Residence time distributions in a co‐kneader: A chemical engineering approach

In this article, we have studied the residence time distributions (RTD) in a modular co‐kneader. Several papers have already addressed the co‐kneader modeling and operating mode but there is still a lack of experimental data on RTD. To investigate the RTD, we have used a colored tracer dispersed in polypropylene (PP) that was injected in the flow during the compounding of neat PP. The effect of operating parameters such as temperature, feed rate, and screw configuration was investigated, focusing on the influence of mixing and conveying elements in a zone where the polymer is molten. As can be expected, results on various screw configurations show that increasing the number of kneading elements makes the RTD longer. More interestingly, for a defined set of elements, their position does not change the experimental RTD. A chemical engineering approach was used to model the RTD, with an equation derived from a cascade of continuous stirred tank reactors. The model allows to retrieve an elementary RTD for each section of a defined type of elements and to propose a law for their combination in good agreement with experiments. POLYM. ENG. SCI., 55:1237–1245, 2015. © 2015 Society of Plastics Engineers     

Residence time distributions in regions of continuous flow systems

The mean residence time of material in any arbitrarily defined internal region of a continuous flow system is shown to equal the holdup in that region divided by the flow rate through the system as a whole: it is thus independent of the flow rate through the region itself and the manner in which the region connects with the remainder of the system. If the region is well mixed, the region residence time distribution consists of an exponential term together with an impulse at time zero.     

A comparative study of fiber breakage in compounding glass fiber-reinforced thermoplastics in a buss kneader,modular Co-rotating and counter-rotating twin screw extruders

The breakage of glass fibers was measured for several different types of continuous mixers including (i) Buss Kneader, (ii) modular intermeshing co-rotating twin screw extruder, and (iii) modular intermeshing counter-rotating twin screw extruder. Comparisons are made using different screw configurations, loadings, feeding ports, and mixing elements. Downstream feeding of glass fibers and milder screw configuration favor less breakage of glass fibers.     

Residence time distributions in mills

The determination of mean residence time is a powerful method for studying the hold-up in a cement mill, and hence whether the mill is operating in the required steel to clinker ratio. To determine the mean residence time accurately it is necessary to correct for the recycle of tracer, and a method of correction is given. Analysis of experimental residence time distributions from two large mills, (one with a circulation ratio of 9.4 the other with a circulation ratio of 1.5) indicates that the results agree with the one dimensional diffusion/mixing model, with a controlling parameter D/uL equal to about 0.07. In the first case the velocity of flow was about 6.5 ft/min and D was 16 ft/min; in the second, 5.7 ft/min and 14 ft²/min.     

Residence time distributions of a series of laminar stages

The Residence Time Distribution (RTD) of a series of j cylindrical (and “slit”) geometry vessels with laminar flow is analyzed. Fully transverse mixing at the points of connection between cells and no significant contribution of molecular diffusion to the mixing process are assumed. This model leads to a one-parameter (j) family of RTD curves, which are more asymmetric and long tailed than those predicted by the “ideal back-mix cells in series” and “axial dispersed plug flow” models.     

Residence time distributions in short tubular vessels

The results of an experimental study of the influence of vessel dimensions and fluid velocity on residence time distributions (RTD's) are presented. Length to diameter ratio (L/D) exerts the major influence on the RTD for the range of sizes and velocities studied. At L/D ≤ 2.6, the RTD resembles the response of a well stirred vessel with by-passing to a pulse signal. Both Reynolds No. (N_Re) and nozzle to vessel diameter ratio (d/D) effect the RTD. At L/D ≥ 5.2, the RTD resembles the response of stirred tanks in series to a pulse. N_Re and d/D do not effect the RTD and can be neglected for scale-up. The second and third moments of the RTD's and parameters of a finite stage model fitted to the RTD relate qualitatively to L/D, d/D and N_Re, but neither the moments or the particular finite stage model used are satisfactory for quantitative correlations.     

Residence time distributions and reaction kinetics in a fuel cell anode

A method which treats the fuel cell anode as a chemical reactor is developed to predict fuel cell performance. The method is based on experimentally measured residence time distribution parameters and differential cell kinetic data. The apparatus and experimental technique used to obtain the gas-phase residence time distributions are described. Kinetic data obtained from differential cell tests of the electrodes are used to evaluate an empirical rate expression.Axial dispersion model solutions for flow with volume change are obtained, based on the measured Peclet numbers and empirical rate expressions, and compared with experimental data from operating large high-temperature molten carbonate fuel cells. Agreement between the model and the experimentally determined data is very good, but only for low conversions of the fuel.Notation A cross-sectional area, cm² - C concentration of hydrogen. (g mole/cm³) - c=C/C _o dimensionless concentration of hydrogen - D dispersion coefficient cm²/s - d _e equivalent diameter, cm - F Faraday's constant - I total current, A - J current density, mA/cm² - k reaction rate constant, appropriate units - L length, cm - M number of moles - N =D/UL dispersion number - n order of reaction - n _e number of electrons transferred - –r rate of reaction based on volume of fluid, moles of reactant reacted/ cm³ s - S _e surface of electrode, cm² - T absolute temperature, °K - mean residence time, s - U velocity component in Z direction, cm/s - u = U/U ₀ dimensionless velocity - V _a volume of system, cm³ - V operating voltage, V - v volumetric flow rate, cm²/s - fractional conversion, degree of conversion of hydrogen - y mole fraction of hydrogen - Z space coordinate, cm - z =Z/L fractional length Greek letters coefficient of expansion - _m molar density of fuel, g mole/cm³ - overvoltage, V - dimensional variance, s² - ² dimensionless variance - =V_a/v ₀ space time, s     

Residence time distributions in systems with internal reflux

A general method for calculating residence time distributions for systems with internal reflux is described. The method allows the derivation of the Laplace transform of any system composed of mixed vessels with both forward and backward flow between them. In particular, the properties of a linear cascade of mixed vessels with forward and backward flow between the vessels is discussed.     

Residence time distributions in discrete recycle systems with crossmixing

An analysis is given of the moments and residence time distributions of a discrete recycle-crossflow model which can be used to account for departures from perfect mixing in stirred tank reactors. The model, which includes the continuous recycle-crossflow model of Hochman and McCord [2] as a special case, contains the number of stages N as an additional parameter. It is particularly useful in situations in which N is small or is known from prior information. Residence time distribution functions of the discrete recycle-crossflow model are also synthesized from known distribution functions of its components using a network decompositions approach. The problem structure disclosed in the analysis and sysnthesis can greatly facilitate conversion and yield calculations at a later stage. Model verification and parameter estimation are briefly discussed in this paper.     

小型气-液-固流化床液相的停留时间分布

采用脉冲示踪技术,研究了3 mm床径的小型气-液-固流化床内液相停留时间分布。以KCl为示踪剂,液相为去离子水,气相为空气,固相为平均粒径0.123~0.222 mm的玻璃微珠和氧化铝颗粒,测量流化床出口液相的电导率,得到其停留时间分布曲线。结果表明,增大表观液速和表观气速,分布曲线变窄,平均停留时间缩短,Peclet数增大;固相的存在使液相的平均停留时间增长。表观液速1.96~15.70 mm×s^-1,表观气速1.18~1.96 mm×s^-1的条件下,流动接近层流;平均停留时间的范围为（19.6±0.34）s~（48.0±0.92）s,建立的Pe经验关联式对实验结果有较好的预测,偏差在±25%以内。研究结果对于小型三相流化床的设计放大具有指导意义。     

Residence time distributions of power law fluids in motionless mixers

Motionless mixers, which are also known as static mixers, can often be modeled as open, circular tubes with parabolic velocity distributions except at a few isolated planes where radial mixing occurs via an instantaneous coordinate transformation. The extension of this idea to the processing of non-Newtonian fluids is straightforward. The parabolic velocity distribution is replaced by whatever fully developed velocity profile is appropriate for the fluid. Experimental confirmation is given for the flow of carboxymethylcellulose solutions through motionless mixers of the Kenics variety. A previous observation that four Kenics elements are equivalent to one plane of complete radial mixing holds for these power law fluids as well as for Newtonian fluids.     

Residence time dependence of molecular weight distributions in continuous polymerizations

Residence time distribution (RTD) is a spectral property of contiuous chemical reactors. Batch reactors may be viewed as having “monodisperse” residence time distributions. This article discusses molecular weight distributions (MWDs) of polymeic materials formed in continuous and in semicontinuos process and how they are affected by reaction time distributions. All synthetic high polymers, even those Prepared in batch reaction, possess a MWD which may sometimes, for a given monomer, be altered chemically by a proper choice of catalyst and diluent. An interesting concept suggested by the present work is the prospect of “tailoring” the MWD for a given monomer-catalyst-diluent system physically by selecting appropriate reactor conditions. Hence, althought this work involves analysis the results may provide a guide to synthesis.     

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.     

Residence time distribution of plug flow in a finite packed-bed chemical reactor

The residence time distributions in a finite packed-bed chemical reactor under plug flow conditions have been studied. Analysis was performed upon the well-known axial dispersion model in one dimension. Of paramount importance it was to construct a high order approximate solution to the corresponding initial-boundary value problem which appeared to be extremely convenient for fast numerical calculations. To this purpose singular perturbation techniq were applied using the reciprocal of the Péclet number as a small parameter. An error analysis was subsequently established for the special case of a pulse-function tracer input. The so-called “tailing phenomenon” of the response curve was simulated by an appropriate parameter-depending boundary condition of diffusion type.     

Residence time effects during capillary flow of a rigid PVC formulation

A typical rigid PVC formulation was rheologically characterized using capillary and parallel plate rheometers within regular processing temperatures and deformations. At 190°C and in an intermediate range of shear rates (10 to 100 l/s) the stress response was a function of the flowing time in the capillary. This behavior was not observed at other temperatures (170 and 210°C). Small amplitude oscillary shear experiments for the same compound but with various thermomechanical histories showed a different behavior as compared to the results of the capillary flow. The specific results of the capillary experiments are consistent with the hypothesis of particulate flow of PVC and also point out the influence of the stabilizers and lubricants in the flow behavior of the compound. The time dependent effect is analyzed in terms of the coupling of thermal and mechanical stresses with the unmelted particles present in the flow field.     

Residence time distribution in continuous flow stirred tank reactors

Numerical values of the cumulative residence time distribution in a continuous flow stirred tank reactor are commonly required. It is shown in the paper that the above distribution is easily transformed into a Chi-squared distribution. This provides a fast easy way of obtaining the desired values from readily available statistical tables.     

Residence time distributions in a fluidised bed in which gas adsorption occurs: stimulus-response experiments

This paper describes stimulus-response experiments with a fluidised bed of porous cracking catalyst in which two tracer gases, one adsorbable and one non-adsorbable, were used. It is shown that the moments of the response curves are strongly dependent on the degree of adsorption of the tracer gas, and that with an adsorbable tracer the dense phase gas is almost completely mixed at gas velocities in excess of 3.3 μ_mf.     

Residence time distributions with a radiotracer in a hydrotreating pilot plant: Upflow versus downflow operation

The objective of the present work is to determine the influence of the two-phase flow direction in hydrotreating bench scale plants on the axial dispersion of the liquid phase. Residence time distribution experiments under ambient conditions in cocurrent upflow and in cocurrent downflow are carried out in a catalytic hydrotreating bench scale plant, which contains a thermowell. Particles that are representative of a commercial catalyst are used. The fluids and flow rates are chosen in order to simulate deep desulfurization conditions of a straight-run gas oil. In order to determine the axial dispersion only within the bed of particles, a radioactive tracer is used.The hydrodynamic parameters are identified using an axial dynamic piston dispersion model. The liquid axial dispersion is found to be significantly higher in the downflow mode than in the upflow mode. The values of the upflow liquid saturation are in a good agreement with the values found in the literature whereas the downflow liquid saturation is lower.Simulations with a multiphase model indicate that the difference of the axial dispersion might have a significant influence on the hydrodesulfurization performances.     

Residence time distributions of gases in lab-scale polymer electrolyte membrane fuel cells (PEMFC)

The paper was aimed at modelling hydrodynamics in lab-scale polymer electrolyte fuel cells, more particularly in the distribution plates. Residence time distributions (RTD) were measured in a wide range of flow rates, using UV absorption of ozone injected as a tracer in the cell. The volume of the inlet and outlet systems, being of the order of the volume of the gas circuit machined in the distribution plates, was taken into account in calculations. Hydrodynamic behaviour of two flow patterns of the commercialised fuel cell investigated was successfully described using ideal reactor models.