Wednesday, January 13, 2021

Increasing ERoEI*

I have been able to imagine increasing an ERoEI* that is less than 1.0, indicating non-renewable, to a value greater than 1.0, indicating renewable, in only two ways: (1) increasing the efficiency of the collector by virtue of a technological breakthrough, (2) reduce the energy invested by virtue of a political or social change - principally getting rid of people who benefit by the enterprise but do not enhance the principal mission, namely, producing energy.

Monday, January 11, 2021

Feet on the Ground

 I have been reading a lot of posts that make me long for solid ground. Let me tell the story of sustainability as I experienced it: It all goes back to the Yahoo! groups: Running on Empty 2, Energy Resources, and Energy Round Table, where we heard horror stories which would begin when the world reached Peak Oil. Indeed, the post-Peak Oil world is similar to the world just before the advent of civilization, except that, whereas the prehistoric world got better day by day, the post-Peak Oil world would get worse. But we did not reach Peak Oil. As we all know various factors intervened and year after year we did not reach Peak Oil. This fed into a great deal of skepticism. "Perhaps we would never reach it." But this idea wasn't coming from chemical engineers. We knew that perpetual growth in a finite world was impossible. So far, sustainability was always about having a perpetual energy supply in a world neither the population nor the economy of which was growing. People kept talking about ERoEI as the criterion for sustainability or else finding some reason why it wouldn't work.

I understood that every economic action has an associated energy action; therefore, it was obvious that people were not computing ERoEI correctly. I devised the thought experiment with the Autonomous Alternative Energy District to demonstrate that. They didn't understand the thought experiment very well or else they thought I would not be able to analyze multiple energy sources and by-products; so, the new exercise which many of you are reviewing for me is still under development at https://www.eroei.net/Mark-III-Economy.pdf and https://www.eroei.net/Mark-III-Economy.html which you might as well defer until last.
The following might be interesting, helpful, or even essential:
https://www.dematerialism.net/MonetarySystem.html and the section on Sustainability in https://www.dematerialism.net/ and relevant pieces on https://eroei.blogspot.com/ and, finally, https://www.eroei.net/Mark-III-Economy.pdf . Also, there is an older version uploaded as a pre-print on ResearchGate. I am having ten times the trouble with Microsoft 365 and OneDrive as I am having with the engineering, which is complete. I just started with MS365 and OneDrive.
If you decide that energy is NOT virtually everything, think about a world that has completely mastered all that social science properly applied can offer. but it has only a small amount of energy and that is dwindling. Picture a nightmare on Earth. Think of all the things you'll miss because you have no energy.Nothing else is so important.
I will put together a package beginning with https://dematerialism.net/MonetarySystem.html continuing with the Sustainability section of https://www.dematerialism.net/ with ancillary pieces in https://eroei.blogspot.com/ and ending
with https://www.eroei.net/Mark-III-Economy.html that show how one supports renewable energy if it is ever attained.

Net Energy and ERoEI* in a Mark III Economy (revised)

 

 


   

  

  

  

  

Structure

 

The Mark I economy had only one economic requirement, namely, that each person had to eat one potato per day or die. This was useful to show that one man's wealth can mean another man's or many men's death. The Mark II economy had four or five economic sectors.   It seemed to validate multiplying qantities of money by the E/GDP ratio tabulated for every country and every year to determine the quantity of energy associated in that year in that part of the world with that economic transaction and many other aspects of monetary behavior. To illustrate the use of ERoEI* and net energy for much more typical communities than the Autonomous Alternative Energy District (AAED), it is convenient to devise a Mark III economy, which is an extension of the AAED with similar boundary conditions.  Sunlight shines on the community territory; junk heat radiates to deep space; electricity sold for biodiesel is exported, biodiesel is imported, motor vehicles are imported, chemicals, and steel are imported, potatoes, saxophones, medical instruments, and robotics are exported.  Other than these, nothing significant crosses the boundaries. Moreover, the energy products and exports are the only net production of the workers all of whom, therefore, live at the expense of energy or exports.  And, since they are entitled to that living because of energy and exports, all of their energy costs are charged nowhere else.  In this exercise a simple example of arbitrary construction is contrived to illustrate how to compute ERoEI*, how to do net energy accounting, and how to determine sustainability. 

Our simple example with the parameters chosen for convenience has six economic sectors, nine syndicates, three forms of energy, and four products other than energy itself, which should be the basis of the monetary currency. The Mark III currency is based upon eMergy.  As in standard business practice, the costing of each product is divided into three parts, namely, materials, µ, labor, λ, and expenses, ϵ, such that µ + λ + ϵ = 1.0 as in the fourth column of Table 3.  “Expenses” usually includes taxes and profits as well as many other items that do not fit well into the materials and labor categories.

The economic sectors: agriculture, energy, manufacturing, transportation, commerce, and health care have their normal meanings. Every worker belongs to a syndicate of workers with similar skills and one characteristic wage. The syndicates that are available to perform specific tasks for the various sectors in the Mark III economy are the farm workers syndicate, non-farm agricultural work, manufacturing, engineering, energy, transportation, commerce, doctors and nurses, and non-medical healthcare workers.

For the sake of a simple example with some opportunity for variety, I have chosen arbitrarily: photovoltaic solar energy, hydroelectric power, and biofuels from algae for my candidates for renewable energy. I reduced the wages until I had positive net energy that permitted the production of (1) food, (2) saxophones, (3) medical equipment, and (4) robotics that will be traded for (1) motor vehicles such as ambulances, fire trucks, snowplows, and tow trucks, (2) chemicals, and (3) steel. In addition, electricity will be traded for biodiesel.  Everything else is found within the AAED.  I have no idea what the correct proportions of material, labor, and expenses are for any of the products, but it doesn’t matter for this imaginary example.   I have picked simple fractions that add to 1.0.   In a real problem, it is important to choose the labor fraction as accurately as possible, as ERoEI* is directly proportional to λ.

In this exercise, the community spent 40% of the net emergy growing potatoes, the standard quantity of which has an energy cost of 0.17 emergy units. The work of producing such potatoes of one emergy unit value is distributed among the six economic sectors (agric, energy, manu, trans, comm, health) respectively in parts of (0.2, 0.2, 0.4, 0.25, 0.3, 0.1) (resp.) emergy units which can be thought of as energy investment for the agricultural syndicate. The percent of human effort assigned to each sector can also be represented as a six-component “vector” (20%, 15%, 10%, 5%, 30%, 10%). For each enterprise, the program prepares a six-by-nine array with a row for the percent of each of the six sectors and nine columns for the time credited to each syndicate for the portion of the work done for that project.  Table 4 is the portion of an MS Excel workbook where ERoEI* is computed and which illustrates the  way I organized the calculations.   The point is to show that multiple primary energy plants and multiple products are not a challenge for ERoEI*.  In this community, there are no free loaders or workers whose only achievement is to get a greater share of the production for themselves or their employers.  The living expenses of freeloaders come from the net energy rather than the energy invested because, if necessary, the community could kick them out.

Computation 

 

For each labor syndicate assigned a single column of the data matrix in Table 4, consider the sum of each sector’s fractional share of each project, 𝜑𝑖𝑛, times the quantity of work per emergy unit, 𝑝𝑖𝑗𝑛, measured in hours for each of the six sectors.  Multiply this six-term sum by the labor cost, 𝑤𝑗, and record the result for each of the nine labor syndicates.  Add these together to find the portion of the energy-invested term that is ascribed to human labor as in the normal business model composed of materials, labor, and expenses.  Thus, the energy returned over energy invested ratio for PV solar satisfies the following equation according to the Wayburn methodology:  

 

The equation is scale invariant. Think of it as "per unit of emergy recovered". So, if there is no energy recovered and ERoEI* = 1.0, it means that the emergy of the output that was used was correct. If ERoEI* > 1.0, emergy of product should be reduced. If ERoEI* < 1.0, the process has an efficiency lower than the industrial standard. The accuracy of the computation is directly proportional to the percent of energy costs due to human effort. I have agreed that we can assume that the data are good enough, as this is supposed to be an approximation.  Nevertheless, it is an approximation of the right thing. It is not necessary to get highly accurate results to do good science.  If we compute 0.5 for ERoEI* of solar, we can be reasonably certain that solar is not truly renewable.  Of course, we can compute material costs more accurately than labor, but expenses are tricky.  Nevertheless, we can add up the three categories of energy costs; and, then, we wont need the fractions.  

 

 

 

 

Table 1 

Symbol

Description

𝛽𝑛

ERoEI* for the nth product

𝜌𝑛

fraction for the nth product of the nominal emergy rating for the entire enterprise

𝜆𝑛

labor fraction of the complete slate of costs for the nth product 

𝑤𝑗

the rate of compensation for the jth syndicate

𝜑𝑛𝑖

the fraction of the nth product produced by the ith sector

𝑝𝑛𝑖𝑗

the time required by the ith sector of the nth product by the jth syndicate

 

 

 

Table 2 shows the results and some of the data for this imaginary sample calculation.  All three of the imaginary renewable energy candidates passed the strict test ERoEI* equal to or greater than 1.0.   The renewable energy candidates were set up to pass to continue the make-believe computation.  It is unlikely that solar or biodiesel would pass with today’s primitive technology – especially recycle technology that has never been tried.   Someday, though, we will have renewable energy that will sustain human civilization for centuries here on Earth.  I hope that a large contingent will oppose “the idea that humanity, having sufficiently corrupted the planet where it arose, must at all costs contrive to seed itself over a larger area: that the vast astronomical distances, which are God’s quarantine regulations, must somehow be overcome.” – C. S. Lewis, Perelandra.  

Thus, in our sample problem, there is enough net energy to imagine by-products that can be used to trade for biodiesel, motor vehicles, chemicals, and steel.  Our neighbors are delighted to receive 10 emergy units (kilowatt-hours) of 110 VAC, 60 Hz, single-phase electric power delivered to their meter for 20 kilowatt-hours of Gibbs availability of biodiesel.  This amounts to a transformity of 0.5 for biodiesel, which is extremely generous.   Electricity carries very little entropy. Hence, emergy or Gibbs availability is nearly pure energy.

The nine labor wage rates, w, were placed in cells D57-L57 of Table 4.  The three ERoEI*s were

stored in cells M30. M37, and M44.  The weighted average for the entire community was stored in  M51. Table 2 shows that production, exports, and imports are balanced.

 

  

 

 

 

 

 

 

Table 2

 

 

Products  

Production  

Sales  

Purchases  

solar  

0.2  

0.2  

   

biodiesel  

   

   

0.3448  

motor vehicles  

   

   

0.2172  

chemical  

   

   

0.1448  

steel  

   

   

0.2172  

food  

0.29  

0.29  

   

saxes  

0.145  

0.145  

   

med instruments  

0.217  

0.217  

   

robotics  

0.072  

0.072  

   

total  

0.924  

0.924  

0.924  

 

Table 3

Product  

βn  

ρn  

(µ λ ϵ)  

biodiesel  

   

   

   

motor vehicles  

   

   

   

chemicals  

   

   

   

steel  

   

   

   

potatoes  

   

0.29  

0.3, 0.3, 0.4  

saxophones  

   

0.145  

0.25, 0.25, 0.5  

medical instruments  

   

0.217  

0.25, 0.25, 0.5  

robotics  

   

0.072  

0.25, 0.25, 0.5  

photovoltaic solar  

1.76  

0.45  

0.3, 0.3, 0.4  

hydroelectric  

1.697  

0.35  

0.3, 0.3, 0.4  

biodiesel from algae  

1.691  

0.2  

0.4, 0.3, 0.3  

combined renewables  

1.724  

   

   

  

 

Table 4

A

B

C

D

E

F

G

H

I

J

K

L

M

 

  

  

A  

P  

M  

E  

T  

C  

Engg  

Docs  

HC  

  

2

Food    

0.290  

0.010

 0.060

 0.036

 0.016

 0.015

 0.015

 0.019

 0.056

 0.008

 1.281

 

0.2  

Agriculture  

0.040

 0.160

 0.120

 0.060

 0.000

 0.000

 0.000

 0.000

 0.000

    

 4 

0.15  

Energy  

0.000

 0.000

 0.120

 0.015

 0.000

 0.000

 0.000

 0.000

 0.000

    

  5

0.1  

Manu  

0.000

 0.000

 0.000

 0.030

 0.070

 0.000

 0.000

 0.000

 0.000

    

  6

0.15  

Trans  

0.000

 0.000

 0.000

 0.000

 0.000

 0.150

 0.000

 0.000

 0.000

    

 

0.3  

Commerce  

0.000

 0.000

 0.000

 0.000

 0.000

 0.090

 0.060

 0.150

 0.000

    

  8

0.1  

Health Care  

0.000

 0.000

 0.000

 0.000

 0.000

 0.000

 0.000

 0.000

 0.050

    

  9

Saxes  

0.145  

0.000

 0.000

 0.027

 0.014

 0.031

 0.019

 0.023

 0.041

 0.014

 1.473

10  

0  

Agriculture  

0.000

 0.000

 0.000

 0.000

 0.000

 0.000

 0.000

 0.000

 0.000

    

11  

0.1  

Energy  

0.000

 0.000

 0.015

 0.015

 0.025

 0.030

 0.005

 0.005

 0.005

    

12  

0.4  

Manu  

0.000

 0.000

 0.120

 0.040

 0.040

 0.120

 0.040

 0.020

 0.020

    

13  

0.1  

Trans  

0.000

 0.000

 0.010

 0.010

 0.030

 0.030

 0.010

 0.005

 0.005

    

14  

0.3  

Commerce  

0.000

 0.000

 0.030

 0.015

 0.030

 0.090

 0.015

 0.060

 0.060

    

15  

0.1  

Health Care  

0.000

 0.000

 0.005

 0.015

 0.020

 0.030

 0.005

 0.020

 0.005

    

16  

Medical  

0.217  

0.000

 0.000

 0.020

 0.016

 0.036

 0.019

 0.041

 0.036

 0.014

 1.376

17  

0  

Agriculture  

0.000

 0.000

 0.000

 0.000

 0.000

 0.000

 0.000

 0.000

 0.000

    

18  

0.15  

Energy  

0.000

 0.000

 0.023

 0.023

 0.038

 0.045

 0.008

 0.008

 0.008

    

19  

0.2  

Manu  

0.000

 0.000

 0.060

 0.020

 0.020

 0.060

 0.010

 0.010

 0.010

    

20  

0.1  

Trans  

0.000

 0.000

 0.010

 0.010

 0.030

 0.030

 0.005

 0.005

 0.005

    

21  

0.3  

Commerce  

0.000

 0.000

 0.030

 0.015

 0.030

 0.090

 0.060

 0.060

 0.060

    

 22 

0.25  

Health Care  

0.000

 0.000

 0.013

 0.038

 0.050

 0.075

 0.050

 0.013

 0.013

    

23  

Robotics  

0.072  

0.000

 0.000

 0.025

 0.015

 0.034

 0.019

 0.034

 0.036

 0.014

 1.414

24  

0  

Agriculture  

0.000

 0.000

 0.000

 0.000

 0.000

 0.000

 0.000

 0.000

 0.000

    

25  

0.2  

Energy  

0.000

 0.000

 0.030

 0.030

 0.050

 0.060

 0.010

 0.010

 0.010

    

26  

0.3  

Manu  

0.000

 0.000

 0.090

 0.030

 0.030

 0.090

 0.015

 0.015

 0.015

    

27  

0.1  

Trans  

0.000

 0.000

 0.010

 0.010

 0.030

 0.030

 0.005

 0.005

 0.005

    

28  

0.3  

Commerce  

0.000

 0.000

 0.030

 0.015

 0.030

 0.090

 0.060

 0.060

 0.060

    

 29 

0.1  

Health Care  

0.000

 0.000

 0.005

 0.015

 0.020

 0.030

 0.020

 0.005

 0.005

    

 30 

Solar  

0.450  

0.000

 0.000

 0.023

 0.015

 0.036

 0.019

 0.022

 0.041

 0.014

 1.760

31  

0  

Agriculture  

0.000

 0.000

 0.000

 0.000

 0.000

 0.000

 0.000

 0.000

 0.000

    

32  

0.2  

Energy  

0.000

 0.000

 0.030

 0.030

 0.050

 0.060

 0.010

 0.010

 0.010

    

 33 

0.25  

Manu  

0.000

 0.000

 0.075

 0.025

 0.025

 0.075

 0.025

 0.013

 0.013

    

34  

0.15  

Trans  

0.000

 0.000

 0.015

 0.015

 0.045

 0.045

 0.015

 0.008

 0.008

    

 35

0.3  

Commerce  

0.000

 0.000

 0.030

 0.015

 0.030

 0.090

 0.015

 0.060

 0.060

 

  

  

 

36 

0.1

Health Care

0.000

0.000

0.005

0.015

0.020

0.030

0.005

0.020

0.005

 

37 

Hydro

0.350

0.000

0.000

0.025

0.015

0.034

0.019

0.034

0.036

0.014

1.697

38 

0

Agriculture

0.000

0.000

0.000

0.000

0.000

0.000

0.000

0.000

0.000

 

39 

0.2

Energy

0.000

0.000

0.030

0.030

0.050

0.060

0.010

0.010

0.010

 

40 

0.3

Manu

0.000

0.000

0.090

0.030

0.030

0.090

0.015

0.015

0.015

 

41 

0.1

Trans

0.000

0.000

0.010

0.010

0.030

0.030

0.005

0.005

0.005

 

42 

0.3

Commerce

0.000

0.000

0.030

0.015

0.030

0.090

0.060

0.060

0.060

 

43 

0.1

Health Care

0.000

0.000

0.005

0.015

0.020

0.030

0.020

0.005

0.005

 

44 

Biofuel

0.200

0.000

0.000

0.023

0.015

0.036

0.019

0.034

0.036

0.014

1.691

45 

0

Agriculture

0.000

0.000

0.000

0.000

0.000

0.000

0.000

0.000

0.000

 

46 

0.2

Energy

0.000

0.000

0.030

0.030

0.050

0.060

0.010

0.010

0.010

 

47 

0.25

Manu

0.000

0.000

0.075

0.025

0.025

0.075

0.013

0.013

0.013

 

48 

0.15

Trans

0.000

0.000

0.015

0.015

0.045

0.045

0.008

0.008

0.008

 

49 

0.3

Commerce

0.000

0.000

0.030

0.015

0.030

0.090

0.060

0.060

0.060

 

50 

0.1

Health Care

0.000

0.000

0.005

0.015

0.020

0.030

0.020

0.005

0.005

 

51 

Combo

 

 

 

 

 

 

 

 

 

 

1.724

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

55 

 

 

 

 

 

 

 

 

 

 

 

 

λ

 

 

A

OF

M

E

T

C

Eng

Med

HC

 

0.3

Food

0.4

0.25

0.38

0.15

0.15

0.21

0.06

0.31

0.38

0.15

 

58 

0.2

Agriculture

0.2

0.8

0.6

0.3

 

 

 

 

 

 

 

0.15

Energy

 

 

0.8

0.1

 

 

 

 

 

 

 

0.1

Manu

 

 

 

0.3

0.7

 

 

 

 

 

 

0.15

Trans

 

 

 

 

 

1

 

 

 

 

 

0.3

Commerce

 

 

 

 

 

0.3

0.2

0.5

 

 

 

0.1

Health Care

 

 

 

 

 

 

 

 

0.5

 

0.25

Saxes

0.2

 

 

 

 

 

 

 

 

 

 

 

0

Agriculture

 

 

0

0

0

0

0

0

0

 

 

0.1

Energy

 

 

0.15

0.15

0.25

0.3

0.05

0.05

0.05

 

 

0.4

Manu

 

 

0.3

0.1

0.1

0.3

0.1

0.05

0.05

 

 

0.1

Trans

 

 

0.1

0.1

0.3

0.3

0.1

0.05

0.05

 

 

0.3

Commerce

 

 

0.1

0.05

0.1

0.3

0.05

0.2

0.2

 

 

0.1

Health Care

 

 

0.05

0.15

0.2

0.3

0.05

0.2

0.05

 

0.25

Medical

0.3

 

 

 

 

 

 

 

 

 

 

 

0

Agriculture

 

 

0

0

0

0

0

0

0

 

 

0.15

Energy

 

 

0.15

0.15

0.25

0.3

0.05

0.05

0.05

 

 

0.2

Manu

 

 

0.3

0.1

0.1

0.3

0.05

0.05

0.05

 

 

0.1

Trans

 

 

0.1

0.1

0.3

0.3

0.05

0.05

0.05

 

 

0.3

Commerce

 

 

0.1

0.05

0.1

0.3

0.2

0.2

0.2

 

 

0.25

Health Care

 

 

0.05

0.15

0.2

0.3

0.2

0.05

0.05

 

0.25

Robotics

0.1

 

 

 

 

 

 

 

 

 

 

 

0

Agriculture

 

 

0

0

0

0

0

0

0

 

 

0.2

Energy

 

 

0.15

0.15

0.25

0.3

0.05

0.05

0.05

 

 

0.3

Manu

 

 

0.3

0.1

0.1

0.3

0.05

0.05

0.05

 

 

0.1

Trans

 

 

0.1

0.1

0.3

0.3

0.05

0.05

0.05

 

 

0.3

Commerce

 

 

0.1

0.05

0.1

0.3

0.2

0.2

0.2

 

 

0.1

Health Care

 

 

0.05

0.15

0.2

0.3

0.2

0.05

0.05

 

0.3

Solar

0.45

 

 

 

 

 

 

 

 

 

 

 

0

Agriculture

0

0

0

0

0

0

0

0

0

 

 

0.2

Energy

0

0

0.15

0.15

0.25

0.3

0.05

0.05

0.05

 

 

0.25

Manu

0

0

0.3

0.1

0.1

0.3

0.1

0.05

0.05

 

 

0.15

Trans

0

0

0.1

0.1

0.3

0.3

0.1

0.05

0.05

 

 

0.3

Commerce

0

0

0.1

0.05

0.1

0.3

0.05

0.2

0.2

 

 

0.1

Health Care

0

0

0.05

0.15

0.2

0.3

0.05

0.2

0.05

 

0.3

Hydro

0.35

 

 

 

 

 

 

 

 

 

 

 

0

Agriculture

0

0

0

0

0

0

0

0

0

 

 

0.2

Energy

0

0

0.15

0.15

0.25

0.3

0.05

0.05

0.05

 

 

0.3

Manu

0

0

0.3

0.1

0.1

0.3

0.05

0.05

0.05

 

 

0.1

Trans

0

0

0.1

0.1

0.3

0.3

0.05

0.05

0.05

 

 

0.3

Commerce

0

0

0.1

0.05

0.1

0.3

0.2

0.2

0.2

 

 

0.1

Health Care

0

0

0.05

0.15

0.2

0.3

0.2

0.05

0.05

 

0.3

Biodiesel

0.2

 

 

 

 

 

 

 

 

 

 

 

0

Agriculture

0

0

0

0

0

0

0

0

0

 

 

0.2

Energy

0

0

0.15

0.15

0.25

0.3

0.05

0.05

0.05

 

 

0.25

Manu

0

0

0.3

0.1

0.1

0.3

0.05

0.05

0.05

 

 

0.15

Trans

0

0

0.1

0.1

0.3

0.3

0.05

0.05

0.05

 

 

0.3

Commerce

0

0

0.1

0.05

0.1

0.3

0.2

0.2

0.2

 

 

0.1

Health Care

0

0

0.05

0.15

0.2

0.3

0.2

0.05

0.05

 

 

 

 

 

 

 

  

 

  

Table 5

  

Syndicates

A

Agriculture on the farm

P

Workers classified as agricultural who do not work on farms

M

Manufacturing both within factories and in the field

E

Workers whose mission is to provide us with energy

T

Those whose mission is to carry raw materials, people, and goods from place to place

C

Those who serve commerce

Engg

Engineering and the practical applications of science

Med

Those who keep us healthy and cure us if we are sick

HC

Those who serve the healthcare business except wellness and healing

  

 

 

 


 


 

  

 

 

Structure

The Mark I economy had only one economic requirement, namely, that each person had to eat one potato per day or die. This was useful to show that one man's wealth can mean another man's or many men's death. The Mark II economy had four or five economic sectors and was useful to demonstrate the use of E/GDP data to convert money to energy and many other aspects of monetary behavior. To illustrate the use of ERoEI* and net energy for much more typical communities than the Autonomous Alternative Energy District, it is convenient to devise a Mark III economy. In this exercise a simple example of arbitrary construction is contrived to illustrate how to compute ERoEI*, Net Energy accounting, and sustainability or not.

Our simple example with most parameters chosen for convenience has six economic sectors, nine syndicates, three forms of energy, and four products other than energy itself, which should be the basis of the monetary currency. With a little bit more trouble, I could have contrived an example wherein a vector currency could have been introduced. To start with, though, the Mark III currency is based upon eMergy.  As in standard business practice, the costing of each product is divided into three parts of unity, namely, materials, µ, labor, λ, and expenses, ϵ, such that µ + λ + ϵ = 1.0 as in the fourth column of Table 2.  Expenses usually includes taxes and profits as well as many other items that do not fit well into the materials and labor categories.

The economic sectors: agriculture, energy, manufacturing, transportation, commerce, and health care, have their normal meanings. Every worker belongs to a syndicate of workers with similar skills and one characteristic wage. The syndicates that are available to perform specific tasks for the various sectors in the Mark III economy are the farm workers syndicate, non-farm agricultural work, manufacturing, engineering, energy, transportation, commerce, doctors and nurses, and non-medical healthcare workers.

For the sake of a simple example with some opportunity for variety, I have chosen arbitrarily: photovoltaic solar energy, hydroelectric power, and biofuels from algae for my candidates for renewable energy. I reduced the wages until I had positive net energy that permitted the production of (1) food, (2) saxophones, (3) medical equipment, and (4) robotics that will be traded for (1 motor vehicles such as ambulances, fire trucks, snowplows, and tow trucks, (2) chemicals, and (3) steel. In addition, electricity will be traded for biodiesel.  I have no idea what the correct proportions of material, labor, and expenses are for any of the products, but it doesn’t matter for this imaginary example.   I have picked simple fractions that add to 1.0.   In a real problem, it is important to choose the labor fraction as accurately as possible, as ERoEI* is directly  proportional to λ.

For example, if there is any positive net energy returned, I have chosen to spend 40% of the net emergy growing some potatoes, the standard quantity of which has an energy cost of 0.17 emergy units. The work of producing such potatoes of one emergy unit value is distributed among the six economic sectors (agric, energy, manu, trans, comm, health) respectively in parts of (0.2, 0.2, 0.4, 0.25, 0.3, 0.1) (resp.) emergy units which can be thought of as energy investment for the agricultural syndicate. The percent of human effort assigned to each sector can also be represented as a six-component vector (20%, 15%, 10%, 5%, 30%, 10%). For each enterprise, the program prepares a six-by-nine array with a row for the percent of each of the six sectors and nine columns for the time credited to each syndicate for the portion of the work done for that project.  Table 4 is the portion of an MS Excel workbook where ERoEI* is computed and which illustrates the organizational scheme I employed.   The point is to show that multiple primary energy plants and multiple products are not a challenge for ERoEI*.  In this community, there are no free loaders or workers whose only achievement is to get a greater share of the production for themselves or their employers.  The living expenses of freeloaders come from the net energy rather than the energy invested because, if necessary, the community could simply not support them.

Computation

For each labor syndicate assigned a single column of the data matrix in Table 3, consider the sum of each sector’s fractional share of each project, 𝜑𝑖𝑛, times the quantity of work per emergy unit, 𝑝𝑖𝑗𝑛, measured in hours for each of the six sectors.  Multiply this six-term sum by the labor cost, 𝑤𝑗, and record the result for each of the nine labor syndicates.  Add these together to find the portion of the energy-invested term that is ascribed to human labor as in the normal business model composed of materials, labor, and expenses.  Thus, the energy returned over energy invested ratio for PV solar satisfies the following equation according to the Wayburn methodology

 

The equation is scale invariant. Think of it as "per unit of emergy recovered". So, if there is no energy recovered and ERoEI* = 1.0, it means that the emergy of the output that was used was correct. If ERoEI* > 1.0, emergy of product should be reduced. If ERoEI* < 1.0, the process has an efficiency lower than the industrial standard. The accuracy of the computation is directly proportional to the percent of energy costs due to human effort. I have agreed that we can assume that the data is good enough as is the rest of it, but this is supposed to be an approximation.  Nevertheless, it is an approximation of the right thing. It is not necessary to get highly accurate results to do good science.  If we compute 0.7 for ERoEI* of solar, we can be reasonably certain that solar is not truly renewable.

 

 

 

Table 1

Symbol

Description

ERoEI* for the nth product

fraction for the nth product of the nominal emergy rating for the entire enterprise

labor fraction of the complete slate of costs for the nth product

the rate of compensation for the jth syndicate

the fraction of the nth product produced by the ith sector

the time required by the ith sector of the nth product by the jth syndicate

 

:

 

 

 

 

 

 

 

 

 

Table 2 shows the results and some of the data for this imaginary sample calculation.  All three of the imaginary renewable energy candidates passed the strict test ERoEI* equal to or greater than 1.0.   The renewable energy candidates were set up to pass to continue the make-believe computation.  It is unlikely that solar or biodiesel would pass with today’s primitive technology – especially recycle technology that has never been tried.   Someday, though, we will have renewable energy that will sustain human civilization for centuries here on Earth.  I hope that a large contingent will oppose “the idea that humanity, having sufficiently corrupted the planet where it arose, must at all costs contrive to seed itself over a larger area: that the vast astronomical distances, which are God’s quarantine regulations, must somehow be overcome.” – C. S. Lewis, Perelandra. 

 

 

 

 

 

 

Thus, in our sample problem, there is enough net energy to imagine by-products that can be used to trade for biodiesel, motor vehicles, chemicals, and steel.  We knew before we established the success of our experiment that we would be able to trade electricity for liquid fuel, which we required for our emergency vehicles.  Moreover, we were permitted to set the transformity of biodiesel to 0.5; therefore, we obtained 20 Gibbs availability units of biodiesel for 10 units (kilowatt-hours) of 110 VAC, 60 Hz, single-phase electric power delivered to the buyer’s meter.  Electricity carries almost no entropy. Hence, emergy or Gibbs availability are nearly pure energy.

 

 

 

Table 2

 

 

Products

Production

Sales

Purchases

solar

0.2

0.2

 

biodiesel

 

 

0.3448

motor vehicles

 

 

0.2172

chemical

 

 

0.1448

steel

 

 

0.2172

food

0.29

0.29

 

saxes

0.145

0.145

 

med instruments

0.217

0.217

 

robotics

0.072

0.072

 

total

0.924

0.924

0.924

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 Table 3

 

 

Product

βn

ρn

(µ λ ϵ)

biodiesel

 

 

 

motor vehicles

 

 

 

chemicals

 

 

 

steel

 

 

 

potatoes

 

0.29

0.3, 0.3, 0.4

saxophones

 

0.145

0.25, 0.25, 0.5

medical instruments

 

0.217

0.25, 0.25, 0.5

robotics

 

0.072

0.25, 0.25, 0.5

photovoltaic solar

1.76

0.45

0.3, 0.3, 0.4

hydroelectric

1.697

0.35

0.3, 0.3, 0.4

biodiesel from algae

1.691

0.2

0.4, 0.3, 0.3

combined renewables

1.724

 

 

 

 

Table 4


 

 

 

  

 

A

P

M

E

T

C

Engg

Docs

HC

 

 

Food

0.290

0.010

0.060

0.036

0.016

0.015

0.015

0.019

0.056

0.008

1.281

 

0.2

Agriculture

0.040

0.160

0.120

0.060

0.000

0.000

0.000

0.000

0.000

 

 

0.15

Energy

0.000

0.000

0.120

0.015

0.000

0.000

0.000

0.000

0.000

 

 

0.1

Manu

0.000

0.000

0.000

0.030

0.070