Minimum stable bubble volumes and bubble collapse rates in gas fluidized beds

Measurements of the collapse rates of small bubbles injected into particulate gas fluidized beds show that the net transfer rate of gas from the bubbles to the continuous phase decreases as the background velocity is increased. The results indicate that the minimum stable bubble volume in a bed fluidized at a velocity equal to twice the minimum fluidizing velocity is 0.08 cc. Evidence of increase in the continuous phase voidage in the path followed by a bubble has been observed; this would explain the formation of stable bubble tracks.     

Effect of bubble interaction on interphase mass transfer in gas fluidized beds

A non-interfering technique has been used to measure the concentration of ozone in pairs of bubbles injected into a bed of inactive 390 μm glass beads fluidized by ozone-free air. The transfer of the ozone tracer from the bubble phase to the dense phase is enhanced when compared to the transfer from isolated bubbles in the same particles and the same column. Bubble growth is also greater for the case where pairs of bubbles are introduced than when bubbles are present in isolation. Enhancement of interphase mass transfer for interacting bubbles in the present work and in previous studies incr with particle size and can be explained in terms of enhancement of the throughflow (or convective) component of transfer while the diffusive component unaltered. This mechanism leads to new equations for estimating interphase mass transfer in freely bubbling fluidized beds.     

Local bubble behavior in three-phase fluidized beds

Bubble behavior, including bubble Sauter diameter, bubble rise velocity, bubble frequency and local gas holdup in different radial and axial positions, was measured using a dual electro-conductivity probe in air-water-glass beads fluidization systems. It has been found that the bubble characteristics differ significantly in various flow regimes, depending on the operating conditions; the radial distribution of bubble parameters also changes from one flow regime to another. Thus, it is necessary to employ local bubble behavior in the modeling of three-phase fluidized beds.     

Correlations for bubble characteristics in fluidized beds

For fluidized bed reactors the available equations for superficial bubble velocity (U_B), bubble fraction (δ), and absolute bubble rise velocity (u_b) do not include bed diameter as a variable. Based on the gross solid circulation model new expressions are derived for U_B, δ, and u_b which explicitly account for bed diameter. Existing data are compared to predicted values from these correlations.     

流化床中气固均匀分布的失稳现象

流化床因其均匀且剧烈的气固相互作用保证了其优异的流动和传递性能,因而广泛应用于化学工业中。因此,构建定量计算气固均匀分布的失稳临界点既是重要的学术问题又具有工程意义。本文分别使用气相和固体颗粒相的质量分数表示气固分布状态;引入颗粒床层压力载荷（Φ _T）描述分布器输入的规则负熵和固体颗粒床层自身混沌熵产生之间相互作用;由于密相颗粒床层远离平衡态且具有强非线性耗散项,因此需基于普利高津最小超量熵增原理给出气固密相流在并联系统均布状态的失稳临界点（Φ _Tc）：分布器和固体颗粒床层总熵增在气固均布和气固非均布情况下相等;由于并联系统的对称性,可将N单元路径并联系统气固均布稳定性分析简化为判断单元路径压降二阶导数正负;在此基础上讨论了操作参数、固体颗粒性质和分布器结构参数对气固密相床层均布稳定性的影响。此外,通过气体示踪和压力脉动频谱分析在直径为300mm冷模实验验证了颗粒床层压力载荷（Φ _T）对密相气固均布稳定性的影响;同时应用该方法论计算了工业流化床反应器临界床层高度、临界表观气速以及分布器临界阻力系数,指导了操作工况的调整和分布器结构设计,对比分析了改造前后的反应情况。     

Pitfalls in gas sampling from fluidized beds

It is shown that gas sampling from fluidized beds can provide misleading information due to hydrodynamic factors, biased sampling from the dense phase and radial gradients. Caution is needed to avoid these problems and in the interpretation of gas-sampling data.     

Utilization of the pressure differential records from gas fluidized beds with internals for bubble parameters determination

Simulated pressure gradient records, based on the theoretical pressure field around a bubble in fluidized bed derived by Davidson, are analysed by statistical methods to determine significant bubble parameters. It is shown that from two records measured by two pairs of pressure differential probes located on common vertical axis the following can be computed: bubble velocity, bubble depth (diameter), vertical spacing of bubbles, bubbling frequency, distributions of bubble sizes and spacings, and local bubble phase fraction. Simulated and actual records of the passage of non-interacting single bubbles over four pairs of probes located in a fluidized bed with internals show good agreement.     

Maximum entropy estimation of the bubble size distribution in fluidized beds

This work presents a new methodology, based on the maximum entropy method, to obtain bubble characteristics in fluidized beds. The probability distributions (PDF) of bubble pierced length and velocity are obtained applying the maximum entropy principle to experimental measurements. In addition, the bubble diameter distribution has been inferred from experimental pierced length measurements. This method is applied to characterize bubbles in fluidized beds for the first time and the most general bubble geometry, a truncated spheroid, is considered. The distance between probes, s, which is the minimum pierced length that is possible to measure accurately using intrusive probes, has been introduced as a constraint in the derivation of the size distribution equation.The maximum entropy method is applied to experimental measurements of bubble characteristics carried out using optical and pressure probes in a three-dimensional fluidized bed of Geldart B particles. Results on bubble size obtained from pressure and optical probes are very similar, although optical probes provide more local information and can be used at any position in the bed. The maximum entropy principle has been found to be a simple method that offers many advantages over other methods applied before for size distribution modeling in fluidized beds.     

Bubble formation and gas leakage in fluidized beds

The Harrison and Leung model for spherical bubble formation in fluidized beds has been extended to account for the dynamics of the emulsion phase. The simplified Davidson-Harrison model is used to obtain the gas and particle velocities in the emulsion phase and includes the effect of the bubble pressure, the change in hydrostatic pressure, grid orifice discharge rate, and gas leakage into the emulsion phase. Computations for the constant flow rate case agree well with measured gas leakage for beds of large particles. For large grid orifices, a simplified model explains the low frequencies observed experimentally for small flow rates.     

Heat transfer mechanisms in gas fluidized beds. Part 3: Heat transfer in circulating fluidized beds

Part 1 of this contribution reported on the effects of system properties on heat transfer between heating or cooling surfaces and bubbling fluidized beds. This investigation produced four correlations which define the respective maximum heat transfer. Part 2 of this study suggests that the heat transfer between exchanger surfaces and bubbling fluidized beds depends on superficial gas velocity, expressed as dimensionless excess gas velocity. The present paper shows that heat transfer coefficients in circulating fluidized beds can be predicted by evaluation of a state diagram, which combines three dimensionless groups: Nusselt number, Archimedes number and a dimensionless pressure gradient. A comparison of coal combustion experiments with own cold model measurements indicates that the radiative component of heat transfer coefficients is only evident at very low dimensionless pressure gradients.     

A critical evaluation of literature correlations for predicting bubble size and velocity in gas–solid fluidized beds

Twenty-five different correlations for bubble size and seven different correlations for bubble rise velocity have been evaluated by comparing their predictions with data available from the open literature. The performance of these correlations has been quantified by calculating the squared difference between the correlation predictions and the experimental data in seven categories for bubble size (Geldart A, B, and D particles, low (less than 10 U_mf) and high (greater than 10 U_mf) excess gas velocity, and perforated and porous plate distributers) and three categories for bubble rise velocity (Geldart A, B, and D particles). The results indicate that the correlations of Cai et al. [Powder Technol. 80 (1994) 99–109] and Werther [Ger. Chem. Eng. 1 (1978) 166–174] are the best choices for calculating the bubble size and bubble rise velocity, respectively.     

Residence times in fluidized beds with secondary gas injection

Experiments were carried out to determine the effects of secondary gas injection on the gas residence time and macromixing characteristics in a bubbling fluidized bed. Primary gas is introduced via a bottom distributor plate, while secondary gas is introduced via a fractal injector submerged in the bed. Results indicate that the average residence time decreases only slightly. Calculated overall reactor Péclet numbers indicate that the gas experiences less back-mixing with secondary gas injection. The bubble size was observed to decrease by up to 70%, indicating improved gas–solid contact. Taking this improved contact and plug flow behavior into account, the conversion in a fluidized bed with secondary gas injection is expected to increase significantly, particularly for mass-transfer limited reactions.