Oil Remains Abundant

Probably a key point of the energy decline movement has been the idea of “peak oil”. The theory has been that oil and gas would imminently decline, leading to catastrophic consequences for civilization, such as collapse. Although this group has a number of different theories (declining net energy, declining EROI, and so on), the primary and central theory of the group has been peak oil. Indeed the energy decline movement (the subject of this blog) was often referred to as the “peak oilers” by the press back in 2008 when the group had publicity. As a result I will discuss the peak oil theory specifically in this post.

As always, I think the theories of this group are quite wrong, including the peak oil theory. To be sure, oil will peak and decline someday, but that will be caused by high oil prices and a switch to alternatives. We will never “run out” of oil, and its decline will have only modest and barely-noticed effects on society. There are clear substitutes for all usages of oil, and the economy will transition when the time is right. Peak oil will be caused by not needing it as much anymore, not by depletion.

Not only do I think the group is wrong about the cause and consequences of peak oil, but I also think the group is wrong in their estimates of how much oil remains and the timing of peak oil. The group has often portrayed peak oil as imminent because of depletion, but that is simply not correct, in my opnion. Even if there is only a very gradual switch to alternatives (EVs), oil supplies are adequate for decades. We do not face any kind of energy shortage during the next 50 years, even if the transition to EVs is very gradual.

In this post I will develop a very simple mathematical model of oil supplies and depletion. I will show that oil supplies are adequate for the next 50 years or so. I should mention that I have no training whatsoever in petroleum engineering or geology. I’m a math/econ sort of guy. However, I’ve noticed that most members of this group (even the thought leaders) have no training in the field either. So it seems fair (to me) to construct an extremely simple model as an amateur, based on very basic math. I will use only a few key facts and very simple math to develop the outline of a basic model.

The Model

The first fact to understand is that oil extraction is a process that currently takes many years and has many stages. First, there are petroleum geologists who scour the earth looking for new oil deposits which haven’t been found yet. After which, there is a planning and engineering effort which can last for many years before any oil comes out of the ground in a particular project. At any time, there is a PIPELINE of oil development projects, at various stages of completion. Old oil wells are continuously depleting and being replaced with newer ones. The oil companies manage of pipeline of projects years in advance so new oil wells will come online as old ones deplete.

At any time, there is a useful figure called the “reserves to production ratio” (henceforth R/P ratio) whcih measures how much oil we have in reserves compared to present usage. Right now, the R/P ratio is about 55, which means that we would have 55 years of oil remaining even if the pipeline discussed above stopped totally and immediately, and no new discoveries were made. Of course, problems would emerge long before the 55 years were up. At some point before the 55 years that we ran out, drilling of new wells could not keep pace with depletion of old ones, and oil production would plummet, probably near the end of the 55 year period.

It is important to understand that oil production for the world will not follow a Hubbert curve. Individual oil fields may well follow a Hubbert curve, but the world will not. This is because any decline in global oil production increases prices, which causes more furious drilling or other technologies which drive the production of oil back up. For example, an individual oil field may undergo depletion, but operators can then use technologies such as steam injection (injecting steam into the well) which drives production back up. As a result, any tiny decline in global oil production will cause increased prices and increased production, preventing any further decline. The eventual decline in conventional global oil production would happen drastically, at the end of the oil era, when no amount of furious drilling or steam injection could overcome the rapid depletion. 

We mentioned before, that we would have 55 years of oil remaining if we stopped all discovery right now, and didn’t develop any unconventional oil reserves. Probably, oil production would continue as normal for 35 years or so then would suddenly plumment to zero during the last 20 years. Furious drilling of existing reserves and techniques such as steam injection would initially prevent a decline in production. However, depletion of existing wells would grow worse and worse over time, until any amount of drilling or technology could not arrest the decline, leading to a sudden plummet at the end.

Thus, at present, we face 35 years or so of steadily increasing prices and then sudden crisis. This assumes all discovery ceases right now and no unconventional oil is ever used.

Of course, we have more time than that. Discovery and development of unconventional resources are ongoing. It is not possible that discovery would suddenly and totally cease, that we would fail to develop any unconventional oil, and so on. Discoveries and development of unconventional resources have been keeping pace with depletion for years. The R/P ratio has remained basically unchanged at higher than 50 since 2010 (https://www.statista.com/statistics/682098/oil-reserves-to-production-ratio-worldwide/). The R/P ratio is the result of exploration and technological advancement by tens of thousands of people in different areas, many years in advance. It’s a statistical phenomenon which follows a smooth curve. It will start declining some day, but it will follow a smooth curve and will not have any kind of sudden discontinuity. As a result, the 55 year figure is a big underestimate of how much oil could ultimately be extracted.

Here we can begin sketching out the basic parts of a model. Oil is being extracted and thereby depleted. This reduces the R/P ratio over time. On the other hand, there is a pipeline of upstream projects, new discoveries, and development of unconventional oil reserves, all of which increases the R/P ratio over time. These two factors are in competition with each other. Production decreases the R/P ratio and discovery and unconventional development increase the R/P ratio.

There is a third factor which needs to be taken into account. At present there is a a transition to electric vehicles underway. At present, 18% of new car sales worldwide are EVs. Electric trucks (the tesla semi and others) are starting to come online also. Any construction of EV factories or deployment of EVs pushes to date of oil depletion back into the future and increases the R/P ratio. It represents oil not burned now. If discoveries kept up the pace they have been doing for the last 13 years, but EVs became more widespread, then discoveries would stay constant but depletion would slow down, leading to an increase in the R/P ratio.

Thus, we have three factors tugging at the R/P ratio: 1) depletion, 2) discovery and unconventional development, and 3) EV adoption. The question is: which factor is winning? What will happen over the next 50 years?

Let’s make some pessimistic assumptions and see the results. Let’s assume that EV adoption is very gradual, much slower than it has been in the last few years, and it takes a full 50 years for half of vehicles on the road to become EVs (here the word “vehicle” is an abstraction which includes cars and trucks in proportion to their fuel usage. For example, a class 8 truck might count as 8 “vehicles” because it burns so much more fuel). At the same time, all oil discovery slows down drastically, starting now, and only little unconventional oil could ever be extracted, so the additions to oil reserves decline to 0 over the next 50 years. These are highly pessimistic assumptions. What would be the result?

The result is that the R/P ratio 50 years from now would be 85, which is much higher than today. We start with 34*55 years of oil, which is 1.87 trillion barrels. However, discoveries and development of unconventional oil declines linearly to zero over 50 years, which implies we gain an additional 0.85 trillion barrels (34*50*.5) during that time, so we have a total of 2.72 trillion barrels to use over the next 50 years. At the same time, EV penetration increases linearly to 50%, gradually, so the total amount of oil burned over the next 50 years is only 75% of what was initially expected (34*.75*50). As a result, we burn 1.275 trillion barrels out of 2.72, so are left with 1.445 trillion at the end. Oil consumption is half at that point (EVs constitute 50% of all vehicles then). The end result is an R/P ratio of 85 (1445/(34*0.5)).

Thus, using very pessimistic assumptions, the R/P ratio INCREASES over time, and the date of exhaustion gets further away. Of course, the R/P ratio won’t really increase to 85 because oil companies will curtail discoveries and curtail development of unconventional resources. Oil companies keep the R/P ratio at 55 as a kind of inventory management, so they will curtail upstream development if it gets too high. Incidentally, the curtailment of discoveries and upstream production has already happened at oil companies, which implies that the date of exhaustion is getting further away.

I pointed out earlier than we cannot just keep production constant until we suddenly run out. Near the end of the oil era, oil production would suddenly plummet despite furious drilling. Here I will define an R/P of 15 as an oil crisis where oil is imminently plummeting and we must rush to convert vehicles and car factories to EVs. 

Using any kind of assumptions, it is very difficult to reach an oil crisis (R/P of 15) over the next 50 years.

Let’s try making drastically pessimistic assumptions. Assume it takes 100 years to reach an EV penetration of 50%. Furthermore, all new oil discoveries and all unconventional development drops linearly to zero over only 40 years (not 50). The result is an R/P ratio of 43.4, fully 50 years from now. Such an R/P ratio is still higher than it was in the 1990s. Even using drastically pessimistic assumptions, oil production is quite adequate 50 years from now, and reserves are quite adequate.

Of course, this has not taken into account the billions of people in China, India, and southeast Asia who wish to start driving and join the middle class, as well as population growth in the developing world. However, those areas are far more densely populated than the USA (which consumes almost 25% of all oil by itself). People there are much more likely to follow the model of Japan in terms of oil consumption, and even that will take many decades. As a result, global oil production has been growing fairly gradually for decades and is only 33% higher than 30 years ago. This factor is obviously greatly outweighed by EV adoption and would not change the above analysis by much.

Conclusion

It does not appear that an oil crisis is imminent. No plausible mathematical analysis yields an imminent oil crisis. At least for the next 50 years, and probably much longer, oil supplies are adequate to meet demand.

I saw a video from Nate Hagens recently showing an imminent drastic drop-off of oil production in the near future. That video made two mistakes, in my opinion. First, it assumed that we are already halfway through our total oil endowment, which is incorrect. Second, it did not mention or take into account EV adoption which is already underway, is growing exponentially, and which pushes out of the date of depletion into the future. When these two factors are included in a basic mathematical model, we see that there is no imminent oil crisis.

So far, I’ve offered some scenarios which stretch 50 years into the future. I don’t like to predict further than 50 years into the future, or even that far, because technological developments occur which render such predictions useless. For example, almost nobody foresaw, 8 years ago, that the biggest car company by far would be an EV company, that EV sales would be increasing at a rate of about 20% per year, and so on. There have repeatedly been technological developments which start out quite small, but which totally change the long-term trajectory. Thus any long-term projection I would have made would have been FAR too pessimistic because of technological developments. The peak oil movement in particular has frequently been very wrong even 5 years out. As a result, the 50 year estimates indicated above are almost certainly far too pessimistic because they ignore technological developments which are disruptive and which could change the picture completely (for the better) over the next 50 years. This makes it even less likely that we face any kind of oil crisis.

Finally, all of this is assuming relatively stable geopolitical conditions. It is always possible there will be a nuclear war because of Ukraine or something similar. I have no way of predicting that, or even calculating its probability. However, we do not face any kind of imminent disruption because of oil depletion, no matter what assumptions are made. Fifty years from now, R/P ratios are likely to be similar to what they are now.

One final thing. Oil is by far the scarcest substance in the world that we use, relative to demand. Nothing else is so concentrated in a single geographical area, so widespread in its usage, and so difficult to substitute. Yet even oil shortages pose no serious problem for the next 50 years. Shortages of other things (like coal and minerals) are MUCH FURTHER AWAY than shortages of oil. Since we don’t face any crisis of oil, we don’t face any crisis of anything else we dig out of the ground either.

There is no energy crisis

In this post, I will show that we don't face an imminent energy crisis. The idea of an imminent energy crisis is badly wrong for several different reasons, as I'll show below.

By "energy crisis" I mean running out of energy or some kind of permanent downslope. I am not referring to global warming here, which is a separate issue.

Coal becomes more abundant over time

I pointed out, in an earlier article, that Hubbert curves would never have worked for global oil. This is because the extraction of oil and its growth were curtailed, which renders Hubbert curves invalid from that point on. Hubbert curves require constant drilling effort in order to work. However, the Middle Eastern countries curtailed their oil output, starting in the 1970s, in order to increase prices. From that point forward, Hubbert curves would understate the amount of oil remaining in those countries. Curtailment leads to an imminent peak in extraction, but it pushes the date of exhaustion further into the future. For this reason, Hubbert curves have not worked for Middle Eastern countries.

The situation with coal is similar, but even more so. Coal production in the USA has been curtailed since 1918. As a result, Hubbert curves will drastically underestimate the amount of coal remaining there. This is probably the reason for the vast discrepancy between the USGS estimates of coal and Hubbert curve estimates of the same resource. Hubbert curves will not work in this case, and the USGS estimate is probably right.

In addition to that, the USA has started curtailing coal production even more severely, starting in 2008. This is because of renewables, and also because fracking drove down the price of gas, leading to a shift towards gas for electricity generation. This decline in coal production pushes out the curve of remaining coal far into the future. The area under the curve remains the same, but the curve is much flatter and wider.

Here in the USA, we had more than 270 years of coal remaining, as of 2008, according to the USGS estimates (Hubbert curves will not work in this case and would drastically underestimate the amount). However, the amount of coal produced per year declined by 38% between 2008 and 2016, because of declining demand.  Thus, the amount of coal remaining 8 years later, at the new lower rate, was not 270 years, but 424 years. Thus we “gained” an additional 154 years of coal in an 8 year period. The decline in demand flattens the curve of remaining resources and pushes it far out into the future.

As a result, we started off (in 2008) a long way from an energy crisis, and we are going further away from an energy crisis quickly.

We began the transition to renewables long before coal reached a geological peak. This totally changes the long-term trajectory of coal extraction. Even a gradual 0.5% linear transition to renewables, begun long in advance, will totally change the long-term trajectory. It's like a ship crossing the Pacific Ocean, which diverts its course by one degree at the beginning of the trip. That small diversion at the beginning results in a massive change in where the ship ends up at the end. Even a 0.5% sustained annual conversion to renewables, begun this early, implies that the energy crisis is getting further away over time, and the date for exhaustion of coal is receding into the future. A 0.5% linear transition to renewables implies that we gain more than 1 year of coal usage for every year that passes (435*0.005-1 = 1.175). Since we are converting the energy system to renewables at a much faster rate than 0.5% per year, we are getting much further away from an energy crisis over time. The possibility of an energy crisis -- always remote -- has now passed, and stands no realistic chance of ever occurring.

There are also "unconventional" coal resources such as underground seams which could be mined using underground gasification. Even if we did nothing to transition to renewables for centuries, it is entirely possible that those unconventional coal resources would then be extracted, just as horizontal fracking was developed and used when necessary. Thus, the estimate of 435 years, indicated above, could be a massive underestimate even if there were no transition to renewables.

Renewables could replace coal very quickly

Not only is coal super-abundant, but we could transition to renewables quickly at any time.

I pointed out in a subsequent article that renewables have a very short doubling time and can grow exponentially and very quickly. Any country could transition entirely to renewables in less than 40 years, using any plausible estimate of EROI and energy payback time, by diverting only a very small amount of its net energy now. As a result, the United States has vastly more time than required to transition to renewables, and is transitioning much faster than required.

As I pointed out in a previous article, the United States, and all other industrial countries, are curtailing their growth of energy and growth of renewables. This is done for several reasons. First, demand for energy in first world countries is flat. Second, we don't wish to prematurely retire our old energy generators such as gas-fired turbines, before the loan has been paid off. It would be uneconomic and more expensive. However, if we were willing to pay more money, the transition could happen faster than it is happening.

As a result, even a massive shortfall in coal resources, compared to USGS estimates, could be compensated by an increased exponential growth of renewables. It would cause an unfortunate financial loss, and higher electricity rates for consumers, but it would imply only a very temporary shortfall of energy. Even a 95% reduction in ultimately recoverable coal reserves would still cause a shortfall of less than a decade, and not a collapse of civilization.

I must also mention that technology continues advancing. The price of solar panels, for example, has dropped by 90% in just the last 15 years. The remaining coal reserves in the USA (435 years) provide a lot of time for further technological development. It is entirely plausible that electricity from solar panels and batteries will become cheaper over time than thermal energy from coal extracted from the ground. At which point, coal is practically useless anyway. And there are other technological developments which could occur in 435 years. Even fusion could be available before then.

Conclusions

Thus, the idea of an imminent energy crisis is badly wrong, in my opinion, for multiple, overlapping reasons. First, the amount of coal remaining is gigantic, leaving centuries for a transition. Second, the transition is happening far earlier than required, which pushes the end date of coal far into the future, so we are getting further away from an energy crisis over time. Third, we could transition to renewables at any time far faster than is required. Any one of those three things would imply that there is no imminent energy crisis. The United States in particular has a vast excess of energy options for at least centuries, and probably much longer.

Oil is a different matter. Oil is much scarcer than coal or gas. It’s possible to argue that we are underinvesting in upstream oil development, which will cause a shortfall in the future, leading to high oil prices. Energy in general, however, remains extremely abundant far into the future, and probably forever, until civilization ends for some other reason.

Of course, many countries have more limited energy supplies than the USA. However, several other countries have similar excessive energy reserves, such as Australia and Norway. Those countries could sell coal to other countries (such as Japan) as they transition to renewables.

A Question of Boundaries

One of the recurring questions in EROI analysis is where the boundaries should be drawn. How wide do you make the boundaries when calculating energy inputs? Do you include the roads wihch are needed to transport solar panels, for example? Should you include first world salaries of solar panel installers?

The new net energy metric I introduced in the prior article, and the ensuing discussion, can inform where the boundaries should be drawn.. When calculating a rate of exponential growth, the boundaries for net energy analysis should include the minimum energy investment to replicate an energy gathering device. Let me provide some examples.

In our scheme outlined in the prior article, energy investments would not include the entire transportation infrastructure or first world standards of living, which would happen after the exponential growth had already occurred. Energy investments would include, however, the energy investment needed to refine oil, in addition to its extraction, because refined oil products (such as diesel) are required to power the machinery to drill new oil wells.

As another example, refinery losses for oil production would count as an ongoing investment, because the refining doesn’t all need to occur at once before any oil from a well is produced. In this case, it makes no difference if the energy comes from the oil itself, or from some external source, since the effect is the same mathematically in either case. However, self-consumption of coal for underground coal gasification (for example) should simply be ignored and not countaed as an investment at all, since it never needed to be extracted in the first place, so it has no effect on replication time.

As another exmaple, the roads needed for installing solar panels would count as an energy investment, but any other transportation infrastructure would count as a return. The rest of the transportation network is not necessary for replication and could come after the exponential growth has occurred.

In this manner, the disagreements over boundaries could be narrowed considerably.

Of course, these above remarks hold only when calculating a replication time and its effect on economic growth. Another use of net energy metrics is to calculate CO2 emissions. In which case, the boundaries should be drawn differently. When calculating CO2 emissions, self-consumption of cola for underground coal gasification should be counted. Also, first-world transportation (car transportation, for example) to a solar power site should be counted. It depends upon the use to which the metric is being put.

Net energy metrics are only useful as part of a broader calculation, and the broader calculation informs where the boundaries should be drawn.

Net Energy and Economic Growth

One of the effects of net energy metrics is their effect on economic growth. A higher EROI or lower payback time would enable faster exponential growth, other things being equal. This is because a shorter energy payback time would allow more generations of exponential growth in a given span of time.

Any energy gathering device (such as a solar panel or oil well) requires an investment of energy now to obtain more energy later. In turn, the output of that energy gathering device allows us to build more such devices in the future. This re-investment over time, across generations of energy gathering devices, is what allows the growth of energy obtained and is one component of economic growth. Net energy metrics determine how much of our net energy we must sacrifice now to obtain more later, and how fast the subsequent growth can occur.

In this article I will examine the effect of net energy on economic growth. I will introduce a new net energy metric — energy replication time — which can be used to measure the effect of net energy on economic growth. I will also provide some simple mathematical examples, using the new metric, which show the effects of net energy on economic growth. At the end, I’ll describe some of the implications of this new metric.

A New Net Energy Metric

As mentioned before, the amount of net energy we obtain is a function of continued re-investment of energy in the past. This continued re-investment of energy, across generations of energy gathering devices, is part of what constitutes economic growth. In order to calculate the rate of growth, for a given sacrifice of net energy now, we must know the replication time of an energy gathering device. After we have determined the replication time, we can plug that number into standard exponential formulas.

Here we define a new net energy metric, namely Energy Replication Time, or ERT. An ERT can be defined as the upfront energy investment from net ongoing returns. Thus, ERT can be defined as follows: 

U_i / (O_r - O_i)

where U_i is an upfront energy investment, O_r is ongoing power returns, and O_i is ongoing power investments. For example, if we had solar panels with a 1 megawatt-year initial investment, and 1.1 megawatts of power returned, and 0.1 megawatts of ongoing investments, then the energy replication time is 1 year. A panel would return enough net energy in one year to build another panel like it.

It is clear that ongoing investments should simply be subtracted from ongoing returns, as above, when calculating the energy replication time. This is because the ongoing returns are diverted to "pay" the energy investment of a subsequent energy gathering device. For example, assume a hypothetical fusion reactor which fires lasers at deuterium to cause fusion. The lasers require 100MW, and the fusion yields 1,000MW. Of course, you could just run a wire from the output of the reactor back around to the input, thereby powering itself. This leaves 900MW  to "pay" the the energy investment of the next reactor. As a result, the denominator is simply the gross ongoing returns minus ongoing investments.

This new metric (ERT) is slightly different from energy payback time (EPBT). Whereas EPBT considers all energy investment (including disposal) as an upfront investment, our new metric (ERT) considers as an upfront investment only the energy needed to construct a new device and start it operating. As a result, ERT cam be plugged into standard exponential formulas whereas EPBT cannot.

Thus, we have defined a new net metric here, Energy Replication Time (ERT), which is defined as U_i / (O_r - O_i), where U_i is an upfront energy investment, O_r is ongoing power returns, and O_i is ongoing power investments. This metric can be plugged into standard exponential formulas and will determine the amount of growth which can be obtained given a sacrifice of net energy now.

A Few Simple Demonstrations

Using this new metric, we can perform some simple mathematical demonstrations. Assume we have a kind of solar panels with an energy replication time (as defined above) of 1 year. If we diverted all of our energy to building new solar panels, the number of panels would double in one year.

However, that is not exactly right. That would only be correct if the new solar panels were all stored in a dark warehouse until the end of the year, then all suddenly deployed at once. If the solar panels were deployed instantaneously, then the number of solar panels would increase faster than that. A solar panel which is manufactured at the start of the year and deployed right away would start contributing to making new solar panels immediately. The faster the panels are deployed, the faster the growth. 

The exponential base can be calculated using the following formula:

(1+1/n)^n

where n is the replication time divided by the average deployment delay. As a result, if the panels are deployed one month after their manufacture, then the number of panels would increase by a factor of ~2.61 every year (because (1+1/12)^12 = ~2.61). Of course, panels which are deployed instantaneously would increase their number by a factor of e each replication period.

For the rest of this article, I will assume that solar panels are deployed instantaneously. This is a theoretical upper bound of the rate of growth for a given replication period.

Using the formulas outlined above, we can perform some simple calculations of economic growth.

Suppose we have panels with an energy replication time of one year. We wish to increase the number of panels by a factor of 100. If we devote all the energy returned to building new panels, how long would it take to increase the number of panels by 100x? The answer is ln(100), or 4.6 years.

Of course, that estimate is theoretically possible, but wildly unrealistic, for several different reasons. No civilization would devote all of its current energy to investment, for example.

Let’s suppose a civilization diverts 1% of its net energy to building new solar panels continuously, in addition to the energy investment it was already making. In which case, how long would it take to increase the total number of panels by a factor of 100x? The answer is:

ln(100 * (100/1) )

… or 9.21 years, with an initial investment of 1%. However, this estimate is still very unrealistic. While theoretically possible, the vast majority of those new panels would be built in the final year. There would be a sudden onrush of panels in the final year until we obtained 100x as many, as per our goal, and then few would be needed for a long time. That would require building many solar panel factories which operated for less than one year then shut down. It would also require retiring all of our coal fired plants (or whatever we were using previously) in a single year, many of them prematurely. It would also probably require diverting much the workforce to installing solar panels for less than a single year, which would be very disruptive.

Instead, let's try installing new solar panels at a constant higher rate. We'll spread out the new solar panels over a period of 25 years, which is the lifetime of a solar panel, and also of a factory. In which case, the solar panels are phased in gradually.

In which case, we can divide our growth into two phases. First, we have a period of exponential growth, during which an initial investment is grown to an amount sufficient to manufacture additional panels at a new higher rate. Second, the output from those panels could power the manufacture of additional panels at a new, constant, higher rate.

Let’s try another simple mathematical example. Assume a hypothetical civilization which obtains 1GW continuously from solar panels now (drawing from batteries at night). We wish to increase our energy obtained by 100x. In which case, we must install solar panels that return 4GW continuously, each year, for 25 years (4*25=100). Furthermore, we are willing to divert only 1% of our net energy now to initiate the growth. How long of a delay is there before the 1% initial investment can be grown exponentially in order to power the solar panel factories continuously and produce new panels at the higher rate for 25 years? The answer is ln(400), or 5.99 years.

Here we have a more realistic example. We start by building new solar panel factories capable of producing panels that return 4GW continuously per year. We assume that the new factories take 7 years to construct. We then divert 1% of our net energy now to making new panels. During the first phase, the output of all the new panels is continuously re-invested to making more panels, enabling exponential growth. This intermediate phase would last 5.99 years. After which, we can manufacture new panels at a constant higher rate, of 4GW per year, leading to 100x more energy obtained after 25 years. Most of the time, the panels are manufactured and deployed a constant higher rate. 

Thus, if we wish to increase the amount of energy we obtain each year from solar panels by a factor of 100, but do so in a non-disruptive way, it would take a total of 7+5.88+25 years, or 37.88 years. It would take 7 years to build additional solar panel factories (assumed), 5.88 years of exponential growth during which the initial 1% investment is continuously re-invested, then 25 years of manufacturing panels at the higher constant rate. At the end of the 37.88 year period, our hypothetical civilization would obtain 100x as much power continuously as originally, by sacrificing 1% of its energy for 5.88 years. Presumably, we would stagger the building of solar panel factories so they would come online exactly when the panels to power them were installed.

We could also perform a basic calculation of how long it would take to replace our current energy system. Suppose we discover that we have a total of 21 years remaining of all coal, oil, gas, and uranium. We’re willing to invest only 1% of our current net energy for 5 years or less to building a replacement energy system of solar panels. No solar panels have been deployed so far, and no panel factories exist. Will we be able to replace our current energy system entirely before running out of fuel? The answer is yes, but barely. It would take 33.9 years (7+1.39+25), using the assumptions above (the term of 1.39 is how long exponential growth of 1% must continue to produce 100%/25 each year). However, during the final 25 years, the energy from fossil fuels would decline linearly to zero, so fossil fuel usage would average only half during that period, so only 12.5 years of fossil fuel usage during that period, so 20.89 years total (7+1.39+12.5) of fossil fuels would be required to replace our current energy system.

It must also be mentioned that the energy investment for disposal has been omitted here. The above calculations would only be correct if we simply abandoned old solar panels and did nothing to dispose of them. This factor is omitted because it considerably complicates the calculations above. However, it is clear that disposal is an extremely minor factor under any regime of exponential growth, because the disposal would happen 25 years after the initiation of growth (assuming solar panels or other energy gathering devices last 25 years).

Conclusions

From the above, we can draw a few preliminary conclusions.

First, the payback time of solar panels is already short enough to enable extremely rapid exponential growth. We could also undergo extremely rapid exponential growth with any other common source of energy, such as coal, gas, oil, uranium, and so on, because they all have payback times shorter than solar PV.

Second, we are curtailing the exponential growth of energy because of insufficient need. The rest of the economy does not grow anywhere near that fast. We can already grow our energy supply quickly enough for any reasonable anticipated need.

Third, the important energy replication time is for solar panels in a desert near the equator, such as the Sahara or northwest Australia. This is because the panel factories, and the panels to power them, could be located there. As a result, the exponential growth could occur there (over only a few years) and then the resulting panels could be exported elsewhere. The rapid exponential growth would occur regardless of the net energy performance elsewhere, and the export of panels would happen after the exponential growth had occurred. It is mathematically obvious that it does not matter much what the net energy performance is of the panels located elsewhere, as long as it remains above a very low level (like low single digits). Even an EROI of lower than 3 for those panels would be perfectly tolerable when considering the amount of energy generated and how quickly we could grow our energy supply.

Fourth, there is no energy crisis. Even if fossil fuels declined to zero over only a few decades, there would still be enough time to replace them with renewables.

In conclusion. We have introduced a new net energy metric in this article: Energy Replication Time (or ERT). ERT is defined as the upfront investment from net ongoing returns for any energy gathering device (such as solar panels). It was shown that the replication time of solar PV is already short enough to enable rapid exponential growth. As a result, no energy crisis will ever occur. Further improvements in net energy for solar PV (or any other energy source) would have only modest benefits.

Oil is easily substituted, and ultimately not important

One of the main claims of the energy decline movement is that oil is somehow an irreplaceable source of energy. Oil somehow has remarkable energy density or other properties which render it a special source of energy that cannot be replaced by anything else.

That point of view is badly wrong, in my opinion. Oil has many easy, obvious substitutes which cost about the same or less. Oil has obvious substitutes for all of its uses. Some of those substitutes would take several decades to implement (we can't all switch to EVs tomorrow, for example). However, all of the substitutes are easy and straightforward for an industrial economy.

In this article I will outline the substitutes for oil, for all of its uses.

Right away, I must point out that more than 60% of oil usage is for light-duty vehicles (cars and SUVs) which can be easily replaced by EVs[1]. Another 15% is used for delivery vans and heavier trucks which travel less than 300 miles per day, which can also be easily electrified. Thus, we can simply use battery-electric vehicles for more than 75% of oil usage. Thus, most of the problem has an extremely obvious solution which is already widespread.

Railroads and long-haul trucking can be electrified using overhead wires. Most of the railroad tracks in the world already have overhead wires. Similar wires could be installed over a few key highways in the United States and elsewhere, thereby placing every populated location within 300 miles of an overhead wire, and therefore within the range of battery-electric heavy trucks such as the Tesla Semi. Railroads and long-haul trucks represent another 10% of oil usage, bringing the total for electrified transport to 85% so far.

The remaining terrestrial vehicles include buses, ferries, construction equipment, agricultural machinery, and mining equipment. All of those vehicles travel back and forth to the same location throughout the day or operate in a small area continuously throughout the day. As a result, they can all use battery swapping.

Finally, ships and airplanes can use synthetic methane. Methane is the main component of natural gas. It is easy to make methane using renewable electricity, water, and the Sabatier process. This has already been done on an industrial scale for many decades and was first discovered more than a century ago. It has always been easy to make methane. This one thing by itself is an obvious substitute for all uses of oil. Vehicles like ships, trucks, and so on, can just use a compressed methane tank and their existing internal combustion engines (with slight modifications). Where I grew up, in the SF Bay Area, there have been methane-powered garbage trucks, taxis, and buses for decades.

There has always been an easy, drop-in substitute (synthetic methane) for all uses of oil. We could have switched to synthetic methane at any point. It was not price-competitive with diesel until recently, but if we were willing to pay today's higher fuel prices then we could have switched to synthetic methane at any time. Thus, the idea that oil is somehow irreplaceable is clearly not correct. The transition to synthetic methane would have been easier than the transition to EVs because existing car designs and production lines could have been used.

Thus, there are multiple, overlapping substitutes for all uses of oil. Almost all of the substitutes are a similar price or lower than oil is at present.

[1] https://www.otherlab.com/blog-posts/us-energy-flow-super-sankey