Residence time distributions and basic studies of flow and melting in a modular buss kneader

Experimental studies of residence time distribution, fill factor, temperature, and melting profiles of thermoplastic resins are presented. Residence time distributions were determined as a function of throughput and screw speed. The melting of polypropylene and low density polyethylene in the entrance region was investigated. Fill factor and temperature profiles are reported.     

Experimental methods in chemical engineering: Residence time distribution—RTD

Reactor performance, solids-(gas)-mixing, flow through porous media, distillation columns, or through granulators improve as the fluid dynamics approach ideal plug flow. The residence time distribution (RTD) is a diagnostic measure of how close fluid flow approaches ideal conditions. The technique introduces a step change to the inlet concentration—a Dirac-δ function, Heaviside step function, or a rectangular pulse (bolus)—while high frequency detectors monitor the concentration along the vessel and/or at the exit. The effluent concentration profile spreads due to the variance in the process lines leading to the vessel and at the exit, the detector response, and the system. We quantify how much each of these contributes to the overall variance in a fluidized bed with 9 g of fluid cracking catalyst in 8 mm diameter quartz tubes. The injection variance is lowest for a GC sample loop configuration, compared to a 3-way valve or 4-way valve geometry. RTD measurements detect bypassing due to dead zones in vessels and the axial-dispersion model and continuous stirred-tank model to characterize deviation from plug flow. However, when the contribution to variance from the ancillary lines and detector is large compared to the system, the uncertainty in the model parameters is high. Research on RTD fundamentals concentrate on boundary conditions while, here, we focus on experimental errors: mechanical, physicochemical mathematical, and instrumental.     

A transport-oriented approach to residence time distributions and two-phase chemical reactors

This paper focuses on two-phase (e.g., fluid-solid catalyst) chemical reactors where one phase participates in the feed and effluent, first order chemical reactions proceed in the other phase and linear, species-dependent, interphase transport connects the phases. A class of reactors exists in which the Laplace transform of the dynamic reaction/interphase transport equations reduces to essentially that of an effective set of first order reactions amongst effluent phase species only, in an imaginary single phase reactor. This result bears on scale-up: Since the imaginary reactor simply scales with the usual residence time distribution, so too do reactors of this class scale with its analog. This easily measurable analog turns out to be just the non-adsorbing tracer experiment. Significantly, certain reactors outside of this class do not scale likewise, even with first order chemistry; an example illustrates. The class in question includes, but is not limited to, fixed bed and Berty (CSTR) reactors. The analysis allows design inferences for two-phase reactors, including fluidized beds.     

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 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 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     

Influence of the melt viscosity and operating conditions on the degree of filling,pressure, temperature,and residence time in a co‐kneader

The effect of the melt viscosity and operating conditions on processing parameters in a co‐kneader with a discharge die was experimentally investigated. Filling ratio, pressure, temperature, and residence time distribution were measured. Experiments were performed with polypropylene resins. The viscosity of the melt was varied either by changing the regulation temperature of the kneader or the molecular weight of the polymer. The filling pattern in the co‐kneader shows the conveying capability of the various elements without any effect of the melt viscosity. Experimental residence time distributions remain the same at a given feed rate and screw speed, regardless of the viscosity of the material. The global degree of filling in a zone combining conveying elements, kneading elements, and restriction ring was found to be nearly constant in the conditions of this study and therefore a simple relation exists between the mean residence time and the feed rate. Beside expected variations of the die pressure and melt temperature when the viscosity, screw speed or feed rates change, a model based on heat equation and experimental data demonstrate the high capability of the co‐kneader for heat exchange and for the control of self‐heating during mixing. POLYM. ENG. SCI., 58:133–141, 2018. © 2017 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.     

Magnetic nanowire synthesis: A chemical engineering approach

Bimetallic one‐dimensional cobalt–nickel magnetic nanowires capped on both sides with conical heads were synthesized using the polyol process. Then, the process was scaled up to produce magnetic nanowires in sample aliquots of approximately 20 g. The scale‐up strategy involved improving the mixing reagents using either axial or radial mixing configurations and was experimentally validated by comparing the structural and magnetic properties of the resulting nanowires. The results indicated a connection between the flow patterns and the size and shape of the nanowires. When a Rushton turbine was used, shorter nanowires with unconventional small heads were obtained. Because the demagnetizing field is strongly localized near or inside these heads, the coercive field was enhanced nearly twofold. These results were confirmed by micromagnetic simulations using isolated nanowires. In addition, the development of flow patterns at the small and pilot scales was predicted and compared using three‐dimensional turbulent computational fluid dynamics simulations. © 2014 American Institute of Chemical Engineers AIChE J, 61: 304–316, 2015     

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.     

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 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.     

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.     

Experimental methods in chemical engineering: Micro‐reactors

Whereas the bulk chemical industry has historically sought economic advantage through economies of scale, a paradigm shift has researchers developing systems on smaller scales. Nano‐cages and nano‐actuators increase selectivity and robustness at the molecular scale. In parallel, micro‐contactors with sub‐millimetre lateral dimensions are decreasing boundary layers that restrict heat and mass transfer and thus meet the objectives of process intensification with great increases in productivity with a smaller footprint. These contactors continue to serve chemical engineers and chemists to synthesize fine chemicals and characterize catalysts; however, they have now been adopted for sensors in biological and biochemical systems. A bibliometric analysis of articles indexed in the Web of Science in 2016 and 2017 identified five major clusters of research: catalysis and bulk chemicals; nanoparticles; organic synthesis and flow chemistry; systems and micro‐fluidics applied to biochemistry; and micro‐channel reactors and mass transfer. In the early 1990s, less than 100 articles a year mentioned micro‐reactors, while over 943 articles mentioned it in 2017. Here, we introduce micro‐reactors and their role in the continuous synthesis of fine chemicals across the various scales to commercialization.     

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.