Damkdhler number

All criteria proposed here are constructed such that if absolutely no gradient of a particular type exists, then the value of the corresponding criterion is zero. For fast catalytic processes this is not reasonable to expect and therefore a value judgment must be made for how much deviation from zero can be ignored. For the dimensionless expressions the Damkdhler numbers are used as these are applied to each particular condition. The approach is that the Damkdhler numbers can be calculated from known system values, which are related to the unknown driving forces for the transport processes. 

Damkdhler (1936) studied the above subjects with the help of dimensional analysis. He concluded from the differential equations, describing chemical reactions in a flow system, that four dimensionless numbers can be derived as criteria for similarity. These four and the Reynolds number are needed to characterize reacting flow systems. He realized that scale-up on this basis can only be achieved by giving up complete similarity. The recognition that these basic dimensionless numbers have general and wider applicability came only in the 1960s. The Damkdhler numbers will be used for the basis of discussion of the subject presented here as follows ... 

It is often useful to write a model equation sueh as Equation 8-121 in terms of dimensionless variables. This introduees the Peelet number Npg = uL/Dg [, whieh represents the ratio of eharaeteristie dispersion time to eharaeteristie eonveetion time (residenee time), and the Damkdhler number,... 

Observe that p is a Damkdhler number since it can be interpreted as the ratio of a characteristic contact time for flow in a thin film (RT/i/aQ), to a characteristic time for adsorption, (rQ/[k... 

Peclet Number and Damkdhler Number Box 22.2 Alternative Definitions of the Damkdhler Number Illustrative Example 22.1 Vertical Distribution of Dichlorodifluoromethane (CFC-12) in a Small Lake... 

As with the external diffusion limitation, a family of curves is obtained which shows that the overall rate of reaction decreases with increase in the Thiele modulus (as compared with the Damkdhler number for the external diffusion limitation). The rate is essentially under kinetic control at low values of 0(0< 1) that is, there is negligible diffusion limitation. In contrast to the case of external diffusion, it may be seen from the curvature of the lines in Fig. 5.53 that the rate of reaction is always a function of the kinetic parameters, even at the higher values of 0. 

The Damkohler is a dimensionless number that can give us a quick estimate of the degree of conversion that can be achieved in continuous-flow reactions. The Damkdhler number is the ratio of the rate of reaction of A to the rate of convective transport of A at the entrance to the reactor. For first- and second-order ineversible reactions the Damkohler numbers are... 

With all three programs, vary the Damkdhler number. Da, over a range from 1 to 500 and explain the results. Note that when Da no longer has any influence on the rate, then mixing must be controlling. 

Pick s law binary diffusivity for the species s and r mixture rn /s) Damkdhler number (—)... 

The parameter Le is a Lewis number, and it includes the heat capacity of the system. The Da is a Damkdhler number and includes the rate of reaction. The parameters are taken as... 

For a second-order irreversible reaction, the Damkdhler number is... 

It is important to know what values of the Damkdhler number. Da, give high and low conversion in continuous-flow reactors. A value of Da = 0.1 or less will usually give less than 10% conversion and a value of Da = lO.O or greater will usually give greaier than 90% conversion that is. the rule of thumb is... 

Figure 13.19 presents the conversion vs. plant Damkdhler number, for two different reaction orders and different values of the recycle concentration. Solid and dashed lines refer to stable and unstable steady states, respectively. It is obvious that one solution is unfeasible, corresponding to zero conversion and infinite recycle flow rate (its stability is presented for 23= 1). The other one is feasible (0 [Pg.525]

---