Average Boiling Point Mixtures Calculation Prediction Estimation Gravity Density Molecular Weight

Overview

Engineering reference data for Average Boiling Point Mixtures Calculation Prediction Estimation Gravity Density Molecular Weight in thermodynamics.

Key Formulas

First Law

$\Delta U = Q - W$

Energy is conserved — heat added minus work done.

Ideal Gas Law

$PV = nRT$

Relates pressure, volume, and temperature of an ideal gas.

Heat Transfer

$Q = mc\Delta T$

Sensible heat transfer.

Carnot Efficiency

$\eta = 1 - T_C/T_H$

Maximum efficiency between two temperatures.

Variables

References

• Original Source

Additional Technical Notes

Equation Applicability

The two Riazi-Daubert correlations cover different molecular weight ranges but have some overlap in applicability.

• Equation (1) is optimized for hydrocarbons with molecular weights between *70 and 300.
• Equation (2) is optimized for molecular weights between *300 and 700. It can also be applied in the 70-300 range, but as noted in Example 1, it yields a less accurate result in that range compared to Equation (1).

When molecular weight data is unavailable, you can derive it from other properties using correlations based on average boiling point and gravity, as referenced in the main content.

Riazi-Daubert Correlations for Average Boiling Point (ABP)

Two empirical correlations from Riazi and Daubert are used to predict the average boiling point (ABP) for hydrocarbons, primarily crude oils and their distillation fractions, based on molecular weight (M) and specific gravity (S).

For Molecular Weights (M) 70-300:

$$T_b = 3.76587 \cdot e^{(3.7741 \times 10^{-3} M + 2.98404 S - 4.25288 \times 10^{-3} M S)} \cdot M^{0.40167} \cdot S^{-1.58262}$$

where $T_b$ is in Kelvin.

For Molecular Weights (M) 300-700:

$$T_b = 9.3369 \cdot e^{(1.6514 \times 10^{-4} M + 1.4103 S - 7.5152 \times 10^{-4} M S)} \cdot M^{0.5369} \cdot S^{-0.7276}$$

where $T_b$ is in Kelvin.

Note: While Equation 2 can be applied to the 70-300 molecular weight range, it is considered less accurate than Equation 1 for that range.

Worked Examples

Example 1: Average Boiling Point of Naphtha

Calculate the average boiling point of a naphtha with specific gravity $S = 0.763$ and a molecular weight of $M = 125$.

Since naphtha is in the low molecular weight range ($M < 300$), Equation (1) applies:

$T_b = 3.76587 \, e^{(3.7741 \times 10^{-3} \cdot 125 + 2.98404 \cdot 0.763 - 4.25288 \times 10^{-3} \cdot 125 \cdot 0.763)} \cdot 125^{0.40167} \cdot 0.763^{-1.58262}$

$T_b = 418 \text{ K} = 145°\text{C} = 293°\text{F}$

Verification with Equation (2): Applying Equation (2) gives $T_b = 423 \text{ K} = 150°\text{C} = 302°\text{F}$. Note that for low molecular weights ($< 300$), this result is considered less accurate than Equation (1).

Example 2: Average Boiling Point of a Vacuum Gas Oil

Calculate the average boiling point of a vacuum gas oil with API gravity $16.7°\text{API}$ and average molecular weight $M = 391$.

Step 1: Convert API gravity to specific gravity:

$S = \frac{141.5}{°\text{API} + 131.5} = \frac{141.5}{16.7 + 131.5} = 0.955$

Step 2: Since $M > 300$, apply Equation (2):

$T_b = 9.3369 \, e^{(1.6514 \times 10^{-4} \cdot 391 + 1.4103 \cdot 0.955 - 7.5152 \times 10^{-4} \cdot 391 \cdot 0.955)} \cdot 391^{0.5369} \cdot 0.955^{-0.7276}$

$T_b = 737 \text{ K} = 464°\text{C} = 867°\text{F}$

API Gravity to Specific Gravity Conversion

API gravity is commonly used in the petroleum industry. To use the Riazi-Daubert correlations, convert to specific gravity at $60°\text{F}$ ($15.6°\text{C}$):

$S = \frac{141.5}{°\text{API} + 131.5}$

where $S$ is specific gravity (dimensionless) and $°\text{API}$ is the API gravity.

Equation Selection Guidelines

Temperature Conversions

$T(°\text{C}) = T(\text{K}) - 273.15$

$T(°\text{F}) = T(°\text{C}) \times \frac{9}{5} + 32$

Practical Application Notes

When applying the Riazi-Daubert correlations for average boiling point estimation, please note the following important guidelines for accurate calculations:

Equation Selection Accuracy:

• Equation (1): Optimized for and most accurate within the molecular weight range of *70-300.
• Equation (2): Required for molecular weights *300-700. While it can be applied to the 70-300 range, doing so yields less accurate results than using Equation (1).

Calculation Workflow:

1. Identify Molecular Weight: Determine if M < 300 or M > 300 to select the primary equation.
2. Prepare Gravity Input: Ensure specific gravity (S) is referenced at 60°F (15.6°C). If API gravity is provided, convert it using the standard formula: $S = \frac{141.5}{\text{API Gravity} + 131.5}$
3. Compute ABP: Apply the selected correlation.
4. Convert Units: The result (Tb) is in Kelvin. Convert to degrees Celsius (°C) or Fahrenheit (°F) as needed: $T_{C} = T_{K} - 273.15$ $T_{F} = (T_{K} - 273.15) \times \frac{9}{5} + 32$

Key Formula Reference (LaTeX): The core Riazi-Daubert correlations are:

• For M = 70-300: $T_b = 3.76587 \cdot \exp\left(3.7741 \times 10^{-3} M + 2.98404 S - 4.25288 \times 10^{-3} M S\right) \cdot M^{0.40167} \cdot S^{-1.58262}$
• For M = 300-700: $T_b = 9.3369 \cdot \exp\left(1.6514 \times 10^{-4} M + 1.4103 S - 7.5152 \times 10^{-4} M S\right) \cdot M^{0.5369} \cdot S^{-0.7276}$

Riazi-Daubert Equations in LaTeX Format

The core Riazi-Daubert correlations for calculating the average boiling point ($T_b$) in Kelvin are:

For molecular weights 70-300:

$$T_b = 3.76587 \times e^{\left(3.7741 \times 10^{-3} M + 2.98404 S - 4.25288 \times 10^{-3} M S\right)} \times M^{0.40167} \times S^{-1.58262}$$

For molecular weights 300-700:

$$T_b = 9.3369 \times e^{\left(1.6514 \times 10^{-4} M + 1.4103 S - 7.5152 \times 10^{-4} M S\right)} \times M^{0.5369} \times S^{-0.7276}$$

where:

• $T_b$ = Average boiling point (K)
• $M$ = Average molecular weight
• $S$ = Specific gravity at 60°F (15.6°C)

Note on Applicability: Equation (2) can be used for molecular weights in the 70-300 range, but with reduced accuracy compared to Equation (1).

API Gravity to Specific Gravity Conversion Formula

The standard formula for converting API gravity ($°API$) to specific gravity ($S$) at 60°F is:

$$S = \frac{141.5}{°API + 131.5}$$

This conversion is necessary when API gravity is provided, as the Riazi-Daubert equations require specific gravity.