Design a packed tower for the absorption SO2 from air. The SO2 feed contain 0.0016 mol frac A into pure water in column that is 1.5 m2 cross sectional area and 3.5 m in height. The flow rates of entering gas and liquid are 111.5 kmol/h and 3860 kmol/h, respectively. The outlet gas has 0.0004 mol frac A. At the conditions in the column, about 25°C, the equilibrium can be represented by

Question

Design a packed tower for the absorption SO2 from air. The SO2 feed contain 0.0016 mol frac A into pure water in column that is 1.5 m2 cross sectional area and 3.5 m in height. The flow rates of entering gas and liquid are 111.5 kmol/h and 3860 kmol/h, respectively. The outlet gas has 0.0004 mol frac A. At the conditions in the column, about 25°C, the equilibrium can be represented by

y = 40.1 x
where x and y are mole fractions of A in the liquid and gas, respectively.

Answer 1

To design a packed tower for the absorption of SO2 from air, we need to calculate the number of theoretical stages and choose an appropriate packing material.

First, we need to calculate the inlet and outlet mole fractions of component A (SO2) in the gas phase and liquid phase.

Given the equilibrium relationship:

y = 40.1x

where y is the mole fraction of A in the gas phase and x is the mole fraction of A in the liquid phase.

We are given:

- Inlet gas flow rate (G) = 111.5 kmol/h
- Inlet liquid flow rate (L) = 3860 kmol/h
- Inlet mole fraction of A in the liquid phase (x_inlet) = 0.0016
- Outlet mole fraction of A in the gas phase (y_outlet) = 0.0004

Using the mole balance equation:

G = L + V (1)

where V is the vapor flow rate leaving the column, we can calculate V:

V = G - L (2)

Next, we can calculate the outlet mole fraction of A in the liquid phase (x_outlet) using the equilibrium relationship:

y_outlet = 40.1 * x_outlet (3)

Now, we can use the overall material balance for component A:

x_inlet * L = x_outlet * (L + V) (4)

Substituting equations (2) and (3) into equation (4):

x_inlet * L = (y_outlet / 40.1) * (L + (G - L)) (5)

Simplifying equation (5):

x_inlet * L = (y_outlet / 40.1) * G (6)

Now, we can solve equation (6) to find the liquid flow rate (L):

L = (x_inlet * G) / ((y_outlet / 40.1) + x_inlet) (7)

Substituting the given values into equation (7), we can calculate L.

Once we have the liquid flow rate, we can calculate the vapor flow rate leaving the column (V) using equation (2).

Now, we can calculate the height equivalent to a theoretical stage (HETP) based on the desired efficiency of the column. The HETP is a characteristic parameter for the packing material and represents the distance required for a theoretical stage. It depends on the type of packing used and can be obtained from literature or vendor data.

Finally, we can calculate the number of theoretical stages (N) using the height of the column (3.5 m) divided by the HETP:

N = Column Height / HETP

With the number of theoretical stages identified, we can choose an appropriate packing material for the absorption tower based on factors such as cost, efficiency, and suitability for the specific application.