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Tue Jun 20, 2017, 04:19 PM

Paper on the Equation of State for High Efficiency Supercritical Carbon Dioxide Driven Turbines.

I came across a very cool paper in a recent issue of one of my favorite scientific journals recently about one of the subjects that's been on my mind a lot recently, the physical chemistry of the dangerous fossil fuel waste carbon dioxide.

The paper is this one: Selection of a Proper Equation of State for the Modeling of a Supercritical CO2 Brayton Cycle: Consequences on the Process Design (Jaubert, et al, Ind. Eng. Chem. Res., 2017, 56 (23), pp 6841–6853)

The introductory paragraph from the paper describes better than I can why this paper is important:

"In recent years, alternative power cycles have received increasing attention as solutions to supply future energy demand, which is expected to rise by 70% by 2035.1 Among different candidates, the supercritical CO[SUB]2[/SUB] (SC-CO[SUB]2[/SUB]) Brayton cycle has emerged as promising solution for high-efficiency power production in nuclear, fossil-thermal, and solar-thermal applications. The investigation carried out by Mecheri and Le Moullec2 has shown that an adapted recompression SC-CO[SUB]2[/SUB] Brayton cycle would theoretically be 5%pt (point) more efficient than the water steam Rankine cycle for similar operating conditions."


If we accept a general working figure for the worldwide generation of electricity of 25,000 TWh per year this translates to about 90 exajoules (EJ) of energy per year of pure electricity, but not, it should be noted, the amount of energy consumed to generate electricity since the production of electricity always (from the second law of thermodynamics) will be less, generally much less, than 100% efficient. While modern combined cycle gas plants utilize both the Brayton cycle as referenced in the title of this paper coupled to a Rankine (steam) cycle can have efficiency values greater than 50%, most thermal plants, including most fossil and nuclear plants operate at roughly 30-35% efficiency.

Let's imagine for argument's sake that all of the 25,000 TWh (90 exajoules) of electricity were generated at 40% efficiency overall, which is probably not all that far from reality. Then the total energy expenditure on electricity generation would be on the order of 90EJ/.4 =225 exajoules, this out of a total energy demand (as of 2015) of 574 exajoules. Increasing the efficiency of by 5% to 90EJ/.45 = 200EJ would result in a total energy savings of 25 exajoules. To put this in perspective, 25 EJ is roughly 5 times as large as all the energy produced by all the so called "renewable energy" plants - solar and wind plants combined on the entire planet. These plants were constructed over 50 years of wild cheering for them and wishful thinking about them and the expenditure in just the last 10 years has been approximately two trillion dollars, with the result that climate change is accelerating, not decelerating.

Twenty five exajoules is also roughly equal to the thermal output of all of the world's nuclear plants, most of which operate on technology developed in the 1960's and were built over a 20 year period from roughly 1965 to 1985.

The author's raison d’être for producing the paper concerns the design of putative power plants which might utilize a carbon dioxide driven Brayton cycle.

The Brayton cycle, for those who do not know, is a power cycle in which the work (turning an turbine connected to a generator in a power plant) is performed without a phase change, i.e. the working fluid is a gas (or perhaps a supercritical fluid) without any liquid being involved. The most familiar example of a Brayton cycle device is a jet engine. In a jet engine, air is compressed and mixed with fuel - a vaporized dangerous fossil fuel in almost every case - and the fuel is ignited heating it and causing it to expand rapidly. In the jet engine, the exhaust pushes a transport device, generally an aircraft; in a power plant the exhaust expands against a turbine, driving its rotary motion.

We may contrast the Brayton cycle with the more common Rankine cycle, in which steam is generated from liquid boiling water (generally under pressure to raise the boiling point significantly beyond 100[sup]o[/sup]C) until it reaches its boiling temperature at the pressure in the boiler, giving steam, and the steam expands against the turbine, driving it, after which it is cooled, and condensed back into a liquid, and returned to the boiler for reboiling.

A combined cycle device uses both cycles. Generally Brayton cycles are conducted at very high temperatures - they depend on so called "superalloys" often coated with refractory ceramics to keep the turbines and combustion systems from melting at these temperatures. The exhaust from the Brayton device is thus generally hot enough to boil water, and thus is available to drive a Rankine cycle. Most combined cycle plants utilize unsustainable dangerous natural gas as a fuel, but as I will point out below, there is no particular reason that this technology cannot be utilized in nuclear plants.

Every gas plant built and operated everywhere, by the way, no matter how high its efficiency level is a crime against all future generations. This includes power plants being built like the one proposed in Superior Wisconsin to help a power company "go renewable."

It's amusing to see people opposing gas lines because so called "renewables" are so wonderful. The entire renewable energy industry is nothing more than a fig leaf for the gas industry.

But I digress.

Returning to the motivation behind this fine paper though, the authors write in paragraphs following the first:

"Currently, the emphasis on such a thermodynamic power cycle is directed toward the demonstration of its performance and the evaluation of its cost and reliability before the possible building of an industrial-scale unit. This step is almost an unrealistic task without the aid of a process simulator able to model and optimize the cycle. Thus, the role of the selected thermodynamic model indecisive because it is the first step which will affect all subsequent tasks in a process evaluation.3 Broadly speaking, the thermodynamic properties determine the feasibility of a given process (e.g.,cycle thermal efficiency), while the transport properties have a major impact on sizing of the equipment.4

Existing studies have pointed out that the property change of CO[SUB]2[/SUB] near the critical point would result in a significant efficiency improvement (i.e., the compression work can be substantially decreased),5 along with a non-negligible influence in the turbo machinery design.6 However, the impact of the choice of the thermodynamic model used to evaluate the properties ofCO[SUB]2[/SUB] has not drawn attention. As an example, Dostal et al.,5Kato et al.,7 Zhang et al.,8 Jeong et al.,9 Lee et al.,10 and Serranoet al.11 all selected the Span−Wagner EoS without justifying their choice. As a second example, the study performed by Clarke et al.12 used a law of corresponding states and highlighted that a small change of the physical properties like the heat capacity and density affect significantly the heat-exchanger design and performance.

Regarding the chemical and energy industries, Whiting et al.13 pointed out that surprisingly, there are only a few studies devoted to the analysis of uncertainty associated with thermodynamic models despite their pivotal role for process design and simulation."


One of the chief thermodynamic penalties paid in Brayton cycles is the energy consumed by the compressor, and the energy, in turn, required to run the compressor is very much a function of the thermodynamic state of the gas, said states being determined by an "equation of state." The state of the gas also plays important roles in turbine design, especially material design, and of course, in heat transfer devices.

There are many examples of gas equations of state, the most familiar to most high school science and freshmen college students being the famous "ideal gas law," PV = nRT. The law is just a loose approximation, not very useful for meeting the requirements of sophisticated engineering devices or for that matter, chemical plants. The trade off between simplicity and accuracy is a difficult one to navigate, and increasingly sophisticated gas laws have been developed over the last century, beginning with the "cubic" laws, the Van der Waal's gas law, then the Reddich Kwong law, it's refined version, the Soave-Reddich-Kwong followed by the widely used "Peng-Robinson" gas law. The latter law was designed to give a method which could generate supporting constants from readily available physically measurable properties of the gas, specifically its critical pressure, critical temperature and a factor known as the "acentric factor," nominally a function of molecular geometry. (The critical pressure is the pressure at which the liquid phase and gas phase become indistinguishable, and the critical temperature is the temperature at which that occurs.)

A very accurate law has been developed for a specific gas, the dangerous fossil fuel waste carbon dioxide, has been developed; this is the Span Wagner equation referred to in the text above. The derivation of this law is an intellectual tour de force; it relies on analysis of the Helmholtz energy, which is the "free energy" equation at constant volume corresponding to the more familiar Gibbs free energy at constant pressure.

It is described in a classic paper, Span and Wagner Journal of Physical and Chemical Reference Data 25, 1509 (1996). Google Scholar has it being cited just over 3000 times; in comparison the Peng Robinson equation paper Ind. Eng. Chem. Fundamen., 1976, 15 (1), pp 59–64 - also a tour de force which is utilized to describe many gases and thus has broader utility - is one of the most cited papers of all time, with just over 8,900 citations.

The Span-Wagner equation in an earlier time - it includes a number of transcendental functions - would have been too complicated for much utility inasmuch it would eat vast amounts of computer time, faster more powerful computers have made it practical to use.

The authors of the paper cited at the beginning of this discussion are, in effect, complaining that people utilize the Span Wagner law without justifying it; the purpose of the paper is to justify it, by comparing five other gas laws and their effect on the design of important power plant components.

The authors write:

:Six candidate EoS were eventually selected for the comparativestudy and are now sorted according to their EoS class:

.• Cubic EoS: the Peng−Robinson EoS (PR) using theclassical Soave alpha function; the Peng−Robinson EoScombined with the Boston−Mathias alpha function(PR-BM), an alternative version of the PR EoS; and theSoave−Redlich−Kwong EoS (SRK) using the Soave alphafunction

• Virial-type EoS: the Lee−Kesler−Plöcker EoS (LKP) andthe Benedict−Webb−Rubin modified by Starling andNushiumi (BWRS)

• Helmholtz-type EoS: the Span−Wagner (SW) EoS."



The authors conclude that the use of the Span Wagner equation, their "reference equation" is in fact justified in making design decisions for power plants. Their goal again was not to disprove the acceptability of the Span Wagner equation, but rather to prove in a formalized sense that the decision to use it - given the power of modern computers - is acceptable.

However, there is a huge caveat: The equation is optimized in a range from the triple point temperature (the temperature at which gas, liquid and solid can coexist) and the corresponding triple point pressure to a limited high temperature, 1100K.

Span and Wagner report the triple point values with high precision as:

"Tt Triple-point temperature: T[sub]t[/sub]=(216.592± 0.002) K;


Pt Triple-point pressure: P[sub]t[/sub]=(0.517 95± 0.000 10) MPa;"

Note that the triple point temperature is on the absolute Kelvin scale, and that this temperature is very cold, -56.558[sup]o[/sup]C, but it is the upper bound that is of concern, 1100K, which translates to a relatively modest 827[sup]o[/sup]C, which is, in theory, hot enough to run a power plant on a combined cycle basis, but still not as high as one might go to achieve broader goals in the elimination of the use of dangerous fossil fuels, that is to completely and totally phase them out, something future generations will be required to do, even if our generation has been too silly and too distracted to do it ourselves.

(As for the triple point pressure, 0.517 MPa is about five times atmospheric pressure. The Span Wagner equation is valid at pressures that are 8000 times higher than atmospheric pressure.)

There are many reasons to explore Brayton Cycles that operate at significantly higher temperatures than 1100 K, particularly if one wishes to thermochemically split water into hydrogen and oxygen. There are many known thermochemical cycles, all of which are significantly more efficient than water electrolysis. Hydrogen and (pure) oxygen are useful chemical intermediates that would in theory allow for the conversion of any source of high temperature gas or supercritical fluid into hydrogen and oxygen at fairly high thermodynamic efficiency.

Probably the best known thermochemical cycle is the sulfur-iodine thermochemical cycle, first advanced many years ago by General Atomics (largely because the patent on it had expired) for use with their high temperature helium Brayton type reactor, the HTGC type reactor. Thousands of papers relating to the sulfur iodine thermochemical cycle are typically published in a given year; for the link I just picked one more or less at random.

When I was a kid, and first heard of the sulfur iodine cycle, I was very excited by it, but in fact, this cycle is more problematic than many other available potential thermochemical water splitting cycles. I've lost my taste for it, because of the issues of corrosion and mass transfer; in particular the production of 1 gram of hydrogen requires the transfer of 128 grams of hydrogen iodide, and in any case, iodine is expensive, even if it is designed to be continuously recycled.

In fact, part of one potential thermochemical cycle is already practiced on a huge industrial scale, in particular the "water gas" reaction by which 99% of the world's current hydrogen production (which is important for the critical industrial enterprise of making ammonia). The water gas reaction is as follows:

CO + H[sub]2[/sub]O ↔ H[sub]2[/sub] + CO[sub]2[/sub].

In this case, as industrially practiced in these energetically irresponsible times, the carbon monoxide is formed by the partial oxidation of methane, the main constituent of dangerous natural gas.

It is, however, very possible to make carbon monoxide by reducing carbon dioxide. Analogously to water splitting thermochemical cycles there, are thermochemical carbon dioxide splitting cycles that carry out the reactions as well that carry out the following reaction:

2 CO[sub]2[/sub] ↔ O[sub]2[/sub] + 2 CO.

The sum of these reactions, after doubling the first, is simply yet another water splitting reaction:

2H[sub]2[/sub]O ↔ 2H[sub]2[/sub] + O[sub]2[/sub]

Thus By coupling this reaction with the water gas reaction we can see that combining these two reactions, one already performed on an industrial scale, we would have in effect, a thermochemical water splitting reaction that potentially would be far less corrosive than the sulfur iodine cycle.

Here’s an example of a thermochemical cycle that works to split either water or carbon dioxide, which I pulled out of my files at random:

Ceria as a Thermochemical Reaction Medium for Selectively Generating Syngas or Methane from H2O and CO2 (ChemSusChem 2009, 2, 735 – 739)

Pretty much any compound now obtained from petroleum can be made with access to syngas, which is a mixture of hydrogen and carbon monoxide as well as, in some cases carbon dioxide.

These cycles generally require temperatures significantly higher than 1100K, usually hundreds of degrees higher, although the cited paper indicates a reaction temperature that is only slightly higher, 1173K. It is notable that there are now many kinds of materials that have been designed that selectively permeate gases, including oxygen, hydrogen (the metal palladium has long been known to conduct hydrogen) and carbon dioxide as well as many other gases. Advances in materials science processing have also been known to produce materials that are biphasic, containing two types of conducting polymers.

Here's an example of a paper that contains two types of oxygen conducting polymers.

Chang et al, Journal of Membrane Science 322 (2008) 429–435

It is therefore possible to imagine advanced materials that allow the permeation of very hot carbon dioxide into them and conduct oxygen out themselves in one direction and carbon monoxide in another. Therefore one can imagine adding a third combined cycle aspect to a supercritical carbon dioxide reactor, a thermochemical portion that allows the production of motor fuels (to the extent we require and accept them), Brayton cycle electricity, and finally, in the final cooling phase, Rankine cycle electricity. We're certainly not there yet by any means, but it certainly is not beyond feasibility, but my readings in materials science suggest that these ideas are not entirely out to lunch.

My son, who is graduating this evening from high school with high honors, is planning to major in materials science engineering in college, with a long term goal of being admitted to a good or great materials science graduate program.. I hope I will be able to stick some of these thoughts into his head, should he decide that his old man actually isn't too stupid to engage.

In any case, to return to the original point, we will certainly need, in order to design these types of devices, advanced equations of state. In order to construct a ternary combined cycle as just imagined, we would need, at the very least, to extend the Span Wagner equation to higher temperatures.

It's worth doing. As I've noted over the years in many different places, the uranium and thorium already mined are sufficient to provide all of humanity's energy needs for centuries if they are utilized in breeding nuclear fuel cycles. This would mean no fracking, no oil platforms, no coal mines, far less excessive and toxic silicon processing, and in fact, no uranium or thorium mining, at least for centuries to come.

Advances in material design, notably in refractory ceramics (including some that are machinable, the so called “MAX phases”) now suggest that such high temperatures will be accessible. It is worth noting that some of the highest melting temperature ceramics include actinide based ceramics that potentially could serve as both structural and fuel elements, examples include thorium oxide (which has been used industrially as a high temperature crucible material), uranium nitride, thorium, uranium and plutonium carbides, etc.

Interesting, if esoteric.

Have a nice evening.

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Reply Paper on the Equation of State for High Efficiency Supercritical Carbon Dioxide Driven Turbines. (Original post)
NNadir Jun 2017 OP
Victor_c3 Jun 2017 #1
NNadir Jun 2017 #4
eppur_se_muova Jun 2017 #2
NNadir Jun 2017 #3

Response to NNadir (Original post)

Wed Jun 21, 2017, 02:13 PM

1. Interesting. Thanks for taking the time to put that together n/t

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Response to Victor_c3 (Reply #1)

Wed Jun 21, 2017, 11:02 PM

4. My pleasure. I wrote it down to clear it in my head and chose to post it here in case anyone was...

...interested.

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Response to NNadir (Original post)

Wed Jun 21, 2017, 03:23 PM

2. Is there an order of magnitude estimate of how many gigaflop-hrs are needed to do such calculations?

Considering all the nuclear explosions that have been simulated in supercomputers, and that QM simulations of solids are being carried out on very large chunks of lattices, it seems a little strange that no one has gotten around to doing these calculations before -- or is it just a matter of priorities ?

(BTW, I don't have access to ACS journals, so I can't get that from the articles.)

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Response to eppur_se_muova (Reply #2)

Wed Jun 21, 2017, 11:00 PM

3. There have been a number of papers written on the topic of reducing the complexity of...

...of the Span Wagner equation, involving the degree to which one is able to tolerate inaccuracies, which may or may not be acceptable depending on the purpose of the calculation.

Examples include Journal of Mechanical Science and Technology May 2007, Volume 21, Issue 5, pp 799–803 and more recently this one, Ind. Eng. Chem. Res. 2012, 51, 1006–1014

The authors of this paper if I understand them correctly are arguing that the investment in computer time in order to design power plant components is a worthy enterprise, since ideally thermal power plants - in my view they should all be nuclear plants - should be designed to operate for appreciable fractions of a century.

None of the papers cited here, nor the one in OP actually give a measure of computer time, since this will depend on the architecture of the computer and the design of the software. It is possible to have a computer with considerable power to do parallel calculations and yet run software on it that does not exploit this capability, as I understand it. There are workstations now that fit on a desktop that can conduct calculations that might have required a super computer 10 or 20 years ago. I am not really competent to discuss this topic however, although I have run across some nice discussions of how engineers and scientists should interact with their computers.

DFT calculations are more broadly applicable than a law for a special gas, in this case carbon dioxide, and so the software and approaches have benefited from considerable investment in time. This is also true of generalized gas laws like the Peng Robinson law which is a cubic equation that suffices for most calculations for at least a first pass. (When I was a kid I programmed my HP41C calculator to solve the Van der Waals equation for a hydrogenation I was doing. It was accurate enough for my purposes.) Even DFT calculations have been subject to theoretical means of simplification. A fine scientist near here at Princeton University has been a pioneer in orbital free density functional theory, OFDFT. (She just got kicked upstairs to the role of Dean of Engineering; hopefully she will keep her scientific efforts moving forward.

Neutron calculations seem to be relatively straight forward and surely are accessible to parallel processing programs. I recently came across a nice paper where people ran a desk top Origen program to calculate an approximate distribution of fission products and actinides in all of the US inventory of used nuclear fuel. Annals of Nuclear Energy Volume 72, October 2014, Pages 277-285.

I wish I had full access to their results, since I think that the utility - especially the economic utility - of fission products to accomplish tasks that need attention, notably the purification of water, soil and air, will depend on their inventory, or to generate heat for remote power systems. There are things that radiation can do that nothing else can do as well.

I'm lucky to live in New Jersey, where we have access to great university library systems that make it possible for visitors to use. I pay Princeton for the privilege and I get two hours a day at Rutgers. I can - and most often do - read pretty much any scientific publication I want to read, with a few exceptions.

If I recall correctly, you live in the South somewhere, and it may involve considerable time and effort to get to a library.

I've been know to travel for access to things, notably to MIT's library in Cambridge. If I'm in the Boston area, I pull out a running list of things I can't get elsewhere that I can get at MIT; notably these are nuclear journals which are only accessible on a limited basis in New Jersey to my knowledge.

The library system in New Jersey is the reason I want to live here until I die.

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