*CE 397: Environmental
Risk Assessment*

**Homework Assignment #2: Transport
and Fate Mechanisms**

**Spring, 1998**

**Table of Contents**

- Partitioning of material between phases
- Gasoline emissions in Austin
- Rainfall washout of organic compounds
- Volatile organic compound emissions from a sewer system

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:

- pure phase
- dissolved in water
- adsorbed to solids
- in the headspace of the tank

**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:

- Reid vapor pressure: 10 psi
- Liquid density: 0.75 kg/L
- Molecular weight (fresh gasoline): 113 g/mole
- MTBE content: 4% by weight

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:

- A typical rain droplet is spherical, with a diameter of 5 mm (a more rigorous approach would be to consider a droplet size distribution).
- Liquid-phase and gas-phase mass transfer coefficients have been measured for methanol scavenging by rain droplets. Typical values are 10 cm/hr and 1000 cm/hr, respectively.
- The average temperature of rain droplets during descent is 10 C.
- Rain droplets fall through a "chemically challenged" mixed layer with a height of 1,000 m.
- Rain droplets have reached their terminal settling velocity by the time they enter the top of the mixed layer.
- The concentration of a specific chemical in the atmosphere does not change appreciably during the time scale required for a single rain droplet to fall through the mixed layer. However, the concentration of chemicals in the atmosphere will decrease with time as the collective effects of many droplets cause washout.

**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.**

**Have fun!**

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:

- Length of sewer reach = 2 km
- Inside diameter of sewer = 0.7 m
- Channel slope = 1.5%
- Manning's roughness coefficient = 0.014
- Uniform flow with sewer flowing 1/2 full (this really simplifies matters!)
- Air flows co-current to wastewater, but at half the mean velocity
- Air exits the sewer at 2 km through a vent on a pump station wet well.
- Tetrachloroethene and MTBE are discharged continuously at the upstream end of the reach and have concentrations of 10 mg/L after mixing with the wastewater (which is assumed to occur instantaneously).
- Wastewater temperature = 25 C.
- For those of you that are good at math, feel free to solve this problem by simultaneously solving the advection-diffusion equation for the liquid and gas phases. If you take this approach, make the assumption that axial dispersion is negligible in both phases.
- For those of you who loathe differential equations, feel free to solve this problem by discretizing the liquid and gas phases into a series of 10 or more equally-sized CFSTRs.

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 k_{l} 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, U_{liq} is the wastewater mean velocity,
S is the slope of the energy grade line (channel slope for uniform flow)
(m/m), and Sc_{l }is the Schmidt number (ratio of the kinematic
viscosity to liquid molecular diffusion coefficient (D_{l }= 9.1E-6
cm^{2}/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 k_{g}/k_{l }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!

*Rich C*

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