Average Boiling Points

Average boiling points are useful in predicting physical properties and for characterization of complex hydrocarbon mixtures. The key here is to represent a mixture of compounds with a range of boiling points by a single characteristic boiling point. Since this is a formidable task, there are five different “average boiling points” that are used in different correlations. They are:

$V A B P (Volume Average Boiling Point)$
$M A B P (Molal Average Boiling Point)$
$W A B P (Weight Average Boiling Point)$
$C A B P (Cubic Average Boiling Point)$
$M e A B P (Mean Average Boiling Point) = (M A B P + C A B P) / 2$

1, 2, and 3 can be defined for a mixture of n components as:

(Vol, ​ Mol, or Weight) A B P = \sum x_{i} T_{b i}

where ABP is is expressed as VABP, MABP, or WABP and x_i is the corresponding volume, mole, or weight fraction of component i, and T_bi is the normal boiling point of component i. Cubic average boiling point (CABP) and Mean Average Boling Points (MeABP) can be calculated as follows.

C A B P = {[\sum x_{i volume} {(T_{b i})}^{1 / 3}]}^{3}

M e A B P = (M A B P + C A B P) / 2

For petroleum streams, volume, weight, or mole fractions of the components are not usually known. In this case, VABP is calculated from standard distillation (ASTM D86 Method) data, and empirical relationships (charts, or equations) are used to calculate the other average boiling points.

Here is the procedure:

Equation 1 (Ts are ASTM D86 temperatures for 10, 30, 50, 70, and 90% volume distilled, respectively):

V A B P = (T_{10 %} + T_{30 %} + T_{50 %} + T_{70 %} + T_{90 %}) / 5

Along with VABP, the slope of the ASTM D86, SL, is used for converting VABP to other average boiling points.

Equation 2:

S L = (T_{90 %} - T_{10 %}) / 80

The following empirical equations can, then, be used to obtain the temperature difference (ΔT) between VABP and other average boiling points (ABP) [2] :

Equation 3:

I n (- Δ T_{Weight Average}) = - 3.64991 - 0.02706 {(V A B P - 273.15)}^{0.6667} + 5.163875

S L 0.25

Equation 4:

I n (Δ T_{Molal Average}) = - 1.15158 - 0.01181 {(V A B P - 273.15)}^{0.6667} + 3.70612 S L^{0.333}

Equation 5:

I n (Δ T_{Cubic Average}) = - 0.82368 - 0.08997 {(V A B P - 273.15)}^{0.45} + 2.456791 S L^{0.45}

Equation 6:

I n (Δ T_{Mean Average}) = - 1.53181 - 0.0128 {(V A B P - 273.15)}^{0.6667} + 3.646064 S L^{0.333}

and

Equation 7:

(Weight, Molal, Cubic, or Mean) A B P = V A B P - Δ T_{(weight, molal, cubic, or mean)}

The temperature unit used for VABP, SL, and ΔT in these correlations is Kelvin.

The following script can be used to calculate VABP, MeABP by entering the distillation temperatures in the table.

You may also use the charts in Figure 4.1a and Figure 4.1b (p. 39) of your textbook [3] to obtain MeABP and MABP, respectively, from VABP. Note that the slope of the distillation curve used in those charts refers to True Boiling Point (TBP) distillation (not to ASTM distillation), and it is calculated as (T_70% -T_10%)/60.

[3] Petroleum Refining, by J. H. Gary, G. E. Handwerk, M. J. Kaiser, 5th Edition, CRC Press NY, 2007, Chapter 4, p.39.

Average Boiling Points

Average Boiling Points

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