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A Termokémiai körfolyamat alatt olyan kémiai reakció sorozatot kell érteni, amiben kizárólag egy hőforrás által szolgáltatott enrgiával vízbontó kémiai folyamatot hajtunk, hidrogén és oxigén előállítása céljából. A körfolyamat jelző azért használatos, mert a víz és alkotói kivételével minden reakciótermék folyamatosan visszajáratásra kerül az eljárásba, keletkező melléktermékek nélkül.

Ha a ciklus során valamelyik lépésben termodinamikai értelemben történő munkavégzés is történik a reakció energiaszükségletének fedezése érdekében, a folyamatot hibrid folyamatként definiáljuk.

Történet

Az eljárások alapjait elsőként Funk és Reinstrom (1966) vetette fel, mint lehetőséget üzemanyagok, alapanyagok (például hidrogén, amónia) hatékonyabb előállítási módjaként, ami nagy tömegben hozzáférhető anyagokra (például víz és légköri nitrogén) és hőforrásokra épül. Annak ellenére, hogy az 1973-as olajválság előtti időkben az üzemanyag rendelkezésreállás nem volt szempont, az elgondolás létjogosultságát néhány szűk piaci szegmens visszaigazolta. Például a katonai logisztika területén távoli elszigetelt harctéren működő járművek üzemanyag ellátásakor kulcsfontosságú ez a terület. A helyszinre telepített üzemanyag gyártó telep hőenergia ellátására elsődlegesen szállítható nukleáris reaktorral -mint hőforrással- rendelkezik, ez a leginkább kutatott alkalmazási területe a témának. Az olajválságot követően több kutatási program (Európa, Japán, USA) indult a polgári célú energiafüggetlenítés területén. A nagy hőmérsékleten (1000 K feletti) üzemelő nukleáris reaktorok alkalmasak ilyen folyamatok hőforrásaként, így az első optimista felvetések után - a termodinamikai vizsgálatokat követően - nyilvánvalóvá vált számos technológiai probléma is. Emiatt a meglévő hagyományos technológia korlátozta az előtérbe kerülést. Ilyen problémák a reaktorok alacsony működési hőmérséklete, a reaktorok lassú reagálása miatti szabályzási problémák, a reaktor szerkezeti anyagainak korróziója, számottevő köztitermék veszteség az eljárás során. Ezek az eljárások évtizedekre háttérbe szorultak, vagy csak kismértékben terjedtek el (hibrid változatok) amik részleges villamos energiát és hulladékhőt használnak. (például a Hibrid kénciklus). Az ujjászületést az ezredforduló utáni energiaválságok és a koncentrált napenergia technológia gyorsütemű fejlődése hozta el: a folyamat számára koncentrált napeneriával fejlesztett magas hőmérséklet az ideális. A technológia környezetbarátsága szintén megalapozza a kutatásokba történő befektetéseket.

Alapvetés

Egy reakcióban történő vízbontás

A kérdéskör vizsgálatához vegyünk egy termodinamikailag egyensúlyban lévő állandó hőmérsékletű rendszert (T), amiben a vízbontási reakciót a következő egyensúlyi folyamattal írhatjuk le:

H₂O(l) $\rightleftharpoons$ H₂(g) + 1/2 O₂(g)    (1)

Egyensúly csak akkor tolódik el jobbra (vízbontás irányába) ha a rendszerhez a vízbontó lépés ΔH entalpiaszükségletét a rendszerhez hozzáadjuk, ez a következő két részből tevődik össze egyértelműen:

• Egyrészt a szükséges termodinamikai értelemben vett munka, reverzibilis munkavégző képesség, amit szabadenergiának, vagy Gibbs féle szabadentalpia változásnak nevezünk (ΔG). Ez az a befektetett hasznos munka, ami a katódfolyamatban a protonok (H⁺) redukálásában, az anódfolyamatban az anionok oxidációjában nyilvánul meg.
• Másrészt a szükséges hőmennyiséget kell fedezni, ami a reakció entrópia változásából (ΔS, az entrópia változás a részecskék számának változásából látható be) és az abszolut hőmérséklet szorzatából származik.

Összegezve az előbbi tényezőket:

$\Delta H=\Delta G+T\Delta S$    (2)

Szobahőmérsékleten, T° = 298K és légköri nyomáson 1 atm (ΔG° and ΔS° közelítőleg egyennlő 237 kJ/mol and 163 J/mol/K, a kiindulási vízmennyiségre vonatkozólag), a befektetett ΔH energia több mint 80%-a hasznosul a víz alkotóira bontásakor.

If phase transitions are neglected for simplicity's sake (e.g. water electrolysis under pressure to keep water in its liquid state), 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,

$\Delta G=\Delta G^{0}-(T-T^{0})\Delta S^{0}$    (3)

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 (equilibrium) only when most of the species have similar excitation levels (a molecule in a highly excited level will quickly return to a lower energy state by collisions) (Entropy (statistical thermodynamics)).

Arbitrary representation of the excitation levels of the H₂O/H₂/O₂ system according to the temperature scale. The higher the temperature (thermal agitation, in transparent red), the more excitation levels at high temperature can be populated.

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,

• A low temperature (T°), thermal agitation allow mostly the water molecules to be excited as hydrogen and oxygen levels required higher thermal agitation to be significantly populated (on the arbitrary diagram, 3 levels can be populated for water vs 1 for the oxygen/hydrogen subsystem),
• At high temperature (T), thermal agitation is sufficient for the oxygen/hydrogen subsystem excitation levels to be excited (on the arbitrary diagram, 4 levels can be populated for water vs 8 for the oxygen/hydrogen subsystem). According to the previous statements, the system will thus evolve toward the composition where most of its excitation levels are similar, i.e. a majority of oxygen and hydrogen species.

One can imagine that if T were high enough in Eq.(3), ΔG could be nullified, meaning that water-splitting would occur even without work (thermolysis of water). Though possible, this would require tremendously high temperatures: considering the same system naturally with steam instead of liquid water (ΔH° = 242 kJ/mol; ΔS° = 44 J/mol/K) would hence give required temperatures above 3000K, that make reactor design and operation extremely challenging.

Hence, a single reaction only offers one freedom degree (T) to produce hydrogen and oxygen only from heat (though using Le Chatelier's principle would also allow to slightly decrease the thermolysis temperature, work must be provided in this case for extracting the gas products from the system)

Vízbontás több kémiai reakció eredményeként

On the contrary, as shown by Funk and Reinstrom, multiple reactions (e.g. k steps) 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 (Eqs.(4) and (5)) for multiple reactions i to be equivalent to water-splitting are trivial (cf. Hess's law):

• $\sum _{i}^{}{\Delta H_{i}^{0}}=\Delta H^{0}$    (4)

• $\sum _{i}^{}{\Delta S_{i}^{0}}=\Delta S^{0}$    (5)

Similarly, the work ΔG required by the process is the sum of each reaction work ΔG_i:

$\Delta G=\sum _{i}^{}{\Delta G_{i}}$    (6)

As Eq. (3) is a general law, it can be used anew to develop each ΔG_i term. If the reactions with positive (p indice) and negative (n indice) entropy changes are expressed as separate summations, this gives,

$\Delta G=\sum _{p}^{}{(\Delta G_{i}^{0}-(T_{i}-T^{0})\Delta S_{i}^{0})}+\sum _{n}^{}{(\Delta G_{i}^{0}-(T_{i}-T^{0})\Delta S_{i}^{0})}$    (7)

Using Eq. (6) for standard conditions allows to factorize the ΔG°_i terms, yielding,

$\Delta G=\Delta G^{0}+\sum _{p}^{}{(T_{i}-T^{0})(-\Delta S_{i}^{0})}+\sum _{n}^{}{(T_{i}-T^{0})(-\Delta S_{i}^{0})}$    (8)

Now consider the contribution of each summation in Eq. (8): in order to minimize ΔG, they must be as negative as possible:

• $\sum _{p}^{}{(T_{i}-T^{0})(-\Delta S_{i}^{0})}$: -ΔS°_i are negative, so (T-T°) must be as high as possible: hence, one choose to operate at the maximum process temperature T_H
• $\sum _{n}^{}{(T_{i}-T^{0})(-\Delta S_{i}^{0})}$: -ΔS°_i are positive, (T-T°) should be ideally negative in order to decrease ΔG. Practically, one can only set T equals to T° as the minimum process temperature in order to get rid of this troublesome term (a process requiring a lower than standard temperature for energy production is a physical absurdity as it would require refrigerators and thus a higher work input than output). Consequently, Eq.(8) becomes,

$\Delta G=\Delta G^{0}-(T_{H}-T^{0})\sum _{p}^{}{\Delta S_{i}^{0}}$    (9)

Finally, one can deduce from this last equation the relationship required for a null work requirement (ΔG ≤ 0)

$\sum _{p}^{}{\Delta S_{i}^{0}}\geq {\frac {\Delta G^{0}}{(T_{H}-T^{0})}}$    (10)

Consequently, a thermochemical cycle with i steps can be defined as sequence of i reactions equivalent to water-splitting and satisfying equations (4), (5) and (10). The key point to remember in that case is that the process temperature T_H can theoretically be arbitrary chosen (1000K as a reference in most of the past studies, for high temperature nuclear reactors), far below the water thermolysis one.

This equation can alternatively (and naturally) 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 (chemical species are thus in a closed loop):

Carnot representation of engines based on thermochemical cycles or on water thermolysis

Carnot representation of engines based on thermochemical cycles or on water thermolysis

• at least two heat sources of different temperatures are required for cyclical operation, otherwise perpetual motion would be possible. This is trivial in the case of thermolysis, as the fuel is consumed via an inverse reaction. Consequently, if there is only one temperature (the thermolysis one), maximum work recovery in a fuel cell is equal to the opposite of the Gibbs free energy of the water-splitting reaction at the same temperature, i.e. null by definition of the thermolysis. Or differently said, a fuel is defined by its instability, so if the water/hydrogen/oxygen system only exists as hydrogen and oxygen (equilibrium state), combustion (engine) or use in a fuel cell would not be possible.
• endothermic reactions are chosen with positive entropy changes in order to be favored when the temperature increases, and the opposite for the exothermic reactions.
• maximal heat-to-work efficiency is the one of a Carnot heat engine with the same process conditions, i.e. a hot heat source at T_H and a cold one at T°,

${\frac {W}{Q}}\leq {\frac {T_{H}-T^{0}}{T_{H}}}$    (11)

• the work output W is the "noble" energy stored in the hydrogen and oxygen products (e.g. released as electricity during fuel consumption in a fuel cell). It thus corresponds to the free Gibbs energy change of water-splitting ΔG, and is maximum according to Eq.(3) at the lowest temperature of the process (T°) where it is equal to ΔG°.
• the heat input Q is the heat provided by the hot source at temperature T_H to the i endothermic reactions of the thermochemical cycle (the fuel consumption subsystem is exothermic):

$Q=\sum _{i}^{}{q_{i}}$    (12)

Hence, each heat requirement at temperature T_H is,

$q_{i}=T_{H}\Delta S_{i}$    (13)

Replacing Eq.(13) in Eq.(12) yields:

$Q=T_{H}\sum _{p}^{}{\Delta S_{i}}$    (14)

Consequently, replacing W (ΔG°) and Q (Eq.(14)) in Eq.(11) gives after reorganization Eq.(10) (assuming that the ΔS_i do not change significantly with the temperature, i.e. are equal to ΔS°_i)

Equation (10) has practical implications about the minimum number of reactions for such a process according to the maximum process temperature T_H. Indeed, a numerical application (ΔG° equals to 229 kJ/K for water considered as steam) in the case of the originally chosen conditions (high-temperature nuclear reactor with T_H and T° respectively equal to 1000K and 298K) 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 (e.g. water-splitting from liquid water: 163 J/mol/K) is twice lower. Consequently, thermochemical cycles composed of less than three steps are practically impossible with the originally planned heat sources (below 1000K), or require "hybrid" versions

Hibrid termokémiai körfolyamat

In this case, an extra freedom degree is added via a relatively small work input W_add (maximum work consumption, Eq.(9) with ΔG ≤ W_add), and Eq.(10) becomes,

$\sum _{p}^{}{\Delta S_{i}^{0}}\geq {\frac {\Delta G^{0}-W_{add}}{(T_{H}-T^{0})}}$    (15)

If W_add is expressed as a fraction f of the process heat Q (Eq.(14)), Eq.(15) becomes after reorganization,

$\sum _{p}^{}{\Delta S_{i}^{0}}\geq {\frac {\Delta G^{0}}{((1+f)T_{H}-T^{0})}}$    (16)

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 (instead of 1000K), 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 (e.g. electrolysis) might sometimes have fewer issues than those using only heat (e.g. distillations)

Speciális eset : Két lépéses termokémiai körfolyamat

According to equation (10), the minimum required entropy change (right term) for the summation of the positive entropy changes decreases when T_H increases. As an example, performing the same numerical application but with T_H equals to 2000K would give a twice lower value (around 140 kJ/mol), 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 (Greece, Germany (German Aerospace Center), Spain, Denmark, England) and of the researches of the solar department of the ETH Zurich and the Paul Scherrer Institute (Switzerland).

Examples of reactions satisfying high entropy changes are metal oxide dissociations, as the products have more excitation levels due to their gaseous state (metal vapors and oxygen) than the reactant (solid with crystalline structure, so symmetry dramatically reduces the number of different excitation levels). 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.(5) is satisfied. Furthermore, assuming similar stabilities of the reactant (ΔH°) for both thermolysis and oxide dissociation, a larger entropy change in the second case explained again a lower reaction temperature (Eq.(3)).

Let us assume two reactions, with positive (1 subscript, at T_H) and negative (2 subscript, at T°) entropy changes. An extra property can be derived in order to have T_H strictly lower than the thermolysis temperature: The standard thermodynamic values must be unevenly distributed among the reactions .

Indeed, according to the general equations (2) (spontaneous reaction), (4) and (5), one must satisfy,

${\frac {\Delta H_{1}^{0}}{\Delta S_{1}^{0}}}<{\frac {\Delta H_{1}^{0}+\Delta H_{2}^{0}}{\Delta S_{1}^{0}+\Delta S_{2}^{0}}}$    (17)

Hence, if ΔH°₁ is proportional to ΔH°₂ by a given factor, and if ΔS°₁ and ΔS°₂ follow a similar law (same proportionality factor), the inequality (17) is broken (equality instead, so T_H equals to the water thermolysis temperature).

Példák

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.

Három lépésnél több lépéses ciklus vagy hibrid ciklus

Kén alapú ciklusok

An advantage of the kén chemical element is its high covalence. Indeed, it can form up to 6 chemical bonds with other elements such as oxygen (e.g. sulfates), 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 (cf. Principles). 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 (e.g. FeSO₄ and CuSO₄) were also performed in Germany and in Japan . However, the cycle which has given rise to the highest interests is probably the (Sulfur-iodine cycle) one (acronym: S-I) 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:

H₂O + Cl₂ → 2 HCl + 1/2 O₂

See also

• Iron oxide cycle
• Cerium(IV) oxide-cerium(III) oxide cycle
• Copper-chlorine cycle
• Hybrid sulfur cycle
• Hydrosol-2
• Sulfur-iodine cycle
• Zinc zinc-oxide cycle
• UT-3 cycle