Peclet number for the liquid phase

The next parameter of importance is the Peclet number of the liquid and the gas phase. For the specified Reynolds number, the Peclet number for the liquid phase using the Michell-Furzer correlation (eq. (3.417)) is 0.74. The minimum value of Z/dp for ethanol conversion between 0.1 and 0.9, evaluated using the Mears criterion (eq. (3.421)), is 2.84 and 62.11 respectively, much lower than the value used in the example, which is about 2500. Thus, the operation can be assumed to follow the plug-flow model. 

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))... 

Equations (8-6) and (8-9) give close answers, whereas Eq. (8-8) predicts a value an order of magnitude lower. The Peclet number for the liquid phase can be calculated from Eqs. (8-11) and (8-12). From (8-11),... 

The experimental studies have shown that, in gas-liquid trickle-bed reactors, significant axial mixing occurs in both gas and liquid phases. When the RTD data are correlated by the single-parameter axial dispersion model, the axial dispersion coefficient (or Peclet number) for the gas phase is dependent upon both the liquid and gas flow rates and the size and nature of the packings. The axial dispersion coefficient for the liquid phase is dependent upon the liquid flow rate, liquid properties, and the nature and size of the packings, but it is essentially independent of the gas flow rate. 

Typical Peclet numbers for the gas phase, based on the length as characteristic dimension, range from 2 to 15 and for the Uquid phase from 0.10 to 0.16. The t/jc and are such that and are of the same magnitude. In fact, they are both high, so that the gas phase and the liquid phase are close to... 

Trickle-bed models assume plug flow for both phases. Thus, it is interesting to evaluate the respective Peclet numbers. The correlations of Michell-Furzer for liquid (eq. (3.417)) and Hochman-Effron for gas (eq. (3.419)) are used and the results are shown in Table 5.15. The Reynolds number for the gas phase is 32.28. 

Commercial reactors are non isothermal and often adiabatic. In a noniso-thermal gas-liquid reactor, along with the mass dispersions in each phase, the corresponding heat dispersions are also required. Normally, the gas and liquid at any given axial position are assumed to be at the same temperature. Thus, in contrast to the case of mass, only a single heat-balance equation (and corresponding heat-dispersion coefficient) is needed. Under turbulent flow conditions (such as in the bubble-column reactor) the Peclet number for the heat dispersion is often assumed to be approximately equal to the Peclet number for the mass dispersion in a slow-moving liquid phase. 

P Peclet number for the dynamic liquid phase (U6LJEA)... 

Finally, we studied the effect of liquid dispersion on catalyst performance by comparing the performance of the powder catalyst in a bubble column reactor with the HyperCat-FT system. As shown in Figure 6, the CO conversion is much lower for a low Peclet number (bubble colunm reactor with a back-mixed liquid phase) as opposed to a higher Peclet number for the HyperCat system. The tests were conducted under the same process conditions and Damkohler number. The change in Peclet number did not change the liquid product... 

In fact, correlations for Peclet numbers required for reactor modeling are available almost exclusively for the liquid phase. Bul am and Rathor (1978) give the following correlation ... 

For determination of the Peclet number in radial direction for the liquid phase Pein the following equation is presenl [274] ... 

The forced fluid flow in heated micro-channels with a distinct evaporation front is considered. The effect of a number of dimensionless parameters such as the Peclet, Jacob numbers, and dimensionless heat flux, on the velocity, temperature and pressure within the liquid and vapor domains has been studied, and the parameters corresponding to the steady flow regime, as well as the domains of flow instability are delineated. An experiment was conducted and demonstrated that the flow in microchannels appear to have to distinct phase domains one for the liquid and the other for the vapor, with a short section of two-phase mixture between them. 

For gas-liquid flows in Regime I, the Lockhart and Martinelli analysis described in Section I,B can be used to calculate the pressure drop, phase holdups, hydraulic diameters, and phase Reynolds numbers. Once these quantities are known, the liquid phase may be treated as a single-phase fluid flowing in an open channel, and the liquid-phase wall heat-transfer coefficient and Peclet number may be calculated in the same manner as in Section lI,B,l,a. The gas-phase Reynolds number is always larger than the liquid-phase Reynolds number, and it is probable that the gas phase is well mixed at any axial position therefore, Pei is assumed to be infinite. The dimensionless group M is easily evaluated from the operating conditions and physical properties. 

The final parameter to be evaluated is the liquid-phase Peclet number, and the graph given by Levenspiel (L10) can be used for this purpose. It must be remembered that the film Reynolds number should be used in estimating the Peclet number. 

Both phases are substantially in plug flow. Dispersion measurements of the liquid phase usually report Peclet numbers, uLdp/D, less than 0.2. With the usual small particles, the wall effect is negligible in commercial vessels of a meter or so in diameter, but may be appreciable in lab units of 50 mm dia. Laboratory and commercial units usually are operated at the same space velocity, LHSV, but for practical reasons the lengths of lab units may be only 0.1 those of commercial units. 

Determinations of Peclet number were carried out by comparison between experimental residence time distribution curves and the plug flow model with axial dispersion. Hold-up and axial dispersion coefficient, for the gas and liquid phases are then obtained as a function of pressure. In the range from 0.1-1.3 MPa, the obtained results show that the hydrodynamic behaviour of the liquid phase is independant of pressure. The influence of pressure on the axial dispersion coefficient in the gas phase is demonstrated for a constant gas flow velocity maintained at 0.037 m s. 

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 ... 

The above equations assume that the liquid-phase reactant C, the product of the reaction, and the solvent are nonvolatile. The effective interfacial area for mass transfer (nL) and the fractional gas holdup (ii0o) arc independent of the position of the column. The Peclet number takes into account any variations of concentration and velocity in the radial direction. We assume that Peclet numbers for both species A and C in the liquid phase are equal. For constant, 4 , Eq. (4-73) assumes that the gas-phase concentration of species A remains essentially constant throughout the reactor. This assumption is reasonable in many instances. If the gas-phase concentration does vary, a mass balance for species A in the gas phase is needed. If the gas phase is assumed to move in plug flow, a relevant equation would be... 

FIGURE 14.11 Axial and radial Peclet numbers for single-phase flow of a gas or liquid through a packed bed of spherical particles. The limits of molecular diffusion are shown hy sohd hues that represent Pe = Re Sc Xg/g, where Xg = bed tortuousity =1.4 and Eg = bed voidage = 0.4 (Sherwood et al., 1975). 

Unlike in MASRs, where liquid mixing is always considered complete, in this case allowance must be made for partial mixing. Thus it may often be necessary to use the dispersion model given by Equation 17.25. The liquid-phase axial diffusion coefficient for estimating the Peclet number in this equation may be calculated from the correlations of Hikita and Kikukawa (1975) or Mangartz and Pilhofer (1981). 

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