scholarly journals Solvability of the Brinkman-Forchheimer-Darcy Equation

2017 ◽  
Vol 2017 ◽  
pp. 1-10 ◽  
Author(s):  
Piotr Skrzypacz ◽  
Dongming Wei
Keyword(s):  
Fixed Bed ◽  
Packed Bed ◽  
Reynolds Numbers ◽  
Fixed Bed Reactor ◽  
Small Data ◽  
Convective Flows ◽  
Finite Element Approximations ◽  
Darcy Equation ◽  
Variable Porosity ◽  
Porous Medium Flow

The nonlinear Brinkman-Forchheimer-Darcy equation is used to model some porous medium flow in chemical reactors of packed bed type. The results concerning the existence and uniqueness of a weak solution are presented for nonlinear convective flows in medium with variable porosity and for small data. Furthermore, the finite element approximations to the flow profiles in the fixed bed reactor are presented for several Reynolds numbers at the non-Darcy’s range.

Design of a continuous flow immobilized-cell reactor for biosynthetical production of L-aspartic acid

1985 ◽  
Vol 50 (10) ◽  
pp. 2122-2133 ◽  
Author(s):  
Jindřich Zahradník ◽  
Marie Fialová ◽  
Jan Škoda ◽  
Helena Škodová
Keyword(s):  
Aspartic Acid ◽  
Continuous Flow ◽  
Immobilized Cells ◽  
Scale Up ◽  
Fixed Bed ◽  
Packed Bed ◽  
Fixed Bed Reactor ◽  
Experimental Program ◽  
Design Parameters ◽  
Immobilized Cell

An experimental study was carried out aimed at establishing a data base for an optimum design of a continuous flow fixed-bed reactor for biotransformation of ammonium fumarate to L-aspartic acid catalyzed by immobilized cells of the strain Escherichia alcalescens dispar group. The experimental program included studies of the effect of reactor geometry, catalytic particle size, and packed bed arrangement on reactor hydrodynamics and on the rate of substrate conversion. An expression for the effective reaction rate was derived including the effect of mass transfer and conditions of the safe conversion-data scale-up were defined. Suggestions for the design of a pilot plant reactor (100 t/year) were formulated and decisive design parameters of such reactor were estimated for several variants of problem formulation.

Hydrate-Based Carbon Capture Process: Assessment of Various Packed Bed Systems for Boosted Kinetics of Hydrate Formation

2020 ◽  
Vol 143 (3) ◽  
Author(s):  
Amit Arora ◽  
Asheesh Kumar ◽  
Gaurav Bhattacharjee ◽  
Chandrajit Balomajumder ◽  
Pushpendra Kumar
Keyword(s):  
Carbon Dioxide ◽  
Carbon Capture ◽  
Carbon Dioxide Capture ◽  
Fixed Bed ◽  
Hydrate Formation ◽  
Packed Bed ◽  
Fixed Bed Reactor ◽  
Capture Process ◽  
Novel Technologies ◽  
Kinetics Of

Abstract The case for developing novel technologies for carbon dioxide (CO2) capture is fast gaining traction owing to increasing levels of anthropogenic CO2 being emitted into the atmosphere. Here, we have studied the hydrate-based carbon dioxide capture and separation process from a fundamental viewpoint by exploring the use of various packed bed media to enhance the kinetics of hydrate formation using pure CO2 as the hydrate former. We established the fixed bed reactor (FBR) configuration as a superior option over the commonly used stirred tank reactor (STR) setups typically used for hydrate formation studies by showing enhanced hydrate formation kinetics using the former. For the various packing material studied, we have observed silica gel with 100 nm pore size to return the best kinetic performance, corresponding to a water to hydrate conversion of 28 mol% for 3 h of hydrate growth. The fundamental results obtained in the present study set up a solid foundation for follow-up works with a more applied perspective and should be of interest to researchers working in the carbon dioxide capture and storage and gas hydrate fields alike.

scholarly journals Synthetic Packed-Bed Generation for CFD Simulations: Blender vs. STAR-CCM+

2019 ◽  
Vol 3 (2) ◽  
pp. 52 ◽  
Author(s):  
Steffen Flaischlen ◽  
Gregor D. Wehinger
Keyword(s):  
Open Source Software ◽  
Fluid Dynamic ◽  
Fixed Bed ◽  
Packed Bed ◽  
Process Industry ◽  
Particle Orientation ◽  
Fixed Bed Reactor ◽  
Cfd Simulations ◽  
Shape Approximation ◽  
Rigid Body Model

A common reactor type in the chemical and process industry is the fixed-bed reactor. Accurate modeling can be achieved with particle-resolved computational fluid dynamic (CFD) simulations. However, the underlying bed morphology plays a paramount role. Synthetic bed-generation methods are much more flexible and faster than image-based approaches. In this study, we look critically at the two different bed generation methods: Discrete element method (DEM) (in the commercial software STAR-CCM+) and the rigid-body model (in the open-source software Blender). The two approaches are compared in terms of synthetically generated beds with experimental data of overall and radial porosity, particle orientation, as well as radial velocities. Both models show accurate agreement for the porosity. However, only Blender shows similar particle orientation than the experimental results. The main drawback of the DEM is the long calculation time and the shape approximation with composite particles.

Steady State Model for Heat Transfer in a Packed Bed Reactor of Elliptic Cylindrical Shape

2008 ◽  
Vol 6 (1) ◽  
Author(s):  
Laércio G. Oliveira ◽  
Ramdayal Swarnakar ◽  
Antonio G. B. de Lima
Keyword(s):  
Heat Transfer ◽  
Steady State ◽  
Fixed Bed ◽  
Packed Bed ◽  
Numerical Results ◽  
Packed Bed Reactor ◽  
Fixed Bed Reactor ◽  
Dimensionless Temperature ◽  
Cylindrical Shape ◽  
Temperature Profiles

The fixed-bed reactors of circular cylindrical geometry with heated or cooled walls are frequently used to carry out heterogeneous reactions of solid-gas type in engineering applications. The design of a fixed bed reactor requires an extensive knowledge of heat transfer characteristics within the packed bed. In this sense, this work presents a three-dimensional mathematical model to predict the heat transfer inside a fixed bed elliptical cylinder heat exchanger. The model considers uniform velocity and temperature profiles of the fluid phase at the entrance of the reactor, and constant thermo-physical properties. The surface of the equipment convective boundary condition is assumed to be constant. The energy equation, written in the elliptical cylindrical coordinates, was discretized using a finite-volume method considering a fully implicit formulation, and WUDS interpolation scheme. Numerical results of the dimensionless temperature profiles inside the packed bed reactor at a steady state are presented and temperature distribution is interpreted. To validate the model, numerical results obtained for the circular cylinder are compared with analytical results from literature and a good agreement was obtained.

Heat Transfer inside Elliptic Cylindrical Reactor: Effect of Bed Porosity

2013 ◽  
Vol 336 ◽  
pp. 97-102
Author(s):  
A.A. Silva Filho ◽  
J.P. Silva de Almeida ◽  
Antônio Gilson Barbosa de Lima
Keyword(s):  
Heat Transfer ◽  
Fixed Bed ◽  
Three Dimensional ◽  
Axial Direction ◽  
Cylindrical Geometry ◽  
Heat Diffusion ◽  
Fixed Bed Reactor ◽  
Three Dimensional Model ◽  
Variable Porosity ◽  
Steady State Heat Transfer

The study of heat transfer phenomenon in porous media by fluids percolated in the axial direction has been of interest to many researchers in various branches of science and technology. Applications are directed to different process such as filtration, distillation, absorption and adsorption in columns, drying and catalytic reactions in fixed beds. The literature has presented several solutions of the heat diffusion / convection equation in fixed bed reactors, but these studies are limited to a cylindrical geometry. In this sense, this work aim to present a pseudo-homogeneous three-dimensional model to describe the steady-state heat transfer within a fixed bed reactor with elliptic cylindrical geometry by considering variable porosity. The energy equation written in elliptical cylindrical coordinates and applied to the porous medium (particulate system) is discretized numerically using the finite volume method. Results of the temperature distribution within the bed are presented analyzed. It was verified that with increased porosity heat transfer inside the reactor tends to be more intense and thus, lower temperature gradients are found in all cross section of the reactor.

Modeling and Simulation of a Packed-bed Reactor for Carrying out the Water-Gas Shift Reaction

2012 ◽  
Vol 10 (1) ◽  
Author(s):  
Yaidelin A. Manrique ◽  
Carlos V. Miguel ◽  
Diogo Mendes ◽  
Adelio Mendes ◽  
Luis M. Madeira
Keyword(s):  
Fixed Bed ◽  
Packed Bed ◽  
Packed Bed Reactor ◽  
Fixed Bed Reactor ◽  
Water Gas Shift ◽  
Small Scale ◽  
Heterogeneous Model ◽  
Co Conversion ◽  
Reactor Operating ◽  
Water Gas

Abstract In this work the water-gas shift (WGS) process was addressed, with particular emphasis in the development of phenomenological models that can reproduce experimental results in a WGS reactor operating at low temperatures. It was simulated the conversion obtained in a fixed-bed reactor (PBR) packed with a Cu-based catalyst making use of a composed kinetic equation in which the Langmuir-Hinshelwood rate model was used for the lowest temperature range (up to 215 ºC), while for temperatures in the range 215 – 300 ºC a redox model was employed. Several packed-bed reactor models were then proposed, all of them without any fitting parameters. After comparing the simulations against experimental CO conversion data for different temperatures and space time values, it was concluded that the heterogeneous model comprising axial dispersion and mass transfer resistances shows the best fitting. This model revealed also good adherence to other experiments employing different feed compositions (CO and H2O contents); it predicts also the overall trend of increasing CO conversion with the total pressure. This modeling work is particularly important for small scale applications related with hydrogen production/purification for fuel cells.

Performance of a multi-slit packed bed microstructured reactor in the synthesis of methanol: Comparison with a laboratory fixed-bed reactor

2011 ◽  
Vol 66 (24) ◽  
pp. 6350-6357 ◽  
Author(s):  
Hamidreza Bakhtiary-Davijany ◽  
Fatemeh Hayer ◽  
Xuyen Kim Phan ◽  
Rune Myrstad ◽  
Peter Pfeifer ◽  
...  
Keyword(s):  
Fixed Bed ◽  
Packed Bed ◽  
Fixed Bed Reactor ◽  
Microstructured Reactor ◽  
Synthesis Of Methanol

Catalytic wet peroxidation of phenol in a fixed bed reactor

2007 ◽  
Vol 55 (12) ◽  
pp. 75-81 ◽  
Author(s):  
F. Martínez ◽  
M.I. Pariente ◽  
J.A. Melero ◽  
J.A. Botas ◽  
E. Gómez
Keyword(s):  
Phenol Degradation ◽  
Fixed Bed ◽  
Methyl Cellulose ◽  
Packed Bed ◽  
Packed Bed Reactor ◽  
Fixed Bed Reactor ◽  
Continuous Treatment ◽  
Catalyst Stability ◽  
Solid Catalyst ◽  
Relevant Role

Iron-containing mesostructured materials (Fe-SBA-15) are suitable for continuous treatment of phenolic aqueous solutions by means of catalytic wet peroxide oxidation (CWPO) in a packed-bed reactor. These materials were successfully extruded, crushed and sieved with a particle size ranging from 1 to 1.6 mm using mineral clay and methyl cellulose as binders. Non-significant changes have been found in the textural and structural properties of the extruded material in comparison to the parent powder Fe-SBA-15 material. Activity of extruded catalyst in terms of phenol degradation and TOC reduction has been monitored in a continuous mode. The increase of residence time enhances significantly the TOC degradation. The catalyst stability, taking into account the loss of iron species from the catalyst into the aqueous solution, has also been examined. The catalytic results of Fe-SBA-15 material in comparison to a homogeneous catalytic test prove the relevant role of the solid catalyst in the oxidation process.

Heat Transfer in Packed Bed Elliptic-Cylindrical Reactor: The Geometry Effect

2019 ◽  
Vol 391 ◽  
pp. 54-59 ◽  
Author(s):  
R. Moura da Silva ◽  
A. Santos Pereira ◽  
A.G. Barbosa de Lima ◽  
Morgana Vasconcellos Araújo ◽  
R.S. Santos
Keyword(s):  
Heat Transfer ◽  
Aspect Ratio ◽  
Temperature Profile ◽  
Fixed Bed ◽  
Three Dimensional ◽  
Packed Bed ◽  
Dimensionless Temperature ◽  
Variable Porosity ◽  
Cylindrical Reactor ◽  
Half Axis

This work aims to develop a transient three-dimensional mathematical model to predict the temperature distribution in a fixed-bed elliptical cylindrical reactor to different geometric aspect ratio (L2/L1=1.5, 2.0 and 3.0). The model considers variable thermo-physical properties, a flat temperature profile at the fluid inlet, as well as a variable porosity model. The governing equation is solved using the finite volume method, coupled with WUDS interpolation scheme and fully implicit method. Results of the temperature profile along the reactor are presented and discussed at different times. As results, it was found that the maximum rate of heat transfer within the reactor occurs near the minor half-axis region of the ellipse (cross-section area of the reactor) and it intensifies over time and that the dimensionless temperature profile is practically unchanged with the aspect ratio.

APLIKASI REAKTOR HIGH RATE PERFORMANCE PADA PENGOLAHAN LIMBAH CAIR INDUSTRI KECIL TAHU = Application of High Rate Performance Rector for Wastewater Treatment in Tofu Small Scale Industries

2016 ◽  
Vol 14 (1) ◽  
pp. 7 ◽  
Author(s):  
Iin Parlina ◽  
Lestari Widodo
Keyword(s):  
Organic Waste ◽  
Fixed Bed ◽  
Packed Bed ◽  
High Rate ◽  
Fixed Bed Reactor ◽  
Upflow Anaerobic Sludge Blanket ◽  
Anaerobic Sludge ◽  
Rate Performance ◽  
Anaerobic Sludge Blanket ◽  
High Rate Performance

Along with the development of biogas and its utilization, biogas reactors also evolved from conventional reactor types to high rate performance reactors, adapts to the needs of increased efficiency and also the characteristics of organic waste that is difficult if processed using ordinary reactor. However, this type of reactor basically has 3 types, namely fixed bed (packed-bed, anaerobic filters, fixed-film), fluidized bed reactor, and UASB/ Upflow Anaerobic Sludge Blanket reactor. From these high rate performance reactors, fixed bed reactor is the type that is pretty much developed and implemented in Indonesia, especially for treating organic wastewater from small industries, for example tofu, tapioca and slaughterhouses. Implementation of fixed bed reactor for the tofu industry until today has reached as much as 5 units that serve the needs of about 132 households in Banyumas District, Central Java Province. The fixed bed reactor’s performance is quite high if it is evaluated from biogas yield and the efficiency of the organic content in tofu industry’s wastewater. Implementation, dissemination, and replication of this reactor for treatment of other types of organic waste or other areas have the potential to support government programs in GHG mitigation actions, renewable energy sources provision, environmental protection and the development of energy self-sufficient villages.Keywords : biogas reactor - performance high - rate, fixed bed reactors, tofu industryAbstrakSeiring dengan perkembangan biogas beserta pemanfaatannya, reaktor biogas juga berkembang dari jenis reaktor konvensional hingga reaktor berunjuk kerja tinggi (high rate performance) menyesuaikan dengan kebutuhan peningkatan efisiensi dan juga karakteristik limbah organik yang sulit jika diolah dengan menggunakan reaktor biogas biasa. Namun, pada dasarnya reaktor ini memiliki 3 jenis, yaitu reaktor unggun tetap (fixed bed, packed-bed, anaerobic filter, fixed-film), reaktor unggun terfluidisasi (fluidized bed reactor), dan reaktor UASB (Upflow Anaerobic Sludge Blanket). Dari ketiga jenis reaktor berunjuk kerja tinggi tersebut, reaktor jenis unggun tetap adalah jenis yang cukup banyak dikembangkan dan diimplementasikan di Indonesia, terutama untuk mengolah limbah cair organik yang berasal dari industri kecil, misalnya tahu, tapioka dan rumah potong hewan. Implementasi reaktor unggun tetap untuk industri tahu hingga saat ini telah mencapai jumlah 5 unit reaktor yang melayani kebutuhan sekitar 132 Rumah tangga di Kabupaten Banyumas secara berkelanjutan. Kinerja reaktor unggun tetap ini dapat dikatakan cukup tinggi jika dinilai dari perolehan biogas dan efisiensi penurunan kandungan organic dalam limbah cair tahu. Program implementasi, diseminasi, dan replikasi reaktor ini untuk pengolahan jenis limbah organik yang lain atau daerah lain memiliki potensi dalam mendukung program pemerintah dalam aksi mitigasi Gas Rumah Kaca, penyediaan sumber energi terbarukan, perlindungan lingkungan dan pengembangan desa mandiri energi.Kata kunci : biogas, reaktor high-rate-performance, reaktor fixed bed, industri tahu

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