Page 222 - Introduction to Petroleum Engineering

FLASH CALCULATION FOR SEPARATORS 209
The k‐value depends on temperature, pressure, and composition. For low pressures
(<100 psi), k‐values are equal to the ratio of vapor pressure to total pressure:
k i P vapi / P. Components with high vapor pressures will have higher k‐values, while
components with lower vapor pressure have lower k‐values. For higher pressures,
equations of state can be used for accurate estimates of k‐values. The ideal gas law
is an example of an equation of state. Charts and tables of k‐values are found in
some reference books. The Wilson equation is often used for qualitative estimates
of k‐values at pressure P and temperature T:

P T
.
k i ci exp 5371 i 1 ci (11.4)
P T
with critical pressure P , critical temperature T , and acentric factor ω for component i.
ci
i
ci
Temperatures for Equation 11.4 must be absolute temperatures.
Example 11.2 Estimate k‐value for Methane

Estimate the k‐value for methane at 100°F and 150 psia. Use P c 666 psia,
.
T 117 F, and 0 010.
c
Answer
First convert from Fahrenheit to absolute temperatures in degrees Rankine:
T 100 F 460 560 R
T ci 117 F 460 343 R
Now, find k :
methane
666 psia 343 R
.
.
k exp 5371 0 010 1 36 3.
methane
150 psia 560 R
Rearranging Equation 11.3, the mole fraction y of component i in the gas phase
i
can be written as

y i k x i (11.5)
i
Using this expression in Equation 11.2 gives

z F k xG xL kG Lx i (11.6)
i
i
i
i
i
The mole fraction x of component i in the liquid phase is
i
zF
x i i (11.7)
kG L
i