Modeling tubular reactor

Specific reactor characteristics depend on the particular use of the reactor as a laboratory, pilot plant, or industrial unit. AH reactors have in common selected characteristics of four basic reactor types the weH-stirred batch reactor, the semibatch reactor, the continuous-flow stirred-tank reactor, and the tubular reactor (Fig. 1). A reactor may be represented by or modeled after one or a combination of these. SuitabHity of a model depends on the extent to which the impacts of the reactions, and thermal and transport processes, are predicted for conditions outside of the database used in developing the model (1-4). 

This model v/as used by Atwood et al (1989) to compare the performance of 12 m and 1.2 m long tubular reactors using the UCKRON test problem. Although it was obvious that axial conduction of matter and heat can be expected in the short tube and not in the long tube, the second derivative conduction terms were included in the model so that no difference can be blamed on differences in the models. The continuity equations for the compounds was presented as ... 

Donnet, M., Jongen, N., Lemaitre, J., Bowen, P. and Hofmann, H., 1999. Better control of nucleation and phase purity using a new segmented flow tubular reactor Model system Precipitation of calcium oxalate. In 14th International Symposium on Industrial Crystallization. Cambridge, U.K., September 12-16, Institution of Chemical Engineers, CD ROM, pp. 1-13. 

The computer model used for this analysis is based on a plug flow tubular reactor operating under restraints of the commonly accepted kinetic mechanism for polymerization reactions ( 5 ) ... 

A theoretical polymerization tubular reactor model was used to study the effects of reactor operating parameters on conversion... 

This section has based scaleups on pressure drops and temperature driving forces. Any consideration of mixing, and particularly the closeness of approach to piston flow, has been ignored. Scaleup factors for the extent of mixing in a tubular reactor are discussed in Chapters 8 and 9. If the flow is turbulent and if the Reynolds number increases upon scaleup (as is normal), and if the length-to-diameter ratio does not decrease upon scaleup, then the reactor will approach piston flow more closely upon scaleup. Substantiation for this statement can be found by applying the axial dispersion model discussed in Section 9.3. All the scaleups discussed in Examples 5.10-5.13 should be reasonable from a mixing viewpoint since the scaled-up reactors will approach piston flow more closely. 

Chapter 3 introduced the basic concepts of scaleup for tubular reactors. The theory developed in this chapter allows scaleup of laminar flow reactors on a more substantive basis. Model-based scaleup supposes that the reactor is reasonably well understood at the pilot scale and that a model of the proposed plant-scale reactor predicts performance that is acceptable, although possibly worse than that achieved in the pilot reactor. So be it. If you trust the model, go for it. The alternative is blind scaleup, where the pilot reactor produces good product and where the scaleup is based on general principles and high hopes. There are situations where blind scaleup is the best choice based on business considerations but given your druthers, go for model-based scaleup. 

Consider the scaleup of a small, tubular reactor in which diffusion of both mass and heat is important. As a practical matter, the same fluid, the same inlet temperature, and the same mean residence time will be used in the small and large reactors. Substitute fluids and cold-flow models are sometimes used to study the fluid mechanics of a reactor, but not the kinetics of the reaction. 

McLaughlin, H. S., Mallikarjun, R., and Nauman, E. B., The Effect of Radial Velocities on Laminar Flow, Tubular Reactor Models, AIChE J., 32, 419-425 (1986). 

Determine the yield of a second-order reaction in an isothermal tubular reactor governed by the axial dispersion model with Pe = 16 and kt = 2. 

Water at room temperature is flowing through a 1.0-in i.d. tubular reactor at Re= 1000. What is the minimum tube length needed for the axial dispersion model to provide a reasonable estimate of reactor performance What is the Peclet number at this minimum tube length Why would anyone build such a reactor ... 

Example 13.9 Illustrate temperature and molecular weight changes in a tubular reactor by constructing a simple model of styrene polymerization in a tube. 

FIGURE 13.8 Temperature profiles using a simplified model of a tubular reactor with pure styrene feed = 135 C and = 20°C. The parameter is the tube diameter in meters. 

Mathematical Modeling of Bulk and Solution Polymerization in a Tubular Reactor... 

Based on the results of these researchers the tubular reactor in this study has been described by the axisymmetric model using effective diffusivities given by Equation 20. 

The catalyst testing was carried out in a gas phase downflow stainless steel tubular reactor with on-line gas analysis using a Model 5890 Hewlett-Packard gas chromatograph (GC) equipped with heated in-line automated Valeo sampling valves and a CP-sD 5 or CP-sil 13 capillary WCOT colunm. GC/MS analyses of condensable products, especially with respect to O-isotopic distribution, was also carried out using a CP-sil 13 capillary column. For analysis of chiral compounds, a Chirasil-CD capillary fused silica column was employed. 

Under steady-state conditions, variations with respect to time are eliminated and the steady-state model can now be formulated in terms of the one remaining independent variable, length or distance. In many cases, the model equations now result as simultaneous first-order differential equations, for which solution is straightforward. Simulation examples of this type are the steady-state tubular reactor models TUBE and TUBED, TUBTANK, ANHYD, BENZHYD and NITRO. 

Mathematical models of tubular chemical reactor behaviour can be used to predict the dynamic variations in concentration, temperature and flow rate at various locations within the reactor. A complete tubular reactor model would however be extremely complex, involving variations in both radial and axial... 

The component mass balance equation, combined with the reactor energy balance equation and the kinetic rate equation, provide the basic model for the ideal plug-flow tubular reactor. 

With respect to reaction rates, an element of fluid will behave in the ideal tubular reactor, in the same way, as it does in a well-mixed batch reactor. The similarity between the ideal tubular and batch reactors can be understood by comparing the model equations. 

The coupling of the component and energy balance equations in the modelling of non-isothermal tubular reactors can often lead to numerical difficulties, especially in solutions of steady-state behaviour. In these cases, a dynamic digital simulation approach can often be advantageous as a method of determining the steady-state variations in concentration and temperature, with respect to reactor length. The full form of the dynamic model equations are used in this approach, and these are solved up to the final steady-state condition, at which condition... 

Figure 4.11. Finite-differencing for a dynamic tubular reactor model.

Axial and radial dispersion or non-ideal flow in tubular reactors is usually characterised by analogy to molecular diffusion, in which the molecular diffusivity is replaced by eddy dispersion coefficients, characterising both radial and longitudinal dispersion effects. In this text, however, the discussion will be limited to that of tubular reactors with axial dispersion only. Otherwise the model equations become too complicated and beyond the capability of a simple digital simulation language. 

Steady-State Tubular Reactor Dispersion Model... 

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