Validation of pressure drop prediction and bed generation of fixed-beds with complex particle shapes using discrete element method and computational fluid dynamics

Catalytic fixed-bed reactors with a low tube-to-particle diameter ratio are widely used in industrial applications. The heterogeneous packing morphology in this reactor type causes local flow phenomena that significantly affect the reactor performance. Particle-resolved computational fluid dynamics has become a predictive numerical method to analyze the flow, temperature, and species field, as well as local reaction rates spatially and may, therefore, be used as a design tool to develop new improved catalyst shapes. Most validation studies which have been presented in the past were limited to simple particle shapes. More complex catalyst shapes are supposed to increase the reactor performance. A workflow for the simulation of fixed-bed reactors filled with various industrially relevant complex particle shapes is presented and validated against experimental data in terms of bed voidage and pressure drop. Industrially relevant loading strategies are numerically replicated and their impact on particle orientation and bed voidage is investigated.     

Local porosity in conical spouted beds consisting of solids of varying density

Local bed voidage has been measured in conical spouted beds by means of an optical fibre, for different geometric factors of the contactor (angle and inlet diameter) and under different experimental conditions (height of the stagnant bed, particle diameter and air velocity). The study has been carried out with glass beads and materials of lower density (high- and low-density polyethylene, polypropylene and extruded and expanded polystyrene). From the results, a correlation has been proposed for calculation of the local bed voidage in the spout and annular zones. The effect of the experimental conditions on the bed voidage in the solid ascent (core) and descent (periphery) regions of the fountain has been studied and the fountain has been proven to be of greater importance in the design of conical spouted beds, as solid density and shape factor are lower.     

A Method to Predict the Minimum Fluidization Velocity of Binary Mixtures Based on Particle Packing Properties

An approach was made to predict the minimum fluidization velocity for binary mixtures of spherical particles differing in size and/or density. The spherical multiparticle model proposed by Panigrahi and Murty was employed to describe the relationship between the bed pressure drop and the gas velocity; the voidage at minimum fluidization was estimated by the Westman equation, which was originally used to calculate the packing voidage of mixtures. The predictions agree fairly well with the reported experimental data in the range of Re = 0.12 ? 156, covering both the regions of laminar flow and intermediate flow.     

Measurements of voidage profiles in spouted beds

A fibre optic probe has been used to measure voidage profiles in the fountain, spout and annulus of spouted beds. The voidage in most of the annulus was found to be somewhat higher than the loose-packed voidage and increased with increasing spouting gas flow rate, contrary to usual assumptions. There is a denser region in the annulus where the voidage was a little lower than the loose-packed bed voidage. In the core of the fountain, the voidage decreased with height for low spouting gas flow rate, consistent with the model of Grace and Mathur (1978); however, at higher gas flow rate, it first increased with height and then decreased towards the fountain top. The radial profiles of local voidage were roughly parabolic in the lower portion of the spout and blunt in the upper portion.     

Simulation and experimental studies on fluidization properties in a pressurized jetting fluidized bed

The influence of pressure on the bubble size and average bed voidage has been investigated experimentally and computationally in a circular three-dimensional cold-flow model of pressurized jetting fluidized bed of 0.2 m i.d. and 0.6 m in height with a central jet and a conical distributor, which roughly stands for the ash-agglomerating fluidized bed coal gasifier. The pressurized average bed voidage and bubble size in the jetting fluidized bed were investigated by using electrical capacitance tomography (ECT) technique. The time-averaged cross-sectional solids concentration distribution in the fluidized bed was recorded. The influence of pressure on the size of bubble and the average bed voidage in a pressurized fluidized bed was studied. Both experimental and theoretical results clearly indicate that there is, at the lower pressure, a small initial increase in bubble size decided by voidage and then a decrease with a further increase in pressure, which proves the conclusion of Cai et.al. [P. Cai, M. Schiavetti, G. De Michele, G.C. Grazzini, M. Miccio, Quantitative estimation of bubble size in PFBC, Powder Technology 80 (1994) 99-109]. At higher pressure, bubbles become smaller and smaller because of splitting. The average bed voidage increases gradually with the pressure at the same gas velocity. However, there is a disagreement between the experimental results and simulation results in the average bed voidage at the higher gas velocity, especially at the higher pressure. It suggests that the increase in density of gas with pressure may result in the drag increase and the drag model needs to be improved and revised at higher pressure.     

Voidage characteristics and prediction of bed expansion in liquid-solid inverse fluidized bed

Studies on voidage fluctuations, axial voidage profile and bed expansion are carried out by measuring the local void fraction using particles of wide ranging characteristics in liquid-solid inverse fluidized bed. The quality of fluidization is elucidated by the local voidage fluctuations. The RMS voidage fluctuation depicts a maximum with respect to average bed void fraction and increases with increase in Archimedes number. The fluidization quality has been quantified using average normalized RMS voidage fluctuation in terms of Transition number. The axial void fraction is almost uniform throughout the bed except for particles with size distribution. All the literature and present experimental data on bed expansion are unified in terms of Richardson and Zaki equation using experimental terminal velocities. A new correlation is proposed for predicting the wall effect corrected experimental terminal velocities, as a substitute for standard drag equation. The bed expansion data are also predicted using the drift flux model.     

垂直气固上行流动系统中颗粒群集聚的最大空隙率

研究了垂直气固上行流动系统的状态与空隙率的关系,指出当气固两相动能相等时,系统处于最稳定状态。此时颗粒集聚具有最大空隙率ε_(max)·根据上述原理推导出ε_(max)的表达式。将计算结果与Matsen等的结果进行了比较,表明本法合理,计算简单,物理意义明确。     

Chaotic characteristics of local voidage fluctuation in a circulating fluidized bed

Local voidage fluctuations have been measured by using an optical transmittance probe at various axial and radial positions in a circulating fluidized bed riser with a 0.1 m i. d. and 10 m height. The chaotic time series analysis of the local voidage fluctuations has been adopted to characterize the nonlinear dynamics of the circulating fluidized bed riser. The variations of the correlation dimension and the Kolmogorov entropy of the voidage fluctuation were found to depend on the local time-average voidage. The axial and radial distributions of the correlation dimension and the Kolmogorov entropy were strongly affected by the solids flow structures (e.g. core-annulus flow) in various operating conditions. The correlation dimension of local voidage fluctuations increases along the riser, except the position near the distributor. Both, the correlation dimension and the Kolmogorov entropy of local voidage fluctuations near the wall, were found to be smaller than those at the center of the riser, independent of the solids circulation rate and the axial position.     

Particle velocity and solids circulation rate in a jet-spouted bed

Radial distribution of particle velocities, solids circulation rate and radial variation in bed voidage in a jet-spouted bed were investigated in a 0.2 m diameter conical-cylindrical column. The upward particle velocity is strongly dependent on gas velocity and its radial profile is the Gaussian. The solids circulation rates are of the same order of magnitude as those in a conventional spouted bed and are proportional to the gas velocity. Estimation of the variation in bed voidage in the radial direction revealed that the annulus voidage of about 0.90 was greater than the spout voidage of around 0.70. This tendency is contrary to that in a conventional spouted bed.     

Radial profiles of solids loading and flux in a gas–solid circulating fluidized bed

An electrical-impedance tomography (EIT) system has been developed to non-invasively measure radial voidage profiles in the riser of a pilot-scale circulating fluidized bed (CFB), yielding quantitative information that is validated by comparison to a gamma-densitometry tomography (GDT) system. EIT and GDT were applied to the CFB riser (14-cm inner diameter, 5.77-m height) containing fluid catalytic cracking particles in air. For all cases, the average and near-wall voidages from EIT and GDT agreed to within 0.03 and 0.07, respectively. This good agreement suggests that, where feasible, EIT can be used in place of GDT, which is advantageous since EIT systems are often safer, less expensive, and faster than GDT systems. The results also compared well to two correlations for radial voidage profile from the literature. Finally, a procedure for determining radial solids flux profiles from radial voidage profiles using an additional correlation [M.J. Rhodes, X.S. Wang, H. Cheng, T. Hirama, B.M. Gibbs, Similar profiles of solids flux in circulating fluidized-bed risers, Chemical Engineering Science 47 (1992) 1635–1643] was investigated. It was found that the accuracy of this correlation strongly depends on the voidage and/or solids flux measurement at the riser center.     

电容层析成像技术在线测量气固流化床空隙率的研究

基于电容层析成像技术，提出了一种在线测量气固流化床空隙率的新方法。建立了相应的12电极电容层析成像气固流化床空隙率测量系统，可同时实现气固 流化床空隙率分布的在线显示和整体空隙率测量。选择加权反投影算法进行图像重建以保证空隙率分布显示的实时性和有效性。采用Tikhonov正则化原理和ART算法相结合的组合型新图像重建算法来实现整体空隙率的测量。Tikhonov正则化原理用于克服图像重建过程中的不适定问题，ART算法用于提高最终重建图像的质量。研究表明以上提出的空隙率测量新方法是有效的。空隙率分布在线测量的速度可达25幅／秒以上，整体空隙率测量的最大误差可小于5％。     

Distributor effects near the bottom region of turbulent fluidized beds

The distributor plate effects on the hydrodynamic characteristics of turbulent fluidized beds are investigated by obtaining measurements of pressure and radial voidage profiles in a column diameter of 0.29 m with Group A particles using bubble bubble-cap or perforated plate distributors. Distributor pressure drop measurements between the two distributors are compared with the theoretical estimations while the influence of the mass inventory is studied. Comparison is established for the transition velocity from bubbling to turbulent regime, U_c, deduced from the pressure fluctuations in the bed using gauge pressure measurements. The effect of the distributor on the flow structure near the bottom region of the bed is studied using differential and gauge pressure transducers located at different axial positions along the bed. The radial voidage profile in the bed is also measured using optical fiber probes, which provide local measurements of the voidage at different heights above the distributor. The distributor plate has a significant effect on the bed hydrodynamics. Owing to the jetting caused by the perforated plate distributor, earlier onset of the transition to the turbulent fluidization flow regime was observed. Moreover, increased carry over for the perforated plate compared with the bubble caps has been confirmed. The results have highlighted the influence of the distributor plate on the fluidized bed hydrodynamics which has consequences in terms of comparing experimental and simulation results between different distributor plates.     

流态化法进行粉体粒度分级实验研究

流化分级是一种有效的粒度分级手段。颗粒群的悬浮速度是流化分级过程中一个重要的操作参数 ,直接影响到分级效率的高低。实验以 11个粒径范围的颗粒群为研究对象 ,在流化床中对颗粒群的悬浮速度进行了测定和研究 ,考察了平均粒径、床层空隙率等因素对颗粒群悬浮速度的影响 ,得出了颗粒群的悬浮速度与颗粒群平均粒径及床层空隙率间的关系曲线 ,为提高粉粒体流化分级的分级效率提供了实验依据     

EFFECT OF HIGH VOIDAGE ON MASS TRANSFER COEFFICIENT IN A FLUIDIZED BED

Experiments were carried out to determine the gas-solid mass transfer coefficient for the air-naphthalene system under fast-fluidized conditions. The data were obtained under conditions of high voidage (as high as 98%) and high gas velocities (0·5 m/s-2·2 m/s). The results indicate that the correlation for the mass-transfer coefficient in a gas-solid fluidized bed under low voidage conditions established by previous investigators can be extended to the fast fluidization regime. Significantly lower mass transfer coefficients were, however, obtained under high voidage compared to low voidage conditions.     

THE EFFECT OF RADIAL DISTRIBUTION OF VOIDAGE ON THE BURNING RATE OF A CARBON SPHERE IN A FLUIDIZED BED

The local void around a sphere in a packed bed or in the emulsion phase of a fluidized bed has been calculated theoretically; and measured as a function of the radial distance from the centre of the sphere. Effects of this distribution on the burning rate and Sherwood number have been investigated for two types of bed e.g. where inerts are of the same size as the carbon particle and where the inerts are smaller than the carbon particle. Even though the present analysis studies the effect on the diffusive component of the mass transfer alone, the results suggest that the distribution of voidage will yield Sherwood numbers higher than that calculated from the constant voidage assumption. The voidage distribution explains the increase in burning rate of carbon with increasing size of the inerts.     

A 3-zone model for protein adsorption kinetics in expanded beds

The adsorption behavior of expanded beds is more complex than that of fixed beds, since the adsorbent particle size, local bed voidage and liquid axial dispersion will vary axially with expanded height. Models applicable to fixed beds maybe not adequately describe the hydrodynamic and adsorption behavior in expanded beds. In this paper, a 3-zone model is developed, in which the model equations are written for the bottom zone, middle zone, and top zone of the column, respectively, and the model parameters, such as the adsorbent particle diameter, bed voidage and liquid axial dispersion coefficient, are zonal values. In-bed breakthrough curves are predicted by the 3-zone model, and tested against literature data for lysozyme adsorption on Streamline SP in an expanded bed.Model parametric sensitivity is analyzed. The effects of film mass transfer resistance, liquid axial dispersion and adsorbent axial dispersion on the breakthrough curves are weaker than that of protein intraparticle diffusion resistance for stable expanded beds. Adsorbent particle size axial distribution and bed voidage axial variation significantly affect in-bed breakthrough curves, therefore, model parameters should not be assigned uniform values over the whole column; instead the model should account for the adsorbent particle size axial distribution and bed voidage axial variation.     

酵母悬浮液进料时膨胀床空隙率和粒径分布的动态变化

引言 膨胀床吸附技术可以直接从细胞破碎液(未澄清液)中提取目标产物[1-3],而无需预先进行固液分离操作,具有快速、高效和集成化的特点.在实际应用中,料液中细胞(碎片)的存在将会影响到膨胀床的床层稳定性和操作性能[4-6].     

XD-1 新型锥度螺旋填料的流体力学特性与机理

XD-1型锥度螺旋填料独特的锥度螺旋结构能使气液二相由逆流接触转变为错流接触,使之与常规填料有完全不同的流体力学特性。在80 mm的冷模实验塔内,用空气-水物系测定了填料的流体力学特性,还与θ环、拉西环和丝网波纹填料进行了比较。实验结果表明,在相同喷淋密度下,锥度螺旋、拉西环、θ环和波纹丝网4种填料的空隙率之比为:0.823∶0.781∶0.947∶0.855时,单位填料层压降之比为:0.58∶1.35∶1.08∶0.65,泛点气速之比为:0.725∶0.280∶0.658∶0.703。     

Transitional packed bed flow in standpipes

A quantitative criterion distinguishing stable from unstable transitional packed bed flow in standpipes is presented. This criterion can be used as an working guideline in actual standpipe operation. A fundamental and simple model based on stress free surface (SFS) theory has been developed. This model also provides a quantitative prediction method for the standpipe voidage.