Manual Tracer Technology: Modeling the Flow of Fluids: 96 (Fluid Mechanics and Its Applications)

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Flow of fluids through porous materials. Aspects of Physical Biology. Elements of Physical Biology. These industries are widespread internationally and are of considerable economic and environmental importance. Moreover, according to the IAEA [ 2 , 3 ], radiotracer techniques have many advantages, such as high detection sensitivity, in-situ detection, availability of a wide range of compatible radiotracers for different phases, rapid response and high reliability, and accuracy of results.

The measurement of homogeneous mixing efficiency is one of the main applications of radiotracers in the industry. Mixing involves the blending of two or more miscible fluids to obtain a predetermined degree of homogeneity. Stirred tanks are widely used in the process industries to perform many different operations, including the blending of miscible liquids into a single liquid phase, the suspension of solids, the promotion of heat and mass transfer, gas-liquid and liquid-liquid mass transfer, crystallisation, and chemical reactions [ 8 , 9 ].

Several objectives must be fulfilled when a mechanically stirred vessel is used.

1. Introduction

Some of these objectives include the homogenisation of single or multiple phases at a specific temperature and concentration of components, which can be affected by the physical properties of the fluids that are being mixed. According to Shekhar and Jayanti [ 10 ], the main requirement of the mixing process is to combine two or more fluids that are initially separated. Rahimi and Parvareh [ 8 ] observed that, in the liquid phase, the use of impellers and jets are two established methods for fluid homogenisation.

Moreover, in the chemical, mineral, and wastewater treatment industries, mechanically stirred tanks are widely used for either simple liquid mixing or for more complex multiphase processes, such as gas-liquid or gas-liquid-solid mixing. Aubin et al. Thus, Montante and Magelli [ 12 ] suggested an investigation of the flow field that is established in a stirred vessel because it is the most important characteristic of the stirred tank reactor in the processes in which the flow field can affect the homogenisation level. Static mixer, another mixing related service of motionless pipeline devices, is widely used throughout the chemical and hydrocarbon processing industries.

This type of mixer is very powerful in the pipeline mixing and is a very dominant option for the laminar flow regime. High reliability over a broad range of flow conditions is achieved when a properly designed static mixer is in operation. Nevertheless, most industrial mixing processes take place in tanks or vessels. Thus, this paper is only concerned with mixing operation in the mixers or vessel. The residence time distribution RTD is one of the important parameters that can provide information on the characteristics of the reactor, such as the flow pattern that occurs [ 13 ].

Tracer technology : modeling the flow of fluids

The RTD, which was first developed by Danckwerts [ 14 ] has been utilised by many researchers to diagnose possible system malfunctions, such as bypassing, leakage, blockage, channel fouling, and backmixing, and to help estimate the quality of mixing. The RTD, which depends on the flow hydrodynamics and the reactor geometry, influences the chemical reactor performance by affecting a number of reaction properties, such as the conversion and yield.

The RTD can be measured by evaluating the concentration of a tracer compound, which is added as a stimulus at the system inlet. Stegowski and Furman [ 15 ] described the fundamentals of the RTD measurement set up, which is illustrated in Figure 2. The RTD curve of a radiotracer experiment is considered measurable after treatment of the raw data.

The treatment of the data involves background correction, radioactive decay correction, starting point correction, filtering, and data extrapolation [ 16 ]. Moreover, according to Ding et al. Levenspiel [ 18 ] mentioned that the quantified RTD can provide a numerical characterisation of the mixing in a reactor, which helps the process engineer better comprehend the mixing performance of the reactor.

In addition, Ding et al. In addition to the RTD, the mixing time is an important parameter that can be used to determine the homogenisation that occurs in a mixing vessel [ 16 , 19 ]. There are many definitions of mixing time, which depend on the selected measurement technique. Jafari and Mohammadzadeh [ 20 ] defined mixing time as the period of time necessary for a system to achieve the desired level of homogeneity in a given vessel, whereas Bujalski et al.

Pramparo et al. The tracer can be a chemical species, any substance that can be tracked, or a thermal disturbance, and the measurement techniques that have been used include liquid crystal thermograph, visual observation [ 21 , 25 ], conductivity, and laser-induced fluorescence [ 24 , 26 , 27 ].

Extensive studies have been conducted to study the efficiency and flow characteristics of mixing vessels using a nonradiotracer approach. The techniques have been successfully implemented and published, but there are some discrepancies when these are compared with radiotracer techniques. Jafari and Mohammadzadeh [ 20 ] and Wang et al. These researchers found large deviations in the mixing time between the different measurement locations and detection methods used and concluded that the mixing time was dependent on the location and the detection of the tracer.

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According to them, this phenomenon was due to the removal of small vortexes, which increases the circulation speed of the liquid vortex. Correlation of the mixing time with the impeller speed by Pramparo et al. There is another drawback associated with the use of nonradioactive tracers. Delvigne et al. However, due to the size constraint of the probe, which was 0. Another technique for the measurement of the mixing time is the use of reagent visualisation. Wabo et al. Wabo and his coworkers also used the electrical resistance tomography ERT system following the adjacent pair protocol to visualise the fluid mixing during a chemical reaction.

They concluded that ERT can suitably image the mixing of reactive tracers and therefore serve as a potential method for quantification of the macrosegregation of reagents in 3D. A total of 16 equally spaced electrodes were used in this study for the current injection; these form a peripheral ring with the 15 voltage pair measurements, as shown in Figure 5. Arratia et al. In addition, the use of these probes involves a complex setup procedure, as described by Wabo et al. Therefore, the use of a radiotracer is the preferred stimulus response technique because of its noninvasive application and online monitoring systems, which avoid the shutdown of the plant.

In addition, Pant and Yelgoankar [ 19 ] also declared that radiotracers often have no competing alternative for troubleshooting full-scale industrial reactors. Thus, the integration of radiotracers with computer simulations resolves the previously mentioned problems. Visualized acid-alkali reactive tracer mixing using the caustic soda-hydrochloric acid-phenolphthalein system conducted by Wabo et al. The 8-plane, electrode tomography sensor system fitted for ERT measurement by Wabo et al.

It helps in troubleshooting reactors and characterises the macromixing and flow within a reactor [ 24 ]. The detected signal is normalised by dividing it by the area under the curve, as shown in 1. The mathematical expression for the first moment in discrete form can be written as follows:.

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  7. Nevertheless, these results should be treated to remove any noises. These models contain many parameters, including the mean residence time, exchange and bypass flow rates, and volume of the dead zone, which can be varied to fit the experimental data. Octave Levenspiel: Books

    Nevertheless, the models mentioned above do not consider the flow field within the reactor, which results in nonideal behaviour. Levenspiel [ 18 ] also noted that there are two commonly cited methods for analysing the RTD curve; these are the dispersion model and the tanks-in-series model. Burrows et al. The dispersion model is based on the ideal plug flow and accounts for the deviations from the ideal flow that is caused by backmixing or random fluctuations. The dispersion number is calculated from the variance of the RTD curve, as shown below:.

    According to Levenspiel [ 18 ] a large dispersion number greater than 0. Additionally, Burrows et al.

    There are several different correlations that can be used for the prediction of the mixing time in an agitated vessel, which achieve a certain degree of mixture uniformity. Pant et al. Moreover, Pant et al. Bujalski et al. The normalized tracer concentration indicates that each collected data were divided by summation of collected data as the denominator. Nevertheless, the values greater than one were due to fluctuations of parasitic signals which were not eliminated or treated earlier as suggested by IAEA and Kasban et al.

    Moreover, Pramparo et al. The above correlations were derived by Zadghaffari et al. A graphical representation of t 90 mixing time using the simulated concentration response by Bujalski et al. Time evolution of the normalized concentration averaged on the monitor surface by Pramparo et al. Extensive radiotracer experiments have been carried out successfully in various industries, which indicate the survival and reliability of radiotracers in hostile environments. To verify its feasibility, the IAEA has developed six mathematical models to analyse the experimentally obtained radiotracer curves.

    The six proposed models are the axial dispersion plug flow model, the axial dispersed plug flow with exchange model, the perfect mixers in series model, the perfect mixers in series with exchange model, the perfect mixers in parallel model, and the perfect mixers with recycle model [ 3 , 16 ]. The optimised model curve that best fits the experimental curve is chosen. A series of radiotracer experiments for the measurement of the RTD, mixing time, and flow rate was conducted by Kasban et al.

    Four paddle impellers were installed and pretreatment of the raw data was carried out using Matlab. A flow rate of approximately 8. The authors concluded that the speed of the impeller affects the mixing time required for the system to reach homogeneity.

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    However, the authors did not describe the calculation of the mixing time or the malfunction that was identified from the findings. They also did not accurately describe the RTD experimental setup and the mixing time measurement. In addition, the authors did not clarify the impeller size and geometry and the parameters used in the mixing process optimisation.