Stochastic Modeling of the Particle Residence Time Distribution in an Opposed Multi‐Burner Gasifier

The gasification technology of impinging streams has been extensively applied to chemical production and power generation. Particle residence time distribution (RTD) is an important parameter required for modeling, designing and optimization of an impinging stream gasifier. A stochastic mathematical model based on the Markov chains model is developed for the opposed multi‐burner gasifier (OMBG), which closely describes the behavior of the flow pattern and particle RTD in the gasification system. The model simulates the motion of single particle moving in the gasifier using the Markov chains. The predicted results give a reasonable fit to the experimental data. This shows that the flow process of particles in the gasifier has recirculation eddies, which have a downward flow direction near the downflow core and an upward flow direction near the wall, but no short‐circuit. Finally, the effect of particle flux rate on the RTD is predicted, and the contrast between gas and particles RTDs at a laboratory scale and in an industrial gasifier are presented.     

撞击流气化炉内颗粒停留时间分布的随机模拟

根据多喷嘴对置式气化炉流场测试,将气化炉划分为若干区域,运用时间离散、状态离散的马尔可夫链随机模型,模拟了气化炉内颗粒相的停留时间分布(RTD)。当颗粒在撞击区和射流区间的回流比为0.5,向下撞击流股区和管流区为平推流模型,其他区域按全混流模型处理时,模拟值与实验值吻合较好。随着进料流量的增大,平均停留时间减小,量纲1方差减小;随着回流比的增加,平均停留时间增大;气固两相平均停留时间接近,但RTD存在一定差异。     

Modeling of the Residence Time Distribution and Application of the Continuous Two Impinging Streams Reactor in Liquid‐Liquid Reactions

The two‐phase monosulfonation of toluene, as an example of liquid‐liquid reactions, has been conducted in a continuous two impinging stream reactor (TISR). The extent of reaction under different operating conditions has been determined. A comparison has been made between the performance capability of the TISR and that of continuous stirred tank reactors (CSTR). Under identical conditions, including mean residence time, temperature, feed compositions and phase ratio, the impinging stream reactor has shown a higher efficiency. Finally, a stochastic model, based on Markov chain processes has been developed for the TISR, which describes the flow pattern and the residence time distribution (RTD) within the reaction system. The RTD model, combined with the kinetic expression, has been applied to calculate the conversion of toluene in the reactor. The predicted values for toluene conversion have been compared with those determined experimentally.     

气流床气化炉停留时间分布的随机模型

基于气流床气化炉流动特征 (区域模型 ) ,进行状态离散 ,建立停留时间分布随机模型。模拟结果与实验值相符 ,显示气化炉内是随机过程 ,证实炉内存在回流和短路 ,流型趋向于全混流     

The Markov process approach to modelling of residence of time distributions in flow systems

The Markov process approach, as used in the modelling of particle residence time distribution in a flow system of interlinked compartments, has been compared with the deterministic model of a complex reaction system of the first order. In the latter model, interfacial reactions take place between flowing phases, corresponding to the compartments in the stochastic model. It has been demonstrated that the two approaches are equivalent. A direct method of calculating the higher moments of the residence time distribution has been verified.     

An impinging–Streams reactor with two pairs of tangential air feeds

The original two–impinging steams devices have proved useful for processes in gas–solid Systems. A modified form of the original two–impinging–streams reactor, with two additional air streams, was explored. All four air streams are fed tangentially to the reactor. The Performance characteristics included the determination of the pressure drop on the reactor, limits of the gas and solid particle mass flow rate, the mean residence time of the particles, and the drying heat transfer, as a function of air flow rates of the secondary and major air streams. The behaviour of the particles and their residence time distribution was investigated by applying a stochastic Markov chain model. It was found that the secondary air stream increases the pressure drop on the reactor and the mean residence time of the particles along with their recycling in the reactor. On the other hand, the secondary air stream decreases the critical mass flow rate of the particles, delays their exit from the reactor and reduces the heat transfer coefficient in drying wet particles.     

连续流动系统停留时间分布的随机模型和模拟

本文提出一个具有吸收态的马尔科夫链(Markov Chain)随机模型,分析和模拟了各种形式的连续流动系统的停留时间分布.模拟结果与确定型模拟结果吻合很好;本模型可以模拟复杂的连续流动系统,但在此情况下,确定型模拟工作是困难的,有时甚至是不可能的.采用本模型还能同时得到停留时间分布的均值和方差;只要选取适当小的时间间隔△t:本模型能满意地逼近连续的随机过程模型.     

运用马尔科夫链模拟气化炉停留时间分布

将连续时间马尔科夫链与多级全混流串联模型结合建立停留时间分布数学模型。通过对气化炉流场的认识,将气化炉划分为几个区域状态,组成马尔科夫链状态转移图,用多级全混流模型表示该各个区域的混合程度。通过对两种气化炉停留时间分布的模拟和实验值进行对比,结果比较吻合,表明该模型模拟气化炉停留时间分布是可行的。     

Application of Markov Chain Analysis and Tanks-in-Series Model in Mathematical Modeling of Impinging Stream Dryers

In spite of the fact that the principles of impinging stream reactors have been developed for more than half a century, the performance analysis of such devices, from a viewpoint of the mathematical modeling, has not been investigated extensively. In this study two models are proposed to describe the drying performance of particulate materials in two-impinging stream dryers. The models are developed based on the Markov chain analysis and the tanks-in-series model. The required parameters for each model are determined by using RTD data obtained in a two-impinging stream dryer and the governing equations are solved numerically. Comparison of the results of the models with available experimental data shows that the stirred tanks-in-series model successfully explains the drying behavior in impinging stream dryers. Nevertheless, the results of the model that is developed based on the Markov chain analysis are not in exact agreement with corresponding experimental data because of the extremely short residence time of the particles inside the dryer. Also, the effects of some operating parameters on the performance of such dryers are investigated. The results indicate that the drying efficiency of the dryer increases when solid-to-gas flow rate ratio, initial moisture content, and diameter of the particles decrease and when the temperature of the carrier gas increases.     

Particle residence time distributions in circulating fluidised beds

This paper gives experimental measurements of the particle residence time distribution (RTD) made in the riser of a square cross section, cold model, circulating fluidised bed, using the fast response particle RTD technique developed by Harris et al. (Chem. Eng. J. 89 (2002a) 127). This technique depends upon all particles having phosphorescent properties. A small proportion of the particles become tracers when activated by a flash of light at the riser entry; the concentration of these phosphorescent particles can subsequently be detected by a photomultiplier. The influence of the solids circulation rate and superficial gas velocity on the RTD were investigated. The results presented are novel because (i) the experiments were performed in a system with closed boundaries and hence give the true residence time distribution in the riser and (ii) the measurement of the tracer concentration is exceedingly fast. The majority of previous studies have measured the RTD in risers with open boundaries, giving an erroneous measure of the RTD.Analysis of the results suggests that using pressure measurements in a riser to infer the solids inventory leads to erroneous estimates of the mean residence time. In particular, the results cast doubt on the assumption that friction and acceleration effects can be neglected when inferring the axial solids concentration profile from riser pressure measurements.An assessment of particle RTD models is also given. A stochastic particle RTD model was coupled to a riser hydrodynamic model incorporating the four main hydrodynamic regions observed in a fast-fluidised bed riser namely (i) the entrance region, (ii) a transition region, (iii) a core-annulus region and (iv) an exit region. This model successfully predicts the experimental residence time distributions.     

旋转圆盘干燥机中物料推进器输送特性研究

研究了旋转圆盘干燥机的转速、推进器角度、推进器个数及排布情况、物料粒径等因素对干燥机中物料输送通量、停留时间和充满度的影响及其变化规律,建立了物理模型和数学模型。得到物料输送通量半经验公式,其与实验数据的均方根误差小于5%。结果表明,干燥机转速越大、推进器向前排布个数越多,在物料粒径较大时体积通量越大,停留时间越短;当干燥机转速较小、物料粒径较小、推进器为前后分布时,能得到较大的充满度。     

STOCHASTIC MODELING AND ANALYSIS OF A TURBULENT FLOW SYSTEM

A stochastic model is developed to describe the axial movement of an element or particle in a turbulent flow system, where diffusion or local transition is not the major mechanism dictating particle motion. The model is a generalization of the diffusion equation for particle movement and includes both diffusion and random displacements. From this model, one can determine the residence time distribution and estimate the parameters characterizing the flow system.     

Residence time distributions in systems governed by the dispersion equation

The theories of discrete and continuous random walks have been applied to systems governed by the dispersion equation. It is shown that residence time distributions can be defined and determined at a particle level of scrutiny and that the resulting distributions are identical to those obtained using continuum methods. Now, however, the appropriate boundary and initial conditions are apparent; and the resulting solutions can he given a clear physical interpretation.The long-sought residence time distribution for dispersion in an open system is shown to be the same as that in a closed system. This result is consistent with Danckwerts' formulation for the yield of first order reactions but invalidates recent results which were based on a transfer function approach to residence time distributions.     

振荡流反应器的物料停留时间分布模型研究

提出了一个基于马尔柯夫链（Markov chains）的考虑腔室间返混的振荡流反应器物料停留时间分布模型。通过对在内径50mm,长1．95m的振荡流反应器进行的理想脉冲示踪试验数据的统计分析,给出了模型的唯一参数回流比R的经验计算公式。发现在试验条件下,存在一个与最小回流比R相对应的振荡条件。这振荡条件可表示为振荡流雷诺数（Reo）与净流雷诺数（Ren）的比值ζ,其范围为1．6〈ζ〈2．5。     

粒径对福建无烟煤在CFB锅炉中燃尽的影响

建立了福建无烟煤细颗粒燃烧模型,计算了其在容量35 t/h循环流化床锅炉炉膛内的燃尽时间和一次通过炉膛的停留时间,分析了不同粒径煤颗粒在不同燃烧温度和不同烟气流速时在CFB锅炉内的燃尽时间和停留时间的变化差异. 实验研究了福建无烟煤粒径对飞灰碳含量的影响及燃尽的影响. 结果表明,细煤颗粒的燃尽时间与停留时间均随粒径增大而增长,但燃尽时间增幅更明显,颗粒一次通过炉膛完全燃尽的临界粒径约为0.15 mm;粒径越大的颗粒其停留时间和燃尽时间对烟气流速和燃烧温度变化越敏感;无烟煤入炉粒径明显影响CFB锅炉飞灰含碳量,选用粒度为3~8 mm的偏粗颗粒为宜.     

Collective dynamics modeling of polydisperse particulate systems via Markov chains

This paper develops an efficient approach to modeling and analyzing the overall dynamics of polydisperse particulate systems, exemplified using a rotating drum with horizontal axis, under both constant and time-varying operating conditions. This approach captures the collective dynamics using stochastic models in the form of Markov chains. The characteristics of such dynamics can be obtained from the Markov chains operator. It provides a systematic way to the analysis of collective dynamical features of particle movements. The obtained operators are used to estimate the spatial particle distribution and the degree of particulate mixing as examples of collective dynamic features of polydisperse particulate systems. In this paper, Markov chains models were developed from discrete element method simulation results to show the effectiveness of the proposed approach.     

The influence of the riser exit on the particle residence time distribution in a circulating fluidised bed riser

This paper reports measurements of the influence of riser exit geometry upon the particle residence time distribution in the riser of a square cross section, cold model, circulating fluidised bed. The bed is operated within the fast fluidisation regime. The fast response particle RTD technique developed by Harris et al. (Chem. Eng. J. 89 (2002) 127-142) was used to measure the residence time distribution.The geometry of the riser exit is shown to have a modest but consistent influence upon the particle RTD; the influence of operating conditions, i.e. superficial gas velocity and solids flux is more significant.Increasing the refluxing effect of the riser exit increases the mean, variance and breakthrough time and decreases the coefficient of variation of the residence time distribution. Changes in reflux do not have a systematic effect upon the skewness of the RTD.     

A model for the devolatilization of EPDM rubber in a series of steam stripping vessels

A mathematical model was developed for the multitank stripping section of industrial ethylene propylene diene monomer (EPDM) rubber processes. Experiments were conducted to determine Henry's law coefficients and diffusivities for hexane solvent and 5‐ethylidene‐2‐norbornene (ENB) comonomer in EPDM particles. Equivalent radii for diffusion within the particles were also determined. A model was developed to predict solvent and comonomer concentrations in a single particle as it moves through a series of tanks with different operating conditions. A second, more‐complicated model was then developed to account for a continuous flow stirred tank residence time distribution for the particles in the tanks. Data from three industrial plants were used to estimate parameters and assess the models' predictive ability. Typical prediction errors are 0.90 wt % for residual hexane and 0.14 wt % for residual ENB. © 2014 American Institute of Chemical Engineers AIChE J, 60: 2596–2606, 2014     

Simulation of flow and drying characteristics of high-moisture particles in an impinging stream dryer via CFD-DEM

Impinging stream dryer (ISD) is an alternative for drying high-moisture particulate materials. Due to the complex multiphase transport phenomena that take place within an ISD, use of a reliable computational model instead of a tedious experimental route to aid the design of the dryer is desirable. In the present study, computational fluid dynamics were used in combination with the discrete element method (CFD-DEM) to predict, for the first time, the multiphase transport phenomena within a coaxial ISD; results from a model that does not consider particle-particle interactions (CFD) were also obtained and compared with those from the CFD-DEM model. In all cases, high-moisture particles having negligible internal transport resistance were assumed. Both models were used to simulate the gas-particle motion behavior, particle mean moisture content, particle mean residence time, and particle residence time distribution. The simulated results from both models were compared with the experimental data whenever possible. The results showed that the CFD-DEM model could be utilized to predict the particle motion behavior and led to more physically realistic results than the CFD model. The CFD-DEM model also gave predictions that were in better agreement with the experimental mean particle residence time and moisture content data.     

Comparing the Markov Chain Model with the Eulerian and Lagrangian Models for Indoor Transient Particle Transport Simulations

Correctly predicting transient particle transport in indoor environments is crucial to improving the design of ventilation systems and reducing the risk of acquiring airborne infectious diseases. Recently, a new model was developed on the basis of Markov chain frame for quickly predicting transient particle transport indoors. To evaluate this Markov chain model, this study compared it with the traditional Eulerian and Lagrangian models in terms of performance, computing cost, and robustness. Four cases of particle transport, three of which included experimental data, were used for this comparison. The Markov chain model was able to predict transient particle transport indoors with similar accuracy to the Eulerian and Lagrangian models. Furthermore, when the same time step size (Courant number ≤1) and grid number were used for all three models, the Markov chain model had the highest calculation speed. The Eulerian model was faster than the Lagrangian model unless a super-fine grid was used. This investigation developed empirical equations for evaluating the three models in terms of computing cost. In addition, the Markov chain model was found to be sensitive to the time step size when the Courant number is larger than 1, whereas the Eulerian and Lagrangian models were not.

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