scholarly journals Analysis of the dynamics of the system of nonlinear differential equations describing a tubular reactor

2017 ◽  
Author(s):  
◽  
Busuyi Ojo Adebayo
Keyword(s):  
Activation Energy ◽  
Flow Reactor ◽  
Nonlinear Differential Equations ◽  
Tubular Reactor ◽  
Damkohler Number ◽  
Continuous Stirred Tank Reactor ◽  
Three Solutions ◽  
Damköhler Number ◽  
Reactor Length ◽  
Parameter Values

A characterization of the solution(s) of nonlinear boundary value problems (BVPs) arising from a class of chemical reactions occurring in a adiabatic tubular reactor when the mass and thermal Peclet numbers are different is performed. Results show that for large Peclet numbers and activation energy, and for sufficiently small Damkohler number and reactor length, the solution to the BVP is unique. While for small Peclet numbers and activation energy, and for large Damkohler number and reactor length, there exist at least three solutions to the BVP. The conclusion is that the number of solution (s) for the BVP depends on the choice of parameter values. Likewise, the first set of parameter values listed above models the adiabatic plug flow reactor, while the other parameter set models the adiabatic continuous stirred tank reactor.

Lewis-number effects on edge-flame propagation

2002 ◽  
Vol 458 ◽  
pp. 219-228 ◽  
Author(s):  
VEDHA NAYAGAM ◽  
F. A. WILLIAMS
Keyword(s):  
Activation Energy ◽  
Propagation Velocity ◽  
Steady Motion ◽  
Lewis Number ◽  
Diffusion Time ◽  
Damkohler Number ◽  
Dimensional Model ◽  
One Dimensional ◽  
Damköhler Number ◽  
Propagation Velocities

Activation-energy asymptotics is employed to explore effects of the Lewis number, the ratio of thermal to fuel diffusivity, in a one-dimensional model of steady motion of edges of reaction sheets. The propagation velocity of the edge is obtained as a function of the relevant Damköhler number, the ratio of the diffusion time to the chemical time. The results show how Lewis numbers different from unity can increase or decrease propagation velocities. Increasing the Lewis number increases the propagation velocity at large Damköhler numbers and decreases it at small Damköhler numbers. Advancing-edge and retreating-edge solutions are shown to exist simultaneously, at the same Damköhler number, if the Lewis number is sufficiently large. This multiplicity of solutions has a bearing on potential edge-flame configurations in non-uniform flows.

Toluene degradation by heterogeneous photocatalysis assisted with ozone in a tubular reactor: analysis over the reactor length

2021 ◽  
Author(s):  
Bárbara Maria Borges Ribeiro ◽  
Renato Carajelescov Nonato ◽  
Tânia Miyoko Fujimoto ◽  
Bianca Gvozdenovic Medina Bricio ◽  
Ursula Luana Rochetto Doubek ◽  
...  
Keyword(s):  
Tubular Reactor ◽  
Heterogeneous Photocatalysis ◽  
Toluene Degradation ◽  
Reactor Length

scholarly journals Development of a tubular continuous flow reactor for the investigation of improved gas–solid interaction in photocatalytic CO2 reduction on TiO2

2019 ◽  
Vol 18 (2) ◽  
pp. 314-318 ◽  
Author(s):  
Martin Dilla ◽  
Ahmet E. Becerikli ◽  
Alina Jakubowski ◽  
Robert Schlögl ◽  
Simon Ristig
Keyword(s):  
Gas Phase ◽  
Continuous Flow ◽  
Flow Reactor ◽  
Tubular Reactor ◽  
Co2 Reduction ◽  
Continuous Flow Reactor ◽  
Reactor Geometry

Newly developed tubular reactor geometry allows intensive gas–solid interaction in photocatalytic gas-phase CO2 reduction.

Modeling of a Fixed-Bed Reactor for the Production of Phthalic Anhydride

2011 ◽  
Vol 6 (1) ◽  
Author(s):  
Amir Rahimi ◽  
Sogand Hamidi
Keyword(s):  
Phthalic Anhydride ◽  
Fixed Bed ◽  
Tubular Reactor ◽  
Operating Conditions ◽  
Fixed Bed Reactor ◽  
Conversion Degree ◽  
Reactor Length ◽  
Reactor Temperature ◽  
Reported Data ◽  
Reactor Pressure

In this study, the performance of a fixed–bed tubular reactor for the production of phthalic anhydride is mathematically analyzed. The conversion degree and reactor temperature values are compared with the measured one in a tubular reactor applied in Farabi petrochemical unit in Iran as well as reported data in the literature for a pilot plate. The comparisons are satisfactory. The effects of some operating parameters including reactor length, feed temperature, reactor pressure, and existence of an inert in the catalytic bed are investigated. The optimum value of each parameter is determined on the basis of the corresponding operating conditions.

A Mass Transport Model for CVD Coating of Optical Fibers

2003 ◽  
Author(s):  
Wei Huang ◽  
Wilson K. S. Chiu
Keyword(s):  
Mass Transport ◽  
Diffusion Model ◽  
Optical Fibers ◽  
Peclet Number ◽  
Flow Reactor ◽  
Transport Model ◽  
Gas Diffusion ◽  
Transfer Model ◽  
Continuous Stirred Tank Reactor ◽  
Péclet Number

Carbon coated optical fibers are produced by the chemical vapor deposition process which includes multi-species mass transport with chemical reactions. A proper numerical model of this process will help elucidate the basic mechanisms and optimize the process to improve coating quality. A heat transfer model has been developed in our research group. We are now developing an applicable chemical kinetics model to include mass transport with gas phase and surface reactions. Several different chemical reactor models have been tried, including a continuous-stirred tank reactor (CSTR) model, a plug flow reactor (PFR) model and a multi-component diffusion model with the Maxwell-Stefan approximations. We found that in reactor conditions with well-mixed or large mass Peclet number, the CSTR and PFR models validate well with experimental results. But a multi-component gas diffusion model is needed for low mass Peclet number conditions. The model has been extended to a wider range of temperatures necessary for this optical fiber coating process.

scholarly journals Optimization of Pd Membrane Reactor for Direct Oxidation of Aromatic Compounds

2011 ◽  
Vol 11 (1) ◽  
pp. 8
Author(s):  
Milad Rasouli ◽  
Sahar Chitsazan ◽  
Mohammad Hossein Sayyar ◽  
Nakisa Yaghobi ◽  
Babak Bozorgi
Keyword(s):  
Fluid Dynamic ◽  
Active Oxygen Species ◽  
Tubular Reactor ◽  
Direct Oxidation ◽  
Design And Optimization ◽  
Reactor Length ◽  
Length Increase ◽  
Principal Reaction ◽  
Complex Chemical Reactions ◽  
Geometrical Factors

Computational fluid dynamic has already become a widely used and indispensable design and optimization tool in many technical areas. In the present work, the CFD simulations have been coupled with complex chemical reactions to model a membrane tubular reactor which is used to produce phenol from benzene in the vapor phase. Hydrogen dissociates on the palladium layer and reacts with oxygen to give active oxygen species, which attack benzene to produce phenol. In principal, reaction occurs in the surface of palladium and conversion of benzene is increased by changing the length and diameter of the Pd coated PSS tubes. The reactor length and diameter are two geometrical factors which are concerned in the present study. Although increasing the reactor length increase the conversion of benzene to phenol but the concentration of the phenol start to decrease. Based on the data provided by the experiments, a mathematical model has been constructed to conduct a simulation which leads us to an optimum design of a new tubular membrane micro-reactor.

Delay-Adaptive Linear Control

2020 ◽  
Author(s):  
Yang Zhu ◽  
Miroslav Krstic
Keyword(s):  
Nonlinear Differential Equations ◽  
Stability Study ◽  
Delay Systems ◽  
Engineering Practice ◽  
Delay Compensation ◽  
Infinite Dimensional ◽  
Controlled Systems ◽  
Finite Dimensional ◽  
And Control ◽  
Parameter Values

Actuator and sensor delays are among the most common dynamic phenomena in engineering practice, and when disregarded, they render controlled systems unstable. Over the past sixty years, predictor feedback has been a key tool for compensating such delays, but conventional predictor feedback algorithms assume that the delays and other parameters of a given system are known. When incorrect parameter values are used in the predictor, the resulting controller may be as destabilizing as without the delay compensation. This book develops adaptive predictor feedback algorithms equipped with online estimators of unknown delays and other parameters. Such estimators are designed as nonlinear differential equations, which dynamically adjust the parameters of the predictor. The design and analysis of the adaptive predictors involves a Lyapunov stability study of systems whose dimension is infinite, because of the delays, and nonlinear, because of the parameter estimators. This book solves adaptive delay compensation problems for systems with single and multiple inputs/outputs, unknown and distinct delays in different input channels, unknown delay kernels, unknown plant parameters, unmeasurable finite-dimensional plant states, and unmeasurable infinite-dimensional actuator states. Presenting breakthroughs in adaptive control and control of delay systems, the book offers powerful new tools for the control engineer and the mathematician.

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