Magnetically resonant, inductively heated thermochemical apparatus and related methods

Abstract

The disclosure relates to inductively heated chemical apparatus and related methods. The apparatus include a magnetically resonant structure coupled with an electromagnetic coil to provide inductive heating to the magnetically resonant structure at near-unity coupling efficiencies. The magnetically resonant structure can be in the form of a coiled sheet, helical coil resonator, of split-ring resonator, for example. The apparatus can provide substantially homogeneous or otherwise tailored radial and axial heating and / or temperature profiles during operation. The apparatus can be used to perform endothermic reactions, separations, and other thermochemical processes.

Description

Atty. Docket No. 33929 / 70726 / US PATENT APPLICATIONMAGNETICALLY RESONANT, INDUCTIVELY HEATED THERMOCHEMICAL APPARATUS AND RELATED METHODS CROSS REFERENCE TO RELATED APPLICATION

[0001] Priority is claimed to U.S. Provisional Application No. 63 / 710,863 (filed October 23, 2024), which is incorporated herein by reference in its entirety.STATEMENT OF GOVERNMENT INTEREST

[0002] None.BACKGROUND OF THE DISCLOSUREField of the Disclosure

[0003] The disclosure relates to inductively heated chemical apparatus and related methods. The apparatus include a magnetically resonant structure coupled with an electromagnetic coil to provide inductive heating to the magnetically resonant structure at near-unity coupling efficiencies. The apparatus can provide substantially homogeneous or otherwise tailored radial and axial heating and / or temperature profiles during operation. The apparatus can be used to perform endothermic reactions, separations, and other thermochemical processes.Background

[0004] The thermochemical industry is a large contributor to the rise of global greenhouse gas emissions. Thus, the demand for sustainable heating of reactors, separators, and thermochemical apparatus is higher than ever.

[0005] The heating of volumetric media to high temperatures is the foundation of many gas-phase chemical reaction systems that involve elevated processing temperatures or endothermic heat requirements. The applications widely range from the selective capture of gases and the production of fuels and chemicals. The predominant source of heating for most high temperature reactor systems is the combustion of chemical fuels, such as methane and propane, which leads to the generation of carbon dioxide. Inductive heating is an established method for clean, efficient heating and is used domestically in inductive stove tops and industrially in the processing of raw materials such as metal smelting. However, an underlying challenge to provide inductively heated chemical reforming reactors that can support tailored volumetric heating profiles, efficient conversion of electricity to internal heat, enhanced heat and mass transfer, and integrated heat management (i.e., heat exchange).

[0006] US 11059719, US 2003 / 0175196, US 8871964, US 11059010, US 7767941 , US 2018 / 0243711 , US 5324904, and US 8647401 relate to the use of induction heating toAtty. Docket No. 33929 / 70726 / US PATENT APPLICATIONpower chemical reactions. There is no disclosure or suggestion of a resonant susceptor to achieve improved coupling.

[0007] RU 2375849C2 describes the resonant power transfer from a primary to secondary coils which is used for zone control. In this system, the resonator is not the structure being heated, there is only melting of conductive materials (i.e., no chemical reaction), and there is only axial power delivery control (i.e., not radial).

[0008] US 8292052 and CN 102201704B describes resonant power transfer, including to Swiss roll like structures. The structures are used as a magnetic field amplifier for improving electrical wireless power transfer (i.e., not used as a susceptor for induction heating), and there is no application thermochemical reactors or reactions.

[0009] US 10302400 describes the ability of Swiss rolls to act as absorbers of electromagnetic energy, but only in the context of cloaking and not for thermochemical reactors or reactions.

[0010] US 11286169 describes a countercurrent Swiss roll reactor. The reactor is only used to perform exothermic reactions in which the reaction itself provides heat, and there is no induction heating of reactants to drive endothermic reactions.

[0011] US 7973296 describes spiral conductors which look like Swiss rolls which are resonantly excited to produce electromagnetic (EM) waves, which then produce a plasma to power a chemical reaction (i.e., there is no induction-based thermal energy from joule heating to drive the reaction or separation process).SUMMARY

[0012] The disclosure relates to inductively heated chemical reactors and other apparatus as well as related methods. The apparatus include a magnetically resonant structure coupled together along with an electromagnetic coil to provide inductive heating to the magnetically resonant structure. The apparatus exhibit near-unity coupling efficiencies, can provide substantially homogeneous or otherwise tailored radial and axial heating and / or temperature profiles during operation, and can be applied to variety of reaction systems, for example endothermic reactions, and well as separation systems and other thermochemical systems.

[0013] In an aspect, the disclosure relates to inductively heated chemical apparatus (e.g., reactor, separator) comprising: a magnetically resonant structure comprising an electrically conductive body (e.g., Swiss roll, helical coil, split ring, or other resonant structure), wherein: the magnetically resonant structure has a characteristic or fundamental resonance frequencyAtty. Docket No. 33929 / 70726 / US PATENT APPLICATION(wR) (and higher order resonance frequencies WR ), and the magnetically resonant structure at least partially defines or occupies an interior volume (e.g., internal flow and reaction volume, such as in combination with an outer reactor / vessel wall); optionally a dielectric material in the interior volume (e.g., as a component / layer of the magnetically resonant structure on the electrically conductive body, or a particulate or other free material adjacent to the electrically conductive body, or as a gas or liquid) and at least one electromagnetic coil proximal to the magnetically resonant structure and adapted to produce an alternating electromagnetic field at a predetermined operating frequency (wE) sufficiently close to the resonance frequency such that the alternating electromagnetic field (i) inductively couples to the magnetically resonant structure, and (ii) inductively heats the magnetically resonant structure (e.g., the electrically conductive body and dielectric material thereof) when AC electrical power at the predetermined operating frequency is applied to the at least one electromagnetic coil.

[0014] Various refinements and embodiments of the disclosed inductively heated chemical apparatus are possible.

[0015] In a refinement, the apparatus further comprises: a vessel (outer) wall enclosing (e.g., immobilizing or retaining) the magnetically resonant structure or structures, wherein the vessel wall optionally at least partially defines the interior volume. In a further refinement, the vessel wall can comprise (e.g., be formed from) an electrically insulating material (e.g., ceramics, glasses, and plastics) or an electrically conductive material (e.g., metals, conductive carbons, conductive ceramics, and combinations thereof). In a further refinement, the apparatus can further include thermal insulation interposed between the vessel wall the at least one electromagnetic coil (e.g., thermal insulation around the outer vessel wall), and / or thermal insulation placed between the outer vessel wall and the magnetically resonator structure.

[0016] In a refinement, the apparatus further comprises: a power supply electrically connected to the at least one electromagnetic coil and adapted to provide the AC electrical power at the predetermined operating frequency, thereby generating an alternating electromagnetic field (e.g., having a wavelength corresponding to the predetermined operating frequency), which transfers power to and inductively heats the magnetically resonant structure. In a further refinement, the predetermined operating frequency can be in a range of 1 kHz to 100 MHz.

[0017] In a refinement, the electrically conductive body is in the form of a (cylindrically) coiled sheet (e.g., a Swiss roll).Atty. Docket No. 33929 / 70726 / US PATENT APPLICATION

[0018] In a refinement, the electrically conductive body is in the form of a helical coil resonator.

[0019] In a refinement, the electrically conductive body is in the form of a split ring resonator.

[0020] In a refinement, the electrically conductive body is in the form of a flat spiral resonator (a thin / flattened analog of a Swiss roll with a circular, rectangular, or other spiral design).

[0021] In a refinement, the electrically conductive body comprises one or more structural features (e.g., surface modifications, geometry selections, etc.) selected from the group consisting of cut-outs (or perforations / gaps / voids, such as in a mesh structure), wrinkles (e.g., non-smooth outer surface), non-uniform spacing (e.g., spacing between adjacent rings or coils in a Swiss roll or helical coil), and combinations thereof. Such structural modifications can be used to tailor or adjust the electromagnetic resonance response (e.g., resonance frequency, coupling efficiency, etc.) of the electrically conductive body.

[0022] In a refinement, the apparatus comprises a plurality of magnetically resonant structures. In a further refinement, the magnetically resonant structures have the same electrically conductive body, the same dielectric material, the same resonance frequency, and the same interior volume. In a further refinement, the magnetically resonant structures have at least one of different electrically conductive bodies, different dielectric materials, different resonance frequencies, and different interior volumes. In a further refinement, at least a portion of the plurality of magnetically resonant structures is removable and / or replaceable from the inductively heated chemical apparatus, while a remainder of the plurality of magnetically resonant structures remains in the inductively heated chemical apparatus. In a further refinement, the inductively heated chemical apparatus contains 2 to 1000 magnetically resonant structures.

[0023] In a refinement, the resonance frequency is in a range of 1 kHz to 100 MHz.

[0024] In a refinement, the magnetically resonant structure has multiple resonance frequencies (WR ).

[0025] In a refinement, the predetermined operating frequency (wE) and the resonance frequency (wR) are different such that (Qx|1 - wE / wR|) is in a range of 0.001 to 2, where Q is a resonance quality factor characteristic of the magnetically resonant structure.Atty. Docket No. 33929 / 70726 / US PATENT APPLICATION

[0026] In a refinement, a coupling efficiency between the electromagnetic coil and the magnetically resonant structure is in a range of 80% to 100%.

[0027] In a refinement, the electrically conducting body comprises a material selected from the group consisting of metals, conductive carbons, conductive ceramics, and combinations thereof.

[0028] In a refinement, the electrically conducting body has an electrical conductivity in a range of 1,000 to 100,000,000 S / m or 10,000 to 10,000,000 S / m; and / or the electrically conducting body has a thermal conductivity in a range of 0.1 to 500 W / (m»K).

[0029] In a refinement, the dielectric material (when present) comprises a material selected from the group consisting of metal oxides and combinations thereof.

[0030] In a refinement, the dielectric material (when present) comprises a material selected from the group consisting of insulating polymers, gas materials, liquid materials, and combinations thereof.

[0031] In a refinement, the apparatus further comprises a catalyst in the interior volume of the magnetically resonant structure (e.g., a catalyst selected or utilized for performing some specific chemical reaction).

[0032] In a refinement, the apparatus further comprises a membrane in the interior volume of the magnetically resonant structure (e.g., to perform separations between reactant or product gases in a reactive system, or between a feed gas mixture in a non-reactive system).

[0033] In a refinement, the apparatus further comprises a sorbent in the interior volume of the magnetically resonant structure (e.g., for use in a separation process, such as a pressure swing or temperature swing adsorption process).

[0034] In a refinement, the at least one electromagnetic coil has a characteristic diameter; and the at least one electromagnetic coil is spaced apart from the magnetically resonant structure by a distance up to the characteristic diameter.

[0035] In a refinement, the magnetically resonant structure is configured to provide a substantially constant heating profile (e.g., by balancing dielectric losses against resistive losses). In a further refinement, a material thickness of the magnetically resonant structure is selected to balance countercurrent and charging current losses in the magnetically resonant structure. In a further refinement, the apparatus comprises the dielectric materialAtty. Docket No. 33929 / 70726 / US PATENT APPLICATIONpositioned at outer radial positions of the inner volume, but not at inner radial positions of the inner volume.

[0036] In a refinement, the magnetically resonant structure is configured to provide a center-dominated heating profile.

[0037] In a refinement, the magnetically resonant structure is configured to provide an edge-dominated heating profile.

[0038] In a refinement, the magnetically resonant structure further defines: an inlet region (e.g., area / plane); and an outlet region (e.g., area / plane) in fluid communication with the inlet region through the interior volume defined by the magnetically resonant structure (e.g., and optionally its vessel). The magnetically resonant structure, typically in combination with an outer vessel wall, would include a single inlet and a single outlet at opposing ends of the interior volume through which fluid flows during reaction in an inlet-interior volume-outlet flow path.

[0039] In another aspect, the disclosure relates to a method for performing a chemical reaction (e.g., an endothermic chemical reaction), the method comprising: feeding a fluid stream comprising a reactant (e.g., one or more reactant species optionally in admixture with one or more diluents in gas and / or liquid phase) to the interior volume of the magnetically resonant structure in the inductively heated chemical apparatus according to the disclosure; applying AC electrical power at a predetermined operating frequency to the at least one electromagnetic coil while the fluid stream flows through the interior volume, thereby generating an alternating electromagnetic field at a predetermined operating frequency (wE) sufficiently close to the resonance frequency such that the alternating electromagnetic field (i) inductively couples to the magnetically resonant structure, (ii) inductively heats the magnetically resonant structure (e.g., the electrically conductive body thereof), (iii) heats the fluid stream flowing through the interior volume, and (iv) chemically reacts the reactant to form a product (e.g., one or more product species optionally in admixture with unreacted reactant species and / or one or more diluents in gas and / or liquid phase); and removing the fluid stream comprising the product from the interior volume.

[0040] In another aspect, the disclosure relates to a method for performing a chemical separation, the method comprising: feeding a fluid stream comprising a target species (e.g., one or more component species to be separated / recovered from a mixture with one or more other component species in gas and / or liquid phase) to the interior volume of the magnetically resonant structure in the inductively heated chemical apparatus according to the disclosure; capturing the target species in a sorbent material in the interior volume of theAtty. Docket No. 33929 / 70726 / US PATENT APPLICATIONmagnetically resonant structure (e.g., adsorbing or absorbing the target species in the sorbent at an ambient or otherwise low temperature); and heating the sorbent material (e.g., via application of AC power to the coil) to release the target species into a product stream (e.g., desorb and recover the target species into a different desorption carrier gas via sorbent heating once the sorbent nears or reaches its saturation point for the target species).

[0041] In another aspect, the disclosure relates to a method for heating a heat transfer fluid, the method comprising: feeding a heat transfer fluid to the interior volume of the magnetically resonant structure in the inductively heated chemical apparatus according to the disclosure and heating the heat transfer fluid therein (e.g., via application of AC power to the coil); and feeding the heated heat transfer fluid exiting the inductively heated chemical apparatus as a hot-side fluid to a heat exchanger.

[0042] In another aspect, the disclosure relates to a method for performing a chemical separation, the method comprising: performing a distillation separation in a distillation column, wherein heat for a reboiler component of the distillation column is provided by the inductively heated chemical apparatus according to the disclosure.

[0043] While the disclosed apparatus, methods, and compositions are susceptible of embodiments in various forms, specific embodiments of the disclosure are illustrated (and will hereafter be described) with the understanding that the disclosure is intended to be illustrative, and is not intended to limit the claims to the specific embodiments described and illustrated herein.BRIEF DESCRIPTION OF THE FIGURES

[0044] Figure 1 illustrates (A) a side view of an inductively heated chemical apparatus according to the disclosure; and (B) a top cross-sectional view of the apparatus with a coiled sheet resonant structure.

[0045] Figure 2 illustrates perspective views of magnetically resonant structures according to the disclosure, including (A) a spiral Swiss roll (or cylindrically coiled sheet) with illustrative dimensions of ro=5mm, d=5mm, N=3, t=2.5mm, and h=50mm; (B) a helical coil resonator; and (C) a split ring resonator.

[0046] Figure 3 illustrates perspective views of magnetically resonant structures according to the disclosure, including (A) a square Swiss roll (or square / rectangular coiled sheet); (B) a lattice of multiple Swiss rolls which could have the same or different geometry and / or could be driven together or individually; and (C) a pair of concentric Swiss rolls.Atty. Docket No. 33929 / 70726 / US PATENT APPLICATION

[0047] Figure 4 illustrates relative positioning between the magnetically resonant structure(s) and the electromagnetic coil, including (A) Swiss roll (or other) resonant structure with electromagnetic driving coil placed centered around it; (B) Swiss roll (or other) resonant structure lattice with coil which can mechanically index over sites at different spatial locations (to selectively couple with a specific resonant structure); and (C) a linear array of Swiss rolls (or other) resonant structures which can be individually driven by frequency multiplexing.

[0048] Figure 5 is a graph illustrating power dissipation as a function of radius for Swiss rolls exhibiting center heating, uniform heating, and edge heating.

[0049] Figure 6 is a graph illustrating power dissipation as a function of radius for the primary and secondary modes of a Swiss roll.

[0050] Figure 7 is a schematic illustrating the current in a roll (or other) resonant structure in which arrow size increases with increasing current, including (A) charging or net current; and (B) surface or circulating current which is proportional in magnitude to the local magnetic field (e.g., where net current in panel (A) is defined as a difference outer minus inner surface currents in panel (B)).

[0051] Figure 8 is a graph illustrating near uniform power profile achieved in a Swiss roll via appropriate selection of metal thickness such that power dissipated by the charging current approximately matches that dissipated by the circulating current.

[0052] Figure 9 is a graph illustrating power dissipation as a function of frequency in a Swiss roll with ro=3mm, d=1 ,75mm, t=.6mm, N=25, and h= infinite for several metal conductivities driven with a uniform 2A / m magnetic field.

[0053] Figure 10 includes graphs illustrating (A) relationship between height of Swiss roll and resonance frequency for a roll with ro=5mm, d=3mm, t=1 mm, and N=10; and (B) the power per meter of height of Swiss roll as a function of frequency. Notably, the shorter Swiss roll shows a lower quality factor.

[0054] Figure 11 is a graph illustrating heating profiles in a Swiss roll with r0=11.75mm, d=1 ,75mm, t=.04mm, N=20, and h=inf inite. The loss tangent of the dielectric is set to tan(delta)=0.02.

[0055] Figure 12 includes graphs illustrating (A) the experimental and simulated impedance as seen by a single turn coil placed around the Swiss roll; (B) experimental and simulated temperature increase profile in the Swiss roll; and (C) experimental temperature increase profile in the Swiss roll with an added silica cloth dielectric layer.Atty. Docket No. 33929 / 70726 / US PATENT APPLICATION

[0056] Figure 13 is a graph illustrating carbon dioxide conversion as a function of gas hourly space velocity (GHSV) using a Swiss roll operating as a reactor (solid line) as compared to an equilibrium conversion curve for a conventional plug flow reactor (dashed line).DETAILED DESCRIPTION

[0057] The disclosure relates to the induction heating of electromagnetically resonant metamaterial structures, including geometries such as split ring resonators, Swiss rolls (or coiled sheets), and helical coils. An external alternating magnetic field, generated by a conductive coil driven with a sinusoidal wave, generates electromotive forces in the structure, inducing currents that dissipate as Joule heat. Operation at or near the resonant frequency of this structure, which is defined by the self-capacitance and inductance of the structure, allows for near-unity coupling efficiencies (i.e., transfer of electrical energy at the input to the driving coil to thermal energy within the resonator structure) for a wide range of possible device and induction coil layouts. Generally, the detailed geometry of the resonant structures can be tailored to produce both radially and axially tailorable temperature profiles.

[0058] The electromagnetically resonant metamaterial structures can be incorporated in various thermochemical systems, for example for in gas phase thermochemical conversion and separations systems which benefit greatly from the desirable properties associated with the resonant coupling. The disclosed resonant structures and corresponding inductively heated apparatus provide efficient, tailored volumetric heat delivery, which is desirable for driving and / or controlling reactive and other thermochemical systems.

[0059] Several advantages of using resonant structures as conductive susceptors of electromagnetic energy ultimately derive from their near-unity efficiency coupling. As discussed in more detail below, these advantages include simpler implementation, higher performance, and altogether distinct operating regimes.

[0060] In common high-power induction heating systems such as those used in metalworking, the l2R (i.e., electrical current I and resistance R) losses associated with the coupling inefficiency between the susceptor and drive coil result in significant parasitic heating of the drive coil. In the case of the resonant structures, high intrinsic coupling efficiency can allow for delivery of significant power to the target while substantially reducing any parasitic heating loss in the coil, thus mitigating the need for complex and expensive coil cooling systems. In particular, this can allow more modular implementation of devices including this technology.Atty. Docket No. 33929 / 70726 / US PATENT APPLICATION

[0061] Additionally, the use of a magnetically resonant structure as a susceptor makes concerns of parasitic coupling to nearby electrical conductors less of a concern, as relative coupling to the resonant susceptor is enhanced compared to non-resonant coupling to other neighboring metallic media. This allows the use of metal elements in, for example, support structures or pressurized shells for the apparatus, without a significant reduction in heating efficiency, whereas in typical non-resonant induction heating systems, any nearby metals will experience relatively high levels of heating, representing both wasted power and potential safety or structural hazards. This is especially useful in applications which utilize pressurized metal shells, where the electromagnetic boundary conditions require the coil to be significantly smaller than the vessel size for efficient coupling, wasting space and reducing performance.

[0062] Induction heating systems are typically driven with a resonant tank circuit, with current resonating back and forth between the inductive coil and an external capacitor. For a system inside a metallic pressure vessel, the significant currents going through the electrical pass throughs in this vessel complicate their design, a problem which the use of resonant devices largely obviates. Further, parasitic capacitance at those passthroughs can complicate matching networks and current profiles, presenting additional design, control, and manufacturing hurdles.

[0063] Another advantage of magnetically resonant structure as a medium for electromagnetic heating is the geometric flexibility it allows due to its intrinsically high coupling efficiency. This allows the position of the drive coil to be flexibly placed relative to the structure, generally at standoff distances that are within the drive coil diameter, without incurring significant reductions in heating efficiency. With conventional non-resonant induction heating, on the other hand, the device to be heated must be co-located with the coil to ensure maximal power transfer. Removing this constraint can simplify system design and allow new operating regimes.

[0064] In the context of thermochemical reactors, an advantage of offsetting the distance of the drive coil from the reactor is that it becomes possible to place additional insulation around the reactor, hence decreasing thermal conduction losses (e.g., of energy that otherwise is used to drive an endothermic reaction). In another embodiment, several resonant structures with different resonant frequencies can be placed near each other and a single coil can heat the rolls in a frequency multiplexed manner, enabling custom power spatial profiles. An array of identical resonant structures over which a coil is mechanicallyAtty. Docket No. 33929 / 70726 / US PATENT APPLICATIONindexed can also be used to heat specific devices, as may be the case in temperature swing absorption systems where only part of a reactor may require heating at any instance in time.

[0065] Using an electromagnetic resonator as a magnetic field enhancement device could be used in more traditional inductive heating applications, wherein a traditional coil excites the resonator which amplifies the magnetic field to heat something in its interior. Such a setup has several possible advantages. First, the outside coil can be made to dissipate near zero power, while the resonator which does dissipate power can be placed inside the insulation and thereby power dissipated in it can be considered useful. Second, as many magnetic resonators naturally exhibit length-wise uniform heating, the coil itself could be made much shorter. The coiled sheet (or Swiss roll) is particularly suitable for this application due to the uniform magnetic field in its interior and the ease of sealing it.

[0066] A variant of the coiled sheet (or Swiss roll) reactor concept includes of two concentric coiled sheets. In this reactor, a fluid travels inwards through one port located at the reactor perimeter and circulates into the interior of the reactor, followed by an outward flow path to an exit port also located at the reactor perimeter. As the inner and outer flow pathways are in adjacent channels throughout the reactor, they are able to effectively exchange heat and thereby naturally form a high-performance countercurrent heat exchanger that can effectively recover sensible heat with high efficiencies. This performs similar to a conventional spiral plate heat exchanger, except it also integrates both heating and chemical reactions into the same structure. This configuration also exhibits high surface area between the two rolls for the occupied volume, implying that a bias could be placed between the two for electrochemical purposes.

[0067] Figure 1 illustrates an inductively heated chemical apparatus 100 according to the disclosure, including side view (panel A) and a top cross-sectional view (panel B). The apparatus 100 can be chemical reactor, a separator, or other thermochemical apparatus. The apparatus 100 includes a magnetically resonant structure 200 having an electrically conducting body 210, a dielectric material 218, and an electromagnetic coil 300 for inductively heating the resonant structure 200 when AC electrical power is applied to the electromagnetic coil 300, and intervening reactor body 400. The magnetically resonant structure 200 has a (characteristic) fundamental resonance frequency (wR) (e.g., and one or more higher order resonance frequencies wR,j). AS described and illustrated in more detail below, the magnetically resonant structure 200 can include structures such as a Swiss roll (or coiled sheet), helical coil, split ring, or other resonant structure. The magnetically resonant structure 200 can at least partially define an interior volume 220. The interiorAtty. Docket No. 33929 / 70726 / US PATENT APPLICATIONvolume 220 can represent an internal flow and / or reaction volume, such as in combination with an outer reactor / vessel wall 400. The dielectric material 218 in the interior volume 220 can be a component / layer of the magnetically resonant structure 200 on the electrically conductive body 210, or a particulate or other free material adjacent to the electrically conductive body 210, or a gas or liquid adjacent to the electrically conductive body 210. The electromagnetic (or induction) coil 300 is positioned proximal to the magnetically resonant structure 200 and is adapted to produce an electromagnetic field when AC electrical power is applied to the at least one electromagnetic coil 300 at a predetermined operating frequency (wE). The predetermined operating frequency is sufficiently close to the resonance frequency such that the alternating electromagnetic field (i) inductively couples to the magnetically resonant structure, and (ii) inductively heats (e.g., via Joule heating) the magnetically resonant structure (e.g., the electrically conductive body and dielectric material thereof) when AC electrical power at the predetermined operating frequency is applied to the at least one electromagnetic coil). The produced electromagnetic field inductively couples to the resonant structure 200, thereby inductively heating the plurality of resonant structure 200 and any contents in the adjacent interior volume 220 (e.g., chemical reactants or products).

[0068] In embodiments, the reactor or apparatus 100 can further include a reactor (or outer) wall 400 enclosing, for example immobilizing or retaining, the resonant structure(s) 200 in the apparatus 100. The vessel wall 400 can at least partially define the interior volume 220, for example in combination with the magnetically resonant structure(s) 200 that together define an enclosed volume corresponding to the reactor or apparatus internal volume. In some embodiments, the reactor or vessel wall 400 advantageously can be formed from stainless steel or other metal alloy suitable for a high-pressure / high-temperature reactor or other chemical application. Because of the high degree of resonant coupling between the electromagnetic coil 300 and the magnetically resonant structure 200, there is little to no appreciable inductive heating of a metal or otherwise electrically conductive vessel 400 material. Accordingly, the vessel 400 may be predominantly comprised of metal and need not be formed from electrically insulating / non-conducting materials as for other inductive heating apparatus). In other embodiments, however, the reactor wall 400 can be an electrically insulating or electrically non-conducting material interposed between the conductive resonant structure 200 and the electromagnetic coil 300, such as being formed from or otherwise including plastic, glass, and / or refractory ceramic material(s).

[0069] In some embodiments, the reactor or apparatus 100 can further include thermal insulation 410 interposed between the vessel wall 400 the at least one electromagnetic coil 300, for example including a thermal insulation material 410 wrapped around or substantiallyAtty. Docket No. 33929 / 70726 / US PATENT APPLICATIONenclosing the outer vessel wall 400. Alternatively or additionally, some amount of thermal insulation 420 may be placed between the outer vessel wall 400 and the magnetically resonator structure 200.

[0070] In embodiments, the reactor 100 can further include or otherwise be electrically connected to a power supply 500 through the electromagnetic coil 300. The power supply 500 is adapted to provide the AC electrical power at a predetermined operating frequency to the coil 300, thereby generating an alternating electromagnetic field (e.g., having a wavelength corresponding to the predetermined operating frequency). The alternating electromagnetic field generated by the coil 300 which transfers power to and inductively heats the magnetically resonant structure 200. The power supply 500 generally can include any suitable power amplifier adapted to receive electrical power and output a periodic electrical signal at a specified / desired frequency, for example a frequency that is selectable or tunable for compatibility with the resonance frequency of a given magnetically resonant structure 200. The predetermined operating frequency suitably can be selected to have a value in a range of 1 kHz to 100 MHz.

[0071] The resonant structure 200 and / or the corresponding interior volume 220 of the apparatus 100 can include a reaction catalyst, for example when the apparatus is intended to operate as a chemical reactor for a given catalytic reaction. In embodiments, the interior volume 220 can be filled with catalyst pellets, or be filled with a structured catalyst component that enhances reaction engineering properties and capabilities. For example, the interior volume 220 of the resonant structure 200 and / or vessel wall 400 can include a catalyst 240 therein. For example, the catalyst 240 can be a coating on the electrically conductive body 210, a loose particle packing in the interior volume 220, a structured catalyst in the interior volume 220, etc. The catalyst 240 can be present in or along a portion or the entire length of the interior volume 220, for example a reactor 100 having a catalystcontaining central region along with no-catalyst pre-heating and / or post-heating regions near the inlet 224 and the outlet 226, respectively. For heterogeneous chemical reactions, the catalyst 240 can be a solid phase material or a component of a solid phase material. For homogenous chemical reactions, the catalyst can be a dissolved species in a liquid reaction medium containing reactants and / or products, or it can be a gaseous species admixed in a gas reaction medium containing reactants and / or products. The specific catalyst 240 used is not particularly limited and can be suitably selected by the skilled artisan based on the specific chemical reaction performed (or intended to be performed) in the reactor 100.Resonant Structure and Apparatus OperationAtty. Docket No. 33929 / 70726 / US PATENT APPLICATION

[0072] Additional features related to structure and operation of the inductively heated chemical apparatus 100 are described in detail below.

[0073] The magnetically resonant structure 200 includes or is formed from an electrically conducting body 210 that at least partially defines an interior volume 220, typically in combination with the vessel wall 400. For example, the vessel wall 400 can define an enclosed volume containing one or more magnetically resonant structures 200 therein, and interstitial or other open spaces defined by the magnetically resonant structure 200 or the electrically conducting body 210 in the enclosed volume correspond to the interior volume 220. The interior volume 220 can correspond to an internal fluid flow and / or reaction volume for fluid phase (e.g., gas and / or liquid) reactants and products being fed to, formed in, and / or removed from the apparatus 100, for example when the apparatus 100 is a reactor performing a chemical reaction. The interior volume 220 can define or otherwise have a longitudinal direction 228 as a (bulk) fluid flow path or direction through the interior volume 220. For example, the longitudinal direction 228 can be an axial direction (e.g., z-direction, such as in a cylindrical r-0-z coordinate system as illustrated, or in a cartesian x-y-z coordinate system (not shown)), and the magnetically resonant structure 200 / wall 400 can define a central axis through the interior volume 220.

[0074] The magnetically resonant structure 200 and vessel wall 400 can define or otherwise include an inlet region 224 and an outlet region 226. The inlet and outlet regions 224, 226 can represent an area or plane across which reactants 110 can flow into the reactor 100 and interior volume 220, and products 120 can flow out of the reactor 100 and interior volume 220. The inlet and outlet regions 224, 226 are in fluid communication with each other via through the interior volume 220 of the magnetically resonant structure 200. A corresponding apparatus (or reactor) 100 typically would include a single inlet 224 and a single outlet 226 at opposing ends of the interior volume 220 through which fluid flows during reaction in an inlet-interior volume-outlet flow path, thus providing a generally axial flow through the apparatus 100 as illustrated in Figure 1 (panel (A)). In other embodiments, the apparatus 100 can include multiple and / or alternate inlets or outlets. For example, the apparatus 100 can include a radial inlet region 225 at an outer circumferential region of the apparatus 100 and / or magnetically resonant structure 200 as illustrated in Figure 1 (panels (A) and (B)). This can be suitable when the magnetically resonant structure 200 has a spiral or coiled structure such that the reactants 110 or other feed materials can flow radially inward in a spiral channel toward the center of the resonant structure 200, where the final products 120 or other outlet materials can then exit the apparatus 100, for example via an axially positioned outlet region 226.Atty. Docket No. 33929 / 70726 / US PATENT APPLICATION

[0075] The specific material(s) used for the magnetically resonant structure 200 and / or its electrically conducting body 210 are not particularly limited as long they have sufficient electrical conductivity for inductive heating and are able to withstand the highest temperatures during any intended chemical reaction or other thermochemical process carried out in the apparatus 100. Suitable electrical conductivity values for the resonant structure materials can be 10 to 100,000,000 S / m, 10,000 to 10,000,000 S / m, or 1000 to 1,000,000 S / m, for example at least 10, 20, 50, 100, 200, 500, 1000, 2000, 5000, 10000, 20000, 50000, 100000, 200000, or 500000 S / m and / or up to 100, 200, 500, 1000, 2000, 5000, 10000, 20000, 50000, 100000, 200000, 500000, 1000000, 2000000, 5000000, 10000000, 20000000, 50000000, or 100000000 S / m. In some embodiments, the resonant structure can be selected to have a desired thermal conductivity to promote heat conduction between adjacent susceptors and further reduce temperature gradients in the apparatus 100. Suitable thermal conductivity values for the susceptor materials can be 0.1 to500 W / (m»K) or 1 to 100 W / (m»K), for example at least 0.1 , 0.2, 0.5, 1, 2, 5, 10, 20, 50, or 100 W / (m»K) and / or up to 1, 2, 5, 10, 20, 50, 100, 200, or 500 W / (m»K). Example materials can include metals, conductive carbons, and conductive ceramics, such as where the resonant structure 200 and / or the body 210 is formed from or otherwise contains one or more of the foregoing materials. For high-temperature applications greater than 600°C, superalloy materials including iron-based superalloys such as FeCr alloy (magnetic), titanium, graphite, and nickel superalloys (non-magnetic) can be inductively heated to very high temperatures of around 1000°C. Similarly for high-temperature applications greater than 600°C, conductive ceramics such as silicon carbide (SiC) and silicon-silicon carbide (SiSiC) can be used as well as various metals able to withstand (e.g., not melt at) higher temperatures, such as steel, stainless steel, and titanium. For temperatures below 600°C, the susceptor materials can include steel, stainless steel, aluminum, brass, titanium, nickel, chromium, copper, and / or alloys including the foregoing. Conductive carbon materials such as reticulated vitreous carbon, carbon nanotubes, and / or graphite can also be used. In cases where low-temperature applications are desired, other electrically conductive materials can be become viable, for example conductive polymers.

[0076] Electromagnetic resonator structures and metamaterials can be modeled as classical LC circuits in which oscillations between charge stored in the self-capacitance and current driven by the self-inductance of the system can be excited via electromagnetic fields. The resonant structures can concentrate low amplitude magnetic fields at their resonant frequencies (wR; or more generally a plurality of frequencies wR,j (e.g., i=1 , 2, 3, etc.) accounting for primary and higher order resonance frequencies), enabling more efficientAtty. Docket No. 33929 / 70726 / US PATENT APPLICATIONwireless power transfer for applications such as wireless charging and wireless heating. When used for heating, an external electromagnetic input produced by an external coil at or near the structure’s resonance frequency can excite a very large response in the structure at steady state, resulting in large induced currents in the resonant structures that dissipate as heat. In this regime, the relative amount of power dissipated in the external coil is small compared to the amount of power dissipated in the resonant susceptor, yielding a highly efficient coupling.

[0077] The high coupling efficiencies between the combined external coil-resonant structure system can be represented with a circuit model of the system which includes a transformer with the secondary coil shorted by a frequency-dependent resistor representing the resonant structure. At resonance, the impedance of this resistor is very large, meaning that parasitic losses in the transformer are comparatively small, yielding efficient power delivery. Phrased differently, the external coil is driven by a high voltage and low current source, minimizing Joule heating losses in the coil, while the large magnitudes of the induced currents in the resonant structure enhance its power dissipation and heating. This operation regime contrasts with typical non-resonant induction heating systems where the effective impedance of the susceptor is relatively low and more current in the external coil is required for equivalent power delivery. There is a broad family of electromagnetic resonator metamaterials which can be selected depending on details such as desired operation frequency, power distributions, manufacturing considerations, and reaction / process of interest. For example, the electrically conductive body 210 can be in the form of a cylindrically coiled sheet (or “Swiss roll”) as illustrated in Figure 2 (panel A). The coiled sheet structure generally exhibits lower resonance frequencies due to higher capacitance and can be used as an internal structural element in a reactor or other apparatus, for example where gaps between adjacent spiral / coil elements define flow channels as the interior volume 220 of the apparatus 100. The coiled sheet can have any suitable shape or geometry other than the illustrated cylindrical shape. For example, the coiled or spiral sheet can have square or rectangular shape for a duct / channel design, a triangular, hexagonal, or other (regular) polygonal shape (not shown) for a structural design, etc. The magnetically resonant structure can include two electrically conductive bodies concentrically aligned or otherwise interlaced with each other, whether with cylindrical shapes or other rectangular / other shapes. Alternatively, the electrically conductive body 210 can be in the form of a helical coil as also illustrated in Figure 2 (panel B). The helical coil can be manufactured cheaply and simply by spring-making machines. Similarly, the electrically conductive body 210 can be in the form of a split-ring resonator as also illustrated in Figure 2Atty. Docket No. 33929 / 70726 / US PATENT APPLICATION(panel C). The split ring resonator has the simplest geometry and the highest resonant frequency.

[0078] The geometry of the resonant structure is generally flexible, and a whole class of similar structures will work equivalently. For example, instead of a cylindrical spiral geometry, a Swiss roll / coiled sheet structure for the electrically conductive body 210 can be a manufactured with rectangular geometry as illustrated in Figure 3 (panel A). Likewise, a coil could be made in a square geometry, or with multiple layers. This could allow the devices to pack more tightly in an array as also illustrated in Figure 3 (panel B). Further, this array can feature structures with similar or distinct resonance frequencies, allowing individual or sets of structures to be controllably heated. The resonant structure 200 can also include two concentric or interleaved electrically conductive bodies 210i, 2102 as also illustrated in Figure 3 (panel C), resulting in a strong coupling between the resonances. This could be beneficial for structural purposes, increasing power density, etc.

[0079] The intrinsically high coupling efficiency of resonant susceptors or structures 200 allows a variety of drive coil 300 setups. The electromagnetic coil 300 suitably can be a single turn coils of copper wire (or other metallic / electrically conductive material), but generally any geometry which generates a magnetic field from input electrical power can be used as well. Figure 4 illustrates several options for the spatial relationship between the electromagnetic coil 300 and the resonant structure(s) 200. For example, placing the coil 300 directly around the electromagnetic resonant structure 200 as shown in Figure 4 (panel A) results in optimal coupling, minimizing the (energy or heating) losses in the coil 300.Alternatively, the coil 300 can be offset from the resonant structure(s) 200, allowing it to be mechanically indexed over an array of structures 200i, 2OO2, etc. as shown in Figure 4 (panel B). The structures in the array could have the same or varying resonant frequencies. Multiple resonant structures 200could also be placed axially or laterally within a surrounding coil 300, and, by frequency multiplexing, different amounts of heat could be selectively delivered to some as shown in Figure 4 (panel C).

[0080] As illustrated in Figure 3 (panel B) and Figure 4 (panels B and C), the apparatus 100 can include a plurality of magnetically resonant structures 200 (e.g., 200i, 2OO2, ... 200nfor n resonant structures). For example, the apparatus 100 can include a plurality of magnetically resonant structures 200 in parallel with fluid flowing through the reactor / apparatus being partitioned between the different resonant structures. The separate magnetically resonant structures 200 can have the same or different shapes, materials, and / or resonant frequencies relative to each other. Additionally or alternatively, theAtty. Docket No. 33929 / 70726 / US PATENT APPLICATIONapparatus can include a plurality of magnetically resonant structures 200 serially positioned relative to each other (e.g., same or different shapes, materials, and / or resonant frequencies) with fluid flowing through the reactor / apparatus passing from one resonant structure to an adjacent downstream resonant structure. Whether in parallel or serial arrangement, the magnetically resonant structures 200 can have the same (or identical) electrically conductive body, the same (or identical) dielectric material, the same (or identical) resonance frequency, and / or the same (or identical) interior volume relative to each other. Alternatively, in parallel or serial arrangement, the magnetically resonant structures 200 can have at least one of different electrically conductive bodies, different dielectric materials, different resonance frequencies, and different interior volumes.

[0081] In some embodiments, at least a portion of the plurality of magnetically resonant structures 200 can removable and / or replaceable from the inductively heated chemical apparatus 100, for example being removable and / or replaceable from within a reactor wall 400 or vessel containing the resonant structures 200. In such cases, a remainder of the plurality of resonant structures 200 remains in the inductively heated chemical apparatus 100, and such remaining resonant structures 200 can be in use performing reactions or other processes while the removed susceptors are still absent. This can reflect a modular design, which provides operational benefits in addition to assembly / manufacturing benefits, for example allowing for selective resonant structure 200 removal for cleaning, replacement, new / fresh catalyst loading, etc., while maintaining operation up-time in other resonant structures 200.

[0082] In some embodiments, the inductively heated chemical apparatus 100 contains 2 to 1000 resonant structures 200. In general, any number resonant structures 200 can be used, for example at least 2, 4, 6, 8, 10, 12, 15, 20, 30, 40, 50, 60, 80, 100, 200, or 500 and / or up to 4, 6, 8, 10, 15, 20, 30, 40, 60, 80, 100, 120, 150, 200, 300, 400, 500, 600, 800, 1000 resonant structures 200.

[0083] In some embodiments, the characteristic (or fundamental / primary) resonance frequency (wR) of the magnetically resonant structure 200 can be in a range of range of 1 kHz to 100 MHz. In general, the resonance frequency can be at least 1 kHz, 2 kHz, 5 kHz, 10 kHz, 20 kHz, 50 kHz, 100 kHz, 200 kHz, 500 kHz, 1 MHz, 2 MHz, 5 MHz, 10 MHz, 20 MHz, or 50 MHz and / or up to 2 kHz, 5 kHz, 10 kHz, 20 kHz, 50 kHz, 100 kHz, 200 kHz, 500 kHz, 1 MHz, 2 MHz, 5 MHz, 10 MHz, 20 MHz, 50 MHz, or 100 MHz. The particular resonance frequency for a magnetically resonant structure 200 can be controlled based on selection of different geometric parameters and / or structural designs. For example, largerAtty. Docket No. 33929 / 70726 / US PATENT APPLICATION(e.g., meter-scale for overall diameter / width) coiled sheet designs with appropriate inclusions of dielectric materials can operate in the kHz range, while smaller-scale designs can operate in the MHz domain. The other resonators typically exhibit higher resonance frequencies, with helical coils reaching down to approximately 100 kHz, and split rings being in the MHz range.

[0084] As noted above, the magnetically resonant structure 200 can be characterized as having a plurality of resonance frequencies wR,j (e.g., i=1 , 2, 3, etc.) accounting for primary (or fundamental) and higher order resonance frequencies). The higher order resonance frequencies can be utilized in place of or in combination with the fundamental frequency in order to achieve distinct power distributions. For example, higher order modes generally exhibit greater uniformity and thus can be used to improve the homogeneity of the heating rate and / or temperature distribution in the apparatus 100. The higher resonance frequencies are generally near an integer multiple of the fundamental resonance frequency (e.g., wR,2~ 2WR.I, W ,3 ~ 3WR.I, ... etc. with index “1” representing the fundamental frequency and indices “2” and higher representing the higher order frequencies). The higher order resonance frequencies are typically within 20% (e.g., within 1 , 2, 5, 10, 15, or 20%) of a given integer multiple relative to the fundamental resonance frequency. For example, a ratio of the second order frequency (WR,2) relative to the fundamental frequency (wR,i) can be in a range of 1.6 to 2.4 (i.e., 2 + / - 20%), 1.8 to 2.2 (i.e., 2 + / - 10%), etc.; and a ratio of the third order frequency (wR,3) relative to the fundamental frequency (wR,i) can be in a range of 2.4 to 3.6 (i.e., 3 + / - 20%), 2.7 to 3.3 (i.e., 3 + / - 10%), etc.

[0085] The predetermined operating frequency for the applied AC electrical power via the electromagnetic coil 300 can vary over wide ranges, and it can be co-designed or otherwise selected in combination with the choice of magnetically resonant structure 200 geometry and / or materials, electrically conductive body 210 material choice, dielectric 218 material choice, and apparatus 100 size (e.g., diameter or width of resonant structure 200 or corresponding vessel 400), to maximize heating efficiency and enable volumetric apparatus heating. In embodiments, the applied AC electrical power can be applied at one or more predetermined operating frequencies across a predetermined range to produce one or more corresponding alternating electromagnetic fields. In embodiments, the predetermined operating frequency (or predetermined range of operating frequencies) can be in a range of 1 kHz to 100 MHz or 100 kHz to 100 MHz. For example, the predetermined operating frequency can be at least 1 kHz, 2 kHz, 5 kHz, 10 kHz, 20 kHz, 50 kHz, 100 kHz, 200 kHz, 500 kHz, 1 MHz, 2 MHz, 5 MHz, 10 MHz, 20 MHz, or 50 MHz and / or up to 2 kHz, 5 kHz,Atty. Docket No. 33929 / 70726 / US PATENT APPLICATION10 kHz, 20 kHz, 50 kHz, 100 kHz, 200 kHz, 500 kHz, 1 MHz, 2 MHz, 5 MHz, 10 MHz, 20 MHz, 50 MHz, or 100 MHz.

[0086] The predetermined operating frequency (wE) is sufficiently close to the resonance frequency (wR) such that the alternating electromagnetic field (i) inductively couples to the magnetically resonant structure, thereby inductively heating the magnetically resonant structure 200 when AC electrical power at the predetermined operating frequency is applied to the electromagnetic coil 300. In some embodiments, the predetermined operating frequency (wE) and the resonance frequency (wR) can be substantially the same. In other embodiments, it can be desirable to intentionally operate with different or otherwise mismatched operating and resonance frequencies (i.e., coRcoE); this achieves slightly less than perfect (or unity) coupling, but provides other advantages related to power electronics and temperature-dependent resonance properties. For example, operating off-resonance improves how stable the resonant structure 200 appears as a load on the drive coil 300, because material properties vary with temperature. Operating off-resonance also improves the drivability of the device by allowing power to be delivered at a lower voltage. These advantages are balanced against the loss in coupling efficiency resulting from operating off-resonance (e.g., resulting in comparatively higher parasitic coil 300 heating losses and / or lower fraction of input power converted to inductive heat in the resonant structure 200). To maintain suitable impedance matching across temperature ranges, either the operating frequency or impedance match may be dynamically tuned. A specific selection can depend on available power electronics, material properties, and operating conditions. The relative degree of frequency difference for off-resonance operation (Wo) can be characterized by Wo = Qx|1 - WE / WR|, where Q is a resonance quality factor characteristic of the magnetically resonant structure 200. The resonance quality factor Q represents the width of the resonance peak when measuring the apparent resistance across the terminals of the drive coil 300 as a function of frequency. Here, the peak is essentially Gaussian and operating off-peak or off-resonance can be characterized as a frequency within a selected number of full-width-half-maximums (FWHMs) for the Gaussian peak. In embodiments, the parameter Wo can be in a range of 0.001 to 2 or 0.001 to 5, for example at least 0.001 , 0.002, 0.005, 0.01 , 0.02, 0.05, 0.1 , 0.2, 0.5, 0.7, 1 , 1 .2, 1.5, 2, 2.5, 3, 3.5, or 4 and / or up to 0.005, 0.01 , 0.02, 0.05, 0.1 , 0.2, 0.5, 0.8, 1 , 1 .2, 1.5, 1.8, 2, 2.5, 3, 3.5, 4, 4.5, or 5. The specific degree of off-resonance operation (Wo) can be selected based on a variety of factors, for example apparatus scale, resonance frequency of the apparatus, desired power delivery and corresponding power electronics to provide same, etc. The foregoing relationships betweenAtty. Docket No. 33929 / 70726 / US PATENT APPLICATIONoperating and resonance frequencies can similarly apply to the higher order resonance frequencies of the resonant structure 200.

[0087] As described above, the inductively heated chemical apparatus can be operated at near-unity coupling efficiencies, although intentional off-resonance operation can also be desirable in some cases. Accordingly, in various embodiments, a coupling efficiency between the electromagnetic coil 300 and the magnetically resonant structure 200 is in a range of 80% to 100%, for example at least 80, 85, 90, 95, 98, 99, or 99.5% and / or up to 85, 90, 95, 98, 99, 99.5, 99.9, or 100%. Alternatively or additionally, a degree of parasitic heating of the electromagnetic coil 300 can be not more than 20% of the electromagnetic coil 300 input power, for example up to 1, 2, 5, 10, 15, or 20% and / or at least 0.001, 0.01, 0.1, 0.2, or 0.5%. The coupling efficiency represents the fraction of electrical energy / power applied to the electromagnetic coil 300 that is converted to thermal energy / inductive heating rate in the magnetically resonant structure 200, while the remainder is dissipated in the coil 300 and other nearby metals. For example, in the presence of electrically conductive walls of the vessel 400, the coupling efficiency to the magnetically resonant structure 200 will be reduced, as the metal walls will absorb some amount of power and partially shield the resonant structure 200. Even in such cases, the amount of lost parasitic heating in the electromagnetic coil 300 can still be relatively low, regardless of the relative partition between inductive heating of the resonant structure 200 and power absorbed by the vessel 400.

[0088] In embodiments, various solid, liquid, and / or gaseous dielectric materials 218 (e.g., non-electrically conducting materials) can be used. Suitable dielectric materials can include metal oxides such as alumina (AI2O3), silica (SiOg), and ceramic materials (e.g., nonconducting ceramics), in particular based on their suitability for high-temperature environments. Further, non-conducting fluids such as gases and liquids can be utilized. In cases where low-temperature applications are desired, other materials can be used, for example insulating polymers, plastics, and / or rubbers such as polytetrafluoroethylene (PTFE), polyamides, etc. In some embodiments, the dielectric material can be coated, adhered, layered, bonded, etc. to or with the electrically conductive body, for example as a layer / coating or as discrete particles / regions. In other embodiments, the dielectric material can be a loose material adjacent to or in contact with the electrically conductive body (but not bound thereto), for example as a particulate filler or packing the interior volume of the magnetically resonant structure. In either case (e.g., bound or loose material), the dielectric material can be a support for catalyst materials. If leaving a void in the dielectric region(s) of the apparatus (or not including one at all) is desired, the input flow stream (e.g., gas orAtty. Docket No. 33929 / 70726 / US PATENT APPLICATIONliquid) during use of the apparatus may simply be allowed to occupy the remaining empty internal volume 220 of the magnetic resonator 200 and to serve as the dielectric material 218. For example, the dielectric material 218 can be a gas phase material that would be present during operation of the apparatus 100, such as an air carrier phase, nitrogen or other inert carrier phase, gas-phase reactant(s) or product(s), etc. that are fed to the reactor or apparatus 100 during operation. The incorporated dielectric materials 218 may range from a gas with relative a dielectric constant (or relative permittivity er) near unity to high dielectric constant materials such as perovskites with a dielectric constant in the hundreds depending on the desired frequency range. For example, the dielectric constant (or relative permittivity) of the dielectric materials 218 can be in a range of 1 to 500, for example being at least 1, 1.5, 2, 3, 5, 8, 10, 20, 30, 50, or 100 and / or up to 10, 20, 30, 50, 100, 200, or 500. Thermal conductivities may range from 0.1 W / (m»K) for instances where the dielectric should be insulating to 100W / (m»K) where heat spreading is important. The dielectric loss tangent at the operating frequency may range from 0 if dielectric loss is not desired as a heating mechanism up to 0.5 if dielectric loss is desired as the dominant heating mechanism, for example at least 0, 0.1 , or 0.2 and / or up to 0.2, 0.3, 0.4, or 0.5.

[0089] In embodiments, the electromagnetic coil 300 need not be wrapped around the magnetically resonant structure 200 or outer vessel wall 400. Further, the coil 300 need not extend the entire (axial) length of the magnetically resonant structure 200, since resonance induced at a given axial location of the magnetically resonant structure proximal to the coil extends axially throughout the entire structure. A single coil is possible, and it can be spaced apart from the magnetically resonant structure and still provide efficient resonant coupling and heating of the magnetically resonant structure. The spacing allows other structures / components to be incorporated into the apparatus / reactor, such as thermal insulation. In some embodiments, the coil can be movable relative to a reactor including a plurality of magnetically resonant structures so that it can selective heat / target some or all of the magnetically resonant structures. In some embodiments, the electromagnetic coil 300 can be spaced apart from the magnetically resonant structure 200 by a distance up to approximately the characteristic diameter of the electromagnetic coil 300, for example being space apart by a distance of at least 0.1 , 0.2, 0.3, 0.4, or 0.5 Dcand / or up to 0.3, 0.5, 0.7, 0.9, 1, 1.1 or 1.2 Dc, where Dcis the characteristic diameter of the electromagnetic coil 300. The coil diameter will typically be on the same size scale as the reactor diameter, for example ranging from a few centimeters to a few meters, such at least 1 , 2, 5, 10, 20, 50, or 100 cm and / or up to 10, 20, 50, 100, 200, 300, 400, or 500 cm for the coil or reactorAtty. Docket No. 33929 / 70726 / US PATENT APPLICATIONdiameter. A larger coil allows for a greater offset between the coil and resonant structure at the expense of increased losses in the coil.

[0090] In embodiments, the magnetically resonant structure 200 can be configured to provide a substantially constant heating profile in the apparatus 100 or internal volume 220 thereof. For example, a heating rate within the magnetically resonant structure 200 at any given location can be about 80% to 100%, 90% to 100%, or 95% to 100% of the maximum local heating rate in the magnetically resonant structure 200. A substantially constant heating profile can be obtained by balancing dielectric losses against resistive losses in the magnetically resonant structure 200. In an embodiment, a substantially constant heating profile can be provided by selecting a resonant structure material thickness (e.g., metal or other material thickness in a coiled or spiral sheet resonant structure) to balance countercurrent and charging current losses. In an embodiment, a substantially constant heating profile can be provided by selectively inserting a dielectric (or high-permeability) material into outer radial portions of the internal volume 220, for example where inner / central radial portions of the internal volume 220 contain no dielectric material (e.g., other than gas or fluid flowing therein during operation). The configuration focuses the resonance effect at the outer radial positions (e.g., the outside turns of a spiral resonant structure), allowing the resonance to exist primarily in the periphery / outside turn, which makes the internal magnetic field (and hence power dissipation) approximately uniform. Other non-uniform heating profiles are possible, for example including center heating (e.g., higher heating rates along a radial centerline as compared to a radial / circumferential edge) or edge heating (lower heating rates along a radial centerline as compared to a radial / circumferential edge). In an embodiment, a center-dominated heating profile can be provided by selecting a resonant structure having a relatively thick material (e.g., metal or other material thickness in a coiled or spiral sheet resonant structure) with a low-loss dielectric, for example where the resonant structure has a large / thick wall dimension relative to the conductor’s skin depth at the resonant frequency. In an embodiment, an edge-dominated heating profile can be provided by including a lossy dielectric such that most power is dissipated by dielectric loss.

[0091] The inductively heated chemical apparatus 100 can be used as a reactor to perform any of a variety of chemical reactions, whether endothermic, exothermic, or otherwise. Representative chemical reactions (e.g., reforming, etc.) are described in more detail below, but the reactor can be used to perform any desired homogeneous or heterogeneous chemical reaction, in particular when precise control of the heating and / or temperature profile in the reactor is desirable.Atty. Docket No. 33929 / 70726 / US PATENT APPLICATION

[0092] Figure 2, panel (A) illustrates a general method for performing a chemical reaction using the inductively heated chemical apparatus 100 in any of its variously disclosed embodiments as a chemical reactor. A feed or reactant stream 110 is fed to the reactor 100 via the inlet 224 to the interior volume 220 of the magnetically resonant structure 200. The feed or reactant stream 110 is generally a fluid stream including one or more reactant species optionally in admixture with one or more diluents in a gas and / or liquid phase, and / or one or more homogeneous catalysts mixed in the gas and / or liquid phase. AC electrical power is applied via the power supply 500 at a predetermined operating frequency to the electromagnetic coil 300 while the fluid stream flows through the interior volume 220. The applied electrical power generates an electromagnetic field having a predetermined wavelength causing inductive heating of the magnetically resonant structure 200. The inductive heating in turn heats the fluid stream flowing through the interior volume 220, for example via conductive heat transfer at the resonant structure / fluid interface, and via convective heat transfer in bulk fluid in the interior volume 220. While the fluid stream flows through the interior volumes 220, the one or more reactant species are chemically reacted to form one or more product species in the fluid stream, optionally in admixture with unreacted reactant species and / or one or more diluents in gas and / or liquid phase. The rate of inductive heating can be adjusted or controlled (e.g., via applied electrical power) to maintain the reactor 100 at a desired heating and / or temperature profile, for example to control reaction kinetics, increase or maximize reactant conversion, increase or maximize product yield, decrease or minimize byproduct formation, and / or prevent reaction runaway (e.g., for an exothermic reaction), etc. The fluid stream that includes one or more products is then removed from the reactor 100 and the interior volume 220 via an effluent or product stream 120 via the outlet 226.Applications

[0093] The disclosed apparatus including one or more magnetically resonant structures coupled with an electromagnetic coil for inductive heating are particularly suitable for performing chemical reactions as generally described above. The disclosed apparatus are particularly useful in any application where tailorable, wireless heat delivery is desirable. The disclosed reactors have significant industrial relevance as they provide induction heating of thermochemical reactors in a manner that is competitive with current reactors that require high grade heat to mass produce materials and chemicals. This scale up scheme applies to any endothermic or exothermic process that benefits from efficient and volumetric heating. More generally, however, the apparatus can be used in non-reactive settings, for example asAtty. Docket No. 33929 / 70726 / US PATENT APPLICATIONa separator, heat storage device, etc. Illustrative applications and uses of the disclosed apparatus, both reactive and non-reactive, are outlined below.

[0094] Endothermic ammonia decomposition (2NH3->N2+3H2) and methanol decomposition (CH3OH->CO+2H2) reactions are of interest. Ammonia and methanol are two promising hydrogen carriers which may be used to generate hydrogen at the site of consumption while generally being easier to store and transport. Given this application, small, modular, efficient reactors may be integrated into systems to supply hydrogen from these carriers. For example, a countercurrent Swiss roll reactor would be highly effective for this purpose. As these reactions occur at elevated temperature (about 500°C for ammonia decomposition and about 250°C for methanol decomposition using typical catalysts), the built-in sensible heat recovery will greatly improve the reactor efficiency without requiring additional bulky, expensive heat exchangers. In combination with the high coupling efficiency of the Swiss roll or other resonant structure, this system would be highly performant. Further, the compact size and excellent manufacturability of the Swiss roll would lend itself well to inexpensive, modular operation.

[0095] The superior coupling of the Swiss roll and other resonant structures also greatly enhances the feasibility, productivity, and efficiency of inductively heated kW to MW scale reactors. In this application, an axial-flow Swiss roll optimized for uniform heating could be used. For example, a few tightly wound outer coils with a dielectric and an air-gapped or catalyst-loaded center would allow for uniform heating in the reaction area while also enabling high pressure operation. In particular, this could be used with reactions like steam methane reforming (CH4+H2O->CO+3H2), which is highly endothermic (AH=206kJ / mol), as well as other endothermic reactions described below. Here, the uniform power delivery can eliminate inefficiencies in catalyst utilization inherent in typical wall-heated, fossil-fuel powered reactors, enabling process intensification and reductions in capital costs.Additionally, the efficient wireless power transfer allows simple incorporation of large quantities of insulation.

[0096] The relatively high surface area the two conductors in a concentric Swiss roll structure would make it excellent as an electrochemical device. In particular, induction heating of the structure could supply a portion of the energy required for electrolysis while simultaneously enhancing kinetics, allowing less expensive catalysts to be used. With appropriate cell construction, it could be used in an elevated temperature alkaline electrolysis cell, an elevated temperature polymer electrolyte membrane electrolysis cell, an elevated temperature ionic conductor cell, a protonic ceramic electrolysis cell, or a solidAtty. Docket No. 33929 / 70726 / US PATENT APPLICATIONoxide electrolysis cell. A uniformly heated Swiss roll construction would be preferred in this application.

[0097] Additionally, the array of Swiss rolls with a coil indexed over them could be used where individual resonant structures only needed to be heated periodically, such as in temperature adsorption systems. This could make it ideal for carbon capture (either atmospheric or from flue gas) wherein individual capture units could be heated as necessary. Depending on available power, part or all of the array could be utilized at any given time. This could be done with solid Swiss rolls in a packed bed, solid Swiss rolls in a fluidized bed, or mesh Swiss rolls in a fluidized bed. A uniform power profile would likely be preferred in this context.

[0098] Further, the excellent heat transfer abilities of Swiss roll would make it ideal as an intermediate or primary reboiler in a distillation column. The in-situ generation of the heat would dramatically simplify the hardware, replacing complex and maintenance heavy reboilers and heat exchangers. High speed modulation of the power delivery would also improve safety and operational flexibility. The wireless nature of the power delivery would further simplify the system. In this case, it is likely that a uniform power profile with a mesh Swiss roll would be optimal.

[0099] The Swiss roll is also highly conducive to reactions in which catalyst needs to be regenerated periodically, as the entire reactor assembly can simply be swapped. This allows for minimal down time in reactor operation, making full usage of the capitally intensive power electronics. This is generally applicable to any reaction in which deactivated catalysts may be regenerated; in particular, cracking of long chain hydrocarbons can produce coking which must be removed. Once again, it is likely that a uniform power profile would be desirable in this context, although the exact details would be dependent on the reaction being performed.

[0100] Gas reforming: The disclosed inductively heated chemical reactor can be applied to all endothermic gas reforming reactions such as steam methane or hydrocarbon reforming (e.g., to produce CO and H2as syngas), dry reforming (e.g., to produce syngas), bireforming, tar reforming to produce syngas, steam cracking to breakdown saturated hydrocarbons into unsaturated hydrocarbons, water gas shift, reverse water gas shift, Sabatier reaction to produce methane from carbon dioxide and hydrogen, hydrogen cyanide production from Andrussow oxidation involving the reaction of methane and ammonia with oxygen, and the Fischer-Tropsch process to produce carbon monoxide and hydrogen to liquid hydrocarbons, to name a few. Representative catalyst materials can include ruthenium, rhodium, nickel, iridium, cobalt, platinum, palladium, iron, copper, and associatedAtty. Docket No. 33929 / 70726 / US PATENT APPLICATIONalloys, which are also electrically conductive. Susceptors made in part or entirely from these catalytic materials can directly heat them to high temperatures. It can be adapted to reformers that utilize catalysts for catalytic-based chemical transformations and to chemical looping systems that couple chemical transformations with reduction and oxidation processes within metal oxides, nitrides, and sulfides. It can be applied also to pyrolysis reactions in which methane, plastics, or biomass utilize heat to decompose into hydrogen or hydrocarbons. The reactor can also be applied to exothermic reactions that require external heat delivery to enhance reaction kinetics. Examples of exothermic reactions include hydrogenation reactions such as the direct conversion of carbon dioxide to liquid hydrocarbons or methanol.

[0101] Chemical separations based on temperature swing adsorption: All separations methods that utilize temperature swing to cycle a sorbent, such as the point source and direct air capture of carbon dioxide, would benefit from the enhanced heat management in the disclosed reactor system. These benefits arise from the ability to scale up and volumetrically heat a large reactor volume quickly, and to simultaneously extract heat from the reactor using integrated heat exchangers or heat removal at the reactor sides. As such, the temperature swing cycle can be shortened, improving the effective capacity of the reactor. This patent is particularly useful for processes that require large reactor volumes, due to the intrinsic scalability of our reactors.

[0102] Cement and ceramic manufacturing: The disclosed reactors apply to applications that require high temperature volumetric solids heating, including cement and ceramic manufacturing. In these electrified kiln concepts, the reactor can operate in fixed bed, moving bed, or a fluidized bed configuration, and heat transfers from the magnetically resonant structure to the solid materials via thermal conduction and radiation.

[0103] Heat storage: Large-scale thermal storage can be realized with the inductively heated resonant structures. The generally metallic construction of the resonators grants high thermal conductivity, allowing rapid energy extraction, and with induction heating, thermal cycling can be rapidly performed with uniform temperature profiles. Further, high heat capacity dielectrics may be utilized to further increase the thermal storage capabilities.

[0104] Fluidic heating: Many applications require the heating of gases or liquids without the need for direct coupling with chemical reactions. These include the heating of fluids for water heaters, heating of various liquids for the food industry, generation of steam from water, and the preheating of gases for use in a chemical reactor. The disclosed apparatus offers low capital costs and process intensification, which allows the form factor for theAtty. Docket No. 33929 / 70726 / US PATENT APPLICATIONheating system to be relatively small. In addition, the disclosed apparatus can eliminate or reduce significant hot spots and / or the presence of high local temperature spikes.

[0105] Mechanical energy conversion technologies: Many mechanical energy conversion technologies couple the heating of fluids together with concepts in thermodynamics to produce mechanical energy. For example, the heating of gases in a vessel will lead to an increase in gas pressure. Inductive heating of the disclosed apparatus, and in particular high power pulsed heating (which is readily accessible with solid state power electronics), can lead to very high heat transfer rates and temperature increases in gases. This high heat transfer is particularly aided by the high surface area to volume ratio of the susceptors. These concepts can be utilized in propulsion devices and be coupled to heat engine concepts based on the Brayton cycle and Rankine cycle, amongst others, to serve in allelectric mechanical systems.

[0106] Steam cracking: Steam cracking is a high temperature process in which saturated hydrocarbons are broken down into smaller and often unsaturated hydrocarbons. Examples of the process include the production of ethylene from ethane and the production of propylene from propane. Steam cracking requires the rapid heating of the gases to high temperatures, typically above 800 degrees Celsius, and maintains this high temperature for endothermic reactions. It is then followed by rapid quenching to mitigate undesirable secondary reactions. Magnetically resonant susceptors in the disclosed reactors can serve as high area, high temperature heating elements that can efficiently provide heat for steam cracking. In general, the excellent thermal contact between volumetric susceptors and fluids is ideal for reactor systems that require low resistance times and low thermal resistance.

[0107] Materials processing through pyrolysis: Pyrolysis involves the thermal decomposition of materials in an inert atmosphere. It is used extensively in industry to convert hydrocarbons to fuels. For example, it is used to convert methane to hydrogen and carbon without the release of carbon dioxide, coke, liquid hydrocarbon and gases from coal, bio-oil, bio-char and syngas from biomass, ethylene and propylene from various hydrocarbons, and liquid oil, wax, char and gases from plastic waste. The disclosed inductively heated chemical reactor can enable clean, efficient, and fast heating of the media to controllable temperatures, enabling fast throughput and reduced reactor sizes. In the case of processes such as methane pyrolysis, the susceptors can serve as both a heating element and catalyst.

[0108] Hydrogen sulfur capture and utilization: Hydrogen sulfide can be removed from a flue or reforming gas stream and converted to hydrogen and sulfur. Hydrogen sulfide, basedAtty. Docket No. 33929 / 70726 / US PATENT APPLICATIONon a reaction-regeneration scheme, can react with iron or iron sulfide compound to form hydrogen and solid products of iron sulfide or iron disulfide compounds. Upon heating of the solid products, sulfur can be released while iron or iron sulfide compound is regenerated. Iron and Iron sulfides are electrically conductive; that is, they can be directly heated through inductive heating. A similar heating principle can be applied to other materials than Fe based material for this reaction scheme.Examples

[0109] The following examples illustrate the inductively heated chemical apparatus and related methods, but are not intended to limit the scope of any claims thereto. In the following examples, a cylindrically coiled sheet (or Swiss roll) is selected as a representative magnetically resonant structure according to the disclosure. The Swiss roll resonant structure is modeled, simulated, and experimentally characterized to several performance characteristics of the disclosed apparatus. Similar results for other resonant structure geometries can be determined to describe the physics and manipulate the system behavior, and many of the results for other resonant structures are qualitatively similar.

[0110] The high self-capacitance and self-inductance of the roll layout allow its resonant frequency to be tuned to frequencies in the range of conventional power electronic inverters, i.e., tens of megahertz to tens of kilohertz, as the scale of the structure increases from centimeters to meters and the material properties of the system are altered. A quantitative framework for determining the resonant frequency of the Swiss roll (1) approximates the capacitance (C) of the Swiss roll by modeling the structure as a concentric cylindrical capacitor with surfaces defined by the inner and outer turns of the roll, and (2) approximates the inductance (L) by modeling the structure as a solenoid. These together define the resonant frequency (COR) as COR = (LC)05. In these examples, the Swiss rolls structures follow the parametric equations r=kd+r0and 0=2TTk, where (1) r and 0 represent the spiral shape of the electrically conductive body in a cylindrical coordinate system (e.g., extending uniformly in the axial direction z by a distance or height h), (2) d is the spacing between layers, (3) r0is the inside diameter, and (4) k is the layer number parameter spanning 0 to N (number of turns). The electrically conductive body has a thickness t, and a height or length h. Figure 1 (panel A) illustrates the cylindrical coordinate system and Figure 2 (panel A) illustrates the specific geometric parameters of the Swiss roll. As previously noted, in general, the Swiss roll can take any form factor consisting of serially connected concentric shapes (e.g., squares, rectangles, triangles, hexagons, etc.).Atty. Docket No. 33929 / 70726 / US PATENT APPLICATION

[0111] The Swiss roll structure may be fabricated in a number of ways, depending on the details of the application. Selection of the electrically conductive roll material is flexible, since the resonance point is determined predominantly by geometry rather than material properties. Accordingly, the ability of the structure to capture electromagnetic energy does not depend substantially on the construction material. Increases in electrical resistivity do decrease the quality factor of the resonance, limiting the coupling efficiency, but this is not a significant concern for most metals. Hence, other concerns such as cost, chemical compatibility, or mechanical properties can drive material choice. Examples of materials that can be used for Swiss roll manufacturing include aluminum, copper, steel, stainless steel, nickel-based superalloys, and carbon. The materials can have the form of solid sheets, felts, foams, or lattices. Similar materials are suitable for other magnetically resonant structure geometries as well.

[0112] Similarly, there is significant freedom to select the interlayer dielectric. The principal constraint is that the dielectric be an adequate insulator for the resonance to have an acceptable quality factor. Further, the resonance frequency can be altered by selection of interlayer dielectrics with non-unity relative permittivity, which enhances the capacitance in the system. This may be desirable if other design considerations such as electromagnetic interference concerns require specific frequency selection. Lossy dielectrics may also be incorporated as a means of altering and tailoring the heating profile.

[0113] Several methods are viable for the manufacturing of Swiss rolls. First, if both the conductor and the dielectric are sufficiently flexible, they may be rolled together. Second, the Swiss roll could be formed via an extrusion process. This results in a free-standing structure and is compatible with mass fabrication. Third, the Swiss roll can be formed via metal 3D printing technologies such as DLMS. This can allow for fine control over structure geometry and therefore heating profile. Fourth, the Swiss roll can be cast, either as a solid structure or a porous one. Fifth, the structure can be rolled from sheet metals, as in the case of flat helical coil springs. Without loss of generality, the sheet metal can be patterned with surface relief structures or holes prior to rolling to customize the heating profile.

[0114] In operation as a thermochemical reactor, a suitable configuration of the Swiss roll is dependent on how the reactants should flow through the system. Specifically, it may be desirable for the gaseous or liquid reactants to pass through just the metal, just the insulator, or both. The first case may be desirable in a system where the conductive material catalyzes the reaction itself or the catalyst is wash coated onto the conductor. It would allow for most direct delivery of heat to the reaction location. This could be constructed by rolling aAtty. Docket No. 33929 / 70726 / US PATENT APPLICATIONmesh material, 3D printing with microstructuring, or casting with pores. Alternatively, if the catalyst were loaded in between the conductive layers, either on supports such as alumina particles or as a powder, it would be preferred to have the gas flow through the insulating region. Any of the mentioned methods could be used to make the conductor gas-impermeable. Finally, allowing the gas to flow in both regions would allow for better mixing, improving temperature uniformity.Example 1 - Power Distribution

[0115] The Swiss roll reactor, consisting of an individual Swiss roll or concentric Swiss rolls, can be configured to support a variety of tailorable radial heating profiles as defined by geometry, material composition, and material loading. In one heating profile instance, Swiss rolls can be heated selectively at its center. This center-heated roll configuration is particularly ideal for counter-current heat exchange within concentric Swiss roll reactors. Alternatively, a uniformly heated roll could be useful for an axial flow reactor where the entire cross section of the gas should ideally be heated the same amount. Finally, a Swiss Roll with selective heating at its outer rings could be useful in a radial flow chemical reactor in scenarios where there is a large initial sensible heat requirement to bring reactants up to a high temperature, after which maintaining temperature requires less power. The power profile as a function of radius for these cases is shown in Figure 5.

[0116] More complex heating profiles can also be realized by exciting higher order resonant modes within Swiss rolls, which exhibit more nuanced radial power profiles. For example, in uniformly spaced systems with larger gap sizes, the primary mode dominantly heats near the center of the Swiss roll as shown in Figure 6; in the language of standing waves, the center of the roll is an antinode with maximal current and the outside edge is a node with approximately no heating. The secondary mode exhibits a second node and antinode, allowing for the same geometric configuration to support multi-zone radial heating via frequency tuning of the drive coil.Example 2 - Resonance Induction Currents

[0117] The resonant coupling to a Swiss roll can be characterized as a three-step process. To begin with, charging currents in the Swiss roll are defined to be those which result in a net displacement of charge from the inside to the outside of the Swiss roll, as shown schematically in Figure 7 (panel A) as a net or charging current 216 in the electrically conducting body 210. These currents are driven by the external magnetic field passing through the turns of a Swiss roll, which creates a time-varying flux, which in turn generatesAtty. Docket No. 33929 / 70726 / US PATENT APPLICATIONan electromotive force about each turn. At the Swiss roll LC resonance, the external magnetic field maximally couples to the Swiss roll to drive this mode.

[0118] Next, the net movement of charge from the charging current results in an enhanced magnetic field as described by Ampere’s Law. In particular, these currents are approximately solenoidal, and hence the magnetic field at any given point is defined by the sum of the magnitudes of the charging currents at greater radii. The magnetic field amplitude is proportional the integral of the charging currents from a given radius to the outside of the roll, which implies that the magnetic field enhancement is greatest at the center of the roll.

[0119] Finally, circulating currents are defined to be currents which run along the perimeter of the Swiss Roll and do not result in a net movement in charge. The circulating currents are shown schematically in Figure 7 (panel B) as an interior or inner surface current 212 and an exterior or outer surface current 214. As the magnetic field is suppressed in the interior sections of the Swiss roll metal layers due to skin effects, a current proportional to the magnitude of that magnetic field arises as described by Ampere’s law. Further, since the direction of magnetic field decay is opposite on the two interfaces of each concentric layer of the Swiss roll, the induced currents are in opposite in direction at these interfaces.Therefore, the circulating currents along the perimeter of the Swiss roll metal layer body generally dissipate a majority of the power in the Swiss roll.Example 3 - Control of Power Profile

[0120] The Swiss roll geometry, which has N turns, can be approximated as a set of N concentric circular rings. Such a structure can be functionally described as a set of N-1 capacitors, where each adjacent set of rings forms a distinct capacitive structure. Further, the capacitors have loops of wire in parallel which produce an electromotive force from the time-varying magnetic flux passing through them. The charging current distribution in this simplified structure is calculated based upon equating this EMF with the capacitive voltage generated by moving charge around that ring. The current distribution in the ithring, , can be determined by solving the following matrix equation (Eq. 1). In Eq. 1, a is a constant equal to CO2PTT, where co is the resonant frequency, Ci is the capacitance of the ithring, and q is the radius of the jthring.Atty. Docket No. 33929 / 70726 / US PATENT APPLICATION

[0121] The Swiss roll structure can be numerically characterized with the AC / DC package of the finite element simulation software COMSOL. Most simulations are performed in 2D (corresponding to an infinite height) along with the impedance boundary condition (valid as long as the metal thickness is multiple times the skin depth of the metal). These simplifying assumptions allow models to be solved in seconds, while more computeintensive models relax them for more accurate results outside of the relevant limiting regimes.

[0122] Simulated and calculated charging current distributions for a roll with r0=3mm, d=1.75mm, t=.1mm, N=25, and h=infinite were evaluated and demonstrated excellent agreement. The resonance frequency was simulated as 19.75±0.13MHz and calculated as 19.77MHz. Notably, for a space-filling Swiss roll (i.e. Nd~R), the diminishing capacitance and flux for the inside turns implies that the charging currents generally reside in the outer turns of the Swiss roll.

[0123] Next, the charging current distribution is used to compute the heating distribution. The magnitude of the alternating magnetic field at a position will be proportional to the amount of resonant current in the turns at a larger radius, which can be used to solve for the magnetic field on either side of the metal of a given turn. Next, the generic solution for the current density inside that metal can be approximated using Eq. 2 below, in which x is the distance into the metal, 5 is the skin depth at the relevant frequency, and Jo and Ji are two constants selected to match the boundary conditions of the magnetic field on either side of the metal. Finally, the power can be calculated using Eq. 3 below, in which t is the metal thickness and a is the metal conductivity.

[0124] In one limiting case, as the metal grows sufficiently thin, the power is primarily dissipated by the charging current and therefore the edge is heated more. On the other hand, if the metal thickness is several times the skin depth, the power is primarily dissipated by the circulating current proportional to magnetic field amplitude, resulting in the center being heated more. At some intermediate value, an approximately uniform power distribution can be achieved as shown in Figure 8. This typically occurs when the metal thickness is on the order of the skin depth.Atty. Docket No. 33929 / 70726 / US PATENT APPLICATION

[0125] The foregoing system can be analytically evaluated to examine the qualitative effects of various deviations from the ideal system, in particular the effects of metal resistivity, finite length, and interlayer dielectric loss (i.e., the presence of material between the metal sheets that can absorb electromagnetic radiation).

[0126] Variations in metal resistivity primarily alter the properties of the resonance by modifying the voltage balance around a turn of the Swiss roll. Importantly, variations in metal resistivity do not alter the distribution of the charging current. However, the added damping term in the LC resonance decreases both the quality factor (i.e., the ratio of the energy stored in the resonator to the energy supplied by a to it) and the resonant frequency, as shown in Figure 9, which plots power dissipation as a function of frequency for three different metal conductivities. As the quality factor of the resonance decreases, a broader range of frequencies can excite the resonance, although the coupling strength at resonance is weaker and the coupling efficiency decreases.

[0127] In the previous analytic analysis, the Swiss roll was assumed to be in the solenoid limit in which the roll height is much longer than the roll width, leading to magnetic fields within the roll that are ideally axially oriented. In a finite height Swiss roll, the magnetic fields within the roll are no longer exclusively axial in orientation and so called “edge effects” can manifest in the form of enhanced magnetic fields. In this finite height limit, the ends of the Swiss roll dissipate more power than the axially middle section of the roll. This enhanced heating region at the roll ends occurs within end section heights of approximately d.Additionally, when h~r0+dN, the resonance frequency increases approximately logarithmically with decreases in the height of the Swiss roll, approaching the infinite height asymptotic value when h»r0+dN as shown in Figure 10 (panel A). Finally, as illustrated in Figure 10 (panel B), it is observed that the quality factor also decreases as the roll height decreases.

[0128] Dielectric losses within the interlayer alter the characteristics of the resonance similarly to the metal resistivity. As dielectric losses increase, the quality factor decreases and the resonance frequency decreases. However, it also represents an additional loss mechanism that is proportional to the generated electric field within the interlayer regions. The magnitude of this electric field is relatively larger at the outer loops of the roll, leading in some cases to power distribution profiles in which more energy is dissipated at the outer layers of the Swiss roll than the inner layers, as illustrated in Figure 11.Example 4 - Tailored Heating ProfilesAtty. Docket No. 33929 / 70726 / US PATENT APPLICATION

[0129] The foregoing model provides a quantitative method of describing the power distribution in a Swiss roll. In practice, depending on application, it could be desirable I to dominantly heat in the center, to heat uniformly, or to dominantly heat at the edge. By modifying the details of the geometry (e.g., either by modifying the turn density or incorporating open area on the conductor), the precise details of the power dissipation can be adjusted while having minor effects on the resonance behavior.

[0130] To design a centrally heated Swiss roll, simply selecting a metal with thickness multiple times the skin depth is sufficient. The magnetic field amplification is by greatest at the center, and so operating in a regime where the circulating currents dissipate most of the power will yield a centrally heated device.

[0131] To achieve a uniform heating profile, metal thickness can be selected to balance charging current losses against circulating current losses. However, this only achieves a roughly uniform heating profile, as there are insufficient degrees of freedom to make the profile completely flat. It also presents some drawbacks in terms of structural stability.Alternatively, in the limit that Ci is much greater for the outside turns (e.g., by reducing the spacing or inserting a dielectric), the charging currents will exist primarily in these outside turns, resulting in uniform magnetic fields and therefore power dissipation in the central turns. The same effect can be achieved by inserting a magnetic material with a large relative permeability prin the outside turns.

[0132] Finally, achieving heating profiles which are outside- (or radial edge-) dominated can be realized by using metal which is a fraction of the skin depth. Alternatively, if this is undesirable for structural reasons, placing dielectrics within the reactor that have an adequate loss tangent can achieve the same effect as the electric field is greater at the outside of the Swiss roll. The dielectric loss may be calculated from the charging currents and the capacitance of the system that together define the electric field magnitude. Further, balancing dielectric losses against resistive losses can be used to finely tune the power profile, although this requires excellent characterization of the constituent materials.

[0133] In the absence of analytic expressions describing power dissipation in the presence of the described non-idealities, the desired behavior of the Swiss rolls can be designed first roughly using the idealized analytical solution and then tailored via numerical studies. In particular, 3D simulations were performed in COMSOL Multiphysics. A closed curve describing the Swiss roll geometry is designed and extruded, and coil with current applied between the two terminals excites it. Layer spacing and material properties can beAtty. Docket No. 33929 / 70726 / US PATENT APPLICATIONadjusted to achieve the desired heating profile and resonance frequency using the results of the simulations.Example 5 - Experimental Validation

[0134] The foregoing modeling and analytical results were validated by comparing simulation and experiment. A stainless steel Swiss roll structure (conductivity of ~1.5x106S / m) was simulated with dimensions ro=2mm, d=2.9mm, N=16, t=1 ,7mm, and h=50mm driven by a single turn of copper wire.

[0135] Next, the same structure was produced with DLMS 3D printing. The impedance curve as seen by a single 120mm diameter loop of copper wire was taken, and a peak at 32.94MHz was observed, which differs from the simulated value of 31 ,55MHz due to imprecise fabrication and deformability of the structure, as shown in Figure 12 (panel A). The fraction of power dissipated in the coil can be computed as RCOH / RSR, such that, at the resonant frequency, just 0.53% of the power is dissipated in the coil. Stainless steel is among the least conductive metals, and therefore most other metals would exhibit superior coupling.

[0136] To experimentally determine the heating profile of a given structure, a FLIR X6901 infrared camera was used to image the temperature of the evolution of the face of the Swiss roll as it was heated via a single turn copper coil. Beginning from room temperature, about 250W power was input until the temperature had increased by about 25°C, requiring about one minute. The radial thermal conductivity of the manufactured structures was insufficient to seriously affect the temperature profile on this timescale, and thus the resultant temperature profile is indicative of the power profile. This is not necessarily a high precision measurement due to variation in the emissivity on account of surface morphology, but it is adequate for qualitative observation. Figure 12 (panel B) shows the radial heating profile comparison between the simulated and experimental values.

[0137] Finally, the heating experiment was repeated, except that two additional turns of aluminum foil with silica cloth were wrapped as a dielectric layer, hence increasing the capacitance of the outer turns and shifting the power profile accordingly. After doing so, the outside two turns show much more heating due to dielectric losses, and that the remaining heating is much more uniform. Figure 12 (panel C) shows the experimental radial heating profile, thus demonstrating that modulating the interlayer capacitance can adjust the power distribution. Accordingly, appropriate design of the geometry and materials may be used to further tailor the profile.Atty. Docket No. 33929 / 70726 / US PATENT APPLICATIONExample 6 - Reactor Operation

[0138] A Swiss roll structure was operated as chemical reactor according to the disclosure. The Swiss roll was fabricated with a 75mm tall stainless steel mesh sheet. The inside 75mm of the roll diameter where reactant gases flowed was packed with a mesoporous alumina to serve as a high-surface-area support for the reaction. Outside of that, several tighter turns with ceramic paper ensured that the interior had a substantially uniform heating profile. The entire construction was placed in a quartz reaction vessel, and a reverse water gas shift reaction was performed with a gas feed mixture with mole fractions of 20% carbon dioxide, 60% hydrogen, and 20% argon inflow. The gas hourly space velocities (GHSVs) were varied from 50 to 360 h-1, and sufficient power was delivered to ensure an exit temperature of 500°C. The results are shown in Figure 13, which illustrates carbon dioxide conversion as a function of GHSV (solid line). Figure 13 demonstrates a clear approach to equilibrium at lower flow rates when using the Swiss roll reactor structure, and a typical equilibrium conversion curve for a plug flow reactor (dashed line) is shown for comparison. Additionally, the enhanced coupling provided by the magnetically resonant Swiss roll structure allowed the use of extra thermal insulation interposed between the outer wall of the reaction vessel and the excitation coil, which was a large, single-turn drive coil. The thermal insulation mitigated thermal conduction losses, but, relative to a traditional induction heating system, still allowed high coupling and efficient energy transfer to the magnetically resonant Swiss roll structure (i.e., showing much lower coupling losses than a traditional induction heating system).

[0139] Because other modifications and changes varied to fit particular operating requirements and environments will be apparent to those skilled in the art, the disclosure is not considered limited to the example chosen for purposes of illustration and covers all changes and modifications which do not constitute departures from the true spirit and scope of this disclosure.

[0140] Accordingly, the foregoing description is given for clearness of understanding only, and no unnecessary limitations should be understood therefrom, as modifications within the scope of the disclosure may be apparent to those having ordinary skill in the art.

[0141] All patents, patent applications, government publications, government regulations, and literature references cited in this specification are hereby incorporated herein by reference in their entirety. In case of conflict, the present description, including definitions, will control.Atty. Docket No. 33929 / 70726 / US PATENT APPLICATION

[0142] Throughout the specification, where the apparatus, compounds, compositions, methods, and processes are described as including components, steps, or materials, it is contemplated that the apparatus, compounds, compositions, methods, and processes can also comprise, consist essentially of, or consist of, any combination of the recited components or materials, unless described otherwise. Component concentrations can be expressed in terms of weight concentrations, unless specifically indicated otherwise.Combinations of components are contemplated to include homogeneous and / or heterogeneous mixtures, as would be understood by a person of ordinary skill in the art in view of the foregoing disclosure.Atty. Docket No. 33929 / 70726 / US PATENT APPLICATIONList of Figure Elements100 reactor, separator, or other thermochemical apparatus110 reactants120 products200 magnetically resonant structure (200i, 2002, 2OO3 ... 200nplurality of n magnetically resonant structures)210 electrically conducting body212 interior or inner surface current214 exterior or outer surface current216 net current218 dielectric material220 interior volume (e.g., internal flow and reaction volume)222 cross section (area)224 inlet (e.g., axial inlet)225 inlet (e.g., radial inlet)226 outlet (e.g., axial outlet)228 flow direction (longitudinal / axial direction)240 catalyst300 electromagnetic coil400 reactor body or wall410 exterior thermal insulation420 interior thermal insulation500 power supply

Claims

Atty. Docket No. 33929 / 70726 / US PATENT APPLICATIONWhat is claimed is:

1. An inductively heated chemical apparatus comprising:a magnetically resonant structure comprising an electrically conductive body, wherein:the magnetically resonant structure has a characteristic resonance frequency (wR), andthe magnetically resonant structure at least partially defines or occupies an interior volume;optionally, a dielectric material in the interior volume andat least one electromagnetic coil proximal to the magnetically resonant structure and adapted to produce an alternating electromagnetic field at a predetermined operating frequency (wE) sufficiently close to the resonance frequency such that the alternating electromagnetic field (i) inductively couples to the magnetically resonant structure, and (ii) inductively heats the magnetically resonant structure when AC electrical power at the predetermined operating frequency is applied to the at least one electromagnetic coil.

2. The inductively heated chemical apparatus of claim 1 , further comprising:a vessel wall enclosing the magnetically resonant structure or structures, wherein the vessel wall optionally at least partially defines the interior volume.

3. The inductively heated chemical apparatus of claim 2, wherein the vessel wall comprises an electrically conductive material selected from the group consisting of metals, conductive carbons, conductive ceramics, and combinations thereof.

4. The inductively heated chemical apparatus of claim 2, wherein the vessel wall comprises an electrically insulating material selected from the group consisting of ceramics, glasses, plastics, and combinations thereof.

5. The inductively heated chemical apparatus of claim 2, further comprising: thermal insulation interposed between the vessel wall the at least one electromagnetic coil.

6. The inductively heated chemical apparatus of claim 1 , further comprising:a power supply electrically connected to the at least one electromagnetic coil and adapted to provide the AC electrical power at the predetermined operating frequency, thereby generating an alternating electromagnetic field, which transfers power to and inductively heats the magnetically resonant structure.Atty. Docket No. 33929 / 70726 / US PATENT APPLICATION7. The inductively heated chemical apparatus of claim 6, wherein:the predetermined operating frequency is in a range of 1 kHz to 100 MHz.

8. The inductively heated chemical apparatus of claim 1 , wherein:the electrically conductive body is in the form of a coiled sheet.

9. The inductively heated chemical apparatus of claim 1 , wherein:the electrically conductive body is in the form of a helical coil resonator.

10. The inductively heated chemical apparatus of claim 1 , wherein:the electrically conductive body is in the form of a split ring resonator.

11. The inductively heated chemical apparatus of claim 1, wherein:the electrically conductive body is in the form of a flat spiral resonator.

12. The inductively heated chemical apparatus of claim 1 , wherein:the electrically conductive body comprises one or more structural features selected from the group consisting of cut-outs, wrinkles, non-uniform spacing, and combinations thereof.

13. The inductively heated chemical apparatus of claim 1, comprising:a plurality of magnetically resonant structures.

14. The inductively heated chemical apparatus of claim 13, wherein:the magnetically resonant structures have the same electrically conductive body, the same dielectric material, the same resonance frequency, and the same interior volume.

15. The inductively heated chemical apparatus of claim 13, wherein:the magnetically resonant structures have at least one of different electrically conductive bodies, different dielectric materials, different resonance frequencies, and different interior volumes.

16. The inductively heated chemical apparatus of claim 13, wherein:at least a portion of the plurality of magnetically resonant structures is removable and / or replaceable from the inductively heated chemical apparatus, while a remainder of the plurality of magnetically resonant structures remains in the inductively heated chemical apparatus.Atty. Docket No. 33929 / 70726 / US PATENT APPLICATION17. The inductively heated chemical apparatus of claim 13, wherein:the inductively heated chemical apparatus contains 2 to 1000 magnetically resonant structures.

18. The inductively heated chemical apparatus of claim 1 , wherein:the resonance frequency is in a range of 1 kHz to 100 MHz.

19. The inductively heated chemical apparatus of claim 1 , wherein:the magnetically resonant structure has multiple resonance frequencies (WR ).

20. The inductively heated chemical apparatus of claim 1 , wherein:the predetermined operating frequency (wE) and the resonance frequency (wR) are different such that (Qx|1 - wE / wR|) is in a range of 0.001 to 2, where Q is a resonance quality factor characteristic of the magnetically resonant structure.

21. The inductively heated chemical apparatus of claim 1 , wherein a coupling efficiency between the electromagnetic coil and the magnetically resonant structure is in a range of 80% to 100%.

22. The inductively heated chemical apparatus of claim 1 , wherein the electrically conducting body comprises a material selected from the group consisting of metals, conductive carbons, conductive ceramics, and combinations thereof.

23. The inductively heated chemical apparatus of claim 1 , wherein:the electrically conducting body has an electrical conductivity in a range of 1 ,000 to 100,000,000 S / m; andthe electrically conducting body has a thermal conductivity in a range of 0.1 to 500 W / (m»K).

24. The inductively heated chemical apparatus of claim 1 , wherein:the dielectric material is present and comprises a material selected from the group consisting of metal oxides and combinations thereof.

25. The inductively heated chemical apparatus of claim 1 , wherein:the dielectric material is present and comprises a material selected from the group consisting of insulating polymers, gas materials, liquid materials, and combinations thereof.Atty. Docket No. 33929 / 70726 / US PATENT APPLICATION 26. The inductively heated chemical apparatus of claim 1 , further comprising:a catalyst in the interior volume of the magnetically resonant structure.

27. The inductively heated chemical apparatus of claim 1 , further comprising:a membrane in the interior volume of the magnetically resonant structure.

28. The inductively heated chemical apparatus of claim 1 , further comprising:a sorbent in the interior volume of the magnetically resonant structure.

29. The inductively heated chemical apparatus of claim 1 , wherein:the at least one electromagnetic coil has a characteristic diameter; andthe at least one electromagnetic coil is spaced apart from the magnetically resonant structure by a distance up to the characteristic diameter.

30. The inductively heated chemical apparatus of claim 1 , wherein:the magnetically resonant structure is configured to provide a substantially constant heating profile.

31. The inductively heated chemical apparatus of claim 30, wherein a material thickness of the magnetically resonant structure is selected to balance countercurrent and charging current losses in the magnetically resonant structure.

32. The inductively heated chemical apparatus of claim 30, wherein the apparatus comprises the dielectric material positioned at outer radial positions of the inner volume, but not at inner radial positions of the inner volume.

33. The inductively heated chemical apparatus of claim 1 , wherein:the magnetically resonant structure is configured to provide a center-dominated heating profile.

34. inductively heated chemical apparatus of claim 1 , wherein:the magnetically resonant structure is configured to provide an edge-dominated heating profile.

35. The inductively heated chemical apparatus of claim 1 , wherein the magnetically resonant structure further defines:an inlet region; andan outlet region in fluid communication with the inlet region through the interiorAtty. Docket No. 33929 / 70726 / US PATENT APPLICATIONvolume defined by the magnetically resonant structure and optionally a surrounding vessel wall.

36. A method for performing a chemical reaction, the method comprising: feeding a fluid stream comprising a reactant to the interior volume of the magnetically resonant structure in the inductively heated chemical apparatus according to any of claims 1 to 35;applying AC electrical power at a predetermined operating frequency to the at least one electromagnetic coil while the fluid stream flows through the interior volume, thereby generating an alternating electromagnetic field at a predetermined operating frequency (wE) sufficiently close to the resonance frequency such that the alternating electromagnetic field (i) inductively couples to the magnetically resonant structure, (ii) inductively heats the magnetically resonant structure, (iii) heats the fluid stream flowing through the interior volume, and (iv) chemically reacts the reactant to form a product; andremoving the fluid stream comprising the product from the interior volume.

37. A method for performing a chemical separation, the method comprising: feeding a fluid stream comprising a target species to the interior volume of the magnetically resonant structure in the inductively heated chemical apparatus according to any of claims 1 to 35;capturing the target species in a sorbent material in the interior volume of the magnetically resonant structure; andheating the sorbent material to release the target species into a product stream.

38. A method for heating a heat transfer fluid, the method comprising:feeding a heat transfer fluid to the interior volume of the magnetically resonant structure in the inductively heated chemical apparatus according to any of claims 1 to 35 and heating the heat transfer fluid therein; andfeeding the heated heat transfer fluid exiting the inductively heated chemical apparatus as a hot-side fluid to a heat exchanger.

39. A method for performing a chemical separation, the method comprising: performing a distillation separation in a distillation column, wherein heat for a reboiler component of the distillation column is provided by the inductively heated chemical apparatus according to any of claims 1 to 35.

Images