Damkoehler number reaction time

The competition between reaction and mixing is given by the Damkoehler number Da), which is the ratio between the reaction rate and the local mixing rate, or conversely, the ratio of the characteristic local mixing time tm and the reaction time tr ... 

An adaptation of the Damkochicr number (Da) is a useful concept for evaluation of mixing effects in crystallization. It is the ratio of the characteristic mixing time to its corresponding process time (nucleation induction time, crystal growth/supersaturation release time, or reaction time). Studies of these times and the resulting predicted Damkoehler number in a laboratory setting can provide evidence of possible scale-up problems. 

It is helpful to visualize the relationship between mixing and nucleation rates through an analogy with the reaction Damkoehler number (Da). The Da number for reaction is defined as Da for reaction = mixing time/reaction time... 

The Damkoehler number Da represents the ratio of a characteristic reaction time to the kinetic time constant of the reaction and is therefore a measure for the reaction time. The attribute characteristic refers to the individual definition necessary for each... 

Based on this value it may be stated from a safety point of view that this thermal potential can in principle be controlled. Furthermore, the ratio of Damkoehler to Stanton number can be calculated, which is independent of the reaction time. 

One possible solution is to reduce the space/time-yield at fixed reactor size. If the reaction system is diluted and the residence time simultaneously prolonged, so that the product of Cbo "t remains constant, then the Damkoehler number and thereby the conversion are left unchanged, but the adiabatic temperature increase is lowered. Due to such a change in the manufacturing recipe, naturally, the amoimt of product manufactured per unit time is reduced. Such a measure and its effect is shown in Figure 4-81 for the example. 

Figure 7-5 shows the dependence of the isothermal conversion on the Damkoehler number for reactions of the first and second order performed in a batch reactor. If the expected conversion is equal to 90%, then the first order reaction will be four times faster than the second order reaction. 

If we compare this equation with the definition of the Damkoehler number [Eq. (4.3.19)], we see that Da can be regarded as the ratio of the reaction time and the characteristic reaction time ... 

Introducing the axial Peclet number for heat Peh,ax=UsCpPgdp/A,ax, the residence time T with regard to the empty tube and the Damkoehler number Da — km,efFPbf = k j Lfu leads to (if an exothermic reaction is taken as example) ... 

For ideal isothermal reactors, the conversion of a reactant A can be calculated by one parameter, the Damkoehler number. (For a cascade of CSTRs we also need the number of CSTRs.) For a reaction order n and a rate constant k, Da equals for a batch reactor (t = reaction time) and r (r = resi-... 

The defining number for this discnssion is the Damkoehler nnmber (Da), the ratio of mixing time to reaction time ... 

Figure 13-2 Normalized yield, Y/Ye p, as a function of Damkoehler number based on ki. This is a qualitative conceptualization of the interaction between mixing rate as expressed by a local mixing time, tm, reaction rate, kiCBo, and reaction yield. As the mixing improves (smaller Da i), the yield increases. As the second reaction gets faster (increasing k2), the mixing time must also drop, to maintain yield.

Relating Mixing and Reaction Time Scales The Mixing Damkoehler Number... 

Figure 13-3 By-product selectivity, Xj, as a function of Damkoehler number based on k2. These data of Bourne in Sharratt (1997) show the increased by-product formation with increasing mixing time based on the engulfment model, Te- As the reaction rate for the second reaction, kiCe, increases, the mixing time must decrease to maintain yield.

Mixing Damkoehler number the ratio of mixing time to reaction time, DaM = Tm/tr. The mixing Damkoehler number may be referred to simply as the Damkoehler number. (Note that the traditional Damkoehler number is the vessel residence time divided by the reaction time.)... 

The Damkoehler number requires characteristic time scales for both mixing and reaction. Calculation of the reaction time scale is relatively straightforward, although the necessary data may be difficult to obtain. Many choices for the mixing time have been proposed, and data are available for many common semibatch geometries. 

These values were combined into a mixing Damkoehler number as the ratio of mixing time constant to reaction time constant ... 

Damkoehler number—system residence time/characteristic reaction time (dimensionless) diameter of microcarrier beads (p,m) energy dissipation/circulation fnnetion P/(kD total force imparted by the impeller, radial and axial (eq. 18-64) (Nm-2)... 

---