CE 397: Environmental Risk Assessment
Homework Assignment #2: Transport and Fate Mechanisms
Table of Contents
Plan for accomplishing homework
1. Partitioning of Material Between Phases
A cylindrical tank has a diameter of 10 m and a height of 4 m. The tank
is effectively sealed with a "fixed roof". It is filled to 30%
of capacity with water containing total and volatile suspended solids concentrations
of 450 and 275 mg/L, respectively. The water is at 25 C, and can be assumed
to be well-mixed. Particle (TSS) settling does not occur over the timeframe
associated with this problem!
A 55-gallon drum containing a mixture of wastes is added to the tank. The drum contains 20 kg (each) of the following chemicals: MTBE, benzene, tetrachloroethene, and hexachlorobenzene.
Determine the fraction of mass (at equilibrium) of each chemical in the following forms:
2. Gasoline Emissions in Austin
Recent studies have suggested that humans inhale and retain a number of gasoline constituents for several hours after pumping gasoline into an automobile (assuming that Stage II vapor recovery is not performed).
Studies of gasoline composition (liquid) in Austin indicate that MTBE levels may be as high as 4% in summer months (The addition of MTBE to gasoline is currently not required in Austin). Assume that a typical summer blend of gasoline in Austin has the following characteristics:
Estimate the total MTBE emissions in Austin (kg/day) assuming a fuel tank temperature of 100 F. You may assume that Austinites are average Americans, using approximately 1 gallon of gasoline per day. State all other assumptions.
The term "washout" refers to the removal of chemicals from the atmosphere as a result of scavenging (mass transfer to) falling rain droplets. Estimate the amount of rain fall (in cm) necessary to washout 50% of each of the chemicals from the atmosphere: MTBE, benzene, hexachlorobenzene. You can make the following assumptions:
Hint: You may want to begin this problem by developing a general relationship for the degree (fraction) of equilibrium achieved by the time a droplet impacts the ground. Begin with a mass balance on the droplet. The next step would then involve a mass balance on the mixed layer itself.
A major pathway for chemical discharges in urban areas is the public sewer system. Estimates the emissions of MTBE and tetrachloroethene following their discharge to a municipal sewer reach. You may assume the following conditions for the sewer of interest:
As part of his Ph.D. dissertation, Jacek Koziel completed a series of experiments to determine liquid and gas-phase mass transfer coefficients in gravity-flow sewers. He has graciously provided you with the following equation to determine liquid-phase mass transfer coefficients for cyclohexane:
where kl has units of m/s, d is the mean depth of flow (m) defined as the cross-sectional area of wastewater divided by the width of the air-water interface, Uliq is the wastewater mean velocity, S is the slope of the energy grade line (channel slope for uniform flow) (m/m), and Scl is the Schmidt number (ratio of the kinematic viscosity to liquid molecular diffusion coefficient (Dl = 9.1E-6 cm2/s for cyclohexane) at 25 C.
Jacek did not observe any mechanistic trends for gas-phase mass transfer coefficients during co-current flow. He did find that the average ratio of kg/kl for co-current flow was 32 (79 for counter-current flow --- which makes sense given a greater shear stress at the air-water interface).
I feel that it is reasonable to expect that problems 1-3 be completed
by next Thursday, and that problem 4 be completed by the following Tuesday.
Let's plan on having assignments submitted by Thursday, February 12. That
will give us time to discuss the problems as you work on them. Have fun!
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