Renewable Tidal Energy
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Renewable Tidal Battery

If you sit in the bathtub and pull an empty cup down into the water you feel the upward force grow as the cup goes deeper.

image.png

This could be a source of power.

The force exerted by the moon on the earth creates a
twice a day.

image.png

This bulge is on average .6 m, but the range between the lowest and highest point of the tide go all the way to
.

Here's a map of tidal ranges throughout the world.


image.png

The idea is that you could put a large water displacing structure in the ocean, tie it to the seafloor, and when it came time for the tide to rise the force exerted by the rising water could be used to generate energy.

image.png

This Coda doc is dedicated to exploring the feasibility of that idea.

Ah, this might actually be a really bad idea:

The claim in this paper is that using tidal energy to provide 1% of the earth’s power requirements will result in the earth ceasing to spin in as little as 1000 years.

But other sources (the guy who runs the Real Engineering youtube channel) claims that this is hogwash. So maybe don’t trust things just because they have stanford affixed to them.

This is to model a cone shaped water displacer

000
13
height
0000
19
radius

4,914
volume (cubic meters)
4,914,498
liters
set a target
4875750
off by
38,748
liters

Save Setting in Combinations Table
This is to compare the effects of certain parameters on power generation, earnings, and structure cost.

standard assumptions
alaska assumptions
000
2
steel thickness (cm)
000
100
tidal range (meters)
0000
0.3
earnings per KWh ($)
7850
steel kg per m^3
603
steel cost per metric ton ($)
124
cement cost per metric ton ($)
1.025
salt water mass per liter (kg)
2
cycles per day
0.1
delta (meters) - step size used when calculating depth pressure

Combinations and consequences
0
Created with Highcharts 9.2.1r (m)years to payoff1002003004005006007008009001000020406080100

I'm pretty sure I'm doing many things wrong

Or else this is completely infeasible

As a point of comparison, a 1 MW solar farm supposedly costs about $1 million to build (though I've seen that number as high as 3 million) and generates on average four megawatt hours per day (it depends on the amount of sunshine). The
@best combination
I found generates about 1 MWh per cycle. With two cycles a day that comes out to 2 MWh per day (half of the output of the solar farm). That means that for this to be competitive with solar it should ideally cost about .5 to $1.5 million to deploy.

That
@best combination
, however, is about
130
times more expensive than a solar farm just in terms of steel cost. But there is good reason to think that I'm dramatically overestimating the cost to build it.

Hopefully my assumptions are somehow extremely incorrect or I made an error in the math (both highly likely).

Possible things that I could be wrong about:
Maybe a cone is the wrong shape (would a cylindrical shape be better? sphere?)
Maybe you could use cement instead of steel (or steel reinforced cement)
Maybe you could use some much cheaper material like plastic
Maybe internally pressurizing the structure would allow you to use significantly less material

I'm also pretty sure that the way I model the forces is incorrect. In particular, I need to model the fact that the deeper you pull the water displacing structure the more forces are exerted on it due to depth pressure. I tried to estimate the total forces acting on the structure in
depth pressure force (bar m^2)
but I would guess I'm doing it wrong. The results I’m getting are on the order of 200 large blue whales worth of force

Manufacturing is definitely a concern, since these things are enormous, but could perhaps be overcome with in situ additive manufacturing. I.e. put the base in the water, then pump water into the base until it falls to a height that can be serviced from the deck of a boat, then add an additional layer of material, pump in more water, add another layer, etc.

Feel free to copy this doc and fix my errors.
if you know where I'm wrong or to tell me why this won’t work

Comparison with the tallest buildings in the world and their costs to build

image.png
By BurjKhalifaHeight.svg: *BurjDubaiHeight.svg: Ramaderivative work: Astronaut (talk)derivative work: WelcometoJurassicPark (talk), Scaling and drawings from https://commons.wikimedia.org/wiki/File:BurjKhalifaHeight.svg and http://www.skyscrapercenter.com All rights reserved. - File:BurjKhalifaHeight.svg http://www.skyscrapercenter.com, CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=54960521

Somehow it only cost 1.5 billion to build the burj, and 700 million to build empire state building, $675 million for hoover dam (
all in today’s dollars
) and yet I'm estimating $500
billion
, clearly I'm doing something wrong

Let's use a submarine as comparison

Australia’s subs are 4 billion a piece and are
volume of cylinder: 4875.75 m^3 which is 4,875,750 liters
which at these parameters:
4 tidal range (meters)
0.3 earnings per KWh ($)
generates this output:

If we straight up used a submarine
0
KWh per cycle
MWh per year
annual earnings
1
1371.2814859029384
1001.0354847091451
$300,311
There are no rows in this table

Subs can withstand up to 300 bar pressure, so clearly these are way over engineered for what we need. If we were to just naïvely scale the cost of the sub to hit 1000 kWh per cycle then we would multiply the $4 billion cost by 18, which is 72 billion dollars.

I've read that Australia’s subs are more than double the cost that most people expect to pay for subs, but reducing our cost down to only 36 billion still doesn't get us close to our $3 million goal, nor is it close to the 500 billion estimate above. Naturally, there is a lot more in a submarine than there would be in one of these structures (a nuclear reactor for one thing), but even as a gut check I’m not sure I’ve made any progress in improving my estimate.

What else can I use as an estimate of the cost to manufacture a highly external pressure resistant structure?

It needs to be able to withstand 10 to 15 bar at most. It would be nice to know how manufacturing costs scale with respect to the ability to withstand pressure


found this (thank you Google recommendation algorithm). The creators claim 25 tons over 15 m generates 250 kWh. Costs $1,385 million to build. We would expect that the idealized output of that sort of system would be (assuming metric tons):
3,675,000
joules gravitational potential energy
1
kWh gravitational potential energy

uh.. that’s not 250 kWh, do they mean per year or do they expect to do this 250 times a day?

So it seems that they actually list it as a
, and the good news article may just be in error

Apparently,
. That means it should be about
694.4
Wh per drop? Asking them

But they also claim 90% efficiency, which would mean 900Wh per drop

Really, all I wanted to know was the efficiency of the winch technology, the claim that 90% efficiency is possible is promising

Exploring possible deployment locations

We basically want places with high tidal ranges and high electricity rates

image.png
image.png
image.png

Chile has pretty good tidal ranges and high prices
Europe also ranks pretty high and would also have decent prices + likely subsidies thanks to carbon markets
New zealand too


The battery approach

There's an alternative way to use this, which is as a massive battery, storing energy when prices are low and releasing it when prices are high
Japan would be a great place to model that approach since it has decently high energy prices and, if you look at the title range map, it has almost 0 tidal range:
image.png
This is important because if you store energy when the prices are low and the tide high, and then you want to release energy while the tide is low you’ll have less potential energy than you previously stored

Some useful information:
Nice!! Has historical data!


best combination
select the height and radius combination you want to model this with

Set tidal range to 100
Press this button to set the tidal range to 100 m. Of course, there's nowhere in the world with a tidal range of 100 m, but we are using energy from the grid to pull the water displacers deeper. So, in theory we could pull them all the way to the seafloor (engineering permitted). At 100 m there are 10 bar of pressure which is 1/3 of what a submarine can handle, so it seemed like a reasonable estimate.

Add Spreads
This button populated the table below with what would happen if we were to perfectly arbitrage the 2020 Japan energy market with the water displacement energy storage solution. This is pretty unrealistic, but it gives us an idea of the maximum market opportunity. In other words,
we are buying energy for the day at the lowest price and selling the energy that same day at the highest price
Japan Daily Max Spread
0
0.0093
dollars per yen

0.9
work conversion efficiency

$4,794,109.41
estimated annual earnings

This estimate is almost definitely wrong due to the depth pressure modeling errors in my calculation. I'll fix it eventually


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