Continuing on the theme I started in my curtailment post, this is a detailed look at a renewable chemical plant centered around a Sabatier reactor, which converts CO2 and hydrogen into methane. The idea here is a floating plant fed with power from wind turbines and solar panels that produce methane that can be used to displace fossil methane from natural gas.

Plant Overview

The plant consists of four main units, the electrolysis unit that splits water into hydrogen and oxygen, a distillation unit that extracts pure water from seawater to feed to the electrolysis unit, an liquid amine-based direct air capture unit to extract CO2 from the air, and a Sabatier reactor that turns hydrogen and carbon dioxide into methane. Not shown is either pipelines to export the methane, oxygen and excess water to shore and a pipeline to import carbon dioxide from carbon capture systems, or liquefaction plants to do the same with cryogenic ships.

I added power and mass flows to the diagram starting with the assumption of 1kW electrical power feed to the electrolysis unit then working out what the rest of the system values needed to be balanced. For simplicity of calculations, I assumed 100% efficiency of transfer between units, which is impossible in practice. Anywhere there is a heat flow, the value in a real plant will be at least 5-10% lower.

Electrolysis Unit

Starting with the starting 1000 Wh electricity to the electrolysis unit, we can calculate the amount of hydrogen after finding a reasonable value for the amount of energy it takes to produce 1kg of hydrogen. The value I used, 55 kWh / 1 kg H2 from here, gives us 18.18g hydrogen for 1000 Wh. Assuming a 70% efficiency (from the same paragraph) gives us 300 Wh waste heat. For an alkaline water electrolysis unit, this waste heat will be about 60-80C. I chose the lower value and feed the heat to the multi-stage flash distillation unit.

For the remaining parts, we need to refer to the chemical equation for water electrolysis to determine the amount of water required and the amount of oxygen produced.

2 H2O + e- ==> 2H2 + O2

Chemical	Molar Mass	Mass	Moles
H2 (given)	2.01568	18.18g	4.50
H2O	18.01528	162.31g	9.01
O2	31.998	143.99g	4.50

Multi-stage Flash Distillation Unit

The hydrogen in the methane that is exported has to come from somewhere, and as this is a floating plant, there is water everywhere, but it needs to be of a quality that it can be feed to the electrolysis unit. When designing this, I had two primary choices: reverse osmosis and multi-stage flash distillation. I chose the latter based on a single parameter: it can operate on waste heat, while the reverse osmosis needs higher-quality mechanical work in the form of the high-pressure pumps to drive the process.

Given the 300 Wh of waste heat from the electrolysis unit, this page gives us a starting point for working out how much water we can expect. Using 27 kWh/m3 of distilled water and applying unit transformations, we get 3g / Wh. For 300 Wh, we get 1107 g of distilled water. Of this water, we need 81.25 g to feed the electrolysis unit, the rest is recycled from the Sabatier reactor. the remaining 1025.75 g of water can be used as make-up water for the DAC unit, or shipped to shore for use in areas experiencing drought (looking at you, California).

Sabatier Reactor

This is the core of the plant, that takes hydrogen and carbon dioxide and forms methane that is a drop-in replacement for natural gas. We start with the 18.18 g of hydrogen from the electrolysis unit to begin our calculations. The Sabatier reaction is the following:

4 H2 + CO2 ==> CH4 + 2 H2O + 165.0 kJ heat

Chemical	Molar Mass	Mass	Moles
H2 (given)	2.01568	18.18g	2.25
CO2	44.009	99.02g	2.25
CH4	16.043	36.09g	2.25
H2O	18.01528	81.06g	4.50

This reaction is exothermic, with the reactor normally running 300-400C, so this is waste heat can be used for several things if there is enough, but in this plant, all the energy that is not going into the methane product will be repurposed elsewhere when possible. All the energy here is intended to drive the boiler in the amine regenerator for the direct air capture unit.

There is 165.0 kJ of heat released for each mole of reaction that occurs. 2.25 moles, gives 371.25 kJ which is the same as 103.12 Wh. There is an additional 50.74 Wh of energy in the water product that is released when it condenses from a vapor to a liquid. The heat of vaporization for water is 2257 kJ/kg = 626.94 Wh/kg = 0.626 Wh/g. For 81.06g of water that gives 50.74 Wh.

Unfortunately, all the energy released here is not enough to drive the regenerator boiler. There would be enough energy if we could use the waste heat from the electrolysis unit to also drive the regenerator, but that would require running the electrolysis at or above 95C and running the regenerator at about the same temperature and I don’t know if the technologies those units use can operate at that temperature.

To make up the shortfall, there are two strategies: use more electricity to provide the extra energy required to run the regenerator boiler thru resistance heaters or import carbon dioxide from elsewhere. Using imported carbon dioxide gives a power to methane efficiency of 55.6%, while running the heaters gives an efficiency of 45.3%, assuming the oxygen and water are dumped as waste products, when it is unlikely to be the case as both are useful in their own right.

Liquid-media Direct Air Capture Unit

Most of the important parts have already been covered, but here is the work for determining the thermal energy to CO2: starting from 0.13Mtoe / 1MtCO2 (from this page) and a number of conversions (1 ton oil equivalent (toe) is 11630 kWh) we arrive at 0.26g CO2 / 1 Wh. As we need 99.02g of CO2 to feed the Sabatier reactor that gives us an energy requirement of 380.84 kWh.

Using pure oxygen to run gas turbines or internal combustion engines to generate electricity allows for easy capture of the resulting carbon dioxide because it is easily separated from the other resulting component, water, by simple condensation. The CO2 could then be sent back to one of these plants to be turned back into methane.

The water would be useful at any location that is currently running a desalinization plant to provide potable water, which is many areas in the Middle East that will be hurting when they run out of oil and gas that can be economically extracted with net energy.

Addendum - November 9, 2020

After some additional thought, I realized I overlooked an important part of using waste heat. The amount of energy that can be provided is proportional to the difference in temperature between the inlet and the outlet of the heat exchanger used to deliver the heat. This is not covered in the above, and so the delivered energy will be less than the stated values by some amount.