An organic compound (A) is to be absorbed out of air (C) using a liquid solvent
ID: 494036 • Letter: A
Question
An organic compound (A) is to be absorbed out of air (C) using a liquid solvent (B) in an absorption tower. The liquid solvent is non-volatile, and does not dissolve air. Assume that A is diffusing through stagnant C and through stagnant B. The inlet gas flow rate is 120 kmol/h and contains 12 mole% A. 88 mole% C. The outlet gas contains 4 mole% A. The inlet liquid contains no A, and the outlet liquid contains 8 mole% A. Equilibrium relation is y = 1.12x + 2.5x^2 where x, y are the liquid and vapor mole fractions of A respectively. Calculate L', V'. Tray tower. Determine the number of trays needed. Packed tower. The tower cross sectional area is 0.4 m^2. Mass transfer coefficient k_x'a is 0.55 kmol/s middot m^3 middot mole fraction. At the bottom of the column, the liquid-side interface mole fraction of A (x_i1) is 0.082. Determine y_i1, k_y'a, K_y'a, x_i2, y_i2, the required height of the column using any expression (for height) that contains k_x'a. For part only, it is permissible to assume dilute solutions.Explanation / Answer
Dear Student,
Counter-current multi-stage absorption (Tray absorber)
In tray absorption tower, multi-stage contact between gas and liquid takes place. In each tray, the liquid is brought into intimate contact of gas and equilibrium is reached thus making an ideal stage. In ideal stage, average composition of liquid leaving the tray is in equilibrium with liquid leaving that tray. The most important step in design of tray absorber is the determination of number of trays. The schematic of tray tower is presented in figure 4.7. The liquid enters from top of the column whereas gas is added from the bottom. The efficiency of the stages can be calculated as:
The following parameters should be known for the determination of “number of stages”
(1) Gas feed rate (2) Concentration of gas at inlet and outlet of the tower (3) Minimum liquid rate; actual liquid rate is 1.2 to 2 times the minimum liquid rate. (4) Equilibrium data for construction of equilibrium curve Now, the number of theoretic stages can be obtained graphically or algebraically
Graphical Method for the Determination of Number of Ideal Stages
Overall material balance on tray tower
Gs(YN+1 -Y1)=Ls(XN -X0) ....................1
This is the operating line for tray tower.
If the stage (plate) is ideal, (Xn, Yn) must lie on the equilibrium line, Y*=f(X)
Top plate is located at P(X0, Y1) and bottom plate is marked as Q(XN, YN+1) in X-Y plane. A vertical line is drawn from Q point to D point in equilibrium line at (XN, YN). From point D in equilibrium line, a horizontal line is extended up to operating line at E (XN-1, YN). The region QDE stands for N-th plate (refer Figure 4.8). We may get fraction of plates. In that situation, the next whole number will be the actual number of ideal plates. If the overall stage efficiency is known, the number of real plates can be obtained from Equation (4.18).
Algebraic Determination of Number of Ideal Stages
If both operating line and equilibrium lines are straight, number of ideal stages can be calculated algebraically.
Let solute transfers from gas to liquid (Absorption) Equilibrium line, Y=X
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