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30 Terawatts, 3250 Years, 13.7 Degrees Surface Temperature

Jim Baird's picture
Owner Thermodynamic Geoengineering

inventor,Method and apparatus for load balancing trapped solar energy Ocean thermal energy conversion counter-current heat transfer system Global warming mitigation method Nuclear Assisted...

  • Member since 2018
  • 368 items added with 442,800 views
  • Mar 17, 2018

The average surface temperature of the Earth is currently 15 C. 

Since the temperature of the ocean at a depth of 1000 is universally 4 C, which is about the average of temperature of the ocean at all levels, and a surface temperature of at least 24 C is needed to derive a result from OTEC, the areas in orange to red (the OTEC zone) below are the only ones where the heat of global warming can be regulated.

The graphic is sectioned into squares of 572 kilometers a side and at a power density estimated at (1kW per km2) the OTEC zone has  an initial global production potential of about 30 terawatts (TW). Roughly twice the amount of energy we are currently deriving from fossil fuels. It should be noted that the graphic is a representation of annual surface temperatures, so since seasons change, and as shown below the red blob representing a surface temperature of 28 C or above can shift with the winds and/or the seasons, so in a year like 2017 the Atlantic can have a red blob of its own that can produce as severe a hurricane season as the one just witnessed.

Another way of looking at the red blob is, a heat black hole. It is a consequence of trade winds driving heat to a depth of 250 meters where during the period of the warming hiatus, 1998 to 2013, a great deal of ocean heat was sequestered. The 64 trillion-dollar question then should be, why aren’t we capitalizing on a massive energy and environmental opportunity that sequesters ocean heat?

In part, it is because back in 1998 a team lead by Physicist Martin Hoffert of New York University concluded that the Earth’s atmospheric CO2 content cannot be stabilized without a tenfold increase in carbon-emission-free power generation over the next 50 years and since only 1.5 TW of carbon-emission-free power was being produced at the time, they concluded that non-fossil-fuel generation would have to account for at least 50 percent of the 30 TW required by 2050.

At the time, and to as late as 2007, the estimated annual available output for OTEC power was only 3 to 5 TW, and so since it takes plants of at least 100 MW capacity, costing about $USD 600 million, for OTEC to be economically viable, compared to 3 MW wind turbines costing $USD 5 million or 400-Watt Solar Panels at $1,200  a piece, at a formative stage of the carbon divestment and renewable investment era OTEC was handicapped by a lowballed potential and a false economy bias associated with small components.

Assuming intermittence of about 70% for wind and solar, at ((5*(100/3))/30) or $555 million per 100 MW then wind is only slightly less costly than OTEC, which is a bargain at (100,000,000 watts/600,000,000 dollars) or $.16 per watt, compared to Solar Panels at 3$ a watt (1200/400). But the real elephant in the room was revealed by the late David MacKay, former Chief Scientific Adviser to the UK Department of Energy and Climate Change in his book Sustainable Energy – Without the Hot Air and in his TED talk A reality check on renewables, where he pointed out, a country like Great Britain, where the energy consumption rate is 125 kWh per day, would have to cover half its land mass by wind farms or between 20 to 25 percent of its area with solar panels to service its citizens.

MacKay used light bulbs to illustrate the UK’s energy consumption and noted that it was as if every person in the country had 125 light bulbs burning continuously 24/7/365. And this analogy has been borrowed for this post. In 2013, OTEC’s maximum annual net power production was reassessed at 30 TW with a rider that persistent cooling of the tropical oceanic mixed-layer would limit net production to about 7 TW.

But by the time of the reassessment, many pioneering OTEC researchers had moved on to other fields, others had retired or had passed away with their vision unfulfilled and the 7 TW limit pertains only to conventional OTEC. As the years after 2013 have demonstrated, the blob isn’t a very efficient heat black hole. In El Niño years the blob spreads across the Pacific as the thermocline rises in the east and descends in the west, as heat rises in the east and sloshes west, with some of the heat being lost from the ocean’s surface to the atmosphere.

To effectively sequester surface heat, it must be moved below the thermocline and retained there for as long possible and how this can be accomplished is the subject of this post. Although a 30 TW potential is ten times what was predicted in the 2007, the following figure from the 2013 study An Assessment of Global Ocean Thermal Energy Conversion Resources With a High-Resolution Ocean General Circulation Model demonstrates this potential is rapidly degraded by upwelling to about 14 TW within about 100 years or  about 2 life cycles of the equipment.

As the following gif shows this degradation is the consequence of an upwelling rate of 20 meters/year and the movement of surface heat to a depth of about 100 meters (the study models heat movement to a depth of only 55 meters).

The legend for the icons shown in the gif above as well as for the gif for Heat Pipe OTEC below are:

The OTEC gif opens on the OTEC producing area and zooms into the red blob and then tilts 90 degrees to show evaporators being serviced by burning light bulbs, heat engines and condensers at a level of 55 meters and cold-water pipes servicing the condensers. The interval between the frames of the gif is 1 second, which is 5 times faster than the interval of the gif for Heat Pipe OTEC, because, as Fig. 3 above shows the upwelling rate for conventional OTEC at a power level of 30 TW is 20 meters/year, compared to a diffusion rate of only 4 meters/year for Heat Pipe OTEC regardless of the power production.

The OTEC gif shows the surface bulbs being burned out at a rate of one every frame because heat moves from the surface to 55 meters and back again within 3 years and upwelling moves the light bulbs away from the evaporators at the same rate. The 2013 study of Rajagopalan and Nihous, per the following graphic, demonstrates that within 1000 years, conventional OTEC cools the surface near the equator by about 4 degrees while the higher latitudes are warmed by the same amount, which is problematic in terms of sea level rise and aquaculture that depends on upwelling adjacent America’s coastlines.

The takeaway from the gif, therefore, should be upwelling doesn’t sequester heat. It only moves it, rapidly, to higher latitudes and the further the heat, in the form of burning light bulbs, is removed from the evaporators the less effective the evaporators are at transferring the heat into the heat engines where the transformation from heat to work has to take place.

The following Heat Pipe OTEC gif shows how the surface heat (light bulbs) are moved to 1000 meters at a rate as high as 75 meters/sec as a consequence of the pressure difference between the evaporating and the condensing ends of the heat pipe. From 1000 meter, at a diffusion rate of 4 meters/year, it takes, 250 years, 10 25-year increments, for the light bulbs to get back to the surface so such systems are an effective way of sequestering heat. They are true, heat, black holes.

Furthermore, for at least the next 500 years, these black holes will draw heat from the entire surface to replenish the heat that is drawn into the evaporators. One thousand years from now, only 0.18 degrees worth of heat will, therefore, have been relocated to higher latitudes, (4C*(4 heat cycles /90 heat cycles)). At which time it becomes advantageous to slowly release heat from the oceans to the atmosphere because the atmosphere will be starting to cool in the absence of the influence of radiative forcing.

It should be noted, with heat pipe OTEC heat is converted to work at an efficiency of 7.6% (see also here).  Per the following gif, therefore, only 1 of the original 15 light bulbs adjacent each evaporator is extinguished each 250-year cycle while the other 14 are moved incrementally back to the surface. Between the evaporator and the condenser, the heat is essentially in a state of thermodynamic limbo once it has passed through the heat engine until it again becomes available to the evaporator back at the surface.

As will be discussed below it will probably take about (((30/18)*2)*60) 200 years to build out the entire fleet of OTEC platforms capable of producing 30TW of power. By that time there will be at least as much added heat to the systems as will have been generated to this point, so by the time today’s heat resurfaces there will be another light bulb’s worth of heat that will have to be added to the topmost level of the following gif.

This additional heat is represented by the orange light bulbs. Burnt out light bulbs are waste heat, so long as they remain within the OTEC producing area they too can be reconverted, at least in part, to work once they are on the surface. They only become anergy outside the OTEC producing area at which point they either melt ice or are radiated to space, which won’t happen for at least 1000 years, until we have stopped adding to the atmospheric greenhouse gas load and have started drawing down that load.

The above gif covers a period of only 500 years during which only 2 light bulbs worth of heat will have been burned out and this  heat will all remain within the red blob. In the alternative, with the upwelling of conventional OTEC, all 15 of light bulbs are burnt after 166 years and have migrated well beyond the blob. With Heat Pipe OTEC, after 1000 years the original heat will have been recycled only 4 times between the surface and 1000 meters as opposed to 90 times between the surface and 55 meters with conventional OTEC. And this has ramification for both the amount of energy that can be extracted from the oceans and the thermal efficiency of the systems.

In the article, “The Long Slow Rise of Solar and Wind” Vaclav Smil points out that every major energy source since coal, then oil, natural gas and now renewable energy that has ever dominated the world supply has taken 50 to 60 years to rise to the top spot. Since 30TW is 1.66 times more energy than is currently derived from all of the world’s energy sources, and no source has ever dominated more than a 50% share of this market, and never for more than 75 years then it will probably take close to 200 years to truly start getting a handle of climate change. In the interim, and out to 3,250 ((100/7.6) * 250) years we can obtain 30 TWs of energy with heat pipe OTEC.

Rajagopalan suggests conventional OTEC cannot sustain a power level of 30TW for more than a few decades without degrading the OTEC resource but in the same breath the paper says 7 TW is sustainable in perpetuity. The difference is the upwelling rate of 20 meters/year as opposed to the 4 meters/year with the heat pipe. Each power cycle leaks heat out of the OTEC producing area, so to get the maximum conversion of warming heat to work the least number of the cycles are required, which would be 13. At which time, an extrapolated version of the heat pipe OTEC gif would reveal 3 light bulbs worth of heat still capable of producing power.

Rajagopalan’s assessment is OTEC sources and sinks relax to pre-OTEC condition at a similar rate to which they are built up. At any time, therefore, before or after full OTEC capacity is attained, production can be throttled back should unanticipated problems arise but it is highly unlikely that you would ever want to shut off such an energy source. Particularly when it is cooling the surface and its curtailment would cause a rapid release of heat from the ocean into the atmosphere. It has to be noted here, an average temperature movement from the surface to a depth of 500 meters results in a significant lowering of the thermal expansion of the oceans and thus sea level rise, which too is a benefit that can be maintained for up to 3,250 years.

OTEC, therefore, represents the only approach, aside from atmospheric- or surface-ocean-based solar radiation management that has the potential to help directly mitigate anthropogenic warming of the surface ocean/atmosphere. One of the main problems confronting systems that experience harsh environments like the deep ocean is tropical cyclones. These don’t form however within 5 degrees latitude of the equator because of the Coriolis effect. In turn, this is the best place for OTEC systems to operate.

The petroleum industry has over 30 years’ experience in harsh environments like the deep ocean and now produce oil and gas from depths of about 2900 meters or about 3 times the depth of a deep-water condenser. The risers used to move gas and fluids between the deep and the surface are similar to the piping used in OTEC, which would use tensioning cables to secure the heat pipe and the deep-water condenser to the surface. The same way oil platforms are secured to the sea floor. Bottom line, what more do you want, beyond long-lived, abundant, power, that will cool the planet?

Should the reader have difficulty deciphering the information in the gifs, larger formats are available here and here.

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Jim Baird on Jul 28, 2018

Revised from original

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