January 1, 2020

Dielectric & Other Properties of CO2 Syn Gas: The Future of an Eq'n of State for Natural Gas.

The motivating paper I'll discuss for this post is this one: Dew Points, Dielectric Permittivities, and Densities for (Hydrogen + Carbon Dioxide) Mixtures Determined with a Microwave Re-Entrant Cavity Resonator (Gergana Tsankova,† Yvonne Leusmann,‡ Roland Span,† and Markus Richter, Ind. Eng. Chem. Res. 2019, 58, 21752?21760). Contemplating it has lead me to review a number of other scientific papers, as linked below.

Much of this post, as is my wont, fairly technical, which is permissible, I think, in the science forum, but as this website is overall a political website, let me begin with a politico-historical comment: As I near the end of my life, it occurs to me that these are the most terrible times in which I have lived. Although this is a political website and we are all engaged in focusing on the bizarre spectacle of the collapse of the American government which is surrendering, without a shot being fired, to the Russians, the terror I see in these times is not concerned the orange Mussolini wannabe in the White House and his empty headed recidivist Fascist council in the Congress. We may be shocked by the American national suicide, but in reality nations fall: The sun set on the British Empire; the Mughal Empire is now nothing more than an answer to a trivia question; the Ming Dynasty, the Qin Dynasty, all are gone, and still "the Earth abides...the sun also rises and the sun also sets..." So may it be with the United States, as much as we, and those among us, have loved our country, its constitution is unraveling in an orgy of stupidity, fear, corruption and intellectual and spiritual rot. We "should have died hereafter."

For me, though, the terror of the times has little to do with politics; rather my terror is the destablization of the planetary atmosphere which - even as it is involved in the political celebration of ignorance, is a physical event, transcending the foolery and threatening the magnificence, such as it is, of humanity, and all the environmental infrastructure on which its future depends.

So it is, I lie awake, dreaming of a better world, and because I am a technical person, my dreams, and hopes that this already impressive Millennial generation will rise to greatness, are very much involved in reflections on possible engineering that will enable them to restore what can be restored after all the destruction that we before them have wrought.

The key to a survivable future is thermodynamics. The etymology of the word is literally changes in a single form of energy, heat, but of course now the term generalized now, for many years in the flows of all forms of energy, notably, exergy, the energy available to be used.

Much of my writing here consists of mocking energy storage schemes that many people imagine will make their reactionary fantasies about a putative "renewable energy" nirvana work. The idea that we can save the world with a massive pile of batteries to store the wind and the solar is every bit as absurd as a Trump tirade; it does not address reality so much as fantasy. Simply it won't work. The belief - and the correct term for it is exactly that, "belief" - that energy storage is a solution to a vast and untenable environmental crisis caused by the use of energy to produce exergy is absurd, since the laws of thermodynamics require that energy storage wastes energy.

All of this said, some forms of very temporary forms of energy storage may be required for systems that are either designed or required to run continuously, such as gasoline engines, addressed in some cases in hybrid cars, or in nuclear power plants during times of low loads, this only being true in a case unfortunately not actually observed, where nuclear energy provides nearly all of the world’s energy supply, as it would were the world’s energy supply to become sustainable in contrast to the status quo. In a thermodynamic sense, some energy storage schemes are better than others, inasmuch as they involve fewer conversions of one form of energy to another and before getting to the paper cited at the outset, it may be useful to examine some of these.

A great deal has been written about the storage of sensible heat itself. The overwhelming majority of electrical power on this planet is produced from thermal sources, primarily through the use of dangerous fossil fuels. Nuclear power plants are also thermal heat devices and there is a trivial, expensive, and mostly useless solar thermal industry as well, although it is a trivial component of the trivial solar industry. The pairing of dangerous fossil fuel plants with so called renewable energy requires dangerous fossil fuel plants to waste heat that they would otherwise use, since shutting them down for a few hours when the sun is shining and the wind is blowing means the heat in their boilers is wasted and needs to be regenerated before the water or other working fluid can return to its boiling point. The majority of nuclear power plants now in operation are also designed to operate continuously; they have, in general, the highest capacity utilization of any generation systems in the world. However the design of these plants was overwhelmingly focused on the 1950’s and pre-1950’s mentality of Rankine steam cycles, a mentality derived from long experience with dangerous fossil fuel plants. My interest in the paper cited at the outset of this post was driven by my interest in extending the utility of nuclear energy way beyond mere electricity, since electricity is inherently a degraded form of energy, convenient to use, but thermodynamically wasteful to produce. Electricity production in thermal system requires four energy conversions: Chemical or nuclear or solar thermal energy is converted to thermal energy which is converted to mechanical energy generally by turbines, and finally to electrical energy.

The storage of sensible heat requires two things, an adiabatic system and materials with very large heat capacities.

The concept of a pure adiabatic system, a system which cannot exchange heat with the environment - in the present context "lose" heat to the environment as entropy - is a theoretical thermodynamic ideal, much the same as the concept of an ideal reversible system. Both are limits that can never be reached as a practical matter; as a practical matter, neither exists. Nevertheless we can come close: thermal isolation materials are well known industrially, although the application is rarely, if ever, for the purpose of energy storage for later use in producing exergy. We call these materials, of course, “insulators,” and they are widely used in buildings, refrigeration systems and ovens. There are, however, insulating materials designed to prevent the flows of heat at extreme temperatures, sometimes as sacrificial materials, for example ablative surfaces on spacecraft, and other materials designed to remain intact, poor heat conducting refractories, such as zirconium oxide thermal barrier coatings on turbines in jet engines and in dangerous natural gas turbines. In theory these latter types of materials could be used to store high temperature heat exchange for later use to produce exergy.

Another way in which energy can be stored is as pressure. I have a favorite paper about storing wind energy that I came across over a decade ago which nevertheless always sticks in my mind. It is this one: Emissions and Energy Efficiency Assessment of Baseload Wind Energy Systems (Denholm et al. Environ. Sci. Technol. 2005, 39, 6, 1903-1911). This is a paper about "CAES," compressed air energy storage. It is notable that 17 years after this discussion was published, no significant amount of wind energy, the total amount of which remains more or less, on an order of magnitude, as trivial as it was then, there is no significant industrial facility that stores wind energy as compressed air. In the proposed scheme of this paper, the inevitable energy loss associated with energy storage is made up by burning dangerous natural gas, the waste of which is dumped directly into the planetary atmosphere.

This paper supports the point I often make: The utility of so called "renewable energy" is entirely dependent on access to dangerous fossil fuels. If you think I am cherry picking by citing this 17 year old paper, I assure you that I vehemently disagree. One can and for half a century always could find papers that claim 100% of the world's energy could be produced by so called "renewable energy," but the experimental results show clearly that these contentions are absurd. After trillions of dollars have been squandered on these schemes, wind, solar, geothermal and tidal energy produced in total, after more than half a century of wild cheering, as of 2018, the last year for which data is available, 12.27 exajoules out of 599.34 exajoules of energy generated in that year.

An improved and less confusing data table combining the 2017, 2018, and 2019 WEO reports.

In a single year the use of dangerous fossil fuels on this planet as a whole grew by 12.69 exajoules, to a total of 485.46 exajoules. Thus the growth in the use of dangerous fossil fuels in a single year, from 2017 to 2018, is greater than the total amount of combined wind, solar, geothermal and tidal energy in use after half a century wild, and frankly delusional, on a Trumpian scale, cheering. Put in even more stark terms the growth in the use, for energy, of combined dangerous fossil fuels in the 21st century, thus far, 148.34 exajoules has exceeded in the growth of combined solar, wind, geothermal and tidal energy, 9.76 exajoules, by an astounding 1,520.6%, in the “percent talk” that advocates of this pixilated scheme use to obscure reality.

And still advocates of so called “renewable energy” insist that “renewable energy” is the best course for the future. I am exceedingly grateful that neither of my sons ever smoked whatever it is they are smoking. The reality is this: So called “renewable energy” is not an alternative to the use of dangerous fossil fuels, but represents something quite different: It is a psychological tool used to generate complacency about the use of dangerous fossil fuels, something at which, in contrast to producing energy, it is quite successful at doing.

But to the extent that so called “renewable energy” is effectively useless in addressing the climate crisis, the science produced from the grants to the agencies funded because of popular enthusiasm for it is decidedly not useless, at least in its entirety. Although I am opposed to the use of wind energy on environmental and economic grounds, thinking about Denholm’s highly cited paper has, over the years, generated certain insights to the issue of energy storage.

At a very low level, one can think about this situation using another theoretical concept that is useful for loose approximations, the “Ideal Gas Law” that one learns in high school, PV = nRT. I’m not sure that high school students are told to focus on this, but the units on both sides of the equation are units of energy, Joules. Although the “law” is clearly quite limited in scope and suggests things we know on inspection that are not true - for example, that as we approach absolute zero matter has no volume - it does make it immediately clear that if the temperature of a gas drops, the amount of energy it contains drops, and that if the volume of a gas increases, the temperature drops. This explains why Denholm’s scheme requires the combustion of dangerous natural gas to recover the putatively stored wind energy.

The efficiency of the scheme, which Denholm discusses at length in the full paper, can also be recognized off the top of one’s head by simply looking at the energy conversions involved: Mechanical energy (the turning wind turbine) is converted to electrical energy (the generator) which is reconverted into mechanical energy, the compressor, and stored as the internal energy of a gas, which can be converted back to mechanical energy with a turbine, and electrical energy with a generator. Before the electricity can be utilized, five energy conversions are required, and all lose heat, but the amount of heat lost from the internal energy of the gas is a function of how long the gas is stored, and the thermal conductivity of the container in which it is stored. If each energy conversion took place at 90% energy efficiency, the overall efficiency would be 100%*0.90^5, which is 59% efficiency. As a practical matter, not all of these steps are 90% efficient. While I think Denholm’s paper is a fine paper, I believe he is being disingenuous in claiming that the energy efficiency of the wind/CAES system is as high as 214%-336% for compressed air stored for 24 hours, and 203%-321% efficient for 50 hour compressed air storage.

Here is table 2 from his paper:



Clearly this dubious calculation is based on the dangerous natural gas burned to reheat the compressed air and the embodied energy that a wind turbine represents. All of this energy is dependent nevertheless, on access to dangerous fossil fuels, coal to make the turbine towers’ steel, gears and housing, degraded electricity and petroleum coke to make aluminum, dangerous natural gas to produce the nitric acid to digest lanthanide ores, coal and/or gas to heat copper ores, etc., etc, and obviously the gas burned to reheat the cooled compressed air. He more realistically assumes that the lifetime of a wind turbine is 20 years, which is somewhat longer than the lifetime one can calculate from the Danish Energy Agency’s Master Register of Wind Turbines, which is a comprehensive data base including detailed data about every Danish wind turbine built since the 1970’s. My last analysis of the data in this database indicated that the average lifetime of decommissioned wind turbines in the Danish database was 17 years and 283 days. Close enough, I presume…

Denholm is more honest about the relative merits of the wind industry, which is not sustainable without access to dangerous fossil fuels, when he notes that the carbon dioxide output for the wind/CAES system he proposes is between 400% to 600% higher than the carbon dioxide cost of nuclear energy for equivalent electricity prediction, stating that the carbon cost of nuclear energy is between 10 and 25 grams of CO2 per kwh for nuclear power and 66-99 grams of CO2 per kwh per kwh for the wind/CAES system. Of course very few, if any, large scale CAES wind systems have been built in the nearly 15 years since his highly cited paper was published, so it is rather impossible to check his figures for accuracy.

Denholm’s paper was published on line on January 21, 2005. The concentration of the dangerous fossil fuel waste carbon dioxide for the week beginning on January 23, 2005 at reported at the Mauna Loa Carbon Dioxide Observatory was 377.85 ppm. On January 20, 2019 the concentration was reported at Mauna Loa as 411.99 ppm. Obviously compressed air storage of wind energy has not saved the world.

All of this is more or less irrelevant to the paper I referenced at the outset of this post, but I engaged in this tortured diversion for one purpose which is to discuss the properties of thermodynamically unstable mixtures of gas. As Denholm briefly describes the putative CAES system he is analyzing, he describes it thusly:

The operative phrase here is "The air is then mixed with fuel and combusted." The dangerous natural gas is not stored in the compressed air but is mixed into it during the release of its internal energy.

One could know as little science as a member of Greenpeace and still understand why this is the case: A mixture of gas and air is potentially explosive. Although many people have been killed by dangerous natural gas explosions, it is generally the case that leaks of dangerous natural gas into do not spontaneously explode; they need a spark or some other kind of ignition. (Recently a neighborhood a few kilometers from where I live was evacuated, and a major thoroughfare through my neighborhood was shut because of a natural gas leak. The leak was located and happily there was no explosion.) Even though a mixture of carbon dioxide and air, dangerous fossil fuel waste, is of lower energy, and thus thermodynamically more stable than a mixture of dangerous and natural gas and air, for combustion, a small amount of initiation energy is required. This, of course, is the activation energy of a chemical reaction, which was first elucidated by development of the still widely used Arrhenius equation by Nobel Laureate Svante Arrhenius - who correctly predicted at the end of the 19th century that climate change would eventually become a problem - and further advanced by a Mormon Mexican immigrant working at Princeton University, Michael Eyring, who proposed the important Eyring equation, which is commemorated with a plaque in a very nice meeting room in Princeton's Chemistry Building, Frick Hall, a room decorated with tributes to Princeton's greatest chemists.

The activation energy can be provided by a spark, and thereafter is maintained by the combustion itself in what is essentially a chain reaction, and is the case with all chain reactions, can either be controlled or explosive. Sparks, of course, can be generated in mixtures of gases when a sufficient voltage difference exists between portions of the otherwise continuous gas: Lightening is the most familiar example; static shocks are another. The way the voltage accumulates is a function of a fundamental property of matter, and in fact, free space, the diaelectric constant, which finally, after the accumulation of a lot of drivel on my part, brings me to the paper cited at the outset of this post.

The theoretical biologist Stuart Kaufman has described life as an “eddy in thermodynamics” – I mentioned this description to Freeman Dyson when I met him and he enthusiastically approved of the description.

The theoretical biologist Stuart Kaufman has described life as an “eddy in thermodynamics” – I mentioned this description to Freeman Dyson when I met him and he enthusiastically approved of the description. The point is that all living things, particularly in atmosphere containing oxygen, but also outside of one, are thermodynamically unstable, which is why they decompose when they die.

Of course, sparks do not generally cause human beings, cats, or slime molds to burst into flame, as they can with a mixture of dangerous natural gas and air, but with the right input of heat, they will all do so. How much heat is required to cause a living or once living thing, for example, wood, to burn is a function of the nature of the material, it’s heat capacity, its density, molecular and supramolecular structure and other physical factors. The release of energy and the rate of energy release is a function of the reactants.

Flames as we generally know them are involved in oxidative reactions, but there are also reductive reactions that release energy much as combustion does.

I have argued in many places over many years that the best, by far, chemical fuel is dimethyl ether, because of its great flexibility – it can displace dangerous natural gas, dangerous petroleum gas, dangerous diesel fuel and dangerous gasoline – while exhibiting a short atmospheric lifetime, roughly five days, and also has properties of a refrigerant while exhibiting a critical temperature higher than the temperature of boiling water, 150°C. It is relatively non-toxic, easily removed from water by aeration, and burns very cleanly giving basically pure water and carbon dioxide as combustion products.

Here are some chemical equations that play a role in the formation of dimethyl ether from a type of “syn gas,” a mixture of carbon monoxide and hydrogen:



Equilibrium calculations for direct synthesis of dimethyl ether from syngas (Moradi et al, Can. J. Chem. Eng. 89:108–115, 2011)

While this particular paper doesn't explicitly state the precise thermodynamic functions represented by the negative values on the right, reference to the Van't Hoff equation suggests that they are the values of the enthalpy, presumably of formation, meaning that the reactions are all exothermic. While the entropy of equation 5 is clearly negative, I happen to know that the reaction has a negative ?G, and thus is a thermodynamically favorable reaction.

In any case, the large negative value of this thermodynamic function suggests that a syn gas mixture might possibly explode forming dimethyl ether or a related compound were a spark to ignite the reaction, but this does not, in general happen.

In any case, the paper features an interesting discussion of correcting the values for the equilibrium as determined by the assumption that the ideal gas law is valid by substituting the "SRK" equation, the Soave modification of the Redich-Kwong equation, a cubic equation of state that is generally more accurate for real gases. Depending on the engineering needs defined by real gases, one can further modify equations of state to derive more accuracy when compared to experimental findings. For example, one of the authors in the paper cited at the outset of this post, Roland Span, derived the Span-Wagner Equation of State for carbon dioxide:

A New Equation of State for Carbon Dioxide Covering the Fluid Region from the Triple-Point Temperature to 1100 K at Pressures up to 800 MPa (R. Span and W. Wagner, Journal of Physical and Chemical Reference Data 25, 1509 (1996))

This paper has been cited a little less than 4,000 times, suggesting that many scientists are willing to "go that extra mile," to make accurate and precise calculations about the properties of carbon dioxide, a good thing.

The equation is not one that would be utilized to solve a problem on a physical chemistry exam however. Here is an amusing note from a paper citing it, Equation of state for carbon dioxide (Kim, Journal of Mechanical Science and Technology 21(2007) 799-803):



Further, the equation is valid "only" up to 1100K, 827°C. In order to address climate change, it would be useful to explore much higher temperatures, suitable for the thermochemical splitting of carbon dioxide into carbon monoxide and oxygen. The Zn/ZnO thermochemical cycle requires temperatures of 2000K, 1727°C, the ceria cycle (my personal favorite) requires temperatures of 1500°C. The iron cobalt cycle, which depends on access to the conflict metal cobalt, can proceed at lower temperatures, 600°C, but depends on vapor phase deposition of a thin layer of these metals which might be industrially challenging, as does the SnO2/SnO cycle, which faces issues with particle size changes with melting with the reaction taking place at approximately 800°C, which is close to the upper limit of where the Span-Wagner equation is valid and precise.

This brings me to the point of discussing the equation of state for dangerous natural gas which is the "GERG 2008" equation which was described by Wagner of the Span and Wagner partnership in this publication:

The GERG-2008 Wide-Range Equation of State for Natural Gases and Other Mixtures: An Expansion of GERG-2004 (Kunz and Wagner, J. Chem. Eng. Data 2012, 57, 11, 3032-3091. )

The standard gas equations of state for pure compounds, the cubic equations like Peng Robinson (PR) and Souave, Redich, Kwong, (SRK) make, put on a somewhat simplistic level, assumptions about molecular size and interatomic forces that become far more complicated in mixtures of gases. For mixtures, the Helmholtz mixing rules apply and can become quite complex especially because highly accurate and precise equations of state for pure compounds which may have the cubic equations as starting points are also highly complex.

Here, for example, is a list of pure compound equations of state utilized in the GERG formulation:



Note that here, Wagner has not evoked his own equation of state for carbon dioxide, but has substituted an equation of state found in the thesis of one of his Ph.D. students, Reinhard Klimeck. (It's in German.)

To give a feel for the complexity of GERG 2008 here is one (of several) tables of applicable functions utilized in its development and use, involving summations, and therefore making use computer dependent:



And another:



However complex, this formulation is valid for dangerous natural gas, and not necessarily for carbon dioxide mixtures, a point that Span apparently made in a presentation built around modifications of the equation for utilization for giant carbon dioxide waste dumps, which fall under the rubric of "CCS," carbon capture and storage, in a conference dedicated to such dumps - which will not work actually to address climate change - in 2015. Here are the slides connected with this presentation:

Experimental Work at RUB and Tsinghua and a New Model Describing Thermodynamic Properties of CO2-rich Mixtures

Too often, in modern times, we define ourselves not by the things in which we believe, but rather by the things we oppose. I am personally not immune from such a flaw: I oppose the use of dangerous natural gas; I oppose solar thermal plants; and I oppose carbon dioxide waste dumps. Here I am, nonetheless, prattling on about the science related to each, equations of state for dangerous natural gas, carbon dioxide splitting cycles that often describe solar thermal schemes as the source of energy to drive them, and the science of carbon dioxide waste dumps. I am for nuclear energy, which in my view, is the only practical means of addressing climate change, albeit increasingly, owing to inattention and appeals to fear and ignorance, a long shot. In order to achieve the address of climate change, and possibly its reversal, it would be necessary to repurpose nuclear energy from merely making electricity to driving reactions involving carbon materials, fuels and waste, and to do this, one must also repurpose the science of dangerous natural gas, putative "solar thermal" carbon dioxide splitting, and the construction of vast theoretical but practically unworkable carbon dioxide waste dumps.

Scientists are people, and as people, they can focus narrowly on purposes for which their work may never be applicable, and miss those for which they might actually apply. This much in no way diminishes the importance and beauty of what they do.

Here, by the way, showing that scientists are people is a picture of the Span group, with Wolfgang Wagner, professor emeritus, the man with white hair in the maroon sweater, wearing glasses, and Roland Span near the front with a maroon tie:



PROF. DR.-ING. ROLAND SPAN MITARBEITER

These equations of state all derive from the Helmholtz energy, that is, the internal energy of the gas available for work; they are functions at constant volume. The modifications proposed by Span at the CCS conference, refer to carbon dioxide dumps, but an alternative to CCS, dumping, is CCU, carbon capture and use. It would seem that Professor Span since the paper cited at the outset considers a mixture of hydrogen and carbon dioxide which contains considerable chemical internal energy, since this mixture is not thermodynamically stable, even if one corrects for the thermodynamic cost of reducing carbon dioxide to carbon monoxide.

Is it likely that an internally generated spark will cause a mixture of hydrogen and carbon dioxide will cause a reductive explosion leading to the exhaust of flammable (in an oxygen atmosphere) dimethyl ether, methane, methanol and other hydrocarbons, ethers and alcohols? Probably not, because the achievement of transition states for the initiation of chemical reactions depends on factors other than energy; this is the purpose of catalysts, to stabilize suitable transition states. Nevertheless, the existence of pressurized syn gas type mixtures of carbon monoxide or carbon dioxide with hydrogen, to exhibit recoverable energy. To return briefly to Denholm, it is as if his compressed air were stored mixed with the dangerous natural gas that his system requires to effectively run. The catalysts for the one step production of dimethyl ether from carbon monoxide and hydrogen include, among others, bifunctional catalysts consisting of copper oxides, zinc oxides, and the ?-alumina (aluminum oxide).

(cf., for one example: Kinetic Modeling of Dimethyl Ether Synthesis in a Single Step on a CuO?ZnO?Al2O3/?-Al2O3 Catalyst (Aguayo et al, Ind. Eng. Chem. Res. 2007, 46, 17, 5522-5530). For an updated zirconium oxide/zeolite catalyst system see Optimization of the Zr Content in the CuO-ZnO-ZrO2/SAPO-11 Catalyst for the Selective Hydrogenation of CO+CO2 Mixtures in the Direct Synthesis of Dimethyl Ether (Miguel Sánchez-Contador et al, Ind. Eng. Chem. Res. 2018, 57, 1169?1178). For an alternate synthesis catalyst see: Optimization of CO2/CO Ratio and Temperature for Dimethyl Ether Synthesis from Syngas over a New Bifunctional Catalyst Pair Containing Heteropolyacid Impregnated Mesoporous Alumina For a review on the reduction of carbon oxides to DME, methanol and related compounds, see Challenges in the Greener Production of Formates/Formic Acid, Methanol, and DME by Heterogeneously Catalyzed CO2 Hydrogenation Processes (Freek Kapteijn et al, Chem. Rev. 2017, 117, 9804?9838))

Passing a stream of syn gas over these catalysts will cause the stream to heat significantly, and, if allowed to expand against a turbine driving a system of compressors and electrical generators, will allow for the recovery of stored energy. The storage of this energy would not involve, by the way, as referenced above, mechanical or electrical intermediates, which are degraded forms of energy but might easily, using known technologies, involve the direct conversion of thermal energy to chemical energy!. How so? There are many options, thermochemical splitting of carbon dioxide into oxygen and carbon monoxide for one example, thermochemical splitting of water, or the water gas generation of hydrogen from carbon monoxide, the dry reforming of biomass with carbon dioxide, and various permutations thereof. All of these processes involve high temperatures, and it follows that these high temperatures can be brought to bear on the generation of electricity as a side product, as is currently done in combined cycle dangerous natural gas plants.

There are two potential reactions, depending on the nature of the starting gases, the temperature, and the morphology and composition of catalysts used:



In each case, six moles of a gas are utilized to form two moles of gas (at high enough temperatures). This, of course, represents a thermodynamically unfavorable reduction in entropy, but with careful utilization of flows and heat exchanges, some of these losses might be recovered by appropriate arrangement of heat exchangers, by utilizing these entropy decreases to enlarge a pressure gradient on either side of a turbine and by utilizing the exotherms of the reactions to heat the expanding syn gas.

What these approaches represent are not losing energy by the practice of energy storage but rather recovering energy that otherwise would have been lost, that is by raising the thermodynamic efficiency of a nuclear plant from the typical 33% efficiency in the majority of the world's plants to something well over 50 or 60 percent, perhaps, depending on the temperatures achieved, to some figure even higher, although the second law requires that it is impossible to reach 100%. Note that the product in this system is also stored energy, DME, the cleanest possible burning fluid carbon based fuel.

In an earlier post here, I referred to the Allam thermal cycle: Considering an Alternative Hybrid Allam Heat Engine Cycle for the Removal of CO2 from the Air.

These types of cycles can be arranged, with appropriate variants, to provide starting materials for truly clean and sustainable energy storage and transport, driven by nuclear heat, with biomass in the line subject to wet or dry reforming rather than combustion, in combination with DME synthetic schemes. It is my feeling that such storage is far more thermodynamically viable than the mass and toxicologically intensive alternatives of solar, wind and chemical batteries.

All this wandering brings me to the point, the storage of energy in the form of compressed syn gas. It is, I think, far less than likely for a syn gas mixture to experience the kinds of breakdown voltages so as to generate a spark that leads to a runaway explosion, irrespective of the internal energy of the mixture. It is of more interest to understand the state of the gas, specifically its density, pressure, and physical state, that is such issues as vapor-liquid relationships. As it turns out, precise information about these factors can be discerned from the diaelectric permittivity.

From the introduction of the paper cited at the very beginning of this long desultory post:



A microwave re-entrant cavity resonator is an esoteric device whereby resonant frequencies of microwaves in a confined space depends on the dielectric permettivity of the material filling that space. More details on the instrument can be found here and in references therein: Densities, Dielectric Permittivities, and Dew Points for (Argon + Carbon Dioxide) Mixtures Determined with a Microwave Re-entrant Cavity Resonator (Richter et al, J. Chem. Eng. Data 2017, 62, 9, 2521-2532)

The introduction continues:



The relationship between density and the diaelectric permittivity is explained as follows:




More explicitly, the relationships between the diaelectric permittivity and the density is described in the paper as follows:



Some graphics from the paper:



The caption:
Figure 1. p, T-diagrams and measurement conditions of (a) (0.05362 H2 + 0.94638 CO2) mixture and (b) (0.25424 H2 + 0.74576 CO2) mixture: ―, phase envelope calculated with the GERG-2008 EOS of Kunz and Wagner 9) ○, experimental dew points. Dielectric permittivity measurements: △, T = 273.06 K; ▽, T = 293.05 K; □, T = 312.74 K; ◇, T = 313.18 K; × and +, in the vicinity of the phase boundary.


The caption:



SRK refers to the Soave modification to the Redlich-Kwong equation of state, a well known standard cubic equation of state, and PR refers to another later widely used cubic equation of state, the Peng-Robinson equation of state.



The caption:




Figure 4:



The caption:



Excerpts from the conclusion:



This is the way I wanted to start this decade, thinking it is likely to be my last, by learning something new. I was personally unaware of the relationship between diaelectric permittivity and density. I write dense posts like this to see what I can learn or review or firm up, and it makes me happy - though I certainly don't expect it will - if someone else finds it interesting.

I wish all DUers a New Year and a decade of healing from this political travesty resulting from the installation of a crude racist in the White House who is unarguably unworthy of this country and in fact, unworthy of the human race as well.

All the best.