A mathematical model for the flotation of waste activated sludge

2002 ◽  
Vol 46 (11-12) ◽  
pp. 203-208
Author(s):  
K. Fujisaki ◽  
M. El-Zahar
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Gas Phase ◽  
Solid Phase ◽  
Growth Curves ◽  
Vertical Axis ◽  
Waste Activated Sludge ◽  
Flotation Process ◽  
Hindered Settling ◽  
Similar Character

A mathematical model that describes a batch flotation process is presented. The model employed a similar method to the hindered settling of flocculated material. This idea is based on our experimental results that the time growth curves of separated liquor zone showed a similar character to the settling curve of flocculated material, when the vertical axis reversed. In this model, it is also assumed that the gas phase and solid phase have the same movement, that is microbubbles and solid sludge particles joined to form aggregated floc. By comparing the numerical prediction with experimental data, the usefulness of the model is confirmed and some examples of flotation simulation are demonstrated.

Mathematical Modeling of Coal Gasification in a Fluidized Bed Reactor Using a Eulerian Granular Description

2011 ◽  
Vol 9 (1) ◽  
Author(s):  
Pablo Cornejo ◽  
Oscar Farías
Keyword(s):  
Experimental Data ◽  
Gas Phase ◽  
Fluidized Bed ◽  
Coal Gasification ◽  
Solid Phase ◽  
Heterogeneous Reaction ◽  
Mass Conservation ◽  
Reaction Rates ◽  
Reaction Model ◽  
Mixing Rate

A three-dimensional computational model was developed to describe the coal-gasification processes inside fluidized-bed reactors. The commercial multi-purpose CFD code FLUENT 6.3 was employed, taking into account drying, volatilization, combustion and gasification processes. Both gas phase and solid phase were described using a eulerian approach to model the exchanges of mass, energy and momentum between phases. The disperse phase was described using the kinetic theory of granular flows. The chemical model involved five heterogeneous and five homogeneous chemical reactions, tracking seven species in the gas phase (CO2, CO, H2O, CH4, H2, O2 and N2) and one specie in the solid phase (C(s)). Drying and volatilization rates were estimated by mass conservation. Heterogeneous reaction-rates were determined by combining an Arrhenius kinetic-rate and a diffusion rate using the kinetics/diffusion Surface Reaction Model; the model was implemented within FLUENT through UDFs (User Defined Functions). Homogeneous reaction-rates were described by a turbulent mixing rate using the Eddy Dissipation Model available in FLUENT. Calibration and validation were performed by using existing experimental data from a benchmark coal-gasification case available in the literature. Results are in good agreement with experimental data, capturing known phenomena like fluidization-bed height, temperature distribution and species concentrations. The main contribution of the present work was implementing the necessary sub-models within the FLUENT code in order to handle reactive fluidized-beds in complex geometries. This allowed combining the flexibility of a commercial CFD code with the accuracy of simplified models developed in academic frameworks.

Mathematical Modeling of Process of Obtaining the Solid Uranium Hexafluoride

2016 ◽  
Vol 683 ◽  
pp. 533-539 ◽  
Author(s):  
Aleksey A. Orlov ◽  
Alexandr F. Tsimbalyuk ◽  
Roman V. Malyugin
Keyword(s):  
Mathematical Modeling ◽  
Experimental Data ◽  
Mathematical Model ◽  
Temperature Distribution ◽  
Solid Phase ◽  
Uranium Hexafluoride ◽  
Tank Wall ◽  
Layer Filling ◽  
Gaseous Uranium ◽  
Good Agreement

A non-stationary mathematical model of desublimation UF6 in vertical tanks considers the movement of gaseous uranium hexafluoride contains in the article. Results of calculation of time dependence of the linear velocity desublimation, the thickness of the resulting layer of the solid phase, the temperature distribution in the tank wall - desublimation layer, filling dynamics of vertical tank B-12 by solid UF6 are presented. Calculations have shown that the 70% of B-12 tank is filled desublimation UF6 by 250 hours, which is in good agreement with the experimental data

Diffusion and sorption of water vapor and benzene within a dry model soil organic matter

1997 ◽  
Vol 35 (7) ◽  
pp. 131-138
Author(s):  
Tsair-Fuh Lin
Keyword(s):  
Experimental Data ◽  
Organic Matter ◽  
Water Vapor ◽  
Soil Organic Matter ◽  
Gas Phase ◽  
Sorption Isotherm ◽  
Solid Phase ◽  
Pore Diffusion ◽  
Desorption Kinetics ◽  
Model Soil

The sorption behavior of water vapor and benzene within a dry model soil organic matter (SOM), peat, was studied. An electrobalance system was employed to determine both the equilibrium sorption isotherm and sorption-desorption kinetics. The sorption isotherm for water vapor was found to resemble that previously reported for this sample, while the sorption isotherm for benzene could not be determined, due to a failure to obtain reproducible sorption capacity. In the kinetic study, strong asymmetries between sorption and desorption rates were observed for both water vapor and benzene. Two diffusion models, accounting for either gas-phase pore diffusion within peat grains or solid-phase diffusion within microspheres of SOM, were used to interpret the asymmetric sorption rate data. Considering gas-phase pore diffusion only, the model resolved the asymmetry of sorption rates and described the experimental data very well for water vapor at three different concentrations. However, the pore diffusion model failed to capture the dominant feature of the experimental data for benzene. As a refinement, a model assuming that solid-phase intra-SOM diffusion is the rate-limiting mechanism produced a better description of the experimental data.

The substantiation of the formalized estimation of effectiveness of technological and production systems

2018 ◽  
Vol 15 (1) ◽  
pp. 169-181
Author(s):  
M. I. Sidorov ◽  
М. Е. Stavrovsky ◽  
V. V. Irogov ◽  
E. S. Yurtsev
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Production Systems ◽  
Van Der Pol

Using the example of van der Pol developed a mathematical model of frictional self-oscillations in topochemically kinetics. Marked qualitative correspondence of the results of calculation performed using the experimental data of researchers.

Comparison of Aerobic and Anoxic-Aerobic Digestion of Waste Activated Sludge

1985 ◽  
Vol 17 (8) ◽  
pp. 1475-1478 ◽  
Author(s):  
A P. C. Warner ◽  
G. A. Ekama ◽  
G v. R. Marais
Keyword(s):  
Experimental Data ◽  
Activated Sludge ◽  
Waste Activated Sludge ◽  
Activated Sludge Process ◽  
Cycle Times ◽  
Waste Sludge ◽  
Volatile Solids ◽  
In Series ◽  
Flow Through ◽  
Theoretical Simulations

The laboratory scale experimental investigation comprised a 6 day sludge age activated sludge process, the waste sludge of which was fed to a number of digesters operated as follows: single reactor flow through digesters at 4 or 6 days sludge age, under aerobic and anoxic-aerobic conditions (with 1,5 and 4 h cycle times) and 3-in-series flow through aerobic digesters each at 4 days sludge age; all digesters were fed draw-and-fill wise once per day. The general kinetic model for the aerobic activated sludge process set out by Dold et al., (1980) and extended to the anoxic-aerobic process by van Haandel et al., (1981) simulated accurately all the experimental data (Figs 1 to 4) without the need for adjusting the kinetic constants. Both theoretical simulations and experimental data indicate that (i) the rate of volatile solids destruction is not affected by the incorporation of anoxic cycles and (ii) the specific denitrification rate is independent of sludge age and is K4T = 0,046(l,029)(T-20) mgNO3-N/(mg active VSS. d) i.e. about 2/3 of that in the secondary anoxic of the single sludge activated sludge stystem. An important consequence of (i) and (ii) above is that denitrification can be integrated easily in the steady state digester model of Marais and Ekama (1976) and used for design (Warner et al., 1983).

Modeling of aerated upflow fixed bed reactors for nitrification

1999 ◽  
Vol 39 (4) ◽  
pp. 85-92 ◽  
Author(s):  
J. Behrendt
Keyword(s):  
Mathematical Model ◽  
Mass Transfer ◽  
Liquid Phase ◽  
Gas Phase ◽  
Fixed Bed ◽  
Fixed Bed Reactor ◽  
Bulk Liquid ◽  
Initial Value ◽  
Fixed Bed Reactors ◽  
Number Of Cells

A mathematical model for nitrification in an aerated fixed bed reactor has been developed. This model is based on material balances in the bulk liquid, gas phase and in the biofilm area. The fixed bed is divided into a number of cells according to the reduced remixing behaviour. A fixed bed cell consists of 4 compartments: the support, the gas phase, the bulk liquid phase and the stagnant volume containing the biofilm. In the stagnant volume the biological transmutation of the ammonia is located. The transport phenomena are modelled with mass transfer formulations so that the balances could be formulated as an initial value problem. The results of the simulation and experiments are compared.

Theoretical analysis of counter-current absorption of a poorly soluble gas based on the PDE-AD model

1986 ◽  
Vol 51 (6) ◽  
pp. 1222-1239 ◽  
Author(s):  
Pavel Moravec ◽  
Vladimír Staněk
Keyword(s):  
Experimental Data ◽  
Liquid Phase ◽  
Gas Phase ◽  
Transfer Functions ◽  
Packed Bed ◽  
Packed Bed Column ◽  
Interfacial Transport ◽  
Gaseous Component ◽  
Poorly Soluble ◽  
Counter Current

Expression have been derived in the paper for all four possible transfer functions between the inlet and the outlet gas and liquid steams under the counter-current absorption of a poorly soluble gas in a packed bed column. The transfer functions have been derived for the axially dispersed model with stagnant zone in the liquid phase and the axially dispersed model for the gas phase with interfacial transport of a gaseous component (PDE - AD). calculations with practical values of parameters suggest that only two of these transfer functions are applicable for experimental data evaluation.

Diffusion model for deposition of epitaxial GaAs layers prepared by the MOCVD method

1991 ◽  
Vol 56 (10) ◽  
pp. 2020-2029
Author(s):  
Jindřich Leitner ◽  
Petr Voňka ◽  
Josef Stejskal ◽  
Přemysl Klíma ◽  
Rudolf Hladina
Keyword(s):  
Experimental Data ◽  
Growth Rate ◽  
Kinetic Model ◽  
Gas Phase ◽  
Substrate Surface ◽  
Deposition Process ◽  
Hydrogen Atmosphere ◽  
Epitaxial Gaas ◽  
Kinetics Of ◽  
Good Agreement

The authors proposed and treated quantitatively a kinetic model for deposition of epitaxial GaAs layers prepared by reaction of trimethylgallium with arsine in hydrogen atmosphere. The transport of gallium to the surface of the substrate is considered as the controlling process. The influence of the rate of chemical reactions in the gas phase and on the substrate surface on the kinetics of the deposition process is neglected. The calculated dependence of the growth rate of the layers on the conditions of the deposition is in a good agreement with experimental data in the temperature range from 600 to 800°C.

An homogeneous growth model of gallium arsenide epitaxial layers from the gas phase

1989 ◽  
Vol 54 (11) ◽  
pp. 2933-2950
Author(s):  
Emerich Erdös ◽  
Petr Voňka ◽  
Josef Stejskal ◽  
Přemysl Klíma
Keyword(s):  
Experimental Data ◽  
Gallium Arsenide ◽  
Kinetic Study ◽  
Gas Phase ◽  
Growth Model ◽  
Epitaxial Layers ◽  
Inhomogeneous Model ◽  
Homogeneous Models ◽  
Active Centres

This paper represents a continuation and ending of the kinetic study of the gallium arsenide formation, where a so-called inhomogeneous model is proposed and quantitatively formulated in five variants, in which two kinds of active centres appear. This model is compared both with the experimental data and with the previous sequence of homogeneous models.

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