Great research starts with great data.

Learn More
More >
Patent Analysis of

Methods for operating solar-thermochemical processes

Updated Time 12 June 2019

Patent Registration Data

Publication Number

US10001298

Application Number

US14/962307

Application Date

08 December 2015

Publication Date

19 June 2018

Current Assignee

NATIONAL TECHNOLOGY & ENGINEERING SOLUTIONS OF SANDIA, LLC

Original Assignee (Applicant)

NATIONAL TECHNOLOGY & ENGINEERING SOLUTIONS OF SANDIA, LLC

International Classification

C01B3/06

Cooperative Classification

C01B31/20,F24S90/00,F24S50/40,C01B3/061,C01B3/063

Inventor

ERMANOSKI, IVAN,MILLER, JAMES E.

Patent Images

This patent contains figures and images illustrating the invention and its embodiment.

US10001298 Methods operating solar-thermochemical processes 1 US10001298 Methods operating solar-thermochemical processes 2 US10001298 Methods operating solar-thermochemical processes 3
See all images <>

Abstract

Methods for controlling or operating solar thermochemical reactions process that maximize the two-step thermochemical energy cycle efficiency by a combination of pressure and temperature swing are disclosed.

Read more

Claims

1. A method for determining an operating oxidation temperature in a thermochemical reactor process, comprising:(a) selecting a thermal reduction temperature for a reactive oxide;(b) selecting an operating pressure in the thermal reduction step in a containment vessel;(c) selecting a solid-solid and a gas-gas recuperation efficiency;(d) selecting an initial oxidation temperature for a feed stream having a heat requirement for oxidizing the feed stream;(e) iterating/repeating steps (a)-(d) to develop a performance/efficiency map as a function of reduction temperature, temperature swing, pressure swing, and recuperation efficiencies;(f) embedding the performance/efficiency map into a solar collection and heating system model to determine the operating oxidation temperature; and(g) utilizing the determined operating oxidation temperature in the thermochemical reactor process which comprises thermal reduction, solid-solid heat exchange in a thermal recuperator, H2 production and steam pre-heating by employing solar radiation to heat and thermally reduce the reactive oxide in a thermal reduction chamber of the reactor, moving the reactive oxide through the recuperator and into an H2 production chamber of the reactor, where the H2 production chamber is operated at the determined operating oxidation temperature by exposing the H2 production chamber to pre-heated steam in a countercurrent flow arrangement, producing H2.

2. The method of claim 1, wherein the thermal reduction temperature is based on materials limitations of the reactive material or containment vessel.

3. The method of claim 1, wherein the thermal reduction temperature is based on thermal receiver performance.

4. The method of claim 1, wherein the thermochemical reactor process is a water splitting process.

5. The method of claim 1, wherein heat requirements for achieving the thermal reduction temperature and the oxide temperature are equal.

6. The method of claim 1, wherein the solar collection and heating system model includes at least one parameter selected from a group consisting of the solar field, receiver, and secondary concentrators.

7. The method of claim 1, wherein the operating pressure is oxygen partial pressure at the thermal reduction temperature.

8. A method for determining an operating oxidation temperature in a thermochemical reactor process, comprising:(a) selectLng a thermal reduction temperature for a reactive oxide;(b) selecting an operating pressure in the thermal reduction step in a containment vessel;(c) selecting a solid-solid and a gas-gas recuperation efficiency;(d) selecting an initial oxidation temperature for a feed stream having a heat requirement for oxidizing the feed stream;(e) iterating/repeating steps (a)-(d) to develop a performance/efficiency map as a function of reduction temperature, temperature swing, pressure swing, and recuperation efficiencies;(f) embedding the performance/efficiency map into a system cost model to determine a configuration of process system components that result in the largest amount of stored chemical energy per unit of capital cost; wherein the operating oxidation temperature is determined at a temperature at which the largest amount of stored chemical energy per unit capital cost is achieved; and(g) utilizing the determined operating oxidation temperature in the thermochemical reactor process which comprises thermal reduction, solid-solid heat exchange in a thermal recuperator, H2 production and steam pre-heating by employing solar radiation to heat and thermally reduce the reactive oxide in a thermal reduction chamber of the reactor, moving the reactive oxide through the recuperator and into an H2 production chamber of the reactor, where the H2 production chamber is operated at the determined operating oxidation temperature by exposing the H2 production chamber to pre-heated steam in a countercurrent flow arrangement, producing H2.

9. The method of claim 7, wherein the process system components comprise thermal recuperation components.

10. The method of claim 7, wherein the thermal reduction temperature is based on materials limitations of the reactive material or containment vessel.

11. The method of claim 7, wherein the thermal reduction temperature is based on thermal receiver performance.

12. The method of claim 7, wherein the thermochemical reactor process is a water splitting process.

13. The method of claim 7, wherein heat requirements for achieving the thermal reduction temperature and the oxide temperature are equal.

14. The method of claim 7, wherein the operating pressure is oxygen partial pressure at the thermal reduction temperature.

Read more

Claim Tree

  • 1
    1. A method for determining an operating oxidation temperature in a thermochemical reactor process, comprising:
    • (a) selecting a thermal reduction temperature for a reactive oxide;
    • (b) selecting an operating pressure in the thermal reduction step in a containment vessel;
    • (c) selecting a solid-solid and a gas-gas recuperation efficiency;
    • (d) selecting an initial oxidation temperature for a feed stream having a heat requirement for oxidizing the feed stream;
    • (e) iterating/repeating steps (a)-(d) to develop a performance/efficiency map as a function of reduction temperature, temperature swing, pressure swing, and recuperation efficiencies;
    • (f) embedding the performance/efficiency map into a solar collection and heating system model to determine the operating oxidation temperature; and
    • (g) utilizing the determined operating oxidation temperature in the thermochemical reactor process which comprises thermal reduction, solid-solid heat exchange in a thermal recuperator, H2 production and steam pre-heating by employing solar radiation to heat and thermally reduce the reactive oxide in a thermal reduction chamber of the reactor, moving the reactive oxide through the recuperator and into an H2 production chamber of the reactor, where the H2 production chamber is operated at the determined operating oxidation temperature by exposing the H2 production chamber to pre-heated steam in a countercurrent flow arrangement, producing H2.
    • 2. The method of claim 1, wherein
      • the thermal reduction temperature is based on materials limitations of the reactive material or containment vessel.
    • 3. The method of claim 1, wherein
      • the thermal reduction temperature is based on thermal receiver performance.
    • 4. The method of claim 1, wherein
      • the thermochemical reactor process is a water splitting process.
    • 5. The method of claim 1, wherein
      • heat requirements for achieving the thermal reduction temperature and the oxide temperature are equal.
    • 6. The method of claim 1, wherein
      • the solar collection and heating system model includes at least one parameter selected from a group consisting of
    • 7. The method of claim 1, wherein
      • the operating pressure is oxygen partial pressure at the thermal reduction temperature.
  • 8
    8. A method for determining an operating oxidation temperature in a thermochemical reactor process, comprising:
    • (a) selectLng a thermal reduction temperature for a reactive oxide;
    • (b) selecting an operating pressure in the thermal reduction step in a containment vessel;
    • (c) selecting a solid-solid and a gas-gas recuperation efficiency;
    • (d) selecting an initial oxidation temperature for a feed stream having a heat requirement for oxidizing the feed stream;
    • (e) iterating/repeating steps (a)-(d) to develop a performance/efficiency map as a function of reduction temperature, temperature swing, pressure swing, and recuperation efficiencies;
    • (f) embedding the performance/efficiency map into a system cost model to determine a configuration of process system components that result in the largest amount of stored chemical energy per unit of capital cost; wherein the operating oxidation temperature is determined at a temperature at which the largest amount of stored chemical energy per unit capital cost is achieved; and
    • (g) utilizing the determined operating oxidation temperature in the thermochemical reactor process which comprises thermal reduction, solid-solid heat exchange in a thermal recuperator, H2 production and steam pre-heating by employing solar radiation to heat and thermally reduce the reactive oxide in a thermal reduction chamber of the reactor, moving the reactive oxide through the recuperator and into an H2 production chamber of the reactor, where the H2 production chamber is operated at the determined operating oxidation temperature by exposing the H2 production chamber to pre-heated steam in a countercurrent flow arrangement, producing H2.
See all independent claims <>

Description

TECHNICAL FIELD

Embodiments of the present invention relate to solar thermochemical processes and reactions and more particularly relate to methods of thermochemical reactor operations using a combination of targeted pressure and temperature swing to efficiently operate a two-step thermochemical cycle for solar fuel production.

BACKGROUND

Solar fuel production has the potential to dramatically change the world's energy posture: from the prospecting and extraction of today, to renewable production using sunlight and atmospheric gases in the future. The issue in solar fuel production is not one of mere feasibility, as this can be accomplished via multiple pathways (e.g. thermochemical, electrochemical, even biological), but one of practical economic viability, expressed via metrics such as the levelized fuel cost, which is strongly tied to efficiency.

Solar concentration systems typically entail optics (mirrors or lenses) to focus a large area of sunlight, or solar thermal energy, onto a small area. The solar thermal energy may drive a heat engine, such as a steam turbine, which may be further coupled to an electrical power generator to convert a portion of the solar thermal energy into electricity. Solar concentration systems may also drive a thermochemical reaction to generate a fuel that chemically stores a portion of the solar thermal energy. Water splitting, gasification of coal, and reforming of methane are all under investigation as potential solar thermochemical fuel production techniques. Solar concentration systems may drive other important reactions on an industrial scale as well, such as CO2 reduction into CO, for example.

Many solar thermochemical reactions entail a redox cycle. Two-step thermochemical fuel production processes are a conceptually simple approach: a working material (oxide) is partially or fully reduced at a high temperature, then cooled and, in the case of water splitting, exposed to steam to be reoxidized and yield H2. The metal oxide is then reduced again to repeat the cycle. While identifying advantageous metal-oxides is currently a subject of research, thermodynamic considerations dictate the thermal reduction portion of the cycle generally requires a high temperature, typically between 1000-2000° C., depending on the reactive oxide chosen and other conditions in the system.

While two-step metal oxide cycles are promising, reduction to practice of these theoretically efficient processes has been challenging. Existing working materials, for example, have a low reversible oxygen capacity, yielding little H2 per mole oxide per cycle. The large energy requirement for heating the reactive material between cycle steps necessitates solid-solid heat recovery at high temperature. Maximizing the per-cycle yield drives operation towards very low thermal reduction pressures and very high thermal reduction temperatures. The former require large vacuum pumps or high-purity sweep gasses, and the latter lead to excessive aperture radiation losses and require the use of specialized materials.

Solar thermochemical reactors in which these materials are implemented can take many forms, affording more or less efficient fuel production, operability, scalability, etc. One conventional system utilizes a honeycomb substrate that is coated with the reactive oxide. The honeycomb substrate is alternately exposed to collected solar energy to heat the system and reduce the reactive oxide, and to a reactant gas, such as H2O in the case of water splitting, to generate fuel. Such a reactor is essentially a fixed bed operating in semi-batch mode, and as such, suffers temperature non-uniformities and low thermal efficiency because much of the solar energy is expended on heating non-reactive portions of the bed (e.g., honeycomb substrate) and is ultimately rejected from the system as waste heat, rather than utilized for fuel production. Also, with each redox cycle, the entire system undergoes extreme thermal cycling, leading to component fatigue and failure.

The broad question of reactor efficiency has been examined in detail by Siegel et al., (N. P. Siegel, J. E. Miller, I. Ermanoski, R. B. Diver, E. B. Stechel “Factors Affecting the Efficiency of Solar-Driven Metal Oxide Thermochemical Cycles” Ind. Eng. Chem. Res., 2013, 52 (9), 3276. DOI: 10.1021/ie400193q) arriving at the concept of the utilization coefficient as an indicator of achievable efficiency for a reactor-material combination in a two-step thermochemical cycle. In a recent analysis Miller et al. (J. E. Miller, A. H. McDaniel, M. D. Allendorf “Considerations in the Design of Materials for Solar-Driven Fuel Production Using Metal-Oxide Thermochemical Cycles” Adv. Energy Mater. 2014, 4, 1300469. DOI:10.1002/aenm.201300469) address efficiency from an even broader thermodynamic viewpoint, and establish a framework for materials design.

The current understanding is that the cost of solar collection is a dominant overall cost factor for solar fuels in general, and for specifically proposed thermochemistry-based system designs. It is therefore of substantial importance for further progress in this field to develop methods for determining the operating and design parameter space that maximize efficiency, given a reactor type and working material properties.

Methods which avoid many of the difficulties and efficiency limitations associated with existing reactor operation would advance the art of solar thermochemical fuel production.

SUMMARY OF THE DISCLOSURE

The present disclosure is directed to methods for controlling solar thermochemical reactions and designing and operating solar thermochemical reactor. The disclosed methods incorporate a methodology for reactor design and controls/operations that maximize energy efficiency of the conversion process.

In an embodiment, methods are disclosed for a non-isothermal two-step cyclic process. In an embodiment, the non-isothermal two-step cyclic process may be non-isothermal water splitting (ITWS) or non-isothermal carbon dioxide splitting. The methods are independent of reactive material properties or reactor design making the results the most generally applicable. In an embodiment, the methods include a combination of pressure and temperature swing, rather than either individually, which emerge as the most efficient mode of operation of a two-step thermochemical cycle. In an embodiment, the methods include determining a map of the relevant operation parameter space. These methods are applicable beyond water splitting (reduction of water to H2), for example to the splitting of carbon dioxide (reduction to CO).

In an embodiment, a method of operating a thermochemical reactor process is disclosed that includes setting a thermal reduction temperature, pressure and oxide mass flow for an oxide in the thermochemical reactor process, and determining an oxidation temperature and oxygen partial pressure where oxide heating requirement and heat requirement of an oxidizing feed stream are equal.

In another embodiment, a method for determining an operating oxidation temperature in a thermochemical reactor process is disclosed that includes the following steps: select a thermal reduction temperature for a reactive material; select an operating pressure in the thermal reduction step in a containment vessel; select a solid-solid and a gas-gas recuperation efficiency; select an initial oxidation temperature for a feed stream having a heat requirement for oxidizing the feed stream; iterate/repeat to develop a performance/efficiency map as a function of reduction temperature, temperature swing, pressure swing, and recuperation efficiencies; and embed the performance/efficiency map into a solar collection and heating system model to determine the operating oxidation temperature.

In yet another embodiment, a method for determining an operating oxidation temperature in a thermochemical reactor process is disclosed that includes the following steps: select a thermal reduction temperature for a reactive material; select an operating pressure in the thermal reduction step in a containment vessel; select a solid-solid and a gas-gas recuperation efficiency; select an initial oxidation temperature for a feed stream having a heat requirement for oxidizing the feed stream; iterate/repeat to develop a performance/efficiency map as a function of reduction temperature, temperature swing, pressure swing, and recuperation efficiencies; and embed the performance/efficiency map into a system cost model to determine a configuration of process system components that result in the largest amount of stored chemical energy per unit of capital cost. The operating oxidation temperature is determined at a temperature at which the largest amount of stored chemical energy per unit capital cost is achieved.

BRIEF DESCRIPTION OF THE DRAWINGS

Embodiments of the present invention are illustrated by way of example, and not limitation, in the figures of the accompanying drawings in which:

FIG. 1 is a reactor schematic according to an embodiment of the disclosure.

FIG. 2a shows the relationship between Tiso(nw/h) and pO2.

FIG. 2b shows the practical efficiency limits for isothermal two-step water-splitting cycles.

FIG. 3 shows the efficiency nR(pTR), for several values of ΔT, εR−0.5,and εGG−0.8, according to an embodiment of the disclosure. In this non-isothermal example, the metal oxide is assumed to be cerium oxide (ceria)

FIG. 4 shows calculated reactor efficiencies as a function of ΔT. Solid lines are for εGG=0.8, whereas dashed lines are for εGG=0.6. Thick lines are for εR−0 and thin ones for εR=0.75. Lines of the same color correspond to the same PTR. The metal oxide in this example is ceria.

FIG. 5 shows calculated reactor efficiencies (left y-axis) as a function of ΔT, for εGG linearly increasing from εGG(1773 K)=0.6 to εGG(1273 K)=0.95 The metal oxide in this example is ceria.

FIG. 6 shows ηR(ΔTopt) as function of pTR, for several εR and εGG. The metal oxide in this example is ceria.

FIG. 7 shows a flow chart of a method of determining the optimal temperature difference between oxidation and reduction for the control of a solar thermochemical process according to an embodiment of the disclosure.

DETAILED DESCRIPTION

The present disclosure is directed to methods for conducting a two-step thermochemical cycle at maximum energy efficiency by controlling solar thermochemical reactions and designing and operating a reactor that drives the two reactions through an appropriate combination of pressure and temperature swings. The term “temperature swings,” as used herein, refers to the situation wherein the two different reactions (oxidation and reduction) are carried out at different temperatures so that the thermodynamic equilibrium state of each of is more favorable. The difference in temperature between the high temperature (oxide reduction) and low temperature (reoxidation) step is the temperature swing. In the following description, numerous details are set forth. It will be apparent, however, to one skilled in the art, that the present invention may be practiced without these specific details. In some instances, well-known methods and devices are shown in block diagram form, rather than in detail, to avoid obscuring the present invention. Reference throughout this specification to “an embodiment” means that a particular feature, structure, function, or characteristic described in connection with the embodiment is included in at least one embodiment of the invention. Thus, the appearances of the phrase “in an embodiment” in various places throughout this specification are not necessarily referring to the same embodiment of the invention. Furthermore, the particular features, structures, functions, or characteristics may be combined in any suitable manner in one or more embodiments. For example, a first embodiment may be combined with a second embodiment anywhere the two embodiments are not mutually exclusive.

The terms “coupled” and “connected,” along with their derivatives, may be used herein to describe structural relationships between components. It should be understood that these terms are not intended as synonyms for each other. Rather, in particular embodiments, “connected” may be used to indicate that two or more elements are in direct physical or electrical contact with each other. “Coupled” my be used to indicated that two or more elements are in either direct or indirect (with other intervening elements between them) physical or electrical contact with each other, and/or that the two or more elements co-operate or interact with each other (e.g., as in a cause and effect relationship).

The reactive particles applicable to the systems and techniques described herein may generally be of any type known for thermochemical reactions that are further suitable for conveyance by the systems and techniques described herein. In an embodiment, the reactive particles may be metal oxides, for example, but not limited to binary, ternary, and quaternary metal oxides, doped or undoped spinels, perovskites, brownmillerites, or other particles including a material having a composition capable of cyclic redox reactions. In this disclosure, exemplary embodiments utilizing a metal oxide (MOx), such as ceria (CeO2), ferrites, manganites, cobaltites, perovskites and the like are disclosed, however, alternative embodiments may employ any known particle composition capable of similar cyclic redox reactions. Reactive particles applicable to the systems and techniques described herein may also vary in size significantly with smaller sizes having higher surface/volume ratios improving reaction rates, but potentially being more susceptible to sintering and/or melting. For one exemplary ceria particle embodiment, particle size is between about 5 μm (microns) and 500 μm (microns).

Although the reactive particles are not consumed significantly with each reaction cycle in the exemplary embodiments described herein, one of skill in the art will note the systems and techniques described herein enable particle continuous addition and extraction and are therefore readily adaptable to embodiments where the reactive particles may be consumed (e.g., attritted or volatilized) and replenished. Reactive particles applicable to the systems and techniques described herein may be a solid media of homogenous or heterogeneous composition (e.g., carrier media coated with reactive media) and of various porosity.

The two step process may be applied to various two-step thermochemical cycle processes, such as, but not limited to solar fuel production, energy storage, and air separations. In an embodiment, the two-step thermochemical cycle is for solar fuel production, and may be a water splitting process or a carbon dioxide splitting process. In water splitting, the reduced metal oxide is reoxidized with steam at a specific temperature to yield H2. Some steam may be unreacted. The newly oxidized material is separated from the steam/H2 gaseous environment and is then thermally reduced by raising the temperature, lowering the oxygen partial pressure, or as described herein a combination of both. The evolved oxygen is pumped or swept away and the material is then ready for reoxidation with steam after the temperature is lowered as prescribed. If material flow through the cycle is continuous, the heat released during cooling may be recuperated to help drive thermal reduction. The net result of the process is that a combination of heat and oxygen pressure manipulation split water into separate streams containing H2 and O2. In carbon dioxide splitting, the process is entirely analogous with CO2 filling the role of H2O, and CO and O2 being the products.

The disclosed methods determine the operating conditions and control parameters for operating a two-step thermochemical cycle at a point wherein the largest fraction of solar energy is converted to chemical energy.

The methods determine the preferred combination of temperature swing and pressure swing between the reduction and oxidation steps for a cyclic two-step thermochemical process for a given set of the reduction temperature, and the effectiveness of recuperation of heat from the gaseous and solid streams. The preferred combination is that which provides the greatest chemical energy output per unit solar energy input. The thermal reduction temperature will typically be at or near an upper limit determined by materials or system limitations while the recuperation will be variable based on design and cost considerations for example; foregoing recuperation is one possible configuration. The methods are applicable to any solid phase metal-oxide system and any reactor embodiment that includes the option of both temperature and pressure swing.

The methods for given reactive material include the following steps:

1. Determine the thermal reduction temperature based on materials limitations or other constraints, e.g. optimizing thermal receiver performance.

2. Determine the operating pressure (oxygen partial pressure) in the thermal reduction step.

3. Determine the solid-solid and gas-gas recuperation efficiencies.

4. Calculate the optimum temperature for the oxidation step.

5. Iterate/repeat to develop efficiency map as a function of reduction temperature, temperature swing, pressure swing, and recuperation efficiencies.

6. For water splitting, the preferred oxidation temperature is that wherein the oxide heating and steam generation heat requirements are equal or approximately equal.

7. Performance/efficiency mapping can be embedded into larger system model including the solar field, receiver, etc. to determine preferred thermal reduction temperature for overall system efficiency.

8. Performance/efficiency mapping can be embedded into larger system cost models to determine preferred configuration of thermal recuperation, pump sizes, etc. that gives the largest amount of stored chemical energy per unit of capital cost.

The methods for operating the two-step thermochemical cycle process are further disclosed by referencing a two-step solar thermochemical reactive metal oxide water splitting cycle discussed below.

Reactions (1) and (2) below, generically describe a two-step thermochemical cycle for H2 production via water splitting, based on a reactive metal oxide (MOx). Reaction (1) is an endothermic thermal reduction of the oxide carried out at a temperature TTR and pressure PTR. Reaction (2) is the mildly exothermic reoxidation of the reduced oxide with H2O, at temperature TWS, which yields H2 and restores the oxide to its initial state. In carbon dioxide splitting, the process can also be used to produce CO from CO2 in reaction (2). The sum of the two reactions is heat-driven H2O splitting, described by reaction (3):

1δTR-δWSMOx-δWS1δTR-δWSMOx-δTR+12O2(4)thermalreductionatTTR,PTR,1δTR-δWSMOx-δTR+H2O1δTR-δWSMOx-δWS+H2(5)H2OsplittingatTWS,H2OH2+12O2(6)H2Othemolysis.

Here, δTR and δWS are the extents of reduction of the oxide following the thermal reduction and water splitting steps. Their difference, Δδ=δTR−δWS, is the reversible oxygen capacity, as realized in the cycle. The oxygen partial pressure for the reduction reaction is PO2.

At any temperature the Gibbs free energies of the above reactions are related:

ΔG1°=ΔG3°−ΔG2°  (4),

meaning that reactions (1) and (2) are thermodynamically spontaneous only in distinct and non-intersecting regions, i.e. ΔG1°(TTR), ΔG2°(TWS),<0 only for ΔT=TTR−TWS>0. If the cycle is carried out in these temperature regions, it is driven entirely by thermal energy, i.e. a primary heat source. However, cyclically heating and cooling the oxide between TTR and TWS opens the possibility for thermal losses that may render H2 production inefficient in practice.

At temperatures where reactions (1) and (2) are not spontaneous, additional energy must be provided to the system (generally in some form other than heat, i.e. a secondary energy source) in order to drive the reactions towards the same endpoints. The minimum amount of thermal energy, Qmin that must be supplied to carry out the cycle in this general case is:

Qmin(TTR,TWS)=ΔH1°(TTR)+(1-ɛR)ΔδFRCpΔT+ΔG1°(TTR)η1+ΔG2°(TWS)η2.(5)

The 1st term on the right-hand side is simply the reduction endotherm. The 2nd term accounts for thermal cycling, where Cp is the molar specific heat capacity of the reactive oxide, FR is the molar fraction of the solid that is reactive (as opposed to inert), and εR is the effectiveness of solid-solid heat recovery. The 3rd and 4th terms generically (the process is not specified) account for the scenario(s) where reactions (1) and/or (2) are carried out at unfavorable temperatures, i.e. when ΔG1°(TTR)>0 and/or ΔG2°(TWS)>0, and represent the minimum work must be performed to drive reaction (1) and/or (2). This work is determined by ΔG1° and/or ΔG2° the respective conditions. Coefficients η1 and η2 account for losses in converting heat to the required amount of work. Additionally, they implicitly include the possibility that waste heat (i.e. heat of reoxidation and unrecovered oxide sensible heat) can be used to provide part of the work in the 3rd and 4th term. (See also discussion of eq. 11.) The limiting case (Qmin=ΔH1°) applies to a system operating in the favorable temperature regimes with ideal heat recovery (εR=1).

To understand the implications of eq. 5, consider the situation where ΔT=0 (ITWS), at a temperature intermediate to those of the thermodynamically favorable regimes. In this case, no energy is required for thermal cycling (the 2nd term is zero), but work must be added to both reactions (1) and (2). As TTR=TWS change in value, the 2nd term remains zero and ΔG1° and ΔG2° increase and decrease in opposition to one another. As discussed below, the thermodynamic limits of this special case can be determined without any knowledge of the reactor design or properties of the working materials.

More interestingly, from an application perspective, if TTR is increased and TWS is decreased (TSWS), the thermal cycling energy requirement (2nd term) becomes nonzero and grows, but the work requirements embodied by ΔG1° and ΔG2° decrease and are eventually eliminated. Thus, eq. 5 suggests that for a given material (defining the thermodynamics) and set of reactor and process designs (defining the various efficiencies, practical and physical limitations, parasitic losses, etc.) there should be such TTR and TWS, that minimize the sum of the last three terms in eq. 5, and therefore Qmin.

Determining the conditions under which a two-step reactor operates at maximum efficiency requires the knowledge of the thermodynamic properties of the working material, as well as a reactor model. Specific thermodynamic properties of reactive oxides are not generally known, and are typically determined by extensive experimentation. Generalizations can therefore be made, but there is no universal solution.

For the purpose of demonstrating efficiency calculations, we use assume CeO2 as the active oxide, a well characterized candidate material for solar thermochemical water splitting. The thermodynamics of CeO2 are obtained from the work of Zinkevich et al. (M. Zinkevich, D. Djurovic, F. Aldinger “Thermodynamic Modelling of the Cerium-Oxygen System” Solid State Ionics, 2006;177, 989.). These authors performed a comprehensive, critical review of the thermodynamic literature concerning cerium oxides and applied a Calphad analysis to derive models covering all relevant phases (including both liquids and solids). This comprehensive approach covers the entire temperature range relevant to our analysis, and is necessary to accurately describe non-stoichiometric phases, such as the ceria fluorite phase (CeO2-δ) of concern here, which persists from δ=0 to δ≈0.3 at 1773 K. This model also generally predicts lower values of δ(p,T) than models based solely on the experiments by Panlener (R. J. Panlener, R. N. Blumenthal, J. E. Gamier “A Thermodynamic Study of Nonstoichiometric Cerium Dioxide” Journal of Physics and Chemistry of Solids 1975, 36, 1213.), used in almost all previous studies. This difference leads to lower overall efficiency predictions for the comprehensive approach, but the conclusions of the analysis remain unchanged by the choice of model. The difference between ceria reduction models is illustrated in FIG. 3.

FIG. 1 is a schematic of a reactor according to an embodiment of the disclosure. As can be seen in FIG. 1, heat exchangers and their effectiveness (εR and εGG) are indicated in the oxide and steam flows. The input solar heat power {dot over (Q)}TH is used to add sensible heat to the ceria (QSH) and to partially reduce it (QTR). If the heat from the H2 production reaction (QMOX) and the unrecovered sensible heat of the oxide (QSH,L), is insufficient to heat steam to TWS (QH2O), part of {dot over (Q)}TH is used. For simplicity and because it is of minor importance, heat recovery from the O2 stream is not shown, but it is included in the calculations (cf. eq. 11).

The reactor is assumed to accomplish four primary unit operations, common to many thermochemical reactor designs. These are a thermal reduction, solid-solid heat exchange in a thermal recuperator, H2 production (water splitting), and steam pre-heating. During operation, concentrated solar radiation heats and thermally reduces the reactive oxide in a thermal reduction chamber. The oxide then moves through the recuperator (entering at the hot inlet) and then into an H2 production chamber, where it is exposed to a pre-heated steam flow in a countercurrent arrangement, producing H2. The reoxidized material is then brought back to the reduction chamber, via the recuperator, where heat is exchanged between the two oxide flows.

The reactor heat-to-H2 efficiency or reactor efficiency, εR, is defined as:

ηR=n.H2HHVH2Q.A,(6)

where {dot over (n)}H2 is the hydrogen molar production rate, HHVH2 is its higher heating value, and {dot over (Q)}A is the solar power at the reactor aperture. Efficiency calculations incorporate an important assumption: Only solar primary energy is used for the entire operation of the reactor. This includes all heat needs, such as thermal reduction, ceria and feedstock heating, and heat equivalents of mechanical work, such as vacuum pumping, compression, oxide moving, etc. Equally importantly, all major losses and inefficiencies are also included, (e.g. black body radiation through the aperture at a concentration ratio CA=3000, conversion efficiency from heat to mechanical work, etc.) Radiation losses are included in the reactor efficiency for completeness and for ease of comparison with other work. The sensible heat of the product gasses is used to preheat steam (with a gas-gas heat recovery effectiveness εGG), and to generate power. Conduction losses through insulated reactor walls are considered negligible in a large device. The sensible heat in the O2 product is comparatively small, and its omission or inclusion has little effect on the efficiency calculations.

The H2 molar production rate in eq. 6 can be expressed in terms of the heat input power ({dot over (Q)}TH) and the heat required for production of 1 mol H2 (Qmol):

n.H2=Q.THQmol.(7)

After losses to aperture intercept (A=0.95) and thermal re-radiation (Prad), {dot over (Q)}TH can be expressed as:

{dot over (Q)}TH=A* {dot over (Q)}A−Prad   (8),

whereas Qmol is:

Qmol=QTR+QSH+QAUX   (9).

Here the individual terms (roughly ordered by decreasing temperature) correspond to those in eq. 5 as follows: QTR=ΔHr(CeO2) is the thermal reduction endotherm. The energy required for heating the oxide (sensible heat) from TWS to TTR (assuming FR=1) is:

QSH=CpΔδΔT(1-ɛR),(10)

where the molar heat capacity of CeO2 is Cp≈80 J/mol K.22 Finally, QAUX encompasses the heat equivalents of other, auxiliary, energy requirements:

QAUX−(QH2O+Qpump+QmechQsep)−(QMOX+QSH,L+QO2)   (11).

Here QH2O is the energy required to heat steam by ΔTI/O=TWS−TO, i.e. from ambient temperature (TO) to TWS, and it includes preheating by hot product streams. The heat equivalents of the pumping of products (in both chambers) and mechanical and separation work are Qpump, Qmech, and Qsep, respectively The negative terms represent the waste heat available from the product gasses, mainly the H2O-H2 mix, which consists of the heat released at TWS in the reoxidation reaction, QMOX=ΔHr-ΔHc0H2, and the unrecovered sensible heat of the oxide, QSH,L. Steam, in the fuel production chamber, acts as both a reactant (oxidizer) and a coolant. The sensible heat in the oxygen exhaust is QO2.

Importantly, QAUX is forced to be non-negative, i.e. it is set to zero when the waste heat exceeds the first three terms in eq. 11, since heat at TWS cannot contribute to either QTR or QSH. The quantities in eq. 11 are heat equivalents, so conversion efficiency terms are included where applicable, such as the conversion of heat to mechanical or pump work. An efficiency of 10% was used for heat-to-pump work and for the oxide moving work. Thermal reduction and water splitting are assumed to end in their thermodynamic equilibrium states, i.e. kinetic limitations are not considered.

The appeal of ITWS lies in the perceived simplification of reactor design and operation, as it eliminates the need for solid-solid heat recovery and, depending on the design, the frequent temperature cycling of reactor components. Coincidentally, this special case lends itself to straightforward theoretical analysis. To begin, we use well-known relationships for each of the reactions (1), (2), and (3):

ΔG°=−RT In K and ΔG°=ΔH°−TΔS°  (12) and (13),

where R is the gas constant. The equilibrium constants for reactions (1) and (2) depend on the reactant and product activities:

K1=(aO2)1/2(aMOx-δTR)1/Δδ(aMOx-δWS)1/ΔδandK2=(aH2)(aMOx-δWS)1/Δδ(aH2O)(aMOx-δTR)1/Δδ.(14)and(15)

At all relevant operating pressures, the gas activities can be expressed as partial pressures:

aO2=pO2andaH2aH2O=pH2pH2O,(16)and(17)

where pO2 is measured relative to standard pressure. Substituting eqs. 12, 13, 16 and 17 into eq. 4 gives:

-RTisoln(pO21/2)-RTisoln(aMOx-δTR1/ΔδaMOx-δWS1/Δδ)=ΔH3°-TisoΔS3°+RTisoln(pH2pH2O)+RTisoln(aMOx-δWS1/ΔδaMOx-δTR1/Δδ).(18)

Here Tiso, is the isothermal operating temperature. Solving for Tiso is facilitated by the exact cancellation of the oxide terms on the left and right side of eq. 18, giving:

Tiso=-ΔH3°R(ln(pO21/2)-ln(pH2OpH2))-ΔS2°.(19)

FIG. 1a shows the relationship between Tiso(nw/h) and pO2. For the water splitting reaction constant thermodynamic values of

ΔH3°=250.8kJmolandΔS3°=57.35Jmol-K

are assumed. These are the values at 1673 K and best represent the temperature range of practical interest. Adopting values for a different temperature introduces very small differences in the results. The fading rectangle in FIG. 2a roughly indicates a reasonable operating parameter space for a practical reactor and shows that ITWS largely falls outside of it.

FIG. 2b shows practical efficiency limits for ITWS. Efficiency curves are plotted for nw/h<105. The lack of results below certain Tiso for the higher pO2 values indicates that ITWS is not possible for nw/h<105. The efficiency scale in FIG. 2b was chosen for ease of comparison with FIGS. 3, 4 and 5.

Referring again to FIG. 2a, the relationship between Tiso and nw/h,for several values of PO2 (nw/h=nH2O/nH2 resulting from the oxidation step (ideal gas behavior is assumed so pH2O/pH2 and nH2O/nH2 are used interchangeably) is shown. It is evident from FIG. 2a that relaxing one parameter results in the restriction of one or both of the other two. For example, decreasing Tiso requires either a pO2 decrease or an nw/h increase, or both. Importantly, FIG. 2a strictly applies to an ideal isothermal cycle. A real isothermal cycle would require even more stringent operating conditions than an ideal one (e.g. a higher Tiso at the same values of pO2 and nw/h), for example due to kinetic limitations.

It is important to understand that the results in FIG. 2a are general in the sense that a cycle represented by a valid combination of the three parameters can be performed by multiple possible materials which must satisfy eq. 4 at Tiso. Conversely, this requirement means that an isothermal cycle, defined by a point in the graph, cannot be realized by arbitrarily chosen materials. The high temperatures (in this case TTR=TWS=Tiso), low pO2, and high nw/h values indicated in FIG. 2a, raise questions regarding the ultimate feasibility of ITWS. To understand the implications of these results and to outline a realistic space of operating parameters, we consider the practical limitations regarding TTR, pO2, and nw/h.

Increasing Tiso corresponds to less strict pO2 (higher) and nw/h (lower) requirements, and isothermal temperatures as high as 2173 K have been considered. However, radiation losses through the reactor aperture, as well as oxide sublimation and reactivity with reactor structures, limit TTR to no more (and possibly substantially less) than 1773 K in devices of practical relevance. To appreciate the challenge of ITWS under the extreme conditions considered in the literature, it is instructive to note that at 2173 K, ceria has a vapor pressure pCeO2≈9.3 Pa, leading to a swift and irreversible oxide loss via sublimation, as observed experimentally by Abanades et al.

It is assumed that low pO2 is achieved by pumping, i.e. lowering of pTR, the total pressure in this step (therefore pO2=pTR). As shown in a previous analysis, the heat equivalent of pump work is not a major contributor to the total energy requirement, but the lowest pTR is limited by other factors, such as oxygen volumetric flow and entering the molecular flow regime, to no less than 1 Pa.

The alternative, isothermal inert gas sweeping, was examined by Bader et al., who showed that, even under best-case conditions, the amount of required N2 by far exceeds the amount of the H2 product (nN2/nH2≈700). In addition to requiring an N2 purification plant, the only manner of somewhat efficient ITWS was found to require exceptionally high levels of heat recovery (>95%) between the incoming and outgoing N2 gas−at Tiso. Finally, the vast majority of the products are the inert-oxygen mix and steam, not H2. It can thus be concluded that sweeping is not an option for ITWS.

The above practical limitations regarding TTR and pTR give context to the results in FIG. 2a: For example, even for very low pTR (e.g. 1 Pa), and the highest operationally relevant Tiso of 1773 K, large amounts of steam must be provided for a very low H2 yield (nh/w=nH2/nH2O<<1); i.e. the majority of the reactor “product” would then be unreacted steam, not H2. In short, ITWS requires impractically high thermal reduction temperatures, or exceptionally low thermal reduction pressures, or results in an exceptionally low H2 fraction in the output stream. As the derivation of eq. 19 shows, these results and associated limitations are a consequence of water thermodynamics and the basic relationship for the Gibbs free energy of the reduction and oxidation reactions (eq. 4), and can therefore not be circumvented by either redox material choice or innovative reactor design.

For a deeper insight into the implications of the tradeoffs associated with ITWS, the low H2 fraction or high nw/h values can be viewed in the context of separation work, i.e. the work that must be performed to separate H2 from the H2-poor output stream. Separation work is directly related to efficiency, and practical ITWS efficiency limits, as defined in eq. 6, can be estimated by including some well-established efficiencies of the constituent processes. Re-radiation losses are given in eq. 8(˜Tiso4). Separation work (2nd law) depends on Tiso, nh/w, and the final H2 purity, assumed here to be a modest xH2=99.9%. The practical separation efficiency (i.e. theoretical 2nd law work vs. actual work) is generally ˜15%, albeit not at the high temperatures considered here. The heat-to-power efficiency of a Rankine cycle in concentrated solar power plants, necessary to perform pump and separation work, is at best ≈40%. Finally, neglecting other work and heat requirements, and keeping the assumption for the heat-to-pumping efficiency (10%) from Section 2.2, plotted in FIG. 2b shows the practical limits for ITWS efficiency (hR).

The results show that the ITWS ηR values are low, even at high Tiso and low pO2. The limits are almost independent of Tiso and depend very weakly on pO2. In light of the outstanding operating conditions shown in FIG. 2a, low efficiencies should not be surprising. The relative insensitivity of the results on Tiso and pO2 may, on the other hand, be initially unexpected. This, however, is a manifestation of the mutual dependence of the operating conditions (pO2, nw/h, and Tiso), which are dictated solely by water thermodynamics as expressed in eq. 19. Simply put, the results in FIG. 2b show that, whether one in practice accepts higher re-radiation losses (to increase Tiso), or chooses to invest work in pumping (to lower pO2) or in H2 separation (to allow higher nw/h), the overall ITWS efficiency limit is roughly the same, in what can be viewed as a thermodynamic zero-sum game.

The above results describe the conditions required for ITWS and indicate the practical difficulties in realizing it, including inherent limitations on efficiency. In this section, the effects of operational parameters on efficiency in the general case where ΔT≥0 are examiner. In this case, both material and reactor assumptions, as discussed above are included. pTR is limited to values between 1 Pa and 1 kPa—low enough to meaningfully facilitate thermal reduction, but not too low to be entirely unfeasible in a reactor in the field. Likewise, TTR=1773 K is set.

The above results describe the conditions required for ITWS and indicate the practical difficulties in realizing it, including inherent limitations on efficiency. In the following paragraphs, the effects of operational parameters on efficiency in the general case where ΔT≥0 are examined. In this case, both material and reactor assumptions as detailed above are included. pTR is limited to values between 1 Pa and 1 kPa—low enough to meaningfully facilitate thermal reduction, but not too low to be entirely unfeasible in a reactor in the field. Likewise, we set TTR=1773 K.

FIG. 3 shows the efficiency ηR(pTR), for several values of ΔT,εR=0.5, and εGG=0.8. In FIG. 3, solid lines show the calculated reactor efficiency as function of pHR, for several values of ΔT (left y-axis). Note the nil efficiency for ITWS above pTR≈75 Pa, and the initial efficiency increase, followed by a decrease, as ΔT increases from 0 K to 400 K. Dashed lines, on the right y-axis, show the extent of thermal reduction, δTR (assuming TTR=1773 K). The black dashed line is for the comprehensive model used in this work (based on Zinkevich et al.), whereas the white line is based on Panlener only.

As can be seen in FIG. 3, two important features are immediately evident in the plot. Firstly, ITWS (ΔT=0) yields the lowest efficiency for every pTR in the range. Secondly, for pTR≈75 Pa and above, ITWS efficiency is zero, whereas TSWS (ΔT>0) for the same pTR yields a positive efficiency.

The latter is a special case of a more general result, also evident in FIG. 3: for low values of ΔT, the efficiency is zero above some critical pTR. This stems from the presence of oxygen in steam as a result of partial dissociation, characterized by a well-known pressure, pO2,d (e.g. PO2,d(1773 K)≈75 Pa) For some values of pTR and TWS, the equilibrium oxygen pressure above the oxide,

pO2,CeO2-δTR

(TWS), exceeds pO2,d(TWS), leading to further oxide reduction (not reoxidation) in steam, and yielding no H2 product.

ΔTopt, defined as the value of ΔT(pTR, εRεGG) for which Qmin (eq. 5) is the smallest, and efficiency (ηR) is the highest, can now be determined. To visually introduce the ΔTopt concept, the efficiency curves in FIG. 3, from yellow to black, at a constant PTR can be followed. A trend is evident: ηR(ΔT) initially increases and then decreases with ΔT. Focusing on this trend, FIG. 4 shows the efficiency as function of ΔT, ηR(ΔT), for εR=0 and εR=0.75, with two values of εGG (0.8 and 0.6) and several values of pTR. The chosen values for εR and εGG reflect the awareness that heat recovery at high temperature is challenging, and a high effectiveness, however desirable, may not be possible in practice.

A peak efficiency, ηR(ΔTopt), exists for any of the combinations of pTR, εR, and εGG in FIG. 4. For the chosen range of parameters, ΔTopt varies roughly between 180 K and 440 K. Furthermore, for most regimes, ITWS efficiency is several-fold lower than that at ΔTopt, and it also yields the lowest efficiency for all εR and εGG. This is especially pronounced for εGG=0.6. Other trends are also apparent. For example, pTR decrease and εR decrease generally lead to a ΔTopt decrease, whereas εGG decrease leads to a ΔTopt increase. Efficiency generally increases with decreasing pTR, and increasing εR and εGG. Conversely, the lowest efficiencies would be realized at high (e.g. atmospheric) pTR, in the absence of heat recovery.

Some of the efficiency curves in FIG. 4 coincide. First, below ΔToptR=0), ηRR=0)=ηRR=0.75). Second, above ΔToptGG=0.6), ηRGG=0.6)=ηRGG=0.8). Finally, curves for pTR and εR=0 coincide with curves for 10*pTR and εR=0.75, below ΔTopt(pTR, εR=0). The first two coincidences result from the balance of energy requirements in the cycle, including those that lead to low isothermal efficiency, and can be understood by considering the interplay of factors that determine ΔTopt. First, we recall that the unrecovered sensible heat of the reduced oxide and the heat of the reoxidation reaction are used to preheat the steam feedstock to near TWS, via the hot H2O-H2 exhaust (FIG. 1). Furthermore, oxide reduction (QTR), oxide heating (QSH), and steam heating (QH2O) are by far the three largest energy requirements in the system (depending on ΔT). Of these, QSH and QH2O can be considered parasitic, since they do not directly contribute to H2 production (whereas QTR does, with an efficiency given by HHVH2/QTR). Therefore, at the point where QSH and QH2O are roughly balanced, the least amount of direct solar input is required for steam heating or the least amount of the oxide sensible heat has to be rejected, thus leading to peak efficiency.

The coinciding efficiencies in FIG. 4 can now be explained as follows: First, below ΔTopt, QH2O is the largest energy requirement and it requires direct solar input (in addition to preheating). Specifically, the region of coincidence, where ηRR=0)=ηRR=0.75),corresponds to a situation in which direct solar input is required for steam heating irrespective of εR. More generally, below ΔToptR=0), QH2O is sufficiently large to make efficiency independent on εR. The situation corresponds to a low and eventually zero 2nd right-hand term in eq. 5 (at ΔT=0), and a large 4th term.

In light of this, the reasons behind the very low efficiency for ITWS are straightforward: While no energy is needed to heat the oxide after the water splitting reaction (QSH=0 in FIG. 1), QH2O is at its maximum, even with extensive preheating by the H2O-H2 output. This is because, at ΔT=0, both nw/h and ΔTI/O are at their maximum values. Since QSH,L=0, virtually all of QH2O requires direct solar input. This dominant role of QH2O in ITWS (but not for ΔT>ΔTopt) also strongly cautions against omitting this energy requirement from efficiency calculations, as is sometimes done.

Second, for ΔT>ΔTopt, oxide heating is the largest energy requirement and it requires direct solar input (to the extent that εR<1). In this region, QH2O is small, mainly because, at low TWS, comparatively little steam is needed to oxidize ceria back to equilibrium (nw/h is small), but also because ΔTI/O is smaller, compared to ITWS. Therefore, QSH/QH2O>1. In fact, at ΔT>ΔTopt, QAUX<0, necessitating heat rejection. Alternatively, this high quality waste heat can be used for other purposes, even though it cannot directly increase reactor efficiency. This corresponds to a small 4th right-hand term in eq. 5 (compared to the 2nd term).

Lastly, coinciding efficiency curves for εR=0 and εR=0.75 reflect the particulars of ceria thermodynamics. As it happens, below ΔTopt(PTR), decreasing PTR by a factor of 10 is equivalent, in efficiency terms, to increasing εR from 0 to 0.75.

The high εGG required for efficient ITWS and low ΔT operation warrants some further consideration. High levels of gas-gas heat recovery (>97%) are attainable at temperatures up to roughly 923 K using stainless steel recuperators. At higher temperatures, creep and corrosion limitations require the use of nickel alloys (up to≈1273 K), and no recuperators operating at 1773 K or higher have been reported. Since in ITWS QH2O is the highest, the role of gas-gas heat exchange is critical. For ITWS at pTR=1 Pa, Tiso=1773 K and ΔTI/O=1475 K, nearly 100 mol of steam must be heated per mole of produced H2 (FIG. 2a). The associated energy requirement considerably exceeds the chemical energy content of the H2 product, even for high εGG.

The above further underscores the challenges associated with ITWS: If an exceptionally high εGG cannot be achieved in practice, the efficiencies for ITWS would be even lower than those shown in FIG. 4. On the other hand, as ΔT increases (i.e. TWS decreases), higher εGG values become more realistic. To account for this, we calculate efficiency in a more flexible fashion, by using a variable εGG, such that it is realistic at both high and low TWS (FIG. 5).

FIG. 5 shows calculated reactor efficiencies (left y-axis) as a function of ΔT, for εGG linearly increasing from εGG (1773 K)=0.6 to εGG (1273 K)=0.95. This roughly corresponds to a situation where heat from the output steam-H2 mixture is rejected above 1273 K. Solid lines are for εR=0, dashed lines are for εR=0.75. The dash-dot line shows εGG on the right y-axis.

The results in FIG. 5 give insight into what might be expected in practice, and show an even larger efficiency advantage of TSWS over ITWS. Although this analysis is for a pumped reactor, it is worth repeating at this point that efficiently recovering heat from a sweep gas would face the same obstacles as in the case of steam, with the added construction difficulty that it must be performed at TTR, irrespective of ΔT. However, operating at ΔTopt and under best-case conditions, would significantly decrease sweep gas requirements compared to ITWS, thus much decreasing, possibly even eliminating the need for heat recovery from the inert-oxygen exhaust and associated hardware complications. An inert gas purification plant would still be necessary.

Solid-solid heat recovery being also challenging, we have consistently included the limiting case of εR=0. Understanding that εR=0.75 is near the upper end of what may be possible in practice, plots such as that in FIG. 5 can be helpful for roughly estimating maximum reactor efficiency: for every pTR, it lies approximately between the peaks of the corresponding solid and dashed lines. The results in FIGS. 4 and 5 in show that for ceria and moderate values of the operating parameters, such as PTR>10 Pa, εR<0.5, and εGG<0.7, efficiency ranges roughly from 10 to 25%, whereas the ΔTopt range is roughly between 250 K and 400 K.

It should be noted at this point that the assumption that all reactions end in their thermodynamic equilibrium states is more important in ITWS, when Δδ is small and the system operates near equilibrium, than for ΔT>0, when Δδ is comparatively large. Therefore, any deviations from this assumption, as is certain to be the case in practice, would further disfavor ITWS.

In addition to maximizing efficiency for a given reactor/material system, knowing ΔTopt can guide reactor design.

FIG. 6 shows calculated reactor efficiencies at ΔTopt (ranging from 130 K to 460 K) as function of PTR. The three groups of lines correspond to three values of εR. Within the groups, solid lines correspond to εGG=0.9, dashed to εGG=0.7, and dash-dot lines to εGG=0.5. It is evident that, for a ceria-based reactor operating at ΔTopt, εR influences efficiency more than εGG does. For example, increasing εR from 0 to 0.5 allows the same efficiency to be achieved at a roughly 10 times higher pTR. This type of plot can be used to help evaluate the cost of achieving a certain pTR, εR, or εGG vs. corresponding efficiency benefits.

SUMMARY

As seen in FIG. 2a, a reactor producing H2 from H2O in an isothermal two-step cycle, must operate at high thermal reduction temperatures, very low thermal reduction pressures, or at an exceptionally high nw/h, or some combination of the three. High operating temperatures place extraordinary demands on reactor materials, and require unrealistically high concentration ratios from the solar collector and concentrator system. Low thermal reduction pressures require very large receivers and pumps—an undertaking of possibly prohibitive cost. Finally, high values of nw/h make water near ambient temperature, not H2, the main reactor product. This necessitates either high temperature H2 separation, or the addition of a high-throughput, high-efficiency steam heat recovery system, which preheats the input water while cooling the output steam-H2 mix. Each of these factors complicate reactor and plant design and compromise economics: Therefore, when the entire balance of plant is considered, ITWS makes matters more difficult, not easier, as one might hope.

Further, in addition to posing extraordinary design and operational demands, ITWS offers no efficiency payoff. On the contrary, it appears to be the most inefficient fashion of producing H2 from H2O in a two-step cycle (FIGS. 3 and 4). Even in the most favorable case, without solid-solid heat recovery, ITWS with a high level of steam-steam heat recovery (εGG=0.8), is less efficient than TSWS at ΔTopt for a far more plausible εGG−0.6 (FIG. 4). This disadvantage only widens for εR>0 or when a realistic TWS-dependent εGG is included (FIGS. 4 and 5).

Recalling that the question in solar fuel production is not one of feasibility, but of efficient solar utilization and minimization of the product cost, no ITWS advantages are evident in our analysis. Rather, requiring that TTR=TWS seems to be an unnecessary and counterproductive limitation. On the other hand, TSWS at ΔTopt maximizes solar resource utilization, and the associated low steam requirement simplifies plant design and operation.

The very existence of ΔTopt may seem peculiar if one thinks of thermochemical reactors as engines that reverse combustion, i.e. where heat is the input and fuel (chemical work) is the output. It may initially appear most plausible that maximizing ΔT would also maximize efficiency. In the case of perfect heat recovery (εRGG=1), this would be correct. It is because of the reality of non-ideal heat recovery that ΔTopt exists at all.

Some general implications regarding reactor operation follow from the above results. Under all conditions, the slopes of the efficiency curves are shallower for ΔT>ΔTopt than for ΔT<ΔTopt. Furthermore, the reasons for suboptimal efficiency are different in these two regions. For ΔT>ΔTopt, the oxide heating requirement results in the production of high quality waste heat (at TWS), which can be used elsewhere in the plant, even if not for H2 production directly. For ΔT<ΔTopt, however, efficiency decreases because of the steam heating requirement, with waste heat available at low temperature (following steam-steam heat recovery) and of little value. This suggests that it may be prudent to err on the side of ΔT>ΔTopt, rather than the opposite, in order to achieve higher average efficiency under the variable environmental conditions present in practice. Even though the feasibility of thermochemical fuel production using ceria as a working oxide has been demonstrated, a consensus exists regarding the need for material improvements. Most notable of them is the need for a material that provides a higher Δδ at a higher pTR and lower TTR than, for example, ceria, yet with similar kinetics and stability. In addition to the possibility of less demanding operation (at a lower required TTR), a higher Δδ would enable higher yields, so that less oxide must be heated per unit produced H2 or fuel in general. Importantly, this increase must not be offset by an equal increase in Cp or more precisely CpΔT (cf. eq. 10 and compare, for example, Cp for ceria with that of LaMnO3 or La1−xSrxMnO3). A material that reduces more easily than ceria (larger δ under identical TTR and pTR) will generally also be more difficult to reoxidize, assuming similar and temperature independent values for ΔS. This assumption is justified as ΔS is largely a function of the evolution of oxygen into the gas phase. Operationally, this suggests that advanced materials may require a lower TWS (larger ΔT) for reoxidation to achieve the same nw/h2. In other words, an insufficiently large Δδ/Cp increase could be offset by an increase in the the 2nd right-hand term in eq. 5, and therefore decrease efficiency.

Understanding this, it is to be expected that optimal operation with advanced materials is likely to involve an increase of ΔTopt, not its decrease in the direction of ITWS. Precise details would additionally depend on reactor design and various internal efficiencies such as εR, εGG, etc. This also follows from general thermodynamic consideration regarding the maximum theoretical efficiency of a two-step thermochemical process. Because of strict thermodynamic limitations, ITWS is unlikely to benefit from the use of advanced materials.

While some key design and operating parameters of a thermochemical reactor for two-step H2 production present obvious tradeoffs between difficulty and efficiency, ΔT is not one of them. For example, the higher the degree of heat recovery (εR or εGG), which is increasingly difficult to accomplish, the higher the efficiency. One must therefore find a balance that minimizes the levelized cost of the H2 product. The choice of ΔT is easier to make: operating difficulty being largely independent of ΔT, it would always be advantageous to operate at ΔT for which efficiency is the highest.

Finally, it should be noted that even though much of this analysis is specific to CeO2 as a reactive oxide, it can be applied to any material for which sufficient thermodynamic information is available. With appropriate small adaptations (mainly heat capacity and dissociation coefficients), the analysis can also be applied to the solar-thermochemical production of CO from CO2, with largely the same conclusions.

Lastly, the conditions (Tiso, pO2 and nw/h) required for isothermal two-step thermochemical water splitting (TTR=TWS) can be determined based on water thermodynamics and are highly mutually dependent: choosing values for any two defines the third. This analysis shows that isothermal water splitting is impractical, being a choice between high thermal reduction temperatures, very low oxygen partial pressures for thermal reduction, or exceptionally high steam requirements (i.e. high separation work)—or some combination of the three.

Isothermal water splitting is substantially less efficient than the same process at ΔT>0. This is true even in the complete absence of solid-solid heat recovery in the latter case, and assuming a high steam heat recovery effectiveness at high temperature. The low efficiency of ITWS is primarily a result of the exceptionally high energy requirement for steam heating in the water splitting step of the cycle.

Given a specific reactor/material combination, an optimal ΔT=TTR−TWS can be found to maximize efficiency. For reasonable values of process parameters in a ceria-based cycle, this ΔTopt ranges roughly between 250 K and 400 K, and is expected to increase in well-designed advanced materials.

A combination of pressure and temperature swing, rather than either individually, is by a wide margin the most efficient mode of operation of a two-step cycle thermochemical reactor for hydrogen production. Efficiency being of paramount importance for the practical application of this technology, temperature and pressure swing reactors appear to be the most promising direction for future research and development.

FIG. 7 shows a flow chart of a method of determining the optimal temperature difference between oxidation and reduction for the control of a solar thermochemical process according to an embodiment of the disclosure. In an embodiment, methods are disclosed for determining oxidation and reduction operating temperatures. It has been unexpectedly disclosed that by setting the thermal reduction temperature, pressure and oxide mass flow, and then determining the oxidation temperature where the oxide heating and steam generation heat requirements are equal or approximately equal, peak efficiency of the cycle is attained.

As so described, the artisan will appreciate that with many independent design parameters, a design protocol for the reactors described herein may include first determining thermal reduction properties of the reactive particles (e.g., reaction kinetics at a chosen reduction temperature and oxygen partial pressure). A solar concentrator power, overall particle mass flow rate through the reduction chamber, and feed stock pumping speed may be independently set to establish the desired reduction temperature, pressure, and residence time within the reactor. Similarly, the production temperature, and production residence time may be set by appropriate component sizing and adjusting the flow of the reactant fluid (two more independent parameters).

It is to be understood that the above description is illustrative, and not restrictive. For example, while flow diagrams in the figures show a particular order of operations performed by certain embodiments of the invention, it should be understood that such order is not required (e.g., alternative embodiments may perform the operations in a different order, combine certain operations, overlap certain operations, etc.). Furthermore, many other embodiments will be apparent to those of skill in the art upon reading and understanding the above description. Although the present invention has been described with reference to specific exemplary embodiments, it will be recognized that the invention is not limited to the embodiments described, but can be practiced with modification and alteration within the spirit and scope of the appended claims. The scope of the invention should, therefore, be determined with reference to the appended claims, along with the full scope of equivalents to which such claims are entitled.

Read more
PatSnap Solutions

Great research starts with great data.

Use the most comprehensive innovation intelligence platform to maximise ROI on research.

Learn More

Patent Valuation

$

Reveal the value <>

19.0/100 Score

Market Attractiveness

It shows from an IP point of view how many competitors are active and innovations are made in the different technical fields of the company. On a company level, the market attractiveness is often also an indicator of how diversified a company is. Here we look into the commercial relevance of the market.

24.0/100 Score

Market Coverage

It shows the sizes of the market that is covered with the IP and in how many countries the IP guarantees protection. It reflects a market size that is potentially addressable with the invented technology/formulation with a legal protection which also includes a freedom to operate. Here we look into the size of the impacted market.

75.0/100 Score

Technology Quality

It shows the degree of innovation that can be derived from a company’s IP. Here we look into ease of detection, ability to design around and significance of the patented feature to the product/service.

81.0/100 Score

Assignee Score

It takes the R&D behavior of the company itself into account that results in IP. During the invention phase, larger companies are considered to assign a higher R&D budget on a certain technology field, these companies have a better influence on their market, on what is marketable and what might lead to a standard.

12.0/100 Score

Legal Score

It shows the legal strength of IP in terms of its degree of protecting effect. Here we look into claim scope, claim breadth, claim quality, stability and priority.

Citation

Patents Cited in This Cited by
Title Current Assignee Application Date Publication Date
Reactor temperature control using probability distribution HUNTSMAN PETROCHEMICAL LLC 18 September 2009 07 July 2011
Controlled relay of media streams across network perimeters MICROSOFT TECHNOLOGY LICENSING, LLC 08 September 2008 29 January 2009
See full citation <>

More like this

Title Current Assignee Application Date Publication Date
Mechanism for production of hydrocarbon by pyrolysis of waste plastics and production method thereof FINERTEC FUELS CENTRO , LDA. 30 November 2015 09 September 2016
Solar receiver using heat pipes and granular thermal storage medium ABENGOA SOLAR LLC. 22 August 2016 02 March 2017
Ultra-high temperature solar-driven gas heating system STELLAR GENERATION, INC. 29 March 2016 06 October 2016
System and method for temperature control in plasma processing system TOKYO ELECTRON LIMITED,TOKYO ELECTRON U.S. HOLDINGS, INC. 22 March 2017 28 September 2017
Method and system for the manufacture of methane as well as heat and electricity by hydrogasification of biomass BICARBO SP.Z O. O. 10 March 2016 15 September 2016
Temperature control measure for slurry bed hydrogenation reactor and design method and use thereof CATECH TECHNOLOGY CO., LTD. 30 November 2015 26 May 2017
An improved temperature control system TURNER, DAVID 06 May 2016 10 November 2016
Solar heat collecting apparatus CHO, YOUNG SANG,CHO, JUNG HEE 04 April 2017 12 October 2017
Hydrogenation process temperature control method, and design method therefor and use thereof CATECH TECHNOLOGY CO., LTD. 20 November 2015 10 November 2016
Solar power collection systems and methods thereof TIBBOTT, GINA, ANNE,KRISHNAN, NEEL 01 April 2016 06 October 2016
Bimetallic tube for solar receiver COCKERILL MAINTENANCE & INGENIERIE S.A. 21 October 2016 01 June 2017
Thermochemical regeneration with oxidant preheating PRAXAIR TECHNOLOGY, INC. 15 August 2016 09 March 2017
Fluid heating system PLOURDE, BRIAN,ABRAHAM, JOHN,PLOURDE, DOUGLAS,PAKONEN, RICHARD,GIKLING, ANDY 01 December 2015 09 June 2016
Rapid solar-thermal conversion of biomass to syngas THE REGENTS OF THE UNIVERSITY OF COLORADO, A BODY CORPORATE 29 August 2007 17 April 2008
Dehydrogenation of alkanes HALDOR TOPSØE A/S 24 October 2016 04 May 2017
Photodetector with integrated temperature control element ELENION TECHNOLOGIES, LLC 23 September 2016 30 March 2017
Method for the generation of power UNIVERSITY OF FLORIDA RESEARCH FOUNDATION, INC. 20 April 2016 27 October 2016
High temperature synthesis for power production and storage THE REGENTS OF THE UNIVERSITY OF CALIFORNIA 27 June 2016 29 December 2016
Fermentation temperature control system and method for animal farm waste pollution treatment HUNAN SAKAL ENVIRONMENTAL SCIENCE AND TECHNOLOGY CO., LTD.,WANG, SHEN 20 July 2016 18 January 2018
Method and installation for thermochemical conversion of raw material containing organic compounds OBSHCHESTVO S OGRANICHENNOJ OTVETSTVENNOSTYU "ENERGOLESPROM" 30 May 2016 07 December 2017
See all similar patents <>

More Patents & Intellectual Property

PatSnap Solutions

PatSnap solutions are used by R&D teams, legal and IP professionals, those in business intelligence and strategic planning roles and by research staff at academic institutions globally.

PatSnap Solutions
Search & Analyze
The widest range of IP search tools makes getting the right answers and asking the right questions easier than ever. One click analysis extracts meaningful information on competitors and technology trends from IP data.
Business Intelligence
Gain powerful insights into future technology changes, market shifts and competitor strategies.
Workflow
Manage IP-related processes across multiple teams and departments with integrated collaboration and workflow tools.
Contact Sales
Clsoe
US10001298 Methods operating solar-thermochemical processes 1 US10001298 Methods operating solar-thermochemical processes 2 US10001298 Methods operating solar-thermochemical processes 3