Heat / energy relation

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xype
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Heat / energy relation

Post by xype »

Hello,

I'm trying to etablish a relation between reactor temperature (Celsius) and power output (Watt).

Let's say I have a single reactor that is not connected to anything, has no fuel and has a base temperature of 1000°C. In such situation the temperature will stay the same because nothing is "consuming" it.

Now let's say I connect a single heat exchanger which consumes 10MW. The temperature of the reactor will slowly decrease beacuse the heat exchanger is consuming it.

The question is : how much time does it take for the reactor to reach 0°C ? In other words, how many power (Joules) are stored in thoose 1000°C ?

Thanks!

mmmPI
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Re: Heat / energy relation

Post by mmmPI »

https://wiki.factorio.com/Heat_exchanger
https://wiki.factorio.com/Nuclear_reactor

Using the value on those pages can help you.
Nuclear reactors have a heat capacity of 10 MJ/C. Thus, they can buffer 5 GJ of heat energy across their working range of 500°C to 1000°C, and require 4.85 GJ of energy to warm up from 15°C to 500°C when initially placed.
The reactor cannot go back to 0° when you use a heat exchanger to cool it because at 500°C the steam productions stops. This is why they call it a 5GJ buffer when a reactor is at 1000°C. From 100O°C down to 500°C there are 5GJ.

1 heat exchanger is able to exchange 10MW of heat into steam which is 10MJ per second. Therefore 5000MJ would require 500 second to consume.

FuryoftheStars
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Re: Heat / energy relation

Post by FuryoftheStars »

mmmPI wrote:
Tue May 31, 2022 6:56 pm
https://wiki.factorio.com/Heat_exchanger
https://wiki.factorio.com/Nuclear_reactor

Using the value on those pages can help you.
Nuclear reactors have a heat capacity of 10 MJ/C. Thus, they can buffer 5 GJ of heat energy across their working range of 500°C to 1000°C, and require 4.85 GJ of energy to warm up from 15°C to 500°C when initially placed.
The reactor cannot go back to 0° when you use a heat exchanger to cool it because at 500°C the steam productions stops. This is why they call it a 5GJ buffer when a reactor is at 1000°C. From 100O°C down to 500°C there are 5GJ.

1 heat exchanger is able to exchange 10MW of heat into steam which is 10MJ per second. Therefore 5000MJ would require 500 second to consume.
This is accurate.

However, because I was bored and curious, and I wanted to see what kind of an effect the buffers of heat exchangers and heat pipes would have in practice (with the below examples, I used the "scientific method" :P ):
  1. In the exact situation of the OP, reactor heated to 1000°C, then a heat exchanger is connected, the exchanger is only able to transfer 4.5 GJ of energy before both it and the reactor settle at ~500°C. (Connecting the heat exchanger without water to produce steam, both it and the reactor will settle at 905°C.)
  2. In a "more normal" use case where the heat exchanger is already connected (but still only 1) and the whole setup is heated to 1000°C (and all fuel consumed) before pumping in water, it's able to transfer 5.5 GJ of energy before they settle to 500°C.
  3. For the sake of it, I did another setup like 2, only I also put one (1) heat pipe segment between the reactor and exchanger. This one was able to transfer 6 GJ of energy.

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Re: Heat / energy relation

Post by mmmPI »

FuryoftheStars wrote:
Tue May 31, 2022 7:22 pm
However, because I was bored and curious, and I wanted to see what kind of an effect the buffers of heat exchangers and heat pipes would have in practice (with the below examples, I used the "scientific method" :P ):

In the exact situation of the OP, reactor heated to 1000°C, then a heat exchanger is connected, the exchanger is only able to transfer 4.5 GJ of energy before both it and the reactor settle at ~500°C. (Connecting the heat exchanger without water to produce steam, both it and the reactor will settle at 905°C.)

That is a torough investigation but it confused me :

the wiki state that
Heat exchangers have a heat capacity of 1 MJ/°C. Thus, they can buffer 500 MJ of heat energy across their working range of 500°C to 1000°C, and require 485 MJ of energy to warm up from 15°C to 500°C when initially placed.

Given those values one could count 1 reactor heated at a 1000° like a 10GJ 100%filled container or 10 000 MJ, to which adding 1 heat exchanger, is like adding 1GJ capacity for the container or 1000 MJ, to make it 11GJ. Some energy is added to the system when you add the heat exchanger, because when built it is at temperature of 15°C. Or 1.5% of the heat exchanger capacity ( 15 MJ )

Therefore at the end one should have a system with a capacity of 11 000 MJ, that contain 10 000 + 15 MJ, under the form of heat. Which means the system is 91.04545% filled. With a max temperature of 1000°C, my expectations would be to have the system settle at around 910°C for the case where you mentionned 905°C.

The difference between the 2 figures is around 5°C which means 55 MJ, (O.5% of the total 11GJ) which is about 0.6875% of a 8GJ nuclear cell that seem missing.

Because if the system loses 55MJ just when being created somehow, then instead of 500 second, the heat exchanger would produce 10MW only during 494.5 second. (10 MW is 10MJ/S so if 55MJ are missing then 5.5 second can be removed to the total).

I know there are potential energy losses when reaching 1000° and that a certain temperature differential is required for the heat to spread, which can cause a bottleneck causing some part to reach 1000° and thus an energy loss, but i didn't expect this to be relevant considering only 2 pieces compose the system. The 0.6875% of an energy cell that it represent makes me disregard it especially knowing that with adjacency bonus, one can consider a fuel cell being 16 24 or 32 GJ.

Still though i wonder what is the science explaining this x)

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Re: Heat / energy relation

Post by FuryoftheStars »

mmmPI wrote:
Tue May 31, 2022 11:42 pm
With a max temperature of 1000°C, my expectations would be to have the system settle at around 910°C for the case where you mentionned 905°C.
I'm glad you said something! I must've mucked something up in the map editor last time, because on a retry, I am getting ~910°C (910.36 in the reactor, and 911.36°C in the exchanger). A rerun of the setup still results in 4.5 GJ in the accumulators, though a 55 MJ difference is minimal enough to not show. Interestingly, too, when the setup shuts down, that 1°C difference between the exchanger and reactor shifts over to the reactor (exchanger @ 500°C, reactor @ 501°C).

Also, a bit infuriating, using the map editor to place accumulators, they are placed with 5 MJ of energy already stored in them. Cut & paste fixes this, but then it appears as though steam turbines have about 97 kJ of energy sitting in them when you place them, too. :?

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Re: Heat / energy relation

Post by Tertius »

FuryoftheStars wrote:
Wed Jun 01, 2022 1:06 am
Also, a bit infuriating, using the map editor to place accumulators, they are placed with 5 MJ of energy already stored in them.
You can change this. Go to the Settings tab of the map editor and change Settings->Interaction->Fill electric buffers when building entities.

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Re: Heat / energy relation

Post by xype »

Nuclear reactors have a heat capacity of 10 MJ/C
Thanks that is exactly what I was looking for, I must have missed it in the wiki.

Very interesting to read all your experiments too!

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Re: Heat / energy relation

Post by mmmPI »

Tertius wrote:
Wed Jun 01, 2022 9:45 am
FuryoftheStars wrote:
Wed Jun 01, 2022 1:06 am
Also, a bit infuriating, using the map editor to place accumulators, they are placed with 5 MJ of energy already stored in them.
You can change this. Go to the Settings tab of the map editor and change Settings->Interaction->Fill electric buffers when building entities.
Cool tip !

i'm glad it's all clear :)

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