Absorber-reactors rate equation

These processes are carried out in a variety of equipment ranging from a bubbling absorber to a packed tower or plate column. The design of the adsorber itself requires models characterizing the operation of the process equipment and this is discussed in Chapter 14. The present chapter is concerned only with the rate of reaction between a component of a gas and a component of a liquid—it considers only a point in the reactor where the partial pressure of the reactant A in the gas phase is and the concentration of A in the liquid is C, that of B, Cg. Setting up rate equations for such a heterogeneous reaction will again require consideration of mass and eventually heat transfer rates in addition to the true chemical kinetics. Therefore we first discuss models for transport from a gas to a liquid phase. 

The approach to be followed in the determination of rates or detailed kinetics of the reaction in a liquid phase between a component of dissolved gas and a component of the liquid is, in principle, the same as that outlined in Chapter 2 for gas-phase reactions on a solid catalyst. In general, the experiments are carried out in flow reactors of the integral type. The data may be analyzed by the integral or the differential method of kinetic analysis. However, for a single reaction, two continuity equations, in general, are required one for the absorbing component A in the gas phase and one for A in the liquid phase. In addition, a material balance is required, linking the consumption of B, the reactant of the liquid phase, to that of A. The continuity equations for A, which contain the rate equations derived in... 

In the Inflow and Outflow terms (1) and (2), the heat flow may be of two kinds the first is transfer of sensible heat or enthalpy by the fluid entering and leaving the element and the second is heat transferred to or from the fluid across heat transfer surfaces, such as cooling coils situated in the reactor. The Heat absorbed in the chemical reaction, term (3), depends on the rate of reaction, which in turn depends on the concentration levels in the reactor as determined by the general material balance equation. Since the rate of reaction depends also on the temperature levels... 

In this equation, Mvoc is the mass flow rate (kilograms per unit time) of the volatile organic compound in the reactor, and it is taken as the average mass flow rate through the reactor. The emissions from the absorber column originate from the offgas vent and this stream contains unreacted raw material, byproducts, and product. Raw material, especially benzene, and one of the byproducts,... 

The determination of the radiation absorption can be accomplished in a Photo-CREC Water-II Reactor. An experimental method for the determination of the rate of photon absorption is described in detail in this section. Tliis experimental method corresponds to a semi-empirical technique of moderate complexity that combines spectroscopic measurements with modeling to obtain sufficient infonnation for the determination of the radiation field distribution in photocatalytic reactors. The radiation absorbed is determined by the use of the Beer-Lambert equation with effective extinction coefficients obtained from spectroscopic measurements. A physical interpretation of these coefficients is also provided later in this chapter. 

Usually, Nr -h 1 reactors will be required to absorb non-productive time (discharge, cleaning and filling of reactor). Solving the equation that represents enzyme inactivation under operation conditions (i.e. Eq. 5.76) and the equation that model conversion profiles within the biocatalyst bed in CPBR (Eq. 5.79), residual enzyme activity in each bioreactor after each time interval can be determined and feed flow-rate to each bioreactor during each interval calculated as ... 

This equation relates the reaction rate (cross section) of a material at the temperature to its cross section at a lower temperature Tn- As in all the preceding analyses, it is assumed that the nuclei are distributed according to the Maxwell-Boltzmann relation (4.198). The above equation may be used then to compute the cross-section curves for a reactor operating at any temperature from the known cross-section data of the reactor material which have been determined at some temperature Tn. Note that U = Tn then Eq. (4.233) reduces to an identity [see also (4.225)]. In general, the indicated integration must be carried out in detail. There is one special case, however, which leads to an especially simple result. If the measured cross-section curve varies as l/v, which is the case for many absorbers in the low-energy range, then it is easily shown that the reaction rate is independent of the moderator temperature. For example, if we take aa v) = Co/y, where Co is some constant, then from (4.233)... 

It was shown in Chapter 4 that the rate of reaction is a function of temperature and concentration. The application of the subsequent equations developed were simplest for isothermal conditions since is then generally solely a function of concentration. If nonisothermal conditions exist, another equation must be developed to describe any temperature variations with position and time in a reactor. For example, in adiabatic operation, the enthalpy (heat) effect accompanying the reaction can be completely absorbed by the system and result in temperature changes in the reactor. As noted earlier, in an exothermic reaction, the temperature increases, which in turn increases the rate of reaction, which in turn increases the conversion for a given interval of time. The conversion, therefore, would be higher than that obtained under isothermal conditions. When the reaction is endothermic, the decrease in temperature of the system results in a lower conversion than that associated with the isothermal case. If the endothermic enthalpy of reaction is large, the reaction may essentially stop due to the sharp decrease in temperature. 

---