Bubble Point and Dew Point Calculations

Notation

i - Subscript for each component in- Subscript for each iterationK - vapor liquid equilibrium constantx - mole Fraction in liquid phasey - mole fraction in vapor phaseF(T) - Newton Raphson function

Equations for Bubble Point

from empirical data

from definition of vapor liquid equilibrium constant

The vapor phase mole fractions add to 1

For Newton Raphson Method

Define a function that iterates to 0

Differentiating F(T)

Newton Raphson Eq.

The bubble point of a system is the temperature at which a liquid mixture begins to vaporize. The dew point is the temperature at which liquid begins to condense out of the vapor. If there is enough volume in the fluid, the bulk fluid concentration will remain unchanged after the first small bubble or drop of liquid is formed. This calculation is important for vapor liquid equilibrium processes such as distillation, adsorption and stripping. The program uses empirical data of vapor liquid equilibrium as a function of temperature and iteratively finds temperature with the Newton Raphson method. There is also a version using the Excel goal seek to demonstrate a easier way to program this.

T - Temperature (OK)

Ki(T) = ai +biT +ciT2 + diT3

yi = xi*Ki(T)

∑i=1

n

K i (T )⋅x i=1

F (T )≡∑i

K i (T )⋅xi−1=0

F '(T )=∑i

(b i+2⋅c i⋅T +3d i⋅T2 )∗xi

T n+1=T n−F (T )/F '(T )

Equations for Dew Point

from empirical data

from definition of vapor liquid equilibrium constant

The liquid phase mole fractions add to 1

For Newton Raphson Method

Define a function that iterates to 0

Differentiating F(T)

SpreadSheets

BBLpt - Bubble point calculation with Newton Raphson IterationDewpt - Dew point calculation with Newton Raphson MethodBBLGS - Bubble point repeated but with Excel Goal Seeker used for iterative solution

Ki(T) = ai +biT +ciT2 + diT3

xi = yi/Ki

Substituting xi for yi/ki

F '(T )=−1⋅y i⋅K i−2 dK (T )

dT

F (T )=∑i

x i−1

F '(T )=∑ (b i+2⋅C iT +3⋅d iT2 )⋅(x i /K i(T ))

∑i

x i=1

Bubble Point Calculation

InputComponent 1 2 3 4 5 6 7

0.493 0.403 0.098 0.006

Number of compounds 4 counts compounds 1.000

Component alpha beta gamma delta Epsilon1 -1.6 0.03 0 0 02 -0.84 0.014 0 0 03 -0.52 0.007 0 0 04 -0.12 0.002 0 0 0567

Temp Initial Guess 200

Run Program

Output

BBL Pt. Temp.

Component Yi 1234567

Total 0.0000 0.0000

Liq Fractions (Xi)

Total Xi=

Xi

Run BBL Point Clear Output

Dew Point Calculation

InputComponent 1 2 3 4 5 6 7

0.007 0.097 0.402 0.494

Number of compounds 4 counts compounds 1.000

Component alpha beta gamma delta Epsilon1 -1.6 0.03 0 02 -0.84 0.014 0 03 -0.52 0.007 0 04 -0.12 0.002 0 0567

Temp Initial Guess 200

Run Program

Output

Dew Pt. Temp.

Component Yi 1234567

Total 0.000 0.000

Vapor Fractions (Yi)

total Yi=

Xi

Run Dew Point Clear Output

Bubble Point CalculationUsing Excel Goal Seeker

Input

Component alpha beta gamma delta Epsilon1 -1.6 0.03 0 0 02 -0.84 0.014 0 0 03 -0.52 0.007 0 0 04 -0.12 0.002 0 0 0

Temperature 250.00 Enter initial guess

CalculationsUses Goal Seek to change Temperature until Sum of the Y's equals 1.000

Component K X Y1 5.900 0.493 2.9092 2.660 0.403 1.0723 1.230 0.098 0.1214 0.380 0.006 0.002

Total 4.104 equals 1.000 after successful calculation

1.000Target Sum of Yi'S

Run BBLpt GS