Direct solar absorption and storage in high-purity glass melts

Terrestial solar spectrum superposed on the absorption spectrum of low-loss glass fibers.

At 1570 °C (a candidate "empty" temperature for a heat-storage glass melt,) the viscosity of soda-lime glass is only about half that of room-temperature honey; at 1800 °C (a candidate "full" temperature for a heat-storage glass melt,) its viscosity has fallen nearly to that of room-temperature motor oil. In a large storage pond of molten glass, convection will easily be turbulent; unfortunately, convection cannot be effectively driven by heating from the top.

Using the relations for the effective conductivity of soda-lime glass melts in Pilon et al. (which likely give values too low for high-purity melts because of the importance of the radiative contribution) the effective thermal conductivity of molten glass at 1570 °C is 95 W/m-°K (nearly twice that of room-temperature steel,) and it increases with temperature: at 1800 °C the effective thermal conductivity is 160 W/m-°K (comparable to room-temperature magnesium.) However, with a thermal diffusivity around 0.00004 m²/sec, a six-hour pulse of solar heating would only travel about 1 meter into the glass melt by conduction/radiation.

The only option for charging the thermal storage is a glass melt that is so transparent to solar radiation that much of the energy is absorbed in the lower half of the pond's depth. If half of the solar energy is absorbed in traveling to a 20 m depth, that is a loss rate of 3 dB/0.02 km = 150 dB/km. Data for very pure glass fibers (see diagram above) show that such transparency can be far exceeded for wavelengths shorter than 2 microns (which account for more than 90% of the AM 1.5 Direct solar spectrum, see diagram below.) It remains to be seen if such high-purity, transparent glass melts can be economical for direct solar absorption and storage.

Solar spectral distribution for AM 1.5 Direct (green line). Image quoted from http://pveducation.org .

Truth in labeling: Solar multiple vs. capacity factor

It is natural to discuss a solar plant in terms of its rated output (i.e., peak electrical power,) but this often gives a false impression of the plant's economic value. For example, a utility might expect a new coal-fired plant to annually generate electric energy equivalent to its producing at full power 20 hours per day (capacity factor = 20/24 = 83%.) A solar plant in a desert climate will, over the course of a year, only produce energy equivalent to its producing at full power about 6 hours per day (capacity factor = 6/24 = 25%)

With energy storage a solar plant can operate with a higher capacity factor (saving money on some aspects of the plant) and making its rated output more directly comparable with a conventional plant. In a simplistic calculation, a 6 hr/day solar plant can become an 18 hr/day solar plant if we divert 2/3 of its output to storage. That is, by later withdrawing the stored energy we can have two more 6 hr periods of full power operation, giving a total of 18 hr/day. Our hypothetical solar plant would be said to have a capacity factor of 75%, 12 hours of storage, and a solar multiple of 3 (i.e., the ratio of its rated power without storage to its rated power with storage.)

In the real world, the above calculation would require a computer simulation, but we can borrow some real world numbers from Gemasolar, a thermal solar plant in Spain, which has 15 hours of storage and a 75% capacity factor. For obvious reasons, solar plants with a significant amount of storage prefer to advertise their annual electricity production rather than their rated power. From Gemasolar's stated annual production of 110,000 MWh/yr, and stated capacity factor of 75%, we can calculate that its rated power is:

110,000 MWhr/yr * (1/0.75) * (1/8760) yr/hr = 16.7 MW

Gemasolar has 304,750 m² of mirrors, so its rated power comes to 55 w_e/m² of mirror area.

Gemasolar and the Ivanpah thermal solar plant differ in detail (and Ivapah has the better solar climate,) but it is relevant to note that Ivanpah has three units rated 123 MW + 133 MW + 133 MW = 389 MW total, no storage, and 1,079,232 MWh/yr annual output—a capacity factor of 32%. In total, Ivanpah has 2,600,000 m² of mirror area, so its rated output of 389 MW comes to 150 W_e/m² of mirror area. That suggests that Gemasolar's solar multiple is about 150/55 = 2.7

The conclusion here is that solar plants without storage should be de-rated by approximately a factor of three before being directly compared with conventional fossil-fueled plants on the basis of rated power.

Solar re-powering Georgia's Plant Bowen in sunny Spain

Solar re-powering Georgia Power's Plant Bowen to 3.2 GWe (75% capacity factor) in Andalucia's climate would require a storage/boiler compartment about 60% as tall as one of its cooling towers—and 130% its diameter. The central optics would be about 110% the height of its smokestacks.

In Andalucia, Spain, the location of the Gemasolar plant, only 15 hours of thermal storage (plus whatever solar multiple, or thermal down-rating, Gemasolar is using) is needed to achieve an annual capacity factor of 75% in a solar thermal generating plant.

Plant Bowen (3.2 GWe and 82% capacity factor) in Euharlee, GA, USA, is the largest coal-fired plant in the United States, and the country's largest point source of CO₂ pollution. This post contemplates what Plant Bowen would look like if re-powered to run on the sun in Andalucia's sunny climate. Of course, it would be more interesting to see what Plant Bowen would look like solar-powered up to its own 82% capacity factor in northwest Georgia's own, somewhat less sunny, climate, but that would involve a detailed simulation. By figuratively moving Bowen to Spain, and adopting Gemasolar's 75% capacity factor, we can just steal data.

Quoting an earlier post:

Here are some statistics for Gemasolar gleaned from the National Renewable Energy Laboratory's site. 

Projected annual output: 110,000 MWhr/yr = 12.6 MWe  annual average.
Rated output  (calculated from the claimed 75% capacity factor): 16.7 MWe rated.
Output per mirror area (304,750 m2) :
       41 We/m2 annual average,
       55 We/m2 rated.
Land yield (1,950,000 m2; mirror/land ratio = 0.156):
        6.4 We/m2-land annual average,
        8.6 We/m2-land rated 

The 15 hours of storage based on 40% thermal efficiency is:
15 hrs * 3600 s/hr * 8.6 We/m2-land * 1/0.40 = 1.2 E6 Jthermal/m2-land 

A plant with telescopic heliostats and glass-melt storage would have some advantages over Gemasolar. Telescopic heliostats can be packed much more closely, increasing the mirror/land ratio to around 0.70, thus increasing land yield about 4.5 times that of Gemasolar. Also, because the glass melt transfers its heat to hotter steam (608°C vs. 565°C) the steam cycle efficiency can be greater, about 46% thermal efficiency as compared with 40%, a factor of 1.15 . 

So here are the Gemasolar statistics if it were rebuilt on the same plot of land with telescopic heliostats and glass-melt storage: 

Projected annual output: 110,000 MWhr/yr * 4.5 * 1.15 = 65 MWe  annual average.
Rated output  (calculated from the claimed 75% capacity factor): 87 MWe rated.

Output per mirror area (304,750 m2 * 4.5 = 1,370,000 m2) :
       41 We/m2 * 1.15 = 47 We/m2 annual average,
       55 We/m2 * 1.15 = 63 We/m2 rated. 

Land yield (1,950,000 m2; mirror/land ratio = 0.156):
        6.4 We/m2 * 4.5 * 1.15 = 33 We/m2-land annual average,
        8.6 We/m2 * 4.5 * 1.15 = 45 We/m2-land rated. 

The 15 hours of storage for the rebuilt plant becomes:
15 hrs * 3600 s/hr * 45 We/m2-land * 1/0.46 = 5.3 E6 Jthermal/m2-land 

Plant Bowen is a plant belonging to Georgia Power in Euharlee, Georgia. It is the largest coal-fired plant in the USA. It has four 800 MWe units, giving an aggregate rating of about 3.2 GWe. A telescopic heliostat / glass-melt power plant in Andalucia with 15 hours of thermal storage, having the same rated output of Plant Bowen, would occupy: 

3.2 GWe-rated / 45 We/m2-land rated = 71 E6 m2,
which is equivalent to a circle 4.8 km in radius.

The height of the central optics will be about 1/14 the field radius, or 340 m, or about 11% taller than Plant Bowen's 305 m smokestacks.

The heat flow to drive rated output is

3.2 GWe-rated * 1/0.46 = 7.0 GWthermal-rated

It remains to calculate storage and boiler dimensions. A boiler's water tube walls usually receive a thermal flux of around 250 kw/m2. Taking that value as a given, the total area of the water tube wall, S_B, will be

S_B = 7.0 GWthermal-rated / 250 kw/m2 = 28,000 m2.

The volumetric storage density in molten glass is

ΔT * 2300 kg/ m3 * 1231 J/kgK = ΔT * 2.8 E6 J/m3-K

Thermal storage needed for 15 hours of rated output is

7.0 GWthermal-rated * 15 hr * 3600 s/hr = 3.8 E14 J

So thermal storage volume V is

V = 1.35 E8/ΔT  m3

For a hemisphere

V = 2/3 π R³

so,

R =  (3/2π V)^0.33 m

R = (3/2π * 1.35 E8/ΔT)^0.33 m

R = (6.4 E7/ΔT)^0.33 m

The height, H, of the water tube wall can be calculated from

2πR * H = S_B


H = S_B * 1/2πR = 28,000 m2 * 0.159 / R = 4,460/R m

Exploring these relations in a Numbers spreadsheet shows that T_empty = 1570 °C (1840 °K) gives a consistent solution with R = 63 m, H = 71, and the flux on the water wall tubes = 250 kw/m2. The glass temperature range from empty to full is just 230 °C. T_empty is approximately the temperature of a glass-making furnace, so it is fair to say that the thermal storage is accomplished by overheating a soda-lime glass-making furnace by about 230 °C.

By comparison, Plant Bowen has four cooling towers that are 47 m in radius and 116 m tall—so the volume of the storage/furnace compartment of a solar-fired Plant Bowen would be comparable in volume to one of its current cooling towers.

Maximum temperatures in glass-melt solar storage

Temperature field in a glass-making furnace in °K. (1820 °K = 1550 °C.)  Image quoted from L. Pilon et al.

As calculated in a previous post, the minimum (i.e., empty) temperature of a glass-melt storage is about 1340 °C (1610 °K) because of the need to supply high radiant flux (about 250 suns) to the steam tubes in order to achieve rated output. The maximum temperature depends on the high temperature materials available for the tank, the furnace roof, and the shading elements that modulate the radiant flux on the stem tubes.

Properties of ultra-high-temperature ceramic insulation. Image quoted from Rath USA.

Being optimistic, I'll say 1800 °C is an acceptable maximum glass-melt temperature—that's 250 °C hotter than a glass making furnace.

The storage temperature range is 1800 °C - 1340 °C = 460 °K, and the mean temperature is 1470 °C.  From Pilon et al., the specific heat, c, of molten glass between 1000 °C and 2000 °C is about 1231 J/kgK, so a 460 °K storage range stores 460 * 1231 = 566,000 J/kg. The density of molten glass in this temperature range is about 2300 kg/m3, so the volumetric energy storage is 1.3 E9 Jthermal/m3.

From the previous post, we need 5.3 E6 Jthermal/m2-land to store 15 hours of heat for rated output, so, spread over the land area of the heliostat field, the storage glass would form a layer 5.3 E6 / 1.3 E9 = 4 mm thick. That is less glass than would be needed for the mirrors!

Again from the previous post, the total land area for 3.2 GWe Gemasolar plant is 71 E6 m2, so the total storage volume is 71 E 6 * .004 = 284,000 m3, equivalent to a hemisphere with radius, r:

pi * 2/3 * r^3 = 284,000

r = 51 m, a pool with a perimeter of 2*pi*r = 320 m

At a thermal efficiency of 0.46, the rated thermal power is 3.2 E9 / 0.46 = 7.0 E9 Wthermal.

At 250 suns, the furnace wall area is 7.0 E9 / 250,000 = 28,000 m2.

With furnace wall area arrayed around the 320 m perimeter of the pool, the furnace wall is 28,000 / 320 = 87 m high, that is close to the height of the actual furnace walls at Plant Bowen, which appear to be about 75 m tall in photos. But I think 87 m is too tall in relation to the pool diameter (102 m) to comport with the earlier assumption of a 0.7 view factor, so this calculation is going to need more iterations.

Capacity factor and hours of solar storage

The Gemasolar plant in Andalucia, Spain operates at an annual capacity factor of 75% using just 15 hours of thermal storage.

The 17 MWe Gemasolar power tower in Fuentes de Andalucía, Spain is designed to operate at an annual capacity factor of 75%, and has run continuously for as long as 36 consecutive days. This remarkable accomplishment is achieved with just 15 hours of thermal storage. Clearly 15 hours of thermal storage is about the right amount for a solar plant!

Here are some statistics for Gemasolar gleaned from the National Renewable Energy Laboratory's site.

Projected annual output: 110,000 MWhr/yr = 12.6 MWe  annual average.
Rated output  (calculated from the 75% capacity factor): 16.7 MWe rated. 

Output per mirror area (304,750 m2) :
       41 We/m2 annual average,
       55 We/m2 rated.  

Land yield (1,950,000 m2; mirror/land ratio = 0.156):
        6.4 We/m2-land annual average,
        8.6 We/m2-land rated

The 15 hours of storage based on 40% thermal efficiency is:

15 hrs * 3600 s/hr * 8.6 We/m2-land * 1/0.40 = 1.2 E6 Jthermal/m2-land

A plant with telescopic heliostats and glass-melt storage would have some advantages over Gemasolar. Telescopic heliostats can be packed much more closely, increasing the mirror/land ratio to around 0.70, increasing land yield about 4.5 times that of Gemasolar. Also, because the glass melt transfers its heat to hotter steam (608°C vs. 565°C) the steam cycle efficiency can be greater, about 46% thermal efficiency as compared with 40%, a factor of 1.15 .

Now, the same Gemasolar statistics if rebuilt on the same land with telescopic heliostats and glass-melt storage:

Projected annual output: 110,000 MWhr/yr  * 4.5 * 1.15 = 65 MWe  annual average.
Rated output  (calculated from the 75% capacity factor): 87 MWe rated. 

Output per mirror area (304,750 m2 * 4.5 = 1,370,000 m2) :
       41 We/m2 * 1.15 = 47 We/m2 annual average,
       55 We/m2 * 1.15 = 63 We/m2 rated. 

Land yield (1,950,000 m2; mirror/land ratio = 0.156):
        6.4 We/m2 * 4.5 * 1.15 = 33 We/m2-land annual average,
        8.6 We/m2 * 4.5 * 1.15 = 45 We/m2-land rated.

The 15 hours of storage for the rebuilt plant becomes:

15 hrs * 3600 s/hr * 45 We/m2-land * 1/0.46 = 5.3 E6 Jthermal/m2-land

Plant Bowen in Euharlee, Georgia, is the largest coal-fired plant in the USA. It has four 800 MWe units, giving an aggregate rating of about 3.2 GWe. A telescopic heliostat / glass-melt power plant in Andalucia with 15 hours of thermal storage, having the same rated output of Plant Bowen, would occupy:

3.2 GWe-rated / 45 We/m2-land rated = 71 E6 m2,

or a circle 4.8 km in radius. The height of the central optics will be about 1/14 the field radius, or 340 m. This is about 11% higher than Plant Bowen's two 305 m smokestacks.

Plant Bowen, 3.2 GWe,