Critical case

On the laboratory scale, it is usually safe to assume that a batch reactor is stirred to uniform composition, but for critical cases such as high viscosities this could be checked with tracer tests. 

If the characteristic equation does not have any roots with positive real parts, but has some roots with zero real parts, the terms in Xt may influence stability. This case belongs to the so-called critical case that requires special investigation. 

This indicates that the deviations are due to systematic errors, for example deficiencies of the applied methods and basis sets. DFT-based methods, such as GIAO/DFT calculations are known to overestimate paramagnetic contributions to the chemical shielding. This results, for critical cases with small HOMO/LUMO separations, in overly deshielded competed chemical shifts. Notorious examples for these deficiencies are 29Si or 13C NMR chemical shift computations of silylenes, silylium ions or dienyl cation .(5/-54) Taking into account the deficiencies of the applied method, and bearing in mind very reasonable correlations shown in Figures 4 and 5, the computational results do support the structural characterization of the synthesized vinyl cations. 

Metabolite (or endogenous compound) cross-reaction may be initially assessed by comparison of displacement curves but in critical cases should also be assessed by addition of metabolite to analyte. 

II processes are subject to disturbances that tend to change operating conditions, compositions, and physical properties of the streams. In order to minimize the ill effects that could result from such disturbances, chemical plants are implemented with substantial amounts of instrumentation and automatic control equipment. In critical cases and in especially large plants, moreover, the instrumentation is computer monitored for convenience, safety, and optimization. 

In critical cases of substantial economic importance, it may be advisable to perform flow tests—Q against A P—in lines of moderate size and to scale up the results to plant size, without necessarily trying to fit one of the accepted models. Among the effects that may not be accounted for by such models are time... 

OHSS is characterized by cystic ovarian enlargement, increased capillary permeability, and third space fluid accumulation (that is in an extracellular compartment that is not in equilibrium with either the extracellular or intracellular fluid, for example the bowel lumen, subcutaneous tissues, retroperitoneal space, or peritoneal cavity). Risk factors include a previous history of OHSS, age under 30 years (probably because more follicles are available), and polycystic ovary syndrome. Non-pregnant patients usually recover within 14 days with supportive treatment. The severe form (with ascites or pleural effusion and hemoconcentration) occurs in 1-10% of patients (64,65). In critical cases, hypoxemia, renal insufficiency, thromboembolism, and rarely death can occur (66). 

A particularly critical case is the exothermal decomposition immediately following the endothermal melting peak. In such cases, the decomposition is faster in the liquid than in the solid state. In an industrial environment, this could mean that a hot spot may melt a small part of the solid, which begins to decompose and the decomposition may propagate through the entire volume of the product. In such cases, the definition of a safe operation temperature becomes critical. 

A set of data on the variation of moisture content of the product with the feed rate under typical operating conditions is given in Fig. 6.21. In critical cases the moisture content may be above the value specified and in more serious cases the material in the annular chamber may completely loss its ability to flow, the system is blocked out, and finally the operation is destroyed. 

Heat must also flow through the walls of a device. DEP utilises electric field inhomogeneities which means that the fields (and heat production) within the liquid tend to be quite localised. The external heat flows can occur over much wider areas so it is sometimes possible to use even poorly conducting materials such as ordinary glasses and quartz. In critical cases, silicon, which has a high thermal conductivity (150 W/m s °C), is used. 

While many of the observed events of the MBH reaction could be included in this scheme, the mechanism failed in some critical cases [47]. First, the mechanism did not provide any clue as to why stereocontrol is so difficult in MBH reactions. Privileged nucleophilic chiral catalysts [48], which in the past have usually allowed good results in related asymmetric transformations, afforded only modest asymmetric induction. This fact was surprising, and pointed to lack of understanding of the basic factors governing the selectivity of the reaction. Other obser-... 

In the transition from a broadband to a narrow band situation, there is a critical case when the positive slope part of Re Z4p(E) becomes parallel to E-E4p (in a point or over a region). On the broad-band side (low Z), we have for all E... 

D-ribonate. In critical cases, such as the study of a mixture in which the presence of small quantities of D-arabinose is being considered, oxidation with bromine and a barium benzoate buffer according to Hudson and Isbell27 may be substituted, even though the procedure becomes more complicated if one wishes to fractionate the aldonic acids through their potassium and barium salts. While other examples of epimerization under these alkaline conditions have not been reported, the possibility of such rearrangements must always be kept in mind. 

This expression is a realistic approximation even though it is assumed here that no diffusion of the aroma substances into the atmosphere takes place. The relative solubility KP/Fof the aroma substance in the packaging material can play an important role in critical cases (high A/mF values) where the ratio mP/mF assumes a maximum... 

In general, metallic pigments are not hygroscopic. The plastic resin should be dried together with the pigment at 60-80°C where necessary. In critical cases (e.g., polyester) the drying can be done under vacuum. 

In critical cases it may well be worthwhile to make a complete analysis of stability. In many cases, however, enough can be learned by studying what Bilous and Amundson (B7) called parametric sensitivity. These authors derived formulas for calculating the amplification or attenuation of disturbances imposed on an unpacked tubular reactor originally in a steady state, with the idea that if the disturbances grow unduly the performance of the reactor is too sensitive to the conditions imposed on it, that is, to the parameters of the system. The effect of feedback from a control system was not considered. As pointed out by the authors, it would be a much more complicated task to apply their procedure to a packed reactor, but it still would entail far less computation than a study of the transient response. 

DADPyOx. (HMX/TNT is a critical case It exhibits an interesting performance/sensitivity ratio when only two tests are taken into account). The IHE TATB and DADPyOx accomplish an important precondition as they possess the best structure for an energetic molecule Cyclic, aromatic, highly nitrated, a stabihzing effect from the intramolecular hydrogen bonding between the nitro and the adjacent amino groups. 

If is not small, this will be a low steady-state concentration, but as tends to zero so [A"]ss increases. For < = 0, d[A"]/dr = = constant and so [AT] would grow linearly until the assumption that the reactant concentration is constant becomes invalid. With < > > 0, [A ] grows exponentially with time again until the consumption of A must be taken into account. The condition for an acceptable steady-state then is clearly (/> < 0, with the condition (/> = 0 being the critical case separating steady-state from explosive runaway. The critical concentration of the reactant obtained from the condition (f> = 0 is then... 

Fig. 5.4. Thermal diagram for Semenov model of thermal explosion the rate of chemical heat release varies with the dimensionless temperature excess 0 according to/(0) = e the rate of heat transfer is given by the straight line with a gradient of l/ifi. For small ifi the loss line is steep and makes two intersections corresponding to two steady-states for large tli the loss line has a low gradient and does not allow steady-state intersection points the critical case corresponds to tangency of the heat release and heat loss lines.

Walas (1988) presented minimum sizes of laboratory and pilot plant drying equipment for full-size plant equipment. Scale-up factors as small as 2 may be required in critical cases however, factors of 5 or more often are practicable, particularly when... 

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