Don’t worry, just a little bump - $70 is just around the corner. Short traders just keep making those margin calls, mortgage the house if you have to. Fortunes await you! PO is for pansies and doomers. At $70 short some more ..... it is going back to $22 .... the world is awash with oil ........ reality has nothing to do with it, its all in those charts!!!!!!!!!!
Joined: Jun 20, 2004 Posts: 250 Location: California
Posted: Tue Jun 27, 2006 12:14 pm Post subject: Mathematics of depletion
I've seen people throwing around alarmingly large depletion rate numbers lately. For example Simmons, using 8%, predicts we'll be down to 25 mbd by 2020. Is this at all plausible?
When I first started crunching the numbers on depletion over a year ago, I concluded that in the long run, the reserve/production (R/P) ratio and the depletion rate must eventually be inverses of each other. Decline slower than the inverse R/P ratio, and the ratio gets ever smaller, decline faster and the ratio gets ever larger. Eventually, you must revert to the inverse ratio, either by experiencing an extremely rapid decent as the ratio gets too small, or by flattening out to a low decline rate as the ratio gets large. This is because the numerator, R, is dropping by an amount equal to the inverse of the R/P ratio, while P is dropping by whatever depletion rate you're using.
Some examples may help. I'll round off numbers from BP's world energy report: let's suppose R is 1200 Gb and P is 30 Gb/year (82 mbd). R/P is 40. Don't believe BP's estimate for R? Fine, use 900 Gb and R/P is 30, it doesn't change the argument. I am assuming zero reserve growth and zero new discoveries - the analysis assumes your reserves are all there is to produce, and the R/P ratio is the inverse of your "burn rate".
With an R/P of 40, you can hold steady at that R/P with a decline of 2.5% per year. Decline slower than that, and R/P will contract. For example, suppose we can prop up world production at 30 Gb for 10 years, a 0% decline rate. R/P will drop to 30 as R drops to 900. At some point, you will be forced to decline, in this example a decline of 3.33% could set in after 10 years of flat production. Hold flat for 20 years and R/P drops to 20, and you can then decline at 5%.
Exactly the opposite happens if you decline faster than inverse R/P. Suppose we take the 8% decline starting year 1. R drops by 30 Gb, to 1170, but P drops by 8%, to 27.6 Gb. R/P then increases to 42.4 years! Compounding it for 14 years as Simmons does will indeed drop P to 9.33 Gb / year (around 26 mbd). However, the cumulative P for that time period has been 259, leaving R at 941. The R/P ratio is now over 100 years, and still climbing!
That just doesn't seem reasonable to me. Experience with mature producers (such as the US) shows that R/P ratios drop as they deplete. Many mature producers have R/P ratios of 10 or lower. An 8% decline rate is consistent with an R/P ratio of 12. Given current world reserves, I could believe a short-term 8% decline due to infrastructure constraints etc., but it's hard to believe we're about to start down at 8% for a prolonged period unless the reserve estimates are inflated by a factor of 4. It also seems unlikely that there really will be zero increases in reserves for the next 14 years.
P.S. if the R/P does soar to 100 in response to a production crash, a 1% decline could set in from 2020 onward. At 8%, at some point absolute production must decline to the point where the trend reverts and the decline rate drops. Based on the experience with depleted producers such as the USA, we won't see R/P numbers like 100 for conventional oil. We might see them for tar sand production, though.
Posted: Tue Jun 27, 2006 12:38 pm Post subject: Re: Mathematics of depletion
One thing that you seem to forget to use is the difference types of oil. It makes perfect sense to have an R/P of 100 if the oil that is left is extremely heavy, spaced far apart, it's source rock is not very porous, etc and simply just doesn't have a high production rate. By your calculations, you seem to give the impression that oil is completely homogenous in its occurrences around the world. It is not. Any complete analysis of oil depletion and its models needs to take this fact into account. Another main factor would be the net energy yielded as it becomes increasingly difficult to extract more energy (that is afterall what we want, not oil). Peace
In this little model, The production increases for the first 8 years, and then declines for the 7 years after that.
The reserves start out at 1200. No reserves growth.
In the beginning, R/P ratio declines, until production reaches its maximum. At this point, R/P increases. In other words, R/P ratio goes through a minimum point at the time of peak production.
So your mature producers are still pretty close to peak. The more their fields get depleted, the higher R/P will get. This is probably a really good functional definition of a post-peak nation, or post-peak global scenario.
I built another model in which reserves are allowed to grow by some amount:
It basically behaves the same way unless reserves growth is greatly larger than the annual extraction. But, if the reserves growth is growing that much, there is no compelling reason for the production to decline unless mekrob's point about heavy oil is considered.
So, either way, I am inclined to say that in a situation where production goes into a peak and decline, R/P ratio will be at its minimum when production is at its maximum.
Joined: Jun 20, 2004 Posts: 250 Location: California
Posted: Tue Jun 27, 2006 8:29 pm Post subject: Re: Mathematics of depletion
MattSavinar wrote:
So basically you're saying you think we're Fark.
Best,
Matt
I'm saying it appears the 8% decline number was either taken out of context or exaggerated for effect.
mekrob wrote:
Any complete analysis of oil depletion and its models needs to take this fact into account.
True. Do you think Simmons did that when he used 8% as an exponential decay rate and gives the number 25 mbd as the 2020 production level? Or do you think he was just trying to scare the crap out of his audience?
mekrob wrote:
Another main factor would be the net energy yielded as it becomes increasingly difficult to extract more energy (that is afterall what we want, not oil).
Also true. Reserves are by definition "economical" to produce. Since new discoveries are down, most of the reserves have been on the books since the days when the price was much lower. We are not talking about trying to squeeze out the 60-70% of OIP that is not currently considered recoverable.
pup55 wrote:
In this little model, The production increases for the first 8 years, and then declines for the 7 years after that.
Interesting model. Of course there's no way production is going to rise 8% a year for the next 8 years, to 140 mbd, is it? Focussing only on the decline, your R/P ratio is starting to shoot up as R drops at a slower rate than P. In the limit you'll reach the point where there's a lot of "reserves" left but you are unable (for some reason) to "produce" them at a meaningful rate. In which case, I submit, they should not have been called reserves in the first place. I am taking the notion of "reserve" at face value, it's oil they expect to produce. I think you are in effect saying you don't believe the reserve numbers. Now if you replace "reserve" with "resource" (OIP), then it seems obvious that you are correct to state that R/P (R = total oil remaining) will skyrocket as you deplete your wells.
WebHubbleTelescope wrote:
So reserves peaked around 1990, if not before, for Norway.
Good point. Indeed I would expect Norway to have a low R/P, and, according to BP's 2006 report, it does:
So, a pop quiz: which of these countries are likely post-peak?
Eyeballing the chart, it looks like Norway was producing around 0.30 Gb when reserves first hit 24 Gb, and was producing 0.80 near the end of the 24 Gb reserve "plateau". That's an R/P of 80 falling to 30, and it's been downhill since, has it not?
It would be interesting to back-date the Norwegian reserves, assuming perfect knowledge of URR as of year 1. (Similar to assuming our current reserve estimates of 1200 Gb represent perfect knowledge of URR for the world as a whole with today as the starting point.) We would then see the reserve number steadily drop as oil is produced. As production ramps up, the R/P ratio would plummet (well, technically it starts at infinity, so take year 1 production as the baseline) until the maximum production rate is reached. Then as the reserves are exhausted production would begin to decline, but of course reserves also continue to decline. The R/P ratio should then converge somewhere. It's not obvious that R/P is at it's lowest at peak production; it will converge to something dictated by geological considerations which could be higher or lower.
Joined: Jun 20, 2004 Posts: 250 Location: California
Posted: Tue Jun 27, 2006 10:51 pm Post subject: Decline rate versus R/P
Here's another take on the same basic issue.
Suppose you have a decline rate R (e.g. R = 8%). This implies that production P asymtotically approaches 0 over an infinitely long time period. Cumulative production over the same infinite amount of time is then given by 1/R (derivation if requested, or you can just look it up in a math textbook).
In other words, 1.00 + 0.92 + 0.84 + ... = 1/.08 = 12.5. So, at 8%, you can expect to recover 12.5 x 30Gb = 375 Gb after an infinite amount of time. Thus the implication is that 1200 - 375 = 825 Gb will never be recovered. This is the problem with a decline rate that exceeds the R/P ratio - you end up asymtotically approaching 0 production but a non-zero "plateau" of reserves never get produced no matter how far out you run the graph.
The problem with a decline rate exceeding the R/P ratio is obvious, but for the sake of completeness, consider the Norwegian example. At some point Norway's production will have to crash. The R/P ratio is 8.9 now, so a decline of 11% (or higher) seems inevitable. If they somehow stave off further decline for another 4 years, the R/P ratio will drop to 5, and a 20% (or greater) decline is inevitable. At an extreme R/P of 1, a 100% decline might reasonably be forecast. Obviously a reversion of the decline rate to something like the inverse R/P is inevitable.
If you believe BP's numbers, current world R/P is 40, where, barring any new discoveries or reserve growth, it could remain forever at a 2.5% decline rate. If a greater decline (e.g. 8%) were to set in immediately, it would at some point be arrested by the ballooning R/P - to believe otherwise is effectively to disbelieve the reserve numbers. Conversely, each year that we go without a decline in P, we will inevitably have that much steeper a decent on the back end.
We could certainly see a prolonged 8% decline on the back-end - but only, in my view, after an initial period of flat or uptrending production. 15 years of 2% growth and you top out at around 110 mbd in 2020, at which point you have 660 Gb remaining and your R/P is down to 16.5, after which a 6% decline could in theory continue forever.
Posted: Tue Jun 27, 2006 11:41 pm Post subject: Re: Mathematics of depletion
DoctorDoom wrote:
When I first started crunching the numbers on depletion over a year ago, I concluded that in the long run, the reserve/production (R/P) ratio and the depletion rate must eventually be inverses of each other.
Let R(t) = Reserve at time t
URR = You know ... the magic number
C(t) = Cummulative Production up to time t
P(t) = Production Rate
k = decline rate
Assuming that technological innovation does not happen i.e. URR is constant from the day the "exponential parasitic growth paradigm" started, the (abused by both doomers and cornocupians) laws of thermodynamics state that:
Eq(1) C(t)+R(t) = URR (Conservation of mass)
Eq(2) P(t) = - dR(t)/dt (Conservation of mass)
Consequently the R/P ratio is a function of time which is quantitatively described by:
Eq(3) R(t)/P(t) = (URR-C(t))/P(t)
irrespective of where one is at the point of the curve i.e. pre or post or at the top of the peak.
The question you posed can be answered by invoking a simple model for the post peak part of the oil production curve ie.
Eq(4) dR(t)/dt = - k*R(t) with initial condition:
Eq(5) R(0) = Rpeak
i.e. t=0 is the peak date and hence the R(0) are the reserves at the "day" of the peak
Hence the last two equations do yield simple exponential asymptotic approximations to the decline/production curves post peak after integration:
Consequently the R/P figure post peak is the ratio of the two equations i.e. :
R(t)/P(t) = 1/k
which is what you said .... ( P(t) should not be zero for this to be a mathematically vaild operation)
As long as:
the post peak part of the curve is faithfully approximated by a first order linear ODE
we are indeed at the post peak phase
URR does not change (as a result of technological innovations, Simmons attempt to maximize the yield of his investments, revelations during REM-IV sleep by the die-off god)
production data are accurate
infrastructure is not blown up by terrorists
investment in the field is limited to maintenance stuff only
the field manager is pumping as fast as he or she can go given the state of the equipment on the field
the R/P number post peak will always be equal to the inverse of the decline rate for a single field (the country or even the world situation will be extremely more complicated). So one should "Eventually... revert to the inverse ratio" some time after the peak
The list of assumptions has to be augmented by a pretty heavy set, to say anything of consequence about the country or the world situation but it would appear that your semi-quantitative analysis of the BP example is ok.
The hypothetical situation you describe is one, of a variable k as a result of infrastructure updates/problems management decisions etc. In this case ,one could decompose the post peak part of the curve into phases each of which has its own value for k.
During each phase, the ratio of the R/P will be numerically equal to the k for that phase as the conservation laws mandate.
Note that this says nothing about the R/P before the peak (we would need a more "accurate" model for reservoir dynamics here), but one objection that one might raise is the constant value of the R/P.
I was pretty specific about that point: the R/P will be constant for a single field as long as the field keeps producing. At some point, a decision will be made to "cap" the field even though trickles are still being pumped out of the ground. The situation at the region/country level will be more complicated as different fields are shut down, or are re-activated in response to price differentials. Hence the empirical observation that R/P declines post peak is consistent with a situation whereby fields are shut down in a non-synchronous manner even though they are still producing stuff.
That;s why simplistic geology-only models are useless in trying to understand and predict the situation. _________________ "Nuclear power has long been to the Left what embryonic-stem-cell research is to the Right--irredeemably wrong and a signifier of moral weakness."Esquire Magazine,12/05
The genetic code is commaless and so are my posts.
Posted: Wed Jun 28, 2006 8:58 am Post subject: Re: Mathematics of depletion
WebHubbleTelescope wrote:
EnergySpin wrote:
Eq(2) P(t) = - dR(t)/dt (Conservation of mass)
Incorrect, IMOO. Rather it should be:
dR/dt = Discoveries(t) - P(t)
as I have further up the thread. Unfortunately, this slip probably screws up the rest of your analysis.
Did not read carefully my post ... I was referring to R/P of a single field AND a constant URR so that no new discoveries are possible.
If you want to incorporate discoveries that's a different beast we are talking about which would also violate the explicit assumption about the "constancy" of the URR I made.
No screw-ups dear Watson (at least as far as this point is concerned).
The analysis of the R/P of a whole region would be an interesting mathematical problem on its own, but the time investment is not justified considering the crappy datasets we currently have. _________________ "Nuclear power has long been to the Left what embryonic-stem-cell research is to the Right--irredeemably wrong and a signifier of moral weakness."Esquire Magazine,12/05
The genetic code is commaless and so are my posts.
Secondly, the industry is dealing with a phenomenon that is exaggerated by the lack of investment over the past 18 years. This phenomenon is the decline rate for the older reservoirs that form the backbone of the world’s oil production, both in and out of OPEC. An accurate average decline rate is hard to estimate, but an overall figure of 8% is not an unreasonable assumption. The maintenance required to slow the rate of decline, and increase the overall recovery, is a key element of the supply picture going forward.
Five factors make the current situation somewhat complex. The first of these is the prevailing high price of oil caused by a combination of increased demand, a lack of renewal of the production base in the twenty years that prices were low, and the re-appearance of the peak oil theorists who amplify the factor of scarcity or fear. Geology and economics do not sit well together in academic arguments, but in my view the availability of new resources at current prices is not in doubt. The resources may not always be where people would like them, and not always of a quality we would like, but they are there.
Posted: Wed Jun 28, 2006 2:11 pm Post subject: Re: Mathematics of depletion
The Simmons 8% comment is a hard one to work out. He knows the context in which it was delivered.
Either Simmons is deliberately misrepresenting here, or he is alluding to the possibilty that a global peak oil downturn cause such instability so as to make infill drilling and new drilling impossible in the middle east.
My money is on the former. My impression is that Simmons is getting frustrated by the difficulties in getting a response on this topic. It must be tempting to exaggerate the meaning of genuinely scary numbers.
Posted: Wed Jun 28, 2006 7:14 pm Post subject: Re: Mathematics of depletion
EnergySpin wrote:
WebHubbleTelescope wrote:
EnergySpin wrote:
Eq(2) P(t) = - dR(t)/dt (Conservation of mass)
Incorrect, IMOO. Rather it should be:
dR/dt = Discoveries(t) - P(t)
as I have further up the thread. Unfortunately, this slip probably screws up the rest of your analysis.
Did not read carefully my post ... I was referring to R/P of a single field AND a constant URR so that no new discoveries are possible.
If you want to incorporate discoveries that's a different beast we are talking about which would also violate the explicit assumption about the "constancy" of the URR I made.
No screw-ups dear Watson (at least as far as this point is concerned).
So for a single field and exponential decline and constant URR, you have a peak that occurs on day 1. Nothing very interesting about this scenario.
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