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。     

Liquid backmixing in oscillatory flow through a periodically constricted meso-tube

This paper deals with the measurement and modelling of axial liquid dispersion in a 4.5 mm internal diameter tube provided with smooth-periodic constrictions (meso-tube) in steady and oscillatory flow conditions. The residence time distribution (RTD) in the meso-tube was monitored for a range of fluid oscillation frequency (f) and amplitude (x₀) at laminar flow. The RTD response was modelled with three hydrodynamic models: (i) tanks-in-series, (ii) tanks-in-series with backflow and (iii) plug flow with axial dispersion. The steady flow through the meso-tube at flow rates up to 21.30 ml/min resulted in broad RTDs, mainly due to the parabolic velocity profile. The use of fluid oscillations allowed a fine-control of the axial liquid dispersion in the meso-tube due to generation of secondary flow in the regions between the constrictions. The axial dispersion coefficient D was reduced by up to 13-fold in comparison with the steady flow situation. Values of x₀ ≤ 1 mm and f = 10 Hz generally resulted in a maximum reduction in axial dispersion through, therefore maximum improvements in RTD. The tanks-in-series model was generally not capable of predicting RTDs in the meso-tube. The potential of this platform for the continuous, sustainable production of added-value products is herein demonstrated.     

Oscillatory flow and axial dispersion in packed beds of spheres

The effect of oscillations in the bulk flow on the axial dispersion coefficient in packed beds of spherical particles has been studied using the imperfect pulse tracer method with two probes located within the bed. Three bed sizes with diameters in the range 25-47.3 mm have been used with oscillation frequencies and amplitudes in the range 0-2.4 Hz and 0-3.5 mm, respectively. In the absence of oscillations, the axial dispersion coefficient increases linearly with interstitial velocity. For a given bulk velocity and oscillation frequency, the axial dispersion coefficient-amplitude relationship shows a minimum. Over the ranges of conditions studied, the best reduction (up to 50%) in the axial dispersion coefficient from the non-oscillation base case occurred at the highest frequency studied and when the wall effect was the greatest, i.e. when the column-to-particle size was the smallest. The axial dispersion coefficient was fitted to a mathematical model, which takes into account the diameters of both the column and the packing, the fluid velocity, and the oscillation intensity (frequency and amplitude). The model was adapted from those developed by Göebel et al. (1986) and Mak et al. (1991) so as to need no a priori assumptions about the relationship between oscillation parameters and the axial dispersion coefficient. The model provides near-perfect fits to the experimental data for the higher frequencies studied.     

管式搅拌反应器中流动特性实验及模型研究

为进一步研究带机械搅拌装置的新型管式反应器内流动特性,采用刺激-响应技术,测定流体在不同操作条件下的停留时间分布(RTD)曲线并与无搅拌停留时间分布曲线作对比,计算了平均停留时间分布的统计特征值。用混合时间表征混合特性,用Peclet操作准数表征轴向扩散特性。结果表明,适当增大转速、流量或降低水位,都有利于反应器内流体的均匀混合。大体上随流量的减少和液位的升高停留时间有延长的趋势,转速变化对停留时间的影响不显著。在搅拌转速不超过400 r/min时,混合时间随着搅拌转速的增大而缩短。在实验范围内,反应器相当于3个串联全混槽反应器。     

Liquid phase mixing in turbulent bed contactor

Axial mixing of the liquid phase in turbulent bed contactor (TBC) is studied through residence time distribution (RTD) experiments over a large range of variables such as flow rate of gas and liquid phases, static bed heights, diameter and density of particles and number of stages in presence of downcomer using air water system. Since all the liquid exits only through the downcomer, it enables the correct estimation of exit concentration of the tracer. The experimental RTD curves are satisfactorily compared with the axial dispersion model. The Peclet numbers evaluated by axial dispersion model and the Peclet numbers reported in the literature are used to propose a unified correlation in terms of operating and geometric parameters. Correlation is also developed for predicting the axial dispersion coefficient. It was observed in the present study that almost plug flow conditions can be achieved in multistage TBC.     

Mixing characteristics in the torus reactor

The hydrodynamic characteristics of propeller-induced toroidal flow in a loop reactor were investigated by performing an RTD analysis. The experimental determination of circulation time allows the calculation of the mean axial velocity with respect to the rotational speed of the impeller. RTD measurements are interpreted with the aid of the dispersion plug flow model, and it is shown that axial dispersion is relatively weak in the torus reactor. The mixing time was also determined experimentally and related to the circulation time. A direct relationship between mixing time and axial dispersion coefficient has been established, leading to a correlation for the mixing time in a torus reactor.     

ANALYSIS OF AXIAL MIXING IN A GAS-LIQUID RECIPROCATING PLATE COLUMN

Axial mixing in the continuous phase in a Landau reciprocating-plate column (LRPC) has been investigated for both single-phase and two-phase gas-liquid flow conditions. A hydrodynamic model is proposed in which axial mixing is described as a process consisting of a backflow through the plate plus longitudinal mixing within the stage. The region in the proximity of the plates is almost perfectly mixed, beyond which there is a low-intensity mixing zone that varies in height and degree of mixing depending on phase velocities as well as the plates design and oscillation velocity. The presence of the dispersed phase affects axial mixing in both the well- and poorly mixed regions of each stage in two opposite ways: it decreases the backflow between the stages due to the hindrance effect caused by the presence of gas bubbles, and it increases the axial dispersion coefficient in the second stage by increasing the turbulence and phase entrainment caused by circulation and bubbles rising. The model adjustable parameters were determined from an experimentally measured dispersion coefficient over a wide range of operating conditions using the transient tracer injection method. The predictions of the model compare favorably with experimental data and can be applied for describing axial mixing in the continuous phase in an LRPC with±14% accuracy.     

Characterisation of fluid mixing in novel designs of mesoscale oscillatory baffled reactors operating at low flow rates (0.3-0.6 ml/min)

For the first time two mesoscale oscillatory baffled designs (central and integral baffles with their volumes of 5.2 ml and 4.4 ml, respectively) were experimentally characterised at net flow rates as low as 0.3 ml/min (Re_n ∼ 1.25), giving a residence time of around 15-17 min over a wide range of oscillation conditions. The purpose was to identify the lower limits of operability, thereby determining the maximum residence time per unit reactor volume for these mesoscale units. The characteristics of fluid flow were found to be strongly affected by Strouhal number at these low net flows. For the integral baffles, the oscillation conditions exhibited little influence on the fluid mixing. For the central baffles, there were three distinct flow regimes, depending on Strouhal numbers which affect the fluid characteristics differently. At two regimes of Sts, St ≥ 0.8 and 0.13 ≤ St ≤ 0.2, an increase in frequency did not alter the axial dispersion. At St ≥ 0.8, the fluid experienced less uniform mixing, representing by right-skewed residence time distribution (RTD) curves. At 0.20 ≤ St ≤ 0.13, the fluid mixing was significantly improved, indicated by narrow and symmetrical RTD curves with Re_o up to 700. At 0.4 ≤ St ≤ 0.27 and St ≤ 0.1, the degree of plug flow was a function of Re_o. The maximum number of tanks achieved at these low flow rates was in the range 30-35, occurring at a velocity ratio (Re_o/Re_n) of 39-40.     

Liquid‐phase axial dispersion of turbulent gas–liquid co‐current flow through screen‐type static mixers

This article discusses the characteristics of turbulent gas–liquid flow through tubular reactors/contactors equipped with screen‐type static mixers from a macromixing perspective. The effect of changing the reactor configuration, and the operating conditions, were investigated by using four different screen geometries of varying mesh numbers. Residence time distribution experiments were conducted in the turbulent regime (4500 < Re < 29,000). Using a deconvolution technique, the RTD function was extracted to quantify the axial/longitudinal liquid‐phase dispersion coefficient. The findings highlight that axial dispersion increases with an increasing flow rate and/or gas‐phase volume fraction. However, regardless of the number and geometry of the mixing elements, reactor configuration, and/or operating conditions, the recorded liquid‐phase axial dispersion coefficients in the presence of screens was lower than that for an empty pipe. Furthermore, the geometry of the screen was found to directly affect the axial dispersion coefficient in the reactor. © 2016 American Institute of Chemical Engineers AIChE J, 63: 1390–1403, 2017     

Trickle bed hydrodynamics and flow regime transition at elevated temperature for a Newtonian and a non-Newtonian liquid

Despite the hydrodynamics of trickle beds experiencing high pressures has become largely documented in the recent literature, trickle bed hydrodynamic behavior at elevated temperatures, on the contrary, largely remains terra incognita. This study's aim was to demonstrate experimentally the temperature shift of trickle-to-pulse flow regime transition, pulse velocity, two-phase pressure drop, liquid holdup and liquid axial dispersion coefficient. These parameters were determined for Newtonian (air-water) and non-Newtonian (air-0.25% Carboxymethylcellulose (CMC)) liquids, and the various experimental results were compared to available literature models and correlations for confrontation and recommendations. The trickle-to-pulse flow transition boundary shifted towards higher gas and liquid superficial velocities with increasingly temperatures, aligning with the findings on pressure effects which likewise were confirmed to broaden the trickle flow domain. The Larachi-Charpentier-Favier diagram [Larachi et al., 1993, The Canadian Journal of Chemical Engineering 71, 319-321] provided good predictions of the transition locus at elevated temperature for Newtonian liquids. Conversely, everything else being kept identical, increasingly temperatures occasioned a decrease in both two-phase pressure drop and liquid holdup; whereas pulse velocity was observed to increase with temperature. The Iliuta and Larachi slit model for non-Newtonian fluids [Iliuta and Larachi, 2002, Chemical Engineering Science 46, 1233-1246] predicted with very good accuracy both the pressure drops and the liquid holdups regardless of pressure and temperature without requiring any adjustable parameter. The Burghardt et al. [2004, Industrial and Engineering Chemistry Research 43, 4511-4521] pulse velocity correlation can be recommended for preliminary engineering calculations of pulse velocity at elevated temperature, pressure, Newtonian and non-Newtonian liquids. The liquid axial dispersion coefficient (D_ax) extracted from the axial dispersion RTD model revealed that temperatures did not affect in a substantial manner this parameter. Both Newtonian and power-law non-Newtonian fluids behaved qualitatively similarly regarding the effect of temperature.     

Residence time distribution and modeling of the liquid phase in an impinging stream reactor

Based on some experimental investigations of liquid phase residence time distribution (RTD) in an impinging stream reactor, a two-dimensional plug-flow dispersion model for predicting the liquid phase RTD in the reactor was proposed. The calculation results of the model can be in good agreement with the experimental RTD under different operating conditions. The axial liquid dispersion coefficient increases monotonously with the increasing liquid flux, but is almost independent of gas flux. As the liquid flux and the gas flux increase, the liquid dispersion coefficient of center-to-wall decreases. The axial liquid dispersion coefficient is much larger than that of center-to-wall, which indicates that the liquid RTD is dominated mainly by axial liquid dispersion in the impinging stream reactor.     

Material transport in a continuous rotary drum. Effect of discharge plate geometry

Experimental results on the influence of the discharge plate geometry on the dimensionless residence time distribution (RTD) for material transport in a continuous rotary drum are described. The RTD obtained by a stimulus-response technique for the different discharge plates can be described well by the axial dispersed flow model. Based on the characteristic Peclet number of the flow regime, material flow tended more towards the plug flow condition at an intermediate size discharge opening. Calculation of the axial dispersion coefficient in each case revealed that the open-ended drum behaved more like an ideal mixer. The implication of these results on the design of continuous rotary devices is discussed.     

Residence time distribution and modeling of the liquid phase in an impinging stream reactor

Based on some experimental investigations of liquid phase residence time distribution (RTD) in an impinging stream reactor, a two-dimensional plug-flow dispersion model for predicting the liquid phase RTD in the reactor was proposed. The calculation results of the model can be in good agreement with the experimental RTD under different operating conditions. The axial liquid dispersion coefficient increases monotonously with the increasing liquid flux, but is almost independent of gas flux. As the liquid flux and the gas flux increase, the liquid dispersion coefficient of center-to-wall decreases. The axial liquid dispersion coefficient is much larger than that of center-to-wall, which indicates that the liquid RTD is dominated mainly by axial liquid dispersion in the impinging stream reactor.     

The measurement and characterisation of residence time distributions for laminar liquid flow in plastic microcapillary arrays

Residence time distributions (RTDs) for a thermoplastic microreactor system were experimentally measured using fibre optic probes and step change concentration inputs. The distributions were then compared to models assuming plug flow superimposed by axial dispersion. The disc-shaped plastic microreactors contained microcapillary arrays of up to 19 parallel channels with diameters around 230 μm and lengths of 10 m. Two different systems were investigated, with either 1 or 19 active capillaries. The magnitude of axial dispersion in those two systems was characterised using Peclet numbers, which were in the range of 15-221 depending on flow rate, demonstrating that molecular dispersion along a single 10 m capillary can provide near plug flow characteristics. The multiple-capillary array showed small perturbations of this plug flow like RTD behaviour as the 19 microcapillaries displayed slight variations in diameter. These results confirm that the flow inside the presented plastic multiple capillary device provides a near plug flow behaviour for the use in continuous microreactors.     

Investigation of the effect of impeller rotation rate,powder flow rate,and cohesion on powder flow behavior in a continuous blender using PEPT

In this paper, we examine the movement of particles within a continuous powder mixer using PEPT (Positron Emission Particle Tracking). The benefit of the approach is that the particle movement along the vessel can be measured non-invasively. The effect of impeller rotation rate, powder flow rate, and powder cohesion on the particle trajectory, dispersive axial transport coefficient, and residence time is examined. Increase in the impeller rotation rate decreased the residence time, increased the axial dispersion coefficient, and resulted in longer total path length. Effect of flow rate was different at two different rotation rates. At lower rotation rate, increase in flow rate increased the residence time, decreased the axial dispersion, and resulted in longer total path length. At higher rotation rate, increase in flow rate decreased the residence time, increased the total path length and showed a complex dependence on the axial dispersion coefficient. Increasing cohesion (measured using the flow index, dilation, and the Hausner ratio) did not affect the axial dispersion coefficient significantly, but had significant effects on the total particle path length traveled and the residence time. These results, relevant to pharmaceutical powders, provide better physical understanding of the influence of operating parameters on the flow behavior in the continuous mixer. In addition, one of the main obstacles of modeling continuous mixing of particles is to know the appropriate values for the modeling parameters as well as validate modeling approaches. One example is the dispersion coefficient which leads to an analytical solution for the axial dispersion model of a continuous blending process.     

Axial dispersion in a reciprocating plate column

Axial mixing in a reciprocating plate column with different amplitudes has been investigated for single-phase and two-phase (air-water) systems. Experiments were performed in water in a semi-batch scheme (no water flow) in a 1.26 m high and 101.6 mm internal diameter column. It was found that the axial dispersion coefficient is a strong function of reciprocation speed and amplitude. The presence of gas considerably affects the axial dispersion coefficient but its contribution appears to saturate at low gas flow rates and then, over a large range of gas flow rates, the axial dispersion coefficient was almost constant. Models are proposed based on experimental data to account for the effects of gas superficial velocity, amplitude and reciprocating frequency. The models predictions are compared with experimental data, obtained over a wide range of operating conditions, and the agreement between them was found to be good. A new class of nonlinear models, for which it is not necessary to have a constant dependency on each operating variable, was also used to correlate the axial dispersion coefficient. This new model allows to carry out sensitivity analysis on each operating variable.     

Axial dispersion in single-phase flow in pulsed packed columns

Axial dispersion in single-phase flow through a pulsed packed column (length 4 m; Raschig-ring packing) has been investigated using an imperfect pulse method. It has been shown that under certain conditions axial dispersion can be reduced by means of pulsation. A three-parameter model based on the Taylor-Aris dispersion equation for tube flow has been developed. This model, which has been verified experimentally, describes the relation between the axial dispersion coefficient and the interstitial and pulsation velocities.     

自热转化炉停留时间分布

以氢气作为示踪剂,运用脉冲法测定自热转化炉内停留时间的分布。实验结果表明:随着催化剂床层的增高,停留时间分布密度函数变窄,平均停留时间和量纲一方差均减小;当进口气量增大时,平均停留时间减小,量纲一方差增大。应用N个全混流反应器(CSTR)、轴向混合模型和平推流模型串联建立自热转化炉停留时间分布模型,由Laplace变换法和阻尼最小二乘法对模型参数进行估算,模型估计停留时间曲线与实验测量曲线吻合良好。     

VELOCITY AND TEMPERATURE EFFECTS ON DISPERSION IN POROUS MEDIA: APPLICATIONS TO UNCONSOLIDATED LIGNITE COAL

A model is derived for the effective axial dispersion coefficient in unconsolidated porous media as a function of temperature and superficial velocity. We also demonstrate a technique for determining the effective axial dispersion coefficient and core porosity from pulse tracer data using a nonlinear parameter estimation routine and a noncapacitive pulse model. Results from pulse tracer experiments using three unconsolidated lignite coals are presented and compared to the analytical predictions. The results indicate that the dispersion coefficient model is valid over the experimental range of temperatures and velocities studied, and can be used as a predictive tool for estimation of the temperature dependence of the dispersion coefficient in porous media.     

Longitudinal mixing in a vibrating-sieve-plate column two-phase flow

Longitudinal mixing in the continuous phase of a vibrating-plate extractor was examined. Particular attention was focused on the effect of the flow of the dispersed phase, which turned out to be of major importance. Three regimes displaying distinctly different character of longitudinal mixing may be observed. The flow within a stage was studied in detail and it was shown that the stage could split into two regions of different character of the flow. A model was proposed which makes up the total effect of longitudinal mixing from the back flow through the plate plus axial dispersion within the stage. Correlations have been proposed relating the axial dispersion coefficient to the hold-up and droplet diameter.