Gasoline from an under-storage storage tank leaked down onto an impermeable clay barrier and collected into a liquid pool. A simplified picture of the situation is provided in the figure below. Directly over this underground pool of liquid gasoline (ii-octane, species A) is a layer of gravel of 1.0 m thickness and width of 10.0 m. The volatile n-octane vapors diffuse through the highly porous gravel layer, and then through a gas boundary layer formed by flow of air over the top surface of the gravel bed, and finally out to the bulk atmosphere where the ii-octane is diluted to below detectable levels. There is no adsorption of ii-octane vapor onto the porous gravel layer, and ii-octane vapor concentration is dilute. Assume that the mass transfer process is allowed to achieve a steady state. The temperature of the system is constant at 15°C, and the total system pressure is 1.0 atm. At this temperature, liquid ii-octane exerts a vapor pressure of 1039 Pa. The void spaces in porous layer create a void fraction (ε) of 0.40, and but the pore size is large enough that Knudsen diffusion can be neglected. 

a. What is the average mole fraction of n-octane vapor at the top surface of the rock layer (y_As = c_As/C) if the air velocity is very low, only 2.0 cm/s? What is the average flux of n-octane vapor emitted to the atmosphere? 

b. What would be the average mole fraction of n-octane vapor at the top surface of the rock layer if the air velocity is 50.0 cm/s? What is the average flux of ii-octane vapor? 

c. The Biot number associated with a mass-transfer process involving diffusion and convection in series is defined as

where L refers to the path length for molecular diffusion within the porous gravel layer and D_Ae refers to the diffusion coefficient of species A within this porous medium, which is not the same as the molecular diffusion coefficient as octane vapor in air. Determine the Biot number for parts (a) and (b), and then assess the relative importance of convective mass transfer in determining the n-octane vapor emissions rate.

Transcribed Image Text:

k.L BiAB DAe air flow (1.0 atm, 15°C) NA Сдо →x = 0 CAS X = L2 z = L, porous gravel layer liquid 1.0 m octane vapors PA octane Z= 0 nonporous rock layer