Combination step CSTRs

To summarize these last examples, we have seen that in the design of reactors that are to be operated at conditions (e.g.. temperature and initial concentration) identical to those at which the reaction rate data were obtained, we can size determine the reactor volume) both CSTRs and PFRs alone or in various combinations. In principle, it may be possible to scale up a laboratory-bench or pilot-plant reaction system solely from knowledge of as a function of X or Q. However, for most reactor systems in industry, a, scale-up proce.s.s cannot be achieved in this manner because knowledge of solely as a function of X is seldom, if ever, available under identical conditions. In Chapter 3. we shall see how we can obtain = yfX) from information obtained either in the laboratory or from the literature. This relationship will be developed in a two-step process. In Step 1, we will find the rate law that gives the rate as a function of concentration and in Step 2, we will find the concentrations as a function of conversion. Combining Steps 1 and 2 in Chapter 3. we obtain -/-.v =JiX). We can then use the method.s developed in this chapter along with integral and numerical methods to size reactors. 

In this case, three time constants in series, X, %2 and X3, determine the form of the final outlet response C3. As the number of tanks is increased, the response curve increasingly approximates the original, step-change, input signal, as shown in Fig. 2.12. The response curves for three stirred tanks in series, combined with chemical reaction are shown in the simulation example CSTR. 

Combine the three first-order ODEs describing the three-CSTR system of Sec. 3.2 into one third-order ODE in terms of Then solve for the response of to a unit step change in C 0 assuming all Jt s and t s are identical. 

Understanding Reactor Flow Patterns As discussed above, a RTD obtained using a nonreactive tracer may not uniquely represent the flow behavior within a reactor. For diagnostic and simulation purposes, however, tracer results may be explained by combining the expected tracer responses of ideal reactors combined in series, in parallel, or both, to provide an RTD that matches the observed reactor response. The most commonly used ideal models for matching an actual RTD are PRF and CSTR models. Figure 19-9 illustrates the responses of CSTRs and PFRs to impulse or step inputs of tracers. 

Salmi (25) set up equations needed to simulate the transient response of both the PFR and the CSTR. The balance equations and the generahzed equations for the rates of the elementary steps are compactly expressed in vector and matrix notation. Details of the computational algorithms are discussed, and they are applied to the N2O decomposition (Eqs. 5 and 6). In another paper (26) these equations are used to simulate (for both PFRs and CSTRs) the responses of sysfems following many mechanisms Eley-Rideal, Langmuir-Hinshelwood. a combination of the two. with and without dissociative adsorption, etc. These curves can be added to those of Kobayashi (22), to expand the general view of how various systems respond. 

Design a two-phase gas-liquid CSTR that operates at 55°C to accomplish the liquid-phase chlorination of benzene. Benzene enters as a liquid, possibly diluted by an inert solvent, and chlorine gas is bubbled through the liquid mixture. It is only necessary to consider the first chlorination reaction because the kinetic rate constant for the second reaction is a factor of 8 smaller than the kinetic rate constant for the first reaction at 55°C. Furthermore, the kinetic rate constant for the third reaction is a factor of 243 smaller than the kinetic rate constant for the first reaction at 55°C. The extents of reaction for the second and third chlorination steps ( 2 and 3) are much smaller than the value of for any simulation (i.e., see Section 1-2.2). Chlorine gas must diffuse across the gas-liquid interface before the reaction can occur. The total gas-phase volume within the CSTR depends directly on the inlet flow rate ratio of gaseous chlorine to hquid benzene, and the impeller speed-gas sparger combination produces gas bubbles that are 2 mm in diameter. Hence, interphase mass transfer must be considered via mass transfer coefficients. The chemical reaction occurs predominantly in the liquid phase. In this respect, it is necessary to introduce a chemical reaction enhancement factor to correct liquid-phase mass transfer coefficients, as given by equation (13-18). This is accomplished via the dimensionless correlation for one-dimensional diffusion and pseudo-first-order irreversible chemical reaction ... 

The situation changes significantly in the case of strains like C. necator, where autocatalytic growth of biomass is followed by a phase of linear PHA production. In this case, biomass production should occur in the first step in a CSTR which is coupled to a subsequent plug flow reactor (PFR). The combination CSTR-PFR not only ensures higher productivity, but also minimizes the loss of substrates and co-substrates. Furthermore, product quality can be enhanced by the fact that the PFR features a narrow residence time distribution, leading to higher uniformity of cell populations. This should also have positive impacts on the distribution of the PHA molecular masses and the composition of polyesters [128]. 

When a steady stream of fluid flows through a vessel, different elements of the fluid spend different times within it. The time spent by each fluid element can be identified by an inert tracer experiment, where a pulse or a step input of a tracer is injected into the flow stream, and the concentration of the pulse in the effluent is detected. As the reader may quickly infer, the tracer must leave the PFR undisturbed. On the other hand, a step pulse may give rise to an exponential distribution in a CSTR. In the beginning of this chapter, we already demonstrated that PFR behavior approaches that of a CSTR under infinite recycle. It follows that infinite CSTRs in series behave like a PFR. Thus, we conclude that any nonideal reactor can be represented as a combination of the PFR and MFR to a certain degree. First, let us show a representative pulse response curve for each of the ideal reactors in Figure 3.5. As seen in the figure, the response to a step input of tracer in a PFR is identical to the input function, whereas the response in a CSTR exhibits an exponential decay. The response curves as shown in Figure 3.5 are called washout functions. The input function of the inert tracer concentration [/] can be mathematically expressed as... 

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