## Steps in Performance Analysis

Pressure Drop Calculation in Vapour Phase

The pressure drop in the vapour phase across a sieve tray is modelled as (Zuiderweg, 1982):

where the dry pressure drop is given by:

Here, g is the acceleration due to gravity, hl is the liquid height or hold-up in metres, ug,h is the vapour velocity in the hole in metres per second, CD is the drag coefficient, and (pG, pl) are the densities of the vapour and liquid, respectively. The second term in eqn [3] represents the static head due to the liquid hold-up on the tray. Hence the liquid height, hl must be predicted from correlations that depend on the hdc = ht + hda # hL [7]

where ht is the pressure difference between points a and b in the vapour phase that is necessary to keep the vapour flowing upwards, hL refers to the effective clear liquid height on the tray deck that must be overcome by the liquid in the downcomer, and hda refers to the pressure loss due to the liquid flow under the downcomer apron. Note that ht is necessary to keep the upward flow of vapour, but acts as a pressure differential that works against the natural liquid flow in the downcomer. If this pressure differential is large, the liquid will back up more in the downcomer. This points out the coupling between the pressure loss in the vapour phase through the tray deck area and the liquid flow in the downcomer. An optimal design must balance these two factors carefully. hL and ht can be estimated from the correlations provided in the previous section. hda can be estimated from:

hda = 165.2Uda where hda is in millimetres of liquid and Uda is the velocity under the downcomer apron in metres per second.

### Froth Height and Density Calculation

The froth density (or the two-phase density) has been measured using gamma ray techniques. The average liquid volume fraction on a sieve tray, defined as £ = hl/hb, is correlated by:

ciency is related to the overall number of transfer units by:

-Nog

Chen and Chuang present the following correlation for Nog using data free of weeping and entrainment. But the data set spans both the froth and spray regimes:

"piF2

Here, hb is the froth or bed height in metres and «g is u , • . • £ ^ E /—

, ' b , . , .. . g Here A = mG/L is the separation factor, Fs = usX/pG

the vapour velocity on bubbling area in metres per second . The constants c1 and n depend on the type of flow regimes . In the spray regime, they take on the values of c1 = 265 and n = 1.7, while in the mixed/emulsion regime, they are 40 and 0.8. This requires one to estimate the flow regime to be expected under a given set of operating conditions. In Figure 3 of Part I, we identified the limits of operation to lie between the weeping and flooding conditions as the vapour rate is increased. Even within this permissible range of operation, the flow condition has been observed to change from spray to froth to emulsion to bubble flow regimes. The transition into the spray regime is given by the capacity factor defined as:

Here, CF is the capacity factor defined as ug^(pG/pL) in metres per second, ug is the vapour velocity in the bubbling area in metres per second, F is the fractional hole area per unit bubbling area and dh is the hole diameter in metres. The transition from the spray/froth to emulsion/bubble flow regime is controlled by the ratio of horizontal liquid momentum to vertical vapour momentum and is given by:

where ul is the horizontal liquid velocity, ug is the vapour velocity on bubbling area in metres per second, and FP is the flow parameter defined in eqn [5], b is the weir length per unit bubbling area in metres"1, hl is the liquid height or hold-up in metres.

### Point Efficiency Calculation

There are many empirical correlations for predicting the mass transfer efficiencies on sieve trays. The most recent one is that proposed by Chen and Chuang (1993). It is based on data from industrial sized columns of Fractionation Research Inc. The point effi-

is the superficial F-factor in kg0 5/m0 5s, tG = hf/us is the vapour-phase contact time in seconds, and hf is the froth height in metres. Note that this correlation combines the geometrical parameters such as q, the fractional perforated area, Ab the bubbling area, the system properties such as densities (pL, pG), diffusivi-ties (Dl, Dg) viscosity (p), the interfacial tension (a) in newtons per metre, the molecular weights (Ml, Mg), and operating conditions such as (L, G), flow rates. This correlation appears to predict the point efficiencies to within 5% of experimental data over a wide range of pressures.

### Murphree Tray Efficiency Calculation

The point efficiency model presented above is based on a detailed examination of mass transfer at the vapour/liquid interface. The ideal equilibrium tray assumption used in the McCabe-Thiele method asserts that the flow condition on a tray is homogeneous everywhere. If that were true, the point efficiency would be the same everywhere on the tray. But there is strong evidence that the flow is not homogeneous, the degree of inhomogeneity being larger in large diameter columns. Several researchers have tried to measure the velocity profiles across a sieve tray and increasingly computational fluid dynamics is being used as a tool to predict such flow fields. (See for example Solari and Bell (1986) and Mehta et al. (1998)). This information on flow profile must be integrated with the point efficiency calculations in order to predict a Murphree tray efficiency. One such method is given below as an illustration. This model considers only the effect of longitudinal mixing. A measure of the effective diffusivity, DE is needed in this model. Models of other flow configuration are discussed in Lockett (1986):

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