Flash Calculations
Engineering fundamentals for vapor-liquid equilibrium
1. VLE Fundamentals
Flash calculations determine how a feed mixture splits into vapor and liquid phases at given conditions. Essential for separator design, distillation, and process simulation.
📊 Flash Separation Schematic
Process diagram showing: Feed stream F (composition z_i, T, P) entering flash drum/separator. Two exit streams: Vapor V (composition y_i) from top, Liquid L (composition x_i) from bottom. Label mole balance: F = V + L. Show equilibrium between phases inside vessel.
Material Balance
Overall: F = V + L
Component: F × z_i = V × y_i + L × x_i
Where:
F, V, L = Feed, vapor, liquid molar flows
z_i = Feed mole fraction of component i
y_i = Vapor mole fraction of component i
x_i = Liquid mole fraction of component i
Phase Behavior
| Condition |
Result |
| T < Bubble point |
All liquid (subcooled) |
| T = Bubble point |
First vapor forms |
| Bubble point < T < Dew point |
Two-phase (V + L) |
| T = Dew point |
Last liquid evaporates |
| T > Dew point |
All vapor (superheated) |
2. K-Values (Equilibrium Ratios)
The K-value relates vapor and liquid compositions at equilibrium:
K_i = y_i / x_i
At equilibrium, each component distributes between phases
according to its K-value at the given T and P.
K-Value Methods
| Method |
Equation |
Application |
| Raoult's Law |
K_i = P_i^sat / P |
Ideal mixtures, low pressure |
| DePriester Charts |
Graphical (T, P) |
Light hydrocarbons, quick estimates |
| Wilson Correlation |
K_i = (Pc_i/P) × exp(5.37(1+ω)(1-Tc_i/T)) |
Hydrocarbons, first approximation |
| Equation of State |
φ_i^V / φ_i^L (fugacity) |
Most accurate, process simulators |
📈 K-Value vs. Pressure (Typical Hydrocarbons)
Log-log plot with P (psia) on X-axis (14.7 to 1000), K-value on Y-axis (0.01 to 100). Show curves for: Methane (K >> 1 at most pressures), Ethane, Propane, n-Butane, n-Pentane, n-Hexane (K << 1 at higher pressures). All curves converge toward K=1 at higher pressure. Mark typical separator pressure range (200-800 psia).
K-Value Interpretation
- K > 1: Component favors vapor phase (light components)
- K < 1: Component favors liquid phase (heavy components)
- K = 1: Equal distribution (near critical or convergence pressure)
Rule of thumb: Methane K ≈ 3–5 at typical separator conditions (500 psia, 80°F). Propane K ≈ 0.5–1.5. Hexane+ K << 1.
3. Rachford-Rice Equation
The Rachford-Rice equation combines material balance and equilibrium to solve for vapor fraction (V/F):
Rachford-Rice Objective Function:
f(V/F) = Σ z_i × (K_i - 1) / (1 + (V/F)(K_i - 1)) = 0
Solve for V/F by iteration (Newton-Raphson or bisection)
Valid range: 0 ≤ V/F ≤ 1
Solution Steps
- Obtain K-values for all components at T and P
- Check if two-phase: Σz_i×K_i > 1 (bubble) and Σz_i/K_i > 1 (dew)
- Solve Rachford-Rice for V/F
- Calculate compositions: x_i = z_i / (1 + (V/F)(K_i - 1)), y_i = K_i × x_i
- Calculate flows: V = F × (V/F), L = F - V
Convergence Checks
| Test |
Result |
Conclusion |
| Σ(z_i × K_i) < 1 |
Below bubble point |
All liquid |
| Σ(z_i / K_i) < 1 |
Above dew point |
All vapor |
| Both sums > 1 |
Two-phase region |
Solve R-R |
Example: Simple Flash
Feed: 60% C1, 25% C2, 15% C3 (mole) at 500 psia, 50°F
K-values: K_C1 = 4.0, K_C2 = 0.80, K_C3 = 0.25
Check: Σz_i×K_i = 0.6(4)+0.25(0.8)+0.15(0.25) = 2.64 > 1 ✓
Check: Σz_i/K_i = 0.6/4+0.25/0.8+0.15/0.25 = 1.06 > 1 ✓
Two-phase → Solve R-R → V/F ≈ 0.54
x_C1 = 0.6/(1+0.54×3) = 0.22, y_C1 = 4×0.22 = 0.88
4. Flash Types
Isothermal Flash (T-P Flash)
Given: T, P, z_i → Find: V/F, x_i, y_i
- Most common flash calculation
- Direct solution via Rachford-Rice
- Used for separator design
Adiabatic Flash
Given: H_feed, P, z_i → Find: T, V/F, x_i, y_i
- Constant enthalpy (isenthalpic)
- J-T valve expansion
- Requires iteration on T
Bubble Point Calculation
Given: T (or P), z_i, V/F = 0 → Find: P (or T)
- Condition: Σ(z_i × K_i) = 1
- First vapor bubble forms
- y_i = z_i × K_i at bubble point
Dew Point Calculation
Given: T (or P), z_i, V/F = 1 → Find: P (or T)
- Condition: Σ(z_i / K_i) = 1
- Last liquid drop evaporates
- x_i = z_i / K_i at dew point
📊 Phase Envelope (P-T Diagram)
P-T diagram showing: Bubble point curve (lower), dew point curve (upper), meeting at critical point (C). Inside envelope: two-phase region with quality lines (10%, 50%, 90% vapor). Outside left: subcooled liquid. Outside right: superheated vapor. Mark cricondenbar (max P) and cricondentherm (max T). Show typical natural gas composition envelope.
5. Applications
Production Separator Sizing
- Flash calculation determines V and L flow rates
- Size vessel for residence time and separation efficiency
- Multi-stage separation optimizes liquid recovery
Stabilizer/Deethanizer Feed
- Determine feed phase condition
- Calculate reboiler/condenser duties
- Product composition specifications
Pipeline Flow Assurance
- Predict liquid dropout vs. pressure/temperature
- Locate slug catchers and pig receivers
- Two-phase flow regime determination
Practical tip: For natural gas systems, always check for retrograde condensation. Rich gas may condense liquid when pressure drops (counterintuitive), requiring slug catchers at pressure letdown points.
References
- GPSA Engineering Data Book, Section 25 (Flash Calculations)
- Campbell Gas Conditioning and Processing, Vol. 1
- Experiment, et al. "Vapor-Liquid Equilibria" (Chemical Engineering Progress)
- API Technical Data Book – Petroleum Refining