ActionPlankton

3 năm trướcdiscuss

Played with these ideas a little:

https://news.ycombinator.com/item?id=24530731

4 năm trướcdiscuss

Keywords: Optimal Control, Bellman. I'm serious.

For a first exercise, forget Dijkstra and just solve a maze by doing Value Iteration, and plot the cost-to-go at each step.

Then consider that this function doesn't have to take a graph vertex or grid cell, but could instead be some continuous function on R^n.

The next step usually is to learn about the Linear Quadratic Regulator problem, where the cost-to-go is a quadratic, and you get to do an iteration of "Value Iteration" by updating the quadratic coefficients.

To connect to physics, see how you'd write the Action Integral in these terms.

ActionPlankton

6 năm trướcdiscuss

Let's do the thermodynamics:

First, some enthalpies of formation (at 298 K and 1 atm, in kJ/mol) (from [1] unless otherwise indicated):

  H2O(l)       -285.8
  
  CO2(g)       -393.509
  CO2(aq)      -419.26
  
  NaOH(g)      -425.93 
  NaOH(aq)     -469.15
  
  Na2CO3(s)   -1130.77
  Na2CO3(l)   -1108.51  (from [2])
  Na2CO3(aq)  -1157.34  (from [3])
  
  CaO(s)       -635.09 
  CaCO3(s)    -1206.9
  Ca(OH)2(s)   -986.09
  Ca(OH)2(aq) -1002.82

The reactions:

1. 2NaOH(aq) + CO2(g) -> Na2CO3(aq) + H2O(l) ... -111.33 kJ/mol (exothermic)

Here I assume that the gas has to dissolve as part of the reaction so use CO2(g) instead of CO2(aq) on the left hand side. I get an enthalpy delta of -111.33 kJ/mol. This differs from some homework answers I find online like [4] because I use NaOH(aq) while they use NaOH(s), etc; I hope I'm right for this application.

2a. CaO(s) + H2O(l) -> Ca(OH)2(aq) .... -81.93 kJ/mol (exothermic)

2b. Na2CO3(aq) + Ca(OH)2(aq) -> 2 NaOH(aq) + CaCO3(s) .... 14.96 kJ/mol (endothermic)

3. CaCO3(s) -> CaO(s) + CO2(g) ... 178.30 kJ/mol (endothermic)

Energy issues:

The easy thing would be to run at least (2b) (causticization) concurrently with (1) so you're always precipitating out CaCO3 and don't accumulate any Na2CO3 solution. It would also be easiest to combine (2a) with (2b) in a single causticization chamber. And it'd be simplest to skip (3) entirely, just treat CaO as a consumable, and be happy that you've sequestered carbon as CaCO3.

However, in a temperate climate, you can imagine doing the following to shift energy around the year (how realistic this is I don't know):

- Only run (2a) during the winter, to heat your home; you'd accumulate Ca(OH)2 solution to be used during the summer in (2b).

- Only run (2b) during the summer, to cool your home. During the winter you'd accumulate Na2CO3 solution from (1), which you'd need to store.

- If you're doing (3), do it during the summer, when a solar furnace can be operated. This gives you a reagent that you'll use in (2a) during the winter.

- You'd want to run (1) all year round, to scrub the CO2.

The main inefficiency this is trying to make useful is that you need to go down in energy with (2a) and back up in (3). And down in energy with (1) and back up in (2b).

I'll next need to understand the soda lime method to compare.

[1] https://en.wikipedia.org/wiki/Standard_enthalpy_of_formation [2] https://webbook.nist.gov/cgi/cbook.cgi?ID=C497198&Mask=2 [3] http://chemistry-reference.com/reaction.asp?rxnnum=454 [4] https://answers.yahoo.com/question/index?qid=20131119075117A...

ActionPlankton

6 năm trướcdiscuss

I'm curious about this cartridge idea. I'm picturing a pipe with quicklime inside and coffee filters on the ends, with a blower to force air through. How tightly would the contents be packed?

This is a little different from what I'd been thinking before your message, which would be more of a fluidized bed reactor -- like quicklime swirling around in air in a garbage can. I think that's closer to how some powerplants treat exhaust.

I've read that there are microscopic changes to the quicklime particles after a couple absorbtion/heating cycles (their pores fill up or something), after which you need to do something to further refresh it, maybe by dissolving it and precipitating it back out of solution.

This led me to considering whether aqueous chemistry might be better.

The simplest would be to react air with calcium hydroxide (would you use a bubbler? Or a packed counterflow tower? Or a spray tower?) and collect the calcium carbonate that precipitates out.

But, based on my shaky chemistry, I understand solubility of calcium hydroxide is low, so you do better with a two-stage process like the Kraft Process:

1. Absorb CO2 in contactor:

2NaOH + CO2 -> Na2CO3 + H2O

2. Regenerate solution in causticizer:

- CaO + H2O -> Ca(OH)2

- Na2CO3 + Ca(OH)2 -> 2 NaOH + CaCO3

3. Decompose calcium carbonate:

CaCO3 -> CaO + CO2

The concentrated NaOH solution would be very caustic, so you'd have to be careful with that, but apart from that none of this seems too terribly scary?

Some parts of the above are endothermic, others exothermic, so maybe this could even let you shift energy from the summer (solar furnace?) to the winter when you need it, as part of the deal.

Or maybe this is all too complicated and you should just use a canister of soda lime granules, like an anesthesia machine? ( https://en.m.wikipedia.org/wiki/Soda_lime )

I'd be interested to hear more from people whose chemistry is better than mine.

ActionPlankton

6 năm trướcdiscuss

Once you have the carbon in biomass, what do you do with it? Dry it out and heat it enough to make biochar?

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