NEW CORRELATION CALCULATES RELIABLE PARAFFIN SOLUBILITIES

Carl L. Yaws, Xiang Pan
Lamar University
Beaumont, Tex.

A new correlation based on boiling point has been developed which accurately calculates paraffin solubilities in water.

The correlation provides reliable solubility values down to very low concentrations (parts per million and less), for which the API correlation is not accurate. It can be used for initial engineering studies, including those involving health, safety, and environmental considerations.

SOLUBILITY ILLUSTRATION

The importance of calculating the solubility of hydrocarbons in water, even at very low concentrations, will increase in the future.

For health considerations, the threshold limit value (TLV) for the exposure of humans to hexane in air is 50 ppm (vol).1 A concentration of only 0.001 ppm (mol) hexane in water will produce about 100 ppm (vol) hexane in air, at the air-water interface. This concentration of 100 ppm exceeds the TLV of 50 PPM.

For safety considerations, the lower explosion limit (LEL) for hexane in air is 1.2 Vol %.2 A concentration of only 0.2 ppm (mol) hexane in water will produce about 2% hexane in air, at the air-water interface. This concentration of 2% exceeds the LEL of 1.2%.

For environmental considerations, if hexane were spilled into water, the water would become saturated with hexane. At saturation, the solubility of hexane in water is about 9.47 ppm (wt), or 1.98 ppm (Mol).3

Hexane in water at 1.98 ppm (mol) will produce about 199,400 ppm (vol), or 19.9% hexane in air, at the air-water interface. This concentration of 199,400 ppm (or 19.9%) greatly exceeds both the TLV of 50 ppm, and the LEL of 1.2%.

This illustration shows that very low concentrations (ppm and less) of hydrocarbons in water can produce concentrations in air, at the air-water interface, that exceed both the TLV for human exposure and the LEL for flammability.

SOLUBILITY CORRELATION

The correlation for the solubility of paraffins in water is based on boiling point, Tb, in K.:

log(S) = A + BTb +

C(Tb)2 + D(Tb)3

where:

S = Solubility in water at 25 C., in ppm (wt)

Tb = Boiling point, in K.

A = 17.652

B = 177.811 x 10-3

C - 500.907 x 10-6

D = 411.124 x 10-9

The correlation applies to normal and isomer paraffins which are liquids at ambient conditions (25 C., 1 atm). Liquid paraffins are C5 and larger molecules. The data range for boiling point temperature is 301 K. to about 561 K.

The correlation is not applicable to paraffins which are solids at ambient conditions. A different solubility curve is obtained for solid paraffins.

The correlation constants (A, B, C, and D) were determined from regression of the available data. In preparing the correlation, a literature search was conducted to identify sources of experimental data.

The data were entered into a computer to provide a data base of solubility values for hydrocarbons. The data base also served as a basis to check the accuracy of the correlation.

A comparison of correlation and experimental values for the solubility of paraffins in water is shown in Fig. 1. The experimental data include a wide variety of normal and isomer (single, double. and triple-substituted) paraffins. Fig. 1 illustrates favorable agreement of correlation and experimental data.

In testing the correlation for C5-C16 liquid paraffins, it was determined that calculated solubility values were in favorable agreement with experimental data, down to very low concentrations. The experimental data covered solubilities of 47.8 to 0.0009 ppm (wt).

In testing the API correlation for C5-C16 liquid paraffins, it was determined that solubility values diverge from experimental data at very low concentrations. The divergence begins at C8 liquid paraffin and increases for larger molecules.

COMPARISON OF CORRELATIONS

The present and API correlations are compared in Table 1. The first data points correspond to C5 liquid paraffins (isopentane and normal pentane). Both correlations exhibit general agreement of calculated values with experimental values for the C5 liquid paraffins.

However, the deviations (or errors) for the present correlation are less, at 3.93% and 1.25% for isopentane and normal pentane, respectively. The corresponding deviations for the API correlation are 33.45% and 15.01%.

For C8 liquid paraffin (normal octane), the deviation of the present correlation is 8.63%, as compared to 22.08% for the API correlation. The pattern of less deviation for the present correlation continues for larger liquid paraffins.

For all the data points covering C5-C16 liquid paraffins, the average deviation from experimental data is about 23.68% for the present correlation. The average deviation for the API correlation is about 40.55%.

A plot of the experimental data and results from the present and API correlations are shown in Fig. 2. Inspection of Fig. 2 indicates that the correlations are roughly equivalent up to a boiling point of about 400 K. and a solubility of about 0.40 ppm (wt).

Since the boiling point and solubility of octane (398.8 K. and 0.431 ppm [wt]) roughly match this condition, the point where the divergence begins roughly corresponds to C8 liquid paraffin. This divergence from experimental data increases for larger liquid paraffins.

The following illustrates the increase in divergence at very low concentrations: For C10 liquid paraffin (normal decane), the experimental value for water solubility is 0.052 ppm (wt). The calculated value from the API correlation is 0.0095 ppm (wt). This calculated value is off by a factor of 5.47 (exp. - calc. 0.052 = 0.0095 = 5.47).

For C12 liquid paraffin (dodecane), the calculated value is off by a factor of 57.8 (exp. calc. 0.0037 0.000064 57.8). For C14 liquid paraffin (tetradecane), the calculated value is off by a factor of 13,750 (exp. calc. 0.0022 0.00000016 = 13,750). For C16 liquid paraffin (hexadecane), the divergence of the calculated value from the experimental value is even greater.

EXAMPLES

Example 1: A hydrocarbon spill of normal pentane occurs into a body of water at ambient conditions (25 C., 1 atm). Substitution of the correlation constants for paraffins and the boiling point of pentane (309.22 K.) into the correlation equation yields:

log(S) = 1.591065, or S = 39.0 ppm (wt)

The calculated and experimental values compare favorably: 39.0 (calc.) vs. 38.50 (exp.).

Example 2: A hydrocarbon spill of normal hexadecane occurs into a body of water at ambient conditions. Substitution of the correlation constants for paraffins and the boiling point of hexadecane (560.5 K.) into the correlation equation yields:

log(S) = -2.9605, or S = 0.0011 ppm (wt)

The calculated and experimental values compare favorably: 0.0011 (calc.) vs. 0.0009 (exp.).

REFERENCES

1. Sax, N.I., Lewis, R.J., Sr., Hawley's Condensed Chemical Dictionary, 11th ed.. Van Nostrand Reinhold Co. Inc., New York, N.Y., 1987.

2. Daubert, T.E., Danner, R.P., "Data Compilation of Properties of Pure Compounds," Parts 1 and 2, DIPPR Project, AIChE, New York, N.Y., 1985.

3. Sorensen, J.M., Arlt, W., "Liquid-Liquid Equilibrium Data Collection," Vol. V, Part 1, Dechema Chemistry Data Series, 6000 Frankfurt/Main, Germany, 1979.

4. McAuliffe, C., J. Phy. Chem., Vol. 70, 1966, p. 1267.

5. Price, L.C., Bull. Am. Assoc. Petrol. Geologists, Vol. 60(2), 1976, p. 213.

6. Sutton, C., Calder, J.A., Environ. Sci. Techn., Vol. 8(7), 1974, p. 654.

7. Yaws, C.L.. Chen, D., Yang, H.C., Tan, L., Nico, D., Hydrocarbon Processing, July 1989, p. 68.

8. McAuliffe, C., Science, Vol. 158, 1969, p. 478.

9. Mackay, D., Shiu, W.Y., J. Phys. Chem. Ref. Data, Vol. 10(4), 1981, p. 1175.

10. Technical Data Book-Petroleum Refining, 4th ed., Vol. 2, American Petroleum Institute, 1983.

Copyright 1991 Oil & Gas Journal. All Rights Reserved.