Level swell correlations

Level swell is characterised by the. void fraction within the swelled liquid, a. This is correlated for each flow regime as a function of 4V the dimensionless ratio of the superficial gas/ vapour velocity to the bubble rise velocity, i.e  

The other correlating parameter is C0. This is intended to take account of channelling of bubbles up the walls, rather than uniform distribution. DIERS[5] recommend the following level swell correlations. 

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The main effect of the presence of solids on level swell will be in changing the liquid viscosity. The mixture viscosity Should be used in place of the liquid viscosity in level swell correlations. ... 

Calculation methods are given here for cases (a) to (c). In section A3.4 below, references are given to a calculation method for case (d). The level swell calculation methods presented here use the drift flux correlations developed by DIERS[11. The DIERS correlations apply to a vertical cylindrical vessel, which is most often the case for chemical reactors. Modifications for horizontal cylindrical vessels are given by Sheppard[2,3]. 

The amount of level swell is correlated with the superficial velocity, jg, of gas or vapour at the surface of the liquid. Superficial velocity is the volumetric flow of gas or vapour, divided by the vessel cross-sectional area (i.e., with no attempt to account for the fraction of the cross-sectional area occupied by liquid). Within a particular flow regime, level swell increases with increasing superficial velocity. 

The terminal bubble rise velocity, ( , is another correlating parameter for level swell. It can be calculated from the following equations, according to the flow regime. ... 

Figure A3.3 is a plot of average void fraction, a, versus the dimensionless superficial velocity, for the different flow regimes and values of C0. The correlations presented here may overestimate level swell for pure vapour pressure systems if there is a non-boiling region (in which static head suppresses boiling) at the bottom of the reactor. This is conservative for relief system sizing and is discussed further by DIERS151.

Equation (A3.6) can now be used to find the level swell. A value is required for the correlating parameter, C0. As two-phase relief is the worst case for relief system sizing, a value of C0 of 1.0 will be used, since this gives the highest predicted level swell ... 

The union of set of data reported in Table XIX of Ref. 43, and the set of data estimated therefrom, as noted in Fig. 61, were then correlated [180] with the relative swelling powers, C, of the corresponding liquids (Fig. 62) at a given level of v ranging from 0 to 1 in increments of 0.2. The data at each respective level of v is represented in Fig. 62 by a unique symbol as noted in the caption for Fig. 62. 

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