Plug Flow Tubular Reactor Research Articles

A mathematical model for a tubular reactor performing ethylene oxidation to ethylene oxide by a catalyst deposited on metallic strips

Catalysts supported on metallic strips may be used advantageously in catalytic processes requiring a severe thermal control, i.e. the catalytic oxidation of ethylene to ethylene oxide. Following the characteristics of such catalysts, reported in two patents, a mathematical model allowing the calculation of the longitudinal temperature of reacting gas and/or the radial temperature of the catalytic module is presented for a tubular plug flow reactor. The pressure drop is also calculated and compared with that of the same reactor filled with traditional spherical pellets. It has been proved that the advantage of catalytic modules, employing metallic strips, are the following: (i) flattening of the longitudinal and radial temperature profiles; (ii) reduction of the pressure drop; (iii) high productivity of ethylene oxide.

Control of Plug-Flow Tubular Reactors by Variation of Flow Rate

Control of Plug-Flow Tubular Reactors by Variation of Flow Rate

Control of Plug-Flow Tubular Reactors by Variation of Flow Rate

Control of Plug-Flow Tubular Reactors by Variation of Flow Rate

Yield optimization for the van de vusse reaction

The Van de Vusse reaction is the classic example of a complex reaction network for which the general guidelines or steady state reactor selection do not apply. It has been shown earlier by simulation for a restricted range of kinetic parameters that maximum yield of the desired product may be higher in a continuous flow stirred tank reactor (CSTR), in a plug flow tubular reactor (PFR) or in a PFR with recycle. Using analytic solutions for all combinations of the kinetic parameters for the CSTR, PFR and PFR with recycle, a classification of the entire kinetic parameter space on the basis of maximum yield of the desired product versus recycle ratio behavior is presented. Thus region wherein a CSTR, a PFR or a PFR with recycle are optimal can be readily indentified.

A method for modelling of complex chemical kinetics

A generalized approach to computation of chemical kinetics is given. In the method presented, the stoichiometry of the reactions and the form of reaction rate expressions are input in matrix form. Nonintegral stoichiometric coefficients are possible and the reaction orders are not limited to being only a subset of the former. With examples of three fundamental reactor types (homogeneous batch, tubular plug-flow and continuous stirred-tank reactor) it is shown that it is possible to formulate in a simple and straightforward way mathematical models of chemical reactors which are general with respect to complex reaction kinetics. The general simulation program, based on this method, was successfully used for the trial-and-error identification of the hypothetical kinetic structure of a biochemical process.

Optimal contaminant removal in fermentation and waste treatment processes

A bifunctional enzymatic catalyst system may be optimally distributed along a plug flow tubular reactor to reduce trace contamination. For the system considered in this study, there are nine possible optimal catalyst distribution policies, depending on the magnitude of the initial concentrations, the relative oxidizing power of the contaminants, and the residence time in the reactor. The effects of these system parameters on the optimal distribution policies are discussed, as is the possibility of replacing the optimal policies with suboptimal decisions. The relative errors caused by the suboptimal policies are found to be insignificant in many cases, but the approximations may not do as well if the oxidizing contaminants have relatively very different effects.

On singular policies in the optimal distribution of a bifunctional catalyst: Part I. Effect of reaction kinetics

AbstractResults are presented on the affects of kinetic changes on optimal, bifunctional, catalyst distribution policies for a consecutive two‐reaction sequence in a plug flow tubular reactor. Earlier results on singular control arising from reversible reactions are extended to include inhibition or activation. These may arise from the affects of any reactant or product on the rate or from a subsequent or preceding reaction in a sequence. The system equations are written in dimensionless form to provide efficient computations and to allow analytic interpretation of numerical results from previous studies.

Optimal Contaminant Removal in Fermentation and Waste Treatment Processes

A bifunctional enzymatic catalyst system may be optimally distributed along a plug flow tubular reactor to reduce trace contamination. For the system considered in this study, there are nine possible optimal catalyst distribution policies, depending on the magnitude of the initial concentrations, the relative oxidizing power of the contaminants, and the residence time in the reactor. The effects of these system parameters on the optimal distribution policies are discussed, as is the possibility of replacing the optimal policies with suboptimal decisions. The relative errors caused by the suboptimal policies are found to be insignificant in many cases, but the approximations may not do as well if the oxidizing contaminants have relatively very different effects.

A radial cell model for a tubular polymerization reactor

AbstractA cell model for the prediction of temperature and concentration gradients in a nonisothermal tubular polymerization reactor at steady state is presented. Both radial and longitudinal gradients are considered. The complete molecular weight distribution is calculated as well as the leading moments of the distribution. The model is easily reduced to predict the performance of a plug‐flow tubular reactor, batch reactor, and continuous stirred tank reactor (CSTR). The specific polymerization mechanism application consists of free‐radical initiation, propagation, and combination termination.

Sufficient conditions for uniqueness and local asymptotic stability for a class of distributed parameter systems: non-adiabatic plug-flow tubular reactors with recycle and feedback control

An analysis of the stability of a non-adiabatic tubular reactor with feedback control, modelled by a plug-flow reactor in which axial dispersion of heat and mass is accounted for by recycle, is presented, A sufficient condition for local stability is developed in terms of system parameters and steady-state profiles. This condition is extended to a condition which is in terms of system parameters and outlet temperature only. Also, a unique stable steady-state criterion, which is in terms of system parameters only, is obtained. These conditions show that under certain assumptions the stability can always be proved for a suitable choice of controller settings.

Solution of non-linear initial value problems by the orthogonal collocation method

The mathematical model of the plug flow tubular reactor (PFTR) in steady state behavior, consisting of a set of initial value ordinary differential equations, is solved by the orthogonal collocation method. The solution to the resulting set of non-linear collocation equations is found by the Newton-Raphson iteration formula, as well as by a method of successive approximations. The computation time required by both techniques for given accuracy is studied as a function of the number of collocation points, the number of subdivisions of the integration interval and the number of differential equations, The method of successive approximations becomes more powerful than the Newton-Raphson technique for larger numbers of differential equations.

A STUDY OF THE CONTROL OF A TUBULAR REACTOR WITH RECYCLE I. Theoretical Results for a Zero-order Exothermic Reaction

The topic of interest in this paper is the behavior of a plug-flow tubular reactor with recycle under feedback control of the rcgutalor type. Attention is devoted mainly to the problem of stabilizing those sicady-slatc profiles which are unstable in the absence of control, but the investigation also includes the controlled behavior of those steady states which arc naturally liable. The study reported in this paper is theoretical; it invokes methods of linear stability analysis and computer simulations in considering two separate cases involving different controlled and manipulated variables. The class of controller functions considered includes the conventional proporIionaI-integraderivative controller. The principal discovery is that the presence of any time delay, regardless of its magnitude, in the controller response prevents stabilization of a naturally unstable state by means of control Strategics of this type. In one of the cases considered, It Is shown that if time delay in the control action is totally absent, stabilization can be achieved; in the other case, stabilization is shown to be possible only if both the time delay in the controller and the transportation lag in the recycle line are zero. The study reported here is based on a hypothetical zero-order reaction, but the icsutls ate linked Io prior experimental observations. Also, other realistic aspects of the basic problem are discussed, and the need for further work is pointed out.

Multivariable PID estimation and control in systems with biased disturbances

A solution is given to yield reset control action in multivariable control systems, where the controller consists of a state reconstructor and feedback from estimated process and environmental states. Integral action in the estimation loop follows from the assumptions about the disturbance model, and if a special choice for the “feed-forward” matrix operating on the estimated environmental states is made, integral, or reset, control action results. The classical least squares optimal control with modeling of the environment is illustrated using a linearized model of a plug flow tubular reactor as a basis for the design. As a second example which illustrates the reset control action, i.e. the tracking of a constant reference vector with zero control error, a simple third order linear system is used.

Control of Plug-Flow Tubular Reactors by Variation of Flow Rate

The control of isothermal and adiabatic plug-flow tubular reactors by variation of flow rate was studied. Proportional feedback, feedforward, and optimal control responses were compared for the regulation of reactor conversion in the presence of inlet disturbances. The optimal control, consisting of a singular solution in each case, produces a considerably improved response over both feedforward and proportional feedback control.

Error in handling finite conversion reactor data by the differential method

The error introduced by using the differential method to handle reaction rate data from reactors operated at finite conversion in order to establish the rate equation is considered. A general method of evaluating this error is developed and several of the more typical kinetic models are analyzed. The results show that even for reversible reactions and for kinetics of the Langmuir-Hinshelwood type with strong adsorption of reactants or products the differential method can be used up to rather large conversions, about 15% for most cases. Although the results are developed for plug-flow tubular reactors, they can easily be extended to batch systems.

Singular solutions in the optimal control of lumped- and distributed-parameter systems

The necessary conditions for a singular optimal subarc in both lumped- and distributed-parameter systems are derived in this paper. Consideration is given to the synthesis of optimal trajectories when such singularities exist. Computational results are presented for a number of systems including the plug-flow tubular reactor to show that such a synthesis can be carried out. A combination of direct search and steepest ascent methods prove quite feasible as a computational tool for handling such optimal systems.

Bounding chemical reactor transients by estimation of growth or decay rates

AbstractIf the transient equations of a plug flow tubular reactor are transformed into a set of corresponding ordinary differential equations, stability information for the former may be obtained graphically from knowledge about the transients of the latter. The analysis presented in this paper combines this simplification with the definitions and theorems of Weiss and Infante to propose a method of direct computation whereby transient bounds may be found for this important class of distributed‐parameter chemical reactor systems.

The effect of dispersion on chemical reactor optimum residence times using perturbation expansion techniques

This work is a mathematical study of the effect of dispersion on the optimum residence times of chemical reactors. Attention is confined to the range of very small and very large dispersions so that perturbation expansions can be used to obtain asymptotic solutions to the equations for the axial dispersed plug flow tubular reactor. Only the consecutive reaction system A → B → C, where B is a desired intermediate product is considered. The optimum residence time is then defined as that which maximizes the yield of B in each isothermal reactor model. It is shown that the expansions for optimum residence time are excellent approximations over a wide range of operating conditions for this reactor model. An interesting maximum effect in the optimum residence time for the axial dispersed tubular reactor is discussed.