Experimental and Analytical Study of Contaminant Transport Resulting from Dissolution of a Flat Surface Buried in a Packed Bed

2010 ◽  
Vol 297-301 ◽  
pp. 1238-1243
Author(s):  
João M.P.Q. Delgado ◽  
M. Vázquez da Silva
Keyword(s):  
Contaminant Transport ◽  
Numerical Solutions ◽  
Flat Surface ◽  
Mathematical Expression ◽  
Mass Conservation ◽  
Mass Transfer Process ◽  
Packed Bed ◽  
Axial Distance ◽  
And Diffusion ◽  
Moving Fluid

The present work describes the mass transfer process between a moving fluid and a slightly soluble flat surface buried in a packed bed of small inert particles with uniform voidage, by both advection and diffusion/dispersion. Numerical solutions of the differential equations describing solute mass conservation were undertaken to obtain the concentration profiles, for each concentration level. A simple mathematical expression that relates the dependence between concentration and axial distance is proposed to describe the approximate size of the diffusion wake downstream of the reactive solid mass.

Concentration Distribution in the Wake of a Plane Surface Buried in a Porous Media in Alignment with the Flow Direction

2009 ◽  
Vol 283-286 ◽  
pp. 553-558
Author(s):  
João M.P.Q. Delgado ◽  
M. Vázquez da Silva
Keyword(s):  
Mass Transfer ◽  
Peclet Number ◽  
Numerical Solutions ◽  
Plane Surface ◽  
Flow Direction ◽  
Mathematical Expression ◽  
Mass Conservation ◽  
Mass Transfer Process ◽  
Packed Bed ◽  
Péclet Number

The present work describes the mass transfer process between a moving fluid and a slightly soluble flat surface buried in a packed bed of small inert particles with uniform voidage, by both advection and diffusion. Numerical solutions of the differential equation describing solute mass conservation were undertaken to obtain the concentration profiles, for each concentration level, the width and downstream length of the corresponding contour surface and the mass transfer flux was integrated to give the Sherwood number as a function of Peclet number. A mathematical expression that relates the dependence with the Peclet number is proposed to describe the approximate size of the diffusion wake downstream of the reactive solid mass.

Multilevel cross flow rotating packed bed to enhance gas film control mass transfer process

2021 ◽  
Vol 161 ◽  
pp. 108321
Author(s):  
Qing-Qing Duan ◽  
Zhi-Guo Yuan ◽  
You-Zhi Liu ◽  
Shan-Shan Duan ◽  
Xi-Fan Duan
Keyword(s):  
Mass Transfer ◽  
Transfer Process ◽  
Cross Flow ◽  
Mass Transfer Process ◽  
Packed Bed ◽  
Rotating Packed Bed

scholarly journals Numerical Modeling of Contaminant Transport with Spatially-Dependent Dispersion and Non-Linear Chemical Reaction

2007 ◽  
Vol 12 (3) ◽  
pp. 329-343 ◽  
Author(s):  
A. J. Chamkha
Keyword(s):  
Contaminant Transport ◽  
Chemical Reaction ◽  
Numerical Solutions ◽  
Dispersion Coefficient ◽  
Transport Model ◽  
Physical Parameters ◽  
Contaminant Concentration ◽  
Dimensionless Time ◽  
Polynomial Type ◽  
Special Cases

A one-dimensional advective-dispersive contaminant transport model with scale-dependent dispersion coefficient in the presence of a nonlinear chemical reaction of arbitrary order is considered. Two types of variations of the dispersion coefficient with the downstream distance are considered. The first type assumes that the dispersivity increases as a polynomial function with distance while the other assumes an exponentiallyincreasing function. Since the general problem is nonlinear and possesses no analytical solutions, a numerical solution based on an efficient implicit iterative tri-diagonal finitedifference method is obtained. Comparisons with previously published analytical and numerical solutions for special cases of the main transport equation are performed and found to be in excellent agreement. A parametric study of all physical parameters is conducted and the results are presented graphically to illustrate interesting features of the solutions. It is found that the chemical reaction order and rate coefficient have significant effects on the contaminant concentration profiles. Furthermore, the scale-dependent polynomial type dispersion coefficient is predicted to obtain significant changes in the contaminant concentration at all dimensionless time stages compared with the constant dispersion case. However, relatively smaller changes in the concentration level are predicted for the exponentially-increasing dispersion coefficient.

scholarly journals Development of in-house lattice-Boltzmann simulator of bioreactors for wastewater treatment: basic concepts and initial results

2017 ◽  
Vol 77 (3) ◽  
pp. 838-847 ◽  
Author(s):  
V. A. Fortunato ◽  
F. L. Caneppele ◽  
R. Ribeiro ◽  
J. A. Rabi
Keyword(s):  
Lattice Boltzmann ◽  
Degradation Kinetics ◽  
Computational Modelling ◽  
Packed Bed ◽  
Packed Bed Reactor ◽  
Proper Order ◽  
Order Of Magnitude ◽  
Boltzmann Method ◽  
And Diffusion

Abstract While computational modelling has increasingly supported wastewater bioreactor engineering, novel numerical techniques have been developed such as the lattice-Boltzmann method (LBM). With vinasse treatment as case study, this work is a first step towards a comprehensive LBM simulator of a continuous-flow anaerobic packed-bed reactor. Extensions from typical models comprise one-dimensional (besides time) dependence, species transport via convection and diffusion, and imposition of either Dirichlet or Danckwerts condition at inlet. The LBM simulator proved to be operational when simulating the bioreactor at different hydraulic retention times (HRTs). Simulated profiles show that stepwise feeding concentrations are smoothed as they are transported towards the bioreactor exit while concentrations increase or decrease in response to generation or degradation kinetics. Good fitting was observed for concentrations of acetic acid (2.1 kg-COD/m3 for HRT = 24 h) and butyric acid (1.3 kg-COD/m3 for HRT = 16 h) at the exit whereas other concentrations were numerically simulated at proper order of magnitude.

CFD modeling of gas–liquid mass transfer process in a rotating packed bed

2016 ◽  
Vol 294 ◽  
pp. 111-121 ◽  
Author(s):  
Yucheng Yang ◽  
Yang Xiang ◽  
Guangwen Chu ◽  
Haikui Zou ◽  
Baochang Sun ◽  
...  
Keyword(s):  
Mass Transfer ◽  
Transfer Process ◽  
Mass Transfer Process ◽  
Packed Bed ◽  
Cfd Modeling ◽  
Liquid Mass ◽  
Rotating Packed Bed ◽  
Liquid Mass Transfer

Adsorption and diffusion of Mg, O, and O2 on the MgO(001) flat surface

2005 ◽  
Vol 122 (17) ◽  
pp. 174707 ◽  
Author(s):  
Grégory Geneste ◽  
Joseph Morillo ◽  
Fabio Finocchi
Keyword(s):  
Flat Surface ◽  
And Diffusion

A Theoretical Approach to the Shift Mechanics of Rubber Belt Variators

2008 ◽  
Vol 130 (12) ◽  
Author(s):  
Francesco Sorge
Keyword(s):  
Numerical Solutions ◽  
Control Volume ◽  
Mass Conservation ◽  
Theoretical Description ◽  
The Other ◽  
Control Surface ◽  
Speed Ratio ◽  
Rubber Belt ◽  
Total Mass Flux ◽  
Inertia Forces

This paper proposes a theoretical description of the mechanical behavior of rubber belt variators during the speed ratio shift. Comparing with the steady operation, the mass conservation of the belt is completely reformulated considering an elementary dihedral control volume between two planes through the pulley axis and balancing the inside mass variation with the total mass flux through the control surface. On the other hand, the belt equilibrium conditions are similar to the steady case, as the inertia forces due to the shifting motion are negligible with respect to the other forces. Assuming a one-dimensional belt model, it is shown that adhesive regions may appear inside the arc of contact, where the belt sticks to the pulley flanges along spiral-shaped paths. It is demonstrated that this type of contact may occur only for the closing pulleys, differently from the steady drives and from the opening pulleys, where only quasiadhesive internal subregions may be observed at most, where the sliding velocity turns out to be quite small along a more or less extended portion of the arc of contact. Numerical solutions are calculated for all types of conditions, and their characteristics are widely described.

scholarly journals Determination of Diffusion Coefficients of Selected Long Chain Hydrocarbons using Reversed- Flow Gas Chromatographic Technique

2011 ◽  
Vol 8 (4) ◽  
pp. 1916-1924 ◽  
Author(s):  
Khalisanni Khalid ◽  
Rashid Atta Khan ◽  
Sharifuddin Mohd Zain
Keyword(s):  
Gas Chromatography ◽  
Diffusion Coefficients ◽  
Elution Curve ◽  
Mathematical Expression ◽  
Chromatographic Technique ◽  
Reversed Flow ◽  
Future Studies ◽  
And Diffusion ◽  
Long Chain

The reversed-flow gas chromatography (RF-GC) technique was used to study the evaporation rate and estimating the diffusion coefficient of samples. The RF-GC system comprises of six-port valve, sampling and diffusion column, detector and modified commercial gas chromatography machine. Selected long chain of hydrocarbons (99.99% purity) was used as samples. The solute (stationary phase) were carried out by carrier gas (mobile phase) to the detector. The data obtained from the RF-GC analysis were analysed by deriving the elution curve of the sample peaks using mathematical expression to find the diffusion coefficients values of respective liquids. The values obtained were compared with theoretical values to ensure the accuracy of readings. The interesting findings of the research showed the theoretical values of equilibrium at liquid-gas interphase lead to profound an agreement with the experimental evidence, which contributes for the references of future studies.

Mass Transfer around a Sphere Buried in a Packed Bed

2014 ◽  
Vol 353 ◽  
pp. 306-310
Author(s):  
João M.P.Q. Delgado ◽  
M. Vázquez da Silva
Keyword(s):  
Boundary Layer ◽  
Layer Thickness ◽  
Boundary Layer Thickness ◽  
Numerical Solutions ◽  
Concentration Field ◽  
Particle Diameter ◽  
Packed Bed ◽  
Concentration Boundary Layer ◽  
Concentration Boundary ◽  
Mass Transfers

The transport phenomenon of mass transfers between a moving fluid and a reacting sphere buried in a packed bed, with “uniform velocity”, was analysed numerically, for solute transport by both advection and diffusion to obtain the concentration field and, from it, the dimensionless concentration boundary layer thickness, , for , and . The bed of inert particles is taken to have uniform voidage. For this purpose, numerical solutions of the partial differential equations describing mass concentration of the solute were undertaken to obtain the concentration boundary layer thickness as a function of the relevant parameters. Finally, mathematical expressions that relate the dependence with the Peclet number and inert particle diameter are proposed to describe the approximate size of the concentration boundary layer thickness.

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