Category Archives: water

Sewage reactor engineering, Stirred tank designs

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Over the past few years, I’ve devoted several of these essays to analysis of first-stage sewage treatment reactors. I described and analyzed the rotating disc reactor found at the plant is Holly here, and described the racetrack,“activated sludge” plug reactor found most everywhere else here. I also described a system without a primary clarifier found near Cincinatti. All of these were effective for primary treatment; soluble organics are removed by bio-catalyzed oxidation:

2 H-C-O-H + O2 –> CO2 + H2O.

A typical plant in Oakland county treats 2,000,000 gallons per day of this stuff, with the bio-reactor receiving liquid waste containing about 200 ppm of soluble and colloidal biomass. That’s 400 dry gallons for those interested, or about 3200 dry lbs./day. About half of this will be oxidized to CO2 and water. The rest (cell bodies) are removed with insoluble components, and applied to farmers fields or buried, or burnt in an incinerator.

There is another type of reactor used in Oakland County. It’s mostly used for secondary treatment, converting consolidated sludge to higher-quality sludge that can be sold or used on farms with less restriction, but it is a type of reactor used at the South Lyon treatment plant, for primary treatment. It is a Continually stirred tank reactor, or CSTR, a design that is shown in schematic below.

As of some years ago, the South Lyon system involved a single largish pond lined with plastic with a volume about 2,000,000 gallons total. About 700,000 gallons per day of sewage liquids went into the lagoon, at 200 ppm soluble organics. Air was bubbled through the liquid providing a necessary reactant, and causing near-perfect mixing of the contents. The aim of the plant managers is to keep the soluble output to the, then-acceptable level of 10 ppm; it’s something they only barely managed, and things got worse as the flow increased. Assume as before, a value V and a flow Q.

We will call the concentration of soluble organics C, and call the initial concentration, the concentration that enters,  Ci. It’s about 200 ppm. We’ll call the output concentration Co, and for this type of reactors, Co = C.  The reaction is first order, approximately, so that, if there were no flow into or out of the reactor, the concentration of organics would decrease at the rate of

dC/dt = -kC.

Here k is a reaction constant, dependent on temperature oxygen and cell content. It’s typically about 0.5/hour. For a given volume of tank the rate of organic removal is VkC. We can now do a mass balance on soluble organics. Since the rate of organic entry is QCi and the rate leaving by flow is QC. The difference must be the amount that is reacted away:

QCi – QC = VkC.

We now use algebra, to find that

Co = Ci/(1 + kV/Q).

V/Q is sometimes called a residence time; for the system. At normal flow, the residence time of the South Lyon system is about 2.8 days or 68.6 hours. Plugging these numbers in, we find that the effluent from the reactor leaves at 1/35 of the input concentration, or 5.7 ppm, on average. This would be fine except that sometimes the temperature drops, or the flow increases, and we start violating the standard. A yet bigger problem was that the population increased by 50% while the EPA standard got more stringent to 2 ppm. This was solved by adding another, smaller reactor, volume = V2. Using the same algebraic analysis, as above you can show that, with two reactors,

Co = Ci/ [(1 + kV/Q)(1+kV2/Q)].

It’s a touchy system, but it meets government targets, just barely, most of the time. I think it is time to switch to a plug-flow reactor system, as used in much of Oakland county. In these, the fluid enters a channel and is reacted as it flows along. Each gallon of fluid, in a sense moves by itself as if it were its own reactor. In each gallon, we can say that dC/dt = -kC. We can thus solve for Co in terms of the total residence time, where t again is V/Q. We can rearrange this equation and integrate: ∫dC/C = – ∫kdt. We then find that, 

      ln(Ci/Co) = kt = kV/Q

To convert 200 ppm sewage to 2 ppm we note that Ci/Co = 100 and that V = Q ln(100)/k = Q (4.605/.5) hours. An inflow of 1000,000 gallons per day = 41,667 gal/ hour, and we find the volume of tank is 41,667 x 9.21 = 383,750 gallons. This is quite a lot smaller than the CSTR tanks at South Lyon. If we converted the South Lyon tanks to a plug-flow, race-track design, it would allow it to serve a massively increased population, discharging far cleaner sewage. 

Robert Buxbaum, November 17, 2019

The chemistry of lead in drinking water

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Our county, like many in the US and Canada, is served by thousands of miles of lead pipes. Some of these are the property of the government, others sit beneath our homes and are the property of the home-owner. These pipes are usually safe, but sometimes poison us. There is also problem of lead-tin solder. It was used universally to connect iron and copper pipes until it was outlawed in 1986. After years of sitting quietly, this lead caused a poisoning crisis in DC in 2004, and in Flint in 2015-16. Last month my town, Oak Park, registered dangerous lead levels in the drinking water. In an attempt to help, please find the following summary of the relevant lead chemistry. Maybe people in my town, or in other towns, will find some clue here to what’s going on, and what they can do to fix it.

lead pipes showing the three oxides: brown, yellow, and red, PbO2, PbO, and Pb2O3.

Left to itself, lead and solder pipe could be safe; lead is not soluble in clean water. But, if the water becomes corrosive, as happens every now and again, the lead becomes oxidized to one of several compounds that are soluble. These oxides are the main route of poisoning; they can present serious health issues including slow development, joint and muscle pain, memory issues, vomiting, and death. The legal limit for lead content in US drinking water is 15 ppb, a level that is far below that associated with any of the above. The solubility of PbO, lead II oxide, is more than 1000 times this limit 0.017 g/L, or 17,000 ppb. At this concentration serious health issues will show up.

PbO is the yellow lead oxide shown in the center of the figure above, right; the other pipes show other oxides, that are less-soluble, and thus less dangerous. Yellow lead oxide and red lead oxides on the right were used as paint colors until well into the 20th century. Red lead oxide is fairly neutral, but yellow PbO is a base; its solubility is strongly dependent on the PH of the water. In neutral water, its solution can be described by the following reaction.

PbO + H2O(l) –> Pb2+(aq) + 2 OH–(aq).

In high pH water (basic water), there are many OH–(aq) ions, and the solubility is lower. In low pH, acidic water the solubility is even higher. For every 1 point of lower pH the lowubility increases by a factor of 10, for every 1 point of higher pH, it decreases by a factor of ten. In most of our county, the water is slightly basic, about pH 8. It also helps that our water contains carbonate. Yellow lead forms basic lead carbonate, 2PbCO3·Pb(OH)2, the white lead that was used in paint and cosmetics. Its solubliity is lower than that of PbO, 110 ppb, in pure water, or within legal limit in water of pH 8. If you eat white lead, though, it reacts with stomach acid, pH 2, and becomes quite soluble and deadly. Remember, each number here is a factor of ten.

A main reason lead levels a very low today are essentially zero, even in homes with lead solder or pipe, involves involves the interaction with hypochlorite. Most water systems add hypochlorite to kill bacteria (germs) in the water. A side benefit is significant removal of lead ion, Pb2+(aq).

Pb2+(aq) + 2 ClO–(aq) –> Pb(ClO)2(s). 

Any dissolved lead reacts with some hypochlorite ion reacts to form insoluble lead hypochlorite. Lead hypochlorite can slowly convert to Lead IV oxide — the brown pyrophilic form of lead shown on the left pipe in the figure above. This oxide is insoluble. Alkaline waters favor this reaction, decreasing solubility, but unlike with PbO, highly alkaline waters provide no significant advantage.

PbClO+(aq) + H2O(l) –> PbO2(s) + 2 H+(aq) + Cl–(aq)

Lead IV oxide, PbO2 was used in old-fashioned matches; it reacts violently with phosphorus or sulfur. People were sometimes poisoned by sucking on these matches. In the stomach, or the presence of acidic drinking water, PbO2 is decomposed forming soluble PbO:

PbO2(s) +2 H+(aq) + 2 e– –> PbO(s) + H2O(l).

You may wonder at the presence of the two electrons in the reaction above. A common source in water systems is the oxidation of sulphite:

SO3-2(aq)–> SO4-2(aq) + 2 e–.

The presence of sulphite in the water means that hypochlorite is removed.

ClO–(aq) + 2 H+(aq) + 2 e– —> Cl–(aq) + H2O(l).

Removal of hypochlorite can present a serious danger, in part because the PbO2(s) slowly reverts to PbO and becomes soluble, but mostly because bacteria start multiplying. In the Flint crisis of 2016, and in a previous crisis in Washington DC, the main problem, in my opinion was a lack of hypochlorite addition. The lead crisis was preceded by an uptick in legionnaires disease; It killed 12 people in Flint in 2014 and 2015, and 87 were sickened, all before the lead crisis. Eventually, it was the rise of legionaries disease that alerted water officials in Virginia that there was something seriously wrong in Flint. Most folks were unaware because Flint water inspectors seem to have been fudging the lead numbers to make things look better.

Most US systems add phosphate to remove lead from the water. Flint water folks could have stopped the lead crisis, but not the legionnaires, by adding more phosphate. Lead phosphate solubility is 14 ppb at 20°C, and my suspicion is that this is the reason that the legal limit in the US is 15 ppb. Regulators chose 15 ppb, I suspect, not for health reasons, but because the target could be met easily through the addition of phosphate. Some water systems in the US and Canada disinfect with chloramine, not hypochlorite, and these systems rely entirely on phosphate to keep lead levels down. Excess phosphate is used in Canada to lower lead levels below 10 ppb. It works better on systems with hypochlorite.

Chloramine is formed by reacting hypochlorite with ammonia. It may be safer than hypochlorite in terms of chlorite reaction products, a real problem when the water source is polluted. But chloramine is not safe. It sickened 72 soldiers, 36 male and 36 female in 1998. They’d used ammonia and bleach for a “cleaning party” on successive days. Here’s a report and first aid instructions for the poisoning. That switching to chloramine can expose people to lead is called “the chloramine catch”.

Unlike PbO, PbO2 is a weak acid. PbO2 and PbO can react to form red lead, PbO•PbO2(s), the red stuff on the pipe at right in the picture above. Red lead can react with rust to form iron plumbable, an insoluble corrosion resister. A simple version is:

PbO•PbO2(s) + Fe2O3(s) —> 2FePbO3(s).

This reaction is the basis of red-lead, anti-rust compounds. Iron plumbable is considered to be completely insoluble in water, but like PbO it is soluble in acid. Bottom line, slightly basic water is good, as are hypochlorite in moderation, and phosphate.

Robert Buxbaum, November 18, 2019. I ran for water commissioner, and might run again. Even without being water commissioner, I’ll be happy to lend my expertise, for free, to any Michigan town or county that is not too far from my home.

Water Towers, usually a good thing.

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Most towns have at least one water tower. Oakland county, Michigan has four. When they are sized right, they serve several valuable purposes. They provide water in case of a power failure; they provide increased pressure in the morning when people use a lot of water showering etc.; and they allow a town to use smaller pumps and to pump with cheaper electricity, e.g. at night. If a town has no tower, all these benefits are gone, but a town can still have water. It’s also possible to have a situation that’s worse than nothing. My plan is to show, at the end of this essay, one of the ways that can happen. It involves thermodynamic properties of state i a situation where there is no expansion headspace or excess drain (most towers have both).

A typical water tower — spheroidal design. A tower of the dimensions shown would contain about 1/2 million gallons of water.

The typical tower stands at the highest point in the town, with the water level about 170 feet above street level. It’s usable volume should be about as much water as the town uses in a typical day. The reason for the height has to do with the operating pressure of most city-level water pipes. It’s about 75 psi and each foot of water “head” gives you about 0.43 psi. You want pressures about 75 psi for fire fighting, and to provide for folks in apartment buildings. If you have significantly higher pressures, you pay a cost in electricity, and you start losing a lot of water to leaks. These leaks should be avoided. They can undermine the roads and swallow houses. Bob Dadow estimates that, for our water system the leakage rate is between 15 and 25%.

Oakland county has four water towers with considerably less volume than the 130 million gallons per day that the county uses. I estimate that the South-east Oakland county tower, located near my home, contains, perhaps 2 million gallons. The other three towers are similar in size. Because our county’s towers are so undersized, we pay a lot for water, and our water pressure is typically quite low in the mornings. We also have regular pressure excursions and that leads to regular water-boil emergencies. In some parts of Oakland county this happens fairly often.

There are other reasons why a system like ours should have water towers with something more like one days’ water. Having a large water reserve means you can benefit from the fact that electric prices are the lowest at night. With a days’ volume, you can avoid running the pumps during high priced, day times. Oakland county loses this advantage. The other advantage to having a large volume is that it gives you more time to correct problems, e.g. in case of an electric outage or a cyber attack. Perhaps Oakland thinks that only one pump can be attacked at one time or that the entire electric grid will not go out at one time, but these are clearly false assumptions. A big system also means you can have pumps powered by solar cells or other renewable power. Renewable power is a good thing for reliability and air pollution avoidance. Given the benefits, you’d expect Oakland county would reward towns that add water towers, but they don’t, as best I can tell.

Here’s one way that a water column can cause problems. You really need those pressure reliefs.

Now for an example of the sort of things that can go wrong in a water tower with no expansion relief. Every stand-pipe is a small water tower, and since water itself is incompressible, it’s easy to see that a small expansion in the system could produce a large pressure rise. The law requires that every apartment hose water system has to have expansion relief to limit these increases; The water tower above had two forms of reliefs, a roof vent, and an overflow pipe, both high up so that pressure could be maintained. But you can easily imagine a plumber making a mistake and installing a stand pipe without an expansion relief. I show a system like that at left, a 1000 foot tall water pipe, within a skyscraper, with a pump at the bottom, and pipes leading off at the sides to various faucets.

Lets assume that the pressure at the top is 20 psi, the pressure at the bottom will be about 450 psi. The difference in pressure (430 psi) equals the weight of the water divided by the area of the pipe. Now let’s imagine that a bubble of air at the bottom of the pipe detaches and rises to the top of the pipe when all of the faucets are closed. Since air is compressible, while water is not, the pressure at the bubble will remain the same as the bubble rises. By the time the bubble reaches the top of the pipe, the pressure there will rise to 450 psi. Since water has weight, 430 psi worth, the pressure at the bottom will rise to 880 psi = 450 + 430. This is enough to damage pump and may blow the pipes as well. A scenario like this likely destroyed the New Horizon oil platform to deadly consequences. You really want those pressure reliefs, and you want a competent plumber / designer for any water system, even a small one.

Robert Buxbaum, September 28- October 6, 2019. I ran for water commissioner is 2016.

Why does water cost what it does?

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Water costs vary greatly about Oakland county, and around the US, and I have struggled in vain to find out why. In part the problem is that each city gets to add as much maintenance and management costs as the city government thinks appropriate. High management and infrastructure fees can increase to the cost of water, but I also not that different cities about Oakland County Michigan get their water at different rates from the multi-county organization that oversees water in South East Michigan: GLWA, The Great Lakes Water Authority.

$112 water bill for zero usage. The base charge is so large that prices are essentially independent of useage.

I’ve attended meetings, both local and multi county and have tried to find out why one town gets its water at a far lower rate than another, near by. Towns get lower rates if they have a water tower, but it is not at all clear what the formula is. It also helps to separate the storm sewage from the sanitary sewage — something that I have proposed for all of Oakland county, but if there is fixed formula of how that affects rates, I’ve not seen it. And I wonder how well communities monitor the amount of storm sewage they generate.

The water itself is free. For the most part, in this county, we pump it from the Detroit river. Some of the rest of the water is pumped from wells. None of this costs anything. There is a pump cost, but it is manicure. Pumping 1 gallon of water up 75 feet, costs about 0.002¢ in pumping cost. The rest of the cost is infrastructure: the cost of the pumps, the pipes, the treatment, the billing and sewage. Among the sewage fees is a pollution penalty, and Oakland county pays plenty of pollution penalties. When it rains, we generate more sewage than the system will handle, and we dump the rest into the rivers and lakes. This results in closed beaches and poisoned fish, and fines too. The county pays the EPA when we do this, and the county passes the cost to the cities. I don’t know what the formula for fee distribution is, and don’t even know what it should be. What I do know is that we do this vastly too often.

Another oddity is that we bill on a per gallon basis. For my home, the bill is about 2¢/ gallon — 100 times the pumping cost. Though the city can claim that we are paying for infrastructure, both clean water infrastructure and sewage infrastructure, it seems odd to bill on a per-gallon used basis, and 1000 times the true per-gallon price. Since most of the price of water is the infrastructure and management cost, it seems like a regressive tax to charge people on the basis of per-gallon used. I also find it odd that cities do a propaganda campaign to tell folks to use less water. Why? I’d much prefer to charge a far lower base charge, and then bill significantly per-gallon. As with much that is socialist, the current system is inefficient, but pleasant for the management.

August 21, 20019, Robert Buxbaum

Kindness and Cholera in California

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California likely leads the nation in socially activist government kindness. It also leads the nation in homelessness, chronic homelessness, and homeless veterans. The US Council on Homelessnesses estimates that, on any given day, 129,972 Californians are homeless, including 6,702 family households, and 10,836 veterans; 34,332 people are listed among “the chronic homeless”. That is, Californians with a disability who have been continuously homeless for one year or cumulatively homeless for 12 months in the past three years. No other state comes close to these numbers. The vast majority of these homeless are in the richer areas of two rich California cities: Los Angeles and San Francisco (mostly Los Angeles). Along with the homeless in these cities, there’s been a rise in 3rd world diseases: cholera, typhoid, typhus, etc. I’d like to explore the relationship between the policies of these cities and the rise of homelessness and disease. And I’d like to suggest a few cures, mostly involving sanitation. 

A homeless encampment in LosAngeles

Most of the US homeless do not live in camps or on the streets. The better off US homelessness find it is a temporary situation. They survive living in hotels or homeless shelters, or they “couch-serf,” with family or friends. They tend to take part time jobs, or collect unemployment, and they eventually find a permanent residence. For the chronic homeless things are a lot grimmer, especially in California. The chronic unemployed do not get unemployment insurance, and California’s work rules tend to mean there are no part time jobs, and there is not even a viable can and bottle return system in California, so the homeless are denied even this source of income*. There is welfare and SSI, but you have to be somewhat stable to sign up and collect. The result is that California’s chronic homeless tend to live in squalor strewn tent cities, supported by food handouts.

Californians provide generous food handouts, but there is inadequate sewage, or trash collection, and limited access to clean water. Many of the chronic homeless are drug-dependent or mentally ill, and though they might  benefit from religion-based missions, Los Angeles has pushed the missions to the edges of the cities, away from the homeless. The excess food and lack of trash collection tends to breed rats and disease, and as in the middle ages, the rats help spread the diseases. 

Total homelessness by state, 2018; California leads the nation. The better off among these individuals do not live on the streets, but in hotels or homeless shelters. For most, this is a short term situation. The rest, about 20%, are chronically homeless. About half of these live on the streets without adequate sewage and water. Many are drug-dependent.

The first major outbreaks of the homeless camps appeared in Los Angeles in August and September of 2017. They reappeared in 2018, and by late summer, rates were roughly double 2017’s. This year, 2019, looks like it could be a real disaster. The first case of a typhoid infected police officer showed up in May. By June there were six police officers with typhoid, and that suggests record numbers are brewing among the homeless.

To see why sanitation is an important part of the cure, it’s worth noting that typhoid is a disease of unclean hands, and a relative of botulism. It is spread by people who go to the bathroom and then handle food without washing their hands first. The homeless camps do not, by and large, have hand washing stations. and forced hygiene is prohibited. Los Angeles has set up porta-potties, with no easy hand washing. The result is typhoid epidemic that’s even affecting the police (six policemen in June!).

rate od disease spread.
R-naught, reproduction number for some diseases, CDC.

Historically, the worst outbreaks of typhoid were spread by food workers. This was the case with “typhoid Mary of the early 20th century.” My guess is that some of the police who got typhoid, got it while trying to feed the needy. If so, this fellow could become another Typhoid Mary. Ideally, you’d want shelters and washing stations where the homeless are. You’d also want to pickup the dirtier among the homeless for forced washing and an occasional night in a homeless shelter. This is considered inhumane in Los Angeles, but they do things like this in New York, or they did.

Typhus is another major disease of the California homeless camps. It is related to typhoid but spread by rodents and their fleas. Infected rodents are attracted to the homeless camps by the excess food. When the rodents die, their infected fleas jump to the nearest warm body. Sometimes that’s a person, sometimes another animal. In a nastier city, like New York, the police come by and take away old food, dead animals, and dirty clothing; in Los Angeles they don’t. They believe the homeless have significant squatters rights. California’s kindness here results in typhus.

Reproduction number and generation time for some diseases.

The last of the major diseases of the homeless camps is cholera. It’s different from the others in that it is not dependent on squalor, just poor health. Cholera is an airborne disease, spread by coughing and sneezing. In California’s camps, the crazy and sick dwell close to each other and close to healthy tourists. Cholera outbreaks are a predictable result. And they can easily spread beyond the camps to your home town, and if that happens a national plague could spread really fast.

I’d discussed R-naught as a measure of contagiousness some months ago, comparing it to the reproductive number of an atom bomb design, but there is more to understanding a disease outbreak. R-naught refers merely to the number of people that each infected person will infect before getting cured or dying. An R-naught greater than one means the disease will spread, but to understand the rate of spread you also need the generation time. That’s the average time between when the host becomes infected, and when he or she infects others. The chart above shows that, for cholera, r-naught is about 10, and the latency period is short, about 9 days. Without a serious change in California’s treatment of the homeless, each cholera case in June will result in over 100 cases in July, and well over 10,000 in August. Cholera is somewhat contained in the camps, but once an outbreak leaves the camps, we could have a pandemic. Cholera is currently 80% curable by antibiotics, so a pandemic would be deadly.

Hygiene is the normal way to prevent all these outbreaks. To stop typhoid, make bathrooms available, with washing stations, and temporary shelters, ideally these should be run by the religious groups: the Salvation Army, the Catholic Church, “Loaveser and Fishes”, etc. To prevent typhus, clean the encampments on a regular basis, removing food, clothing, feces and moving squatters. For cholera, provide healthcare and temporary shelters where people will get clean water, clean food, and a bed. Allow the homeless to work at menial jobs by relaxing worker hiring and pay requirements. A high minimum wage is a killer that nearly destroyed Detroit. Allow a business to hire the homeless to sweep the street for $2/hour or for a sandwich, but make a condition that they wash their hands, and throw out the leftovers. I suspect that a lot of the problems of Puerto Rico are caused by a too-high minimum wage by the way. There will always be poor among you, says the Bible, but there doesn’t have to be typhoid among the poor, says Dr. Robert Buxbaum.

*California has a very strict can and bottle return law where — everything is supposed to be recycled– but there are very few recycling centers, and most stores refuse to take returns. This is a problem in big government states: it’s so much easier to mandate things than to achieve them.

July 30, 2019. I ran for water commissioner in Oakland county, Michigan, 2016. If there is interest, I’ll run again. One of my big issues is clean water. Oakland could use some help in this regard.

How to avoid wet basements

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My house is surrounded my mulch — it absorbs enough rainwater that I rarely have to water.

Generally speaking water gets to your basement from rain, and the basic way you avoid wet basements is by providing some more attractive spot for the rainwater to go to. There are two main options here: divert the water to a lake or mulch-filled spot at least 8 feet away from your home, or divert it to a well-operated street or storm drain. My personal preference is a combination of both.

At right I show a picture of my home taken on a particularly nice day in the spring. Out front is a mulch-filled garden and some grass. On the side, not shown is a driveway. Most of the rain that hits our lawn and gardens is retained in 4 inches of mulch, and waters the plants. Four inches of mulch-covered ground will hold at least four inches of rainwater. Most of the rain that hits the house is diverted to downspouts and flows down the driveway to the street. Keeping some rainwater in the mulch means you don’t have to pay so much to water the trees and shrubs. The tree at the center here is an apple tree. I like fruit trees like this, they really suck up water, and I like the apples. We also have blueberries and roses, and a decorative pear (I like pears too, but they are messy).

In my opinion, you want some slope even in the lawn area, so excess rainwater will run to the sewers and not form a yard-lake, but that’s a professional preferences; it’s not always practical and some prefer a brief (vernal ) lake. A vernal lake is one that forms only in the spring. If you’ve got one, you may want to fill it with mulch or add trees that are more water tolerant than the apple, e.g. swamp oak or red cedar. Trees remove excess water via transpiration (enhanced evaporation). Red Cedars grow “knees” allowing them to survive with their roots completely submerged.

For many homes, the trick to avoiding a flooded basement is to get the water away from your home and to the street or a retention area.

When it comes to rain that falls on your hose, one option is to send it to a vernal lake, the other option is to sent it to the street. If neither is working, and you find water in your basement, your first step is to try to figure out where your rainwater goes and how it got there. Follow the water when it’s raining or right after and see where it goes. Very often, you’ll discover that your downspouts or your driveway drain into unfortunate spots: spots that drain to your basement. To the extent possible, don’t let downspout water congregate in a porous spot near your house. One simple correction is to add extenders on the downspouts so that the water goes further away, and not right next to your wall. At left, I show a simple, cheap extender. It’s for sale in most hardware stores. Plastic or concrete downspout pans work too, and provide a good, first line of defense agains a flood basement. I use several to get water draining down my driveway and away from the house.

Sometimes, despite your best efforts, your driveway or patio slopes to your house. If this is the case, and if you are not quite ready to replace your driveway or patio, you might want to calk around your house where it meets the driveway or patio. If the slope isn’t too great, this will keep rainwater out for a while — perhaps long enough for it to dry off, or for most of the rainwater to go elsewhere. When my driveway was put in, I made sure that it sloped away from the house, but then the ground settled, and now it doesn’t quite. I’ve put in caulk and a dirt-dam at the edge of the house. It keeps the water out long enough that it (mostly) drains to the street or evaporates.

A drain valve. Use this to keep other people’s sewer water out of your basement.

There is one more source of wet basement water, one that hits the houses in my area once a year or so. In our area of Oakland county, Michigan, we have combined storm and sanitary sewers. Every so often, after a big rain, other people’s rainwater and sanitary sewage will come up through the basement drains. This is really a 3rd world sewer system, but we have it this way because when it was put in, in the 1900s, it was first world. One option if you have this is to put in a one-way drain valve. There are various options, and I suggest a relatively cheap one. The one shown at right costs about $15 at Ace hardware. It will keep out enough water, long enough to protect the important things in your home. The other option, cheaper and far more hill-billy, is to stuff rags over your basement drains, and put a brick over the rags. I’ll let you guess what I have in my basement.

Robert Buxbaum, June 13, 2019

Why concrete cracks and why sealing is worthwhile

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The oil tanker Palo Alto is one of several major ships made with concrete hulls.

The oil tanker Palo Alto is one of several major ships made with concrete hulls.

Modern concrete is a wonderful construction material. Major buildings are constructed of it, and major dams, and even some ships. But under the wrong circumstances, concrete has a surprising tendency to crack and fail. I thought I’d explain why that happens and what you can do about it. Concrete does not have to crack easily; ancient concrete didn’t and military or ship concrete doesn’t today. A lot of the fault lies in the use of cheap concrete — concrete with lots of filler — and with the cheap way that concrete is laid. First off, the major components of modern concrete are pretty uniform: sand and rock, Portland cement powder (made from cooked limestone, mostly), water, air, and sometimes ash. The cement component is what holds it all together — cements it together as it were — but it is not the majority of even the strongest concretes. The formula of cement has changed too, but the cement is not generally the problem. It doesn’t necessarily stick well to the rock or sand component of concrete (It sticks far better to itself) but it sticks well enough that spoliation, isn’t usually a problem by itself.

What causes problem is that the strength of concrete is strongly affected (decreased) by having lots of sand, aggregate and water. The concrete used in sidewalks is as cheap as possible, with lots of sand and aggregate. Highway and wall concrete has less sand and aggregate, and is stronger. Military and ship concrete has little sand, and is quite a lot stronger. The lowest grade, used in sidewalks, is M5, a term that refers to its compressive strength: 5 Mega Pascals. Pascals are European (Standard International) units of pressure and of strength. One Pascal is one Newton per square meter (Here’ a joke about Pascal units). In US (English) units, 5 MPa is 50 atm or 750 psi.

Ratios for concrete mixes of different strength.

Ratios for concrete mixes of different strength; the numbers I use are double these because these numbers don’t include water; that’s my “1”.

The ratio of dry ingredients in various concretes is shown at right. For M5, and including water, the ratio is 1 2 10 20. That is to say there is one part water, two parts cement, 10 parts sand, and 20 parts stone-aggregate (all these by weight). Added to this is 2-3% air, by volume, or nearly as much air as water. At least these are the target ratios; it sometimes happens that extra air and water are added to a concrete mix by greedy or rushed contractors. It’s sometimes done to save money, but more often because the job ran late. The more the mixer turns the more air gets added. If it turns too long there is extra air. It the job runs late, workers will have to add extra water too because the concrete starts hardening. I you see workers hosing down wet concrete as it comes from the truck, this is why. As you might expect, extra air and water decrease the strength of the product. M-10 and M-20 concrete have less sand, stone, and water as a proportion to cement. The result is 10 MPa or 20 MPa strength respectively.

A good on-site inspector is needed to keep the crew from adding too much water. Some water is needed for the polymerization (setting) of the concrete. The rest is excess, and when it evaporates, it leaves voids that are similar to the voids created by having air mix in. It is not uncommon to find 6% voids, in commercial concrete. This is to say that, after the water evaporates, the concrete contains about as much void as cement by volume. To get a sense of how much void space is in the normal concrete outside your house, go outside to a piece of old concrete (10 years old at least) on a hot, dry day, and pour out a cup of water. You will hear a hiss as the water absorbs, and you will see bubbles come out as the water goes in. It used to be common for cities to send inspectors to measuring the void content of the wet (and dry) concrete by a technique called “pycnometry” (that’s Greek for density measurement). I’ve not seen a local city do this in years, but don’t know why. An industrial pycnometer is shown below.

Pyncnometer used for concrete. I don't see these in use much any more.

Pycnometer used for concrete. I don’t see these in use much any more.

One of the main reason that concrete fails has to do with differential expansion, thermal stress, a concept I dealt with some years ago when figuring out how cold it had to be to freeze the balls off of a brass monkey. As an example of the temperature change to destroy M5, consider that the thermal expansion of cement is roughly 1 x 10-5/ °F or 1.8 x10-5/°C. This is to say that a 1 meter slab of cement that is heated or cooled by 100°F will expand or shrink by 10-3 m respectively; 100 x 1×10-5 = 10-3. This is a fairly large thermal expansion coefficient, as these things go. It would not cause stress-failure except that sand and rock have a smaller thermal expansion coefficients, about 0.6×10-5 — barely more than half the value for cement. Consider now what happens to concrete that s poured in the summer when it is 80°F out, and where the concrete heats up 100°F on setting (cement setting releases heat). Now lets come back in winter when it’s 0°F. This is a total of 100°F of temperature change. The differential expansion is 0.4 x 10-5/°F x 100°F =  4 x10-4 meter/meter = 4 x10-4 inch/inch.

The force created by this differential expansion is the elastic modulus of the cement times the relative change in expansion. The elastic modulus for typical cement is 20 GPa or, in English units, 3 million psi. This is to say that, if you had a column of cement (not concrete), one psi of force would compress it by 1/3,000,000. The differential expansion we calculated, cement vs sand and stone is 4×10-4 ; this much expansion times the elastic modulus, 3,000,000 = 1200 psi. Now look at the strength of the M-5 cement; it’s only 750 psi. When M-5 concrete is exposed to these conditions it will not survive. M-10 will fail on its own, from the temperature change, without any help needed from heavy traffic. You’d really like to see cities check the concrete, but I’ve seen little evidence that they do.

Water makes things worse, and not only because it creates voids when it evaporates. Water also messes up the polymerization reaction of the cement. Basic, fast setting cement is mostly Ca3SiO5

2Ca3SiO5 + 6 H2O –> 3Ca0SiO2•H2O +3Ca(OH)2•H2O.

The former of these, 3Ca0SiO2•H2O, forms something of a polymer. Monomer units of SiO4 are linked directly or by partially hydrated CaO linkages. Add too much water and the polymeric linkages are weakened or do not form at all. Over time the Ca(OH)2 can drain away or react with  CO2 in the air to form chalk.

concrete strength versus-curing time. Slow curing of damp concrete helps; fast dry hurts. Carbonate formation adds little or no strength. Jehan Elsamni 2011.

Portland limestone cement strength versus curing time. Slow curing and damp helps; fast dry hurts. Carbonate formation adds little or no strength. Jehan Elsamni 2011.

Ca(OH)2 + CO2 → CaCO3 + H2O

Sorry to say, the chalk adds little or no strength, as the graph at right shows. Concrete made with too much water isn’t very strong at all, and it gets no stronger when dried in air. Hardening goes on for some weeks after pouring, and this is the reason you don’t drive on 1 too 2 day old concrete. Driving on weak concrete can cause cracks that would not form if you waited.

You might think to make better concrete by pouring concrete in the cold, but pouring in the cold makes things worse. Cold poured cement will expand the summer and the cement will detach from the sand and stone. Ideally, pouring should be in spring or fall, when the temperature is moderate, 40-60°F. Any crack that develops grows by a mechanism called Rayleigh crack growth, described here. Basically, once a crack starts, it concentrates the fracture forces, and any wiggling of the concrete makes the crack grow faster.

Based on the above, I’ve come to suspect that putting on a surface coat can (could) help strengthen old concrete, even long after it’s hardened. Mostly this would happen by filling in voids and cracks, but also by extending the polymer chains. I imagine it would be especially helpful to apply the surface coat somewhat watery on a dry day in the summer. In that case, I imagine that Ca3SiO5 and Ca(OH)2 from the surface coat will penetrate and fill the pores of the concrete below — the sales pores that hiss when you pour water on them. I imagine this would fill cracks and voids, and extend existing CaOSiO2•H2O chains. The coat should add strength, and should be attractive as well. At least that was my thought.

I should note that, while Portland cement is mostly Ca3SiO5, there is also a fair amount (25%) of Ca2SiO4. This component reacts with water to form the same calcium-silicate polymer as above, but does so at a slower rate using less water per gram. My hope was that this component would be the main one to diffuse into deep pores of the concrete, reacting there to strengthen the concrete long after surface drying had occurred.

Trump tower: 664', concrete and glass. What grade of concrete would you use?

Trump tower: 664′, concrete and glass. What grade of concrete would you use?

As it happened, I had a chance to test my ideas this summer and also about 3 years ago. The city inspector came by to say the concrete flags outside my house were rough, and thus needed replacing, and that I was to pay or do it myself. Not that I understand the need for smooth concrete, quite, but that’s our fair city. I applied for a building permit to apply a surface coat, and applied it watery. I used “Quickrete” brand concrete patch, and so far it’s sticking OK. Pock-holes in the old concrete have been filled in, and so far surface is smooth. We’ll have to see if my patch lasts 10-20 years like fresh cement. Otherwise, no matter how strong the concrete becomes underneath, the city will be upset, and I’ll have to fix it. I’ve noticed that there is already some crumbling at the sides of flags, something I attribute to the extra water. It’s not a problem yet, but hope this is not the beginning of something worse. If I’m wrong here, and the whole seal-coat flakes off, I’ll be stuck replacing the flags, or continuing to re-coat just to preserve my reputation. But that’s the cost of experimentation. I tried something new, and am blogging about it in the hope that you and I benefit. “Education is what you get when you don’t get what you want.” (It’s one of my wise sayings). At the worst, I’ll have spent 90 lb of patching cement to get an education. And, I’m happy to say that some of the relatively new concrete flags that the city put in are already cracked. I attribute this to: too much sand, air, water or air (they don’t look like they have much rock): Poor oversight.

Dr. Robert E. Buxbaum. March 5, 2019. As an aside, the 664 foot Trump Tower, NY is virtually the only skyscraper in the city to be built of concrete and glass. The others are mostly steel and glass. Concrete and glass is supposed to be stiffer and quieter. The engineer overseeing the project was Barbara Res, the first woman to oversee a major, NY building project. Thought question: if you built the Trump Tower, which quality of concrete would you use, and why.

Great waves, small circles, and the spread of ideas.

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Simplified wave motion, GIf by Dan Russel (maybe? I think?).

The scientific method involves looking closely at things. Sometimes we look closely for a purpose — to make a better mouse-trap, say. But sometimes it’s just to understand what’s happening: to satisfy curiosity, to understand the way the world works, or to answer a child. Both motivations bring positive results, but there is a difference in how people honor the product of these motivations. Scientific knowledge developed for curiosity is considered better; it tends to become the model for social understanding, and for art and literature. Meanwhile, science developed for a purpose is considered suspect, and often that suspicion is valid. A surprising amount of our knowledge was developed for war: for the purpose of killing people, destroying things, and occupying lands.

Waves provide a wonderful example of science exploration that was developed mostly for curiosity, and so they have become models of social understanding and culture — far more so than the atom bomb and plague work discussed previously.

Waves appear magical: You poke a pond surface with a stick, and the influence of that poke travels, as if by magic, to all corners of the pond. Apparently the initial poke set off something, and that sets off something else, and we’ve come to use this as a model for cultural ideas. Any major change in music, art, or cultural thought is described as a wave (and not as a disease). The sense of wave is  that a small push occurs, and the impact travels across a continent and across an ocean. The Gifs above and below shows how this happens for the ordinary wave — the one with a peaked top. As shown, the bits of water do not move with the wave. Instead they just circulate in a small circle. The powerful waves that crosses an ocean are composed of many small circles of water rolling in the general direction of the wave. With ideas too, I think, one person can push a second, and that second a third, each acting in his or her own circle, and a powerful transmission of ideas results. Of course, for a big wave, you need a big circle, but maybe not in cases of reflection (reflected waves can add, sometimes very destructively).

simplified wave movement

In the figures I’ve shown, you will notice that the top of the circle always moves in the same direction as the top of the wave. If the wave moves to the right, the circle is clockwise. There are also Rayleigh waves. In these, the top of the wave is not peaked, but broad, with little indents between ripples. For Rayleigh wave the motion is not circular, but elliptical, and the top of the ellipse moves in the opposite direction to that of the wave. These waves go slower than the normal waves, but they are more destructive. Most of the damage of earthquakes is by the late-arriving Rayleigh waves.

If regular waves are related to fast-moving ideas, like rock n roll, Rayleigh waves might be related to slower-traveling, counter-intuitive ideas, paradigm shifts: Religions, chaos, entropy, feminism, or communism. Rayleigh waves are mostly seen in solids, and the destructive power of counter-intuitive ideas is mostly seen in rigid societies.

Then there are also pressure waves, like sound, and wiggle waves (transverse waves). Pressure waves travel the fastest, and work in both solids and liquids. Wiggle waves travel slower (and don’t travel in liquids). Both of these involve no circles at all, but just one bit of material pushing on its neighbor. I think the economy works this way: bouncing springs, for the most part. Life is made up of all of these, and life is good. The alternative to vibration, I should mention, is status. Status is a form of death. There is a certain sort of person who longs for nothing more than an unchanging, no-conflict world: one government and one leadership. Avoid such people.

Robert Buxbaum, February 10, 2019

Water Conservation for Michigan – Why?

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The Michigan Association of Planners is big on water conservation, joining several environmental groups to demand legislation requiring water conservation:

POLICY 4. Water Conservation: The Michigan Association of Planning supports state legislation requiring water conservation for public, and private users.

Among the classic legislation passed so far are laws requiring low flush toilets, and prohibiting high-volume shower heads as in this Seinfeld episode. I suppose I should go along: I’m running for water commissioner, and consider myself a conservationist. The problem is, I can’t see a good argument for these laws for most people here in Oakland County, or in neighboring Macomb and Wayne Counties. The water can’t run out because most users take it from the river and return it to the river, cleaned after it’s used; it’s all recycled.

Map of the main drinking-water pipes serving south-east Michigan

Map of the main drinking-water pipes serving south-east Michigan

The map above shows the clean water system for south-east Michigan. The high-population areas, the ones that are colored in the map, get their water from the Detroit River or from Lake Huron. It’s cleaned, pumped, and carried to your home along the pipes shown. Then after you’ve used the water, it travels back along another set of pipes to the water treatment plant and into the Detroit River.

Three-position shower head -- a wonderful home improvement I got it at universal plumbing.

Three-position shower head — a wonderful home improvement. I got it at universal plumbing.

When the system is working well, the water we return to the Detroit River is cleaner than the water we took in. So why legislate against personal use? If a customer wants to enjoy a good shower, and is willing to pay for the water at 1.5¢ per gallon, who cares how much water that customer uses? I can understand education efforts, sort-of, but find it hard to push legislation like we have against a high-volume shower head. We can not run out, and the more you use, the less everyone pays per gallon. A great shower head is a great gift idea, in my opinion.

The water department does not always work well, by the way, and these problems should be solved by legislation. We give away, for $200/year, high value clean water to Nestle company and then buy it back for $100,000,000. That’s a problem. Non-flushable toilet wipes are marketed as flushable; this causes sewer blockades. Our combined sewers regularly dump contaminated water into our rivers, lakes, and basements. These problems can be solved with legislation and engineering. It’s these problems that I’m running to solve.

Robert Buxbaum, January 6, 2019. If you want to save water, either to save the earth, or because you are cheep, here are some conservation ideas that make sense (to me).

We don’t need no stinking primary clarifier

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Virtually every sewage plant of Oakland County uses the activated sludge process, shown in the layout below. Raw sewage comes in, and goes through physical separation — screening, grit removal, and a first clarifier – settling tank before moving to the activated sludge oxidation reactor. The 1st clarifier, shown at left below, removes about half of the incoming organics, but it often stinks and sometimes it “pops” bubbles of fart. This is usually during periods of low flow, like at night. When the flow is slow, it arrives at the plant as a rotting smelly mess; it’s often hard to keep the bubbles of smell down.

Typical Oakland Sewage plant, activated sludge process with a primary clarifier.

Typical Oakland County Sewage treatment plant, activated sludge process with a primary clarifier.

The smell is much improved in the oxidation reactor, analyzed here, and in the 2nd clarifier, shown above at right. Following that is a filter, an ultraviolet cleanup stage, and the liquids are discharged to a local river. In Oakland county, the solids from the two clarifiers are hauled off to a farm, or buried in a landfill. Burial in a landfill is a costly waste, as I discuss here. The throughputs for most of these treatment plants is only about 2-3 million gallons of sewage per day. But Oakland county can produce 500 million gallons of sewage per day. The majority of this goes to Detroit for treatment, and sometimes the overflow is dumped rotting and smelly, in the rivers.

A few months ago, I visited the Sycamore Creek Wastewater facility outside of Cincinnati. This is an 8 million gallon per day plant that uses the “extended aeration process”, shown in the sketch below. I noticed several things I liked: the high throughput (the plant looks no bigger than our 2-3 million gallon plants) and the lack of a bad smell, primarily. The Sycamore Creek plant had an empty hole where the primary clarifier had once been. Lacking this clarifier, the screened sewage could not sit and pop. Instead it goes directly from grit removal to the oxidation reactor, a reactor that looks no bigger than in our plants. This reactor manages a four times higher throughput, I think, because of a higher concentration of cellular catalyst. Consider the following equation derived in a previous post:

ln C°/C = kV/Q.

Here, C° and C are the incoming and exit concentrations of soluble organic; k is the reaction rate, proportional to cellular concentration, V is the volume of the reactor, Q is the flow, and ln is natural log. The higher cellular concentration in the extended aeration plant results in an increased reaction rate, k. The higher the value of k, the higher the allowed flow, Q, per reactor volume, V.

The single clarifier at the end of the Sycamore Creek plant does not look particularly big. My sense is that it deals with a lot more sludge and flow than is seen in our 2nd clarifiers because (I imaging) the sludge is higher density, thus faster settling. I expect that, without the 1 clarifier, there is extra iron and sulfate in the sludge, and more large particles too. In our plants, a lot of these things are removed in the primary clarifier. Sludge density is also increased, I think, because the Cincinnati plant recycle a greater percentage of the sludge (I list it as 90% in the diagram). Extra iron in the reactor also helps to remove phosphates from the water effluent that flows back to the river, an important pollution concern. Iron phosphates are insoluble, and thus leave with the sludge. In Oakland county’s activated sludge plants, it is typical to add iron to the reactor or clarifier. In Cincinnati’s extended aeration plant, I’m told, iron addition is generally not needed.

Typical Oakland Sewage plant, activated sludge process with a primary clarifier.

Cincinnati sewage treatment plant, extended aeration process with no primary clarifier.

The extended aeration part of the above process refers to the secondary sludge oxidizer, the continuously stirred tank reactor, or CSTR shown at lower right above. The “CSTR” is about 1/5 the volume of the main oxidation reactor and about the size of a clarifier. Oxidation in the CSTR compliments that in the main oxidizer removing organics, making bio-polymer, and improving (I think) the quality of the sludge that goes to the farms. Oxidation in the CSTR reduces the amount of sludge that goes to the farms. The sludge that does go, is  less-toxic and more concentrated in organics and minerals. I’m not sure if the CSTR product is as good as the product from an anaerobic digester, or if the CSTR is cheaper to operate, but it looks cheaper since there is no roof, and no (or minimal) heating. This secondary oxidizer is very efficient at removing organics because the cellular catalyst concentration is very high – much higher than in the main oxidizer.

During periods of high load, early morning, the CSTR seems to serve as a holding tank so that sludge does not build up in the clarifier. Too much sludge in the clarifier can start to rot, and ruin the effluent quality. The way you tell if there is too much sludge, by the way, is through a device called the “sludge judge.” I love that name. The Cincinnati plant used a centrifugal drier; none of our plants do. The Cincinnati plant had gap the bubble spots of the main oxidizer. This is good for denitrification, I’m told, an important process that I discuss elsewhere.

The liquid output of their clarifier (or ours) is not pure enough to be sent directly to the river. In this plant, the near-pure water from the clarifier is sent to a trickling filter, a bed of sand and anthracite that removes colloidal remnants. Some of our plants do the same. I suspect that the large surface area in this filter is also home to some catalysis: last stage oxidation of remaining bio-organics. On a regular basis, the filter bed is reverse-flushed to remove cellular buildup, slime, and send it to the beginning of the process. The trickling filter output is then sent to an ultraviolet, bacteria-killing step before being released to the rivers. All in all, I suspect that an extended aeration process like this is worth looking into for Oakland County, especially for our North Pontiac sewage treatment facility. That plant is particularly bad smelling, and clearly too small to treat all its sewage. Perhaps we can increase the throughput and decrease the smell at a minimal cost.

Dr. Robert E. Buxbaum, December 18, 2018. I’m running for water commissioner of Oakland county, MI. If you like, visit my campaign site. Here are some sludge jokes and my campaign song.