*[ The Hill’s group consists of energy insiders, and I must admit I was impressed by the predictions they said their model had already gotten right, such as the drop in oil price when everyone was expecting the price to rise. And much of what they say matches the predictions and timeline of others as well as how the net energy cliff will unfold. The charts and calculus are very impressive, and for years their paper has been discussed on peak oil forums. *

*A scientist I know working in Saudi Arabia thinks we’ve got at least 20 years, and that if Exxon, Chevron, and other oil and gas companies go bankrupt, no problem — the government will nationalize them. Another scientist pointed out that “Modern society runs on oil, thus the oil industry will be the absolute LAST industry to fail. It will be supported by hook or crook until then. Even at $200 a barrel we get energy a thousand times cheaper than human labor. Just not 20,000 times as much anymore”.*

*Dennis Coyne, who published Seppo Korpela’s article here says: “Oil prices are not determined primarily by thermodynamics as the Hill’s Group suggests. Geology and technology will affect the cost to supply the oil and World economic growth and technology will affect the demand for oil, the price of oil will mostly be determined by these factors along with policy and political choices made by individual nations.”*

*After Bardi’s post I’ve added some of the predictions Bill Hill said their model predicted on various forums — many sound plausible, but perhaps not an outcome of their model… And at the very bottom, an English translation of one of the Spanish articles. Stay tuned for a peer-reviewed critique of their paper, which I’ve heard is in the works.*

*Alice Friedemann **www.energyskeptic.com** author of “**When Trucks Stop Running: Energy and the Future of Transportation**”, 2015, Springer and “**Crunch! Whole Grain Artisan Chips and Crackers**”. Podcasts: **Practical Prepping**, **KunstlerCast 253**, **KunstlerCast278**, **Peak Prosperity** , **XX2 report** ]*

**Ugo Bardi. Feb 26, 2017. ***Catastrophism is popular, but not necessarily right. Debunking the “Hill’s Group” analysis of the future of the oil industry*. Cassandra’s Legacy.

*Catastrophism is popular, but not necessarily right. Debunking the “Hill’s Group” analysis of the future of the oil industry*. Cassandra’s Legacy.

*“The Hill’s Group” has been arguing for the rapid demise of the world’s oil industry on the basis of a calculation of the entropy of the oil extraction process. While it is true that the oil industry is in trouble, the calculations by the Hill’s group are, at best, irrelevant and probably simply plain wrong. Entropy is an important concept, but it must be correctly understood to be useful. It is no good to use it as an excuse to pander unbridled catastrophism.*

Catastrophism is popular. I can see that with the “Cassandra’s Legacy” blog. Every time I publish something that says that we are all going to die soon, it gets many more hits than when I publish posts arguing that we can do something to avoid the incoming disaster. The latest confirmation of this trend came from three posts by Louis Arnoux that I published last summer (link to the first one). All three are in the list of the ten most successful posts ever published here.

Arnoux argues that the problems we have today are caused by the diminishing energy yield (or net energy, or EROI) of fossil fuels. This is a correct observation, but Arnoux bases his case on a report released by a rather obscure organization called “The Hill’s Group.” They use calculations based on the evaluation of the entropy of the extraction process in order to predict a dire future for the world’s oil production. And they sell their report for $28 (shipping included).

Neither Arnoux nor the “Hill’s Group” are the first to argue that diminishing EROEI is at the basis of most of our troubles. But the Hill’s report gained a certain popularity and it has been favorably commented on many blogs and websites. It is t is understandable: the report has an aura of scientific correctness that comes from its use of basic thermodynamic principles and of the concept of entropy, correctly understood as the force behind the depletion problem. There is just a small problem: the report is badly flawed.

When I published Arnoux’s posts on this blog, I thought they were qualitatively correct, and I still think they are. But I didn’t have the time to look at the details of the report of Hill’s group. Now, some people did that and their analysis clearly shows the many fundamental flaws of the treatment. You can read the results in English by Seppo Korpela, and in Spanish by Carlos De Castro and Antonio Turiel. [ *NOTE: at the very bottom I have an english translation minus the equations* ].

Entropy is a complex subject and delving into the Hill’s report and into the criticism to it requires a certain effort. I won’t go into details, here. Let me just say that it simply makes no sense to start from the textbook definition of entropy to calculate the net energy of oil production. The approximations made in the report are so large to make the whole treatment useless (to say nothing of the errors it contains). Using the definition of entropy to analyze oil production is like using quantum mechanics to design a plane. It is true that all the electrons in a plane have to obey Schroedinger’s equation, but that’s not the way engineers design planes.

Of course, the problem of diminishing EROEI exists and can be studied. The way to do that is known and it is based on the “life cycle analysis” (LCA) of the process. This method takes into account entropy indirectly, in terms of heat losses, without attempting the impossible task of calculating it from first principles. By means of this method we can see that, at present, oil production still provides a reasonable energy return on investment (EROEI) as you can read, for instance, in a recent paper by Brandt et al.

But if producing oil still provides an energy return, why is the oil industry in such dire troubles? (see this post on the SRSrocco report, for instance). Well, let me cite a post by Nate Hagens:

In the last 10 years the global credit market has grown at 12% per year allowing GDP growth of only 3.5% and increasing global crude oil production less than 1% annually. We’re so used to running on various treadmills that the landscape doesn’t look all too scary. But since 2008, despite energies fundamental role in economic growth, it is access to credit that is supporting our economies, in a surreal, permanent, Faustian bargain sort of way. As long as interest rates (govt borrowing costs) are low and market participants accept it, this can go on for quite a long time, all the while burning through the next higher cost tranche of extractable carbon fuel in turn getting reduced benefits from the “Trade” creating other societal pressures.

Society runs on energy, but thinks it runs on money.In such a scenario, there will be some paradoxical results from the end of cheap (to extract) oil. Instead of higher prices, the global economy will first lose the ability to continue to service both the principal and the interest on the large amounts of newly created money/debt, and we will then probably first face deflation. Under this scenario, the casualty will not be higher and higher prices to consumers that most in peak oil community expect, but rather the high and medium cost producers gradually going out of business due to market prices significantly below extraction costs. Peak oil will come about from the high cost tranches of production gradually disappearing.

I don’t expect the government takeover of the credit mechanism to stop, but if it does, both oil production and oil prices will be quite a bit lower.

In the long run it’s all about the energy. For the foreseeable future, it’s mostly about the credit

In the end, it is simply dumb to think that the system will automatically collapse when and because the net energy of the oil production process becomes negative (or the EROEI smaller than one). No, it will crash much earlier because of factors correlated to the control system that we call “the economy”. It is a behavior typical of complex adaptative systems that are never understandable in terms of mere energy return considerations. Complex systems always kick back.

The final consideration of this post would simply be to avoid losing time with the Hill’s report (to say nothing about paying $28 for it). But there remains a problem: a report that claims to be based on thermodynamics and uses resounding words such as “entropy” plays into the human tendency of believing what one wants to believe. Catastrophism is popular for various reasons, some perfectly good. Actually, we should all be cautious catastrophists in the sense of being worried about the catastrophes we risk to see as the result of climate change and mineral depletion. But we should also be careful about crying wolf too early. Unfortunately, that’s exactly what Hill&Arnoux did and now they are being debunked, as they should be. That puts in a bad light all the people who are seriously trying to alert the public of the risks ahead.

Catastrophism is the other face of cornucopianism; both are human reactions to a difficult situation. Cornucopianism denies the existence of the problem, catastrophism (in its “hard” form) denies that it can be solved or even just mitigated. Both attitudes lead to inaction. But there exists a middle way in which we don’t exaggerate the problem but we don’t deny it, either, and we do something about it

A defense of the Hills Group (one of the comments at Cassandra’s Legacy):

Your preference for Life Cycle Analysis over the Thermodynamics of Steady State is just that…your preference. The ETP model includes as a cost the cost of replacing reserves as they are used. The method used in the ETP model is similar to what one might use for a biological system…that is, the parents have to provide for the children…adult birds need to look for caterpillars to feed the young. Now, if, as Hubbert assumed, we have a boundless supply of nuclear energy just waiting in the wings, a Life Cycle study would be appropriate. But since oil is part of the very biological business of keeping humans alive and functioning, there is nothing wrong with the ETP method. Whichever method is used, the user is responsible for understanding the assumptions and applying them appropriately.

*You fail to see that the numbers quoted by Nate Hagens MIGHT just have a more fundamental cause than ‘just because’. If the falling value of energy, and particularly oil, as displayed by the output from the ETP model is correct, then we would expect the numbers that Hagens quotes. Hagens is not ‘disproving’ the ETP model.

*After accusing other people of confusing the EROEI methodology, you fall into the same trap. The ETP model does not claim that EROEI is going below 1. As estimated from the ETP model, the ‘dead state’ is arrived at when the EROEI is around 7 (as I remember). Such numbers are reasonably consistent with what Charles Hall and others have called ‘extended EROEI’. That is, they count the costs beyond the well-head. The ETP methodology estimates that, with a well-head EROEI of 7, we will no longer be able to sustain the industrial economy as it is presently configured.

*While the ETP model does not model the human reaction to the recognition that the economic and social system cannot go on much longer as it has been going for the last decades and centuries, Mr. Hill has been very clear that he thinks the situation is dire. The oil companies could lose enormous amounts of equity values overnight. The recognition would reverberate through the economy and the social system. The ETP model tells us something about the physical world, which we must interpret in terms of the financial and social world.

**And FYI, some of the predictions the Hills Group claim that their model predicts for the future**:

**The 2012 energy half way point, set out by the Etp Model, marked the point where the world started being better off without oil than with it. That conversion will be complete by no later than 2030.**

Our** model indicates that conventional crude production will fall to 44 mb/d by 2030**. Thereafter, it goes into catastrophic decline.

**Our analysis indicates that it will probably be in the range of 15 to 20 years after that when the majority of petroleum production will cease**. **The oil age is coming to an end. The Etp Model provides a very important time line; one that informs us that we have at most 14 years to put into place an alternate energy system; one beyond oil.** **Past that point the world will have fallen into such a deep depression that it will no longer be able to help itself.**

**We expect to have reached permanent depression by the end of 2017 (prediction made June 2016).**

T**he reduction will not hit all nations the same way. The richer Western countries will be able to afford fuels for longer than smaller poorer counties. But, how that will feed back into their general economies is yet an unknown. It will definitely have a negative impact, and perhaps a gigantic one. Like the S&P collapsing, an explosion of corporate bankruptcies, and supply chains breaking. But all and all we will just have to wait and see. It has been four years since petroleum hit its energy half way point. We should not have to wait much longer. We are likely to see the first major impacts this year**!

**Things are a lot worse than oil producers are admitting. The Etp Model indicates that in the present price environment that only about 35% of the world’s producers are making money over their full life cycle costs. Their desperation for cash ensures that production will not decline until many of them start to fail. The energy dynamics of the situation point to falling prices until at least 2020. By then much of the world’s petroleum production capacity will be gone forever**!

Damage is being inflicted on the industry that will never be repaired. CapEx is being cut everywhere in the industry, and future development is likely to never fully recover. The Etp Model indicates that only **about an additional 320 Gb will now ever be extracted**. In 2012 petroleum contributed $6.22 trillion to the $16.16 trillion GDP of the US. That contribution will fall by more than half during the next decade.

**Very low priced oil is a catastrophe for the petroleum industry, and the world. Whereas the oil age might have staggered forward for another 14 to 15 years, it might all come unglued over the next 5 or 6**.

**The Etp Model indicates that only about an additional 320 Gb will now ever be extracted.**

The industry’s net worth is now declining by 24% per year. If the price decline continues, as expected, trillions of dollars will be lost to bond and equity holders over the next few years. Pension funds, and Sovereign wealth fund will be hit particularly hard.

**EROEI**

Year |
EROEI : 1 |

1945 |
167.0 |

1980 |
30.4 |

2014 |
9.1 |

2015 |
8.9 |

**At 6.9 : 1 it will have reached its the theoretical limit, or were the PPS (Petroleum Production System) reaches the “dead state”**. That will be dependent on its accumulated production, which has had a very consistent rate of increase for the last 100 years. The accumulated production has followed Hubbert’s curve almost exactly; by 2009 it had deviated from that curve by 0.04 Gb. In other words the amount remaining to be extracted is a product of how much has already been removed. Any amount after 1,780 Gb will remain in the ground as it will no longer be able to act as an energy source.

**The highest ERoEI crude left in the world is probably coming out of the Middle East and Nigeria; and both of them are about to explode. **

Saudi Arabia

**When Ghawar will start to collapse has been the subject of heated discussion for a very long time. Looking at its water cut, as reported by Aramco reserve engineers, and the fact that they have been drilling horizontal wells to skim the last few feet off the top of the oil column indicates that it probably won’t be long in coming. A better indication is probably the price. The Affordability Curve gives a pretty good indication as to what is likely to transpire, and **** The Price of Oil** puts the maximum affordability at:

2015 – $77.28

2016 – 65.94

2017 – 54.18

2018 – 41.16

2019 – 26.88

By the looks of the above graph sometime between 2018 and 2019 the Saudi’s will no longer be able to cover their lifting cost. Once that happens their production will collapse, and they will likely break the peg. My WAG (wild ass guess) would be sometime in that time frame. Of course, the Iranians may decide to blow the crap out of them at any time, and that would put a real crimp onto their production. It looks like the best case scenario is 2 to 3 years before Saudi Arabia implodes.

Shale / Light Tight Oil

U.S. LTO production will not start to decline because of a lack of drilling opportunities, lack of funds (the FED has their back), or because of high well decline rates. **It will decline when it runs out of buyers for it. That will happen in the next couple of years**.

**It now requires about 74,000 BTU to extract, process, and distribute a gallon of petroleum**. **Only the lower API fractions have an energy content that is sufficient to provide a surplus of energy after their process energy is subtracted.**

**The energy dynamics imply that once conventional crude is depleted, that other alternative liquid fuels will not be able to maintain enough of the economy needed to produce them, or provide for their demand**. **Shale is a good example of this phenomenon. Most shale is incapable of driving the economy, and its only use is as a feedstock for other processes**.

**Civilization is likely to experience something resembling a brown out. Voltage drops until the motors grind to halt, and burn up. Imagine billions of people milling around trying to figure out why things are running slower, and slower. Not much has yet fully stopped working, but nothing is working quite right**!

**Petroleum is providing just enough energy at this point in time to keep what is running going. If any additional load is placed on the system, like having to bail out the banks again, a good sized war, or even some natural disaster something is going to burn up. Maybe a big chunk of the health care system, the consumer economy, or the petroleum industry but something will no longer be maintainable. The world no longer has the extra energy to expend on anything but what it is presently using. The danger is that when it starts it could cascade into a black out**!

**An analysis of the theoretical foundations of the ETP model **By Antonio Turiel

Last February 20^{th}, we held a monographic session in the Transition Forum organized by FUHEM (a Spanish foundation concerned with social issues, basically a NGO of many intellectuals and scarce funds), to analyze the ETP model. This model created by the Hill’s Group tries to forecast the global oil production evolution in the next years. It is based in the decreasing net energy that oil is offering.

To start the discussion, FUHEM asked me to make an analysis to validate and check the theoretical robustness of the said model. They were trying to see, among other things, if their conclusions (quite terrible, by the way) could be used in their discussions with political agents.

I have deemed convenient to write this post explaining the conclusions of my analysis, due to its importance and the raising interest on this subject.

This is a rather technical post, but I will try to explain the basic concepts in the most intuitive possible form. The formulas and concepts treated are those included in the document “Depletion: A determination for the world’s petroleum reserve”, release 2 of March 1^{st}. 2015.

The following critique is not exhaustive; there are many aspects in the model that will not be treated. I will mainly focus on the most relevant theoretical aspects, but not even all of them, and I will deliberately sidestep the discussion on use of data. Carlos de Castro, on his turn, made a detailed analysis for the same session on the data processing in the ETP model. This analysis can be accessed as post in the blog of the Energy, Economy and System Dynamics Group of the Valladolid University.

The Hill’s Group Report (hereinafter HGR) states in its introduction that they intend to estimate the energy needed by the oil production and distribution system (so called Petroleum Production system, or PPS) to make its products reach the society and to check if this energy is approaching to the energy efficiency limit, which corresponds with the energy that can be obtained just burning this oil.

All the HGR is based on the equations used to calculate the energy needed by the PPS to continue working. This needed energy is called Total Production Energy or ETP. They use some thermodynamic equations to this effect and I will precisely focus my analysis on the theoretical derivation of these equations.

**Theoretical foundations of the ETP**

One of the weakest points of the report is the inadequate definition of the validity boundaries. By the treatment given to the variables, it could be thought that calculations are made at the well head and therefore, that the calculated ETP refers to the energy spent to just extract the oil. However, as per other considerations, it is mentioned that the calculations include all the PPS.

Making a calculation for the whole PPS is a rather complex issue, even introducing simplifying hypothesis, such as taking typical or mean values, as there are a huge amount of mixed processes with different efficiencies. The conditions under which extraction, refining and distribution take place greatly change from one place to another in the planet (the spatial dimension, as quoted to Antonio Serrano in his analysis of these problems).

In fact, the biggest problem to tackle the analysis with thermodynamic equations is to define and accurately enclose the limits of the system under study and to be sure that the hypotheses are correctly applied to it. In fact, sometimes implicit hypothesis are included inadvertently. So, one has to be extremely careful with the data handling and with the terms included in the equations.

Other conceptual problems observed from the start is that the analysis takes the PPS isolated from the rest of the economy and specifically form other energy sources that could back the oil extraction, (oil could still be interesting when no net energy can be extracted from it due to its possibly bigger added value). That makes the statements on the collapse of the PPS questionable, to say the least. The collapse may finally happen, but it is not unavoidable in pure logic, from what is being theoretically analyzed.

The basic variable to derive the ETP is the calculation of the entropy variation rate. As the “entropy” word appears, you can bet that 90% of the readers will just jump over the part of the report with the formulas and go directly to the graphs and the conclusions.

This post has precisely the aim to analyze to which extent these equations are physically sound, if they are well applied and to which system they are applied. I will try to make the explanation as simple as possible, complementing each theoretical concept with a more simple explanation. In any case, I recommend the (Spanish speaking) readers with time and will to know about this in more detail, to read an old post of this blog, called “Entropía”

The first equation introduced in the HGR is a general one, valid for any system, on the entropy variation rate with time:

Equation 1.

Intimidating, as it appears, this equation shows, in fact, a very simple equality

(Notation: **S** is the symbol to denote entropy). The first term of the equation is the derivative of entropy with time. This term does not say anything specific, being at the left of the sign equal. The equation is issued to calculate this term in the left side. The terms in the right side will give information on which things change the entropy.

(Notation: **Q** means heat. The dot on top means the variation with (respect) time. **T **means temperature). The entropy of a given body is intimately associated to its temperature. This term includes all the changes of the entropy produced in the considered system due to heat flows. The sigma letter **Σ** heading the term is a sum indicating that we have to add all the transferences of associated entropies due to all possible heat flows: there exists an undefined amount of heat sources Qj, each of them associated to a temperature Tj and we have to add all of them (for all the values of ** j **index).

(Notation: **m** is the mass of a substance or a given body and **s** is the entropy per mass unit of this substance or body; it is also called “specific entropy”). This term is just telling that if there are substances or bodies entering into the system, they bring their entropy with them. The dot on top of the **m** means variation of the mass of the entering substance or body with time and as in the previous term, it is added over all the possible entering bodies, in this case numbered with the ** i** index.

Analog to the previous term, but in this case, referred to the substances or bodies abandoning the system. That’s why the negative sign before the summation, because leaving the system also removes entropy from the total.

This is the last term of the equation and refers to all the changes in the entropy associated to irreversible processes taking place in the system. This term is a complete hotchpotch where it can be included everything that could not be counted in the other terms. That’s why is the most difficult to evaluate.

The equation just dissected is correct. It is a general one specifying the different factors contributing to the increase of entropy and it can be applied to any system without exceptions. The problem of this equation is that has an undefined number of terms (the sums could easily contain thousands of terms), which makes hard to use it in practice. When this general equation is applied to simple systems, it is possible to make approximations that allow to simplify it and make it manageable. But each of these approximations implies certain hypothesis that could determine the particular system for which they are of application. This implicit specification of the system of application may happen and pass unnoticed to the person who is applying it, that could even claim that the system of application is another one. This is precisely the case of the ETP model, as we shall see below.

The first hypothesis in the HGR is to assume that there are no entering masses in the system; only outgoing masses: the oil flow that leaves the wellhead and enters into the PPS. Besides, there is a simplification, when considering only one temperature, taken in a first approach as the typical temperature of the oil deposits. For the outgoing mass the HGR considers the total oil mass leaving all oil deposits. Therefore, the equation is reduced to the following form:

Equation 2.

Simplifying sums and substituting the quantities by typical values (or by mean values, the report is not explicit on that) is an approximation, but that is not the main problem of this equation. Such kind of simplification is what in Statistical Mechanics is called “mean field” and is applied to systems containing a large number of parts, all of them with the same type of interaction. The mean field gives a good first approach to the reality, maybe incurring in some degree of error but correctly capturing trends.

But the problem is not the mean field approximation. It is that the HGR ignores all type of interactions that a real PPS system has. For instance, all the intense flow of materials (steel, concrete, electronics of many different types, etc.) which are required to build and maintain the wells, to build and repair the distribution system (pipelines, trucks, supertankers, etc.). The report also ignores the intense heat inflows and outflows associated to all these processes. All these interactions are of diverse types and cannot be managed with a mean field approximation. Simply because the system is extremely heterogeneous and there are no mean or typical values that could properly describe such complex systems.

I will put an example to make myself better understood.

Talking about fusion or freezing temperatures of water is useful in practical terms, even if we could be talking of waters from different origins with different mineral salts diluted and therefore slightly different freezing points. In all cases, we are talking of liquids with homogeneous aspects, suffering similar processes. At the end, all the water samples considered will freeze into ice at approximately the same temperature, with slight differences among them. So, it has some sense to talk of a fusion temperature at zero degrees Celsius, and this allow us to understand how ice behaves.

Now, let’s think in a heterogeneous system; one constituted by different parts with different behaviors. One apparently simple like ice cream in a vanilla cornet. If we increase the temperature of the system over the melting point of the ice cream, the ice cream will melt, but it will still be contained within the wafer cone. If we continue increasing the temperature, the water content of the ice cream will eventually evaporate, leaving a viscous mass than then a dry mass. If we still increase the temperatures, the system will burn, but the way it will do it, will depend on the different combustion points; it will depends on how the wafer will be softened, the amount of remaining water in the ice cream, etc.

The cornet ice cream system cannot be understood with the temperature changes and even less with a given fusion temperature. All the ice cream cornet interactions are rather complex and to understand how the system behaves it is not enough with assessing the behavior of each part (ice cream and wafer cone) separately; it depends also on how the two parts interact with each other for the particular ice cream and wafer cone under consideration. And if the ice cream cornet is complex, we have to imagine how complex should be all the global production and distribution system.

This is the reason why the mean field approach used in the equation above cannot be applied (apart from the fact that there are incoming masses and this term cannot be neglected). The conclusion is that the simplified equation applies to the liquid oil contained in the geological deposits, although the interactions with the rocks are also neglected and they may not be so negligible when, for instance, the reservoir rock is collapsing and cementing when the oil is extracted from its interstices.

There is a new formula introduced in this point of the report, even it is not used until later, that confirms that the report refers to liquid oil. The formula tells about the entropy variation for an uncompressible, non-reactive liquid, when its temperature is modified from T1 to T2

Equation 3

The variable **c** is the specific (per unit of mass) heat capacity of a liquid (it is explicitly stated in the report that the constant-volume specific heat equals the pressure-constant specific heat, what means that we are talking about uncompressible liquids. Therefore, this formula has only sense when applied to uncompressible liquids that are not undergoing any type of chemical reaction (nor a phase change, as we shall discuss later). In fact, when this equation is used later one, it evidences that all the derivation of the ETP equation refers to liquid oil.

If the first hypothesis is very restrictive and determines the system to which is applied, the second hypothesis has much more implications and is regrettably more inconsistent. It is enounced as follows:

Given

(that is, the entropy variation is diminishing as the outgoing mass is decreasing), so the author of the model concludes that

Equation 4

There are many problems with this deduction. First, limits of applicability. To obtain Equation 4 we have been told that we can neglect the total entropy variation and the entropy associated to outgoing mass because the outgoing mass flow is decreasing. This means that the formula could only be valid for wells that are already in an advanced terminal decline. This hypothesis is not true if we consider the total global number of wells.

Equation 4 is not valid for wells not yet in final decline because even if the entropy change due to heat fluxes equals the entropy change due to irreversible processes when the outgoing mass flow is very low, it does not imply that those two terms are equal at any other time.

But the situation is even worse: if the oil outflow tends to zero, not only the entropy will tend to vanish, but also the heat flow (there is less heat to transfer, by lacking its source, the oil still to be extracted) and also the change in entropy due to irreversibility will bend to zero. All four terms from Equation 3 tend to zero in the final terminal decline, and for assuming that some terms become negligible in front of others (they go to zero faster, we could say), a very detailed analysis is required. This analysis is not done in the report.

The small detail that on top of equation 4 there is a wrong sign (the entropy variation due to irreversibility should appear with a sign minus, when solving equation 2) is in fact a minor issue (the entropy transference could be redefined with a different convention of signs).

Equation 4 is the starting point to calculate what the report calls “rate of irreversibility production” identified with the letter I and defined as follows:

Equation 5

This amount, as per equation 4, corresponds exactly with the heat Q (being rigorous, the variations are the both quantities are equal), so what can be calculated solving this equation is the associated flow of heat. Coming back to the expression of equation 3 and combining it with that of equation 5 (it is exactly what the report does), what they calculate is the heat flow obtained when taking a uncompressible, non-reactive liquid, that does not experiment any phase transition and taking it from a given temperature (the one of the geological deposit) to other (the one at the surface).

In this last pirouette, without any theoretical explanation, the heat flow is identified with the specific ETP; that is, per unit of oil mass extracted and surprisingly divided by billions of barrels (Gb), thus obtaining the fundamental formula of the report:

Equation 6

Where **m** represent the extracted masses (of oil if with subscript **c, **and water, if with subscript **w**) and the letters **c** represent the specific heat capacity of the substance (oil if with subscript **c **and water, if with subscript **w**)

It is worth to spend some time analyzing this expression. The important thing is the numerator, because the rest consist in dividing by some quite arbitrary amounts (the extracted mass of oil and the Gigabarrels). The numerator has a form that should sound familiar even to a secondary grade student:

Expression 1. Sensible heat of the oil and water mix.

We must remember that the specific heat capacity of a given substance is the amount of heat that has to be given to a gram of it to increase its temperature by 1 degree Celsius. For instance the heat capacity of pure water at 25 º C and normal pressure is one calorie per gram and per centigrade degree, or otherwise, 4.18 joules per gram and centigrade degree. Taking this into account and that the heat capacities of the liquids are “quite” constant (with many nuances), the expression 1 is simply the amount of released heat by a mixture of oil and water when it goes from a temperature TR (that of the deposit) to a T0 (that of the environment). In this point, the problems of this theoretical digression are so numerous that it is difficult to list them all.

There is no reason whatsoever to identify this heat flow from the mixture of oil and water leaving a deposit with that of the energy ETP (Etp by definition has to be the energy consumed by the PPS to obtain, refine and distribute oil).

It is not just that the theoretical rationale implies only a minimum part of the PPS (oil in the deposit) and that there are errors in the approximations (the direst one that invalids everything, in obtaining equation 4). It is not only that the HGR only computes the heat derived from the extracted mixture. Even discarding these errors, the ETP, as well as the heat, should be a variable of process, not a variable of state. This means that the amount of energy consumed by PPS depends on the specific processes used to move from one state to the other. Which has the following logic: we do not use the same energy to extract oil with a specialized brand new drilling machine, that using a more deteriorated and obsolete equipment. We do not incur in the the same energy consumption when transporting oil by a tortuous and long road, that sending it through a well-maintained pipeline system, etc. etc. That is precisely the difficulty implied by trying to assess the ETP from first principles: it is necessary to know in detail the specific processes used. Besides, these processes can be improved with time (in fact this is what usually happens). Therefore, any attempt to make forecasts has to consider these factors as well as many others (financial, geopolitical technological, or demand) that the report does not even mention.

Even from the point of view of evaluating this heat flow (which by the way has a minor importance with respect to many other processes that need to be described) there are many errors. Specifically, given the fact that the temperature of the deposit is of several hundreds degrees Celsius, it could be assumed that in some point from the deposit and the wellhead, the mix of oil and water could suffer a liquid to gas transition, as the pressure decreases, and the subsequent latent heat should be accounted. In any case this heat flow has no much sense, because the oil does not come out at the deposit temperature (it will be very dangerous, as the contact with the oxygen could lead to a deflagration). There must be a temperature exchange process in the extraction (likely favored by the well design), that will introduce irreversible processes that should be accounted in the last term of the equation (and there are not).

It is rather curious to see the water fraction appearing in the last moment of the derivation, when in fact this water is entering basically pumped in from the surface to favor the oil extraction; but it was precisely the incoming mass term what was the first one to be eliminated in the first simplification. In fact the water inflow also implies a heat flow not considered, of opposite sign to the one considered in the formula, that will probably tend to diminish in the left side of equation 4.

The entropy is a variable of state and it characterizes, as such, the state of the system; but knowing just the entropy does not suffice to completely characterize a state; other complementary variables are needed, such as temperature, pressure, internal energy, chemical potentials…That’s why even knowing completely the specific process involved in the ETP for the PPS system, the entropy alone will not be enough for evaluation ETP; other complementary variables that the report does not contemplate will also be required.

This flaw is severe: apart from the need to introduce more terms in the sums of equation 1 and making consistent hypothesis, it will be necessary to define a good number of additional equations, as many as the state variables, also containing a good number of terms in each of them. In this sense the ETP model has only scratched the surface of the thermodynamic modeling of the energy required for the continuity of the PPS.

Some more observations could be made, but I believe it is crystal clear that there is no theoretical reason for the ETP curve, derived from this thermodynamic model. As such, at most the model could work in an effective way, assuming that the curve resembles the right one and that the model parameters can be adjusted a posteriori to produce meaningful results Therefore, data processing in the model is crucial. Regrettably, data processing has many problems on itself, as described by Carlos de Castro.. I will leave them out to shorten this post.

**Discussion of the ETP model.**

The emergence of the ETP model some months ago raised big expectations among the experts in energy depletion, especially because the convincing nature of a fast collapse of the oil industry. The present strong divestment in upstream by oil companies, that started in 2014 and still lasts today, seems to be in perfect agreement with the problems anticipated with the HGR and with the posts by Louis Arnoux

In this sense, the appearance of the report whose theoretical grounds have been discussed here, it is something positive, as it opens a necessary debate on the decline of the net energy to still today reluctant sectors to this type of discussion. On the other hand the application of the thermodynamic principles to the assessment of the net energy limits, it is something that has sense and it seems an interesting path to explore, even if this will imply a very exhaustive and meticulous work, with a good comprehension of the many aspects of the oil industry, to ensure a correct accounting.

In the negative side, there are many things: an incorrect application of the theory, wrong deductions, definitions with no physical meaning, defective data processing, lack of interaction with the economy and other energy sources, etc.

Taking into account these deficiencies, it is obvious that the ETP model cannot be used for a serious discussion of the energy depletion problems; at least not until a whole review is made.

My work in this post, has been somehow similar (although more informal) than the one I would have made as a peer reviewer if sent to a scientific media. In fact, once the Hill’s Group released the report, it should have been desirable to send it to a scientific journal to be peer reviewed, to be later released and disseminated in the scientific community, general public and stakeholder. Passing this revision would have been a guarantee that the work had been assessed by experts and the results are trustworthy. I understand the authors may already be working on that. My advice is that they wait for the reviewers to finish and apply the suggested corrections, before giving more publicity to a model that as it is today can only serve to discredit to a community that deserves to be heard more than ever.

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**Personal assessment**

The appearance of the ETP model has prompted the necessity to endow the community with the adequate models to describe the growing non-linearity of the system, that will be growing if there are no short term reactions to the problems already detected.

However, the ETP model has been received with a surprising lack of criticism by the community, in a collective gap in which I myself have participated in some way. It may have happened a confirmation bias: as one colleague said, a brilliant and enlightened physicist, the model started with correct premises and arrived to coherent conclusions; therefore, it was reasonable to expect that the model will work properly.

In reality, very few had bothered to calmly analyze the model and point out the deficiencies. I hope this should serve to maintain a critical thinking and do not accept things that seem to confirm what we believe. All hypothesis must be examined and all the works revised to obtain the highest efficiency, yielding the best results to all of us. I do hope that this post and similar others could contribute to improve the model and to improve our understanding of the troubled way ahead of all of us.

Bests.

Antonio