Heat Pipes for a Single Well Engineered Geothermal System

Abstract

A heat pipe or a bundle of heat pipes for transporting geothermal heat in a well is provided. As the temperature rises at one end of the heat pipe, the operating fluid turns to a vapor which absorbs the latent heat. The hot vapor within the heat pipe flows to the cooler end of the heat pipe where it then condenses and releases the latent heat. The condensed fluid then flows back to the hot side of the heat pipe and the process repeats itself.

Claims

1. An apparatus for transporting geothermal heat from a geothermal well to a surface comprising: at least one heat pipe comprising a wall surrounding a central tube or chamber; a fluid contained within the central tube or chamber; a first apparatus end that is closed and positioned at a first end of the heat pipe, and a second apparatus end that is closed and positioned at a second end of the heat pipe; wherein the apparatus is configured to be in a vertical or inclined position in the geothermal well, and wherein the fluid absorbs geothermal heat at the first apparatus end as it transitions to a vapor, rises to the second apparatus end, releases geothermal heat at the second apparatus end as it condenses back to a liquid state, and returns to the first apparatus end.

2. The apparatus of claim 1, wherein the first apparatus end is configured for placement in the geothermal well and the second apparatus end is configured for placement near the surface.

3. The apparatus of claim 1, wherein the wall of the at least one heat pipe further comprises: a copper layer surrounding the central tube or chamber; a steel layer surrounding the copper layer; and a titanium layer surrounding the steel layer; and wherein at least the copper layer and the titanium layer are non-porous to water.

4. The apparatus of claim 1, wherein the wall of the at least one heat pipe further comprises: an internal coating layer surrounding the central tube or chamber; an iron layer surrounding the internal coating layer, which is configured to protect the iron layer from the fluid in the central tube or chamber; and an external coating layer of a caustic resistant material surrounding the iron layer; and wherein at least the internal and external coating layers are non-porous to water.

5. The apparatus of claim 1, wherein the at least one heat pipe is made from titanium.

6. The apparatus of claim 1, wherein the at least one heat pipe comprises: a plurality of pipes welded together vertically; a base section secured to a base of the plurality of pipes; a threaded plug configured to be secured to an uppermost pipe of the plurality of pipes, which comprises corresponding threading; and a port comprised in the uppermost pipe of the plurality of pipes and positioned so as to be covered by the threaded plug when the threaded plug is fully inserted into the uppermost pipe; and wherein during assembly of the at least one heat pipe, the threaded plug is partially inserted into the plurality of pipes, the fluid is injected into the at least one heat pipe through the port, and the threaded plug is then inserted further into the plurality of pipes to cover the port.

7. The apparatus of claim 6, wherein the plurality of pipes, the threaded plug and the base section are made from titanium.

8. The apparatus of claim 1, wherein the at least one heat pipe comprises a plurality of heat pipes arranged in a bundle surrounding a bundle central tube or chamber comprising the fluid.

9. The apparatus of claim 8, wherein the bundle of heat pipes comprises at least six heat pipes surrounding the bundle central tube or chamber, each of the heat pipes comprising the wall surrounding the central tube or chamber.

10. The apparatus of claim 8, wherein the bundle of heat pipes comprises a plurality of bundles of heat pipes.

11. The apparatus of claim 10, wherein the plurality of bundles of heat pipes comprises at least six bundles of heat pipes and comprises a total of at least seventy-two heat pipes.

12. The apparatus of claim 11, wherein the plurality of bundles of heat pipes are arranged to surround a further central tube or chamber comprising the fluid.

13. The apparatus of claim 1, wherein the at least one heat pipe comprises appendages branching outwardly from a central heat pipe configured to insertion into horizontal or angled bore holes in the geothermal well.

14. The apparatus of claim 1, wherein the at least one heat pipe is made from copper.

15. The apparatus of claim 1, wherein the at least one heat pipe is made from a copper-nickel alloy.

16. The apparatus of claim 1, wherein the fluid is water.

Description

BRIEF DESCRIPTION OF THE FIGURES

[0017] FIG. 1 shows a heat pipe according to an embodiment of the invention.

[0018] FIG. 2 shows a heat delivery system according to an embodiment of the invention.

[0019] FIG. 3 shows a cross-section of a first embodiment of a heat pipe according to the present invention.

[0020] FIG. 4 shows a cross-section of a second embodiment of a heat pipe according to the present invention.

[0021] FIG. 5 shows a cross-section of a third embodiment of a heat pipe according to the present invention.

[0022] FIG. 6 shows an embodiment of converting a titanium pipe into a heat pipe according to the third embodiment of the present invention.

[0023] FIG. 7a shows a first heat pipe design option according to the present invention.

[0024] FIG. 7b shows a second heat pipe design option according to the present invention.

[0025] FIG. 7c shows a third heat pipe bundle design option according to the present invention.

[0026] FIG. 8 shows a graph of estimated well electric power output for a geothermal field.

[0027] FIG. 9 shows an embodiment of a heat nest according to the invention having appendages.

[0028] FIGS. 10a-10b show embodiments of a heat pipe according to the invention having appendages.

[0029] FIGS. 11a-11d show an example of typical brine flow in a well.

[0030] FIG. 12 shows an example of creating appendages in a well.

[0031] FIG. 13 shows an example of an entrainment model.

[0032] FIGS. 14a-14c show examples of heat pipe bundle designs according to the invention in two dimensions.

[0033] FIGS. 15a-15c show examples of heat pipe bundle designs according to the invention in three dimensions.

DETAILED DESCRIPTION OF THE FIGURES

[0034] The present invention will now be described with reference made to FIGS. 1-15c.

[0035] A heat pipe 10 is shown in FIG. 1 having a first end 11 and a second end 12. The heat pipe 10 is self-contained and includes fluids operating in a vacuum. As the temperature rises at one end 11 of the heat pipe 10, the operating fluid turns to a vapor which absorbs the latent heat. The hot vapor within the heat pipe 10 flows to the cooler end 12 of the heat pipe where it then condenses and releases the latent heat. The condensed fluid then flows back to the hot end 11 of the heat pipe 10. The process of the liquid vaporizing and condensing at the two ends 11 and 12 of the heat pipe 10 repeats itself. In a preferred embodiment, the heat pipe 10 is slanted at a minimum angle of three degrees to facilitate the condensate returning to the bottom end 11 of the heat pipe 10. This transfer of heat takes place in only a few seconds. Conversely, when the heat source is removed, the heat pipes cool in only a few seconds.

[0036] Many heat pipes 10 can be used in a geothermal well 201. One or more geothermal well 201, as shown in FIG. 2, are drilled into the earth until the required temperature is encountered in an area referred to as a heat reservoir 210. For example, the well 201 may have a diameter of 17.5 inches (0.45 meters) drilled into a region of hot rock. The well 201 may include lateral bore holes 207 drilled into the rock which are installed with heat pipes 208 to harvest heat and deliver it to the central well. A heat exchanger 209 transfers the heat from the heat pipes 208 to the closed cycle system 204. The heat is then pumped to the surface using a pump 202, and delivered to the production well. Insulation 203, 206 and a high heat conductive material 205 are provided in the well to minimize heat loss. The heat delivered is based on the heat resource encountered in the earth. If enough heat is encountered the operational cost of the heat source is minimized because no fossil fuel is burned to generate the required amount of heat to change the oil viscosity. The geothermal well 201 can be depreciated over a long period of time and thus the operational costs are composed of running the pumps. Geothermal well 201 can be used alone or in combination with a boiler 212 and waste heat 213 to provide the required thermal energy.

[0037] A boiler 212 can be used to augment the geothermal well 201 or replace the geothermal well 201 for the heat required. The boiler 212 can also burn fossil fuel, crude oil or gas that naturally comes from an oil well, such as flaring gas.

[0038] Additionally, if an additional heat source 213, such as waste heat or electrical resistant heat, is available, the other heat source 213 can be used to supply additional heat. For example, on an offshore oil platform where it would be more difficult to implement a geothermal well, waste heat or a combination of waste heat, electrical heat and/or a boiler can be used to supply the heat source for heating and/or flooding the oil reservoir. The other heat source 213 supplies heat to a manifold 218, such as a hot water manifold, for providing the hot water to applications requiring the thermal output.

[0039] In accordance with the invention, multiple constructions of the heat pipe can be provided According to a first embodiment shown in FIG. 3, a heat pipe 30 is provided that includes a central chamber 31 surrounded by a layer of copper 32. The internal copper layer 32 may have a thickness of 1.25 millimeters, but can vary in other embodiments. A steel layer 33 is provided around the copper layer 32 and an outer layer 34 of titanium is provided. The outer layer 34 of titanium may have a thickness of one millimeter, but can vary in other embodiments. The heat pipe 30 has an inner diameter D.sub.1 of twenty-eight millimeters and an outer diameter D.sub.2 of 44.5 millimeters. The titanium 34 and copper 32 in the heat pipe 30 are non-porous to water. In a preferred embodiment, the heat pipe 30 has a length of forty feet and can tolerate a temperature inside the central chamber 31 of approximately 600° F.

[0040] According to a second embodiment, shown in FIG. 4, a heat pipe 40 is provided that includes a central chamber 41 surrounded by iron 43. The iron 43 piping has a layer of an internal coating 42 that protects the iron 43 from water flowing through the central chamber 41 of the heat pipe 40. The internal coating layer 42 may have a thickness of 1.25 millimeters, but can vary in other embodiments. Another layer of caustic resistant coating 44 is provided around the exterior of the iron layer 42. The outer layer of coating 44 may have a thickness of one millimeter, but can vary in other embodiments. The coating layer 44 protects the iron 43 from exposure to caustic materials. The heat pipe 40 may have an inner diameter D.sub.3 of twenty-eight millimeters and an outer diameter D.sub.4 of 44.5 millimeters. The exterior coating 44 and interior coating 42 of the heat pipe 40 are non-porous to water. In a preferred embodiment, the heat pipe 40 has a length of forty feet and can tolerate a temperature inside the central chamber 41 of approximately 600° F.

[0041] A third embodiment of a heat pipe 50 is shown in FIG. 5. The heat pipe 50 includes a central chamber 51 surrounding by a titanium pipe 52. The titanium pipe 52 can have a thickness of 3.63 millimeters. In certain embodiments, the thickness of the titanium pipe 52 can vary depending on the depth of the well and other factors. The inner diameter D.sub.5 of the heat pipe 50 can be forty-one millimeters and the outer diameter D.sub.6 can be 48.26 millimeters (1.9 inches).

[0042] An embodiment for converting titanium pipes into a heat pipe 60 is shown in FIG. 6. Several titanium pipes 61 are attached by welds 62. A base 63 is provided and welded to the titanium pipes 61. The topmost pipe 61 is highly threaded, and a threaded plug 64 is screwed into the threaded pipe 61. A port 65 is provided near the top of the titanium pipes 61. When the threaded plug 64 is screwed into the threaded pipe 61, the port 65 is left uncovered by the plug 64. Water is injected into the heat pipe 60 through the port 65. After the appropriate amount of water is pumped into the heat pipe 60, the port 65 is used to create a vacuum. The threaded plug 64 is then further screwed into titanium pipes 61 in order to cover the port 65, thereby securing the vacuum. The threaded plug 64 can then be welded to the titanium pipes 61.

[0043] FIG. 7a shows a design for a heat pipe 70a having an outer diameter of 3.25 inches and four inch appendages. The heat pipe 70a includes a central chamber surrounded by a wall 72a. The thermal capacity of the design is approximately 60 kW and may cost approximately $0.20/W.

[0044] FIG. 7b shows a design for a heat pipe 70b having an outer diameter of 5.25 inches and six inch appendages. The heat pipe 70b includes a central chamber 71b surrounded by a wall 72b. The thermal capacity of the design is approximately 120 kW and may cost approximately $0.22/W.

[0045] In contrast to the single tube designs of FIGS. 7a and 7b, FIG. 7c shows a heat pipe 70c having a six-tube bundle design. Six individual pipes 72c are bundled together around a central chamber 71c. Each of the individual heat pipes 72c includes a tube or chamber 73c.

[0046] The thermal capacity of the design is approximately 100 kW and may cost approximately $0.18/W.

[0047] FIG. 8 shows the estimated well electric power output for a geothermal field. The chart shown is based on a performance estimate based on Well PGM-11 Characteristics for a 1500 meter well depth and a 0.3 meter well diameter. The elliptical region 80 represents the performance estimate range. The brine natural convection defines the production limit in the 10 to 1000 mD (millidarcy) mid-porosity region. The maximum values are set by a two millimeter per second brine flow rate, which is approaching pure fluid natural convection flow velocities. There is no performance decay over time projected. In certain embodiments of the invention, the heat pipe in a heat nest is provided with a plurality of appendages. As shown in FIGS. 9-10b, a heat pipe 90 can have several appendages 91 that branch outwardly from the heat pipe 90. The appendages 91 may have a single pipe design, such as the design of FIG. 7a or 7b, or can have a bundle of pipes, such as the design of FIG. 7c.

[0048] FIGS. 11a-11d show typical brine flow in a well. Large scale brine circulation enables long term heat harvesting from the hottest zones. Heat pipes lower in the well benefit from higher fluid speed, but suffer from lower brine temperatures. The net effect is that all heat pipes transport about the same amount of heat. Large scale brine flow circulation also enables heat harvesting from a large reservoir volume with little impact on far field temperatures, as shown in FIGS. 11c-11d.

[0049] FIG. 12 shows an exemplary embodiment for drilling a bore hole 120 into a formation 125 for receiving an appendage of a heat pipe and providing the appendage. The bore hole 120 can be drilled laterally either before or after casing the well, if a well casing 123 is used. The drilling whip stock 121 is anchored at a vertical location. Individual appendage bore holes 120 are drilled. The drilling apparatus is rotated and cleared from the bore hole 120. A heat pipe and grout feed tube are fed down the central bore hole 122 of the well by way of coiled tubing. The whip stock 121 guides the heat pipe into the appendage 120. Grout 124 is pumped into the appendage 120 to fill voids in non-aqueous or highly corrosive environments. The whip stock 121 can be raised to the next height and rotated 90 degrees for use in creating another bore hole and providing an appendage. It is estimated that using this method, four appendages can be produced per day. Additional examples of creating an appendage can be found in applicant's co-pending U.S. patent application Ser. No. 14/202,778 titled “Creation of SWEGS Appendages and Heat Pipe Structures”, filed Mar. 3, 2014, (U.S. Patent Application Publication No. 2015/0013981) which is incorporated by reference in its entirety.

[0050] In accordance with the present invention, there are several factors relevant to determining the appropriate construction of a heat pipe, including mechanical, thermal and environmental requirements.

[0051] A thermal evaluation of the potential effectiveness of the heat pipe includes examining the heat pipe power capacity limits of the fluid, or thermosiphon, used in the heat pipe. There are limiting factors for thermosiphons, including entrainment of flooding limits and boiling or evaporative limits. For example, water has a greater power capacity than methanol or other fluids when in the 100° C. to 200° C. range. The power limit of the thermosiphon depends on the gravity return of the condensate form of the fluid. The capillary limit does not apply and the viscosity limit is not an issue at higher temperatures. The sonic limit exceeds 2 kW at 100° C. and scales with the cross-sectional area of the heat pipe. The surface smoothness of the heat pipe also effects boiling of the thermosiphon. It is expected that entrainment is the main limiting factor where shear stress from the vapor flows up the heat pipe, which can prevent the counter flow of the condensate to the evaporator. This leads to “flooding” of the condenser.

[0052] A model can be used to estimate or project the entrainment or flooding limit of the thermosiphon. Suitable models found in the art include, for example: ESDU-81038 (1981) as reported in “Heat Pipes” by Dunn and Reay; Wallis (1969): Gas-liquid velocity criteria for flooding in counter-flow; Nguyen-Chi, H. and Groll, M.: Flooding Limit based on Wallis criteria with additional term for tube inclination; Taitel-Duckler (1976): Criteria for Kelvin-Helmholtz instability for finite waves in liquid films on inclined surfaces; and Weber number criteria with length scale based on the liquid film thickness. An example of an entrainment model estimating the liquid film thickness (t) in a tube 130 is shown in FIG. 13. In the example shown, the tube 130 has width (w).

[0053] The liquid velocity profile is integrated to get mass flow according to the following equation:

[00001]$Q=\frac{{\rho }_f^2.Math.h_{\mathrm{fg}}.Math.\mathrm{wg}.Math..Math.\cos .Math..Math.\theta }{{\mu }_f}\left[\frac{{t_1\left(t_1+t_2\right)}^2}{2}-\frac{{\left(t_1+t_2\right)}^3}{6}\right]$

[0054] The shear stress balance can be determined according to the following equation:

[00002]$t_2=\frac{{\tau }_v}{{\rho }_f.Math.g.Math..Math.\cos .Math..Math.\theta }$

[0055] The unity Weber number can be determined according to the following equation:

[00003]$Q\cong {\left(\frac{2.Math.{\mathrm{\pi \sigma \rho }}_g.Math.h_{\mathrm{fg}}^2}{Z}\right)}^{0.5}.Math.w\left(w-t\right)$

[0056] Table 2 shows predicted entrainment limited power:

TABLE-US-00002 TABLE 2 T.sub.vapor = 121° C., Inclination = 60 degrees from vertical Tube ID (in.) 0.237 1.1 3.31 Tube ID (mm) 6.02 27.9 84.1 Annulus ID (mm) 0 0 28 Number in Bundle 72 6 1 Entrainment Limited Power for Individual Pipes (kW) ESDU *0.5 0.35 15.5 102 Chi-Groll *2.2 0.40 18.2 141 Wallis 0.43 20.3 156 Taitel Duckler *1.4 0.41 21.0 192 Entrainment Limited Power for Assembly (kW) ESDU *0.5 25 93 102 Chi-Groll *2.2 29 109 141 Wallis 31 122 156 Taitel Duckler *1.4 29 126 192 minimum 25 93 102 maximum 31 126 192

[0057] With respect to the possibility of power capacity being limited by boiling, it is estimated that there would be heat flux levels of 3.4, 7.5 and 22 W/cm.sup.2 for tubes having inner diameters of 6, 28 and 84 millimeters, respectively. At 100 kW total power over a 15 meter length for the evaporator, the heat flux levels are 0.49, 1.26 and 2.53 W/cm.sup.2 for tubes having inner diameters of 6, 28 and 84 millimeters, respectively. As a result, it is not expected that boiling of the thermosiphon should be a limiting condition for the heat pipes according to the invention.

[0058] It is estimated that for a heat pipe having a sixty degree inclination from vertical and at 121° C., the power transport for a heat pipe including pipes having a ⅜ inch outer diameter and a seventy-two pipe bundle (FIG. 14c) would be 30 kW. It is further estimated the power transport for a heat pipe under similar conditions having a 1.75 inch outer diameter and a six pipe bundle (FIG. 14b) would be 100 kW. And it is further estimated that for a heat pipe under similar conditions having a 5.25 inch outer diameter and a single pipe (FIG. 14a) would be 120 kW.

[0059] A vapor shear test can be conducted with the purpose of determining the entrainment or flooding limited power capacity of a thermosiphon and to provide a baseline for scaling to other tube sizes. The return of liquid condensate by gravity down a thermosiphon tube is opposed by the shear stress from the counter-flow in vapor. The same shear stress conditions can be created in an air-water analog in an open tube. Tests can be done at different tube inclinations and liquid and gas flow rates to determine the conditions where liquid is unable to flow down the tube. An apparatus for the test can include a glass tube having a length of eight feet and an inner diameter of eight millimeters, pure deionized water introduced at the top of the tube, which flows down by gravity, and clean nitrogen gas introduced at the bottom of the tube, which flows to the top and exits. Water wets the glass tube just as it wets the thermosiphon wall material and the normal liquid flow and flow reversal at higher gas velocities can be observed. The tests can be performed at room temperature and the tube can be inclined at 30, 45 and 60 degrees from horizontal.

[0060] An energy equation is used to calculate mass flow rate of vapor and liquid and velocity of vapor. The shear stress is calculated based on vapor velocity for the round tube using standard friction factor correlations. The equivalent velocity of N.sub.2 gas is calculated to match vapor shear stress. Table 3 below shows test conditions to simulate water liquid vapor counter-flow at 100° C. The flow becomes unsteady at the conditions labeled with an asterisk in Table 3.

TABLE-US-00003 TABLE 3 Angle Fluid N.sub.2 Gas Power Level of incline Flow rate Flow rate T.sub.a [watts] From horizontal [mL/min] [gm/min] [° C.] 400 30° 10.645 13.872 25 500 30° 13.306 17.340 25 600 30° 15.968 20.808 25 650 30° 17.298 22.542 24.4 660 30° 17.564 22.889 24.4  670*  30°* 17.831*  23.235* 24.4*  680*  30°* 18.097*  23.582* 24.4*  690*  30°* 18.363*  23.929* 24.4*  700*  30°* 18.629* .sup. 24.276 * 24.4* 650 45° 17.298 22.542 24.4 660 45° 17.564 22.889 24.4 670 45° 17.831 23.235 24.4 680 45° 18.097 23.582 24.4 690 45° 18.363 23.929 24.4 700 45° 18.629 24.276 24.8 710 45° 19.002 24.623 24.8 720 45° 19.27 24.969 24.8 730 45° 19.54 25.316 24.8  740*  45°* 19.8*  25.663* 24.8*  750*  45°* 19.96* 26.01* 24.8* 710 60° 18.895 24.623 23.6 720 60° 19.161 24.969 23.6 730 60° 19.427 25.316 23.6 740 60° 19.694 25.663 23.6  750*  60°* 19.96* 26.01* 23.6*  760*  60°* 20.226*  26.357* 23.6*  770*  60°* 20.492*  26.703* 23.6*  780*  60°* 20.758* 27.05* 23.6*

[0061] A shear test shows that as the angle of inclination of the pipe or tube increases, the power carrying capacity also increases to a limit. From testing an eight feet section of eight millimeter (inner diameter) tubing, it is estimated a pipe can carry from 600 W at an angle of inclination from horizontal of 30 degrees up to 750 watts at an angle of inclination of 60 degrees. Increasing the angle from 30 to 45 improves the power capacity by approximately 10%, but increasing the 45 to 60 improves the power carrying capacity by only 1.3%. Further, a second tube shaped with helical swirls around a W″ mandrel was built and tested which produced similar results, indicating the heat pipe will function with a transposed tube winding.

[0062] As shown and described in reference to FIGS. 7a-7c, there are several design options for heat pipes and heat pipe bundles. Further examples of heat pipe bundle design options are shown in FIGS. 14a-14c.

[0063] FIG. 14a shows a heat pipe 150 having a single pipe 152 with a central chamber 151 defining an inner diameter. FIG. 14b shows a heat pipe bundle 160. The bundle 160 is formed by six heat pipes 162 around a central chamber 161, with each of the six heat pipes 162 having a tube or chamber 163 defining an inner diameter of the heat pipe 162. FIG. 14c shows a further heat pipe bundle 170. The heat pipe bundle 170 includes six smaller heat pipe bundles 174 around a central chamber 171. Each smaller heat pipe bundle 174 includes twelve heat pipes 172, each having a tube or chamber 173 defining an inner diameter of the heat pipe 172. There are a total of seventy-two heat pipes 172 in the bundle 170.

[0064] FIGS. 15a-15c show the heat pipes 150, 160, 170 of FIGS. 14a-14c in three-dimensional representations.

[0065] As the number of heat pipes increases from a heat pipe 150 to the heat pipe bundle 170, the diameter of the individual heat pipes 150, 162, 172 decreases. Exemplary dimensions for the heat pipes 150, 160, 170 of FIGS. 14a-14c that would fit a bore hole are listed in Table 4.

TABLE-US-00004 TABLE 4 Single Tube Six tubes 72 tubes (FIG. 14a) (FIG. 14b) (FIG. 14c) # of tubes 1    6    72-90 Outer Diameter (OD) 5.25″ 1.75″ 0.375″ Inner diameter (ID) 3.31″ 1.10″ 0.237″ Wall Thickness (WT)  0.970″ 0.32″ 0.069″ OD/WT Ratio 5.4  5.4  5.4   Center hole diameter 1.5″  1.75″ 1.75″  Length 100′    100′    100′   

[0066] The material used for making the heat pipe wall may also vary based on compatibility with water as the working fluid, corrosion resistance to brine in the well bore, availability of tubes in the appropriate diameter and wall thickness material cost and ability to manufacture. One possible material is copper, which has a high thermal conductivity, compatibility with water as the working fluid, has well-known fabrication processes and is readily available at the lowest cost. A second material option is 70/30 cupro-nickel alloy, which is considered because of its excellent corrosion resistance and higher mechanical strength over copper. It is expected that it is compatible for making heat pipes having water, as a related material, Monel, is known to be acceptable. A third material for possible use is titanium KS50, which has superior mechanical strength, half of the weight of copper and excellent corrosion resistance. It is also known to be compatible with water for heat pipe use.

[0067] These three pipe materials are further compared in Table 5 below:

TABLE-US-00005 TABLE 5 Cu—Ni Titanium Copper 70/30 Grade 2 CP (CDA 102, (CDA (ASTM Commercial Availability Units 122, 110) 715) B-338) Density lb./in.sup.3 .321 .322 .163 Yield Strength kpsi 10 35 40 Ultimate strength kpsi 35 65 50 Young's Modulus ×10.sup.6 psi 15.1 18 15.2 Weight to Stiffness ratio 47 47 93 (2x) Percent Elongation % 40% 29% 10% to failure Coefficient of Thermal 10.sup.−6 in/ 9.4 8.6 5.2 Expansion (@350° F.) in - ° F. Thermal Conductivity W/m-K 390 29.4 18.5 (RT) Corrosion Resistance Good Better Best

[0068] A stress analysis, as a result of bending of the material, can be performed for each of these materials. Because the metals being considered are ductile, the analysis compares the calculated stress values to the yield stress. Yield stress is usually measured as 0.2% yield or proof strength, which is the stress that produces a 0.2% strain without recovering. Stresses investigated in the analysis include bending around a large radius during installation and hoop stresses caused from internal tube pressures at 350° F. and 600° F. temperatures and external pressures at 6,000, 8,000 and 10,000 feet below ground level. The bending stresses are calculated using Hooke's Law, where the strain at the extreme fiber of the tube outer diameter, and E is the modulus of elasticity in 10.sup.6 pounds per square inch (psi). Strain rate is determined from bending around the large radius, the appendage that must pass through during deployment into the hole. Strains can be determined for a forty feet and fifty feet bend radius. Hoop stresses can be determined using Lame's equation.

[0069] A summary of the bending stress analysis is shown in Table 6. The results labeled (*) indicate a possibility of the tube to yield during deployment, the results labeled (**) indicate an elastic tube, and the results with no asterisks indicate the tube will yield during deployment.

TABLE-US-00006 TABLE 6 Bending Stress, kpsi 5.25″ 1.75″ ⅜″ Bend Temp, OD OD OD Radius ° F. Material tube tube tube 40 350 Cu, annealed 82.5 27.5 5.9 ** 40 600 Cu, annealed 77.7 25.9 5.6 ** 50 350 Cu, annealed 66 22   4.7 ** 50 600 Cu, annealed 62.2 20.7 4.4 ** 40 350 70/30 Cu—Ni, annealed 98.3 32.8 7.0 ** 40 600 70/30 Cu—Ni, annealed 92.8 30.9 6.6 ** 50 350 70/30 Cu—Ni, annealed 78.7   26.2 * 5.6 ** 50 600 70/30 Cu—Ni, annealed 74.2  24.7* 5.3**  40 350 KS-50 Titanium 83.3  27.8** 5.9**  40 600 KS-50 Titanium 75.3  25.1** 5.4**  50 350 KS-50 Titanium 66.6  22.2** 4.8**  50 600 KS-50 Titanium 60.3  20.1** 4.3** 

[0070] A sample analysis of the estimated cost for the three example raw materials is shown in Table 7:

TABLE-US-00007 TABLE 7 Units Cu Cu—Ni Ti Raw material cost $USD/lb. $4 $22 Tube Cost $/lb. 5.33 9.14 $30-60 (?) Weight of Heat Pipe Assembly per foot Single tube Lbs./ft. 50.28 50.44 25.42 Six Tubes Lbs./ft. 33.52 33.63 16.95 72 Tubes Lbs./ft. 18.47 18.53 9.34 Estimated Cost Per Heat Pipe Single tube $/ft. $268 $461 $782 Six Tubes $/ft. $178 $307 $522 72 Tubes $/ft. $98 $169 $287

[0071] A summary of the estimated raw material cost tradeoffs for the three example materials is shown in Table 8:

TABLE-US-00008 TABLE 8 Units Single Tube 6 Tube 72 Tube Power Carrying Capacity kW 120 100 30 Cost Per Watt Cu $/watt $.22 $.18 $.32 Cu—Ni $/watt $.38 $.31 $.56 Ti $/watt $.65 $.52 $.96

[0072] While there have been shown and described and pointed out fundamental novel features of the invention as applied to preferred embodiments thereof, it will be understood that various omissions and substitutions and changes in the form and details of the devices and methods described may be made by those skilled in the art without departing from the spirit of the invention. For example, it is expressly intended that all combinations of those elements and/or method steps which perform substantially the same function in substantially the same way to achieve the same results are within the scope of the invention. Moreover, it should be recognized that structures and/or elements and/or method steps shown and/or described in connection with any disclosed form or embodiment of the invention may be incorporated in any other disclosed or described or suggested form or embodiment as a general matter of design choice.