# Activated sludge sewage treatment bioreactors

I ran for water commissioner of Oakland county in 2016, a county with 1.3 million people and eight sewage treatment plants. One of these plants uses the rotating disk contractor, described previously, but the others process sewage by bubbling air through it in a large tank — the so-called, activated sludge process. A description is found here in Wikipedia, but with no math, and thus, far less satisfying than it could be. I thought I might describe this process relevant mathematics, for my understanding and those interested: what happens to your stuff after you flush the toilet or turn on the garbage disposal.

Simplified sewage plant: a bubbling, plug-flow bio-reactor with 90% solids recycle and a settler used to extract floc solids and bio-catalyst material.

In most of the USA, sanitary sewage, the stuff from your toilet, sink, etc. flows separately from storm water to a treatment plant. At the plant, the sewage is first screened (rough filtered) and given a quick settle to remove grit etc. then sent to a bubbling flow, plug-flow bioreactor like the one shown at right. Not all cities use this type of sludge processes, but virtually every plant I’ve seen does, and I’ve come to believe this is the main technology in use today.

The sewage flows by gravity, typically, a choice that provides reliability and saves on operating costs, but necessitates that the sewage plant is located at the lowest point in the town, typically on a river. The liquid effluent of the sewage, after bio-treatment is typically dumped in the river, a flow that is so great more than, during dry season, more than half the flow of several rivers is this liquid effluent of our plants – an interesting factoid. For pollution reasons, it is mandated that the liquid effluent leaves the plant with less than 2 ppm organics; that is, it leaves the plant purer than normal river water. After settling and screening, the incoming flow to the bio-reactor typically contains about 400 ppm of biomaterial (0.04%), half of it soluble, and half as suspended colloidal stuff (turd bits, vegetable matter, toilet paper, etc). Between the activated sludge bio-reactor and the settler following it manage to reduce this concentration to 2 ppm or less. Soluble organics, about 200 ppm, are removed by this cellular oxidation (metabolism), while the colloidal material, the other 200 ppm, is removed by adsorption on the sticky flocular material in the tank (the plug-flow tank is called an oxidation ditch, BTW). The sticky floc is a product of the cells. The rate of oxidation and of absorption processes are proportional to floc concentration, F and to organic concentration, C. Mathematically we can say that

dC/dt = -kFC

where C and F are the concentration of organic material and floc respectively; t is time, and k is a reaction constant. It’s not totally a constant, since it is proportional to oxygen concentration and somewhat temperature dependent, but I’ll consider it constant for now.

As shown in the figure above, the process relies on a high recycle of floc (solids) to increase the concentration of cells, and speed the process. Because of this high recycle, we can consider the floc concentration F to be a constant, independent of position along the reactor length.

The volume of the reactor-ditch, V, is fixed -it’s a concrete ditch — but the flow rate into the ditch, Q, is not fixed. Q is high in the morning when folks take showers, and low at night. It’s also higher — typically about twice as high — during rain storms, the result of leakage and illegal connections. For any flow rate, Q, there is a residence time in the tank, τ where τ = V/Q. We can now solve the above equation assuming an incoming concentration C° = 400 ppm and an outgoing concentration Co of 2 ppm:

ln (C°/Co) = kFτ

Where τ equals the residence time in the tank. Since τ = V/Q,

ln (C°/Co) = kFV/Q.

The required volume of reactor, V, is related to the flow rate, Q, as follows for typical feed and exit concentrations:

V = Q/kF ln( 400/2) = 5.3 Q/kF.

The volume is seen to be dependent on F. In Oakland county, thank volume V is chosen to be one or two times the maximum expected value of Q. To keep the output organic content to less than 2 ppm, F is maintained so that kF≥ 5.3 per day. Thus, in Oakland county, a 2 million gallon per day sewage plant is built with a 2-4 million gallon oxidation ditch. The extra space allows for growth of the populations and for heavy rains, and insures that most of the time, the effluent contains less than 2 ppm organics.

Bob Martin chief engineer the South Lyon, MI, Activated Sludge plant, 2016. His innovation was to control the air bubblers according to measurements of the oxygen content. The O2 sensor is at bottom; the controller is at right. When I was there, some bubblers were acting up.

As you may guess, the activated sludge process requires a lot of operator control, far more than the rotating disk contractor we described. There is a need for constant monitoring and tweaking. The operator deals with some of the variations in Q by adjusting the recycle amount, with other problems by adjusting the air flow, or through the use of retention tanks upstream or downstream of the reactor, or by adding components — sticky polymer, FeCl3, etc. Finally, in have rains, the settler-bottom fraction itself is adjusted (increased). Because of all the complexity. sewer treatment engineer is a high-pay, in demand, skilled trade. If you are interested, contact me or the county. You’ll do yourself and the county a service.

I’d mentioned that the effluent water goes to the rivers in Oakland county. In some counties it goes to the fields, a good idea, I think. As for the solids, in Oakland county, the solid floc is concentrated to a goo containing about 5% solids. (The goo is called unconsolidated sludge) It is shipped free to farmer fields, or sometimes concentrated to more than 5% (consolidated sludge), and provided with additional treatment, anaerobic digestion to improve the quality and extract some energy. If you’d like to start a company to do more with our solids, that would be very welcome. In Detroit the solids are burned, a very wasteful, energy-consuming process, IMHO. In Wisconsin, the consolidated sludge is dried, pelletized, and sold as a popular fertilizer, Milorganite.

Dr. Robert Buxbaum, August 1, 2017. A colleague of mine owned (owns?) a company that consulted on sewage-treatment and manufactured a popular belt-filter. The name of his company: Consolidated Sludge. Here are some sewer jokes and my campaign song.

# Nestle pays 1/4,000 what you pay for water

When you turn on your tap or water your lawn, you are billed about 1.5¢ for every gallon of water you use. In south-east Michigan, this is water that comes from the Detroit river, chlorinated to remove bacteria, e.g. from sewage, and delivered to you by pipe. When Nestle’s Absopure division buys water, it pays about 1/4000 as much — \$200/ year for 218 gallons per minute, and they get their water from a purer source, a pure glacial aquifer that has no sewage and needs no chlorine. They get a far better deal than you do, in part because they provide the pipes, but it’s mostly because they have the financial clout to negotiate the deal. They sell the Michigan water at an average price around \$1/gallon, netting roughly \$100,000,000 per year (gross). This allows them to buy politicians — something you and I can not afford.

Absopure advertises that I t will match case-for-case water donations to Flint. That’s awfully white of them.

We in Michigan are among the better customers for the Absopure water. We like the flavor, and that it’s local. Several charities purchase it for the folks of nearby Flint because their water is near undrinkable, and because the Absopure folks have been matching the charitable purchases bottle-for bottle. It’s a good deal for Nestle, even at 50¢/gallon, but not so-much for us, and I think we should renegotiate to do better. Nestle has asked to double their pumping rate, so this might be a good time to ask to increase our payback per gallon. So far, our state legislators have neither said yes or no to the proposal to pump more, but are “researching the matter.” I take this to mean they’re asking Nestle for campaign donations — the time-honored Tammany method. Here’s a Detroit Free Press article.

I strongly suspect we should use this opportunity to raise the price by a factor of 400 to 4000, to 0.15¢ to 1.5¢ per gallon, and I would like to require Absopure to supply a free 1 million gallons per year. We’d raise \$300,000 to \$3,000,000 per year and the folks of Flint would have clean water (some other cities need too). And Nestle’s Absopure would still make \$200,000,000 off of Michigan’s, clean, glacial water.

Robert Buxbaum, May 15, 2017. I ran for water commissioner, 2016, and have occasionally blogged about water, E.g. fluoridationhidden rivers, and how you would drain a swamp, literally.

# pee in the shower and other water savers

Do you want to save the planet and save money at the same time? Here are some simple tips:

The first money and planet saver, is to pee in the shower. For those who don’t have a lawn, or who don’t water, your single biggest water cost is likely the toilet. Each person in your household will use it several times per day, at roughly 1.6 gallons per flush. In Oak Park, Michigan the cost of water is 1.5¢/gallon, so each flush costs you, roughly 2.5¢. If you pee in the shower every morning, you’ll save yourself about one flush per day, or 2.5¢. Over the course of a year you’ll have used about 500 gallons less, and will have saved yourself somewhere between \$5 and \$10. Feel good about yourself every morning; the effort involved is truly minimal.

Related to peeing in the shower, I should mention that many toilets leak. A significant part of your water bill can often be cut by replacing the “flapper valve on the inside of your toilet tank, and/or by cleaning the needle fill valve. To see if you need this sort of help, put a few drops of food dye in the toilet when you leave in the morning. If the color is largely gone by the time you get back, the toilet is leaking the equivalent of a few volumes per day, that is at least as much water as is flushed. If the color goes faster, or you hear the tank refill when no one used it, you’re leaking more. Check the flapper and replace it if it’s worn — it’ll cost about \$3 — and check the needle-fill valve. They don’t work forever. Cleanliness is near godliness.

Mulch is good, this is too much concentrated by the tree trunk. Use only 2-3 inches and spread it out from the trunk to save water and weeding without attracting bugs.

If your valve is leaking and you decide to replace it, you may want to replace with a variable flush valve. Typically, there are two options: a big vale for big flush (1.6 gal) and a small valve for small flush (1 gal or less). These are widely used in Europe. You can make up for this cost rather quickly at 1.5¢/gallon.

A little more work than the above is to add a complete rain garden or bioswale. Build it at the bottom of any large incline on your property, where the water runs off (It’s likely a soggy swamp already). Dig the area deeper and put, at the bottom of the hole, a several-inch layer of mulch and gravel. Top it off with the soil you just removed, ideally raising the top high enough that, if the rain garden should fill, the water will run off to the street. Plant in the soil at the top long-rooted grasses, or flowers, vegetables, or water-tolerant trees. You may want to direct the water from your home’s sump pump here too (It can help to put a porous pipe at the bottom to distribute this water). If you do this right, you’ll get vegetables or trees and you won’t have to water the garden, ever. Also, you’ll add value to your property by removing the swampy eyesore. You’ll protect your home too, since a major part of home flooding comes from the water surge of sump water to the sanitary sewer.

Robert E. Buxbaum, April 14, 2017. I ran for water commissioner, Oakland County, MI, Nov. 2016. Among my other thoughts: increased retention to avoid flooding, daylighting rivers, and separating the sanitary from the storm sewers. As things stand, the best way to save money on water– get the same deal the state gave to Nestle/ Absopure: they pay only \$200/year to pump 200 gal/minute. That is, they pay only 1/3000 of what you and I pay. It helps to have friends in government.

# Rethinking fluoride in drinking water

Fluoride is a poison, toxic tor a small child in doses of 500 mg, and toxic to an adult in doses of a few thousand mg. It is a commonly used rat poison that kills by robbing the brain of the ability to absorb oxygen. In the form of hydrofluoric acid, it is responsible for the deaths of more famous chemists than any other single compound: Humphrey Davy died trying to isolate fluorine; Paul Louyet and Jerome Nickles, too. Thomas Knox nearly died, and Henri Moissan’s life was shortened. Louis-Joseph Gay Lussac, George Knox, and Louis- Jacques Thenard suffered burns and similar, George Knox was bedridden for three years. Among the symptoms of fluoride poisoning is severe joint pain and that your brain turns blue.

In low doses, though, fluoride is thought to be safe and beneficial. This is a phenomenon known as hormesis. Many things that are toxic at high doses are beneficial at low. Most drugs fall into this category, and chemotherapy works this way. Diseased cells are usually less-heartythan healthy ones. Fluoride is associated with strong teeth, and few cavities. It is found at ppm levels many well water systems, and has shown no sign of toxicity, either for humans or animals at these ppm levels. Following guidelines set by the AMA, we’ve been putting fluoride in drinking water since the 1960s at concentrations between 0.7 and 1.2 ppm. We have seen no deaths or clear evidence of any injury from this, but there has been controversy. Much of the controversy stems from a Chinese study that links fluoride to diminished brain function, and passivity (Anti-fluoriders falsely attribute this finding to a Harvard researcher, but the Harvard study merely cites the Chinese). The American dental association strongly maintains that worries based on this study are groundless, and that the advantage in lower cavities more than off-sets any other risks. Notwithstanding, I thought I’d take another look. The typical US adult consumes 1-3 mg/day the result of drinking 1-3 liters of fluoridated water (1 ppm = 1 mg/liter). This < 1/1000 the toxic dose,

While there is no evidence that people who drink high-fluoride well water are any less-healthy than those who drink city water, or distilled / filtered water, that does not mean that our city levels are ideal. Two months ago, while running for water commissioner, I was asked about fluoride, and said I would look into it. Things have changed since the 1960s: our nutrition has changed, we have vitamin D milk, and our toothpastes now contain fluoride. My sense is we can reduce the water concentration. One indication that this concentration could be reduced is shown below. Many industrial countries that don’t add fluoride have similar tooth decay rates to the US.

World Health Organization data on tooth decay and fluoridation.

This chart should not be read to suggest that fluoride doesn’t help; all the countries shown use fluoride toothpaste, and some give out fluoride pills, too. And some countries that don’t add fluoride have higher levels of cavities. Norway and Japan, for example, don’t add fluoride and have 50% more cavities than we do. Germany doesn’t add fluoride, and has fewer cavities, but they hand out fluoride pills, To me, the chart suggests that our levels should go down, though not to zero. In 2015, the Department of Health recommend lowering the fluoride level to 0.7 ppm, the lower end of the previous range, but my sense from the experience of Europe is that we should go lower still. If I were to pick, I’d choose 1/2 the original dose: 0.6 to 0.35 ppm. I’d then revisit in another 15 years.

Having picked my target fluoride concentration, I checked to see the levels in use in Oakland county, MI, the county I was running in. I was happy to discover that most of the water the county drinks, that provided by Detroit Water and Sewage, NOCWA and SOCWA already have decreased levels of 0.43-0.55 ppm. These are just in the range I would have picked, Fluoride concentrations are higher in towns that use well water, about  0.65-0.85 ppm. I do not know if this is because the well water comes from the ground with these fluoride concentrations or if the towns add, aiming at the Department of Health target. In either case, I don’t find these levels alarming. If you live none of these town, or outside of Oakland county, check your fluoride levels. If they seem high, write to your water commissioner. You can also try switching from fluoride toothpaste to non-fluoride, or baking soda. In any case, remember to brush. That does make a difference, and it’s completely non-toxic.

Robert Buxbaum, January 9, 2017. I discuss chloride addition a bit in this essay. As a side issue, a main mechanism of sewer pipe decay seems related to tooth decay. That is the roofs of pipe attract acid-producing, cavity causing bacteria that live off of the foul sewer gas. The remedies for pipe erosion include cleaning your pipes regularly, having them checked by a professional once per year, and repairing cavities early. Here too, it seems high fluoride cement resists cavities better.

# How do you drain a swamp, literally

The Trump campaign has been claiming it wants to “drain the swamp,” that is to dispossess Washington’s inbred army of academic consultants, lobbyists, and reporter-spin doctors, but the motto got me to think, how would you drain a swamp literally? First some technical definitions. Technically speaking, a swamp is a type of wetland distinct from a marsh in that it has no significant flow. The water just, sort-of sits there. A swamp is also unlike a fen or a bog in that swamp water contains enough oxygen to support life: frogs, mosquitos, alligators,., while a fen or bog does not. Common speech ignores these distinctions, and so will I.

If you want to drain a large swamp, such as The Great Dismal Swamp that covered the south-east US, or the smaller, but still large, Hubbard Swamp that covered south-eastern Oakland county, MI, the classic way is to dig a system of open channel ditches that serve as artificial rivers. These ditches are called drains, and I suppose the phrase, “drain the swamp comes” from them. As late as the 1956 drain code, the width of these ditch-drains was specified in units of rods. A rod is 16.5 feet, or 1/4 of a chain, that is 1/4 the length of the 66′ surveyor’s chains used in the 1700’s to 1800’s. Go here for the why these odd engineering units exist and persist. Typically, 1/4 rod wide ditches are still used for roadside drainage, but to drain a swamp, the still-used, 1956 code calls for a minimum of a 1 rod width at the top and a minimum of 1/4 rod, 4 feet, at the bottom. The sides are to slope no more than 1:1. This geometry is needed. experience shows, to slow the flow, avoid soil erosion and help keep the sides from caving in. It is not unusual to add one or more weirs to control and slow the flow. These weirs also help you measure the flow.

The main drain for Royal Oak and Warren townships, about 50 square miles, is the Red Run drain. For its underground length, it is 66 foot wide, a full chain, and 25 feet deep (1.5 rods). When it emerges from under ground at Dequindre rd, it expands to a 2 chain wide, open ditch. The Red Run ditch has no weirs resulting in regular erosion and a regular need for dredging; I suspect the walls are too steep too. Our county needs more and more drainage as more and more housing and asphalt is put in. Asphalt reduces rain absorption and makes for flash floods following any rain of more than 1″. The red run should be improved, and more drains are needed, or Oakland county will become a flood-prone, asphalt swamp.

Small ditch drain, Bloomfield, MI. The ditches connect to others and to the rivers via the culvert pipes in the left and center of the picture. A cheap solution to flooding.

Ditch drains are among the cheapest ways to drain a swamp. Standard sizes cost only about \$10/lineal foot, but they are pretty ugly in my opinion, they fill up with garbage, and they tend to be unsafe. Jaguars running back Denard Robinson was lucky to have survived running into one in his car (above) earlier this year. Ditches can become mosquito breeding grounds, too and many communities have opted for a more expensive option: buried, concrete or metal culverts. These are safer for the motorist, but reduce ground absorption and flow. In many places, we’ve buried whole rivers. We’ve no obvious swamps but instead we get regular basement and road flooding, as the culverts still have combined storm and sanitary (toilet) sewage, and as more and more storm water is sent through the same old culverts.

Given my choice I would separate the sewers, add weirs to some of our ditch drains, weirs, daylight some of the hidden rivers, and put in French drains and bioswales, where appropriate. These are safer and better looking than ditches but they tend to cost about \$100 per lineal foot, about 10x more than ditch drains. This is still 70x cheaper than the \$7000/ft, combined sewage tunnel cisterns that our current Oakland water commissioner has been putting in. His tunnel cisterns cost about \$13/gallon of water retention, and continue to cause traffic blockage.

Bald cypress in a bog-swamp with tree knees in foreground.

Another solution is trees, perhaps the cheapest solution to drain a small swamp or retention pond, A full-grown tree will transpire hundreds of gallons per day into the air, and they require no conduit connecting the groundwater to a river. Trees look nice and can complement French drains and bioswales where there is drainage to river. You want a species that is water tolerant, low maintenance, and has exceptional transpiration. Options include the river birch, the red maple, and my favorite, the bald cypress (picture). Bald cypress trees can live over 1000 years and can grow over 150 feet tall — generally straight up. When grown in low-oxygen, bog water, they develop knees — bits of root-wood that extend above the water. These aid oxygen absorption and improve tree-stability. Cypress trees were used extensively to drain the swamps of Israel, and hollowed-out cypress logs were the first pipes used to carry Detroit drinking water. Some of these pipes remain; they are remarkably rot-resistant.

Robert E Buxbaum, December 2, 2016. I ran for water commissioner of Oakland county, MI 2016, and lost. I’m an engineer. While teaching at Michigan State, I got an appreciation for what you could do with trees, grasses, and drains.

# just water over the dam

Some months ago, I posted an engineering challenge: figure out the water rate over an non-standard V-weir dam during a high flow period (a storm) based on measurements made on the weir during a low flow period. My solution follows. Weir dams of this sort are erected mostly to prevent flooding. They provide secondary benefits, though by improving the water and providing a way to measure the flow.

A series of compound, rectangular weir dams in Maine.

The problem was stated as follows: You’ve got a classic V weir on a dam, but it is not a knife-edge weir, nor is it rectangular or compound as in the picture at right. Instead it is nearly 90°, not very tall, and both the dam and weir have rounded leads. Because the weir is of non-standard shape, thick and rounded, you can not use the flow equation found in standard tables or on the internet. Instead, you decide to use a bucket and stopwatch to determine the flow during a relatively dry period. You measure 0.8 gal/sec when the water height is 3″ in the weir. During the rain-storm some days later, you measure that there are 12″ of water in the weir. Give a good estimate of the storm-flow based on the information you have.

A V-notch weir, side view and end-on.

I also gave a hint, that the flow in a V weir is self-similar. That is, though you may not know what the pattern will be, you can expect it will be stretched the same for all heights.

The upshot of this hint is that, there is one, fairly constant flow coefficient, you just have to find it and the power dependence. First, notice that area of flow will increase with height squared. Now notice that the velocity will increase with the square root of hight, H because of an energy balance. Potential energy per unit volume is mgH, and kinetic energy per unit volume is 1/2 mv2 where m is the mass per unit volume and g is the gravitational constant. Flow in the weir is achieved by converting potential height energy into kinetic, velocity energy. From the power dependence, you can expect that the average v will be proportional to √H at all values of H.

Combining the two effects together, you can expect a power dependence of 2.5 (square root is a power of 0.5). Putting this another way, the storm height in the weir is four times the dry height, so the area of flow is 16 times what it was when you measured with the bucket. Also, since the average height is four times greater than before, you can expect that the average velocity will be twice what it was. Thus, we estimate that there was 32 times the flow during the storm than there was during the dry period; 32 x 0.8 = 25.6 gallons/sec., or 92,000 gal/hr, or 3.28 cfs.

The general equation I derive for flow over this, V-shaped weir is

Flow (gallons/sec) = Cv gal/hr x(feet)5/2.

where Cv = 3.28 cfs. This result is not much different to a standard one  in the tables — that for knife-edge, 90° weirs with large shoulders on either side and at least twice the weir height below the weir (P, in the diagram above). For this knife-edge weir, the Bureau of Reclamation Manual suggests Cv = 2.49 and a power value of 2.48. It is unlikely that you ever get this sort of knife-edge weir in a practical application. Be sure to measure Cv at low flow for any weir you build or find.

Robert Buxbaum, vote for me for water commissioner. Here are some thoughts on other problems with our drains.

# A plague of combined sewers

The major typhoid and cholera epidemics of the US, and the plague of the Al Qaeda camps, 2009 are understood to have been caused by bad sewage, in particular by the practice of combining sanitary + storm sewage. Medieval plagues too may have been caused by combined sewers.

A combined sewer system showing an rain-induced overflow, a CSO.

A combined system is shows at right. Part of the problem is that the outfall is hard to contain, so they tend to spew sewage into the lakes and drinking water as shown. They are also more prone to back up during rain storms; separated systems can back up too, but far less often. When combined sewers back up, turds and other infected material flows into home basements. In a previous post, “follow the feces,” I showed the path that Oakland county’s combined sewers outfalls take when they drain (every other week) into Lake St. Clair just upstream of the water intake, and I detailed why, every few years we back up sewage into basements. I’d like to now talk a bit more about financial cost and what I’d like to do.

The combined sewer system shown above includes a small weir dam. During dry periods and small rain events, the dam keeps the sewage from the lake by redirecting it to the treatment plant. This protects the lakes so that sometimes the beaches are open, but there’s an operation cost: we end up treating a lot of rain water as if it were sewage. During larger rains, the dam overflows. This protects our basements (usually) but it does so at the expense of the drinking water, and of the water in Lake St. Clair and Lake Erie.

As a way to protect our lakes somewhat Oakland county has added a retention facility, the George W. Kuhn. This facility includes the weir shown above and a huge tank for sewage overflows. During dry periods, the weir holds back the flow of toilet and sink water so that it will flow down the pipe (collector) to the treatment plant in Detroit, and so it does not flow into the lake. Treatment in Detroit is expensive, but nonpolluting. During somewhat bigger rains the weir overflows to the holding tank. It is only during yet-bigger rains (currently every other week) that the mixture of rain and toilet sewage overwhelms the tank and is sent to the river and lake. The mess this makes of the lake is shown in the video following. During really big rains, like those of August 2014, the mixed sewage backs up in the pipes, and flows back into our basements. With either discharge, we run the risk of plague: Typhoid, Cholera, Legionnaires…

Some water-borne plagues are worse than others. With some plagues, you can have a carrier, a person who can infect many others without becoming deathly sick him or herself. Typhoid Mary was a famous carrier of the 1920s. She infected (and killed) hundreds in New York without herself becoming sick. A more recent drinking water plague, showed up in Milwaukee 25 years ago. Some 400,000 people were infected, and 70 or so died. Milwaukee disinfected its drinking water with chlorine and a bacteria that entered the system was chlorine tolerant. Milwaukee switched to ozone disinfection but Detroit still uses chlorine.

Combined sewers require much larger sewage treatment plants than you’d need for just sanitary sewage. Detroit’s plant is huge and its size will need to be doubled to meet new, stricter standards unless we bite the bullet and separate our sewage. Our current system doesn’t usually meet even the current, lower standards. The plant overflows and operation cost are high since you have to treat lots of rainwater. These operation costs will keep getter higher as pollution laws get tougher.

In Oakland county, MI we’ve started to build more and more big tanks to hold back and redirect the water so it doesn’t overwhelm the sewage plants. The GWK tank occupies 1 1/2 miles by about 100 feet beneath a golf course. It’s overwhelmed every other week. Just think of the tank you’d need to hold the water from 4″ of rain on 900 square mile area (Oakland county is 900 square miles). Oakland’s politicians seem happy to spend money on these tanks because it creates jobs and graft and because it suggests that something is being done. They blame politics when rain overwhelms the tank. I say it’s time to end the farce and separate our sewers. My preference is to separate the sewers through the use of French drains or bio-swales, and through the use of weir dams. I’m running for drain commissioner. Here’s something I’ve written on the chemistry of sewage, and on the joy of dams.

Dr. Robert E. Buxbaum, July 1-Sept 16, 2016.

# The chemistry of sewage treatment

The first thing to know about sewage is that it’s mostly water and only about 250 ppm solids. That is, if you boiled down a pot of sewage, only about 1/40 of 1% of it would remain as solids at the bottom of the pot. There would be some dried poop, some bits of lint and soap, the remains of potato peelings… Mostly, the sewage is water, and mostly it would have boiled away. The second thing to know, is that the solids, the bio-solids, are a lot like soil but better: more valuable, brown gold if used right. While our county mostly burns and landfills the solids remnant of our treated sewage, the wiser choice would be to convert it to fertilizer. Here is a comparison between the composition of soil and bio-solids.

The composition of soil and the composition of bio-solid waste. biosolids are like soil, just better.

Most of Oakland’s sewage goes to Detroit where they mostly dry and burn it, and land fill the rest. These processes are expensive and engineering- problematic. It takes a lot of energy to dry these solids to the point where they burn (they’re like really wet wood), and even then they don’t burn nicely. As shown above, the biosolids contain lots of sulfur and that makes combustion smelly. They also contain nitrate, and that makes combustion dangerous. It’s sort of like burning natural gun powder.

The preferred solution is partial combustion (oxidation) at room temperature by bacteria followed by conversion to fertilizer. In Detroit we do this first stage of treatment, the slow partial combustion by bacteria. Consider glucose, a typical carbohydrate,

-HCOH- + O–> CO+ H2O.    ∆G°= -114.6 kcal/mol.

The value of ∆G°, is relevant as a determinate of whether the reaction will proceed. A negative value of ∆G°, as above, indicates that the reaction can progress substantially to completion at standard conditions of 25°C and 1 atm pressure. In a sewage plant, many different carbohydrates are treated by many different bacteria (amoebae, paramnesia, and lactobacilli), and the temperature is slightly cooler than room, about 10-15°C, but this value of ∆G° suggests that near total biological oxidation is possible.

The Detroit plant, like most others, do this biological oxidation treatment using either large stirred tanks, of million gallon volume or so, or in flow reactors with a large fraction of cellular-material returning as recycle. Recycle is needed also in the stirred tank process because of the low solid content. The reaction is approximately first order in oxygen, carbohydrate, and bacteria. Thus a 50% cell recycle more or less doubles the speed of the reaction. Air is typically bubbled through the reactor to provide the oxygen, but in Detroit, pure oxygen is used. About half the organic carbon is oxidized and the remainder is sent to a settling pond. The decant (top) water is sent for “polishing” and dumped in the river, while the goop (the bottom) is currently dried for burning or carted off for landfill. The Holly, MI sewage plant uses a heterogeneous reactors for the oxidation: a trickle bed followed by a rotating disk contractor. These have higher bio-content and thus lower area demands and separation costs, but there is a somewhat higher capital cost.

A major component of bio-solids is nitrogen. Much of this in enters the form of urea, NH2-CO-NH2. In an oxidizing environment, bacteria turns the urea and other nitrogen compounds into nitrate. Consider the reaction the presence of washing soda, Na2CO3. The urea is turned into nitrate, a product suitable for gun powder manufacture. The value of ∆G° is negative, and the reaction is highly favorable.

NH2-CO-NH2 + Na2CO3 + 4 O2 –> 2 Na(NO3) + 2 CO2 + 2 H2O.     ∆G° = -177.5 kcal/mol

The mixture of nitrates and dry bio-solids is highly flammable, and there was recently a fire in the Detroit biosolids dryer. If we wished to make fertilizer, we’d probably want to replace the drier with a further stage of bio-treatment. In Wisconsin, and on a smaller scale in Oakland MI, biosolids are treated by higher temperature (thermophilic) bacteria in the absence of air, that is anaerobically. Anaerobic digestion produces hydrogen and methane, and produces highly useful forms of organic carbon.

2 (-HCOH-) –> COCH4        ∆G° = -33.7 Kcal/mol

3 (-HCOH-) + H2O –> -CH2COOH + CO2 +  2 1/2 H2        ∆G° = -21.9 kcal/mol

In a well-designed plant, the methane is recovered to provide heat to the plant, and sometimes to generate power. In Wisconsin, enough methane is produced to cook the fertilizer to sterilization. The product is called “Milorganite” as much of it comes from Milwaukee and much of the nitrate is bound to organics.

Egg-shaped, anaerobic biosolid digestors, Singapore.

The hydrogen could be recovered too, but typically reacts further within the anaerobic digester. Typically it will reduce the iron oxide in the biosolids from the brown, ferric form, Fe2O3, to black FeO.  In a reducing atmosphere,

Fe2O3 + H2 –> 2 FeO + H2O.

Fe2O3 is the reason leaves turn brown in the fall and is the reason that most poop is brown. FeO is the reason that composted soil is typically black. You’ll notice that swamps are filled with black goo, that’s because of a lack of oxygen at the bottom. Sulphate and phosphorous can be bound to ferrous iron and this is good for fertilizer. Generally you want the reduction reactions to go no further.

Weir dam on the river Dour in Scotland. Dams of this type increase residence time, and oxygenate the flow. They’re good for fish, pollution, and flooding.

When allowed to continue, the hydrogen produced by anaerobic digestion begins to reduce sulfate to H2S.

NaSO4 + 4.5 H2 –>  NaOH + 3H2O + H2S.

I’m running for Oakland county, MI water commissioner, and one of my aims is to stop wasting our biosolids. Oakland produces nearly 1000,000 pounds of dry biosolids per day. This is either a blessing or a curse depending on how we use it.

Another issue, Oakland county dumps unpasteurized, smelly black goo into Lake St. Clair every other week, whenever it rains more than one inch. I’d like to stop this by separating the storm and “sanitary” sewage. There is a capital cost, but it can save money because we’d no longer have to pay to treat our rainwater at the Detroit sewage plant. To clean the storm runoff, I’d use mini wetlands and weir dams to increase residence time and provide oxygen. Done right, it would look beautiful and would avoid the flash floods. It should also bring natural fish back to the Clinton River.

Robert Buxbaum, May 24 – Sept. 15, 2016 Thermodynamics plays a big role in my posts. You can show that, when the global ∆G is negative, there is an increase in the entropy of the universe.

# Weird flow calculation

Here is a nice flow problem, suitable for those planning to take the professional engineers test. The problem concerns weir dams. These are dams with a notch in them, somethings rectangular, as below, but in this case a V-shaped notch. Weir dams with either sort of notch can be used to prevent flooding and improve the water, but they also provide a way to measure the flow of water during a flood. That’s the point of the problem below.

A series of weir dams with rectangular weirs in Maine.

You’ve got a classic V weir on a dam, but it is not a knife-edge weir, nor is it rectangular or compound as in the picture at right. Instead it is nearly 90°, not very tall, and both the dam and weir have rounded leads. Because the weir is of non-standard shape, thick and rounded, you can not use the flow equation found in standard tables or on the internet. Instead, you decide to use a bucket and stopwatch to determine that the flow during a relatively dry period. You measure 0.8 gal/sec when the water height is 3″ in the weir. During the rain-storm some days later, you measure that there are 12″ of water in the weir. The flow is too great for you to measure with a bucket and stopwatch, but you still want to know what the flow is. Give a good estimate of the flow based on the information you have.

As a hint, notice that the flow in the V weir is self-similar. That is, though you may not know what the pattern of flow will be, you can expect it will be stretched the same for all heights.

As to why anyone would use this type of weir: they are easier to build and maintain than the research-standard, knife edge; they look nicer, and they are sturdier. Here’s my essay in praise of the use of dams. How dams on drains and rivers could help oxygenate the water, and to help increase the retention time to provide for natural bio-remediation.

If you’ve missed the previous problem, here it is: If you have a U-shaped drain or river-bed, and you use a small dam or weir to double the water height, what is the effect on water speed and average retention time. Work it out yourself, or go here to see my solution.

Robert Buxbaum. May 20-Sept 20, 2016. I’m running for drain commissioner. send me your answers to this problem, or money for my campaign, and win a campaign button. Currently, as best I can tell, there are no calibrated weirs or other flow meters on any of the rivers in the county, or on any of the sewers. We need to know because every engineering decision is based on the flow. Another thought: I’d like to separate our combined sewers and daylight some of our hidden drains.

# Weir dams to slow the flow and save our lakes

As part of explaining why I want to add weir dams to the Red Run drain, and some other of our Oakland county drains, I posed the following math/ engineering problem: if a weir dam is used to double the depth of water in a drain, show that this increases the residence time by a factor of 2.8 and reduces the flow speed by 1/2.8. Here is my solution.

A series of weir dams on Blackman Stream, Maine. Mine would be about as tall, but wider and further apart. The dams provide oxygenation and hold back sludge.

Let’s assume the shape of the bottom of the drain is a parabola, e.g. y = x, and that the dams are spaced far enough apart that their volume is small compared to the volume of water. We now use integral calculus to calculate how the volume of water per mile, V is affected by water height:  V =2XY- ∫ y dx = 2XY- 2/3 X3 =  4/3 Y√Y. Here, capital Y is the height of water in the drain, and capital X is the horizontal distance of the water edge from the drain centerline. For a parabolic-bottomed drain, if you double the height Y, you increase the volume of water per mile by 2√2. That’s 2.83, or about 2.8 once you assume some volume to the dams.

To find how this affects residence time and velocity, note that the dam does not affect the volumetric flow rate, Q (gallons per hour). If we measure V in gallons per mile of drain, we find that the residence time per mile of drain (hours) is V/Q and that the speed (miles per hour) is Q/V. Increasing V by 2.8 increases the residence time by 2.8 and decreases the speed to 1/2.8 of its former value.

Why is this important? Decreasing the flow speed by even a little decreases the soil erosion by a lot. The hydrodynamic lift pressure on rocks or soil is proportional to flow speed-squared. Also, the more residence time and the more oxygen in the water, the more bio-remediation takes place in the drain. The dams slow the flow and promote oxygenation by the splashing over the weirs. Cells, bugs and fish do the rest; e.g. -HCOH- + O2 –> CO2 + H2O. Without oxygen, the fish die of suffocation, and this is a problem we’re already seeing in Lake St. Clair. Adding a dam saves the fish and turns the run into a living waterway instead of a smelly sewer. Of course, more is needed to take care of really major flood-rains. If all we provide is a weir, the water will rise far over the top, and the run will erode no better (or worse) than it did before. To reduce the speed during those major flood events, I would like to add a low bicycle path and some flood-zone picnic areas: just what you’d see on Michigan State’s campus, by the river.

Dr. Robert E. Buxbaum, May 12, 2016. I’d also like to daylight some rivers, and separate our storm and toilet sewage, but those are longer-term projects. Elect me water commissioner.