Non-adiabatic operation

For finite, rather than infinite, values of the dimensionless Newtonian cooling time, the stationary-state condition is given by eqn (7.21). Thus, even with the exponential approximation, both R and L involve the residence time. The correspondence between tangency and ignition or extinction still holds, 

With the exponential approximation (y 0) and the assumption that the inflow and ambient temperatures are equal, we have a stationary-state equation which links ass to tres and which involves two other unfolding parameters, 0ad and tn. Depending on the particular values of the last two parameters the (1 — ass) versus rres locus has one of five possible qualitative forms. These different patterns are shown in Fig. 7.4 as unique, single hysteresis loop, isola, mushroom, and hysteresis loop plus isola. The five corresponding regions in the 0ad-rN parameter plane are shown in Fig. 7.5. This parameter plane is divided into these regions by a straight line and a cusp, which cut each other at two points. 

It cuts. the axis at 0ad = 4 as 1/tn tends to zero (adiabatic limit). We have already seen that this is the condition for transition from multiple stationary states (hysteresis loop) to unique solutions for adiabatic reactors, so the line is the continuation of this condition to non-adiabatic systems. Above this line the stationary-state locus has a hysteresis loop this loop opens out as the line is crossed and does not exist below it. Thus, as heat loss becomes more significant (l/iN increases), the requirement on the exothermicity of the reaction for the hysteresis loop to exist increases. 

however, possible to have multiple stationary states even for parameter values lying below the hysteresis line. These multiplicities are associated with the cusp in the parameter plane. The equation describing the full cusp is most easily presented in the form 

The cusp curve begins at the cusp point which has coordinates 

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Comparison with Eq. (7) shows that the the non-adiabatic operator matrix, A, has been added. This is responsible for mixing the nuclear functions associated with different BO PES. 

The non-adiabatic operator matrix, A can be written as a sum of two terms a matrix of numbers, G, and a derivative operator matrix... 

The superaiatrix notation emphasizes the structure of the problem. Each diagonal operator drives a wavepaclcet, just as in the adiabatic case of Eq. (10), but here the motion of the wavepackets in different adiabatic states is mixed by the off-diagonal non-adiabatic operators. In practice, a single matrix is built for the operator, and a single vector for the wavepacket. The operator matrix elements in the basis set <() are... 

Finally, we shall look briefly at the form of the non-adiabatic operators. Taking the kinetic energy operator in Cartesian form, and using mass-scaled coordinates where Ma is the nuclear mass associated with the ath... 

The extra factor 1 + (rres/rN) in eqn (7.19) for non-adiabatic operation allows for the transfer of heat through the vessel walls as well as by outflow. As Newtonian heat transfer becomes more important (tn decreases) or at long residence times (large rres), the value of this factor increases. Consequently, the fraction of the adiabatic temperature rise achieved for a given extent of reaction decreases. 

Based on eqs. A.11-A.13, one can now determine the non-adiabatic operator H from the relation... 

In the adiabatic approximation, H in Eq. 4 is neglected. H is called the non-adiabaticity operator, and causes phenomena deviating from the adiabatic approximation such as nonradiative transitions between adiabatic states. The adiabatic-coupling scheme is a procedure for investigating such phenomena on the basis of H. ... 

Spontaneous ignition and associated features of organic gases and vapours are a consequence of the exothermic oxidation chemistry discussed in Chapter 1, but the way in which events unfold is determined by the physical environment within which reaction takes place. The heat transfer characteristics are probably most important, as may be illustrated with respect to the different consequences of adiabatic and non-adiabatic operation in a CSTR (Section 5) [117]. The notion of adiabatic operation may seem remote from any practical application, but this idealized condition may be approached if the chemical time-scale is considerably shorter than the time-scale for heat losses. 

Table 5-6 Conversion vs reactor length for chlorination of propylene NON ADIABATIC OPERATION...

If a distillation column loses heat to the environment (non-adiabatic operation), how would that affect the separation ... 

Figure 8.15 Conversion-temperature trajectories for exothermic reversible reaction in non-adiabatic operation...

According to Junge [89] a proper application of partial condensation within a cohniin can increase its efficiency. The effect in question is a partial wall condensation due to a heat loss in the column, i.e., to non-adiabatic operation. Trenne [90] has reported a similar process. On the other hand the extensive calculations of Kuhn [91] promote the view that the most effective procedure is to avoid all condensation except at the upper end of the column. Von Weber [92] has pointed out that partial condensation offers advantages if it is applied in connection with a column narrowing towards its top (see Fig. 172). Owing to the increase in concentration... 

Adrover et al. [52] discussed heat effects in membrane WGS reactor. They proposed that for non-adiabatic operation the proper selection of operating conditions is important to avoid the undesired temperature raises. They also proposed that heat effects are negligible in small-scale laboratory designs. However, for intermediate or larger scale applications the temperature variations have significant effects on chemical kinetics and equilibrium. 

Fii . 1. Effect of non-adiabatic operation on column performance according to Byron, Bowman and Coull (48). 

Fijj. 2. Variation of relative coLuim performance for non-adiabatic operation of a distillation column at different ratios ... 

Figure 9. Gas and wall dimensionless temperature history and superficial dimensionless velocity at the outlet end during adsorption step for the propylene / propane /nitrogen system over 13X zeolite under non-isothermal non-adiabatical operating conditions.

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