Some problems concerning the non-adiabatic tubular reactor a-priori bounds,qualitative behavior,preliminary uniqueness and stability considerations

An investigation of the non-adiabatic tubular reactor, in which a single chemical reaction occurs, is presented. The steady state mass and heat balance equations are shown to be a pair of coupled, nonlinear differential equations, and are shown to uncouple into a single functional-differential equation for the case Le = 1. A-priori bounds on the steady state concentration and temperature are developed, and some remarks about the shape of the steady state profiles made. Sufficient conditions ensuring uniqueness of steady states and their asymptotic stability are derived.     

An experimental study of instability in a non-adiabatic multi-reaction tubular reactor

An experimental study of instability in a non-adiabatic packed bed reactor using NO reduction with CO over a fiber glass supported Ru catalyst is presented. A 2-reaction kinetic model is used. The results are compared to the predictions of two different TRAM ignition criteria which are expanded to cover the non-adiabatic, single reactant but multireaction case. Although there were difficulties in experimentally evaluating some of the transport parameters, the results show that one of the expanded ignition criteria in particular does satisfactorily model the data. Data are also presented which show how the temperature profile in an ignited bed moves as the inlet temperature is lowered to the quench point. Additional quench data are provided which show that the quench point is strongly affected by the feed concentration of the reactant and only a mild function of gas velocity.     

Modelling channel interactions in a non-adiabatic multichannel catalytic combustion reactor

The development of a mathematical model to account for channel interactions in a multichannel monolith with square shaped channels is described. As an example of the application of the code, channel interactions are modelled that result from a maldistribution in fuel supply into a catalytic monolith combustor. The response of a metal and a ceramic monolith are compared, demonstrating the advantages of conduction as a method of dissipating heat in the radial direction.     

Emulsion copolymerization in a tubular reactor

A study was conducted on the emulsion copolymerization of vinyl acetate and butyl acrylate in a tubular reactor. It was performed at a constant temperature of 60°C and at different fluid velocities and feed compositions. Conversion, particle size distribution, and copolymer composition were measured, respectively, with gravimetric method, laser light scattering, and nuclear magnetic resonance. Maximum conversions were found for each of the monomer compositions; this maximum conversion varied, however, with the recipe used. The amount of butyl acrylate has a direct effect on the number of particles and on the final conversion. In lower levels of butyl acrylate particle size distribution is wide and bimodal. High levels of butyl acrylate leads to narrow and monomodal particle size distribution. Therefore the level of butyl acrylate and the velocity of fluid flowing inside the tube have strong effects on the shape (monomodal‐bimodal) and the width of particle size distributions. This effect may vary at different levels of butyl acrylate and flow rate. The results obtained from copolymer composition show that an alternating block copolymer is made during the reaction. © 2000 John Wiley & Sons, Inc. J Appl Polym Sci 75: 833–842, 2000     

Modeling an annular flow tubular reactor

A stochastic model representing annular flow in a tubular reactor is proposed. Numerical simulation was utilized to generate sample paths fitting the residence time distributions (RTD) of the system. The model was constructed from basic diffusion equations with the additional consideration of random effects disturbing the system, thus yielding a stochastic partial differential equation. The stochastic model is simulated using the Euler–Maruyama procedure. Experimental data from three tubular polymerization reactors were well fitted by the model. The model encompassed the two deterministic parameters, mean residence time and Peclet number, as well as three stochastic parameters: stochastic relevance (b), updated time (ΔT) and the seed that begins the Wiener process. The satisfactory results indicate that the model constitutes an important step toward comprehending the complex fluid dynamics of tubular flow systems.     

Transient behaviour of a non-ideal tubular reactor

Experimental data are reported for the unsteady state behaviour of a laminar flow reactor with first order homogeneous liquid phase reaction. The data are in agreement with the predictions of the dispersion model, using previously reported reaction-dependent dispersion coefficients which directly gives the bulk mean concentration. The use of proper boundary conditions, ignored in a recent paper on this topic⁽¹⁹⁾, is found to significantly influence the predictions. Unlike the conclusion drawn in⁽¹⁹⁾ it is shown that the Taylor model is unable to correctly predict the reactor length for fast reactions even for high conversions.     

Numerical simulation of a tubular polymerization reactor

A mathematical model for a tubular emulsion polymerization reactor is developed. The partial differential equations describing the mass balances on initiator, monomer, and number of polymer particles are numerically solved using an implicit–explicit scheme based on the Crank–Nicholson method. The model adequately simulates experimental results reported by Rollin and co-workers and sufficiently explains the unusual behavior of the reactor when operating at relatively low emulsifier concentrations.     

Calcination of limestone in a tubular reactor

Theoretical expressions were developed for the design of a tubular reactor for the calcination of limestone, pneumatically conveyed by flue gas. The total residence time and the length of the reactor are affected in particular by the particle size, the excess thermal capacity of the gas and the heat transfer coefficient. High throughput can be achieved in relatively small reactors. An experimental investigation verified a theoretical prediction, that a considerable part of the decomposition takes place in the first few centimeters of the reactor length. The rate of heat transfer in this section was high, with Nusselt numbers of 9.9 to 31.7.     

Some general observations on tubular reactor stability

A sufficient condition under which a tubular reactor with axial diffusion is globally stable is derived by use of the maximum principle for parabolic equations. It is shown that by use of some topological concepts the asymptotic stability of a steady state can be determined without the necessity of performing any computations. If a unique steady state exists it is asymptotically stable. If three steady states exist, the high and low temperature steady states are asymptotically stable, while the intermediate one is unstable.     

Startup of an industrial adiabatic tubular reactor

The dynamic behaviour of an adiabatic tubular plant reactor during the startup is demonstrated, together with the impact of a feed-pump failure of one of the reactants. A dynamic model of the reactor system is presented, and the system response is calculated as a function of experimentally-determined, time-dependent, manipulated variables. The values of model parameters are estimated by using the SimuSolv (1991) computer program. The data set collected during the reactor start-up is used for the parameter estimation procedure. An excellent agreement is obtained between the experimental and the calculated system response. Many continuously-operated commercial reactors require a complete conversion of one of the main reactants at the reactor exit. It is shown that for an industrial tubular reactor a much higher initial reactor temperature is required during the startup, compared to the reactor inlet temperature during normal steady-state operation, to ensure a complete reactant conversion. Much more research is necessary to determine whether this is a generally valid rule.     

The unsteady-state solution for a finite dispersion-type catalytic packed-bed tubular reactor

The unsteady-state solution is obtained by an operator theory in functional analysis setting for a general finite catalytic packed-bed tubular reactor model with axial dispersion in the bed, mass transfer between the catalyst particles and the flowing phase, and intraparticle diffusion and surface reaction in the catalyst particles.     

Hydrodeoxygenation of vegetable oil in batch reactor: Experimental considerations

The generation of reliable experimental data in any experimental scale requires proper procedures not only for the reaction step but also for the feed preparation, separation, and characterization of products as well as calculations of conversion and product yields. Batch reactor is the most used experimental setup for carrying out exploratory studies for catalyst screening and development. This work is focused on describing and discussing a step-by-step methodology for conducting experiments for catalytic hydrotreating of vegetable oils in batch reactor. The proposed methodology considers literature and own experiences on advantages and disadvantages of different feed types, catalysts, experimental setup and procedures, effect of reaction parameters, separation and characterization of products, and calculations.     

Simulation of an industrial nylon 6 tubular reactor

A commonly used energy-efficient nylon 6 reactor is simulated under steady-state conditions. The effects of various operating conditions and parameters, e.g., feed composition, temperature and flow rate, heat transfer coefficients, and reactor dimensions, on the temperature and molecular weight profiles are studied. A temperature maximum is observed in the reactor under usual conditions of operation. The maximum value of the temperature is sensitive to the feed conditions, and one has to ensure that degradation reactions speeded up at high temperatures do not affect product characteristics. The model and the numerical technique used are fairly simple and account for most of the important features of industrial reactors. Hence, these can be used in the development of digital-control algorithms in the future.     

Qualitative and quantitative observations on the tubular reactor

The tubular reactor in the steady state is considered for a single chemical reaction. It is shown that almost all of the qualitative features of the temperature and concentration profiles may be deduced from the equations themselves without solving them. Extensive numerical calculations are also presented both for the finite and semi-infinite reactor. Comparisons are made with the lumped constant system. It is shown that the solution for the semi-infinite reactor is always unique and serves as a bounding solution for all finite reactors with the same parameters.