Introduction
Energy Returned over Energy Invested (EROI) Computed Five Different Ways
My first simplified economy, the Mark I Economy, had only one economic good, which I referred to as a “potato”. Every citizen required one potato per day and nothing else to live; but, if he did not get it, he would die. The economy was capable of producing precisely one potato per day per person; thus, if someone took more than one, someone else would die. This was fine for my purpose, which was to show the necessity of wealth sharing in a world with limited resources and a steady-state economy; but, now, I require more complexity.
If you have read this paper previously, always look in What’s New first; and, if something has been added since your last reading, look there next. Unfortunately, the changes made today will necessitate a complete re-reading. Normally, you will find everything you need to read here and in any experiments you have not yet seen. I hope you have taken my advice about downloading new copies of this paper and the spreadsheets whenever you work on this project. This is an intentionally open-ended paper that takes advantage of web publication to do something that cannot be done in the print literature – except that, because of the pressure of publish-or-perish, many academics write paper after paper that are no more than progress reports on work done previously and contain no new ideas.
After the rest of this paper was written I wrote the brief note at http://dematerialism.net/eroeistar.htm that provides EROEI* to delimit strictly the boundary between feasible energy technologies (if EROEI* ≥ 1.0) and unsustainable energy technologies (if EROEI* < 1.0). That paper uses the section from this paper on the Autonomous Alternative Energy District.
This is the beginning of a complete revision of this paper to exploit a new relation between emergy and the ratio of Energy Returned to Energy Invested (EROI) and to introduce a new routine for computing five types of EROI:
1. EROIo. The energy invested (EI) is the direct energy overhead of the energy sector.
2. EROI1. EI1 includes, in addition to the direct energy overhead, the indirect energy costs associated with the energy overhead of the manufacturing and transportation portions of the overhead of the energy sector but not the overhead due to commerce.
3. EROI2. EI2 includes, in addition, the overhead due to the activities of commerce in connection with the sale of energy.
4. EROI3. EI3 includes, in addition, the consumption of energy associated with that portion of the salaries paid to the energy sector in excess of what they would have been if no one earned more than the workers do. This is thought to account for over-consumption associated with profit taking in connection with the sale of energy.
5. EROI4. EI4 includes, in addition, the consumption of energy by the workers in the energy sector and the pro-rata shares of the energy expenses of the workers and managers in other sectors insofar as they support the energy sector.
Note (12.05.2011) It’s about time I entered a reference to yet another, even more comprehensive, EROI (or ERoEI as I write nowadays). Please see http://dematerialism.net/eroeistar.htm.
It has come to my attention that some people do not see the point of building an economy that models the American and other hypothetical economies in an idealized way that is guaranteed to be less wasteful than every real economy of the same type. This paper assumes that the reader is familiar with the notions of Peak Oil, Overshoot, and Die Off.
The Base Case (BC) is a steady-state idealization of an American-style market economy that is guaranteed to be less wasteful than the real economy because there is no financial or monetary system with banks and stock exchanges and so on, and there is no government and military sector. However, even the idealization of an American-style market economy is certain to be more wasteful than any real economy in which every single person receives exactly the same share of the national economic dividend regardless of what he does or doesn’t do. Although there is the cost of buying and selling and there is a middleman from the commercial sector interposed between consumers and the sectors and between sectors, no one can become richer by means of the market. Therefore, the savings indicated for a move from BC to the No-Managers Case (NM) are certain to occur in real life and they will probably exceed the savings indicated by the model.
The situation is the same for moves from NM to the No-Commerce Case (NC) and from NC to the No-Commerce-No-Managers Case (NCNM). Let us characterize the worst-case scenario for each case with an asterisk and the best-case idealization with an unembellished symbol since the cases in the model are the best-case idealizations. Then, the order of energy consumption from greater to less for identical standards of living for workers whether on active duty or furloughed is as follows: EBC* > EBC > ENM* > ENM > ENC* > ENC > ENCNM* > ENCNM or, more likely, ENCNM* = ENCNM. Since the reader is aware of the vital nature of our need to reduce our energy budget in the wake of Peak Oil, the purpose of the exercise should now be abundantly clear, however see the list of four educational goals in To the Reader below.
Speaking of things that I have had “no need to say”, when I say No Managers, I do not mean that no one will manage. I mean that managers will be paid the same as other workers; and, since the worker is the manager’s client, the workers ought to select their managers from among themselves. The comic strip Dilbert reminds me that managers who are not competent workers are generally incompetent managers as well.
Since the macros are re-written frequently, it would not be a bad idea to learn their names so that you can click on the Tools Menu, click on Macros, click on Macros on the macro list, and find what keys to press for each macro. See the tables of macro names and what each one does in the new Appendix A. In the meantime, follow my instructions in the experiments but look up each macro in Excel’s drop down menu before you use it. Before long, you should become familiar with my style in naming macros with Init standing for initialize, Iter standing for iteration, etc.
In http://dematerialism.net/Mark-II-Economy.xls the fractions retained for salaries is the same for every sector; therefore, only the commercial equation is used to find the one fraction, and the other equations that balance salaries with expenses can be used to compute the fraction of the population attached to that sector. The fraction of the population supported by commerce makes the sum of the fractions equal to 1.0. In the Base Case, I have found the set of δij and ηi that match the cash fractions spent by consumers on the four commodities and the energy fractions consumed by the four sectors tabulated by the DOE for the United States on or about the year 2000. Also, I have chosen the factor by which the consumption of residential units and manufacturing units for managers exceeds that of workers to match the income distribution in the United States between the upper 10% and the lower 90%.
The Mark II Economy provides a computational laboratory in which the energy analyst can perform experiments on a simplified economy that replicates many of the important features of a real economy. The Mark II Economy is simple but not very simple. The governing equations are troublesome enough that mathematical analysis might be replaced by numerical experiments in most instances. Also, numerical simulation is a useful tool to verify conclusions reached analytically. When you download the spreadsheet, be sure to Enable Macros. They are needed to follow this discussion, and they are safe. If you are unable to do this, lower the security level under Security under Macros on the Tools menu in MS Excel.
The Mark-II-Economy achieves four important goals:
1. To show how energy is related to money. One may estimate the increase in the total energy budget (E) associated with a diversified monetary investment by multiplying the capital, operating, and other costs of the investment by the E/GDP ratio. See Experiment 1.
2. To eliminate the confusion regarding the ratio (EROI) of energy returned (ER) to energy invested (EI), five separate EROIs were defined depending upon what was included in the EI term. The quantity EIo includes only the direct energy costs of providing the net energy to the economy; EI1 includes the indirect expenses but not those incurred by commerce; EI2 includes, in addition, the energy costs of commerce; EI3 includes, in addition, the energy costs of paying the managers in the energy sector more than the workers are paid; ER4 includes, in addition, the rest of the energy expenses of workers and managers in the energy sector and the pro-rata shares of the energy expenses of the workers and managers in other sectors insofar as they support the energy sector. EROIo is independent of political economy as the standard of living of the workers remains constant when the political economy changes.
3. To illustrate the effect of lowering the EROI due to substituting a less efficient technology for the technology that preceded it chronologically. One sees the total energy budget, E, approaching infinity as EROI diminishes toward 1.0. In this paper, I have defined Energy Returned to be the total energy extracted or produced. This is the sum of the energy delivered and the energy invested. An alternative definition counts only the energy delivered. This has the advantage that it is easily computed in practice. For example, if a Concentrated Solar Power (CSP) installation is rated at 500 MW with an operating factor of 0.3 and a plant life of 30 years, ER = 500 MW · 0.000001 TW/MW · 0.3 · 30 years = 0.012 terawatt-years = 39 billion kilowatt-hours. If the alternative definition is used, each of EROIs is reduced by exactly 1.0 and the total energy budget approaches infinity as EROI-1 approaches zero. This result is illustrated graphically in Chart 2 on each of the two spreadsheets http://dematerialism.net/Mark-II-Economy.xls and http://dematerialism.net/Mark-II-Economy-CSP.xls.
4. To examine the changes in total energy budget, EROI, and the amount of work performed in each sector to maintain a constant standard of living when an American-style market economy (Base Case) changes to a market economy where everyone is paid the same (No-Managers Case), that changes to a planned economy with a commissar class that earns what managers earned in the Base Case (No-Commerce Case), that changes to a planned economy (or, better yet, a give-away economy) where everyone is paid the same (No-Commerce-No-Managers Case). This result is illustrated graphically in Chart 1 on each of the two spreadsheets http://dematerialism.net/Mark-II-Economy.xls and http://dematerialism.net/Mark-II-Economy-CSP.xls.
In a Mark II Economy, every converged solution balances the Total Energy Budget (E) with the Energy Invested (EI) under the broadest interpretation of EI (see the first note below); therefore, I have not attempted to model feasibility by computing an energy budget that is less than the energy produced by whatever alternative energy technology is under investigation. However, impracticality occurs at a higher ER/EI than does strict infeasibility.
Note. Permit me to define two, perhaps new, meanings of the words "profane" and "transcendent". Let us consider an act of man profane if its purpose is to provide for life the energy that supports life all of which comes ultimately from Nature, e. g., agriculture. Let us consider an act of man transcendent if its purpose can be said to be to build a monument to God whether God exists or not, e. g., art. Let us consider all other acts of man to be "frivolous". Then, one can choose to place the energy costs, EP, of all profane acts in the Energy Invested (EI). One can include the energy costs, ET, of transcendent activity in EI if the transcendent be considered necessary to the profane. One can include the energy costs, EF, of frivolous activity provided we associate an efficiency to EI equal to [EP + ET]/[ EP + ET + EF] at which point we have arrived at the balance equation approach to feasibility because the ER/EI will be exactly 1.0 for a real society running on the energy technology under investigation.
Note. We all know that energy is conserved according to the First Law of Thermodynamics and may be defined to be that which is represented by any of the additive terms in the First Law of Thermodynamics expressed as a balance equation. By looking at the Combined First and Second Laws, we understand that by energy consumed what we really mean is change in Helmholtz or Gibbs (depending upon context) availability, i.e., energy corrected for entropy. Thus, in the sequel, I shall continue to use the popular term “energy” when I mean “availability”.
Note. The difference between the Gibbs availability of the reactants and the Gibbs availability of the reaction products associated with the combustion of a primary fuel is often referred to as ‘exergy’. Exergy is the total quantity of reversible work that can be obtained by burning the fuel and bringing the products of combustion into equilibrium with the environment. It represents an upper bound on the amount of work of any description that can be performed by consuming that fuel. The reversible work that can be performed by the combustion of methane is computed here.
On both of the spreadsheets, it is important to change parameters gradually to stay within the domain of convergence of Newton’s method if you plan to do experiments on the spreadsheet that take you away from a converged solution. If you are not within the domain of convergence, the computation can diverge and destroy the spreadsheet. That’s why it’s important to save frequently after successes and exit without saving when the computation blows up. For example, suppose you want to reduce the ER/EI as far as you can: Change the factor by which δEE is multiplied by one unit at a time. (δEE is the number of energy units that must be spent by the energy sector to deliver one energy unit to the economy.) Go from 1.0 to 2.0 not 1.0 to 9.0. (This represents a sort of artificial homotopy – just the sort of thing my doctoral thesis was all about. As it turns out, topological degree is invariant under homotopy, which is why a new solution is guaranteed to be found so long as the variables continue to be defined on your computer. See Wayburn, T. L. and J. D. Seader, "Homotopy Continuation Methods for Computer-Aided Process Design," Computers and Chemical Engineering, 11, No.1 (1987).
Convergence on Mark-II-Economy.xls is obtained with <CS>O for all the cases. On Mark-II-Economy-CSP.xls, use <CS>O for the Base Case and <CS>Z for the other cases. It is extremely important to be on Sheet 1 when you take a Newton step. Moreover, the results can be unfortunate if you press the wrong button. Use the macros carefully and save often after your successes. I regret that these spreadsheets are not foolproof.
Please return to http://dematerialism.net/Mark-II-Economy.html.
Thomas L Wayburn
Houston, Texas
October 15, 2006