Uniformity Fast Chemical Reactions

Comparison of Eq. (184) with Eq. (183) shows the effect of size distribution for the case of fast chemical reaction with simultaneous diffusion. This serves to emphasize the error that may arise when one applies uniform-drop-size assumptions to drop populations. Quantitatively the error is small, because 1 — is small in comparison with the second term in the brackets [i.e., kL (kD)112). Consequently, Eq. (184) and Eq. (183) actually give about the same result. In general, the total average mass-transfer rate in the disperser has been evaluated in this model as a function of the following parameters ... 

The plug-flow model indicates that the fluid velocity profile is plug shaped, that is, is uniform at all radial positions, fact which normally involves turbulent flow conditions, such that the fluid constituents are well-mixed [99], Additionally, it is considered that the fixed-bed adsorption reactor is packed randomly with adsorbent particles that are fresh or have just been regenerated [103], Moreover, in this adsorption separation process, a rate process and a thermodynamic equilibrium take place, where individual parts of the system react so fast that for practical purposes local equilibrium can be assumed [99], Clearly, the adsorption process is supposed to be very fast relative to the convection and diffusion effects consequently, local equilibrium will exist close to the adsorbent beads [2,103], Further assumptions are that no chemical reactions takes place in the column and that only mass transfer by convection is important. 

In the case of the fast binary reaction we could eliminate the reaction term from the reaction-diffusion-advection equation. But in general this is not possible. In this chapter we consider another class of chemical and biological activity for which some explicit analysis is still feasible. We consider the case in which the local-reaction dynamics has a unique stable steady state at every point in space. If this steady state concentration was the same everywhere, then it would be a trivial spatially uniform solution of the full reaction-diffusion-advection problem. However, when the local chemical equilibrium is not uniform in space, due to an imposed external inhomogeneity, the competition between the chemical and transport dynamics may lead to a complex spatial structure of the concentration field. As we will see in this chapter, for this class of chemical or biological systems the dominant processes that determine the main characteristics of the solutions are the advection and the reaction dynamics, while diffusion does not play a major role in the large Peclet number limit considered here. Thus diffusion can be neglected in a first approximation. 

Following a rapid initial dispersion to the Kolmogorov scale, the packets continue to evolve in size and shape but at a relatively slow rate. Molecular-level mixing occurs by diffusion between packets, and the rates of diffusion and of the consequent chemical reaction can be calculated. Early versions of the model assumed spherical packets of constant and uniform size. Variants now exist that allow the packet size and shape to evolve with time. Regardless of the details, these packets are so small that they typically equilibrate with their environment in much less than a second. This is so fast compared to the usual reaction half-lives and to the mean residence time in the reactor that the vessel behaves as if it were perfectly mixed. 

Consider an explosive comprising uniform spherical grains all of the same size and radius. According to the Eyring model, chemical reaction in the detonation wave occurs via a particular very fast combustion flame proceeding radially inward toward the center of the grain. The rate of reaction thus follows the equation... 

Coal Residence Time. Because the oxidation rate is fast, there is essentially no residence time required for chemical reaction. In a plug flow reactor, coal feed rate would depend only on the oxygen input rate and the unit oxygen consumption. Moreover, if gas distribution is uniform, the oxidation would be uniform. In a continuous fluidized-bed reactor, however, residence time must be long enough to minimize the effect of the short-circuiting of untreated feed into the product. The... 

The analysis of turbulent motion physics for a reaction mtjcture in tubular channels of various designs can open the way to a quantitative and scientifically grounded approach for the selection of the optimal geometry, for any fast chemical process, to reduce the diffusion limitation and create uniform conditions for making synthetic products. However, it is necessary to find a solution for another very important problem of theoretical and applied science the temperature mode control of fast chemical processes with high local heat generation in a reaction zone. 

---