Please refer to Problem 27.1) Gasoline from an under-storage storage tank leaked down onto an impermeable clay barrier and collected into a liquid pool 2 cm deep. Directly over this underground pool...

Please refer to Problem 27.1) Gasoline from an under-storage storage tank leaked down onto an impermeable clay barrier and collected into a liquid pool 2 cm deep. Directly over this underground pool of liquid gasoline (n-octane) is a layer of gravel 1 m thickness (L) and width (W) of 10 m. The volatile noctane vapors diffuse through the highly porous gravel layer of void fraction 0.4, through a gas film formed by flow of air over the flat surface, and then out to the bulk atmosphere where the noctane is instantaneously diluted to below detectable levels. A simplified picture of the situation was provided in Problem 27.1. There is no adsorption of n-octane vapor onto the porous gravel layer, and n-octane vapor concentration inside the porous gravel layer is dilute. Assume that the mass-transfer process is allowed to achieve a steady state. The temperature is constant at 15C. At this temperature, liquid n-octane exerts a vapor pressure of 1039 Pa. The void spaces between the rocks are large enough so that the molecular-diffusion coefficient can be used for the gas phase. The system is at atmospheric pressure.

a. What is the average mole fraction of n-octane vapor at the surface (z
 L) of the rock layer if the air velocity is only 2 cm/s? What is the flux of n-octane vapor across both the porous gravel layer and the concentration boundary layer at the surface?

b. What would be the average mole fraction of n-octane vapor at the surface of the rock layer if the air velocity is 50 cm/s? What would the new flux be?

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_AB
refers to the diffusion coefficient of species A within medium B for molecular diffusion. 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.