Reactors transient behavior

The analysis of the transient behavior of the packed bed reactor is fairly recent in the literature 142-145)- There is no published reactor dynamic model for the monolith or the screen bed, which compares well with experimental data. 

In industry, as well as in a test reactor in the laboratory, we are most often interested in the situation where a constant flow of reactants enters the reactor, leading to a constant output of products. In this case all transient behavior due to start up phenomena have died out and coverages and rates have reached a constant value. Hence, we can apply the steady state approximation, and set all differentials in Eqs. (142)-(145) equal to zero ... 

The kinetic equations describing these four steps have been summarized and discussed in the earlier paper and elsewhere (1,5). They can be combined with conservation laws to yield the following non-linear equations that describe the transient behavior of the reactor. In these equations the units of the state variables T, M, and I are mols/liter, while W is in grams/liter. The quantity A (also mols/liter) represents that portion of the total polymer that is unassociated — i.e. reactive. 

Analysis of CSTR Cascades under Nonsteady-State Conditions. In Section 8.3.1.4 the equations relevant to the analysis of the transient behavior of an individual CSTR were developed and discussed. It is relatively simple to extend the most general of these relations to the case of multiple CSTR s in series. For example, equations 8.3.15 to 8.3.21 may all be applied to any individual reactor in the cascade of stirred tank reactors, and these relations may be used to analyze the cascade in stepwise fashion. The difference in the analysis for the cascade, however, arises from the fact that more of the terms in the basic relations are likely to be time variant when applied to reactors beyond the first. For example, even though the feed to the first reactor may be time invariant during a period of nonsteady-state behavior in the cascade, the feed to the second reactor will vary with time as the first reactor strives to reach its steady-state condition. Similar considerations apply further downstream. However, since there is no effect of variations downstream on the performance of upstream CSTR s, one may start at the reactor where the disturbance is introduced and work downstream from that point. In our generalized notation, equation 8.3.20 becomes... 

What equations would have to be solved to determine transient behavior in a tubular reactor How would you guess that temperatures might vary with time for step changes in Tf, Tco, or flow rates ... 

The steady state approximation eliminates transient behavior in the kinetics. However, it is only the transient behavior of the rates and coverages that has been eliminated. The expression for the rate obtained through the steady state approximation is perfectly suitable for the simulation of e g the conversion through a catalyst bed or most aspects of the transient behavior of a reactor. 

A minor transient feature was also manifested when ammonia was admitted to the reactor (t — 0 s) the NO outlet concentration immediately decreased, went through a weak minimum near 150 s and finally slightly increased, reaching steady state in correspondence of the end of the ammonia feed phase (tx 2,800 s). Again, the nitrogen evolution was symmetrical to that of NO. The same ammonia inhibition effect invoked to explain the enhancement in the deNOx conversion at ammonia shutdown can explain this transient behavior, too. In fact both features suggest the existence of an optimal ammonia surface concentration, which is lower than the coverage established at steady state. 

Some problems in the analysis of transient behavior and stability of chemical reactors. First International Symposium on Chemical Reaction Engineering no. 109. Washington, D.C. American Chemical Society, 1972. 

With the introduction of micro reactors, transient reactor operations also became of interest for production owing to their low internal reactor volume and thus fast dynamic behavior. In 1999, liauw et al. presented a periodically changing flow to prevent coke development on the catalyst and to remove inhibitory reactants in a micro channel reactor [88], This work was preceded in 1997 by Emig and Seiler, of the same group, who presented a fixed-bed reactor with periodically reversed flow [89]. In 2001, Rouge et al. [27] reported the catalytic dehydration of isopropanol in a micro reactor. 

Nowadays, the most common small-scale application of hydrogen is the use in residential or mobile fuel cell systems. Special requirements of this application are compact design, integrated CO-removal, high energetic efficiency, quick start-up and fast transient behavior. The proposed solutions comprise unit-operation-based concepts as well as multifunctional, micro-structured reactors. 

The model described in Section 13.6 is used to simulate the transient behavior of the reactor operated isothermally at 50 °C. 

Altshuller, D., "Design Equations and Transient Behavior of the Countercurrent Moving-Bed Chromatographic Reactor,"... 

A mathematical formulation of the transient behavior of pressure in an HDS reactor is, of course, extremely complex and. as yet, has not been analyzed. In the limiting case, when the catalyst bed is heavily plugged with solid deposits, the problem of pressure-drop calculations is very similar to the pressure drop through an oil reservoir.72 The well-known Darcy type of equation should be applicable in this case. 

Some work has already been done on the simulation of transient behavior of moving bed coal gasifiers. However, the analysis is not based on the use of a truly dynamic model but instead uses a steady state gasifier model plus a pseudo steady state approximation. For this type of approach, the time response of the gasifier to reactor input changes appears as a continuous sequence of new steady states. 

Yoon, H. Wei, J. Denn, M. "Modeling and Analysis of Moving Bed Coal Gasifiers" EPRI Report No. AF-590, Vol 2, 1978.. "Transient Behavior of Moving Bed Coal Gasification Reactors" 71st Annual AIChE Meeting, Miami, 1978.. AIChE J. 1979, (3), 429. 

EXAMPLE 11.2-2 Transient Behavior of a Stirred-Tank Reactor... 

Dynamic regime (T When the period of the oscillation is of the order of the system s characteristic response lime, the system is in intermediate or dynamic periodic operation. The transient behavior of the system has to be determined to predict the effects of periodic operation. Dynamic reactor operation may result in considerably higher performance if resonance phenomena are involved, and therefore this range of operation is of particular interest for optimization of the reactor. 

Two different modeling approaches are used for simulated moving bed reactors. The first approach combines the model of several batch columns with the mass balances for the external inlet and outlet streams. By periodically changing the boundary conditions the transient behavior of the process is taken into account. The model is based on the SMB model introduced in Chapter 6 and is, therefore, referred to as the SMBR model. The second approach assumes a true counter-current flow of the solid and the liquid phase like the TMBR. Therefore, this approach is called the TMBR model. 

In section 2.2.7, multiple steady states in a heterogeneous chemical reaction (one dependent variable) and a jacketed stirred tank reactor (two dependent variables) were analyzed. Both stable and unstable steady states were obtained. The transient behavior of the system was found to depend on the initial conditions. The methodology and Maple programs presented in this chapter should be valid for any system of IVPs with multiple steady states. In section 2.2.8, phase plane behavior of a jacketed stirred tank reactor was analyzed. The program provided should be of use for analyzing phase plane behavior of different chemical systems. A total of ten different examples were presented in this chapter. 

To summarize we may say the following about the applications of Markov chains. Markov chains provide a solution for the dynamical behavior of a system in occupying various states it can occupy, i.e., the variation of the probability of the system versus time (number of steps) in occupying the different states. Thus, possible applications of Markov chains in Chemical Engineering, where the transient behavior is of interest, might be in the study of chemical reactions, RTD of reactors and complex processes employing reactors. 

In all these cases, the correct design must grow from the equations of mass, energy, and momentum balance to which we now turn in the next few sections. From these we proceed to the design problem (Sec. 9.5) and hence to elementary considerations of optimal design (Sec. 9.6). The stability and sensitivity of a tubular reactor is a vast and fascinating subject. Since the steady state equations are ordinary differential equations, the equations describing the transient behavior are partial differential equations. This... 

However, the parameter estimates in Figures 9.1 and 9.2 and Equations 9.6 and 9.7 were developed for random packing, and even the boundary condition of Equation 9.4 may be inappropriate for monoliths or structured packing. Also, at least for automotive catalytic converters, the pressure drop and the transient behavior of the reactor during startup is of paramount importance. Transient terms da/dt and dT/dt are easily added to Equations 9.1 and 9.3, but the results will mislead. These... 

The next task was to model the reformer itself to understand design issues and be able to predict performance of various reactor/catalyst types and transient behavior. However, upon trying to obtain kinetic rate expressions for the reforming reactions, it was found that very little information existed in the public domain. This led to the decision/need to develop reaction kinetics for catalytic partial oxidation and steam reforming at National Energy Technology Laboratory s (NETL s) onsite research facility. 

Compute the transient behavior of the dispersed plug-flow reactor for the isothermal, liquid-phase, second-order reaction... 

The residence-time distribution of the PFR was shown to be arbitrarily sharp because all molecules spend identical times in the PFR. We introduced the delta function to describe this arbitrarily narrow RTD. We added a dispersion term to the PFR equations to model the spread of the RTD observed in actual tubular reactors. We computed the full, transient behavior of the dispersed plug-flow model, and displayed the evolution of the concentration profile after a step change to the feed concentration. 

In this chapter we have found that a reactor type that is familiar to us and that has intuitively obvious usefulness, namely, the well-mixed semibatch reactor, is also very complex to treat—at least analytically—due to its transient behavior. It is also evident that we would never use this kind of reactor to evaluate even the most basic chemical kinetics. Thus we need a simpler type of reactor that is mathematically more tractable and experimentally more feasible to operate. We will see instances of these in the next chapter. Along the way we have now added the final element that we needed in our Mathematica toolbox, the writing of Modules. We will build on this to produce even more useful Packages in what follows. 

---