Flash Calculation Theory

Flash calculations determine the phase split and compositions when a mixture at specified conditions partially vaporizes.

What is a Flash?

A flash (or flash drum) is a unit operation where a liquid feed is partially vaporized by reducing pressure or adding heat. The resulting vapor and liquid phases are in equilibrium and can be separated.

Applications: Crude oil distillation, refrigeration systems, natural gas processing, chemical reactors, evaporators.

Material Balance

For a flash drum with feed F splitting into vapor V and liquid L:

F = V + L (Overall balance)

F·z_i = V·y_i + L·x_i (Component balance)

Where z_i is feed composition, y_i is vapor composition, and x_i is liquid composition.

K-Value (Equilibrium Ratio)

The K-value relates vapor and liquid compositions at equilibrium:

K_i = y_i / x_i

Raoult's Law (Ideal Mixtures)

K_i = P_i^sat / P

Where P_i^sat is the saturation pressure from Antoine equation.

Rachford-Rice Equation

Combining material balance with equilibrium relationships gives the Rachford-Rice equation:

f(ψ) = Σ z_i(K_i - 1) / (1 + ψ(K_i - 1)) = 0

Where ψ = V/F is the vapor fraction. This equation is solved iteratively using Newton-Raphson method.

Composition Calculations

Once ψ is found:

x_i = z_i / (1 + ψ(K_i - 1))

y_i = K_i · x_i

Bubble & Dew Points

Bubble Point

Temperature where the first bubble of vapor forms from a liquid.

At bubble point: Σ K_i·x_i = 1 (V/F = 0)

Dew Point

Temperature where the first drop of liquid forms from a vapor.

At dew point: Σ y_i/K_i = 1 (V/F = 1)

Antoine Equation

Vapor pressure is calculated using the Antoine equation:

log₁₀(P^sat) = A - B / (C + T)

Where A, B, C are component-specific constants, T is temperature (°C), and P^sat is in mmHg.

Flash Types

Type	Given	Calculate
Isothermal (TP)	T, P	V/F, x_i, y_i
Bubble Point	P, x_i	T_bubble, y_i
Dew Point	P, y_i	T_dew, x_i
Adiabatic	H_feed, P	T, V/F, x_i, y_i

References

Rachford, H.H. and Rice, J.D. (1952). "Procedure for Use of Electronic Digital Computers in Calculating Flash Vaporization". J. Petroleum Technology.
Smith, J.M., Van Ness, H.C., and Abbott, M.M. (2005). Introduction to Chemical Engineering Thermodynamics. McGraw-Hill.
Seader, J.D. and Henley, E.J. (2006). Separation Process Principles. Wiley.

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