As one can see in the diagram, there are energy inputs on the left of the graph (such as the chemical potential energy in coal, natural gas, & oil as well as nuclear potential energy and solar energy potential.) In the middle of the graph are power plants as well as the four "users" of energy. At the far right of the graph is the end points, which are "Energy Services" and "Rejected Energy."
This is of course, for those of you who have studied biology, a really distorted and linear view of the world. On the left: inputs and on the right: outputs
The real world course is not linear in this sense because the "Energy Services" outputs are but inputs into finding, collecting, and moving the raw energy inputs into our power plants and transportation vehicles.
As such, what I've done is to plot the "Energy Services" that LLNL has calculated since 2000 and to compare the values that they calculate with the values of "Useful Work" that I've been calculating using data from the BP Statistical World Energy Review. In the figure, I've plotted LLNL's "Energy Services" along with this blog's definition of "Useful Work."
One thing to notice is that there are a few major jumps in the LLNL values for "Energy Services." This is likely due to uncertainty on their part on what "Energy Services" really means. The other thing to notice is that their values are roughly double the values that I calculate when both are plotted in units of [TWh]. This difference is in part due to the fact that they count 100% of the HHV energy value of the natural gas used in our homes as "Energy Services", whereas I only count 10% of the HHV energy values of the natural gas used in our homes as "Useful Work." The reason is that the natural gas that we use in our homes is used to heat objects near room temperature, and as such the useful work of the natural gas is really small (10% is likely even an over-estimate of the useful work associated with the hot water and hot air.)
The next question is: which of the two definitions ("Energy Services" or "Useful Work") is a better indicator of economic growth? To answer this question, I've plotted below the yearly rate of growth of "Energy Services", "Useful Work", and "Real GDP" between 2000 and 2012. (The second figure is just a zoom-in of the first picture that makes it easier to see most of the data.)
One can see from these figures that both "Energy Services" and "Useful Work"do a decent, but not perfect job of tracking "Real GDP." For example, to be quantitative here, the correlation coefficient between "Useful Work" and "Real GDP" is 78% between 2000 and 2012. That's pretty good (considering that this is not my real job...just something I do on the weekends.) The correlation coefficient between "Energy Services" and "Real GDP" between the same time period is only 18%. However, if one only looks at the time period in between the two "jumps" in the LLNL data, then the correlation coefficient between "Energy Services" and "Real GDP" is 71% between 2003 and 2011. During this same time period, the correlation coefficient between "Useful Work" and "Real GDP" is 85%.
The conclusions I draw from these graphs are the following:
(1) "Useful Work" is a pretty good, but not perfect indicator or economic growth. Though, the question remains: what is the cause of the slight difference between "Useful Work" and "Real GDP" ? Is it due to errors on my part in estimating useful work generation? Is it due to errors in calculating Real GDP? Or is it due to the fact that Real GDP and Useful Work are not really 100% correlated?
(2) LLNL's concept of "Energy Services" is less useful than "Useful Work" in predicting growth in "Real GDP". There are some obvious problems with the concept of "Energy Services". The main problem with LLNL's definition is that it mixes actual generation of useful work with the potential to do useful work. I've tried to avoid this problem in the definition of "Useful Work" by only counting "useful work," such as (a) the useful work required to overcome air and road friction in our vehicles, (b) the useful work required to run computers, refrigerators, air conditioners, electrolysis units, etc..., and (c) the useful work equivalent of the energy that goes into making hot water or hot air.
(3) The flow of energy is not linear. The LLNL graph hides the self-replicating nature of energy flows. The useful work generated from one process can either be wasted (i.e. used to dig a ditch and fill it back in) or the useful work can be used to make more power plants and hence grow the amount of useful work available. As such, it's important to graph how useful work generation increases or decreases over time (hence the plots above.)