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.     

Regional stability for a tubular reactor with axial mixing

A graphical phase-plane procedure is suggested by which regions of stability can be estimated for a tubular reactor. The technique uses a super-position of limits for primary flow and reaction effects and those arising from secondary axial dispersion. Several detailed numerical tests are reported to substantiate the conjecture.     

Some general observations on the recycle flow model

Recycle around a plug flow reactor is considered for all possible recycle rates, both positive and negative. For a first order reaction in such a system performance predictions are made. System behaviour as the recycle rate tends to infinity is discussed.     

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.     

Multiplicity,stability, and oscillatory dynamics of the tubular reactor

Numerical bifurcation techniques were developed for studying the multiplicity, stability, and oscillatory dynamics of the nonadiabatic tubular reactor with a single A → B reaction. The techniques illustrate the existence of one, three, five, or seven steady states and bifurcating periodic solutions. We present numerical procedures for computing the Hopf bifurcation formulas which can determine the stability and location of the oscillation without integrating the parabolic partial differential equations. The combination of our Hopf techniques with steady state bifurcation methods enables us to determine all possible steady and stable oscillatory solutions exhibited by distributed parameter models such as the tubular reactor.     

Some general considerations of reversible chemical reactions in batch and tubular reactors

The possibility of change in the algebraic sign of the net reaction rate of a single reversible reaction occurring in adiabatic or non-adibatic batch and tubular reactors is investigated. This change is shown not to occur for adiabatic reactors; it may depending on the operating conditions and the system parameters for non-adiabatic reactors. These and the related aspects of approach to system equilibrium are analyzed by an examination of the mathematical models describing these chemical reactors. Important results are summarized throughout the paper as Conclusions 1 - 10. The results have direct applications in reactor design and operation. From a practical point of view it means that yield may be reduced in some cases by allowing too long a residence time even for a single reaction. Numerical examples are given to illustrate the results.     

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.     

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.     

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.     

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 observations on food allergy

Conclusions Some fundamenally important concepts of allergy and the methods of identification of the extrinsic causative factors in allergic disease have been reviewed. Clinical evidence beasung upon the occurrence of allergic sisturbances attributed to allergens othe cottonseed has been assembled and examined to illustrate the fact that effective discrimination against, a single class of food products may result from faulty interpretation of valid clinical data.     

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 non-adiabatic tubular reactor: Stability considerations

This paper is a continuation of four previous ones in this journal ^{(1, 2, 3, 4)} and is involved with the transient and stability behavior of a non-adiabatic unpacked tubular reactor. The steady states found earlier are tested for stability both by computing transient profiles and by computing the eigenvalues of the appropriate linearized problem. It is found in all cases that the two computations predict the proper stability behavior. It is shown that in some cases all steady states for a given set of parameters may be unstable and that a unique steady state may give rise to an oscillatory system.     

筒式光催化反应器降解养殖废水研究

以柔性纤维负载Ti O2为光催化剂,自制筒式光催化反应器,进行光催化模拟水产养殖废水实验,考察了曝气量、p H值、催化剂投加量与初始浓度等因素对氨氮去除率的影响。结果表明,在曝气量为1.0 L/min,催化剂用量12.5 g,碱性条件及初始浓度在90 mg/L时,氨氮降解率最高为85.3%。不同初始浓度氨氮的光催化降解速率符合准一级动力学模型,模拟养殖箱连续运行15 d表明,氨氮浓度降低,可满足水产养殖废水标准。