Multi-Piece Corrugated Waveguide

Abstract

The device includes a tube having an inner surface, an inner diameter, and a length. The device also includes a coil spring. The coil spring includes an outer surface, an outer diameter, and a plurality of coil elements disposed along a length of the coil spring. The coil spring can be positioned within the tube, and the outer diameter of the coil spring can be smaller than an inner diameter of the tube. The coil spring can form a waveguide. Related manufacturing methods and systems are also described herein. In one embodiment, a gap is defined between the outer surface of the coil spring and the inner surface of the tube.

Description

[Technical field]

[0001] CROSS-REFERENCE TO RELATED APPLICATIONS This application claims priority under 35 U.S.C. § 119 to U.S. patent application Ser. No. 17 / 367,800, entitled "MULTI-PIECE CORRUGATED WAVEGUIDE," filed July 6, 2021, the entire contents of which are expressly incorporated herein by reference in their entirety.

[0002] The subject matter described herein relates to waveguides for use in transmitting electromagnetic waves. [Background technology]

[0003] A waveguide is a structure that guides waves, such as electromagnetic waves or sound, restricting the transmission of energy to one direction, thereby minimizing energy loss. Waveguides can be used in non-conventional drilling techniques, such as thermal and / or millimeter wave drilling, to form a borehole in a well. Waveguides can be used to transmit electromagnetic waves into a borehole to allow drilling at greater subterranean depths than conventional rotary drilling. Certain internal features, such as corrugated grooves, can be included in the waveguide and can increase the transmission efficiency of the electromagnetic waves provided into the borehole. Forming and deploying a corrugated waveguide in a single length of tubing can be expensive, require specialized materials and equipment, and can be prone to manufacturing errors, which can result in wasted inventory, well downtime, and inefficient transmission of electromagnetic energy. Summary of the Invention [Means for solving the problem]

[0004] In one aspect, a device is provided. In one embodiment, the device can include a tube having an inner surface, an inner diameter, and a length. The device can also include a coil spring. The coil spring can include an outer surface, an outer diameter, and a plurality of coil elements disposed along the length of the coil spring. The coil spring can be positioned within the tube, and the outer diameter of the coil spring can be smaller than the inner diameter of the tube.

[0005] In another embodiment, a gap can be defined between an outer surface of the coil spring and an inner surface of the tube. In another embodiment, the coil spring can form a waveguide. In another embodiment, the inner surface of the coil spring can include a conductive material. In another embodiment, the coil spring can include a coating of copper, gold, silver, or platinum. In another embodiment, the device can further include an insulating layer between the tube and the coil spring. In another embodiment, the outer surface of the coil spring can include a dielectric material.

[0006] In another embodiment, at least one coil element of the plurality of coil elements can be defined by one revolution of the at least one coil element about a circumference of the coil spring. In another embodiment, at least one coil element of the plurality of coil elements can include a base portion and a protruding portion extending from the base portion, the protruding portion including one of a trapezoidal cross-sectional shape, a circular cross-sectional shape, a square cross-sectional shape, a rectangular cross-sectional shape, or a sinusoidal cross-sectional shape. In another embodiment, the plurality of coil elements can include one of a trapezoidal cross-sectional shape, a circular cross-sectional shape, a rectangular cross-sectional shape, an elliptical cross-sectional shape, or a tapered shape along a length of the plurality of coil elements.

[0007] In another embodiment, the coil spring can include copper wire and / or aluminum wire. In another embodiment, the tube can include a carbon steel tube. In another embodiment, a plurality of coil springs can be positioned within the tube. In another embodiment, a first coil spring and a second coil spring of the plurality of coil springs can be coupled via a coupling spring positioned within the tube. In another embodiment, a first end of the coupling spring can be attached to a first end of the first coil spring and a second end of the coupling spring can be attached to a second end of the second coil spring, and the coupling spring can be configured to reduce axial movement of the first coil spring and the second coil spring relative to each other due to thermal expansion of the first coil spring and / or the second coil spring.

[0008] In another embodiment, the cross-sectional profile of the coil spring and / or each coil element of the plurality of coil elements can be dimensioned to propagate electromagnetic waves. In another embodiment, the coil spring and the cross-sectional profile of the coil spring can be dimensioned to propagate electromagnetic waves in a HE11 mode. In another embodiment, the length of the tube can be greater than 1 meter. In another embodiment, the length of the tube can be greater than 5 meters. In another embodiment, the length of the tube can be greater than 9 meters.

[0009] In another embodiment, the plurality of coil elements can be dimensioned to include a space between two or more coil elements of the plurality of coil elements, the space can be dimensioned to be 1 / 6 of a wavelength of the electromagnetic waves injected into the borehole of the well via the waveguide assembly. In another embodiment, the plurality of coil elements can be dimensioned to include a pitch between two or more coil elements of the plurality of coil elements, the pitch can be dimensioned to be 1 / 3 of a wavelength of the electromagnetic waves injected into the borehole of the well via the waveguide assembly. In another embodiment, the plurality of coil elements can be dimensioned to include a width dimensioned to be less than a wavelength of the electromagnetic waves injected into the borehole of the well via the waveguide assembly.

[0010] In another embodiment, the coil spring within the tube can form a helical groove. In another embodiment, the helical groove can be configured to propagate electromagnetic waves. In another embodiment, the helical groove can be configured to propagate electromagnetic waves in a HE11 mode, a transverse electric mode, a transverse magnetic mode, or a combination of a transverse electric mode and a transverse magnetic mode. In another embodiment, the tube can be a tapered tube and the coil spring can be a tapered coil spring. In another embodiment, the tube can be a curved tube. In another embodiment, the tube and the coil spring can be contained within a casing and configured to extend from or retract into the casing.

[0011] In another aspect, a method is provided. In one embodiment, the method can include extruding a wire including a cross-sectional profile. The method can also include forming the wire into a coil spring having an outer diameter and a plurality of coil elements disposed along a length of the coil spring. The method can further include inserting the coil spring into a tube having an inner diameter larger than the outer diameter of the coil spring, the tube can have a length along which the coil spring extends within the tube.

[0012] In another embodiment, the method can include coating the wire with a conductive material. The method can also include coating the coil spring with a conductive material. The method can further include coating the inner surface of the tube with an insulating material. In another embodiment, the conductive material can include one or more of copper, silver, or gold. In another embodiment, a gap can be formed between the inner surface of the tube and the outer surface of the coil spring when the coil spring is inserted into the tube.

[0013] In another embodiment, the method can further include forming a channel in an inner surface of the tube, the channel can extend axially along a length of the tube. In another embodiment, the cross-sectional profile of the wire can include a base portion and a protruding portion extending from the base portion, the protruding portion can include one of a trapezoidal profile, a circular profile, a square profile, a rectangular profile, or a sinusoidal profile. In another embodiment, forming the wire into a coil spring can include wrapping the wire around a mandrel such that a shape of each coil element of the plurality of coil elements can correspond to a cross-sectional shape of the mandrel along at least a portion of a length of the coil spring. In another embodiment, the cross-sectional shape of the mandrel can include at least one of a trapezoidal shape, a circular shape, a rectangular shape, an elliptical shape, or a tapered shape.

[0014] In another embodiment, the wire can be a copper wire or an aluminum wire.In another embodiment, the method can further include forming a plurality of coil springs and inserting the plurality of coil springs into a tube.

[0015] In another aspect, a device is provided. In one embodiment, the device can include an outer tube. The outer tube can have an inner surface, an inner diameter, and a length. The device can also include an inner tube. The inner tube can have an inner surface, an outer surface, an outer diameter, and a spiral shaped groove formed in the inner surface and extending along the length of the inner tube. The inner tube can be positioned within the outer tube, and the outer diameter of the inner tube can be smaller than the inner diameter of the outer tube.

[0016] In another embodiment, a gap can be defined between an outer surface of the inner tube and an inner surface of the outer tube. In another embodiment, the spiral shaped groove can form a waveguide. In another embodiment, the inner surface of the inner tube and / or the spiral shaped groove can comprise a conductive material. In another embodiment, the device can further comprise an insulating layer between the outer tube and the inner tube. In another embodiment, the outer surface of the inner tube can comprise a dielectric material. In another embodiment, the spiral shaped groove can be configured to propagate millimeter electromagnetic waves. In another embodiment, the spiral shaped groove can be configured to propagate millimeter electromagnetic waves in a HE11 mode.

[0017] In another aspect, a system is provided. In one embodiment, the system can include a waveguide assembly. The waveguide assembly can include a tube. The tube can include an inner surface, an inner diameter, and a length. The waveguide assembly can also include a coil spring. The coil spring can include an outer surface, an outer diameter, and a plurality of coil elements disposed along a length of the coil spring. The coil spring can be positioned within the tube, and the outer diameter of the coil spring is smaller than the inner diameter of the tube. The system can also include a millimeter wave drilling rig. The millimeter wave drilling rig can include a gyrotron configured to inject millimeter wave radiation energy into a borehole of the well through the waveguide assembly.

[0018] In another embodiment, the system may include multiple waveguide assemblies underground for directing millimeter wave radiation energy to excavate a portion of the borehole or to remove material from the borehole. In another embodiment, multiple coil springs may be stacked in one or more tubes up to a distance of 15 km below the surface of the well.

[0019] In another aspect, a method is provided. In one embodiment, the method can include forming a plurality of corrugation features on a first side of a metal stock sheet. The sheet can include a first edge and a second edge. The method can also include forming the metal stock sheet into a first tube. The method can also include welding the first edge and the second edge together to seal the first tube. The sealed first tube can form a corrugated waveguide.

[0020] In another embodiment, the method can include inserting a sealed first tube into a second tube to form a multi-piece corrugated waveguide.

[0021] In another aspect, a method is provided. In one embodiment, the method can include receiving a metal stock sheet having a first surface, a first edge, and a second edge. The method can also include receiving a corrugated element on top of the first surface of the metal stock sheet. The corrugated element can include a plurality of corrugation features. The method can further include forming the metal stock sheet into a first tube including the corrugated element within the first tube. The method can also include welding the first edge and the second edge together to seal the first tube. The sealed first tube can form a multi-piece corrugated waveguide.

[0022] In another embodiment, the corrugation element is a coil spring.In another embodiment, the corrugation element is a second tube including a plurality of corrugation features formed on an inner surface of the second tube.

[0023] These and other features will be more readily understood from the following detailed description taken in conjunction with the accompanying drawings. [Brief description of the drawings]

[0024] [Figure 1]FIG. 1 illustrates an exemplary embodiment of a millimeter wave drilling system including a multi-piece corrugated waveguide as described herein. [Diagram 2] FIG. 1 illustrates a cross-sectional view of a borehole containing a waveguide for low-loss transmission of millimeter wave radiation as described herein. [Diagram 3] 4 is a flow chart illustrating an exemplary embodiment of a method for forming a multi-piece corrugated waveguide as described herein. [Figure 4] 4 is a flow chart illustrating an exemplary embodiment of a method for coating a portion of a multi-piece corrugated waveguide as described herein. [Diagram 5] FIG. 2 illustrates a cross-sectional view of an exemplary embodiment of a multi-piece corrugated waveguide as described herein. [Figure 6] FIG. 2 illustrates a cross-sectional view of an exemplary embodiment of a multi-piece corrugated waveguide including a dielectric material and / or a thermal insulating material on the outer surface of the coil spring of the multi-piece corrugated waveguide described herein. [Figure 7] FIG. 2 illustrates a cross-sectional view of an exemplary embodiment of a multi-piece corrugated waveguide including an insulating layer between a tube and a coil spring of the multi-piece corrugated waveguide described herein. [Figure 8] FIG. 2 illustrates a cross-sectional view of an exemplary embodiment of a multi-piece corrugated waveguide including dielectric and / or insulating materials on the inner surface of the tube of the multi-piece corrugated waveguide as described herein. [Figure 9] FIG. 2 illustrates a cross-sectional view of an exemplary embodiment of a multi-piece corrugated waveguide including an inner tube having a spiral groove formed on the inner surface of the inner tube as described herein. [Figure 10] FIG. 2 illustrates a cross-sectional view of an exemplary embodiment of a multi-piece corrugated waveguide including an inner tube having a spiral groove and a dielectric material on the outer surface of the inner tube of the multi-piece corrugated waveguide described herein. [Figure 11]FIG. 1 illustrates a cross-sectional view of an exemplary embodiment of a multi-piece corrugated waveguide including an inner tube having a spiral groove and an insulating layer between the tube and a coil spring of the multi-piece corrugated waveguide described herein. [Figure 12] FIG. 2 illustrates a cross-sectional view of an exemplary embodiment of a multi-piece corrugated waveguide including a tapered tube and a tapered coil spring as described herein. [Figure 13] FIG. 2 illustrates a cross-sectional view of an exemplary embodiment of a multi-piece corrugated waveguide including a bent tube as described herein. [Figure 14A] FIG. 2 illustrates a cross-sectional view of an exemplary embodiment of a multi-piece corrugated waveguide including a casing through which the tubes and coil springs described herein can extend. [Figure 14B] FIG. 2 illustrates a cross-sectional view of an exemplary embodiment of a multi-piece corrugated waveguide including a casing through which the tubes and coil springs described herein can extend. [Figure 15] FIG. 1 illustrates an exemplary embodiment of manufacturing a coiled tubing product for use in the multi-piece corrugated waveguide described herein. [Figure 16] FIG. 1 illustrates an exemplary embodiment of manufacturing a multi-piece corrugated waveguide as described herein, including a coiled tubing product. [Figure 17A] 1A-1C illustrate exemplary embodiments of coil springs included in a multi-piece corrugated waveguide as described herein. [Figure 17B] 1A-1C illustrate exemplary embodiments of coil springs included in a multi-piece corrugated waveguide as described herein. [Figure 17C] 1A-1C illustrate exemplary embodiments of coil springs included in a multi-piece corrugated waveguide as described herein. [Figure 17D] 1A-1C illustrate exemplary embodiments of coil springs included in a multi-piece corrugated waveguide as described herein. [Figure 17E]1A-1C illustrate exemplary embodiments of coil springs included in a multi-piece corrugated waveguide as described herein. [Figure 17F] 1A-1C illustrate exemplary embodiments of coil springs included in a multi-piece corrugated waveguide as described herein. [Figure 17G] 1A-1C illustrate exemplary embodiments of coil springs included in a multi-piece corrugated waveguide as described herein. [Figure 18A] 1A-1C illustrate exemplary embodiments of cross-sectional shapes of multiple coil elements included in a multi-piece guide described herein. [Figure 18B] 1A-1C illustrate exemplary embodiments of cross-sectional shapes of multiple coil elements included in a multi-piece guide described herein. [Figure 18C] 1A-1C illustrate exemplary embodiments of cross-sectional shapes of multiple coil elements included in a multi-piece guide described herein. [Figure 18D] 1A-1C illustrate exemplary embodiments of cross-sectional shapes of multiple coil elements included in a multi-piece guide described herein. [Figure 18E] 1A-1C illustrate exemplary embodiments of cross-sectional shapes of multiple coil elements included in a multi-piece guide described herein. [Figure 19A] FIG. 2 illustrates an exemplary embodiment of a square cross-sectional profile of a protruding portion of a coil element of a multi-piece corrugated waveguide as described herein. [Figure 19B] FIG. 2 illustrates an exemplary embodiment of a plurality of coil elements, each of which includes a square cross-sectional profile of a protruding portion as described herein. [Figure 20A] FIG. 2 illustrates an exemplary embodiment of a trapezoidal cross-sectional profile of a protruding portion of a coil element of a multi-piece corrugated waveguide as described herein. [Figure 20B] FIG. 2 illustrates an exemplary embodiment of a plurality of coil elements, each of which includes a trapezoidal cross-sectional profile of a protruding portion as described herein. [Figure 21A]FIG. 13 illustrates another exemplary embodiment of a trapezoidal cross-sectional profile of a protruding portion of a coil element of a multi-piece corrugated waveguide described herein. [Figure 21B] FIG. 13 illustrates another exemplary embodiment of a plurality of coil elements, each of which includes a trapezoidal cross-sectional profile of a protruding portion as described herein. [Figure 22A] FIG. 2 illustrates an exemplary embodiment of a rectangular cross-sectional profile of a protruding portion of a coil element of a multi-piece corrugated waveguide as described herein. [Figure 22B] FIG. 2 illustrates an exemplary embodiment of a plurality of coil elements, each of which includes a rectangular cross-sectional profile of a protruding portion as described herein. [Figure 23A] FIG. 2 illustrates an exemplary embodiment of a circular cross-sectional profile of a protruding portion of a coil element of a multi-piece corrugated waveguide as described herein. [Figure 23B] FIG. 2 illustrates an exemplary embodiment of a plurality of coil elements, each of which includes a circular cross-sectional profile of a protruding portion as described herein. [Figure 24A] FIG. 2 illustrates an exemplary embodiment of a sinusoidal cross-sectional profile of a protruding portion of a coil element of a multi-piece corrugated waveguide as described herein. [Figure 24B] FIG. 2 illustrates an exemplary embodiment of a plurality of coil elements, each of which includes a sinusoidal cross-sectional profile of a protruding portion as described herein. [Figure 25A] FIG. 2 illustrates an exemplary embodiment of a protruding portion of a coil element including multiple cross-sectional profiles as described herein. [Figure 25B] FIG. 2 illustrates an exemplary embodiment of multiple coil elements, each of which includes a protruding portion having multiple cross-sectional profiles as described herein. [Figure 26] FIG. 1 illustrates an exemplary embodiment of a multi-piece corrugated waveguide formed from two nested coil springs as described herein. [Figure 27] FIG. 26D illustrates an exemplary embodiment of the multi-piece corrugated waveguide of FIG. 26C.

[0025] It should be noted that the drawings are not necessarily to scale. The drawings are intended to depict only typical aspects of the subject matter disclosed herein, and therefore should not be considered as limiting the scope of the present disclosure. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0026] A waveguide is a structure that guides waves, such as electromagnetic waves or sound, minimizing energy loss by restricting the transmission of energy to one direction. Waveguides can be used, for example, in millimeter wave drilling operations to efficiently transport electromagnetic waves to the required depth to form a wellbore. The design and materials used to form the waveguide can affect the transmission efficiency of electromagnetic waves transmitted in a particular transmission mode. For example, radio frequency (RF) waves can be transmitted over long distances using a waveguide that includes a series of corrugated features. The corrugated features can include a pattern of repeating ridges or grooves that can extend within the length of the tube. The pattern of corrugated features (e.g., ridges, grooves, etc.) can be shaped to aid in the propagation of electromagnetic waves and can be dimensioned according to the characteristics of the waves (e.g., frequencies) that the waveguide is designed to propagate efficiently. Often, corrugated waveguides can include a dielectric or conductive coating that can improve the transmission efficiency of the waveguide.

[0027] Some existing techniques for forming corrugated waveguides include machining, rotary cutting, tapping, or drilling the inner surface of the tube to form the corrugation features. It is also possible to construct a stack of rings within the tube to form the corrugation features. However, these techniques can be difficult to perform when the length of the waveguide is long, and therefore can introduce errors in the dimensions of the corrugation features. Such errors can reduce the transmission efficiency of the waveguide.

[0028] In addition, forming long lengths of waveguide using some existing methods may leave residual material, such as shavings, burrs, etc., which may also reduce the transmission efficiency of the waveguide. Also, some existing methods are not suitable for subsequent machining of long lengths of tube to correct imperfections in the corrugation features. Thus, repair and replacement costs of waveguides formed in long lengths of tube using some conventional methods may be high. Coating the interior surface of long lengths of tube (and corrugation features therein) with, for example, a conductive coating, may be difficult, expensive, and labor intensive.

[0029] The multi-piece corrugated waveguides described herein can be used in various industries and applications where electromagnetic waves are transmitted, such as the oil and gas production industry, nuclear energy, nuclear fusion reactors, drilling and mining operations, and sound or audio applications. The design and manufacturing approach of the multi-piece corrugated waveguide can provide a cheaper alternative for any industry or application compared to purchasing long corrugated waveguides with corrugation features formed via traditional manufacturing methods. Thus, some implementations of the present subject matter can include a multi-piece corrugated waveguide formed from a coil spring disposed within a tube. The coil spring can be shaped to provide the corrugation features of the waveguide, while the tube can provide structural support. By utilizing the coil spring inside the tube as a waveguide, longer lengths of waveguide can be manufactured without the dimensional errors of the corrugation features that are introduced by some existing approaches to forming waveguides. By reducing the dimensional tolerance of the corrugated features, the waveguide can propagate electromagnetic waves (eg, millimeter waves) more efficiently, thereby resulting in an improved waveguide.

[0030] In some embodiments, the multi-piece corrugated waveguide can be configured for use in millimeter wave drilling during well formation. In some implementations, the coil spring and the inner surface of the tube can be coated, for example, with a conductive coating. The transmission efficiency of some implementations of the multi-piece corrugated waveguide described herein can also be improved by dimensioning the features of the coil spring, such as the width, depth, and pitch of the coil spring for a particular transmission mode. Some implementations of the multi-piece corrugated waveguide described herein can provide efficient transmission of electromagnetic waves in various transmission modes.

[0031] Some implementations of the multi-piece corrugated waveguide described herein can be formed by assembling multiple individual components. In some implementations, each of the individual components can be formed with greater precision compared to existing methods of machining corrugation features into a single long piece of tube. Forming the components individually can ensure that corrugation features are formed with the desired properties necessary for efficient and frequency-dependent transmission of electromagnetic waves. Also, individually manufacturing the components of some implementations of the multi-piece corrugated waveguide described herein can reduce labor and maintenance costs because the coil spring and tube can be assembled together over a longer range of lengths compared to machining a fixed length of tube.

[0032] In some implementations, repair and replacement costs can be reduced because the coil spring can be easily removed and replaced within the tube. In contrast, existing methods can require specialized equipment and long downtime to re-machine long lengths of tube, resulting in higher repair and replacement costs. Additionally, re-machining the tube multiple times can result in insufficient material remaining to re-form the desired corrugation features of the waveguide.

[0033] FIG. 1 illustrates an exemplary embodiment of a millimeter wave drilling (MMWD) system 100 including an exemplary multi-piece corrugated waveguide 108. The MMWD system 100 shown in FIG. 1 includes a gyrotron 102 connected via a power cable 104 to a power supply 106 that provides power to the gyrotron 102. A high power millimeter wave beam output by the gyrotron 102 is guided by a waveguide 108, such as a multi-piece corrugated waveguide as described herein. The waveguide 108 can include a waveguide bend 118, a window 120, and a waveguide section 126 having an opening 128 for off-gas venting and pressure control. A section of the waveguide is below ground level 130 to help seal the borehole.

[0034] As part of the transmission line of the waveguide 108, there is an isolator 110 to prevent reflected power from returning to the interface for the gyrotron 102 and diagnostic access 112. The diagnostic access is connected by a low power waveguide 114 to the diagnostic electronics and data acquisition 116. At the window 120, there is a pressurized gas supply unit 122 connected by piping 124 to the window to inject a clean gas flow over the inside of the window to prevent deposition on the window. A second pressurized unit 136 is connected by piping 132 to the waveguide opening 128 to control the pressure in the borehole 148 and to help introduce and remove borehole gas as needed. The window gas injection unit 122 can be operated at a slightly higher pressure relative to the borehole pressure unit 136 to maintain a gas flow over the entire window surface. A branch line 134 in the borehole pressurization piping 132 may connect to a pressure relief valve 138 to allow volatilized borehole material and window gases to be exhausted to the atmosphere 146 through a gas analysis monitoring unit 140 followed by a gas filter 142 and an exhaust duct 144. In some embodiments, the exhaust duct 144 may return the gases to the pressurization unit 136 for reuse.

[0035] The pressure within the borehole may be partially or fully increased by partial volatilization of the molten subsurface material. A thermal melt front 152 at the end of the borehole 148 may propagate under the combined action of mmWave power and gas pressure into the subsurface formation leaving behind a ceramic (e.g., vitreous) borehole wall 150. This wall may act as a dielectric waveguide to transmit the mmWave beam to the thermal front 152.

[0036] FIG. 2 illustrates a cross-sectional view of an exemplary borehole including a multi-piece corrugated waveguide that can be configured to transmit millimeter-wave radiation with low loss. FIG. 2 provides a more detailed view corresponding to the MMWD and MMWD system described in U.S. Patent No. 8,393,410, entitled "Millimeter-wave Drilling System" to Woskov et al. A borehole 200 with annulus 205, vitreous / ceramic wall 210, and transparent glass 215 has a waveguide assembly 220 inserted to improve the propagation efficiency of the millimeter-wave beam. In some embodiments, the waveguide assembly can include a multi-piece corrugated waveguide as described herein. In some embodiments, multiple waveguide assemblies can be inserted into the borehole. For example, multiple waveguide assemblies can be stacked on top of each other up to 1 km, 5 km, 10 km, or more below the surface of the well.

[0037] As shown in FIG. 2, the diameter of the waveguide assembly 220 can be smaller than the borehole diameter to create an annular gap 225 for evacuation / extraction. The standoff distance 230 of the leading edge of the multi-piece corrugated waveguide 220 from the thermal fusion front 235 of the borehole is far enough to allow the launched millimeter wave beam spread 240 to fill 245 the dielectric borehole 200 with the guided millimeter wave beam. The standoff distance 230 is also far enough to keep the temperature of the waveguide assembly 220 low enough for survivability. The inserted waveguide assembly 220 also acts as a conduit for a pressurized gas flow 250 from the surface. This gas flow keeps the waveguide clean and contributes to the extraction / removal of rock material from the borehole. The gas flow from the surface 250 mixes 255 with the volatilized outgassed rock material 260 and transports the condensed rock vapor through the annular space 225 to the surface. The exhaust gas stream 265 is large enough to limit the size of the volatilized rock particles and transport them to the surface.

[0038] FIG. 3 is a flow chart illustrating an exemplary embodiment of a method for forming a multi-piece corrugated waveguide as described herein. At 305, a wire including a cross-sectional profile can be extruded. Extruding or rolling a wire to form a coil spring (e.g., a corrugated feature of a waveguide as described herein) can advantageously improve the quality of the manufactured waveguide, since extrusion is less likely to leave burrs or machined material in the waveguide compared to conventional methods that can machine, tap, or otherwise drill corrugated grooves into the inner surface of the waveguide. The wire can be made from any standard metallic or non-metallic material. In some embodiments, the wire can include a metal wire or other conductive material, such as copper wire, aluminum wire, or copper chromium zirconium alloy wire. The extrusion can form the cross-sectional profile of the wire. The cross-sectional profile can include a base portion and a protruding portion extending from the base portion, as shown and described with respect to FIGS. 19-25.

[0039] The base portion and the protruding portion can include profiles that can be shaped in a variety of geometries and dimensions. For example, in some embodiments, the profile of the protruding portion can include a trapezoidal profile, a circular profile, a square profile, a rectangular profile, or a sinusoidal profile. In some embodiments, the base portion can include a rectangular profile or a curved profile. Other profile shapes are possible.

[0040] The protruding portion can include a width and depth that can accommodate the mode and / or frequency of the electromagnetic wave to be transmitted through the multi-piece corrugated waveguide described herein. For example, the width and depth of the protruding portion can be formed to accommodate optimal transmission of electromagnetic waves, such as millimeter waves and microwaves in the HE11 mode or any other mode with low attenuation.

[0041] The width and depth of the protruding parts of the corrugated waveguide can be configured with respect to the frequency of the wave transmitted through the waveguide. For example, for optimal transmission of the HE11 mode, the width of the corrugations can be less than 1 / 6 of the wavelength and the depth of the corrugations can be about 1 / 4 of the wavelength of the beam. For other propagation modes, the corrugations can take on different geometrical characteristics.

[0042] At 310, the wire can be formed into a coil spring having an outer diameter and a plurality of coil elements disposed along the length of the coil spring. In some embodiments, the coil spring can be formed by wrapping the wire around a form, such as a mandrel, to form the wire into the coil spring. In this manner, the cross-sectional shape of the coil spring (e.g., the shape observed when the coil spring is viewed from a perspective parallel to an axis extending along the length of the coil spring) and the shape of each coil element of the coil spring can correspond to the cross-sectional shape of the mandrel (e.g., the shape observed when the mandrel is viewed from a perspective parallel to an axis extending along the length of the mandrel). The cross-sectional shape of the mandrel (and thus the coil element, the plurality of coil elements, and the cross-sectional shape of the coil spring) can include, for example, a trapezoidal shape, a circular shape, a rectangular shape, a square shape, or an elliptical shape as shown in Figures 18A-18E. Other shapes are possible.

[0043] In some embodiments, the coil spring can be a tapered coil spring, which can be formed using a tapered mandrel. In some embodiments, the cross-sectional shape of the plurality of coil elements, and therefore the coil spring, can vary along the length of the plurality of coil elements and / or the coil spring. In some embodiments, the coil spring can include multiple cross-sectional profiles along the length of the coil spring.

[0044] A coil element of the coil spring can correspond to one turn of the wire around the mandrel. Each coil element can have a circumference and a diameter. The diameter of each coil element can correspond to the diameter of the coil spring and the number of coil elements forming the coil spring. As shown with respect to FIG. 17A, the number of coil elements can include a pitch defined between the centers of two coil springs. The pitch can correspond to the mode and / or frequency of the electromagnetic wave transmitted through the multi-piece corrugated waveguide described herein. In addition, the coil element can include a protruding portion. The protruding portion can be formed with a width and depth corresponding to optimal transmission of millimeter waves in, for example, HE11 mode. The coil element geometry showing the width and depth of the protruding portion is shown and described with respect to FIGS. 19-25.

[0045] In some embodiments, the coil spring can be formed as a compression spring or a tension spring. Depending on the desired pitch between the coil elements, it may be advantageous to use a compression spring (e.g., a coil spring having a larger pitch between the coil elements, as shown in FIG. 17A) instead of a tension spring (e.g., a coil spring having a smaller pitch between the coil elements, as shown in FIG. 17B). In some embodiments, multiple coil springs can be formed in the manner described with respect to operation 310. In some embodiments, as shown in FIGS. 17B and 17C, the coil spring can be formed to include attachment points at each end of the coil spring such that multiple coil springs can be linked or joined together. For example, the attachment points can include semicircular attachment points configured at each end of the coil spring. A semicircular attachment point at one end of one coil spring can be joined with a semicircular attachment point at one end of another adjacent coil spring.

[0046] At 315, the coil spring can be inserted into the tube. The tube can provide structural rigidity to the coil spring and can be designed to provide an air-tight or liquid-tight (e.g., pressurized) containment. In some embodiments, the tube can be a continuous tube, a coiled tube product, or a pipe tube product. In some embodiments, the tube can be a gas injector or pump evacuation device. The tube can have an inner diameter that can be larger than the outer diameter of the coil spring. The tube can have a length along which the coil can extend within the tube. As shown in Figures 5-8, 12-13, and 14A-14B, the coil spring can form a plurality of corrugation features within the tube when inserted into the tube. The corrugation features can enable the coil spring and tube to efficiently transmit electromagnetic waves therethrough in various transmission modes, such as the HE11 mode. The corrugation features can be further defined as a result of extruding a wire with a specific cross-sectional profile and pitch such that transmission efficiency is achieved by the cross-sectional profile of the coil spring and the plurality of coil elements within the tube. In some embodiments, the tube can be made of a metallic or non-metallic material. In some embodiments, the tube can be made of carbon steel, stainless steel, Inconel, titanium alloy, molybdenum alloy, tungsten alloy, copper alloy, aluminum alloy, or copper chromium zirconium. In some embodiments, a plurality of coil springs can be inserted into the tube.

[0047] In some embodiments, as shown in Figures 5-8 and 12-13, when the coil spring is inserted into the tube, a gap can be formed between the inner surface of the tube and the outer surface of the coil spring. The gap can allow deformation of the coil spring material due to thermal expansion during electromagnetic wave transmission through the tube and the coil spring. The gap allows gas to flow from the surface to the bottom of the borehole while allowing cooling of the inner and outer corrugations of the coil spring, which cannot be achieved with conventional waveguide pipes. The tube can act as an additional barrier for any electromagnetic waves that may leak through the coil spring to the environment. In some embodiments, a channel can be formed on the inner surface of the tube, which can allow gas to flow from the surface to the bottom of the borehole. In some embodiments, the channel can extend axially along the length of the tube.

[0048] FIG. 4 is a flow chart illustrating an exemplary embodiment of a method 400 for coating a portion of a multi-piece corrugated waveguide as described herein. Coating or dipping a portion of a multi-piece corrugated waveguide as described herein can increase the transmission efficiency of transmitted electromagnetic waves and can also help manage thermal conditions within the multi-piece corrugated waveguide. Compared to conventional methods of coating the inner surface of a long tube that has been drilled or machined to form corrugated waveguide features within the long tube, coating a portion of a multi-piece corrugated waveguide as described herein can be performed more easily because the coil spring and tube can be formed and coated separately. In addition, the use of a shorter length coil spring as described herein can also make it easier to apply the coating material prior to insertion into the tube.

[0049] At 405, the wire can be coated with a conductive material. In some embodiments, the wire can be coated with a conductive material such as copper, silver, platinum, or gold. The coating process can include vapor deposition, chemical or electrochemical coating, spraying, spinning, dipping, applying a film, etc. In some embodiments, the wire can be coated with a dielectric material.

[0050] At 410, the coil spring can be coated with a conductive material. In some embodiments, the outer diameter of the coil spring can be coated with a conductive material, as shown in FIG. 17B. In some embodiments, the coil spring can be coated with a conductive material, such as copper, silver, platinum, or gold. In some embodiments, the coil spring can be coated with a dielectric material. The coating process can include vapor deposition, chemical or electrochemical coating, spraying, spinning, dipping, applying a film, and the like.

[0051] At 415, the inner surface of the tube can be coated with an insulating material. For example, as shown in FIG. 8, the inner surface of the tube can be coated with a dielectric material. The insulating material can be thermally insulating and can be used between the inner surface of the tube and the outer surface of the coil spring to isolate the heat in the well bore annulus 205 from the coil spring. This can allow purge gas from the surface to cool the coil spring down to the bottom of the borehole without losing cooling capacity due to interaction with the inner surface of the tube (contact with the hot gases rising through the annulus 205). In some embodiments, the insulating material can include fiberglass, open cell foam, closed cell foam, polystyrene, ceramic fiber, carbon composite, silica fiber, rock wool, and the like.

[0052] Although the multi-piece corrugated waveguide is described herein with respect to drilling operations, the multi-piece corrugated waveguide embodiments herein can be deployed in a variety of other configurations for transmitting electromagnetic waves. Although drilling operations require the insertion of an MCG into the earth and possibly flowing gas through or around the MCG, other applications of the MCG embodiments described herein can be performed using a fixed placement of the MCG on the ground. For example, in nuclear energy or sound transmission applications, the MCG can be configured on the ground surface and positioned relative to a target to which the electromagnetic waves are transmitted.

[0053] Figure 5 is a diagram illustrating a cross-sectional view of an exemplary embodiment of a multi-piece corrugated waveguide 500 as described herein. Some implementations of the multi-piece corrugated waveguide (MCG) as described herein can be formed according to the methods 300 and 400 described with respect to Figures 3 and 4. The exemplary MCG described herein can be configured to operate within the system 100 described with respect to Figure 1 and to deploy the borehole 200 described with respect to Figure 2.

[0054] As shown in FIG. 5, the MCG 500 can be deployed in a borehole 505 at a surface 510 where a well or other subsurface drilling operation is being performed. The MCG 500 can deliver electromagnetic energy 515, such as RF waves, to the borehole 505. The MCG 500 can include a tube 520 and a coil spring 525 positioned within the tube 520. The tube 520 can include an inner surface, an outer surface, an inner diameter defined between the opposing inner surfaces, an outer diameter defined between the opposing outer surfaces, and a length defined between a first tube end 520 and a second tube end 520. In some embodiments, the length of the tube 520 can be greater than 1 meter, greater than 5 meters, or greater than 9 meters. In embodiments where the tube comprises a continuous tube, a coiled tube product, or a pipe tube product, the length of the tube 520 can be greater than 10 km. When forming a borehole, dozens to hundreds of pipes 520 may be deployed to reach a sufficient depth required to form a well.

[0055] The coil spring 525 can include a plurality of coil elements 530 disposed along the length of the tube 520 and can form a waveguide. The plurality of coil elements 530 can include two or more coil elements 535. The coil spring 525 can include an outer surface that contacts the inner surface of the tube 520 and an outer diameter defined between the opposing outer surfaces of the coil spring 525. The outer diameter of the coil spring 525 can be smaller than the inner diameter of the tube 520.

[0056] 5, a gap 540 may be defined between an outer surface of the coil spring 525 and an inner surface of the tube 520. This gap may allow the coil spring 525 to expand within the tube 520 as a result of thermal expansion of the coil spring 525 during transmission of the electromagnetic waves through the MCG 500. The gap 540 may also allow gas to pass from the surface to the bottom of the borehole. Additionally, a second gap 545 may be defined between the outer surface of the tube 520 and the wall of the borehole 505.

[0057] In some embodiments, the cross-sectional profile of each of the coil springs 525 and the coil elements 535 can be dimensioned to propagate electromagnetic waves through the MCG 500. For example, the cross-sectional profile of the coil springs 525 and the coil elements 535 can be shaped and dimensioned to propagate millimeter electromagnetic waves having low attenuation. The cross-sectional profile of the coil springs 525 and the coil elements 535 can be dimensioned to propagate electromagnetic waves in one or more transmission modes. For example, the cross-sectional profile of the coil springs 525 and the coil elements 535 can be dimensioned to propagate millimeter electromagnetic waves in the HE11 mode.

[0058] In some embodiments, the cross-sectional profile of the coil spring 525 and coil element 535 may be sized based on the wavelength and / or frequency of the transmitted electromagnetic waves.

[0059] 5, the coil spring 525 can form a helical groove 550. In some implementations, the helical groove 550 can extend continuously on an inner surface of the coil spring 525 along the length of the coil spring 525. The helical groove 550 can be formed by opposed protruding portions of each coil element 535. In some embodiments, the coil spring 525 can include an inner diameter 555 measured between the protruding portions of each coil element 535. In some embodiments, the inner diameter 555 can include a diameter of 5.0 mm to 15.0 mm, 10.0 mm to 20.0 mm, 15.0 mm to 25.0 mm, 20.0 mm to 30.0 mm, 25.0 mm to 35.0 mm, 30.0 mm to 40.0 mm, 45.0 mm to 55.0 mm, 50.0 mm to 60.0 mm, 55.0 mm to 65.0 mm, 60.0 mm to 70.0 mm, 65.0 mm to 75.0 mm, 70.0 mm to 80.0 mm, 75.0 mm to 90.0 mm, or 85.0 mm to 200.0 mm. In some embodiments, the inner diameter can be greater than 200.0 mm or less than 5.0 mm. Other inner diameters are possible. In some embodiments, the inner diameter 555 can include a tolerance range of ±0.075 mm, ±0.1 mm, ±0.125 mm, ±0.150 mm, ±0.175 mm, or ±0.2 mm, ±0.225 mm, or ±0.25 mm, etc., although other tolerance ranges are possible.

[0060] FIG. 6 illustrates a cross-sectional view of an exemplary embodiment of a multi-piece corrugated waveguide 600 including a dielectric material and / or thermal insulation material on the outer surface of the coil spring of the multi-piece corrugated waveguide described herein. As shown in FIG. 6, the MCG 600 can include a tube 605, a coil spring 610, and a dielectric material 615 on the outer surface of the coil spring 610. In some embodiments, the dielectric material can include glass, ceramic, porcelain, and most plastics. The dielectric material 615 can be applied to the outer diameter of the coil spring 610 as a coating, or the dielectric material 615 can be a separate component added to the assembled MCG 600. The dielectric material 615 can electrically insulate the tube 605 from the coil spring 610 to prevent electrical shorts between them.

[0061] In some embodiments, the coil spring 610 can include an inner diameter 620 measured between the protruding portions of each coil element of the coil spring 610. In some embodiments, the inner diameter 620 can include a diameter of 5.0 mm to 15.0 mm, 10.0 mm to 20.0 mm, 15.0 mm to 25.0 mm, 20.0 mm to 30.0 mm, 25.0 mm to 35.0 mm, 30.0 mm to 40.0 mm, 45.0 mm to 55.0 mm, 50.0 mm to 60.0 mm, 55.0 mm to 65.0 mm, 60.0 mm to 70.0 mm, 65.0 mm to 75.0 mm, 70.0 mm to 80.0 mm, 75.0 mm to 90.0 mm, or 85.0 mm to 200.0 mm. In some embodiments, the diameter can be greater than 200.0 mm or less than 5.0 mm. Other diameters are possible. In some embodiments, the inner diameter 620 can include a tolerance range, such as ±0.075 mm, ±0.1 mm, ±0.125 mm, ±0.150 mm, ±0.175 mm, ±0.2 mm, ±0.225 mm, or ±0.25 mm, although other tolerance ranges are possible.

[0062] FIG. 7 illustrates a cross-sectional view of an exemplary embodiment of a multi-piece corrugated waveguide 700 including an insulating layer between the tube and the coil spring of the multi-piece corrugated waveguide described herein. As shown in FIG. 7, the MCG 700 can include a tube 705, a coil spring 710, and an insulating layer 715. The insulating layer 715 can be thermally insulating and can be positioned between the tube 705 and the coil spring 710. In some embodiments, the insulating layer can be formed from insulating materials such as fiberglass, open / closed cell foam, polystyrene, ceramic fiber, carbon composite, silica fiber, rock wool, and the like. The insulating material can be positioned between the inner surface of the tube 705 and the outer surface of the coil spring 710 to isolate heat within the well bore annulus 205 from the coil spring 710. This can allow purge gas from the surface to cool the coil spring 710 all the way to the bottom of the borehole without losing cooling capacity due to interaction with the inner surface of the tube 705 (contact with the hot gases rising through the annulus 205).

[0063] In some embodiments, the coil spring 710 can include an inner diameter 720 measured between the protruding portions of each coil element of the coil spring 710. In some embodiments, the inner diameter 720 can include a diameter of 5.0 mm to 15.0 mm, 10.0 mm to 20.0 mm, 15.0 mm to 25.0 mm, 20.0 mm to 30.0 mm, 25.0 mm to 35.0 mm, 30.0 mm to 40.0 mm, 45.0 mm to 55.0 mm, 50.0 mm to 60.0 mm, 55.0 mm to 65.0 mm, 60.0 mm to 70.0 mm, 65.0 mm to 75.0 mm, 70.0 mm to 80.0 mm, 75.0 mm to 90.0 mm, or 85.0 mm to 200.0 mm. In some embodiments, the diameter can be greater than 200.0 mm or less than 5.0 mm. Other diameters are possible. In some embodiments, the inner diameter 720 can include a tolerance range, such as ±0.075 mm, ±0.1 mm, ±0.125 mm, ±0.150 mm, ±0.175 mm, ±0.2 mm, ±0.225 mm, or ±0.25 mm, although other tolerance ranges are possible.

[0064] 8 is a diagram illustrating a cross-sectional view of an example embodiment of a multi-piece corrugated waveguide 800 including a dielectric material and / or insulating material on an inner surface of the tube of the multi-piece corrugated waveguide described herein. As shown in FIG. 8, the MCG 800 can include a tube 805, a coil spring 810, and a dielectric material 815 on an inner surface of the tube 815. In some embodiments, the dielectric material and / or insulating material can include fiberglass, open / closed cell foam, polystyrene, ceramic fiber, carbon composite, silica fiber, rock wool, and the like.

[0065] In some embodiments, the coil spring 810 can include an inner diameter 820 measured between the protruding portions of each coil element of the coil spring 810. In some embodiments, the inner diameter 820 can include a diameter of 5.0 mm to 15.0 mm, 10.0 mm to 20.0 mm, 15.0 mm to 25.0 mm, 20.0 mm to 30.0 mm, 25.0 mm to 35.0 mm, 30.0 mm to 40.0 mm, 45.0 mm to 55.0 mm, 50.0 mm to 60.0 mm, 55.0 mm to 65.0 mm, 60.0 mm to 70.0 mm, 65.0 mm to 75.0 mm, 70.0 mm to 80.0 mm, 75.0 mm to 90.0 mm, or 85.0 mm to 200.0 mm. In some embodiments, the diameter can be greater than 200.0 mm or less than 5.0 mm. Other diameters are possible. In some embodiments, the inner diameter 820 can include a tolerance range, such as ±0.075 mm, ±0.1 mm, ±0.125 mm, ±0.150 mm, ±0.175 mm, ±0.2 mm, ±0.225 mm, or ±0.25 mm, although other tolerance ranges are possible.

[0066] FIG. 9 is a diagram illustrating a cross-sectional view of an exemplary embodiment of a multi-piece corrugated waveguide 900 including an inner tube having a spiral groove formed on the inner surface of the inner tube as described herein. As shown in FIG. 9, the MCG 900 can include an outer tube 905. The outer tube 905 can include an inner surface, an inner diameter defined between an opposing inner surface, and a length defined between a first tube end 905 and a second tube end 905. The MCG 900 can also include one or more inner tubes, such as inner tubes 910 and 915. Each inner tube can include an inner surface, an outer surface, an outer diameter defined between an opposing outer surface, and a spiral shaped groove 920 formed on the inner surface of the inner tubes 910 and 915. The inner tubes 910 and 915 can be positioned within the outer tube 905 as a result of the outer diameter of the inner tubes 910 and 915 being smaller than the inner diameter of the outer tube 905. In some embodiments, for example, when multiple inner tubes are positioned within the outer tube 905, two or more inner tubes 910 and 915 can be joined via a threaded connection, via welding one inner tube to a second inner tube, or via bolting one inner tube to a second inner tube. In some embodiments, the inner tubes 910 and / or 915 can be secured within the outer tube 905 via protrusions formed on the inner surface of the outer tube 905. In some embodiments, the inner tubes 910 and 915 can be joined via a magnetic coupling or a retainer ring that can encircle the overlapping portions of the inner tubes 910 and 915. In some embodiments, the inner tubes 910 and 915 can be formed from a flat sheet plate of stock material that is rolled into a tubular shape. In such embodiments, corrugation features can be formed in the surface of the flat sheet of stock material, where the corrugation features can include helical corrugations as well as non-helical corrugations that are formed as peaks and valleys in the surface of the flat sheet of stock material. In some embodiments, the inner tubes 910 and 915 may be formed via additive manufacturing processes.

[0067] The spiral shaped groove 920 may be formed as a continuous or semi-continuous groove that may extend along the length of the inner tubes 910 and 915. The spiral shaped groove 920 may form a waveguide configured to transmit electromagnetic waves through the MCG 900. For example, the spiral shaped groove 920 may be configured to propagate millimeter electromagnetic waves in one or more transmission modes. In some embodiments, the spiral shaped groove 920 may be configured to propagate millimeter electromagnetic waves in a HE11 transmission mode, although other transmission modes, such as a transverse electric mode (TE) or a transverse magnetic mode (TM), or a combination of TE and TM, may also propagate through the spiral shaped groove 920.

[0068] 9, in some embodiments, a gap 925 can be defined between the outer surface of the inner tubes 910 and 915 and the inner surface of the outer tube 905. The gap 925 can allow the inner tubes 910 and 915 to expand within the tube 905 as a result of thermal expansion of the inner tubes 910 and 915 during electromagnetic wave transmission through the MCG 900. The gap 925 can also allow gas to pass from the surface to the bottom of the borehole.

[0069] 9, in some embodiments, the spiral shaped groove 920 can include a conductive material 930. The conductive material 930 can be present on a surface of the spiral groove 920. In some embodiments, the interior surface of the inner tubes 910 and / or 915 can include a conductive material 935. The conductive material can include copper, silver, platinum, or gold.

[0070] In some embodiments, the MCG 900 can include an inner diameter 940 measured between the protruding portions of each inner tube 910 and 915. The protruding portions can be formed by a spiral shaped groove 920. In some embodiments, the inner diameter 940 can include a diameter of 5.0 mm to 15.0 mm, 10.0 mm to 20.0 mm, 15.0 mm to 25.0 mm, 20.0 mm to 30.0 mm, 25.0 mm to 35.0 mm, 30.0 mm to 40.0 mm, 45.0 mm to 55.0 mm, 50.0 mm to 60.0 mm, 55.0 mm to 65.0 mm, 60.0 mm to 70.0 mm, 65.0 mm to 75.0 mm, 70.0 mm to 80.0 mm, 75.0 mm to 90.0 mm, or 85.0 mm to 200.0 mm. In some embodiments, the diameter can be greater than 200.0 mm or less than 5.0 mm. Other diameters are possible. In some embodiments, the inner diameter 940 can include a tolerance range, such as ±0.075 mm, ±0.1 mm, ±0.125 mm, ±0.150 mm, ±0.175 mm, ±0.2 mm, ±0.225 mm, or ±0.25 mm, although other tolerance ranges are possible.

[0071] FIG. 10 illustrates an exemplary embodiment of a multi-piece corrugated waveguide 1000 including an inner tube having a spiral groove and a dielectric material on the outer surface of the inner tube of the multi-piece corrugated waveguide described herein. As shown in FIG. 10, the MCG 1000 can include an outer tube 1005 and an inner tube 1010. In the embodiment shown in FIG. 10, a single inner tube 1010 is configured inside the outer tube 1005. The inner tube 1010 includes a spiral shaped groove 1015 formed on the inner surface of the inner tube 1010. The spiral shaped groove 1015 can be a continuous groove formed along the length of the inner tube 1010 and can form a waveguide. The MCG 1000 can include a dielectric material 1020 on the outer surface of the inner tube 1010. The dielectric material 1020 may include glass, ceramic, porcelain, or plastic and may be applied to the outer diameter of the inner tube 1020 as a coating, or the dielectric material 1020 may be a separate component added to the MCG 1000 assembly. The dielectric material 1020 may electrically insulate the outer tube 1005 from the inner tube 1010 and may prevent electrical shorts between them.

[0072] In some embodiments, the MCG 1000 can include an inner diameter 1025 measured between the protruding portions of the inner tube 1010. The protruding portions can be formed by a spiral shaped groove 1015. In some embodiments, the inner diameter 1025 can include a diameter of 5.0 mm to 15.0 mm, 10.0 mm to 20.0 mm, 15.0 mm to 25.0 mm, 20.0 mm to 30.0 mm, 25.0 mm to 35.0 mm, 30.0 mm to 40.0 mm, 45.0 mm to 55.0 mm, 50.0 mm to 60.0 mm, 55.0 mm to 65.0 mm, 60.0 mm to 70.0 mm, 65.0 mm to 75.0 mm, 70.0 mm to 80.0 mm, 75.0 mm to 90.0 mm, or 85.0 mm to 200.0 mm. In some embodiments, the diameter can be greater than 200.0 mm or less than 5.0 mm. Other diameters are possible. In some embodiments, the inner diameter 1025 can include a tolerance range, such as ±0.075 mm, ±0.1 mm, ±0.125 mm, ±0.150 mm, ±0.175 mm, ±0.2 mm, ±0.225 mm, or ±0.25 mm, although other tolerance ranges are possible.

[0073] FIG. 11 illustrates a cross-sectional view of an exemplary embodiment of a multi-piece corrugated waveguide 1100 including an inner tube with a spiral groove and an insulating layer between the tube and a coil spring of the multi-piece corrugated waveguide described herein. As shown in FIG. 11, the MCG 1100 can include an outer tube 1105, an inner tube 1110, and a spiral shaped groove 1115 formed on the inner surface of the inner tube 1110. The MCG 1100 can also include an insulating layer 1120. The insulating layer 1120 can be positioned between the outer tube 1105 and the inner tube 1110. In some embodiments, the insulating layer 1120 can be formed from an insulating material such as fiberglass, open cell foam, closed cell foam, polystyrene, ceramic fiber, carbon composite, silica fiber, rock wool, and the like. An insulating material 1120 can be positioned between the inner surface of the outer tube 1105 and the outer surface of the inner tube 1110 to isolate the heat in the well bore annulus 205 from the inner tube 1110. This can allow purge gas from the surface to cool the inner tube 1110 all the way to the bottom of the borehole without losing cooling capacity due to interaction with the inner surface of the outer tube 1105 (contact with the hot gases rising through the annulus 205).

[0074] In some embodiments, the MCG 1100 can include an inner diameter 1125 measured between the protruding portions of the inner tube 1110. The protruding portions can be formed by a spiral shaped groove 1115. In some embodiments, the inner diameter 1125 can include a diameter of 5.0 mm to 15.0 mm, 10.0 mm to 20.0 mm, 15.0 mm to 25.0 mm, 20.0 mm to 30.0 mm, 25.0 mm to 35.0 mm, 30.0 mm to 40.0 mm, 45.0 mm to 55.0 mm, 50.0 mm to 60.0 mm, 55.0 mm to 65.0 mm, 60.0 mm to 70.0 mm, 65.0 mm to 75.0 mm, 70.0 mm to 80.0 mm, 75.0 mm to 90.0 mm, or 85.0 mm to 200.0 mm. In some embodiments, the diameter can be greater than 200.0 mm or less than 5.0 mm. Other diameters are possible. In some embodiments, the inner diameter 1125 can include a tolerance range, such as ±0.075 mm, ±0.1 mm, ±0.125 mm, ±0.150 mm, ±0.175 mm, ±0.2 mm, ±0.225 mm, or ±0.25 mm, although other tolerance ranges are possible.

[0075] 12 is a diagram illustrating a cross-sectional view of an exemplary embodiment of a multi-piece corrugated waveguide 1200 including a tapered tube and a tapered coil spring as described herein. As shown in FIG. 12, the MCG 1200 can include a tube 1205 and a coil spring 1210 within the tube 1205. The tube 1205 can be a tapered tube. The tapered tube 1205 can have a first diameter defined between opposing faces of the tube 1205 at a first end 1215 of the MCG 1200 and a second diameter defined between opposing faces of the tube 1205 at a second end 1220 of the MCG 1200. Thus, the diameter of the tube 1205 can change from the first end 1215 to the second end 1220. For example, a first diameter of the tube 1205 at the first end 1215 can be smaller than a second diameter of the tube 1205 at the second end 1220. As further shown in FIG. 12, the coil spring 1210 can be a tapered coil spring. Similar to the tube 1205, the coil spring 1210 can have a diameter that varies from the first end 1215 to the second end 1220. The tapered coil spring 1210 can be formed using a tapered mandrel as described with respect to FIG. 3. The two-piece design can advantageously reduce the machining difficulty of creating tapered corrugation features in the tapered tube 1205.

[0076] In some embodiments, the MCG 1200 can include an inner diameter 1225 measured between the protruding portions of the inner tube 1210 at the first end 1215 of the MCG 1200. In some embodiments, the inner diameter 1225 can include a diameter between 5.0 mm and 15.0 mm, 10.0 mm and 20.0 mm, 15.0 mm and 25.0 mm, 20.0 mm and 30.0 mm, 25.0 mm and 35.0 mm, 30.0 mm and 40.0 mm, 45.0 mm and 55.0 mm, 50.0 mm and 60.0 mm, 55.0 mm and 65.0 mm, 60.0 mm and 70.0 mm, 65.0 mm and 75.0 mm, 70.0 mm and 80.0 mm, 75.0 mm and 90.0 mm, or 85.0 mm and 200.0 mm. In some embodiments, the diameter can be greater than 200.0 mm or less than 5.0 mm. Other diameters are possible. In some embodiments, the inner diameter 1225 can include a tolerance range, such as ±0.075 mm, ±0.1 mm, ±0.125 mm, ±0.150 mm, ±0.175 mm, ±0.2 mm, ±0.225 mm, or ±0.25 mm, although other tolerance ranges are possible.

[0077] In some embodiments, the MCG 1200 can include an inner diameter 1230 measured between the protruding portions of the inner tube 1210 at the second end 1230 of the MCG 1200. In some embodiments, the inner diameter 1230 can include a diameter of 5.0 mm to 15.0 mm, 10.0 mm to 20.0 mm, 15.0 mm to 25.0 mm, 20.0 mm to 30.0 mm, 25.0 mm to 35.0 mm, 30.0 mm to 40.0 mm, 45.0 mm to 55.0 mm, 50.0 mm to 60.0 mm, 55.0 mm to 65.0 mm, 60.0 mm to 70.0 mm, 65.0 mm to 75.0 mm, 70.0 mm to 80.0 mm, 75.0 mm to 90.0 mm, or 85.0 mm to 200.0 mm. In some embodiments, the diameter can be greater than 200.0 mm or less than 5.0 mm. Other diameters are possible. In some embodiments, the inner diameter 1230 can include a tolerance range, such as ±0.075 mm, ±0.1 mm, ±0.125 mm, ±0.150 mm, ±0.175 mm, ±0.2 mm, ±0.225 mm, or ±0.25 mm, although other tolerance ranges are possible.

[0078] FIG. 13 is a diagram illustrating a cross-sectional view of an exemplary embodiment of a multi-piece corrugated waveguide 1300 including a curved tube as described herein. As shown in FIG. 13, the MCG 1300 can include a tube 1305 (only the inner surface is shown for clarity) and a coil spring 1310 within the tube 1305. The curved tube 1305 can allow the MCG 1300 to be deployed in various borehole configurations that are not mostly vertical or mostly horizontal geometries. For example, the MCG 1300 can be utilized when transitioning between a vertical borehole configuration and a horizontal borehole configuration, or vice versa. The MCG 1300 can be deployed to steer or steer electromagnetic waves around subsurface obstacles or geological formations that may otherwise limit the transmission efficiency of the transmitted electromagnetic waves. In some embodiments, the tube 1305 can be a bellows tube including multiple contractible segments configured to form a bend in the tube 1305.

[0079] In some embodiments, the coil spring 1310 can include an inner diameter 1315 measured between the protruding portions of each coil element of the coil spring 1310. In some embodiments, the inner diameter 1315 can include a diameter of 5.0 mm to 15.0 mm, 10.0 mm to 20.0 mm, 15.0 mm to 25.0 mm, 20.0 mm to 30.0 mm, 25.0 mm to 35.0 mm, 30.0 mm to 40.0 mm, 45.0 mm to 55.0 mm, 50.0 mm to 60.0 mm, 55.0 mm to 65.0 mm, 60.0 mm to 70.0 mm, 65.0 mm to 75.0 mm, 70.0 mm to 80.0 mm, 75.0 mm to 90.0 mm, or 85.0 mm to 200.0 mm. In some embodiments, the diameter can be greater than 200.0 mm or less than 5.0 mm. Other diameters are possible. In some embodiments, the inner diameter 1315 can include a tolerance range, such as ±0.075 mm, ±0.1 mm, ±0.125 mm, ±0.150 mm, ±0.175 mm, ±0.2 mm, ±0.225 mm, or ±0.25 mm, although other tolerance ranges are possible.

[0080] 14A-14B are diagrams illustrating a cross-sectional view of an exemplary embodiment of a multi-piece corrugated waveguide 1400 including a casing through which the tubes and coil springs described herein can extend. The MCG 1400 can include a tube 1405, a coil spring 1410 within the tube 1405, and a casing 1415. As shown in FIG. 14A, the MCG 1400 is shown in a retracted position. The tube 1405 and coil spring 1410 are retracted into the casing 1415. In FIG. 14B, the MCG 1400 is shown in an extended position. In FIG. 14B, the tube 1405 and coil spring 1410 extend from within the casing 1415. In this manner, the tube 1405 and coil spring 1410 can be telescopically retracted into and extended from the casing 1415. By having the coil spring 1410 span the length of the casing 1415 and tube 1505, the mm-waves can be contained no matter what position or bend angle the MCG 1400 is in. Also, because the spring 1405 is one piece, there is no step between the inner diameter of the casing 1415 and the inner diameter of the tube 1405. This eliminates the power loss of the mm-waves that can be associated with sudden diameter changes.

[0081] In some embodiments, the coil spring 1410 can include an inner diameter 1420 measured between the protruding portions of each coil element of the coil spring 1410. In some embodiments, the inner diameter 1420 can include a diameter of 5.0 mm to 15.0 mm, 10.0 mm to 20.0 mm, 15.0 mm to 25.0 mm, 20.0 mm to 30.0 mm, 25.0 mm to 35.0 mm, 30.0 mm to 40.0 mm, 45.0 mm to 55.0 mm, 50.0 mm to 60.0 mm, 55.0 mm to 65.0 mm, 60.0 mm to 70.0 mm, 65.0 mm to 75.0 mm, 70.0 mm to 80.0 mm, 75.0 mm to 90.0 mm, or 85.0 mm to 200.0 mm. In some embodiments, the diameter can be greater than 200.0 mm or less than 5.0 mm. Other diameters are possible. In some embodiments, the inner diameter 1420 can include a tolerance range, such as ±0.075 mm, ±0.1 mm, ±0.125 mm, ±0.150 mm, ±0.175 mm, ±0.2 mm, ±0.225 mm, or ±0.25 mm, although other tolerance ranges are possible.

[0082] FIG. 15 illustrates an exemplary embodiment of manufacturing a coiled tube product for use in the multi-piece corrugated waveguide described herein. In some embodiments, the multi-piece corrugated waveguide can be formed from a continuous tube, a coiled tube product, or a pipe tube product. The continuous tube and the coiled tube product or the pipe tube product can be formed from a long strip of sheet metal. The long strip of metal can be configured on a reel. The strip of metal can be welded together at the ends of the strip of metal and then rolled to form a tube via a roller. The tube can then be welded closed to form an extremely long continuous length of tube, such as a tube over 10 km in length. In embodiments including a continuous tube, a coiled tube product, or a pipe tube product, the length of the tube can be greater than 10 km.

[0083] In some embodiments, corrugation features, such as ridges and / or grooves, can be rolled or stamped into the strip of sheet metal. In this manner, the corrugation features are provided on the inner surface of the coiled tube when the coiled tube is formed from the strip of sheet metal. In this manner, a first tube can be formed to include pre-configured corrugation features on the inner surface of the first tube. The first tube can then be inserted into a second tube to form a multi-piece corrugated waveguide as described in the embodiments herein.

[0084] As shown in FIG. 15, a long strip of stock metal 1505 can be contacted with a roller 1510. The roller 1510 can include grooves and ridges that can form corrugation features 1515 in the strip of metal. The corrugation features 1515 can be formed on a surface of the metal stock 1505 that can correspond to the inner surface of the tube being formed. The metal stock 1505 can be conveyed through one or more shaping rollers 1520 to transform the metal stock 1505 into a tube 1525. The tube 1525 can have an open seam where opposing edges of the metal stock 1505 are adjacent to one another. The seam can be welded via a welding device 1530 to form a fully enclosed tube or pipe 1535 that includes the corrugation features 1515.

[0085] FIG. 16 illustrates an exemplary embodiment of manufacturing a multi-piece corrugated waveguide that includes a coiled tube product as described herein. For example, a long strip of metal stock 1605 can be received within one or more shaping rollers 1610. A coil spring 1615 or previously formed coiled tube product 1615 can be fitted into a portion of the metal stock 1605 as it is being formed by the shaping rollers 1610. In some embodiments, the coiled tube product 1615 can be formed as described with respect to FIG. 15. Once fitted, the metal stock 1605 can be completely formed into a tube and welded closed. The resulting tube 1620 can include the coil spring 1615 or coiled tube product 1615 therein and can provide the corrugation features as described herein. In some embodiments, the coil spring or coiled tube product 1605 can be fitted before completely surrounding the tube and welding closed. In some embodiments, the coil spring or coiled tube product 1615 can be fitted into the coiled tube as the tube is being formed and welded closed.

[0086] 17A-17G illustrate exemplary embodiments of coil springs included in the multi-piece corrugated waveguides described herein. The coil springs illustrated in FIGs. 17A-17G can correspond to the coil springs described in the embodiments herein and can include embodiments of coil springs configured as compression springs or tension springs. In some embodiments, a combination of compression and tension coil springs can be used in the tubes described herein.

[0087] As shown in Figure 17A, one embodiment of a compression coil spring is shown having a length 1705. The coil spring can include an inner diameter 1710 and a width 1715. In some embodiments, the inner diameter 1710 can include a diameter of 5.0mm to 15.0mm, 10.0mm to 20.0mm, 15.0mm to 25.0mm, 20.0mm to 30.0mm, 25.0mm to 35.0mm, 30.0mm to 40.0mm, 45.0mm to 55.0mm, 50.0mm to 60.0mm, 55.0mm to 65.0mm, 60.0mm to 70.0mm, 65.0mm to 75.0mm, 70.0mm to 80.0mm, 75.0mm to 90.0mm, or 85.0mm to 200.0mm. In some embodiments, the diameter can be greater than 200.0 mm or less than 5.0 mm. Other diameters are possible. In some embodiments, the inner diameter 1710 can include a tolerance range, such as ±0.075 mm, ±0.1 mm, ±0.125 mm, ±0.150 mm, ±0.175 mm, ±0.2 mm, ±0.225 mm, or ±0.25 mm, although other tolerance ranges are possible.

[0088] In some embodiments, the width 1715 can be dimensioned to be less than the wavelength of the electromagnetic waves provided through the MCGs described herein. For example, the width 1715 can be less than the wavelength of millimeter electromagnetic waves injected into the borehole of a well. In some embodiments, the width 1715 can be 1 / 3 to 1 / 4 the frequency of the RF signal transmitted in the MCGs described herein. The width 1715 of the coil can correspond to the pitch and corrugation features of the springs formed in the MCGs described herein.

[0089] A coil element 1720 of the coil spring can be defined as one turn (e.g., 360 degrees) of the coil spring as measured along the circumference of the coil spring. A plurality of coil elements 1720 can form the coil spring to have a length 1705. The coil spring can include a space 1725 between two or more coil elements 1720. For example, the space 1725 can be wider than the frequency of the electromagnetic waves injected into the MCG described herein, but the spring can be configured to compress such that the space 1725 is reduced to at least 1 / 10 of the frequency of the injected electromagnetic waves to prevent the electromagnetic waves from leaking out. In some embodiments, the space 1715 can be 0.1-0.2 mm, 0.15-0.25 mm, 0.3-0.4 mm, 0.35-0.45 mm, or 0.5-0.6 mm. In some embodiments, the space can be greater than 0.6 mm or less than 0.1 mm. Other space sizes can be included.

[0090] In some embodiments, the coil spring and the plurality of coil elements 1720 can include a pitch 1730 between the coil elements 1720. The pitch can be measured from a center point of a first coil element to a center point of a second coil element adjacent to the first coil element. In some embodiments, the pitch 1730 can be dimensioned to be 1 / 3 of a wavelength of an electromagnetic wave provided through the MCG described herein. For example, the pitch 1730 can be 1 / 3 of a wavelength of a millimeter electromagnetic wave injected into the borehole of the well. For example, the pitch can be 0.3 mm to 7.0 mm.

[0091] 17B-17G show additional exemplary embodiments of coil springs for use with the MCG embodiments described herein. Any and all of the coil springs shown in FIG. 17B-17G can have the coil spring diameter, coil element width, pitch between coil elements, and space between coil elements described with respect to the coil spring shown and described in FIG. 17A. For example, in FIG. 17B, a tension spring is shown. The tension spring can be coated with a material 1735, such as a conductive material. The spring can also be coated with a highly conductive metallic material, such as gold, platinum, copper, or aluminum, which can optimize transmission efficiency. The tension spring can include a first coupling portion at a first end and a second coupling portion at a second end. As shown in FIG. 17C, a compression coil spring is shown. The compression spring can include a first coupling portion at a first end and a second coupling portion at a second end.

[0092] As shown in Figure 17D, in some embodiments, the coil spring can include a tapered coil spring. A tapered coil spring can include a diameter that varies along the length of the coil spring. As shown in Figure 17E, in some embodiments, the coil spring can include multiple tapered sections. In the embodiment shown in Figure 17E, the coil spring has an upper tapered section and a lower tapered section with a non-tapered section between the upper and lower tapered sections.

[0093] As shown in FIG. 17F, in some embodiments, the coil spring can include a tapered portion having a larger diameter than a non-tapered portion between the upper and lower tapered portions. As shown in FIG. 17G, in some embodiments, the coil spring can include multiple pitch configurations between the coil elements at two or more locations along the length of the coil spring. For example, the coil spring can include a first pitch 1740 and a second pitch 1750. The first pitch 1740 can be smaller than the second pitch 1750. In some embodiments, the first pitch can be larger than the second pitch. Similarly, in some embodiments, the coil spring can have a first space 1745 between the first plurality of coil elements and a second space 1755 between the second plurality of coil elements.

[0094] 18A-18E are diagrams illustrating example embodiments of cross-sectional shapes of the coil elements included in the multi-piece guide described herein. The cross-sectional shapes of the coil elements included in the coil spring described herein can be formed according to operation 310 of FIG. 3. As shown in FIG. 18A, in some embodiments, the coil elements can include a rectangular cross-sectional shape. As shown in FIG. 18B, in some embodiments, the coil elements can include an elliptical cross-sectional shape. As shown in FIG. 18C, in some embodiments, the coil elements can include an oval cross-sectional shape. As shown in FIG. 18D, in some embodiments, the coil elements can include a circular cross-sectional shape. As shown in FIG. 18E, in some embodiments, the coil elements can include a trapezoidal cross-sectional shape. In some embodiments, the coil elements can include a square shape, a triangular shape, or a polygonal shape. Although the cross-sectional shapes illustrated in FIG. 18A-18E are described in the context of the cross-sectional shapes of the coil elements, the cross-sectional shapes illustrated in FIG. 18A-18E can also correspond to the cross-sectional shape of a mandrel used to form the coil elements.

[0095] 19A-25B show various embodiments of cross-sectional profiles of the coil elements. The cross-sectional profiles can be formed as described in operation 305 of FIG. 3. The wire forming the coil spring and the coil elements of the coil spring can be extruded to have the cross-sectional profiles shown in FIGS. 19A-25B. A variety of cross-sectional profiles can be formed in this manner and configured for use with the various MCG embodiments described herein. For example, in some embodiments, the cross-sectional profiles can include triangular or pointed cross-sectional profiles in addition to the cross-sectional profiles shown in FIGS. 19A-25B. Other cross-sectional profiles are possible.

[0096] 19A illustrates an exemplary embodiment of a square cross-sectional profile of a protruding portion of a coil element of a multi-piece corrugated waveguide described herein. As shown in FIG. 19A, the coil element 1900 can include a base portion 1905 and a protruding portion 1925 extending from the base portion 1905. The base portion 1905 can include a height 1910, a width 1915, and a back surface 1920. The base portion 1905 is shown with a rectangular profile, but additional base portion profile shapes can be implemented. Similarly, the back surface 1920 is shown as a flat shaped back surface, but additional back surface shapes or profiles can be implemented. In some embodiments, the height 1910 can include a height of 0.2 mm to 0.4 mm, 0.3 mm to 0.5 mm, 0.4 mm to 0.6 mm, 0.5 mm to 0.7 mm, 0.6 mm to 1.0 mm, 2.0 mm to 5.0 mm, 4 mm to 8 mm, 6 mm to 10 mm, or 12 mm to 15 mm. In some embodiments, the height can be greater than 15 mm or less than 0.2 mm. Other heights are possible.

[0097] As shown in FIG. 19A, the coil element 1900 can include a protruding portion 1925 extending from a base portion 1905. The protruding portion 1925 can include a square-shaped profile as shown in FIG. 19A, although other profile shapes can be implemented. The protruding portion 1925 can include a height 1930, a width 1935, and an offset 1940. In some embodiments, the height 1930 can include a height of 0.2 mm to 0.4 mm, 0.3 mm to 0.5 mm, 0.4 mm to 0.6 mm, 0.5 mm to 0.7 mm, or 0.6 mm to 1.0 mm. In some embodiments, the height can be greater than 1.0 mm or less than 0.2 mm. Other heights are possible. In some embodiments, the height 1930 can include a tolerance range, such as ±0.010 mm, ±0.020 mm, ±0.030 mm, ±0.040 mm, or ±0.050 mm, although other tolerance ranges are possible.

[0098] In some embodiments, width 1935 can include a width of 0.2 mm to 0.4 mm, 0.3 mm to 0.5 mm, 0.4 mm to 0.6 mm, 0.5 mm to 0.7 mm, 0.6 mm to 0.8 mm, 0.7 mm to 0.9, or 0.8 mm to 1.0 mm. In some embodiments, the width can be greater than 1.0 mm or less than 0.2 mm. Other widths are possible. In some embodiments, width 1935 can include a tolerance range, such as ±0.050 mm, ±0.060 mm, ±0.070 mm, ±0.080 mm, or ±0.090 mm, although other tolerance ranges are possible.

[0099] In some embodiments, the offset 1940 can include an offset of 0.2 mm to 0.4 mm, 0.3 mm to 0.5 mm, 0.4 mm to 0.6 mm, 0.5 mm to 0.7 mm, 0.6 mm to 0.8 mm, 0.7 mm to 0.9, or 0.8 mm to 1.0 mm. In some embodiments, the offset can be greater than 1.0 mm or less than 0.2 mm. Other offsets are possible. In some embodiments, the offset 1940 can include a tolerance range, such as ±0.050 mm, ±0.060 mm, ±0.070 mm, ±0.080 mm, or ±0.090 mm, although other tolerance ranges are possible.

[0100] FIG. 19B illustrates an exemplary embodiment of a plurality of coil elements, each of which includes a square cross-sectional profile of the protruding portion as described herein. As shown in FIG. 19B, the plurality of coil elements 1945 can be formed such that each coil element (e.g., coil elements 1900A-1900C) has the same cross-sectional profile and dimensions as described for the coil element illustrated in FIG. 19A. The plurality of coil elements 1945 can include a space 1950 between adjacent protruding portions 1925 of adjacent coil elements. In some embodiments, the space 1950 can be dimensioned to be ¼ of a wavelength of the electromagnetic wave provided through the MCG described herein. For example, the space 1950 can be ⅙ of a wavelength of the millimeter electromagnetic wave injected into the borehole of the well. As further shown in FIG. 19B, the plurality of coil elements 1945 can include a pitch 1955. The pitch 1955 can be dimensioned to be ⅓ of a wavelength of the electromagnetic wave provided through the MCG described herein. For example, the pitch 1955 may be 1 / 3 of the wavelength of millimeter electromagnetic waves injected into the borehole of the well. Other dimensions may also be implemented.

[0101] 20A illustrates an exemplary embodiment of a trapezoidal cross-sectional profile of a protruding portion of a coil element of a multi-piece corrugated waveguide described herein. As shown in FIG. 20A, the coil element 2000 can include a base portion 2005 and a protruding portion 2025 extending from the base portion 2005. The base portion 2005 can include a height 2010, a width 2015, and a back surface 2020. The base portion 2005 is shown with a rectangular profile, but additional base portion profile shapes can be implemented. Similarly, the back surface 2020 is shown as a flat shaped back surface, but additional back surface shapes or profiles can be implemented. In some embodiments, the height 2010 can include heights between 0.2 mm and 0.4 mm, between 0.3 mm and 0.5 mm, between 0.4 mm and 0.6 mm, between 0.5 mm and 0.7 mm, between 0.6 mm and 1.0 mm, between 2.0 mm and 5.0 mm, between 4 mm and 8 mm, between 6 mm and 10 mm, or between 12 mm and 15 mm. In some embodiments, the height can be greater than 15 mm or less than 0.2 mm. Other heights are possible.

[0102] As shown in FIG. 20A, the coil element 2000 can include a protruding portion 2025 extending from a base portion 2005. The protruding portion 2025 can include a trapezoidal shaped profile as shown in FIG. 20A, although other profile shapes can be implemented. The protruding portion 2025 can include a height 2030, a width 2035, and an offset 2040. In some embodiments, the height 2030 can include a height of 0.2 mm to 0.4 mm, 0.3 mm to 0.5 mm, 0.4 mm to 0.6 mm, 0.5 mm to 0.7 mm, or 0.6 mm to 1.0 mm. In some embodiments, the height can be greater than 1.0 mm or less than 0.2 mm. Other heights are possible. In some embodiments, the height 2030 can include a tolerance range, such as ±0.010 mm, ±0.020 mm, ±0.030 mm, ±0.040 mm, or ±0.050 mm, although other tolerance ranges are possible.

[0103] In some embodiments, width 2035 can include a width of 0.2 mm to 0.4 mm, 0.3 mm to 0.5 mm, 0.4 mm to 0.6 mm, 0.5 mm to 0.7 mm, 0.6 mm to 0.8 mm, 0.7 mm to 0.9, or 0.8 mm to 1.0 mm. In some embodiments, the width can be greater than 1.0 mm or less than 0.2 mm. Other widths are possible. In some embodiments, width 2035 can include a tolerance range, such as ±0.010 mm, ±0.020 mm, ±0.030 mm, ±0.040 mm, or ±0.050 mm, although other tolerance ranges are possible.

[0104] In some embodiments, the offset 2040 can include an offset of 0.2 mm to 0.4 mm, 0.3 mm to 0.5 mm, 0.4 mm to 0.6 mm, 0.5 mm to 0.7 mm, 0.6 mm to 0.8 mm, 0.7 mm to 0.9, or 0.8 mm to 1.0 mm. In some embodiments, the offset can be greater than 1.0 mm or less than 0.2 mm. Other offsets are possible. In some embodiments, the offset 2040 can include a tolerance range, such as ±0.010 mm, ±0.020 mm, ±0.030 mm, ±0.040 mm, or ±0.050 mm, although other tolerance ranges are possible.

[0105] In some embodiments, the protruding portion 2025 can include an angle 2060 formed with respect to a surface of the base portion 2005 from which the protruding portion 2025 extends. In some embodiments, the angle 2060 can be between 0 and 3.0 degrees, between 1.5 and 5.0 degrees, between 4.0 and 6.0 degrees, between 5.5 and 7.0 degrees, between 6.0 and 8.0 degrees, between 7.5 and 9.0 degrees, between 8.0 and 10.0 degrees, between 9.0 and 12.0 degrees, between 11.0 and 13.0 degrees, or between 12.0 and 15.0 degrees, although other angles are possible. In some embodiments, the angle can be greater than 15 degrees. Other angles are possible.

[0106] FIG. 20B illustrates an exemplary embodiment of a plurality of coil elements, each of which includes a trapezoidal cross-sectional profile of the protruding portion as described herein. As shown in FIG. 20B, the plurality of coil elements 2045 can be formed such that each coil element (e.g., coil elements 2000A-2000C) has the same cross-sectional profile and dimensions as described for the coil element illustrated in FIG. 20A. The plurality of coil elements 2045 can include a space 2050 between adjacent protruding portions 2025 of adjacent coil elements. In some embodiments, the space 2050 can be dimensioned to be 1 / 6 of a wavelength of the electromagnetic wave provided through the MCG described herein. For example, the space 2050 can be 1 / 6 of a wavelength of the millimeter electromagnetic wave injected into the borehole of the well. As further shown in FIG. 20B, the plurality of coil elements 2045 can include a pitch 2055. The pitch 2055 can be dimensioned to be 1 / 3 of a wavelength of the electromagnetic wave provided through the MCG described herein. For example, the pitch 2055 may be 1 / 3 of the wavelength of a millimeter electromagnetic wave injected into the borehole of the well. Other dimensions may also be implemented.

[0107] 21A illustrates another exemplary embodiment of a trapezoidal cross-sectional profile of a protruding portion of a coil element of a multi-piece corrugated waveguide described herein. As shown in FIG. 21A, the coil element 2100 can include a base portion 2105 and a protruding portion 2125 extending from the base portion 2105. The base portion 2105 can include a height 2110, a width 2115, and a back surface 2120. The base portion 2105 is shown with a rectangular profile, but additional base portion profile shapes can be implemented. Similarly, the back surface 2120 is shown as a flat shaped back surface, but additional back surface shapes or profiles can be implemented. In some embodiments, the height 2110 can include a height of 0.2 mm to 0.4 mm, 0.3 mm to 0.5 mm, 0.4 mm to 0.6 mm, 0.5 mm to 0.7 mm, 0.6 mm to 1.0 mm, 2.0 mm to 5.0 mm, 4 mm to 8 mm, 6 mm to 10 mm, or 12 mm to 15 mm. In some embodiments, the height can be greater than 15 mm or less than 0.2 mm. Other heights are possible.

[0108] As shown in FIG. 21A, the coil element 2100 can include a protruding portion 2125 extending from a base portion 2105. The protruding portion 2125 can include a trapezoidal shaped profile as shown in FIG. 21A, although other profile shapes can be implemented. The protruding portion 2125 can include a height 2130, an offset 2135, and a width 2140. In some embodiments, the offset 2135 can be the same or different on both sides of the protruding portion 2125. In some embodiments, the height 2130 can include a height of 0.2 mm to 0.4 mm, 0.3 mm to 0.5 mm, 0.4 mm to 0.6 mm, 0.5 mm to 0.7 mm, or 0.6 mm to 1.0 mm. In some embodiments, the height can be greater than 1.0 mm or less than 0.2 mm. Other heights are possible. In some embodiments, the height 2130 can include a tolerance range, such as ±0.010 mm, ±0.020 mm, ±0.030 mm, ±0.040 mm, or ±0.050 mm, although other tolerance ranges are possible.

[0109] In some embodiments, the offset 2135 can include an offset of 0.2 mm to 0.4 mm, 0.3 mm to 0.5 mm, 0.4 mm to 0.6 mm, 0.5 mm to 0.7 mm, 0.6 mm to 0.8 mm, 0.7 mm to 0.9, or 0.8 mm to 1.0 mm. In some embodiments, the offset can be greater than 1.0 mm or less than 0.2 mm. Other offsets are possible. In some embodiments, the offset 2135 can include a tolerance range, such as ±0.010 mm, ±0.020 mm, ±0.030 mm, ±0.040 mm, or ±0.050 mm, although other tolerance ranges are possible.

[0110] In some embodiments, width 2140 can include a width of 0.2 mm to 0.4 mm, 0.3 mm to 0.5 mm, 0.4 mm to 0.6 mm, 0.5 mm to 0.7 mm, 0.6 mm to 0.8 mm, 0.7 mm to 0.9, or 0.8 mm to 1.0 mm. In some embodiments, the width can be greater than 1.0 mm or less than 0.2 mm. Other widths are possible. In some embodiments, width 2140 can include a tolerance range, such as ±0.010 mm, ±0.020 mm, ±0.030 mm, ±0.040 mm, or ±0.050 mm, although other tolerance ranges are possible.

[0111] In some embodiments, the protruding portion 2125 can include an angle 2160 formed with respect to a surface of the base portion 2105 from which the protruding portion 2125 extends. In some embodiments, the angle 2160 can be between 0 and 3.0 degrees, 1.5 and 5.0 degrees, 4.0 and 6.0 degrees, 5.5 and 7.0 degrees, 6.0 and 8.0 degrees, 7.5 and 9.0 degrees, 8.0 and 10.0 degrees, 9.0 and 12.0 degrees, 11.0 and 13.0 degrees, or 12.0 and 15.0 degrees, although other angles are possible. In some embodiments, the angle can be greater than 15 degrees. In some embodiments, the angle 2160 can be the same on both sides of the protruding portion 2125. In some embodiments, the angle 2160 on one side of the protruding portion 2125 can be different than the angle 2160 on the other side of the protruding portion 2125.

[0112] FIG. 21B illustrates another exemplary embodiment of a plurality of coil elements, each of which includes a trapezoidal cross-sectional profile of the protruding portion as described herein. As shown in FIG. 21B, the plurality of coil elements 2145 can be formed such that each coil element (e.g., coil elements 2100A-2100C) has the same cross-sectional profile and dimensions as described for the coil element illustrated in FIG. 21A. The plurality of coil elements 2145 can include a space 2150 between adjacent protruding portions 2125 of adjacent coil elements. In some embodiments, the space 2150 can be dimensioned to be 1 / 6 of a wavelength of the electromagnetic wave provided through the MCG described herein. For example, the space 2150 can be 1 / 6 of a wavelength of the millimeter electromagnetic wave injected into the borehole of the well. As further shown in FIG. 21B, the plurality of coil elements 2145 can include a pitch 2155. The pitch 2155 can be dimensioned to be 1 / 3 of a wavelength of the electromagnetic wave provided through the MCG described herein. For example, the pitch 2155 may be 1 / 3 of the wavelength of a millimeter electromagnetic wave injected into the borehole of the well. Other dimensions may also be implemented.

[0113] 22A is a diagram illustrating an example embodiment of a rectangular cross-sectional profile of a protruding portion of a coil element of a multi-piece corrugated waveguide described herein. As shown in FIG. 22A, the coil element 2200 can include a base portion 2205 and a protruding portion 2225 extending from the base portion 2205. The base portion 2205 can include a height 2210, a width 2215, and a back surface 2220. The base portion 2205 is shown with a rectangular profile, but additional base portion profile shapes can be implemented. Similarly, the back surface 2220 is shown as a flat shaped back surface, but additional back surface shapes or profiles can be implemented. In some embodiments, the height 2210 can include a height of 0.2 mm to 0.4 mm, 0.3 mm to 0.5 mm, 0.4 mm to 0.6 mm, 0.5 mm to 0.7 mm, 0.6 mm to 1.0 mm, 2.0 mm to 5.0 mm, 4 mm to 8 mm, 6 mm to 10 mm, or 12 mm to 15 mm. In some embodiments, the height can be greater than 15 mm or less than 0.2 mm. Other heights are possible.

[0114] As shown in Fig. 22A, the coil element 2200 can include a protruding portion 2225 extending from a base portion 2205. The protruding portion 2225 can include a rectangular profile as shown in Fig. 22A, although other profile shapes can be implemented. The protruding portion 2225 can include a height 2230, an offset 2235, and a width 2240. In some embodiments, the offset 2235 can be the same or different on either side of the protruding portion 2225.

[0115] In some embodiments, height 2230 can be greater or less than 0.2 mm to 0.4 mm, 0.3 mm to 0.5 mm, 0.4 mm to 0.6 mm, 0.5 mm to 0.7 mm, or 0.6 mm to 1.0 mm, although other heights are possible. In some embodiments, height 2230 can include a tolerance range, such as ±0.010 mm, ±0.020 mm, ±0.030 mm, ±0.040 mm, or ±0.050 mm, although other tolerance ranges are possible.

[0116] In some embodiments, the offset 2235 can include an offset of 0.05 mm to 0.1 mm, 0.075 mm to 0.15 mm, 0.1 mm to 0.15 mm, 0.125 mm to 0.175 mm, 0.15 mm to 0.2 mm, 0.175 mm to 0.25 mm, 0.2 mm to 0.4 mm, 0.3 mm to 0.5 mm, 0.4 mm to 0.6 mm, 0.5 mm to 0.7 mm, or 0.6 mm to 1.0 mm. In some embodiments, the offset can be greater than 1.0 mm or less than 0.2 mm. Other offsets are possible. In some embodiments, the offset 2235 can include a tolerance range, such as ±0.010 mm, ±0.020 mm, ±0.030 mm, ±0.040 mm, or ±0.050 mm, although other tolerance ranges are possible. In some embodiments, the offset 2235 can be the same on both sides of the overhanging portion 2225. In some embodiments, the offset 2235 on one side of the overhanging portion 2225 can be different from the offset 2235 on the opposite side of the overhanging portion 2225.

[0117] In some embodiments, width 2240 can include a width of 0.2 mm to 0.4 mm, 0.3 mm to 0.5 mm, 0.4 mm to 0.6 mm, 0.5 mm to 0.7 mm, 0.6 mm to 0.8 mm, 0.7 mm to 0.9, or 0.8 mm to 1.0 mm. In some embodiments, the width can be greater than 1.0 mm or less than 0.2 mm. Other widths are possible. In some embodiments, width 2240 can include a tolerance range, such as ±0.010 mm, ±0.020 mm, ±0.030 mm, ±0.040 mm, or ±0.050 mm, although other tolerance ranges are possible.

[0118] FIG. 22B illustrates an exemplary embodiment of a plurality of coil elements, each of which includes a rectangular cross-sectional profile of the protruding portion as described herein. As shown in FIG. 22B, the plurality of coil elements 2245 can be formed such that each coil element (e.g., coil elements 2200A-2200C) has the same cross-sectional profile and dimensions as described for the coil element illustrated in FIG. 22A. The plurality of coil elements 2245 can include a space 2250 between adjacent protruding portions 2225 of adjacent coil elements. In some embodiments, the space 2250 can be dimensioned to be 1 / 6 of a wavelength of the electromagnetic wave provided through the MCG described herein. For example, the space 2250 can be 1 / 6 of a wavelength of the millimeter electromagnetic wave injected into the borehole of the well. As further shown in FIG. 22B, the plurality of coil elements 2245 can include a pitch 2255. The pitch 2255 can be dimensioned to be 1 / 3 of a wavelength of the electromagnetic wave provided through the MCG described herein. For example, the pitch 2255 may be 1 / 3 of the wavelength of a millimeter electromagnetic wave injected into the borehole of the well. Other dimensions may also be implemented.

[0119] 23A is a diagram illustrating an example embodiment of a circular cross-sectional profile of a protruding portion of a coil element of a multi-piece corrugated waveguide described herein. As shown in FIG. 23A, the coil element 2300 can include a base portion 2305 and a protruding portion 2325 extending from the base portion 2305. The base portion 2305 can include a height 2310, a width 2315, and a back surface 2320. The base portion 2305 is shown with a rectangular profile, but additional base portion profile shapes can be implemented. Similarly, the back surface 2320 is shown as a flat shaped back surface, but additional back surface shapes or profiles can be implemented. In some embodiments, the height 2310 can include a height of 0.2 mm to 0.4 mm, 0.3 mm to 0.5 mm, 0.4 mm to 0.6 mm, 0.5 mm to 0.7 mm, 0.6 mm to 1.0 mm, 2.0 mm to 5.0 mm, 4 mm to 8 mm, 6 mm to 10 mm, or 12 mm to 15 mm. In some embodiments, the height can be greater than 15 mm or less than 0.2 mm. Other heights are possible.

[0120] As shown in Fig. 23A, the coil element 2300 can include a protruding portion 2325 extending from a base portion 2305. The protruding portion 2325 can include a circular shaped profile as shown in Fig. 23A, although other profile shapes can be implemented. The protruding portion 2325 can include a height 2330, an offset 2335, and a width 2340. In some embodiments, the offset 2335 can be the same or different on either side of the protruding portion 2325.

[0121] In some embodiments, height 2330 can include a height of 0.2 mm to 0.4 mm, 0.3 mm to 0.5 mm, 0.4 mm to 0.6 mm, 0.5 mm to 0.7 mm, or 0.6 mm to 1.0 mm. In some embodiments, the height can be greater than 1.0 mm or less than 0.2 mm. Other heights are possible. In some embodiments, height 2330 can include a tolerance range, such as ±0.010 mm, ±0.020 mm, ±0.030 mm, ±0.040 mm, or ±0.050 mm, although other tolerance ranges are possible.

[0122] In some embodiments, the offset 2335 can include an offset of 0.05 mm to 0.1 mm, 0.075 mm to 0.15 mm, 0.1 mm to 0.15 mm, 0.125 mm to 0.175 mm, 0.15 mm to 0.2 mm, 0.175 mm to 0.25 mm, 0.2 mm to 0.4 mm, 0.3 mm to 0.5 mm, 0.4 mm to 0.6 mm, 0.5 mm to 0.7 mm, or 0.6 mm to 1.0 mm. In some embodiments, the offset can be greater than 1.0 mm or less than 0.2 mm. Other offsets are possible. In some embodiments, the offset 2335 can include a tolerance range, such as ±0.010 mm, ±0.020 mm, ±0.030 mm, ±0.040, or ±0.050 mm, although other tolerance ranges are possible. In some embodiments, the offset 2335 can be the same on both sides of the overhanging portion 2325. In some embodiments, the offset 2335 on one side of the overhanging portion 2325 can be different from the offset 2335 on the opposite side of the overhanging portion 2325.

[0123] In some embodiments, width 2340 can include a width of 0.2-0.4 mm, 0.3-0.5 mm, 0.4 mm-0.6 mm, 0.5 mm-0.7 mm, 0.6 mm-0.8 mm, 0.7 mm-0.9, or 0.8 mm-1.0 mm. In some embodiments, the width can be greater than 1.0 mm or less than 0.2 mm. Other widths are possible. In some embodiments, width 2340 can include a tolerance range, such as ±0.010 mm, ±0.020 mm, ±0.030 mm, ±0.040, or ±0.050 mm, although other tolerance ranges are possible.

[0124] FIG. 23B illustrates an exemplary embodiment of a plurality of coil elements, each of which includes a circular cross-sectional profile of the protruding portion as described herein. As shown in FIG. 23B, the plurality of coil elements 2345 can be formed such that each coil element (e.g., coil elements 2300A-2300C) has the same cross-sectional profile and dimensions as described for the coil element shown in FIG. 23A. The plurality of coil elements 2345 can include a space 2350 between adjacent protruding portions 2325 of adjacent coil elements. In some embodiments, the space 2350 can be dimensioned to be 1 / 6 of a wavelength of the electromagnetic wave provided through the MCG described herein. For example, the space 2350 can be 1 / 6 of a wavelength of the millimeter electromagnetic wave injected into the borehole of the well. As further shown in FIG. 23B, the plurality of coil elements 2345 can include a pitch 2355. The pitch 2355 can be dimensioned to be 1 / 3 of a wavelength of the electromagnetic wave provided through the MCG described herein. For example, the pitch 2355 may be 1 / 3 of the wavelength of a millimeter electromagnetic wave injected into the borehole of the well. Other dimensions may also be implemented.

[0125] 24A is a diagram illustrating an example embodiment of a sinusoidal cross-sectional profile of a protruding portion of a coil element of a multi-piece corrugated waveguide described herein. As shown in FIG. 24A, the coil element 2400 can include a base portion 2405 and a protruding portion 2425 extending from the base portion 2405. The base portion 2405 can include a height 2410, a width 2415, and a back surface 2420. The base portion 2405 is shown with a rectangular profile, but additional base portion profile shapes can be implemented. Similarly, the back surface 2420 is shown as a flat shaped back surface, but additional back surface shapes or profiles can be implemented. In some embodiments, the height 2410 can include a height of 0.2-0.4 mm, 0.3-0.5 mm, 0.4 mm-0.6 mm, 0.5 mm-0.7 mm, 0.6 mm-1.0 mm, 2.0 mm-5.0 mm, 4 mm-8 mm, 6 mm-10 mm, or 12 mm-15 mm. In some embodiments, the height can be greater than 15 mm or less than 0.2 mm. Other heights are possible.

[0126] As shown in FIG. 24A, the coil element 2400 can include a protruding portion 2425 extending from a base portion 2405. The protruding portion 2425 can include a symmetrical sinusoidal profile as shown in FIG. 24A, although other shapes of sinusoidal profiles can be implemented. In some embodiments, the protruding portion 2425 can have an angular profile, such as a triangular shaped profile. In some embodiments, multiple protruding portions 2425 can extend from the base portion, and each protruding portion can have the same or different profile shapes. The protruding portion 2425 can include a height 2430, an offset 2435, and a width 2440. In some embodiments, the protruding portion 2425 can be disposed between two offsets 2435.

[0127] In some embodiments, height 2430 can include a height of 0.2 mm to 0.4 mm, 0.3 mm to 0.5 mm, 0.4 mm to 0.6 mm, 0.5 mm to 0.7 mm, or 0.6 mm to 1.0 mm. In some embodiments, the height can be greater than 1.0 mm or less than 0.2 mm. Other heights are possible. In some embodiments, height 2430 can include a tolerance range, such as ±0.010 mm, ±0.020 mm, ±0.030 mm, ±0.040 mm, or ±0.050 mm, although other tolerance ranges are possible.

[0128] In some embodiments, the offset 2435 can include an offset of 0.05 mm to 0.1 mm, 0.075 mm to 0.15 mm, 0.1 mm to 0.15 mm, 0.125 mm to 0.175 mm, 0.15 mm to 0.2 mm, 0.175 mm to 0.25 mm, 0.2 mm to 0.4 mm, 0.3 mm to 0.5 mm, 0.4 mm to 0.6 mm, 0.5 mm to 0.7 mm, or 0.6 mm to 1.0 mm. In some embodiments, the offset can be greater than 1.0 mm or less than 0.2 mm. Other offsets are possible. In some embodiments, the offset 2435 can include a tolerance range, such as ±0.010 mm, ±0.020 mm, ±0.030 mm, ±0.040 mm, or ±0.050 mm, although other tolerance ranges are possible. In some embodiments, the offset 2435 can be the same on both sides of the overhanging portion 2425. In some embodiments, the offset 2435 on one side of the overhanging portion 2425 can be different from the offset 2435 on the opposite side of the overhanging portion 2425.

[0129] In some embodiments, width 2440 can include a width of 0.2 mm to 0.4 mm, 0.3 mm to 0.5 mm, 0.4 mm to 0.6 mm, 0.5 mm to 0.7 mm, 0.6 mm to 0.8 mm, 0.7 mm to 0.9, or 0.8 mm to 1.0 mm. In some embodiments, the width can be greater than 1.0 mm or less than 0.2 mm. Other widths are possible. In some embodiments, width 2440 can include a tolerance range, such as ±0.010 mm, ±0.020 mm, ±0.030 mm, ±0.040 mm, or ±0.050 mm, although other tolerance ranges are possible.

[0130] FIG. 24B illustrates an exemplary embodiment of a plurality of coil elements, each of which includes a sinusoidal cross-sectional profile of the protruding portion as described herein. As shown in FIG. 24B, the plurality of coil elements 2445 can be formed such that each coil element (e.g., coil elements 2400A-2400C) has the same cross-sectional profile and dimensions as described for the coil element illustrated in FIG. 24A. The plurality of coil elements 2445 can include a space 2450 between adjacent protruding portions 2425 of adjacent coil elements. In some embodiments, the space 2450 can be dimensioned to be 1 / 6 of a wavelength of the electromagnetic wave provided through the MCG described herein. For example, the space 2450 can be 1 / 6 of a wavelength of the millimeter electromagnetic wave injected into the borehole of the well. As further shown in FIG. 24B, the plurality of coil elements 2445 can include a pitch 2455. The pitch 2455 can be dimensioned to be 1 / 3 of a wavelength of the electromagnetic wave provided through the MCG described herein. For example, the pitch 2455 may be 1 / 3 of the wavelength of a millimeter electromagnetic wave injected into the borehole of the well. Other dimensions may also be implemented.

[0131] 25A is a diagram illustrating an exemplary embodiment of a protruding portion of a coil element including multiple cross-sectional profiles as described herein. As shown in FIG. 25A, the coil element 2500 can include a base portion 2505 and a protruding portion 2525 extending from the base portion 2505. The base portion 2505 can include a height 2510, a width 2515, and a back surface 2520. The base portion 2505 is shown with a rectangular profile, but additional base portion profile shapes can be implemented. Similarly, the back surface 2520 is shown as a flat shaped back surface, but additional back surface shapes or profiles can be implemented. In some embodiments, the height 2510 and / or back surface 2520 can include heights between 0.2 mm and 0.4 mm, between 0.3 mm and 0.5 mm, between 0.4 mm and 0.6 mm, between 0.5 mm and 0.7 mm, between 0.6 mm and 1.0 mm, between 2.0 mm and 5.0 mm, between 4 mm and 8 mm, between 6 mm and 10 mm, or between 12 mm and 15 mm. In some embodiments, the height can be greater than 15 mm or less than 0.2 mm. Other heights are possible.

[0132] As shown in FIG. 25A, the coil element 2500 can include a plurality of protruding portions 2525 extending from a base portion 2505. The protruding portions 2525 can each include a rectangular profile as shown in FIG. 25A, although other profile shapes can be implemented. In some embodiments, each of the plurality of protruding portions 2525 can include a profile with the same shape as shown in FIG. 25A. In some embodiments, one or more of the protruding portions 2525 can include a profile that is shaped differently than the profile shape of the other protruding portions 2525. The protruding portions 2525 can include a height 2530, a width 2535, an offset 2540, and a combined protruding portion width 2545. In some embodiments, the height 2530 can include a height of 0.2 mm to 0.4 mm, 0.3 mm to 0.5 mm, 0.4 mm to 0.6 mm, 0.5 mm to 0.7 mm, or 0.6 mm to 1.0 mm. In some embodiments, the height can be greater than 1.0 mm or less than 0.2 mm. Other heights are possible. In some embodiments, the height 2530 can include a tolerance such as ±0.010 mm, ±0.020 mm, ±0.030 mm, ±0.040 mm, or ±0.050 mm, although other tolerances are possible. In some embodiments, the height 2530 can be the same or different from adjacent or non-adjacent overhanging portions 2525.

[0133] In some embodiments, the width 2535 can include a width of 0.2 mm to 0.4 mm, 0.3 mm to 0.5 mm, 0.4 mm to 0.6 mm, 0.5 mm to 0.7 mm, 0.6 mm to 0.8 mm, 0.7 mm to 0.9, or 0.8 mm to 1.0 mm. In some embodiments, the width can be greater than 1.0 mm or less than 0.2 mm. Other widths are possible. In some embodiments, the width 2535 can include a tolerance range, such as ±0.010 mm, ±0.020 mm, ±0.030 mm, ±0.040 mm, or ±0.050 mm, although other tolerance ranges are possible. In some embodiments, the width 2535 can be the same or different than adjacent or non-adjacent protruding portions 2525.

[0134] In some embodiments, the offset 2540 can include an offset of 0.05-0.1 mm, 0.075-0.15 mm, 0.1 mm-0.15 mm, 0.125 mm-0.175 mm, 0.15 mm-0.2 mm, 0.175 mm-0.25 mm, 0.2 mm-0.4 mm, 0.3 mm-0.5 mm, 0.4 mm-0.6 mm, 0.5 mm-0.7 mm, or 0.6 mm-1.0 mm. In some embodiments, the offset can be greater than 1.0 mm or less than 0.2 mm. Other offsets are possible. In some embodiments, the offset 2540 can include a tolerance range, such as ±0.010 mm, ±0.020 mm, ±0.030 mm, ±0.040 mm, or ±0.050 mm, although other tolerance ranges are possible. In some embodiments, the offset 2540 can be the same on both sides of the overhanging portion 2525. In some embodiments, the offset 2540 on one side of the overhanging portion 2525 can be different from the offset 2540 on the opposite side of the overhanging portion 2525. In some embodiments, the offset 2540 can be the same or different for non-adjacent overhanging portions 2525.

[0135] In some embodiments, the combined protrusion width 2545 can include a width of 0.2 mm to 0.4 mm, 0.3 mm to 0.5 mm, 0.4 mm to 0.6 mm, 0.5 mm to 0.7 mm, 0.6 mm to 0.8 mm, 0.7 mm to 0.9, 0.8 mm to 1.0 mm, 0.9 mm to 2.0 mm, 1.5 mm to 3.0 mm, 2.5 mm to 5.0 mm, 4.0 mm to 8.0 mm, 6.0 mm to 10.0 mm, 8.0 mm to 15.0 mm, or 10.0 mm to 20.0 mm. In some embodiments, the width can be greater than 20 mm or less than 0.2 mm. Other combined protrusion widths are possible. In some embodiments, the combined protrusion width 2545 can include a tolerance range, such as ±0.010 mm, ±0.020 mm, ±0.030 mm, ±0.040 mm, or ±0.050 mm, although other tolerance ranges are possible.

[0136] FIG. 25B illustrates an exemplary embodiment of a plurality of coil elements, each of which includes a protruding portion having a plurality of cross-sectional profiles, as described herein. As shown in FIG. 25B, the plurality of coil elements 2550 can be formed such that each coil element (e.g., coil elements 2500A-2500C) has the same cross-sectional profile and dimensions as described for the coil element shown in FIG. 25A. The plurality of coil elements 2550 can include a space 2555 between adjacent protruding portions 2525 of adjacent coil elements. In some embodiments, the space 2555 can be dimensioned to be 1 / 6 of a wavelength of the electromagnetic wave provided through the MCG described herein. For example, the space 2555 can be 1 / 6 of a wavelength of the millimeter electromagnetic wave injected into the borehole of the well. As further shown in FIG. 25B, the plurality of coil elements 2550 can include a pitch 2560. The pitch 2560 can be dimensioned to be 1 / 3 of a wavelength of the electromagnetic wave provided through the MCG described herein. For example, pitch 2560 can be 1 / 3 of the wavelength of millimeter electromagnetic waves injected into the borehole of the well. Other dimensions can also be implemented. Coil elements 2550 can be axially fixed inside the outer tube of the MCG described herein by bolts or with the aid of current fittings to connect the coil elements together and / or to the outer tube of the MCG described herein.

[0137] 26A-C illustrate an exemplary embodiment of a multi-piece corrugated waveguide formed from two nested coil springs as described herein. As shown in FIG. 26A, a first coil spring 2605 can be inserted into a second coil spring 2610 by rotating the first coil spring 2605 into the second coil spring 2610, so that the coil elements of each coil spring are threaded together, as shown in the assembled two-piece coil spring 2615 shown in FIG. 26B. FIG. 26C illustrates a cross-sectional view of the two-piece coil spring 2615.

[0138] FIG. 27 is a diagram illustrating an example embodiment of the multi-piece corrugated waveguide of FIG. 26C. As shown in FIG. 27, detail A of FIG. 26C is shown to illustrate nesting two coil springs together to create a profile of corrugation features that correspond to the diameter and pitch of the first coil spring 2605 and the second coil spring 2610. The first coil spring 2605 can have an inner diameter 2705 that is larger than the inner diameter 2710 of the second coil spring 2610. In some embodiments, the first coil spring 2605 can be coated with a first material, such as a dielectric or ferromagnetic material. The second coil spring 2610 can be coated with a second material, such as a conductive material.

[0139] Some implementations of the present subject matter can provide a multi-piece corrugated waveguide suitable for use with the transmission of electromagnetic waves. For example, some implementations of the present subject matter can enable the formation and use of a corrugated waveguide suitable for drilling a borehole in a well using millimeter electromagnetic waves in various transmission modes, such as the HE11 mode. Some implementations of the multi-piece configuration of the corrugated waveguide described herein can reduce the complexity of manufacturing such devices by providing the corrugated waveguide features via coil springs that can be inserted into the tube, instead of machining the corrugation features into a long length of tube. As a result, some implementations of the MCG described herein can be manufactured to closer tolerances than forming the corrugated features via machining, tapping, or drilling, where machined material may remain in the waveguide and reduce electromagnetic permeability. Additionally, coating or plating of MCG components may be more easily accomplished because the insulating, dielectric, or conductive material can be applied to the individual components during manufacture, instead of machining corrugation features into a long length of tubing and then coating or plating the long length of tubing with an insulating, dielectric, or conductive material.

[0140] Certain exemplary embodiments are described to provide a general understanding of the principles of the structure, function, manufacture, and use of the systems, devices, and methods disclosed herein. One or more examples of these embodiments are illustrated in the accompanying drawings. Those skilled in the art will appreciate that the systems, devices, and methods specifically described herein and shown in the accompanying drawings are non-limiting exemplary embodiments, and that the scope of the present invention is defined only by the claims. Features illustrated or described in connection with one exemplary embodiment may be combined with features of other embodiments. Such modifications and variations are intended to be included within the scope of the present invention. Furthermore, in this disclosure, similarly named components of an embodiment generally have similar characteristics, and therefore, within a particular embodiment, each feature of each similarly named component is not necessarily described in detail.

[0141] Approximate language used herein throughout the specification and claims may be applied to modify any quantitative expression that may vary within acceptable limits without causing a change in the basic function to which it pertains. Thus, values ​​modified by terms such as "about," "approximately," and "substantially" are not limited to the exact value specified. In at least some cases, the approximation language may correspond to the precision of the instrument for measuring the value. Throughout the specification and claims, unless the context or language indicates otherwise, range limitations may be combined and / or substituted, and such ranges may be specified and include all subranges contained therein.

[0142] Those skilled in the art will appreciate further features and advantages of the present invention based on the above-described embodiments. Accordingly, the present application should not be limited by what has been particularly shown and described, except as indicated by the appended claims. All publications and references cited herein are expressly incorporated by reference in their entirety.

Claims

1. An apparatus comprising: a tube including an inner surface, an inner diameter, and a length; and a coil spring including an outer surface, an outer diameter, and a plurality of coil elements arranged along the length of the coil spring, the coil spring being positioned within the tube and the outer diameter of the coil spring being smaller than the inner diameter of the tube.

2. The apparatus according to claim 1, wherein a gap is defined between the outer surface of the coil spring and the inner surface of the tube.

3. The apparatus according to claim 1, wherein the coil spring forms a waveguide.

4. The apparatus according to claim 1, wherein the inner surface of the coil spring includes a conductive material.

5. The apparatus according to claim 1, wherein the coil spring includes a coating of copper, gold, silver, or platinum.

6. The apparatus according to claim 1, further comprising an insulating layer between the tube and the coil spring.

7. The apparatus according to claim 1, wherein the outer surface of the coil spring includes a dielectric material.

8. The apparatus according to claim 1, wherein at least one of the plurality of coil elements is defined by one rotation of the at least one coil element about the perimeter of the coil spring.

9. The apparatus according to claim 1, wherein at least one of the plurality of coil elements includes a base portion and a protruding portion extending from the base portion, the protruding portion including one of a trapezoidal cross-sectional shape, a circular cross-sectional shape, a square cross-sectional shape, a rectangular cross-sectional shape, or a sinusoidal cross-sectional shape.

10. The apparatus according to claim 1, wherein the plurality of coil elements includes one of a trapezoidal cross-sectional shape, a circular cross-sectional shape, a rectangular cross-sectional shape, an elliptical cross-sectional shape, or a tapered shape along the length of the plurality of coil elements.

11. The apparatus according to claim 1, wherein the coil spring includes copper wire and / or aluminum wire.

12. The apparatus according to claim 1, wherein the tube includes a carbon steel tube.

13. The apparatus according to claim 1, wherein a plurality of coil springs are positioned within the tube.

14. The apparatus according to claim 13, wherein a first coil spring and a second coil spring among the plurality of coil springs are coupled via a coupling spring positioned within the tube.

15. The first end of the coupling spring is attached to the first end of the first coil spring, the second end of the coupling spring is attached to the second end of the second coil spring, and the coupling spring is configured to reduce the amount of axial movement of the first coil spring and the second coil spring relative to each other due to thermal expansion of the first coil spring and / or the second coil spring. The device according to claim 14.

16. The cross-sectional outer shape of each coil element of the coil spring and / or the plurality of coil elements is dimensioned to propagate electromagnetic waves. The device according to claim 1.

17. The coil spring and the cross-sectional outer shape of the coil spring are dimensioned to propagate the electromagnetic wave in the HE11 mode. The device according to claim 16.

18. The length of the tube is longer than 1 meter. The device according to claim 1.

19. The length of the tube is longer than 5 meters. The device according to claim 1.

20. The length of the tube is longer than 9 meters. The device according to claim 1.

21. The plurality of coil elements are dimensioned to include a space between two or more of the plurality of coil elements, and the space is dimensioned to be 1 / 6 of the wavelength of the electromagnetic wave injected into the borehole of the well through the waveguide assembly. The device according to claim 1.

22. The plurality of coil elements are dimensioned to include a pitch between two or more of the plurality of coil elements, and the pitch is dimensioned to be 1 / 3 of the wavelength of the electromagnetic wave injected into the borehole of the well through the waveguide assembly. The device according to claim 1.

23. The plurality of coil elements are dimensioned to include a width that is shorter than the wavelength of the electromagnetic wave injected into the borehole of the well through the waveguide assembly. The device according to claim 1.

24. The coil spring in the tube forms a helical groove. The device according to claim 1.

25. The helical groove is configured to propagate electromagnetic waves. The device according to claim 24.

26. The apparatus according to claim 25, wherein the spiral groove is configured to propagate the electromagnetic wave in the HE11 mode, transverse electric mode, transverse magnetic mode, or a combination of transverse electric mode and transverse magnetic mode.

27. The apparatus according to claim 1, wherein the tube is a tapered tube and the coil spring is a tapered coil spring.

28. The apparatus according to claim 1, wherein the tube is a curved tube.

29. The apparatus according to claim 1, wherein the tube and the coil spring are contained within a casing and are configured to extend from within the casing or retract into the casing.

30. A method comprising: extrusion-molding a wire including a cross-sectional outer shape; forming the wire into a coil spring, the coil spring having a plurality of coil elements arranged along an outer diameter and a length of the coil spring; inserting the coil spring into a tube having an inner diameter larger than the outer diameter of the coil spring, the tube having a length along which the coil spring extends within the tube.

31. coating the wire with a conductive material; coating the coil spring with a conductive material; and / or coating an inner surface of the tube with an insulating material, the method according to claim 30.

32. The method according to claim 31, wherein the conductive material includes one or more of copper, silver, or gold.

33. The method according to claim 30, wherein a gap is formed between an inner surface of the tube and an outer surface of the coil spring when the coil spring is inserted into the tube.

34. The method according to claim 30, further comprising forming a channel in an inner surface of the tube, the channel extending axially along the length of the tube.

35. The method according to claim 30, wherein the cross-sectional outer shape of the wire includes a base portion and a protruding portion extending from the base portion, the protruding portion including one of a trapezoidal outer shape, a circular outer shape, a square outer shape, a rectangular outer shape, or a sine wave outer shape.

36. The method according to claim 30, wherein forming the wire into a coil spring includes winding the wire around the mandrel such that the shape of each of the plurality of coil elements corresponds to the cross-sectional shape of the mandrel along at least a portion of the length of the coil spring.

37. The method according to claim 36, wherein the cross-sectional shape of the mandrel includes at least one of a trapezoidal shape, a circular shape, a rectangular shape, an elliptical shape, or a tapered shape.

38. The method according to claim 30, wherein the wire is a copper wire or an aluminum wire.

39. The method further includes forming a plurality of coil springs and inserting the plurality of coil springs into the tube. The method according to claim 30, further comprising inserting the plurality of coil springs into the tube.

40. An apparatus comprising an outer tube having an inner surface, an inner diameter, and a length, and an inner tube having an inner surface, an outer surface, an outer diameter, and a helical groove formed on the inner surface and extending along the length of the inner tube, wherein the inner tube is positioned within the outer tube and the outer diameter of the inner tube is smaller than the inner diameter of the outer tube.

41. The apparatus according to claim 40, wherein a gap is defined between the outer surface of the inner tube and the inner surface of the outer tube.

42. The apparatus according to claim 40, wherein the helical groove forms a waveguide.

43. The apparatus according to claim 40, wherein the inner surface of the inner tube and / or the helical groove includes a conductive material.

44. The apparatus according to claim 40, further comprising an insulating layer between the outer tube and the inner tube.

45. The apparatus according to claim 40, wherein the outer surface of the inner tube includes a dielectric material.

46. The apparatus according to claim 40, wherein the helical groove is configured to propagate millimeter electromagnetic waves.

47. The apparatus according to claim 46, wherein the helical groove is configured to propagate the millimeter electromagnetic waves in the HE11 mode.

48. A system comprising a waveguide assembly comprising a tube including an inner surface, an inner diameter, and a length, and a coil spring including an outer surface, an outer diameter, and a plurality of coil elements arranged along the length of the coil spring, wherein the coil spring is positioned within the tube and the outer diameter of the coil spring is smaller than the inner diameter of the tube. A system comprising a gyrotron configured to inject millimeter-wave radiation energy into a borehole of a well through the waveguide assembly.

49. The system according to claim 48, further comprising a plurality of waveguide assemblies underground for directing the millimeter-wave radiation energy to excavate a portion of the borehole or to remove material from the borehole.

50. The system according to claim 49, wherein the plurality of coil springs are stacked in one or more tubes to a distance of 15 km below the surface of the well.

51. A method comprising: forming a plurality of corrugation features on a first side of a metal material sheet, the sheet including a first edge and a second edge; forming the metal material sheet into a first tube; sealing the first tube by welding the first edge and the second edge together, the sealed first tube forming a corrugated waveguide.

52. The method according to claim 51, further comprising inserting the sealed first tube into a second tube to form a multi-piece corrugated waveguide.

53. A method comprising: receiving a metal material sheet having a first surface, a first edge, and a second edge; receiving a corrugation element at the top of the first surface of the metal material sheet, the corrugation element including a plurality of corrugation features; forming the metal material sheet into a first tube including the corrugation element within the first tube; sealing the first tube by welding the first edge and the second edge together, the sealed first tube forming a multi-piece corrugated waveguide.

54. The method according to claim 53, wherein the corrugation element is a coil spring.

55. The method according to claim 53, wherein the corrugation element is a second tube including a plurality of corrugation features formed on an inner surface of the second tube.

56. An apparatus comprising: an outer tube having an inner surface, an inner diameter, and a length; At least one inner tube having an inner surface, an outer surface, an outer diameter, and at least one corrugation feature formed on the inner surface and extending along the length of the at least one inner tube, wherein the at least one inner tube is positioned within the outer tube and the outer diameter of the at least one inner tube is smaller than the inner diameter of the outer tube, the at least one inner tube An apparatus comprising.

57. The apparatus according to claim 56, further comprising a dielectric material adjacent to the inner surface of the outer tube or the outer surface of the at least one inner tube.

58. The apparatus according to claim 57, wherein the outer surface of the at least one inner tube includes a coating of the dielectric material.

59. The apparatus according to claim 57, wherein the dielectric material is a material layer positioned between the inner surface of the outer tube and the outer surface of the at least one inner tube.

60. The apparatus according to claim 57, wherein the dielectric material includes one of glass, ceramic, porcelain, or plastic.

61. The apparatus according to claim 56, further comprising an insulating layer positioned between the outer tube and the at least one inner tube.

62. The apparatus according to claim 61, wherein the insulating layer includes one of glass fiber, continuous bubble foam, closed cell foam, polystyrene, ceramic fiber, carbon composite, silica fiber, or rock wool.

63. The apparatus according to claim 56, wherein the at least one inner tube includes a plurality of inner tubes longitudinally disposed within the outer tube.

64. The apparatus according to claim 63, wherein each of the plurality of inner tubes is joined together within the outer tube via one of a screw connection, a weld, a magnetic connection, or a bolt connection.

65. The apparatus according to claim 63, wherein each of the plurality of inner tubes is joined to each other via a retaining ring surrounding adjacent ends of two inner tubes.

66. The apparatus according to claim 56, wherein the at least one inner tube is formed via additive manufacturing.

67. The apparatus according to claim 56, wherein the outer tube includes a continuous tube, a coiled tube, or a pipe tube.

68. The apparatus according to claim 56, wherein the outer tube includes a gas injector or a pump discharge device.

69. The apparatus according to claim 56, wherein the outer tube includes a non-metallic material.

70. The apparatus according to claim 56, wherein the outer tube comprises carbon steel, stainless steel, Inconel, titanium alloy, molybdenum alloy, tungsten alloy, copper alloy, aluminum alloy, or copper chromium zirconium alloy.

71. The apparatus according to claim 56, wherein the at least one corrugation feature comprises at least one groove adjacent to at least one ridge.

72. The apparatus according to claim 56, wherein the at least one corrugation feature comprises a helical groove.

73. The apparatus according to claim 71, wherein the at least one corrugation feature is configured to propagate millimeter-wave electromagnetic waves in the HE11 mode.

74. The apparatus according to claim 71, wherein the at least one corrugation feature is configured to propagate millimeter-wave electromagnetic waves, and the width of the at least one corrugation feature is shorter than 1 / 6 of the wavelength of the millimeter-wave electromagnetic waves.

75. The apparatus according to claim 71, wherein the at least one corrugation feature is configured to propagate millimeter-wave electromagnetic waves, and the depth of the at least one corrugation feature is 1 / 4 of the wavelength of the millimeter-wave electromagnetic waves.

Images