Dispersion model first order reactions

FIGURE 4.33 Reactor size predicted by an axial dispersion model compared with the size predicted by a plug flow model. First-order reaction, — ta = aca-... 

FIG. 23-15 Chemical conversion by the dispersion model, (a) First-order reaction, volume relative to plug flow against residual concentration ratio, (h) Second-order reaction, residual concentration ratio against kC t. 

Example 9.6 Compare the nonisothermal axial dispersion model with piston flow for a first-order reaction in turbulent pipeline flow with Re= 10,000. Pick the reaction parameters so that the reactor is at or near a region of thermal runaway. 

Given k fit) for nny reactor, you automatically have an expression for the fraction unreacted for a first-order reaction with rate constant k. Alternatively, given ttoutik), you also know the Laplace transform of the differential distribution of residence time (e.g., k[f(t)] = exp(—t/t) for a PER). This fact resolves what was long a mystery in chemical engineering science. What is f i) for an open system governed by the axial dispersion model Chapter 9 shows that the conversion in an open system is identical to that of a closed system. Thus, the residence time distributions must be the same. It cannot be directly measured in an open system because time spent outside the system boundaries does not count as residence but does affect the tracer measurements. 

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. 

The dispersion model of example DISRE is extended for non-isothermal reactions to include the dispersion of heat from a first-order reaction. 

Fig. 18. General design chart for the dispersion model for first-order reaction A R with no change in volume (e = 0). Ordinate gives the dispersed flow reactor volume divided by the volume of an ideal PFR which achieves the same conversion. - - -, Constant kr ------, constant DIuL.

Figure 17.4. Dispersion model. Conversion of first-order reaction as function of the Peclet number.

We will consider a dispersed plug-flow reactor in which a homogeneous irreversible first order reaction takes place, the rate equation being 2ft = k, C. The reaction is assumed to be confined to the reaction vessel itself, i.e. it does not occur in the feed and outlet pipes. The temperature, pressure and density of the reaction mixture will be considered uniform throughout. We will also assume that the flow is steady and that sufficient time has elapsed for conditions in the reactor to have reached a steady state. This means that in the general equation for the dispersed plug-flow model (equation 2.13) there is no change in concentration with time i.e. dC/dt = 0. The equation then becomes an ordinary rather than a partial differential equation and, for a reaction of the first order ... 

To incorporate mixing by the dispersed plug flow mechanism into the model for the bubble column, we can make use of the equations developed in Chapter 2 for dispersed plug flow accompanied by a first-order chemical reaction. In the case of the very fast gas-liquid reaction, the reactant A is transferred and thus removed from the gas phase at a rate which is proportional to the concentration of A in the gas, i.e. as in a homogeneous first-order reaction. Applied to the two-phase bubble column for steady-state conditions, equation 2.38 becomes ... 

LPCVD Reactor Models. First-Order Surface Reaction. The traditional horizontal-wafer-in-tube LPCVD reactor resembles a fixed-bed reactor, and recent models are very similar to heterogeneous-dispersion models for fixed-bed reactors (21,167,213). To illustrate CVD reactor modeling, this correspondence can be exploited by first considering a simple first-order surface reaction in the LPCVD reactor and then discussing complications such as complex reaction schemes, multicomponent diffusion effects, and entrance phenomena. 

Pavlica and Olson38 outlined a generalized axial dispersion model for the isothermal bubble-column reactor in which a pseudo-first-order reaction occurred in both the gas and liquid phases. The model considered axial mixing in both the gas and the liquid phases. Here, we review a model for the reactor in which a generalized (m, n)th-order reaction between a gaseous species A and a liquid species C is carried out in the liquid phase. There are many chlorination, nitration, sulfonation, alkylation, and hydrogenation reactions which can be... 

The model described above assumes constant gas velocity and pressure in the reactor. Recently, Deckwer6 outlined a dispersion model which took into account the opposite effects of gas shrinkage and expansion caused by absorption and reduced hydrostatic head. A first-order reaction in the liquid phase was assumed. Both slow and fast reaction regimes were considered. The governing nonlinear differential equations were solved on the computer. 

As illustrated above, dispersion models can be used to described reactor behavior over the entire range of mixing from PFR to CSTR. Additionally, the models are not confined to single-phase, isothermal conditions or first-order, reaction-rate functions. Thus, these models are very general and, as expected, have found widespread use. What must be kept in mind is that as far as reactor performance is normally concerned, radial dispersion is to be maximized while axial dispersion is minimized. 

Direct contact heat transfer, 185 Dispersion model, 560-562 first order reactions, 561 second order reactions, 562 Distillation, 371-457 batch, 390 binary, 379 column assembly, 371 flash, 375... 

Tanks-in-Series Model Versus Dispersion Model. We have seen that we can apply both of these one-parameter models to tubular reactors using the variance of the RTD. For first-order reactions the two models can be applied with equal ease. However, the tanks-in-series model is mathematically easier to use to obtain the effluent concentration and conversion for reaction orders other than one and for multiple reactions. However, we need to ask what would be the accuracy of using the tanks-in-series model over the dispersion model. These two models are equivalent when the Peclet-Bodenstein number is related to the number of tanks in series, n, by the equation ... 

Dispersion model For a first-order reaction, use the Danckwerts boimdaiy conditions... 

If the pathogens exist in a disperse form, the UV light can directly reach them and hence a complete disinfection can occur. The disinfection rate can then be described by first-order reaction kinetics, which is also called as Chick-Watson model (11) ... 

---