WO2019126726A1

WO2019126726A1 - Calibrating a reactor hosting an exothermic reaction based on active site formation energy

Info

Publication number: WO2019126726A1
Application number: PCT/US2018/067251
Authority: WO
Inventors: Dennis G. LETTS
Original assignee: Ih Ip Holdings Limited
Priority date: 2017-12-22
Filing date: 2018-12-21
Publication date: 2019-06-27

Abstract

Methods are disclosed for calibrating the power output by a reactor hosting an exothermic reaction that involves a fuel material and a catalyst. The calibration is based on an activation energy and the volume of the catalyst. The activation energy is an energy required to excite a catalyst into a catalytic state. In some embodiments, the exothermic reaction involves deuterons and the calibration uses the deuteron precession rate to predict the power output from the exothermic reaction.

Description

Calibrating A Reactor Hosting An Exothermic Reaction Based On

Active Site Formation Energy

CROSS-REFERENCE TO RELATED APPLICATION

[0001] This application claims the benefit of priority of U.S. provisional patent application no. 62/609,377, titled“Calibrating A Reactor Hosting An Exothermic Reaction Based On Active Site Formation Energy,” filed on December 22, 2017, which is incorporated herein in its entirety by this reference.

Technical Field

[0002] The present invention relates generally to energy generation in an exothermic reaction, and more specifically, to calibration of a reactor hosting an exothermic reaction based on active site formation energy.

Background

[0003] In an exothermic reaction, the amount of heat generated during the reaction is proportional to the amount of the fuel involved in the reaction. To be more precise, the amount of heat generated is directly linked to the chemicals involved in the reaction. The chemicals can be reactant or catalyst. In the case of a catalyst, the exact amount of heat that will be generated in an exothermic reaction depends on the weight or volume of the reactant or the catalyst, and the mechanism involved in the catalytic process.

[0004] In one type of exothermic reactions known as Low Energy Nuclear Reaction (LENR), a deuterium gas is loaded into a transition metal lattice. The nuclear reaction occurs between two deuterium atoms or ions loaded into the metal. In some

embodiments, the amount of deuterium loaded into the transition metal as measured by the deuterium loading ratio is an important factor in triggering an exothermic reaction. Estimating the power output from an LENR requires knowledge of the amount of deuterium atoms or ions loaded in the metal lattice. A deuterium atom or ion loaded into the metal lattice forms an active site where an LENR may take place. The power output from an LENR depends on the number of active sites formed in the metal lattice. The present disclosure teaches how to estimate the concentration of active sites in a metal catalyst for use in power output estimation of an exothermic reaction.

Summary

[0005] The present invention relates to power output estimation of an exothermic reaction. The exothermic reaction involves a reactor fuel and a catalyst. The reactor fuel comprises deuterons and the catalyst comprises a transition metal capable of absorbing the deuterons. When the exothermic reaction is hosted in a reactor, the reactor can be calibrated using the power estimates. For example, the reactor can be graded or evaluated based on the estimated power output.

[0006] In some embodiments, the power output from an exothermic reaction is estimated by determining an active site formation energy (ASFE) of the catalyst and measuring a volume of the catalyst. The reactor is calibrated using the determined ASFE, the volume of the catalyst, the deuteron precession rate of the deuterons that are part of the reactor fuel. The deuteron precession rate is dependent on the strength of the magnetic field inside the reactor and the deuteron gyromagnetic ratio of a deuteron. The magnetic field can be either a component of the earth’s magnetic field or an externally imposed magnetic field.

[0007] In some embodiments, the ASFE is determined by measuring a first power output at a first temperature and a second power output at a second temperature. In some embodiments, the ASFE is estimated based on measurement data.

[0008] In some embodiments, the catalyst is a transition metal, a metal alloy, a transition metal oxide, or a metal hydride. The catalyst is used in an exothermic reaction in which deuterons are used as a fuel material.

[0009] In at least one embodiment, a method is provided for estimating a power output of a reactor hosting an exothermic reaction, in which the reactor includes a reactor fuel and a catalyst, the reactor fuel includes deuterons, and the catalyst includes one or more transition metals. The method includes: determining an active site formation energy (ASFE) of the catalyst; calculating a deuteron precession rate; measuring a volume of the catalyst; and estimating a power output of the reactor based on the ASFE, the deuteron precession rate, and the volume of the catalyst.

[0010] The deuteron precession rate may be calculated based on the magnitude of a magnetic field and the deuteron gyromagnetic ratio. The magnetic field may be externally imposed, and may be the earth’s magnetic field.

[0011] The estimated power output is used to evaluate the power output of the reactor. The reactor may be operated at a real power output without exceeding the estimated power output. [0012] The method may include controlling the real power output without exceeding the estimated power output by controlling at least one of a concentration, pressure, and amount of the reaction fuel available in the reactor.

[0013] The method may include controlling the real power output without exceeding the estimated power output by controlling at least one electrical characteristic of an electrode or surface.

[0014] The estimated power output is used to estimate a useful lifetime of the reactor, and, when a time of real use of the reactor meets or exceeds the estimated useful lifetime of the reactor, the reactor may be retired, refueled, or serviced.

[0015] In at least one embodiment, a method of calibrating a reactor is provided. The reactor includes a reactant material and a catalyst. The method includes: measuring a volume of the catalyst; estimating a power output of the reactor based on the volume of the catalyst and an activation energy of the catalyst; and calibrating the reactor using the estimated power output.

[0016] The activation energy of the catalyst may be determined based on power outputs of an exothermic reaction measured at different temperatures, and wherein the catalyst is involved in an exothermic reaction. The estimated power output of the reactor may be further based on a deuteron precession rate.

Brief Description of Figures

[0017] FIG. 1 illustrates an exemplary reactor for heat generation, according to at least one embodiment.

[0018] FIG. 2 illustrates the power output from an exemplary exothermic reaction. [0019] FIG. 3 illustrates the power output from another exemplary exothermic reaction.

[0020] FIG. 4 illustrates an exemplary gyromagnetic motion of a deuteron.

[0021] FIG. 5 is a flowchart illustrating an exemplary method of estimating the power output by an exothermic reaction, according to at least one embodiment.

[0022] FIG. 6 is a flowchart illustrating an exemplary method of estimating the power output of an exothermic reaction based on the energy required (ASFE) to form a single active site in the catalyst, according to at least one embodiment.

Detailed Description

[0023] These descriptions are presented with sufficient details to provide an understanding of one or more particular embodiments of broader inventive subject matters. These descriptions expound upon and exemplify particular features of those particular embodiments without limiting the inventive subject matters to the explicitly described embodiments and features. Considerations in view of these descriptions will likely give rise to additional and similar embodiments and features without departing from the scope of the inventive subject matters. Although the term“step” may be expressly used or implied relating to features of processes or methods, no implication is made of any particular order or sequence among such expressed or implied steps unless an order or sequence is explicitly stated.

[0024] Any dimensions and materials expressed or implied in the drawings and these descriptions are provided for exemplary purposes. Thus, not all embodiments within the scope of the drawings and these descriptions are made according to such exemplary dimensions and materials. The drawings are not made necessarily to scale. Thus, not all embodiments within the scope of the drawings and these descriptions are made according to the apparent scale of the drawings with regard to relative dimensions in the drawings. However, for each drawing, at least one embodiment is made according to the apparent relative scale of the drawing.

[0025] Unless described or implied as exclusive alternatives, features throughout the drawings and descriptions should be taken as cumulative, such that features expressly associated with some particular embodiments can be combined with other embodiments.

[0026] The present application discloses methods for calibrating a reactor configured to host an exothermic reaction. FIG. 1 illustrates a reactor 100. The reactor 100 comprises a primary container 102, an electrode 104, and a lid 106. The primary container 102 may be constructed, for example, of metal having an interior wall or surface first plated with gold 108 or another material (e.g., silver). The plated gold or silver functions as a seal to prevent reaction gasses in the chamber from escaping through the wall of the reaction chamber 100. On top of the gold 108, a layer of hydrogen absorbing material 110 is plated. Outside the reactor 100, a magnet 112 may be optionally placed.

[0027] In FIG. 1, the lid 106 is placed at one end of the reactor 100 and is used to accommodate the electrode 104, input/output ports 114, and a removable electrical pass through 116. The electrode 104 may be made of tungsten, molybdenum, cobalt, or nickel, or other rugged metal that can withstand high voltage and high temperature environment. On the electrode 104, a sleeve of dielectric material 108, such as Teflon, may be placed or coated on the electrode 104 to prevent discharges between the electrode 104 and any exposed (i.e., un-plated) areas of the interior of the reactor, for example the interior wall of the primary container 102 of the reactor 100. The input/output ports 114 are used to introduce reaction gases into the reactor 100 or extract resultant gases from the reactor 100. The input/output ports 114 can also be used to accommodate pressure controlling devices.

[0028] In at least one embodiment, the input/output ports 114 are gaseous communication with one or more gas control devices 120, which may include one or more valves, one or more mass-flow controllers, and may define or be part of a gas flow and control manifold. The gas control device(s) 120 may be used to supply and regulate reaction gases to the reactor 100 via the input/output ports 114 and to further remove spent, depleted, or reacted gases. The gas control device(s) 120 can thus be used to control reactor output power by governing the concentration, pressure, and amount of reaction gases available in the reactor.

[0029] In at least one embodiment, the electrode 104 is in electrical communication with one or more electrical control devices 130, which may include one or more voltage regulators, one or more current regulators, and may send and/or receive, separately or concurrently, electrical power and/or signals via DC, AC, and/or other wave or pulse modalities. The electrical control device(s) 130 may be used to supply and regulate voltage and current to the electrode 104 via the electrical pass-through 116. The electrical control device(s) 130 can thus be used to control reactor output power by governing electrical characteristics and conditions at the electrode 104, for example relative to the interior wall of the primary container 102 and the layers (108, 110) thereon. [0030] In at least one embodiment, a controller 140 regulates the reactor, for examples via at least the gas control device(s) 120 and electrical control device(s) 130, which are operatively coupled to the controller 140. The controller 140 may include a processor that executes reactor control software stored in memory and/or non-transient computer readable instructions. The controller 140 may include user/operator interface devices for manual operation, assistance, and/or monitoring. The controller 140 may regulate the reactor in automatic and/or manual modes, and may regulate in hybrid automatic / manual-assist modes.

[0031] The controller 140 can thus be used to control reactor output power by:

controlling the electrical control device(s) 130 to govern electrical characteristics and conditions at the electrode 104; and, independently or concurrently, controlling the gas control device(s) 120 to govern the concentration, pressure, and amount of reaction gases available in the reactor.

[0032] A type of exemplary exothermic reactions is the so-called Low Energy Nuclear Reaction (LENR), in which two deuterium atoms or ions fuse to form helium and release energy in the process. The reactor 100 shown in FIG. 1 can be configured for LENR type of reactions.

[0033] In an exemplary low energy nuclear reaction, experiments suggest that a fusion nuclear reaction takes place between two deuterium atoms or ions that are loaded into a metal lattice, for example, palladium. The metal lattice functions as a catalyst. The metal lattice comprises vacancies, which deuterium atoms or ions can fill. The energy required to form an active site is referred to as the active site formation energy (ASFE). An active site refers to the vacancy filled by a deuterium atom or ion. When the ASFE is near or below 1 eV, the number of vacancies in the catalyst reaches a concentration of sufficient magnitude to support measurable exothermic reactions. In certain cases, as the amount of energy required to form an active site increases, fewer active sites will be formed. According to the thermodynamic theory, the number of active sites is

_ E_

proportional to e fcr, where E is the amount of energy required to form an active site, k is the Boltzmann constant, and T is the temperature of the catalyst. With a constant N representing the total number of lattices in the catalyst, the number of active sites can be expressed as:

ASFE

Ne r (Equation 1), with ASFE standing for active site formation energy. In some embodiments, the ASFE can be measured or calculated using experimental data, as explained below.

[0034] Active site formation energy (ASFE) and vacancy formation energy (VFE) are terms used synonymously in these descriptions. The VFE for unloaded palladium is 1.8 eV. As hydrogen enters the lattice, the Pd atoms move apart slightly and the bonding strength is reduced. When the lattice is "full" there are 4 atoms of palladium and 4 atoms/ions of hydrogen. At this degree of loading, the VFE has declined to 1 eV or slightly below, and the Pd lattice spacing has increased from 3.89A to slightly more than 4.026A.

[0035] In one exemplary process, two exothermic reactions are conducted and the excess power output is measured in each of the exothermic reactions. FIG. 2 illustrates the power output from a first exothermic reaction. In FIG. 2, the excess power generated in the first exothermic reaction is recorded during a time period of 5770 minutes. The average power output (XPi) from the exothermic reaction over the entire time period is calculated to be 2.82W and the average temperature for the same time period is 65.59° C.

[0036] FIG. 3 illustrates the measurement data from a second exothermic reaction. In FIG. 3, the excess power generated in the second exothermic reaction is recorded over a time period of 13000 minutes. The average power output (XP₂) from the exothermic reaction over the entire time period is estimated to be 3.835W and the average temperature for the same time period is 69.86° C.

[0037] Excess power, heat, or energy as used herein refers to joule energy released by conversion, for example as heat, by exothermic reactions. Thus, excess power, heat, or energy refers to, for example, thermal energy that is released, detected, or harnessed beyond what stimulate are applied to trigger reactions or provide heated conditions. For example, energy may be provided to the reactor via the electrode 104 and via one more heating elements. Excess power, heat, or energy refers to net production and generation of energy at the reactor, for example via the reactants and their exothermic reactions, after accounting for electrical or thermal stimulate applied to trigger reactions or provide heated conditions. It is understood the excess power, heat, or energy come from conversion with respect to the conservation of energy.

[0038] Based on the measurement data from these two exothermic reactions, the active site formation energy can be estimated as follows.

[0039] Under Equation 1, the ratio between the average power outputs of the two exothermic reactions can be expressed as:

ASFE

Ne ^kTi XPi

A^SFE XP₂ (Equation 2).

Ne ^kT2 [0040] Solving for ASFE yields:

ASFE = kln(—) AA (Equation 3).

A -A

[0041] Substituting the values for Ti, T₂, XP₂, and XPi:

XP₁ = 2.82 W, XP₂ = 3.83SW, 7 = (65.59 + 273.15 )K, T₂ = (69.86 + 273.15)X, yields:

ASFE = 0.7209eE.

[0042] With the knowledge of the ASFE, the power output from the catalyst contained in the reactor can be estimated using the following formula:

XP = no. of vacancies x deuter on precession rate x 23.78 MeV (4).

[0043] In Equation 4, the number of active sites can be estimated statistically using:

(Equation 4)

[0044] The deuteron precession rate is the precession rate of a deuteron in a magnetic field. As shown in FIG. 4, a deuteron, having a gyromagnetic ratio y_D, processes in a magnetic field B. The magnetic field can be provided by the earth’s magnetic field, from permanent or electromagnets, or from magnetic fields produced at the atomic scale within the catalyst. The precession rate (Hz) of a deuteron can be expressed as:

(Equation 5), where y_D is 2 (m_p+m_n) g_n and g_n is the so-called g-factor constant, which for deuteron is numerically the same as its magnetic moment 0.857438 nuclear magnetons, m_p is the mass of a proton, and m_n is the mass of a neutron. [0045] With the knowledge of the active site formation energy of the catalyst and the deuteron precession rate, the power output from a reactor that contains a fixed amount of catalyst and fuel can be estimated. FIG. 5 illustrates an exemplary method for estimating the power output of a reactor that hosts an exothermic reaction involving a deuterium gas as fuel and a catalyst. First the active site formation energy (ASFE) of the catalyst is estimated (step 502). Then the deuteron precession rate in a magnetic field, as provided by the earth’s magnetic field, for example, is calculated (step 504). The volume of the catalyst is measured (step 506). The power output of the reactor can be estimated based on the ASFE, the deuteron precession rate and the volume of the catalyst (step 508).

[0046] The exemplary process 500 described in FIG. 5 is applicable to exothermic reactions that involve deuterium and a catalyst that absorbs deuterium into the vacancies inside the catalyst. The principle embodied in the process 500 can be applied to a variety of reactions, either chemical or nuclear, involving a catalyst in a catalytic state, which is an elevated energy state or excited state. The catalyst is effective when in the catalytic state. The amount of energy needed to excite a chemical unit of the catalyst from the base energy state to the catalytic state is referred to as the activation energy (AE). Statistically,

AE

the amount of the catalyst in the catalytic state is proportional to e kr and the output

AE

from the reactor is proportional to e kr as well. FIG. 6 is a flow chart illustrating an exemplary method 600 for estimating the output of a reaction that involves a catalyst. In the method 600, the volume of the catalyst used in the reaction is measured (step 602). Based on the volume of the catalyst and an activation energy of the catalyst needed to bring the catalyst to an elevated energy state or an excitation state, the output of the reaction can be determined (step 604).

[0047] The calculations and calibrations described herein have industrial utility in a range of practical applications, of which numbered descriptions are provided in the following as non-limiting examples.

[0048] 1 - Based on the volume of catalyst present, a reactor's performance can be evaluated and assigned an efficiency level so comparisons with other reactors can be made.

[0049] 2 - Underperforming reactors can be identified.

[0050] 3 - Catalysts can be evaluated quickly to assist in optimizing catalyst production. See section "Cathode Testing Protocol" below, and United States patent application publication number 20180196026A1, entitled“Methods and Apparatus for Testing Fuel Materials for Exothermic Reactions,” which is incorporated herein by this reference. These methods permit catalyst evaluation by lab technicians rather than metallurgical specialists.

[0051] 4 - An operating range for the ASFE can be identified. If the ASFE is too high, then output power is low. If the ASFE is too low, energy output can disrupt the metal lattice structure and halt reactor operation. See section“Concentration Limit for Vacancies” below.

[0052] 5 - The methods expressly described and implicitly enabled by these descriptions can be embedded in reactor control software so that expected reactor power output can be computed in real time using live data. Expected reactor performance can then be compared to actual reactor performance in real time. This has significant engineering and safety utility.

[0053] Cathode Testing Protocol - Cathodes can be loaded with hydrogen or deuterium to serve as heat producers in LENR devices. As new materials are developed, it will be desirable to test these materials to determine the number of vacancies, the number of lattices in the cathodic material, the effective vacancy formation energy, and the vacancy formation energy limit. This section describes how such data can be calculated from laboratory results, beginning with testing for excess power at Tl and T2, and determining XPi and XP₂. Calculate the VFE for the material as:

(Equation 6)

[0054] Calculate number of vacancies as:

Nv = XP2

Q zL (Equation 7)

2/r

[0055] Calculate the number of lattices as:

[0057] Calculate the mass of LENR metal as:

(Equation 10)

[0058] Calculate the lattice energy as:

[0060] Calculate the minimum lattice number as:

N min Nvi Q

(Equation 13)

E_L

[0061] Calculate the minimum atoms as:

N atoms 4N (Equation 14)

mm

[0062] Calculate the minimum mass as Mass:

(Equation 15)

[0063] These calculations can be made using known physics constants and experimental data obtained in testing for excess power at Tl and T2 (determining XPi and XP₂).

[0064] The constants used in this Cathode Testing Protocol are listed below in order of appearance.

Tl = lower cathode temperature in Kelvin

T2 = higher cathode temperature in Kelvin

XP1 = excess power in watts measured at Tl XP2 = excess power in watts measured at T2

E_v = Vacancy formation energy (VFE) of material in eV

K_B = Boltzmann’s constant = l.38xl0²³ JK

Ny = number of vacancies in the cathode material

Q = Energy release for the conjectured reaction = 3.81x10 -12 Joule

g = magnetogyric ratio for deuterium = 4106.6 rad/(Gauss-sec)

B = External magnetic field in gauss; earth’s magnetic field -0.5 gauss

V _metal = volume of metal in cathode in cm3

a = lattice volume in cm

a = lattice dimension in cm = 4.026 xlO -8 cm

M_metai = mass of cathode material tested in grams

= density of cathode material in grams/cm = 12 grams/cm for palladium E_L = lattice cohesive energy in eV

M = Madelung constant for face centered cubic lattice = 1.747

q = electric charge = l.602lxl0 ¹⁹ Coulomb

Ro = nearest neighbor distance in beta phase, meters; Pd = 2.884xlO ¹⁰ m.

p = repulsive interaction distance = 0.35 Angstroms

So = Permittivity of vacuum = 8.8542x10 Joule · coulomb meter

E_min = minimum value for the VFE to avoid lattice rupture, in eV

N_min = total number of lattices required to avoid lattice rupture

N_atoms =total number of atoms of cathodic material required

Mass = mass of cathode material needed in grams

[0065] Furthermore:

[0066] E_L, the lattice cohesive energy can be calculated:

Mq²{-R_Q÷p )

E_L = 4 U_A 7 (Equation 18)

[0067] Concentration Limit for Vacancies - Given the LENR reaction Q = 23.78

MeV, there is a vacancy concentration limit that is likely related to the lattice energy for the palladium hydride/deuteride. From MathCAD calculations in the file’’Lattice Energy”, the Pd lattice has a cohesive energy of 20.934 eV when the D/Pd ratio -0.98 and is associated with the beta phase of the deuteride.

[0068] The concentration limit can be computed:

EL (Equation 19)

Q e KT

(Equation 20)

[0069] At a cell temperature of 50C, the lower limit for the vacancy formation energy is 0.388 eV. If the VFE declines below this limit, then the deuterated Pd lattices will rupture. At 300C, the lower limit of the VFE is -0.688 eV. The MathCAD worsheet is shown below in Table 1.

Table 1: Vmm%f Concentration Limit

[0070] A single palladium lattice is held together by its lattice energy which was computed when the D/Pd ratio reached 0.98. The lattice energy for palladium at high deuterium loading is 20.934 eV. When a LENR reaction occurs, it is conjectured that 23.78 MeV of energy is released in the cathode. The minimum number of palladium lattices to absorb the released energy is calculated as 23.78 MeV/20.934 eV = 1.136c10⁶. This means that each vacancy must be surrounded by 1.136c10⁶ palladium lattices to absorb the energy to keep the energy per lattice below 20.934 eV, so the implied maximum concentration is 1/1.136c10⁶ = 8.803xl0⁷. There are 4 palladium atoms associated with each lattice, suggesting that each vacancy should be surrounded by at least 4.4 million palladium atoms. This ratio suggests the minimum amount of absorbing material required for a given vacancy concentration, which will be especially important when considering thin film cathodes. The vacancy concentration is controlled by the vacancy formation energy of the cathode material and the cathode temperature. At a typical electrolysis cell temperature of 50C, the lower limit for the VFE is 0.388 eV. At a typical gas system temperature of 300C, the minimal VFE is 0.688 eV, as shown in the calculation above.

[0071] The present invention may be carried out in other specific ways than those herein set forth without departing from the scope and essential characteristics of the invention. The present embodiments are, therefore, to be considered in all respects as illustrative and not restrictive, and all changes coming within the meaning and equivalency range of the appended claims are intended to be embraced therein.

Claims

1. A method of estimating a power output of a reactor hosting an exothermic

reaction, the reactor comprising a reactor fuel and a catalyst, the reactor fuel comprising deuterons, the catalyst comprising one or more transition metals, said method comprising:

determining an active site formation energy (ASFE) of the catalyst;

calculating a deuteron precession rate;

measuring a volume of the catalyst; and

estimating a power output of the reactor based on the ASFE, the deuteron

precession rate, and the volume of the catalyst.

2. The method of claim 1, wherein the ASFE is determined by measuring a first power output of the exothermic reaction at a first temperature and a second power output of the exothermic reaction at a second temperature.

3. The method of any preceding claim, wherein the deuteron precession rate is

calculated based on the magnitude of a magnetic field and the deuteron gyromagnetic ratio.

4. The method of claim 3, wherein the magnetic field is externally imposed.

5. The method of claim 4, wherein the externally imposed magnetic field is the earth’s magnetic field.

6. The method of any preceding claim, wherein the ASFE is estimated based on measured data.

7. The method of any preceding claim, wherein the catalyst comprises a metal or a metal alloy.

8. The method of any preceding claim, wherein the catalyst comprises a transition metal oxide.

9. The method of any preceding claim, wherein the catalyst comprises a metal hydride.

10. The method of any preceding claim, wherein the estimated power output is used to evaluate the power output of the reactor.

11. The method of any preceding claim, further comprising operating the reactor at a real power output without exceeding the estimated power output.

12. The method of claim 11, further comprising controlling the real power output without exceeding the estimated power output by controlling at least one of a concentration, pressure, and amount of the reaction fuel available in the reactor.

13. The method of claim 11 or 12, further comprising controlling the real power

output without exceeding the estimated power output by controlling at least one electrical characteristic of an electrode or surface.

14. The method of claim 11, wherein the estimated power output is used to estimate a useful lifetime of the reactor.

15. The method of claim 14, further comprising, when a time of real use of the reactor meets or exceeds the estimated useful lifetime of the reactor, at least one of:

retiring the reactor; refueling the reactor; and servicing the reactor.

16. A method of calibrating a reactor, said reactor comprising a reactant material and a catalyst, said method comprising:

measuring a volume of the catalyst;

estimating a power output of the reactor based on the volume of the catalyst and an activation energy of the catalyst; and

calibrating the reactor using the estimated power output.

17. The method of claim 16, wherein the activation energy of the catalyst is determined based on power outputs of an exothermic reaction measured at different temperatures, and wherein the catalyst is involved in an exothermic reaction.

18. The method of any one of claims 16-17, wherein the estimated power output of the reactor is further based on a deuteron precession rate.

19. The method of any one of claims 16-18, wherein the catalyst comprises a metal or a metal alloy.

20. The method of any one of claims 16-19, wherein the catalyst is a metal hydride.

21. The method any one of claims 16-20, wherein the estimated power output is used to evaluate the power output of the reactor.

22. The method any one of claims 16-21, further comprising operating the reactor at a real power output without exceeding the estimated power output.

23. The method of claim 22, further comprising controlling the real power output without exceeding the estimated power output by controlling at least one of a concentration, pressure, and amount of the reactant material available in the reactor.

24. The method any one of claims 22-23, further comprising controlling the real power output without exceeding the estimated power output by controlling at least one electrical characteristic of an electrode or surface.

25. The method any one of claims 16-24, wherein the estimated power output is used to estimate a useful lifetime of the reactor.

26. The method of any one of claims 25, further comprising, when a time of real use of the reactor meets or exceeds the estimated useful lifetime of the reactor, at least one of: retiring the reactor; refueling the reactor; and servicing the reactor.