Overall Material Balance
In a countercurrent stripping operation, the overall material balance for the solute $S$ is given by:
$L x_L + V y_V = L x_S + V y_S$
Given: Liquid phase inlet mole fraction ($x_L$) = $0.1$ Liquid phase outlet mole fraction ($x_S$) = $0.01$ Carrier gas is pure, so gas phase inlet mole fraction ($y_V$) = $0$ Molar feed rate of carrier gas ($V$) is twice the liquid stream ($L$), so $V = 2L$.
Substituting the values:
$L(0.1) + (2L)(0) = L(0.01) + (2L)y_S$ $0.1L = 0.01L + 2Ly_S$
Dividing by $L$:
$0.1 = 0.01 + 2y_S$ $0.09 = 2y_S$ $y_S = \frac{0.09}{2} = 0.045$
The mole fraction of $S$ in the gas leaving the last stage ($y_S$) is $0.045$.
Operating Line Equation
The operating line for a countercurrent stripping process relates the mole fraction of solute in the gas entering a stage ($y$) to the mole fraction of solute in the liquid entering that same stage ($x$). It is derived from a material balance around a section of the column.
The general equation is:
$y = \frac{L}{V} x - \frac{L}{V} x_S + y_V$
Using $L/V = 0.5$, $x_S = 0.01$, and $y_V = 0$:
$y = 0.5 x - 0.5(0.01) + 0$ $y = 0.5x - 0.005$
This operating line passes through the points $(x_S, y_V) = (0.01, 0)$ and $(x_L, y_S) = (0.1, 0.045)$.
Equilibrium Line
The equilibrium distribution is given by $y_e = x_e$. This is a straight line with a slope of 1 passing through the origin.
Minimum Number of Ideal Stages
The minimum number of ideal stages required for the separation is determined using a graphical method (similar to McCabe-Thiele) by stepping off stages between the operating line and the equilibrium line.
The procedure involves:
- Plotting the equilibrium line ($y_e = x_e$) and the operating line ($y = 0.5x - 0.005$).
- Starting at the point representing the liquid outlet and gas inlet: $(x_S, y_V) = (0.01, 0)$.
- Moving vertically to the operating line, then horizontally to the equilibrium line, and repeating this process.
- The number of steps required to reach the liquid inlet composition ($x_L = 0.1$) gives the minimum number of ideal stages.
Applying this graphical stepping method to the given conditions results in 3 steps. Therefore, the minimum number of ideal stages required is 3.
Important Questions from Absorption
- A gas stream with $2.01 \text{ mol }\%$ ammonia is to be scrubbed in a counter-current isothermal packed bed absorber using pure water to reduce its concentration to $0.01 \text{ mol }\%$. Assume that dilute conditions apply, operating line is linear and the mass transfer coefficients are constant throughout the column. The liquid and the gas flows inside the absorber (in $\text{kmol m}^{-2}\text{ h}^{-1}$) are 1000 and 200, respectively. The equilibrium relationship is $y = 0.9 x$, where, $y$ is the mole-fraction of ammonia in the gas phase and $x$ is that in the liquid. Under these conditions, the height of overall gas transfer unit ($H_{tOG}$) is $0.8 \text{ m}$ and the number of overall gas transfer units ($N_{tOG}$) is given by the following integral.
$$ N_{tOG} = \int_{y_1}^{y_2} \frac{dy}{y - y^*} $$
The integration is performed between the two ends of the column, and $y^*$ is the equilibrium mole fraction in the gas phase, corresponding to the composition of the liquid at corresponding location. Which one of the following is the minimum length of the packing (in m) necessary to achieve the desired scrubbing? Benzene is removed from air by absorbing it in a non-volatile wash-oil at 100 kPa in a counter-current gas absorber. Gas flow rate is 100 mol/min, which includes 2 mol/min of benzene. The flow rate of wash-oil is 50 mol/min. Vapor pressure of benzene at the column conditions is 50 kPa. Benzene forms an ideal solution with the wash-oil and the column is operating at steady state. Gas phase can be assumed to follow ideal gas law. Neglect the change in molar flow rates of liquid and gas phases inside the column.
For this process, the value of the absorption factor (up to two decimal places) is ________________- Pure gas P is being absorbed into a liquid. The dissolved P undergoes an irreversible reaction in the liquid film. The reaction is first order with respect to P. Which one of the following represents the concentration profile of P in the liquid film at steady state?
A countercurrent absorption tower is designed to remove 95% of component A from an incoming binary gas mixture using pure solvent B. The mole ratio of A in the inlet gas is 0.02. The carrier gas flow rate is 50 kmol/h. The equilibrium relation is given by $Y = 2X$, where Y and X are the mole ratios of A in the gas and liquid phases, respectively. If the tower is operated at twice the minimum solvent flow rate, the mole ratio of A in the exit liquid stream is ________ (rounded off to three decimal places).
- For absorption of $H_2S$ from a mixture with hydrocarbon vapour into an aqueous alkanolamine solution, the liquid phase mass transfer resistance is
