In chemistry, thermochemical cycles combine solely heat sources (thermo) with chemical reactions to split water into its hydrogen and oxygen components.Producing Hydrogen: The Thermochemical Cycles - Idaho National Laboratory (INL) 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 (1966) as a maximally efficient way to produce fuels (e.g. hydrogen, ammonia) from stable and abundant species (e.g. water, nitrogen) and heat sources.Funk, J.E., Reinstrom, R.M., 1966. Energy requirements in the production of hydrogen from water. I&EC Process Design and Development 5(3):336-342. 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 (a nuclear reactor was considered) was being investigated with utmost interest. Following the oil crisis, multiple programs (Europe, Japan, United States) were created to design, test and qualify such processes for purposes such as energy independence. High-temperature (around operating 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 (thermodynamic cycles for electricity generation, coupled with the electrolysis of water) and by numerous practical issues (insufficient temperatures from even nuclear reactors, slow reactivities, reactor corrosion, significant losses of intermediate compounds with time...).Shinnar, R., Shapira, D., Zakai, S., 1981. Thermochemical and hybrid cycles for hydrogen production. A differential economic comparison with electrolysis. I&EC Process Design and Development 20(4):581-593. Hence, the interest for this technology faded during the next decades,Funk, J.E., 2001. Thermochemical hydrogen production: past and present. International Journal of Hydrogen Energy 26(3):185:190. or at least some tradeoffs (hybrid versions) were being considered with the use of electricity as a fractional energy input instead of only heat for the reactions (e.g. Hybrid sulfur cycle). 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,Steinfeld, A., 2005. Solar thermochemical production of hydrogen - a review. Solar Energy 78(5):603-615 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 (e.g. water splitting) in thermodynamic equilibrium at constant pressure and thermodynamic temperature T:
H2O(l) H2(g) + 1/2 O2(g) (1)
Equilibrium is displaced to the right only if energy (enthalpy change ΔH for water-splitting) is provided to the system under strict conditions imposed by thermodynamics: one fraction must be provided as work, namely the Gibbs free energy change ΔG of the reaction: it consists of "noble" energy, i.e. under an organized state where matter can be controlled, such as electricity in the case of the electrolysis of water. Indeed, the generated electron flow can reduce protons (H+) at the cathode and oxidize anions (O2−) at the anode (the ions exist because of the chemical polarity of water), yielding the desired species. the other one must be supplied as heat, i.e. by increasing the thermal agitation of the species, and is equal by definition of the entropy to the absolute temperature T times the entropy change ΔS of the reaction. (2) Hence, for an ambient temperature T° of 298K (kelvin) and a pressure of 1 atm (atmosphere (unit)) (ΔG° and ΔS° are respectively equal to 237 kJ/mol and 163 J/mol/K, relative to the initial amount of water), 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 (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, (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)).
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.Lédé, J., Lapicque, F., Villermaux, J., Cales, B., Ounalli, A., Baumard, J.F., Anthony, A.M., 1982. Production of hydrogen by direct thermal decomposition of water: preliminary investigations. International Journal of Hydrogen Energy 7(12):939-950.
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)
Water-splitting with multiple reactions 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.Kogan, A., 1998. Direct solar thermal splitting of water and on-site separation of the products - II. Experimental feasibility study. International Journal of Hydrogen Energy 23(9):89-98.
The first pre-requisites (Eqs.(4) and (5)) for multiple reactions i to be equivalent to water-splitting are trivial (cf. Hess's law):
(4)
(5) Similarly, the work ΔG required by the process is the sum of each reaction work ΔGi:
(6)
As Eq. (3) is a general law, it can be used anew to develop each ΔGi term. If the reactions with positive (p indice) and negative (n indice) entropy changes are expressed as separate summations, this gives,
(7)
Using Eq. (6) for standard conditions allows to factorize the ΔG°i terms, yielding,
(8)
Now consider the contribution of each summation in Eq. (8): in order to minimize ΔG, they must be as negative as possible: : −ΔS°i are negative, so (T − T°) must be as high as possible: hence, one choose to operate at the maximum process temperature TH : −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,
(9)
Finally, one can deduce from this last equation the relationship required for a null work requirement (ΔG ≤ 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 TH 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):
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 TH and a cold one at T°,
(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 TH to the i endothermic reactions of the thermochemical cycle (the fuel consumption subsystem is exothermic): (12)