# Example 3-8: Diesel fuel characterization

A diesel fuel has been characterised in laboratory by a TBP curve, as shown in table 1. Its average specific gravity is given as 0.8113. For simulation purposes, this diesel must be split in 10 °C cuts.

1. Find the volume percentage corresponding to each cut.
2. Provide the characteristic (critical) parameters for each cut.
Table 1: Constants for example 1
Fraction distillate 0 3 7 17 29 40 50 59
Boiling temperature ( °C) 123 162 185 206 226 244 262 279
Fraction distillate 67 73 80 85 88 92 100
Boiling temperature ( °C) 295 309 324 338 350 362 375

## Analysis:

The properties given are the boiling temperature as a function of fraction.

Components are a mixture of a large number of components and will be evaluated as pseudo-components.

Phases are vapour and liquid at atmospheric pressure.

## Solution:

### See complete results in file (xls):

Some help on nomenclature and tips to use this file can be found here.

### In a first step, the cut procedure is illustrated:

The curve is obtained by an interpolation method. One of the best choices is to use a cubic spline interpolation. Once the natural condition for extrapolation is chosen, the solution of the linear system gives all the curvatures at all points (table 2). This information is used to calculate the coefficients of each cubic polynomial.

The cuts are constructed on a 10 °C width basis which requires an inverse interpolation. An iterative procedure must be implemented. The volume percent corresponding to each cut is given in the table 2 and in figure 1.

Table 2: Percent volume of each cut obtained by the spline approximation of the TBP sample data
Cut 123-133 133-143 143-153 153-163 163-173 173-183 183-193 193-203
% volume 0.69341 0.71810 0.77799 0.91208 1.24396 2.06761 3.44645 5.24822
Cut 213-223 223-233 233-243 243-253 253-263 263-273 273-283 283-293
% volume 5.92534 6.10119 6.10784 5.70905 5.41591 5.29662 5.28176 4.97780
Cut 303-313 313-323 323-333 333-343 343-353 353-363 363-373 373-375
% volume 4.40797 4.71684 3.96873 2.74591 2.56800 3.60710 6.00210 1.55911

### In a second step, the characterization procedure is illustrated:

Once the petroleum mixture has been cut into pseudo-components, as shown in figure 1, each of the pseudo-component must be characterized for further calculation.

First, the average value of KW must be determined, as:

The average specific gravity, SG, is given (SG = 0.81130), but the average temperature is not known. It is computed from

Interpolating the curve, one can take:

% volume Tb (°C)

10 188
50 258
90 353

Which yields: = 264°C

And therefore: =12.19 (rather paraffinic)

Using , where this time is the normal boiling temperature of the pseudo-component, the density of each of these components can be calculated (Table 3).

Before any calculation can be performed, the volume fractions must be converted into molar fractions. This requires the knowledge of the molecular masses. As an example, the method by Twu is used in Table 3.

Table 3: Percent volume of each cut obtained by the spline approximation of the TBP sample data
Pseudos Tb Pseudos Density MW % mol Tc Pc
°C (kg/kmol) (K) (kPa)
Pseudo1 128 0.7360 114.8 0.0044 1.08% 580.5
Pseudo2 138 0.7420 120.1 0.0044 1.08% 591.0
Pseudo3 148 0.7480 125.6 0.0046 1.12% 601.4
Pseudo4 158 0.7539 131.2 0.0052 1.27% 611.7
Pseudo5 168 0.7596 136.9 0.0069 1.67% 622.0
Pseudo6 178 0.7653 142.8 0.0111 2.69% 632.2
Pseudo7 188 0.7710 148.9 0.0179 4.33% 642.3
Pseudo8 198 0.7765 155.0 0.0263 6.37% 652.3
Pseudo9 208 0.7819 161.4 0.0299 7.25% 662.2
Pseudo10 218 0.7873 167.8 0.0278 6.74% 672.1
Pseudo11 228 0.7926 174.5 0.0277 6.72% 681.8
Pseudo12 238 0.7979 181.3 0.0269 6.52% 691.5
Pseudo13 248 0.8030 188.3 0.0244 5.90% 701.1
Pseudo14 258 0.8081 195.4 0.0224 5.43% 710.7
Pseudo15 268 0.8132 202.7 0.0212 5.15% 720.1
Pseudo16 278 0.8182 210.2 0.0206 4.98% 729.5
Pseudo17 288 0.8231 217.9 0.0188 4.56% 738.9
Pseudo18 298 0.8279 225.8 0.0159 3.85% 748.2
Pseudo19 308 0.8327 233.9 0.0157 3.80% 757.4
Pseudo20 318 0.8375 242.2 0.0163 3.95% 766.5
Pseudo21 328 0.8422 250.8 0.0133 3.23% 775.6
Pseudo22 338 0.8468 259.5 0.009 2.17% 784.7
Pseudo23 348 0.8514 268.6 0.0081 1.97% 793.7
Pseudo24 358 0.8560 277.8 0.0111 2.69% 802.7
Pseudo25 368 0.8605 287.3 0.018 4.36% 811.6
Pseudo26 374 0.8631 293.2 0.0046 1.11% 817.0

### Comparison of the methods available for characterization:

In order to compare the various methods that exist a single component was taken (normal boiling temperature = 348 K and specific gravity 0.8479), and the characteristic properties calculated in table 4:

Table 4: Comparison of the various characterization methods using a heavy component (normal boiling temperature = 348 K and specific gravity 0.8479)
MW (kg/kmol) Tc (K) Pc (kPa) Vc (cm3/mol) Zc (-)
Twu [1] 77.7 553.7 4745.9 277.1 0.286
Cavett and Simsci [2] 544.0 4258.9 291.0 0.274
Lee Kesler [3] 77.8 550.3 4743.0 262.2 0.272
Winn and Mobil + Hall-Yarborough[4] 72.7 552.5 5248.7 246.0 0.281
Riazi and Daubert 1[5] 75.0 562.4 5001.5 268.1 0.287
Riazi and Daubert 2 = API method[6] 555.2 4338.1 291.1 0.274

We can see that all methods give similar results. This is so because the cut is a light one. In order to compare the various methods for heavy compounds a single component was taken (normal boiling temperature = 1165.35 K and specific gravity 1.045), and the characteristic properties calculated in table 5:

Table 5: Comparison of the various characterization methods using a heavy component (normal boiling temperature = 1165.35 K and specific gravity 1.045)
MW (kg/kmol) Tc (K) Pc (kPa) Vc (cm3/mol) Zc (-)
Twu [1] 1663.1 1270.7 476.4 2858.2 0.129
Cavett and Simsci [2] 1320.4 4925.6 -194.7 -0.087
Lee Kesler [3] 957.7 1220.3 234.1 5395.5 0.125
Winn and Mobil + Hall-Yarborough[4] 1163.0 1269.2 536.0 5050.8 0.257
Riazi and Daubert 1[5] 861.8 1234.8 496.5 3359.9 0.162
Riazi and Daubert 2 = API method[6] 1178.7 615.7 16604.9 1.043

The component chosen is rather heavy in order to stress that the differences may be large for such components. The method by Cavett and Simsci should clearly be avoided in that case (negative vc). The API recommended method by Riaizi and Daubert also provides a critical compressibility factor that is not realistic. Among the most realistic values, that proposed by Twu is probably most reasonable, because it is based on the extrapolation of the well-known behaviour of n-alkanes.

#### References

[1] TWU C.H., An internally consistent correlation for predicting the critical properties and molecular weights of petroleum and coal-tar liquids, Fluid Phase Equilibria, 1984, 16, n°2, p. 137-150. http://dx.doi.org/10.1016/0378-3812(84)85027-X

[2] CAVETT R.H., Physical Data for Distillation Calculations- Vapor-Liquid Equilibria, 1962.

[3] KESLER M.G., LEE B.I., Improve prediction of enthalpy of fractions, Hydrocarbon Processing, 1976, 55, p. 153-158.

[4] WINN F.W., Physical Properties by Nomogram, Petroleum Refiner, 1957, 36, p. 157-159.

[5] RIAZI M.R., DAUBERT T.E., Simplify property predictions, Hydrocarbon Processing, 1980, 59, n°3, p. 115-116.

[6] RIAZI M.R., Characterization and Properties of Petroleum Fluids, American Society for Testing and Materials, Philadelphia, 2005.