Estimation—Liquids

Many more correlations are available for diffusion coefficients in the liquid phase than for the gas phase. Most, however, are restricted to binary diffusion at infinite dilution or to self-diffusivity DA A. This reflects the much greater complexity of liquids on a molecular level. For example, gas-phase diffusion exhibits negligible composition effects and deviations from thermodynamic ideality. Conversely, liquid-phase diffusion almost always involves volumetric and thermodynamic effects due to composition variations. For concentrations greater than a few mole percent of A and B, corrections are needed to obtain the true diffusivity. Furthermore, there are many conditions that do not fit any of the correlations presented here. Thus, careful consideration is needed to produce a reasonable estimate. Again, if diffusivity data are available at the conditions of interest, then they are strongly preferred over the predictions of any correlations. Experimental values for liquid mixtures are listed in Table 2-325. 

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Example 16 Estimate Liquid Heat Capacity of 2-Butanol. 

Example 17 Estimate liquid heat capacity at 293.15 K of 1,4-pentadiene, CH2 =CH-----CH2---CH =CH2- The atomic groups are ... 

TABLE 2-394 Atomic Group Contributions to Estimate Liquid Heat Capacity at 293.15 K... 

Establish liquid and vapor flow rates and densities. Obtain or estimate liquid surface tension. If conditions vary significantly across the tower, apply this method to each section of interest wherein conditions can be considered constant. 

The following relation is used in estimating liquid film transfer units [62]. For the proper systems Hl may be assumed to be equal to Hql-... 

For vapours, use the equation of state selected for predicting the vapour-liquid equilibria. For liquids, use the same equation if it is suitable for estimating liquid density. 

Chueh, C. F. and Swanson, A. C. (1973b) Chem. Eng. Prog. 69 (July) 83. Estimating liquid heat capacity. 

The UNIQUAC and UNIFAC equations can be used to estimate liquid-liquid equilibria, see Chapter 8. 

Elshout, R. Graphs Determine Time to Drain Vessels, Chemical Engineering, Sept. 23,1968, p. 246. Tate, R.W. Estimating Liquid Discharge from Pressurized Vessels, Chemical Engineering, Nov. 2, 1970, p. 126. 

Data Estimated liquid-phase mass transfer coefficient, kL = 4.0 x 10-4 m/s. 

More frequently, empirical relationships are used to estimate liquid thermal conductivities. A linear relationship with temperature is adequate, since liquid thermal conductivities do not vary considerably with temperature, and hardly at all with pressure. 

To estimate liquid viscosity using Porter equation (6.2.1)... 

To estimate liquid viscosity with Grain s method (eq. 6.4.7)... 

The dimensionless criterion factor f = qv/a is of great importance in estimating liquid flow parameters the discussion of its values is beyond the frames of the present work (as outlined in the references cited). It may be noted, however, that the same expression appears in the equation evaluating the ability of polymers for thread and fiber spinning 15>. To the first approximation, the criterion f = qv/o may be treated as a measure of shape-keeping ability of liquid in flow. 

A relatively simple example of a group contribution technique is the method for estimating liquid and solid heat capacities (159). This method is a modification of Kopp s rule (160,161) which was originally proposed in 1864. Kopp s rule states that, at room temperature, the heat capacity of a solid compound is approximately equal to a stoichiometric summation of the heat capacities of its atoms (elements). The Hurst-Harrison modified equation is as follows ... 

Figure 12 shows the estimated liquid flow rate versus the actual liquid flow rate. The tests for Qa — 0.6 m3/h are of the stratified flow type. The tests of 1.8 < Qa < 7.5 m3/h are of the elongated bubble and slug flow type (Brennen, 2005 Govier and Aziz, 1972). In this study, the flow conditions are compared with the flow regime charts of Govier and Omer (1962 in Govier and Aziz, 1972) and Mendhane (1974 in Brennen, 2005). 

The expected average and standard deviations between the actual liquid flow rate and the estimated liquid flow rate are —1.9% and 5.1%, respectively, in the range 0.6standard deviation is due to the tests of Qa — 0.6m3/h. Small differences between the estimated liquid flow rate and the actual liquid flow rate represent a large 8e value. 

All of the thermodynamic properties of the gas phase should be calculated using an equation of state. This is typically true for the liquid as well, with the exception of the density. The commonly used equations of state do a poor job of estimating liquid density. Often the liquid density from the equation of state is rejected in favor of one from the more accurate empirical expression such as the COSTALD equation. In this case the following equation can be used ... 

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