Reaction superficial liquid velocity

Here, the parameter F = Uo]dJ2De( — t) considers the effect of intraparticle diffusion, Pe = V dJlEzi. takes into account the effect of axial dispersion, S = 3(1 — e)Kt/U0L considers the effect of total external mass-transfer resistance, and A0 = /j (l — )k dp/2UoL considers the effect of surface reaction on the conversion. In these reactions L/0l, s the superficial liquid velocity, dp is the particle... 

Surface reaction (pore diffusion negligible) dp, [ ], [fiJb temperature, replacement of active by inactive catalyst particles Superficial liquid velocity (above certain minimum) Superficial gas velocity ... 

All the balances have accumulation, convection, axial dispersion, and reaction terms. The equations include liquid holdup, Bi, and superficial liquid velocity, w. Langmuir-type rate equation, for the main reaction, Equation 15.4, included also an activity correction term a. Kst and in Equations 15.5-15.7 indicate the adsorption parameters for stearic acid and heptadecene, respectively. Equation 15.4 corresponds to a monomolecular transformation of stearic acid via the adsorption of the reactant to the main product. Adsorption terms for stearic acid and heptadecene were used, since both of these compounds contain functional groups enabling adsorption on the active sites of the catalyst Reaction rates were assumed not to be limited by heptadecane adsorp-UoiL Thus, the adsorption term of heptadecane was n ected. In line with the experimental observations indicating catalyst deactivation. Equation 15.4 (Table 15.2) was modified to incorporate the decrease in catalyst activity. In particular, the activity was assumed... 

Experimental data of stearic acid decarboxylation in a laboratory-scale fixed bed reactor for formation of heptadecane were evaluated studied with the aid of mathematical modeling. Reaction kinetics, catalyst deactivation, and axial dispersion were the central elements of the model. The effect of internal mass transfer resistance in catalyst pores was found negligible due to the slow reaction rates. The model was used for an extensive sensitivity study and parameter estimation. With optimized parameters, the model was able to describe the experimentally observed trends adequately. A reactor scale-up study was made by selecting the reactor geometry (diameter and length of the reactor, size and the shape of the catalyst particles) and operating conditions (superficial liquid velocity, temperature, and pressure) in such a way that nonideal flow and mass and heat transfer phenomena in pilot scale were avoided. 

Figure 2. Superficial liquid velocity dependence of reaction rates...

In evaluating their results they assumed the film theory, and, because the oxygen is sparingly soluble and the chemical reaction rate high, they also assumed that the liquid film is the controlling resistance. The results were calculated as a volumetric mass-transfer coefficient based, however, on the gas film. They found that the volumetric mass-transfer coefficient increased with power input and superficial gas velocity. Their results can be expressed as follows ... 

Hydraulic analysis Using Figure 3.27, the appropriate gas superficial velocity and the column diameter for the heterogeneous flow regime can be selected. An appropriate choice for the reactor diameter and the superficial gas velocity is 0.5 m and 0.1 m/s, respectively. The height to diameter ratio in columns is greater than unity and a value of 5 is reasonable. Therefore, the value of 2.5 m has been selected for the column height. As a result, the reactor volume is equal to 0.49 m3. This volume is occupied by the reaction mixture, which is the gas, the liquid, and the solid phase. 

Fig. 4.8. Alternative bubble columns each using the same volume of liquid, and the same total gas flowrate, (a) Low aspect-ratio column low superficial gas velocity ue small interfacial area a low rate of reaction, (b) High aspect-ratio column high superficial gas velocity u0 large interfacial area <2 higher rate of reaction. Note For case (b) it must not be assumed that both gas and liquid phases are well-mixed...

As mentioned earlier, the same rotor internals used in pilot tests should be used upon scale-up. The rotor dimensions of inner diameter and axial height are determined by maintaining a constant superficial gas velocity at the rotor eye. The radial packing depth, and thus the outer diameter, is based on the number of transfer units required. Adjustments in packing depth and packing type may be necessary to achieve the desired liquid holdup or residence time, e.g., for chemical reaction (26). 

Johnson et al. (J3) suggest the use of the hydrogenation reaction of a-methylstyrene with a suspended palladium-alumina catalyst as an alternative test system to establish the effect of agitation variables on liquid-phase mass-transfer coefficients. They found the over-all hydrogen transfer coefficient to vary in a complex manner with agitator speed, and to increase with the 0.6 power of the superficial gas velocity up to a point beyond which the transfer showed no further change with gas velocity. 

Here A0 and E are the frequency factor and the activation energy for the reaction, respectively, Rg is the universal gas constant, 7] is the reactor inlet temperature pG and pi are the gas and liquid densities, respectively, Cpr. and CpL are the gas and liquid heat capacities respectively, V0G and U0L are the superficial gas and liquid velocities respectively, e. is the void fraction of the undiluted catalyst, r is the space time, C-, is the reactor inlet concentration of the reactant, m is the order of the reaction, and A7/r is the heat of reaction. The results shown in Figs. 4-5... 

Ariga et al. [48] have investigated the behavior of the monolith reactor in which Echerichia coli with P-galactosidase or Saccharomyces cerevisiae was immobilized within a thin film of K-carragcenan gel deposited on the channel wall. The effects of mass transfer resistance and axial dispersion on the conversion were studied. Those authors found that the monolith reactor behaved like the plug-flow reactor. The residence-time distribution in this reactor was comparable to four ideally mixed tanks in series. The influence of gas evolution on liquid film resistance in the monolith reactor was also investigated. It was shown that at low superficial gas velocities, the gas bubble may adhere to the wall, which decreases the effective surface area available for the reaction. The authors concluded that the reactor was very effective in the reaction systems accompanied by gas evolution, such as fermentations. 

Nevertheless, as a first approximation for design, use of Eq. (Ill) is recommended with the coefficient doubled for a gas-liquid reaction in pulse or spray flow over inert packing. For the bubble flow regime, with G > 0.01 kg/m sec, it is conservative to assume Al = 0.15 sec for any gas-liquid reaction. For the dependence of effective interfacial area, despite the lack of a general correlation, it is judicious to consider that this area will vary with the 0.5 power of superficial gas velocity regardless of packing size and type, column diameter, and liquid superficial velocity. 

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