Wastewater containing volatile species A dissolved in the water at a dilute inlet concentration of 0.50 gmole A/m³(c_AL,0) is pumped into a well-mixed open holding pond at a volumetric flow rate (v₀) of 2.0 m³/s, as shown in the figure below. The volatile species A partitions into the atmosphere by an inter phase mass-transfer process so that the wastewater exiting the pond contains a concentration of dissolved A of 0.35 gmole A/m³(CAL). Fresh air very gently blows across surface of the 10.0 m width of the pond, so that the bulk gas composition of species A is effectively zero (e.g. p_A‰ˆ 0, c^*_AL ‰ˆ 0). Equilibrium distribution data for solute A between air and water at 20°C is described by Henry€™s law with H = 0.50 m³atm/gmole (500 m³atm/kgmole).

Potentially useful data (1.0 atm total system pressure, 20°C) 

Gas film: k_c = 2.67 × 10^-4 m/s 

Liquid film: k_L = 5.5 × 10^-3 m/s 

Air at 1.0 atm, 20°C: ρ = 1.206 kg/m³, µ = 1.8 13 × 10^-5 kg/m-s, D_A-air = 0.08 cm²/s (gas)

Liquid water at 20°C: ρ = 998.2 kg/m³, µ = 9.32 × 10^-4 kg/m-s, D_A-H2O = 2.0 × 10^-5 cm²/s (liquid) 

a. What is the mass-transfer coefficient based on the overall liquid phase driving force, K_L? 

b. Develop a material balance model in algebraic form using the following variables: c_AL, c_AL,0, K_L, p_A, v₀, and surface area S. At the conditions of operation, what is the surface area S of the liquid pond? 

c. What is the velocity of the air flow over the surface of the pond, assuming laminar flow? 

d. What is the partial pressure of species A on the gas side of the gas€”liquid interface, p_A,i?

Transcribed Image Text:

Bulk gas, pa =0 PAi kG Gas/liquid interface CALI KL Bulk liquid, CAL Air flow Pond W = 10.0 m surface, Well-mixed liquid CAL = 0.35 gmol A/m3 V, = 2.0 m/sec CALO = 0.50 gmol A/m³ V, = 2.0 m/sec