Stirred-tank reactor kinetic energy

Figure 15.5 Measured and simulated turbulent kinetic energies (normalized with the impeller tip speed) at the impeller plane in a stirred tank reactor (From [17]).

In 1991, Lima Neto, Pardey, Ford and coworkers121 reported a detailed kinetics investigation of the RhCl3 catalyst in aqueous picoline using a continuously stirred tank reactor (CSTR). Some of the data are tabulated in Table 31. The activation energy (80-120 °C) was 7.4 kcal/mol (31 kJ/mol). 

Consider an exothermic irreversible reaction with first order kinetics in an adiabatic continuous flow stirred tank reactor. It is possible to determine the stable operating temperatures and conversions by combining both the mass and energy balance equations. For the mass balance equation at constant density and steady state condition,... 

X H kJ/mol. Since the sticking coefficient of H2 on Cu( 111) is not known, the prefactor for the sticking and the activation energy of the Cu(l 10) surface was used as areliable approximation. From the kinetic gas theory, a preexponential factor Aads = 9.2 x 10 (torr-s) was derived for our model. In our calculation we assumed 132 /xmol/gr active sites based on theexperimental results of Muhler et al. [6] for the Cu/Zn0/Al203 based on a H/ = H (2 Cu) = 1 1 stoichiometry. Under the conditons of perfect mixing gas phase condition is uniform throughout the bed. The reactor mass balance for a transient continuous stirred tank reactor was used in the form... 

Two basic approaches are often used for fluidized bed reactor modeling. One approach is based on computational fluid dynamics developed on the basis of the mass, momentum, and energy balance or the first principle coupled with reaction kinetics (see Chapter 9). Another approach is based on phenomenological models that capture the main features of the flow with simplifications by assumption. The flow patterns of plug flow, CSTR (continuous-stirred tank reactor). 

At the high recycling ratios the loop reactor operates as an ideal stirred-tank reactor. Therefore, the reaction rate can immediately be determined from the difference in concentration between the feed and the outlet, the throughput and the quantity of catalyst.The rate equation, describing the consumption of xylene and the formation of the reaction products, are considered to be pseudo first order. The parameter of the rate equations, which are the frequency factors and the activation energies, are determined by least square methods. In the above function (Fig. 6b) r is the measured rate, r is calculated with estimated parameters, w represent appropriate weight factors and N is the number of measured values. Because the rate equations could be differentiated v/ith respect to the unknown kinetic parameters, the objective function was minimized by a step-wise regression. 

Fig. 7.27 Simulated turbulent kinetic energy in horizontal plane of stirred tank reactor...

Fermentation systems obey the same fundamental mass and energy balance relationships as do chemical reaction systems, but special difficulties arise in biological reactor modelling, owing to uncertainties in the kinetic rate expression and the reaction stoichiometry. In what follows, material balance equations are derived for the total mass, the mass of substrate and the cell mass for the case of the stirred tank bioreactor system (Dunn et ah, 2003). 

Based on these observations [93] proposed a modified model containing two time constants, one for the liquid shear induced turbulence and a second one for the bubble induced turbulence. The basic assumption made in this model development is that the shear-induced turbulent kinetic energy and the bubble-induced turbulent kinetic energy may be linearly superposed in accordance with the hypothesis of [128, 129]. Note, however, that [82] observed experimentally that this assumption is only valid for void fractions less than 1 %, whereas for higher values there is an amplification in the turbulence attributed to the interactions between the bubbles. The application of this model to the high void fraction flows occurring in operating multiphase chemical reactors like stirred tanks and bubble columns is thus questionable. 

Like many other exothermic reactions in stirred tanks, three steady stages are possible for polymerizations beginning with monomer a lower one where there is essentially zero conversion an intermediate, metastable condition and an upper, runaway condition where conversion to polymer is nearly complete. It is usually desired to operate at the intermediate, metastable condition. To illustrate this, assume that the polymerization kinetics are pseudo-first order and write material and energy balances based on perfect mixing in the reactor. A material balance on monomer gives... 

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