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On the Thermodynamic Model of Oil Extraction by the Hill’s Group


SK is a professor emeritus in the department of Mechanical and Aeronautical Engineering at a Major University in the USA.

Corrections to the first and third equations were made on Feb 25, 2017.

The report reviewed here claims to rely on thermodynamics arguments to predict oil’s price-volume trajectory going forward.

Classical Thermodynamic analysis

First a few lines about thermodynamic analysis. The early contributions to thermodynamics by Carnot, a military engineer by training, were based on study of heat engines. The same theme was followed by Clausius, Kelvin, Planck and others. The study of heat engines is still an important aspect of mechanical engineering and as such appears in engineering thermodynamic textbooks with one chapter devoted to the analysis steam power plants, and another on the thermodynamic cycles that model, spark ignition engines, diesel engines, and gas turbine power plants. Similar analysis is next extended to refrigeration cycles and performance of heat pumps.

The fundamental analysis is based on the first law of thermodynamics together with a mass balance. The second law of thermodynamics introduces the entropy as a thermodynamic property and the related concepts of reversible processes and reversible heat transfer. Irreversibilities of real processes are taken into account by assigning a value of experimentally determined efficiency to equipment such as pumps, compressors and turbines and this way the reversible processes are related to the actual ones.

A relatively recent development has been a systematic use of an exergy balance to examine where in a complex energy system irreversibilities take place. Exergy is defined as the maximum theoretical work that can be obtained from a system and its environment as the system comes to equilibrium with its environment. By combining the first and second laws of thermodynamics an exergy balance can be written down. Rudimentary exergy analysis can be found in the 1941 book Thermodynamics by Joseph Keenan. It was called availability analysis at that time. The most systematic development of the exergy analysis is in the textbook Fundamentals of Engineering Thermodynamics by M. Moran, H. Shapiro, D. Boettner and M. Bailey, 7th ed. John Wiley, 2011.

Developments over the last century have led to increases in the thermodynamic efficiency of systems such as a coal or nuclear power plants, mainly by increasing the maximum steam temperature of the plant. As the hot steam from a boiler or a superheater flows into the steam turbine, the first row of blades encounters a hot environment. This requires that these blades be made of materials that withstand the stresses generated at these temperatures. Such developments have increased the maximum temperature of these power plants to about 1000 F, but further improvements have stalled over the last half a century. To be sure, in the interim feedwater heaters and reheating have been used to increase the efficiency of the plant. For gas fired power plants combustion temperature is higher and turbine designers implement both cooling technology and use high temperature materials for the blades. Today they are made of single crystals, capable of withstanding the hot combustion gases.

Although the entropy balance equation can be used (although typically only for steady state systems) to determine the entropy production, to carry it out requires that sufficient number of thermodynamic properties and interactions are known at the system boundaries. Since such a calculation needs to be carried out after the thermodynamic analysis has been completed, it is seldom done in engineering practice because the knowledge of the same properties allows also the determination of the thermodynamic efficiency of the system.

The advocates of exergy accounting claim that knowing where the exergy destruction takes place in a system is a good way of allocating development money to improve it. This kind of analysis has not taken hold in industry either, simply because, manufacturers of, say turbines, know that the efficiency of the turbine is a measure of the irreversibilities and they direct their efforts toward understanding how the blades of the turbine can be shaped in order to reduce these irreversibilities. Such a task is based on aerodynamic calculations. Compressors and pump are, by the nature of the flow through them, machines with lower efficiency than turbines and their improvement requires again experts with fluid dynamic knowledge to improve them. Similarly improving the heat transfer in a heat exchanger is carried out by making improvements in the heat exchanger surfaces and reducing pressure losses. If these improve the heat transfer, the entropy production is reduced. Here the expertise of a heat transfer specialist rather than a thermodynamicists is needed.

One interesting application of exergy analysis is to calculate the second law efficiency. A high second law efficiency means that the source of energy is well matched with the application. Thus heating shower water with a thermal solar heater is a good match, as unfocused solar energy raises the water temperature high enough to serve as shower water, but not nearly so high as to create superheated steam to power a steam turbine. Thus the most important insight to be obtained is to match the source of energy to the application, and once this insight is internalized, calculation of the second law efficiency adds only marginally to understanding. For this reason it is seldom used in industry. To be sure, optimization of a system’s second law efficiency is still worthwhile, but using other metrics this can be done with topics based on heat transfer and fluid dynamics, with stress analysis, material selection and related fields as further aids. Interestingly exergy analysis shows that most of the exergy destruction takes place in the combustion of the fuel, but there is not much one can do to reduce this destruction. For this reason a naive application of exergy analysis may lead the poor allocation of development funds. Besides, the manufacturer of the turbine does not design heat exchangers so their coordination would be difficult to carry out.

Thermodynamic analysis in the report by the Hill’s Group

The report uses the second law of thermodynamics as the starting point. The unsteady entropy balance for a control volume with one exit and no inlet is given as

Next comes the assumption that at all times

It is based on the observation that because at the end of oil production when the reservoir has been completely depleted the flow will stop and nothing much takes place, then both of these terms are zero. After cancelling these terms the entropy production is seen to be related to the heat transfer. But his assumption is clearly unjustified while the oil is being extracted and these two terms do not cancel each other. The neglect of the terms leads to an equation that omits the entropy production that is caused by the irreversibilities of the oil flow through the permeable reservoir rock.

The incorrect canceling leads to the equation

and the former choice assumes that the entropy production is known and then this equation is used to calculate the heat transfer. If one the other hand, the aim is to calculate the entropy production in the reservoir, there is no indication in the report how the heat transfer is calculated. In thinking about the heat transfer, for a control volume that includes the reservoir only, it appears that the heat interaction between the system and the surroundings is mainly caused by the geothermal gradient. That is, heat enters from the lower boundary and leaves across the upper boundary. This is a passive process. The fact that the oil and water in the reservoir have some average temperature in the geological setting only influences the viscosity of the fluids and thus how well they move through the reservoir, but from the energetic standpoint the sensible energy is not important. That is, there is no attempt made to extract this energy in a heat exchanger, nor is the high pressure used to extract energy in an expander. Rather the oil and water mixture flows through a set of throttling valves, in which the exergy is destroyed.

If one the other hand the entropy production were known independently, then this equation could be used to calculate the heat transfer, but the answer would be incorrect because entropy production is caused by both heat transfer and irreversible processes taking place inside the control volume. For the control volume consisting of the reservoir, entropy production takes place mainly in the pores of the permeable reservoir rock as the flow is forced out. This takes place by viscous dissipation and although it can be calculated in principle, in practice such a calculation is nearly impossible to carry out from first principles. The entropy production rate for the system would then be calculated by integration of the local values over the entire reservoir.

There does not seem to be much point in attempting to relate the entropy of crude oil in the reservoir to that of the output stream. Whereas entropy of pure substances are tabulated in thermodynamic tables, for mixtures such as crude oil it is not known. It appears that the attempt in the report is to relate the efficiency of oil extraction to the reversible work needed to accomplish the same task.

Next in the analysis is a calculation of ETp. It is defined as the total production energy, or the total work required to extract, process, and distribute a volumetric quantity (a gallon) of crude oil. The report offers the equation

as a way to calculate it. But this is the energy of the sensible part of the oil-water mixture above the reference temperature To. It does not include the chemical energy of the crude oil and the formula cannot be reconciled with the definition of ETp.

The following equation also appears in the report

Thus there are two equations to use for calculating ETp and there is no mention what the independent variables are and what is calculated using these equations. If the value of ETp is calculated this way then how is the previous equation used? The only unknowns are the reservoir temperature Tr and the oil-water ratio, if the total flow rate is determined from the depletion rate equation. The reservoir temperature can be measured, so the unknown seems to be the water oil ratio. However, the report makes use of an empirical equation for the oil/water ratio as a function of the percent depletion of the reservoir. Finally the last equation can only be used to calculate the change in exergy, and this would necessitate a new symbol to be introduced for exergy, e.g. XTp, for exergy is not the same as energy.

The report next presents calculation of the oil extraction trajectory that is based on Hubbert’s methodology. The calculations are in close agreement what others have found, with cumulative production 2357 Gb that is somewhat larger than Campbell and Laherrere’s value of 2123 Gb. It is now well known that in the calculations based on logistic equation, there is a slow drift to large values of the ultimate production as more data has been included in the calculations with the passing of the years.

In the same section is also a discussion of the surface water cut as a function of the percent of oil extracted from a reservoir. The curve is then rotated in order to satisfy two criteria set by the authors. Now a rotation of a curve is a mathematical transformation and a curve cannot be arbitrarily rotated without destroying the underlying mathematical theory. Furthermore, the report states that ETp cannot exceed EG, the crude oil’s specific exergy. With the calculation of ETp suspect, this condition is also meaningless. Here again energy and exergy are used interchangeably.

Returning to the calculation in Section 4.1 of the report for calculating ETp by the equation

The statement on top of page 19 suggests that the water cut is an input parameter, in which case the value of ETp depends only on the reservoir temperature. The reservoir temperature in turn is a function of the depth of the well, owing to the geothermal gradient. This would allow this equation to be used to calculate the sensible energy of oil-water mixture. But what purpose does this serve? The sensible energy of the crude oil is not used in any significant way. The crude oil cools as it enters the ground facilities and it cools further as it is transported in the pipelines. No power is generated from the sensible part of the crude oil’s energy. Only the chemical energy is valuable upon combustion. The rest of the report relates to how prices are linked to the energy delivered.

From what has been discussed above, the thermodynamic analysis is incorrect and therefore any calculations and graphs based on this analysis must also be unreliable. Readers may note that the incorrect analysis predicts that one threshold based on their analysis was passed in 2012 and another will take place in 2022. That this coincides with the time others have judged to be when great difficulties to appear, seems to give the report a superficial credibility.

Since the chemical energy is the only significant energy of crude oil, this is the energy returned in the EROEI calculation. If the authors have a better handle on how much energy is expended in oil production, they can form the EROEI ratio and it would constitute an independent check on the work of Hall and his coworkers on EROEI. Such an independent analysis would be valuable.

 Peak Oil Barrel

26 Comments on "On the Thermodynamic Model of Oil Extraction by the Hill’s Group"

  1. Cloggie on Sat, 25th Feb 2017 12:02 pm 

    Let’s hope that the mistakes will be addressed in the second version of the report.

  2. shortonoil on Sat, 25th Feb 2017 2:01 pm 

    This writer is making up a whole bunch of stuff that is NOT in the report. Anyone can compare the report to what they saying by going here:

    Pay close attention to the Q/T = σ . That is the third equation that they list, and is on page 8 of the report. They have a minus sign in front of the theta term. There is none in the report. This has been intentionally alternated to deceive readers.

    If Coyne can’t do any better than this, he had better get back to his fictional lines for fictional reserves.

  3. Dennis Coyne on Sat, 25th Feb 2017 2:28 pm 

    Hi Shortonoil,

    I guess you will have to publish your model in a peer reviewed journal to see if PhD level mechanical engineers such as Professor SK think it is correct.

  4. shortonoil on Sat, 25th Feb 2017 2:32 pm 

    Whomever wrote this is a complete idiot. His minus sign in front of the σ term is ridiculous. Entropy is never negative. If it could be it would be possible to build a perpetual motion machine. That is guaranteed to not to happen by the definition of entropy as put forth by the Clausius inequality.

    Whom ever this is, is as much a mechanical engineer as Abraham Lincoln was a brain surgeon. The site that this was taken from is obviously a good place to stay away from!

  5. Dennis Coyne on Sat, 25th Feb 2017 2:36 pm 

    Hi Shortonoil,

    On fictional reserves, my “low” model based on Paul Pukite’s (aka Webhubbletelescope) Oil Shock model is consistent with the estimates of Jean Lahererre, using Hubbert Linearization to estimate a URR of 2500 Gb for C+C less extra heavy oil (Venezuela Orinoco and Canadian oil sands).

    The high scenario is similar to estimates by Steve Mohr and is lower than the estimate of the USGS and are also based on the oil shock model and reasonable estimates of future extraction rates.

    I doubt all this oil will be extracted because lower cost of alternatives will eventually drive down prices, maybe by 2050 or 2060 and a lot of oil will be left in the ground due to low oil prices.

    Thermodynamics will have very little to do with it.

  6. Dennis Coyne on Sat, 25th Feb 2017 3:01 pm 

    Hi Shortonoil,

    Interesting, Q/T is not entropy, Q (with a dot on top) is a flow of heat and T is the absolute temperature in Kelvin of the system.
    Heat can flow into a system or out of a system, there is not a single direction for heat flow.

  7. Ghung on Sat, 25th Feb 2017 3:10 pm 

    I doubt all this oil will be extracted because Systemic contraction will create demand destruction well before 2050 or 2060 and a lot of oil will be left in the ground due to an inability to sustain anywhere near current levels of industrialism. When you are economically, politically and ecologically screwed, current levels of oil production will be history. Forever.

    Thermodynamics will have very little to do with it, at least as far as the average Deluded Joe is concerned.

  8. James boags on Sat, 25th Feb 2017 3:13 pm 

    Troll alert ! They’ll be coming in thick and fast on this topic

  9. James boags on Sat, 25th Feb 2017 3:17 pm 

    The etp model is there worst nightmare they will do anything to discredit it

  10. Ghung on Sat, 25th Feb 2017 3:19 pm 

    It’s not a troll thing, James. One just needs to get one’s head out of the oil sands to figure out that a lot of things need to go right to maintain anywhere near current levels of production. It’s forest/tree thing.

  11. onlooker on Sat, 25th Feb 2017 3:37 pm 

    Yes James, certain people and for sure the Establishment do NOT wish the realization to sink in that our energy dependence is now on life support as the Oil Industry begins to crumble as the Etp predicts. Too much money involved and too much at stake in the disruption of business as usual/ Ironically, this attitude has prevented us for years from taking a different path. Now change will be forced upon everyone. Ghung, people do not wish to take their head out of the sand just like the ostrich, the future is too scary so they look away.

  12. Dennis Coyne on Sat, 25th Feb 2017 4:01 pm 

    Hi Ghung,

    Note that I expect oil to peak between 2020 and 2030 (probably closer to 2020, maybe 2025 for end of plateau, 2030 very doubtful).
    In the mean time oil prices will increase and there might be an energy transition to non-fossil fuel energy from 2020 to 2055.

    I expect when peak oil does arrive and is actually accepted by most people as a reality (by 2025 or maybe 2030 at the latest) the economy will be disrupted and there will be a Worldwide depression, around 2030 +/-5 years for the start. It will last 5 to 10 years and possibly there will be a Worldwide WW2 like effort to transition to non-fossil fuel energy. I believe it is possible with proper policy for such a transition to be complete by 2055+/-5 years.

    May be wishful thinking though as this is one of many problems.

  13. Dennis Coyne on Sat, 25th Feb 2017 4:12 pm 

    Hi Onlooker,

    I expect oil will peak and decline, but Hill’s analysis of oil price based on net energy is flawed. Time will show that this view is correct, but oil output will peak and decline leading to higher prices for oil.

    Imagine oil prices fell to $10/b, would people use more or less oil?

    What would happen to oil supply at $10/b would it be higher or lower?

    What do you think will happen to the price of oil under these circumstances?

    This is pretty basic stuff.

  14. onlooker on Sat, 25th Feb 2017 6:03 pm 


  15. onlooker on Sat, 25th Feb 2017 6:08 pm 

    Dennis, I replied to you on the Etp thread in the main section

  16. makati1 on Sat, 25th Feb 2017 6:18 pm 

    What all of these “predictions” do NOT take into account are all of the events happening in the rest of the world that will prevent them from ever coming true. That is why I do not bother to read anything that starts with “Future this” or “Peak that”. All are just bad guesses and most are just used to prop up the oily lies that have been spewing since at least the 1970s. Capitalism is dying, and with it is the oily industry. No profit, no oil. The serfs are becoming less and less able to buy oily products at any price. Food and shelter will be the main priority soon, not anything else.

    If you are not preparing for a world with a lot less energy available in the near future, you are the one who will suffer the most, not the ones who face what is coming and are preparing their life boats. But then, denial is easy. Preparing is not. Buckle Up!

  17. Truth Has A Liberal Bias on Sat, 25th Feb 2017 7:39 pm 

    A great amount of confusion seem to have grown up in the use of words ‘forecast’, ‘prediction’ and ‘projection’. A prediction is an estimate based solely in past data of the series under investigation. It is purely mechanical extrapolation. A projection is a prediction where the extrapolated values are subjects to a certain numerical assumptions. A forecast is an estimate which relates the series in which we are interested to external factors. Forecasts are made by estimating future values of the external factors by means of prediction, projection or forecast and from these values calculating the estimate of the dependent variable.

  18. Truth Has A Liberal Bias on Sat, 25th Feb 2017 8:06 pm 

    Clearly the Etp model is severely flawed. The best Hill can do to defend his model is point to a typo in this article. At least Hill now posts a fre link to his article instead of trying to sell it.

  19. James boags on Sat, 25th Feb 2017 9:40 pm 

    Yes that’s about right years of research by the hills group to come up with the etp model debunked by a troll saying its flawed and that’s it nothing to see here move along. So far is been on the money and $54 max for a barrel in 2017 looks spot on

  20. Truth Has A Liberal Bias on Sat, 25th Feb 2017 10:08 pm 

    i read some talk from Steve at SRS a short time ago that the Etp report was gonna be published in a peer reviewed scientific journal. Anybody have any updates on that?

  21. carval on Sun, 26th Feb 2017 1:39 am 

    In Spain have been published recently, in Spanish, a couple of articles about the ETP model. Both with a liking for the project, but quite critical:

  22. Cloggie on Sun, 26th Feb 2017 5:46 am 

    This whole discussion is a rear-guard fight as it pretends that conventional oil (+dregs from Venezuela and Canada) are all there is.

    In reality we are entering a “third carbon age” of unconventional fossil:

    At least in North-America; Europe in contrast has chosen a renewable energy future, regardless of what Michael Klare says.

    The real significant point is that there is more than enough fossil fuel available to guarantee that the renewable energy transition will succeed, most likely in Europe first (2050).

  23. Davy on Sun, 26th Feb 2017 8:06 am 

    “The real significant point is that there is more than enough fossil fuel available to guarantee that the renewable energy transition will succeed, most likely in Europe first (2050).”
    What we lack is the wisdom to continue as a civilization. We lack a healthy planetary system. We will soon have an economy that is in a death spiral of stagflation combine with population overshoot and in an underlying basis of ecological failure. A new renewable word that is an energy and societal transition is not remotely possible without a healthy basis.

    Clog you are pissing on yourself. I hope I am crazy and you are right but I am honest and I see little reality with what you are preaching. There are too many things that don’t add up. There is too much fantasy and hopium for a transition that must happen now. The scale of the undertaking and the time frame it needs to happen in is fantasy. The population must stop growing “Now”. Attitudes and lifestyles must change “Now”. Humans want affluence “Now”. Try to reconcile all those incongruities. All you are doing is projecting techno optimism without the economic basis nor the social wisdom needed to make this a reality. You cannot do this transition just with technology. You cannot transcend earthly limits. The only way there will be such a transition is through a holistic transformation of man and that appears unlikely without a population dropping to 500MIL. I see absolutely nothing to be optimistic about.

  24. Cloggie on Sun, 26th Feb 2017 9:15 am 

    I see little reality with what you are preaching. There are too many things that don’t add up. There is too much fantasy and hopium for a transition that must happen now. The scale of the undertaking and the time frame it needs to happen in is fantasy.

    So what do you suggest we should do?

  25. Davy on Sun, 26th Feb 2017 9:40 am 

    Do what you are doing Clog but with sobriety that embraces honesty. If you say for example “it is a long shot but we have to try”. I would say bravo for the spirt. If you admit that technology has and is killing the planet but we are stuck with it again bravo. But please don’t blow smoke up my ass. Your motivation is good but with a poor presentation.

  26. Nony on Mon, 27th Feb 2017 6:53 pm 

    ETP is beyond silly. Nutter mumbo jumbo about thermo from guys that I wouldn’t trust to run a hot water boiler. It reminds me of Blacklight Power or Cold Fusion. That POB ran this story makes them look bad.

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