Furnace temperature and pressure math

The data used was collected in version 0.2.2800. It was obtained with regular furnaces only, the advanced furnace is untested. If there is any difference between them, it would probably be the internal volume, the regular furnace holds 1000 L.

Furnace behaviour

• Only the gas inside the furnace have temperature, the furnace itself does not and absorbs no heat
• Combustion will consume 95% of the limiting ingredient, O2 or H2 (if there is 10 mol O2, and excess H2, 0.5 mol O2 will remain afterwards)
• Reaction formula: 1 O2 + 2 H2 -> 6 CO2 + 3 X + 595kJ
• No side reactions with other gases have been observed so far

Using perfect 2:1 fuel

Temperature peak

• T(after) = (T(before) * 61.9 + 0.95 * 595k) / (243.6 * 0.95 + 61.9 * 0.05)
  • Temperature in Kelvin (Celsius + 273)
  • 61.9 = heat capacity before combustion (based on reaction formula, so 3 moles total) = sum(specific heat * moles of each gas before) = 21.1 + 2*20.4
  • 243.6 = heat capcity for gas after combustion = sum(specific heat * moles of each gas after) = 0.05*(21.1 + 2*20.4) + 0.95*(6*28.2 + 3*24.8)
  • 0.95 and 0.05 refers to the 95% combustion efficiency
• The number of moles combusted doesn't matter under perfect conditions, the temperature increase is the same since the reagent/product ratio determines this outcome. The number of moles will however effect how quickly the gas cools.

Pressure peak

• P = nRT/V
  • n = total moles
  • R = 8314
  • V = 1000
• P (before) = n(before) * 8314 * T(before) / 1000
• P (after) = n(before) * (0.05*1 + 0.05*2 + 0.95*6 + 0.95*3) / (1 + 2) * 8314 * T(after) / 1000

Using diluted fuel

Unreactive gases can be added before the ignition to increase pressure and decrease temperature. An excess of either O2 or H2 also counts as unreactive. The outcome can be calculated like this.

Temperature peak

1. O2 moles reacted = min(moles O2, moles H2 * 0.5) * 0.95
2. released energy = O2 moles reacted * 595k
3. heat capacity (before) = sum(specific heat * moles of each gas (before))
4. heat capacity (after) = heat capacity (before) + O2 moles reacted * 181.7†
5. thermal energy (before) = temp (before) * heat capacity (before)
6. thermal energy (after) = thermal energy (before) + released energy
7. temperature (after) = thermal energy (after) / heat capacity (after)

† 181.7 comes from 243.6 - 61.9 (the change in the heat capacity for the gas before and after combustion, see above)

Pressure peak

1. total moles (before) = pressure(Pa) * 1000 / (8314 * Temp (before)
2. total moles (after) = total moles (before) + O2 moles reacted * 6†
3. Pressure (after) = total moles (after) * 8314 * Temperature (after) / 1000

†6 comes from 9 - 3, combustion consumes 3 moles and produces 9 moles

Using Ice(Oxite) and Ice(Volatiles)

There is a minor difference between which ice is added first. One can also observe a fluctuation in the combustion efficiency compared to when a furnace is fueled with gas. The end result also matters a little bit on how fast the ignition button is pressed when the first ice type is added while doing larger batches.

small batch, oxite first

• Adding 1 oxite + 1 volatile, in that order
  • Temperature: 2222K, Pressure: 2.03MPa, moles of O2/H2 combusted: 11/21, Combustion ratio (H2): 95%
• Adding 1 oxite + 2 volatiles, in that order
  • Temperature: 2514K, Pressure: 4.13MPa, moles of O2/H2 combusted: 22/43, Combustion ratio (H2): 98%

small batch, volatiles first

• Adding 1 volatile + 1 oxite, in that order
  • Temperature: 2224K, Pressure: 2.03MPa, moles of O2/H2 combusted: 11/21, Combustion ratio (H2): 95%
• Adding 2 volatiles + 1 oxite, in that order
  • Temperature: 2432K, Pressure: 3.93MPa, moles of O2/H2 combusted: 21/42, Combustion ratio (H2): 95%

large batch, oxite first

• Adding 5 oxite + 10 volatiles, in that order
  • Temperature: 2463K, Pressure: 18.76MPa, moles of O2/H2 combusted: 96/190, Combustion ratio (H2): 86%
• Adding 8 oxite + 16 volatiles, in that order
  • Temperature: 2537K, Pressure: 33.28MPa, moles of O2/H2 combusted: 172/344, Combustion ratio (H2): 98%

The difference in combustion efficiency is a mystery. Fuel temperature doesn't seem to matter (seen by furnace tests with 2:1 gas on both Mars and Europa). One possibility is that this deviation is a result of multiple consecutive ignitions. Whatever the reason, using ice in a furnace creates some unpredictability.

Furnace cooling rate

unknown

Observations

• the rate of cooling is temperature dependent, hotter cools faster (furnace temp - surrounding temp? how do vaccum behave?)
• the rate of cooling is time dependent (game tick speed is once per 0.5 seconds)
• the rate of cooling is mol dependent (small amounts cool faster, appears to be a linear correlation)
• adding ores decreases the temperature (do melting cost energy? or is this just from heating the trapped gases inside the ore?)

Possible experimental setup to measure dT/dt

• Hold a tablet with an atmos cartridge in the right hand (so it can be read when the game is paused). Aim the tablet against the furnace and pause with ESC, double tap ESC to move the game forward one tick, record the temperatures.
• Remember to record the total amount of moles as well

Resetting the furnace

Since only gas have temperature, evacuating all gas means resetting the temperature

Calculating how to reach a desired Temperature and Pressure on ignition

There are only 4 variables required for this calculation.

1. Intial fuel mix temperature (furnace temperature before ignition)
2. Desired temperature on ignition (you choose)
3. Desired pressure on ignition (you choose)
4. The specific heat value of the gas used to dilute the fuel (if a mix of gases is used, the specific heat to use is the average specific heat per mol, example calculation below)

Diluting the fuel correctly isn't hard, but if there are issues one can easily double check if the mix is correct by using the tablet and looking at the mol% values for the fuel mix. The fuel ratio calculated with the big equation below uses the entire 1O2+2H2 combination, to get the individual ratios for O2 and H2, these must first be calculated. This is actually very easy and the equations used are written under Diluting the fuel.

The equations below will give these values

1. The ratio(fuel) in the fuel-dilutant mix. (0.75 means 75% perfect 1:2 fuel mols (O2 and H2 added together)† and 25% are dilutant gas mols)
2. The pressure of the fuel mix to put into the furnace before ignition

†It's important to separate out fuel part like this so either O2 or H2 can be used as dilutant gas if desired

Calculating the fuel ratio

• ratio(fuel) = n(fuel)/(n(fuel)+n(dilutant)) = s*(T(after) - T(before)) / ( T(before)*(61.9/3-s) + (0.95*595k/3) ) - T(after)*(61.9-s) - T(after)*(0.95*181.7/3) )
  • k = 1000
  • s = specific heat of diluting gas
    • if the dilutant is a mix of gases, calculate the average specific heat in the mix per mol
    • example: 8 mol N2 and 17 mol CO2 as dilutant -> specific heat = (8*20.6 + 17*28.2) / (8+17) = 25.77
  • n(fuel) = total mols of fuel = n(O2)+n(H2) together (always in the perfect 1:2 ratio, if either O2 or H2 are in excess the extra amount is considered a dilutant)
  • n(dilutant) = total mols of non-combusting gas (this can be an excess of O2 or H2 if that is used as dilutant)
  • ratio(fuel), 1 = 100% fuel = 33.3% O2 and 66.7% H2, no dilutant present

Diluting the fuel

• desired mol ratio of O2 inside the fuel mix (used to help with dilution if there is H2 in excess) = ratio(fuel)/3
• desired mol ratio of H2 inside the fuel (used to help with dilution if there is O2 in excess) = ratio(fuel)*2/3

When diluting fuel with a gas mixer the temperature of the fuel and dilutant must be the same. One simple way to get around this is by using a tablet to check the number of mols in the mix instead, and comparing with the result of one of the two tiny equations just above.

Calculating the pressure before ignition

• P(before) = P(after)*R*T(before) / ( (R*T(after)) * (1 + ratio(fuel)*2*0.95) )
  • r(fuel) is the result from the temperature calculation above
  • R = 8314
  • P(after) = desired value, in Pa
  • T(before) = temperature of fuel mix in the furnace before ignition
  • T(after) = the chosen value used in the temperature calculation above

Example calculation

It's a warm and sunny day on Europa and a stationeer wants to make some invar. The desired temperature and pressure will chosen as be the upper limit for invar, so 1500K and 20MPa. Adding ore to the furnace will reduce its temperature and increase the amount of gas (and pressure) inside of it, but the stationeer is pretty sure that making just 100g of invar should be doable. The furnace is exposed to the atmosphere and will be loosing temperature and pressure fairly fast which could be an issue, but making the alloy should be quick enough. The dilutant gas will be pure O2 from the atmosphere, which has a specific heat value of 21.1. The starting temperature of the fuel and the atmosphere are both at -140°C.

• ratio(fuel) = s*(T(after) - T(before)) / ( T(before)*(61.9/3-s) + (0.95*595000/3) ) - T(after)*(61.9-s) - T(after)*(0.95*181.7/3) )
  • s = specific heat of the dilutant = 21.1
  • T(after) = 1500K (this is the chosen value)
  • T(before) = -140C = 133K (temperature inside the furnace before ignition)

ratio(fuel) = 0.281

since O2 is also the dilutant here, the ratio of H2 is limiting value for the fuel, knowing this value will help when diluting it

ratio(H2) = 0.281 * 2/3 = 0.187

the fuel mix should have 18.7% moles of H2, the rest of it will be O2

The necessary pressure of the pre-ignition fuel mix inside the furnace will be

• P(before) = P(after)*R*T(before) / ( (R*T(after)) * (1 + ratio(fuel)*2*0.95) )
  • ratio(fuel) = 0.281
  • P(after) = 20MPa (this is the chosen value)
  • T(before) = -140C = 133K
  • T(after) = 1500K (this is the chosen value used in the temperature calculation)

P(before) = 1156.5kPa

The furnace will be fed 1.16MPa of a O2/H2 gas mix containing 19% H2. This will produce the desired 1500K and 20MPa.

Making 100g of invar this way is possible, but the ores chilling effect on the temperature and the increase in pressure is definately noticeable. One has to wait for a few seconds to let the pressure drop down below 20MPa after adding the ore, when this happens the temperature is still a bit over 1200K, leaving a big enough time window to easily get the ingot out.

Experiment used to determine the amount of released energy from combustion (so it can be verified)

1. Place a frame, build a furnace partially inside the frame, complete the frame. The furnace is now perfectly insulated and will no longer loose temperature (unless ore is added) nor explode from high pressure
2. Add fuel (2:1 not required) via a pipe, use over 1000 mol of O2, remove the pipe attached to the furnace
3. Record all mol amounts and temp with a tablet (atmos cartridge), convert temp to K (add +273)
4. Ignite furnace, record all mol amounts and temp with tablet, convert temp to K
5. Calculate moles of combusted O2 (= moles before - moles after)
6. Calculate the Thermal energy in the gas, before and after (Thermal energy = Temp * sum(mol of each gas * specific heat)
7. Calculate energy released per mol of combusted O2 (= TE.after - TE.before) / moles of combusted O2)
8. Deconstruct the furnace completely to disarm it safely, or connect a single pipe so it can burst and act as a vent
9. Alternatively: A circuit can probably also be used to capture the temperature and pressure at the point of ignition