I looked around myself and I thought,
What would I give the world if I could give them anything? What would everyone find useful — what would no one turn down? What could I afford to give them?
I could give them all water, I thought.
[The below concept is not patented and is now in the public domain, so now that it’s been made plain/obvious it’ll be harder to patent/shelve/ignore. The only thing I would request is lunch with Elon Musk, who inspired the work. Maybe even just a symbolic glass of water.]
The modest success of my previous post, “Why I know the world isn’t real” — has prompted me to write this follow up.
After all, what would subsurface ‘artificial river’ hydro (a.k.a. Boring Company tunnels) be without reverse osmosis desalinated water to drive it, offshore wind to supply it, geothermal pumps to leverage the inevitable heat gradients, and countercurrent compressed air heat exchangers to reduce the cost of operating our carbon-unfriendly HVAC systems?
Um, don’t answer that…
Since I’ve already shown the ruse is up — that the world isn’t real — this time I’ll get right to it…
- Reverse osmosis desalinated water
Okay, I must digress briefly…my water ‘pitch’…
Humans run on water.
Both literally and figuratively. A liter an hour for actual running running, more or less depending on temperature and humidity (and yes, I studied that, too.) In first world countries, their all-uses consumption aggregate averages about 75 gallons per day. About two cubic meters per seven people.
Yeah, we “forgot” about this. Almost a third of a cubic meter per person daily, which is currently provided, for the most part, no-questions-asked-at-the-end-of-the-day by weather systems.
And there’s no sense crying about it, either, because not only are tears salty (no shortage of salt water), but as sophisticated as water treatment facilities may be, they will NEVER do their jobs for a lower total energy cost per unit water than weather systems (or reverse osmosis of seawater, for that matter.)
Here…
Source: https://www.epa.gov/sites/production/files/2017-06/documents/wastewater-guide.pdf
From the EPA data above, a quick conversion from MG (million gallons) to m³ translates to a conveyance energy of 0–3.7 kWh/m³, a treatment energy of 0.026–4.22 kWh/m³, and a distribution energy of 0.184–0.317 kWh/m³.
The aggregate range is thus
(0+0.026+0.184) to (3.7+4.22+0.317) or 0.21–8.24 kWh/m³
For end-to-end water treatment as compared to conventional seawater desalination (3–10 kWh/m³) and subsurface desalination methods (2.46 kWh/m³)
At this point, I’d be pretty surprised if you weren’t asking, “Er…what?” and that’s even before I remind you that the conveyance and distribution costs are almost 100% determined by
THE ENERGY COST OF MOVING WATER
…which is what I tried to explain in my last post.
We’re literally attempting to micromanage the most important substance on the planet. All while
- noticing water shortages everywhere
- projecting increased resource usage (food, electricity, land) as the population grows
but…
- considering water consumption of increasingly modern civilizations essentially as an afterthought
and
- forgetting that as human civilizations grow — projected to be by about another 50% in the next 30 years — they will outpace the natural movements of water about the hydrosphere by approximately that same 50% — considering our current (relatively water-starved) populations as a reference point
In other words, we don’t have any choice but to scale up our water processing very significantly (and very soon), unless you consider widespread water rationing or otherwise overly restricting a resource that is 100% renewable when treated by renewable energy sources a sensible plan.
Pardon the emphasis, but the latter there doesn’t make any sense!
Look, even at the most aggressive (first world) estimate of 75 gallons (0.284 m³) water used per person per day, we’re still only talking about a total MAXIMUM energy cost for the processing itself of 1–2 kWh/day/person. Which, provided commercially (and sans carbon), is on the order of FIVE CENTS’ worth. Maybe even less than a nickel if we’re even moderately competent at engineering and conservation.
There is no reasonable argument to the contrary:
Of all things, we’re being Scrooges with WATER!
We haven’t focused *anywhere near* enough attention (or energy) on water and assuring that it’s going to be widely available. We’re basically taking it for granted, and we cannot afford to do that anymore. The conventional attitude in Western culture is “it’ll keep showing up” and the primary reason is because barely anyone in ‘proper culture’ thinks about or cares about ‘a few pennies.’
Here we have plenty of water and don’t care about pennies…virtually everywhere else in the world both the water AND the pennies matter.
Eventually, the fact that both those pennies and that water are meaningful to everyone else on the planet correspondingly means a conflict is brewing. To put it plainly, if we don’t sort this out (using an approach such as the one outlined below, or something better) sooner or later there will be fighting.
Do we really want to rely on having the most numerous and biggest guns at that point? a.k.a. the point when conventional weapons no longer matter and computerized warfare has become the norm? I for one hope not.
We’re couchsurfing it through the most epic challenge in human history, folks.
Where was I…?
Oh yes, reverse osmosis desalination.
We know we can do it, and we know it can be done cost effectively — with 100% renewable energy. And so, since we know we can, and we know we eventually have to anyway, the only question is how do we scale it up massively and efficiently? Yes, that’s where I was…
Berkeley has already done some work on this (thank you):
https://news.berkeley.edu/berkeley_blog/the-cost-of-irrigation-water-and-urban-farming/
The above study shows nonpotable (=the least treated) water to have a cost of about $1650/acre-foot and potable to be about $2115/acre-foot.
An acre-foot is equivalent to about 1233 m³ yielding a cost of:
$1.34/m³ (nonpotable) and $1.72/m³ (potable.)
which can also be expressed as:
$0.0051/gallon (nonpotable) and $0.0065/gallon (potable)
…with, AGAIN, the highest cost being associated with MOVING IT AROUND.
(Fair warning: I’m going to keep coming back to this point. It’s important.)
Are you ready to have your brain bleed a little?
What if I told you that the second highest cost isn’t even in the processing — at least not exactly?
Water is thermally resistant. It costs about 1 calorie per cm³ to heat by 1 Celsius degree. Assuming conventional subsurface temperatures of about 15°C (~59°F) and wastewater averages just 20°C, a mere 5 C differential…
(reference: http://web.deu.edu.tr/atiksu/ana52/aryen3.html)
and the average per-person use of 75 gallons per day…
=75 gallons/day * 264 gallons/m³ * 1.0 x 10⁶ cm³/m³ * 5 C°
= 1,420,455 calories/day
Wait, calories?
Yes, and since 860,420 thermochemical calories is equivalent to 1 kilowatt hour…
=1,420,455/860,420 = 1.65 kWh daily per person waste heat in water
*(without even considering inefficiencies in heating methods)*
At the U.S. average residential energy price of $0.126/kWh, this equals:
$0.208/day/person
The minimum cost of the waste heat in the water we use, per person!
Not even remotely debatable, sorry. And you’re worried about the vampiric energy draw of the little green LED on your dishwasher? Seriously?
This compared to the entire cost (Berkeley) of the (potable) water itself:
75 gallons * $0.0065/gallon = $0.4875/day/person
…and the treatment cost differential between potable and nonpotable:
$1.72–1.34 = $0.38/m³ * m³/264 gallons = $0.0014/gallon
which yields a per-person daily cost of $0.105 to have our water be drinkable versus nondrinkable water for residential use (In other words, it costs us almost exactly twice as much in residual heat FLUSHED DOWN THE DRAIN as it does to make sure the faucet water is drinkable versus not.)
and finally, comparing to the energy cost of reverse osmosis of seawater:
3–10 kWh/m³ (conventional) * $0.126/kWh (residential) = $0.378–1.26/m³
=$0.378–1.26/m³ * 75 gallons/person/day * 1 m³/264 gallons
= $0.107–0.358/day/person (reverse osmosis, conventional)
or via subsurface techniques:
= 2.46 kWh/m³ * $0.126/kWh (residential) = $0.310/m³
Which translates to:
$0.310/m³ * 75 gallons/person/day * 1 m³/264 gallons
= $0.088/day/person (reverse osmosis, subsurface)
We quite literally waste more than twice as much heat daily in the water we flush down the drain than it would cost us in energy to purify it by reverse osmosis.
I know it seems impossible, but it’s 100% true. And the reason is both simple and impossible to debate:
Not only is water terribly costly to move it’s also extremely resistant to temperature change.
In fact, as mentioned above, it requires about 1 calorie per cm³ to heat water by 1 Celsius degree, which means 1,000,000 calories for 1 m³…
=1.16 kWh/C° {to raise the temperature of a single m³ of water.}
Wait, but that means the per unit cost of reverse osmosis…is about the same as raising the same unit’s temperature just three degrees C…
Yep. Actually 2.59–8.62 degrees (vs. conventional approaches) and only 2.12 degrees using subsurface techniques.
Oh but it gets better. So very much better!
This is a reasonably mature technology. There’s nothing particularly challenging about implementing it, the difficulty in implementing it is doing so
1. at scale
2. using renewable energy
3. efficiently
Actually, that’s not challenging either. There’s literally no challenge at all to it. Well, aside from the regular humans arguing about it part.
We already know that:
- we have to source it from seawater.
Wastewater treatment is okay but excessive wastewater treatment (i.e. treating it beyond the nonpotable stage) is unnecessary. It’s actually harmful, in a way. Remember, we’re emptying aquifers all over the place and almost nowhere do we bother to consciously replenish them. And we’ve got farmers hurting for water. We seriously need to stop squeezing the farmers, guys. Remember, they are the ones most ultimately responsible for our food. They’re second in importance only to water.
I know tons of people are going to have a conniption fit about the above [true] statement but the reality is, considering the differential cost of potable versus nonpotable water ($465/acre-foot, or $0.377/m³) what possible reason would anyone have for processing it beyond the nonpotable stage? When an essentially infinite amount of seawater can be desalinated for far less than that price?
An even better question (then the answers):
Considering that the energy cost of seawater desalination trends to about $0.10/m³ [using renewable energy]— what possible reason would anyone have for paying $1650/acre-foot (=$1.34/m³) for NONPOTABLE water? When they could quite literally purify seawater for less than a tenth of that price?!
Obvious answer: Water is TERRIBLY hard to move.
Non-obvious answer: The effluent from RO desalination still represents a significant hurdle.
The approach I outline below overrides both of those problems. I detail it extensively, with actual figures. Like I said, Merry Christmas.
Conventional RO desalination, as mentioned, does require 3–10 kWh per cubic meter of purified water produced. To remove an objection which might otherwise be distracting, yes, it does require a facility and yes, it does require at least some human management. There ARE other costs associated with it.
Here:
The Claude “Bud” Lewis Carlsbad Desalination Plant — which cost $1B to build and was estimated by its opponents to cost San Diego County $108M per year — processes about 50 million gallons per day, and has been operational for four years. [I’m using the cost figures of its opponents as the outside (high) estimate of its operational cost. The true figure is undoubtedly somewhat lower. I did this to establish the (upper) boundary cost of water production.]
$1B + $108M*4 = $1.432B
4*365 = 1,460 days * 50M gallons/day = peak output of 73B gallons
Assuming ~90% up time yields about 65.7B gallons (actual uptime probably higher, resulting in marginally lower per unit water cost)
$1.432B/65.7B gallons
$0.0218/gallon inclusive of construction and operation TO DATE
or
$432M/65.7 billion gallons =
$0.0066/gallon considering operation alone
or
$432M + ($1B/40) = $457M/40 billion =
$0.0070/gallon if we assume the facility has a 40-year lifecycle at the current production rate.
Wait, that’s $1.85 per cubic meter assuming 40 year depreciation!
That’s like paying $2,278.58 for an acre-foot of potable water!
Yeah, and Berkeley came up with a figure of $2,115, so humor me for a few more minutes — because we know the figure above is probably pretty close.
What we’re trying to establish here are the component costs of clean water. We now know that the all-encompassing cost at the largest desalination facility in North America — one which incidentally uses 3.6 kWh/m³ of energy for the RO process itself — has an overall cost of $1.85/m³ produced.
We also know that’s made up of $1B for the plant itself, and approximately $108M per 18B gallons of peak production, or $0.006/gallon ($1.584/m³) of which 3.6 kWh * $0.1351/kWh (average commercial rate of power, San Diego) = $0.486/m³, or 30.7%, is due to RO process power consumption.
Most of the remaining 69.3% is for facility management and the energy cost of moving water, though it’s quite difficult to determine the breakdown any further.
Let’s at least figure out the minimum cost of moving the water…
Current research¹ shows a brine discharge rate 49.5% higher than the volume of purified water produced. Using this figure, assuming 90% pump efficiency and 85% pump energy recovery with a minimal 10m vertical pumping distance, we can readily arrive at the following figures for additional (pumping-related) net energy consumption:
190,000 m³ production, assume 90% facility uptime: 170,500 m³/day
Pump requirement: 170,500*2.49 (includes subsequent effluent volume) =
424,500 m³/day * 10 m vertical distance =
4.91 m³/s * 10 m * 1000kg/m³ * 0.9 (efficiency) =
434 kW * 24 =10,416 kWh/day (minimal pumping energy used)
…and assuming 85% reclamation of effluent gravitational potential energy:
170,500*1.49 =
2.94 m³/s * 10 m * 1000kg/m³ * 0.85 (return efficiency) =
245 kW * 24 = 5,880 kWh/day reclaimed
=4,536 kWh pumping energy per 170,500 m³ processed, or
0.027 kWh/m³ — per 10 m vertical distance pumped, minimum
¹https://www.sciencedirect.com/science/article/pii/S0048969718349167
In reality, even though the facility itself is located very near sea level, the required pumping must happen from a vertical displacement significantly greater than just 10 meters — considering especially that the effluent can’t merely be dumped directly adjacent to the coast. Requiring a more realistic minimum 30 m displacement, even with our conservative processing figures, yields 0.08 kWh/m³ — or 2.2% of the energy cost of the RO process itself.
This, actually, is all we needed to know.
Why, you ask?
Because I can show that 3.68 kWh*$0.1351 = $0.497/m³ plus infrastructure costs is significantly higher than an alternative process which can work much more effectively — simply by rearranging the parts and using existing technology.
A floating desalination plant can be built for not significantly more than a land-based plant, and with all things considered, possibly far less. This is known because:
(1) the footprint of the Carlsbad example above is comparable to the deck area of a ULCC supertanker
(2) the cost of a supertanker ($120M) is only 12% of the cost to install the Carlsbad plant
1+2 = floating desalination plant can be built for a rough cost of $1.12B
And that’s being very generous, because that comparison assumes the cost of six acres of Carlsbad, California coastline is zero, when in reality it’s more like $360,000/acre (~$2.1M/six acres) or more.
The land-based solution also carries with it significant local legal resistance, greater permitting costs, less operational freedom…
The reason why this is important is because:
(1) offshore wind is significantly more powerful than onshore wind, and it generally costs less per unit to produce than fossil-fuel based electricity production methods
(2) part of offshore wind’s higher cost is the requirement of power lines with which to transmit its power (~$9M/mile)¹, and associated transmission losses — conservatively not less than 2%
(3) moving liquid by tanker is second only to moving it by pipeline in terms of aggregate cost²
(4) moving already desalinated water costs approximately 60% less than moving (a greater volume of) seawater and then subsequently desalinating it, and this implies that when the system is designed correctly, moving desalinated water by tanker is cheaper than moving seawater by pipeline and only afterwards processing it
¹ https://www.nytimes.com/2010/03/17/business/energy-environment/17power.html
“And underwater lines are still more expensive than lines on transmission towers. Mr. Stern’s 65-mile cable cost about $600 million, and a 53-mile cable under San Francisco Bay cost about $505 million. Much of the cost in each case is to transform the electricity to direct current, a form that is easier to use in buried cables. Standard lines hung on towers run from $1 million to $4 million a mile, depending on terrain and other factors. If more underwater lines are built, the higher costs would have a small impact on electric bills.”
$600M/65 miles = $9.23M/mile
$505M/53 miles = $9.53M/mile
²https://transportgeography.org/?page_id=5711
Shows:
1 gal-US (3.785 l, 0.833 gal-imp) of fuel can move a ton of cargo 857 km by barge, or 337 km (209 mi) by rail, or 98 km (61 mi) by truck.
Pipelines, at roughly three times the efficiency of rail, would check in at 1,011 km/gallon, or about 18% better than conventional seabound shipping. Thus moving seawater to desalinate it by pipeline costs significantly more energy than moving the product (desalinated water) by conventional shipping the same or similar distance.
This is nothing more than an energy and cost balance equation, so I’m actually not giving the world water, per se. I’m giving it basic math.
Taken in aggregate, this data shows that:
(a) not only is it only marginally less expensive to locate desalination facilities terrestrially (more expensive when the data is taken in aggregate)
but
(b) it’s also significantly more expensive to power them
and
(c) it’s more expensive to process with them (!) — [as a consequence of having to move the costly-to-move raw material a further distance to the facility AND the 1.49X as heavy waste product a further distance away. Which is essentially done merely to save moving the (lighter) desired product a further, more economical distance. The whole point is to separate fresh water from salty; it’s rather obvious that the best way of doing this is clearly NOT to move a huge volume of salty water to where the desalination plant happens to be, process off just 40% of it and then put the other 60% back! DS plants have needed to be designed around this problem for a very long time.]
AND
(d) they’re functionally less versatile: “Hmm…where will we take this water today?”
AND
(e) locating them terrestrially ignores the problems of effluent (for them) and transmitting offshore wind energy (for ‘others’)—despite that the latter is one of our most promising green technologies
If that were only all, but that ISN’T all. It gets even better!
To break these points down one by one:
A. We know that a floating DS facility can be built for less than $120M more than the comparable (Carlsbad) facility. We also know that it would require an extreme amount of electricity:
For 190,000 m³/day of purified water, the RO process alone is equivalent to
190,000 * 3.6 kWh = 684,000 kWh required per day = 28.5 MW*24 hours
Running at 25% capacity consistently, this translates to a floating array of 114 MW capacity, or roughly 12–15 turbines at current maximum size.
We know that locating offshore (floating) wind turbines at 20 miles off the coast (~600m depth) would require something on the order of $180M in transmission lines. This cost would obviously one and a half of the envisioned DS tankers, but in order to appropriately assign an opportunity cost value to removing the line, we’d need to assume that if we had such a transmission line, we’d use it to maximum capacity.
Considering that undersea cables typically transmit at 150kV/600A =
90 MW
Source: https://www.emworks.com/blog/high-voltage/3-phase-high-voltage-submarine-power-cables
…and the fact that we generally do not want to throttle capacity when we can avoid it…
It appears as though a 114 MW capacity floating turbine array twenty miles off the coast and capable of filling one floating desalination facility/tanker per day could save us roughly $180M in transmission lines while costing less than $120M more than a domestic facility to build and simultaneously giving us access to cheaper, cleaner power AND more operational versatility.
Not only that, but considering that a significant percentage of the installation cost of offshore installations is due to the transmission cables themselves, the proposed solution correspondingly drops the generation price of the power. Yeah, those values DO stack.
To roughly calculate this:
If we assume a 90 MW offshore wind installation, operating at a consistent 25% capacity, can produce
90 MW * 0.25 * 365.25 days/year * 24 hours/day * 25 years/lifetime =
4.9 x 10⁶ MWh over its lifetime
In other words, 4.9 x 10⁹ kilowatt hours…the fractional cost of the installation of transmission line ($180M, assuming $9M/mile and 20 mile offshore site) is then:
$1.8 x 10⁸/4.9 x 10⁹ = $0.0367/kWh amortized (exclusive of transmission losses)
With the turbines themselves — at commercial grade, ~$1000/kW, ~$1M/MW = $90M/90MW— only costing about half that!
I’m sure you wish I were kidding at this point, but I’m not. Almost two-thirds of the cost of the installations are made up of getting the energy where it needs to go, and about half the end user cost of the electricity is in the transmission in this case.
[Note: our installation is larger than the comparison transmission line would support, but that’s okay because we’re not going to be transmitting the electricity back to shore. The per kWh comparison is valid regardless of the size of the offshore installation, assuming the same relative size and distance and correspondingly similar per kWh transmission line costs. ]
Yes, you say, but you still have to move the purified water back to shore. And that’s gonna cost you.
You’re quite right, it will. In fact, let’s calculate an annual cost:
- ULCC’s (that is, oil tankers of similar capacity) generally cost between $60–100K per day to the end lessor. On the low side, the vast majority of this cost is typically made up of bunker fuel — the high side changes primarily due to market volatility.
- Using $80,000/day as our estimate (and assuming, at first, we’ll use bunker fuel) yields an annual every-day-of-the-year lease price of about $29.2M, of which about a 75% is comprised of the bunker fuel costs. This figure jibes with the known operational life of the vehicles (40+ years) and cost to build (~$120M).
- Because we know that roughly $60,000 of this daily operational cost is associated with bunker fuel and we also know that the vessels conventionally spend about 85% of their time in motion…and because we also know that the rate at which they move (~15 knots = 17.3 mph) corresponds to a total in-motion time of approximately two and a half hours per day were they to be used as shuttles to a point 20 miles distant from the coast, we can similarly determine that their comparison fuel use would be about
2.5/24 = 1/12 versus 0.85/24
or 10.4% of a day versus 85%, a ratio of about 12.2% give or take.
This then yields a reduced even assuming they used bunker fuel total daily price of $27,320 — or an annual price of $9.98M.
You’ll note here that I calculated the facility costs two different ways — first by assuming ownership of the base vehicle ($120M) and now, here, by considering it a lease. In the final calculation, I’ll use the (higher) lease cost along with the corresponding facility depreciation figure I used before. While this will obviously make the costs considerably higher, it also serves to use a more realistic estimate of operational and maintenance costs than the one offered for the terrestrial location. Even though the calculation for the terrestrial facility’s production cost jibed with the Berkeley figure.
You’ll recall that I used a 40-year facility lifespan, and a $1B build cost.
Also that annual production was determined (at 90% uptime) to be (in m³ this time):
190,000 * 0.90 (% uptime) * 365.25 days/year = 62.46 x 10⁶ m³
…and over lifetime:
62.46 x 10⁶ m³ * (40) = 2.5 x 10⁹ m³ of water produced.
Adding the facility’s build cost and total RO process energy consumption to the annual lease cost times the facility lifespan gives us this:
$1B + (2.5 x 10⁹ m³ * ($0.07/kWh*3.6 kWh/m³) + $9.98M *40 =
$1B + ($630M) + ($399M) = $2.03B
$2.03B for 2.5B m³ of water, or $0.812/m³
Importantly, this includes basic staffing of the tanker and it includes the cost of transporting the water from the offshore facility to shore. [Note: I haven’t yet addressed where the turbine energy goes while the ship is in transit to or from shore, but you ought to know by now that I shortly will.]
This figure considers a very high estimate for the cost of offshore wind and a similarly aggressive estimate for the cost of the ship’s operation. It doesn’t factor in vertical integration — ownership of the component parts — and it doesn’t factor in what I keep referring to as the best part.
Adding that second tanker, but making it a ferry tanker rather than a desalination plant in itself — yields an added cost of $399M over its lifetime.
This would then total $2.43B for 2.5B m³ of water, or $0.972/m³
Which is about half (52.5%) of the conventional price of potable water calculated from the terrestrial plant ($1.85/m³), and more than 40% lower (56.6%) than the rate quoted in the Berkeley study.
And no, I still haven’t gotten to the best part — though if you’ve already read my last post you might have figured it out by now.
The summary, to this point, is not only can you
(1) use cheaper and 100% renewable energy (via offshore wind) to provide energy for the process
but you can
(2) transport it more cost effectively
(3) build the facility to process it for a roughly comparable cost
and
(4) essentially eliminate the problem of effluent water and its proximity to high concentrations of sea life/the shoreline
Wind power!
As of October, 2019, offshore wind prices amounted to $78/MWh, or $0.078/kWh. This is significantly less than the $0.1351/kWh commercial energy cost in the comparison county, but as mentioned, the offshore wind price assumes significant transmission line costs (~$0.0367/kWh) which are not required in the proposed plan. A more realistic estimate for the cost of energy is closer to the $47–51/MWh cost of onshore wind, perhaps even less. We know that offshore wind turbines experience much more consistent wind exposure, can be constructed far larger, experience less public resistance, etc. Their main downfall is transmission of their product energy. I used a figure of $0.07/kWh in the above calculations, reasoning that transmission losses and transmission line costs, in aggregate, amount to at the very least 10–12%.
It may ultimately be that locating our generation offshore — and using what we easily can of it, offshore — is one key to our sustainable economy and renewable energy future.
Wikipedia, supertankers:
As of 2011, the world’s two largest working supertankers are the TI-class supertankers TI Europe and TI Oceania. These ships were built in 2002 and 2003 as Hellespont Alhambra and Hellespont Tara for the Greek Hellespont Steamship Corporation. Hellespont sold these ships to Overseas Shipholding Group and Euronav in 2004. Each of the sister ships has a capacity of over 441,500 DWT a length overall of 380.0 metres (1,246.7 ft) and a cargo capacity of 3,166,353 barrels (503,409,900 l).
Alhambra, shown above, can carry 475,000 m³ — or 1.71 Gigawatt hours’ worth of reverse osmosis purified water. It would process that water via offshore wind power using a conformation of pipelines and turbines similar to that shown in the diagrams below.
Recalling the model of the Carlsbad plant, at 190,000 m³/day, the daily energy requirement is 684 Megawatt-hours, or 28.5 MW continuous. Assuming a capacity factor of 25%, this corresponds to an offshore wind facility rated at 114 MW — or, again, about 12–15 turbines of approximately the current maximum size. [The above wind farm is 12 turbines drawn at 9MW capacity, or 108MW total. An average capacity of ~26.4% yields the necessary energy to energize the floating DS plant shown.]
Incidentally, this makes up only 7% of the water requirement of San Diego County, so it could obviously be scaled up by a factor of ten or more — considering especially that doing so would enable production and delivery to ports all along the coast.
The tanker in the image above would fill in approximately 2.5 days, but would more likely be continuously emptied by smaller, more maneuverable ships shuttling its production to various points along the shoreline. And while the total market value of the purified water — using Berkeley’s price of $2,115/acre foot — is only $325,912/day, the cost to produce has already been established as $0.972/m³, or $184,680/day.
WITHOUT vertically integrating the wind turbines for a lower energy cost than $0.07/kWh.
Cutting that cost to a more realistic generation-integrated figure of $0.045/kWh yields another $17,100/day in daily savings, brings the production-to-coast cost down to $167,580/day and raises the profit margin from 76.5% to 94.5%.
For WATER.
Almost inarguably the most important, most impossible-to-replace, most universally necessary and incredibly easy to sell commodity in the entire world. A commodity which is used worldwide in a volume on the order of 10–100 billion gallons per day for drinking and household use alone.
It should never again cost more than at most $0.005/gallon (=$1.32/m³) making it possible for the entire world to live at least without the threat of dying of thirst.
You mean to tell me that you, Steve Jurvetson, or you, Brock Pierce, or you, Bill Gates, or you Jeff Bezos, or you Mark Zuckerberg, or you, Mark Cuban, or you [insert 100 other billionaires here] can’t get behind an idea which is essentially guaranteed to profit
EVEN THOUGH I JUST GAVE IT TO YOU FOR FREE?
If so, you’re hopeless. Let’s get it done.
The kicker?
I haven’t even mentioned the even more valuable result: using it to generate, store, and transfer both energy and heat.
The above envisioned floating desalination plant would use an electrically driven propulsion system, and periodically move along a series of intake pipes located beneath the wind turbines which are used to energize the system pumps. This process would facilitate diffusing the effluent water around the surrounding area, minimizing the repercussions to nearby marine life and improving diffusion of the brine.
It would also filter impurities (such as the intolerable amount of plastic we’ve thrown into the oceans) out of our ocean water. A relative drop at a time, but a helpful drop where there wasn’t one before. It would drive down the cost of terrestrial farming with the hope of drastically cutting the overfishing that is threatening marine species everywhere.
The solution is infinitely scalable, and as such, it will help us drive the power and energy systems described below.
Transferring purified water laterally to reservoir ferries (and then to the shoreline) would simply require the total volume of the ferries times the shore cycle time to be equivalent to the daily production volume. In other words, if the time required for one to fill itself at the station, carry its payload to the shore, empty it, and return to the station were one full day, the total volume of comparable ferries required would be equivalent to the average daily production of the station, i.e. two ships of 95,000+ m³ payload, three ships of 83,333+ m³ payload, etc.
Since the time required for a full cycle to the coastline and back, including filling and dumping, is likely far less than one day (at 15 knots = 17.3 mph, the transit time to a desalination station 20 miles from the coast and back is less than 3 hours) the job could probably be accomplished by a single modest ferry. Even rounding the three hour figure to six to allow ample pumping time, etc. allows four trips per day for a ferry of comparatively modest 47,500 m³ payload to accomplish the task. Merely by spending its life essentially continuously in motion.
Driven by a lithium ion battery propulsion system, but that’s another article…
The Receiver Station
As I’ve mentioned, the properties of water which make it challenging can also serve to make it more rewarding. Let’s take two of these:
- energy cost to move
- thermal resistance
The law of conservation of energy indicates that whatever energy we put into water can in theory be taken back out. How we have managed to fail to leverage this property fully by now is beyond me, but I do know this:
- However high we pump water, current technology allows us to recover about 90–95% of the energy we invest in doing so.
We already do this in places we find convenient. What’s left is to build one to our convenience and use parameters in keeping with our current state of technology. The only serious requirement is appropriate engineering designs.
2. However much heat we put into water, we can draw a reasonably high percentage back off — provided we have a reasonably closed and insulated system to contain it.
In aggregate, these two things strongly suggest subsurface tunnels. To a certain extent, the deeper the better.
Let’s first consider a 3.8 m internal diameter, 500-m deep tunnel drilled by the Boring Company, with one of its ends adjacent to the shoreline…
A conduit connecting a coastline water drop off point to the intake of the tunnel can readily be envisioned. Hydropower generators of appropriate size can similarly be envisioned at the base of the intake tunnel, directly adjacent to said tunnel — 500 meters vertically displaced from sea level.
Francis turbine generators comparable to those used in the Three Gorges Dam, in China (10.4 m wide) might be used at the base of each intake, outputting a maximum of about 700 MW at a flow rate of 150 m³/second and high pressure 2° the extreme vertical (500m) head. Roughly four such generators would be necessary to meet the energy requirements of the Los Angeles metro area.
They would also require a daily flow rate average of about 13,000,000 m³.
This part may be less challenging than it first appears. The reason is because
…however high we pump water, current technology allows us to recover about 90–95% of the energy we invest.
Which conversely means that no matter how low we drop it, we can always pick it back up again, losing on the order of 10% of the energy cost in the exchange. The below video describes this more succinctly.
Boring Company tunnels have a final internal diameter of 3.8 m. Elon Musk has said that they can been drilled “at any depth.”
While tunnels significantly deeper than the company has to date built likely cost more to complete than the reference $10M/mile stated cost, the company has stated a goal of reducing those costs “by up to a factor of ten.”
The below analysis assumes the current figure, $10M/mile, throughout the calculations. This should make it easier to do proportional cost analyses, and it assumes that over time and volume, costs will drop at least to the extent necessary to construct the tunnels at the stated depth, sea level minus 500 m, for the stated cost, $10M/mile.
Moving water, as it turns out, is much more cost effective than moving people. You can move a LOT more of it and it actually gives you several advantages that moving people/freight doesn’t.
Cost of boring
A $10M, a one mile long tunnel of diameter 3.8 m has a volume of
volume = pi * r² * length
= 3.14159 * (1.9m)² * 1609.344m/mile
= 18,250 m³/mile
…and a volumetric excavation/build cost of $548 per m³
Correspondingly, a 255 mile long tunnel connecting the coastline at Los Angeles with the Hoover Dam at Lake Mead, at depth, would cost:
$2.55B and enclose a volume of 46,540,000 m³
From above, we can see that dropping this volume of water a vertical distance of 500 m from a corresponding tunnel of equivalent dimensions in a single day could generate:
46,540,000 m³/day = 1,939,167 m³/hr = 32,319 m³/min = 539 m³/sec
at 700 MW capacity per 150 m³/sec * 500 m this yields this proportionality:
Q capacity at 539 m³/sec = 700 MW capacity at 150 m³/sec
Q = 2.52 GW
And would therefore require 2.52 GW*(1.05)² in energy input (in addition to the tunnels) to store the gravitational potential energy, accounting for round trip inefficiencies in both the front end pump and the back end generators, and assuming continuous use of hydro generation potential on the user side to balance with continuous investment of renewable energy on the generation side.
2.52 GW * (1.05)² = 2.78 GW if generation were continuous and evenly distributed temporally.
In reality, the generation source — most likely a very large scale commercial solar farm near Baker, California (think: Mohave Desert)— would need to be significantly higher than 2.78 GW in capacity, for the reason that solar power is intermittent and we measured the average power rate. Although the area referenced collects an average of 6.77 hours of solar radiation daily (at an array angle of 35°) it also experiences a low of 5.19 hours’ insolation in its low month (December).
This invariably means that if we’d like to draw a minimum of
2.52 GW * 24 hours = 60.48 GWh (one full volume exchange)
out of the system daily, year-round, we’d need the equivalent of:
2.78 GW * 24 = 66.72 GWh/5.19 h (Dec. solar avg, at array angle 35°) =
12.86 GW of array
Which requires about 21,200 acres of panels at 35° — a mere 1.37% of the area of the nearby Mohave National Preserve — and would cost, at ~$1.50/watt:
$1.50 * 1000 (kilowatt) * 1000 (Megawatt) * 1000 (Gigawatt)* 13 =
$19.5 billion
On the plus side, the end user cost of that power *(considering only the initial generation and efficiency loss in transmission/recovery)* assuming linear 10% degradation to year 25, would be:
=$19.5 x 10⁹/[12.86 GW * 6.77 hours/d average (PVWatts)* 365.25 * 25 * 0.95 * (1/(1.05*1.05))]
= $19.5 x 10⁹/6.85 x 10⁵ GWh
= $28,467.15/GWh
Or $28.47/MWh, which as we all know is $0.02847/kWh
Carbon free, stored in an energy volume up to 60.48 Gigawatt-hours, and with a maximum aggregate power output of 2.52 GW.
Obviously, we still need to:
- Factor in the cost of tunneling.
- Connect the tunnels with hydro turbines. Yikes, those are pricey!
- Computerize management of the assets.
And a whole host of other human-argument associated garbage like permits and legal discussions…who gets what, when, for how much, etc.
We also have to factor in that people are going to keep using water, which invariably means we need to conserve it much better than we do, despite the fact that it starts to look pretty limitless at the costs shown.
The encouraging part is that once we balance the offshore water generation with our daily population use parameters, we can dump the percentage associated with our hot water use into the hole near the shoreline and access the preheated water extant to the tunnel system for our hot water systems.
This means our cold water will in aggregate come in colder and our hot water will require less energy to heat. The amount of energy savings in that process is both mind boggling and very hard to calculate.
Let’s start by adding the tunneling cost to the photovoltaic generation…
We used an estimate of $10M per mile for the tunnels, and originally thought two such tunnels would suffice. Price tag?
$2.55B each, and we still haven’t connected them. Ouch.
Okay, let’s make a third tunnel, too. Just for giggles. [Actually, the reason will become obvious in a minute, trust me on this one.]
$2.55B * 3 = $7.65B
Let’s also add nine separate vertical tunnels, assume that they have a volumetric production cost comparable to the horizontal tunnels, and make them three times as wide (9X cross sectional area) so we can make sure to fully accommodate putting nine (9) known 700MW hydroturbines (10.4 m) down there.
Wiki, Three Gorges:
“Turbine diameter is 9.7/10.4 m (VGS design/Alstom’s design) and rotation speed is 75 revolutions per minute.”
The vertical tunnels are thus 3.8*3 = 11.4 m in diameter, vary from a low of 500 m (coast intake) to
693 m (Pasadena)
1,093 m (Barstow)
717 m (Baker)
804 m (Lake Mead)
and, using the average of each of these figures (to approximate stations between them, roughly at 25–30 mile average horizontal displacements) gives:
597 m
893 m
905 m
761 m
Which totals 6,963 meters of vertical drilling at a bore of 11.4 meters, yielding a volume of:
6,963 m* (5.7 m)² *3.14159 = 710,715 m³
and a cost of
$548/m³ * 710,715 m³ =$389.5M
At this point, we have yet to determine or account for the hydro turbine costs, and I haven’t told you what the third (middle) tunnel is for or where exactly it’s located, but we do know that:
$19.5B (from generation) corresponds to an end-user electricity cost of $0.02847/kWh lifetime
Adding $7.65B (horizontal tunnels) and $389.5M (vertical) yields a total of $27.54B, or a cost of $0.0402/kWh
This also gives us a hyperloop route and an extremely easy way to energize it.
By locating a hyperloop — or maglev — tunnel between the other two tunnels, we further reduce transmission losses and can energize the vehicles while they’re in transit rather than waste time and assets essentially forcing them to remain stationary when they’re depleted of charge.
This can also function as a secondary energy distribution system, with consumers delivering discharged cars to transit connect points and picking up cars which have been charged during their movements in the middle tunnel. Additionally, vehicles could travel in what amounts to an infinite loop — stopping for only enough time to pick up freight, passengers, or discharged vehicles. This would significantly reduce the impact of air resistance, if designed correctly, and help reduce the problematic necessity of depressurizing the tunnels to achieve energy efficiency at speed. One method of accomplishing this might be to allow vehicles to ingress and egress the middle tunnel at speed. Think of it like an amusement park slide.
Another arrangement might make the central passageway alternating and unidirectional, which, while it complicates management, allows for much faster travel and much more lavish accommodations en route (by accommodating wider-bodied transit vehicles.) Perhaps on odd days passenger travel would be west bound only, and on even, eastbound. Freight might be moved at night, with directional change hour determined in part by which direction had a higher scheduled quantity of freight on any given day.
Obviously, any such an arrangement would greatly improve the utilization rates of the vehicles, and would allow faster and safer travel — the economics of which are beyond the scope of this discussion.
Let’s take a brief break and look at a few interesting facts about offshore wind — which may well be the lynchpin allowing this overall system to be built, and to run, cost effectively:
“But we still have to move the water…”
Aren’t we embarrassed about this yet? Women and children carrying 40 pounds of water on their head as a primary activity of daily living?
How heartless we can be, to allow tens or hundreds of millions of people in the world live without access to clean water. What can any of us do, aside with come up with solutions and talk about them?
We still have to move the water. Ten billion gallons a day worldwide as the requirement for basic life.
We have to move it, and the fact that we can do it much more easily than we are — which was already proven by Muammar Gaddafi of all people —
— means it would be awful embarrassing if twenty years from now, when I’m dead and the rest of the world is having its predictable water wars — someone stumbles across this article and says, “If only we’d have seen this earlier!”
In other words, please share this. Tag Elon if you would. If he can’t figure this out, one of the people on his team will be able to.
Some highlights of the “Great Man-Made River” (wikipedia):
- It consists of more than 1,300 wells most more than 500 m deep and supplies 6,500,000 m³ of fresh water per day to the cities of Tripoli, Benghazi, Sirte, and elsewhere. The late Libyan Leader Muammar Gaddafi described it as the “Eighth Wonder of the World.”
- It was conceived in the 1960’s and began construction thirty five years ago, in 1984.
- The first phase alone required excavation of 85,000,000 m³ — almost as much as the sum of the two tunnels required for operation of the envisioned hydrosystem — and was finished in 1991. Almost thirty years ago and before computers were even much of ‘a thing.’
- The system was estimated to cost $25B, as compared to the $27.54B cost projected for the three-tunnel system envisioned, which importantly included a 12.86 GW solar array on public land.
The artificial river system envisioned is designed to store a maximum capacity of 46,540,000 m³ of water, and could theoretically deliver even more than that quantity in a day. It already has ample precedent.
As for the reason why anyone or anything would need more than that much in a single day? The only conceivable reason would be energy production, or storage. But we’re simply too accustomed to water as a scarce resource — even though it is plentiful — to think at the scale necessary to allow it to do its finest work.
Remember, regardless of how we produce water — the cost floor has still been near $2000/acre foot for quite a while. Remember that no matter how much we produce of it — provided we don’t allow it to evaporate — we’ll still use it at some point. It isn’t going to go to waste. Remember that all the pain of water shortages could go away forever if we just had the gumption to think ahead.
Remember that hydropower is no more limited than the water to drive it, or the imagination required to use our existing technologies to build it.
Next up: Part III, countercurrent heat exchangers…
