I think it is easy to get hung up on Hubbert. He is not a magical guru, nor our religious leader who must be revered. He was simply a guy doing modelling of oil production, that's all. Perhaps he was the first or most famous, and deserves a special spot as an inspirational pioneer.

He was working with the best data and techniques he had at the time. Subsequent people have refined the techniques and have more data. As for predictions, they are always extrapolations of current trend assuming "all other conditions stay equal". It's a weather forecast, not a messianic prediction. Like a hurricane track, we should use it for planning. If the hurricane doesn't hit this time, we don't say "hurrah! hurricanes don't exist!"

So don't worry whether Hubbert had every detail right. He didn't, but it doesn't matter. Equally, to those who eagerly find fault with any detail of Hubbert's predictions : big deal. It doesn't disprove any of the modelling now being performed, nor does it mean that the whole concept of oil production peaking goes out the window.

Hubbert ignored external factors such as economics and technology improvements, and it was IMO a mistake to do so. There is no a priori reason why the production curve needs to be symmetric. Pre-peak production curves may have looked symmetric simply because, with other sources available, there was no economic incentive to do anything other than let natural geological flow rates dominate. Post-peak, don't be surprised if aggressive efforts are made to maintain production, resulting in a lopsided curve with a very steep downslope following a sort-of plateau. Also don't be surprised if the plateau is a bumpy one as price rises kill demand which causes price drops which etc etc. And as prolonged price rises put more unconventional oil into production. Long term of course we will see the downslope, there is no disputing that.

I don't understand why people think the only options are a symetrical profile or a peak followed by a cliff. A third option is that the peak is followed by a long slow decline. Too many factors affect the production profile to say which is the most likely.

I don't understand why people think that the oil crisis in the 70s caused oil production to deviate from some 'ideal' hubbert curve. The production profile has always been affected by economics and politics. There is no geological reason why oil production should follow a hubbert curve. No reason at all. The production profile is what it is. If it doesn't follow the hubbert curve, then the hubbert curve was wrong simple as that. It is a crude approximation used only because no one has a better model.

Symmetry of the curve is being discussed (along with other issues) here-->
http://peakoil.com/post195998.html#195998
I'm still waiting for Rockdock to comment on the conceptual accuracy of my approximation (and yes I'm fully aware of the contradiction between "accuracy" and "approximation")

I've been unsuccesful in finding enough of Hubbert's own writings to answer this question myself, therefore I ask it here. (50 words or less
if possible).

Why did Hubbert believe total world oil production would follow the same
basic form as US domestic production? Or did he?

My limited knowledge seems to imply he believed what was true of the
part(US) was true of the whole(world). This might be true and might not.

Until we are well into the downward slope of the peak oil bell curve that will be derived afterwards with 100% known data. That

If the yet to be found oil supplies that are it is assumed will be found are not found. Then the bell curve's 'peak' will show a peak occurring earlier than the actual production graphical representation does currently.

Only history will really show the true curve. Much relies on future discoveries. Mr. King Hubbert only showed what the CURRENT DATA showed. As data changes so does the results of any mathematics performed.

Even if the peak date changed he still showed the need for mankind to think about the realities of the future production of petroleum products.

So if the peak date is 25 years later. Mankind has a chance to change our ways. If he is more correct and only 9 years off we have less time.

I think that the hardest thing for many to come to terms with is the fact that we live in a world of limits. The earth has a finite physical size with finite amounts of oil deposits.

Whether all of Hubberts math was perfect, or when exactly the peak will occur will be debated indefinitely. The fact that oil is finite in supply is not debateable.

The painful coming to terms with this fact is similar to an infant realizing that the world doesn't revolve around them. People will kick, claw and scream and go in to serious denial before finally accepting this.

A good thing about peak oil. Is that people will have to grow up, finally.

Umm, can you say DOUBLETHINK?

no...

He's saying that the exceptions prove the rule.

We found the posting by Smiley in which he or she proposes a simple physical model for Hubbert’s peak to be quite interesting. In the posting, Smiley comments that he or she can solve the model numerically but doesn’t know if there is an algebraic solution. In fact, it is possible to solve the model algebraically and to show that the solution for the volume of liquid extracted follows the s-shaped logistic curve and that the rate of extraction (the derivative of the logistic curve) has the characteristic bell shape with its peak at the halfway point for total volume extracted. This solution requires a specific algebraic form for the area of the hole A(t) through which liquid is being extracted. However, this particular form is quite reasonable. It is itself peaked, with a peak which lags behind the peak in the extraction rate. This can be interpreted as wells being shut down (due to water encroachment, etc.) as production falls. A very rough draft of the details of our solution can be found at http://www.tam.cornell.edu/~dma32/oil/o ... oBookmark3.

Welcome to the forum Hybrid....

This is really interesting. Hope you don't mind me taking you into the realm of economics:

There ought to be a way to model the cost of maintaining the pressure of the vessel at P sub 0, that is, as a little fluid is extracted, the pressure can be brought back up to P sub O at some cost. In the real world, this would represent the injection of water or CO2 or something to maintain the flow rate. Obviously, as the fluid is extracted, the cost of maintaining the pressure at some rate will increase. Also, increasing the diameter of the hole (or drilling more holes) will make necessary an even greater increase in cost to maintain the pressure.

What I am thinking is at some point after the peak, the incremental cost of maintaining the pressure at a given rate can be pretty close to asymptotic, which is to say, at some point, you reach "the wall" and the incremental cost of maintaining the flow rate will exceed the incremental benefit of extracting the fluid. There is an economic breakeven rate, and also, an energy breakeven rate (EROEI).

It would be interesting to know how far to the right of the peak that will occur. From that, you could make some estimates for a given field as to the point at which you would abandon production, and therefore, get some understanding of how much of the "proven reserves" in a given field might be unrecoverable.

The reason that this is interesting to us, is the historical data for production and consumption of NGl in Saudi Arabia.



Presumably Saudi is using natural gas or some oil-derivative to pump seawater down into their holes to keep the pressure stable on their small number of oilfields. As you can see, over the past five or six years, the amount of oil extracted per BCF of gas has been getting lower and lower every year. This suggests that they are having to pump the hell out of water into their holes to keep production constant.

Using the above equations, along with a cost factor, you should be able to estimate how close Saudi is to "peak" and also model how many years they have until it becomes too costly to pump the incremental amount.

It would be really interesting to know this.

I don't understand how the term A(t) can be separated out of the solution. If this really did solve the partial differential equation, A(t) should reduce to a constant. Otherwise A(t) is a function of Ve(t), which is what you are trying to solve for!

A contrived example:
du(t)/dt = A(t) u(t)

but I WANT the solution u(t) = k*t

so I set A(t) = 1/t = k/u(t).

then I can solve for du/dt = k/u(t) * u(t) = k
or u(t) = k*t.

But we all know that this is bogus, because IT IS NOT CALCULUS. It is just a bunch of sleight-of-hand, masquerading as calculus. I think in your desire to force it into the logistic equation you took some misguided shortcuts.

Indeed. Generally speaking hydrostatic or water pressure increases with depth by about 0.45 psi/ft. There are cases of overpressure in real life due to factors such as undercompaction, an isolated reservoir etc. In terms of temperature it depends on where you are drilling. Offshore in ultradeep water it is possible you are drilling into rocks sitting above oceanic crust in which case the geothermal gradient is somewhere around 35 - 45 C/km. If you are drilling onshore on an old cold craton like central US it can be as low as 10 C/km...if you are drilling near a modern rift (eg. East Africa Rift in Uganda) you can have geothermal gradients as high as 60 - 100 C/km locally.

By the way there are a bunch of engineering formulae constructed for these exact issues.....usually allow you to look a single phase or multi phase flow, water drive versus gas depletion drive, input porosity, permeability...etc etc. Not sure if you guys were just interested in modeling to understand how it works (very commendable) or wanting to solve a problem (commendable as well). I can probably dig the relevant stuff up in some of my dusty reservoir engineering texts.

Thanks for the info! so if P= f(depth) and T= g(depth), the initial conditions of the above model can be known and derived from the reservoir depth.

I guess I should qualify a bit with the need to take a simple case....onshore in a craton would be good. Also with temperature there can be oddities...for example salt is pretty conductive so it will change geothermal gradients locally. The thermal gradient through water bearing, oil bearing and gas bearing sediments is also slightly different. But again a simple case is best.

Also there are a bunch of other issues regarding fluids one has to take into account. For example in the model here gas and oil are used together. The added bit of difficulty this adds to the problem is that at reservoir conditions there will be a fair bit of gas entrained within the oil if it is at conditions above bubble point. As the produced fluid moves up the borehole it's P & T drops and gas begins to bubble out. An added concern if you were looking at detail might be the change in fluid friction along the tubing as the fluid moves and changes properties. Seems complex but actually is pretty logical step by step. Also best to start without sulphur....this creates another problem....don't make me tell you about the well I sat as a youth that ended up spewing chunks of sulphur .