Isothermal reactor with axial dispersion

DISRE - Isothermal Reactor with Axial Dispersion... 

Adiabatic reactor with radial dispersion and chemical reaction Adiabatic reactor with axial dispersion and chemical reaction Not isothermal reactor with axial dispersion. 

DISRET - Non-Isothermal Tubular Reactor with Axial Dispersion 340... 

Kinetic/transport for Isothermal Laminar-Flow Reactor with Axial Dispersion under Transient Open-Loop Operation... 

Consider a simple trickle-bed for which one can assume uniform gas and liquid distributions, a nonvolatile liquid, trickling flow, isothermal pellets, and complete wetting. For an isothermal reactor with a uniform distribution of the gas and liquid phases, there will be no radial gradients of concentration. Although axial dispersion is more important in trickle-beds than in fixed-beds because of relatively low fluid velocities, we will assume that the dispersion is negligible. Under the assumptions, one can write for the gas phase (refer to Figure 12.3) ... 

Kirelic/lranspon for Isothermal Laminar-Flow Reactor with no Axial Dispersion [See Shinohara and Christiansen (I974J for ilie non-isoihermul... 

Adiabatic Reactors. Like isothermal reactors, adiabatic reactors with a flat velocity profile will have no radial gradients in temperature or composition. There are axial gradients, and the axial dispersion model, including its extension to temperature in Section 9.4, can account for axial mixing. As a practical matter, it is difficult to build a small adiabatic reactor. Wall temperatures must be controlled to simulate the adiabatic temperature profile in the reactor, and guard heaters may be needed at the inlet and outlet to avoid losses by radiation. Even so, it is hkely that uncertainties in the temperature profile will mask the relatively small effects of axial dispersion. 

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. 

Most biochemical reactors operate with dilute reactants so that they are nearly isothermal. This means that the packed-bed model of Section 9.1 is equivalent to piston flow. The axial dispersion model of Section 9.3 can be applied, but the correction to piston flow is usually small and requires a numerical solution if Michaehs-Menten kinetics are assumed. 

A one-dimensional isothermal plug-flow model is used because the inner diameter of the reactor is 4 mm. Although the apparent gas flow rate is small, axial dispersion can be neglected because the catalj st is closely compacted and the concentration profile is placid. With the assumption of Langmuir adsorption, the reactor model can be formulated as. 

This example models the dynamic behaviour of an non-ideal isothermal tubular reactor in order to predict the variation of concentration, with respect to both axial distance along the reactor and flow time. Non-ideal flow in the reactor is represented by the axial dispersion flow model. The analysis is based on a simple, isothermal first-order reaction. 

In this section, we apply the axial dispersion flow model (or DPF model) of Section 19.4.2 to design or assess the performance of a reactor with nonideal flow. We consider, for example, the effect of axial dispersion on the concentration profile of a species, or its fractional conversion at the reactor outlet. For simplicity, we assume steady-state, isothermal operation for a simple system of constant density reacting according to A - products. 

The solution of Eq. (173) poses a rather formidable task in general. Thus the dispersed plug-flow model has not been as extensively studied as the axial-dispersed plug-flow model. Actually, if there are no initial radial gradients in C, the radial terms will be identically zero, and Eq. (173) will reduce to the simpler Eq. (167). Thus for a simple isothermal reactor, the dispersed plug flow model is not useful. Its greatest use is for either nonisothermal reactions with radial temperature gradients or tube wall catalysed reactions. Of course, if the reactants were not introduced uniformly across a plane the model could be used, but this would not be a common practice. Paneth and Herzfeld (P2) have used this model for a first order wall catalysed reaction. The boundary conditions used were the same as those discussed for tracer measurements for radial dispersion coefficients in Section II,C,3,b, except that at the wall. 

The importance of dispersion and its influence on flow pattern and conversion in homogeneous reactors has already been studied in Chapter 2. The role of dispersion, both axial and radial, in packed bed reactors will now be considered. A general account of the nature of dispersion in packed beds, together with details of experimental results and their correlation, has already been given in Volume 2, Chapter 4. Those features which have a significant effect on the behaviour of packed bed reactors will now be summarised. The equation for the material balance in a reactor will then be obtained for the case where plug flow conditions are modified by the effects of axial dispersion. Following this, the effect of simultaneous axial and radial dispersion on the non-isothermal operation of a packed bed reactor will be discussed. 

First we introduce the reader to the principles of such problems and their solution in Sections 5.1.2 and 5.1.2. As an educational tool we use the classical axial dispersion model for finding the steady state of one-dimensional tubular reactors. The model is formulated for the isothermal case with linear kinetics. This case lends itself to an otherwise rare analytical solution that is given in the book. From this example our students can understand many characteristics of such systems. 

The axial dispersion plug flow model is used to determine the performance of a reactor with non-ideal flow. Consider a steady state reacting species A, under isothermal operation for a system at constant density Equation 8-121 reduces to a second order differential equation ... 

We now look at the mathematical equations for a general isothermal steady-state model for the trickle-bed reactor, which takes into account external mass-transfer resistances, i.e., gas-liquid and liquid-solid, axial dispersion, and the intraparticle mass-transfer resistances, along with the intrinsic kinetics occurring at the catalyst surface. Since many practical reactions can be characterized as... 

The above discussion can be illustrated for an isothermal packed bed tubular reactor with negligible diffusional resistances ( /= 1.0) and negligible axial dispersion (plug flow) and instantaneous radial dispersion (one-dimensional model) ... 

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