NSF Case: Numerical Problems for Gilbane Gold

Gilbane Gold is a video in which David Jackson, a young environmental engineer, finds himself in a predicament. He works for Z-Corp, a computer chip manufacturer. They are currently discharging lead (and arsenic) at the allowable limits set by the city of Gilbane. Z-Corp is anticipating a major expansion which is expected to increase their lead discharge by five times. The law allows for this lead to be diluted down to the acceptable limit. However, the diluted lead will be absorbed by the city's sewage sludge and ultimately end up on farmers' fields, thus disproving the adage "dilution is the solution to pollution."

As the story unfolds in the video, David becomes a whistleblower which will likely lead to disasterous consequences for him personally and Z-Corp. The purpose of this problem is to explore technical options available to David Jackson. Perhaps the story could have resulted in a happier ending had David followed an alternate path.

1. The city of Gilbane allows lead concentrations of 1.00 ounce per million gallons. Express this concentration as micrograms per liter (mg/L). Also, express this concentration as parts per billion (ppb), i.e. grams of lead per billion grams of total solution.

2. To help you visualize the concentration of lead in the water, imagine you have one billion Ping-Pong balls to be placed in a tank. Some of the Ping-Pong balls will be painted black (corresponding to lead) and the rest will remain white (corresponding to water). Approximately how many of the Ping-Pong balls will be painted black?

The Ping-Pong balls are 1-1/4 inch in diameter and will be loaded into the tank in a "face-centered cubic" fashion in which the "packing factor" (i.e. Ping-Pong ball volume divided by total tank volume) is 0.74. What is the tank volume in cubic feet? What is the length (in feet) of each wall assuming the tank is a cube?

To separate the black Ping-Pong balls from the white Ping-Pong balls, you could pick up each ball, inspect it, and place all the white balls in one tank and all the black balls in another tank. Assuming you work eight hours per day, five days per week, with two weeks vacation each year and that you can process one ball each second, how many years will you require to sort all the balls?

3. Z-Corp produces 250,000 gallons per day of effluent at its current capacity. In one year, how many pounds of lead are discharged? Assume the concentration is the allowable limit, i.e. 1.00 ounce per million gallons.

4. When Z-Corp expands its chip capacity by five times, the lead discharge will increase by five times. In one year, how many pounds of lead will be discharged from the plant?

5. The city regulations are written so that Z-Corp can discharge as much wastewater as it wishes provided the concentration never exceeds 1.00 ounce per million gallons. Z-Corp decides that one option is to add additional clean water to the effluent to dilute the lead down to the allowable limit. If they follow this option, what will be the volume of effluent emitted from their plant when the chip capacity increases by five times?

Low-grade water costs $0.25/thousand gallons. The increased production is expected to last three years. During this period of increased production, how much money must be spent purchasing the dilution water? The city charges $0.75/thousand gallons to treat sewage water. During the period of increased production, how much additional must be spent for sewer charges? What is the total additional cost of pursuing the dilution option?

6. The city of Gilbane treats its wastewater using the standard "activated sludge process" (see Figure 1). The houses and industry (such as Z-Corp) discharge their water effluent into a common sewer. The total solids content in the raw sewer water is about 700 mg/L (0.07%). The raw sewer water flows into an aerobic digestor which is stirred and aerated to encourage microbial growth. The effluent from the aerobic digestor flows to a clarifier, an unstirred tank that allows the microorganisms to settle out in the sludge. Most of the sludge is returned to the aerobic digestor to maintain a high cell concentration. This encourages rapid consumption of the "food" in the sewer water. (It might not be food to you, but the microorganisms love it.) Because new microorganisms are constantly made from the food in the raw sewer water, it is necessary to purge sludge from the system. The city sells their sludge to farmers as "Gilbane Gold." When operating properly, the water discharged to the river will have a total solids concentration of 20 mg/L (0.002%).

The city of Gilbane produces 15 million gallons per day of raw sewage from which 60.0 tons per day of sewage sludge is produced. Given that the sludge is 75% water, how much dry sludge is produced each day?

7. The microorganisms that grow on raw sewer water have the ability to bind heavy metals and pull them out of the water. The concentration of heavy metals in the microorganisms can be thousands of times greater than the concentration in the water.

Except for Z-Corp, no other industry or household in Gilbane has lead in their effluent. At current Z-Corp production levels, what is the concentration of lead (in ppb) in the raw sewer water? Also, what is the lead concentration in the Gilbane Gold? (Express your answer in pounds of lead per dry ton of sludge and ppb)? Compared to the raw sewer water, by what factor is the lead concentration increased in the sludge? Also, at the increased production level, what will be the lead concentration in the Gilbane Gold? In all cases, assume that 95% of the lead entering the activated sludge process is bound to the microorganisms.

8. A farmer applies Gilbane Gold to his land at an annual rate of 5.00 dry ton/acre. At current Z-Corp production levels, over a 50-year period, how much lead would be applied to an acre of his land? At the increased production level, over a 50-year period, how much lead would be applied to an acre of his land?

9. The current law is written so that the lead concentration in industrial effluent can be 1.00 ounce per million gallons regardless of how much lead actually ends up in the final sludge. David Jackson, the young engineer in the "hot seat," anticipates that the law will change once the city becomes aware of the higher lead content in the Gilbane Gold when Z-Corp produces chips at a higher rate. He decides that he must investigate alternative ways to process the wastewater from Z-Corp.

One possible treatment technology is ion exchange. If you have a water softener in your home, you are already familiar with the benefits of ion exchange technology. In this case, undesirable calcium and magnesium ions (divalent ions that form soap scum) are replaced with desirable sodium ions (monovalent ions that do not form soap scum).

As shown in Figure 2, an ion exchange process is operated in three stages: exchange, saturation, and regeneration. During exchange, H+ ions bound to the resin beads exchange with Pb2+ ions in the water. During saturation, all the H+ ions have been leached out of the resin beads and replaced by Pb2+ ions. During regeneration, the beads are contacted with a high concentration of acid which washes out the Pb2+ ions and replaces them with H+ ions. The washed-out lead can be recovered and further concentrated for ultimate disposal as a hazardous waste.

At saturation, the entire bed of resin beads is in equilibrium with the incoming high-lead concentration feed. The equilibrium relationship between the lead loading on the beads and the concentration of lead in the water is

where L is the actual equilibrium lead loading (g lead/kg of beads), Lmax is the maximum possible equilibrium loading (g lead/kg of beads), C is the equilibrium lead concentration in the water (mg/L), and K is the affinity constant (mg/L). Experiments with PB2-ZX ion exchange resin indicate that Lmax is 265 g lead/kg beads and K is 53 mg/L. Plot the actual equilibrium loading L versus the lead concentration in the water. For a lead concentration of 5.00 ounce per million gallons, what is the equilibrium loading of lead on the resin beads? With an arrow, indicate this equilibrium loading on your graph.

10. Figure 3 shows the lead concentration in the effluent from the ion exchange bed as a function of time. Initially, nearly all the lead is removed from the effluent. As time proceeds, the effluent concentration slowly increases. At a critical point, called "breakthrough," the effluent concentration rapidly increases. Typically, the bed would not be operated past the breakthrough point; influent would be discontinued and the bed would be regenerated.

David Jackson contacts an ion exchange vendor. They supply a small ion exchange test unit. David feeds a lead concentration of 5.00 ounce per million gallons. At breakthrough, he determines that the average effluent concentration is 1.00 ounce per million gallons, the concentration allowed by the city. Further, he determines that the average lead loading of the bed is 80% of its equilibrium loading. At breakthrough, what is the average lead loading (g lead/kg of beads) on the beads?

11. For $15,000, the vendor sells a "turn-key," skid-mounted ion exchange unit with 200 kg of ion exchange beads, a tank, a pump, and controller. It can process 10 gallons per minute of contaminated water. The inlet concentration is 5 ounces per million gallons at a flow rate of 250,000 gallons per day. How many skid-mounted ion exchange units must be purchased? What is the capital cost required to treat this wastewater? After a regeneration, how many days does it take for breakthrough to occur?

12. David Jackson belongs to a professional society. To stay abreast of current technology, he subscribes to their journals and attends their meetings. Through these sources, he learns of a new technology called "artificial wetlands" (see Figure 4). An artificial wetland consists of a shallow swamp lined with plastic. Above the plastic liner grow aquatic plants such as cattails, duckweed, etc. These plants have microorganisms growing on their roots that have the ability to bind heavy metals and digest organic pollutants into harmless carbon dioxide and water. After many years, the heavy metals eventually build up in the plants. At this point, some of the plants are harvested to remove the heavy metals. To dispose of the harvested plants, a number of options are available:

David Jackson is unfamiliar with this technology so he hires a consultant to design the system. The consultant determines that Option 3 is the most viable. Given specifications of 250,000 gallons per day with an inlet concentration of 5.00 ounces per million gallons, he estimates the cost of the artificial wetland and anaerobic digestor is $150,000.

After performing the above analysis, David Jackson surveys his options. He can do the following:

In light of the above options, assess the behavior of David Jackson (the young engineer), Phil Port (his boss), Tom Richards (the environmental consultant), and Diane Collins (the vice-president of Z-Corp) as depicted in the video.

[The numerical solutions are currently being digitized for presentation. Therefore, only a solution to number 12 is available at this time. Please Check back later for an update to the solutions.]

Option	Description	Cost
1	Dilution	$1,095,000
2	Ion Exchange	$270,000
3	Artificial Wetland	$150,000

It should be noted that this economic analysis is not complete. Option 1 reports total operating costs for a three-year period. In constrast, Options 2 and 3 report capital costs only and do not include operating costs. However, from this simple economic evaluation, it is pretty clear that Option 1 is the most expensive. This is an interesting result because it shows that avoiding pollution can actually save money. Of the remaining two options, Option 3 appears to be the least expensive. This too is an interesting result. The very nature of the pollution problem is that microorganisms tend to concentrate heavy metals in the sludge. Option 3 uses this property of microorganisms to its advantage. This result also emphasizes the necessity for engineers to stay abreast of the latest technical advances.

From this analysis, David Jackson should recommend to his boss that the company construct an artificial wetland. The initial capital outlay could be reduced further by delaying the construction of the digestor for a number of years because the plants need not be harvested until then.

After the above analysis, we can conclude the following about the behavior of the following characters portrayed in the video:

1. David Jackson - Rather than seeking an economical technical solution to the problem, he became a whistleblower. He seemed to lack technical skill either because of poor schooling or a lack of commitment to keeping current in his field. Some of this could be excused because he was a young engineer and perhaps did not have enough experience to be fully aware of all the technical options.

David would have been much more effective had he done his homework and presented his analysis of the situation so management could make an informed decision about what steps to take.

2. Phil Port - He also seemed to lack technical skill, but perhaps he does not have a technical background and cannot be faulted for this. He told David Jackson that if he could solve the problem without spending a lot of money, he would be viewed in a whole new light by the company. In a way, he was challenging David Jackson to apply his technical skills to solve the problem. However, he probably should have been more supportive and less confrontational. He should have been more explicit and directed David to investigate various options and make explicit recommendations to management by a given date.

3. Tom Richards - Presumably, Tom is the most technically informed engineer in the video. He, of all people, could have informed Z-Corp that economical waste treatment options were available. Unfortunately, he was fired, so he could not justify putting in the time to assess the various options.

4. Diane Collins - It was wrong for her to fire the environmental consultant at a time when they badly needed technical expertise not available within Z-Corp. This was a very bad management decision.