Patent Publication Number: US-2023144856-A1

Title: High-temperature shock heating for thermochemical reactions

Description:
CROSS-REFERENCE TO RELATED APPLICATION 
     The present application claims the benefit of U.S. Provisional Application No. 62/989,110, filed Mar. 13, 2020, entitled “System and Method for High-Temperature Shock Heating for Thermochemical Reactions,” and U.S. Provisional Application No. 63/154,191, filed Feb. 26, 2021, entitled “System, Device, and Method for High-Temperature Shock Heating for Thermochemical Reactions,” each of which is incorporated by reference herein in its entirety. 
    
    
     STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH 
     This invention was made with government support under DE-FE0031877 awarded by the United States Department of Energy (DOE). The government has certain rights in the invention. 
    
    
     FIELD 
     The present disclosure relates generally to thermochemical reactions, and more particularly, high-temperature Joule-based heating for thermochemical reactions, such as pyrolysis, thermolysis, synthesis, hydrogenation, dehydrogenation, hydrogenolysis, or combinations thereof. 
     BACKGROUND 
     Conventional thermochemical reactions are typically conducted by continuous heating under near-equilibrium conditions, in part because conventional heating devices exhibit poor heat transfer and large thermal inertia. As a result, many of the reaction schemes currently employed in industrial-scale chemical production systems suffer from low yield with respect to desired products due to the constraints of chemical equilibrium. For example, selective methane (CH 4 ) transformation to value-added products remains difficult to achieve. Similar to other thermochemical reactions, conventional methane conversion methods, such as steam reforming, dry reforming, direct non-oxidative methane conversion (DNMC), oxidative coupling, partial oxidation, and methane pyrolysis, are all conducted with continuous heating at a relatively mild temperature (e.g., &lt; 1300 K), which limits conversion. While higher temperatures are preferred for higher methane conversion in view of the endothermic nature of these transformations, such higher temperatures cause secondary and subsequent reactions that skew product yield toward undesired low-value products, such as heavy aromatics and coke, thereby reducing selectivity, conversion, or both. Achieving high yield and high selectivity to value-added products through methane conversion remains an unmet challenge. 
     In another example, ammonia (NH 3 ) synthesis (N 2 +3H 2  → 2NH 3 , ΔH = -91.8 kJ/mol) is typically conducted at a constant temperature under high pressure (e.g., ~200 bar). While a higher temperature may be preferred to provide the activation energy to break N 2  bonds, thermodynamically the synthesis reaction is not favored at such higher temperatures because of the exothermic nature of the reaction, which would otherwise shift the reaction equilibrium to ammonia decomposition at the higher temperatures. Accordingly, conventional ammonia synthesis methods require a compromise between reaction kinetics (e.g., where a higher temperature is desired for N 2  activation) and thermodynamics (e.g., where a lower temperature is desired due to the exothermic nature of the synthesis reaction) by adopting a mid-range temperature (e.g., -500° C.) and associated reduced reaction rate. 
     Embodiments of the disclosed subject matter may address one or more of the above-noted problems and disadvantages, among other things. 
     SUMMARY 
     Embodiments of the disclosed subject matter provide gas-flow reactor systems and methods for high-temperature shock heating to conduct thermochemical reactions under non-equilibrium conditions with kinetic control over the mechanistic reaction process. Such thermochemical reactions can include pyrolysis, thermolysis, synthesis, hydrogenation, dehydrogenation, hydrogenolysis, or combinations thereof. As used herein, “shock heating” or “programmable heating and quenching” (PHQ) refers to rapid heating and quenching with tunable heating patterns (e.g., non-continuous or discontinuous heating) with time scales on the order of seconds or sub-seconds (e.g., milliseconds). The shock heating can employ a porous electrical Joule heating element within or part of a gas-flow reactor system. Compared with conventional steady-state approaches that operate with continuous heating at constant temperatures, embodiments of the disclosed subject matter provide rapid switching between low (e.g., 800 K to near room temperature) and high temperatures (e.g., 1200 K or above) in milliseconds or seconds. During the heating cycle, reactants (e.g., gases) are provided in thermal contact with the heating element by flowing into contact with and through pores of the heating element to enable efficient heat transfer therebetween. Accordingly, the temperature of the reactants closely follows the temperature profile of the heating element, thereby allowing for precise control of the reaction pathway under non-equilibrium conditions. With the disclosed shock heating approach, the high temperature applied during part of a heating cycle can enable bond activation while the chemical reaction is allowed to proceed during the low temperature part of the heating cycle, thereby decoupling thermodynamics and kinetics, and improving reaction rate and energy-efficiency. 
     In one or more embodiments, a method can comprise, for a first time period, providing one or more reactants in thermal contact with a first heating element in a reactor. The method can further comprise, during a first part of a heating cycle, providing the one or more reactants with a first temperature by heating with the first heating element, such that one or more thermochemical reactions is initiated. The method can also comprise, during a second part of the heating cycle, providing the one or more reactants with a second temperature less than the first temperature. A duration of the first time period can be equal to or greater than a duration of the heating cycle, and the duration of the heating cycle is less than five seconds. The first heating element can operate by Joule heating and can have a porous construction that allows gas to flow therethrough. The one or more thermochemical reactions can comprise pyrolysis, thermolysis, synthesis, hydrogenation, dehydrogenation, hydrogenolysis, or any combination thereof. 
     In one or more embodiments, a method can comprise, for a first time period, providing one or more reactants within a reactor. The method can further comprise, during the first time period, using one or more Joule heating elements to change a temperature of the one or more reactants between a first peak temperature and a first minimum temperature for a first heating cycle. The first peak temperature can initiate one or more thermochemical reactions of the one or more reactants. The one or more thermochemical reactions can comprise pyrolysis, thermolysis, synthesis, hydrogenation, dehydrogenation, hydrogenolysis, or any combination thereof. The method can also comprise, during the first time period, using the one or more Joule heating elements to change the temperature of the one or more reactants between a second peak temperature and a second minimum temperature for a second heating cycle. The second peak temperature can also initiate the one or more thermochemical reactions of the one or more reactants. A duration of the first time period can be equal to or greater than a combined duration of the first and second heating cycles, and the duration of each of the first heating cycle and the second heating cycle can be less than five seconds. A difference between the first peak temperature and the first minimum temperature can be at least 600 K, and a difference between the second peak temperature and the second minimum temperature can be at least 600 K. 
     In one or more embodiments, a thermochemical reaction system can comprise a gas-flow reactor, a Joule heating element, and a control system. The gas-flow reactor can have an inlet port and an outlet port. The inlet port can be constructed to receive input of a gas flow to an internal volume of the gas-flow reactor. The outlet port can be constructed to receive output of a gas flow from the internal volume of the gas-flow reactor. The Joule heating element can be disposed within the gas-flow reactor. The Joule heating element can have a porous construction that allows gas to flow therethrough. The control system can be operatively coupled to the Joule heating element and can be configured to apply a signal to the Joule heating element that changes temperature thereof between a peak temperature and a minimum temperature during a corresponding heating cycle. A duration of the heating cycle can be less than five seconds, a difference between the peak temperature and the minimum temperature can be at least 600 K, and the peak temperature can be at least 1200 K. 
     In one or more embodiments, a thermochemical reaction system can comprise an array of membrane reactors, an outer conduit, and electrical connections to each of the array of membrane reactors. The array of membrane reactors can be arranged in parallel within the outer conduit. Each membrane reactor can comprise a circumferential membrane wall that surrounds an internal flow volume. The circumferential membrane wall can be constructed to allow a first gas from the internal flow volume to pass therethrough while retaining a second gas within the internal flow volume. The outer conduit can define a product collection flow volume between outer circumferential surfaces of the membrane walls and an inner circumferential surface of the outer conduit. The electrical connections can be constructed to allow application of electrical power thereto, such that each membrane wall acts as a Joule heating element. 
     Any of the various innovations of this disclosure can be used in combination or separately. This summary is provided to introduce a selection of concepts in a simplified form that are further described below in the detailed description. This summary is not intended to identify key features or essential features of the claimed subject matter, nor is it intended to be used to limit the scope of the claimed subject matter. The foregoing and other objects, features, and advantages of the disclosed technology will become more apparent from the following detailed description, which proceeds with reference to the accompanying figures. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       Embodiments will hereinafter be described with reference to the accompanying drawings, which have not necessarily been drawn to scale. Where applicable, some elements may be simplified or otherwise not illustrated in order to assist in the illustration and description of underlying features. Throughout the figures, like reference numerals denote like elements. 
         FIG.  1 A  is a simplified schematic diagram of a thermochemical reaction system, according to one or more embodiments of the disclosed subject matter. 
         FIG.  1 B  is a graph depicting aspects of an exemplary non-continuous or discontinuous heating profile that can be employed in a thermochemical reaction system, according to one or more embodiments of the disclosed subject matter. 
         FIG.  1 C  is a graph of an exemplary pulse heating profile that can be employed in a thermochemical reaction system, according to one or more embodiments of the disclosed subject matter. 
         FIG.  1 D  is a graph of an exemplary stepped heating profile that can be employed in a thermochemical reaction system, according to one or more embodiments of the disclosed subject matter. 
         FIG.  1 E  is graph of an exemplary arbitrary heating profile that can be employed in a thermochemical reaction system, according to one or more embodiments of the disclosed subject matter. 
         FIG.  2    illustrates reactant input, heating, and product output stages in an exemplary batch operation of a thermochemical reaction system, according to one or more embodiments of the disclosed subject matter. 
         FIG.  3 A  illustrates reactant flow initialization and heating stages in an exemplary continuous operation of a thermochemical reaction system, according to one or more embodiments of the disclosed subject matter. 
         FIG.  3 B  illustrates another exemplary continuous operation of a thermochemical reaction system employing reactant recirculation, according to one or more embodiments of the disclosed subject matter. 
         FIG.  4 A  illustrates an exemplary operation of a thermochemical reaction system for processing of preloaded solid or liquid reactants, according to one or more embodiments of the disclosed subject matter. 
         FIG.  4 B  illustrates an exemplary operation of thermochemical reaction system for processing of solid or liquid reactants in a gas flow, according to one or more embodiments of the disclosed subject matter. 
         FIG.  5 A  is a process flow diagram of an exemplary thermochemical reaction method, according to one or more embodiments of the disclosed subject matter. 
         FIG.  5 B  is a simplified schematic diagram depicting a generalized example of a computing environment in which the disclosed technologies may be implemented. 
         FIG.  6 A  illustrates an exemplary configuration for a heating element arranged parallel to reactant flow in a thermochemical reaction system, according to one or more embodiments of the disclosed subject matter. 
         FIG.  6 B  illustrates an exemplary variation of the configuration of  FIG.  6 A  that employs employing multiple heating elements arranged parallel to each other. 
         FIG.  6 C  illustrates an exemplary variation of the configuration of  FIG.  6 A  that employs multiple heating elements serially arranged with respect to reactant flow and electrically connected together in parallel. 
         FIG.  6 D  illustrates an exemplary variation of the configuration of  FIG.  6 C  that employs multiple heating elements serially arranged with respect to reactant flow and electrically connected together in series. 
         FIG.  7 A  illustrates an exemplary configuration for a heating element arranged non-parallel to reactant flow in a thermochemical reaction system, according to one or more embodiments of the disclosed subject matter. 
         FIG.  7 B  illustrates an exemplary variation of the configuration of  FIG.  7 A  that employs a heating element arranged perpendicular to reactant flow. 
         FIG.  8 A  illustrates an exemplary configuration for a heating element having a three-dimensional structure in a thermochemical reaction system, according to one or more embodiments of the disclosed subject matter. 
         FIG.  8 B  illustrates another exemplary configuration for a heating element forming a flow conduit of a reactor in a thermochemical reaction system, according to one or more embodiments of the disclosed subject matter. 
         FIG.  9 A  illustrates an exemplary configuration for a heating element forming an asymmetric membrane reactor in a thermochemical reaction system, according to one or more embodiments of the disclosed subject matter. 
         FIG.  9 B  is a cross-sectional view of a fabricated asymmetric membrane for use in the system configuration of  FIG.  9 A . 
         FIG.  9 C  illustrates an exemplary configuration for a heating element forming a symmetric membrane reactor in a thermochemical reaction system, according to one or more embodiments of the disclosed subject matter. 
         FIG.  10 A  is a simplified perspective view of an exemplary setup employing a bundle of membrane reactors for parallel processing in a thermochemical reaction system, according to one or more embodiments of the disclosed subject matter. 
         FIG.  10 B  is a simplified cross-sectional view illustrating exemplary operational aspects of the reactor bundle setup of  FIG.  10 A . 
         FIG.  11    is a simplified schematic diagram illustrating an exemplary thermochemical reaction system for producing ammonia from hydrogen and nitrogen gases, according to one or more embodiments of the disclosed subject matter. 
         FIG.  12    is a simplified schematic diagram of an experimental setup that was used for thermochemical processing of methane. 
         FIG.  13 A  is a graph illustrating conventional thermochemical processing of methane using continuous heating technique. 
         FIG.  13 B  is a graph illustrating thermochemical processing of methane using discontinuous heating technique (referred to as, programmable heating and quenching (PHQ)), according to one or more embodiments of the disclosed subject matter. 
         FIG.  14 A  is a graph comparing products resulting from pyrolysis of methane using the continuous heating technique with products resulting from pyrolysis of methane using the PHQ heating technique. 
         FIG.  14 B  is a graph comparing C 2  selectivity resulting from pyrolysis of methane using the PHQ heating technique to C 2  selectivity using continuous heating techniques employing catalysts. 
         FIG.  14 C  is a graph of temperature profile of the heating element for input electrical pulses of different peak powers but with the same pulse durations. 
         FIG.  14 D  is a graph of temperature profiles of the heating element for input electrical pulses of different durations but with same the peak temperature. 
         FIG.  15 A  is a graph comparing C 2  selectivity resulting from pyrolysis of methane using the PHQ heating technique to C 2  selectivity using continuous heating techniques under various conditions. 
         FIG.  15 B  is a graph of methane conversion versus peak temperature using the PHQ heating technique with the same pulse duration. 
         FIG.  15 C  is a graph of product selectivity from pyrolysis of methane versus peak temperature using the PHQ heating technique with the same pulse duration. 
         FIG.  15 D  is a graph of product selectivity from pyrolysis of methane versus pulse duration using the PHQ heating technique with the same peak temperature. 
         FIG.  16 A  is a graph illustrating thermochemical processing of ammonia using the PHQ technique, according to one or more embodiments of the disclosed subject matter. 
         FIG.  16 B  is a graph comparing activity and stability of ammonia products synthesized using the PHQ heating technique to that of ammonia products synthesized using continuous heating. 
         FIG.  16 C  is a graph comparing size and distribution of an Ru catalyst loaded on a carbon heating element before and after being subject to the PHQ heating technique for 1 hour. 
         FIG.  16 D  is a graph comparing size and distribution of an Ru catalyst loaded on a heating element before and after being subject to the continuous heating technique for 1 hour. 
     
    
    
     DETAILED DESCRIPTION 
     General Considerations 
     For purposes of this description, certain aspects, advantages, and novel features of the embodiments of this disclosure are described herein. The disclosed methods and systems should not be construed as being limiting in any way. Instead, the present disclosure is directed toward all novel and nonobvious features and aspects of the various disclosed embodiments, alone and in various combinations and sub-combinations with one another. The methods and systems are not limited to any specific aspect or feature or combination thereof, nor do the disclosed embodiments require that any one or more specific advantages be present, or problems be solved. The technologies from any embodiment or example can be combined with the technologies described in any one or more of the other embodiments or examples. In view of the many possible embodiments to which the principles of the disclosed technology may be applied, it should be recognized that the illustrated embodiments are exemplary only and should not be taken as limiting the scope of the disclosed technology. 
     Although the operations of some of the disclosed methods are described in a particular, sequential order for convenient presentation, it should be understood that this manner of description encompasses rearrangement, unless a particular ordering is required by specific language set forth below. For example, operations described sequentially may in some cases be rearranged or performed concurrently. Moreover, for the sake of simplicity, the attached figures may not show the various ways in which the disclosed methods can be used in conjunction with other methods. Additionally, the description sometimes uses terms like “provide” or “achieve” to describe the disclosed methods. These terms are high-level abstractions of the actual operations that are performed. The actual operations that correspond to these terms may vary depending on the particular implementation and are readily discernible by one of ordinary skill in the art. 
     The disclosure of numerical ranges should be understood as referring to each discrete point within the range, inclusive of endpoints, unless otherwise noted. Unless otherwise indicated, all numbers expressing quantities of components, molecular weights, percentages, temperatures, times, and so forth, as used in the specification or claims are to be understood as being modified by the term “about.” Accordingly, unless otherwise implicitly or explicitly indicated, or unless the context is properly understood by a person of ordinary skill in the art to have a more definitive construction, the numerical parameters set forth are approximations that may depend on the desired properties sought and/or limits of detection under standard test conditions/methods, as known to those of ordinary skill in the art. When directly and explicitly distinguishing embodiments from discussed prior art, the embodiment numbers are not approximates unless the word “about” is recited. Whenever “substantially,” “approximately,” “about,” or similar language is explicitly used in combination with a specific value, variations up to and including 10% of that value are intended, unless explicitly stated otherwise. 
     Directions and other relative references may be used to facilitate discussion of the drawings and principles herein, but are not intended to be limiting. For example, certain terms may be used such as “inner,” “outer,”, “upper,” “lower,” “top,” “bottom,” “interior,” “exterior,” “left,” right,” “front,” “back,” “rear,” and the like. Such terms are used, where applicable, to provide some clarity of description when dealing with relative relationships, particularly with respect to the illustrated embodiments. Such terms are not, however, intended to imply absolute relationships, positions, and/or orientations. For example, with respect to an object, an “upper” part can become a “lower” part simply by turning the object over. Nevertheless, it is still the same part and the object remains the same. 
     As used herein, “comprising” means “including,” and the singular forms “a” or “an” or “the” include plural references unless the context clearly dictates otherwise. The term “or” refers to a single element of stated alternative elements or a combination of two or more elements, unless the context clearly indicates otherwise. 
     Although there are alternatives for various components, parameters, operating conditions, etc. set forth herein, that does not mean that those alternatives are necessarily equivalent and/or perform equally well. Nor does it mean that the alternatives are listed in a preferred order, unless stated otherwise. Unless stated otherwise, any of the groups defined below can be substituted or unsubstituted. 
     Although dimensions, materials, and methods similar or equivalent to those described herein can be used in the practice or testing of the presently disclosed subject matter, suitable dimensions, materials, and methods are described below. The dimensions, materials, methods, and examples are illustrative only and not intended to be limiting. Features of the presently disclosed subject matter will be apparent from the following detailed description and the appended claims. 
     Introduction 
     Embodiments of the disclosed subject matter provide a programmable heating and quenching (PHQ) technique (also referred to as shock heating, pulse heating, non-continuous heating, or discontinuous heating) for conducting thermochemical reactions with a high selectivity, rate, and yield to value-added products at high energy efficiency. Thermochemical reactions can include, but are not limited to, one or more of pyrolysis, thermolysis, synthesis, hydrogenation, dehydrogenation, and hydrogenolysis. Embodiments of the disclosed subject matter can be applied to conduct other non-equilibrium thermochemical reactions that require high temperatures (e.g., &gt; 1000 K) for reaction initiation and where reactants, products, or both do not react with the heating element. 
     Unlike continuous heating under near-equilibrium conditions, the PHQ technique disclosed herein employs periodic or non-continuous heating on a second or sub-second scale to conduct non-equilibrium thermochemical reactions. In embodiments, a porous electrical heater (also referred to as a Joule heating element) is disposed such that gaseous reactants (or reactants supported in a gas flow) flow into contact with and through pores of the heater (e.g. in thermal contact with the heater) to enable efficient heat transfer therebetween. The direct contact between the gas-phase reactants and porous heating element can offer temporal tunability, spatial tunability, or both, with more complex temperature profiles (e.g., square wave, triangle wave, zoned heating, etc.) to accurately manipulate reaction pathways. 
     Driven by electrical energy, the PHQ technique may also enable process intensification and distributed chemical manufacturing with improved energy efficiency, which are currently unattainable by conventional thermochemical synthesis. Compared with conventional steady-state approaches that employ continuous heating at constant temperatures (e.g., less than 1300 K), the PHQ technique allow for rapid switching between a low temperature (e.g., 800 K or below) and a high temperature (e.g., 1200 K or above) in the second or sub-second regime simply by varying the electric current applied to the heater, in order to achieve non-equilibrium thermochemical reactions. In some embodiments, the high temperature offered by the PHQ technique can enable fast activation of reactants for high reaction rates (e.g., synthesis, conversion, etc.). The rapid quenching can provide high selectivity and good catalyst stability, as well as lowers the average reaction temperature to improve energy efficiency and reduce energy costs. 
     Generalized Thermochemical Reaction System 
     Embodiments of the disclosed subject matter further provide systems having a gas-flow reactor for conducting such thermochemical reactions. The porous electrical heating element can be disposed within or form a part of the gas-flow reactor. In general, the reactor system can include a source of one or more reactants and the heating element. Variations in system parameters can be made to accommodate different thermochemical reactions. Such variations can include, but are not limited to, heating process and pattern for the heating element (e.g., waveform, peak temperature and duration, minimum temperature and duration, heating cycle duration), reactor construction (e.g., flow path geometry, heating element geometry, materials for reactor and heating element, operation with or without catalysts), reaction configuration (e.g., reaction medium material, reactor temperature, flow rates, pressures), and reactant configuration (e.g., reactant types, reactant composition). 
     For example,  FIG.  1 A  illustrates a generalized thermochemical reaction system  100  according to one or more embodiments of the disclosed subject matter. The reaction system  100  can have a reactor  102 , a porous heating element  104 , and a control system  108 . In some embodiments, the reactor  102  is not pressurized during operation, such that thermochemical reactions proceeding therein occur at or near atmospheric pressure (e.g., ~1 bar). Alternatively, in some embodiments, the reactor  102  is pressurized during operation, for example, by being constructed as or being disposed in a pressure chamber. In such embodiments, the thermochemical reactions proceeding therein (e.g., hydrogenolysis, hydrogenation, synthesis, etc.) occur at an elevated pressure, such as 20 MPa (~200 bar). 
     The reactor  102  can define a flow path for gases provided to inlet  110  thereof to flow into thermal contact with the porous heating element  104 . As used herein, thermal contact refers to a gas flowing into and through pores of the heating element  104  such that the temperature of the gas closely follows (e.g., within 10%) a temperature of the heating element  104 . The duration of thermal contact (also referred to as residence time or first time period) between the heating element  104  and the gas may be based on a flow rate of the gas through the reactor  102  and a length, L, of the heating element  104  along the direction of flow. In some embodiments, the residence time of the reactant is selected such that the gas (e.g., a molecule in the gas flow) is exposed to multiple heating cycles of the heating element  104 , as described in more detail below. 
     In some embodiments, the reactor  102  is constructed as a flow-through chamber, with a single inlet  110  for gaseous reactants  112  and/or carrier gas  114  flows, and at least one outlet  116  for gaseous products  118 . Alternatively, in some embodiments, the reactor is provided with more than one inlet, more than one outlet, or both. For example, the reactor can be provided with a separate inlet for introduction of different reactants or carrier gases, or the reactor  102  can be provided with a second outlet  120  for removal of unreacted reactants, as discussed further below. In some embodiments, the reactor can also include separate ports or other structures to allow routing of electrical connections between the control system  108  and the heating element  104 . Alternatively or additionally, in some embodiments, the electrical connections can be provided through the same inlet port and/or outlet port as the gas flows. 
     In some embodiments, for example, where at least one of the reactants is not in the gas phase, the reactor  102  can include a support structure disposed within the internal flow volume in close proximity (e.g., less than 1 cm) to the heating element  104  to hold solid or liquid reactants (e.g., biomass, polymers such as polyolefins or other plastics, etc.) for non-continuous heating by the heating element  104 . Although such solid or liquid reactants are not in direct contact with the heating element  104 , the close proximity allows the temperature of the reactants to closely follow the temperature of the heating element. 
     The porous heating element  104  is constructed to provide Joule heating based on electrical power (e.g., current) applied thereto. The heating element  104  can have a porosity or gas permeability tailored to a particular thermochemical reaction in order to allow reactants to flow therethrough. For example, in some embodiments, the heating element  104  can have a pore size of about 1 µm, a gas permeability of at 200 L/m 3  at 200 Pa, or both. In some embodiments, the pore sizes of the heating element  104  can be characterized by imaging the pores in a portion of the heating element  104  or in an entirety thereof. For example, the pore sizes of the heating element  104  can be characterized by optical microscopy, electron microscopy (e.g., scanning electron microscopy), or X-ray micro-computed-tomography (micro-CT) imaging (e.g., American Society for Testing and Materials (ASTM) F2450-18,  Standard Guide for Assessing Microstructure of Polymeric Scaffolds for Use in Tissue-Engineered Medical Products , ASTM International, West Conshohocken, PA, 2018, which is incorporated herein by reference). Alternatively or additionally, in some embodiments, the pore sizes of the heating element can be characterized by performing one or more porometry or porosimetry tests on the heating element. For example, the pore sizes can be characterized by capillary flow porometry, bubble point testing (e.g., ASTM F316-03(2019)  Standard Test Methods for Pore Size Characteristics of Membrane Filters by Bubble Point and Mean Flow Pore Test , ASTM International, West Conshohocken, PA, 2019, which is incorporated herein by reference), or mercury intrusion porosimetry (e.g., UOP578-11,  Automated Pore Volume and Pore Size Distribution of Porous Substances by Mercury Porosimetry , ASTM International, West Conshohocken, PA, 2011, or U.S. Pharmacopeial Convention for Micromeritics and Particulate Systems Instruments &lt;267&gt;,  Porosimetry by Mercury Intrusion , U.S. Pharmacopeial Convention, Rockville, MD, 2012, both of which are incorporated herein by reference). 
     The porous heating element  104  can be formed to have any two-dimensional (e.g., having a dimension at least 2 orders of magnitude less than orthogonal dimensions) or three-dimensional (3-D) shape, for example, planar, tubular, cylindrical, disk-shaped, as well as complex non-standard geometries. In some embodiments, multiple heating elements can be provided with the reactor. The multiple heating elements can be operated in series or in parallel, for example, to provide a longer residence time for reactants, to provide temporal or spatial variations in temperature, or for any other reason. The heating element  104  can be constructed of any material that has sufficient electrical resistivity (e.g., to achieve peak operating temperature for a given power input in a range of 500-3000 K), high temperature resistance (e.g., a melting temperature much greater than planned peak operating temperature), and low heat capacity (e.g., to enable rapid, sub-second heating and cooling rates in a range of 10 2  K/s to 10 5  K/s). For example, in some embodiments, the heating element  104  is constructed to provide a heating rate (R H ), cooling rate (Rc), or both of at least 10 3  K/s (e.g., ≥ 10 4  K/s). In some embodiments, the heating element  104  can be formed of pure carbon or a carbon-containing material, such as silicon carbide (SiC). For example, in some embodiments, the heating element  104  is composed only of carbon fibers, carbon felt, carbon nanotube fibers, carbon nanofibers, graphene, or combinations thereof. 
     In some embodiments, the reactor  102  is provided with a catalyst for the thermochemical reaction to be conducted therein. For example, the catalyst can be incorporated on or embedded within the heating element  104 . Alternatively or additionally, the catalyst can be provided separate from the heating element  104 , for example, as a flow conduit surface of the reactor. In some embodiments, the catalyst can be a single element or multi-elemental (e.g., binary, ternary, high-entropy, etc.). For example, the catalyst can comprise a metal (e.g., Ru, Fe, Ni, etc.) or alloys thereof, or any other known or later developed catalyst for a particular thermochemical reaction conducted by the reaction system  100 . In some embodiments, the catalysts can be nanoparticles formed in situ within the heating element  104 , for example, by using a high-temperature shock synthesis method, such as that described in U.S. Pat. Application Publication No. 2019/0161840, which is incorporated by reference herein. 
     In some embodiments, the reactor  102  can optionally include a separator  106 . For example, the separator  106  can be constructed to receive a flow of products and unreacted reactants from the heating element  104  and to isolate the products from the reactants. The unreacted reactants can then be directed via outlet  120  to a recirculating flow circuit  122  for reintroduction to the reactor inlet  110  for reprocessing. In some embodiments, the recirculating flow circuit  122  can optionally include a recirculating pump  124  for conveying the reactants between outlet  120  and union  126  (or valve or other fluid circuit feature to allow the reactant flow to be reintroduced to reactor  102 ). 
     In some embodiments, the separator  106  is a passive separation mechanism, for example, by being constructed as a size-selective filter membrane. In such embodiments, the pore size of the filter membrane can be selected to separate products from reactants (or vice versa), for example, based on the kinetic diameter of the respective molecules in the product and reactant flows. For example, in some embodiments, the pore size of the separator filter membrane can be microporous (e.g., &lt; 2 nm, such as ~0.3 nm for separation of ammonia product from H2 and N 2  reactant gases). Alternatively or additionally, the separator  106  can employ an active separation mechanism, for example, by being constructed as ultrasonic-based gas separation device, such as that described in U.S. Pat. No. 8,231,707, issued Jul. 31, 2012, which is incorporated by reference herein. Although shown separately from heating element  104 , in some embodiments, the functions of the heating element  104  and the separator  106  can be integrated together. For example, concurrently with provision of heating cycles, the heating element  104  may allow diffusion of products therethrough to a second flow path while retaining reactants to a first flow path in order to provide the desired separation. In such embodiments, the heating element  104  may be considered a membrane reactor. 
     In operation of thermochemical reaction system  100 , one or more reactant gases from source(s)  112  are provided to the inlet  110  of reactor  102 , and the gases within the reactor are subjected to multiple heating cycles (e.g., each with its own peak temperature and minimum temperature) of the heating element  104  in either a continuous mode of operation (e.g., gas flow from the inlet  110 , through the interior of the reactor  102 , to the outlet  116  or  120  remains substantially constant or at least active during the multiple heating cycles) or batch mode of operation (e.g., gas flow into the inlet  110  and/or gas flow from outlets  116  and  120  is paused during one or more of the multiple heating cycles). For example, the residence time (e.g., the time period during which the reactants are in thermal contact with the heating element) for the reactants can be on the order of tens of seconds or minutes (or even greater), while the period of each heating cycle may be on the order of seconds (e.g., 5 seconds or less, such as ~ 1 second). Referring to  FIG.  1 B , an exemplary heating profile or waveform  130  for two heating cycles is shown. During each heating cycle, the reactants are subjected to a peak temperature, T H , (e.g., at least 1000 K, such as 1200 K or greater) for a first part  132  of the heating cycle and a lower quenching temperature, T L , (e.g., no more than 800 K, at least 600 K less than the peak temperature, or both) for a second part  134  of the heating cycle. In some embodiments, the duration, t H , of the first part  132  for peak temperature is less than the remainder of the heating cycle, for example, no more than 35% of the cycle period, τ (e.g., a first part of 10-400 millisecond duration (or 15-150 milliseconds) for a total cycle duration of 1-1.5 seconds). Conversely, the duration, t L , of the second part  134  for quench temperature can constitute the majority of the heating cycle period, τ. 
     Although shown in idealized form in  FIG.  1 B , temperatures experienced in practical implementations of the disclosed reaction system  100  may deviate slightly from the idealized form. For example,  FIG.  1 C  illustrates an example of a pulsed heating profile  136  for operating the heating element  104 . While the waveform  138  of the applied electrical power follows the desired rectangular pulse configuration, with a first part  140  defining peak temperature and a second part  142  defining quench temperature, the actual temperature  144  generated by the heating element  104  deviates slightly therefrom, in particular by having a longer cooling rate due to slower cooling effect. Nevertheless, the system  100  is constructed such that the temperature of the gaseous reactants can be rapidly changed between a peak temperature and a minimum temperature in each heating cycle in the second or sub-second regime. 
     Although the discussion above and elsewhere herein focuses on pulsed heating, embodiments of the disclosed subject matter are not limited thereto. Rather, other waveforms are also possible according to one or more contemplated embodiments. For example,  FIG.  1 D  illustrates a stepped heating profile  150 . Similar to the above-described profiles, each cycle of the stepped heating waveform  150  has a first part  152  corresponding to the desired peak temperature and a second part  154  corresponding to the desired quench or minimum temperature. However, the waveform  150  also includes intermediate temperatures between the peak and minimum. The rapid heating/cooling rates offered by the disclosed heating elements can allow obtention of these multiple different temperature levels on the second or sub-second time scale. Such a waveform may be useful in multi-step thermochemical reactions, such as conversion of methane to higher carbon number compounds (e.g., C 6 H 6 ), where the conversion step of each intermediate (e.g., C 2 , C 3 , C 4 , C 5  species) may have different preferred peak temperatures for reaction activation. 
     While  FIGS.  1 B- 1 D  describe the waveform for each cycle as being identical, embodiments of the disclosed subject matter are not limited thereto. Rather, more complex waveform patterns that are non-repeating are also possible. For example,  FIG.  1 E  illustrates an arbitrary waveform  160 . Although the waveform  160  is non-periodic (not repeating), a cycle period can be defined as the time between peak temperature applications, for example, between first peak application part  162  and second peak application part  164 . Between the peak application parks  162 ,  164 , at least one quench application part  166  is provided. Even with arbitrary waveforms such as waveform  160 , the time between successive peak application parts is selected to be less than five seconds, such that each the time of each peak application is in the second or sub-second regime. 
     Returning to  FIG.  1 A , the control system  108  can be operatively coupled to the heating element  104  to control heating thereof. For example, in some embodiments, control system  108  can comprise a processor programmed to generate and/or apply electrical power signals to the heating element  104  to provide a desired shock heating profile to reactants within the reactor  102 . Alternatively or additionally, control system  108  can comprise an electrical power supply and/or a signal generator (e.g., source meter or source measure unit with solid-state relay). In some embodiments, the control system  108  can comprise multiple components that each separately control elements of the reaction system  100 , for example, a first controller for the heating element, a second controller for fluid circuit components, etc. In some embodiments, the control system  108  can also control operation of the separator  106 , pump  124 , or any other fluid circuit components such as pumps, valves, etc. within system  100 . 
     For example, when the reactants  112  include methane (CH4), the reactants can undergo a conversion/transformation reaction (e.g., pyrolysis) to generate products  118  such as C 2  hydrocarbons, aromatics, or both. For example, when the reactants  112  include ethane (C 2 H 6 ), propane (C 3 H 8 ), and/or higher hydrocarbons, the reactants can undergo a dehydrogenation reaction (e.g., pyrolysis) to generate products  118  such as other hydrocarbons, aromatics, or both. For example, when the reactants  112  include hydrocarbons, the reactants can undergo a dehydrogenation reaction (e.g., pyrolysis) to generate products  118  such as olefins and/or a hydrogenolysis reaction to generate products  118  such as other forms of hydrocarbons. For example, when the reactants  112  include hydrogen (H 2 ) and nitrogen (N 2 ), the reactants can undergo a synthesis reaction to generate products  118  such as ammonia (NH3). For example, when the reactants  112  include methane (CH 4 ) and nitrogen (N 2 ), the reactants can undergo conversion/transformation (e.g., pyrolysis) and synthesis reactions to generate products  118  such as ammonia (NH3), hydrocarbons, aromatics, or any combination thereof. For example, when the reactants  112  include methane (CH 4 ) and carbon dioxide (CO 2 ), the reactants can undergo conversion/transformation (e.g., pyrolysis) to generate products  118  such as synthesis gas (syngas). For example, when the reactants  112  include polymers (e.g., plastics such as polyolefin), the reactants can undergo conversion/transformation (e.g., pyrolysis) to generate products  118  such monomers, oligomers, hydrocarbons, aromatics, or any combination thereof. Thermochemical reactions other than those specifically described above are also possible according to one or more contemplated embodiments. 
     In some embodiments, one or more carrier gases from source(s)  114  can optionally be provided to the reactor  102  (e.g., via inlet  110 ). For example, the carrier gas can comprise hydrogen (H 2 ), nitrogen (N 2 ), or a noble gas (e.g., argon (Ar) or helium (He)). In some embodiments, the carrier gas can be supplied to a flowpath in the reactor separate from the reactants, for example, to act as a sweep gas to carry resulting products from the separator  106 . Alternatively or additionally, in some embodiments, the carrier gas can also serve as a reactant as well as providing a carrying function. For example, solid or liquid reactant particles can be disposed within (e.g., via atomizer, aerosolizer, nebulizer, etc.) the carrier gas for transport to the heating element, whereby the heating therein initiates a thermochemical reaction between the particles (e.g., polymer particles) and the carrier gas (e.g., H 2 ). 
     Reactor Operation Examples 
       FIG.  2    illustrates a thermochemical reaction system  200  operating in a batch mode. Thermochemical reaction system  200  includes a porous heating element  202  disposed in an internal volume  210  within reactor  204 . In an input stage of the batch mode (left panel of  FIG.  2   ), an inlet  206  of the reactor  204  is opened and one or more reactants gases  208  flow into the internal volume  210 , such that the reactant gases  208  are in thermal contact with the heating element  202 . The inlet  206  is then closed to seal the reactant gases  208  within the reactor  204 . In a heating stage of the batch mode (center panel of  FIG.  2   ), multiple cycles of a non-continuous heating profile  212  are applied to the heating element by a control system to cause corresponding heating thereof. The peak temperature part of each heating cycle initiates thermochemical reaction of the reactant gases  208  in thermal contact with the heating element  202 , which reaction proceeds under non-equilibrium conditions during the remaining part of each heating cycle to generate products  214 . The system can transition to an output stage once all reactants within the internal volume  210  have been converted to products  214 , after expiration of a predetermined time period, after a predetermined number of heating cycles, or according to any other criteria. In the output stage of the batch mode (right panel of  FIG.  2   ), an outlet  216  of the reactor  204  is opened and one or more product gases  214  are removed via flow  218 . In some embodiments, during the input stage, the output stage, or both, heating element may be active (e.g., undergoing heating cycles); however, in general, the heating element is inactive (e.g., completely de-energized, or at least not undergoing heating cycles) during the input and output stages. 
       FIG.  3 A  illustrates a thermochemical reaction system  300  operating in a continuous flow mode. Thermochemical reaction system  300  includes a porous heating element  302  disposed in an internal volume  310  within reactor  304 . In an initial stage of the flow mode (left panel of  FIGS.  3   ), a flow  308  of one or more reactant gases is provided to open inlet  306  of the reactor  304 , such that the one or more reactants gases  208  flow through the internal volume  310  and out of the reactor  304  via outlet  318  as flow  316 . While within the internal volume  310 , the reactants flow in thermal contact with the heating element  302  (e.g., contacting surfaces and through pores of the heating element) for a residence time based at least in part on the inlet flow rate, outlet flow rate, and heating element length  320  along the reactant flow path. The system  300  can transition to the heating stage (right panel of  FIG.  3 A ), where multiple cycles of a non-continuous heating profile  312  are applied to the heating element by a control system to cause corresponding heating thereof. The peak temperature part of each heating cycle initiates thermochemical reaction of the reactant gases  308  in thermal contact with the heating element  302 , which reaction proceeds under non-equilibrium conditions during the remaining part of each heating cycle to generate products  322 , which are subsequently removed from the reactor  304  via flow  324  through outlet  318  in a substantially continuous manner. 
     In some embodiments, less than all of the reactants in the internal volume  310  may be converted to products, for example, due to insufficient residence time or other factors. Accordingly, in some embodiments, reactants can be separated from products and returned to the reactor for reprocessing. For example,  FIG.  3 B  illustrates a thermochemical reaction system  330  operating in a continuous flow mode with recirculation. Similar to the system  300  of  FIG.  3 A , reactant gases are provided to reactor  334  via flow  308  through the inlet. The heating element  332  in system  330 , however, is constructed to separate reactants and products into different flow paths within the reactor  334 . For example, the heating element  332  can be constructed as a separate membrane, the pore size of which allows product molecules to pass through while retaining reactant molecules, or vice versa. While the heating element  332  performs the multiple heating cycles, the products can be simultaneously separated from the reactants into different flow streams. In the illustrated example of  FIG.  3 B , unreacted reactants  338  are separated to first flow path  340 , and products  322  are separated to second flow path  344 . Similar to  FIG.  3 A , the products  322  can be removed from flow path  344  via flow  324  through outlet  318  in a substantially continuous manner. Meanwhile, unreacted reactants can be removed from flow path  340  via outlet  336  and returned via recirculation flow circuit  342  to the inlet of the reactor  334  for reprocessing. 
     In some embodiments, one or more of the reactants may be in the form of a solid or liquid. In such embodiments, the reactant can be provided within the reactor, and gaseous products resulting from application of the non-continuous heating cycles of the heating element can be removed in a substantially continuous manner. For example,  FIG.  4 A  illustrates a thermochemical reaction system  400  operating in continuous flow mode with preloaded solid or liquid reactants  420 . Similar to system  300  of  FIG.  3 A , a gas flow  408  is provided to reactor  404  via inlet  406 . In some embodiments, the gas flow  408  acts a carrier gas, to direct products evolving from the solid or liquid reactants  420  to the outlet port  418  for removal as flow  416 . Alternatively or additionally, gas flow  408  is a reactant in the thermochemical reaction with reactants  420 . The reactants  420  are loaded within the inner volume  410  proximal to porous heating element  402  (e.g., less than 1 cm). In some embodiments, the solid or liquid reactants  420  may be loaded on a thermally-stable holder, for example, comprised of one or more ceramic materials, such as Al 2 O 3 , ZrO 2 , SiO 2 , etc. or combinations thereof (e.g., mullite (3Al 2 O 3 ·2SiO 2  or 2Al 2 O 3 ·SiO 2 )). Similar to system  300  of  FIG.  3 A , multiple cycles of a non-continuous heating profile  412  are applied to the heating element  402  by a control system to cause corresponding heating thereof. The peak temperature part of each heating cycle initiates thermochemical reaction of the preloaded reactants  420  (and/or any reactants in flow  408 ), which reaction proceeds under non-equilibrium conditions during the remaining part of each heating cycle to generate products  422 . Such products  422  can be removed from the reactor  304  in a substantially continuous manner via flow  416  through outlet  418 . 
     In some embodiments, rather than pre-loading the reactor with solid or liquid reactants, such reactants can be added to an inlet gas flow of carrier gas or co-reactant gas. For example,  FIG.  4 B  illustrates a thermochemical reaction system  430  operating in a continuous flow mode with solid or liquid reactants  434 . For example, the solid or liquid reactants  434  can be converted to particles  436  (e.g., via atomizer, aerosolizer, etc.) that are incorporated into and carried by inlet gas flow  438 . Similar to system  400  of  FIG.  4 A , inlet gas flow  438  is introduced into internal volume  410  via inlet  406 , where it flows into contact with and through porous heating element  402 . In some embodiments, the gas flow  438  acts a carrier gas, to carry the reactant particles  436  through the reactor  404  and to direct products evolving from the solid or liquid reactants to the outlet port  418  for removal as flow  442 . Alternatively or additionally, gas flow  438  is a reactant in the thermochemical reaction with reactant particles  436 . Similar to system  400  of  FIG.  4 A , multiple cycles of a non-continuous heating profile  412  are applied to the heating element  402  by a control system to cause corresponding heating thereof. The peak temperature part of each heating cycle initiates thermochemical reaction of the reactant particles  436  (and/or any reactant gas in flow  438 ), which reaction proceeds under non-equilibrium conditions during the remaining part of each heating cycle to generate products  440 . Such products  440  can be removed from the reactor  304  in a substantially continuous manner via flow  442  through outlet  418 . 
     Method Examples 
       FIG.  5 A  illustrates a method  500  for thermochemical reactions employing the PHQ (non-continuous heating) technique. The method  500  can initiate at process block  502 , where a reactor of a thermochemical reaction system is provided. The reactor can have a structure according to any of the examples described herein. In some embodiments, the reactor can be provided with a separate heating element therein (or multiple heating elements). Alternatively, in some embodiments, the heating element can be constructed as a structural part of the reactor, for example, as a membrane reactor that separates products from reactants. Each heating element can be porous so as to be permeable with respect to the gases employed in the thermochemical reaction (e.g., reactants) and/or gases employed in the system (e.g., non-reacting carrier gases). 
     The method  500  can proceed to decision block  504 , where it is determined if a catalyst is desired. For some thermochemical reactions, the use of the PHQ technique can result in efficient and effective chemical production even without any catalyst (e.g., metal catalysts) within the system. In such examples (e.g., methane pyrolysis), the method  500  can proceed directly to decision block  508  without otherwise providing a catalyst. Otherwise, if a catalyst is desired, the method  500  can proceed to process block  506 , where the reactor is provided with an appropriate catalyst. In some embodiments, the catalyst can be provided within the reactor (e.g., an internal volume thereof, such as surfaces of a flow path) separate from the porous heating element. Alternatively or additionally, in some embodiments, the catalyst is provided on and/or integrated with the porous heating element. For example, the catalyst can be a metal catalyst (e.g., Ru, Fe, Ni, alloys thereof), a multi-elemental catalyst (e.g., binary, ternary, high-entropy, etc.), any other known or later developed catalyst, or combinations thereof. In embodiments where the catalyst is loaded in the heating element, the loading can be in the range of 0.5-40 wt% inclusive, for example, about 2 wt%. In some embodiments, the loading of the catalyst in the heating element comprises forming catalyst nanoparticles by a high-temperature shock synthesis method, such as that described in U.S. Pat. Application Publication No. 2019/0161840, which is incorporated by reference herein. The method  500  can then proceed to decision block  508 . 
     At decision block  508 , the process flow can diverge based on the phase of the reactant used in the thermochemical reaction system. For example, for reactions where any of the reactants are solid or liquid (e.g., biomass or a polymer, such as plastic), the method  500  can proceed to decision block  510 ; otherwise, if all reactants are gases, the method can proceed directly to process block  514 . At decision block  510 , it is determined if a carrier gas is desired for flowing reactants. If a carrier gas is not desired for flowing reactants, the method  500  can proceed to process block  512 , where the reactants are preloaded into the reactor. For example, the solid or liquid reactants (e.g., in particle form) can be loaded onto a support (e.g., formed of one or more ceramic materials) within the reactor. The support can position the reactants proximal to the heating element, for example, within 1 cm. Alternatively, solid or liquid reactants can be continuously supplied to a heating location within the reactor (e.g., within 1 cm of the heating element), for example, by a fluid pump, particle conveyor belt, or any other mechanical conveyance. For example, gravity can be used, together with surface features of the reactor, to channel particles added to the reactor at a location remote from the heating element to the heating region proximal the heating element. In some embodiments, a carrier gas is provided regardless of the decision made at decision block  510 , for example, to transport products generated within the reactor to an outlet or to as a co-reactant (e.g., H2 gas) with the solid/liquid reactants preloaded within the reactor. 
     At decision block  510 , if it is determined that a carrier gas is desired for flowing solid or liquid reactants, the method  500  can proceed to process block  514 , where the carrier gas is used to flow the reactants into the reactor and into thermal contact with the porous heating element therein. For example, the carrier gas can include hydrogen (H 2 ), nitrogen (N 2 ), a noble gas (e.g., helium, argon, etc.), or any combination thereof. If not already in such form, the method  500  can further include preparing the solid/liquid reactant in suitable form for inclusion in the carrier gas, for example, by forming into separate particles or droplets (e.g., by an aerosolizer, atomizer, nebulizer, etc.). 
     At process block  514 , one or more reactants (e.g., either in gaseous form or particles carried by a carrier gas) are flowed into the reactor into thermal contact with the porous heating element. For example, reactants can include, but are not limited to, methane, ethane, propane, other hydrocarbons, hydrogen, nitrogen, carbon dioxide, polymer (e.g., plastics, such as polyolefin), biomass, or any combination thereof. In particular, the gas flow can be around and through the heating element via pores therein, such that the temperature of the flowing reactants in thermal contact with the heating element substantially matches the temperature of the heating element and will substantially follow temperature changes produced by the waveform applied to heating element during the heating cycle. The size of the heating element, gas flow rate, and heating cycle period are selected such that reactants remain in thermal contact with the heating element for residence time period (e.g., on the order of tens of seconds, minutes, or even hours) that exceeds a duration of each heating cycle (e.g., such that each reactant molecule in the gas flow experiences multiple heating cycles in a single pass through the reactor). In some embodiments, the flowing of process block  514  can also include flowing a carrier or sweep gas through the reactor with the reactant gas flow (e.g., in a same flow path or a different flow path as the reactant gas flow). For example, a sweep gas of hydrogen or a noble gas can be provided to a product isolated flow path (e.g., separated from a reactant flow path by a separator membrane) to flow the gaseous products out of the reactor. 
     The method  500  can proceed to process block  516 , where the reactants in the reactor are heated for a single heating cycle by applying a predetermined waveform (e.g., current or power signal) to the porous heating element within the reactor. The heating in process block  516  is generally non-continuous and includes at least a first part  518 , where a peak temperature (e.g., at least 1000 K, such as 1200 K or greater) is applied to the reactants for a duration ti, and a second part  520 , wherein a minimum or quench temperature (e.g., less than 800 K, such as 700 K or less) is applied to the reactants for a duration t 2 . In some embodiments, the duration t 1  of the first part  518  is less than a remainder of the heating cycle in process block  516 , for example, no more than 35% of the heating cycle duration (e.g., 10-400 milliseconds for a total cycle duration less than 5 seconds, for example, 1-1.5 seconds). In some embodiments, the duration t 2  of the second part  520  constitutes a majority of the heating cycle in process block  516 , for example, at least 50% of the heating cycle duration. Although shown separately from process block  514 , in some embodiments, process block  516  occurs concurrently with process block  514 , such that heating occurs while reactants flow into and through the reactor. Alternatively, in some embodiments employing batch processing, the flowing of process block  514  can be stopped prior to initiating heating in process block  516 . 
     The peak temperature generated in process block  516  can be effective to initiate (e.g., enable bond activation) one or more thermochemical reactions of the reactants in thermal contact with the porous heating element. The thermochemical reactions can include pyrolysis, thermolysis, synthesis, hydrogenation, dehydrogenation, hydrogenolysis, and/or any other non-equilibrium thermochemical reaction that requires high temperatures (e.g., &gt; 1000 K) for initiation and where reactants, products, or both do not react with the heating element. The provision of a quench temperature within the heating cycle of process block  516  can help tune selectivity for particular reaction products or alter reaction equilibrium. For example, in some embodiments, the heating cycle of process block  516  can yield high selectivity toward light hydrocarbon chemicals while limiting coke formation in CH4 conversion. In some embodiments, the provision of a quench temperature within the heating cycle of process block  516  can help compensate for the exothermic nature of the initiated thermochemical reaction, which would otherwise elevate temperature beyond that controlled by heating element and lead to product decomposition. In some, the provision of a quench temperature within the heating cycle of process block  516  may also improve catalyst stability, and/or lower energy costs for product generation by reducing average temperature in the reactor. 
     The method  500  can proceed to decision block  522 , where it is determined if additional heating cycles should be applied. In some embodiments, heating cycles can be repeated in a substantially continuous manner, for example, as long as reactants are provided as input to the reactor. However, even in batch operations, the heating can be repeated at least once and preferably multiple times, in order to subject reactants within the reactor to multiple heating cycles. If additional heating cycles are desired, the method  500  can return to process block  516  for repetition. 
     Otherwise, the method  500  can proceed to process block  524 , where products generated by the thermochemical reactions in the reactor are removed for storage or use. Such products can include, but are not limited to, C 2  hydrocarbons, higher hydrocarbons, aromatics, ammonia, syngas, or combinations thereof. In some embodiments, the removal for process block  516  involves flowing a carrier or sweep gas to carry products within the reactor to an appropriate outlet. For example, as described above a sweep gas of hydrogen or a noble gas can be provided to a product-isolated flow path (e.g., separated from a reactant flow path by a separator membrane) to flow the gaseous products out of the reactor. Although shown separately from process block  516 , in some embodiments, process block  524  occurs concurrently with process block  516 , such that heating occurs while products flow out of the reactor. Alternatively, in some embodiments employing batch processing, the removing of process block  524  can occur after the heating in process block  516  is completed. 
     Although blocks  502 - 524  of method  500  have been separately illustrated in  FIG.  5 A , in some embodiments, blocks may be combined and performed together (simultaneously or sequentially). Moreover, although  FIG.  5 A  illustrates a particular order for blocks  502 - 524  of method  500 , embodiments of the disclosed subject matter are not limited thereto. Indeed, in certain embodiments, the blocks may occur in a different order than illustrated or simultaneously with other blocks. For example, the reactant flow of process block  514 , non-continuous heating of process block  516 , and product removal of process block  524  may all occur simultaneously in a continuously operating thermochemical reaction setup. Accordingly, embodiments of the disclosed subject matter are not limited to the specific order illustrated in  FIG.  5 A  and described above. 
       FIG.  5 B  depicts a generalized example of a suitable computing environment  550  in which the described innovations may be implemented, such as control system  108 , controller  212 , controller  312 , controller  412 , method  500 , controller  612 , controller  712 , controller  812 , controller  832 , controller  922 , and/or a controller for system  1100 . The computing environment  550  is not intended to suggest any limitation as to scope of use or functionality, as the innovations may be implemented in diverse general-purpose or special-purpose computing systems. For example, the computing environment  550  can be any of a variety of computing devices (e.g., desktop computer, laptop computer, server computer, tablet computer, etc.). In some embodiments, the computing environment is an integral part of a thermochemical reaction system or chemical processing system. Alternatively, in some embodiments, the computing environment is a separate system connected to the thermochemical reaction system or chemical processing system, for example, by making operative electrical connections (e.g., wired or wireless) to the thermochemical reaction system or chemical processing system, or components thereof. 
     With reference to  FIG.  5 B , the computing environment  550  includes one or more processing units  554 ,  556  and memory  558 ,  560 . In  FIG.  5 B , this basic configuration  552  is included within a dashed line. The processing units  554 ,  556  execute computer-executable instructions. A processing unit can be a general-purpose central processing unit (CPU), processor in an application-specific integrated circuit (ASIC) or any other type of processor. In a multi-processing system, multiple processing units execute computer-executable instructions to increase processing power. For example,  FIG.  5 B  shows a central processing unit  554  as well as a graphics processing unit or co-processing unit  556 . The tangible memory  558 ,  560  may be volatile memory (e.g., registers, cache, RAM), non-volatile memory (e.g., ROM, EEPROM, flash memory, etc.), or some combination of the two, accessible by the processing unit(s). The memory  558 ,  560  stores software  562  implementing one or more innovations described herein, in the form of computer-executable instructions suitable for execution by the processing unit(s). 
     A computing system may have additional features. For example, the computing environment  550  includes storage  564 , one or more input devices  566 , one or more output devices  568 , and one or more communication connections  570 . An interconnection mechanism (not shown) such as a bus, controller, or network interconnects the components of the computing environment  550 . Typically, operating system software (not shown) provides an operating environment for other software executing in the computing environment  550 , and coordinates activities of the components of the computing environment  550 . 
     The tangible storage  564  may be removable or non-removable, and includes magnetic disks, magnetic tapes or cassettes, CD-ROMs, DVDs, or any other medium which can be used to store information in a non-transitory way, and which can be accessed within the computing environment  550 . The storage  564  can store instructions for the software  562  implementing one or more innovations described herein. 
     The input device(s)  566  may be a touch input device such as a keyboard, mouse, pen, or trackball, a voice input device, a scanning device, or another device that provides input to the computing environment  550 . The output device(s)  566  may be a display, printer, speaker, CD-writer, or another device that provides output from computing environment  550 . 
     The communication connection(s)  570  enable communication over a communication medium to another computing entity. The communication medium conveys information such as computer-executable instructions, audio or video input or output, or other data in a modulated data signal. A modulated data signal is a signal that has one or more of its characteristics set or changed in such a manner as to encode information in the signal. By way of example, and not limitation, communication media can use an electrical, optical, RF, or other carrier. 
     Any of the disclosed methods can be implemented as computer-executable instructions stored on one or more computer-readable storage media (e.g., one or more optical media discs, volatile memory components (such as DRAM or SRAM), or non-volatile memory components (such as flash memory or hard drives)) and executed on a computer (e.g., any commercially available computer, including smart phones or other mobile devices that include computing hardware). The term computer-readable storage media does not include communication connections, such as signals and carrier waves. Any of the computer-executable instructions for implementing the disclosed techniques as well as any data created and used during implementation of the disclosed embodiments can be stored on one or more computer-readable storage media. The computer-executable instructions can be part of, for example, a dedicated software application or a software application that is accessed or downloaded via a web browser or other software application (such as a remote computing application). Such software can be executed, for example, on a single local computer (e.g., any suitable commercially available computer) or in a network environment (e.g., via the Internet, a wide-area network, a local-area network, a client-server network (such as a cloud computing network), or other such network) using one or more network computers. 
     For clarity, only certain selected aspects of the software-based implementations are described. Other details that are well known in the art are omitted. For example, it should be understood that the disclosed technology is not limited to any specific computer language or program. For instance, aspects of the disclosed technology can be implemented by software written in C++, Java, Perl, any other suitable programming language. Likewise, the disclosed technology is not limited to any particular computer or type of hardware. Certain details of suitable computers and hardware are well known and need not be set forth in detail in this disclosure. 
     It should also be well understood that any functionality described herein can be performed, at least in part, by one or more hardware logic components, instead of software. For example, and without limitation, illustrative types of hardware logic components that can be used include Field-programmable Gate Arrays (FPGAs), Program-specific Integrated Circuits (ASICs), Program-specific Standard Products (ASSPs), System-on-a-chip systems (SOCs), Complex Programmable Logic Devices (CPLDs), etc. 
     Furthermore, any of the software-based embodiments (comprising, for example, computer-executable instructions for causing a computer to perform any of the disclosed methods) can be uploaded, downloaded, or remotely accessed through a suitable communication means. Such suitable communication means include, for example, the Internet, the World Wide Web, an intranet, software applications, cable (including fiber optic cable), magnetic communications, electromagnetic communications (including RF, microwave, and infrared communications), electronic communications, or other such communication means. In any of the above described examples and embodiments, provision of a request (e.g., data request), indication (e.g., data signal), instruction (e.g., control signal), or any other communication between systems, components, devices, etc. can be by generation and transmission of an appropriate electrical signal by wired or wireless connections. 
     Heating Element Examples 
     As noted above, a porous heating element can be formed to have any two-dimensional (e.g., having a dimension at least 2 orders of magnitude less than orthogonal dimensions) or three-dimensional (3-D) shape, for example, planar, tubular, cylindrical, disk-shaped, as well as complex non-standard geometries. For example,  FIG.  6 A  illustrates a thermochemical reaction system  600  employing a porous heating element  602  with a planar or flat configuration. Similar to other examples described herein, thermochemical reaction system  600  has heating element  602  disposed in an internal volume within reactor  604 , for example, with a center thereof being substantially aligned with a central axis  610  of the reactor  604 . For example, the heating element  602  can have a thickness (along x-direction) that is less than 1 cm (e.g., sub-millimeter, such as ~250 µm), a width (along y-direction) that spans or is less than a corresponding diameter/width of the reactor, and a length (along z-direction) that is selected in conjunction with inlet gas flow rate and outlet gas flow rate to provide a predetermined residence time for reactants within reactor  604 . A controller  612  is operatively coupled to the heating element  602  via appropriate electrical connections in order to apply a desired power waveform to the heating element  602  to provide multiple heating cycles during the predetermined residence time. 
     An inlet flow  606  of reactant and/or carrier gases can be provided to one axial end of the reactor  604 , and an outlet flow  608  of product, reactant, and/or carrier gases can be extracted from an opposite axial end of the reactor. In some embodiments, a flow rate (e.g., mass flow rate) of the inlet flow  606  is substantially identical to that of the outlet flow  608 . Alternatively, in some embodiments, the inlet flow rate is different from the outlet flow rate. In the illustrated example, the inlet flow  606  and the outlet flow  608  are aligned with the central axis  610  of the reactor, and the porous heating element  602  is arranged with a major surface thereof (e.g., having the largest exposed surface area) being substantially parallel to the direction of gas flow through the reactor. Alternatively, in some embodiments, the inlet flow  606  and outlet flow  608  can be offset from each other and/or from the central axis. For example, in the x-y plane, an axis of the inlet flow  606  can be disposed on one side of the heating element  602 , and an axis of the outlet flow  608  can be disposed on an opposite of heating element  602 . 
     In some embodiments, multiple heating elements can be provided with a single reactor. The multiple heating elements can be operated in series or in parallel, for example, to provide a longer residence time for reactants, to provide temporal or spatial variations in temperature (e.g., multi-step reactions and/or chain reactions), or for any other reason. For example,  FIG.  6 B  illustrates a thermochemical reaction system  620  employing an array  622  of porous heating elements  602   a - 602   c  oriented parallel to the directions of inlet flow  606  and outlet flow  608 . Each of the heating elements  602   a - 602   c  of the array  622  can have substantially the same shape and operating characteristics. Alternatively, the heating elements  602   a - 602   c  can have different shapes, for example, to accommodate differences in reactor geometry in regions away from the central axis  610 . The heating elements of the array  622  can be connected together in series or in parallel, so as to be energized together by controller  612 . Alternatively, in some embodiments, the heating elements of the array  622  can be separately connected to controller  612  or be separately connected to respective controllers, such that each of the heating elements is capable of independent operation from others within the array  622 . 
     In another example,  FIG.  6 B  illustrates a thermochemical reaction system  640  employing a linear array  642  of porous heating elements  644   a - 644   c  oriented serially with respect to the directions of inlet flow  606  and outlet flow  608 . In  FIG.  6 B , each of the heating elements  644   a - 644   c  are connected together in parallel and to controller  612 .  FIG.  6 C  illustrates a thermochemical reaction system  660  substantially similar to that of  FIG.  6 B , but the linear array  662  of porous heating elements  664   a - 664   c  are connected together in series and to controller  612 . In the illustrated examples of  FIGS.  6 B- 6 C , the linear arrays  642 ,  662  are aligned with the central axis  610  of the reactor  604 . However, other arrangements for the array that are not aligned with the central axis  610  (e.g., at off-axis locations in the x-y plane) are also possible. In some embodiments, the heating elements of array  642 ,  662  can be operated in parallel, for example, to provide simultaneous heating cycles with the same heating waveform and peak temperature. Alternatively, in some embodiments, at least some of the heating elements of array  642  or array  662  can have different properties (e.g., size, material composition, etc.) resulting in different heating operation (e.g., peak temperature) for the same applied power waveform. Alternatively or additionally, in some embodiments, the heating elements of the array  622  can be separately connected to controller  612  or be separately connected to respective controllers, such that each of the heating elements is capable of independent operation from others within the array  622 , for example, to provide a spatial variation of temperature within the reactor (e.g., along the z-direction). 
     Although the flat parallel configurations of  FIGS.  6 A- 6 D  provides a simple and convenient approach for arranging the heating elements within the reactor, other configurations may enhance interaction of the heating element with the flowing gas molecules to improve thermal performance. For example, in some embodiments, the heating element is angled with respect to the inlet flow direction, so as to force the reactants therein to flow through the pores of the heating element. For example,  FIGS.  7 A- 7 B  illustrate thermochemical reaction systems employing porous heating elements arranged at a non-zero angle with respect to the inflow direction. Thermochemical reaction system  700  in  FIG.  7 A  has heating element  702  disposed in an internal volume within reactor  704 , and the thermochemical reaction system  720  in  FIG.  7 B  has heating element  722  disposed in an internal volume of reactor  704 . In  FIGS.  7 A- 7 B , a controller  712  is operatively coupled to the respective heating element via appropriate electrical connections in order to apply a desired power waveform thereto to provide multiple heating cycles during the predetermined residence time. Although  FIGS.  7 A- 7 B  illustrate a single heating element within the reactor, multiple heating elements can also be provided in a manner similar to that described with respect to  FIGS.  6 C- 6 D . 
     Similar to other examples described herein, an inlet flow  706  of reactant and/or carrier gases can be provided to one axial end of the reactor  704 , and an outlet flow  708  of product, reactant, and/or carrier gases can be extracted from an opposite axial end of the reactor  704 . However, in  FIG.  7 A , the porous heating element  702  is arranged with a major surface thereof (e.g., having the largest exposed surface area) at a non-zero angle (e.g., angle  716  between surface normal  714  and central axis  710 ) with respect to the direction of gas flow through the reactor. In  FIG.  7 B , the porous heating element  722  is further rotated from the parallel arrangements of  FIGS.  6 A- 6 D  so as to have its major surface arranged substantially perpendicular to the central axis  710  and/or the inlet flow  706  direction. Thus, rather than passing around top and bottom parallel surfaces of the heating element as in  FIGS.  6 A- 6 D , the configurations of  FIGS.  7 A- 7 B  forces the inlet flow  706  to pass through the thickness of the respective porous heating element  702 ,  722 , which may enable better heat exchange between reactants and the heating element and/or more precise temperature control. 
     Although  FIGS.  6 A- 7 B  illustrate simple planar shapes, heating elements can have any geometric shape (e.g., oval, triangle, etc.) or any arbitrary shape. Indeed, when the heating element is formed of carbon, the resulting structure can have sufficient flexibility to be manipulated into custom shapes for enhanced interaction with flowing reactants. Moreover, in some embodiments, the heating element can be formed into a 3-D structure (e.g., size in each dimension on a same order of magnitude) rather than just a thin planar structure. For example,  FIG.  8 A  illustrates a thermochemical reaction system  800  employing a 3-D structure for porous heating element  802 . The thermochemical reaction system  800  has heating element  802  disposed in an internal volume within reactor  804 . A controller  812  is operatively coupled to the heating element  802  via appropriate electrical connections in order to apply a desired power waveform thereto to provide multiple heating cycles during the predetermined residence time. Although  FIG.  8 A  illustrates a single heating element within the reactor, multiple heating elements can also be provided in a manner similar to that described with respect to  FIGS.  6 C- 6 D . 
     Similar to other examples described herein, an inlet flow  806  of reactant and/or carrier gases can be provided to one axial end of the reactor  804 , and an outlet flow  808  of product, reactant, and/or carrier gases can be extracted from an opposite axial end of the reactor  804 . Similar to the arrangement in  FIG.  7 B , the porous heating element  802  is disposed with an inlet face thereof arranged substantially perpendicular to central axis  810  of the reactor  804  and/or the inlet flow  806  direction. However, in contrast to the heating element in  FIG.  7 B , the porous heating element  802  has a substantial length (e.g., greater than 1 cm, for example, on the order of tens of centimeters) along the flow direction (e.g., z-direction). The length of heating element  802  can be selected in conjunction with inflow flow  806  rate, outflow flow  808  rate, or both, in order to provide a desired residence time in thermal contact with the heating element. In some embodiments, optional flow channels  814  can be provided within the porous body  816  of the heating element  802 . In some embodiments, the flow channels  814  can have a cross-sectional size greater than the pore size of body  816  of the heating element  802 , for example, to help reduce flow resistance through the reactor  804 . 
     In some embodiments, the heating element can be formed into more complex shapes or structures than those illustrated in  FIGS.  6 A- 8 A , for example, to allow the heating element to define flow paths for gaseous reactants and/or products. For example,  FIG.  8 B  illustrates a thermochemical reaction system  820  employing a 3-D structure for porous heating element  822 . In the illustrated example, heating element  822  is formed as a substantially annular tube (cutaway to show interior for illustration purposes only) that defines a fluid conduit  824  within or of the reactor  820 . Similar to other examples described herein, an inlet flow  826  of reactant and/or carrier gases can be provided to one axial end of the heating element  822  acting as fluid conduit, and an outlet flow  828  of product, reactant, and/or carrier gases can be extracted from an opposite axial end of the heating element  822 . A controller  832  is operatively coupled to the heating element  822  via appropriate electrical connections in order to apply a desired power waveform thereto, to provide multiple heating cycles to gas flow within conduit  824  during the predetermined residence time. Although  FIG.  8 B  illustrates a single heating element  822 , multiple heating elements can also be provided in parallel (e.g., with central axes  830  parallel to, but offset from each other in x-y plane) or in series (with central axes  830  substantially coaxial). 
     Membrane Reactor Examples 
     In some embodiments, the heating element can be formed into more complex shapes or structures than those illustrated in  FIGS.  6 A- 8 B , for example, to allow the heating element to act as a separation membrane as well as provide heating. For example,  FIGS.  9 A- 9 B  illustrates a membrane reactor  900  configuration for a thermochemical reaction system employing a multi-function heating element  912 . The multi-function heating element  912  comprises an asymmetric membrane formed by an outer annular layer  914   a  and an inner annular layer  914   b . The inner annular layer  914   b  defines a first flow volume  906 , to which an inlet flow  908  of reactants is provided and from which an outlet flow  910  of un-reacted reactants exists. The membrane reactor  900  also has an outer tube  902  (e.g., quartz or ceramic tube) that surrounds the outer annular layer  914   a  of the heating element  912 . A second flow volume  904  is defined in the annular space between the outer tube  902  and the outer annular layer  914   a . A controller  922  is operatively coupled to the heating element  912  via appropriate electrical connections in order to apply a desired power waveform thereto, in particular, to provide multiple heating cycles to gas flow within conduit first flow volume  906  during a predetermined residence time. 
     In operation, reactants within first flow volume  906  undergo thermochemical reactions upon application of the heating cycles by the heating element  912 . The asymmetric membrane of the heating element  912  is constructed to allow products  916  generated in the first flow volume  906  to pass therethrough to the second flow volume  904  (e.g., via diffusion), where the products are collected via outlet flow  918 . In some embodiments, the second flow volume  904  is provided with an optional carrier or sweep gas flow  920  to help collect the products  916  into outlet flow  918 . For example, the sweep gas flow  920  can comprise hydrogen gas, nitrogen gas, a noble gas, or any combination thereof. In some embodiments, in addition to carrying products from the membrane surface, the sweep gas can be used for heat recovery or preheating of gases. 
     For example, when the membrane reactor is employed for ammonia synthesis, the membrane of the heating element  912  can remove the formed ammonia in situ to drive equilibrium toward ammonia formation and avoid ammonia decomposition. The quenching following peak temperature application in the heating cycle can prevent, or at least reduce, ammonia decomposition. Prior to the next heating cycle, ammonia can be separated by membrane of the heating element  912  due to the size exclusion effect and removed from the membrane reactor  900  via outlet flow  918 . 
     The bilayer construction of the asymmetric membrane can allow for separate optimizations of the heating element functionalities. For example, the radially-outer layer  914   a  of the heating element  912  can be optimized for separation, for example, by having a pore size selected based on the kinetic diameters of reactant and product molecules. To that end, the radially-outer layer  914   a  may also have a relatively narrow thickness to allow efficient diffusion of products therethrough. In contrast, the radially-inner layer  914   b  of the heating element  912  can be optimized for diffusion, for example, by having a larger pore size (e.g., a pore size at least 1000 times greater than that of layer  914   a ). To that end, the radially-inner layer  914   b  can be made relatively thicker, for example, to providing Joule heating effect, provide structural support and/or offer increased surface area for loading of catalysts (e.g., nanoparticles  924 ) therein or thereon. In some embodiments, the radially-outer layer  914   a  and the radially-inner layer  914   b  can be formed of the same material (e.g., elemental carbon or a carbon-containing material), but with different thicknesses and pore sizes. For example, in an ammonia synthesis reaction, the radially-outer layer  914   a  can have a pore size of &lt; 2 nm (e.g., ~0.3 nm) and a thickness, t a , less than 1 µm, and the radially-inner layer  914   b   can have a pore size of &gt; 100 nm (e.g., ~1 µm) and a thickness, t b , of 1-2 mm. The formed ammonia will be separated by the nanoporous layer  914   a  due to size exclusion (e.g., based on kinetic diameters: d NH3 =2.6 Å, d H2 =2.9 Å, d N2 =3.6 Å). 
     Alternatively, in some embodiments, the heating element comprises a symmetric membrane construction. For example,  FIG.  9 C  illustrates a thermochemical reaction system  930  employing a heating element  932  with symmetric membrane (e.g., a single layer  934 ). The single membrane layer  934  can be constructed similar to outer layer  914   a  in  FIGS.  9 A- 9 B  but thicker (e.g., intermediate between thickness t a  and thickness t b  described with respect to  FIGS.  9 A- 9 B ), in order to provide a combination of functions, for example, product separation, Joule heating effect, structural support and/or surface area for loading of catalysts. Operation of thermochemical reaction system  930  would otherwise be substantially identical to that of system  900 . Although  FIGS.  9 A- 9 C  illustrate a particular membrane reactor configuration, embodiments of the disclosed subject matter are not limited thereto. Indeed, other membrane reactor setups or configurations also possible, for example, similar to those disclosed in U.S. Pat. No. 10,525,407, incorporated herein by reference, but with the presently disclosed heating elements replacing the membrane and/or support tubes described in the ‘407 patent. 
     In some embodiments, membrane reactors similar to that illustrated in  FIGS.  9 A- 9 C  can be bundled together in a single thermochemical reaction system, for example, to increase processing capacity or throughput. For example,  FIGS.  10 A- 10 B  illustrate a thermochemical reaction system  1000  employing multiple membrane reactors, in particular, individual membrane heating elements  1002  shaped as tubes and arrayed in parallel within a common outer conduit  1004 . Inlet gas flow  1008  is provided to the reaction volume defined by the internal conduit  1006  of each membrane heating element  1002 , for example, using an inlet manifold  1022  for parallel distribution of reactants. A controller (not shown) is operatively coupled to the membrane heating elements  1002  via appropriate electrical connections in order to apply a desired power waveform thereto, to provide multiple heating cycles to gas flow within conduits  1006  during the predetermined residence time. 
     Products  1012  produced by the thermochemical reactions of the reactants in conduits  1006  are separated by the membrane heating elements  1002  to a shared flow volume  1010  defined in the interstitial space between the outer conduit  1004  and the bundle of heating elements  1002 . The products in flow volume  1010  are collected as outlet flow  1014 , for example, by application of a sweep gas  1032  applied to the flow volume  1010  via header  1030 . The outlet flows  1014  can be collected by header  1034  as outlet flow  1036  for removal of the products from the system for use or storage. Meanwhile, unreacted reactants in each internal conduit  1006  can be collected together at outlets thereof by another manifold  1024 . The resulting outlet stream  1026  can be recirculate back as inlet gas flow  1008  via recirculation fluid circuit  1028 . 
     Thermochemical Reaction System Examples 
       FIG.  11    illustrates an example of a thermochemical reaction system  1100  employing membrane reactor bundles  1102  in the production of ammonia from nitrogen gas and hydrogen gas feeds  1110 . In the designed system, reactant gases can be preheated by the heat of reaction. After the thermochemical reaction in each membrane reactor (as shown at  1104 ), the outlet flow containing ammonia and sweep gas (e.g., H 2 ) can be directed to a first circuit loop  1108 . In addition to directing the ammonia product to an outlet of the membrane reactor, the sweep gas can also provide cooling to the exothermic ammonia synthesis reaction and thereby avoid or at least reduce the occurrence of ammonia decomposition. For example, first circuit loop  1108  can provide product separation (e.g., separation of the ammonia from the sweep gas), product storage (e.g., by condensing the ammonia), and/or energy recovery (e.g., by using heat in the outlet flow to produce steam under pressure for electricity generation). The separated sweep gas can be returned to the membrane reactor bundle, for example, for reuse as sweep gas or repurposed as a reactant with feed stocks  1110 . Meanwhile, the outlet flow of unreacted reactants from each membrane reactor (as shown at  1104 ) can be directed to a second circuit loop  1106 . For example, second circuit loop  1110  can provide reactant recycling (e.g., by combining with new feed stock at  1110 ) and/or energy recovery (e.g., by using heat in the outlet flow to produce steam under pressure for electricity generation). Other configurations for thermochemical reaction systems employing membrane reactor bundles  1102  are also possible according to one or more contemplated embodiments. 
     Fabricated Examples and Experimental Results 
       FIG.  12    illustrates a reactor setup  1200  employed in experiments for thermochemical processing of gaseous reactants. In the setup  1200 , a planar heating element  1210  (e.g., rectangular parallelepiped with narrow thickness) is disposed within an internal flow volume of reactor  1206  (e.g., high-temperature tube). In fabricated examples, a porous carbon material with high gas permeability was used as the heating element  1210  in the reactor setup  1200 . Electrical connections  1212   a ,  1212   b  were made at opposite ends of the planar heating element  1210  in order to pass a current therethrough to effect Joule heating. Due to its low heat capacity, the planar heating element  1210  was able to achieve heating and cooling rates of ~10 4  K/s. During heating cycles of the heating element  1210 , the gas-phase reactants (e.g., molecules  1208  in inlet flow  1202 ) flow through the reactor  1206  and come into direct contact with the porous carbon material of heating element  1210 , passing through and directly interacting with its microstructure, thereby closely following the programmed heating pattern of the heating element  1210  (e.g., in a noncontinuous or discontinuous manner). Over 90% of the electrical energy applied to the heating element via connections  1212   a ,  1212   b  can be converted to heat the gas molecules  1208 , resulting in a more energy efficient process as compared to conventional approaches. The high temperatures (e.g., greater than 1000 K) resulting from the heating element during each heating cycle initiates a thermochemical reaction or reactions that generate a product gas (e.g., hydrocarbon molecules  1218 ). The resulting product gas and any un-reacted reactant gas can be removed from the reactor via flow  1216  from outlet port  1214 . 
     In the fabricated examples, carbon paper (Freudenberg H23 gas diffusion layer, manufactured by Freudenberg Performance Materials SE, Germany, having a thickness of 210 µm, a through-plane electrical resistivity of 4.5 mΩ-cm 2  at 1 MPa and an in-plane electrical resistance of 0.8 Ω, and a through-plane air permeability of 400 L/m 2 -s (DIN EN ISO 9237)) or carbon felt (AvCarb G475A soft graphite battery felt, manufactured by AvCarb Material Solutions, Lowell, Massachusetts, having a thickness of 4.7 mm, and an electrical resistivity of 200 mΩ-cm 2  at 6.3 psi or activated carbon felt ACF 1000, sold by Fuel Cell Earth) was used for the heating element. In some examples, the carbon felt was loaded with Ru (2 wt%) or Fe catalyst (2 wt%), for example, using the method described in U.S. Pat. Application Publication No. 2019/0161840, published May 30, 2019, which is incorporated herein by reference. For electrical connection to the heating element, multipurpose  110  copper wire (99.9%, also known as electrolytic-tough-pitch (ETP) copper, 0.04 ” diameter) and multipurpose 110 copper sheets (99.9% pure copper, also known as ETP copper, 0.002 ” thickness) were used. Alumina ceramic protection tubes (99.8%, 0.125 ” outer diameter and 0.062 ” inner diameter, maximum temperature 2223 K) were used to cover the copper wires and prevent the copper wires from heating the sealing materials. 
     In the fabricated examples involving methane pyrolysis, carbon paper having planar dimensions of 40 mm x 8 mm was used, of which a central section of 20 mm x 8 mm was exposed within the reactor volume as a heating element and 10 mm x 8 mm sections at each end were otherwise wrapped in copper foil to provide electrical connection. In the fabricated examples involving ammonia synthesis, carbon felt having planar dimensions of 35 mm x 8 mm was used, of which a central section of 15 mm x 8 mm was exposed within the reactor volume as a heating element and 10 mm x 8 mm sections at each end were otherwise wrapped in copper foil to provide electrical connection. In the fabricated examples, the copper-foil-wrapped regions were connected with copper wire, without the need for conductive glue or paste. The copper wires extended out of the alumina ceramic protection tube. In the fabricated example, each end of the alumina ceramic protection tube was sealed with epoxy. The carbon heating element, copper material, and alumina ceramic protection tubes were further placed in a quartz tube reactor (½″ diameter), which was connected with union fittings (Swagelok Ultra-Torr Union Tee, sold by Swagelok Company, Solon, Ohio) on each end. One port of the union fitting was used for the electrical connection, while the other was used for the gas inlet or outlet. The copper wire from the port was connected to an appropriate signal generation setup. 
     In particular, to provide the appropriate electrical control signal to the heater, a solid-state relay device (sold by Omega Engineering, Inc., Norwalk, Connecticut) with DC input and DC output (maximum current 25 A) was used. The input signal to the solid-state relay was provided by a source meter (Keithley Model 2425 SourceMeter, sold by Tektronix, Inc., Beaverton, Oregon), and the output signal was provided by a variable DC power source (Volteq Variable Switching DC Power Supply HY7520 EX, 75 V, 20 A, sold by Acifica, Inc., San Jose, California). In programmed heating and quenching (PHQ) operation of the reactor setup  1200 , depending on the length of the high-temperature pulse desired, for each heating cycle the initial time duration was set as “power on” (e.g., 20 ms on), while the remaining time up to 1100 ms was set as “power off” (e.g., 1080 ms off). Due to changes in defect level and crystallinity of the carbon heater during heating operations that can decrease its resistance, the electrical signal was adjusted during operations to maintain peak temperature. 
     To generate heat, an electric current is passed through the porous carbon heating element, which due to its low heat capacity (e.g., &lt; 6.6x 10 -6  J/K) is able to reach heating and cooling rates of ~10 4  K/s, as shown in  FIG.  14 C . Since the gas-phase reactants flow into direct contact with the heating element, passing through and directly interacting with its microstructure, the reactants closely following the programmed heating pattern of the heating element. And since the heating element is capable of efficiently generating high temperatures (e.g., greater than 1200 K and up to 2400 K) that can exponentially increase the methane activation rate for high conversion, the reactor setup of  FIG.  12    requires no additional catalyst in order to perform methane pyrolysis. 
     In fabricated examples, the heating cycles for PHQ operation of the reactor setup employed a pulse profile, where electrical power was applied to the heating element from an “off” state (e.g., no current applied) to an “on” state (e.g., full current applied) and held for 20 ms, followed by removing the electrical power for the remainder of the heating cycle (e.g., to turn the heating element back off for 1080 ms to complete a cycle period of 1100 ms). Each heating cycle was repeated multiple times while the reactants remained in thermal contact with the heating element (e.g., where residence time of the gaseous reactants in contact with the heating element is based on flow rate and heater length). By adjusting the input power for a specific pulse duration, the peak temperature (T high ) of the carbon heater can also be accurately controlled, as shown in  FIG.  14 C . And by adjusting the pulse duration of the input power, the resulting temperature profile can be tuned in a similar manner, as shown in  FIG.  14 D . Increased pulse duration can require decreased power input to reach the same peak temperature. 
     Fabricated examples of the reactor setup employing PHQ operation (e.g., the temperature profile illustrated in  FIG.  13 B ) to drive thermochemical reactions were compared against continuous heating (e.g., the temperature profile illustrated in  FIG.  13 A ) to drive the same reactions. For methane pyrolysis examples, continuous heating was conducted using a tube furnace in a catalyst-free setup under near-equilibrium conditions. In general, the continuous heating of  FIG.  13 A  creates a variety of products due to the lack of tunability over the temperature profile, and thus the resulting reaction pathways. In contrast, the PHQ operation of  FIG.  13 B , which is enabled by the disclosed reactor setups, can selectively produces value-added C 2  products. The high temperature of the PHQ operation ensures high conversion even without any catalyst present, while the transient heating time enables high selectivity. Without being bound to any particular theory of operation, it is hypothesized that the high temperature of the PHQ heating cycle contributes to the fast activation of the C-H bond, while the transient reaction time can effectively prevent secondary and subsequent reactions toward undesired heavy aromatics and coke. As shown in  FIG.  14 A , the PHQ operation of  FIG.  13 B  demonstrates much higher selectivity (e.g., &gt; 75% versus &lt; 35% without using a catalyst) to value-added C 2  hydrocarbons at comparable methane conversions (e.g., -13%) as compared to the conventional continuous heating operation of  FIG.  13 A . It is further noted that the periodic switching between high and low temperatures (e.g., heating on for 20 ms and off for 1080 ms) made possible by PHQ technique translates to a much lower average temperature (815 K in  FIG.  13 B ) than continuous heating (1273 K in  FIG.  13 A ), thereby reducing the energy cost for comparable methane conversions. 
     With respect to C 2  product selectivity, the metal-catalyst-free PHQ technique with the fabricated reactor examples also outperformed continuous heating that had optimized catalysts, for example, the catalyst-based approaches for methane pyrolysis and direct non-oxidative methane conversion (DNMC) reactions shown in  FIG.  14 B .  FIG.  15 A  further shows the product selectivity and methane conversion for four different reaction techniques, in particular (1) non-catalytic methane pyrolysis using continuous furnace heating at 1273 K; (2) catalytic methane pyrolysis with a state-of-the-art Fe/silica catalyst using continuous furnace heating at 1273 K; (3) methane pyrolysis with the carbon paper heating element (as shown in  FIG.  12   , but without any PHQ operation) using continuous furnace heating at 1273 K; and (4) methane pyrolysis using the reactor setup of  FIG.  12    with PHQ operation. In the PHQ operation, the peak temperature, T high  was 2200 K, and the pulse duration was 55 ms over a heating cycle period of 1100 ms (e.g., 55 ms on, 1045 ms off). 
     Using the same flow rate (e.g., 24 standard cubic centimeters per minute (sccm), 90 mol% methane and 10 mol% argon) and pressure (1 atm) for each reaction technique, the product distribution of the PHQ method was found to offer a significant improvement compared to the other techniques, with a much higher selectivity (-80%) for C 2  products, as illustrated in  FIG.  15 A . In comparison, only ~40% C 2  products were measured using continuous heating by a furnace at 1273 K with the Fe/silica catalyst. For the non-catalytic system, continuous furnace heating at 1273 K produced nearly zero product. Meanwhile, continuous heating in the presence of the carbon paper (e.g., using a furnace, without PHQ) showed some methane conversion (-15%), but with a large amount of undesired coke (~30%) and lower C 2  product selectivity (~40%). 
     These results suggest that low C 2  selectivity is intrinsic to the continuous heating method due to significant secondary and subsequent reactions resulting in the formation of low-value compounds, such as naphthalene and coke. In contrast, in the fabricated examples employing PHQ operation (e.g., 55 ms on, 1045 ms off during eating heating cycle), the average temperature (T avg ) is &lt; 900 K. Yet, PHQ operation is still able to achieve a comparable methane conversion (~15%) and much higher value-added C 2  product selectivity than those achieved by the Fe/silica catalyst using continuous heating. Without being bound to any particular theory, the high temperature of the PHQ technique promotes fast methane activation according to the Arrhenius law to achieve enhanced conversion, while the transient heating time and fast quenching gives rise to high selectivity to value-added C 2  intermediate products in the reaction network of methane pyrolysis. 
     The effect of peak temperature, T high , and pulse duration (e.g., heating time) on the methane pyrolysis reaction was further investigated. In particular, a lower flow rate (e.g., 4 sccm, 75 mol% methane and 25 mol% argon) was employed to increase the methane conversion. With a fixed pulse duration of 20 ms on and 1080 ms off, methane conversion monotonically increased with peak temperature, T high , as shown in  FIG.  15 B . Such increased peak temperature at fixed pulse duration, however, leads to slightly lower selectivity to C 2  products but higher selectivity to benzene (C 6 H 6 ) due to the increased reaction rate at higher temperatures, as shown in  FIG.  15 C . As shown in  FIG.  15 D , increasing the pulse duration at a constant peak temperature (e.g., T high  = 1800 K) can achieve similar results by increasing reaction time (e.g., longer reaction progress), thereby offering another way to toggle between C 2  and C 6 H 6  products. In general, the observed selectivities of the total C 2  products (e.g., &gt; 75%) by the metal-catalyst-free PHQ process shown in  FIGS.  15 A- 15 D  are better than those obtained by continuous heating with comparable methane conversions, even those that employ optimized catalysts. 
     For ammonia synthesis examples, continuous heating was conducted using the Ru-loaded or bare carbon felt as the heating element in a continuous operation mode. In general, continuous heating at a high temperature undermines catalyst stability in ammonia synthesis by accelerating its ripening process. In contract, the PHQ operation of  FIG.  16 A  provides transient high-temperature heating and therefore a high ammonia production rate, while also ensuring good catalyst stability by rapidly quenching the reaction temperature. Ru supported on a carbon felt heater was selected as a model catalyst, as it exhibits activity for N 2  activation. While industrial ammonia synthesis is normally conducted at high pressures, fabricated examples operated under ambient pressure conditions (e.g., atmospheric pressure) to compare ammonia synthesis rates by PHQ operation and continuous heating, both using carbon felt as the heating element. 
     Employing the heating cycles illustrated in  FIG.  16 A  (e.g., 110 ms on, 990 ms off; peak temperature, T high , of 1400 K), the PHQ operation showed a stable performance that lasted for ~20 hours with an ammonia synthesis rate of ~7000 µmol/g Ru /h, after which the activity started to decay ( FIG.  16 B ), as measured by the Berthelot method. For comparison, the ammonia synthesis rates were also measure by continuous heating at T high  (1400 K), T low  (~700 K), and T avg . (~900 K). As shown in  FIG.  16 B , continuous heating at T high  exhibited good activity that was comparable with PHQ operation, but only lasted for ~2 hours, and continuous heating at T avg . showed much worse activity although with comparable reaction time during which the ammonia synthesis rate was relatively stable. Finally, continuous heating at T low  showed an almost zero ammonia synthesis rate due to the poor N 2  activation under low temperature. 
     Note that the presence of an active catalyst (e.g., Ru) for ammonia synthesis may be necessary, as without it the synthesis rate drops to close to zero whether the heating operation is continuous or PHQ. This also suggests that the heating element (e.g., carbon felt) and the electric circuit components (e.g., Cu wire) are themselves catalytically inactive in these processes. Scanning electron microscopy (SEM) was used to compare the size evolution of the Ru catalyst during PHQ and continuous heating at T high . As shown in  FIG.  16 C , the Ru nanoparticles retained their original size and distribution after PHQ for 1 hour. In contrast, the Ru nanoparticles severely ripened after continuous heating at T high  for the same duration, as shown in  FIG.  16 D . 
     Due to the improved catalyst stability offered by the PHQ operation (e.g., 110 ms on, 990 ms off; T high  of 1200 K), a fabricated example of the reactor system was able to maintain stable ammonia production for ~100 hours with an average synthesis rate (r NH3 ) of ~4000 µmol/g Ru /h using a non-optimized Ru catalyst. In another fabricated example of the reactor system using a non-optimized Fe catalyst, stable ammonia production for &gt; 100 hours was obtained with an average synthesis rate (r NH3 ) of ~6000 µmol/g Fe /h. Without being bound to any particular theory, this improvement over conventional ammonia synthesis techniques may be attributed to the higher temperature that is enabled by the PHQ method without sacrificing the catalyst stability because of the rapid temperature quenching. Moreover, other catalysts optimized for the ammonia synthesis in combination with the disclosed PHQ operation can yield even greater improvements in synthesis rates. 
     Additional Examples of the Disclosed Technology 
     In view of the above described implementations of the disclosed subject matter, this application discloses the additional examples in the clauses enumerated below. It should be noted that one feature of a clause in isolation, or more than one feature of the clause taken in combination, and, optionally, in combination with one or more features of one or more further clauses are further examples also falling within the disclosure of this application. 
     Clause 1. A method, comprising:
     (a) for a first time period, providing one or more reactants in thermal contact with a first heating element in a reactor;   (b) during a first part of a heating cycle, providing the one or more reactants with a first temperature by heating with the first heating element, such that one or more thermochemical reactions is initiated; and   (c) during a second part of the heating cycle, providing the one or more reactants with a second temperature less than the first temperature, 
   wherein a duration of the first time period is equal to or greater than a duration of the heating cycle,   the duration of the heating cycle is less than five seconds,   the first heating element operates by Joule heating and has a porous construction that allows gas to flow therethrough, and   the one or more thermochemical reactions comprises pyrolysis, thermolysis, synthesis, hydrogenation, dehydrogenation, hydrogenolysis, or any combination thereof.   
   

     Clause 2. The method of any clause or example herein, in particular Clause 1, further comprising, after (c) removing one or more gaseous products of the one or more thermochemical reactions from the reactor. 
     Clause 3. The method of any clause or example herein, in particular any one of Clauses 1-2, wherein (b) comprises applying a first electrical power level to the first heating element, and (c) comprises applying a second electrical power level or no electrical power to the first heating element, the second electrical power level being less than the first electrical power level. 
     Clause 4. The method of any clause or example herein, in particular any one of Clauses 1-3, wherein (b) and (c) comprise applying an electrical power waveform to the first heating element, the waveform comprising at least a first electrical power level corresponding to the first temperature and a second electrical power level corresponding to the second temperature. 
     Clause 5. The method of any clause or example herein, in particular Clause 4, wherein the waveform comprises a pulse, a rectangular wave profile, a stepped profile, a triangular wave profile, a sine wave profile, or any combination thereof. 
     Clause 6. The method of any clause or example herein, in particular any one of Clauses 1-5, wherein the second part of the heating cycle immediately follows the first part of the heating cycle, a duration of the first part is 10-400 milliseconds (e.g., 15-150 ms), and/or a duration of the second part is 1-1.5 seconds. 
     Clause 7. The method of any clause or example herein, in particular any one of Clauses 1-6, wherein the second temperature is at least 600 K less than the first temperature. 
     Clause 8. The method of any clause or example herein, in particular any one of Clauses 1-7, wherein the first temperature is greater than or equal to 1200 K. 
     Clause 9. The method of any clause or example herein, in particular any one of Clauses 1-8, wherein the second temperature is less than or equal to 800 K. 
     Clause 10. The method of any clause or example herein, in particular any one of Clauses 1-9, wherein the one or more thermochemical reactions occur with the reactor at atmospheric pressure or at a pressure less than or equal to 20 MPa. 
     Clause 11. The method of any clause or example herein, in particular any one of Clauses 1-10, wherein (a) comprises flowing a first reactant of the one or more reactants into contact with or through the first heating element, wherein the first time period is based on at least a flow rate of the first reactant and a size of the first heating element. 
     Clause 12. The method of any clause or example herein, in particular any one of Clauses 1-11, wherein (b) comprises supplying an electrical current to the first heating element, and (c) comprises reducing or removing the electrical current from the first heating element. 
     Clause 13. The method of any clause or example herein, in particular any one of Clauses 1-12, wherein the duration of the first time period is at least two times greater than the duration of the heating cycle, and the method comprises repeating (b) and (c) at least once during the first time period. 
     Clause 14. The method of any clause or example herein, in particular any one of Clauses 1-13, wherein (a) comprises recirculating reactants unreacted by a previous heating cycle back into thermal contact with the first heating element, and the method further comprises: (d) repeating (b)-(c). 
     Clause 15. The method of any clause or example herein, in particular Clause 14, wherein (a) and (d) are continuously performed for at least 100 hours. 
     Clause 16. The method of any clause or example herein, in particular any one of Clauses 1-15, wherein the reactor, the first heating element, or both include one or more catalysts. 
     Clause 17. The method of any clause or example herein, in particular Clause 16, wherein the one or more catalysts comprise single element nanoparticles, multi-element nanoparticles, or any combination thereof. 
     Clause 18. The method of any clause or example herein, in particular any one of Clauses 1-17, wherein the first heating element comprises a pure carbon or carbon-containing material. 
     Clause 19. The method of any clause or example herein, in particular Clause 18, wherein the first heating element comprises porous carbon or porous silicon carbide (SiC). 
     Clause 20. The method of any clause or example herein, in particular any one of Clauses 1-19, wherein the first heating element has a heat capacity less than 1 x 10 -5  J/K. 
     Clause 21. The method of any clause or example herein, in particular any one of Clauses 1-20, wherein a heating rate to the first temperature, a cooling rate to the second temperature, or both is at least 10 3  K/s. 
     Clause 22. The method of any clause or example herein, in particular Clause 21, wherein the heating rate, the cooling rate, or both is about 10 4  K/s. 
     Clause 23. The method of any clause or example herein, in particular any one of Clauses 1-22, wherein the first heating element is formed as a porous membrane that allows at least one gaseous product of the one or more thermochemical reactions to pass therethrough to a second flow path while retaining the one or more reactants in a first flow path. 
     Clause 24. The method of any clause or example herein, in particular any one of Clauses 1-22, wherein the first heating element is formed as a porous membrane that allows one or more reactants to pass therethrough to a second flow path while retaining the one or more reactants in a first flow path. 
     Clause 25. The method of any clause or example herein, in particular any one of Clauses 23-24, wherein the porous membrane has a bilayer structure comprising first and second layers, the first layer faces the first flow path and has a first pore size, and the second layer faces the second flow path and has a second pore size different than the first pore size. 
     Clause 26. The method of any clause or example herein, in particular Clause 25, wherein one of the first and second pore sizes is at least 1000 times greater than the other of the first and second pore sizes. 
     Clause 27. The method of any clause or example herein, in particular any one of Clauses 25-26, wherein one of the first and second pore sizes is greater than or equal to 1 µm and the other of the first and second pore sizes is less than or equal to 2 nm, for example, about 0.3 nm. 
     Clause 28. The method of any clause or example herein, in particular any one of Clauses 25-27, wherein one of the first and second layers has a thickness of 2 mm or less, and the other of the first and second layers has a thickness of 1 µm or less. 
     Clause 29. The method of any clause or example herein, in particular any one of Clauses 23-24, wherein the porous membrane comprises a single layer facing the first flow path on one side and the second flow path on an opposite side. 
     Clause 30. The method of any clause or example herein, in Clause 29, wherein the single layer has a pore size less than or equal to 10 nm. 
     Clause 31. The method of any clause or example herein, in particular any one of Clauses 29-30, wherein the pore size is less than or equal to 2 nm, for example, about 0.3 nm. 
     Clause 32. The method of any clause or example herein, in particular any one of Clauses 1-31, wherein the first heating element comprises multiple heating sub-elements electrically connected together, each heating sub-element being formed as a porous membrane that separates a respective first flow path from a common second flow path, the one or more reactants being provided to each first flow path, gaseous products of the one or more thermochemical reactions passing through the respective porous membrane to the common second flow path. 
     Clause 33. The method of any clause or example herein, in particular any one of Clauses 1-32, wherein the reactor has one or more second heating elements therein arranged in series or in parallel with the first heating element. 
     Clause 34. The method of any clause or example herein, in particular Clause 33, wherein (b), (c), or both comprise using one, some, or all of the second heating elements so as to provide a spatial temperature gradient, a temporal temperature gradient, or both. 
     Clause 35. The method of any clause or example herein, in particular any one of Clauses 1-34, wherein the one or more reactants comprise methane (CH 4 ), the one or more thermochemical reactions comprise pyrolysis, and a gaseous product of the thermochemical reactions comprises C 2  and higher hydrocarbons and/or aromatics. 
     Clause 36. The method of any clause or example herein, in particular Clause 35, wherein the thermochemical reactions within the reactor occur without a catalyst. 
     Clause 37. The method of any clause or example herein, in particular any one of Clauses 35-36, wherein at least 65% of the reacted methane is converted to C 2  hydrocarbons, or about 75% of the reacted methane is converted to C 2  hydrocarbons. 
     Clause 38. The method of any clause or example herein, in particular any one of Clauses 35-37, wherein the first temperature is at least 1200 K (e.g., 1800 K or greater), the duration of the first part of the heating cycle is less than 400 milliseconds (e.g., 100 ms or less), and the duration of the heating cycle is less than 1.5 seconds. 
     Clause 39. The method of any clause or example herein, in particular any one of Clauses 1-34, wherein the one or more reactants comprise nitrogen gas (N 2 ) and hydrogen gas (H 2 ), the one or more thermochemical reactions comprise synthesis, and a gaseous product of the thermochemical reactions comprises ammonia (NH 3 ). 
     Clause 40. The method of any clause or example herein, in particular Clause 39, wherein the first temperature is at least 1200 K, the duration of the first part of the heating cycle is less than 150 milliseconds, and the duration of the heating cycle is less than 1.5 seconds. 
     Clause 41. The method of any clause or example herein, in particular any one of Clauses 1-34, wherein the one or more reactants comprise a polymer, the one or more thermochemical reactions comprise pyrolysis and hydrogenation, and a product of the thermochemical reactions comprises monomers, oligomer, hydrocarbons, aromatics or any combination thereof. 
     Clause 42. The method of any clause or example herein, in particular any one of Clauses 1-34, wherein the one or more reactants comprises methane (CH 4 ) and nitrogen gas (N 2 ), the one or more thermochemical reactions comprise pyrolysis and synthesis, and a gaseous product of the thermochemical reactions comprises ammonia (NH 3 ), hydrocarbons, aromatics, or any combination thereof. 
     Clause 43. A method, comprising:
     (a) for a first time period, providing one or more reactants within a reactor;   (b) during the first time period, using one or more Joule heating elements to change a temperature of the one or more reactants between a first peak temperature and a first minimum temperature for a first heating cycle, the first peak temperature initiating one or more thermochemical reactions of the one or more reactants; and   (c) during the first time period, using the one or more Joule heating elements to change the temperature of the one or more reactants between a second peak temperature and a second minimum temperature for a second heating cycle, the second peak temperature initiating one or more thermochemical reactions of the one or more reactants,   wherein a duration of the first time period is equal to or greater than a combined duration of the first and second heating cycles, the duration of each of the first heating cycle and the second heating cycle is less than five seconds, a difference between the first peak temperature and the first minimum temperature is at least 600 K, a difference between the second peak temperature and the second minimum temperature is at least 600 K, and the one or more thermochemical reactions comprises pyrolysis, thermolysis, synthesis, hydrogenation, dehydrogenation, hydrogenolysis, or any combination thereof.   

     Clause 44. The method of any clause or example herein, in particular Clause 43, further comprising, after (c) removing one or more gaseous products of the one or more thermochemical reactions from the reactor. 
     Clause 45. The method of any clause or example herein, in particular any one of Clauses 43-44, wherein (b) comprises applying a first electrical power waveform to the Joule heating elements, (c) comprises applying a second electrical power waveform to the Joule heating elements, the first electrical power waveform comprising a first electrical power level corresponding to the first peak temperature and a second electrical power level corresponding to the first minimum temperature, the second electrical power waveform comprising a third electrical power level corresponding to the second peak temperature and a fourth electrical power level corresponding to the second minimum temperature. 
     Clause 46. The method of any clause or example herein, in particular Clause 45, wherein each waveform has a pulse profile, a rectangular wave profile, a stepped profile, a triangular wave profile, a sine wave profile, or any combination thereof. 
     Clause 47. The method of any clause or example herein, in particular any one of Clauses 45-46, wherein the first and second electrical power waveforms are substantially identical, and a period of each electrical power waveform is a duration of each of the first and second heating cycles. 
     Clause 48. The method of any clause or example herein, in particular any one of Clauses 45-47, wherein a period of each of the first and second electrical power waveforms is 1-1.5 seconds, and a duration of the first peak temperature, the second peak temperature, or both is 10-400 milliseconds (e.g., 15-150 ms). 
     Clause 49. The method of any clause or example herein, in particular any one of Clauses 43-48, wherein:
     the first peak temperature, the second peak temperature, or both is at least 1200 K;   the first minimum temperature, the second minimum temperature, or both is less than or equal to 800 K (e.g., less than or equal to 600 K); or   any combination of the above.   

     Clause 50. The method of any clause or example herein, in particular any one of Clauses 43-49, wherein the one or more thermochemical reactions occur with the reactor at atmospheric pressure or at a pressure less than or equal to 20 MPa. 
     Clause 51. The method of any clause or example herein, in particular any one of Clauses 43-50, wherein:
     for at least 65% of the duration of the first heating cycle, the one or more reactants are at a temperature less than the first peak temperature;   for at least 65% of the duration of the second heating cycle, the one or more reactants are at a temperature less than the second peak temperature; or   any combination of the above.   

     Clause 52. The method of any clause or example herein, in particular any one of Clauses 43-51, wherein the one or more thermochemical reactions proceed within the reactor without a catalyst. 
     Clause 53. The method of any clause or example herein, in particular any one of Clauses 43-51, wherein the reactor, the one or more Joule heating elements, or both include one or more catalysts. 
     Clause 54. The method of any clause or example herein, in particular any one of Clauses 43-53, wherein:
     each Joule heating element has a porous construction that allows gas to flow therethrough;   each Joule heating element is formed of pure carbon or carbon-containing material;   each Joule heating element has a heat capacity of less than 1 x 10 -5  J/K;   each Joule heating element is constructed and controlled to provide a heating rate, a cooling rate, or both of at least 10 3  K/s; or   any combination of the above.   

     Clause 55. The method of any clause or example herein, in particular any one of Clauses 43-54, wherein each Joule heating element is constructed as a porous separation membrane that allows at least one of the reactants or gaseous products to pass therethrough while retaining the other of the reactants or gaseous products. 
     Clause 56. A thermochemical reaction system, comprising:
     a gas-flow reactor having an inlet port and an outlet port, the inlet port being constructed to receive input of a gas flow to an internal volume of the gas-flow reactor, the outlet port being constructed to receive output of a gas flow from the internal volume of the gas-flow reactor;   a Joule heating element disposed within the gas-flow reactor, the Joule heating element having a porous construction that allows gas to flow therethrough; and   a control system operatively coupled to the Joule heating element and configured to apply a signal to the Joule heating element that changes temperature thereof between a peak temperature and a minimum temperature during a corresponding heating cycle,   wherein a duration of the heating cycle is less than five seconds, a difference between the peak temperature and the minimum temperature is at least 600 K, and the peak temperature is at least 1200 K.   

     Clause 57. The thermochemical reaction system of any clause or example herein, in particular Clause 56, wherein the control system is configured to repeat the heating cycle by re-applying the signal to the Joule heating element. 
     Clause 58. The thermochemical reaction system of any clause or example herein, in particular any one of Clauses 56-57, wherein the control system comprises one or more processors, and computer-readable storage media storing computer-readable instructions that, when executed by the one or more processors, cause the one or more processors to apply the signal and/or re-apply the signal to the Joule heating element. 
     Clause 59. The thermochemical reaction system of any clause or example herein, in particular any one of Clauses 56-58, wherein each signal comprises an electrical power waveform having at least a first electrical power level corresponding to the peak temperature and a second electrical power level corresponding to the minimum temperature. 
     Clause 60. The thermochemical reaction system of any clause or example herein, in particular any one of Clauses 56-59, wherein each signal comprises an electrical power waveform having a pulse profile, rectangular wave profile, stepped profile, triangular wave profile, sine wave profile, or any combination thereof. 
     Clause 61. The thermochemical reaction system of any clause or example herein, in particular any one of Clauses 56-60, wherein the control system is configured to apply the signal or re-apply the signal such that the duration of the respective heating cycle is 1-1.5 seconds, a duration of the peak temperature is 10-400 milliseconds (e.g., 15-150 ms), or both. 
     Clause 62. The thermochemical reaction system of any clause or example herein, in particular any one of Clauses 56-61, wherein the control system is configured to apply the signal or re-apply the signal such that the peak temperature is applied for no more than 35% of the duration of the respective heating cycle. 
     Clause 63. The thermochemical reaction system of any clause or example herein, in particular any one of Clauses 56-62, wherein:
     the Joule heating element is formed of pure carbon or carbon-containing material;   the Joule heating element has a heat capacity of less than 1 x 10 -5  J/K;   the Joule heating element is constructed and controlled to provide a heating rate, a cooling rate, or both of at least 10 3  K/s; or   any combination of the above.   

     Clause 64. The thermochemical reaction system of any clause or example herein, in particular any one of Clauses 56-63, wherein the Joule heating element comprises porous carbon or porous silicon carbide (SiC). 
     Clause 65. The thermochemical reaction system of any clause or example herein, in particular any one of Clauses 56-64, wherein the gas-flow reactor, the Joule heating element, or both include one or more catalysts. 
     Clause 66. The thermochemical reaction system of any clause or example herein, in particular Clause 65, wherein the one or more catalysts comprise single element nanoparticles, multi-element nanoparticles, or any combination thereof. 
     Clause 67. The thermochemical reaction system of any clause or example herein, in particular any one of Clauses 56-66, wherein gas-flow reactor is provided with multiple Joule heating elements arranged in series or in parallel with respect to a gas flow through the internal volume of the gas-flow reactor. 
     Clause 68. The thermochemical reaction system of any clause or example herein, in particular any one of Clauses 56-67, further comprising a separator constructed to separate gaseous products of a thermochemical reaction within the internal volume of the gas flow reactor from reactants of the thermochemical reaction. 
     Clause 69. The thermochemical reaction system of any clause or example herein, in particular any one of Clauses 56-68, wherein the Joule heating element is constructed as a porous separation membrane that allows a first gas to pass therethrough while retaining a second gas. 
     Clause 70. The thermochemical reaction system of any clause or example herein, in particular Clause 69, wherein the porous separation membrane has a bilayer structure comprising first and second layers, the first layer having a first pore size, the second layer having a second pore size different than the first pore size. 
     Clause 71. The thermochemical reaction system of any clause or example herein, in particular Clause 70, wherein:
     one of the first and second pore sizes is at least 1000 times greater than the other of the first and second pore sizes;   one of the first and second pore sizes is greater than or equal to 1 µm and the other of the first and second pore sizes is less than or equal to 2 nm, for example, about 0.3 nm;   one of the first and second layers has a thickness of 2 mm or less, and the other of the first and second layers has a thickness of 1 µm or less; or   any combination of the above.   

     Clause 72. The thermochemical reaction system of any clause or example herein, in particular Clause 69, wherein the porous separation membrane is a single layer that is substantially homogeneous throughout its thickness. 
     Clause 73. The thermochemical reaction system of any clause or example herein, in particular Clause 72, wherein the single layer has a pore size less than or equal to 10 nm. 
     Clause 74. The thermochemical reaction system of any clause or example herein, in particular Clause 73, wherein the pore size is less than or equal to 2 nm, for example, about 0.3 nm. 
     Clause 75. The thermochemical reaction system of any clause or example herein, in particular any one of Clauses 56-74, wherein the gas-flow reactor comprises a thermally-stable holder disposed proximal to the Joule heating element, the thermally-stable holder being constructed to hold solid or liquid reactants for heating during each heating cycle. 
     Clause 76. The thermochemical reaction system of any clause or example herein, in particular Clause 75, wherein the thermally-stable holder comprises quartz, ceramic, or any combination thereof. 
     Clause 77. A thermochemical reaction system, comprising:
     an array of membrane reactors arranged in parallel, each membrane reactor comprising a circumferential membrane wall that surrounds an internal flow volume, the circumferential membrane wall being constructed to allow a first gas from the internal flow volume to pass therethrough while retaining a second gas within the internal flow volume;   an outer conduit containing the array of membrane reactors, the outer conduit defining a product collection flow volume between outer circumferential surfaces of the membrane walls and an inner circumferential surface of the outer conduit; and   electrical connections to each of the array of membrane reactors, the electrical connections being constructed to allow application of electrical power thereto, such that each membrane wall acts as a Joule heating element.   

     Clause 78. The thermochemical reaction system of any clause or example herein, in particular Clause 77, further comprising:
     a control system operatively coupled to the membrane reactors via said electrical connections, the control system being configured to apply an electrical power signal to each membrane wall that changes temperature thereof between a peak temperature and a minimum temperature during a corresponding heating cycle,   wherein a duration of the heating cycle is less than five seconds, a difference between the peak temperature and the minimum temperature is at least 600 K, and the peak temperature is at least 1200 K.   

     Clause 79. The thermochemical reaction system of any clause or example herein, in particular Clause 78, wherein the control system is configured to repeat the heating cycle by re-applying the electrical power signal to each membrane wall. 
     Clause 80. The thermochemical reaction system of any clause or example herein, in particular any one of Clauses 78-79, wherein the control system comprises one or more processors, and computer-readable storage media storing computer-readable instructions that, when executed by the one or more processors, cause the one or more processors to apply the electrical power signal and/or re-apply electrical power signal to each membrane wall. 
     Clause 81. The thermochemical reaction system of any clause or example herein, in particular any one of Clauses 77-80, wherein each electrical power signal comprises a waveform having at least a first power level corresponding to the peak temperature and a second power level corresponding to the minimum temperature. 
     Clause 82. The thermochemical reaction system of any clause or example herein, in particular any one of Clauses 77-81, wherein each electrical power signal comprises a waveform having a pulse profile, rectangular wave profile, stepped profile, triangular wave profile, sine wave profile, or any combination thereof. 
     Clause 83. The thermochemical reaction system of any clause or example herein, in particular any one of Clauses 78-82, wherein the control system is configured to apply the electrical power signal or re-apply the electrical power signal such that the duration of the respective heating cycle is 1-1.5 seconds, a duration of the peak temperature is 10-400 milliseconds (e.g., 15-150 ms), or both. 
     Clause 84. The thermochemical reaction system of any clause or example herein, in particular any one of Clauses 78-83, wherein the control system is configured to apply the electrical power signal or re-apply the electrical power signal such that the peak temperature is applied for no more than 35% of the duration of the respective heating cycle. 
     Clause 85. The thermochemical reaction system of any clause or example herein, in particular any one of Clauses 77-84, wherein:
     each membrane wall is formed of pure carbon or carbon-containing material;   each membrane wall has a heat capacity of less than 1 x 10 -5  J/K;   each membrane wall is constructed and controlled to provide a heating rate, a cooling rate, or both of at least 10 3  K/s; or   any combination of the above.   

     Clause 86. The thermochemical reaction system of any clause or example herein, in particular any one of Clauses 77-85, wherein each membrane wall comprises porous carbon or porous silicon carbide (SiC). 
     Clause 87. The thermochemical reaction system of any clause or example herein, in particular any one of Clauses 77-86, wherein each membrane reactor includes one or more catalysts. 
     Clause 88. The thermochemical reaction system of any clause or example herein, in particular Clause 87, wherein the one or more catalysts comprise single element nanoparticles, multi-element nanoparticles, or any combination thereof. 
     Clause 89. The thermochemical reaction system of any clause or example herein, in particular any one of Clauses 77-88, further comprising:
     a first inlet manifold that directs an inlet of gaseous reactants to the internal flow volume of each of the membrane reactors;   a first outlet manifold that collects unreacted gaseous reactants exiting the internal flow volume of each of the membrane reactors;   a second inlet manifold that directs an inlet of carrier or sweep gas to the product collection flow volume surrounding the membrane reactors;   a second outlet manifold that collects carrier gas, sweep gas, gaseous products, or any combination thereof exiting from the product collection flow volume; or   any combination of the above.   

     Clause 90. The thermochemical reaction system of any clause or example herein, in particular any one of Clauses 77-89, further comprising:
     a first fluid circuit loop that couples an outlet of the first outlet manifold to an inlet of the first inlet manifold so as to recirculate reactants to the membrane reactors;   a second fluid circuit loop that couples an outlet of the second outlet manifold to an inlet of the first inlet manifold, the second inlet manifold, or both, so as to recirculate carrier or sweep gas to the membrane reactors or to reuse the carrier or sweep gas as a reactant; or   any combination of the above.   

     Clause 91. The thermochemical reaction system of any clause or example herein, in particular any one of Clauses 77-90, wherein 
     the first fluid circuit loop comprises a heat exchanger constructed to remove heat from the recirculated reactants;   the second fluid circuit loop comprises a heat exchanger constructed to remove heat from an outlet flow from the second outlet manifold so as to separate or condense a gaseous product in the outlet flow;   the first fluid circuit loop, the second fluid circuit loop, or both comprise an electricity generator constructed to use the removed heat to generate electricity; or   any combination of the above.   

     Clause 92. The thermochemical reaction system of any clause or example herein, in particular any one of Clauses 77-91, further comprising:
     a hydrogen gas source and a nitrogen gas source,   wherein each gas source is coupled to the array of membrane reactors to provide the respective gas as input to the internal flow volumes of the membrane reactors,   the membrane reactors are constructed to discontinuously heat the hydrogen and nitrogen gases flowing within the internal flow volumes to cause a thermochemical reaction of the gases to produce ammonia.   

     Clause 93. The thermochemical reaction system of any clause or example herein, in particular any one of Clauses 77-91, further comprising:
     a source of first hydrocarbon gas,   wherein the source is coupled to the array of membrane reactors to provide the first hydrocarbon gas as input to the internal flow volumes of the membrane reactors,   the membrane reactors are constructed to discontinuously heat the first hydrocarbon gas flowing within the internal flow volumes to cause a thermochemical reaction of the first hydrocarbon gas to cause transformation thereof to other hydrocarbons and/or aromatics.   

     Clause 94. The thermochemical reaction system of any clause or example herein, in particular any one of Clauses 77-91, further comprising:
     a methane gas source and a nitrogen gas source,   wherein each gas source is coupled to the array of membrane reactors to provide the respective gas as input to the internal flow volumes of the membrane reactors,   the membrane reactors are constructed to discontinuously heat the methane and nitrogen gases flowing within the internal flow volumes to cause thermochemical reactions of the gases to produce ammonia, hydrocarbons, aromatics, or any combination thereof.   

     Clause 95. The thermochemical reaction system of any clause or example herein, in particular any one of Clauses 77-91, further comprising:
     a methane gas source and a carbon dioxide gas source,   wherein each gas source is coupled to the array of membrane reactors to provide the respective gas as input to the internal flow volumes of the membrane reactors,   the membrane reactors are constructed to discontinuously heat the methane and carbon dioxide gases flowing within the internal flow volumes to cause a thermochemical reaction of the gases to produce syngas.   

     Clause 96. The thermochemical reaction system of any clause or example herein, in particular any one of Clauses 77-91, further comprising:
     a source of hydrogen gas with particles or droplets of a polymer therein,   wherein the source is coupled to the array of membrane reactors to provide the hydrogen gas with the particles or droplets as input to the internal flow volumes of the membrane reactors,   the membrane reactors are constructed to discontinuously heat the particles or droplets in the hydrogen gas flowing within the internal flow volumes to cause a thermochemical reaction of the polymer to produce monomers, oligomers, hydrocarbons, aromatics, or any combination thereof.   

     Conclusion 
     Any of the features illustrated or described with respect to  FIGS.  1 A- 16 D  can be combined with any other features illustrated or described with respect to  FIGS.  1 A- 16 D  to provide systems, methods, devices, and embodiments not otherwise illustrated or specifically described herein. For example, the heating element configurations described with respect to  FIGS.  6 A- 10 B  can be applied to any of the reactor operations described with respect to  FIGS.  2 A- 4 B . Moreover, the heating element arrangement variations described with respect to  FIGS.  6 B- 6 D  can be applied to the heating element configurations described with respect to  FIGS.  7 A- 10 B , and vice versa. In still another example, the system configuration illustrated in  FIG.  11    could be applied to other thermochemical reaction processes besides ammonia production. Other combinations and variations are also possible according to one or more contemplated embodiments. Indeed, all features described herein are independent of one another and, except where structurally impossible, can be used in combination with any other feature described herein. 
     In view of the many possible embodiments to which the principles of the disclosed technology may be applied, it should be recognized that the illustrated embodiments are only preferred examples and should not be taken as limiting the scope of the disclosed technology. Rather, the scope is defined by the following claims. We therefore claim all that comes within the scope and spirit of these claims.