Monday, May 12, 2014

Exponential Remediation of Civilization's Footprint

Introduction

"The extinction of the human race will come from its inability to emotionally comprehend the exponential function." - Edward Teller

"The greatest shortcoming of the human race is our inability to understand the exponential function." - Al Bartlett

Below is a first-order (approximate) description of a fast (potentially very fast) doubling time system for remediation of civilization's environmental damage. The fast doubling time drives exponential growth that could, at enormous profit and in under 15 years, drastically reduce civilization's ecological impact while, incidentally, sequestering large amounts of CO2. It is not intended to overcome Dr. Bartlett's accusation that sustainable growth is impossible and cornucopian thinking is "The New Flat Earth Society". It is intended merely to argue that imminent environmental catastrophes may, with appropriate refinements and corrections of the described system, be averted within the time estimated for environmental catastrophes by some of the more pessimistic projections (usually several decades rather than a mere 15 years).

An important principle to keep in mind is that as baseload electricity costs decrease, recycling beats other sources of raw materials. This means that if one is targeting zero environmental footprint, the most compelling path is through lower baseload electric cost simply because recycling is more economical than waste.

Baseload electric generation in the following scenario is the Atmospheric Vortex Engine for six reasons:
  1. The AVE's theory is quite basic and, if located in an environment with low winds, such as the tropical doldrums, quite representative of reality -- hence projections based on it are likely to be sound for the tropical doldrums.
  2. AVE technology is scalable to hundreds of terawatts without significant environmental impact.
  3. The AVE, unique among prospective baseload electric generation systems, is inherently suited to scrubbing the atmosphere of pollutants.
  4. The AVE complements any baseload electric generation systems that produce waste heat (including prospective ones such as cold fusion, thorium breeder, hot fusion, advanced fission, solar collection, etc.) in that only the AVE can reach a virtually limitless heat sink of the very low temperatures required for high Carnot efficiency cogeneration. 
  5. If located in the tropical doldrums and produced by rapid reproduction to macroengineering scales, the projected cost of a kWh of baseload electricity from the AVE, alone, drawing heat only from renewable oceanic heat, is on the order of a few mils (tenths of a cent of a USD) -- 5 mils is a conservatively high figure.
  6. The AVE's primary construction cost is structural materials which, given electric power are economically derived from in situ resources.
Another important principle to keep in mind is that civilization's primary environmental impact is agriculture. The primary objective must be to reduce agriculture's environmental footprint -- where agriculture includes all sources of food to sustain civilized populations including not only land-based agriculture but also exploitation of natural fisheries. Moreover, if you focus on agriculture, you must focus on "primary production" -- the photosynthesis of food calories (proteins, carbohydrates or oils).

Finally, it is important to co-locate human habitats with the primary production systems but this is of no avail if those habitats are not more attractive than current human habitats. People must spontaneously relocate to these systems where their wastes are recycled.

Overview of the Fast Doubling-Time System

The fast doubling time system is a tropical-doldrums, artificial floating atoll, sheltering a low sea state lagoon upon which floats algae photobioreactors of exceedingly high primary production for the food chain. The atoll is produced from in situ resources available in the air and ocean by the application of very low cost baseload electricity generated by an Atmospheric Vortex Engine, the primary structure of which is also produced from the same in situ resources, the electricity for which is from a pre-existing such AVE.

A reference design is based on the 500MW capacity maritime AVE projected by AVE patent-holder, Louis Michaud. The projected per capita electric power use will be 4 times higher than the US at present in order to support total recycling with most energy for industry and transportation derived from electricity. This yields a near-zero environmental-footprint carrying capacity of 100,000 people per atoll.  These 100,000 people enjoy not only beach front lifestyle but also sufficient population and density to substitute for current urban amenities.

The doubling time is potentially on the order of months, with an estimate of 3 months justified below.

A system with a 3 month doubling time could remediate the environmental impact of civilization's 7 billion people in under 15 years.

If you have an emotional reaction against this "outrageous" claim, try to recall the words of Edward Teller and Al Bartlett about human emotions and exponentials (doubling times).

Emotions are no substitute for arithmetic.

The Fast Doubling AVECarbocrete Core

The core of the system is the electric power from the AVE coupled to the Carbocrete production process. Doubling time of the whole system is limited by the doubling time of the AVECarbocrete core because once an AVECarbocrete exists, the rest of the surrounding atoll can be constructed without increasing the doubling time of the system.

Carbocrete(TM) is 75% lighter and more durable than steel reinforced concrete. It is a very good candidate for AVE arenas in general but is particularly well suited for the maritime AVE for a number of reasons, not the least of which is that the electricity from the AVE can be used to manufacture Carbocrete entirely from maritime materials available in the air, seawater and sand from the sea floor (Carbocrete requires 50% less sand than normal concrete and requires no rock aggregates).

The Calera process is a promising* way to create concrete (CaCO3) from electricity, air and sea water. The carbon for the Carbocrete is available from CO2 and can be extracted by a sub-process of the Calera process -- a process in which very high pH media (NaOH) absorbs CO2 either from sea water or from air that is passing over its surface (as would be the case with the AVE). Magnesium is also available from sea water with electric extraction and could form, along with carbon fiber parts, much of the remaining materials of an AVE, such as turbine blades.

The Calera process requires 3.3GJ of electricity to produce one tonne of concrete**. If a system design focused on self-replication (with human labor inputs of course) from in situ materials and AVE electricity, the doubling time of these maritime AVECarbocrete systems could be exceedingly short -- hence the resulting AVE electricity cost brought much lower.

The initial system could be constructed from a floating Calera 500MW input plant designed to be constructed primarily out of Carbocrete from Calera cement reinforced with carbon fiber. To bootstrap the very first AVECarbocrete system, the 500MW input to that Calera plant could be 3 natural gas turbines from GE (GE9281F @ 217MW each and @ $40M each) floating on barges, fueled by LNG ships. These would be rented and the rental costs, paid for out of capital, rapidly amortized by subsequent rapid self-replication of the AVECarbocrete systems.

If we had a rough idea of how many cubic meters of Carbocrete a 500MW maritime arena would require, it would then be straight forward to calculate the amount of time the 500MW maritime AVE would have to run in order to manufacture its own Carbocrete construction materials.

A very rough calculation with some guesses of my own to illustrate how such a calculation would work using Unicalc:

A 200m diameter, 80m high AVE arena might be approximated as a cylinder with two circular "lids" -- all averaging 1ft thickness:

((pi*200m*80m)+(2*(100m)^2*pi))*1ft?m^3
([{pi * (200 * meter)} * {80 * meter}] + [{2 * ([100 * meter]^2)} * pi]) * (1 * foot) ? meter^3
= 34472.067 m^3

So that's the volume of Carbocrete required. Now the time required to produce that Carbocrete given 500MW input to a floating Calera plant given Carbocrete is 2.7tonne/m^3 and it takes 3.3GJ/tonne of Calera concrete (and that approximates the energy to produce the Carbocrete):

(34472.067 m^3/500MW);(2.7tonne/m^3);3.3GJ/tonne?days
([{34472.067 * (meter^3)} / {500 * (mega*watt)}] * [{2.7 * ton_metric} / {meter^3}]) * ([3.3 * {giga*joule}] / ton_metric) ? ...
= 7.1098638 days

This incredibly fast doubling time illustrates that raw materials are the least of our worries. Keep in mind, these constitute the majority of the materials that, otherwise, would need to be transported by ship thousands of miles to the tropical doldrums.

Let's double that amount of Carbocrete to reproduce the floating Calera plant that is paired with each AVE, and double it again to account for inefficiencies and double it again to be on the safe side: we multiply by 2^3 = 8 -- so that's 57 days or about 2 months doubling time for the AVECarbocrete core's construction materials.

A doubling time of 2 months still seems ridiculously fast, but if modern automation and construction techniques, such as concrete printing, are applied, a reasonable argument can be made that the primary structure of this system need not be the limiting factor in reducing the doubling time. Other critical components such as machined parts, electronics, etc. are far smaller and can be transported much more easily from high production volume facilities. Ultimately these, too, would be incorporated into the system but such is not essential.

Lets tack on another 50% for various bottlenecks in the critical path of construction and we have:

Doubling time of 3 months.

Agriculture -- The New Green Revolution

As has been previously discussed, the next green revolution will provide at least a factor of 10 lower area requirement for agriculture, based on floating photobioreactors. These photobioreactors require wave-break shelter from even moderate sea states -- shelter naturally provided in the lagoon of an artificial atoll. In the tropical doldrums the primary production of agricultural feedstocks would be far higher than the annualized 35g/m^2/day measured for more northerly (Mediterranean) climates, but let's stick with 35g/m^2/day to be conservative.

Although the total agricultural system would be aquaponic, yielding high-value produce in symbiosis with high value sea food, let's look only at the sea food protein resulting from a food chain based on a natural species of algae: arthrospira platensis aka "spirulina".

Spirulina consists of better than 50% protein. The trophic loss in fish aquaculture is approximately 2 to 1 -- or about 2 units of feed for 1 unit of fish. Lets further say that an additional factor of 4 is required to provide a wide array of kinds of sea food -- not just algae grazers like tilapia and sockeye salmon -- including predator fish as well as invertebrates such as mollusks, crab, lobsters, shrimp, etc. Each square meter of photobioreactor's primary production of algae is therefore reduced by a factor of 16 (50%*(1/2)*(1/4)) before it is consumed by humans. Each square meter therefore produces a little over 2 grams per day of human consumable food.

How big must the lagoon be to support the atoll's population?

Well, first we need to know how big the atoll's population would be and for that, we need to look at the per capital electricity consumption of the 500MW AVE capacity. Since we are positing electricity-intensive infrastructure for all energy needs, including replacing most raw materials with recycled materials, let's increase the per capita electric consumption by a factor of 4 over the current US per capita electric consumption.

Each 500MW AVE could support a population of 100,000 people.

If that 100,000 people needed to consume 1lb of protein equivalent per day (remember we aren't including fruits and vegetables that would be hydroponically produced in conjunction with the sea food production of the aquaponics system), then the photobioreactor area, hence the lagoon area, would need to be about:

2g/m^2/day;1lb/person/day;100000person?(km)^2
([{(2 * gramm) / (meter^2)} / day]^-1 * [{(1 * poundm) / person} / day]) * (100000 * person) ? (kilo*meter)^2
= 22.6796 (km)^2
or about 23 square kilometers.

Assuming the atoll is perfectly circular, that represents a radius of:

sqrt(23(km)^2/pi)?km
sqrt((23 * [{kilo*meter}^2]) / pi) ? kilo*meter
= 2.7057582 km

So the atoll has a diameter of about 6km.

Closing the Deal With Tropical Beachfront Real Estate

A 6km diameter represents a potential of:

pi*6km?m
pi * (6 * [kilo*meter]) ? meter
= 18849.556 m

or about 20,000 meters of beach front real estate.

Recalling that each atoll's population is about 100,000 people, that yields population density of about 5 per meter. This indicates a high-rise condominium beach front, as with Miami Beach. People have shown a clear preference for these kinds of urban beachfront environments.

Let's therefore stick with that figure and calculate how many stories of family-of-four condominiums averaging 4000ft^2 each with 40ft of beachfront would be needed to accommodate this 5 people per beachfront meter population density.  First, lets calculate how many people must be stacked on a 40ft beachfront to achieve 5people per meter:

5people/m;40ft?people
([5 * people] / meter) * (40 * foot) ? people
= 60.96 people

Now let's calculate how many stories this requires at one home per story:

60.96 people/(4people/story)?story
(60.96 * people) / ([4 * people] / story) ? story
= 15.24 story

Or about 16 stories in our beachfront condo.

Comparable condominium complexes in Miami Beach go for on the order of $3 million for each condo.

Obviously, this is price, not cost of these beachfront condominiums -- and it is only the price for early units. However, if it were possible to sell these condos for $3 million each, the real estate value, alone, of the atoll would dwarf its food production value, let alone the electric generation.

100000people;3e6usd/home;4people/home?usd
([100000 * people] * [{3E6 * usd} / home]) * ([4 * people] / home)^-1 ? usd
= 7.5E10 usd

or about $75 billion.

The food at approximately $300/person/month with a 12% zero amortization schedule has a present value of approximately:

100000people*300usd/people/month;100*month?usd
([{(100000 * people) * (300 * usd)} / people] / month) * (100 * month) ? usd
= 3E9 usd

or $3 billion.

The electricity at approximately 5mil/kWh with a 12% zero amortization schedule has a present value of approximately:

0.005usd/kWh;500MW;100*month?usd
([{0.005 * usd} / {kilo*Wh}] * [500 * {mega*watt}]) * (100 * month) ? usd
= 1.825E8 usd

In other words, the value of the early atolls is dominated by their real estate value, with food value coming in second and electricity value negligible.

Now lets figure how long it would take for an AVECarbocrete core to produce the Carbocrete for these beachfront condos.

Let's say we want the 16 story condos to rest on a flotation platform that extends the beach 200 feet to the water and another 200 feet beyond that for the breakwater. We'll let the lagoon-side terminate at only 100 feet. With the condos being 100ft in radial length, we have a total of 200ft+200ft+100ft+100ft of flotation platform in radial dimension. Since the condo's weight determines the amount of water displaced to float it, we'll estimate that first:

((40ft+100ft)*12ft+100ft*100ft)*1ft?m^3
([{(40 * foot) + (100 * foot)} * {12 * foot}] + [{100 * foot} * {100 * foot}]) * (1 * foot) ? meter^3
= 330.74077 m^3

or about 400 cubic meters of Carbocrete per condominium with stories each 12 feet high and 1ft thick walls and ceilings/floors that are shared with adjacent condos.

The volume of Carbocrete per length of beachfront per condo is then:

400m^3/40ft?m^3/ft
(1000 * [meter^3]) / (100 * foot) ? (meter^3) / foot
= 10 m^3/ft

And for 16 stories it is  obviously 160 m^3/(ft beachfront).

Given a Carbocrete density of 2.7tonne/m^3 we have:

160m^3/(ft beachfront);2.7tonne/m^3?tonne/(m beachfront)
([160 * {meter^3}] / [foot * beachfront]) * ([2.7 * ton_metric] / [meter^3]) ? ton_metric / (meter * beachfront)
= 1417.3228 tonne/(m beachfront)

That means the flotation platform has to displace approximately 1500m^3 of ocean water for each meter of beachfront.

Keeping in mind the 200ft+200ft+100ft+100ft of flotation platform in radial dimension, to displace that 1500m^3 per meter of ocean water we need:

(200ft+200ft+100ft+100ft);1500m^3/m?m
([{(200 * foot) + (200 * foot)} + {100 * foot}] + [100 * foot])^-1 * ([1500 * {meter^3}] / meter) ? meter
= 8.2020997 m

or about 10 meters of air space below water for the entire radial length of the platform.

That means the flotation hull has to have a Carbocrete perimeter in the atoll's radial dimension of about:

(200ft+200ft+100ft+100ft+10m)*2?m
([{([200 * foot] + [200 * foot]) + (100 * foot)} + {100 * foot}] + [10 * meter]) * 2 ? meter
= 385.76 m

or about 400m (0.4 a kilometer).

Assuming this flotation vessel averages about 1ft thick the mass per beachfront length of the flotation hull is about:

1ft*400m*2.7tonne/m^3?tonne/m
([{1 * foot} * {400 * meter}] * [2.7 * ton_metric]) / (meter^3) ? ton_metric / meter
= 329.184 tonne/m

Adding that to the condominium's mass we have:

1417.3228 tonne/m+329.184 tonne/m?tonne/m
([1417.3228 * ton_metric] / meter) + ([329.184 * ton_metric] / meter) ? ton_metric / meter
= 1746.5068 tonne/m

or about 2000tonne/m of Carbocrete per meter of beachfront real estate.

How rapidly, then, can our 500MW AVECarbocrete core produce this?

3.3GJ/tonne;500MW;2000tonne/m?m/day
([{3.3 * (giga*joule)} / ton_metric]^-1 * [500 * {mega*watt}]) * ([2000 * ton_metric] / meter)^-1 ? meter / day
= 6.5454545 m/day

or about 6m of beachfront real estate per day per AVECarbocrete core.

How long would it take to complete the atoll?
20000(m beachfront)/(6m beachfront/day)?years
(20000 * [meter * beachfront]) / ([{6 * meter} * beachfront] / day) ? year
= 9.1324201 years

or about a 10 years to complete an atoll once its AVECarbocrete core is producing its Carbocrete.

(At this point please note that it is likely feasible*** to build more than one 500MW AVECarbocrete core by diverting early Carbocrete, that would ordinarily go into the atoll, toward constructing at least one more AVECarbocrete core.  This would bring the atoll completion time to 5 years instead of 10.)

Obviously there is a limited market for $3million condos, and 10 years is a long construction time, but, with automation brought on by industrial learning curve, the cost of beachfront condo real estate approaches the limit imposed by the cost of producing the materials which, by that time, is the levelized marginal cost of another AVECarbocrete core. 

A condominium has a material requirement (including flotation) of:

2000tonne/m;40ft/40condo?tonne/condo
([2000 * ton_metric] / meter) * ([40 * foot] / [40 * condo]) ? ton_metric / condo
= 609.6 tonne/condo

At 5mil/kWh this costs:

3.3GJ/tonne; 609.6tonne/condo;0.005usd/kWh?usd/condo
([{3.3 * (giga*joule)} / ton_metric] * [{609.6 * ton_metric} / condo]) * ([0.005 * usd] / [kilo*Wh]) ? usd / condo
= 2794 usd/condo

or about $3000 per family of four.



So How Do You Get To World Salvation In 15 Years???

Here's how:

Each AVECarbocrete core grows into an atoll supporting 100,000 people.  The time it takes to exponentially reproduce the number of AVECarbocrete cores for 7 billion people is:

100000people*2^doublings = 7e9people
doublings  = log2(7e9people/100000people)
doublings = log(7e9people/100000people)/log(2)
= 16.095067 doublings

And, as we recall, the doubling time for the AVECarbocrete core was 3months, which means:

16.095067 doublings;3month/doubling?years
(16.095067 * doublings) * ([3 * month] / doublings) ? year
= 4.0237668 years

Or under 5 years until the last AVECarbocrete core produced starts on constructing its atoll which, as we saw previously, takes 10 years to complete.

5 years plus 10 years is, through the miracle of addition:

15 years.

*The Calera process has to dispose of chlorine evolved during electrolysis of sea salt.  This is a serious environmental issue that will be addressed in a future article.  Considerations are  1) that the estimated US capacity, alone, for CO2 geologic sequestration is greater than that which would be required to sequester all of the chlorine resulting from the global scale of this project -- a project which not only sequesters virtually the same amount of CO2, but terminates further CO2 emissions, while restoring natural carbon sinks such as rainforests, 2) CPVC/carbon fiber/CaCO3/MgOH2 composites have shown properties superior to fiberglass, and the majority of the mass of such composites is chlorine -- a fact that could radically change the in situ structural materials approach so as to de-emphasize the Calera process and emphasize scrubbing CO2 directly from the air by recycled NaOH rather than liberating Cl2 from CaCl2.  This would radically reduce the amount of chlorine produced while using what little is produced as structural mass, 3) Chlorine in the troposphere -- usually derived from photochemical separation of oceanic NaCl -- is a major sink for methane and methane is 25 times more potent as a greenhouse gas than is CO2.

**See footnote at Greenhouses Are Not the Next Green Revolution.  The cost of deep sea dredging for sand is assumed to be similar to the energy cost of synthesizing CaCO3.

***The feasibility of additional AVECarbocrete cores per atoll is limited by the thermal flow from the surrounding ocean water pulled in by downward convection of cooled water expelled from the AVE.  It is reasonable to posit at least two 500MW AVECarbocrete cores would have the requisite heat flow because the vast majority of the incident solar energy is absorbed by the floating photobioreactors, which are only about 5% efficient in turning solar energy to food energy.  That means 95% of the insolation would be available as heat flow colocated with the AVECarbocrete cores.  That amount of solar thermal power is:

23((km)^2);300W/m^2?MW
(23 * [{kilo*meter}^2]) * ([300 * watt] / [meter^2]) ? mega*watt
= 6900 MW

Or nearly 7GW, whereas the output of the AVE is 0.5GW -- and that the Carnot efficiency of the 500MW AVE is estimated to be 12% which means even without resorting to inward flow of ocean water outside of the atoll, the electric power available is:

12%*7GW?MW
(12 * percent) * (7 * [giga*watt]) ? mega*watt
= 840 MW

So we are very close to the 1000MW for two 500MW AVECarbocrete cores per atoll.