Kinetic steady-state flow conditions

The occurrence of kinetic instabilities as well as oscillatory and even chaotic temporal behavior of a catalytic reaction under steady-state flow conditions can be traced back to the nonlinear character of the differential equations describing the kinetics coupled to transport processes (diffusion and heat conductance). Studies with single crystal surfaces revealed the formation of a large wealth of concentration patterns of the adsorbates on mesoscopic (say pm) length scales which can be studied experimentally by suitable tools and theoretically within the framework of nonlinear dynamics. [31]... 

Open systems far from equilibrium will be the subject of this chapter. This situation is, for example, given for catalytic reactions under steady-state flow conditions. Apart from oscillatory or chaotic kinetics as described in Chapter 7, the interplay between reaction and transport processes may lead to the formation of concentration patterns on mesoscopic... 

The conventional steady-state flow methods that are used widely to investigate the kinetics of heterogeneous catalytic reactions are limited because under steady-state conditions, the... 

Under steady-state conditions, as in the Couette flow, the strain rate is constant over the reaction volume for a long period of time (several hours) and the system of Eq. (87) could be solved exactly with the matrix technique developed by Basedow et al. [153], Transient elongational flow, on the other hand, has two distinctive features, i.e. a short residence time (a few ps) and a non-uniform flow field, which must be incorporated into the kinetics equations. In transient elongational flow, each rate constant is a strongfunction of the strain-rate which varies with time in the Lagrangian frame moving with the center of mass of the macromolecule the local value of the strain rate for each spatial coordinate must be known before Eq. (87) can be solved. 

Experiments at different flow rates and with difierent catalyst grain sizes confirmed that the reaction kinetics is not influenced by external or internal mass transfer. Catechol conversions (X) were always less than 0.05 allowing the reaction to be carried out in the differential kinetic region. The initial yields (Yi,o) for the monomethylated isomers were measured under steady-state conditions (after 8-10 hours of the catalyst activity stabilisation) and were used to compare the catalysts selectivities ... 

While alkane metathesis is noteworthy, it affords lower homologues and especially methane, which cannot be used easily as a building block for basic chemicals. The reverse reaction, however, which would incorporate methane, would be much more valuable. Nonetheless, the free energy of this reaction is positive, and it is 8.2 kj/mol at 150 °C, which corresponds to an equihbrium conversion of 13%. On the other hand, thermodynamic calculation predicts that the conversion can be increased to 98% for a methane/propane ratio of 1250. The temperature and the contact time are also important parameters (kinetic), and optimal experimental conditions for a reaction carried in a continuous flow tubiflar reactor are as follows 300 mg of [(= SiO)2Ta - H], 1250/1 methane/propane mixture. Flow =1.5 mL/min, P = 50 bars and T = 250 °C [105]. After 1000 min, the steady state is reached, and 1.88 moles of ethane are produced per mole of propane consmned, which corresponds to a selectivity of 96% selectivity in the cross-metathesis reaction (Fig. 4). The overall reaction provides a route to the direct transformation of methane into more valuable hydrocarbon materials. 

Fig. 17. Comparison of the variation of the time-average S02 conversion and the maximum bed temperature predicted for stationary cycling condition by an unsteady-state and a steady-state kinetic model for a packed-bed S02 converter operating with periodic flow reversal...

Characterization of the reaction intermediate is facilitated by studies in a flow system in which the sample cell and a reference cell are mounted in series in a double beam spectrometer (IS). Not only can we observe the intermediate bands under rigorous steady state conditions, but we can monitor the conversion by sampling the effluent. In addition, the reference cell assures the spectrum we see is that of surface species. Primitive analysis of the kinetics reveals the intermediate is favored by relatively high ethylene pressures hence, use of a reference cell to cancel contributions of the gas phase is an important factor. 

We can, however, consider the stability of each of the three operating points in Example 14-7 with respect to the inevitable small random fluctuations in operating conditions, including cA, in steady-state operation. Before doing this, we note some features of the rate law as revealed in Figure 14.4. There is a maximum value of (- rA) at cA = 1.166 mol m-3. For cA < 1.166, the rate law represents normal kinetics ( rA) increases as cA increases for cA > 1.166, we have abnormal kinetics (—rA) decreases as cA increases. We also note that (-rA) in equation (C), the rate law, represents the (positive) rate of disappearance of A by reaction within the CSTR, and that (—rA) in equation (D), the material balance, represents the (positive) net rate of appearance of A by flow into and out of the reactor. As noted above, in steady-state operation, these two rates balance. 

In a transported PDF simulation, the chemical source term, (6.249), is integrated over and over again with each new set of initial conditions. For fixed inlet flow conditions, it is often the case that, for most of the time, the initial conditions that occur in a particular simulation occupy only a small sub-volume of composition space. This is especially true with fast chemical kinetics, where many of the reactions attain a quasi-steady state within the small time step At. Since solving the stiff ODE system is computationally expensive, this observation suggests that it would be more efficient first to solve the chemical source term for a set of representative initial conditions in composition space,156 and then to store the results in a pre-computed chemical lookup table. This operation can be described mathematically by a non-linear reaction map ... 

Kinetic data are frequently acquired in continuous reactors rather than batch reactors. These data permit one to determine whether a process has come to steady state and to examine activation and deactivation processes. These data are analyzed in a similar fashion to that discussed previously for the batch reactor, but now the process variables such as reactant flow rate (mean reactor residence time) are varied, and the composition will not be a function of time after the reactor has come to steady state. Steady-state reactors can be used to obtain rates in a differential mode by maintaining conversions small. In this configuration it is particularly straightforward to vary parameters individually to find rates. One must of course wait until the reactor has come to steady state after any changes in feed or process conditions. 

As pointed out earlier, CVD is a steady-state, but rarely equilibrium, process. It can thus be rate-limited by either mass transport (steps 2, 4, and 7) or chemical kinetics (steps 1 and 5 also steps 3 and 6, which can be described with kinetic-like expressions). What we seek from this model is an expression for the deposition rate, or growth rate of the thin film, on the substrate. The ideal deposition expression would be derived via analysis of all possible sequential and competing reactions in the reaction mechanism. This is typically not possible, however, due to the lack of activation or adsorption energies and preexponential factors. The most practical approach is to obtain deposition rate data as a function of deposition conditions such as temperature, concentration, and flow rate and fit these to suspected rate-limiting reactions. 

---