Process Engineering

Flash Calculations & VLE

Calculate vapor-liquid equilibrium using K-values, Rachford-Rice equation, and phase behavior correlations for separator design, distillation, and process simulation per GPSA standards.

Launch Calculator Rachford-Rice method

Typical K-values

0.01 to 100

K>1 for light components (methane ≈3-5), K<1 for heavy components at separator conditions.

Separator pressure

200-800 psia

Typical production separator operating pressure for optimal vapor-liquid split efficiency.

Phase split

0-100% vapor

Vapor fraction (V/F) ranges from 0 (subcooled liquid) to 1 (superheated vapor) in two-phase region.

Contents

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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 showing feed stream F with total moles and composition z_i entering flash drum, vapor stream V with composition y_i exiting top, liquid stream L with composition x_i exiting bottom, equilibrium symbol between phases, and material balance equations F=V+L and F×z_i=V×y_i+L×x_i
Flash drum separation with material balance: F = V + L, and Ki = yi/xi at equilibrium.

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
Equilibrium K-values vs pressure log-log chart for light hydrocarbons at 100°F showing curves for methane C1, ethane C2, propane C3, n-butane nC4, n-pentane nC5, and n-hexane nC6, with K=1 reference line and typical separator operating range of 200-800 psia
Equilibrium K-values for light hydrocarbons at 100°F. K > 1 favors vapor phase; K < 1 favors liquid phase.

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

  1. Obtain K-values for all components at T and P
  2. Check if two-phase: Σz_i×K_i > 1 (bubble) and Σz_i/K_i > 1 (dew)
  3. Solve Rachford-Rice for V/F
  4. Calculate compositions: x_i = z_i / (1 + (V/F)(K_i - 1)), y_i = K_i × x_i
  5. 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
Natural gas phase envelope P-T diagram showing bubble point curve, dew point curve, critical point C, two-phase region with quality lines at 10%, 30%, 50%, 70%, 90% vapor, cricondenbar (max P), cricondentherm (max T), retrograde condensation zone, and typical pipeline P-T path
Natural gas phase envelope with quality lines. Retrograde condensation occurs when liquid forms on pressure decrease.

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, Section 25 (Flash Calculations)
  • Campbell Gas Conditioning and Processing, Vol. 1
  • Experiment, Inc. "Phase Equilibria in Hydrocarbon Systems" (Chemical Engineering Progress)
  • API Technical Data Book – Petroleum Refining

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