5. Logistics of sodium hydroxide and sodium metal

anode and cathode electrodes, where the electrodes can be moved closer together to compen-

It is possible to calculate the quantity of Na metal produced throughout the year by the selfcontained sodium (Na) metal production plant sited in the different geographic locations given in Table 2, based on the hours of daylight and the prevailing air mass conditions. It is not necessary to specify a detailed design for the NaOH electrolytic cell to generate an accurate daily estimate of Na metal production yield throughout the year, if it is assumed that maximum electric power available from the solar tower PV device panel array can always be supplied to the electrolytic cells by appropriately controlling the electrical resistance of the NaOH electrolytic cells together with the set point reference voltage VSET of the PWM DC-DC converter. It is assumed that electrolysis of NaOH, and thereby Na metal production can only occur if the available current supplied by the solar tower PV device panel array has a minimum threshold value of IST ¼ 3,000 A. In Figure 10, the production yield of Na metal is calculated for each day of the hypothetical year 2015, for electrolysis of pure NaOH according to Eq. (2), for the four geographic locations listed in Table 2, using the solar position algorithm (SPA) described in Solar position algorithm for solar radiation applications written by Reda & Andreas in 2004, that is a refined algorithm based on the book, The Astronomical Algorithms written by Meeus in 1998, and is presently regarded as the most accurate [73, 74]. The SPA allows the solar zenith θsz, and azimuth γs, angles to be calculated

The calculation in Figure 10 provides the expected daily sodium (Na) metal production yield under the assumption that the energy conversion efficiency ηPV ¼ 90% for the solar tower PV device panel array and furthermore, current is only transmitted to the electrolytic cells when the solar tower PV device panel array receives sufficient solar irradiance to produce the minimum threshold value of current IST ¼ 3,000 A. The calculation in Figure 10, uses the SPA algorithm to determine the solar zenith angle θsz, throughout the day from sunrise to sunset for each day of

Figure 10. Calculated sodium (Na) metal daily production yields throughout the hypothetical year 2015, for El Paso, Texas (thick solid), Alice Springs, Australia (thin solid), Bangkok, Thailand (thick dash) and Mbandaka, DRC (thin dash).

sate the loss of reactant volume as it is consumed in the cell.

174 Recent Improvements of Power Plants Management and Technology

with uncertainties of �0.0003� in the range between -2000 to 6000 years.

For the full benefits of the hydrogen (H2(g)) fuel based sustainable clean energy economy to be realized, it is essential to overcome the logistical problems inherent with H2(g) fuel. The H2(g) fuel possesses the unique characteristic that it can be combusted directly inside an internal combustion engine (ICE) to produce useful work without emission of carbon dioxide (CO2) or sulfur oxides (SOX) and with minimal emission of nitrogen oxides (NOX). It can also be converted to electricity directly in a fuel cell to produce useful work with substantially higher efficiency than in an ICE. Regardless of how the versatile H2(g) fuel is applied to produce useful work, it is essential to provide safe, reliable and economical logistics for its use. The major drawback of H2(g) fuel remains the difficulty of direct storage. Fortunately, the element sodium (Na) positioned two rows below hydrogen in Group I of the periodic table of elements, is sufficiently electropositive to be capable of chemically releasing the H2(g) fuel stored in either ordinary salinated (sea) or desalinated (fresh) water (H2O) over a wide temperature range [37]. Sodium (Na) is also sufficiently abundant in nature in the form of sodium chloride (NaCl) in seawater, to make its use economical for H2(g) fuel generation [103]. Therefore, sodium (Na) metal and the sodium hydroxide (NaOH) byproduct resulting from the H2(g) fuel producing chemical reaction in Eq. (1), constitute the ideal intermediate materials needed to render H2(g) into a practical and usable fuel by storing the sun's radiated energy as Na metal.

A hydrogen (H2(g)) fuel clean energy economy based on a sustainable, closed clean energy cycle that uses sodium (Na) metal recovered by electrolysis from sodium hydroxide (NaOH) as a means of storing the sun's radiant energy collected during daytime hours, provides numerous benefits including safe, reliable and economical logistics. The scalable, selfcontained sodium (Na) metal production plant that stores the sun's radiant energy in sodium (Na) metal, can be constructed in almost any geographic location on earth benefitting from ample solar irradiance and clear weather all year. In the U.S.A., the arid, southwestern desert region offers the requisite conditions, including sufficient undeveloped land area to construct scalable, self-contained solar powered electrolytic sodium (Na) metal production plants by the thousands. Using the southwestern desert region that includes West Texas, New Mexico, Arizona and Southern California as a hub for solar powered sodium (Na) metal production by electrolysis of sodium hydroxide (NaOH), it is possible to develop sufficient Na metal production capacity based on the scalable, self-contained sodium (Na) metal production plant described, to meet the U.S.A.'s energy needs for motor vehicle transport and for broader clean electric power applications.

The physical and chemical properties of sodium (Na) metal and sodium hydroxide (NaOH) render these materials ideal from an operational logistical standpoint. The sodium (Na) metal is a solid at room temperature and therefore has negligible vapor pressure. As a result, Na metal can be stored almost indefinitely in hermetically sealed packaging that can be opened much as a sardine can, only when the Na metal must be loaded into a hydrogen generation apparatus to react with either salinated (sea) or desalinated (fresh) water (H2O) according to Eq. (1), to produce hydrogen (H2(g)) fuel on demand [37]. The sodium hydroxide (NaOH) byproduct of the hydrogen producing chemical reaction in Eq. (1), is also a solid at room temperature in its pure form and has negligible vapor pressure. The NaOH is miscible with water in all proportions, enabling the aqueous NaOH(aq) solution to be readily transferred by pumping into and out of sealed tanks for transport by truck, rail car or pipeline to the remotely located self-contained sodium (Na) metal production plant units for reprocessing by electrolysis according to Eqs. (2) and (3), to recover the Na metal for reuse in generating H2(g) fuel. The NaOH(aq) transportation/storage tanks of the type shown in Figure 2, can be fiberglass or metal with a corrosion resistant internal rubber liner, and must seal hermetically to exclude ambient air that contains carbon dioxide (CO2) which slowly degrades the NaOH(aq), albeit not irreversibly.

To obtain a sense for the magnitude of the logistical effort needed to produce and distribute sufficient sodium (Na) metal to fuel all of the motor vehicles in the U.S.A. while recovering the sodium hydroxide (NaOH) byproduct for reprocessing by electrolysis, it is necessary to consider the total number of vehicles in circulation. According to the Bureau of Transportation Statistics at the United States Department of Transportation (DOT), the total number of registered vehicles in the year 2013 in the U.S.A. numbered 255,876,822 [104]. The figure includes passenger cars, motorcycles, light duty vehicles, other 2-axle/4-tire vehicles, trucks with 2-axles/6-tires or more and buses. If it is further assumed that each motor vehicle on average consumes the energy equivalent of 16.2 gallons of 100 octane gasoline (2,2,4- Trimethylpentane) per week, then the corresponding quantity of H2(g) fuel having an equivalent heating value is given as 15.8 kg. The generation of 15.8 kg of H2(g) fuel according to Eq. (1), requires that 361.6 kg of Na metal react with approximately 300 kg of water (H2O) [37]. Therefore, the total quantity of Na metal consumed per week in the U.S.A. can be calculated as 255,876,822 vehicles · 361.6 kg/week ¼ 92,525,058,835 kg/week. If each solar tower produces a mass mNa ¼ 30,000 kg/day of Na metal, then in one week the Na metal yield per solar tower will be given as 30,000 kg · 7 days ¼ 210,000 kg/week. The number of solar towers required to meet demand for Na metal will be given as NST ¼ 92,525,058,835 kg/ week / 210,000 kg/week ¼ 440,596 solar towers or approximately NST ≈ 450,000 solar towers. While the number of solar towers required might seem very large and the task of constructing them onerous, it is in fact possible to construct the sufficient number of towers to provide Na metal for all the motor vehicles in the U.S.A. The self-contained sodium (Na) metal production plants can be constructed at a density of approximately ρplant ¼ 30 plant units per square mile to prevent mutual shading when the towers are elevated and rotated to track the sun. The solar tower density and layout necessitate a land area given as Aland ¼ NST / ρplant ¼ 450,000 / 30 ¼ 15,000 square miles, to meet the Na metal demand for all the motor vehicles in the U.S.A. using PV device panels with an efficiency ηPV ¼ 90%, and a land area Aland ¼ 75,000 square miles using PV device panels with an efficiency ηPV ¼ 18% that currently exist commercially. The land area required can be placed into perspective when considering that the area of the state of New Mexico is approximately 121,000 square miles and thus, there exists more than sufficient desert land area for constructing the scalable, selfcontained sodium (Na) metal production plants in the U.S.A.

Our company believes that hydrogen (H2(g)) fuel will earn an important role in motor vehicle transport applications for powering smaller 1–5 kW class secondary power fuel cells for onboard continuous recharging of battery electric vehicles (BEVs), a concept implemented successfully in the 1960s using H2(g) fuel stored in high pressure cylinders [23]. The concept of a smaller hydrogen fuel cell operating at a fixed power output level to continuously recharge an electric storage battery can be extended not only to motor vehicle propulsion systems but also for a broad range of clean electric power applications, including general ground transport that includes commercial trucks, trains, maritime transport as well as powering single family homes, commercial establishments and industrial enterprises. Such an approach will ultimately enable mankind to dispense with use of carbon based fossil fuels for motor vehicle transport applications and most other types of ground based electric power generation.

## 6. Conclusion

A hydrogen (H2(g)) fuel clean energy economy based on a sustainable, closed clean energy cycle that uses sodium (Na) metal recovered by electrolysis from sodium hydroxide (NaOH) as a means of storing the sun's radiant energy collected during daytime hours, provides numerous benefits including safe, reliable and economical logistics. The scalable, selfcontained sodium (Na) metal production plant that stores the sun's radiant energy in sodium (Na) metal, can be constructed in almost any geographic location on earth benefitting from ample solar irradiance and clear weather all year. In the U.S.A., the arid, southwestern desert region offers the requisite conditions, including sufficient undeveloped land area to construct scalable, self-contained solar powered electrolytic sodium (Na) metal production plants by the thousands. Using the southwestern desert region that includes West Texas, New Mexico, Arizona and Southern California as a hub for solar powered sodium (Na) metal production by electrolysis of sodium hydroxide (NaOH), it is possible to develop sufficient Na metal production capacity based on the scalable, self-contained sodium (Na) metal production plant described, to meet the U.S.A.'s energy needs for motor vehicle

The physical and chemical properties of sodium (Na) metal and sodium hydroxide (NaOH) render these materials ideal from an operational logistical standpoint. The sodium (Na) metal is a solid at room temperature and therefore has negligible vapor pressure. As a result, Na metal can be stored almost indefinitely in hermetically sealed packaging that can be opened much as a sardine can, only when the Na metal must be loaded into a hydrogen generation apparatus to react with either salinated (sea) or desalinated (fresh) water (H2O) according to Eq. (1), to produce hydrogen (H2(g)) fuel on demand [37]. The sodium hydroxide (NaOH) byproduct of the hydrogen producing chemical reaction in Eq. (1), is also a solid at room temperature in its pure form and has negligible vapor pressure. The NaOH is miscible with water in all proportions, enabling the aqueous NaOH(aq) solution to be readily transferred by pumping into and out of sealed tanks for transport by truck, rail car or pipeline to the remotely located self-contained sodium (Na) metal production plant units for reprocessing by electrolysis according to Eqs. (2) and (3), to recover the Na metal for reuse in generating H2(g) fuel. The NaOH(aq) transportation/storage tanks of the type shown in Figure 2, can be fiberglass or metal with a corrosion resistant internal rubber liner, and must seal hermetically to exclude ambient air that contains carbon dioxide (CO2) which

To obtain a sense for the magnitude of the logistical effort needed to produce and distribute sufficient sodium (Na) metal to fuel all of the motor vehicles in the U.S.A. while recovering the sodium hydroxide (NaOH) byproduct for reprocessing by electrolysis, it is necessary to consider the total number of vehicles in circulation. According to the Bureau of Transportation Statistics at the United States Department of Transportation (DOT), the total number of registered vehicles in the year 2013 in the U.S.A. numbered 255,876,822 [104]. The figure includes passenger cars, motorcycles, light duty vehicles, other 2-axle/4-tire vehicles, trucks with 2-axles/6-tires or more and buses. If it is further assumed that each motor vehicle on average consumes the energy equivalent of 16.2 gallons of 100 octane gasoline (2,2,4- Trimethylpentane) per week, then the corresponding quantity of H2(g) fuel having an equivalent heating value is given as 15.8 kg. The generation of 15.8 kg of H2(g) fuel according to

transport and for broader clean electric power applications.

176 Recent Improvements of Power Plants Management and Technology

slowly degrades the NaOH(aq), albeit not irreversibly.

The technical and economic viability of a novel, scalable, self-contained solar powered electrolytic sodium (Na) metal production plant has been demonstrated for meeting the hydrogen (H2(g)) fuel clean energy needs of the U.S.A. The scalable, self-contained sodium (Na) metal production plant uses a solar tower PV device panel array to collect and convert the sun's vast radiant energy emission produced by hydrogen fusion, into electric power that is used to recover sodium (Na) metal from sodium hydroxide (NaOH) or from a mixture of NaOH and NaCl by electrolysis. The Na metal can subsequently be reused to

generate H2(g) fuel and NaOH byproduct by reacting with either ordinary salinated (sea) or desalinated (fresh) water (H2O). The scalable, self-contained sodium (Na) metal production plant operation is enabled by a specially designed voltage step down PWM DC-DC converter consisting of a multiphase converter topology with up to 32 synchronous voltage step down converter circuits connected in parallel. The PWM DC-DC converter has a fixed output voltage VOUT ≈ 124 V and variable input voltage VIN ¼ VST, that corresponds to the output voltage of the solar tower PV device panel array and can be controlled to maintain the PV device panel array operating near the maximum power point (MPP). Each scalable, self-contained sodium (Na) metal production plant consists of two voltage step down PWM DC-DC converters, wherein each unit supplies 25 NaOH electrolytic cells, electrically connected in series, with a current ICELL ¼ 96,500 A, corresponding to approximately one mole of electrons per second. The scalable electrical design of the solar tower allows the PV device panel array to be upgraded with newer and more efficient PV device panels as they become available as a result of progress in scientific research and development. Once PV device panels with an efficiency ηPV ¼ 90% will become available, the power output of the solar tower PV device panel array can reach PST ¼ 23.9 MW that is sufficient for producing a mass quantity of approximately mNa ¼ 30,000 kg of Na metal per day from the electrolysis of NaOH. It therefore becomes possible to meet the hydrogen (H2(g)) fuel clean energy needs of all the motor vehicles in the U.S.A. by constructing approximately 450,000 scalable, self-contained sodium (Na) metal production plant units of the type described, in the southwestern desert region of the U.S.A. that includes West Texas, New Mexico, Arizona and Southern California. If the land area needed for the scalable, self-contained sodium (Na) metal production plant units becomes scarce, then purpose built ships equipped with the Na metal production plants can be dispatched into the vast ocean expanses near the equator where high solar irradiance occurs, to convert aqueous NaOH(aq) stored onboard into sodium (Na) metal before returning to port.

## Nomenclature



generate H2(g) fuel and NaOH byproduct by reacting with either ordinary salinated (sea) or desalinated (fresh) water (H2O). The scalable, self-contained sodium (Na) metal production plant operation is enabled by a specially designed voltage step down PWM DC-DC converter consisting of a multiphase converter topology with up to 32 synchronous voltage step down converter circuits connected in parallel. The PWM DC-DC converter has a fixed output voltage VOUT ≈ 124 V and variable input voltage VIN ¼ VST, that corresponds to the output voltage of the solar tower PV device panel array and can be controlled to maintain the PV device panel array operating near the maximum power point (MPP). Each scalable, self-contained sodium (Na) metal production plant consists of two voltage step down PWM DC-DC converters, wherein each unit supplies 25 NaOH electrolytic cells, electrically connected in series, with a current ICELL ¼ 96,500 A, corresponding to approximately one mole of electrons per second. The scalable electrical design of the solar tower allows the PV device panel array to be upgraded with newer and more efficient PV device panels as they become available as a result of progress in scientific research and development. Once PV device panels with an efficiency ηPV ¼ 90% will become available, the power output of the solar tower PV device panel array can reach PST ¼ 23.9 MW that is sufficient for producing a mass quantity of approximately mNa ¼ 30,000 kg of Na metal per day from the electrolysis of NaOH. It therefore becomes possible to meet the hydrogen (H2(g)) fuel clean energy needs of all the motor vehicles in the U.S.A. by constructing approximately 450,000 scalable, self-contained sodium (Na) metal production plant units of the type described, in the southwestern desert region of the U.S.A. that includes West Texas, New Mexico, Arizona and Southern California. If the land area needed for the scalable, self-contained sodium (Na) metal production plant units becomes scarce, then purpose built ships equipped with the Na metal production plants can be dispatched into the vast ocean expanses near the equator where high solar irradiance occurs, to convert aqueous NaOH(aq) stored onboard

into sodium (Na) metal before returning to port.

178 Recent Improvements of Power Plants Management and Technology

a Length of the semi-major axis of earth's elliptical orbit around the sun (m)

A<sup>P</sup> Photovoltaic (PV) panel area (m2

APA Photovoltaic (PV) panel array area (m2

Aland Land area (mi<sup>2</sup>

B<sup>l</sup> Solar tower branch length (m) Bsec<sup>l</sup> Solar tower branch section length (m) B<sup>h</sup> Solar tower branch height (m)

)

)

)

Nomenclature

A, B Matrices

AM Air mass at mean sea level

d DC-DC converter duty cycle

AM<sup>a</sup> Air mass at actual atmospheric pressure



N<sup>P</sup> Number of photovoltaic (PV) panels

NB-ST Number of branches on the solar tower

Nday Day number in a year from 1 to 365

N<sup>φ</sup> Number of phases NST Number of solar towers

t Time duration

T<sup>P</sup> Time period for a cycle u, U Vector, vector DC component

NP-B Number of photovoltaic (PV) panels per branch NP-Bsec Number of photovoltaic (PV) panels per branch section NB-L/R Number of branches on the left or right of the solar tower

180 Recent Improvements of Power Plants Management and Technology

P Absolute pressure (Pa)

P<sup>w</sup> Photovoltaic (PV) panel width (m) P<sup>l</sup> Photovoltaic (PV) panel length (m) rsun Distance from the center of the sun to the center of the earth (m) R Resistor value (Ω) RP, R<sup>S</sup> Photovoltaic (PV) device parallel resistance, series resistance (Ω) RTH Thevenin equivalent resistance (Ω) R<sup>C</sup> Electrolytic cell resistance (Ω) S<sup>h</sup> Solar tower structure height (m) S<sup>w</sup> Solar tower structure width (m)

T Absolute temperature, ITS-90 or Celsius temperature (K) or (C)

C)

T<sup>C</sup> Surface temperature of IC package (

T<sup>f</sup> Fusion temperature (K)

VNaOH(aq) Aqueous sodium hydroxide volume (Gal) VST Solar tower output voltage (V) VST-MAX Solar tower maximum output voltage (V) VST-DROP Solar tower central column conductor voltage drop (V) VIN DC-DC converter input voltage (V) VOUT DC-DC converter output voltage (V) VBAT Utility scale battery voltage (V) VCELL Electrolytic cell voltage (V) VOC Photovoltaic (PV) panel open circuit voltage (V) VMPP-C Photovoltaic (PV) single cell maximum power point voltage (V)

PST-L/R Solar tower left or right half output power (W) or (MW) PST Solar tower output power (W) or (MW) PST-50 Solar tower output power (50 towers) (W) or (MW)


## Author details

Alvin G. Stern

Address all correspondence to: inquiries@agstern.com

AG STERN, LLC, Newton, MA, USA

## References


Author details

Address all correspondence to: inquiries@agstern.com

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Irr<sup>0</sup> Solar constant 1367 (W/m<sup>2</sup>

182 Recent Improvements of Power Plants Management and Technology

P<sup>0</sup> Standard atmospheric pressure 101325 (Pa) Psun Power output of the sun 3.8 · 10<sup>26</sup> (W) Pearth Power output of the sun reaching the earth 1.7 · 10<sup>17</sup> (W) Rsun Radius of the sun 6.96 · 10<sup>8</sup> (m) rsun-m Mean distance from center of sun to center of earth 1.496 · 10<sup>11</sup> (m) T<sup>0</sup> Celsius zero point, ITS-90 273.15 (K) TEu Eutectic temperature of NaCl-H2O solution �21.2 (�C) Tsun Surface temperature of the solar black body 5800 (K) Tes Period of earth's rotation around the sun 365.24 (days) Tea Period of earth's rotation on its axis (mean solar day) 86,400 (sec) ε Obliquity or tilt angle of earth's rotation axis 23.44 (�)

δ Solar angle of declination �23.44 ≤ δ ≤ þ23.44 (�)

ωea Angular velocity of earth's rotation on its axis 7.292115 · 10�<sup>5</sup> (rad/sec)

ηPVmax Thermodynamic efficiency limit of PV device panels 93 (%) ϕT-CAN Latitude at Tropic of Cancer þ23.44 (�) ϕT-CAP Latitude at Tropic of Capricorn �23.44 (�) λPM Longitude at Greenwich Prime Meridian 0 (�) π Number, pi 3.14

)

AG STERN, LLC, Newton, MA, USA

Alvin G. Stern

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