Net Energy and ERoEI* in a Mark III Economy

 

 

 

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*, how to do net energy accounting, and how to determine 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.  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 average 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.

The community will spend 40% of the net emergy growing 0.17 emergy units worth of potatoes per emergy unit of community energy production. The work of producing potatoes 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 for the portion of the work done for that project with a row for the percent of each of the six sectors and a column for each syndicate.  Table 4 is the portion of an MS Excel workbook where ERoEI* is computed and which illustrates the way I organized the computation. 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 can kick them out, which, in our system, is a fate worse than death.

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, 𝜑_𝑖^𝑛, times the quantity of work per emergy unit, 𝑝_𝑖𝑗^𝑛, measured in hours for each of the six sectors.  Multiply this six-term sum by the labor cost, 𝑤_𝑗, 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. This is 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.

 

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 personally 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.  Our neighbors are delighted to receive 10 units (kilowatt-hours) of 110 VAC, 60 Hz, single-phase electric power delivered to the buyer’s meter for 20 kilowatt-hours of biodiesel, which means the transformity of biodiesel is 0.5.  Electricity carries very little entropy, hence, the Gibbs availability of electricity is 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	0.000	0.000	0.000	0.000
	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
	0.1	Health Care	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.050
	Saxes	0.145	0.000	0.000	0.027	0.014	0.031	0.019	0.023	0.041	0.014	1.473
	0	Agriculture	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000
	0.1	Energy	0.000	0.000	0.015	0.015	0.025	0.030	0.005	0.005	0.005
	0.4	Manu	0.000	0.000	0.120	0.040	0.040	0.120	0.040	0.020	0.020
	0.1	Trans	0.000	0.000	0.010	0.010	0.030	0.030	0.010	0.005	0.005
	0.3	Commerce	0.000	0.000	0.030	0.015	0.030	0.090	0.015	0.060	0.060
	0.1	Health Care	0.000	0.000	0.005	0.015	0.020	0.030	0.005	0.020	0.005
	Medical	0.217	0.000	0.000	0.020	0.016	0.036	0.019	0.041	0.036	0.014	1.376
	0	Agriculture	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000
	0.15	Energy	0.000	0.000	0.023	0.023	0.038	0.045	0.008	0.008	0.008
	0.2	Manu	0.000	0.000	0.060	0.020	0.020	0.060	0.010	0.010	0.010
	0.1	Trans	0.000	0.000	0.010	0.010	0.030	0.030	0.005	0.005	0.005
	0.3	Commerce	0.000	0.000	0.030	0.015	0.030	0.090	0.060	0.060	0.060
	0.25	Health Care	0.000	0.000	0.013	0.038	0.050	0.075	0.050	0.013	0.013
	Robotics	0.072	0.000	0.000	0.025	0.015	0.034	0.019	0.034	0.036	0.014	1.414
	0	Agriculture	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000
	0.2	Energy	0.000	0.000	0.030	0.030	0.050	0.060	0.010	0.010	0.010
	0.3	Manu	0.000	0.000	0.090	0.030	0.030	0.090	0.015	0.015	0.015
	0.1	Trans	0.000	0.000	0.010	0.010	0.030	0.030	0.005	0.005	0.005
	0.3	Commerce	0.000	0.000	0.030	0.015	0.030	0.090	0.060	0.060	0.060
	0.1	Health Care	0.000	0.000	0.005	0.015	0.020	0.030	0.020	0.005	0.005
	Solar	0.450	0.000	0.000	0.023	0.015	0.036	0.019	0.022	0.041	0.014	1.760
	0	Agriculture	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000
	0.2	Energy	0.000	0.000	0.030	0.030	0.050	0.060	0.010	0.010	0.010
	0.25	Manu	0.000	0.000	0.075	0.025	0.025	0.075	0.025	0.013	0.013
	0.15	Trans	0.000	0.000	0.015	0.015	0.045	0.045	0.015	0.008	0.008
	0.3	Commerce	0.000	0.000	0.030	0.015	0.030	0.090	0.015	0.060	0.060

 

 

	0.1	Health Care	0.000	0.000	0.005	0.015	0.020	0.030	0.005	0.020	0.005
	Hydro	0.350	0.000	0.000	0.025	0.015	0.034	0.019	0.034	0.036	0.014	1.697
	0	Agriculture	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000
	0.2	Energy	0.000	0.000	0.030	0.030	0.050	0.060	0.010	0.010	0.010
	0.3	Manu	0.000	0.000	0.090	0.030	0.030	0.090	0.015	0.015	0.015
	0.1	Trans	0.000	0.000	0.010	0.010	0.030	0.030	0.005	0.005	0.005
	0.3	Commerce	0.000	0.000	0.030	0.015	0.030	0.090	0.060	0.060	0.060
	0.1	Health Care	0.000	0.000	0.005	0.015	0.020	0.030	0.020	0.005	0.005
	Biofuel	0.200	0.000	0.000	0.023	0.015	0.036	0.019	0.034	0.036	0.014	1.691
	0	Agriculture	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000
	0.2	Energy	0.000	0.000	0.030	0.030	0.050	0.060	0.010	0.010	0.010
	0.25	Manu	0.000	0.000	0.075	0.025	0.025	0.075	0.013	0.013	0.013
	0.15	Trans	0.000	0.000	0.015	0.015	0.045	0.045	0.008	0.008	0.008
	0.3	Commerce	0.000	0.000	0.030	0.015	0.030	0.090	0.060	0.060	0.060
	0.1	Health Care	0.000	0.000	0.005	0.015	0.020	0.030	0.020	0.005	0.005
	Combo											1.724
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
	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