Study of fluid dynamic conditions in the selected static mixers part II‐determination of the residence time distribution

Stec, Magdalena; Synowiec, P.

doi:10.1002/cjce.22879

Cited by 16 publications

(26 citation statements)

References 24 publications

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“…The shape of these peaks depends on eddy diffusion, longitudinal diffusion, and mass transfer between the mobile phase and stationary phase . RTD measurements to study hydrodynamics of vessels generally rely on non‐adsorbing tracers with a pulse input that injects a known amount of tracer for a shorter time than the vessel residence time, like GCs . This technique is fast, direct, and the small quantity of tracer identifies non‐standard behaviour that becomes clear in a graph.…”

Section: Theorymentioning

confidence: 99%

“…The second moment, variance ( σ 2 ), represents the spread of the curve and how far the fluid elements deviate from plug flow . The larger value corresponds to a higher amplitude of the distribution and, thereby, an elevated deviation from plug flow, while lower values signify less intermixing effect between fluid elements:

σ^{2} = \frac{\int_{0}^{\infty} t^{2} E ((), t) normald t}{\int_{0}^{\infty} E ((), t) normald t} - {\overset{false¯}{t}}^{2}

= \int_{0}^{\infty} {(t - \overset{false¯}{t})}^{2} E ((), t) normald t = \frac{\int_{0}^{\infty} {(t - \overset{false¯}{t})}^{2} C normald t}{\int_{0}^{\infty} C normald t}

≅ \frac{\sum t_{i}^{2} C_{i} normalΔ t_{i}}{\sum C_{i} normalΔ t_{i}} - {\overset{false¯}{t}}^{2}

…”

Section: Theorymentioning

confidence: 99%

“…We compare the mean residence time with the theoretical residence time ( τ ) to identify dead volumes and short‐circuiting:

τ = \frac{V_{m}}{Q}

where, V m = V empty − V internals (m 3 ) and Q is the volumetric flow rate (m 3 · s −1 ). Thus, when

\overset{t}{true} > τ

, the fluid is possibly bypassing or channelling …”

Section: Theorymentioning

confidence: 99%

“…The boundary conditions are considered open‐open when the detectors are positioned along the column of the vessel. When injecting and detecting in the lines leading to the reactor and at the exit, we might consider the inlet boundary condition as closed‐closed if we consider that backmixing (reverse flow) is negligible and their volume is orders of magnitude smaller than the vessel, which is best to confirm experimentally …”

Section: Uncertaintymentioning

confidence: 99%

“…[37] RTD measurements to study hydrodynamics of vessels generally rely on nonadsorbing tracers with a pulse input that injects a known amount of tracer for a shorter time than the vessel residence time, like GCs. [24,38] This technique is fast, direct, and the small quantity of tracer identifies non-standard behaviour that becomes clear in a graph. An instantaneous injection pulse is ideal and it is best to minimize residence time between the injector and the entrance of the reactor and the reactor effluent and detector.…”

Section: Theorymentioning

confidence: 99%

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Experimental methods in chemical engineering: Residence time distribution—RTD

2020

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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.

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Section: Theorymentioning

confidence: 99%

σ^{2} = \frac{\int_{0}^{\infty} t^{2} E ((), t) normald t}{\int_{0}^{\infty} E ((), t) normald t} - {\overset{false¯}{t}}^{2}

= \int_{0}^{\infty} {(t - \overset{false¯}{t})}^{2} E ((), t) normald t = \frac{\int_{0}^{\infty} {(t - \overset{false¯}{t})}^{2} C normald t}{\int_{0}^{\infty} C normald t}

≅ \frac{\sum t_{i}^{2} C_{i} normalΔ t_{i}}{\sum C_{i} normalΔ t_{i}} - {\overset{false¯}{t}}^{2}

…”

Section: Theorymentioning

confidence: 99%

“…We compare the mean residence time with the theoretical residence time ( τ ) to identify dead volumes and short‐circuiting:

τ = \frac{V_{m}}{Q}

where, V m = V empty − V internals (m 3 ) and Q is the volumetric flow rate (m 3 · s −1 ). Thus, when

\overset{t}{true} > τ

, the fluid is possibly bypassing or channelling …”

Section: Theorymentioning

confidence: 99%

Section: Uncertaintymentioning

confidence: 99%

Section: Theorymentioning

confidence: 99%

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Experimental methods in chemical engineering: Residence time distribution—RTD

2020

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Fluidized bed hydrodynamic modeling of CO₂ in syngas: Distorted RTD curves due to adsorption on FCC

2021

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Bubbles rising through fluidized beds at velocities several times superficial velocities contribute to solids backmixing. In micro-fluidized beds, the walls constrain bubble sizes and velocities. To evaluate gas-phase hydrodynamics and identify diffusional contributions to longitudinal dispersion, we injected a mixture of H 2 , CH 4 , CO, and CO 2 (syngas) as a bolus into a fluidized bed of porous fluid catalytic cracking catalyst while a mass-spectrometer monitored the effluent gas concentrations at 2 Hz. The CH 4 , CO, and CO 2 trailing RTD traces were elongated versus H 2 demonstrating a chromatographic effect. An axial dispersion model accounted for 92% of the variance but including diffusional resistance between the bulk gas and catalyst pores and adsorption explained 98.6% of the variability. At 300 C, the CO 2 tailing disappeared consistent with expectations in chromatography (no adsorption). H 2 and He are poor gas-phase tracers at ambient temperature. We recommend measuring RTD at operating conditions.

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Issue Highlights

2017

Can J Chem Eng

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This work presents a three-dimensional CFD model that considers thermal cracking and gas generation inside the tubes of petrochemical furnaces. Thermal cracking is represented by a kinetic net with six pseudo-components. The CFD model was able to predict the petroleum thermal cracking to lighter fractions and the gas generation as well as the coke formation inside the tube. Coke concentration increases along the pipe as the average temperature of the mixture increases. The graphical abstract shows that coke formation is greater near tube walls, where temperature is higher. The blue on top shows the gas phase, where no coke is formed. High Catalytic Effi ciency of Pd Nanoparticles Immobilized on TiO 2 Nanorods-Coated Ceramic MembranesShuai Zhang, Hong Jiang, Yefei Liu and Rizhi Chen A highly effi cient and reusable catalyst was designed and constructed by loading Pd nanoparticles on a ceramic membrane modifi ed with TiO 2 nanorods (NRs). The TiO 2 NRs can provide more areas for the deposition of Pd nanoparticles, and then more Pd nanoparticles with better dispersion can be loaded on the membrane, leading to superior catalytic activity. The interaction between Pd nanoparticles and TiO 2 NRs makes less leaching of Pd nanoparticles in the liquid-phase p-nitrophenol hydrogenation, thereby higher catalytic stability. Study of Fluid Dynamic Conditions in the Selected Static Mixers Part II -Determination of the Residence Time Distribution Magdalena Stec and Piotr Maria SynowiecThe development of new technologies or intensifi cation of the existing ones requires the use of very effi cient, multi-tasking devices with, if possible, small space requirements. As an example of such equipment, replacing a typical stirred tank reactors, static mixers may be mentioned. However, to decide if the selected type is appropriate for the considered application, the knowledge of fl uid-dynamic conditions (like pressure drops, residence time distribution, mixing effi ciency) is mandatory.The presented paper takes into account the detailed analysis of the residence time distribution (RTD) in two types of static mixers: Kofl o and Kenics and an empty pipe used as a background, respectively. Within the work, the description of RTD moments (like mean residence time t m and spread 2 ), as well as the recognition of mixing characteristics, were made. What is more, according to the differences between real and theoretical residence times, such phenomena like channeling, bypassing or the existence of stagnant zones were also examined.

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Study of fluid dynamic conditions in the selected static mixers part II‐determination of the residence time distribution

Cited by 16 publications

References 24 publications

Experimental methods in chemical engineering: Residence time distribution—RTD

Experimental methods in chemical engineering: Residence time distribution—RTD

Fluidized bed hydrodynamic modeling of CO₂ in syngas: Distorted RTD curves due to adsorption on FCC

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Study of fluid dynamic conditions in the selected static mixers part II‐determination of the residence time distribution

Cited by 16 publications

References 24 publications

Experimental methods in chemical engineering: Residence time distribution—RTD

Experimental methods in chemical engineering: Residence time distribution—RTD

Fluidized bed hydrodynamic modeling of CO2 in syngas: Distorted RTD curves due to adsorption on FCC

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Resources

About

Fluidized bed hydrodynamic modeling of CO₂ in syngas: Distorted RTD curves due to adsorption on FCC