LPG Vaporization and Entropy Calculator

How Do We Calculate the Vaporization Rate of Your LPG Mixture?

Our calculator uses advanced thermodynamic principles to predict whether your propane and butane mixture will undergo flash vaporization when passing through a restriction. Here's how to explain the process in simple language:

1. We Determine the Pure Vapor Pressures

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For each component (propane and butane), we calculate the pressure exerted by their vapors at the temperature you specify. We use proven scientific equations (Antoine's Equation) that mathematically relate temperature to vapor pressure.

2. We calculate the vapor pressure of your mixture

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Depending on the model you choose:

Ideal Model (Raoult): We simply average the pressures based on the percentage of each gas

Real Model (Margules): We adjust the calculation considering how different molecules interact with each other

3. We compare it to your downstream pressure

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The moment of truth: if the pressure after the restriction (P₂) is lower than the vapor pressure we calculated, vaporization will occur! This is because the liquid cannot remain stable at that pressure.

4. We show you what percentage vaporizes

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We don't just say "yes" or "no," but we calculate exactly what part of your mixture will change to vapor and what part will remain liquid, representing this in an easy-to-understand graph.

5. We calculate the energy involved

We determine the entropy of vaporization, which tells you how much energy is required for this phase change—valuable information for designing efficient systems.

 

Model Limitations

 

1. Range of Validity
-Temperature: -50°C to 100°C (outside this range, results may lose accuracy).
-Pressure: Up to 20 bar (not applicable for cryogenic or ultra-high-pressure conditions).
-Composition: Only valid for binary mixtures of propane/butane. Does not consider:

• Impurities (methane, ethane, pentane).

• Additives (odorizers, corrosion inhibitors).

2. Calculation Assumptions

• Raoult's Law: Assumes ideal behavior (no molecular interactions).

• Margules Model: Considers interactions, but with fixed coefficients (A₁₂ = 0.143, A₂₁ = 0.128).

• Antoine Equation: Reduced accuracy near the critical point (T > Tc).

3. Factors Not Considered
-Kinetic effects: Does not evaluate expansion rate or residence time.
-Heat losses: Assumes an adiabatic process (no heat exchange with the environment).
-Restriction geometry: Does not take into account the type of plate/valve (orifice, globe, etc.).

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Uncertainty in Results

 

Vapor pressure (Pv) ±2-5% Antoine equation (experimental setup)

Composition ±1% Rounding in % propane/butane

Temperature ±0.5°C Thermocouple accuracy (if actual measurement is used)

Margules model ±3-8% Approximate interaction coefficients

*Reference values for standard conditions (25°C, 70/30 mixture).

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Recommendations for Professional Use

✔ Validate with specialized software for critical designs. ✔ Consider a safety factor of 10-15% in industrial applications.
✔ Do not use for:

Pressure vessel design (ASME/API standards require more rigorous methods).

Blends with >5% other hydrocarbons.

Interpretation:

• If P₂ is within the uncertainty range of Pv, further analysis is recommended.

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Equations used by the calculator

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1. Vapor pressure of each component (Antoine equation, P in mmHg and T in °C): log₁₀ P = A − B / (T + C). The result is divided by 750.062 to convert it to bar absolute.

Propane: A = 6.80398, B = 803.997, C = 246.78 · Butane: A = 6.80776, B = 935.773, C = 238.789.

2. Ideal mixture (Raoult's law): Pv = x₁·Pv,propane + x₂·Pv,butane, where x₁ and x₂ are the propane and butane fractions.

3. Real mixture (Margules): ln γ₁ = x₂²·[A₁₂ + 2·(A₂₁ − A₁₂)·x₁] and ln γ₂ = x₁²·[A₂₁ + 2·(A₁₂ − A₂₁)·x₂], with A₁₂ = 0.143 and A₂₁ = 0.128; then Pv = x₁·γ₁·Pv,propane + x₂·γ₂·Pv,butane.

4. Criterion: flash vaporization occurs if the downstream pressure P₂ (absolute) is lower than the mixture's Pv.

5. Vaporization entropy: ΔS = ΔHvap / T, with T in kelvin and ΔHvap = x₁·425.5 + x₂·385.6 kJ/kg (with Margules it is multiplied by x₁·γ₁ + x₂·γ₂).

6. Vaporized fraction (adiabatic flash): find the temperature T₂ at which the mixture's Pv equals P₂ and apply x = 1 − exp(−cp·(T₁ − T₂) / ΔHvap), with liquid cp = x₁·2.52 + x₂·2.39 kJ/(kg·K). Assumes constant composition during the expansion.

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Worked example: 70/30 LPG at 25 °C

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Data: 70% propane, 30% butane, T = 25 °C and downstream pressure P₂ = 6 bar absolute.

1. Propane: log₁₀ P = 6.80398 − 803.997 / (25 + 246.78) = 3.84572 → P = 7,010 mmHg = 9.346 bar.

2. Butane: log₁₀ P = 6.80776 − 935.773 / (25 + 238.789) = 3.26033 → P = 1,821 mmHg = 2.428 bar.

3. Raoult: Pv = 0.70 × 9.346 + 0.30 × 2.428 = 7.270 bar. With Margules: γ₁ = 1.0110, γ₂ = 1.0694 and Pv = 7.393 bar.

4. Since P₂ = 6 bar is lower than 7.27 bar, the LPG flashes when it passes the restriction. With P₂ = 8 bar it would stay liquid.

5. Entropy: ΔHvap = 0.70 × 425.5 + 0.30 × 385.6 = 413.53 kJ/kg; ΔS = 413.53 / 298.15 = 1.3870 kJ/(kg·K) (1.4266 with Margules).

6. Vaporized fraction: the mixture's Pv drops to 6 bar at T₂ = 17.7 °C; cp = 0.70 × 2.52 + 0.30 × 2.39 = 2.481 kJ/(kg·K); x = 1 − exp(−2.481 × (25 − 17.7) / 413.53) = 4.3%. 95.7% stays liquid (with Margules: T₂ = 17.1 °C and 4.5% vapor).

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LPG vapor pressure by temperature and blend (Raoult, bar absolute)

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−20 °C: propane 2.42 · 70/30 1.83 · 50/50 1.44 · 30/70 1.04 · butane 0.45

−10 °C: propane 3.41 · 70/30 2.60 · 50/50 2.06 · 30/70 1.51 · butane 0.70

0 °C: propane 4.69 · 70/30 3.59 · 50/50 2.86 · 30/70 2.13 · butane 1.03

10 °C: propane 6.28 · 70/30 4.84 · 50/50 3.88 · 30/70 2.92 · butane 1.48

20 °C: propane 8.23 · 70/30 6.38 · 50/50 5.15 · 30/70 3.92 · butane 2.07

30 °C: propane 10.57 · 70/30 8.25 · 50/50 6.70 · 30/70 5.15 · butane 2.83

40 °C: propane 13.35 · 70/30 10.47 · 50/50 8.56 · 30/70 6.64 · butane 3.77

To convert to gauge pressure, subtract atmospheric pressure (about 1.013 bar at sea level).

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Frequently asked questions

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Should P₂ be absolute or gauge pressure? Absolute, because the Antoine vapor pressure is absolute. If your gauge reads 5 bar, at sea level that is about 6.01 bar absolute.

Why does butane vaporize less than propane? Its vapor pressure is about four times lower (2.43 vs 9.35 bar at 25 °C). That is why butane-rich blends stay liquid at lower pressure but vaporize poorly in cold weather: at −10 °C pure butane has only 0.70 bar, below atmospheric pressure.

When should I use Raoult and when Margules? Raoult assumes an ideal mixture and is usually enough for propane and butane, which are similar molecules. Margules corrects with activity coefficients and gives slightly higher pressures (7.39 vs 7.27 bar in the example).

What does it mean if P₂ is lower than Pv? The liquid drops below its bubble-point pressure and part of it boils suddenly (flash). In orifice plates and valves this causes flow measurement errors, noise and wear.

What is the vaporization entropy used for? It shows how much energy per kilogram and per kelvin the phase change absorbs; it helps estimate the cooling caused by vaporization.

How does it calculate the percentage that vaporizes? When the pressure drops, the liquid boils and cools down to the temperature T₂ at which its vapor pressure equals P₂. The heat it gives up while cooling is what evaporates part of it. For example, pure butane at 25 °C released to the atmosphere cools to about −0.5 °C and roughly 15% of it vaporizes.

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Final Note
This tool is useful for preliminary estimates, but technical decisions should be based on international standards (API, ISO) and experimental measurements.