Thermochemical cycle


Thermochemical cycles combine solely heat sources with chemical reactions to split water into its hydrogen and oxygen components. The term cycle is used because aside of water, hydrogen and oxygen, the chemical compounds used in these processes are continuously recycled.
If work is partially used as an input, the resulting thermochemical cycle is defined as a hybrid one.

History

This concept was first postulated by Funk and Reinstrom as a maximally efficient way to produce fuels from stable and abundant species and heat sources. Although fuel availability was scarcely considered before the oil crisis efficient fuel generation was an issue in important niche markets. As an example, in the military logistics field, providing fuels for vehicles in remote battlefields is a key task. Hence, a mobile production system based on a portable heat source was being investigated with utmost interest.
Following the oil crisis, multiple programs were created to design, test and qualify such processes for purposes such as energy independence. High temperature nuclear reactors were still considered as the likely heat sources. However, optimistic expectations based on initial thermodynamics studies were quickly moderated by pragmatic analyses comparing standard technologies and by numerous practical issues. Hence, the interest for this technology faded during the next decades, or at least some tradeoffs were being considered with the use of electricity as a fractional energy input instead of only heat for the reactions. A rebirth in the year 2000 can be explained by both the new energy crisis, demand for electricity, and the rapid pace of development of concentrated solar power technologies whose potentially very high temperatures are ideal for thermochemical processes, while the environmentally friendly side of thermochemical cycles attracted funding in a period concerned with a potential peak oil outcome.

Principles

Water-splitting via a single reaction

Consider a system composed of chemical species in thermodynamic equilibrium at constant pressure and thermodynamic temperature T:
Equilibrium is displaced to the right only if energy is provided to the system under strict conditions imposed by thermodynamics:
Hence, for an ambient temperature T° of 298K and a pressure of 1 atm , more than 80% of the required energy ΔH must be provided as work in order for water-splitting to proceed.
If phase transitions are neglected for simplicity's sake, one can assume that ΔH et ΔS do not vary significantly for a given temperature change. These parameters are thus taken equal to their standard values ΔH° et ΔS° at temperature T°. Consequently, the work required at temperature T is,
As ΔS° is positive, a temperature increase leads to a reduction of the required work. This is the basis of high-temperature electrolysis. This can also be intuitively explained graphically.
Chemical species can have various excitation levels depending on the absolute temperature T, which is a measure of the thermal agitation. The latter causes shocks between atoms or molecules inside the closed system such that energy spreading among the excitation levels increases with time, and stop only when most of the species have similar excitation levels .
Relative to the absolute temperature scale, the excitation levels of the species are gathered based on standard enthalpy change of formation considerations; i.e. their stabilities. As this value is null for water but strictly positive for oxygen and hydrogen, most of the excitation levels of these last species are above the ones of water. Then, the density of the excitation levels for a given temperature range is monotonically increasing with the species entropy. A positive entropy change for water-splitting means far more excitation levels in the products. Consequently,
One can imagine that if T were high enough in Eq., ΔG could be nullified, meaning that water-splitting would occur even without work. Though possible, this would require tremendously high temperatures: considering the same system naturally with steam instead of liquid water would hence give required temperatures above 3000K, that make reactor design and operation extremely challenging.
Hence, a single reaction only offers one freedom degree to produce hydrogen and oxygen only from heat

Water-splitting with multiple reactions

On the contrary, as shown by Funk and Reinstrom, multiple reactions provide additional means to allow spontaneous water-splitting without work thanks to different entropy changes ΔS°i for each reaction i. An extra benefit compared with water thermolysis is that oxygen and hydrogen are separately produced, avoiding complex separations at high temperatures.
The first pre-requisites and ) for multiple reactions i to be equivalent to water-splitting are trivial :
Similarly, the work ΔG required by the process is the sum of each reaction work ΔGi:
As Eq. is a general law, it can be used anew to develop each ΔGi term. If the reactions with positive and negative entropy changes are expressed as separate summations, this gives,
Using Eq. for standard conditions allows to factorize the ΔG°i terms, yielding,
Now consider the contribution of each summation in Eq. : in order to minimize ΔG, they must be as negative as possible:
Finally, one can deduce from this last equation the relationship required for a null work requirement
Consequently, a thermochemical cycle with i steps can be defined as sequence of i reactions equivalent to water-splitting and satisfying equations, and . The key point to remember in that case is that the process temperature TH can theoretically be arbitrary chosen, far below the water thermolysis one.
This equation can alternatively be derived via the Carnot's theorem, that must be respected by the system composed of a thermochemical process coupled with a work producing unit :
Consequently, replacing W and Q in Eq. gives after reorganization Eq.
Equation has practical implications about the minimum number of reactions for such a process according to the maximum process temperature TH. Indeed, a numerical application in the case of the originally chosen conditions gives a minimum value around 330 J/mol/K for the summation of the positive entropy changes ΔS°i of the process reactions.
This last value is very high as most of the reactions have entropy change values below 50 J/mol/K, and even an elevated one is twice lower. Consequently, thermochemical cycles composed of less than three steps are practically impossible with the originally planned heat sources, or require "hybrid" versions

Hybrid thermochemical cycles

In this case, an extra freedom degree is added via a relatively small work input Wadd, and Eq. becomes,
If Wadd is expressed as a fraction f of the process heat Q, Eq. becomes after reorganization,
Using a work input equals to a fraction f of the heat input is equivalent relative to the choice of the reactions to operate a pure similar thermochemical cycle but with a hot source with a temperature increased by the same proportion f.
Naturally, this decreases the heat-to-work efficiency in the same proportion f. Consequently, if one want a process similar to a thermochemical cycle operating with a 2000K heat source, the maximum heat-to-work efficiency is twice lower. As real efficiencies are often significantly lower than ideal one, such a process is thus strongly limited.
Practically, use of work is restricted to key steps such as product separations, where techniques relying on work might sometimes have fewer issues than those using only heat

Particular case : Two-step thermochemical cycles

According to equation, the minimum required entropy change for the summation of the positive entropy changes decreases when TH increases. As an example, performing the same numerical application but with TH equals to 2000K would give a twice lower value, which allows thermochemical cycles with only two reactions. Such processes can be realistically coupled with concentrated solar power technologies like Solar Updraft Tower. As an example in Europe, this is the goal of the Hydrosol-2 project and of the researches of the solar department of the ETH Zurich and the Paul Scherrer Institute.
Examples of reactions satisfying high entropy changes are metal oxide dissociations, as the products have more excitation levels due to their gaseous state than the reactant . Consequently, these entropy changes can often be larger than the water-splitting one and thus a reaction with a negative entropy change is required in the thermochemical process so that Eq. is satisfied. Furthermore, assuming similar stabilities of the reactant for both thermolysis and oxide dissociation, a larger entropy change in the second case explained again a lower reaction temperature.
Let us assume two reactions, with positive and negative entropy changes. An extra property can be derived in order to have TH strictly lower than the thermolysis temperature: The standard thermodynamic values must be unevenly distributed among the reactions .
Indeed, according to the general equations , and, one must satisfy,
Hence, if ΔH°1 is proportional to ΔH°2 by a given factor, and if ΔS°1 and ΔS°2 follow a similar law, the inequality is broken.

Examples

Hundreds of such cycles have been proposed and investigated. This task has been eased by the availability of computers, allowing a systematic screening of chemical reactions sequences based on thermodynamic databases. Only the main "families" will be described in this article.

cycles with more than 3 steps or hybrid ones

Cycles based on the sulfur chemistry

An advantage of the sulfur chemical element is its high covalence. Indeed, it can form up to 6 chemical bonds with other elements such as oxygen, i.e. a wide range of oxidation states. Hence, there exist several redox reactions involving such compounds. This freedom allows numerous chemical steps with different entropy changes, and thus offer more odds to meet the criteria required for a thermochemical cycle. Most of the first studies were performed in the USA, as an example at the Kentucky University for sulfide-bases cycles. Sulfate-based cycles were studied in the same laboratory and also at Los Alamos National Laboratory and at General Atomics. Significant researches based on sulfates were also performed in Germany and in Japan
. However, the cycle which has given rise to the highest interests is probably the one discovered by General Atomics.

Cycles based on the reversed Deacon process

Above 973K, the Deacon reaction is reversed, yielding hydrogen chloride and oxygen from water and chlorine: