Backmixed liquid phase

Satterfield and Huff (32) have developed a model based on the plug flow of the gas phase and completely backmixed liquid phase and the model equation is based on the summation of mass transfer and reaction resistances. These authors analyzed the data of Schlesinger et al. (35) and the pilot plant scale data of Farley and Ray (36) and concluded that the overall rate is equally Influenced by mass transfer and reaction resistances at normal operating temperatures (around 503 K) and the mass transfer resistance becomes increasingly more important at higher temperatures. ... 

Eq. (60) corresponds with eq. (7) for constant gas flow. As usual, it is now necessary to eliminate Cj i by accounting for the reaction rate in the backmixed phase. Assuming m-th order reaction of A in the backmixed liquid phase one obtains... 

Fig. 4 Effect of gas phase mixing on conversion and absorption rate for first order reaction - Comparison of models <11> and <13> both with backmixed liquid phase...

The kinetic models for the gas phase polymerization of propylene in semibatch and continuous backmix reactors are based on the respective proven models for hexane slurry polymerization ( ). They are also very similar to the models for bulk polymerization. The primary difference between them lies in the substitution of the appropriate gas phase correlations and parameters for those pertaining to the liquid phase. 

Assuming the liquid phases remain immiscible, the modelling approach for multicomponent systems remains the same, except that it is now necessary to write additional component balance equations for each of the solutes present, as for the multistage extraction cascade with backmixing in Section 3.2.2. Thus for component j, the component balance equations become... 

In packed-bed reactors, the catalyst is fully wetted, whereas the heat and mass transfer efficiency is higher than that observed in trickle-bed reactors. However, low operation efficiency may appear due to backmixing of the liquid phase. Moreover, high liquid-phase residence times can result in the occurrence of homogeneous side reactions. 

Continuous flow of both phases in upflow and complete mixing of phases For packed bubble columns (upflow of both gas and liquid phases), under the assumption of complete mixed flow, the backmixing model of Ramachandran and Chaudhari (1980) is applicable. The relevant equations are presented in Section 3.5.1 for the continuous flow of gas and slurry phases in complete mixed-flow conditions (slurry CSTR reactor). 

Concerning packed bubble bed reactors, the evaluation of the Peclet number of the liquid-phase is important in order to decide if we have to use a plug- or backmixed-flow model. The liquid-phase can be considered well mixed if (Ramachandran and Chaudhari, 1980)... 

Concerning packed bubble bed reactors, the evaluation of the Peclet number of the liquid phase is important in order to decide if we have to use a plug- or backmixed-flow model. For the specified Reynolds number, the Peclet number for the liquid phase using the Stiegel-Shah correlation (eq. (3.422)) is 0.15, much lower than in the trickle bed, which was expected as the backmixing in the liquid phase in packed bubble bed reactors is relatively high. The liquid phase can be considered to be well mixed if (Ramachandran, and Chaudhari, 1980) (eq. (3.423))... 

Concentration modulation experiments have been reported for applications to heterogeneous catalysis (48). The experimental implementation was accomplished by periodically flowing solutions with different (reactant) concentrations over the catalyst immobilized on the IRE. Fast concentration modulation in the liquid phase is limited by mass transport (diffusion and convection), and an appropriately designed cell is essential. The cell depicted in Fig. 12 has two tubes ending at the same inlet (65). This has the advantage that backmixing in the tubing upstream of the cell can be avoided. With this cell, concentration modulation periods of about 10 s were achieved (45,65). 

In a gas-inducing reactor, both gas and liquid phases are generally considered to be completely backmixed. The use of Eqs. (2.39) and (2.40) for the calculations of the critical speed for gas induction is recommended. The rate of gas induction can be expressed by a dimensionless relation NA = /(FrdJH, Ga, dT/du HJdj). The most important parameters are Fr dJH and dT/di. For a given power input per unit volume, the turbo aerator appears... 

Finally, some remarks on the operation of mechanically agitated gas-liquid reactors are worth mentioning. The mode of operation (i.e., batch, semibatch, continuous, periodic, etc.) depends on the specific need of the system. For example, the level of liquid-phase backmixing can be controlled to any desired level by operating the gas-liquid reactor in a periodic or semibatch manner. This provides an alternative to the tanks in series or plug flow with recycle system and provides a potential method of increasing the yield of the desired intermediate in complex reaction schemes. In some cases of industrial importance, the mode of operation needs to be such that the concentration of the solute gas (such as Cl2, H2S, etc.) as the reactor outlet is kept at a specific value. As shown by Joshi et al. (1982), this can be achieved by a number of different operational and control strategies. 

In spite of these advantages of slurry reactors, some technical difficulties are involved in the operation of these reactors. For example, separation of the catalyst and handling of the slurry is difficult the solids can produce erosion of the equipment and significant backmixing of the liquid phase does not allow operation in a plug-flow manner. 

In slurry reactors, the liquid phase is completely backmixed, whereas backmixing in the gas and solid phases may not be complete. The gas-phase mixing depends on the design of the impeller and the nature of the bubbles, as well as the superficial gas velocity. The presence of gas reduces liquid-phase mixing however, an increase in gas flow increases the mixing. The mixing is also dependent upon the coalescence rate of the bubbles. 

Further, the liquid-phase backmixing is considerably lower in horizontal sparged contactors compared to that in bubble columns. Some comparison may be valid between horizontal and vertical agitated contactors. 

Finally, the rotating-disk reactor provides efficient gas-liquid mass transfer by constant renewal of the gas-liquid film on the rotating disk. The mass-transfer coefficient in such a reactor can be calculated using Eq. (6.49). The reactor provides a low pressure drop and partially backmixed gas and liquid phases. The extent of backmixing can be further reduced by the use of baffles. Once again, power consumption and mechanical difficulties may limit the size of such vessels. 

Two-parameter time-delay model (Buffham,14 Buflham and Gibilaro,15 and Buflham el al.18) This model is based on the concept of fluid elements being randomly delayed in time on their passage through the bed. The model has been mainly applied to the liquid-phase backmixing in a trickle-bed reactor. The model assumes that the liquid would flow in plug flow except for the fact that molecules... 

Three-parameter mixing-cell model (Van Swaaij et aL106) This is a stagewise model for liquid-phase backmixing in a trickle-bed reactor. According to this model, an elementary mixing pattern for trickle flow is expressed as106... 

Four-parameter model of Rao and Varma85 This model combines the concepts of the bypass model of Michell and Furzer86 and the PDE model of Van Swaaij et al.106 The model is applied to the liquid-phase backmixing in a trickle-bed... 

The residence-time distribution in the liquid phase of a cocurrent-upflow fixed-bed column was measured at two different flow rates. The column diameter was 5.1 cm and the packing diameter was 0.38 cm. The bed void fraction was 0.354 and the mass flow rate was 50.4 g s l. The RTD data at two axial positions (which were 91 cm apart in Run 1 and 152 cm apart in Run 2) are summarized in Table 3-2. Using the method of moments, estimate the mean residence time and the Peclet number for these two runs. If one assumes that the backmixing characteristics are independent of the distance between two measuring points, what is the effect of gas flow rate on the mean residence time of liquid and the Peclet number Hovv does the measured and the predicted RTD at the downstream positions compare in both cases ... 

Recommendations Under trickle-flow conditions, for the gas-phase axial dispersion, Eq. (6-53) is recommended. For the liquid-phase axial dispersion in hydrocarbon systems, use of Eq. (6-51) is recommended. More experimental data with a variety of hydrocarbon systems are, however, needed. Backmixing under pulsed-flow conditions has not been yet studied. Both experimental as well as theoretical work on this subject is needed. 

Case II Liquid phase - plug flow, gas phase - backmixed ... 

Kim et al.56 correlated their data for liquid-phase backmixing in a three-phase rectangular column by a dimensionless correlation ... 

The analytical problems associated with differential reactors can be overcome by the use of the recirculation reactor. A simplified form, called a Schwab reactor, is described by Weisz and Prater . Boreskov.and other Russian workers have described a number of other modifications " . The recirculation reactor is equivalent kinetically to the well-stirred continuous reactor or backmix reactor , which is widely used for homogeneous liquid phase reactions. Fig. 28 illustrates the principle of this system. The reactor consists of a loop containing a volume of catalyst V and a circulating pump which can recycle gas at a much higher rate, G, than the constant feed and, withdrawal rates F. 

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