A mathematical solution for response of tracer pulse in a loop reactor with open boundary and recycle

Takao, Masaharu; Ono, S.; Hirose, Tsutomu; Murakámi, Yasuhiro

doi:10.1016/0009-2509(82)85044-6

Cited by 13 publications

(3 citation statements)

References 1 publication

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“…Eq. (4) can be used to describe the RTD for a pulse injection when injection and detection are at different points in a loop reactor (Takao et al, 1982) and can be fit to the experimental tracer response curve by estimating the Peclet number, Pe,…”

Section: Residence Time Distributionmentioning

confidence: 99%

Oxygen mass transfer and hydrodynamics in a multi-phase airlift bioscrubber system

Littlejohns

2009

Chemical Engineering Science

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Section: Residence Time Distributionmentioning

confidence: 99%

Oxygen mass transfer and hydrodynamics in a multi-phase airlift bioscrubber system

Littlejohns

2009

Chemical Engineering Science

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“…As in Benkhelifa et al (2000), the global flow behaviour was modelled by an axial dispersed plug flow with complete recirculation; it is based on the Voncken's equation generalized to reactors in which injection and detection are located at different points (Takao et al, 1982):…”

Section: Hydrodynamics Of the Liquid Phasementioning

confidence: 99%

Investigations in an external-loop airlift photobioreactor with annular light chambers and swirling flow

Loubière

Pruvost

Aloui

et al. 2011

Chemical Engineering Research and Design

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a b s t r a c tPhotosynthetic microorganisms could serve as valuable compounds, but also for environmental applications. Their production under controlled conditions implies to design specific reactors, named photobioreactors, in which light supply is the main constraint. This paper was devoted to an original external-loop airlift photobioreactor (PBR) with annular light chambers in which a swirling motion was induced. The aim was to characterize this novel geometrical configuration in terms of gas-liquid hydrodynamics, and to test its potentiality for algal cultures. This PBR consisted of two identical columns connected by flanges defining tangential inlets, each column being made of two transparent concentric tubes (6 L in liquid volume, 50 m −1 in specific illuminated area). Firstly, the global flow characteristics (circulation and mixing times) were determined by a tracer method and modelled by an axial dispersed plug flow with complete recirculation (Péclet number). By means of a double optical probe, both local and global time-averaged parameters of the gas phase were measured, namely void fraction, bubble velocity, frequency and size. The gas-liquid mass transfer were also characterized, in tap water and in culture medium, by measuring overall volumetric mass transfer coefficients. In a second time, cultures of the microalga Chlamydomonas reinhardtii were run in batch mode. The variations of biomass concentration and pigment content with time from inoculation were successfully obtained. All these findings highlighted: (i) some significant differences in terms of gas-liquid hydrodynamics between the present PBR and the usual airlift systems, (ii) the interest of this configuration for algal cultures, even if complementary studies and technological improvements are still required for definitively validating its scale-up.

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“…The fluid concentration of the aforementioned model is given using Laplace integral transform. 21 (i) The liquid phase is at batch operation mode; therefore, the liquid concentration is given by…”

Section: Axial Dispersion Models (Adms)mentioning

confidence: 99%

Hydrodynamics and Axial Dispersion in a Gas−Liquid−(Solid) EL-ALR with Different Sparger Designs

Chen

Dong

Geng

et al. 2008

Ind. Eng. Chem. Res.

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The gas-liquid-(solid) three-phase hydrodynamics in an external-loop airlift reactor (EL-ALR) with an upward pipe 0.47 m in diameter and 2.5 m in height, two external loop downward pipes 0.08 m in diameter and 2.5 m in height, were investigated using four different gas sparger designs. The microconductivity probe and the three-dimensional (3-D) laser Doppler anemometry (LDA) techniques were, respectively, implemented to measure the local gas holdup in the riser (R Gr ) and liquid phase velocity in the downcomer (U Ld ) using air as the gas phase, water as the liquid phase, and alginate gel beads as the solid phase, over a wide range of operation conditions. The tracer age distribution was measured using the pulse-pursuit response technology. Axial dispersion model (ADM) was used to estimate the model parameter Peclet number (Pe) values as a fitted parameter with the measured data, using the gold partition method for nonlinear programming strategy inequation restrict conditions. The ADM gave better fits to the experimental data at high axial locations and lower superficial gas velocity (U G ) for an EL-ALR used with a large L/D R ratio. A synergistic effect of U Ld , R Gr , Pe, solids loading (SL), and sparger designs on the performance of an EL-ALR was observed in our experiments. The sparger designs were determined to have a noticeable effect on the R Gr and Pe in the lower gas velocity and lower solid loading ranges (U G < 0.025 m/s and SL < 2%), but only a slight effect in the high gas velocity and high solid loading ranges (U G > 0.030 m/s and SL > 3%). However, the effect of sparger designs on the U Ld is greater in the gas velocity from 0.025 m/s to 0.045 m/s. For the lower solids loading, the increase of orifice diameter leads to a decrease in R Gr . This is in accordance with what was presented in the gas-liquid two-phase system. Moreover, the influence of orifice diameters of the spargers is negligible for solids loading of >3%. Although the Pe values decreased with the operating gas velocity, the gas velocity change from 0.03 m/s to 0.04 m/s yielded lower Pe values, as a result of the reduced bubble size. As the gas velocity further increased to 0.06 m/s, the R Gr and the U Ld values increased, while the Pe values negligibly increased. For a gas-liquid two-phase system, Pe decreases with the orifice diameter and, for 1% of solids, Pe is also lower for sparger P-2 (φ 0.6 mm) than for sparger P-1 (φ 0.3 mm). For higher amounts of solids (3%), Pe does not have a defined trend. In addition to the gas velocity and sparger design effects, the solids loading had the effect of decreasing the U Ld values, while such effect became small and flattened at high solid loadings. The U Ld values, especially with VO ) 100%, are 20% lower in three-phase flow than that in two-phase flow. In addition, the U Ld profiles in three-phase flow are flatter than that in two-phase flow with VO ) 50%-100%, actually showing a parabolic shape rather than the almost linear one encountered in two-phase flow. This is very important for ...

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A mathematical solution for response of tracer pulse in a loop reactor with open boundary and recycle

Cited by 13 publications

References 1 publication

Oxygen mass transfer and hydrodynamics in a multi-phase airlift bioscrubber system

Oxygen mass transfer and hydrodynamics in a multi-phase airlift bioscrubber system

Investigations in an external-loop airlift photobioreactor with annular light chambers and swirling flow

Hydrodynamics and Axial Dispersion in a Gas−Liquid−(Solid) EL-ALR with Different Sparger Designs

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