时间。
Biomass density and the char thermal conductivity exhibit the highest sensitivity.
生物质密度和焦炭热导率表现出最高的敏感性。

Miller and Bellan (3) performed a parametric investigation of reactor temperature, heating rate, porosity, initial particle size, and initial temperature effects on char yields and conversion times using a spherically symmetric particle pyrolysis model.
米勒和贝兰（3）利用球对称颗粒热解模型，对反应器温度、加热速率、孔隙率、初始颗粒尺寸及初始温度对焦炭产率和转化时间的影响进行了参数化研究。
An increase in heating rate decreased both the char yield and the conversion time for both cellulose and wood. Additionally, both char yield and conversion time are increasing functions of initial particle size. (3) The char yield increase arises from secondary reactions between tar vapor and solids in the particle and the lower temperature heat-up.
加热速率的提高减少了纤维素和木材的炭产率以及转化时间。此外，炭产率和转化时间均随初始颗粒尺寸的增大而增加。（3）炭产率的增加源于颗粒内焦油蒸气与固体之间的二次反应以及较低温度的升温过程。

Baxter and Robinson (4) applied engineering models of kinetics, heat transfer, and mass transfer to predict the effects of particle size and density, shape, internal temperature gradients, and composition.
巴克斯特和罗宾逊（4）运用了动力学、传热和质量传递的工程模型，以预测颗粒尺寸和密度、形状、内部温度梯度及成分的影响。
The results of mass loss history of biomass particles were compared with data collected from several highly instrumented furnaces.
生物质颗粒质量损失历史的结果与从多个高度仪器化的炉膛中收集的数据进行了比较。
Drying and devolatilization were found to be primarily heat-transfer controlled whereas oxidation was found to be primarily mass-transfer controlled for most biomass of practical concern. In their later research, they found devolatilization removes most of the mass.
干燥和挥发分的析出过程主要受热传递控制，而氧化反应则主要受质量传递控制，这一发现适用于大多数实际关注的生物质。在后续研究中，他们进一步发现挥发分的析出带走了大部分质量。
Under rapid, high-temperature pyrolysis conditions, up to 95 wt % (daf) of the mass is released during devolatilization, significantly more than ASTM tests.
在快速、高温热解条件下，挥发分析出过程中最多可释放高达 95 wt%（干基）的质量，远超 ASTM 测试结果。

The effects of particle size, reactor heating rate, and final reactor temperature were theoretically and experimentally investigated by Di Blasi. (5) Similar results were obtained: large particle size increases char yields; higher heating rates result in higher volatile yields and lower char yields.
Di Blasi 从理论和实验两方面研究了颗粒尺寸、反应器加热速率及最终反应器温度对燃烧过程的影响。(5) 研究结果相似：颗粒尺寸增大导致焦炭产率增加；较高的加热速率则使挥发分产率提高，同时焦炭产率降低。
This researech indicates three main regimes of solid-fuel pyrolysis: the thermally thick (diameter = 0.625 cm), the thermally thin (diameter = 0.04 cm), and the pure kinetic regime.
本研究揭示了固体燃料热解的三个主要区域：热厚区（直径=0.625 厘米）、热薄区（直径=0.04 厘米）以及纯动力学区。
The pure kinetic limit involves only particles at least 1 order of magnitude smaller than those allowing conversion in the thermally thin regime, except at very low temperatures.
纯动力学极限涉及的颗粒尺寸至少比在热薄状态下允许转化的颗粒小一个数量级，除非在极低温度下。

As for particle shape, a spherical particle shape is usually assumed in modeling work for convenience. Other particle shapes have been considered. Jalan and Srivastava (6) studied pyrolysis of a single cylindrical biomass particle, and particle size and heating rate effects were investigated. In Horbaj’s model (7) and Liliddahl’s model (8), a particle geometric factor was introduced to account for the particle shape, which can deal with a prism (or slab), a cylinder (or rod), and a sphere.
关于颗粒形状，通常在模型工作中假设为球形以方便处理。其他颗粒形状也已被考虑。Jalan 和 Srivastava（6）研究了单个圆柱形生物质颗粒的热解，并探讨了颗粒尺寸和加热速率的影响。在 Horbaj 的模型（7）和 Liliddahl 的模型（8）中，引入了颗粒几何因子来考虑颗粒形状，这些模型能够处理棱柱（或平板）、圆柱（或棒状）以及球形颗粒。

In 2000, Janse and Westerhout (9) simulated the flash pyrolysis of a single wood particle. To investigate the influence of particle shape, simulations included spherical, cylindrical, and flat particles.
2000 年，Janse 与 Westerhout（9）模拟了单个木质颗粒的闪速热解过程。为探究颗粒形状的影响，模拟中涵盖了球形、圆柱形及扁平形颗粒。
Results show that spherical particles react most quickly compared to other particle shapes if the characteristic size is taken as the minimum particle dimension.
结果表明，若以最小颗粒尺寸作为特征尺寸，球形颗粒相较于其他形状的颗粒反应最为迅速。
The higher surface-area-to-volume ratio of spherical particles on this basis explains this observation; flat particles react most slowly.
基于此，球形颗粒具有更高的表面积与体积比，这一现象得到了解释；而扁平颗粒反应最为缓慢。
In the work reported later in this document, the characteristic dimension is taken as the spherical-equivalent diameter: the diameter of a sphere with the same volume/mass as the aspherical particle.
在本文件后续的研究中，特征尺寸取为球形等效直径：即与非球形颗粒体积/质量相同的球体的直径。
As will be shown, using the spherical-equivalent diameter results in the opposite trend—spherical particles react most slowly. There is no inconsistency in these results, just a difference in basis of comparison.
正如将展示的，使用球形等效直径会导致相反的趋势——球形颗粒反应最慢。这些结果并无矛盾，只是比较基准不同。
At small particle diameters (typically less than 200 μm), the rate of reaction becomes dominant and the different particle shapes exhibit nearly equal conversion times. Flat particles seem to yield less gas and more char.
在颗粒直径较小的情况下（通常小于 200 微米），反应速率占主导地位，不同形状的颗粒表现出几乎相等的转化时间。扁平颗粒似乎产生较少的气体和较多的焦炭。
This research also showed that an increase in particle diameter (or conversion time) caused no change in bio-oil yield, a slight decrease in gas yield, and a slight increase in char yield.
本研究还表明，颗粒直径（或转化时间）的增加并未改变生物油产率，气体产率略有下降，而焦炭产率则略有上升。
This might be due to the low reactor temperature (surface temperature 823 K) they used to simulate this process.
这可能是由于他们用于模拟该过程的反应器温度较低（表面温度 823 K）所致。

Coal char reactivity and oxidation processes enjoy an extensive literature developed during the last decades.
煤焦反应性和氧化过程在过去几十年中积累了丰富的文献资料。
Char, either from coal or biomass, is usually considered to be mainly composed of carbon, containing far fewer heteroatoms (O, H, S, and N) than the fuels from which they derive but nonetheless retaining some heteroatoms and in any case having structures and reactivity very different from graphite.
无论是来自煤炭还是生物质的炭，通常被认为主要由碳组成，其含有的杂原子（氧、氢、硫和氮）远少于其来源燃料，但仍保留一定数量的杂原子，且其结构和反应性与石墨截然不同。
In this sense, the chemical structure of biomass char is similar to coal char, but large physical differences exist between them, such as density, thermal conductivity, porosity, surface area, and particle shape and size.
从这个角度看，生物质焦的化学结构与煤焦相似，但它们在密度、导热性、孔隙率、表面积以及颗粒形状和大小等物理特性上存在显著差异。

Mermoud and his co-workers (10) collected experimental steam gasification reactivity data with beech char and compared with model predictions.
梅尔穆德及其同事（10）收集了山毛榉焦炭的实验蒸汽气化反应性数据，并与模型预测进行了比较。
The usual homogeneous or shrinking core particle models produced unacceptable results and that only the assumption of thermal equilibrium between the particle and the surrounding gas is valid for a model at bed scale.
传统的均匀模型或收缩核粒子模型产生了不可接受的结果，只有假设颗粒与周围气体之间存在热平衡，才对床尺度模型有效。

With birch wood chars obtained from a free-fall tubular reactor and a thermobalance, Chen et al. (11) studied char reactivity with carbon dioxide and steam in the thermobalance. Reaction rates of the char depend strongly on particle temperature history during char formation.
陈等（11）利用从自由落管反应器和热天平获得的桦木炭，在热天平中研究了炭与二氧化碳和蒸汽的反应活性。炭的反应速率强烈依赖于炭形成过程中颗粒的温度历史。
Chars obtained from rapid pyrolysis possessed higher reactivity (2.3−2.4 times higher) in the reaction with carbon dioxide or steam compared with chars from slow pyrolysis.
快速热解获得的焦炭在二氧化碳或蒸汽反应中的反应活性更高（高出 2.3 至 2.4 倍），相较于慢速热解得到的焦炭。
In other words, kinetic rates of char increase with increasing particle heating rate during the thermal decomposition process.
换言之，在热分解过程中，随着颗粒加热速率的增加，焦炭的反应速率也随之提高。

The reactivity of two kinds of biomass chars from Southern pine and switchgrass was investigated by Wornat et al. (12) Results showed that, at early stages of char conversion, both of the chars were quite reactive.
Wornat 等人（12）研究了南方松和柳枝稷两种生物质焦的反应性。结果表明，在焦转化初期，这两种焦均表现出较高的反应活性。
However, their reactivity decreased somewhat during char conversion as more reactive carbon is preferentially depleted and the inorganic constituents of the chars underwent physical and chemical transformations that render them less catalytically active.
然而，在炭转化过程中，它们的反应性有所下降，因为更具反应性的碳优先被消耗，同时炭中的无机成分经历了物理和化学变化，导致其催化活性降低。
They also found that even with small biomass char particles (75−106 μm), the irregular morphologies and their wide range of burning rates made a more rigorous and detailed kinetic analysis quite difficult.
他们还发现，即使对于较小的生物质焦炭颗粒（75−106 微米），其不规则形态和广泛的燃烧速率范围也使得进行更为严格和详细的反应动力学分析变得相当困难。

Results from Di Blasi and co-workers (13) indicate that in the kinetically controlled regime (low temperature ∼873 K) and under nonisothermal conditions (10, 20−80 K/min heating rate), the reactivities (d m/d t) of three biomass chars (wheat straw, olive husks, and grape residues) increased with conversion first, reaching a maximum, and decreased or remained constant, then increased again as a function of conversion.
Di Blasi 及其同事的研究结果（13）表明，在动力学控制区（低温约 873 K）和非等温条件下（加热速率为 10, 20−80 K/min），三种生物质焦（小麦秸秆、橄榄壳和葡萄残渣）的反应性（d m/d t）随转化率先增加，达到峰值后下降或保持不变，随后又随转化率再次增加。
A one-step global model interprets the mass loss curves in their work with conversion-dependent parameters. At low temperatures in a TGA, Adanez and his co-workers (14) determined combustion reactivities of five biomass chars with a combined method, with similar results.
一步全局模型通过依赖于转化率的参数解释了他们工作中的质量损失曲线。在热重分析（TGA）的低温条件下，Adánez 及其同事（14）采用综合方法测定了五种生物质焦的燃烧反应性，并得到了相似的结果。

A recent paper (15) investigated the combustion characteristics of moving and suspended biomass particles both experimentally and mathematically. It was found that isothermal particle assumption is no longer valid when particle size exceeds 150−200 μm.
最近的一篇论文（15）通过实验和数学模型研究了移动和悬浮生物质颗粒的燃烧特性。研究发现，当颗粒尺寸超过 150−200 微米时，等温颗粒假设不再适用。

Detailed single biomass particle combustion data, including particle mass loss and temperature history as functions of time, is rarely reported in the above literature.
上述文献中很少报道详细的单个生物质颗粒燃烧数据，包括颗粒质量损失和温度随时间变化的历史记录。
This investigation summarizes experimental drying, devolatilization conversion, and char oxidation rates for poplar particles in a single particle reactor, as well as a model that predicts these data nearly within their experimental uncertainty, providing detailed descriptions of particle mass and temperature change for a single particle during combustion.
本研究总结了在单颗粒反应器中对杨木颗粒进行的实验干燥、挥发分转化及焦炭氧化速率，并提出一个模型，该模型能在实验不确定度范围内近似预测这些数据，详细描述了燃烧过程中单颗粒的质量和温度变化。

2 Experimental Method 2 实验方法

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A single-particle reactor (16) is used to investigate the drying, devolatilization, and char oxidation/gasification behaviors of biomass particles. Figure 1 schematically illustrates the experimental facility for the single particle combustion study.
单颗粒反应器（16）用于研究生物质颗粒的干燥、挥发分释放以及焦炭氧化/气化行为。图 1 以示意图形式展示了单颗粒燃烧研究的实验装置。

Figure 1. Single-particle reactor schematic diagram.
图 1. 单颗粒反应器示意图。

Poplar particles with two regular shapes, cylinder and near-sphere, were obtained by cutting 9.5 mm diameter poplar dowel rod to different aspect ratios: 1.0 for near-spherical and 4.0 for cylindrical particles. Moisture content of the samples is usually about 6%.
杨木颗粒具有两种规则形状，即圆柱形和近球形，通过将直径为 9.5 毫米的杨木棒切割成不同长径比获得：近球形颗粒的长径比为 1.0，圆柱形颗粒的长径比为 4.0。样品的水分含量通常约为 6%。
To study the drying behavior of biomass particles, samples with higher moisture contents were also prepared by soaking in water for different periods and kept in closed sample bottles.
为研究生物质颗粒的干燥行为，还通过在水中浸泡不同时间并存放在密封样品瓶中，制备了含水量较高的样品。

Single biomass particles suspended on a type B or type K thermocouple and connected to a wireless data logger, from PACE Scientific, provided internal temperature data at a speed of 20 Hz.
单个生物质颗粒悬挂在 B 型或 K 型热电偶上，并连接至 PACE Scientific 的无线数据记录仪，以 20 赫兹的速率提供内部温度数据。
The data logger, thermocouple, and the biomass particle were placed on top of a balance to provide dynamic mass loss data. A small hole of about the same size of the thermal couple wire (∼0.25 mm) was drilled through the center the particle for thermocouple suspension.
数据记录仪、热电偶与生物质颗粒被放置在电子天平上，以提供动态质量损失数据。在颗粒中心钻了一个与热电偶线径相近的小孔（约 0.25 毫米），用于热电偶的悬挂。
Mass loss data were collected and recorded with the balance with a resolution of 0.1 mg. The imaging system and optical pyrometer recorded the physical changes and surface temperature distribution of the biomass particle.
质量损失数据通过分辨率为 0.1 毫克的称重仪采集并记录。成像系统和光学高温计则记录了生物质颗粒的物理变化及表面温度分布情况。
The data logger, balance, and imaging system collect data simultaneously. All equipment and devices are synchronized within 1 s. For particle devolatilization processes, particle surface temperature was also measured by a thermocouple.
数据记录仪、天平及成像系统同步采集数据，所有设备和装置的同步精度在 1 秒以内。对于颗粒的挥发分释放过程，还通过热电偶测量了颗粒表面温度。
To reduce the influence of thermal conduction on surface temperature measurement, a shallow and narrow groove was cut on the particle surface and the wire was buried next to the surface.
为减少热传导对表面温度测量的影响，在颗粒表面刻出浅窄槽，并将导线埋设于靠近表面处。

This single-particle reactor produces experimental data, including mass loss, and surface and center temperature, as functions of time for poplar dowel particles during drying, pyrolysis, and char oxidation/gasification processes.
该单颗粒反应器生成实验数据，包括杨木销颗粒在干燥、热解及焦炭氧化/气化过程中质量损失、表面和中心温度随时间变化的关系。

3 Particle Mathematical Model
3 颗粒数学模型

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As a biomass particle hovers in the single-particle reactor with air as carrier gas, it exchanges energy by both radiation and convection and by chemical reactions.
当生物质颗粒在以空气为载气体的单颗粒反应器中悬浮时，它通过辐射、对流以及化学反应进行能量交换。
The biomass particle undergoes the following processes: drying, devolatilization, volatiles combustion, char gasification, and char oxidation. These processes may occur sequentially or simultaneously, depending on particle properties and reactor conditions.
生物质颗粒经历以下过程：干燥、挥发分析出、挥发分燃烧、焦炭气化和焦炭氧化。这些过程可能依次发生或同时进行，具体取决于颗粒特性和反应器条件。

Mechanisms of Drying, Devolatilization, and Char Gasification and Oxidation
干燥、挥发分释放及焦炭气化和氧化机制

Moisture in biomass occurs in two forms: free water and bound water. (17) Moisture content above the fiber saturation point (FSP) is free water, that is, exists in liquid form in pores and cells. Below the FSP, moisture is bound water, that is, exists as moisture physically or chemically bound to surface sites or as hydrated species.
生物质中的水分以两种形式存在：自由水和结合水。（17）纤维饱和点（FSP）以上的水分含量为自由水，即以液态形式存在于孔隙和细胞中。低于 FSP 时，水分则为结合水，即以物理或化学方式结合在表面位点上，或以水合物的形式存在。
The average FSP is about 30%, (17) which is the weight of water in the wood as a percentage of the weight of oven-dry wood (essentially water content on a dry basis). Traditionally, the forest products industries express moisture on this basis, so that 100% moisture means essentially half of the mass is water.
平均 FSP 约为 30%，（17）即木材中水分重量占烘干木材重量的百分比（基本上是基于干基的水分含量）。传统上，林产品行业以此基准表示水分，因此 100%水分意味着质量的一半是水。
Nuclear magnetic resonance (NMR) can determine free water and bound water contents. (18) Free moisture vaporizes from both the internal and external surface at a rate determined by the surface saturated vapor pressure, the partial pressure of vapor in the gas phase.
核磁共振（NMR）可测定自由水和结合水含量。(18) 自由水分从内外表面蒸发，其速率由表面饱和蒸汽压和气相中蒸汽分压决定。
Bound water does not vaporize in a manner similar to free moisture but rather is released as a result of chemical reactions releasing bound hydrates and similar processes.
结合水并非以自由水分蒸发的方式挥发，而是通过释放结合水合物及类似化学反应过程释放出来。
Four basic methods, including a thermal model, equilibrium model, and chemical reaction model, describe wood drying under combustion heat fluxes. (19) In this model, a mass transfer expression, with the difference between equilibrium vapor pressure and vapor partial pressure as the driving force, describes both the evaporation of free water and recondensation of vapor.
四种基本方法，包括热模型、平衡模型和化学反应模型，描述了在燃烧热流作用下的木材干燥过程。(19) 在该模型中，以平衡蒸汽压与蒸汽分压之差为驱动力的质量传递表达式，既描述了自由水的蒸发，也描述了蒸汽的再凝结。
The evaporation rate of bound water proceeds by a chemical reaction rate expression. (20) Figure 2 illustrates the drying scheme of moisture. Poplar particles used in the single-particle reactor usually have 6% moisture content, which is categorized as bound water.
结合水的蒸发速率遵循化学反应速率表达式。（20）图 2 展示了水分的干燥过程。在单颗粒反应器中使用的杨木颗粒通常含有 6%的水分，这些水分被归类为结合水。
Samples with higher moisture content, up to 50%, were also prepared and used to collect free-water drying process data and validate the drying model.
含水量高达 50%的样品也被制备并用于收集自由水干燥过程数据，并验证干燥模型。

Figure 2. Moisture drying scheme.
图 2. 水分干燥方案。

Devolatilization or pyrolysis involves heating of raw biomass components or organic materials in the absence of oxidizer, thermal degradation of the biomass components, mass transport of the devolatilization products by advection and diffusion, and escape of products at the surface of the particle.
挥发分释放或热解过程涉及在无氧化剂条件下对生物质原料或有机材料进行加热，生物质组分的热降解，挥发分产物通过对流和扩散的质量传递，以及产物在颗粒表面的逸出。
A few authors distinguish between pyrolysis and devolatilization, with the former occurring in a neutral or reducing environment and the latter in an oxidizing environment.
一些作者区分了热解和挥发分的析出，前者发生在中性或还原性环境中，而后者则发生在氧化性环境中。
Most particles thermally decompose within a volatile cloud (reducing environment) even when the overall environment is oxidizing, making this distinction somewhat ambiguous. The two terms are used interchangeably in this document, consistent with most of the literature.
大多数颗粒在挥发物云（还原环境）中发生热分解，即使整体环境是氧化性的，这使得这种区分有些模糊。在本文件中，这两个术语可互换使用，与大多数文献保持一致。
The two-stage wood pyrolysis kinetics model, shown in Figure 3, is chosen for this particle model since it is capable of predicting the product yields and distribution variations with temperature and heating rate which are significantly influenced by particle shape and size.
图 3 所示的两阶段木材热解动力学模型被选用于此颗粒模型，因为它能够预测产品产率和分布随温度和加热速率的变化，这些变化显著受到颗粒形状和大小的影响。

Figure 3. Two-stage wood pyrolysis model. (21)
图 3. 两阶段木材热解模型。(21)

The volatile yield from pyrolysis includes a complex mixture and more than 100 hydrocarbons were found. (22-24) Pyrolysis product distribution depends strongly on reactor temperature, heating rate, residence time, and mass transfer velocity and pressure. (24) This complex mixture mainly consists of CO, CO ₂, H ₂O, H ₂, light hydrocarbons, and heavy hydrocarbons. The first five components are classified as light gas, and the last one as tar. For the light gas composition, reaction kinetics from Thunman et. al (25) predict wood pyrolysis volatile components in this model, with the mass fraction of each species listed in Table 1. To simplify the combustion behaviors of volatiles, the light hydrocarbon and heavy hydrocarbon are lumped together as hydrocarbons in the current investigation, and the lumped hydrocarbon molecule is C ₆H _6.2O _0.2, consistent with published results. (25) In this model, hydrocarbon combustion in the gas phase occurs through a one-step global reaction according to the approximate composition of hydrocarbon, even though the combustion chemistry of a simple gas could be a complex phenomenon. (26) The reaction mechanism and kinetic parameters for the hydrocarbon combustion are based on the recommendations of Smoot and Smith. (27)
热解挥发分的产率包含复杂的混合物，发现了超过 100 种的烃类化合物。（22-24）热解产物分布强烈依赖于反应器温度、加热速率、停留时间、质量传递速度及压力。（24）这一复杂混合物主要由 CO、CO₂、H₂O、H₂、轻质烃类和重质烃类组成。前五种成分归类为轻气体，最后一种为焦油。对于轻气体组成，Thunman 等人（25）的反应动力学预测了本模型中木材热解挥发分成分，各物种的质量分数列于表 1 中。为简化挥发分的燃烧行为，本次研究将轻质烃类和重质烃类合并为烃类，合并后的烃分子为 C₆H₆.₂O₀.₂，与已发表的结果一致。（25）在本模型中，气相中的烃类燃烧通过一步全局反应进行，依据的是烃类的大致组成，尽管单一气体的燃烧化学可能是一个复杂的现象。 (26) 烃类燃烧的反应机理和动力学参数基于 Smoot 和 Smith 的推荐。 (27)

Table 1. Light Gas Composition Produced during Devolatilization
表 1. 热解过程中产生的轻质气体组成

components 成分	H ₂ H₂	CO	CO ₂ 二氧化碳	H ₂O 水	light hydrocarbon 轻质烃
mass fraction 质量分数	0.109	0.396	0.209	0.249	0.127

Char gasification and oxidation include five classic heterogeneous and homogeneous reactions, indicated as reactions 8−12 in Table 2. In coal char combustion, reaction 8 is described by both first- and half-order expressions. (28, 29) Biomass char reactivity literature is less substantial than that for coal char, but some report that biomass char has slightly higher reactivity than that of coal. (12, 13, 30, 31) The oxidation rate of biomass char varies between a half- and first-order, as demonstrated by Janse et al. (32) According to Bryden’s (33) analysis, lignite’s kinetic parameters are used for wood char oxidation since wood char more closely resembles lignite than other coal types.
生物质焦的气化和氧化过程涉及五个经典的异相和均相反应，如表 2 中的反应 8−12 所示。在煤焦燃烧中，反应 8 既可以用一级反应表达式描述，也可以用半级反应表达式描述。（28, 29）相比煤焦，生物质焦反应性方面的文献较少，但有研究指出，生物质焦的反应性略高于煤焦。（12, 13, 30, 31）Janse 等人（32）的研究表明，生物质焦的氧化速率介于半级与一级反应之间。根据 Bryden（33）的分析，由于木质焦与褐煤的相似性高于其他煤种，因此木质焦氧化反应的动力学参数采用了褐煤的数据。
The oxidation kinetic mechanisms make this model more robust, but in practice oxidation occurs mostly under diffusion-controlled conditions, in which case the details of the kinetics are immaterial.
氧化动力学机制使该模型更加稳健，但在实际应用中，氧化过程大多处于扩散控制条件下，此时动力学的细节变得无关紧要。

Table 2. Chemical Reactions, Phase Change and Rate Expressions
表 2. 化学反应、相变及速率表达式

reaction index 反应指数	reaction description 反应描述	rate expression 速率表达式	ref 参考文献
1	biomass → light gas 生物质 → 轻质气体	r₁ = ∂ρ _B/∂ t = k₁ρ _B r1 = ∂ρ_B/∂t = k1ρ_B
2	biomass → tar 生物质 → 焦油	r₂ = ∂ρ _B/∂ t = k₂ρ _B r2 = ∂ρ_B/∂t = k2ρ_B
3	biomass → char 生物质 → 炭	r₃ = ∂ρ _B/∂ t = k₃ρ _B r3 = ∂ρB/∂t = k3ρB
4	tar → light gas 焦油 → 轻质气体	r₄ = ∂ρ _G/∂ t = ε k₄ρ _gY_T r4 = ∂ρG/∂t = εk4ρgYT
5	tar → char 焦油 → 炭	r₅ = ∂ρ _C/∂ t = ε k₅ρ _gY_T
6	H ₂O(l,free) ↔ H ₂O(g) H₂O(l,自由) ↔ H₂O(g)	r₆ = ∂ρ _fw/∂ t = s_a(ρ _fw/ρ _fw⁰) h_m,pore(ρ _v^sat − Y_Vρ _g) r6 = ∂ρ_fw/∂t = sa(ρ_fw/ρ_fw0) hm,pore(ρ_vsat − YVρ_g)
7	H ₂O(l,bound) → H ₂O(g) H₂O(l,bound) → H₂O(g)	r₇ = ∂ρ _bw/∂ t = k₇ρ _bw r7 = ∂ρ_bw/∂t = k7ρ_bw	20
8	C + ¹/ ₂O ₂ → CO C + 1/2O₂ → CO	r₈ = ∂ C_{O ₂}/∂ t = s_a,char[ρ _C/(ρ _C + ρ _B + ρ _A)] k₈ε C_{O ₂} r8 = ∂CO₂/∂t = sa,char[ρC/(ρC + ρB + ρA)] k8εCO₂	31
9	C + CO ₂ → 2CO C + CO₂ → 2CO	r₉ = ∂ C_{CO ₂}/∂ t = s_a,char[ρ _C/(ρ _C + ρ _B + ρ _A)] k₉ε C_{CO ₂} r9 = ∂CCO₂/∂t = sa,char[ρC/(ρC + ρB + ρA)] k9εCCO₂	29
10	C + H ₂O → CO + H ₂ C + H₂O → CO + H₂	r₁₀ = ∂ C_{H ₂O}/∂ t = s_a,char[ρ _C/(ρ _C + ρ _B + ρ _A)] k₁₀ε C_{H ₂O} r10 = ∂CH₂O/∂t = sa,char[ρC/(ρC + ρB + ρA)] k10εCH₂O	29
11	¹/ ₂O ₂ + CO → CO ₂ 1/ 2O₂ + CO → CO₂	r₁₁ = ∂ C_CO/∂ t = k₁₁C_COC_{O ₂}^0.25C_{H ₂O}^0.5 r11 = ∂CCO/∂t = k11CCOCO²⁰·²⁵CH²O⁰·⁵	34
12	H ₂ + ¹/ ₂O ₂ → H ₂O H₂ + 1/2O₂ → H₂O	r₁₂ = ∂ C_{H ₂}/∂ t = k₁₂C_{H ₂}C_{O ₂}^1.42 r12 = ∂CH₂/∂t = k12CH₂CO₂¹·⁴²	34
13	C ₆H _6.2O _0.2 + 2.9O ₂ → 6CO + 3.1H ₂	r₁₃ = ∂ C_HC/∂ t = k₁₃C_HC^0.5C_{O ₂} r13 = ∂CHC/∂t = k13CHC^0.5CO2	27

Parameters describing chemical reactions and phase changes, together with their corresponding rate expressions during drying, devolatilization, and char oxidation processes, appear in Table 2.
表 2 列出了描述干燥、挥发分释放和焦炭氧化过程中化学反应及相变参数及其相应的速率表达式。

Arrhenius expressions describe the temperature dependence of the kinetic rate coefficients for reactions 1−5 and 7−13, as indicated in eqs 1 and 2.
Arrhenius 表达式描述了反应 1−5 和 7−13 的反应速率系数对温度的依赖关系，如方程 1 和 2 所示。

In reactions 1−5, 7, and 11−13
在反应 1−5、7 以及 11−13 中

(1) and in reactions 8−10,
并在反应 8−10 中，

(2)

The literature-based kinetic parameters for wood pyrolysis vary widely. They are usually measured at low to moderate temperature (usually <900 K). No high-temperature kinetic data for the two-stage scheme appear in the literature. Font et al. (35) presented kinetic data for the three primary reactions that are found to be comparable to what Nunn et al. (36) reported for the single reaction kinetic data for hardwood in the high-temperature range (573−1373 K). Font et al.ʼs results are used in this model for sawdust samples, and Wagenaar’s (37) pine wood pyrolysis kinetics data are applied for poplar samples. The pre-exponential factors, activation energy, and standard heats of reaction for all the reactions used in this model appear in Table 3.
基于文献的木材热解动力学参数差异较大，通常在低温至中温条件下（通常<900 K）测得。目前文献中尚未见关于两阶段方案的高温动力学数据。Font 等人（35）提供了与 Nunn 等人（36）所报告的高温范围（573−1373 K）内硬木单反应动力学数据相媲美的三种主要反应的实验数据。本模型中，Font 等人的结果用于锯末样品，而 Wagenaar（37）的松木热解动力学数据则应用于杨木样品。表 3 列出了本模型中所有反应的指前因子、活化能及标准反应热。

Table 3. Kinetic Data and Heats of Reaction
表 3. 动力学数据与反应热

reaction index 反应指数	A (1/s) A (1/秒)	E (kJ/mol) E（千焦/摩尔）	ref 参考文献	temp range (K) 温度范围（K）	Δ H (kJ/kg) ΔH (千焦/千克)	ref 参考文献
1 (hardwood sawdust) ^a 1（硬木锯屑）	1.52 × 107 1.52 × 10⁷	139.2	35	733−878	−418 -418	20
1 (poplar) ^a 1（杨木）	1.11 × 1011 1.11 × 10¹¹	177	37	573−873
2 (hardwood sawdust) ^a 2（硬木锯屑）	5.85 × 106 5.85 × 10⁶	119	35	733−878	−418 -418	20
2 (poplar) ^a 2（杨木）	9.28 × 109 9.28 × 10⁹	149	37	573−873
3 (hardwood sawdust) ^a 3（硬木锯屑）	2.98 × 103 2.98 × 10³	73.1	35	733−878 733-878	−418 -418	20
3 (poplar) ^a 3（杨木）	3.05 × 107 3.05 × 10⁷	125	37	573−873
4	4.28 × 106 4.28 × 10⁶	107.5	38	−	42	39
5	1.0 × 105 1.0 × 10⁵	107.5	40	−	42	39
6	5.13 × 1010 5.13 × 10¹⁰	88	19	−	−2440 -2440	19
8	0.658 (m/(s·K)) 0.658 (米/(秒·开))	74.8	31	−	9212	19
9	3.42 (m/(s·K)) 3.42 (米/(秒·开))	130	29	−	14370	41
10	3.42 (m/(s·K)) 3.42 (米/(秒·开))	130	29	−	10940	41
11	1012.35	167	34	−	10110	41
12	1012.71	171.3	34	−	120900	41
13	104.32 × T × 0.3 P 104.32 × 温度 × 0.3 / 压力	80.2	27	−	41600	33

These are all one-step kinetics for pyrolysis.

这些都是用于热解的一步动力学模型。

Heat, Mass, and Momentum Transfer Control Equations
热量、质量和动量传递控制方程

The following assumptions allow tractable mathematical combustion model development:
以下假设有助于简化数学燃烧模型的开发：

• a transient one-dimensional model sufficiently describes particle behavior;
• 一个瞬态一维模型足以描述颗粒行为；

• local thermal equilibrium exists between the solid and gas phase in the particle, so internal temperatures and their gradients are the same for the solid and gas;
• 颗粒内固相与气相之间存在局部热平衡，因此固相和气相的内部温度及其梯度相同；

• gases behave as ideal gases, including both relationships between pressure, temperature, and specific volume and dependence of heat capacity on temperature only;
• 气体表现为理想气体，包括压力、温度与比体积之间的关系，以及热容仅对温度的依赖性；

• particle aspect ratios and shapes do not change during devolatilization, though size does change dynamically. The shape and aspect ratio is a simplifying assumption for this case but not required by the model in general;
• 颗粒的纵横比和形状在挥发分释放过程中不会改变，尽管尺寸会动态变化。在此情况下，形状和纵横比是一个简化的假设，但并非模型所必需的；

• heat and mass transfer at particle boundaries increase relative to that of a sphere by the ratio of the particle surface to that of a volume-equivalent sphere—a close approximation to results from more detailed analyses for similarly sized particles.
• 颗粒边界处的热量和质量传递相对于球体的增加量，与颗粒表面积与等体积球体表面积之比成正比——这一近似结果与针对类似尺寸颗粒的更详细分析所得结果相当接近。

Particle shapes represented by a parameter n include a sphere ( n = 2), cylinder ( n = 1), and flat plate ( n = 0). The biomass particle initially contains inert gas or air. In total, 12 species appear in the model: biomass, char, free water, bound water, ash, CO, CO ₂, H ₂O, H ₂, O ₂, lumped hydrocarbon (tar), and inert gas. The mass conservation of each species, the momentum, and the total energy equations, as well as the initial and boundary conditions, appear as eqs 3– 33.
颗粒形状由参数 n 表示，包括球体（n=2）、圆柱体（n=1）和平板（n=0）。生物质颗粒最初含有惰性气体或空气。模型中总共出现 12 种组分：生物质、焦炭、自由水、结合水、灰分、CO、CO₂、H₂O、H₂、O₂、复合烃类（焦油）及惰性气体。各组分的质量守恒、动量及总能量方程，以及初始和边界条件，均以方程 3 至 33 的形式呈现。

The biomass temporal mass balance contains three consumption terms, one each for the reactions to light gas, tar, and char, where all terms in this expression and most terms in subsequent expressions depend on both time and position.
生物质时间质量平衡包含三个消耗项，分别对应于生成轻气体、焦油和焦炭的反应，其中此表达式及后续表达式中的所有项大多同时依赖于时间和位置。

(3)

Similarly, the char temporal mass balance contains five source terms, one from the conversion of biomass to char and one for the char yield from the secondary reactions of tar, as well as the gasification and oxidation reactions.
同样地，焦炭的时间质量平衡包含五个源项，一个来自生物质向焦炭的转化，一个来自焦油二次反应的焦炭产率，以及气化和氧化反应。

where 其中

(4)

The temporal free-water mass balance contains a loss associated with conversion to vapor and a source term associated with water vapor readsorption into the particle, as determined by reaction 6 in Table 2. The free water also migrates due to the pressure gradient in the liquid phase (42, 43). The migration flux is based on Darcy’s law for this porous media, which is proportional to the total liquid pressure gradient. The total liquid pressure is equal to the pressure of the gas phase minus the capillary pressure of the gas−liquid interface.
时间自由水质量平衡包含与转化为蒸汽相关的损失项，以及由表 2 中反应 6 确定的水蒸气再吸附到颗粒中的源项。自由水还因液相中的压力梯度而迁移（42, 43）。迁移通量基于达西定律适用于这种多孔介质，与总液相压力梯度成正比。总液相压力等于气相压力减去气液界面的毛细压力。
An effective free water diffusivity D_eff,fwis derived to describe the migration with Fick’s law applied based on the Darcy’s law results. (43) Equation 5 gives the mass balance for free water. The mass transfer coefficient of vapor in the pore h_m,pore, which appears in the evaporation rate reaction 6, is determined by eq 6. (44)
基于达西定律结果，推导出一种有效的自由水扩散系数 Deff,fw，以描述应用菲克定律的迁移过程。(43) 方程 5 给出了自由水的质量平衡。孔隙中蒸汽的质量传递系数 hm,pore，出现在蒸发速率反应 6 中，由方程 6 确定。(44)

where 其中

(5)

(6)

Bound water has similar migration in the radial direction but responds to a chemical potential gradient rather than a pressure/concentration gradient, and the phase change follows the chemical reaction r7, shown in Equation 7.
结合水在径向方向上的迁移方式相似，但其响应的是化学势梯度而非压力/浓度梯度，相变则遵循化学反应 r7，如方程 7 所示。

where 其中

(7)

Several different correlations describe diffusivities of free water and bound water; (42, 43, 45) Olek et al.ʼs method is applied in this investigation. The diffusivities of both free water and bound water are direction dependent, and the diffusivity in the axial direction is larger than that in the tangential direction.
几种不同的相关性描述了自由水和结合水的扩散性；（42, 43, 45）本研究采用了 Olek 等人提出的方法。自由水和结合水的扩散性均具有方向依赖性，轴向方向的扩散性大于切向方向。
Details appear at the end of this section in the physical property list.
详细信息见本节末尾的物理性质列表。

The ash in the particle is assumed to be inert, so that ash density is constant for nonshrinking/swelling particle
颗粒中的灰分被假定为惰性，因此对于非收缩/膨胀颗粒，灰密度保持恒定

(8)

(9)

The conservation equations for all gas-phase components (CO, CO ₂, H ₂O, O ₂, H ₂, HC, and inert gas) include temporal and spatial gradients, convection, and source terms as follows.
所有气相组分（CO、CO₂、H₂O、O₂、H₂、HC 及惰性气体）的守恒方程包括时间与空间梯度、对流项以及源项，具体如下。

Source terms for each gas-phase species appear below:
各气相物种的源项如下所示：

(10) The overall gas-phase continuity equation results from the sum of these species and has the form
总体气相连续性方程由这些组分的总和得出，其形式为

where 其中

(11)

The gas-phase velocity in the particle obeys a Darcy law type expression
颗粒中的气相速度遵循达西定律类型的表达式

where 其中

(12)

The gas mixture is ideal, and the permeability, η, is a mass-weighted function of the individual solid-phase permeabilities:
气体混合物为理想状态，渗透率η是各固相渗透率的以质量为权重的函数：

(13) The energy conservation equation includes the following terms:
能量守恒方程包括以下各项：

(14) where Ĥ_l = Ĥ_l,f⁰ + ∫ _T₀^T C _{p, l} ( T) d T, l is any species involved, i = any species or component in the solid phase, j = any species or component in the gas phase, and k = free water and bound water.
其中，Ĥ = Ĥ,f 0 + ∫ T0T C p, ( T) d T，表示任意涉及的物种，= 固相中的任意物种或组分，= 气相中的任意物种或组分，k = 自由水和结合水。

This form of the energy equation relates to standard theoretical analyses (46) for multicomponent systems. In eq 14, the first term represents the energy accumulation, the second term represents energy convection, the third term (first term after the equality) accounts for conduction heat transfer, and the last term accounts for energy associated with species diffusion in the gas phase and the liquid phase.
这种形式的能量方程与多组分系统的标准理论分析（46）相关。在公式 14 中，第一项表示能量积累，第二项表示能量对流，第三项（等式后的第一项）表示导热传热，最后一项表示与气相和液相中物种扩散相关的能量。
The last term generally contributes only negligibly to the overall energy balance and is commonly justifiably ignored.
最后一项对整体能量平衡的贡献通常微乎其微，因此通常可以合理地忽略不计。
No heats of reaction appear in the expression since the energy balances total enthalpy (both phases) and is not written in terms of temperature or separate particle and gas phases.
反应热未出现在表达式中，因为能量平衡考虑了总焓（包括两相），并且不是以温度或单独的颗粒相和气相来表示的。
Heats of reaction only become apparent when separately modeling the particle and gas phases or using temperature instead of enthalpy. Radiation between the gas and solid phase in the particle is incorporated into the effective conductivity, as explained below.
反应热仅在分别建模颗粒和气体相或使用温度代替焓时才显现出来。颗粒中气相与固相之间的辐射被纳入有效导热系数中，如下文所述。

The effective diffusivity of gas species in the particle can be calculated by the parallel pore (47) model, as shown in eq 15.
颗粒内气体组分的有效扩散系数可通过平行孔模型（47）计算，如公式 15 所示。

where 其中

(15)

An identical diffusivity for each species and Fickian diffusion assumptions, as implied here, avoid the complexity of more formal multicomponent diffusion calculations.
此处所指的各物种相同扩散系数及菲克扩散假设，避免了更为正式的多组分扩散计算的复杂性。

The effective particle thermal conductivity includes radiative and conductive components with some theoretical basis (48, 49) and with empirical verification for wood. (9)
颗粒有效热导率包括辐射和传导分量，具有一定的理论基础（48, 49），并对木材进行了经验验证（9）。

(16) where the particle structure is assumed to be close to the upper limit for thermal conductivity; that is, it is assumed to have high connectivity in the direction of conduction
假设颗粒结构接近导热率的上限，即假定其在导热方向上具有高连通性

(17) and where radiation contributes approximately to the third power of the temperature
辐射对温度的贡献大约与温度的三次方成正比

(18)

The emissivity of the particle is the mass-weighted result of each solid component: biomass, ash, and char. A volume-weighted emissivity might be more appropriate, but it is not available in this case: all components are assumed to occupy the same total volume.
颗粒的发射率是生物质、灰分和炭各固体成分的质量加权结果。体积加权发射率可能更为合适，但在本例中无法获取：所有成分均假设占据相同的总体积。

(19)

The thermal conductivity of a wet biomass particle is based on Ouelhazi’s (42) empirical correlation which states that the effective thermal conductivity is a function of temperature and moisture contents. Thermal conductivity is anisotropic, with the value in the fiber direction 2.5 times that in the transversal direction.
湿生物质颗粒的热导率基于 Ouelhazi（42）的经验相关性，该相关性指出有效热导率是温度和水分含量的函数。热导率具有各向异性，纤维方向的值是横向方向的 2.5 倍。
An average value of both the fiber and transveral directions is adopted in this paper. Details of the thermal conductivity of the wet biomass particle appear at the end of this section.
本文采用纤维方向和横向方向的平均值。湿生物质颗粒的热导率详细信息见本节末尾。

Initial conditions depend on experimental conditions for a nonreacting particle. That is, at t = 0
初始条件取决于非反应颗粒的实验条件。即在 t = 0 时。

(20)

Boundary conditions at the particle center reflect the spherical symmetry, that is, at r = 0
颗粒中心处的边界条件反映了球对称性，即在 r = 0 处

(21)

During biomass particle combustion, the flame surrounding the particle may affect particle surface temperature by heat generated in the flame that feeds back to the surface and further heats the particle.
在生物质颗粒燃烧过程中，围绕颗粒的火焰可能通过火焰中产生的热量反馈到颗粒表面，从而影响颗粒表面温度，并进一步加热颗粒。
The model describes both the particle domain and the boundary layer domain, which includes the flame during combustion. The boundary layer flame, as with many other model features, can be turned on or off during simulation.
该模型描述了颗粒域和边界层域，后者包括燃烧过程中的火焰。与其他许多模型特征一样，边界层火焰在模拟过程中可以被开启或关闭。

If the boundary layer domain is off, boundary conditions at the particle outer surface depend on external conditions of pressure and heat and mass flux:
如果边界层域关闭，颗粒外表面的边界条件取决于压力、热通量和质量通量的外部条件：

(22) where θ _m and θ _T represent the blowing factors (46) for mass transfer and heat transfer, respectively. RSA represents the exterior surface area ratio, which is the surface area of the particle divided by the characteristic surface area, as follows:
其中，θ_m 和 θ_T 分别表示质量传递和热量传递的吹拂因子（46）。RSA 代表外表面面积比，即颗粒表面积与特征表面积之比，具体如下：

(23) for spheres, cylinders, and flat plates, respectively.
分别针对球体、圆柱体和平板。

Each shape employs heat transfer coefficients developed for that particular shape. Correlations suitable for random particle orientation during flight appear in the literature for some particles. (50) Where such a model is not available, the characteristic length of the particle is the arithmetic average length of the particle. For near-spherical particles, Masliyah’s prolate spheroid model (50) provides a suitable correlation, as indicated in eq 24.
每种形状采用为其特定形状开发的热传递系数。文献中针对某些颗粒在飞行过程中随机取向的情况提供了适用的关联式。(50) 若无此类模型，颗粒的特征长度为其长度的算术平均值。对于近似球形的颗粒，Masliyah 的长椭球模型(50) 提供了合适的关联，如式 24 所示。

(24)

Cylinders at low Reynolds numbers adopt the correlation of Kurdyumov (51) (eq 25).
低雷诺数下的圆柱体采用 Kurdyumov 的相关性（51）（公式 25）。

(25)

The heat transfer coefficient for a flat plate appears in Equation 26.
平板的热传递系数出现在公式 26 中。

(26)

Mass transfer coefficient calculations are analogous to heat transfer correlations respectively for each specific particle shape.
质量传递系数计算类似于每种特定颗粒形状的热传递关联式。

If the boundary layer domain is turned on, the boundary conditions assume those in the bulk flow (indicated by infinity subscripts), as shown in eq 27.
如果边界层域被启用，边界条件将采用主流中的条件（用无穷大下标表示），如式 27 所示。

(27) where BLT _m and BLT _T are boundary layer thickness of mass transfer and heat transfer, respectively. The determination of these two types of boundary layer thicknesses is straightforward if the particle stays in inert carrier gas (nitrogen).
其中，BLT_m 和 BLT_T 分别为质量传递和热传递的边界层厚度。若颗粒处于惰性载气（氮气）中，这两种边界层厚度的确定是直接的。
A linear method is adopted to approximate the boundary layer thicknesses, as illustrated below.
采用线性方法近似边界层厚度，如下所示。

The linear approximation assumes that the gradient at the particle surface can be approximated by an algebraic difference:
线性近似假设颗粒表面的梯度可以用代数差来近似：

(28)

The mass transfer at the particle surface is also correlated with the empirical mass transfer correlation:
颗粒表面的质量传递也与经验质量传递相关性相关：

(29) where the mass transfer coefficient can be calculated by
其中质量传递系数可通过以下公式计算：

(30)

So, substituting eqs 29 and 30 into eq 28 leads to the boundary layer thickness for mass transfer:
因此，将方程 29 和 30 代入方程 28，得到质量传递的边界层厚度：

(31)

Similarly, the boundary layer thickness of heat transfer based on the linear approximation is
同样地，基于线性近似的热传递边界层厚度为

(32)

When the particle is surrounded by air instead of nitrogen, a flame forms in the boundary layer.
当颗粒被空气而非氮气包围时，边界层中会形成火焰。
The resulting temperature and species concentration distributions in the boundary layer may influence the boundary layer thickness, making it different from that calculated based on the heat and mass transfer correlations illustrated above.
边界层内产生的温度和物种浓度分布可能会影响边界层厚度，使其与基于上述热质传递关联式计算的结果有所不同。
The determination of the exact boundary layer thickness for such a burning particle with surrounding flame could be complicated due to bulk flow convection (slip velocity) in the reactor axial direction and the off-gases from the particle.
确定这种燃烧颗粒及其周围火焰的精确边界层厚度可能会因反应器轴向方向上的整体流动对流（滑移速度）和颗粒释放的废气而变得复杂。
A two-dimensional model might be needed to predict the exact boundary layer thickness. In this investigation, eqs 31 and 32 are applied to determine the thickness of the boundary layer, where flame is formed during combustion. Model predictions agree well with experimental data.
可能需要一个二维模型来预测精确的边界层厚度。在本研究中，通过应用方程 31 和 32 来确定燃烧过程中形成火焰的边界层厚度。模型预测与实验数据吻合良好。

To simplify momentum conservation, constant boundary-layer pressure is assumed, equal to the atmospheric pressure. The secondary cracking reactions of tar and soot formation in the boundary layer are neglected, although combustion reactions are included.
为了简化动量守恒，假设边界层压力恒定，等于大气压。尽管包含了燃烧反应，但边界层中焦油和炭黑的二次裂解反应被忽略。
A radiation energy flux has to be added to the energy equation for the node on the particle physical surface due to the radiation between the particle surface and reactor wall.
由于颗粒表面与反应器壁之间的辐射，需要在颗粒物理表面节点处的能量方程中加入辐射能通量。

Particle shrinking or swelling during drying, pyrolysis, and char gasification and oxidation depends on the following empirical correlation:
颗粒在干燥、热解、焦炭气化和氧化过程中的收缩或膨胀取决于以下经验相关性：

(33) which can be used to describe both shrinking and swelling behaviors of a burning solid particle or droplet. In eq 33, v is the current control volume of each cell and v⁰ initial control volume of each cell; x_m, x_B, x_C are conversion of moisture, biomass, and char; β _M is the swelling/shrinking factor of moisture drying, 0.9 for wood particle drying shrinking; β _B is the swelling/shrinking factor of biomass devolatilization, 0.9 for wood particle shrinking; β _C is the shrinking factor of char burning, 0.0 for constant char density shrinking (conceptually consistent with the typically external diffusion controlled oxidation rates).
可用于描述燃烧固体颗粒或液滴的收缩和膨胀行为。在公式 33 中，v 为各单元的当前控制体积，v0 为各单元的初始控制体积；xm、xB、xC 分别为水分、生物质和焦炭的转化率；βM 为水分干燥的膨胀/收缩因子，木材颗粒干燥收缩时为 0.9；βB 为生物质挥发分的膨胀/收缩因子，木材颗粒收缩时为 0.9；βC 为焦炭燃烧的收缩因子，恒定焦炭密度收缩时为 0.0（概念上与通常外扩散控制的氧化速率一致）。

The density change of each species in the solid phase is determined by the following equation due to volume change.
固相中各组分的密度变化由以下方程确定，以反映体积变化的影响。

(34) where i = char, ash, and biomass.
其中 = 炭、灰分和生物质。

The physical properties of the biomass particles significantly affect the heat and mass transfer rates. (2, 52) In this work, temperature-dependent heat capacity correlations are used for all species. The heat capacity of biomass and char adopt the model suggested by Merrick. (53) Gronli et al. (54) suggested a correlation for tar heat capacity, which is based on some typical pyrolysis tar components (closely related to benzene). All physical properties appear in Table 4.
生物质颗粒的物理性质显著影响热质传递速率。(2, 52) 本研究中，所有物种均采用温度相关的热容关联式。生物质和焦炭的热容采用 Merrick 提出的模型。(53) Gronli 等人(54)提出了一种焦油热容的关联式，该关联式基于一些典型的热解焦油成分（与苯密切相关）。所有物理性质列于表 4 中。

Table 4. Physical Properties of Biomass Particles
表 4. 生物质颗粒的物理性质

property 性质	value 值	ref
wood density ρ _B 木材密度 ρB	650 kg/m ³ (sawdust), 580 kg/m ³ (poplar particle) 650 kg/m³（锯末），580 kg/m³（杨木颗粒）
porosity ϵ 孔隙率 ϵ	0.4
emissivity ω 发射率 ω	ω _A = 0.7, ω _B = 0.85, ω _C = 0.95
permeability η (Darcy) 渗透率 η (达西)	η _B = 1, η _C = 100 η_B = 1, η_C = 100	54
thermal conductivity k (W/(m·K)) 导热系数 k (W/(m·K))	k_j, gas species thermal conductivity is calculated based on DIPPR correlations 气体物种的热导率是基于 DIPPR 关联式计算的	55
	k_A = 1.2
	wet biomass in tangential direction: 湿生物质在切向方向：	42
	if C_w > 0.4: 如果 Cw > 0.4:
	k_B = (9.32 × 10 ⁻² + 6.5 × 10 ⁻³C_w)(1 + 3.65 × 10 ⁻³( T − 273.15))(0.986 + 2.695 C_w) kB = (9.32 × 10⁻² + 6.5 × 10⁻³Cw)(1 + 3.65 × 10⁻³(T − 273.15))(0.986 + 2.695 Cw)
	if C_w ≤ 0.4: 如果 Cw ≤ 0.4:
	k_B = (0.129−4.9 × 10 ⁻²C_w)(1 + (2.05 + 4 C_w) × 10 ⁻³( T − 273.15))(0.986 + 2.695 C_w) kB = (0.129 − 4.9 × 10⁻²Cw)(1 + (2.05 + 4Cw) × 10⁻³(T − 273.15))(0.986 + 2.695Cw)
	thermal conductivity in axial direction is 2.5 times of the tangential one 轴向热导率是切向的 2.5 倍。
	k_C = 0.071	56
biomass particle specific surface area S_a (m ²/m ³) 生物质颗粒比表面积 Sa (m²/m³)	9.04 × 10 ⁴ 9.04 × 10⁴	BET
char particle specific surface area S_a,char (m ²/m ³) 炭粒比表面积 Sa,char (m²/m³)	1.0 × 10 ⁶ 1.0 × 10⁶	BET
pore size d_pore (m) 孔径 dpore (米)	3.2 × 10 ⁻⁶ 3.2 × 10⁻⁶	BET
hydraulic pore diameter, d_{pore,hydraulic} 水力孔径，dpore，水力	d_{pore,hydraulic} = 4.0ε/ S_a(1.0 − ε) dpore,hydraulic = 4.0ε / Sa(1.0 − ε)
molecular weight M (kg/kmol) 分子量 M (kg/kmol)	M_T = 145	9
viscosity μ (Pa·s) 粘度 μ (帕·秒)	μ _gas = 3 × 10 ⁻⁵ for all gas species μ_gas = 3 × 10⁻⁵ 适用于所有气体物种	57
diffusivity DAB (m ²/s) 扩散系数 DAB (m²/s)	DAB = 3.0 × 10 ⁻⁵ for all gas species DAB = 3.0 × 10⁻⁵ 对于所有气体物种	9
	where C_bw is bound water content, D₀ = 5 × 10 ⁻⁵ m/s, a₁ = 31030 J/mol, and a₂ = 10000 J/mol 其中 Cbw 为结合水含量，D0 = 5 × 10⁻⁵ m/s，a1 = 31030 J/mol，a2 = 10000 J/mol	45
	S_ir = 0.1, irreducible saturation, k_fw^φ = 3.0 × 10 ⁻¹⁵ m ² Sir = 0.1，不可还原饱和度，kfwφ = 3.0 × 10⁻¹⁵ m²	43
heat capacity C_p (J/(kg·K)) 热容 Cp (J/(kg·K))		53
	where 其中	53
	C_{p, T} = −100 + 4.4 × T − 0.00157 × T₂ Cp, T = −100 + 4.4 × T − 0.00157 × T²	(54)
	C_{p, j} of all gas species except hydrocarbon is based on DIPPR database correlations 除烃类气体外，所有气体物种的 Cp 均基于 DIPPR 数据库的相关性	(55)

This one-dimensional complete mathematical model for the combustion of a single biomass particle includes a set of partial differential equations (PDEs) to describe the mass, heat, and momentum transfer in the particle domain and the flame layer domain. A control volume method (58) reformulates these differential equations into a set of algebraic equations amenable to computer simulation.
该一维完整的生物质颗粒燃烧数学模型包含一组偏微分方程（PDEs），用于描述颗粒域和火焰层域中的质量、热量和动量传递。通过控制体积法（58），将这些微分方程重构为一组适合计算机模拟的代数方程。
A fully implicit scheme is applied for the transient term in the energy conservation equation, each species conservation equation, and momentum equation; the convection and diffusion/conduction terms are solved by the power law scheme; control volume faces occur midway between the grid points; a staggered grid is used for velocity component; the SIMPLE algorithm is applied for the momentum transfer to calculate the flow field.
全隐式格式应用于能量守恒方程、各组分守恒方程及动量方程中的瞬态项；对流项和扩散/传导项采用幂律格式求解；控制体面位于网格点中间位置；速度分量采用交错网格；应用 SIMPLE 算法进行动量传递以计算流场。

4 Results and Discussion 4 结果与讨论

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点击复制章节链接Section link copied!

The single-particle combustion model comparisons with mass loss data and particle temperature data collected on the single-particle reactor provide model validation below.
单颗粒燃烧模型与在单颗粒反应器上收集的质量损失数据和颗粒温度数据进行了比较，以下为模型验证结果。
Then, a series of model predictions with different levels of complexity illustrate the necessity of such a sophisticated structure model for biomass particle combustion modeling. Finally, more model investigations and experimental data are presented and discussed.
随后，一系列不同复杂程度的模型预测展示了为生物质颗粒燃烧建模设计如此精细结构模型的必要性。最后，展示了更多的模型研究与实验数据，并进行了讨论。

Single-Particle Combustion Model Validation
单颗粒燃烧模型验证

Combustion experiments in the single-particle reactor validate the combustion model by comparisons of particle surface temperature, internal temperature, and mass loss during drying, devolatilization, and char oxidation.
单颗粒反应器中的燃烧实验通过对比颗粒表面温度、内部温度及干燥、挥发分释放和焦炭氧化过程中的质量损失，验证了燃烧模型。

The single-particle reactor wall temperature is not uniform in the axial direction due to reactor configurations, so an average wall temperature determined at the location of the particle is used in the model as the reactor wall temperature.
由于反应器结构配置，单颗粒反应器壁温在轴向方向上并不均匀，因此在模型中采用颗粒所在位置确定的平均壁温作为反应器壁温。
Both a type K thermocouple and the imaging pyrometer measure this temperature. The thermocouple reading was 1303 K and the average pyrometer measurement was 1276 K. The imaging pyrometer data are taken as the wall temperature here.
K 型热电偶和成像高温计均测量了该温度。热电偶读数为 1303 K，而成像高温计的平均测量值为 1276 K。此处将成像高温计的数据作为壁面温度。
A type K thermocouple monitors the center gas temperature. The actual gas temperature was corrected for radiative and other losses from the thermocouple bead based on the wall temperature, bulk gas velocity, and the thermocouple bead size.
K 型热电偶用于监测中心气体温度。根据壁温、气体主流速度及热电偶珠粒尺寸，对热电偶珠粒的辐射及其他损失进行了修正，从而得到实际气体温度。
This resulted in a gas temperature of 1050 K.
这导致了气体温度达到 1050 K。

Particle Devolatilization
颗粒挥发分释放

Data for a near-spherical particle ( d_p = 11 mm) with aspect ratio of 1.0 and a moisture content of 6.0 wt %, including mass loss, center and surface temperature during pyrolysis, appear with model predictions in Figures 4 and 5. The nominal conditions of this experiment include a reactor wall temperature of 1273 K and gas temperature of 1050 K. All the following validation experiments used the same conditions.
对于近似球形颗粒（dp = 11 mm），其长宽比为 1.0，水分含量为 6.0 wt%，包括热解过程中的质量损失、中心及表面温度数据，与模型预测结果一同展示在图 4 和图 5 中。该实验的名义条件包括反应器壁温 1273 K 和气体温度 1050 K。所有后续的验证实验均采用相同条件。

Figure 4. Temperature of near-spherical particle during pyrolysis in nitrogen ( d_p = 9.5 mm, AR = 1.0, MC = 6 wt %, T_w = 1276 K, T_g = 1050 K).
图 4. 近球形颗粒在氮气中热解时的温度（dp = 9.5 mm，AR = 1.0，MC = 6 wt %，Tw = 1276 K，Tg = 1050 K）。

Figure 5. Mass loss of near-spherical particle during pyrolysis in nitrogen ( d_p = 9.5 mm, AR = 4.0, MC = 40 wt %, T_w = 1276 K, T_g = 1050 K).
图 5. 近球形颗粒在氮气中热解的质量损失（dp = 9.5 mm，AR = 4.0，MC = 40 wt %，Tw = 1276 K，Tg = 1050 K）。

The particle mass loss and particle surface temperature predictions generally agree with experimental data except that the measured particle center temperature increases faster than the model predictions at the beginning.
颗粒质量损失及颗粒表面温度预测总体上与实验数据吻合，唯初始阶段测得的颗粒中心温度上升速度较模型预测为快。
This discrepancy likely arises from thermal conduction through the thermocouple wire, as discussed later.
这种差异可能源于热电偶丝的热传导，这一点将在后文讨论。
In principle, the measured particle surface temperature and center temperature should reach the same value at the end of pyrolysis, but a small discrepancy exists in differences in thermocouple bead size and shape and ash coating on the center temperature bead.
原则上，测得的颗粒表面温度和中心温度在热解结束时应达到相同值，但由于热电偶珠粒大小和形状的差异以及中心温度珠粒上的灰分覆盖，存在微小偏差。
A more detailed discussion of the features of these data appears after discussion of the potential cause of the discrepancy in the center temperature data.
关于这些数据特征的更详细讨论将在中心温度数据差异潜在原因的讨论之后进行。

To determine the thermocouple lead wire impact on the measured center temperature, a second experiment at the same conditions used a cylindrical particle of the same diameter but with aspect ratio of 4.0. Two thermocouples monitored the center temperature, one passing axially and a second passing radially through the particle.
为了评估热电偶引线对测量中心温度的影响，在相同条件下进行了第二次实验，使用了一个直径相同但长径比为 4.0 的圆柱形颗粒。两个热电偶监测中心温度，一个沿轴向穿过颗粒，另一个沿径向穿过颗粒。
The axial thermocouple should be less impacted by heat conduction through the leads since the particle provides some insulation from the radiation and buoyancy-driven bulk-flow convection. In Figure 6, lines 1 and 2 are particle center temperatures measured in the radial direction; lines 3 and 4 are results measured in axial direction.
轴向热电偶受到导线热传导的影响应较小，因为颗粒提供了一定的辐射和对流隔热作用，减少了辐射和浮力驱动的整体流动对热传导的影响。在图 6 中，线 1 和线 2 为径向测得的颗粒中心温度；线 3 和线 4 为轴向测得的结果。
As indicated, the center temperature measured in the radial direction increases much faster than that measured in axial direction at the beginning, indicating that the thermocouple wire conduction influences initial center temperature measurements.
如所示，径向测量的中心温度在初期上升速度远快于轴向测量值，这表明热电偶丝传导对初始中心温度测量产生了影响。
The model prediction for the center temperature generally agrees with the average of the axial direction data.
模型对中心温度的预测通常与轴向方向数据的平均值相符。

Figure 6. Temperature comparison of a cylindrical particle during pyrolysis in nitrogen ( d_p = 9.5 mm, AR = 4.0, MC = 6 wt %, T_w = 1276 K, T_g = 1050 K).
图 6. 氮气中圆柱形颗粒热解过程中的温度对比（dp = 9.5 mm，长径比 AR = 4.0，含水率 MC = 6 wt %，壁温 Tw = 1276 K，气体温度 Tg = 1050 K）。

Mass loss data collected in several runs for the cylindrical particle appear with model predictions in Figure 7.
图 7 中展示了圆柱形颗粒在多次运行中收集的质量损失数据，并与模型预测结果一同呈现。

Figure 7. Mass loss comparison of a cylindrical particle during pyrolysis in nitrogen ( d_p = 9.5 mm, AR = 4.0, MC = 6 wt %, T_w = 1276 K, T_g = 1050 K).
图 7. 氮气中圆柱形颗粒热解过程中的质量损失对比（dp = 9.5 mm，长径比 AR = 4.0，含水率 MC = 6 wt %，壁温 Tw = 1276 K，气体温度 Tg = 1050 K）。

The shapes of the temperature histories illustrate the complexity of this large-particle pyrolysis process even in the absence of complications arising from surface oxidation and surrounding flames.
温度历史曲线的形状展示了即使在没有表面氧化和周围火焰引起的复杂因素的情况下，这种大颗粒热解过程的复杂性。
The initial low center temperature is associated with vaporization, which occurs at subboiling temperatures under nearly all conditions. Experiments with more moist particles reported later illustrate more clearly the impacts of vaporization.
初始的中心低温与蒸发相关，这在几乎所有条件下都在低于沸点的温度下发生。后续对更湿润颗粒的实验更清晰地展示了蒸发的影响。
After vaporization, particles heat up relatively slowly, mainly because devolatilization reactions in outer layers of the particle generate significant gas velocities in the pores (commonly reaching 0.2 m/s), thereby impeding internal heat transfer.
气化后，颗粒加热相对缓慢，这主要是因为颗粒外层的挥发分反应在孔隙中产生了显著的气体速度（通常可达 0.2 m/s），从而阻碍了内部传热。
After devolatilization, particle temperature increases rapidly, mainly because the particle mass is greatly reduced relative to the early data by virtue of volatile losses but significantly because the internal heat transfer impediment from rapid outgassing also subsides.
挥发分释放后，颗粒温度迅速升高，这主要是因为相对于早期数据，颗粒质量因挥发物损失而大幅减少，但更重要的是，由于快速排气导致的内部传热阻碍也显著减弱。
By contrast, the surface particle temperature increases rapidly and is less susceptible to slow heat transfer rates or even significant impacts from the blowing factor, in this case because radiation is the dominant heating mechanism.
相比之下，颗粒表面温度迅速升高，不易受到缓慢传热速率的影响，甚至在此情况下，由于辐射是主要的加热机制，吹扫因子带来的显著影响也较小。
If convection were the primary heating mechanism, surface temperature heating rates would decrease by factors of up to 10 during rapid mass loss due to the outgassing effects.
如果对流是主要的加热机制，由于排气效应导致的快速质量损失期间，表面温度加热速率将减少多达 10 倍。
These processes result in temperature differences between the surface and the center of many hundreds of degrees Kelvin during particle heatup.
这些过程导致颗粒加热期间表面与中心之间存在数百开尔文的温差。

Particle Drying and Devolatilization
颗粒干燥与挥发分释放

The drying model was further tested using wet particles with higher moisture content.
干燥模型进一步通过含水量更高的湿颗粒进行了测试。
Particle surface temperature and center temperature were measured with type K thermocouples in a cylinder particle with 40 wt % moisture (based on total wet particle mass) during drying and devolatilization.
颗粒表面温度和中心温度在干燥和挥发分释放过程中，通过 K 型热电偶在一个含水量为 40%（基于湿颗粒总质量）的圆柱形颗粒中进行了测量。
Similar to the previous experiments, particle center temperature measured in both axial and radial directions produced different results, with those in the axial direction more reliable. Results appear in Figure 8, which includes model predictions and data. Lines 1 and 2 indicate the center temperature measured in the radial direction, and lines 3 and 4 indicate the axial measurement.
与之前的实验类似，在轴向和径向测得的颗粒中心温度产生了不同的结果，其中轴向测量的结果更为可靠。结果如图 8 所示，包含了模型预测和数据。线 1 和线 2 表示径向测量的中心温度，而线 3 和线 4 表示轴向测量。
Both the model prediction and experimental data showed that the particle temperature first rises to a constant value near but below the boiling point, with evaporation mainly occurring in this stage.
模型预测与实验数据均表明，颗粒温度首先上升至接近但低于沸点的恒定值，此阶段以蒸发为主。
Following drying, the particle temperature increases rapidly until biomass devolatilization slows the particle heating rate due to endothermic decomposition of biomass materials (minor effect) and the effect of rapid mass loss on the heat transfer coefficient, often called the blowing parameter (major effect if convection dominates the particle heatup).
干燥后，颗粒温度迅速升高，直到生物质挥发分的析出减缓了颗粒的加热速率，这是由于生物质材料分解的吸热效应（较小影响）以及快速质量损失对传热系数的影响，通常称为吹扫参数（若对流传热占主导，则为主要影响）。
Once all biomass material converts to char, light gas, and tar, the residual char undergoes a rapid center temperature rise due to its lower mass (major effect), lower heat capacity (minor effect) and return of the blowing factor to near 1.
一旦所有生物质材料转化为焦炭、轻质气体和焦油，剩余的焦炭会因质量较小（主要影响）、热容较低（次要影响）以及吹扫因子恢复至接近 1 而经历快速的中心温度上升。

Figure 8. Temperature comparisons of a cylindrical particle during drying and pyrolysis in nitrogen ( d_p = 9.5 mm, AR = 4.0, MC = 40 wt %, T_w = 1276 K, T_g = 1050 K).
图 8. 氮气中圆柱形颗粒干燥和热解过程中的温度对比（dp = 9.5 mm，AR = 4.0，MC = 40 wt %，Tw = 1276 K，Tg = 1050 K）。

During most of the particle history, the predicted surface temperature is approximately 200 K below the average measured surface temperature.
在颗粒物历史的大部分时间里，预测的表面温度比平均测量表面温度低约 200 K。
The predicted surface temperature depends primarily on radiative heating, convective heating, the impact of the blowing factor on heat transfer, and the rate and thermodynamics of water vaporization.
预测的表面温度主要取决于辐射加热、对流加热、吹扫因子对传热的影响以及水蒸发的速率和热力学特性。
As discussed later, the blowing factor in this radiation-dominated environment has little impact on the predictions. The thermodynamics of water vaporization are in little doubt, although the thermodynamics of the chemically adsorbed water losses are relatively uncertain.
如后文所述，在这种以辐射为主导的环境中，吹扫因子的影响对预测结果影响甚微。水蒸发的物态变化过程毋庸置疑，然而化学吸附水损失的热力学特性则相对不确定。
It is also possible that the reactions of the particle with its attendant changes in size and composition compromise the thermal contact between the surface thermocouple and the particle.
颗粒与其伴随的尺寸和成分变化可能影响了表面热电偶与颗粒之间的热接触，这也是有可能的。
There is no clear indication of whether the discrepancy arises from experimental artifacts or from uncertainties in emissivity and transport coefficients or other factors.
目前尚无明确迹象表明这种差异是由实验误差引起的，还是由于发射率和传输系数的不确定性或其他因素导致的。

Figure 9 compares the predicted and measured mass loss data. The model does not predict the measured trend within its uncertainty though the predictions and measurements are in qualitative agreement.
图 9 对比了预测与实测的质量损失数据。尽管预测与实测在定性上一致，模型并未在其不确定性范围内准确预测实测趋势。
The disagreement is likely related to the temperature issues discussed above, including the nonuniformity of reactor temperature distribution.
这种分歧很可能与上述温度问题有关，包括反应器温度分布的不均匀性。
For a cylindrical particle horizontally oriented in the center of the reactor, its ends were exposed to higher temperature environment but the model applied an average bulk gas center temperature.
对于水平放置在反应器中心的圆柱形颗粒，其端部暴露于较高温度的环境中，但模型采用了平均的气体中心温度。

Figure 9. Mass loss of a cylindrical particle during drying and pyrolysis in nitrogen ( d_p = 9.5 mm, AR = 4.0, MC = 40 wt %, T_w = 1276 K, T_g = 1050 K).
图 9. 氮气中圆柱形颗粒干燥和热解过程中的质量损失（dp = 9.5 mm，长径比 AR = 4.0，含水率 MC = 40 wt %，壁温 Tw = 1276 K，气相温度 Tg = 1050 K）。

Particle Combustion 颗粒燃烧

Figure 10 shows the temperature profiles of a wet, near-spherical particle with 40 wt % moisture content (based on the total wet particle mass) and aspect ratio of 1.0 during combustion.
图 10 展示了含水量为 40 wt%（基于湿颗粒总质量）且接近球形、长宽比为 1.0 的湿颗粒在燃烧过程中的温度分布。

Figure 10. Temperature profiles of a near-spherical wet particle during combustion in air ( d_p = 9.5 mm, AR = 1.0, MC = 40 wt %, T_w = 1276 K, T_g = 1050 K).
图 10. 近球形湿颗粒在空气中燃烧时的温度分布（dp = 9.5 mm，AR = 1.0，MC = 40 wt %，Tw = 1276 K，Tg = 1050 K）。

A type B thermocouple provides temperature data for combustion experiments since the peak temperatures exceed the reliable range of type K thermocouples.
B 型热电偶为燃烧实验提供温度数据，因为峰值温度超出了 K 型热电偶的可靠测量范围。
The measured particle surface temperatures are not consistent with model prediction due to experimental artifacts associated with a shrinking particle. The surface contact is lost as the particle shrinks, and the bead becomes exposed to the surrounding flame.
由于与收缩颗粒相关的实验伪影，测得的颗粒表面温度与模型预测不一致。随着颗粒收缩，表面接触丢失，珠粒暴露于周围火焰中。
The measured particle center temperatures appear to disagree with model predictions, though the disagreement arises primarily from thermocouple wire conduction.
测得的颗粒中心温度似乎与模型预测不符，但这种差异主要源于热电偶丝的导热。
Both experimental data and model predictions show that during the char burning stage the particle temperature increases to a peak value and then declines dramatically.
实验数据和模型预测均显示，在焦炭燃烧阶段，颗粒温度会上升至峰值，随后急剧下降。
This supports theoretical descriptions of large-particle combustion mechanisms. Oxidizer diffusion rates primarily control combustion rates in char consumption, which proceeds largely with constant density and shrinking particle diameter.
这为大颗粒燃烧机理的理论描述提供了支持。氧化剂扩散速率主要控制着焦炭消耗中的燃烧速率，其过程基本上在密度恒定和颗粒直径缩小的条件下进行。
The char particle oxidation front finally reaches the center of the particle as particle size gets smaller with ash built up in the outer layer of the particle.
随着颗粒尺寸减小且颗粒外层积聚灰分，焦炭颗粒的氧化前沿最终会到达颗粒中心。
The pseudo-steady-state combustion rate/temperature of the particle first increases then decreases with size due to changes in the relative importance of radiation losses, convection, and diffusion.
颗粒的伪稳态燃烧速率/温度首先随尺寸增大而增加，随后因辐射损失、对流和扩散相对重要性的变化而减小。
Once the char is completely consumed, the particle (ash) cools rapidly to near the convective gas temperature, depending on the radiative environment.
一旦焦炭完全消耗，颗粒（灰分）会根据辐射环境迅速冷却至接近对流气体温度。

The corresponding mass loss curves as functions of time appear in Figure 11. In this case, the data and predictions nearly overlap, though there remains a slight underprediction of the mass loss rate. This consistent underprediction could be partially caused by convective drag on the particle, making it appear less massive on the scale than it is.
相应的质量损失随时间变化的曲线如图 11 所示。在此情况下，数据与预测几乎重合，但仍存在轻微的质量损失速率低估现象。这种持续的低估可能部分归因于颗粒所受的对流拖曳力，使其在秤上显得比实际质量更轻。

Figure 11. Mass loss of a near-spherical wet particle during combustion in air ( d_p = 9.5 mm, AR = 1.0, MC = 40 wt %, T_w = 1276 K, T_g = 1050 K).
图 11. 近球形湿颗粒在空气中燃烧时的质量损失（dp = 9.5 mm，AR = 1.0，MC = 40 wt %，Tw = 1276 K，Tg = 1050 K）。

For a low moisture content (6 wt %), near-spherical particle ( d_p = 9.5 mm, AR = 1.0), the flame temperatures are measured with both thermocouple and camera pyrometry. A type B thermocouple mounted near the particle surface provides some measurements of the flame temperature surrounding the particle.
对于低水分含量（6 wt%）、近似球形颗粒（dp = 9.5 mm，AR = 1.0），火焰温度通过热电偶和摄像测温法进行了测量。一种 B 型热电偶安装在颗粒表面附近，提供了颗粒周围火焰温度的一些测量数据。
The upper limit of a type B thermocouple is about 2100 K, and the thermocouple data above this value are not accurate, as shown in Figure 12. The flame temperature was also interpreted by the imaging pyrometer with gray-body emission assumption, where the results are combinations of flame and particle surface radiations. Both thermocouple and pyrometry data are compared with model predictions in Figure 12, where the flame receded away from the thermocouple after devolatilization. The thermocouple measurements fluctuate due to the turbulence and two-dimensional effects caused by the bulk gas convection, which is not captured in this one-dimensional model.
B 型热电偶的上限约为 2100 K，超过此值的热电偶数据不再准确，如图 12 所示。火焰温度还通过假设灰体发射的成像高温计进行了解释，其结果是火焰和颗粒表面辐射的组合。图 12 中将热电偶和高温计数据与模型预测进行了比较，其中挥发分析出后火焰远离了热电偶。由于整体气体对流引起的湍流和二维效应，热电偶测量值出现波动，而这一维模型未能捕捉到这些现象。
In the camera pyrometry measurements, soot was assumed as gray-body emitter, although there is some spectral character to soot emission and the camera pyrometry measurements can be improved if spectral-dependent emissivity is applied in the calculation. (59) The model prediction of the flame indicates the transition of combustion from devolatilization stage to char burning stage, appearing in Figure 12. Results show that model predictions generally agree with both the camera-measured data and thermocouple data, and the difference is within measurements uncertainty.
在摄像测温法测量中，假设炭黑为灰体发射体，尽管炭黑发射具有一定的光谱特性，若在计算中应用光谱依赖的发射率，摄像测温法的测量精度可得到提升。（59）模型预测的火焰显示了燃烧从挥发分阶段向焦炭燃烧阶段的转变，如图 12 所示。结果表明，模型预测总体上与摄像测量数据和热电偶数据相符，差异在测量不确定度范围内。

Figure 12. Flame temperature comparison during a near-spherical particle combustion in air ( d_p = 9.5 mm, AR = 1.0, MC = 6 wt %, T_w = 1273 K, T_g = 1050 K).
图 12. 近球形颗粒在空气中燃烧时的火焰温度对比（dp = 9.5 mm，AR = 1.0，MC = 6 wt %，Tw = 1273 K，Tg = 1050 K）。

This now-validated particle combustion model predicts the relative importance of effects of different factors such as temperature gradients, blowing, and flame reaction, as illustrated below.
这一经过验证的颗粒燃烧模型预测了温度梯度、吹扫和火焰反应等不同因素的相对重要性，如下所示。

Nonisothermal Effects 非等温效应

Both experimental data and model predictions showed that large temperature gradients exist in large biomass particles during combustion. An isothermal particle assumption incorrectly predicts both temperature and mass loss for large particles, as illustrated in Figure 13, where pyrolysis experimental data of a 9.5 mm dry, near-spherical particle are compared with model predictions with isothermal and nonisothermal assumptions.
实验数据和模型预测均表明，在大型生物质颗粒燃烧过程中存在显著的温度梯度。等温颗粒假设会错误地预测大型颗粒的温度和质量损失，如图 13 所示，图中将 9.5 毫米干燥、近似球形颗粒的裂解实验数据与等温和非等温假设下的模型预测进行了对比。
The model with isothermal assumptions predicts overall conversion rates approximately three times faster than the nonisothermal model, the latter being in good agreement with experimental data.
等温假设模型预测的整体转化速率比非等温模型快约三倍，而后者的结果与实验数据吻合良好。
In the isothermal prediction, the surface temperature, which controls the rate of convective and radiative heat transfer, is the same as the average particle temperature.
在等温预测中，控制对流和辐射传热速率的表面温度与颗粒平均温度相同。
The prediction with the temperature gradient indicates the surface temperature increases much faster than the average temperature, decreasing the average driving force for heat transfer and prolonging the reaction time of the particle.
温度梯度的预测表明，表面温度比平均温度上升得快得多，这降低了平均传热驱动力，并延长了颗粒的反应时间。
The difference between isothermal predictions and predictions with temperature gradients decreases with decreasing particle size, but the predicted conversion times do not become comparable (within 10%) until the size is less than 100 μm, which is much smaller than the average particle size used in commercial operation.
等温预测与考虑温度梯度的预测之间的差异随着颗粒尺寸的减小而减小，但预测的转化时间在颗粒尺寸小于 100 微米之前不会变得相当（在 10%以内），这远小于商业运行中使用的平均颗粒尺寸。

Figure 13. Effects of temperature gradients on particle pyrolysis in nitrogen Nonisothermal assumption for model 1 and isothermal assumption for model 2 ( d_p = 9.5 mm, AR = 1.0, MC = 6 wt %, T_w = 1273 K, T_g = 1050 K).
图 13. 温度梯度对氮气中颗粒热解的影响。模型 1 采用非等温假设，模型 2 采用等温假设（dp = 9.5 mm，AR = 1.0，MC = 6 wt%，Tw = 1273 K，Tg = 1050 K）。

Effects of Blowing on Particle Temperature
吹扫对颗粒温度的影响

During pyrolysis, the blowing factor of the 9.5 mm particle becomes as low as 0.1, as shown in Figure 14. This pronounced impact on heat transfer is not observed when radiation dominates particle heating, as illustrated by the predicted temperature profiles of a biomass particle in the single-particle reactor with and without blowing factor correction in Figure 15, where the particle heating history is nearly independent of the blowing effects correction.
在热解过程中，如图 14 所示，9.5 毫米颗粒的吹扫因子降至 0.1。当辐射主导颗粒加热时，并未观察到这种对传热显著的影响，如图 15 中单颗粒反应器中生物质颗粒在有无吹扫因子修正下的预测温度曲线所示，颗粒加热历程几乎不受吹扫效应修正的影响。
However, for environments dominated by convective heating, the blowing factor has a major impact on overall heat transfer rates, and the blowing factor slows down the particle pyrolysis process by about 20%, as indicated in Figure 16.
然而，在以对流加热为主的环境中，吹扫因子对整体传热速率有重大影响，并且如图 16 所示，吹扫因子使颗粒热解过程减缓约 20%。

Figure 14. Blowing factor during particle pyrolysis process in nitrogen ( d_p = 9.5 mm, AR = 1.0, MC = 6 wt %, T_w = 1273 K, T_g = 1050 K).
图 14. 氮气中颗粒热解过程中的吹扫因子（dp = 9.5 mm，AR = 1.0，MC = 6 wt %，Tw = 1273 K，Tg = 1050 K）。

Figure 15. Particle temperature profile during particle pyrolysis in nitrogen with and without blowing factor correction when radiation dominates (model 1 with blowing factor correction and model 2 without blow factor correction; d_p = 9.5 mm, AR = 1.0, MC = 6 wt %, T_w = 1303 K, T_g = 1050 K).
图 15. 辐射主导条件下，氮气中颗粒热解时的颗粒温度分布图，包含与不包含吹扫因子修正（模型 1 含吹扫因子修正，模型 2 不含吹扫因子修正；dp = 9.5 mm，AR = 1.0，MC = 6 wt %，Tw = 1303 K，Tg = 1050 K）。

Figure 16. Effects of blowing factor on particle temperature during pyrolysis in nitrogen when convection dominates (Model-1 with blowing factor correction and model-2 without blow factor correction; d_p = 9.5 mm, AR = 1.0, MC = 6 wt %, T_w = 298 K, T_g = 1400 K).
图 16. 当对流占主导时，吹扫因子对氮气中热解颗粒温度的影响（模型-1 采用吹扫因子修正，模型-2 未采用吹扫因子修正；dp = 9.5 mm，AR = 1.0，MC = 6 wt %，Tw = 298 K，Tg = 1400 K）。

Effects of Surrounding Flame during Particle Combustion
颗粒燃烧过程中周围火焰的影响

The current single-particle combustion model simulates the boundary layer and the flame formed around the particle surface in the boundary layer, as well as predicting the boundary layer thickness.
当前的单颗粒燃烧模型模拟了颗粒表面周围的边界层及其形成的火焰，并预测了边界层厚度。

Figure 17 illustrates the effects of the boundary layer simulation and surrounding flame on the particle temperature profiles during combustion. Simulations both including and neglecting the surrounding flame appear in this graph.
图 17 展示了边界层模拟及周围火焰对燃烧过程中颗粒温度分布的影响。图中包含了考虑与忽略周围火焰的两种模拟结果。
As expected, essentially no difference exists between the two simulations early in devolatilization (flame not yet ignited).
正如预期，在热解初期（火焰尚未点燃），两种模拟之间几乎没有差异。
Slight differences in the surface temperature start to appear during the late devolatilization stage and early oxidation stage of combustion, but the flame actually decreases the predicted surface temperature in this case.
在燃烧的挥发分后期和氧化初期阶段，表面温度开始出现细微差异，但在此情况下，火焰实际上降低了预测的表面温度。
This counterintuitive decrease is associated with the flame consuming oxygen in the boundary layer that otherwise would have reacted with the particle.
这种反直觉的减少与火焰消耗了边界层中的氧气有关，否则这些氧气会与颗粒发生反应。
The relatively minor thermal feedback from the flame to the particle impacts the particle surface temperature less than the reduction in surface reaction associated with the decreased oxygen concentration.
火焰对颗粒的相对较小的热反馈对颗粒表面温度的影响，小于因氧气浓度降低而导致的表面反应减少的影响。
During the bulk of oxidation, the flame increases the predicted surface temperature by about 100 K. The modeled particle final temperatures differ from each other by about 20 K. This minor discrepancy arises from the method applied to determine the boundary layer thickness.
在氧化反应的大部分过程中，火焰使预测的表面温度升高约 100 K。模型颗粒的最终温度彼此相差约 20 K。这种微小的差异源于确定边界层厚度所采用的方法。
In the model including flame layer the boundary layer thickness is based on the linear heat and mass transfer correlations which were used in the model without flame layer.
在包含火焰层的模型中，边界层厚度基于线性热质传递相关性，这些相关性在无火焰层的模型中被采用。
In the boundary layer, temperature distribution is not linear for a spherical coordinate and the tangent (slope) on the surface becomes greater than linear distribution.
在边界层中，对于球坐标系，温度分布并非线性，且表面上的切线（斜率）大于线性分布。
This increases the convection heat transfer in the boundary and hence decreases the particle surface temperature.
这增强了边界层中的对流热传递，从而降低了颗粒表面温度。

Figure 17. Effects of flame on near-spherical particle temperature during combustion in air (model 1 stands for results without flame included, model 2 for those with flame included; d_p = 9.5 mm, AR = 1.0, MC = 6 wt %, T_w = 1273 K, T_g = 1050 K).
图 17. 火焰对近球形颗粒在空气中燃烧时温度的影响（模型 1 表示未包含火焰的结果，模型 2 表示包含火焰的结果；dp = 9.5 mm，AR = 1.0，MC = 6 wt %，Tw = 1273 K，Tg = 1050 K）。

Model results also indicate that particle temperature becomes dramatically more uniform during char burning, although the flame feedback maintains a surface temperature greater than the center temperature, unlike theoretical predictions for particles with oxygen penetration but no flame feedback.
模型结果还表明，在焦炭燃烧过程中，颗粒温度变得显著更加均匀，尽管火焰反馈使得表面温度高于中心温度，这与理论预测的具有氧气渗透但无火焰反馈的颗粒情况不同。
These relatively subtle effects on flame temperatures are too small for accurate measurements by our techniques.
这些对火焰温度的相对微妙的影响，以我们的技术手段难以进行精确测量。

Generally speaking, nonisothermal effects will slow down the heat transfer (both radiation and convection) between the bulk gas and particle surface due to the decrease of temperature difference.
一般来说，非等温效应会因温度差的减小而减缓主体气体与颗粒表面之间的传热（包括辐射和对流）。
Also for convection-dominated particle heat transfer, the blowing factor (which is caused by high mass transfer in the boundary layer) will dramatically reduce the heating rate to the particle.
对于以对流为主的颗粒传热，吹扫因子（由边界层内高传质引起）将显著降低颗粒的加热速率。
Surrounding flame affects the particle temperature mainly during the char burning stage.
周围火焰主要在焦炭燃烧阶段影响颗粒温度。

The modeled particle radius, boundary layer thickness, and off-gas velocity as functions of residence time during drying, devolatilization, and char burning appear in Figure 18.
图 18 展示了干燥、挥发分释放和焦炭燃烧过程中，颗粒半径、边界层厚度和逸出气体速度随停留时间变化的模拟结果。

Figure 18. Particle radius, boundary layer thickness, and off-gas velocity during a wet particle combustion process in air ( d_p = 9.5 mm, AR = 1.0, MC = 6 wt %, T_w = 1273 K, T_g = 1050 K).
图 18. 湿颗粒在空气中的燃烧过程中，颗粒半径、边界层厚度和废气速度的变化情况（dp = 9.5 mm，AR = 1.0，MC = 6 wt %，Tw = 1273 K，Tg = 1050 K）。

Although the three processes of drying, devolatilization, and char oxidation occur simultaneously for large particles such as the 11 mm poplar particle used in this investigation, they can still be approximately identified from both experimental data and model predictions, as shown in Figures 10 and 18. Drying mainly finishes in the first 20 s followed by primary devolatilization that lasts about 30 s; char oxidation requires an additional 30 s. The modeling results also show that the particle shrinks slightly during drying and shrinks more rapidly during char burning.
尽管对于本研究中使用的 11 毫米杨木颗粒而言，干燥、挥发分释放和焦炭氧化这三个过程是同时进行的，但仍可从实验数据和模型预测中近似识别出它们，如图 10 和图 18 所示。干燥过程主要在前 20 秒内完成，随后是持续约 30 秒的一次挥发分释放；焦炭氧化则需要额外 30 秒。模型结果还显示，颗粒在干燥过程中略有收缩，而在焦炭燃烧期间收缩更为迅速。

The comparisons between experimental data and model predictions with different levels of complexity demonstrate that for biomass particle combustion a model with such a sophisticated structure is necessary, which takes particle shape, size, surface area, temperature and concentration gradients, and flame effects into account.
实验数据与不同复杂度模型预测结果的对比表明，对于生物质颗粒燃烧过程，必须采用具备如此精细结构的模型，该模型需综合考虑颗粒形状、尺寸、表面积、温度与浓度梯度以及火焰效应等因素。

5 Conclusions 5 结论

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A relatively general purpose particle combustion model capable of simulating drying, recondensation, devolatilization, and char oxidation and gasification, and swelling/shrinking as well as gas-phase combustion surrounding biomass particles was developed to compare with original data.
开发了一种相对通用的颗粒燃烧模型，能够模拟干燥、再凝结、挥发分释放、焦炭氧化与气化，以及膨胀/收缩现象，并能模拟生物质颗粒周围的气相燃烧，以便与原始数据进行比较。
Comparisons were made of particle center and surface temperatures and overall mass loss. Model predictions included many additional features of biomass combustion less amenable to direct measurement.
对颗粒中心和表面温度以及整体质量损失进行了比较。模型预测涵盖了生物质燃烧的许多额外特征，这些特征较难通过直接测量获得。

The data and model developed in this investigation describe single-particle biomass combustion rates reasonably well.
本研究中开发的数据和模型能较好地描述单颗粒生物质燃烧速率。
Generally, agreement within a few percent of the measured values is achieved, though in most cases there remain generally small but statistically signficant differences between predictions and measurements.
通常情况下，预测值与实测值之间的误差在几个百分点以内，但在大多数情况下，预测与测量之间仍存在虽小但具有统计学意义的差异。

Isothermal spherical mathematical approximations for fuels that either originate in or form aspherical shapes during combustion poorly represent combustion behavior when particle size exceeds a few hundred microns.
当燃料起源于或燃烧过程中形成非球形形状时，等温球形数学近似在颗粒尺寸超过几百微米时，难以准确反映燃烧行为。
This includes a large fraction of the particles in both biomass and black liquor combustion.
这涵盖了生物质和黑液燃烧中大量颗粒的部分。
In particular, composition and temperature gradients in particles strongly influence the predicted and measured rates of temperature rise and combustion, with large particles reacting more slowly than is predicted from isothermal models.
特别是颗粒中的成分和温度梯度对预测和测量的升温速率及燃烧速率有显著影响，大颗粒的反应速度比等温模型预测的要慢。

Author Information 作者信息

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Corresponding Author 通讯作者
- Hong Lu - Chemical Engineering Department, Brigham Yong University, Provo, Utah 84602; Email: honglu@research.ge.com
  洪亮 - 化学工程系，杨百翰大学，普罗沃，犹他州 84602；电子邮件：honglu@research.ge.com
Authors 作者
- Warren Robert - Chemical Engineering Department, Brigham Yong University, Provo, Utah 84602
  沃伦·罗伯特 - 化学工程系，杨百翰大学，普罗沃，犹他州 84602
- Gregory Peirce - Chemical Engineering Department, Brigham Yong University, Provo, Utah 84602
  格雷戈里·皮尔斯 - 化学工程系，杨百翰大学，普罗沃，犹他州 84602
- Bryan Ripa - Chemical Engineering Department, Brigham Yong University, Provo, Utah 84602
  布莱恩·里帕 - 化学工程系，杨百翰大学，普罗沃，犹他州 84602
- Larry L. Baxter - Chemical Engineering Department, Brigham Yong University, Provo, Utah 84602
  拉里·L·巴克斯特 - 化学工程系，杨百翰大学，普罗沃，犹他州 84602

Acknowledgment 致谢

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This investigation is supported by US Department of Energy (DOE)/EE Office of Industrial Technologies. Thanks are given to Drs. Thomas Fletcher, Søren Kær, and Dale Tree for helpful discussions.
本研究得到了美国能源部（DOE）/能源效率办公室工业技术部的支持。感谢 Thomas Fletcher 博士、Søren Kær 博士和 Dale Tree 博士的有益讨论。
Justin Scott, Paul Foster, Kelly Echoes, Brian Spears, and Russ Johnson contributed to this project.
贾斯汀·斯科特、保罗·福斯特、凯利·艾科斯、布莱恩·斯皮尔斯和拉斯·约翰逊为本项目做出了贡献。

Nomenclature 命名法

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A = pre-exponential factor, s ⁻¹; area, m ²
A = 指前因子，s⁻¹；面积，m²
AR = aspect ratio AR = 长宽比
BLT = boundary layer thickness, m
BLT = 边界层厚度，米
C_p = heat capacity, J·kg ⁻¹·K ⁻¹
Cp = 热容，J·kg⁻¹·K⁻¹
d = diameter, m
d = 直径，米
D_eff = effective diffusivity, m ²·s ⁻¹
Deff = 有效扩散系数，m²·s⁻¹
D _AB = molecular diffusivity, m ²·s ⁻¹
D_K = Knudson diffusivity, m ²·s ⁻¹
E_i = activation energy, J·mol ⁻¹
h_f = heat transfer coefficient, W·m ⁻¹·K ⁻¹
h_m = mass transfer coefficient, m·s ⁻¹
Ĥ = enthalpy, J·kg ⁻¹
k = rate constant; devolatilization reaction = s ⁻¹; heterogeneous reaction = m·s ⁻¹
K = thermal conductivity, W/m·s
M = molecular weight, kg·kmol ⁻¹
M_W = gas average molecular weight, kg·kmol ⁻¹
n = shape factor
Nu = Nusselt number
p = pressure, Pa
Pr = Prandtl number
r = radius coordinate, m; reaction rate, kg·m ⁻³·s ⁻¹
Re = Reynolds number
R/ R_g = universal gas constant, J·mol ⁻¹·K ⁻¹
R_p = particle radius, m
R_SA = surface area ratio
t = time, s
S_a = particle specific surface area, m ²·m ⁻³
SA = surface area, m ²
T = temperature, K
u = gas velocity, m·s ⁻¹
v = volume, m ³
x = conversion
Y = mass fraction

Greek symbols
α = proportional factor
β = particle/droplet swelling/shrinking factor
ϵ = porosity
µ = viscosity, Pa·s
η = permeability, Darcy
θ = blowing factor
ρ = density, kg·m ⁻³
Δ H = heat of reaction, J·kg ⁻¹

Subscripts
0 = initial value or reference state
A = ash
B = biomass
C = char
con = conductivity
eq = equivalent
G = gas phase
G = light gas
HC = hydrocarbon
I = species or component in solid phase
J = species or component in gas phase
K = species or component in liquid phase
I = inert gas
M = moisture
P = particle
rad = radiation
V = water vapor
T = tar
w = wall

References

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A theory for detn. of the pyrolysis rate of a single infinite slab, infinite cylinder, or sphere in a const. temp. furnace is suggested. In analogy with the shrinking-core model a pyrolysis propagation front velocity is defined. The velocity is thereafter used in a compartment-model approach for deriving a set of ordinary differential equations for solving the burn-off over time. A comparison with exptl. and published data is also made.
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Janse, A. M. C.; Westerhout, R. W. J.; Prins, W. Modelling of Flash Pyrolysis of a Single Wood Particle Chem. Eng. Process. 2000, 39, 239– 252
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Modelling of flash pyrolysis of a single wood particle
Janse, A. M. C.; Westerhout, R. W. J.; Prins, W.
Chemical Engineering and Processing (2000), 39 (3), 239-252CODEN: CENPEU; ISSN:0255-2701. (Elsevier Science S.A.)
Reactors for flash pyrolysis of biomass are designed to maximize the yield of bio-oil, at the expense of the byproducts gas and char. To understand which chem. and phys. factors influence the yield to bio-oil, the flash pyrolysis of a cylindrical wood particle with a max. diam. of 1000 μm has been simulated by solving the governing equations for mass, enthalpy and momentum conservation for the reactant and products (one dimensional). The flow of vapors is described using the Dusty Gas model (1985), and the structure of wood is incorporated in the model by applying the random pore model of N. Wakao, J.M. Smith (1962). Typical conversion times for a cylindrical particle increase from 1 to 10 s when the diam. increases from 200 to 1000 μm at a surface temp. of 823 K. The bio-oil yield (approx. 77%) is hardly affected by the particle size (200-1000 μm diam.). Obviously tar cracking inside the particle does not occur for the simulated conditions. The heating of a particle is notably delayed by the outflow of vapors. While assuming that they leave the particle in a direction perpendicular instead of parallel to the heat flux, the simulated conversion times appear to decrease with sometimes more than 50%. Finally, the sign and size of the pyrolysis reaction heat is shown to have a distinct effect on the calcd. particle conversion time. As an overall conclusion, the results of this work show that an extensive description of internal mass transport phenomena in flash-pyrolysis modeling is not necessary, while accurate knowledge of the reaction kinetics and heat transfer parameters is crucial.
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Mermoud, F.; Golfier, F.; Salvador, S.; Van de Steene, L.; Dirion, J. L. Experimental and numerical study of steam gasification of a single charcoal particle Combust. Flame 2006, 145, 59– 79
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11
Chen, G.; Yu, Q.; Sjostrom, K. Reactivity of Char from Pyrolysis of Birch Wood J. Anal. Appl. Pyrolysis 1997, 40−41, 491– 499
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Reactivity of char from pyrolysis of birch wood
Chen, Guanxing; Yu, Qizhuang; Sjoestroem, Krister
Journal of Analytical and Applied Pyrolysis (1997), 40,41 (), 491-499CODEN: JAAPDD; ISSN:0165-2370. (Elsevier)
Pyrolysis of biomass from birch was carried out both in a free-fall tubular reactor and a thermobalance. The char obtained was further gasified with carbon dioxide and steam in the thermobalance. It was obsd. that the reaction rates of the char with the reagents were strongly affected by the time-temp. history of the char formation. A rapid heating rate of the raw material in free-fall reactor gives a char which possesses higher reactivity in reaction both with carbon dioxide and steam compared with the char formed under slow heating rate in the thermobalance. The treatment condition and environment of the char precursor during devolatilization are the most important factors affecting the reactivity of the char in gasification with the used reagents. The kinetic study focused on whether a surrounding pyrolysis gas atm. exerts neg. effects on the reactivity of the formed char.
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Wornat, M. J.; Hurt, R. H.; Davis, K. A.; Yang, N. Y. C. Single-Particle Combustion of Two Biomass Chars. In Twenty-Sixth Symposium (International) on Combustion; The Combustion Institute: Pittsburgh, PA, 1999.
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13
Di Blasi, C.; Buonanno, F.; Branca, C. Reactivities of Some Biomass Chars in Air Carbon 1999, 37, 1227– 1238
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Reactivities of some biomass chars in air
Di Blasi, Colomba; Buonanno, Federico; Branca, Carmen
Carbon (1999), 37 (8), 1227-1238CODEN: CRBNAH; ISSN:0008-6223. (Elsevier Science Ltd.)
The reactivities in air of biomass chars, obtained using conventional pyrolysis, are investigated for applications in fixed-bed gasification. Biomasses considered are wheat straw, olive husks and grape residues. Char particles are spread to form a 150 μm thick layer and are radiatively heated, to achieve a kinetically controlled conversion. Time-wt. loss curves, detd. under non-isothermal conditions (heating rates of 10 K/min and a final temp. of 873 K), indicate that the reactivity continuously increases with conversion. The olive husk chars present the highest value, whereas that of grape residue chars is the least. All biomass chars are also combusted at different heating rates (20-80 K/min) and final temps. of 713 K (grape residues) and 673 K (olive husks and straw), so that conversion consists of a dynamic stage, followed by an isothermal period. Again, grape residue chars are the less reactive. Furthermore, the reactivity first attains a max., decreases or remains almost const. and then increases again as a function of conversion. This behavior can be explained by the different roles played by the reaction temp., the development of surface area as combustion proceeds and the increase in the ratio of ashes (catalytically active) to carbon. Finally, the wt. loss curves are well interpreted by a one-step global reaction, whose rate presents a power law dependence on the solid conversion and activation energies in the range 75-94 kJ/mol.
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Adanez, J.; de Diego, L. F.; Garcia-Labiano, F.; Abad, A.; Abanades, J. C. Determination of Biomass Char Combustion Reactivities for FBC Applications by a Combined Method Ind. Eng. Chem. Res. 2001, 40, 4317– 4323
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15
Yang, Y. B.; Sharifi, V. N.; Swithenbank, J.; Ma, L.; Darvell, L. I.; Jones, J. M.; Pourkashanian, M.; Williams, A. Combustion of a Single Particle of Biomass Energy Fuels 2008, 22, 306– 316
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Combustion of a Single Particle of Biomass
Yang, Yao B.; Sharifi, Vida N.; Swithenbank, Jim; Ma, Lin; Darvell, Leilani I.; Jones, Jenny M.; Pourkashanian, Mohamed; Williams, Alan
Energy & Fuels (2008), 22 (1), 306-316CODEN: ENFUEM; ISSN:0887-0624. (American Chemical Society)
Biomass is one of the important renewable energy sources. Biomass fuels exhibit a range of chem. and phys. properties, particularly size and shape. Investigations of the behavior of a single biomass particle are fundamental to all practical applications, including both packed and fluidized-bed combustion, as well as suspended and pulverized fuel (pf) combustion. In this paper, both exptl. and math. modeling approaches are employed to study the combustion characteristics of a single biomass particle ranging in size from 10 μm to 20 mm. Different subprocesses such as moisture evapn., devolatilization, tar cracking, gas-phase reactions, and char gasification are examd. The sensitivity to the variation in model parameters, esp. the particle size and heating rates, is investigated. The results obtained from this study are useful in assessing different combustion systems using biomass as a fuel. It helps to clarify the situations where the thermally thin and thermally thick cases interface. Simple models of particle combustion assuming const. particle temp. are sometimes inadequate and that for large particles a more detailed math. representation should be applied.
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Ip, L.-T. Comprehensive black liquor droplet combustion studies. Chemical Engineering; Brigham Young University: Provo, UT, 2005.
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17
Forest Products Laboratory United States Department of Agriculture Forest Service.
Physical Properties and Moisture Relations of Wood. In Wood Handbook: Wood as an Engineering Material; Forest Products Society: Madison, WI, 1999; Chapter 3, pp 3− 5.
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18
Guzenda, R.; Olek, W. Identification of free and bound water content in wood by means of NMR relaxometry. In 12th International Symposium on Nondestructive Testing of Wood; Sopron: Budapest, Hungary, 2000.
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Bryden, K. M.; Hagge, M. J. Modeling the combined impact of moisture and char shrinkage on the pyrolysis of a biomass particle Fuel 2003, 82, 1633– 1644
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Chan, W.-C.R.; Kelbon, M.; Krieger, B. B. Modeling and experimental verification of physical and chemical processes during pyrolysis of a large biomass particle Fuel 1985, 64 (11) 1505– 1513
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Di Blasi, C. Heat, Momentum and Mass Transport through a Shrinking Biomass Particle Exposed to Thermal Radiation Chem. Eng. Sci. 1996, 51 (7) 1121– 1132
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Heat, momentum and mass transport through a shrinking biomass particle exposed to thermal radiation
Di Blasi, Colomba
Chemical Engineering Science (1996), 51 (7), 1121-32CODEN: CESCAC; ISSN:0009-2509. (Elsevier)
A coupled transport and reaction model is formulated to investigate the effects of various parameters on biomass pyrolysis. The model takes into account formation of chars, tars and gases through mechanisms including both primary reactions of the virgin biomass degrdn. and secondary reactions of the primary tar. All main transport phenomena, unsteadiness of the gas/vapor-phase processes, variation of the reacting medium properties and particle shrinkage are also described. Numerical simulation of the problem of wooden particle, subjected to an assigned external radiation, is used to analyze time and space evolution of the main variables and product distribution as the shrinkage parameters and the intensity of the heat flux are varied. The effects of the orientation of the anisotropic wood grain relative to the one-dimensional heat flux are also investigated.
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Evans, R. J.; Milne, T. A. Molecular Characterization of the Pyrolysis of Biomass. 1. Fundamentals Energy Fuels 1987, 1, 123– 137
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Evans, R. J.; Milne, T. A. Molecular Characterization of the Pyrolysis of Biomass. 2. Applications Energy Fuels 1987, 1, 311– 319
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Demyirbas, A. Hydrocarbons from Pyrolysis and Hydrolysis Processes of Biomass Energy Sources 2003, 25, 67– 75
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Thunman, H.; Niklasson, F.; Johnsson, F.; Leckner, B. Composition of Volatile Gases and Thermochemical Properties of Wood for Modeling of Fixed or Fluidized Beds Energy Fuels 2001, 15, 1488– 1497
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Warnatz, J. Hydrocarbon oxidation high-temperature chemistry Pure Appl. Chem. 2000, 72 (11) 2101– 2110
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Smoot, L. D.; Smith, P. J. Coal Combustion and Gasification; Plenum Press: New York, 1985.
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Smith, K. L.; Smoot, L. D.; Fletcher, T. H.; Pugmire, R. J. The structure and reaction processes of coal. In The Plenum Chemical Engineering Series; Luss, D., Ed.; Plenum Press: New York, 1994.
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Brewster, B. S.; Hill, S. C.; Radulovic, P. T.; Smoot, L. D. Fundamentals of Coal Combustion for Clean and Efficient Use; Smoot, L. D., Ed.; Elsevier Applied Science Publishers: London, 1993; Vol. 20.
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Blackham, A. U.; Smoot, L. D.; Yousefi, P. Rates of oxidation of millimetre-sized char particles: simple experiments Fuel 1994, 73 (4) 602– 612
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Evans, D. H.; Emmons, H. W. Combustion of wood charcoal Fire Res. 1977, 1) 57– 66
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31
Combustion of wood charcoal
Evans, D. D.; Emmons, H. W.
Fire Research (Lausanne) (1977), 1 (1), 57-66CODEN: FIRED9; ISSN:0378-7761.
The lowest mainstream air velocity at which the charcoal from basswood (Tilia americana) would self-sustain its own combustion was 7.7 m/s, and at the highest air velocity (43 m/s), the surface temp. of burning charcoal was 1055° as detd. by filament pyrometer with surface emissivity of 0.85, assuming that the influence of the ash was negligible at this high air velocity. An expression for the effective reaction rate of charcoal oxidized in air was developed, and predictions of the internal temp. distribution in the burning sample were made based on a simple 1-dimensional conduction model in a semi-infinite solid, assuming a value for thermal diffusivity appropriate to charcoal at elevated temp. and adequate insulation of the burning sample. Both a gas-phase reaction and substantial combustion in pores may be involved in the oxidn. of charcoal in air.
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Janse, A. M. C.; de Jonge, H. G.; Prins, W.; van Swaaij, W. P. M. Combustion kinetics of char obtained by flash pyrolysis of pine wood Ind. Eng. Chem. Res. 1998, 37, 3909– 3918
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Combustion Kinetics of Char Obtained by Flash Pyrolysis of Pine Wood
Janse, Arthur M. C.; De Jonge, Harald G.; Prins, Wolter; Van Swaaij, Wim P. M.
Industrial & Engineering Chemistry Research (1998), 37 (10), 3909-3918CODEN: IECRED; ISSN:0888-5885. (American Chemical Society)
The combustion kinetics of rapidly pyrolyzed wood have been investigated within the temp. range of 573-773 K and the oxygen concn. range of 2.25-36 vol.%. These kinetics are, for instance, required for the design of a char combustion section in an integrated flash pyrolysis pilot plant. Two different exptl. techniques were used: a std. thermogravimetric technique (TGA) and flue gas anal. after combustion in a dild. packed bed. The pyrolysis char was prepd. in a small screen heater reactor, enabling heating rates of >300 K/s. The results of the TGA and the packed-bed measurements are in good agreement for temps. >648 K. Below that temp., the reaction rate obsd. in the TGA appears to be (up to 1.5 times) lower than that in the packed-bed reactor. The combustion kinetics can be described by a simple rate equation which has an av. deviation of 20%. Several pore models reported in the literature were tested against the exptl. data, but they could not improve the accuracy of the fit. In comparison with available data, this specific type of char shows a notably higher rate of combustion.
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Bryden, K. M. Computational Modeling of Wood Combustion; Mechanical Engineering Department, University of Wisconsin-Madison: Madison, WI, 1998.
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34
Hautman, D. J.; Dryer, L.; Schug, K. P.; Glassman, I. A multiple-step overall kinetic mechanism for the oxidation of hydrocarbons Combust. Sci. Technol. 1981, 25, 219– 235
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A multiple-step overall kinetic mechanism for the oxidation of hydrocarbons
Hautman, D. J.; Dryer, F. L.; Schug, K. P.; Glassman, I.
Combustion Science and Technology (1981), 25 (5-6), 219-35CODEN: CBSTB9; ISSN:0010-2202.
Extensive exptl. results were obtained on the oxidn. of many aliph. hydrocarbons in a high temp., turbulent flow reactor developed for kinetic studies. These results indicated the viability of presenting this complex kinetic situation in the format of a simplified, overall kinetic scheme which could accurately predict the major species formed and the temp.-time history (rate of heat release) of the system.
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Font, F.; Marcilla, A.; Verdu, E.; Devesa, J. Kinetics of the pyrolysis of almond shells and almond shells impregnated with CoCl2 in a fluidized bed reactor and in a pyroprobe 100 Ind. Eng. Chem. Res. 1990, 29, 1846– 1855
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36
Nunn, T. R.; Howard, J. P.; Longwell, T.; Peters, W.A. Product compositions and kinetics in the rapid pyrolysis of sweet gum hardwood Ind. Eng. Chem., Process Des. Dev. 1985, 24, 836– 844
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Product compositions and kinetics in the rapid pyrolysis of sweet gum hardwood
Nunn, Theodore R.; Howard, Jack B.; Longwell, John P.; Peters, William A.
Industrial & Engineering Chemistry Process Design and Development (1985), 24 (3), 836-44CODEN: IEPDAW; ISSN:0196-4305.
Yields, compn., and rates of evolution of major products from batch pyrolysis of predried sweet gum hardwood were measured for 600-1400 K under 5 psig He, at heating rates 1000 K/s and residence time at final temp. 0 s. Approx. 100-mg layers of 45-88 μ wood powder, thinly spread on a hot stage, were heated so that volatiles residence times at elevated temps. were minimized. Total wt. loss increased strongly with temp. to an asymptote of 93% at 1100 K. Tar was the major pyrolysis product at >800 K. It exhibited a max. yield of 55% at 900 K and declined to an asymptote of 46% at 1300 K. Secondary cracking of the tar was significant at >900 K and contributed substantially to the yields of CO, CH4, C2H4, and other light gases. CO dominated the gas produced at >850 K and attained as asymptote of 17% above 1300 K. A single-reaction first-order decompn. model described well the global rates of evolution of most major products except tar. However, the data implied that most products were evolved by more complex kinetic pathways.
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Wagenaar, B. M.; Prins, W.; Van Swaaij, W. P. Flash pyrolysis kinetics of pine wood Fuel Process. Technol. 1993, 36, 291
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Flash pyrolysis kinetics of pine wood
Wagenaar, B. M.; Prins, W.; van Swaaij, W. P. M.
Fuel Processing Technology (1993), 36 (1-3), 291-8CODEN: FPTEDY; ISSN:0378-3820.
The kinetic parameters of sawdust pyrolysis at 300-600° was measured. A thermogravimetric analyzer was used for expts. at 300-450°, while for measurements at 450-600° an entrained flow reactor was used. The kinetic expression that describes the mass loss of sawdust due to pyrolysis is assumed to be of first-order in wood feed. The first-order rate const. (k0) obtained from the measurements can be described by an Arrhenius equation with k0 = 1.4 1010 kg/kg-s and activation energy Ea = 150 KJ/mol.
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Liden, C. K.; Berruti, F.; Scott, D. S. A kinetic model for the production of liquids from the flash pyrolysis of biomass Chem. Eng. Commun. 1988, 65, 207– 221
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A kinetic model for the production of liquids from the flash pyrolysis of biomass
Liden, A. G.; Berruti, F.; Scott, D. S.
Chemical Engineering Communications (1988), 65 (), 207-21CODEN: CEGCAK; ISSN:0098-6445.
A kinetically based prediction model for the prodn. of org. liqs. from the flash pyrolysis of biomass is proposed. Wood or other biomass is assumed to be decompd. according to two parallel reactions yielding liq. tar and (gas + char). The tar is then assumed to further react by secondary homogeneous reactions to form mainly gas as a product. The model provides a very good agreement with the exptl. results obtained using a pilot plant fluidized-bed pyrolysis reactor. The proposed model is able to predict the org. liq. yield as a function of the operating parameters of the process, within the optimal conditions for maximizing the tar yields, and the reaction rate consts. compare reasonably well with those reported in the literature.
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Koufopanos, C. A.; Papayannakos, N.; Maschio, G.; Lucchesi, A. Modelling of the Pyrolysis of Biomass Particles. Studies on Kinetics, Thermal and Heat Transfer Effects, Can. J. Chem. Eng. 1991, 69 (4) 907– 915
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Modeling of the pyrolysis of biomass particles. Studies on kinetics, thermal and heat transfer effects
Koufopanos, C. A.; Papayannakos, N.; Maschio, G.; Lucchesi, A.
Canadian Journal of Chemical Engineering (1991), 69 (4), 907-15CODEN: CJCEA7; ISSN:0008-4034.
A rationally-based model to describe the pyrolysis of a single solid particle of biomass is presented. As the phenomena governing the pyrolysis of a biomass particle are both chem. (primary and secondary reactions) and phys. (mainly heat transfer phenomena), the model couples heat transport with chem. kinetics. The thermal properties included in the model are considered to be linear functions of temp. and conversion, and were estd. from literature data or by fitting the model with exptl. data. The heat of reaction is represented by 2 values: one endothermic, which prevails at low conversions, and the other exothermic, which prevails at high conversions. Pyrolysis phenomena are simulated by a scheme consisting of 2 parallel reactions and a 3rd reaction for the secondary interactions between charcoal and volatiles. The model predictions are in agreement with exptl. data regarding temp. and wt.-loss histories of biomass particles over a wide range of pyrolysis conditions.
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Di Blasi, C. Analysis of convection and secondary reaction effects within porous solid fuels undergoing pyrolysis Combust. Sci. Technol. 1993, 90, 315– 340
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Analysis of convection and secondary reaction effects within porous solid fuels undergoing pyrolysis
Di Blasi, Colomba
Combustion Science and Technology (1993), 90 (5-6), 315-40CODEN: CBSTB9; ISSN:0010-2202.
A math. model of transport phenomena (heat, momentum, and mass transfer) and chem. processes (primary and secondary reactions) of the thermal degrdn. of wood is presented. Implicit finite difference equations for energy, momentum, and chem. species mass balances are formulated and numerically solved. The progress of the pyrolysis process along a wooden slab, radiatively heated on one side, is characterized by the following main processes: (1) a virgin wood region, crossed by a slow flow of pyrolysis products, where temp. and pressure values decrease as the nonirradiated boundary is approached, (2) a primary pyrolysis region where, due to the relatively low temps., secondary reactions are not active, and (3) a char layer where volatile products of primary pyrolysis mainly flow and, due to higher temp., undergo secondary reactions. For low medium permeabilities, a peak in the gas overpressure is obsd., sepg. the virgin wood and the pyrolysis region and two velocity distributions, directed towards the virgin wood and the char layer. Time and space evolution of main variables and reaction product distribution, as internal flow convection varies as a function of wood and char permeabilities, are simulated. The effects of variations in the kinetic data and energetics of primary and secondary reactions, with special emphasis on the coupling between flow convection and extent of secondary reactions, are also analyzed.
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Turns, S. R. An Introduction to Combustion: Concepts and Applications, 2nd ed.; McGraw-Hill: New York, 2000.
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Ouelhazi, N.; Arnaud, G.; Fohr, J. P. A Two-dimensional study of wood plank drying. The effect of gaseous pressure below boiling point Transp. Porous Media 1992, 7 (1) 39– 61
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A two-dimensional study of wood plank drying. The effect of gaseous pressure below boiling point
Ouelhazi, N.; Arnaud, G.; Fohr, J. P.
Transport in Porous Media (1992), 7 (1), 39-61CODEN: TPMEEI; ISSN:0169-3913.
The internal gaseous pressure of a plank of softwood, during drying below the b.p. of water is examd. A one-dimensional numerical study showed a depression inside the plank that depends on permeability and initial satn. With a two-dimensional numerical study, a redn. in this depression was obsd. Because the longitudinal permeability is much greater than the transversal one (radial or tangential), the air flow can more easily fill the water vol. that is evacuated. The simulation exhibits displacement of drying fronts from the transversal faces and extremities. Because the exchange area of the extremities is weak, the two-dimensional effect was limited to a specific distance. The coeffs. of the model were derived from literature data. An exptl. study confirmed the progression of the moisture field. The moisture profiles were obtained by cond. measurements between needles. The improvement of two-dimensional drying can be evaluated using drying kinetics.
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De Paiva Souza, M. E.; Nebra, S. A. Heat and mass transfer model in wood chip drying Wood Fiber Sci. 2000, 32 (2) 153– 163
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Heat and mass transfer model in wood chip drying
De Paiva Souza, Maria Eugenia; Nebra, Silvia Azucena
Wood and Fiber Science (2000), 32 (2), 153-163CODEN: WFSCD4; ISSN:0735-6161. (Society of Wood Science and Technology)
A model of simultaneous transport of heat and mass in a hygroscopic capillary porous medium was developed and applied to the drying of wood. Water is considered to be present in three forms-free water, bound water, and vapor-which remain in local equil. It is assumed that the heat and mass transport mechanisms are: capillarity of free water, diffusion of vapor due to the concn. gradient, and diffusion of bound water due to the gradient of chem. potential between the water mols. The consts. of the phenomenol. coeffs. were adjusted. Finally, the drying process in wood chips was simulated in a unidimensional mesh. The results were compared with exptl. data on drying kinetics obtained from the literature. Concn. profiles are shown, and the wt. of each of the mechanisms present in the drying phenomenon is shown in graphic form and discussed.
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Incropera, F. P.; Dewitt, D. P. Fundamentals of Heat and Mass Transfer, 4th ed.; John Wiley & Sons: New York, 1996.
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Figure 1
Figure 1. Single-particle reactor schematic diagram.
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Figure 2
Figure 2. Moisture drying scheme.
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Figure 3
Figure 3. Two-stage wood pyrolysis model. (21)
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Figure 4
Figure 4. Temperature of near-spherical particle during pyrolysis in nitrogen ( d_p = 9.5 mm, AR = 1.0, MC = 6 wt %, T_w = 1276 K, T_g = 1050 K).
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Figure 5
Figure 5. Mass loss of near-spherical particle during pyrolysis in nitrogen ( d_p = 9.5 mm, AR = 4.0, MC = 40 wt %, T_w = 1276 K, T_g = 1050 K).
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Figure 6
Figure 6. Temperature comparison of a cylindrical particle during pyrolysis in nitrogen ( d_p = 9.5 mm, AR = 4.0, MC = 6 wt %, T_w = 1276 K, T_g = 1050 K).
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Figure 7
Figure 7. Mass loss comparison of a cylindrical particle during pyrolysis in nitrogen ( d_p = 9.5 mm, AR = 4.0, MC = 6 wt %, T_w = 1276 K, T_g = 1050 K).
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Figure 8
Figure 8. Temperature comparisons of a cylindrical particle during drying and pyrolysis in nitrogen ( d_p = 9.5 mm, AR = 4.0, MC = 40 wt %, T_w = 1276 K, T_g = 1050 K).
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Figure 9
Figure 9. Mass loss of a cylindrical particle during drying and pyrolysis in nitrogen ( d_p = 9.5 mm, AR = 4.0, MC = 40 wt %, T_w = 1276 K, T_g = 1050 K).
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Figure 10
Figure 10. Temperature profiles of a near-spherical wet particle during combustion in air ( d_p = 9.5 mm, AR = 1.0, MC = 40 wt %, T_w = 1276 K, T_g = 1050 K).
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Figure 11
Figure 11. Mass loss of a near-spherical wet particle during combustion in air ( d_p = 9.5 mm, AR = 1.0, MC = 40 wt %, T_w = 1276 K, T_g = 1050 K).
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Figure 12
Figure 12. Flame temperature comparison during a near-spherical particle combustion in air ( d_p = 9.5 mm, AR = 1.0, MC = 6 wt %, T_w = 1273 K, T_g = 1050 K).
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Figure 13
Figure 13. Effects of temperature gradients on particle pyrolysis in nitrogen Nonisothermal assumption for model 1 and isothermal assumption for model 2 ( d_p = 9.5 mm, AR = 1.0, MC = 6 wt %, T_w = 1273 K, T_g = 1050 K).
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Figure 14
Figure 14. Blowing factor during particle pyrolysis process in nitrogen ( d_p = 9.5 mm, AR = 1.0, MC = 6 wt %, T_w = 1273 K, T_g = 1050 K).
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Figure 15
Figure 15. Particle temperature profile during particle pyrolysis in nitrogen with and without blowing factor correction when radiation dominates (model 1 with blowing factor correction and model 2 without blow factor correction; d_p = 9.5 mm, AR = 1.0, MC = 6 wt %, T_w = 1303 K, T_g = 1050 K).
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Figure 16
Figure 16. Effects of blowing factor on particle temperature during pyrolysis in nitrogen when convection dominates (Model-1 with blowing factor correction and model-2 without blow factor correction; d_p = 9.5 mm, AR = 1.0, MC = 6 wt %, T_w = 298 K, T_g = 1400 K).
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Figure 17
Figure 17. Effects of flame on near-spherical particle temperature during combustion in air (model 1 stands for results without flame included, model 2 for those with flame included; d_p = 9.5 mm, AR = 1.0, MC = 6 wt %, T_w = 1273 K, T_g = 1050 K).
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Figure 18
Figure 18. Particle radius, boundary layer thickness, and off-gas velocity during a wet particle combustion process in air ( d_p = 9.5 mm, AR = 1.0, MC = 6 wt %, T_w = 1273 K, T_g = 1050 K).
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References
This article references 59 other publications.
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  A detailed math. model is presented for the temporal and spatial accurate modeling of solid-fluid reactions in porous particles for which volumetric reaction rate data is known a priori and both the porosity and the permeability of the particles are large enough to allow for continuous gas phase flow. The methodol. is applied to the pyrolysis of spherically sym. biomass particles by considering previously published kinetics schemes for both cellulose and wood. A parametric study is performed to illustrate the effects of reactor temp., heating rate, porosity, initial particle size, and initial temp. on char yields and conversion times. It is obsd. that while high temps. and fast heating rates minimize the prodn. of char in both reactions, practical limits exist due to endothermic reactions, heat capacity, and thermal diffusion. Three pyrolysis regimes are identified: (1) initial heating, (2) primary reaction at the effective pyrolysis temp., and (3) final heating. The relative durations of each regime are independent of the reactor temp. and are approx. 20, 60, and 20% of the total conversion time, resp. The results show that models which neglect the thermal and species boundary layers exterior to the particle will generally over-predict both the pyrolysis rates and exptl. obtainable tar yields. An evaluation of the simulation results by comparisons with exptl. data indicates that the wood pyrolysis kinetics is not accurate, particularly at high reactor temps.
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  The present work involves the development of a math. model to describe the pyrolysis of a single solid biomass particle. Generally, the phenomena governing the pyrolysis of a single biomass particle is based on both phys. and chem. changes. The chem. changes include primary and secondary pyrolysis reactions, and both chem. and phys. changes are controlled by the heat transfer phenomena. The proposed energy balance model equation takes into account the non-isothermal reaction of the biomass particle. The equation for the model is solved for a cylindrical pellet under a wide range of operating conditions. The numerical scheme employed is a finite difference, backward implicit scheme for the heat transfer equation and the Runge-Kutta 4th order predictor-corrector method for the equations involving chem. kinetics. Results for various size particles have been obtained to predict the temp. profile as a function of the radial distance at varying time intervals. The results obtained from the model are compared with exptl. data from the literature.
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  The math. model of heat transfer and the kinetics of pyrolysis of biomass at lower temps. are presented. The model serves for detn. of surface and core temp. and d. of obsd. solid particle as well as the time of thermal decompn. of biomass and can be use for the improvement of the charcoal-making procedure.
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  A theory for detn. of the pyrolysis rate of a single infinite slab, infinite cylinder, or sphere in a const. temp. furnace is suggested. In analogy with the shrinking-core model a pyrolysis propagation front velocity is defined. The velocity is thereafter used in a compartment-model approach for deriving a set of ordinary differential equations for solving the burn-off over time. A comparison with exptl. and published data is also made.
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  Chemical Engineering and Processing (2000), 39 (3), 239-252CODEN: CENPEU; ISSN:0255-2701. (Elsevier Science S.A.)
  Reactors for flash pyrolysis of biomass are designed to maximize the yield of bio-oil, at the expense of the byproducts gas and char. To understand which chem. and phys. factors influence the yield to bio-oil, the flash pyrolysis of a cylindrical wood particle with a max. diam. of 1000 μm has been simulated by solving the governing equations for mass, enthalpy and momentum conservation for the reactant and products (one dimensional). The flow of vapors is described using the Dusty Gas model (1985), and the structure of wood is incorporated in the model by applying the random pore model of N. Wakao, J.M. Smith (1962). Typical conversion times for a cylindrical particle increase from 1 to 10 s when the diam. increases from 200 to 1000 μm at a surface temp. of 823 K. The bio-oil yield (approx. 77%) is hardly affected by the particle size (200-1000 μm diam.). Obviously tar cracking inside the particle does not occur for the simulated conditions. The heating of a particle is notably delayed by the outflow of vapors. While assuming that they leave the particle in a direction perpendicular instead of parallel to the heat flux, the simulated conversion times appear to decrease with sometimes more than 50%. Finally, the sign and size of the pyrolysis reaction heat is shown to have a distinct effect on the calcd. particle conversion time. As an overall conclusion, the results of this work show that an extensive description of internal mass transport phenomena in flash-pyrolysis modeling is not necessary, while accurate knowledge of the reaction kinetics and heat transfer parameters is crucial.
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  Chen, G.; Yu, Q.; Sjostrom, K. Reactivity of Char from Pyrolysis of Birch Wood J. Anal. Appl. Pyrolysis 1997, 40−41, 491– 499
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  Pyrolysis of biomass from birch was carried out both in a free-fall tubular reactor and a thermobalance. The char obtained was further gasified with carbon dioxide and steam in the thermobalance. It was obsd. that the reaction rates of the char with the reagents were strongly affected by the time-temp. history of the char formation. A rapid heating rate of the raw material in free-fall reactor gives a char which possesses higher reactivity in reaction both with carbon dioxide and steam compared with the char formed under slow heating rate in the thermobalance. The treatment condition and environment of the char precursor during devolatilization are the most important factors affecting the reactivity of the char in gasification with the used reagents. The kinetic study focused on whether a surrounding pyrolysis gas atm. exerts neg. effects on the reactivity of the formed char.
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  Di Blasi, C.; Buonanno, F.; Branca, C. Reactivities of Some Biomass Chars in Air Carbon 1999, 37, 1227– 1238
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  Di Blasi, Colomba; Buonanno, Federico; Branca, Carmen
  Carbon (1999), 37 (8), 1227-1238CODEN: CRBNAH; ISSN:0008-6223. (Elsevier Science Ltd.)
  The reactivities in air of biomass chars, obtained using conventional pyrolysis, are investigated for applications in fixed-bed gasification. Biomasses considered are wheat straw, olive husks and grape residues. Char particles are spread to form a 150 μm thick layer and are radiatively heated, to achieve a kinetically controlled conversion. Time-wt. loss curves, detd. under non-isothermal conditions (heating rates of 10 K/min and a final temp. of 873 K), indicate that the reactivity continuously increases with conversion. The olive husk chars present the highest value, whereas that of grape residue chars is the least. All biomass chars are also combusted at different heating rates (20-80 K/min) and final temps. of 713 K (grape residues) and 673 K (olive husks and straw), so that conversion consists of a dynamic stage, followed by an isothermal period. Again, grape residue chars are the less reactive. Furthermore, the reactivity first attains a max., decreases or remains almost const. and then increases again as a function of conversion. This behavior can be explained by the different roles played by the reaction temp., the development of surface area as combustion proceeds and the increase in the ratio of ashes (catalytically active) to carbon. Finally, the wt. loss curves are well interpreted by a one-step global reaction, whose rate presents a power law dependence on the solid conversion and activation energies in the range 75-94 kJ/mol.
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  Adanez, J.; de Diego, L. F.; Garcia-Labiano, F.; Abad, A.; Abanades, J. C. Determination of Biomass Char Combustion Reactivities for FBC Applications by a Combined Method Ind. Eng. Chem. Res. 2001, 40, 4317– 4323
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  Yang, Y. B.; Sharifi, V. N.; Swithenbank, J.; Ma, L.; Darvell, L. I.; Jones, J. M.; Pourkashanian, M.; Williams, A. Combustion of a Single Particle of Biomass Energy Fuels 2008, 22, 306– 316
  15
  Combustion of a Single Particle of Biomass
  Yang, Yao B.; Sharifi, Vida N.; Swithenbank, Jim; Ma, Lin; Darvell, Leilani I.; Jones, Jenny M.; Pourkashanian, Mohamed; Williams, Alan
  Energy & Fuels (2008), 22 (1), 306-316CODEN: ENFUEM; ISSN:0887-0624. (American Chemical Society)
  Biomass is one of the important renewable energy sources. Biomass fuels exhibit a range of chem. and phys. properties, particularly size and shape. Investigations of the behavior of a single biomass particle are fundamental to all practical applications, including both packed and fluidized-bed combustion, as well as suspended and pulverized fuel (pf) combustion. In this paper, both exptl. and math. modeling approaches are employed to study the combustion characteristics of a single biomass particle ranging in size from 10 μm to 20 mm. Different subprocesses such as moisture evapn., devolatilization, tar cracking, gas-phase reactions, and char gasification are examd. The sensitivity to the variation in model parameters, esp. the particle size and heating rates, is investigated. The results obtained from this study are useful in assessing different combustion systems using biomass as a fuel. It helps to clarify the situations where the thermally thin and thermally thick cases interface. Simple models of particle combustion assuming const. particle temp. are sometimes inadequate and that for large particles a more detailed math. representation should be applied.
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16. 16
  Ip, L.-T. Comprehensive black liquor droplet combustion studies. Chemical Engineering; Brigham Young University: Provo, UT, 2005.
  There is no corresponding record for this reference.
17. 17
  Forest Products Laboratory United States Department of Agriculture Forest Service.
  Physical Properties and Moisture Relations of Wood. In Wood Handbook: Wood as an Engineering Material; Forest Products Society: Madison, WI, 1999; Chapter 3, pp 3− 5.
  There is no corresponding record for this reference.
18. 18
  Guzenda, R.; Olek, W. Identification of free and bound water content in wood by means of NMR relaxometry. In 12th International Symposium on Nondestructive Testing of Wood; Sopron: Budapest, Hungary, 2000.
  There is no corresponding record for this reference.
19. 19
  Bryden, K. M.; Hagge, M. J. Modeling the combined impact of moisture and char shrinkage on the pyrolysis of a biomass particle Fuel 2003, 82, 1633– 1644
  There is no corresponding record for this reference.
20. 20
  Chan, W.-C.R.; Kelbon, M.; Krieger, B. B. Modeling and experimental verification of physical and chemical processes during pyrolysis of a large biomass particle Fuel 1985, 64 (11) 1505– 1513
  There is no corresponding record for this reference.
21. 21
  Di Blasi, C. Heat, Momentum and Mass Transport through a Shrinking Biomass Particle Exposed to Thermal Radiation Chem. Eng. Sci. 1996, 51 (7) 1121– 1132
  21
  Heat, momentum and mass transport through a shrinking biomass particle exposed to thermal radiation
  Di Blasi, Colomba
  Chemical Engineering Science (1996), 51 (7), 1121-32CODEN: CESCAC; ISSN:0009-2509. (Elsevier)
  A coupled transport and reaction model is formulated to investigate the effects of various parameters on biomass pyrolysis. The model takes into account formation of chars, tars and gases through mechanisms including both primary reactions of the virgin biomass degrdn. and secondary reactions of the primary tar. All main transport phenomena, unsteadiness of the gas/vapor-phase processes, variation of the reacting medium properties and particle shrinkage are also described. Numerical simulation of the problem of wooden particle, subjected to an assigned external radiation, is used to analyze time and space evolution of the main variables and product distribution as the shrinkage parameters and the intensity of the heat flux are varied. The effects of the orientation of the anisotropic wood grain relative to the one-dimensional heat flux are also investigated.
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22. 22
  Evans, R. J.; Milne, T. A. Molecular Characterization of the Pyrolysis of Biomass. 1. Fundamentals Energy Fuels 1987, 1, 123– 137
  There is no corresponding record for this reference.
23. 23
  Evans, R. J.; Milne, T. A. Molecular Characterization of the Pyrolysis of Biomass. 2. Applications Energy Fuels 1987, 1, 311– 319
  There is no corresponding record for this reference.
24. 24
  Demyirbas, A. Hydrocarbons from Pyrolysis and Hydrolysis Processes of Biomass Energy Sources 2003, 25, 67– 75
  There is no corresponding record for this reference.
25. 25
  Thunman, H.; Niklasson, F.; Johnsson, F.; Leckner, B. Composition of Volatile Gases and Thermochemical Properties of Wood for Modeling of Fixed or Fluidized Beds Energy Fuels 2001, 15, 1488– 1497
  There is no corresponding record for this reference.
26. 26
  Warnatz, J. Hydrocarbon oxidation high-temperature chemistry Pure Appl. Chem. 2000, 72 (11) 2101– 2110
  There is no corresponding record for this reference.
27. 27
  Smoot, L. D.; Smith, P. J. Coal Combustion and Gasification; Plenum Press: New York, 1985.
  There is no corresponding record for this reference.
28. 28
  Smith, K. L.; Smoot, L. D.; Fletcher, T. H.; Pugmire, R. J. The structure and reaction processes of coal. In The Plenum Chemical Engineering Series; Luss, D., Ed.; Plenum Press: New York, 1994.
  There is no corresponding record for this reference.
29. 29
  Brewster, B. S.; Hill, S. C.; Radulovic, P. T.; Smoot, L. D. Fundamentals of Coal Combustion for Clean and Efficient Use; Smoot, L. D., Ed.; Elsevier Applied Science Publishers: London, 1993; Vol. 20.
  There is no corresponding record for this reference.
30. 30
  Blackham, A. U.; Smoot, L. D.; Yousefi, P. Rates of oxidation of millimetre-sized char particles: simple experiments Fuel 1994, 73 (4) 602– 612
  There is no corresponding record for this reference.
31. 31
  Evans, D. H.; Emmons, H. W. Combustion of wood charcoal Fire Res. 1977, 1) 57– 66
  31
  Combustion of wood charcoal
  Evans, D. D.; Emmons, H. W.
  Fire Research (Lausanne) (1977), 1 (1), 57-66CODEN: FIRED9; ISSN:0378-7761.
  The lowest mainstream air velocity at which the charcoal from basswood (Tilia americana) would self-sustain its own combustion was 7.7 m/s, and at the highest air velocity (43 m/s), the surface temp. of burning charcoal was 1055° as detd. by filament pyrometer with surface emissivity of 0.85, assuming that the influence of the ash was negligible at this high air velocity. An expression for the effective reaction rate of charcoal oxidized in air was developed, and predictions of the internal temp. distribution in the burning sample were made based on a simple 1-dimensional conduction model in a semi-infinite solid, assuming a value for thermal diffusivity appropriate to charcoal at elevated temp. and adequate insulation of the burning sample. Both a gas-phase reaction and substantial combustion in pores may be involved in the oxidn. of charcoal in air.
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32. 32
  Janse, A. M. C.; de Jonge, H. G.; Prins, W.; van Swaaij, W. P. M. Combustion kinetics of char obtained by flash pyrolysis of pine wood Ind. Eng. Chem. Res. 1998, 37, 3909– 3918
  32
  Combustion Kinetics of Char Obtained by Flash Pyrolysis of Pine Wood
  Janse, Arthur M. C.; De Jonge, Harald G.; Prins, Wolter; Van Swaaij, Wim P. M.
  Industrial & Engineering Chemistry Research (1998), 37 (10), 3909-3918CODEN: IECRED; ISSN:0888-5885. (American Chemical Society)
  The combustion kinetics of rapidly pyrolyzed wood have been investigated within the temp. range of 573-773 K and the oxygen concn. range of 2.25-36 vol.%. These kinetics are, for instance, required for the design of a char combustion section in an integrated flash pyrolysis pilot plant. Two different exptl. techniques were used: a std. thermogravimetric technique (TGA) and flue gas anal. after combustion in a dild. packed bed. The pyrolysis char was prepd. in a small screen heater reactor, enabling heating rates of >300 K/s. The results of the TGA and the packed-bed measurements are in good agreement for temps. >648 K. Below that temp., the reaction rate obsd. in the TGA appears to be (up to 1.5 times) lower than that in the packed-bed reactor. The combustion kinetics can be described by a simple rate equation which has an av. deviation of 20%. Several pore models reported in the literature were tested against the exptl. data, but they could not improve the accuracy of the fit. In comparison with available data, this specific type of char shows a notably higher rate of combustion.
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33. 33
  Bryden, K. M. Computational Modeling of Wood Combustion; Mechanical Engineering Department, University of Wisconsin-Madison: Madison, WI, 1998.
  There is no corresponding record for this reference.
34. 34
  Hautman, D. J.; Dryer, L.; Schug, K. P.; Glassman, I. A multiple-step overall kinetic mechanism for the oxidation of hydrocarbons Combust. Sci. Technol. 1981, 25, 219– 235
  34
  A multiple-step overall kinetic mechanism for the oxidation of hydrocarbons
  Hautman, D. J.; Dryer, F. L.; Schug, K. P.; Glassman, I.
  Combustion Science and Technology (1981), 25 (5-6), 219-35CODEN: CBSTB9; ISSN:0010-2202.
  Extensive exptl. results were obtained on the oxidn. of many aliph. hydrocarbons in a high temp., turbulent flow reactor developed for kinetic studies. These results indicated the viability of presenting this complex kinetic situation in the format of a simplified, overall kinetic scheme which could accurately predict the major species formed and the temp.-time history (rate of heat release) of the system.
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35. 35
  Font, F.; Marcilla, A.; Verdu, E.; Devesa, J. Kinetics of the pyrolysis of almond shells and almond shells impregnated with CoCl2 in a fluidized bed reactor and in a pyroprobe 100 Ind. Eng. Chem. Res. 1990, 29, 1846– 1855
  There is no corresponding record for this reference.
36. 36
  Nunn, T. R.; Howard, J. P.; Longwell, T.; Peters, W.A. Product compositions and kinetics in the rapid pyrolysis of sweet gum hardwood Ind. Eng. Chem., Process Des. Dev. 1985, 24, 836– 844
  36
  Product compositions and kinetics in the rapid pyrolysis of sweet gum hardwood
  Nunn, Theodore R.; Howard, Jack B.; Longwell, John P.; Peters, William A.
  Industrial & Engineering Chemistry Process Design and Development (1985), 24 (3), 836-44CODEN: IEPDAW; ISSN:0196-4305.
  Yields, compn., and rates of evolution of major products from batch pyrolysis of predried sweet gum hardwood were measured for 600-1400 K under 5 psig He, at heating rates 1000 K/s and residence time at final temp. 0 s. Approx. 100-mg layers of 45-88 μ wood powder, thinly spread on a hot stage, were heated so that volatiles residence times at elevated temps. were minimized. Total wt. loss increased strongly with temp. to an asymptote of 93% at 1100 K. Tar was the major pyrolysis product at >800 K. It exhibited a max. yield of 55% at 900 K and declined to an asymptote of 46% at 1300 K. Secondary cracking of the tar was significant at >900 K and contributed substantially to the yields of CO, CH4, C2H4, and other light gases. CO dominated the gas produced at >850 K and attained as asymptote of 17% above 1300 K. A single-reaction first-order decompn. model described well the global rates of evolution of most major products except tar. However, the data implied that most products were evolved by more complex kinetic pathways.
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37. 37
  Wagenaar, B. M.; Prins, W.; Van Swaaij, W. P. Flash pyrolysis kinetics of pine wood Fuel Process. Technol. 1993, 36, 291
  37
  Flash pyrolysis kinetics of pine wood
  Wagenaar, B. M.; Prins, W.; van Swaaij, W. P. M.
  Fuel Processing Technology (1993), 36 (1-3), 291-8CODEN: FPTEDY; ISSN:0378-3820.
  The kinetic parameters of sawdust pyrolysis at 300-600° was measured. A thermogravimetric analyzer was used for expts. at 300-450°, while for measurements at 450-600° an entrained flow reactor was used. The kinetic expression that describes the mass loss of sawdust due to pyrolysis is assumed to be of first-order in wood feed. The first-order rate const. (k0) obtained from the measurements can be described by an Arrhenius equation with k0 = 1.4 1010 kg/kg-s and activation energy Ea = 150 KJ/mol.
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38. 38
  Liden, C. K.; Berruti, F.; Scott, D. S. A kinetic model for the production of liquids from the flash pyrolysis of biomass Chem. Eng. Commun. 1988, 65, 207– 221
  38
  A kinetic model for the production of liquids from the flash pyrolysis of biomass
  Liden, A. G.; Berruti, F.; Scott, D. S.
  Chemical Engineering Communications (1988), 65 (), 207-21CODEN: CEGCAK; ISSN:0098-6445.
  A kinetically based prediction model for the prodn. of org. liqs. from the flash pyrolysis of biomass is proposed. Wood or other biomass is assumed to be decompd. according to two parallel reactions yielding liq. tar and (gas + char). The tar is then assumed to further react by secondary homogeneous reactions to form mainly gas as a product. The model provides a very good agreement with the exptl. results obtained using a pilot plant fluidized-bed pyrolysis reactor. The proposed model is able to predict the org. liq. yield as a function of the operating parameters of the process, within the optimal conditions for maximizing the tar yields, and the reaction rate consts. compare reasonably well with those reported in the literature.
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39. 39
  Koufopanos, C. A.; Papayannakos, N.; Maschio, G.; Lucchesi, A. Modelling of the Pyrolysis of Biomass Particles. Studies on Kinetics, Thermal and Heat Transfer Effects, Can. J. Chem. Eng. 1991, 69 (4) 907– 915
  39
  Modeling of the pyrolysis of biomass particles. Studies on kinetics, thermal and heat transfer effects
  Koufopanos, C. A.; Papayannakos, N.; Maschio, G.; Lucchesi, A.
  Canadian Journal of Chemical Engineering (1991), 69 (4), 907-15CODEN: CJCEA7; ISSN:0008-4034.
  A rationally-based model to describe the pyrolysis of a single solid particle of biomass is presented. As the phenomena governing the pyrolysis of a biomass particle are both chem. (primary and secondary reactions) and phys. (mainly heat transfer phenomena), the model couples heat transport with chem. kinetics. The thermal properties included in the model are considered to be linear functions of temp. and conversion, and were estd. from literature data or by fitting the model with exptl. data. The heat of reaction is represented by 2 values: one endothermic, which prevails at low conversions, and the other exothermic, which prevails at high conversions. Pyrolysis phenomena are simulated by a scheme consisting of 2 parallel reactions and a 3rd reaction for the secondary interactions between charcoal and volatiles. The model predictions are in agreement with exptl. data regarding temp. and wt.-loss histories of biomass particles over a wide range of pyrolysis conditions.
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40. 40
  Di Blasi, C. Analysis of convection and secondary reaction effects within porous solid fuels undergoing pyrolysis Combust. Sci. Technol. 1993, 90, 315– 340
  40
  Analysis of convection and secondary reaction effects within porous solid fuels undergoing pyrolysis
  Di Blasi, Colomba
  Combustion Science and Technology (1993), 90 (5-6), 315-40CODEN: CBSTB9; ISSN:0010-2202.
  A math. model of transport phenomena (heat, momentum, and mass transfer) and chem. processes (primary and secondary reactions) of the thermal degrdn. of wood is presented. Implicit finite difference equations for energy, momentum, and chem. species mass balances are formulated and numerically solved. The progress of the pyrolysis process along a wooden slab, radiatively heated on one side, is characterized by the following main processes: (1) a virgin wood region, crossed by a slow flow of pyrolysis products, where temp. and pressure values decrease as the nonirradiated boundary is approached, (2) a primary pyrolysis region where, due to the relatively low temps., secondary reactions are not active, and (3) a char layer where volatile products of primary pyrolysis mainly flow and, due to higher temp., undergo secondary reactions. For low medium permeabilities, a peak in the gas overpressure is obsd., sepg. the virgin wood and the pyrolysis region and two velocity distributions, directed towards the virgin wood and the char layer. Time and space evolution of main variables and reaction product distribution, as internal flow convection varies as a function of wood and char permeabilities, are simulated. The effects of variations in the kinetic data and energetics of primary and secondary reactions, with special emphasis on the coupling between flow convection and extent of secondary reactions, are also analyzed.
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41. 41
  Turns, S. R. An Introduction to Combustion: Concepts and Applications, 2nd ed.; McGraw-Hill: New York, 2000.
  There is no corresponding record for this reference.
42. 42
  Ouelhazi, N.; Arnaud, G.; Fohr, J. P. A Two-dimensional study of wood plank drying. The effect of gaseous pressure below boiling point Transp. Porous Media 1992, 7 (1) 39– 61
  42
  A two-dimensional study of wood plank drying. The effect of gaseous pressure below boiling point
  Ouelhazi, N.; Arnaud, G.; Fohr, J. P.
  Transport in Porous Media (1992), 7 (1), 39-61CODEN: TPMEEI; ISSN:0169-3913.
  The internal gaseous pressure of a plank of softwood, during drying below the b.p. of water is examd. A one-dimensional numerical study showed a depression inside the plank that depends on permeability and initial satn. With a two-dimensional numerical study, a redn. in this depression was obsd. Because the longitudinal permeability is much greater than the transversal one (radial or tangential), the air flow can more easily fill the water vol. that is evacuated. The simulation exhibits displacement of drying fronts from the transversal faces and extremities. Because the exchange area of the extremities is weak, the two-dimensional effect was limited to a specific distance. The coeffs. of the model were derived from literature data. An exptl. study confirmed the progression of the moisture field. The moisture profiles were obtained by cond. measurements between needles. The improvement of two-dimensional drying can be evaluated using drying kinetics.
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43. 43
  De Paiva Souza, M. E.; Nebra, S. A. Heat and mass transfer model in wood chip drying Wood Fiber Sci. 2000, 32 (2) 153– 163
  43
  Heat and mass transfer model in wood chip drying
  De Paiva Souza, Maria Eugenia; Nebra, Silvia Azucena
  Wood and Fiber Science (2000), 32 (2), 153-163CODEN: WFSCD4; ISSN:0735-6161. (Society of Wood Science and Technology)
  A model of simultaneous transport of heat and mass in a hygroscopic capillary porous medium was developed and applied to the drying of wood. Water is considered to be present in three forms-free water, bound water, and vapor-which remain in local equil. It is assumed that the heat and mass transport mechanisms are: capillarity of free water, diffusion of vapor due to the concn. gradient, and diffusion of bound water due to the gradient of chem. potential between the water mols. The consts. of the phenomenol. coeffs. were adjusted. Finally, the drying process in wood chips was simulated in a unidimensional mesh. The results were compared with exptl. data on drying kinetics obtained from the literature. Concn. profiles are shown, and the wt. of each of the mechanisms present in the drying phenomenon is shown in graphic form and discussed.
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44. 44
  Incropera, F. P.; Dewitt, D. P. Fundamentals of Heat and Mass Transfer, 4th ed.; John Wiley & Sons: New York, 1996.
  There is no corresponding record for this reference.
45. 45
  Olek, W.; Perre, P.; Weres, J. Inverse analysis of the transient bound water diffusion in wood Holzforschung 2005, 59 (1) 38– 45
  There is no corresponding record for this reference.
46. 46
  Bird, R. B.; Stewart, W. E.; Lightfoot, E. N. Transport Phenomena, 2nd ed.; John Wiley & Sons, Inc.: New York, 2002.
  There is no corresponding record for this reference.
47. 47
  Wheeler, A. Advances in Catalysis; Academic Press: New York, 1951; p 250.
  There is no corresponding record for this reference.
48. 48
  Robinson, A. L.; Buckley, S. G.; Baxter, L. L. Thermal Conductivity of Ash Deposits 1: Measurement Technique Energy Fuels 2001, 15, 66– 74
  There is no corresponding record for this reference.
49. 49
  Robinson, A. L.; Buckley, S. G.; Yang, N. Y. C.; Baxter, L. L. Thermal Conductivity of Ash Deposits 2: Effects of Sintering Energy Fuels 2001, 15, 75– 84
  There is no corresponding record for this reference.
50. 50
  Masliyah, J. H.; Epstein, N. Numerical solution of heat and mass transfer from spheroids in steady axisymmetric flow Prog. Heat Mass Transfer 1972, 6, 613– 632
  50
  Numerical solution of heat and mass transfer from spheroids in steady axisymmetric flow
  Masliyah, Jacob H.; Epstein, Norman
  Progress in Heat and Mass Transfer (1972), 6 (), 613-32CODEN: PGHMB9; ISSN:0079-631X.
  Heat (or mass) transfer from oblate and prolate spheroids with a ratio of minor to major axis of 0.2, as well as from a sphere, were studied by numerically solving the energy (or diffusion) equation for const. fluid properties, in conjunction with the previously solved equations of continuity and motion, in spheroidal coordinates. A Reynolds no. range of 1-100 was covered for a Prandtl no. Pr of 0.7, as well as creeping flow for Peclet no. <70. Streamlines, isotherms, and local Nusselt nos. are presented. Surface mean Nusselt nos. computed for Pr = 0.7 are compared with exptl. data in the literature, while those computed for creeping flow are compared with results obtained by more approx. methods, and by anal. theory for limiting values of Peclet no.
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51. 51
  Kurdyumov, V. N.; Fernandez, E. Heat transfer from a circular cylinder at low Reynolds numbers J. Heat Transfer, Trans. ASME 1998, 120 (1) 72– 75
  51
  Heat transfer from a circular cylinder at low Reynolds numbers
  Kurdyumov, V. N.; Fernandez, E.
  Journal of Heat Transfer (1998), 120 (1), 72-75CODEN: JHTRAO; ISSN:0022-1481. (American Society of Mechanical Engineers)
  A correlation formula, Nu = W0(Re)Pr1/3 + W1(Re), that is valid in a wide range of Reynolds and Prandtl nos. was developed based on the asymptotic expansion for Pr → ∞ for the forced heat convection from a circular cylinder. For large Prandtl nos., the boundary layer theory for the energy equation is applied and compared with the numerical solns. of the full Navier Stokes equations for the flow field and energy equation. It is shown that the two-terms asymptotic approxn. can be used to calc. the Nusselt no. even for Prandtl nos. of order unity to a high degree of accuracy. The formulas for coeffs. W0 and W1 are provided.
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52. 52
  Raveendran, K.; Ganesh, A.; Khilart, K. C. Influence of Mineral Matter on Biomass Pyrolysis Characteristics Fuel 1995, 74 (12) 1812– 1822
  52
  Influence of mineral matter on biomass pyrolysis characteristics
  Raveendran, K.; Ganesh, Anuradda; Khilar, Kartic C.
  Fuel (1995), 74 (12), 1812-22CODEN: FUELAC; ISSN:0016-2361. (Elsevier)
  Studies on wood and twelve other types of biomass showed that in general, deashing increased the volatiles yield, initial decompn. temp., and rate of pyrolysis. However, coir pith, groundnut shell, and rice husk showed an increase in char yield on deashing, which is attributed to their high lignin, potassium, and zinc contents. These results were supported by studies on salt-impregnated, acid-soaked, and synthetic biomass. A correlation was developed to predict the influence of ash on volatiles yield. Upon deashing, liq. yields increased and gas yields decreased for all the biomass studied. The active surface area increased upon deashing. The heating value of the liq. increased, whereas the increase in char heating value was only marginal.
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53. 53
  Merrick, D. Mathematical models of the thermal decomposition of coal - 2. Specific heats and heats of reaction Fuel 1983, 62 (5) 540– 546
  There is no corresponding record for this reference.
54. 54
  Gronli, M. G.; Melaaen, M. C. Mathematical model for wood pyrolysis - comparison of experimental measurements with model predictions Energy Fuels 2000, 14, 791– 800
  There is no corresponding record for this reference.
55. 55
  DIPPR. Design Institute of Physical Property Data.
  http://dippr.byu.edu/index.asp [cited; available from: http://dippr.byu.edu/index.asp.
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56. 56
  Lee, C. K.; Chaiken, R. F.; Singer, J. M. Charring pyrolysis of wood in fires by laser simulation Symp. (Int.) Combust, 16th, MIT, Aug 15−20 1976, 1459– 1470
  There is no corresponding record for this reference.
57. 57
  Kansa, >E. J.; Perlee, H. E.; Chaiken, R. F. Mathematical model of wood pyrolysis including internal forced convection; 1977, 29, 3) 311− 324.
  There is no corresponding record for this reference.
58. 58
  Patankar, S. V. Numerical Heat Transfer and Fluid Flow. In Series in Computational Methods in Mechanics and Thermal Sciences; Taylor & Francis: New York, 1980.
  There is no corresponding record for this reference.
59. 59
  Murphy, J. J.; Shaddix, C. R. Influence of scattering and probe-volume heterogeneity on soot measurements using optical pyrometry Combust. Flame 2005, 143 (1−2) 1– 10
  There is no corresponding record for this reference.

Comprehensive Study of Biomass Particle Combustion生物质颗粒燃烧的综合研究Click to copy article link点击复制文章链接Article link copied!

Energy & Fuels

Abstract 摘要

1 Introduction 1 引言

2 Experimental Method 2 实验方法

Figure 1 图 1

3 Particle Mathematical Model3 颗粒数学模型

Mechanisms of Drying, Devolatilization, and Char Gasification and Oxidation干燥、挥发分释放及焦炭气化和氧化机制

Figure 2 图 2

Figure 3 图 3

Heat, Mass, and Momentum Transfer Control Equations热量、质量和动量传递控制方程

4 Results and Discussion 4 结果与讨论

Single-Particle Combustion Model Validation单颗粒燃烧模型验证

Particle Devolatilization颗粒挥发分释放

Figure 4 图 4

Figure 5 图 5

Figure 6 图 6

Figure 7 图 7

Particle Drying and Devolatilization颗粒干燥与挥发分释放

Figure 8 图 8

Figure 9 图 9

Particle Combustion 颗粒燃烧

Figure 10 图 10

Figure 11 图 11

Figure 12 图 12

Nonisothermal Effects 非等温效应

Figure 13 图 13

Effects of Blowing on Particle Temperature吹扫对颗粒温度的影响

Figure 14 图 14

Figure 15 图 15

Figure 16 图 16

Effects of Surrounding Flame during Particle Combustion颗粒燃烧过程中周围火焰的影响

Figure 17 图 17

Figure 18 图 18

5 Conclusions 5 结论

Author Information 作者信息

Acknowledgment 致谢

Nomenclature 命名法

Greek symbols

Subscripts

References

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References

Comprehensive Study of Biomass Particle Combustion
生物质颗粒燃烧的综合研究
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3 Particle Mathematical Model
3 颗粒数学模型

Mechanisms of Drying, Devolatilization, and Char Gasification and Oxidation
干燥、挥发分释放及焦炭气化和氧化机制

Heat, Mass, and Momentum Transfer Control Equations
热量、质量和动量传递控制方程

Single-Particle Combustion Model Validation
单颗粒燃烧模型验证

Particle Devolatilization
颗粒挥发分释放

Particle Drying and Devolatilization
颗粒干燥与挥发分释放

Effects of Blowing on Particle Temperature
吹扫对颗粒温度的影响

Effects of Surrounding Flame during Particle Combustion
颗粒燃烧过程中周围火焰的影响