Feasibility Conditions

A catalyst offers an alternative, energetically favorable mechanism to the non-catalytic reaction, thus enabling processes to be carried out under industrially feasible conditions of pressure and temperature. 

The understanding that the computers controlling the equipment might possess could be contained within a kinetic and thermodynamic model that encapsulates the detailed chemistry of the process. This would include a description of all the reactions that might be expected to occur under the conditions achievable in the plant, together with a list of the relevant rate constants and activation energies for each reaction. In addition, process variables, such as maximum flow rates or pump pressures that are needed for a full description of the behavior of the system under all feasible conditions, would be provided. 

In choosing rows according to the optimality criteria, certain feasibility conditions must also be met ... 

We note that the feasibility condition of steady combustion (5.13) may be written... 

The following optimal or feasible conditions and structural parameters were determined liquid to gas flow rate ratio VJVG = 0.85-1.OxlO 3 m3m 3 impinging velocity u0 = 10-15 m-s 1 dimensionless impinging distance S/d0> 4 molar ratio Ca/S = 1.0 for pseudo flue gas without C02 the nozzles were mounted at the outlets of the gas conduits ... 

The exploration of new process regimes is tightly correlated to the task of chemical production [3, 8, 25]. Microreactors will then not only serve to investigate processes of macroreactors under ideal or otherwise not feasible conditions, but are expected to partially replace macroreactors for different applications. An example for a reaction which can hardly be achieved even on a laboratory scale is the direct fluorination of aromatics. 

Activation of the diene system must be present in order for any cycloaddition to occur under experimentally feasible conditions 42. In fact, distillation of ethyl ( )- and/or (Z)-6-azido-2-vinyl-2-hexenoate produced the same mixture of cis- and trans- isomers of vinylaziridines 4, although only one isomer was isolated, the other one was converted during purification to a monocyclic dihydropyrrole143. Although the stereochemistry was lost after conversion to the bicyclic dihydropyrrole, further reduction and isomerization steps were utilized in order to obtain the desired alkaloids diastereoselectively143,144... 

It is important to get adequate heat transfer in the zone however, if the contact has too many theoretical stages, the liquid will leave the column too hot and may deposit solids in the downstream heat exchangers. One theoretical stage of contact for the entire zone is a feasible condition in most cases. 

Such a feasibility constraint, characteristic to recycle systems, does not appear for stand-alone reactors. It can be explained by simple material balance reasons. The separation section does not allow the reactant to leave the process. Therefore, for a given a reactant input (Fa) either large reactor volume V) or fast kinetics ( CTref)) are necessary to consume entirely the reactant fed and avoid accumulation. These three variables are conveniently grouped in the plant Damkdhler number. The factor Zj accounts for the degradation of reactor performance due to impure reactant recycle. We note that a similar feasibility conditions also holds when the concentration of the reactant in the product stream is nonzero. Moreover, systems containing a purge stream of fixed flow rate have the same qualitative behaviour as the simple system described here. Finally, we remark that the condition 13.17 applies also to the system PFR -Separator - Recycle. 

The conversion of the key component, Xp, is presented in Fig. 13.23 for high purity separation (z j =Zbj =1). For given values of the fixed flow rate ( ec,B or/) and separation performance (za,3 and zb,5), two feasible steady states exist when the plant DamkShler number exceeds the critical value corresponding to the turning point of the Da - Xp, diagram. The following feasibility conditions can be derived ... 

Interestingly, in general [Pg.212]

These four feasibility conditions are summarized graphically in Figure 7.28. The arrows in these illustrations indicate the direction in which compositions change in a... 

Conditions (49) and (50) are called primal feasibility, conditions (51) and (52) are called dual feasibility, and condition (53) is called complementary slackness. To interpret these results geometrically, it is helpful to rewrite (51) in a more compact notation using gradients. 

Checking points obtained from backward CSTR and PFR points is identical to checking if points lie within the convex region defined by a set of inequality constraints. The feasibility condition given by Equation 8.9 may be used to check if points intersect the current region Pj.,... 

A further and probably more relevant issue in radiopharmaceutical drug finding and drug development is the fact that the (radio)pharmaceutical must be synthesized in the clinic immediately prior to its use. This means that the organometallic precursor must be synthesized from saline in high purity and under feasible conditions. Chemists familiar with organometallic compounds are well aware that this task is very difficult since the reaction conditions usually result in different end products and a wild mixture of potentially coordinating... 

Equation (6.2.3) is viewed to free the analysis from the constraint of dilute populations through the time dependence of the equivalent frequency (6.2.2) so that denser populations can be admitted to the scope of this treatment. The feasibility condition for self-similarity (5.2.12), derived in Section 5.2 of... 

All physically feasible conditions of the flibe communication channel from the external world to the reactor are bounded by the physically limited extremes listed in Table XXIV-3. These are innate physical bounds - they span the space of all possible conditions communicated to the reactor from outside the vessel. 

Feasibility conditions for transferring material from pipeline runs to depots... 

The transfer of material from run i el to depot jeJ is feasible only if the pipeline outlet to depot j is reachable from run i. Fulfillment of such feasibility conditions while pumping a later run i e 7"" requires that (a) the lower coordinate of run i at time C,-. must be less than the depot coordinate Pj and (b) the upper coordinate of run i at time Cr, decreased by the interface volume WiFi, should be greater than Pj. 

The critical value Da" represents a limit point of the balance equations. Then, the following feasibility conditions (i.e. existence of steady states) can be derived ... 

The designer should be aware that there is a critical reactor volume, which generally corresponds to a bifurcation point of the mass balance equations. For stable operation the reactor should be larger than this critical value. As example, for essentially first-order reaction with pure product and recycle, the feasibility condition is simply Da>. The definition of the plant Damkohler number includes reactor volume, reaction kinetics and fresh reactant feed flow rate. Similar expressions hold for more complex stoichiometry. 

Another approach has recently been described by Cuetos et al. for the dynamic kinetic resolution of a-substituted p-amino esters [77]. Several ra-transaminases and acyclic alkyl-p-keto esters were tested, leading to high conversion rates and high ee and de values. With this result in mind it seems feasible that novel transaminases will be designed to create enantiomeric pure molecules under mild and economically feasible conditions. 

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