Application of residence time distribution technique to the study of the hydrodynamic behaviour of a full‐scale wastewater treatment plant plug‐flow bioreactor

The hydrodynamic behaviour of a full‐scale wastewater treatment plant (WWTP) bioreactor treating municipal wastewater, situated in Granollers (Barcelona, Spain), has been studied by means of a residence time distribution (RTD) technique using lithium (chloride) as tracer. The bioreactor studied is designed to work as a plug‐flow reactor and it is divided into two independent lanes (1 and 2), each one composed of four compartments in series resulting in a total volume of 3970 m³ per lane. During the RTD experiments, working flow was 1000 m³ h^?1 per lane, which implied an ideal mean residence time of 3.97 h. When a lithium chloride tracer was injected in the bioreactor, both lanes showed a similar highly non‐ideal hydrodynamic behaviour, which had an important effect on the reactor's performance. This global RTD was complemented by means of local RTDs in different locations of the bioreactor in order to determine qualitatively the reactor's mixing regime. Different non‐ideal models (namely axial dispersion, tanks‐in‐series and some simple compartment models) have been tested for the modelling of the experimental RTD. The best model fitting RTD data for Lanes 1 and 2 was a configuration consisting of four mixed tanks in series. The RTD study proposed in this work will permit improvement of the reactor's mixing performance, which is of special interest in future projects including simultaneous removal of carbon, nitrogen and phosphorus. Copyright © 2005 Society of Chemical Industry     

Residence Time Distribution Models Derived from Non‐Ideal Laminar Velocity Profiles in Tubes

The theoretical E‐curve for the laminar flow of non‐Newtonian fluids in circular tubes may not be accurate for real tubular systems with diffusion, mechanical vibration, wall roughness, pipe fittings, curves, coils, or corrugated walls. Deviations from the idealized laminar flow reactor (LFR) cannot be well represented using the axial dispersion or the tanks‐in‐series models of residence time distribution (RTD). In this work, four RTD models derived from non‐ideal velocity profiles in segregated tube flow are proposed. They were used to represent the RTD of three tubular systems working with Newtonian and pseudoplastic fluids. Other RTD models were considered for comparison. The proposed models provided good adjustments, and it was possible to determine the active volumes. It is expected that these models can be useful for the analysis of LFR or for the evaluation of continuous thermal processing of viscous foods.     

Hydrodynamic Behavior and Residence Time Distribution of Industrial‐Scale Bale Packings

The hydrodynamic behavior of bale packing was tested in a catalytic distillation column. Models and empirical equations for predicting pressure drop and dynamic liquid holdup were proposed and compared with experimental results. The examination of residence time distribution (RTD) relied on the pulse method and a conductivity meter which deduced the axial Péclet number, axial dispersion coefficient, and dynamic liquid holdup. The relations of dynamic liquid holdup obtained from gravimetric draining experiments and RTD studies were discussed with static and total liquid holdup. Potential impacts of the liquid distributor and conductivity cell were also assessed. The results prove that models and empirical equations fit well and are reliable in design and scale‐up.     

多段多点进料搅拌设备的停留时间分布与返混特性

本文对多段多点进料均相系统建立了两种进料分别脉冲时的停留时间分布模型,给出平均停留时间和方差计算式。在四段实验设备内测定了停留时间分布,并估算出段间返混流率。对无因次返混流率与操作参数和几何参数进行了关联。     

A study of residence time distribution in co‐rotating twin‐screw extruders. Part II: Experimental validation

In the first part of this paper, a new approach to model the residence time distribution (RTD) in a co‐rotating twin‐screw extruder was proposed. It consists of coupling a continuum mechanics approach with a chemical engineering one, yielding an RTD curve without any fitting parameter. However, the choice of ideal reactors that depict the behavior of each particular profile is not evident. In this second part, we present an experimental study based on two types of extruder (Leistritz 30–34 and Clextral BC45), different screw profiles and two measurement techniques (off‐line and in‐line). Global, partial and local RTD curves were obtained, both experimentally and by means of a deconvolution technique. This series of experiments permitted the definition of the best association between ideal reactors and screw elements. Using this association, a comparison has been made between experimental results and theoretical calculations. A good agreement was generally obtained in terms of the RTD shape, delay time, mean residence time and variance.     

Hydrodynamic behaviour of a full‐scale anaerobic contact reactor using residence time distribution technique

BACKGROUND: The knowledge of the fluid pattern of full‐scale anaerobic reactors is of fundamental importance for the optimisation of biological processes. High solids concentrations often lead to inefficient mixing conditions, which may reduce treatment capacity due to heterogeneity within the biomass. RESULTS: The hydrodynamic characteristics of a full‐scale anaerobic contact reactor treating evaporator condensate from a sulphite pulp mill were investigated. The methodology applied was based on the residence time distribution (RTD) technique using lithium as a tracer. Different non‐ideal hydraulic flow models were tested and the best model fitting RTD data was the Gamma distribution model with by‐pass. It was concluded that the full‐scale bioreactor presents a good degree of mixing with about 22% of non‐effective volume due to the presence of high amounts of inorganic materials. CONCLUSION: As a result of this study it was possible to both improve the full‐scale bioreactor performance and decrease the running costs by changes in the plant operation strategies which allowed reduction of the huge amount of inorganic materials contributing to the non‐effective volume. The methodology is simple and results from a unique RTD experiment and confirms the importance of considering mixing characteristics when assessing complex full‐scale treatment processes. Copyright © 2009 Society of Chemical Industry     

A study of residence time distribution in co‐rotating twin‐screw extruders. Part I: Theoretical modeling

A theoretical model to determine the residence time distribution (RTD) in a co‐rotating twin‐screw extruder is proposed. The method consists of coupling a continuum mechanics approach with a chemical engineering one and allows us to obtain the RTD without any adjustable parameter. The process parameters are obtained using Ludovic® twin‐screw modeling software, and ideal reactors are chosen to depict the screw profile. The influence of screw speed, feed rate and viscosity on RTD are described on a fictive screw profile. The predictions of the model are in qualitative agreement with literature data. The key point of this procedure is obviously the correct association between an ideal reactor and a screw element.     

Particle Flow Modelling in Slurry‐Fed Stirred Vessels

Despite its importance, experimental information on the Residence Time Distribution (RTD) of solid particles in continuous‐flow stirred vessels is still scant. In this work, experimental data on particle RTD in a high‐aspect‐ratio vessel stirred by three equally‐spaced Rushton turbines, obtained by means of Twin Systems Approach (TSA), are employed to assess the suitability of the well known Axial‐Dispersion Model to describe particle behavior in the investigated system. The data analysis and model parameter assessment are preceded by a discussion on the utility of self‐recirculated systems in carrying out experiments concerning continuous slurry‐fed apparatuses. In particular, the suitability of single recirculated systems is discussed and a way to extract numerical RTD data from the relevant experiments is proposed. The advantages and disadvantages of employing instead a couple of twin systems, as it was actually done to obtain the experimental data employed in this work, is shortly discussed.     

Gas Flow Behavior in a Two‐Phase Reactor Stirred with Triple Turbines

Gas behavior was studied in a gas‐liquid reactor stirred with multiple turbines. Triple PBTs pumping either down or up and BT‐6's were used. The behavior of coalescing (water) and non‐coalescing (sodium sulfate solution) systems was investigated. The gas phase behavior was characterized by means of the RTD and modeled with the axial dispersion model. This model was confirmed to interpret the experimental data well for water and satisfactorily for the coalescence‐inhibiting solutions. The influence of the operating conditions, turbine type and system coalescing behavior on the model parameters is discussed. Comparison is also made with similar data regarding Rushton turbines and high‐solidity ratio hydrofoils, as well as gas holdup.     

Estimation of liquid phase mixing due to solids in a turbulent bed contactor

The mixing in two-phase gas-liquid and three-phase gas-liquid-solid system (turbulent bed contactor) is evaluated through residence time distribution (RTD) studies in terms of Peclet number. RTD experiments are conducted for various gas and liquid velocities, and number of stages for two- and three-phase systems. Since the mean residence time is very short in both the systems, a mixed flow tank with exponential decay RTD is used in series. After deconvolution, the RTD of the system is obtained. The experimental RTD curves are satisfactorily compared with the axial dispersion model and Peclet numbers are evaluated for all the experiments. The axial dispersion coefficients are calculated from Peclet numbers. With this study, it is thought that liquid phase mixing may be controlled by changing the quantity of solid particles in the bed.     

Time Series Modeling of Two‐ and Three‐Phase Flow Boiling Systems with Genetic Programming

The time series of the physical parameters in boiling evaporators with vapor‐liquid (V‐L) two‐phase and vapor‐liquid‐solid (V‐L‐S) three‐phase external natural circulating flows exhibit nonlinear features. Hence, proper system evolution models may be built from the point of view of nonlinear dynamics. In this work, genetic programming (GP) was utilized to find the nonlinear modeling functions necessary to develop global explicit two‐variable iteration models, using wall temperature signals measured from the heated tube in ordinary two‐phase and three‐phase fluidized bed evaporators. The model predictions agree well with the experimental data of the time series, which means that the models established with GP can adequately describe the dynamic evolution behavior of multi‐phase flow boiling systems.     

液固搅拌槽中固、液相停留时间分布

本文以海沙和自来水为介质研究了在标准搅拌槽内影响固液两相停留时间分布的主要因素,以便比较两相之间的差异,并利用双区模型描述出口流体中固体和液体的停留时间分布。对所建立模型中的参数进行估值后,建立了模型参数与搅拌雷诺数、固体颗粒浓度及搅拌槽几何参数之间的关联式。     

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     

In‐line measurement of residence time distribution in melt extrusion via video analysis

Residence time distribution (RTD) is an important factor in melt extrusion as it strongly influences the product quality. It can cause degradation of the active pharmaceutical ingredient (API), which can be reduced by shorter mean residence times, and the content uniformity, which can be improved by broadening the RTD caused by axial mixing. In our study, we developed an inline video analysis that to date has mainly been applied offline. For extrusion, hydrophilic polymer and a surfactant were used as a molten matrix, in which an API was embedded. The video analysis consisted of four steps: (1) segmentation of the image to mask the strands, (2) calculation of average color values for the segmented pixels of each frame, (3) fitting of the obtained color curve with an analytical solution, and (4) calculating several RTD measures (e.g., the minimal and mean RT) for better comparison of the results. The RTD measures were responses in the design of experiments (DoE), which included the process parameters screw design, screw speed, and throughput. This analysis clearly showed that screw design had the strongest effect on the RTD measures. The results suggest that video analysis is a suitable tool for inline RTD measurements. POLYM. ENG. SCI., 58:170–179, 2018. © 2017 Society of Plastics Engineers     

Empirical likelihood in long‐memory time series models

This article studies the empirical likelihood method for long‐memory time series models. By virtue of the Whittle likelihood, one obtains a score function that can be viewed as an estimating equation of the parameters of a fractional integrated autoregressive moving average (ARFIMA) model. This score function is used to obtain an empirical likelihood ratio which is shown to be asymptotically chi‐square distributed. Confidence regions for the parameters are constructed based on the asymptotic distribution of the empirical likelihood ratio. Bartlett correction and finite sample properties of the empirical likelihood confidence regions are examined.     

Modeling of a cokneader for the manufacturing of composite materials having absorbent properties at ultra‐high‐frequency waves. Part 1: Modeling of flow from residence time distribution investigations

The purpose of this study is to gain better understanding of flow patterns and mixing conditions in a particular single‐screw extruder: the Buss Cokneader. To this end, the residence time distribution (RTD) of the polymer was investigated experimentally for different combinations of the operating variables (i.e. feed rate, screw rotation speed). The measurement of RTD used a standard stimulus‐response technique. Two kinds of tracer were used: free anthracene and anthracene grafted on the polymer. It was shown that only the second could characterize the actual flow of the polymer in the extruder. It does not perturb the flow and has the same rheological behavior as the studied fluid. Thanks to the RTD data, a model of the extruder based on the combination of ideal reactors, such as continuous stirred tank reactors or plug flow reactors, was finally set up. The establishment of relationships between model parameters and extrusion conditions allowed the prediction of RTD with good agreement.     

The effect of adsorption on mass transfer in fluidized bed catalytic reactors

Tracer gas residence time distributions (RTD) in a laboratory scale fluidized bed system have been measured for pulses of three different tracer gases (methane, ethane and propane) at different temperatures in the range 323 to 435 K. The fluidized solid was a commercial zeolite based FCC catalyst (CBZ‐2), and measurements were carried out in a superficial air velocity range of 0.01 to 0.04 m/s. The data were interpreted with two‐phase dense phase dispersion models for adsorptive tracers, available in the literature. In addition, modified models were considered by assuming a stationary dense phase and neglecting axial dispersion in this phase. Mean residence time, μ₁, and the variance of the residence time, σ², of RTD data were calculated for each experimental run. Applying the moment technique in the Laplace domain, the differential equations for all models considered were analytically solved. Mass transfer coefficients obtained from dynamic experiments were compared with the values estimated from the relations available in the literature. It was found that methods considering convective flux alone between the bubble and emulsion phases give closer values to the experimental ones than the methods also including the diffusive flux.     

Liquid phase residence time distribution for a two-phase countercurrent flow in a packed column with a novel internal

The liquid phase residence time distribution (RTD) for gas–liquid countercurrent flow in a packed column with a novel internal was measured by conductivity measurements and an air–water system. The RTD of a liquid tracer is well represented by the ADM and PDE models. At lower gas flow rates, the Peclet number of the liquid in the packed column with the internal is lower than that without the internal; at higher gas flow rates, it is vice versa, especially with an internal with a higher volume fraction. The distribution of the liquid RTD can be improved by using suitable geometric parameters of the internal to give a larger volume fraction and a lower stage height.     

管式反应器中Casson流体层流停留时间分布

本文对管式反应器中Casson流体层流流动的停留时间分布进行了理论分析,导出了停留时间分布密度函数的精确数学模型和简化数学模型。在较宽的参数范围内,简化模型与精确模型吻合程度较好。还得出等温管式反应器中一、二级不可逆反应的转化率计算式,并对转化率作了计算和比较。     

Advance in research on residence time distribution in mixers

研究混合器的停留时间分布对进一步研究混合器内的流型、混合等具有重要的意义。首先介绍了用于描述停留时间分布（RTD）的统计特征参量,根据测试原理及示踪剂输入方式等对停留时间的实验方法进行分类介绍。着重回顾了化学反应工程方法中RTD模型的发展,对有关RTD流场模拟中的常用模型进行了对比分析,并对统计学方法在RTD中的应用加以描述。最后展望了对上述方法在停留时间分布中的进一步应用。