A natural gas stream $($containing methane and ethane$)$ is to be contacted with a

non$-$volatile liquid hydrocarbon oil to remove $($via counter$-$current absorption$)$ a significant

portion of the ethane. Methane solubility in the liquid oil is to be considered

negligible$).$ The flow configuration is given below. The inlet rates for the gas stream

are $500$kmol$\frac{e}{h}r$ methane and $15$kmole$\frac{s}{h}r$ ethane at $298K$ and $2$atm $($absolute

pressure$),$ and we wish to remove $90\%$ of the ethane from the gas stream. The liquid

inlet rate is $3500$kmol$\frac{e}{h}r.$

Additional Information:

$H=4$:$10$ Henry's constant for ethane: $y=Hx$

Ky a $=355$kmol$\frac{e}{h}r-m3$ overall mass transfer coefficient

$S=1\mathrm{.}70m^2$ column cross$-$sectional area

a$)$ Since there is a significant amount of ethane in the feed gas, it is best to work

with molar ratios $(Y$ and $x)$ rather than molar fractions. From the problem

specification, calculate values for the inlet and outlet molar ratios for the gas

phase: $Y_{N-1}$ and $Y_L.(10$ pts$)$

b$)$ Determine the number of equivalent equilibrium stages, $N,$ needed to reach the target outlet

ethane fraction.