PUMA — A New Mathematical Model for the Rapid Calculation of Steady-State Concentration Profiles in Mixer-Settler Extraction, Partitioning, and Stripping Contactors Using the Purex Process

1986 ◽  
Vol 75 (2) ◽  
pp. 160-167 ◽  
Author(s):  
John F. Geldard ◽  
Adolph L. Beyerlein ◽  
Houn-Lin Chiu
Keyword(s):  
Mathematical Model ◽  
Steady State ◽  
Purex Process ◽  
Concentration Profiles ◽  
Steady State Concentration ◽  
Rapid Calculation ◽  
State Concentration

scholarly journals Modelling of non-steady-state concentration profiles at ISFET-based coulometric sensor—actuator systems

1990 ◽  
Vol 229 ◽  
pp. 71-81 ◽  
Author(s):  
W. Olthuis ◽  
J. Luo ◽  
B.H. Van der Schoot ◽  
P. Bergveld ◽  
M. Bos ◽  
...  
Keyword(s):  
Steady State ◽  
Concentration Profiles ◽  
Steady State Concentration ◽  
Sensor Actuator ◽  
State Concentration

scholarly journals Gas Dispersion and Bubble-to-Emulsion Phase Mass Exchange in a Gas-Solid Bubbling Fluidized Bed: A Computational and Experimental Study

2003 ◽  
Vol 1 (1) ◽  
Author(s):  
Dhaneshwar J. Patil ◽  
Martin van Sint Annaland ◽  
J.A.M. Kuipers
Keyword(s):  
Mass Transfer ◽  
Steady State ◽  
Fluidized Bed ◽  
Mass Exchange ◽  
Concentration Profiles ◽  
Steady State Concentration ◽  
Tracer Gas ◽  
Gas Dispersion ◽  
Bubbling Fluidized Bed ◽  
State Concentration

Knowledge of gas dispersion and mass exchange between the bubble and the emulsion phases is essential for a correct prediction of the performance of fluidized beds, particularly when catalytic reactions take place. Test cases of single rising bubble and a bubbling fluidized bed operated with a jet without a chemical reaction were studied in order to obtain fundamental insights in the prevailing mass transfer phenomena. Numerical simulations were carried out to predict the dispersion of tracer gas using a two-fluid model based on Kinetic Theory of Granular Flow (KTGF). The simulations of a single-bubble rising through an incipiently fluidized bed revealed that the assumptions often made in phenomenological models in the derivation of correlations for the mass transfer coefficient, mainly that the bubble diameter remains constant and that the tracer concentration is uniform in the bubble, are not valid. The predicted bubble-to-emulsion phase mass transfer coefficient showed good agreement with the estimated values from the literature correlations assuming additive convection-diffusion transport for different bubble sizes and different particle sizes, indicating the importance of the convective distribution even for relatively small particles. Experiments were carried out to measure the steady state concentration profiles of a tracer gas in a pseudo two-dimensional bubbling fluidized bed operated with a jet. The simulated steady state concentration profiles of the tracer gas agreed well the experimental measurements. The radial convection of the gas is significantly influenced by the bubble ‘throughflow’ and therefore depends upon the particle and bubble size. The experimental comparison of theoretical results was extended to study the influence of the jet velocity and the particle diameter on the radial dispersion of the tracer gas in the bed.

Analytical Solution of Cubic Autocatalytic Reaction-Diffusion Equations

2011 ◽  
pp. 199-218
Author(s):  
D. Shanthi ◽  
L. Rajendran
Keyword(s):  
Steady State ◽  
Analytical Solution ◽  
Chemical Species ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations ◽  
Concentration Profiles ◽  
Diffusion Cell ◽  
Steady State Concentration ◽  
State Concentration

The system is considered here with two chemical species, the reactant a and autocatalyst b. The Gray-Scott model of cubic-autocatalysis with linear decay is coupled with diffusion and considered in a one-dimensional reactor (a reactor-diffusion cell). Steady-state and non steady- state concentration profiles of the reactant and autocatalyst in Gray-Scott model are obtained using He’s Homotopy pertuburation method for small values parameters. A satisfactory agreement with analytical and numerical results are noted.

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