The Kaya Identity, as posted earlier on SLB, is back for another round. see link. Apparently, even more bloggers are weighing in, with Dr. Roy Spencer posting his take on his blog, and WattsUpWithThat also having more. Dr. Spencer, for those who may not
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| Oil Refinery source: Wikipedia commons |
In my earlier post, I wrote that the units on both sides do indeed cancel, and in this post I will demonstrate that even when the same variable appears on each side, an equation is quite useful. The blog-blather seems to be that, if the equation reduces to CO2 = CO2, then it is useless (where CO2 is in tons per year).
Background
A bit of background, first. In a somewhat analogous situation to the current climate scare, in which the entire Earth is said by alarmists to overheat because man's activities emit carbon dioxide, CO2, into the atmosphere, we had an actual energy disruption in the early 1980s. This was no vague, arm-waving exercise by some data-manipulating maniacs, this was hard, cold fact of oil price increase. I was a small part of that back then. But, owing to my recent graduation from college and being early in my engineering career, I did not participate in developing our version of the Kaya Identity, nor in policy discussions on which aspects were to be pursued. I was, however, on the front line for our private-sector company (multiple oil refineries, gas processing plants, an ethylene plant, various petrochemical plants) and obtaining the desired results in the most profitable manner.
Thirty-five years ago, in 1979, the oil cartel OPEC increased the price of oil dramatically, to $36 per barrel, more than double the price only a few months earlier. One of the results, in the US, was a government mandate to reduce energy consumption in the process industries, I believe the target was 25 percent.
The Equations
The equation that (perhaps) was used back then, very similar to the Kaya Identity, was
1) Eg = P x T/P x Ec/T x Eg/Ec
Where
Eg = Energy, trillion Btu/y, e.g. gross energy consumed
P = Process plants, a number
T = Throughput per process plant, tons per year
Ec = Energy consumed in the process plant, trillion Btu/y
Note the similarity to the Kaya Identity, equation 2:
2) CO2 = P x GDP/P x E/GDP x CO2/E
Each equation 1) and 2) has four terms on the right hand side, the numerator of the fourth term is identical to the left hand side, and all the other units cancel out on the right hand side (P / P, GDP / GDP, E / E all cancel.)
Therefore, if the Kaya Identity naysayers are correct, then equation 1) should also be useless. After all, in equation 1), the cancelled units on the right hand side are (P / P, T / T, and Ec / Ec), leaving Eg = Eg
Yet, equation 1) was indeed useful.
The Usefulness
To accomplish the energy reduction, which at the time was deemed not only necessary but crucial to US economic survival, there were quite a number of things that could be done. Each will be discussed in turn.
First, variable P, the number of plants, could be reduced by 25 percent. That single act would have reduced gross energy. That path was indeed partly pursued, as a number of inefficient, smaller plants were shut down. The result was not 25 percent reduction, though, in Eg.
Second, the throughput per plant, T/P, could be reduced by 25 percent. That also, alone, would have reduced Eg. However, the US needed the products from those plants. Instead, throughput per plant was increased, to make up for the plants previously shutdown. It is true that a recession also occurred, so overall demand was somewhat less than it had been previously. This was especially true in some industries, such as oil refining. Drivers suddenly found ways to cut their gasoline consumption, by driving less or carpooling, for example. It was found that Eg was reduced, also because the remaining plants were somewhat more efficient in energy use per ton of throughput.
Third, the energy consumed per ton of throughput at each plant could be reduced. This is the third term in equation 1), Ec/T. This area generated the most interest and activity among the process engineers, our supervisors and managers, the group of which I was a part. As good process engineers, we developed more than 40 different items, or process changes, that could be implemented with a reduced energy consumption. I won't detail the entire list here, but will provide a few as examples.
A brief note about how Ec differs from Eg in the above equation 1). Ec is the energy consumed in the process, not including certain inefficiencies or wasted energy such as the hot gas exiting the smokestack on a fired heater. Examples of Ec include electrical power required to run motors, steam required to run steam turbines, heat absorbed in the reboiler of a distillation column, etc. In contrast, Eg includes all the inefficiencies, such as the gross fuel burned in a boiler, which includes the heat loss out the smokestack.
Examples of process changes that can (and do) reduce Ec, energy consumed, included but were not limited to:
a) replacing steam turbines with electric motors as drivers on pumps and compressors, and gas-driven compressors with electric motor-drives.
b) installing new heat exchangers with increased surface area to increase the inlet temperature of streams heated in a fired heater.
c) installing different catalysts that operate at a lower temperature, thus requiring a lower temperature exiting a fired heater
d) installing different catalysts that provide better yields, thus requiring less feed to a process to obtain the same output
e) installing improved process units that consume less energy intrinsically (e.g. low-pressure catalytic reforming in oil refineries, compared to high-pressure units)
f) improve process control to reduce reflux and reboil on distillation columns where over-reboiling was the normal practice
g) add more trays to distillation columns, to reduce reflux and reboil requirements, similarly, more efficient packing could be installed in packed columns
h) use waste process heat (e.g. medium temperature streams) to preheat boiler feedwater, or generate low-pressure steam
i) recover more steam condensate and return it to the boiler
j) install better insulation, also electric heat tracing instead of steam heat tracing
k) install bottoms-to-feed heat exchangers on distillation columns
l) run process unit intermediate streams hot from upstream to downstream units
m) purchase less energy-intensive feed, e.g. light crude oil instead of heavier crude oil
n) reduce waste and consequent reprocessing of off-spec product
o) install variable-speed motors on large motors
p) install cogeneration utilities, especially combined cycle gas turbine plants.
There are many, many more items on the list of process changes that reduce Ec. We evaluated them all, and implemented those that met our criteria for return on investment.
Fourth and finally, the gross energy per unit of energy consumed could be reduced, Eg/Ec. This involved increasing the efficiency of fired heaters, among other things. For example, a furnace that operated initially at 85 percent efficiency and consumed 300 million Btu per hour (a common, ordinary furnace in a refinery), wasted fifteen percent or 45 million Btu per hour out the smokestack as hot flue gases. By careful engineering, the furnace could be improved to 90 or perhaps 92 percent efficiency, corresponding to approximately 280 million Btu per hour of fuel consumed. The savings was 300 minus 280, or 20 million Btu per hour. This was approximately 7 percent savings. The same could be done in a boiler, and other furnaces across the refinery or chemical plant.
Details of all these process improvements are not given here, but will be familiar to the process engineers. Many of us lived this, we designed the improvements, supervised the installation, started up the new systems, and documented the energy reductions.
All in, the process industries exceeded the target, as I recall we accomplished approximately 27 percent reduction.
The equation 1) , which does reduce in mathematical terms to Eg = Eg, after cancelling out the various terms on the right hand side, was quite useful. We made use of each and every term, to a greater or lesser extent.
Perhaps those who stoutly insist that the Kaya Identity is useless because it, too, reduces to CO2 = CO2, are unaware of the energy crisis of 1979 and the subsequent events in the US. Perhaps knowing this now, they will pause and reconsider. One can ask any of us who were engineers at the time, between about 1980 and 1985. We lived it.
Roger E. Sowell, Esq.
Marina del Rey, California
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