HW3_solutions_v2

HW3_solutions_v2 - Chemical Engineering 150B- Fall 2005...

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Chemical Engineering 150B- Fall 2005 Problem Set #3 Solutions Problem 1. (15 points) A common procedure for increasing the moisture content of air is to bubble it through a column of water. The air bubbles are assumed to be spheres having a radius of 1 mm, and are in thermal equilibrium with the water at 298 K. Determine how long the bubble should remain in the water to achieve a vapor concentration at the center that is 90% of the maximum possible (saturation) concentration. Assume the air dry when it enters the column of water, and that the air inside the small bubble is very small. The vapor pressure of water is available from many sources, including the steam tables. Use Gurney Lurie charts for spherical geometry from the back of W3R. Problem 2. (35 points) Liquid benzene leaked from a storage tank and seeped into the ground below. Since the density of benzene is less than the density of water, the liquid benzene formed a light nonaqueous-phase liquid layer on top of the water-saturated solid as shown: Dissolved benzene diffusion Nonporous rock layer Benzene storage tank Liquid benzene spill (on top of soil) 1m 5 pt 5 pt 5 pt for using charts
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At a depth of 1 m below the water-saturated soil layer is a nonporous, impermeable rock layer. There is no ground water flow through the water-saturated solid layer; it is completely stagnant. Initially, there is no benzene dissolved in the water-saturated soil layer. Although water- saturated solid is a complex mixture, as a medium for benzene diffusion you may assume that it approximates the properties of a homogenous substance. The pure liquid benzene layer resting on top of the solid is essentially a constant source due to the low solubility of benzene in water. Finally, you may assume that benzene does not diffuse into the nonporous rock layer. We are interested in the transport of benzene into the water-saturated soil layer, so that we identify how much solid must be dug up and treated after 72 hours. Useful Information: Liquid benzene is sparingly soluble in water, and its solubility limit is 24 mol/m 3 at 293 K. Density of benzene is 0.88 g/cm 3 . The effective diffusion coefficient of benzene in water-saturated solid is 1 x 10 -9 m 2 /s at 293 K. Partial differential equation, Y t = Y zz , can be solved using a separation of variables approach, Y = T(t)Z(z). (a) To approximate this process as semi-infinite diffusion, what physical assumption must we make? Write down the partial differential equation with appropriate boundary/initial conditions. (b) Calculate the concentration of dissolved benzene at a position of 5 cm into the water- saturated soil layer 72 hours after the benzene spill using a semi-infinite medium. Please provide utilize an analytical solution. 5 pt 5 pt
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(c) Calculate the concentration of dissolved benzene at a position of 5 cm into the water- saturated soil layer 72 hours after the benzene spill using a semi-infinite medium. Please provide utilize an analytical solution and use a computer program (e.g., Mathcad or Excel) to calculate the concentration.
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HW3_solutions_v2 - Chemical Engineering 150B- Fall 2005...

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