Provide a preliminary design for an air stripping column that removes toluene from groundwater. The toluene concentration ranges from 0.1 to 2.1 mg/L and must be reduced to less than or equal to 50 µg/L. According to a hydrogeologic study, the flow rate should be 110 gallons per minute to prevent the spread of contamination. Laboratory investigations determined the overall mass transfer coefficient (KLa) to be 0.020 sec^-1. Design the column with a 2.0-foot diameter and an air-to-water ratio of 15. Calculate the liquid loading rate, stripping factor, and tower height. Provide a sketch of the column, including all required accessories.

 The design of an air stripping column involves several considerations, including sizing the column, determining the height, the air-to-water ratio, and ensuring that the liquid loading rate falls within acceptable limits for optimal operation. Below are the steps to calculate the liquid loading rate, stripping factor, and tower height:

1. Liquid Loading Rate (LLR): The LLR is the volume of water to be treated per unit area of the column per unit time. It's expressed in units such as cubic meters per hour per square meter (m^3/h/m^2) or gallons per minute per square foot (gpm/ft^2).

First, calculate the area of the column using the diameter: Area (A) = π * (D/2)^2 A = π * (2.0 ft/2)^2 A = π * 1.0 ft^2 ≈ 3.1416 ft^2

Next, convert the flow rate to the correct units (if it's not already in gpm): Flow rate = 110 gpm (given)

Now, calculate the LLR with: LLR = Flow rate / Area LLR = 110 gpm / 3.1416 ft^2 LLR ≈ 35 gpm/ft^2

2. Stripping Factor: The stripping factor (SF) is an essential design parameter that determines the potential of the air stripping process. SF is the ratio of the air-to-water volumetric flow rates. You were given an air-to-water ratio (A/W) of 15. This ratio is a volume/volume ratio, so no further calculation is required for the stripping factor as it is given.

SF = A/W = 15 (by design)

3. Tower Height: To estimate the tower height, we need to combine the desired outlet contaminant concentration (Cout) with the initial concentration range and the stripping factor, using the overall mass transfer coefficient (KLa). Since KLa and SF are known, we need to establish a relationship between these and the removal efficiency required to lower toluene concentration to acceptable levels (50 µg/L). The simplified design equation using the log mean concentration difference is:

N = (1/KLa) * ln[(Cin - Cout)/(Cout * SF - Cout) ]

Assuming the worst-case scenario, use the maximum toluene concentration: Cin = 2.1 mg/L = 2100 µg/L Cout = 50 µg/L (desired concentration)

Convert KLa to appropriate units if necessary (keeping it consistent with the units being used for SF and concentration): KLa = 0.020 sec^-1

Now, calculate the number of transfer units (N): N = (1/0.020 sec^-1) * ln[(2100 µg/L - 50 µg/L)/(50 µg/L * 15 - 50 µg/L)] N ≈ 115.78

The height of the packing (H) needed can be calculated using the number of transfer units (N) and the height of a transfer unit (HTU), an empirical value which can be determined from vendor specifications or laboratory data. However, this information is not provided in the question. As such, we would need additional data on HTU to calculate the tower height.

Given HTU (if provided as 'x' ft per transfer unit): H = N * HTU

4. Sketch of the Unit: Illustrate a cylindrical tower with the following:

- Water inlet at the top - Water distribution system atop the packed bed - Packed bed section where the mass transfer takes place - Air inlet at the bottom (with specifications in accordance to design) - Air distribution system - Air outlet on top of the unit - Water collection system at the bottom