A Carnot engine between the Earth's poles and equator

[NTL2009]

I was assuming (maybe incorrectly) that the idea was to use solar collectors (maybe concentrated) to raise the temperature of the working fluid for the (Sterling? Turbine?) engine, and use the ocean at ~ 1 km depth (or at the poles) to cool the fluid back down to maintain a large temperature delta. Working with just the relatively small delta of surface water temperature to near freezing deep water temperatures is just not much to work with.

 

[Prathyush]

I was assuming (maybe incorrectly) that the idea was to use solar collectors (maybe concentrated) to raise the temperature of the working fluid for the (Sterling? Turbine?) engine, and use the ocean at ~ 1 km depth (or at the poles) to cool the fluid back down to maintain a large temperature delta.

Yes. That as the basic idea. I am hoping it would become economical at a large scale implementation. Once a tunnel/pipe is build it is a thermodynamic resource you can use for a very long time.

Per NOAA, the average deep (below 200m) ocean temperature at the North pole is about 4 deg C, and the temperature near the equator is 30 deg C.

One way to implement is to dig a tunnel 1-2 KM deep from deep ocean to a hot spot of solar radiation. You can let high pressure at deep sea to do most of the work in transporting water. It's an altitude sensitive thing.

The cost of tunneling is significantly lower(~100-1000KM) and can have benefits of network effects. You can then use a lower condensation temperature. You still need to deal with brine water, unless you dig another tunnel to discard the water ( or the extract salts and freshwater as a resource)

Assume a design for the heat exchanger, but not the heat exchange area.

I need to learn heat exchanger physics. I was hoping that practical efficiency numbers could abstract out the details.(but it is something I will look into slowly)

 

[Keith_McClary]

 

[Prathyush]

I did quick search on papers discussing extracting energy from the gulf stream.

They typical estimates seem to range around 10 GW .

https://www.researchgate.net/publication/256495742_Theoretical_Assessment_of_Ocean_Current_Energy_Potential_for_the_Gulf_Stream_System
"Assuming a 30% conversion efficiency from energy removal from the flow to electrical power, turbines yield
a peak energy potential for electricity production of about 13 GW from the Gulf Stream system"

EVALUATING THE POTENTIAL FOR ENERGY EXTRACTION FROM TURBINES IN THE GULF STREAM SYSTEM
"providing an estimate by assuming a 30% power conversion efficiency for energy removal from the flow to electrical power [19] yields an average potential for electricity production of about 1.5 GW from the Florida Current and 5.6 GW from the entire US portion of the Gulf Stream system or 13 and 49 TWh/yr, respectively. "

In comparison peak power recorded in US is about 700 GW. It seems (not sure) the gulf stream can only contribute a modest part of the energy mix.

 

[jbriggs444]

I was assuming (maybe incorrectly) that the idea was to use solar collectors (maybe concentrated) to raise the temperature of the working fluid for the (Sterling? Turbine?) engine, and use the ocean at ~ 1 km depth (or at the poles) to cool the fluid back down to maintain a large temperature delta. Working with just the relatively small delta of surface water temperature to near freezing deep water temperatures is just not much to work with.

Yes. That as the basic idea. I am hoping it would become economical at a large scale implementation. Once a tunnel/pipe is build it is a thermodynamic resource you can use for a very long time.

If you have a high temperature solar heat source then I do not see the point of going to huge expense to put your cooling towers one kilometer deep in an ocean that is (perhaps) tens or hundreds of miles away.

If you are gathering solar input from a large surface area then air cooling over that surface area is clearly sufficient -- because it was already sufficient before building the solar collector.

You only need low temperature cooling if you have a low temperature heat source.

 

[NTL2009]

If you have a high temperature solar heat source then I do not see the point of going to huge expense to put your cooling towers one kilometer deep in an ocean that is (perhaps) tens or hundreds of miles away.
...
You only need low temperature cooling if you have a low temperature heat source.

That makes sense - I think I got drawn into the OPs idea of using near freezing water on the sink side.

The ocean would make a very good sink, due to size and thermal characteristics of water. Whether that water is at surface temperatures, or near freezing wouldn't be that significant if the hot side is near or above boiling. As an example, 200F - 70F is a 130F delta, get that water cooled to 35F, and you've only increased the delta to 165F, unlikely to be worth the construction costs and ongoing pumping costs to push that water through the heat exchange, plus maintenance.

Let's see, convert to Kelvin for that efficiency value... 366C, 294K, 275K

1 − ((294 ∕ 366)^0.5) ≈ 0.10374184
1 − ((275 ∕ 366)^0.5) ≈ 0.13318623

About a 28% improvement in efficiency (relative improvement, ~ 10% to 13%, ~ 3 points, not 28 points!)
Significant, but I'm certain it would not warrant the expense and complexity. Even less of an improvement if you use an intermediate fluid with a higher boiling point, or pressurize water as the working fluid in a concentrated solar collector.

 

[jbriggs444]

if the hot side is near or above boiling

After a little Googling on concentrated solar power generation, it seems that the hot side temperature is often higher than this. There are a variety of designs.

[In a parabolic trough design]
Common fluids are synthetic oil, molten salt and pressurized steam.
[...]
[In a power-tower design]
Within the receiver the concentrated sunlight heats molten salt to over 1,000 °F (538 °C)

 

[Prathyush]

Significant, but I'm certain it would not warrant the expense and complexity.

I will do a detailed estimate sometime in the future. The economics roughly works like this.

Consider, Ouarzazate Solar Power Station.

Water consumption for the Ouarzazate Noor complex is estimated at 2.5 to 3 million $m^3$ per year for cleaning and cooling. It produces 1470 GWH of energy annually.

China built, Dahuofang water tunnel 85.3 Km of water tunnel at 750 million USD. It's cross section is 50 $m^2$ and diameter is 8m.

Assume we need 10x the size of tunnel and we can estimate the cost at 7.5 billion USD. At 10 cents a KWh. We need to produce 75 Billion KWh = 75,000 GWh of extra energy energy.

Ouarzazate Noor complex produces 1470 GWh of energy annually.

Estimating efficiency gain between cooling between 45 degrees and 5 degrees as (there is no water in Sahara, so should be efficiency should be compared to Air cooled thermal plants which I believe is less efficient.)

$$ \frac{ 1- \sqrt{\frac{278}{600}} }{1- \sqrt{\frac{318}{600}} } - 1 = .174 $$

If we can produce 17.4 pc of 1470 GWh ~ 255 GWh extra annually. You have a pay back period of 294 years.
If you should dump the brine water back in the ocean. You need 2 tunnels, so 588 years

If you can make a Plant 25X in size (assuming same sized tunnel), you get a pay back period of 23.5 years.

At .5 m/s a 50 m^3 cross section tunnel is capable of transporting 788 million $m^3$ of water a day.
Well above 3 million*25 = 75 million $m^3$ obtained from extrapolating.

That is a very very rough estimate, which I will sharpen slowly. I have not estimated the cost of pumping in this estimate.(I will work it out sometime. If you can collect energy when the water is pumped back into the ocean it can be made lower. Typical altitude of Sahara is under a KM)

One you have a tunnel network the incremental cost of more plants should should also be considered. For instance Libya built Great Man made river. It's a tragedy that the country has now been destroyed.

You can also extract fresh water from such a setup using a vapor pump. So economic value of water in Sahara can also be estimated. In principle concentrated brine can be used to extract certain minerals using osmotic methods, further optimizing economic value.

It requires more careful consideration, especially with a detailed project on where and how. The construction cost of Ouarzazate Solar Power Station is 2.5 billion. A plant 25X larger plant is 62.5 billion. So it may start making economical sense if the project size is in the order of 70 Billion.