  # Simple Vapour-Liquid Equilibrium Flash

Category: Chemical Engineering

Demonstrates: Non-Linear simultaneous equations; Array variables

## Problem Description

A mixture of 3 chemical components: benzene, toluene and xylene is fed continuously into a vapour-liquid separator, or flash drum. Vapour and liquid in the separator are at equilibrium.

Given the feed composition and the conditions in the drum, calculate the flow rate and composition of the vapour and liquid phases. Ideal behaviour is assumed.

The mole fractions of the 3 components in the feed are 0.4, 0.4 and 0.2 respectively. Feed flow is 100 kmol/hr. Temperature and pressure of the separator are 118°C and 1140 mmHg.

The following equations will be used:

Material Balance:

 L + V = F Lxi + Vyi = Fzi

Vapour-Liquid Equilibrium:

 yi = Kixi Ki = pi0 / P

Vapour Pressure (Antoine Equation):

 log(pi0) = Ai - Bi / (t + Ci)

Summation of Mole Fractions:

 Σ (yi - xi) = 0

The EQUATRAN source text for this problem is:

 /* Equilibrium Flash Calculation */ LOCAL N = 3 /* Number of components */ VAR F = 100 "Feed rate [kgmol/h]",.. t = 118 "Temperature [C]",.. P = 1140 "Pressure [mmHg]",.. L "Liquid flow rate [kgmol/h]",.. V "Vapor flow rate [kgmol/h]",.. z(N) = ( 0.4, 0.4, 0.2 ) .. "Feed mole fraction [-]",.. x(N) "Liquid mole fraction [-]",.. y(N) "Vapor mole fraction [-]",.. K(N) "K value [-]",.. p(N) "Vapor pressure [mmHg]",.. A(N) "Antoine constants A",.. B(N) "Antoine constants B",.. C(N) "Antoine constants C" /* Material balance */ L + V = F L*x + V*y = F*z /* Liquid vapor equilibrium */ y = K*x K = p/P /* Antoine equation p[mmHg], t[C] */ LOG10(p) = A - B/(t+C) /* Antoine constants (p[mmHg],t[C]) */ /* Benzene, Toluene and Xylene */ A = ( 6.90565, 6.95464, 7.00988) B = ( 1211.03, 1344.80, 1462.27) C = ( 220.790, 219.482, 215.105) SUM(y-x) = 0 OUTPUT L,V,x,y,K

Enter the lines above into a new source text window, then click the Run button. EQUATRAN will determine that an itereative solution is required and will select the variable L to be estimated to start the calculation loop. An input window is shown and an initial value for L can be entered. We know the value must be between 0 and 100, so 50 is a good value to use, but this is a simple and any reasonable value can be entered. The calculation result is displayed:

 /* Equilibrium Flash Calculation */                                      <<   results   >> L               =  56.35664       : Liquid flow rate [kgmol/h]               V               =  43.64336       : Vapor flow rate [kgmol/h]                x               =                 : Liquid mole fraction [-]                   1) 0.2889993        2) 0.4344453        3) 0.2765554      y               =                 : Vapor mole fraction [-]                    1) 0.5433351        2) 0.3555209        3) 0.101144       K               =                 : K value [-]                                1) 1.880057         2) 0.8183329        3) 0.3657279