Last year I wrapped up my Master’s studies at Cambridge with a year-long thesis project in the Whittle Laboratory, doing some very exciting work optimising ISRU components for Martian operation at scale. In the aftermath I continued pulling on threads in the thermodynamic optimisation space at the kilo- and mega-scale, and got to some equally fun conclusions. I’ve neglected to share these, apart from with some select people who asked, until I got a poke from a colleague that they might be appreciated. So enjoy – this is part 3 of 3 shortform reports that accompany the main thesis text.
Read more: Large-Scale Energy Storage for MarsThis post is available in PDF format, in case you prefer LaTeX formatting.
This is the last of the three reports I wrote on Mars thermodynamic engineering, but isn’t the end of the work I was doing on the subject. More to follow!
1. Overview
- Four “novel energy storage” systems were analysed for Starship-scale Mars operations: a liquid-storage hydrogen fuel cell, a liquid carbon dioxide expander turbine, a methalox turbine and a methalox fuel cell. Each of these makes use of ISRU materials as a means of energy storage. These were compared to current technology of lithium-ion batteries and hydrogen fuel cells with compressed gas storage.
- As with most surface ISRU systems, the total system mass of an energy storage system is dominated by the mass of electrical generation and heat rejection systems. This emphasises the need to improve system efficiency and reduce the weight of both of these subsystems.
- In general, novel systems have a higher fixed mass than traditional, but a substantially lower weight per energy stored. This makes them higher performing at larger scales.
- Assuming equal charge and discharge times, batteries are highest performing below around 50MWh, gas-storage hydrogen fuel cells below 200MWh, carbon dioxide expander turbines below 800MWh and methalox turbines above this point.
- Liquid hydrogen fuel cells and methalox fuel cells are likely never competitive, unless the underlying technology were to improve, as they are outperformed by similar alternatives.
- All novel systems have much heavier charging than discharging systems, so may be well suited for slow charge and relatively rapid discharge, ie not for diurnal energy storage.
- Both liquid carbon dioxide and methalox experience substantial boiloff from uninsulated tanks, on the order of 0.3-3% per day. Liquid carbon dioxide levels are best replenished by recapturing new carbon dioxide, while methalox is best kept with a cryocooler to achieve zero boiloff
2. Working Assumptions
Data on the performance of traditional systems, as well as the mass equivalency factors for power
and thermal systems, were obtained from Baseline Values and Assumptions Document [1]. Additional data on fuel cells was obtained from relevant NASA publications [2] [3]. The general assumptions are given in Table 2.1.
| Parameter | Value | Unit | Source |
| Mass equivalency of solar cells | 100 | kg/kWe | BVAD [1] |
| Mass equivalency of Martian radiators | 121 | kg/kWth | BVAD [1] |
| Methane-oxygen reaction energy | 10 | MJ/kg reactant | Cambridge University databook |
| Hydrogen-oxygen reaction energy | 13.3 | MJ/kg reactant | Cambridge University databook |
| Cryocooler mass equivalency | 50 | kg/kWth | Prior work (see Master’s thesis) |
| Methalox production energy from water and compressed CO2 | 50 | MJ/kg output | Prior work (see Process Engineering At Scale) |
| Maximum polytropic turbine efficiency | 85 | % | Prior Work (see Master’s thesis) |
3. Results
The results of the study are laid out in Table 3.1, with the mass efficiency of each system broken down by column. The charging specific power is the mass of the subsystem required to charge up the energy storage system, per unit input power. The discharge specific power is the mass
of the subsystem required to discharge the energy storage system, per unit output power. The storage specific energy is the mass of the actual energy storage subsystem, per unit output energy, neglecting any boiloff mitigation. The estimated round-trip efficiency of each system is also given. No single figure of merit is calculated as this depends on the required charging and discharging power and the quantity of energy stored. Instead, the subsystems of each energy storage system are separated as described, allowing for a calculation of total mass for a given
design requirement.
To calculate the total mass of an energy storage system, the specific input, output and stored power of the system should each be multiplied by the relevant design value. For instance, a liquid carbon dioxide system storing 100kWh with a charging power of 50kW and discharging power of 200kW would weigh (100 kW-hr × 0.29 kg/kWh) + (50 kWin × 241 kg/kWin) + (200 kWout ×14 kg/kWout) = 14879 kg. This is true for all systems apart from batteries, where each mass value for charge, discharge and storage is calculated separately and the largest taken.
| Approach | Charge specific power (kg/kW input) | Discharge specific power (kg/kW output) | Storage specific energy (kg/kW-h output) | Round-trip efficiency |
| Li-Ion batteries | 2* | 2* | 5* | ~99% |
| H2 regenerative fuel cell, pressurised gases stored | 0.5 | 0.5 | 1 | ~50% |
| H2 regenerative fuel cell, cryogenic liquids stored | 0.5(electrolyser) 20 (liquefier) 48 (radiator, 0.4kWth/kWin) 69 total | 0.5 | 0.12 | 14% |
| CO2 expander turbine | 1.4 (compressor) 240 (radiator, 1.98kWth/kWin) 241 total | 14 | 0.29 | 90% |
| Methalox turbine | 0.2 (CO2 compressor) 13 (methalox production) 28 (radiator, 1.30kWth/kWin) 241 total | 0.2 | ~1e-5 | 18% |
| Methalox fuel cell | 1 (low confidence) | 1 (low confidence) | ~1e-5 | 10% (low confidence) |
4. Hydrogen fuel cell, liquid reactant storage
Hydrogen fuel cells with liquefaction of reactants to increase storage density perform very poorly. While the efficiency of the electrolyser and fuel cell remain high, over 70% of the energy output of the fuel cell is required to liquify the reactants. This reduces efficiency from a respectable 50% to around 14%. This low efficiency hugely increases the mass of power generation and heat rejection to support the large liquefaction plant. A substantial improvement in liquefaction efficiency may improve the performance of this system, but the deep cryogenic temperature of liquid hydrogen make this unlikely.
5. Liquid Carbon Dioxide Expander Turbine
A liquid carbon dioxide expander turbine operates similarly to a reheated steam cycle for terrestrial power generation, using carbon dioxide rather than water as a working fluid. Cold liquid carbon dioxide is pressurised with a pump to high pressure (tens of bar), boiled in a heat exchanger and expanded through a turbine to generate mechanical power. After each turbine, the cold gaseous carbon dioxide is reheated in another heat exchanger to increase the specific work of each turbine and prevent the carbon dioxide condensing to liquid or solid inside the system. The carbon dioxide is eventually either exhausted to atmosphere or returned to a carbon dioxide acquisition compressor. Carbon dioxide is a relatively benign working fluid with substantial chemical and nuclear industry heritage, so the design of this system is not expected to be particularly novel.
This approach can theoretically produce substantial amounts of net power (ie, a round-trip efficiency greater than 100%) with sufficient reheat temperature. This would be a strong candidate for a nuclear energy power generation cycle on Mars. However, for this study the temperature of reheat was limited to 400K (127C) as might be achieved from waste process heat utilisation. Under these conditions, an optimal cycle might achieve a round-trip efficiency of 90-100% with a boiler pressure of 50 bar and 12 turbines. The dominant system weight is the radiator needed to reject heat from liquid carbon dioxide compression.
A plot of accessible system performance is given in Figure 5.1, showing the range of available round-trip efficiencies and power outputs at a given mass flow, for different boiler pressures and reheat temperatures. Some regions of the design space are not accessible due to limitations of the carbon dioxide vapour pressure line. High efficiencies and high power outputs for a given mass flow (or high specific works) occur for high boiler pressures and high reheat temperatures as expected.
flow (215g/s). Round-trip efficiency is given on the left, varying from 48% to 102%. Turbine power output is given on the right, varying from 48kW to 96kW (specific power of 223kJ/kg to 446kJ/kg). Some regions are inaccessible due to the approach of the carbon dioxide in the turbine to the vapour dome or sublimation line.
6. Methalox Turbines
Methalox turbine generation presents the opportunity to directly utilise methane and oxygen rocket propellants as fuel and oxidiser in a more conventional gas turbine arrangement. Due to the need to limit turbine blade temperature to substantially below the flame temperature, carbon dioxide is also injected into the combustor. This is analagous to the air-rich operation of all industrial and aviation gas turbines. To limit the combustor temperature to reasonable values, 77% of mass flow in the turbine is composed of additional carbon dioxide. Similar to the carbon dioxide turbine, the turbine string is also limited by the formation of liquid water and liquid and solid carbon dioxide. It is assumed that water is removed by a condensing heat exchanger just above the point where it would be problematic, and the turbine string terminates when carbon dioxide condensation would be problematic.
As expected, this approach is extremely lightweight due to the small size of the turbines required and lack of need for multiple reheating heat exchangers. However, it suffers from poor efficiency of the methalox production process. Based on prior work (see At-Scale Process Engineering) it was found that current technology assumes a 20% production efficiency with an electrochemical process. Even with the roughly 85% energy conversion efficiency of the turbine stack, the round trip efficiency is still low. This makes the methalox turbine well-suited for extremely large-scale energy storage systems, and means it benefits the most from improvements to the methalox production process.
7. Methalox Fuel Cells
Methalox fuel cells suffer from the same issues with methalox production efficiency as turbines, but with lower round-trip efficiency and thus a higher overall system mass. Even with an optimistic fuel cell efficiency of 50%, higher than the well-studied hydrogen fuel cell, efficiency is substantially worse than the turbine equivalent. This is unlikely to change in the near future, making methalox fuel cells an unattractive option.
8. Starship Tanks for Energy Storage
The potential of Starship propellant tanks for energy storage are given below. Data for propellant tank volumes are taken from Twitter use @fael097, and are presumed correct for SN15 as of February 2021. These values are expected to have shifted with the introduction of Starship V2 (or whatever version we’re on now) and are likely to change again with a future Mars landing variant, but are presented as indicative of the energy storage potential of a single landed Starship.
Given an approximate ISRU power consumption of 1MW, a single Starship filled with liquid CO2 can store around a week of energy consumption. This 1MW expander turbine would weigh around 14 tonnes.
| CH4 main | O2 main | CH4 header | O2 header | Total | |
| Volume (m3) | 603 | 796 | 16.2 | 18.6 | 1433.8 |
| Fluid capacity of each tank (kg) | |||||
| Liquid CO2 (6 bar) | 703,000 | 928,000 | 18,900 | 21,700 | 1,671,600 |
| Liquid oxygen (1 bar) | 908,000 | 21,000 | 929,000 | ||
| Liquid methane (1 bar) | 254,000 | 6,800 | 260,800 | ||
| Oxygen gas (6 bar, 273K) | 5,100 | 6,800 | 174 | 158 | 12,232 |
| Hydrogen gas (6 bar, 273K) | 320 | 423 | 8.6 | 9.9 | 761.5 |
| Energy storage capacities (MW-h) | |||||
| Liquid CO2 expander | 69.2 | 91.4 | 1.86 | 2.14 | 164.6 |
| Methalox turbine, CO2 stored | CO2, 12% full | CH4, 77% full | O2, 100% full | 67.4 | |
| Methalox turbine, no CO2 stored | CH4, 89% full | O2, 100% full | CH4, 100% full | O2, 100% full | 2740 |
| Hydrogen gas fuel cell | O2, 15% full | H2, 100% full | H2, 100% full | H2, 100% full | 2.2 |
8.1 Heat gain into Starship tanks
In each case where liquid reactants are stored in the Starship main tanks, the temperature must be maintained to prevent substantial boiloff. The significance of this boiloff must be considered when evaluating the effectiveness of any system of energy storage that uses liquids as energy stores. To calculate this heat loading, the Syrtis one-dimensional heat transfer modelling code was used. This Python code solves heat transfer from radiation, convection, solar insolation and conduction on the Martian surface to assess heat transfer to habitats and other pressure vessels [4].
The Starship tanks were modelled as bare stainless steel with thickness 3.2mm and diameter 9m, placed at a latitude of 30 degrees north (the approximate target Starship landing sites). Heat gains per metre of tank length are given in Table 8.2, along with calculated boiloff quantities in kilograms per metre of tank length and percent total load.
The maximum heat load into liquid carbon dioxide is 2.8kW per metre, or 70kW for both main tanks. Rejecting this heat in a cryocooler would require around 700kW of electrical input with a 3.5t system. Instead replenishing boiloff gas by producing additional carbon dioxide from the atmosphere would require 18,000kg of production per day or 180kW of constant energy input. The boiling off carbon dioxide could be used to drive an expander turbine with 53kW of output power, so a net power input of just 127kW would be needed. Replacing rather than re-condensing carbon dioxide is thus an optimal choice for this power system. As the vehicle tanks store 164.6MWh, the boiloff figure of merit (energy stored over energy required for zero boiloff) is 1300.
| Summer condition | Winter condition | |
| Daily heat gain Liquid CO2 | 2.5 x 108 J/m 2.8kW/m | 0.7 x 108 J/m 2.8kW/m |
| Daily boiloff Liquid CO2 | 720kg/m 1.0% | 200kg/m 0.3% |
| Daily heat gain Cryogen | 4.5 x 108 J/m 2.8kW/m | 2.8 x 108 J/m 2.8kW/m |
| Daily boiloff Cryogenic O2 | 2110kg/m 2.9% | 1310kg/m 1.8% |
| Daily boiloff Cryogenic CH4 | 880kg/m 3.3% | 550kg/m 2.1% |
| Daily heat gain gas | 0.7 x 108 J/m 0.8kW/m | -1.0 x 108 J/m -1.0kW/m |
The maximum heat load into cryogenic tanks is around twice as large, requiring 128kW of cooling power or 1275kW of electrical input for a cryocooler. Replacing the roughly 40,000kg of reactant boiloff per day would require a much larger 22,500kW of input power to a methalox pro-
duction stack, so cryocooling is the appropriate choice. This would be a substantially heavier overall boiloff reduction system due to increased cooler mass, power system and heat rejection. The boiloff figure of merit is 2150.
A thermal control coating on the surface of a storage Ship would reduce heat loads considerably, particularly for liquid carbon dioxide which is stored relatively close to Mars ambient temperature. An idealised titanium dioxide coating reduces the diurnal total heat load into carbon dioxide tanks to zero, and cuts the heat load for cryogens roughly in half. However, this would require a fairly substantial engineering effort to remove thermal protection tiles from the Ship after landing and keep the surface free of accumulated dust. If such measures are being taken, further insulating materials such as closed-cell foams or MLI blankets may also be used.
Bibliography
[1] M. Anderson et al. Life Support Baseline Values and Assumptions Document. 2015.
[2] K. A. Burke. Fuel Cells for Space Science Applications. Technical Memorandum NASA-TM-212730. Glenn Research Center, Cleveland, OH: National Aeronautics and Space Administration, 2003.
[3] C. P Garcia et al. Round Trip Energy Efficiency of NASA Glenn Regenerative Fuel Cell System. Technical Memorandum NASA-TM-214054. Glenn Research Center, Cleveland, OH: National Aeronautics and Space Administration, 2006.
[4] S. Ross. Syrtis: A Python package for Martian heat transfer analysis. https://github.com/smross106/Syrtis. 2023.