涓流床反应器中流区过渡的气相渗透率表征

由于Ergun方程可适用于气液间无相互作用的两相流动压降计算,并且由气相单相和气液两相并流下的气相压降比值可计算气相相对渗透率,因此,Ergun方程可用于涓流床中不同流区过渡和气液相互作用程度的表征。为检验这一方法的有效性,实验测定了空气-水体系在内径140mm有机玻璃塔中不同粒径玻璃珠(1.9、3.6、5.2、9.3mm)组成的床层压降和持液量。由于采用了压力传感器和电容层析成像仪,因此可测定脉冲流状态下的瞬态数据。通过压降的实验值与理论值比较,发现Ergun方程的适用范围有限,在没有进入脉冲流前先已失效,说明此时气液间作用已经相当显著。鉴于此,改用气液两相压降实验值代替理论值进行了气体渗透率的计算,发现不同气液流速和颗粒直径下出现脉冲流时的气体渗透率均低于0.08。     

Experimental investigation of pressure drop in packed beds of irregular shaped wood particles

The knowledge of the pressure drop across a packed bed of irregular shaped wood particles is of great importance for achieving optimal control and maximum efficiency in many applications, such as wood drying, pyrolysis, gasification and combustion. In this work the effect of porosity, average particle size and main particle orientation on the pressure drop in a packed bed is investigated. To this end, particle size distributions and porosities are determined experimentally.Based on the experimental results obtained in this study, the form coefficient C and the permeability K of the Forcheimer equation are calculated for different packed beds. The Ergun equation requires an average equivalent particle diameter that is derived from the measured particle size distribution. This equivalent diameter and the corresponding bed porosity are used in the well known Ergun equation in order to derive adapted shape factors A and B.Since a change in bed porosity and particle size, caused by the degradation of the wood particles and gravity, can be expected in a reacting packed bed, a set of shape factors for use with the Ergun equation is determined that are independent of porosity and particle diameter and fit the experimental data very well.     

FLUIDIZED BED PRESSURE DROP IN PROMOTED GAS-SOLID BEDS WITH COAXIAL ROD, DISK, AND BLADE TYPE PROMOTERS

Bed pressure drop equations have been formulated for gas-solid fluidized beds with different types of promoters using Ergun's equation (Ergun, 1952) and experimental data. Four rod promoters, seven disk promoters, along with one blade promoter were used in beds supported on five different distributors with open areas of 12.9%, 8.96%, 5.74%, 3.23%, and 1.43% of the column section. The predicted values of bed pressure drop using a modified (i.e., modified numerical constant) Burke-Plummer (Burke and Plummer, 1928) equation were compared with the corresponding experimental as well as the respective values obtained with the help of Kumar et al. (submitted) and traditional gas-solid fluidized bed equations.     

Numerical calculation with experimental validation of pressure drop in a fixed-bed reactor filled with the porous elements

To study flow dynamics in a fixed-bed reactor, experiment and numerical simulation are used. In this work, the flow dynamics in a fixed-bed reactor filled with porous particles was simulated. For verification, experimental data were used. Porous particles were prepared from grains with sizes from 0.2 to 2.0 mm. Porous particles made by sintering grains in a muffle furnace. The study of pressure drop was performed in the velocity range up to 3 m/s. Numerical calculation was performed for a realistic computational domain obtained by RBD-algorithm (rigid body dynamics). It was found that if the pore size is less than 0.5 mm, then the flow through the porous medium of particles is minimal; if the pore size is larger than 0.5 mm, then there is a flow through the porous elements of the fixed-bed reactor. To take into account the porosity of the particles, γ correlation coefficient was proposed for the Ergun equation.     

Fluid flow through compressible soft particle beds

The fluid flow through a soft particle bed was studied theoretically and experimentally in this report. Several correction factors were introduced to modify the Ergun equation and account for the deformed shape and reduced volume of compressed particles in a compressible soft particle bed. To acquire the correction factors, both uni‐compression tests and computational fluid dynamics simulation methods were used. The pressure drop estimated from the customized modeling equation was further compared with the experimental data obtained from a bed composed of calcium‐alginate gel particles. In contrast to the conventional Ergun equation, the pressure drop estimated from the customized modeling equation was highly consistent with the experimental data. The result suggests that the customized modeling equation is a convenient tool for accurately predicting the pressure drop across a compressible soft particle bed. © 2016 American Institute of Chemical Engineers AIChE J, 62: 1716–1727, 2016     

Interfacial stress in non-Newtonian flow through packed bed

This study investigates the pressure drop characteristics, shear stress in packed bed with shear thinning power law type non-Newtonian liquid. A mechanistic model has also been developed to analyze the pressure drop and interfacial stress in packed bed with non-Newtonian liquid by considering the loss of energy due to wettability. The Ergun's and Foscolo's equations were used for comparison with the experimental data. The Ergun equation was modified to account for the effect of flow behavior index of non-Newtonian fluid in the column. The intensity factor of shear stress and the friction factor were analyzed based on energy loss due to wettability effect of liquid on the solid surface.     

Pressure buildup in gas‐liquid flow through packed beds due to deposition of fine particles

In order to understand the increase in pressure drop in hydrotreating reactors due to deposition of fine solids, experiments were conducted with a model suspension of kaolin clay in kerosene. The suspension was circulated through packed beds of catalyst pellets in the trickle‐flow and pulse‐flow regimes, and the increase in pressure drop measured as a function of particle concentration in the bed. The increase in pressure drop was linear with particle concentrations over the range 0–60 kg.m^?3. A consistent approach to modeling the pressure drop behavior was to determine an effective porosity of the packed bed as a function of the concentration of fine particles, then use this porosity in the Ergun equation as a basis for calculating the two‐phase pressure drop.     

气体的温度和压力及颗粒形状对固定床压降的影响

本文在Ａ－Ｓ方程的基础上推导出气体流经固定床时的压降表达式。     

Mathematical model for gas flow through a packed bed in the presence of sources and sinks

Flow within a packed bed is normally calculated by attempting to simultaneously satisfy the continuity and Ergun equations. However, the presence of gas sources/sinks within the bed escalates the complexity of the problem, particularly when the flow is two-dimensional and a solution to the full Ergun equation is required. In quest of an efficient and dependable algorithm for the calculation of gas flow, a critical review of existing solution methods was undertaken and a new method, ‘FLOW’, is now proposed. The technique retains the viscous and inertial pressure gradient terms of the Ergun equation, and both are treated as linear functions of the flow. Solutions are approached iteratively; using finite difference techniques, the continuity and linearized Ergun equations are solved for the pressure field; a new flow field is then calculated from which is derived an adjustment to the inertial resistance term of the Ergun equation. The sequence is repeated until satisfactory convergence is obtained. Relatively few iterations are normally required and, for the case of negligible inertial pressure drop, one calculation cycle is sufficient. A comparison of results obtained using the ‘FLOW’, modified ‘SIMPLE’ and vorticity procedures is presented. The proposed method allow flexibility in the specification of boundary conditions and can be applied to compressible or incompressible flow, as well as for the case of nonisothermal beds.     

Pressure drop measurements of ceramic sponges—Determining the hydraulic diameter

This paper presents experimental results of pressure drop measurements for different solid ceramic sponges. In the experiments, the material, pore sizes and porosity were varied. Furthermore, this data is correlated using an Ergun-type equation. It was possible to obtain Ergun constants for sponges independently of the varied parameters. In the future, the presented pressure drop correlation will provide a simple method for determining hydraulic diameters for solid ceramic sponges with unknown geometric parameters (strut, window and pore diameter,…) based on pressure drop measurements. Furthermore a correlation is given to derive the hydraulic diameter from the ppi (pores per inch) number.     

垂直矩形窄缝通道内气液两相流型的研究

本文研究了矩形窄缝通道内气液两相流的流型.用目测和摄影方法得到气液两相向上并流的流型.用x-y函数记录仪测得各种流型下的压差频谱图.作出了以1/X_(tt)～G_t和j_(?)～Re为坐标的流型图.作者还用Lockbart-Martinelli方法计算了矩形通道内气液两相流的压降,并与实测值进行了比较.     

加压流化床冷态模拟初探（Ⅰ）─压力及内部构件对细颗粒物料初始流化状况的影响

本实验初步探讨了压力状况下（０．５～２．５ＭＰａ）细颗粒的流化特性,对众多流化床设计的基本参数进行了测定。本文着重讨论压力和内部构件两因素对初始流化状况的影响并用Ｅｒｇｕｎ方程进行理论分析和计算。结果发现与实验现象相符较好,进一步说明Ｅｒｇｕｎ方程在加压情况下的适用性。     

Pressure-drop predictions in a fixed-bed coal gasifier

In the Sasol Synfuels plant in Secunda, Sasol-Lurgi fixed-bed dry-bottom gasifiers are used for the conversion of low-grade bituminous coals to synthesis gas (syngas). The gasifiers are fed with lump coal having a particle size in the range from 5 to 100 mm. Operating experience shows that the average particle size and particle-size distribution (PSD) of feed coal, char and ash influence the pressure drop across the bed and the gas-flow distribution within the bed. These hydrodynamic phenomena are responsible for stable gasifier operation and for the quality and production rate of the syngas. The counter-current operation produces four characteristic zones in the gasifier, namely, drying, de-volatilization, reduction and combustion. The physical properties of the solids (i.e. average particle size, PSD, sphericity and density) are different in each of these zones. Similarly, the chemical composition of the syngas, its properties (temperature, density and viscosity) and superficial velocity vary along the height of the bed. The most popular equation used to estimate the pressure drop in packed beds is that proposed by Ergun. The Ergun equation gives good predictions for non-reacting, isothermal packed beds made of uniformly sized, spherical or nearly spherical particles. In the case of fixed-bed gasifiers, predictions by the Ergun equation based on the average or inlet values of bed and gas flow parameters are unsatisfactory because the bed structure and gas flow vary significantly in the different reaction zones. In this study, the Ergun equation is applied to each reaction zone separately. The total pressure drop across the bed is then calculated as the sum of pressure drops in all zones. It is shown that the total pressure drop obtained this way agrees better with the measured result.     

Spouted bed and spout-fluid bed behaviour in a column of diameter 0.91 m

Hydrodynamic measurements were obtained in a half-column of diameter 0.91 m equipped with a conical base using particles of diameter 3.3 to 6.7mm with operation both as pure spouted beds and in the spout-fluid bed mode. Comparison of the experimental results for minimum spouting velocity with equations in the literature generally gave unsatisfactory agreement. On the other hand, the correlations of McNab (1972) and Had?isdmajlovi? et al. (1983) gave reasonable predictions of spout diameters in spouted and spout-fluid beds respectively. Hydrodynamic regimes with auxiliary air present were broadly similar to those determined in smaller columns. However, there were substantial dead regimes at the bottom of the column. A finite difference model based on the vector form of the Ergun equation gave good predictions of air flow distribution and longitudinal pressure profiles.     

Attrition of char agglomerates

A 15.2 cm diameter fluidized bed system with single- and multiple-jet distributors was designed and constructed to study the attrition behavior and mechanism of Kentucky No. 9 char from IGT's U-GAS fluidized bed gasifier. The effects of the jet and auxiliary gas velocities, the number of jets, the bed height, and the roughness of the fluidized bed wall on the attrition of char particles were studied. Particle shape variation during attrition was calculated by comparing our experimental data on pressure drop for a packed bed with the Ergun equation prediction. A mathematical procedure was developed to translate the size distribution variation of particles in the fluidized bed to the attrition rate expression.     

Resistance to airflow through bulk pistachio nuts (Kalleghochi variety) as affected by moisture content, airflow rate, bed depth and fill method

The prediction of airflow resistance is fundamental to the design of efficient drying and aeration systems for pistachio nuts. Using a laboratory unit, the pressure drop across a column of pistachio nuts (Kalleghochi variety) was investigated to determine the effect of moisture content, airflow rate, bed depth and fill method. Five levels of moisture contents (4.80, 14.50, 23.70, 37.60 and 45.60 w.b.%), four bed depths (25, 50, 75 and 100 cm) and two fill methods (loose and dense) were studied with airflow rates ranging from 0.08-1.00 m³/S m². Results indicated that resistance to airflow through a column of pistachio nuts increased with increasing bed depth, moisture content and airflow rate for both dense and loose fill method. Airflow rate was the most significant factor affecting the pressure drop of pistachio nuts followed by fill method and moisture content. The dense fill of pistachio nuts produced higher resistance to airflow compared with the loose fill. Among the three models (Shedd, Hukill and Ives, and Ergun equation) investigated to describe pressure drop data of pistachio nuts, Ergun equation was found to be the most suitable for describing the pressure drop data of pistachio nuts.     

低、高压滴流床中压降和持液量计算的统一关系式

基于对滴流床中气液两相流动特征尺度的分析,提出以修正的相摩擦系数对相Reynolds数进行关联,获取低、高压滴流床中压降和持液量计算的统一关联式的方法.对于滴流床中单相不饱和流（液体流动,气体静止）情形,以及低压和高压滴流床中两相流、高气液作用情形,收集了文献报道的不同大小颗粒、不同物系的大量实验数据,以相摩擦系数对相Reynolds数进行关联,得到新的压降和持液量计算式,其物理意义明确,计算精度得以提高.     

The flow of non-Newtonian solutions through packed beds

The rheological behavior of aqueous solutions of Separan AP-30®, polymethylcellulose, and polyvinylpyrrolidone was studied experimentally. These solutions exhibit non-Newtonian flow behavior in simple shear, and are characterized by one of several 2, 3, or 4 parameter rheological equations. The equations used included the power law, the Ellis model, Spriggs equation, the Herschel-Bulkley equation, and Meter's model. The power law model fits the data for each of the solutions over a limited range of shear rates, whereas the other models, which include either a lower shear rate limiting Newtonian viscosity, and/or an upper shear rate limiting Newtonian viscosity, or a yield stress, fit the data well over a wide range of shear rates from 0.00675 to 1076 sec^?1. The pressure drop-flow rate data for the same aqueous solutions flowing through packed beds were correlated well by the Ergun equation using the various rheological models applied in this work to evaluate a modified fluid viscosity. In each case it was found that the rheological model which best fit the viscometric data also gave the best packed bed friction factor correlation, and that no one model, such as the powerlaw, or the Ellis model, is the best one to use in all cases for all solutions. For polyvinylpyrrolidone solutions large deviations between experimental values of friction factor and those from the Ergun equation occurred for modified Reynolds numbers greater than one. A pseudo viscoelastic parameter was used to improve the friction factor correlation empirically at high Reynolds numbers.     

The Effect of Particle Size Distribution on Pressure Drop through Packed Beds of Cooked Wood Chips

The pressure drop of process liquors through columns of wood chips determines the operability, efficiency and control of both batch and continuous pulp digesters and the quality of the pulp produced from them. Pressure drop was measured through columns of industrial white spruce chips (produced with a chipping head‐rig) as a function of the chip size distribution and the extent of delignification. Flow resistance depended on the porosity of the chip bed which was affected by the kappa number of the chips (which affected their flexibility) and chip size distribution, the compaction forces applied to the column, and the liquid superficial velocity. The chip beds were compressible and inelastic. Previous work from the literature using the Ergun equation to characterize pressure losses through chip beds is examined and compared with results of this work.     

Flow through packed bed reactors: 1. Single-phase flow

Single-phase pressure drop was studied in a region of flow rates that is of particular interest to trickle bed reactors . Bed packings were made of uniformly sized spherical and non-spherical particles (cylinders, rings, trilobes, and quadralobes). Particles were packed by means of two methods: random close or dense packing (RCP) and random loose packing (RLP) obtaining bed porosities in the range of 0.37–0.52. It is shown that wall effects on pressure drop are negligible as long as the column-to-particle diameter ratio is above 10. Furthermore, the capillary model approach such as the Ergun equation is proven to be a sufficient approximation for typical values of bed porosities encountered in packed bed reactors. However, it is demonstrated that the original Ergun equation is only able to accurately predict the pressure drop of single-phase flow over spherical particles, whereas it systematically under predicts the pressure drop of single-phase flow over non-spherical particles. Special features of differently shaped non-spherical particles have been taken into account through phenomenological and empirical analyses in order to correct/upgrade the original Ergun equation. With the proposed upgraded Ergun equation one is able to predict single-phase pressure drop in a packed bed of arbitrary shaped particles to within ±10% on average. This approach has been shown to be far superior to any other available at this time.