The Roman Philosopher Lucius Anneaus Seneca (4 BCE-65 CE) was perhaps the first to note the universal trend that growth is slow but ruin is rapid. I call this tendency the "Seneca Effect."
Showing posts with label fossil fuels. Show all posts
Showing posts with label fossil fuels. Show all posts

Sunday, May 14, 2023

Renewables are not a cleaner caterpillar, they are a new butterfly. A Discussion with Dennis Meadows


Dennis Meadows (left in the image) and Ugo Bardi in Berlin, 2016

A few days ago, I received a message from Dennis Meadows, one of the authors of the 1972 study "The Limits to Growth," about a previous post of mine on "The Seneca Effect." I am publishing it here with his kind permission, together with my comments, and his comments on my comments. I am happy to report that after this exchange we are "99% in agreement."


I read with interest you review of the Michaux/Ahmed debate. Normally I greatly benefit from your writing. But in this case it seemed to me that your text totally avoided addressing the central point - replacing fossil fuels as an energy source with renewables will require enormous amounts of metals and other resources which we have no reasonable basis for assuming will be available. It is not true that peak oil was presented principally as a prediction. Rather critics of Hubert's original analysis misrepresented it as an effort to predict in order to ridicule it -  just as Bailey did for the Limits to Growth natural resource data from World3. I was struck that your critique of Michaux did not contain a single piece of empirical data - the strong point of his research. Rather you engaged in what I term "proof by assertion."

I am personally convinced that there is absolutely no possibility for renewables to be expanded sufficiently that they will support current levels of material consumption. I attach the text of a memo I recently wrote to other members of the Belcher group stating this belief (*). 

Best regards Dennis Meadows


Dear Dennis, 

first of all, it is always a pleasure to receive comments from you. It is not a problem to be in disagreement on some subjects -- the world would be boring if we all were! Besides, I think our disagreement is not so large once we understand certain assumptions. 

Let me start by saying that I fully agree with your statement that "there is absolutely no possibility for renewables to be expanded sufficiently that they will support current levels of material consumption." Not only is it impossible, but even if it were, we would not want that!

So, what do we disagree about? It is about the direction to take.  The fork in the path leads in two different directions depending on the efficiency of renewable technologies: Path 1): renewables are useless, and Path 2): renewables are just what we need

I strongly argue for Path 2) in the sense that we definitely do NOT need to "support current levels of material consumption" to create a sustainable and reasonably prosperous society. But let me explain what I mean by that.  

First, in my opinion, the problem with Michaux's report is that it underestimates the efficiency of renewable technologies. He says that renewables are not really renewable, just "replaceable." He, like others who use this term, means that the plants that we are now building will not be replaceable once fossil fuels are gone. In this case, creating a renewable infrastructure will be a waste of resources and energy (Path 1). 

This view may have been correct until a few years ago, but it is now obsolete. The recent scientific literature on the subject indicates that the efficiency of renewable technologies (expressed in terms of EROI, energy return on energy invested) is now significantly better than that of fossil fuels. Furthermore, it is large enough that the materials used can be recycled using renewable energy. There is a vast literature on this subject. On the specific question of the EROI, I suggest to you this paper by Murphy et al. You can also find an extensive bibliography of the field in our recent paper,  "On the history and future of 100% renewable research." 

Of course, not everything is easy to recycle, and a future renewable infrastructure will have to avoid the use of rare metals (such as platinum for fuel cells) or metals that are not rare, but not abundant enough for the task (such as copper, that will have to be largely replaced by aluminum). That is possible: the current generation of wind and PV plants is mostly based on abundant and recyclable materials. Doing even better is part of the natural evolution of technology. What we can't recycle, we won't use. 

There is a much more fundamental point in this discussion. It is the very concept that we need renewables to be able to "replace fossil fuels," in the sense of matching in quantitative terms the energy produced today (in some views, even exceeding it in order to "keep the economy growing"). This is impossible, as we all agree. The point is that renewables will greatly reduce the need for energy and materials to keep a complex civilization working. If you think, for instance, of how inefficient and wasteful our fossil-based transportation system is, you see that by switching to electric transportation and shared vehicles, we can have the same services for a much smaller consumption of resources. This concept has been expressed by Tony Seba in a form that I interpret as, "Renewables are not a cleaner caterpillar-- they are a new butterfly"

That doesn't mean that the geological limits of the transition aren't to be taken into account; the butterfly cannot fly higher than a certain height. Then, it may well be that we won't be able to move to renewables fast enough to avoid a societal, or even ecosystemic, crash. On this point, please take a look at a paper that I co-authored, where we used the term "the sower's strategy" to indicate that the transition is possible, but it will need hard work, as the peasants of old knew. But staying with fossil fuels is leading us to disaster (as you correctly say in the document for the Balaton group) while moving to nuclear fission simply means exchanging a fossil fuel (hydrocarbons) for another fossil fuel (uranium). Going renewables is a fighting chance, but I believe it is the only chance we have.   

There is an even more fundamental point that goes beyond a certain technology being more efficient than another. Going renewables, as Nafeez Ahmed correctly points out, is a switch from a predatory economy to a bioeconomy.  Our industrial sphere should imitate the biosphere that has been using minerals from the Earth's crust on land for the past 350 million years (at least) and never ran out of anything. As I said elsewhere, we need to do what the biosphere does, that is:

1. Use only minerals that are abundant.
2. Use them sparingly and efficiently.
3. Recycle ferociously. 

If we can do that, we have a unique opportunity in the history of humankind. It means we can build a society that does not destroy everything in order to satisfy human greed. Can we do it? As always, reality will be the ultimate judge. 


The answer from Dennis Meadows


Thank you for sending me your article. I agree that the main difference of opinion lies in the direction to take. I am reminded of the defining characteristic of professors - two people who agree on 99% and spend all their time focusing on and debating the other one percent. Because I largely agree with you, my only relevant comment on what you say is that you have overly limited our options: 

So, what do we disagree about? It is about the direction to take.  The fork in the path leads in two different directions depending on the efficiency of renewable technologies: Path 1): renewables are useless, and Path 2): renewables are just what we need

I would not choose either path; rather I believe it is time to quit focusing on fossil energy scarcity as a source of our problems and start concentrating on fragility. The debate -renewables versus fossil - is a distraction from considering the important options for increasing the resilience of society.

Dennis Meadows


A minor point. You say, "It is not true that peak oil was presented principally as a prediction." I beg to differ. I have been a member of ASPO (the Association for the Study of Peak Oil) almost from inception and part of its scientific committee as long as the association existed. And I can say that one of the problems of the approach of peak oilers was a certain obsession with the date of the peak. That doesn't disqualify a group of people whom I still think included some of the best minds on this planet during that period. The problem was that few of them were experts in modeling, and models are like weapons: you need to know the rules before you try to use them. By the way, you and your colleagues didn't make this mistake in your "Limits to Growth" in 1972; correctly, you were always careful of presenting a fan of scenarios, not a prediction. Later on, Bailey and his ilk accused you of having done what you didn't do: "wrong predictions." But that was politics, another story. 


(*) Statements about being realistic about technology, alternative energy, and sustainability
Dennis Meadows

April 11, 2023 message to the Balaton Group

Dear Colleagues,

I have often described politics as the art of choosing which of several impossible outcomes you most prefer. It is important to envision good outcomes. It may be useful to strive for them. But it is important to be realistic. The recent discussion about technology, alternative energy, and sustainability are based on several implicit assumptions, which I believe are unrealistic. At the risk of being an old grump, and recognizing my own limited vision, I list here some statements that I believe from the study of science, history, and human nature to be realistic.

#1: There is no possibility that the so-called renewable energy sources will permit the elimination of fossil fuels and sustain current levels of economic activity and material well- being. The scramble for access to declining energy sources is likely to produce violence. 

#2: The planet will not sustain anywhere close to 9 billion people at living standards close to their aspirations (or our views about what is fair).

#3: Sustainable development is about how you travel, not where you are going.

#4: The privileged will not willingly sacrifice their own advantages to reduce the gap between the rich and the poor (witness the US.) They will lose their advantages, but unwillingly.

#5: The rapidly approaching climate chaos will erode society's capacity for constructive action before it prompts it.

#6: Expansion and efficiency are taken as unquestioned goals for society. They need to be replaced by sufficiency and resilience.

#7: History does not unfold in a smooth, linear, gradual process. Big, drastic discontinuities lie ahead - soon. 

#8: When a group of people believe they must choose between options that offer more order or those affording greater liberty, they will always opt for order. 

Unfortunately so, since it will have grave implications for the evolution of society’s governance systems. Dictators will always promise less chaos than Democrats.

Monday, January 10, 2022

How to keep gasoline prices low: bomb your gas station


An Italian fighter plane (note the "fasci" symbols on the wings) shot down in England in November 1940 during the bombing campaign mounted by the Italian Air Force during WW2 (source). Sending obsolete biplanes with open cockpits against the modern British Spitfires is one of the most glaring examples of military incompetence in history. Among other things, this old tragedy may give us hints about the current situation in the world and, in particular, why the consumers of fossil fuels tend to bomb their suppliers. 

Not everyone in Europe has understood exactly what is happening with gas prices, yet, but the consequences could be heavy. For a brief moment, prices rose of a factor ten over what was considered as "normal." Then, prices subsided a little, but still remain way higher than before. Electricity prices are directly affected by the trend and that is not only traumatic for consumers, but also for the European industry. 

So, what's happening? As usual, interpretations are flying free in the memesphere: those evil Russians, the conspiracy of the Americans, it is all a fault of those ugly Greens who don't want nuclear energy, the financial lobby conspiring against the people, etcetera.

Let me try an approach a little different. Let me compare the current situation with that of the 1930s in Europe. Back then, fossil fuels were already fundamental for the functioning of the economy, but coal was the truly critical resource: not for nothing it was called "King Coal."

The coal revolution had started to appear in Europe in the 19th century. Those countries that had large coal reserves England, Germany, and France, could start their industrial revolutions. Others were cut off from the bonanza: the lack of coal was the main cause of the decline of the Southern Mediterranean countries. The Turkish empire, the "sick man of Europe," was not really sick, it was starved. Of coal. 

But it was not strictly necessary to have coal mines to industrialize: it could be done by importing coal from the producing countries. Sailing ships could carry coal at low cost just about everywhere in the world, the problem was to transport it inland. Coal is bulky and heavy, the only way to do that is to have a good network of waterways. And having that depends on climate: the Southern Mediterranean countries are too dry to have it. But Northern Mediterranean countries had the network and could industrialize: it was the case of Italy. 

Italy went through its industrial revolution much later than the Northern European countries but succeeded using British coal. That, of course, meant that Italy became dependent on British coal imports. Not a problem as long as the two countries were friendly to each other. Unfortunately, as it often happens in life, money may well take the priority over friendship. 

In the early 1920s, coal production in England reached a peak and couldn't be increased any more. That, of course, led to higher prices and cuts in exports. At that time, nobody could understand how depletion affects production (not even nowadays people do). So most Italians took the reduced coal supply from Britain as a geopolitical attack. It was an evil strategy of the decadent plutocracy called the Perfidious Albion, specifically designed to harm the young and growing southern countries.  

The Italian conquest of Ethiopia was the turning point of the struggle. Britain reacted by stopping the exports of coal to Italy. That, and other international economic sanctions, pushed the Italian economy, already crippled by the cost of the war, to the brink of collapse. Given the situation, events played out as if following a prophecy written down long before. Italy had to rely more and more on German coal and that had obvious political consequences. 

The tragedy became a farce when old Italian biplanes tried to bomb Britain into submission in 1940. The campaign lasted just two months, enough for the Italian contingent to take heavy losses before it was withdrawn (*). It was not just a tactical blunder, but a strategic disaster since it gave the British and their allies an excuse to bomb Italy at will. Which they did, enthusiastically and very successfully. 

The curious thing about this disastrous campaign is how it inaugurated a tradition: bombing one's supplier of fossil fuels. Italy's bombing of Britain was just the first of a long series: in August 1941, the British attacked and bombed Iran to secure the Iranian oil wells. They were much more successful than the Italians against Britain and Iran surrendered in less than a week. In the same year, in November, the Japanese attempted the same trick by bombing the United States, their main supplier of oil. The Japanese attack on Pearl Harbor was a tactical success, but a major strategic disaster, as we all know. 

After WWII, the "Carter Doctrine" implied the strategic value of oil producers in the Middle East. One of the outcomes was the protracted bombing of Iraq from 1991, still intermittently ongoing. Other oil suppliers bombed by Western states were Libya and Syria. 

In short, the tradition of bombing one's suppliers of fuels remains alive and well. Whether it can accomplish anything better than the disastrous attempt of Italy in 1941 is debatable, to say the least. After all, it is equivalent to blasting away your neighborhood gas station in order to get the gas you need, but this is the way the human mind seems to work. 

So, on the basis of this historical tradition, let's try to build a narrative about what's going on, right now, with the gas supply to Europe. We just need to translate the roles that some countries had in the 1930s with those of today. 

Coal --> Natural Gas
Italy --> Western Europe (EU)
Britain --> Russia
Germany --> USA

The correspondence is very good: we have a consumer of fossil energy (now Europe, then Italy) which is militarily weak, but threatens the supplier (Now Russia, then Britain) with military action despite the obvious superiority of the latter. The weak consumer (Europe/Italy) feels that it can get away with this suicidal strategy because it has the backup of a powerful ally (Now the USA, then Germany). 

Just like Britain did in 1936 to Italy, Russia appears to have reduced the supply of gas to Europe. In both cases, the result was/is a crisis in the economy of the consumers. Just as it happened in the late 1930s, the stronger ally is coming to the rescue: in 1936, Germany started supplying coal to Italy by rail, now the US is sending cryogenic gas to Europe -- both are expensive methods of transportation, but allow the supplier to access a market that would have been barren, were it not for political reason. But becoming the customers of a militarily powerful country has political costs. 

The correspondence is so good that the current situation could easily develop into a similar outcome as in 1941, with the European Union doing something completely idiotic: attacking Russia, hoping for the support of the powerful US ally. (also, traditionally, attacking Russia is done in Winter: what could go wrong?). 

One conclusion of this story is that humans always tend to worsen whatever major problem they happen to face. Apart from this, perhaps there is an alternative scenario that could lead Europe away from the perspective of nuclear annihilation: maybe we can learn something from the Italian experience. 

In 1936, during the coal embargo imposed by Britain, Italy carried out an attempt to reduce its consumption of fossil fuels that went under the name of "autarchy" (Autarchia). It was based on the renewable technologies available at that time, and it involved some crazy ideas, such as making shoe soles out of cardboard and dresses out of fiberglass. But, on the whole, the idea of relying as much as possible on national and local products made plenty of sense. It didn't work, mainly because the government squandered the Italian resources in useless wars, but, who knows? Today it might work better if we don't make the same mistake. 

(*) The Italian pilots had to fight with obsolete canvas biplanes: much slower than the British Spitfires, poorly armed, without an armored cockpit (the pilots used sandbags as makeshift armor), without sufficient heating, without the right training. And, of course, poor reliability of almost every mechanical system in a cold climate. Most of the Italian losses were due to mechanical failures, while no British planes are reported to have been lost to the Italians. If the definition of "epic" involves fighting against an overwhelming superior enemy, then the experience of the Italian force in the Battle of Britain can surely be defined in this way: an epic disaster. Whoever had this absurd idea deserved to be hanged, and at least one of them was.    

Monday, April 19, 2021

Peak Water: Are we Running out of a Critical Resource?

"Peak Water" is an idea that has been going in parallel with that of "Peak Oil." Both assume that the production of limited resources, fossil fuels and fossil water, will follow a "bell shaped" curve. The production peak of liquid fuels may have been passed during the past few years. About "peak water" the situation is less clear, but the data indicate depletion problems in several areas of the world. Above, you see the historical and predicted water production from the Texas section of the Ogallala Aquifer. The data approximately follow a "Bell Shaped" (Hubbert) curve, typical of the depletion of non-renewable resources. In this case, the peak seems to have arrived in the late 1990. 

Freshwater is a fundamental resource in our world, even more than crude oil. Without freshwater, it would be impossible to maintain the current agricultural production that manages to feed nearly 8 billion human beings. Most of the world's agriculture, nowadays, is based on irrigation. It means that production depends on water that has been stored somewhere, naturally or artificially. And once you start depending on a limited stock of resources, you face a problem. Even though your resource may be renewable, if you exploit it faster than it renews itself, you will eventually run out of it. It is the phenomenon called "overexploitation"

There lies a truly nasty problem that we may be facing in the near future. A lot of water used for irrigation nowadays is "fossil water." It means it has been stored underground by natural processes that may have been active only in the ancient past or that may be very slow, sometimes of the order of thousands or even hundreds of thousands of years. Underground water deposits are called "aquifers." Some are fast replenished by natural phenomena, but in most cases, the rate of water withdrawal is much faster than that of the natural flow into the aquifer. That's a recipe for disaster.

A classic case of an agricultural region that ran out of fossil water is that of Saudi Arabia. Starting with the 1980s, Saudi Arabian farmers started extracting water that had been lying underground for hundreds of thousands of years, from a time when the Arabian peninsula was green. That was true fossil water in the sense that the replenishment rate of the aquifers was practically zero. The result was a boom in agricultural production that quickly peaked in 1990 following an evident bell-shaped curve. The curve had a second cycle during the 2010s, but that changed little to the situation. Right now, Saudi Arabia's agricultural production is reduced to practically zero and all the food must be imported.

Saudi Arabia's freshwater production was a classic case of a "Hubbert cycle." That is, water production followed the same kind of "bell-shaped" curve observed for crude oil and other mineral resources. The "Hubbert Theory" (the one that generated the concept of "Peak Oil") is far from being perfect, but it is true that in most cases oil production cycles generate bell-shaped curves. 

With aquifers, the core of the question is the same: you exploit a limited resource, you make a profit, you invest part of it in more exploitation. And that leads to depletion. The result is expected to be the same kind of curve. 

It doesn't matter that, in most cases, aquifers are partially replenished by natural phenomena. The curve will be the same, although it will not go to zero at the end of the cycle, but will return to the natural groundwater recharge rate. (source)

 But that may be an optimistic estimate: with aquifers, there is always the issue of subsidence. It means that once you remove the water from porous rock, the rock becomes more compact and it won't be filled again with water. It happens also with oil wells, but in that case, you don't care: it is known that oil is a one-time resource. Some aquifers may be in the same category, and may be gone forever after that they have been emptied. As an additional effect of subsidence, your home may sink into a hole in the ground. (image: subsidence in Jakarta).

So, it is perfectly possible to run out of water, even though water is theoretically a renewable resource. During the first millennium CE, an entire civilization, that of the Garamantes of central Sahara, disappeared when their supply of fossil water ran out.

So, how do we stand today? Overall, one would tend to say that the situation is not so good (to say the least). Most of the aquifers in use are being overexploited. The table below, from Wikipedia, is impressive (again, to say the least). 


If we continue in this way, it is unavoidable that sooner or later humans will run out of freshwater. It will be"peak water," but when could it happen, exactly? 

The problem with freshwater is that we don't have the same wealth of data for water resources and consumption that we have for crude oil. There exist a large number of aquifers, most of them are exploited only locally and it is difficult to obtain reliable data on what is being done in all the regions of the world. Nevertheless, we have some rough estimates: the total amount of freshwater accessible to humans is estimated as some 200,000 km3. The total consumption of freshwater worldwide is estimated at around 1,000 km3 per year

That these estimates are such round numbers tells us something about the uncertainty involved. But we can still say that aquifers contain huge amounts of water, about one thousand times more than the estimated volume of the world reserves of crude oil (about 200 km3). Even just the Ogallala aquifer in the central US is larger, estimated to have contained some 3,600 km3 of water before pumping started, in the 1950s. Then, we also consume huge amounts of water. We can compare again with crude oil, and we find that oil consumption (about 4 km3/year) is again dwarfed by water consumption that turns out to be about 250 times larger. 

Unfortunately, these data are not enough for an estimate of when peak water could occur. Not only there are too many uncertainties involved, but the main point is that water is mostly a local resource, unlike oil, which is global. It means that the depletion cycle is spaced differently in different regions, depending on the rate of consumption to reserves. So, the fact that Saudi Arabia mostly ran out of water during the past decade had no significant effect on the world's agricultural production. But if a truly major agricultural region, such as the Central Plains in the US, were to run out of water, then the situation would quickly become dire for all the regions in the world that depend on food imported from the US.

So, what's happening in the US in terms of water production and consumption? The good news, here, is that consumption has been declining. That happened not because of water depletion, but because of the switch from coal to natural gas as the main energy source for electricity production. Natural gas plants are more efficient than coal-fired plants and the result is a reduced need for cooling water. (data below from USGS)

So, it is possible to reduce the consumption of water and that leaves plenty of it available for agriculture, but that doesn't solve the problem. As you see in the figure, the second largest sector of water consumption is irrigation and that sector has been declining, too. Nobody can say for sure if (or when) the wells of the Ogallala aquifer will run dry, bur these data are worrisome

Then, can we find new aquifers? Maybe, but even here the situation is not promising, to say the least. In 2013, the discovery of a new, large aquifer in Kenya was reported with much fanfare in the media. The aquifer was described as containing 250 billion cubic meters of water. Less than one-tenth of the Ogallala aquifer, but still a remarkable discovery.  Too bad that it was soon found that it was brackish water, not freshwater. So is life, you can't have everything, you know?

But we can desalinate brackish water, can't we? We can desalinate seawater, too. And you won't tell us that we will run out of seawater, will you? Sure we can. But that's not a panacea, either.

Agriculture is an economic activity that lives on very small profit margins. You increase the cost of some agricultural inputs and a lot of things change and farmers go in the red. Water for irrigation is often subsidized and farmers can't usually afford to pay it much more than $0.01 per cubic meter. In comparison, desalinated water may cost around one dollar per cubic meter, maybe a little less but not much. It is a factor of 10, at best. How much would an eggplant cultivated using desalinated water cost? More than most people would be able to afford.

As things stand, there is no way to use desalinated water in agriculture: we should go back to the dreams of "energy too cheap to meter" and that doesn't seem to be closer today than it was in the 1950s, when it was proposed. Besides, as long as our energy supply comes mainly from fossil fuels, using a substantial fraction of it to produce the huge amounts of freshwater needed for irrigation would be an environmental disaster.

That doesn't mean that desalinated water is a bad idea. Not at all and, in the future, it may cost much less than it costs right now. Just think of the possibility of producing freshwater using the excess energy that renewable energy plants generate at some moments during the day. It would be a smart way to store energy that otherwise would have to be wasted.  

Smart, yes, but problematic in many ways. One is that at present we are still far away from having excess energy production from renewable plants sufficient to produce the huge amounts of water needed in agriculture. The second - probably worse - is that desalinated water is mostly produced from seawater, near the seashore. But agriculture is mainly performed inland, so you would need a gigantic infrastructure to transport enormous amounts of water where it is needed. Again, not an impossible task, but a steep barrier to overcome, and the costs would be gigantic, too.

In the end, the problem is not so much having sufficient energy to desalinate water. It is that irrigated agriculture is just not a good idea. In most cases, it is a trap that leads to the destruction of the fertile soil, something that the ancient Sumerians already experimented around 2,200 BC. It seems that the Sumerians depleted the aquifers they had been using for about one thousand years and couldn't avoid the soil to become too salty to be cultivated

Are we facing the same destiny? Maybe. But there are many ways open for a kind of agriculture that's more respectful of the soil and that doesn't need so much water as the current methods do. It is to be seen if we can change fast enough to avoid having to adapt the hard way, that is rebuilding after collapse. In this field, as in many others, the Seneca Cliff is awaiting.

Sunday, December 7, 2014

Fossil fuels: are we on the edge of the Seneca cliff?

Originally published on "Cassandra's Legacy" on Sunday, December 7, 2014

"It would be some consolation for the feebleness of our selves and our works if all things should perish as slowly as they come into being; but as it is, increases are of sluggish growth, but the way to ruin is rapid." Lucius Anneaus Seneca, Letters to Lucilius, n. 91

This observation by Seneca seems to be valid for many modern cases, including the production of a nonrenewable resource such as crude oil. Are we on the edge of the "Seneca cliff?"

It is a well known tenet of people working in system dynamics that there exist plenty of cases of solutions worsening the problem. Often, people appear to be perfectly able to understand what the problem is, but, just as often, they tend to act on it in the wrong way. It is a concept also expressed as "pushing the lever in the wrong direction."

With fossil fuels, we all understand that we have a depletion problem, but the solution, so far, has been to drill more, to drill deeper, and to keep drilling. Squeezing out some fuel by all possible sources, no matter how difficult and expensive, could offset the decline of conventional fields and keep production growing for the past few years. But is it a real solution? That is, won't we pay the present growth with a faster decline in the future?

This question can be described in terms of the "Seneca Cliff", a concept that I proposed a few years ago to describe how the production of a non renewable resource may show a rapid decline after passing its production peak. A behavior that can be shown graphically as follows:

It is not just a theoretical model: there are several historical cases where the production of a resource collapsed after having reached a peak. For instance, here are the data for the Caspian sturgeon, a case that I termed "peak caviar".

Do we risk to see something like this in the case of the world production of oil and gas? In my opinion, yes. There are some similarities; both fossil fuels and caviar are non-replaceable resources; and in both cases prices went rapidly up at and after the peak. So, if Caspian sturgeon showed such a clear Seneca cliff, oil and gas could do the same. But let me go into some details.

In the first version of my Seneca model, the fast decline of production was interpreted in terms of growing pollution that places an extra burden on the productive system and reduces the amount of resources available for the development of new resources. However, I found that the Seneca behavior is rather robust in these systems and it appears every time people try to "stretch out" a system to force it to produce more and faster than it would naturally do.

So, in the case of the Caspian sturgeon, above, growing pollution is unlikely to be the cause of the rapid collapse of production (even though it may have contributed to the problem). Rather, the main factor in the collapse is likely to have been the effect of the growing prices of a rare and non replaceable resource (caviar). High prices enticed producers to invest more and more resources in raking out of the sea as much fish as possible. It worked, for a while, but, in the end, you can't fish sturgeon which isn't there. It ended up in disaster: a classic case of a Seneca Cliff.

Can this phenomenon be modeled? Yes. Below, I describe the model for this case in some detail. The essence of the idea is that producers need to reinvest a fraction of their profits in developing new resources in order to keep producing. However, the yield of the new investments declines as time goes by because the most profitable resources (e.g. oilfields) are exploited first. As a result, less and less capital is available for new investments. Eventually production reaches a maximum, then it declines. If we assume that companies re-invest a constant fraction of their profits in new resources, the model leads to the symmetric bell shaped curve known as the "Hubbert Curve."

However, as I describe in detail below, decline can be postponed if high prices provide extra capital for new productivedevelopments. Unfortunately, growth is obtained at the cost of a fast burning out of capital resources. The final result is not any more the symmetric Hubbert curve, but a classic Seneca curve: decline is more rapid than growth.

Is this what we are facing for fossil fuels? Of course, we are only dealing with qualitative models, but, on the other hand, qualitative models are often robust and give us an idea of what to expect, even though they can't tell us much in terms of predicting events on a precise time scale. The ongoing collapse of oil prices may be a symptom that we are running out of the capital resources necessary to keep developing new fields. So, what we can say is that there are some good chances of rough times ahead - actually very rough. The Seneca cliff may well be part of our near term future.


The Seneca curve as the result of increasing fractions of profits allocated to the production of a non renewable resource

by Ugo Bardi - 07 Dec 2014

Note: this is not a formal scientific paper; it is more a rough "back of the envelope" calculation designed to show how increasing capex fractions can affect the production rate of a non renewable resource. If someone could give me a hand to make a more refined and publishable study, I would be happy to collaborate!

The basics of a system dynamics model describing the exploitation of a non renewable resource in a free market are described in detail in a 2009 paper byBardi and Lavacchi. According to the model developed in that paper, it is assumed that the non renewable resource (R) exists in the form of an initial stock of fixed extent. The resource stock is gradually transformed into a stock of capital (C) which in turn gradually declines. The behavior of the two stocks as a function of time is described by two coupled differential equations.

R' = - k1*C*R
C' = k2*C*R - k3*C,

where R' and C' indicate the flow of the stocks as a function of time (R' is what we call "production"), while the "ks" are constants. This is a "bare bones" model which nevertheless can reproduce the "bell shaped" Hubbert curve and fit some historical cases. Adding a third stock (pollution) to the system, generates the "Seneca Curve", that is a skewed forward production curve, with decline faster than growth. 

The two stock system (i.e. without taking pollution into account) can also produce a Seneca curve if the equations above are slightly modified. In particular, we can write: 

R' = - k1*k3*C*R
C' = ko*k2*C*R - (k3+k4)*C.

Here, "k3" explicitly indicates the fraction of capital reinvested in production, while k4 which is proportional to capital depreciation (or any other non productive use). Then, we assume that production is proportional to the amount of capital invested, that is to k3*C. Note how the ratio of R' to the flow of capital into resource creation describes the net energy production (EROI), which turns out to be equal to k1*R. Note also that "ko" is a factor that defines the efficiency of the transformation of resources into capital; it can be seen as related to technological efficiency. These points will not be examined in detail here.

Here is the model as implemented using the Vensim (TM) software for system dynamics. The "ks" have been given explicit names. I am also using the convention of "mind sized models" with higher free energy stocks appearing above lower free energy stocks

If the k's are kept constant over the production cycle, the shape of the curves generated by this model is exactly the same as with the simplified version, that isa symmetric, bell shaped production curve. Here are the results of a typical run:

Things change if we allow "k3" to vary over the simulation cycle. The characteristic that makes "k3" (productive investment fraction) somewhat different than the other parameters of the model, is that it is wholly dependent on human choice. That is, while the other ks are constrained by physical and technological factors, the fraction of the available capital re-invested into production can be chosen almost at will (of course, there remains the limit of the total amount of available capital!). 

Higher prices will lead to higher profits for producers and to the tendency to increase the fraction reinvested in new developments. It is also known that in the region near the production peak prices tend to be higher - as in the historical cases of whale oil and caviar and whale oil. In the case of caviar, the price rise was nearly exponential, in the case of whale oil, more like a logistic curve. Assuming that the fraction of reinvested capital varies in proportion to prices, some modeling may be attempted. Let me show here the results obtained for an exponential increase of the fraction of reinvested Capex.

I have also tried other functions for the rising trend of k3. The results are qualitatively the same for a linear increase and for a logistic one: the Seneca behavior appears to be robust, as long as we assume a significant increase of the fraction of the reinvested capex

Let me stress once more that these are not supposed to be complete results. These are just tests performed with arbitrary assumptions for the constants. Nevertheless, these calculations show that the Seneca cliff is a general behavior that occurs when producers stretch out their system allocating increasing fractions of capital to production.