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1

A sensitivity analysis of kinetic characterizations in continuous flotation circuits under moderate deviations with respect to perfect mixing

Vinnett Luis, Pino-Muñoz Catalina A., Yianatos Juan, Díaz Francisco, Henríquez Felipe

Physicochemical Problems of Mineral Processing

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2022

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Vol. 58, iss. 5

art. no. 152420

EN

This paper studies the effect of moderate deviations with respect to perfect mixing on the estimated kinetic parameters in industrial flotation banks. Radioactive tracer tests and mass balance surveys were performed to characterize the mixing regimes and Cu kinetic responses. For three models (Single Rate Constant, Rectangular and Gamma), two approaches to incorporate the residence time distributions (RTD) in the kinetic characterizations of rougher banks were compared: (i) RTDs measured from the radioactive tracer tests; and (ii) pure perfect mixing in each flotation machine. The measured RTDs did not present significant bypass in the evaluated banks. In all cases, comparable model fitting was obtained with both RTD approaches, which indicates that the kinetic models add sufficient flexibility to compensate for moderate biases in the mixing regime. The studied kinetic models showed non-significant differences in the estimated maximum recoveries (R∞), mean (kmean) and median (k50) rate constants when comparing the process modelling from measured RTDs and pure perfect mixing. However, the Gamma model was more sensitive to the RTD assumption in terms of the shapes of the flotation rate distributions. From the results, kinetic characterizations focused only on model fitting, or on R∞ and kmean (or k50) estimations have low sensitivity to the assumption of perfect mixing when the RTDs present moderate deviations with respect to this regime. Special attention must be paid when characterizing floating components as the perfect mixing assumption may bias the shapes of the flotation rate distributions.

2

Modeling and simulation of vertical roller mill using population balance model

Fatahi Rasoul, Barani Kianoush

Physicochemical Problems of Mineral Processing

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2020

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Vol. 56, iss. 1

24--33

EN

There are few studies concerning the process simulation of vertical roller mills (VRMs). In this research work, the application of population balance model for simulation of a VRM in a cement clinker grinding circuit was investigated. The residence time distribution (RTD) was measured, and the tank-in-series and Weller models were employed to describe the residence time distribution. Two sampling surveys were carried out on the VRM circuit. The data from the first survey were used for model calibration, and the specific breakage rates were back-calculated. The model parameters obtained were used for simulation of the second survey, and validation of the model. The results showed that the clinker particle spent a short time inside the VRM and the mean residence time is about 67s. The tanks-in series model compares to Weller model was more proper to describe the residence time distributions in the VRM. The simulation results showed that the specific breakage rates increased with increasing particle size. However, the particles larger than 25.4 mm particles sizes are too large to be properly nipped by master rollers. Finally, it can be concluded that the grinding process of the VRM is very well-predictable with the population balance model.

3

Application of Twin Screw Extrusion for Continuous Processing of Energetic Materials

Dombe G., Mehilal D., Bhongale C., Singh P. P., Bhattacharya B.

Central European Journal of Energetic Materials

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2015

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Vol. 12, no. 3

507--522

EN

Continuous processing of energetic materials using a twin screw extruder is gaining importance as it is a safe and cost-effective alternative to conventional batch processing. The continuous process based on a twin screw extruder combines the capabilities of intensive mixing and high pressure extrusion. It is used for processing a variety of energetic materials, such as gun and rocket propellants, plastic bonded explosives, pyrotechnics, thermo-baric explosives, etc. The twin screw extruder process demands various safety features for the processing of energetic materials. Therefore, exhaustive characterisation of the energetic materials in terms of safety and rheology, coupled with characterisation of the mechanical components of the extruder, are essential for designing a safe continuous process. In this article, a technological overview of continuous processing for energetic materials is presented, along with its various features, process design methodology and safety issues.

4

Numerical Investigation of the Hydrodynamic Conditions in A Multi-Strand Cc Tundish with Closed Outlets

Merder T.

Archives of Metallurgy and Materials

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2014

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Vol. 59, iss. 3

887--892

EN

In industrial conditions there are situations when the CC machine works under emergency. It can be result of mechanical or electrical causes, breakout of billet or problem with supplying new parts of liquid steel to the CC machine. As a consequence one or two outlets of the tundish should be closed. However, closing one of the outlets influences the hydrodynamic and thermal conditions occurring in the tundish. Thus, the important information is which of the outlets should be closed to conduct further continuous casting process correctly. The following research was conducted to analyze the influence of liquid steel flow behaviour in the multi-strand tundish when all outlets do not work. Such problem was solved by means of numerical methods based on Navier-Stokes equations (k–ɛ standard turbulence model). Numerical simulations were done using the educational version of CFD program (Computational Fluid Dynamics) – ANSYSFluent. As a result forecasted velocity fields and RTD curves (Residence Time Distribution) were obtained. RTD characteristics were used to determine kinetics of liquid steel mixing and also to calculate parts of particular flow areas for studied cases.

PL

W warunkach przemysłowych zdarzają się sytuacje, kiedy maszyna COS pracuje w stanie awaryjnym. Wynikać to może z powodu usterek mechanicznych lub elektrycznych, przerwania wlewka ciągłego lub być wywołane dostarczeniem nowej partii ciekłej stali na stanowisko COS. Prowadzi to do zamknięcia jednego lub dwóch wylewów w kadzi pośredniej. Zamknięcie któregokolwiek z wylewów wpływa na warunki hydrodynamiczne i termiczne panujące wewnątrz kadzi. Istotną informacją jest więc to, które z otworów wylewowych powinny być zamknięte, aby proces ciągłego odlewania przebiegał prawidłowo. Niniejsze badania mają na celu analizę wpływu zachowania przepływu ciekłej stali w wielowylewowej kadzi pośredniej, kiedy nie pracują wszystkie otwory wylewowe. Tak postawiony problem rozwiązywano metodami numerycznymi opartymi na równaniach Naviera-Stokesa przy użyciu modelu turbulencji standard k–ɛ. Symulacje numeryczne przeprowadzono z wykorzystaniem edukacyjnej wersji programu CFD (Computational Fluid Dynamics) – ANSYSFluent. W wyniku obliczeń numerycznych otrzymano prognozowane rozkłady pól prędkości i krzywe RTD (Residence Time Distribution). Opracowane charakterystyki RTD posłużyły do określenie kinetyki mieszania stali, oraz wyliczenia udziałów poszczególnych stref przepływu dla rozpatrywanych przypadków.

5

Experimental study and mathematical modeling of the residence time distribution in magnetic mixer

Rakoczy R., Kordas M., Grądzik P., Konopacki M., Story G.

Polish Journal of Chemical Technology

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2013

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Vol. 15, nr 2

53--60

EN

This study reports on research results in the field of a mixing process under the action of a transverse rotating magnetic field (TRMF). The main objective of this paper is to present the effect of this type of a magnetic field on residence time distribution (RTD) measurements. This paper evaluates the performance of a magnetic mixer by comparing the results of an experimental investigations in a pilot set-up and theoretical values obtained from mathematical model. This model consisting of the set of ideal continuous stirred tank reactors (CSTR) fitted well the experimental data.

6

Simulation of Residence Time Distribution and Mixing in Reactors with Recirculation using 2D Approach

Zima P.

TASK Quarterly : scientific bulletin of Academic Computer Centre in Gdansk

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2011

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Vol. 15, No 3-4

297-315

EN

In this paper, we propose a 2D approach in order to create a mathematical model for the determination of the residence time distribution for a flow reactor with recirculation. Apart from characterizing the functional residence time distribution, this model can help improve the operation of the reactor at the design stage. The mathematical model was validated by comparison with experiments carried out in a hydraulic laboratory.

7

Charakterystyka strefy przejściowej kadzi pośredniej typu "delta"

Mender T., Jowsa J., Wierzcha M., Misiak A.

Hutnik, Wiadomości Hutnicze

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2007

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Vol. 74, nr 8

398-402

PL

W artykule przedstawiono analizę warunków hydrodynamicznych i przejściową strefę mieszania dla przemysłowej kadzi pośredniej typu "delta". Dla oceny warunków kształtowania się przejściowej strefy mieszania przeprowadzono badania zmiany stężenia pierwiastków znacznikowych w trakcie odlewania stali. Na podstawie otrzymanych danych uzyskano charakterystyki opisujące strefę przejściową.

EN

The article presents an analysis of hydrodynamic conditions and the transient mixing zone for industrial "delta "-shaped tundish. To evaluate conditions of transient mixing zone forming ezamination for the change of marker elements concentration during steel casting was performed. On the basis of results charakteris tics describing the transient zone have been obtained.

8

Charakterystyki mieszania podczas odlewania stali przy użyciu sześciowylewowej kadzi pośredniej

Jowsa J., Merder T., Bogusławski A., Mendrek A.

Hutnik, Wiadomości Hutnicze

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2005

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Vol. 72, nr 7-8

377-383

PL

Kadź pośrednia stanowi nieodzowny element procesu ciągłego odlewania stali. Konstrukcja i geometria obiektu decydują o warunkach hydrodynamicznych przepływającej stali. Warunki te kształtują proces przejściowego mieszania stali oraz w różnym stopniu wpływają na proces flotacyjnego usuwania wtrąceń niemetalicznych. Charakterystyka ruchu metalu i procesu mieszania może być odwzorowana przez krzywe typu F i E. Krzywe E i F stanowią prezentację graficzną rozkładów czasu przebywania znacznika w kadzi pośredniej w zależności od przyjętej metody badawczej. Dla kadzi sześciootworowej o pojemności 15 Mg podjęto badania teoretyczne oraz przemysłowe zmierzające do opracowania charakterystyk rozkładu czasu przebywania (F, E). Wyniki badań posłużyły także do zweryfikowania modelu matematycznego przepływu stali w kadzi, opartego na rozwiązaniu równania Naviera-Stokesa. Otrzymane charakterystyki pozwalają na oszacowanie wielkości udziałów poszczególnych rodzajów przepływu cieczy, a w szczególności przepływu idealnego mieszania i przepływu tłokowego.

EN

The tundish is a necessary element of continuous steel casting process. The desing and geometry of this facility determine the hydrodynamic conditions of flowing steel. These conditions shape the transient process of steel mixing and influence in different grade the process of nonmetallic inclusion removal by flotation. The characteristics of mixing process can be represented by curves of F and E types. For a six-way tundish of a capacity of 15 Mg theoretical studies and industrial tests were undertaken for developing characteristics of the distribution of residence time (F, E). The investigation results were used also for verifying the mathematical model of steel flow in the tundish based on the Navier-Stokes equation. The obtained characteristics enable the estimation of the quantity of volume fraction of separate types of liquid flow and in particular the ideal mixing and the plug flow.

9

Radiotracer investigations of municipal sewage treatment stations

Farooq M., Khan I., Ghiyas-ud-Din, Gul S., Palige J., Dobrowolski A.

Nukleonika

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2003

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Vol. 48, nr 1

57-61

EN

Tracer techniques, which are well-established methods in process dynamics studies in industry, were applied to investigate the dynamics of sewage treatment process. The concept of residence time distribution (RTD) was used to investigate the efficiency of the primary clarifier, aeration tank and secondary clarifier of a sewage treatment plant. Preliminary treatment and modeling of the tracer data was performed using the software DTS Pro Ver. 4.20. A big short - circuiting (by-passing) with a large volume of stagnant zones were found in the primary and secondary clarifiers, while no stagnant zone was detected in the aeration tank.

10

Radioisotope tracer study in an indirectly heated rotary dryer

Pant H.

Nukleonika

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2002

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Vol. 47, nr 4

173-176

EN

A radioisotope tracer study was carried-out in a pilot scale indirectly heated rotary dryer to measure residence time distribution (RTD) of sand particles. Lanthanum-140 labeled sand was used as a tracer. Mean residence time (MRT) and variance of the tracer distribution curves were calculated from the measured RTD curves. From the calculated MRTs, solid holdup in the dryer was estimated. The qualitative comparison of the dimensionless variance with the data published in the literature led to the conclusion that the rotary dryer behaves as a plug flow system. The results of the study were used to design a full-scale industrial rotary dryer.

11

Measurement of liquid holdup and axial dispersion in trickle bed reactors using radiotracer technique

Pant H., Saroha A., Nigam K.

Nukleonika

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2000

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Vol. 45, nr 4

235-241

EN

The holdup and axial dispersion of aqueous phase has been measured in trickle bed reactors as a function of liquid and gas flow rates using radioisotope tracer technique. Experiments were carried out in a glass column of inner diameter 15.2´10-2 m column for air-water system using three different types of packings i.e. non-porous glass beads, porous catalysts of tablet and extrudate shape. The range of liquid and gas flow rates used were 8.3´10-5-3.3´10-4 m3/s and 0-6.67´10-4 m3/s, respectively. Residence time distributions of liquid phase were measured and mean residence times were determined. The values of liquid holdup were calculated from the measured mean residence times. It was observed that liquid holdup increased with increase in liquid flow rates and was independent of increase in gas flow rates used in the study. Two-parameter axial dispersion model was used to simulate measured residence time distribution data and values of mean residence time and Peclet number were obtained. It was observed that values of Peclet number increases with increase in liquid flow rate for glass beads and tablets and remains almost constant for extrudates. The values of mean residence time obtained from model simulation were found to be in good agreement with the values measured experimentally.

12

Tracer testing of processes under variable flow and volume

Niemi A. J., Zenger K., Thereska J., Martinez J. G.

Nukleonika

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1998

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Vol. 43, nr 1

73-94

EN

Continuous flow vessel system of pilot scale was constructed and provided with computer control for programmed variation of flow rate and volume of liquid. Radioisotope and chemical tracer pulses were used for determination of residence time distributions (RTDs). It has been shown earlier that the RTDs of such vessels are invariable under variations of flow or volume and flow, if they are presented as functions of an appropriate, integrated variable, and if the process flow pattern is not affected by the stated variations. The experimental responses of the individual vessels tested were therefore converted to RTD functions of such a variable. It turned out that they converged close to each other within a wide range of steady states and dynamic variations of flow and volume. This is considered to indicate the expediency of the integrated variable used and invariance of the vessel flow pattern within the same range. Additional tests with continuous, randomly variable tracer feed support these conclusions.

PL

Zbudowano system zbiorników o ciągłym przepływie z komputerową kontrolą zaprogramgwanych zmian szybkości przepływu i objętości cieczy. W celu wyznaczenia rozkładów czasów prze,iywania (RDT) stosowano wskaźniki promieniotwórcze i chemiczne. Wykazano wcześniej, że RDT w takich zbiornikach nie zmieniają się ze zmianą przepływu lub objętości, jeżeli przedstawi się je w postaci funkcji odpowiedniej zcałkowanej zmiennej i jeżeli w.w. zmiany nie wpływają na strukturę rozkładu przepływu procesu. Odpowiedzi doświadczalne z poszczególnych badanych zbiorników przekształcono więc w odpowiednie funkcje RDT takich zmiennych. Okazało się, że są one ze sobą silnie zbieżne w szerokim zakresie stanów statycznych i dynamicznych zmian przepływu i objętości. Wskazuje to na praktyczne korzyści ze stosowanej zcałkowanej zmiennej i na niezmienność struktur przepływu w zbiornikach w tym samym zakresie. Dodatkowe próby przy ciągłym zmiennym losowo podawaniu wskaźnika potwierdzają powyższe wnioski.

13

RTD prediction, modelling and measurement of gas flow in reactor

Thyn J., Ha J. J., Strasak P., Zitny R.

Nukleonika

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1998

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Vol. 43, nr 1

95-114

EN

Problems of the measurement and evaluation of RTD of gas phase in chemical reactors are presented and discussed. The measurement of RTD in an industry is mostly used in trouble shooting or for process intensification or optimization. Special PC-programs have been prepared for selection of an RTD model and for its verification by parametrical analysis. An example of the procedure used in trouble shooting is demonstrated on basis of data of radiotracer impulse response of gas flow in a heat exchanger. The results of methods for identification (deconvolution) with regularization, from so called nonparametrical analysis are presented. A combined model described by a set of differential equations has been suggested for gas flow in the reactor with baffles. The model identification by nonlinear regression yields important process parameters, the relative dead volume and mass exchange coefficient e.g. The prediction of RTD for other steady state conditions (e.g. for another flow rate) can be done on the basis of dimensionless impulse response. However the similarity assumption should be verified by other experiments, because the same flow pattern as well as the same relative active volume must be assured at different steady conditions. Another possibility is the prediction of a change of RTD (change of the values of RTD model parameters) on the basis of numerical solution of transport equations for fluid dynamics using particle tracking method or transient analysis of temperature pulse spreading. The results of the RTD prediction for a broad range of Reynolds numbers using software Fluent are presented.

PL

Omówiono problemy pomiaru i wyznaczania rozkładu czasu przebywania (RTD) fazy gazowej w reaktorach chemicznych. Pomiar RTD w przemyśle stosuje się najczęściej przy ocenie niezawodności lub w celu intensyfikacji lub optymalizacji procesu. Opracowano specjalne programy komputerowe umożliwiające wybranie optymalnego modelu RTD i jego weryfikację na drodzeprocedury optymalizacyjnej. Podano przykład postępowania przy badaniu niesprawności wymiennika ciepła oparty na analizie odpowiedzi impulsowej otrzymanej w eksperymencie radioznacznikowym dla fazy gazowej. Przedstawiono wyniki uzyskane z zastosowaniem procedury identyfikacyjnej (dekonwolucji) z regularyzacją tzw. metodą analizy nieparametrycznej. Dla przepływu gazu w reaktorze z przegrodami zaproponowano złożony model opisany układem równań różniczkowych. Identyfikacja modelu na drodze regresji nieliniowej pozwala na wyznaczenie podstawowych parametrów procesu, np. względnej objętości martwej i współczynnika wymiany masy. Określenie RTD dla innych stanów stacjonarnych (np. innego natężenia przepływu) można przeprowadzić w oparciu o analizę bezwymiarowej odpowiedzi impulsowej. Jednakże należy sprawdzić założone podobieństwo na drodze innych doświadczeń, ponieważ należy się upewnić, że w różnych warunkach stacjonarnych struktura przepływu i względna objętność czynna są takie same. Można również przewidzieć zmiany RTD (zmiany wartości parametrów modelu RTD) na podstawie numerycznego rozwiązania równań transportu dla dynamiki cieczy, stosując metodę "cząstek znakowanych" lub analizę stanów przejściowych dyspersji impulsu temperaturowego. Przedstawiono wyniki wyznaczania RTD dla szerokiego zakresu liczb Reynoldsa stosując oprogramowanie Fluent.