Instantaneous reactions

Tubular Reactors. The tubular reactor is exceUent for obtaining data for fast thermal or catalytic reactions, especiaHy for gaseous feeds. With sufficient volume or catalyst, high conversions, as would take place in a large-scale unit, are obtained conversion represents the integral value of reaction over the length of the tube. Short tubes or pancake-shaped beds are used as differential reactors to obtain instantaneous reaction rates, which can be computed directly because composition changes can be treated as differential amounts. Initial reaction rates are obtained with a fresh feed. Reaction rates at... 

R = estimated instantaneous reaction force or moment at installation temperature, Ibf or in lbf (N or N mm)... 

Instantaneous reaction A- - B —A P. The reaction between the two feed solutions occurs instantaneously as soon as they are mixed. 

The solution that is obtained for the instantaneous reaction rate per unit area is ... 

Subsequent kinetic work has amply confirmed the mechanistic picture described above. For example, the reaction of diphenylmercury with Ph(COOEt).CH.HgBr gives an almost instantaneous reaction with precipitation of phenylmercuric bromide, whereas reaction of the soluble product with a second molar equivalent of mercuric bromide gave a very slow (ca. 2 weeks) precipitation of phenylmercuric bromide722, i.e. reaction involves (287) and (288)... 

A continuous process was described in 1939 [29] consisting of bringing together continuously flowing streams of sulfuric acid and alcohol without restraining the resulting rise of temperature, but with an immediate neutralization and cooling of the reaction flow. Inert solvents were used in instantaneous reactions. 

From these general characteristics a number of criteria for sulfonation configurations can be derived. The combination of an instantaneous reaction, with considerable exothermic heat effect and a factor 50-100 increase in viscosity in the organic phase, makes it clear that proper temperature control in the organic phase is the main problem in practice. 

Efficient mixing of the organic acid and the alkaline phase is essential to promote the instantaneous reaction and to avoid undesired degradation reactions in isolated acid spots and pH drift occurring in the neutralized product storage... 

To determine the reaction rate at a given instant in the course of the reaction, we should make our two concentration measurements as close together in time as possible. In other words, to determine the rate at a single instant we determine the slope of the tangent to the plot of concentration against time at the time of interest (Fig. 13.4). This slope is called the instantaneous rate of the reaction. The instantaneous reaction rate changes in the course of the reaction (Fig. 13.5). 

The instantaneous reaction rate is the slope of a tangent drawn to the graph of concentration as a function of time for most reactions, the rate decreases as the reaction proceeds. 

The E-model was also applied to a system of parallel reactions (Baldyga and Bourne, 1990a). It was found that selectivity depends on compositions of both the initial reactor content and the stream added for chemically equivalent mixtures of three reactants (see reaction system given by Eqns. (5.4-143) and (5.4-144)). For an instantaneous reaction, the yield of 5 varies from 0 to 100 % depending on the mode of composing the feeding stream. 

The parameter p (= 7(5 ) in gas-liquid sy.stems plays the same role as V/Aex in catalytic reactions. This parameter amounts to 10-40 for a gas and liquid in film contact, and increases to lO -lO" for gas bubbles dispersed in a liquid. If the Hatta number (see section 5.4.3) is low (below I) this indicates a slow reaction, and high values of p (e.g. bubble columns) should be chosen. For instantaneous reactions Ha > 100, enhancement factor E = 10-50) a low p should be selected with a high degree of gas-phase turbulence. The sulphonation of aromatics with gaseous SO3 is an instantaneous reaction and is controlled by gas-phase mass transfer. In commercial thin-film sulphonators, the liquid reactant flows down as a thin film (low p) in contact with a highly turbulent gas stream (high ka). A thin-film reactor was chosen instead of a liquid droplet system due to the desire to remove heat generated in the liquid phase as a result of the exothermic reaction. Similar considerations are valid for liquid-liquid systems. Sometimes, practical considerations prevail over the decisions dictated from a transport-reaction analysis. Corrosive liquids should always be in the dispersed phase to reduce contact with the reactor walls. Hazardous liquids are usually dispensed to reduce their hold-up, i.e. their inventory inside the reactor. 

For the instantaneous reaction, the rate is equal to the reactant feed rate. The energy balance then becomes... 

Very high values of Da correspond to instantaneous reactions. ... 

Show by simulation that the corresponding conversion of B for instantaneous reaction is given by solving the equation... 

The instantaneous reaction rate can be expressed in terms of the fraction conversion by combining equations A, C, and D. 

Disposal of a benzene solution of phosphoryl chloride into a waste drum containing carbon disulfide (and other solvents) caused an instantaneous reaction, with evolution of (probably) hydrogen chloride. Presence of a hydroxylic compound seems likely. 

Acid-base reactions are the archetypical instantaneous reactions. If we let A denote the acid concentration and B the base concentration, the chemical source term for both the acid and base can be expressed as... 

Finally, to conclude our discussion on coupling with chemistry, we should note that in principle fairly complex reaction schemes can be used to define the reaction source terms. However, as in single-phase flows, adding many fast chemical reactions can lead to slow convergence in CFD simulations, and the user is advised to attempt to eliminate instantaneous reaction steps whenever possible. The question of determining the rate constants (and their dependence on temperature) is also an important consideration. Ideally, this should be done under laboratory conditions for which the mass/heat-transfer rates are all faster than those likely to occur in the production-scale reactor. Note that it is not necessary to completely eliminate mass/heat-transfer limitations to determine usable rate parameters. Indeed, as long as the rate parameters found in the lab are reliable under well-mixed (vs. perfect-mixed) conditions, the actual mass/ heat-transfer rates in the reactor will be lower, leading to accurate predictions of chemical species under mass/heat-transfer-limited conditions. 

Fig. 16.1. Results of reacting quartz sand at 100°C with deionized water, calculated according to a kinetic rate law. Top diagram shows how the saturation state Q/K of quartz varies with time bottom plot shows change in amount (mmol) of quartz in system (bold line). The slope of the tangent to the curve (fine line) is the instantaneous reaction rate, the negative of the dissolution rate, shown at one day of reaction.

Figpre 9.6 Two-film model (profiles) for instantaneous reaction A(g) + bB( ) - products... 

For an instantaneous reaction, equation 9.2-27 is an alternative to equation 9.2-22. An expression for E can be obtained from these two equations, and special cases can be examined in terms of E (see problems 9-11 and 9-12). 

The cases above, reaction in bulk liquid only and instantaneous reaction in the liquid film, have been treated by considering rate processes in series. We can t use this approach if diffusion and reaction of A and B are both spread over the liquid film. Instead, we consider solution of the continuity equations for A and B, through the liquid film. 

As shown in Figure 9.8, the solution for E for a fast second-order reaction given by equation 9.2-51 is bounded by E for two other cases fast first-order or pseudo-first-order reaction, given by equation 9.2-49 and instantaneous reaction, given by equation... 

Note that the enhancement factor E is relevant only for reaction occurring in the liquid film. For an instantaneous reaction, the expressions may or may not involve E, except that for liquid-film control, it is convenient, and for gas-film control, its use is not practicable (see problem 9-12(a)). The Hatta number Ha, on the other hand, is not relevant for the extremes of slow reaction (occurring in bulk liquid only) and instantaneous reaction. The two quantities are both involved in rate expressions for fast reactions (occurring in the liquid film only). 

Consider a packed tower for the absorption of A from a gas containing inert material (in addition to A) by a liquid containing B (nonvolatile) under continuous, steady-state conditions. Absorption is accompanied by the instantaneous reaction A(g) + bB(() - products. Assume the overall process is liquid-film controlled. 

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