First up is carbon dioxide. People exhale around 0.998 kg of CO2 per day and consume 0.835 kg O2 per day. The OSHA limit for normal exposure is 1000 ppm, while NASA's 1000-day limit is 5000 ppm. (Granted, NASA is specifying a 70-kg man in peak condition; the population will be mixed gender and age including children, but a little excess capacity doesn't hurt.)
Zeolites (a type of molecular sieve that can be used for CO2 capture) work by adsorbing a specific gas until the structure is full, then releasing the gas under heat and/or vacuum. This release is called the regeneration phase and normally takes less time than the adsorption phase. For continuous operation the system requires twice the amount of zeolite needed for the adsorption phase; adding a third measure provides a good safety factor and could also provide emergency capacity if needed. The behavior of zeolites depends strongly on their molecular structure and they can trap more than one kind of molecule, so a detailed design will consider water vapor and other gases.
NASA currently uses a four-bed system with silica/13X beads to adsorb water and 4A beads to adsorb CO2; the beds are exposed to vacuum and strongly heated to reject the CO2 into space. This takes a lot of power and wastes the CO2. The silica beds also have to be heated over 100 °C to force the water out.
Let's look at an alternative sorbent, MIL-101(Cr). The two important characteristics are the low-temperature regeneration and the fact that it will adsorb CO2 in the presence of water vapor. The capacity is low, about 21 grams CO2 per kg; however, we can choose to regenerate at 45 °C under vacuum and get 95% capacity in 10 minutes with a much smaller heat demand. The linked report shows performance in a 10% CO2 stream where the sorbent is saturated after about 10 minutes; we will be operating at less than 0.1% CO2 for about 60 minutes or until saturation. Let's also use the NASA CO2 value and consider the system on a mass basis. We need to handle 998 / 24 = 41.6 grams CO2 per hour. Also of concern is that the material loses some of its effectiveness over time and it can lose some mass as fine dust due to wear; let's allow up to 10% loss of effectiveness, or 0.95 * 0.9 = 0.855 of rated capacity, 17.96 grams per kg. At 17.96 grams CO2 per kg sorbent we need 2.316 kg for each bed (per person). NASA uses two beds, but let's spec three beds. If one fails or requires maintenance that can't be done between regeneration and onlining then there is a third bed available. As an emergency capability, two beds can capture CO2 at the same time while a third is regenerated; since regeneration takes much less time than saturation this means the system can more than double its performance when necessary. Sorbent mass is then 6.949 kg per person and could need replacement as often as annually. (The metal salts in this material can be recovered fairly easily and the organic linking compounds can be reconstituted from base elements, so it is recyclable.)
The temperature difference between 25 °C input air and 45 °C regenerating bed is only 20 K, easily within reach of a high-performance heat pump at a COP of around 5. The adsorption process generates heat equal to the heat of vaporization of CO2, or 121.3 kJ/kg at 25 °C. At 45 °C CO2 is supercritical, so there is no heat of vaporization to speak of; we need only heat it and apply vacuum for it to desorb. Also of note, this material can adsorb water vapor in excess of its own mass; we will assume that all water vapor in the input air is adsorbed.
ASHRAE recommends whole-house ventilation of 25 l per second, which is presumably for a standard American house and a family of four. In addition, the make-up air for this ventilation will contain 350-450 ppm CO2. The habitat's makeup air will contain nearly zero CO2, so ventilation requirements may be as low as 5 l per second per person. In areas with high humidity (kitchen, bathroom, etc.) additional humidity management will be required, either as a dehumidifier or as ventilation. Countering this is the need to trap particulates, remove sufficient CO2 and properly cool the space. It seems that a central or at least regional air-processing facility would have fairly steady loads, while a local facility would have downtime paired with high-demand periods. Minimizing the number of complex parts and using economies of scale means each air handling facility will serve a diverse volume and steady demand. For this reason let's assume each room has a supply vent and a return vent, and these vents are ducted to the nearest air facility as efficiently as possible. Return vents in high-humidity areas will have fans to increase the volume of air moved. Return vents will have low pressure drop filters (plant fiber with activated carbon) to adsorb volatiles and trap some dust; these will be burned off periodically and replaced. Supply vents will be operable so an unoccupied volume is not serviced unnecessarily. The air facility will provide HEPA-grade particle filtration and activated carbon volatiles filtration, possibly including electrostatic equipment.
We are handling 41.6 grams of CO2 which generates 5.046 kJ of heat. The specific heat of CO2 at 25 °C is 0.846 kJ/kg*K and 0.865 kJ/kg*K at 45 °C, a value that is nearly linear over this range; we will use the average value of 0.856 kJ/kg*K. We also handle some amount of water vapor; our input air is assumed to be 50% rH, but the mass of water handled depends on what volume of air we handle in an hour.
NASA specifies 2.277 kg per person per day of water vapor as perspiration and respiration, which is 94.875 grams per hour. At 25 °C the saturation pressure is 3159(3158.502) Pa and vapor density is 0.02331 kg/m³, while the air density is 1.105 kg/m³. The air has a specific heat of 1.005 kJ/kg-K and the water vapor has a specific heat of 4186 kJ/kg-K. At 50% rH the water vapor density is 11.65 g/m³. We require 8.14 m³/hr (2.26 l per second) of processed air to remove that much water vapor. The water is condensed directly onto the adsorbent, yielding 2256 kJ/kg * 0.094857 kg = 214.04 kJ of heat. As mentioned above, the CO2 produces 5.05 kJ of heat. The dry, filtered air can now be cooled to whatever level is necessary. The dewpoint at 25 °C and 50% rH is 14 °C, so a minimum value is probably 15 °C. We're handling 8.995 kg of air and dropping by 10 °C, which removes 90.4 kJ of heat. Ignoring the CO2 contribution, the combination of air and water vapor removes 304.44 kJ per hour or 84.57 watts of heat. This is definitely not enough; we need to handle about 137 watts just for body heat plus around 15 watts for lighting. The difference will be made up by processing more air and introducing some water vapor back into the return air.
30% rH is a reasonable value to avoid static electricity problems. At 15 °C the saturation pressure is 1700.13 Pa and vapor density is 0.01298 kg/m³, while the air density is 1.225 kg/m³, or 0.902 m³ of output air per 1 m³ of input air. At 30% rH the water vapor density is 3.89 g/m³, or 3.51 g/m³ of input air. Now we are removing only 8.14 grams of water per m³ of input air, so we need to handle 11.654 m³/hr. The output air will contain 40.91 g of water vapor at 15 °C which will later rise to 25 °C, carrying 1,712.3 kJ of heat. The air itself masses 12.878 kg and carries 129.4 kJ of heat. Now we're up to 512 W of heat, about three times as much as we need for metabolism. That leaves some leeway for other equipment, around 360 W per person.
The sorbent bed needs to handle 135.77 g water vapor per hour plus 41.6 g CO2 per hour. These produce 311.35 kJ of heat to be removed from the bed. To regenerate, the loaded bed needs to be heated 20 °C under vacuum. The water requires 11,366.67 kJ to reach this temperature and the CO2 needs 0.71 kJ. The sorbent needs less than 1 kJ/kg*K, which is considerably less than the margin of error for my many assumptions and will be ignored. At low pressure (0.09 bar), the boiling point of water is below 45 °C. The heat of vaporization rises to about 2400 kJ/kg, so another 325.8 kJ are required to boil it out. The CO2 is supercritical and passes freely out of the bed. We reach a total of 11,693 kJ of heat required for regeneration.
There are three sources of heat readily available: the active sorbent bed (311.35 kJ/hr), the input air stream (129.4 kJ/hr) and the regeneration exhaust. Drawing heat out of the exhaust under reduced pressure means we can condense and separate the water (slightly carbonated), then compress and cool the remaining high-concentration CO2. The first step is to condense the water while still above the critical temperature of CO2; dropping 5 °C yields 3,167.47 kJ as the water condenses (reducing the water vapor volume and easing the load ono the vacuum pump), then a further 6,252 kJ to bring it back to 29 °C. This is a total of 9,860 kJ scavenged. Moving it with a heat pump possessing a COP of 5 (reasonable for such a low temp swing) will cost 1,972 kJ per hour or about 550 watts. The heat pump's waste heat goes into the regen cycle. This is not perfect; some heat is lost into the output air and not all of the heat pump's heat can be moved into the regen bed. Still, these numbers are close enough to work with and have a lot of margin built in. For comparison to imperial units, a 550-watt heat pump with a COP of 5 is roughly 0.8 tons of refrigeration or about a fourth of a whole-house AC.
Further work will be to find the energy needs of the vacuum pumps and fans. These values will be substantial and cannot be ignored.
6.95 kg sorbent MIL-101(Cr) per person, reprocess annually
11.654 m³/hr ventilation per person
550 watts heat pump per person
40.91 g/hr clean water for makeup humidity per person
135.77 g/hr water recovered per person
41.6 g/hr CO2 recovered per person
bagasse or other plant fiber filters with activated carbon for local particulate and volatiles control
HEPA-grade central filtration
vacuum pumps for regen
describe air system in hydro areas
describe heat flow from regen system to radiators
volume of air handling equipment (spec for 100 people each?)
gut-check duct volumes and air velocities to ensure this is reasonable