[ExI] Power Satellite payback analysis

[Keith Henson]

On Sat, Jun 10, 2023 at 9:24 PM Kennedy, Robert
<Robert.Kennedy at tetratech.com> wrote:
>
> Keith,
>
> you can repost this to [extropy-chat] for me.
>
> That methane propellant doesn't get into the rocket all by itself, so divide by say 0.5 to account for the industrial effort (penalty) to get the methane out of the ground, liquefy it, and into the fuel tank.  That 15 kWh/kg becomes 30 kWh/kg.  On the other hand, that methane is not synthesized, it is primarily fossil in origin, so I'm not sure its energy should even be counted.  In other words, in terms of energy from human sources, that methane could be considered almost free for accounting purposes.  How free?  In the oil & gas sector, the "embedded energy" of hydrocarbon fuels is about 25%.  So multiply the 30 kWh/kg by 25%: say 8 kWh/kg of payload for the fuel.
>
> You should also factor in the cost of liquefying oxygen to a cryo-propellant.  It's 1 kWh per kg of LOX, times a factor of 30 (30 kg of LOX per kg of payload).  So, 30 kWh/kg of payload for the oxidizer.

Good point, I was only considering the fuel.

> However, you left out of your accounting the energy cost of the portions of the launcher's dry mass that are not recovered, plus a charge to amortize the reusable bits, since they won't last forever.

I think SpaceX intends to get the whole thing back.  If you assume 100
flights, the financial and energy cost of the vehicle gets down into
the noise.  This is a really rough calculation and did not go that
deep.

>To save you the effort of detailed calculations, you can do a horseback estimate of the energy embedded in manufactured products based on the USA's primary energy input of 97 quads, divided by GDP of $23 trillion, then triple the result for the higher intensity of the manufacturing sector.  This yields 13 MJ/dollar.  Now multiply that by the entire cost of Elon Starship, $100M, to get 1300 TJ.  Then discount by whatever proportion gets reused.  Looks like he gets both the booster and upper stage back.  Let's say 95% re-use, leaving 66 TJ for the 5% that's not recovered.  Then divide by your payload mass, 100,000 kg. I get a specific dry launcher charge of 667 MJ per kg, or 185 kWh/kg of payload.
>
> 8 + 30 + 185 = 223 kWh/kg of payload.

If it is really that high, then power satellites are not worth doing.
I have also looked at the problem from the economic return.  A power
satellite can't cost more than $2400/kW to keep the power cost at 3
cents/kWh.

> I don't think you should ignore the embedded energy of your SBSP.  So, take your estimated manufacturing cost per kilo, whatever it is, and go thru the energy-per-dollar process above to get a figure for specific embedded energy of the SBSP payload in kWh/kg.
>
> Add that to the 223.
>
> Then at last, you can divide the output of delivered electricity by the figure above to figure out how long it takes to hit energy breakeven.
>
> One last step, a simple one: take your total useful lifetime of the SBSP, and divide that by the time to breakeven above.  This will give you a dimensionless term called "energy return on energy invested" or EROEI for short.

I tend to use energy breakeven for comparison.  Wind in good locations
is around 6 months, PV solar is about a year.

> Wonks use this figure of merit all the time.  FYI, for terrestrial solar, wind, and nuclear, the EROEIs are all in the middle teens.**  Be curious what you get.  I'll bet it'll be huge.

It hardly matters.  The scale of the project is far too large on this
side of the singularity.  If you were going to replace 1/3rd of the
current energy use over 20 years, it would require 25,000 launches a
year.  Starting to consider mining an asteroid.

Keith

> ** you would be amazed/apalled how bad the EROEI for oil exploration and production has become.
>
> Robert (K3TVO)
>
> Robert G. Kennedy III, PE -- Senior Systems Engineer VI
> Direct:  865.220.4736 -- Main:  Mobile:  865.405.5806 -- Main:  865.220.4700 -- Fax:  865.482.6647 (new)
> robert.kennedy at tetratech.com
>
> Tetra Tech, Complex World, Clear Solutions™
> 1093 Commerce Park Drive, Suite 100 -- Oak Ridge, Tennessee 37830 -- www.tetratech.com
>
> -----Original Message-----
> From: Keith Henson <hkeithhenson at gmail.com>
> Sent: Saturday, June 10, 2023 11:17 PM
> To: ExI chat list <extropy-chat at lists.extropy.org>
> Subject: Power Satellite payback analysis
>
> I wrote this for the blog OFW, but I thought it might amuse people here.
>
> Someone bitched about me saying that a power satellite would repay the energy to lift it in
>
> “a bit over two months” with
>
> " Keith, I call rubbish on this. Post the study/paper documenting this silly claim."
>
> My response:
>
> I can reconstruct this from a few numbers right here.
>
> The mass of a power satellite is around 6.5 kg/kW (my work, but it is about the center for others),
>
> SpaceX big rocket burns about 4,600 tons of LOX and LNG to take 100 tons to orbit
>
> CH4 takes 2 O2 to burn.
>
> 16 and 32 so the LNG is 1/3 of 4600 or 1533 tons of LNG to lift 100 tons. Or 15.3 kg of LNG to lift one kg.
>
> So to lift enough for a kW would take 15.3 times 6.5 or 100 kg.
> Methane is 55.5 MJ/kg or 15.4 kWh/kg. 100 kg would be 1540 kWh worth of LNG. Davide by 24 hours per day and you get 64 days for the lift energy to be paid back, little over two months.
>
> This does not account for the energy it took to make the power satellite parts, but that is small compared to the lift energy, even aluminum is only around 1%.
>
> I also left out the reaction mass to move the power satellite to GEO, which might push the mass you have to lift up to 10 kg/kW.
>
> But if you burned the LNG for power, the best you can do in a combined cycle power plant is 60%. This factor makes the payback somewhat shorter.
>
> So using LNG for rocket fuel seems like a good idea compared with just using it to make electricity.
>
> If you find an error in my analysis, please let me know.
>
>
> Keith