Holdup 572 INDEX

The same index n is used for the timings of the polymerization starts and the timings of the mixing vessel holdup steps since each mixing vessel holdup step corresponds exactly to one polymerization start. 

Small bubbles and flow uniformity are important for gas-liquid and gas-liquid-solid multiphase reactors. A reactor internal was designed and installed in an external-loop airlift reactor (EL-ALR) to enhance bubble breakup and flow redistribution and improve reactor performance. Hydrodynamic parameters, including local gas holdup, bubble rise velocity, bubble Sauter diameter and liquid velocity were measured. A radial maldistribution index was introduced to describe radial non-uniformity in the hydrodynamic parameters. The influence of the internal on this index was studied. Experimental results show that The effect of the internal is to make the radial profiles of the gas holdup, bubble rise velocity and liquid velocity radially uniform. The bubble Sauter diameter decreases and the bubble size distribution is narrower. With increasing distance away from the internal, the radial profiles change back to be similar to those before contact with it. The internal improves the flow behavior up to a distance of 1.4 m. 

Fig. 4. Radial maldistribution index of the local gas holdup at different axial positions.

The dynamic formulation of the model equations requires a careful analysis of the whole system in order to prevent high-index problems during the numerical solution (144). As a consequence, a consistent set of initial conditions for the dynamic simulations and suitable descriptions of the hydrodynamics have to be introduced. For instance, pressure drop and liquid holdup must be correlated with the gas and liquid flows. 

A subset of the type IV model equations can be obtained using the assumption of constant molar holdup in the condenser and in intermediate plates and fast energy dynamics. These assumptions will make the resulting set of DAEs an index 1 rather than index 2 system. In the literature this type of model is referred to as the rigorous constant molar holdup model. Galindez and Fredenslund (1988), Mujtaba and Macchietto (1988, 1992, 1993, 1996, 1998) used this type of model in their studies. Refer to Mujtaba and Macchietto (1998) for the model equations. 

A first prediction attempt of GCxGC retention using this strategy was carried out by Beens et al. [10]. Retention times in the D column were calculated from those of n-alkanes and the analyte retention index. For the analyte retention times in D, k was first obtained by interpolation for the n-alkane series at the elution temperatures, the retention times f of these compounds were calculated using the corresponding holdup times, and then t Ri for the analyte was calculated from its RI at the elution temperature using Equation (3). Differences between calculated and experimental values were observed for D retention times, although predicted elution profiles were similar to the experimental patterns. A similar approach [27] used k values measured at several temperatures to obtain a better interpolation. The accuracy of the prediction of retention times was... 

This suggests that any correction factor which will cause the holdup data for shear-thinning fluids to collapse onto the Newtonian curve, must become progressively smaller as the liquid velocity increases and the flow behaviour index, n, decreases. Based on such intuitive and heuristic considerations, Farooqi and Richardson [1982] proposed a correction factor, J, to be applied to the Lockhart-Martinelli parameter, x, so that a modified parameter Xmod is defined as ... 

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