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Book The Impact of Heat Exchanging Internals on Hydrodynamics of Bubble Column Reactor

Download or read book The Impact of Heat Exchanging Internals on Hydrodynamics of Bubble Column Reactor written by Ahmed Jasim and published by . This book was released on 2016 with total page 96 pages. Available in PDF, EPUB and Kindle. Book excerpt: "In this study, the impact of configuration and size of vertical heat exchanging internals in bubble columns on gas holdup, specific gas-liquid interfacial area, bubble chord length, and bubble rise velocity were investigated. Three different configurations of internals, each covering 25% of the column's cross-sectional area, were used to simulate the heat exchanging tubes utilized in the F-T process. The First configuration is a circular-like arrangement of 0.5 inch diameter vertical rods, whereas the second is a hexagonal-like arrangement of 0.5 inch diameter vertical rods. The third configuration is also a circular arrangement but of 1 inch diameter vertical rods used to examine the effect heat exchanging tubes diameter on the hydrodynamics. The experiments were carried out in a 14 cm inner diameter Plexiglas bubble column using air-water system, at superficial gas velocities in the range of 0.02 to 0.45 m/s, measured based on free cross-sectional area of the column available for fluid flow. 4-point optical fiber probe technique was used to collect the diameter profiles of the hydrodynamic parameters. In comparison to bubble column without internals, the obtained result showed that the configuration of the internals significantly affect the hydrodynamics and also the flow resistance inside the column. Steeper gas holdup and specific interfacial area profiles observed when the 0.5 inch circular arrangement internals is used. A distinct asymmetrical radial profiles of gas holdup and specific interfacial area were obtained when the hexagonal arrangement is used. The 1 inch internals enhanced the gas holdup and specific interfacial area near to the wall regions. In the churn turbulent regime, Bubbles chord length and bubbles rise velocity were found to be larger with the presence of internals when compared to bubble column without internals"--Abstract, page iv.

Book Effect of Dense Heat Exchanging Internals on the Hydrodynamics of Bubble Column Reactors Using Non invasive Measurement Techniques

Download or read book Effect of Dense Heat Exchanging Internals on the Hydrodynamics of Bubble Column Reactors Using Non invasive Measurement Techniques written by Mohammed Khloofh Al Mesfer and published by . This book was released on 2013 with total page 412 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Given their efficiency and capital cost reduction, bubble/slurry bubble column reactors are the reactors of choice for Fischer-Tropsch (FT) synthesis, offering clean alternative fuels and chemicals. FT synthesis is an exothermic process that requires many heat exchanging tubes in order to remove heat efficiently and maintain the desired temperature and isothermal operating condition. The impact of the heat exchanging tubes (internals) on the hydrodynamics is not fully understood. Reliably designing and scaling up bubble column reactors requires proper understanding of hydrodynamics, as well as heat and mass transfer parameters. The main objective of this work is to advance the understanding of the effect of internals (25% covered cross-sectional area to meet FT needs) on hydrodynamics (gas holdup distribution, 3D liquid velocity, Reynolds stresses, turbulent kinetic energy, eddy diffusivity, etc.) in bubble columns. Single-source y-ray Computed Tomography (CT) and Radioactive Particle Tracking (RPT) were used for the first time to study the effect of dense internals and gas velocity on the phase holdup distribution and radial profiles, liquid velocity field and turbulent parameter profiles. The main findings obtained for the first time in this study can be summarized as follows: [I] The presence of internals at a given superficial gas velocity causes: [a] An increase in gas holdup and the axial centerline liquid velocity [b] A sharp decrease in turbulence parmeters [II] The increase in superficial gas velocity in the presence of internals causes: [a] An increase in gas holdup, axial centerline liquid velocity and turbulent parameters"--Abstract, leaf iii.

Book Effects of Internals Configurations on Heat Transfer and Hydrodynamics in Bubble Columns   with and Without Solid Particles

Download or read book Effects of Internals Configurations on Heat Transfer and Hydrodynamics in Bubble Columns with and Without Solid Particles written by Anil Kumar Jhawar and published by . This book was released on 2011 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: Internals of different types are required in a number of industrial applications of bubble columns to achieve the desired mixing or to remove the heat of reaction to maintain desired temperature and isothermal conditions of operation. Some of these applications include Fischer-Tropsch synthesis, methanol synthesis, and production of dimethyl ether (DME). The presence of internals however can alter the column hydrodynamics and mixing patterns which could influence reactor performance. A fast response probe capable of capturing bubble dynamics, as well as detecting flow direction is used to study the effect of internals on local heat transfer and column hydrodynamics in a bubble column with and without solid particles. It captured the temporal variations in heat transfer coefficients due to changes in local hydrodynamic conditions. Measurements obtained in presence of different configurations and combinations of internals are compared with those without internals to elucidate the effects of internals design and configurations. Comparisons are based on average values and fluctuating component of local temporal variations of the heat transfer coefficient obtained with the fast response probe. The average gas holdup, center line liquid, and bubble rise velocities obtained with and without internals are also compared. The observed differences are discussed based on the insights provided by these comparisons. The heat transfer coefficient and gas holdup increases in presence of internals. Relationships between local heat transfer measurements and hydrodynamic conditions with internals are shown and discussed. The observed increase in heat transfer coefficients with scale can be related to increase in liquid circulation velocity with column diameter, which in turn is related to an increase in large bubbles rise velocity.

Book Hydrodynamics  Mixing  and Mass Transfer in Bubble Columns with Internals

Download or read book Hydrodynamics Mixing and Mass Transfer in Bubble Columns with Internals written by Mohamed Hamed and published by . This book was released on 2012 with total page 123 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bubble columns and slurry bubble columns are considered reactors of choice for a wide range of applications in the chemical, biochemical, and petrochemical industries. Most of the chemical applications of bubble columns include exothermic processes and hence they require some means of heat removal to maintain a steady process. The most practical means for heat removal in these reactors is the utilization of vertical cooling internals since they provide high heat transfer area per reactor volume. However, the effects of these internals on the reactor performance are poorly understood in the open literature. This causes the design of the internals to be based on empirical rules not on the applications of fundamentals. The main objective of this study is to enhance the understanding of the effects of vertical cooling internals on the gas hydrodynamics, gas mixing, and mass transfer. In addition, this study attempts to develop and validate models that can simulate the radial gas velocity profile and axial gas mixing in the presence and absence of internals. Finally, this work aims to validate all the observed experimental results and models in larger columns with and without internals to have a better understanding of the scale-up effects in the presence of internals. This is accomplished by carrying out experiments in a lab-scale 8-inch bubble column and a pilot-scale 18-inch bubble column in the absence and presence of internals. The studied % occluded area by internals (~ 25%) is chosen to match the % occluded area used in the Fischer-Tropsch synthesis. The radial gas velocity profiles are measured using the 4-point optical probe and are used to validate the 1-D gas velocity model developed by Gupta (2002). Gar tracer techniques are used to study the effect of internals on the overall axial gas mixing and mass transfer. A 2-D model, that considers the radial variations of the gas velocity and gas holdup, is developed and used to analyze the tracer data allowing the estimation of the turbulent diffusivities of the gas phase. The 2-D model along with the axial dispersion coefficient model developed by Degaleesan and Dudukovic (1998) are used to determine the contribution of different mixing mechanisms to the overall axial gas mixing. The effect of internals and column diameter on the gas velocity profile, gas mixing, and mass transfer is assessed. The presence of internals causes: The effect of internals and column diameter on the gas velocity profile, gas mixing, and mass transfer is assessed. The presence of internals causes: An increase in the center-line gas velocity. A significant decrease in axial gas mixing. A decrease in the gas-liquid mass transfer coefficient. The increase in column diameter causes: Enhancement of the gas circulation. An increase in axial gas mixing. The model developed by Gupta (2002) to predict radial gas velocity profiles is validated at different operating conditions in the presence and absence of internals. A 2-D convection-diffusion model is developed and proven useful in interpreting gas tracer data and simulating the overall axial gas mixing in the presence and absence of internals.

Book Fluid Dynamics and Scale up of Bubble Columns with Internals

Download or read book Fluid Dynamics and Scale up of Bubble Columns with Internals written by Ahmed Abouelfetouh Youssef and published by . This book was released on 2010 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bubble columns and slurry bubble columns, as multiphase reactors, are favored for a wide range of applications in the chemical, biochemical, petrochemical and metallurgical industries. They are considered the reactor of choice for the Fischer Tropsch synthesis, among other applications, offering an alternative energy source and providing clean liquid fuels as compared to other reactors. Most of the industrial applications of bubble column reactors require the utilization of heat exchanging tubes, the effect of which on the reactor's performance is not fully understood. This study proposes detailed investigations of selected local hydrodynamics in bubble columns with and without internal heat exchanging tubes. The main focus of this dissertation is to enhance the understanding of the phenomena associated with the local gas holdup and the bubble dynamics (specific interfacial area, frequency, velocity, and chord length) and their radial profiles via detailed experimentations by means of the four-point optical fiber probe as a measuring technique. In addition, the liquid phase mixing is investigated. The effects of the presence of cooling tubes, which are commonly used in industrial applications of bubble columns, are thoroughly investigated in columns of different diameters to assess the effect of scale. Based on the insights gained from the above, one of the main limitations in bubble columns, scale up, is to be tackled in this study. A new approach, yet simple, for designing the reactor in order to reduce the scale-up risk is developed making use of the necessary heat exchanging vertical internals in controlling the effect of scale through reactor compartmentalization leading to an optimized, yet efficient, design of large scale bubble columns. The main findings of this work can be summarized as follows: The impact of vertical internals on bubble dynamics and liquid phase mixing is assessed: Increase in gas holdup, interfacial area. Decrease in bubble size due to higher break-up rates. Enhancement in the large scale recirculation cells. Increase in the liquid phase mixing. The new scaling methodology was proposed and proven viable.

Book Investigations in Hydrodynamics and Mixing Patterns in the Bubble Column Equipped with Internals

Download or read book Investigations in Hydrodynamics and Mixing Patterns in the Bubble Column Equipped with Internals written by Keller George and published by . This book was released on 2015 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bubble column reactors, with or without solid particles, have a number of applications in the chemical, petrochemical, biochemical and environmental industries. A number of these industrial applications require internals such as baffles, heat transfer surfaces and special distributors to meet demands. Proper selection and design of these internals can lead to the improved performance and efficiency of a bubble column reactor. Several experiments are carried out in a bubble column equipped with a concentric tube bundle (CT) and an internal combination consisting of a concentric tube bundle and concentric baffle (or static mixer) (CTB) respectively. Neutrally buoyant particles are used to determine the effect of the CT and CTB internals on the local flow structures in the equipped column respectively. More upward, near-linear particle movements are observed with the CTB internal over the CT internal. Several non-linear particle movements are also observed. Overall bulk liquid circulation flow patterns are proposed for the intermediate to high gas velocity range based on the observed local flow structures for both internals. Comparisons are made between the gas holdups obtained during internal equipment and that of a comparable hollow bubble column from the literature. Both internals increase the gas holdup of a hollow bubble column. However, the increases with the CT internal are higher by more than 25% of that obtained with the CTB internal on average. The effect of the internals on average bubble size is investigated for the small bubble class. Smaller average diameters are obtained when the CT internal is used. The interfacial area in the presence of the two internals is determined respectively. Higher interfacial areas are obtained with the CT internal. The average difference in interfacial area is 54.0 m2/m3. The effect of the internals on mixing time is determined through dye and aqueous salt tracer studies. In both instances, higher mixing times are obtained with the CTB internal. Liquid backmixing is quantified through the axial dispersion coefficients obtained from the salt tracer studies. The axial dispersion coefficients obtained with the CT internal are higher than that of the CTB internal by about 15% on average.

Book Population Balances

    Book Details:
  • Author : Doraiswami Ramkrishna
  • Publisher : Elsevier
  • Release : 2000-08-08
  • ISBN : 0080539246
  • Pages : 373 pages

Download or read book Population Balances written by Doraiswami Ramkrishna and published by Elsevier. This book was released on 2000-08-08 with total page 373 pages. Available in PDF, EPUB and Kindle. Book excerpt: Engineers encounter particles in a variety of systems. The particles are either naturally present or engineered into these systems. In either case these particles often significantly affect the behavior of such systems. This book provides a framework for analyzing these dispersed phase systems and describes how to synthesize the behavior of the population particles and their environment from the behavior of single particles in their local environments. Population balances are of key relevance to a very diverse group of scientists, including astrophysicists, high-energy physicists, geophysicists, colloid chemists, biophysicists, materials scientists, chemical engineers, and meteorologists. Chemical engineers have put population balances to most use, with applications in the areas of crystallization; gas-liquid, liquid-liquid, and solid-liquid dispersions; liquid membrane systems; fluidized bed reactors; aerosol reactors; and microbial cultures. Ramkrishna provides a clear and general treatment of population balances with emphasis on their wide range of applicability. New insight into population balance models incorporating random particle growth, dynamic morphological structure, and complex multivariate formulations with a clear exposition of their mathematical derivation is presented. Population Balances provides the only available treatment of the solution of inverse problems essential for identification of population balance models for breakage and aggregation processes, particle nucleation, growth processes, and more. This book is especially useful for process engineers interested in the simulation and control of particulate systems. Additionally, comprehensive treatment of the stochastic formulation of small systems provides for the modeling of stochastic systems with promising new areas of applications such as the design of sterilization systems and radiation treatment of cancerous tumors. - A clear and general treatment of population balances with emphasis on their wide range of applicability. Thus all processes involving solid-fluid and liquid-liquid dispersions, biological populations, etc. are encompassed - Provides new insight into population balance models incorporating random particle growth, dynamic morphological structure, and complex multivariate formulations with a clear exposition of their mathematical derivation - Presents a wide range of solution techniques, Monte Carlo simulation methods with a lucid exposition of their origin and scope for enhancing computational efficiency - An account of self-similar solutions of population balance equations and their significance to the treatment of data on particulate systems - The only available treatment of the solution of inverse problems essential for identification of population balance models for breakage and aggregation processes, particle nucleation and growth processes and so on - A comprehensive treatment of the stochastic formulation of small systems with several new applications

Book Hydrodynamics and Mass Transfer in Downflow Slurry Bubble Columns

Download or read book Hydrodynamics and Mass Transfer in Downflow Slurry Bubble Columns written by Subrata Kumar Majumder and published by CRC Press. This book was released on 2019-01-02 with total page 168 pages. Available in PDF, EPUB and Kindle. Book excerpt: Slurry bubble column reactors are intensively used as a multiphase reactor in the chemical, biochemical, and petrochemical industries for carrying out reactions and mass transfer operations in which a gas, made up of one or several reactive components, comes into contact or reacts with a liquid. This volume describes the hydrodynamics of three-phase gas-liquid-solid flow in a downflow slurry bubble column. The efficiency of the downflow gas interacting system is characterized by the self-entrainment of secondary gas. The book covers the gas entrainment phenomena, gas holdup characteristics, pressure drop, gasliquid mixing characteristics, bubble size distribution, interfacial phenomena, and the mass transfer phenomena in the downflow slurry system. This volume will be useful in chemical and biochemical industries and in industrial research and development sectors, as well as in advanced education courses in this area. The book will be helpful for further understanding the multiphase behavior in gas interacting multiphase systems for research and development. The hydrodynamic and mass transfer characteristics discussed will be useful in the design and installation of the modified slurry bubble column in industry for specific applications.

Book Bubble Column Reactions

    Book Details:
  • Author : Wolf-Dieter Deckwer
  • Publisher : John Wiley & Sons
  • Release : 1992-04-08
  • ISBN :
  • Pages : 564 pages

Download or read book Bubble Column Reactions written by Wolf-Dieter Deckwer and published by John Wiley & Sons. This book was released on 1992-04-08 with total page 564 pages. Available in PDF, EPUB and Kindle. Book excerpt: This technology, though used for many years, has shown great vitality recently and is still in a state of flux. Provides an account of developments up to the present and also an orderly evaluation of literature already published on the subject. Considerable space is devoted to bubble column reactor performance predictions based on mathematical models and the importance of each is explained with practical examples.

Book Hydrodynamics and Mass Transfer in Bubble Columns

Download or read book Hydrodynamics and Mass Transfer in Bubble Columns written by Onkar N. Manjrekar and published by . This book was released on 2016 with total page 101 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bubble columns and slurry bubble columns are multiphase reactors used for a wide range of applications in the biochemical, chemical, petrochemical, and metallurgical industries. In spite of their widespread usage, the scale-up of bubble columns remains an ongoing challenge. Various scale-up approaches, based on concepts ranging from ideal mixing to complex 3-D multiphase CFD models, have been used for assessing the effect of column size and gas and liquid flow rates on column hydrodynamics and reactor performance. Among these approaches, phenomenological models based on either single-class or multi-class bubbles that were validated on cold flow systems have been successful in predicting the residence time distributions of gas and liquid in pilot-scale bubble columns (Chen et al., 2004) (Gupta, 2002). However, such models are not entirely predictive, since they are validated using columns having the same size as hot operating units. To provide better predictive capability, we need prior knowledge of local hold-up, transport coefficients, and bubble dynamics. This dissertation provides an improved understanding of the key design parameters (gas hold-up, volumetric mass transfer coefficients, gas-liquid interfacial area, and their spatial distribution) for predictive scale-up of bubble columns. In this work, a 4-point optical probe is used to estimate local gas hold-up and bubble dynamics (specific interfacial area, frequency, bubble velocity, and bubble chord-lengths) and their radial profiles in a cold-flow slurry bubble column and a bubble column photo-bioreactor. Along with local bubble dynamics, the effect of superficial gas velocity on volumetric mass transport coefficients in several sizes of bubble columns, with and without internals, and in slurry bubble columns and photo-bioreactors are studied. Key findings: In the bubbly flow regime, bubble dynamics in photo-bioreactors with suspended algae were dominated by the physicochemical properties of the liquid, as distinguished from the churn-turbulent flow regime in the slurry bubble columns, where bubble dynamics were mainly affected by turbulent intensities. In the bubbly-flow regime, volumetric mass transfer coefficients increased with an increase in superficial gas velocity. However, in the churn-turbulent flow regime, they approached a constant value with an increase in the superficial gas velocity. A new methodology was proposed to identify the flow regime from optical probe signals based on the support vector machine algorithm, which can uniquely classify flow regimes for various systems on a single flow regime map. A new model for the liquid phase mixing, that with a proper choice of the mass transfer coefficients enables a good match of the predicted and measured tracer response is described. This model provides a better prediction of volumetric mass transfer coefficients than the currently used well mixed model for the liquid phase (CSTR). The dissertation improves the fundamental understanding of the connection between bubble dynamics and mass transfer. Using the 4-point optical probe as a tool, it demonstrates a connection between bubble dynamics and volumetric mass transfer coefficients. Present work addresses the need of industries to have a method that can be used as an online process control tool to identify flow regime, this method has been tested at cold flow conditions and needs to be implemented at hot flow conditions. The parameters (radial distributions of gas hold-up, bubble velocities, and volumetric mass transfer coefficient) that are evaluated in the present work can be used to validate phenomenological models and CFD results at cold flow conditions, which can later be combined with process chemistry to accomplish scale-up (Chen et al., 2004). The open literature on multiphase reactors is mainly limited to cold flow condition, and techniques such as the optical probe need to be extended to hot flow conditions. The optical probe described here can withstand high temperature and pressure, but for hot flow conditions it requires a better binding agent to hold the probe tips together, one that will not dissolve in industrial solvents.

Book Hydrodynamics of Bubble Column Reactors Operating with Non Newtonian Liquids

Download or read book Hydrodynamics of Bubble Column Reactors Operating with Non Newtonian Liquids written by Amin Esmaeili Khalil Saraei and published by . This book was released on 2015 with total page 223 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Book Bubbly Flows

    Book Details:
  • Author : Martin Sommerfeld
  • Publisher : Springer Science & Business Media
  • Release : 2012-12-06
  • ISBN : 3642185401
  • Pages : 354 pages

Download or read book Bubbly Flows written by Martin Sommerfeld and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book summarises the outcom of a priority research programme: 'Analysis, Modelling and Computation of Multiphase Flows'. The results of 24 individual research projects are presented. The main objective of the research programme was to provide a better understanding of the physical basis for multiphase gas-liquid flows as they are found in numerous chemical and biochemical reactors. The research comprises steady and unsteady multiphase flows in three frequently found reactor configurations, namely bubble columns without interiors, airlift loop reactors, and aerated stirred vessels. For this purpose new and improved measurement techniques were developed. From the resulting knowledge and data, new and refined models for describing the underlying physical processes were developed, which were used for the establishment and improvement of analytic as well as numerical methods for predicting multiphase reactors. Thereby, the development, lay-out and scale-up of such processes should be possible on a more reliable basis.

Book Hydrodynamics and Heat Transfer of Baffled and Unbaffled Slurry Bubble Columns

Download or read book Hydrodynamics and Heat Transfer of Baffled and Unbaffled Slurry Bubble Columns written by S. C. Saxena and published by . This book was released on 1994 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Book Heat Transfer and Hydrodynamics in a Three phase Slurry Bubble Column

Download or read book Heat Transfer and Hydrodynamics in a Three phase Slurry Bubble Column written by and published by . This book was released on 1998 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Book Direct Contact Heat Transfer

    Book Details:
  • Author : Frank Kreith
  • Publisher : Springer Science & Business Media
  • Release : 2013-11-11
  • ISBN : 3662301822
  • Pages : 400 pages

Download or read book Direct Contact Heat Transfer written by Frank Kreith and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt: to increase the use of direct contact processes, the National Science Foundation sup ported a workshop on direct contact heat transfer at the Solar Energy Research Insti tute in the summer of 1985. We served as organizers for this workshop, which em phasized an area of thermal engineering that, in our opinion, has great promise for the future, but has not yet reached the point of wide-spread commercial application. Hence, a summary of the state of knowledge at this point is timely. The workshop had a dual objective: 1. To summarize the current state of knowledge in such a form that industrial practi tioners can make use of the available information. 2. To indicate the research and development needed to advance the state-of-the-art, indicating not only what kind of research is needed, but also the industrial poten tial that could be realized if the information to be obtained through the proposed research activities were available.

Book The Effects of Low Aspect Ratio and Heat Exchanging Internals on the Bubble Properties and Flow Regime in a Pilot plant Bubble slurry Bubble Column for Fischer Tropsch Synthesis

Download or read book The Effects of Low Aspect Ratio and Heat Exchanging Internals on the Bubble Properties and Flow Regime in a Pilot plant Bubble slurry Bubble Column for Fischer Tropsch Synthesis written by Hayder Al-Naseri and published by . This book was released on 2019 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Fischer-Tropsch synthesis (F-T) is a process utilized to convert the syngas mixture of CO and H2 to synthetic fuel and chemicals that executed commercially by using the bubble/slurry bubble column reactor. The experimental results reveal that the investigated parameters, in terms the presence of internals, and reducing the aspect ratio and the solids loading, increase the local gas holdup, interfacial area, bubble passage frequency, and decrease the bubble rise velocity, bubble chord length. Meanwhile, the aspect ratio H/D = 4, and 5 provide enough height to established the fully developed flow regime. As a result of the variation in the bubble properties that in turn reflected on the flow regime transition, therefore, the presence of internals and decreasing the aspect ratio delay the transition from the transition flow regime to churn turbulent flow regime. The validated CFD codes, using Eulerian-Eulerian approach incorporated with the population balance model PBM, exhibit the capability to simulate the bubble column in bubbly and turbulent flow regimes. However, results revealed that the presence of internals enhanced the gas holdup significantly in the wall region of the column. The gas holdup radial profiles in the presence of internals in different configurations provide a uniform gas holdup profile. While the results of the effect of internals diameter exhibit that the gas holdup was increased remarkably in the center and the wall regions of the bubble column equipped by internals of 1-inch diameter more than in using internals of 0.5-inch. However, the effect of internals configurations reported that the internals with hexagonal arrangement increases the gas holdup in the center region more than the circular arrangement, and less in the wall region comparing with the circular arrangement"--Abstract, page iv.