Category Archives: water

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 plug-flow reactor with a 90+% solids recycle used to maintain a high concentration of bio-catalyst material.

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 by the South Lyon, MI, Activated Sludge reactor

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.

A rotating disk bio-reactor for sewage treatment

One of the most effective designs for sewage treatment is the rotating disk bio-reactor, shown below. It is typically used in small-throughput sewage plants, but it performs quite well in larger plants too. I’d like to present an analysis of the reactor, and an explanation of why it works so well.

A rotating disc sewage reactor.

A rotating disk sewage reactor; ∂ is the thickness of the biofilm. It’s related to W the rotation rate in radians per sec, and to D the limiting diffusivity.

As shown, the reactor is fairly simple-looking, nothing more than a train of troughs filled with sewage-water, typically 3-6 feet deep, with a stack of discs rotating within. The discs are typically 7 to 14 feet in diameter (2-4 meters) and 1 cm apart. The shaft is typically close to the water level, but slightly above, and the rotation speed is adjustable. The device works because appropriate bio-organisms attach themselves to the disk, and the rotation insures that they are fully (or reasonably) oxygenated.

How do we know the cells on the disc will be oxygenated? The key is the solubility of oxygen in water, and the fact that these discs are only used on the low biological oxygen demand part of the sewage treatment process, only where the sewage contains 40 ppm of soluble organics or less. The main reaction on the rotating disc is bio oxidation of soluble carbohydrate (sugar) in a layer of wet slime attached to the disc.

H-O-C-H + O2 –> CO2 + H2O.

As it happens, the solubility of pure oxygen in water is about 40 ppm at 1 atm. As air contains 21% oxygen, we expect an 8 ppm concentration of oxygen on the slime surface: 21% of 40 ppm = 8 ppm. Given the reaction above and the fact that oxygen will diffuse five times more readily than sugar at least, we expect that one disc rotation will easily provide enough oxygen to remove 40 ppm sugar in the slime at every speed of rotation so long as the wheel is in the air at least half of the time, as shown above.

Let’s now pick a rotation speed of 1/3 rpm (3 minutes per rotation) and see where that gets us in terms of speed of organic removal. Since the disc is always in an area of low organic concentration, it becomes covered mostly with “rotifers”, a fungus that does well in low nutrient (low BOD) sewage. Let’s now assume that mass transfer (diffusion) of sugar in the rotifer slime determines the thickness of the rotifera layer, and thus the rate of organic removal. We can calculate the diffusion depth of sugar, ∂ via the following equation, derived in my PhD thesis.

∂ = √πDt

Here, D is the diffusivity (cm2/s) for sugar in the rotifera slime attached to the disk, π = 3.1415.. and t is the contact time, 90 seconds in the above assumption. My expectation is that D in the rotifer slime will be similar to the diffusivity sugar in water, about 3 x 10-6 cm2/s. Based on the above, we find the rotifer thickness will be ∂ = √.00085 cm2 = .03 cm, and the oxygen depth will be about 2.5 times that, 0.07 cm. If the discs are 1 cm apart, we find that, about 14% of the fluid volume of the reactor will be filled with slime, with 2/5 of this rotifer-filled. This is as much as 1000 times more rotifers than you would get in an ordinary constantly stirred tank reactor, a CSTR to use a common acronym. We might now imagine that the volume of this sewage-treatment reactor can be as small as 1000 gallons, 1/1000 the size of a CSTR. Unfortunately it is not so; we’ll have to consider another limiting effect, diffusion of nutrients.

Consider the diffusive mass transfer of sugar from a 1,000,000 gal/day flow (43 liters/sec). Assume that at some point in the extraction you have a concentration C(g/cc) of sugar in the liquid where C is between 40 ppm and 1 ppm. Let’s pick a volume of the reactor that is 1/20 the normal size for this flow (not 1/1000 the size, you’ll see why). That is to say a trough whose volume is 50,000 gallons (200,000 liters, 200 m3). If the discs are 1 cm apart, this trough (or section of a trough) will have about  4×10^8 cm2 of submerged surface, and about 9×10^8 total surface including wetted disc in the air. The mass of organic that enters this section of trough is 44,000 C g/second, but this mass of sugar can only reach the rotifers by diffusion through a water-like diffusion layer of about .06 cm thickness, twice the thickness calculated above. The thickness is twice that calculated above because it includes the supernatant liquid beyond the slime layer. We now calculate the rate of mass diffusing into the disc: AxDxc/z = 8×10^8 x 3×10-6 x C/.06 cm = 40,000 C g/sec, and find that, for this tank size and rotation speed, the transfer rate of organic to the discs is 2/3 as much as needed to absorb the incoming sugar. This is to say that a 50,000 gallon section is too small to reduce the concentration to ln (1) at this speed of disc rotation.

Based on the above calculation, I’m inclined to increase the speed of rotation to .75 rpm. At this speed, the rotifer-slime layer will be 2/3 as thin 0.2 mm, and we expect an equally thinner diffusion barrier in the supernatant. At this faster speed, there is now 3/2 as much diffusion transfer per area because the thinner diffusion barrier, and we can expect a 50,000 liter reactor section to reduce the initial concentration by a fraction of 1/2.718 or C/e. Note that the mass transfer rate to the discs is always proportional to C. If we find that 50,000 gallons of tank reduces the concentration to 1/e, we find that we need 150,000 gallons of reactor to reduce the concentration of sugar from 40 ppm to 2 ppm, the legal target, ln (40/2) = 3. This 150,000 gallons is a remarkably small volume to reduce the sBOD concentration from 40 ppm to 2 ppm (sBOD = soluble biological oxygen demand), and the energy use is small too if the disc bearings are good.

The Holly sewage treatment plant is the only one in Oakland county, MI using the rotating disc contacted technology. It has a flow of 1,000,000 gallons per day, and has a contactor trough that is 215,000 gallons, about what we’d expect though their speed is somewhat higher, over 1 rpm and their input concentration is likely lower than 40 ppm. For the first stage of sewage treatment, the Holly plant use a vertical-draft, trickle-bed reactor. That is they drizzle the sewage-liquids over a slime-coated packing to reduce the sBOD concentration from 200 ppm to before feeding the flow to the rotating discs. My sense of the reason they don’t do the entire extraction with a trickle bed is that the discs use far less energy.

I should also add that the back-part of the disc isn’t totally useless oxygen storage, as it seems from my analysis. Some non-sugar reactions take place in the relatively anoxic environment there and in the liquid at the bottom of the trough. In these regions, iron reacts with phosphate, and nitrate removal takes place. These are other important requirements of sewage treatment.

Robert E. Buxbaum, July 18, 2017. As an exercise, find the volume necessary for a plug flow reactor or a stirred tank reactor (CSTR) to reduce the concentration of sugar from 40 ppm to 2 ppm. Assume 1,000,000 gal per day, an excess of oxygen in these reactors, and a first order reaction with a rate constant of dC/dt = -(0.4/hr)C. At some point in the future I plan to analyze these options, and the trickle bed reactor, too.

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. Isn't that white of them.

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.

May 1, St. Tammany day

May 1 is St. Tammany day, a day to rejoice in the achievements of Tammany Hall, and of St Tammany, the guardian of crooked politicians everywhere. The Sons of St. Tammany started in 1773 as a charitable club of notable revolutionary-era individuals including Benjamin Franklin, John Hancock, and John Dickenson, but evolved into perhaps the most corrupt, and American, of political organizations. The picture of a US politician – the cartoon version at least — is the Tammany Democrat: a loud, drunken, womanizer, willing to do or promise whatever the people seem to want at the moment. Tammany and its bosses helped form this image. They helped new immigrants, but did so by creating needless government jobs, by filling them often with incompetent loyalists, and by overcharging on government contracts. Today, these Tammany ways rule in every major American city; the other clubs of the day are gone or influence-less.

John Hancock leads a meeting of the St. Tammany (Columbian) society. Note the "Appeal to Heaven flag and the Indian, real or imagined. Indians participated in several, early St. Tammany meetings.

John Hancock leads a meeting of the St. Tammany society. Note the “Appeal to Heaven” flag. While Indians participated in some, early meetings, the one here is, I suspect, a ghost: St. Tammany.

In revolutionary-era America, the Sons of St. Tammany was just one of many social-charitable clubs (Americans like to form clubs), in many ways it was similar to the Masons and the Cincinnati, but those clubs were international and elitist. The sons of Tammany was purely American, and anti-elitist. It was open to anyone born on this side of the Atlantic, and had Indian customs. The Cincinnati society, for comparison, started with members who were as notable (Alexander Hamilton, George Washington, Marie, Marquis de Lafayette, Henry Knox, etc.) but was originally open only to high officers of the regular army, including foreigners like Lafayette, but not ordinary soldiers, minutemen (militia), or the general public. The symbols of the Tammanies were American: the liberty-cap and the “Appeal to Heaven” flag, now a popular symbol of the Tea Party; the leader was called by an Indian name: Sachem. By contrast, the Cincinnati society symbol was the Imperial Eagle (Washington’s was gold with diamonds), and the leader was called “general”. The Tammany society began admitting immigrants in 1810 or so, while the Cincinnati society remains closed to this day, except to descendants of Revolutionary officers — an aristocratic affectation in the eyes of some.

It was Aaron Burr who first saw the opportunity to use the Tammany organization as a for-profit, political machine. In the years 1795-9, New York was suffering from yellow fever and a variety of other diseases that were taken to be caused by a lack of clean water. Burr proposed, with Tammany support, the creation of a corporation to build a new water system to bring fresh, clean water from the Bronx River to lower Manhattan via iron pipes. The Manhattan company was duly chartered, with directors who were primarily Tammany men, Republican-Democrats, and not Federalists. Federalists (Hamilton, primarily) controlled the only NY banks at the time and controlled the directorate of every chartered company in the city. The Manhattan company requested a $2,000,000 perpetual charter, twice as big as the charter of Hamilton’s Bank of New York, and a monopoly on water distribution. These were reasonable requests given the task, but unusual in the lack of Federalist or governmental oversight. But the Manhattan company was a water company, and water was needed. But Burr’s intent, all along, it seems was to build a bank, not a water company. After the charter was approved, but before signing, he amended it to allow any excess funds to be used for any legal purpose. 

In this cartoon by Dr. Seuss, The Tammany Tiger says, "Today is the Big Day Folks. Vote Early and Often."

In this cartoon by Dr. Seuss, The Tammany Tiger says, “Today is the Big Day Folks. Vote Early and Often.”

Money was raised, but only $100,000 used for the water system. The remaining 95% of the charter funds, $1,900,000, went to found “The Bank of The Manhattan company” — later to be known as “The Chase Manhattan Bank” or “The Manhattan Bank of Cholera.” Instead of building the reservoir in upper Manhattan and filling it with clean water as originally proposed, Burr’s Tammany trustees voted to dig wells in lower Manhattan, and placed its reservoir in lower Manhattan too, near Chamber’s St,  next to a cemetery where Cholera victims were buried. New York suffered with Cholera, Typhoid, and leaky, wooden pipes until 1842 when Peter Cooper brought clean water to lower Manhattan from the Groton River via iron pipes. To this day, crooked water contracts are a staple of Tammany politics

The Bank of the Manhattan company opened at 40 Wall St on September 1, 1799, a mere four months after the water company’s incorporation. Hamilton was furious. The company continues today as The JP Morgan, Chase Manhattan Bank, one of the largest banking institutions in the world. Burr used the money and power of his company to reward supporters and to run for vice president with Thomas Jefferson’s tacit support. Except for his Tammany candidacy, John Adams would have won New York and a second term as president. Burr’s career pretty-well died after the Hamilton duel, but Tammany did well without him. By 1812, the Society built its first Tammany Hall, officially called the Wigwam, a $55,000, five-story building with a meeting hall for 2000. New York Democratic politics would center on Tammany Hall for the next century at least.

Following disappointment with John Quincy Adams, “the bitter branch of the bitter tree,” Tammy leaders went national. They recruited Andrew Jackson, a war hero and early recruit of Burr’s. They’d support Jackson if he’d hand over spoils, control of government jobs. He agreed and, as president, fired perfectly good, long-standing government employees He replaced them with Democratic loyalists. When Jackson stepped down in 1833, Tammany elected an equally corrupt New Yorker, Martin van Buren. Though there were periodic Whig and Republican reforms, Tammany learned they could wait those out. They always re-emerged like mushrooms after a rain.

Boss Tweed and other Tammany leaders: who stole the money?

Boss Tweed and other Tammany leaders in a cartoon by Nast, Tammany Ring. “Who stole the money? He did.”  

A key vote-getter in the Tammany system is to provide Thanksgiving dinners and other charitable giveaways for the poor, as well as promises of jobs. By the late 1800s, William J. Brian added promises of soft money and wealth redistribution, cornerstones of the Democratic platform to this day. Tammany also tends to be for low tariffs as opposed to the high tariff ideas of Hamilton and many Whigs and 19th century Republicans. A case can be made for either view.

Tammany helped New York immigrants, particularly the Irish to get citizenship and avoid legal troubles in return for votes and occasional muscle. In other cities, Democratic clubs were less open to Catholics, reflecting the views of the common voter in each state. In the North they were pro-union, in the South anti, electing Klu Kluxers like George Wallace, Sam Ervin, and Robert Byrd. This lead to a famous split in the Democratic party about the 1968 convention. Famous Tammany leaders include William M. “Boss” Tweed, “Big” Tim Sullivan, and “Gentleman” Jimmy Walker. Sullivan famously authored the first anti-gun law, the Sullivan act; it was designed to protect his thugs against private citizens shooting them. It didn’t always work.

Edwin Edwards, Democratic Governor of Louisiana. 1972-1996. Who would not trust this man?

Hon. (?) Edwin Edwards, Governor of Louisiana. 1972-1996. Tammany lives

If you want to see Tammany politics in action, visit almost any large US city, or read its newspaper. In Chicago, the dead vote, and 4 of the last 6 governors have gone to jail. Mayor Daily famously told Kennedy that 90 percent of the registered voters of Cook County would vote for him. They did (sort of); because of this, JFK won Illinois and the presidency. In New York, voters discovered only in the 1960s that Tammany’s leader, Carmine DeSapio had been working for 30 years with known gangland murderer, Charles “Lucky” Luciano. In Detroit, where I live and corruption in the water department is legendary. Race-based job handouts, unemployment is high along with high minimum (living) wages. We’re now in the process of a $70,000,000 project to replace 100 feet of sewer pipe, and we’re building a $140 million, 3.3 mile trolley. Tammany loves all public works.

Then there is Louisiana, home to St Tammany parish. Louisiana Democrats like Huey Long and Edwin Edwards (shown at left) are unusual in that they’re proud to say that their corrupt methods are corrupt. Edwards has had two long runs as governor despite several convictions for doing illegal things he admits to doing. When Edwards was asked why he did favors for his friends. He responded: “Who should I do them for? My enemies?” Or, to quote one of Edwin Edwards campaign ads. Vote Edwin EdwardsPeople seem to love it, or did until the levy broke. There is a particularly American grandeur to all this. As Will Rodgers said, “America has the best politicians money can buy.” Today is the day to be proud of that uniquely American tradition. You too can grow up to buy a president.

Robert Buxbaum, April 28, 2017. I ran for water commissioner, and have written about sewage treatment, flood avoidance, and fluoride, as well as the plusses and minuses of trade unionization, and the difference between Republicans and Conservatives.

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 inches and spread it out to save water and weeding.

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.

The next big issue is lawn-care. If you water your lawn and flowers daily, you’ve likely noticed that you pay about $300/month for water in the summer: a lot more than in the winter, or than your lazes-faire neighbor in the summer. Every $150 of summer-excess, water bill you pay represents about 10,000 gallons applied to your lawn. That’s a cubic foot, or 1¢ to 2¢ of water applied per ft2 per month for typical watering. While many sites advise that you can save by adding a rain barrel, I disagree. Rain barrels are costly, ugly, and are a lot of work ago plumb in. And each barrel only holds 55 gallons of water, 82¢ worth when full. You do a lot better, IMHO by putting down an inch or two of mulch around your flowers and vegetables. This mulch requires no work and will keep you from needing to water these areas for the 3-4 days after every rainfall. A layer of 1″ to 2″ will help your soil hold 0.5 to 1 gallon of water per square foot. At typical prices of mulch and water, this will pay for itself in 1-2 years and will help you avoid weeding. Mulch is a far better return than the rain-barrels that are often touted, and there’s far less effort involved. Buy the mulch, not the barrel, but don’t put down too more than 2″ on flowers and vegetable. Trees can take 3 -4″; don’t use more. Avoid a mulch mountain right next to a tree, it causes the roots to grow weird, and provides a home for bugs and undesirable anaerobic molds.

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.

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.report__jaguars_running_back_denard_robi_0_5329357_ver1-0_640_360

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.

Classic ditch drain, Bloomfiled MI. Notice the culverts used to convey water from the ditch under the road.

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 swamp

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.

The straight flush

I’m not the wildest libertarian, but I’d like to see states rights extended to Michigan’s toilets and showers. Some twenty years ago, the federal government mandated that the maximum toilet flush volume could be only 1.6 gallons, the same as Canada. They also mandated a maximum shower-flow law, memorialized in this Seinfeld episode. Like the characters in those shows, I think this is government over-reach of states rights covered by the 10th amendment. As I understand it, the only powers of the federal government over states are in areas specifically in the constitution, in areas of civil rights (the 13th Amendment), or in areas of restraint of trade (the 14th Amendment). None of that applies here, IMHO. It seems to me that the states should be able to determine their own flush and shower volumes.

If this happen to you often, you might want to use more water for each flush, or  at least a different brand of toilet paper.

If your toilet clogs often, you might want to use more flush water, or at least a different brand of toilet paper.

There is a good reason for allowing larger flushes, too in a state with lots of water. People whose toilets have long, older pipe runs find that there is insufficient flow to carry their stuff to the city mains. Their older pipes were designed to work with 3.5 gallon flushes. When you flush with only 1.6 gallons, the waste only goes part way down and eventually you get a clog. It’s an issue known to every plumber – one that goes away with more flush volume.

Given my choice, I’d like to change the flush law through the legislature, perhaps following a test case in the Supreme court. Similar legislation is in progress with marijuana decriminalization, but perhaps it’s too much to ask folks to risk imprisonment for a better shower or flush. Unless one of my readers feels like violating the federal law to become the test case, I can suggest some things you can do immediately. When it comes to your shower, you’ll find you can modify the flow by buying a model with a flow restrictor and “ahem” accidentally losing the restrictor. When it comes to your toilet, I don’t recommend buying an older, larger tank. Those old tanks look old. A simpler method is to find a new flush cistern with a larger drain hole and flapper. The drain hole and flapper in most toilet tanks is only 2″ in diameter, but some have a full 3″ hole and valve. Bigger hole, more flush power. Perfectly legal. And then there’s the poor-man solution: keep a bucket or washing cup nearby. If the flush looks problematic, pour the extra water in to help the stuff go down. It works.

A washing cup.

A washing cup. An extra liter for those difficult flushes.

Aside from these suggestions, if you have clog trouble, you should make sure to use only toilet paper, and not facial tissues or flushable wipes. If you do use these alternatives, only use one sheet at a flush, and the rest TP, and make sure your brand of wipe is really flushable. Given my choice, I would like see folks in Michigan have freedom of the flush. Let them install a larger tank if they like: 2 gallons, or 2.5; and I’d like to see them able to use Newman’s Serbian shower heads too, if it suits them. What do you folks think?

Dr. Robert E. Buxbaum, November 3, 2016. I’m running for Oakland county MI water resources commissioner. I’m for protecting our water supply, for better sewage treatment, and small wetlands for flood control. Among my less-normative views, I’ve also suggested changing the state bird to the turkey, and ending daylight savings time.

Most flushable wipes aren’t flushable.

I’m a chemical engineer running for Oakland county water resources commissioner, and as the main job of the office is sewage, and as I’ve already written on the chemistry, I thought I might write about an aspect of the engineering. Specifically about toilet paper. Toilet paper is a remarkable product: it’s paper, compact and low in cost; strong enough to clean you, smooth on your bum, and beyond that, it will disintegrate in turbulent water so it doesn’t clog pipes. The trick to TP’s dry strength and wet-weakness, is that the paper pulp, wood cellulose, is pounded very thin, yet cast fluffy. For extra softness, the paper is typically coated with aloe or similar. Sorry to say, the same recipe does not work for wet-wipes, paper towels or kleenex (facial tissues); all of these products must have wet-strength, and this can cause problems with sewer clogs.

Patent 117355 for perforated toilet paper claimed it as an improved wrapping paper.

Patent 117,355 for perforated toilet paper on a roll. It’s claimed as an improved wrapping paper.

Before there was toilet paper, the world was a much sadder, and smellier place. Much of the world used sticks, stones, leaves, or corn cobs, and none of these did a particularly thorough job. Besides, none of these is particularly smooth, or particularly disposable, nor did it fall apart — not that most folks had indoor plumbing. Some rich Romans had plumbing, and these cleaned themselves with a small sponge on the end of a stick. They dipped the sponge ned in water for each use. It was disgusting, but didn’t clog the pipes. I’ve seen this in use on a trip to Turkey 25 years ago — not in actual use, but next to the commode.

The first reasonably modern toilet was invented in 1775 by Alexander Cummings, and by 1852 the first public flush toilets were available. The design looked pretty much like it looks today and the cost was 1¢. You got a towel and a shoe-shine too for that penny, but there was no toilet paper as such. Presumably one used a Roman sponge or some ordinary, standard paper. A popular wipe, back int he day  was the Sears-Roebuck catalog. It came free to most homes, and included a convenient hole in the corner allowing one to hang it in and outhouse or near the commode. It was rough on the bum, and didn’t fall apart. My guess is that it clogged the pipes too, for those who used it with flush toilets. The first toilet-specific paper wasn’t invented till 1859. Joseph Gayetty, an American, patented a product from pulverized hemp, a relatively soft fiber, softened further with aloe. The paper softer than standard, and had less tendency to clog pipes.

Toilet paper has to be soft

Toilet paper is either touted to be soft or strong; Modern Charmin touts wet strength, while Cottonelle touts completeness of wipe: ‘go commando.” 

The next great innovation was to make toilet paper as a perforated product on a roll. These novelties appear as US Patent #117,355 awarded to Seth Wheeler of Albany, NY 25 July 1871 (Wheeler also invented the classic roll toilet paper dispenser). Much of the sales pitch was that a cleaner bum would prevent the spread of cholera, typhoid, and other plagues and that is a legitimate claim. As the  market expanded, advertising followed. Some early brands of paper touted their softness, others their strength. Facial tissues, e.g. Kleenex, were sold specifically as a soft TP-like product that does not fall apart when wet. Sorry to say, this tends to go along with clogged toilets; do not flush more than one kleenex down at a flush. Kleenex is made with the same short fibers and aloe as toilet paper, but it contains binders (glue) to give it wet-strength. My guess is that Charmin is made the same way and that it isn’t great on your plumbing.

Paper towels and most baby wipes are worse to flush than Kleenex. They are made with lots of binder and they really don’t fall apart in water. Paper towels should never be flushed, and neither should most baby wipes, even brands that claim to be ‘flushable.” When flushed, these items tend to soak up fat and become fat bergs – the bane of sewer workers everywhere. There is a class action law suit against flushable wipe companies, and New York City is pursuing legislation to prevent them from claiming to be flushable. Still, as with everything, there are better and worse moist-wipe options. “Cottonelle” brand by Kleenex, and Scott flushable wipes will eventually (In a day or less) dissolve in water. These products are made with binders like kleenex, but the binder glue is a type that dissolves in any significant amount of water. As a result, these brands fall apart when flushed. For now, these are the only flushable brands I’d recommend flushing, and even then I suggest you only flush one at a time. In tests by Consumer Reports, other brands, e.g. Charmin and Equate flushable wipes do not dissolve. These manufacturers either have not quite figured out how to make dissolvable binders, or they can’t get around Kleenex’s patents.

Robert Buxbaum. October 10, 2016. If you live in Oakland county, MI vote for me for water commissioner. Here’s my web-site with other useful essays. I should mention Thomas Crapper, too. He invented the push-button flush and made some innovations in the water cistern, and he manufactured high-end commodes for Parliament and the royal family, but he’s irrelevant to the story here.

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 weir dams on Blackman Stream, Maine. These are thick, rectangular weirs.

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.

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.