scholarly journals Modelling and Dynamic Simulation of One-Dimensional Isothermal Axial Dispersion Tubular Reactors with Power Law and Langmuir-Hinshelwood-Hougen Watson Kinetics

2021 ◽  
Vol 8 (2) ◽  
pp. 834-858
Author(s):  
Almoruf Olajide Fasola Williams
Keyword(s):  
Mass Transfer ◽  
Dynamic Response ◽  
Power Law ◽  
Axial Dispersion ◽  
Operating Parameters ◽  
Orthogonal Collocation ◽  
Feed Concentration ◽  
One Dimensional ◽  
Tubular Reactors ◽  
The One

In this paper, the modelling, numerical lumping and simulation of the dynamics of one-dimensional, isothermal axial dispersion tubular reactors for single, irreversible reactions with Power Law (PL) and Langmuir-Hinshelwood-Hougen-Watson (LHHW)-type kinetics are presented. For the PL-type kinetics, first-order and second-order reactions are considered, while Michaelis-Menten and ethylene hydrogenation or enzyme substrate-inhibited reactions are considered for the LHHW-type kinetics. The partial differential equations (PDEs) developed for the one-dimensional, isothermal axial dispersion tubular reactors with both the PL and LHHW-type kinetics are lumped to ordinary differential equations (ODEs) using the global orthogonal collocation technique. For the nominal design/operating parameters considered, using only 3 or 4 collocation points, are found to adequately simulate the dynamic response of the systems. On the other hand, simulations over a range of the design/operating parameters require between 5 to 7 collocations points for better results, especially as the Peclet number for mass transfer is increased from the nominal value to 100. The orthogonal collocation models are used to carry out parametric studies of the dynamic response behaviours of the one-dimensional, isothermal axial dispersion tubular reactors for the four reaction kinetics. For each of the four types of reaction kinetics considered, graphical plots are presented to show the effects of the inlet feed concentration, Peclet number for mass transfer and the Damköhler number on the reactor exit concentration dynamics to step-change in the inlet feed concentration. The internal dynamics of the linear (or linearized) systems are examined by computing the eigenvalues of the linear (or linearized) lumped orthogonal collocation models. The relatively small order of the lumped orthogonal collocation dynamic models make them attractive and useful for dynamic resilience analysis and control system analysis/design studies.

On Standard Eigenvalues of Variable-Coefficient Heat and Rod Equations

1989 ◽  
Vol 56 (1) ◽  
pp. 146-148 ◽  
Author(s):  
H. P. W. Gottlieb
Keyword(s):  
Heat Equation ◽  
Power Law ◽  
Heat Conductivity ◽  
Variable Coefficient ◽  
Continuous Case ◽  
Coefficient Function ◽  
Heat Conductivity Coefficient ◽  
One Dimensional ◽  
Variable Heat ◽  
The One

Forms of the variable-heat-conductivity coefficient function in the one-dimensional heat equation are determined which yield a standard harmonic eigenvalue sequence as in the case of homogeneity. The continuous case is found to correspond to a four-thirds power law dependence on coordinate. For the stepped case, the condition on the ratio of segmental heat conductivities in terms of the junction location is presented.

QUANTUM HALL EDGE PHYSICS AND ITS ONE-DIMENSIONAL LUTTINGER LIQUID DESCRIPTION

2012 ◽  
Vol 26 (22) ◽  
pp. 1244001 ◽  
Author(s):  
ORION CIFTJA
Keyword(s):  
Correlation Function ◽  
Power Law ◽  
Quantum Hall ◽  
Luttinger Liquid ◽  
Edge States ◽  
One Dimensional ◽  
Liquid Model ◽  
Experimental Values ◽  
The One ◽  
The Relationship

We describe the relationship between quantum Hall edge states and the one-dimensional Luttinger liquid model. The Luttinger liquid model originated from studies of one-dimensional Fermi systems, however, it results that many ideas inspired by such a model can find applications to phenomena occurring even in higher dimensions. Quantum Hall systems which essentially are correlated two-dimensional electronic systems in a strong perpendicular magnetic field have an edge. It turns out that the quantum Hall edge states can be described by a one-dimensional Luttinger model. In this work, we give a general background of the quantum Hall and Luttinger liquid physics and then point out the relationship between the quantum Hall edge states and its one-dimensional Luttinger liquid representation. Such a description is very useful given that the Luttinger liquid model has the property that it can be bosonized and solved. The fact that we can introduce a simpler model of noninteracting bosons, even if the quantum Hall edge states of electrons are interacting, allows one to calculate exactly various quantities of interest. One such quantity is the correlation function which, in the asymptotic limit, is predicted to have a power law form. The Luttinger liquid model also suggests that such a power law exponent should have a universal value. A large number of experiments have found the quantum Hall edge states to show behavior consistent with a Luttinger liquid description. However, while a power law dependence of the correlation function has been observed, the experimental values of the exponent appear not to be universal. This discrepancy might be due to various correlation effects between electrons that sometimes are not easy to incorporate within a standard Luttinger liquid model.

Fundamental Study on Transport Model for Radionuclides under Unsaturated Condition around Near-Surface Underground

MRS Advances ◽  
2020 ◽  
Vol 5 (5-6) ◽  
pp. 223-232
Author(s):  
Takenori Ozutsumi ◽  
Masayuki Kogure ◽  
Yuichi Niibori ◽  
Taiji Chida
Keyword(s):  
Mass Transfer ◽  
Unsaturated Zone ◽  
Transport Model ◽  
Path Model ◽  
Local Flow ◽  
Near Surface ◽  
One Dimensional ◽  
Retardation Coefficient ◽  
The One ◽  
Unsaturated Condition

ABSTRACTThe low-level nuclear wastes such as decontamination waste from Fukushima are disposed in near-surface underground, where the intermittent recharge of rain and groundwater causes spatial distribution of water content. Therefore, pores of soils are not filled with water, that is, an unsaturated zone will be formed. In such a condition, since the water flow path are detoured by clogged gas in pores of soil in the unsaturated zone, the migration path of radionuclide would be different from the saturated zone. So far, the one-dimensional advection-dispersion equation (ADE) model has been widely used in order to explain experimental results under an unsaturated condition. However, the detouring of local flow-paths remarkably affects the mass transfer. The one-dimensional ADE evaluates such a detouring effect by using Peclet number and retardation coefficient as fitting parameters. In other words, the one-dimensional ADE model is difficult to explain mass transfer under an unsaturated condition. Therefore, the purpose of this study is explaining such complicated transport of radionuclides using a multi-path model based on phenomena in underground. The proposed multi-path model considering both water saturation and permeability distributions showed good agreement with the experimental data under an unsaturated condition.

Numerical Simulation of Heat and Mass Transfer of Lump Coal Falling in the Freeboard Zone of COREX Melter-Gasifier

2012 ◽  
Vol 455-456 ◽  
pp. 74-79
Author(s):  
Gang Pan ◽  
Xun Liang Liu ◽  
Gan Wang ◽  
Zhi Wen
Keyword(s):  
Mathematical Model ◽  
Mass Transfer ◽  
Heat And Mass Transfer ◽  
Mass Transfer Process ◽  
Operating Parameters ◽  
Distribution Law ◽  
Moisture Evaporation ◽  
One Dimensional ◽  
Corex Melter Gasifier ◽  
Lump Coal

. A one-dimensional mathematical model was developed for describing heat and mass transfer process of lump coal falling in the freeboard zone of COREX melter-gasifier. The temperature distribution, law of moisture evaporation and removal of volatile of lump coal were obtained. Further more, the effects of operating parameters on heat and mass transfer phenomena of lump coal were studied.

The Dissipation Function-Based Efficiency for Turbomachinery—Part I: The Efficiency of a Cooled Turbine Row1

2016 ◽  
Vol 139 (3) ◽  
Author(s):  
Chong M. Cha
Keyword(s):  
Mass Transfer ◽  
Dissipation Function ◽  
One Dimensional ◽  
Specific Heats ◽  
Gas Streams ◽  
Blade Row ◽  
The One ◽  
Turbine Airfoils ◽  
The Impact ◽  
Mixing Problem

The effect of coolant addition or “mixing loss” on aerodynamic performance is formulated for the turbine, where mixing takes place between gas streams of different compositions as well as static temperatures. To do this, a second-law efficiency measure is applied to a generalization of the one-dimensional mixing problem between a main gas stream and a single coolant feed, first introduced and studied by Hartsel (1972, “Prediction of Effects of Mass-Transfer Cooling on the Blade-Row Efficiency of Turbine Airfoils,” AIAA Paper No. 1972-11) for the turbine application. Hartsel's 1972 model for mass transfer cooling loss still remains the standard for estimating mixing loss in today's turbines. The present generalization includes losses due to the additional contributions of “compositional mixing” (mixing between unlike compositions of the main and coolant streams) as well as the effect of chemical reaction between the two streams. Scaling of the present dissipation function-based loss model to the mainstream Mach number and relative cooling massflow and static temperature is given. Limitations of the constant specific heats assumptions and the impact of fuel-to-air ratio are also quantified.

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