An astounding variety of data supports the conclusion that our earth’s climate is changing due to increasing greenhouse gas (GHG) concentrations in the atmosphere. The economic, social, and environmental implications could be catastrophic. Moreover, scientists have reached a consensus that the increase in GHGs is indeed anthropogenic, caused by fossil fuel burning and deforestation. Carbon dioxide (CO2) is the GHG that contributes the most to climate change because of both its abundance and long atmospheric lifetime. With the rapid economic development of China (the world’s leading CO2 emitter) and India’s increasing energy demands, the rate of CO2 emissions is accelerating, leaving politicians, scientists, and engineers with an international problem of an enormous scale.

More long-term technological development is required to substantially shift to renewable energy sources that do not emit CO2. Thus, short-term solutions are being considered that enable us to continue using fossil fuels. At present, coal-burning power plants provide 42% of electricity in the US, but at the expense of accounting for ~36% of US CO2 emissions. Among a portfolio of strategies to mitigate anthropogenic CO2 emissions, one high-impact option is carbon capture and storage (CCS). The idea is to capture the CO2 from the flue gas emitted from the smokestacks of coal-burning power plants and subsequently store it underground in a geological formation. The geological formation can be thought of as a sponge for CO2, sequestering it from the atmosphere where it would, otherwise, instigate global warming.

An advantage of the CCS process is that it can in principle be retrofitted to existing coal power plants. A coal power plant retires after a long 45 years of use; a plant built today will, if left unchecked, continue to emit CO2 for 45 years coming. The economics of completely abandoning a prodigious investment in a young plant to curb CO2 emissions are unfeasible. CCS technologies are attractive because they can prevent climate change while protecting current investments.

Already, commercial-scale CCS technologies are in operation, but not at the scale of a large coal power plant. Its market-readiness for mass-adoption is complicated by two broad issues. The first issue is related to the tremendous rate of CO2 emissions. A back-of-the-envelope calculation reveals that the US alone releases from its coal-burning power plants enough CO2 to fill the Empire State Building 100 times every hour. Even given the magic chemical or material that captures CO2 from the flue gas, imagine how much of it we would need. The second issue is that the CCS process places a parasitic energy load on the plant, and that is the focus of this article. The most energetically intensive part of the CCS scheme is capturing the CO2 from the flue gas, separating it from the other components mainly nitrogen (- then why even separate the CO2? - see Note below) Capture technologies at present are estimated to cost 25-30% of a plant’s power output, driving up the price of electricity by around 80%.

Can we improve capture technologies to reduce the energy costs for separating CO2 from the flue gas? The laws of thermodynamics allow us to calculate the minimum theoretical energy requirement for the separation of the CO2 from the flue gas. That is, the same thermodynamic laws that preclude the construction of a perpetual motion machine say that, no matter how ingenious of a capture process we design, there will always be an energy cost for separating the CO2 from the flue gas. Fig 1 shows a plot of the minimum energy required (per mole of CO2) to separate the CO2 from an ideal gas mixture as a function of the CO2 concentration in the starting mixture. As a sanity check, note that a mixture that is already pure CO2 takes zero energy to separate. For the flue gas from a coal-burning power plant, the CO2 concentration is ~13 mol %, and the minimum theoretical energy requirement from the graph (green dot) turns out to be ~5% of the output of the coal power plant, suggesting that there is room for improvement in current carbon capture technologies.

One might ask, instead, why not just capture CO2 from the very air we breathe? Fig 1 shows that, as the fraction of CO2 in the mixture decreases, we need more and more energy to separate it from the mixture. The CO2 concentration in the air is a measly 0.039 mol % (red dot), rendering energy costs for a separation from air four times that of a separation performed on the flue gas from a coal power plant-- even if we were to develop the most efficient separation process nature allows. Another reason to avoid separating CO2 from air is that, for every liter of CO2 to be recovered from the atmosphere, 2500 liters of air must be processed. This excessive air flow rate through a capture process and the increased separation energy costs for such a small CO2 concentration in the air lead to the following conclusion. Procrastinating CCS on coal power plants and instead resolving to capture CO2 out of the the air we breathe-- after the flue gas mixes with the atmosphere-- will lead to larger separation costs in the future. This is important to consider given that a CO2 molecule released today will stay in the atmosphere for a time comparable to our life span, absorbing sunlight and warming our planet throughout the entire duration.

The separation energy requirement stems from the tendency of all physical systems to increase a mathematical quantity called entropy; an intuitive, qualitative definition of entropy is “disorder”. The second law of thermodynamics states that an isolated system will maximize its disorder. Fig 2 shows an isolated system (the black box) containing the flue gas in two disparate states (both at the same temperature and pressure). CO2 molecules are depicted as red spheres, whereas all other components of the flue gas are depicted as blue spheres. In state 1, a barrier exists that separates CO2 molecules from the rest. If we remove the barrier, the second law tells us that CO2 will spontaneously mix with the other components, entering state 2, without the help of some outside influence. Because each of the molecules can now explore a greater volume, the disorder of the system has increased, as nature prefers.

In carbon capture, we are starting off in state 2, and we desire to move to state 1. Unfortunate for CCS, going from state 2 to state 1 involves a decrease in disorder (entropy), and this will not happen spontaneously without some outside influence. That is, isolated physical systems tend to maximize their entropy, and if we want to decrease a system’s entropy, we must input energy into the system. In the context of carbon capture, if we want to separate the CO2 from the flue gas, it is inevitably going to cost energy. The laws of thermodynamics allow us to calculate the minimum energy requirement by considering a reversible process from state 2 to state 1, and this is a lower bound-- for the most efficient, ingenious process yet-to-be-discovered.

The utility of the entropy of mixing concept is to check how much more progress we can possibly make with capture technology and set realistic targets. The conclusion is that there is room for improvement, but CCS technologies will inevitably incur a sizeable parasitic energy cost on a coal-fired power plant. Since the energy cost is a decreasing function of the concentration of CO2 in the starting mixture (Fig 1), we see the energetic benefits of capturing CO2 from coal power plants now, rather than later, after it mixes in the air.

------- The math behind the generation of Fig 1 for those interested ----

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Note: If capturing the CO2 out of the flue gas is the most expensive part, why do we need to separate the CO2 from the flue stream? Why not just pump the entire flue gas stream into the geological reservoir? Well, fortunately, CO2 can be compressed into a supercritical fluid at a reasonable pressure and temperature, endowing it with liquid-like densities and gas-like viscosities-- both ideal properties for it to be transported and pumped underground relatively easily. The most obvious reason for not sending the entire flue gas underground is that ~13% of the flue gas stream is CO2, so, even assuming that the other components of the flue gas have exactly the same desirable properties as CO2, storing the entire flue stream requires 7-8 times of (i) the volume of the storage reservoir and (ii) compression and pumping throughput for transporting the flue gas underground. However, the other flue gas components do not have nearly as desirable properties as CO2, and the compression, pumping, and subsequent storage of these components would impose enormous energy costs that make storing the entire flue gas stream unfeasible. Furthermore, a key idea with geological sequestration is that the CO2 will undergo chemical reactions with minerals in the geological formation and, after thousands of years, turn into a mineral. At this point, the CO2 has zero probability of escaping back into the atmosphere. Nitrogen, on the other hand, is too inert to react and form minerals.

** The idea for this blog post came from a course I am taking at Berkeley titled “Carbon Capture and Sequestration”. An interactive iBook is coming soon: Berkeley Lectures on Energy: Carbon Capture and Sequestration by Berend Smit, Jeffrey Reimer, Curt Oldenburg, and Ian Bourg.

Sources:

A Brown and B Freeman. Analysis and Status of Post-Combustion Carbon Dioxide Capture Technologies. Environmental Science and Technology. (2011) 45 (20), pp 8624–8632.

Smith, Van Ness, and Abbott. Introduction to Chemical Engineering Thermodynamics.

Sponge analogy for a geological formation: https://www.youtube.com/watch?v=ROEFaHKVmSs