Jose Vicente GomezMaraven S.A. Punto

Fijo, Venezuela

An empirical equation estimates the liquid density of petroleum fractions and hydrocarbon mixtures at specific temperatures.

The specific gravity and Watson K factor of the fraction are the only properties required, keeping characterization work to a minimum.

The equation is applicable to fractions having boiling points ranging from 40 to 650 C. It has been found to be in good agreement with the American Petroleum Institute (API) nomograph.

Prediction accuracy is also reasonable for some coal liquids.

### BACKGROUND

Liquid density is one of the most commonly needed physical properties in process engineering computations. Accurate density data are required in a broad variety of calculations. Among these are the sizing of process equipment and pipelines, material and energy balances, interconversions of volumetric and mass flow rates, and estimation of other properties.

Several graphical and analytical methods have been proposed in the past for the prediction of liquid densities.1 6 However, because of their intrinsic limitations, the applicability or accuracy of such methods in practice leaves something to be desired.

Graphs and charts, for example, involve a graphical interpretation step and therefore are unsuitable for computer applications. Furthermore, extrapolation for conditions other than those specified in the graph is often difficult.

On the other hand, analytical methods such as those proposed by O'Donnell and Huggins are not accurate enough because they rely on the assumption that density can be predicted in terms of specific gravity and temperature only, overlooking the contribution of the relative paraffinicity of the fraction (Watson K factor).5-6

The importance of the Watson K factor on the estimation of liquid densities has been demonstrated.7 Fig. 1 shows the effect of temperature on liquid densities of petroleum fractions having the same specific gravity at 60 F., but different paraffinic contents.

As can be seen, the density at a given temperature decreases in the order of paraffinic, naphthenic, and aromatic content. This has to do with the value of the fraction's critical temperature.

The lower the paraffinic content of the fraction (i.e., the lower the value of the Watson K factor), the lower its critical temperature. As a result, fractions having relatively low Watson K factors are located more closely to the critical region because of their higher reduced temperatures.

Consequently, the slope of the density-temperature curve is greater, and thus the density is lower.

Like the correlations published by the author in 1989, the equation presented here also takes the Watson K factor of the cut into account.7 It represents an improvement over the previous expressions, however, in that it yields better predictions in the locality of the critical region.

Another mathematical method that allows for characterization effects is the one recently proposed by Valderrama and Abu-Sharkh.8 This method will be compared with density values obtained from the new equation.

### NEW EQUATION

To provide an analytical expression for computer applications, an equation has been developed for predicting the liquid density of petroleum fractions and hydrocarbon mixtures as a function of temperature, specific gravity (60/60 F.), and Watson K factor (Equation 1).

Equation 1, together with Equations 2 and 3, covers the density of fractions having a normal boiling point between 40 C. and 650 C.

Results from Equation 1 are consistent with those from correlations previously developed.7 The only exception occurs in the critical region, where the new equation gives better estimates.

Coefficients ao through a2l for Equations 2 and 3 are given in Table 1.

For very heavy fractions with normal boiling points greater than 650 C., Equation 4, developed earlier, should be used.7

Although Equation 4 is not intended for estimates at temperatures near the critical one, it yields good predictions for the range of processing temperatures commonly found for such heavy fractions.

For clarity, three examples are presented in this section. The fractions chosen for illustration are one light FCC gasoline, one straight-run kerosine, and one bitumen.

First, the characterization schemes used for the selected fractions will be explained. Then, density values will be estimated from Equation 1, as well as from methods proposed by Gomez, Valderrama and Abu-Sharkh, and AP1.4 7 8

### CHARACTERIZATION

Table 2 shows the experimental data and computed properties for the chosen fractions.

As has been mentioned, the characterization requirements for the new equation are minimal. Only the values of K and SG (nomenclature box), which are commonly available to the process engineer, are needed for this task.

That is not the case for the Valderrama/Abu-Sharkh method, however, which needs a more rigorous characterization scheme to evaluate the pseudocritical properties and the molecular weights of the fractions. This is why Table 2 includes additional information, besides the values of K and SG.

Fig. 2 shows the flowsheets for the calculation of key properties in Table 2. The characterization scheme employed for both light FCC gasoline and kerosine is a classical approach and requires no further comment.

The Riazi-Daubert property-prediction method is used, as recommended by Valderrama and Abu-Sharkh.8 10 In the case of bitumen, distillation data are not usually available; hence, properties such as specific gravity and viscosity at standard temperatures are normally used for characterization purposes.

While the bitumen scheme shown in Fig. 2 is not the only possible approach, it is one of the few feasible choices for an engineer having limited data and time.

It is important to clarify that, in this case, the property prediction method developed by Twu is preferable to that of Riazi-Daubert.10 14 The Riazi-Daubert method is recommended for use with fractions having normal boiling points up to 454 C. (850 F.) and is thus unsuitable for heavy cuts and bitumen.

### METHODS COMPARISON

Table 3 compares the results of Equation 1 with those of the previously mentioned methods to calculate densities. On this point, some clarifications are needed:

- In the Valderrama/Abu-Sharkh work, two correlations were originally proposed: the generalized ZRA equation and the generalized A and B equation. Because the authors report the generalized A and B form to be more accurate, it has been chosen for evaluation purposes.
- From the conceptual standpoint, it is important to note that, although Equation 1 gives liquid density values at atmospheric pressure, values from the Valderrama/Abu-Sharkh correlation correspond to liquid densities at saturation pressure.
Nevertheless, because saturation pressures in the examples shown here are relatively low (less than 35 atm abs.), the effect of pressure is slight and densities from both methods can be directly compared.

- Predicted critical densities are contrasted with values from Equation 5. Equation 5 was derived from the ideal gas equation, corrected for nonideality. An average value of 0.28 has been taken for the critical compressibility factor Zc.15 16

For the light FCC gasoline, both Equation 1 and the Valderrama/Abu-Sharkh method yield quite similar results, which are in reasonable agreement with the API nomograph.

Critical densities resulted in values almost identical to the value computed from Equation 5.

The advantage of Equation 1 over the one previously developed is evident when the critical region is approached.7

It is important to remark that, while extensive characterization work was needed to execute the Valderrama/Abu-Sharkh correlation, only two parameters were required to get comparable predictions from Equation 1.

Density predictions for the kerosine show that Equation 1 gives closer estimates to the values read from the API nomograph. Again, the new equation performs better in the critical region than the author's former correlation.

The superiority of the new equation is also clear where bitumen is concerned. Predictions from Equation 1 are in good agreement with the API nomograph, whereas the Valderrama/Abu-Sharkh correlation yields unrealistic values. (Note that predicted densities at 350 C. and 450 C. are even higher than the specific gravity of bitumen at 60 F.)

From these results, it seems that the Valderrama/Abu-Sharkh method is unable to handle heavy fractions, in spite of the extensive characterization work required. The same conclusion also applies to the generalized ZRA equation, although the results are not reported here.

### COAL LIQUIDS

Because of their high content of polynuclear aromatic hydrocarbons, coal liquids are, in general, much more aromatic than petroleum fractions. The API nomograph cannot be used to estimate the liquid density of these products because their Watson K values fall well below the lower limit of 10.5 found in the API chart.4

Although Equation 1 has been primarily developed for petroleum fractions, it has also been found to yield reasonable estimates for some coal liquids.

Table 4 compares Equation 1 results with experimental data for three coal liquids studied by Hwang and by Holder.17 18 It can be observed that predicted densities agree well with the experimental data throughout a broad range of temperatures.

### ACKNOWLEDGMENT

The author wishes to thank Tom Beckwith for his collaboration in the preparation of this article.

### REFERENCES

- Bland, W.F., and Davidson, R.L., eds., Petroleum Processing Handbook, McGraw-Hill Book Co., New York, 1967, pp. 12-26.
- Kern, D.Q., Process Heat Transfer, McGraw-Hill Book Co., New York, 1950, p. 809.
- Edmister, W.C., Applied Hydrocarbon Thermodynamics, Gulf Publishing Co., Houston, 1961, Chapter 5.
- American Petroleum Institute Technical Data Book, Petroleum Refining, 4th ed., 1983, Vol. 1, Ch. 6, pp. 6 61.
- O'Donnell, R.J., "Predict Thermal Expansion of Petroleum," Hydrocarbon Processing, April 1980, pp. 229 231.
- Huggins, P., "Program produces wide range of distillate properties," OGJ, Nov. 30, 1987, pp. 38-45.
- Gomez, J.V., "Correlations allow calculation of density of petroleum fractions," OGJ, Mar. 27, 1989, pp. 66-67.
- Valderrama, J.O., and Abu-Sharkh, B.F., "Generalized Rackett-type Correlations to Predict the Density of Saturated Liquids and Petroleum Fractions," Fluid Phase Equilibria, Vol. 51, 1989, pp. 87-100.
- Zhou, P., "Correlation of the Average Boiling Points of Petroleum Fractions with Pseudocritical Constants," International Chemical Engineering, Vol. 24, No. 4, October 1984, pp. 731-741.
- Riazi, M.R., and Daubert, T.E., "Simplify Property Predictions," Hydrocarbon Processing, March 1980, pp. 115-116.
- Riazi, M.R., and Daubert, T.E., "Molecular weight of heavy-oil fractions estimated from viscosity," OGJ, Dec. 28, 1987, pp. 110-112.
- American Petroleum Institute Technical Data Book, Petroleum Refining, 4th ed., 1983, Vol. 1, Ch. 2, pp. 2 19.
- American Petroleum Institute Technical Data Book, Petroleum Refining, 4th ed., 1983, Vol. 1, Ch. 2, pp. 2 31.
- Twu, C.H., "An Internally Consistent Correlation for Predicting the Critical Properties and Molecular Weights of Petroleum and Coal-Tar Liquids," Fluid Phase Equilibria, Vol. 16, 1984, pp. 137-150.
- Gas Processors Suppliers Association Engineering Data Book, Tulsa, 10th ed., 1987, Vol. 2, p. 23-12.
- Reid, R.C., Prausnitz, J.M., and Poling, B.E., The Properties of Gases and Liquids, McGraw-Hill Book Co., New York, 4th ed., 1987, p. 33.
- Hwang, S.C., Tsonopoulos, C., Cunningham, J.R., and Wilson, G.M., "Density, Viscosity, and Surface Tension of Coal Liquids at High Temperatures and Pressures," Supplementary Material, Ind. Eng. Chem. Process Des. Dev., Vol. 21, No. 1, 1982, pp. 127-134.
- Holder, G.D., and Gray, J.A., "Thermophysical Properties of Coal Liquids 2. Correlating Coal Liquid Densities," Ind. Eng. Chem. Process Des. Dev., Vol. 22, No. 3, 1983, pp. 424-429.

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