[DoctorDoom]

Just for laughs, I tried running some computer simulations of the peak. What I found, I think, is that there is something a bit fishy with the baseline numbers people are using to forecast the peak year by 2010. The main problem is this: if the peak occurs too soon in relationship to the reserves, then declines at a 3% rate, the R/P ratio will bottom out too soon and then begin to rise again. This is because cumulative production, deducted from the reserves, is not keeping pace if you allow the drop to proceed at 3%. This seems counter-intuitive to me; most past-peak fields around the world see their R/P ratios drop to fairly low numbers, like 10-15 years. This implies that rather than computing production as X% of prior year, it might make more sense to compute it as X% of remaining reserves. If you do this you get a later peak followed by a steeper decline.

Using 2% demand growth, BP's current reserve estimates, and low numbers for all remaining yet-to-find/reserve-growth, it's very easy to put the peak out in 2020-2025 while not allowing the R/P ratio to drop below 15. The post-peak decline is breathtaking, of course.

The worst-case scenario peaks at 118 Mb/day, with an R/P ratio of 15 on the remaining 608 Gb of reserves. Production has to fall to half this by 2035 to stay at R/P = 15, a disastrous descent. Any earlier than that, say 2010 or 2015, and you can hold a plateau until 2025 while allowing the R/P to drop to no worse than around 20 years.

My point is this - if the peak is near, we can probably count on a long plateau; it's not reasonable to assume that we'd allow ourselves to starve while the R/P ratio bottoms at 30 and then heads back up. The only way to make the R/P ratio continue to slide is to reduce the rate of decline to 1-2%, or put a decade of flat production into the model. Either way, there's a good 15 years in which to get our act together. Perversely, peaking later is worse because of the steepness of the decline. Even then, you still have 15 years before the SHTF.

Here's the 2025 crash-and-burn:

Code: Select all

      Production     USA       Reserves   Conv
Year  Conv  Hvy    mbd w% ef%  Conv  Hvy  R/P
2005    80    0     20 25   0  1126  100   38
2006    81    0     20 24   1  1107  100   37
2007    83    0     20 24   3  1086  100   35
2008    84    0     20 23   5  1066  100   34
2009    86    0     19 23   7  1044  100   33
2010    88    0     19 22   9  1022  100   31
2011    90    0     19 22  10   999  100   30
2012    91    0     19 21  12   976  100   29
2013    93    0     19 21  13   952  100   28
2014    95    0     19 20  14   928  100   26
2015    97    0     19 20  16   902  100   25
2016    98    0     19 19  17   876   99   24
2017   100    1     19 19  18   850   98   23
2018   101    2     19 19  19   823   97   22
2019   102    2     19 18  20   796   96   21
2020   104    3     19 18  21   768   94   20
2021   105    4     19 17  24   740   92   19
2022   108    4     19 17  26   710   90   18
2023   110    4     18 16  28   680   87   16
2024   112    4     18 16  30   649   85   15
2025   112    4     18 15  33   608   83   14
2026   111    4     18 15  35   568   81   14
2027   103    4     17 16  36   530   79   14
2028    96    4     17 17  38   495   77   14
2029    90    4     17 18  40   462   74   14
2030    84    4     16 18  42   432   72   14
2035    60    4     14 22  50   306   61   14
2040    42    4     14 31  49   218   50   14
2045    30    4     14 42  49   155   39   14
2050    21    4     14 57  49   110   28   14
2055    15    4     14 76  49    79   17   14


Here's the not-quite-right 2010 plateau that has us starving ourselves while the R/P climbs in the out years:

Code: Select all

      Production     USA       Reserves   Conv
Year  Conv  Hvy    mbd w% ef%  Conv  Hvy  R/P
2005    80    0     20 25   0  1126  100   38
2006    81    0     20 24   1  1107  100   37
2007    83    0     20 24   3  1086  100   35
2008    84    0     20 23   5  1066  100   34
2009    86    0     19 23   7  1044  100   33
2010    86    0     19 23   9  1023  100   32
2011    86    0     19 23  10  1002  100   31
2012    86    0     19 23  12   980  100   31
2013    86    0     19 22  13   959  100   30
2014    86    0     19 22  14   937  100   29
2015    86    0     19 22  16   916  100   29
2016    83    0     19 23  17   896   99   29
2017    80    1     19 24  18   877   98   30
2018    78    2     19 24  19   858   97   30
2019    76    2     19 25  20   840   96   30
2020    73    3     19 25  21   824   94   30
2021    71    4     19 25  24   808   92   31
2022    69    4     19 26  26   793   90   31
2023    67    4     18 26  28   778   87   31
2024    65    4     18 26  30   764   85   32
2025    63    4     18 27  33   741   83   32
2026    61    4     18 27  35   719   81   32
2027    59    4     17 28  36   698   79   32
2028    57    4     17 28  38   677   77   32
2029    56    4     17 28  40   656   74   32
2030    54    4     16 28  42   637   72   32
2035    46    4     14 28  50   547   61   32
2040    40    4     14 32  49   470   50   32
2045    34    4     14 38  49   404   39   32
2050    29    4     14 43  49   347   28   32
2055    25    4     14 49  49   299   17   32


Here's an in-between case with the plateau in the 2015-2020 range; we still starve in the out years but it's not for lack of trying as the R/P falls to 15:

Code: Select all

      Production     USA       Reserves   Conv
Year  Conv  Hvy    mbd w% ef%  Conv  Hvy  R/P
2005    80    0     20 25   0  1126  100   38
2006    81    0     20 24   1  1107  100   37
2007    83    0     20 24   3  1086  100   35
2008    84    0     20 23   5  1066  100   34
2009    86    0     19 23   7  1044  100   33
2010    88    0     19 22   9  1022  100   31
2011    90    0     19 22  10   999  100   30
2012    91    0     19 21  12   976  100   29
2013    93    0     19 21  13   952  100   28
2014    95    0     19 20  14   928  100   26
2015    95    0     19 20  16   903  100   26
2016    95    0     19 20  17   878   99   25
2017    95    1     19 20  18   854   98   24
2018    95    2     19 20  19   829   97   23
2019    95    2     19 20  20   804   96   23
2020    95    3     19 20  21   780   94   22
2021    92    4     19 20  24   756   92   22
2022    89    4     19 20  26   733   90   22
2023    86    4     18 20  28   712   87   22
2024    84    4     18 21  30   691   85   22
2025    81    4     18 21  33   662   83   22
2026    79    4     18 21  35   633   81   21
2027    76    4     17 22  36   605   79   21
2028    74    4     17 22  38   578   77   21
2029    72    4     17 22  40   552   74   21
2030    70    4     16 22  42   526   72   20
2035    60    4     14 22  50   411   61   18
2040    51    4     14 26  49   311   50   16
2045    44    4     14 30  49   226   39   14
2050    31    4     14 41  49   161   28   14
2055    22    4     14 55  49   114   17   14


[Aaron]

could you graph that for us?

[DoctorDoom]

Assumptions:

Reserves = 1146 Gb (from BP)
Yet-to-find = 100 Gb at 5 Gb / year for 20 years, 0 afterwards
Reserve growth = 100 Gb at 5 Gb / year for 20 years, 0 afterwards
Venezuela heavy crude: 100 Gb (conservative, based on quoted numbers that 15% of their over 1000 Gb of reserves is produceable at $15/barrel; assumes energy profit ratio is 3:1, meaning each of these barrels is effectively 2/3 of a conventional barrel.
Baseline 2005 = 80 Mb/day.
Growth = 2% / year until peak
Decline = 3% / year post-peak until R/P limit reached
R/P minimum = 15 years (production max = 7% of remaining reserves)
Heavy crude cannot be produced at greater than 6 Mb/day (4 net of energy costs).

Legend for charts:
Production numbers are in Mb / day
Reserves are in Gb
R/P is in years and doesn't include the "heavy" numbers

USA numbers can be ignored. They represent an attempt to see what effect a change in US policy might have. US demand starts at 20 Mb/day and grows at 1.5% per year before policy effects. The policy modelled is to increase mpg requirements from current average of 20 to an average of 40, this is done over 15 years as the US fleet of autos is turned over. After this, efficiency of everything including autos must improve at 3% per year until the US is using energy at the same rate as Germany (50% of current US per-capita consumption). The numbers printed are the US demand in Mb/day, % of world production that represents, and the % energy efficiency the US has achieved (maximum of 50%).

[DoctorDoom]

could you graph that for us?

Assuming I could, how would I post an image to your server?

More thoughts on the rate of decline:

The decline by a fixed percentage can be viewed as a phenomenon similar to radioactive decay. Thus, limiting the decline to a fixed % of the remaining reserves, you ensure that each year, the amount is 1-X% of the previous year. For example, at 10% decine starting from 100, the first year you lose 10, leaving 90, the next year you lose 9, leaving 91, etc. What is interesting is that this is the same as decreasing the amount of the previous year's production by a fixed % - you get the same results either by that method or by using a %-of-remaining. So that implies that a 3% decline rate is the same as saying that in the limit you can produce at most 3% of what you've got left. And that means you approach an R/P ratio of 33 as you go out far enough. Conversely, if you believe the R/P ratio actually goes to something like 12, then by the same logic as above the long-term decline rate approaches 8%.

Unless I've screwed up somewhere, I think the decline rate is just the inverse of the R/P ratio. Not sure what good a graph would do - it's going to show the same exponential decline as the Hubbert graphs, the only difference would be how steep it is and what year the peak occurs.

The Hubbert model assumes you reach peak when you've burned half of the endowment. But the data that supports that view is all subject to bias due to human decision-making. It could just as easily be true that you reach peak when you've burned up enough of the endowment and/or ramped up production to the point that you've reached the maximum rate from which oil can be "withdrawn" from the field while still maximizing total recovery.

So the thrust of my argument is this: decline rate is the inverse of R/P, mature fields easily get down to 15 year R/Ps (e.g. Alaska, North Sea), therefore the world should also be able to get to 15 R/P, and hence the eventual world decline rate will be able to get to 7%. If you work backward from 7% and the existing reserves, it puts the peak out at least 15 years from now (unless growth increases). Any sooner and you get a more rounded plateau of longer duration, and the 7% rate is not reached for another decade or so after the plateau period.

[Pops]

I'm a real visual guy too Doc.

Go to: www.zippimages.com there is free hosting and no registration, although there is a limit to the time it will appear.

Then click {Img} in the post reply window and point it at the host.

[rowante]

DoctorDoom's work needs to be in the submit to the experts forum. Aaron?

[Cool Hand Linc]

I have trouble with it too. What does it all mean?

[Onyered]

In the last paragraph you said, “unless growth increases”. So are you factoring in the world demand increase? Maybe that would account for the difference in the dates.

[Aaron]

Assuming I could, how would I post an image to your server?

Send me a copy, and I'll post it. Or mail me a spreadsheet with the data & I'll graph it.

Or post it anywhere, and we can do as Pops suggests and link it from here directly.

And yes, this is exactly what we want for "Ask the Experts".

I sent a beta of the questions to a friend from a seismic survey company for a baseline opnion... publish ASAP.

Keep this one going... great work DD.

[smiley]

I’ve been thinking about that myself since I noticed that R/P ratios in S&C America where increasing despite falling production. I came to the conclusion that R/P ratios can run higher despite falling production.

I was first seeing the R/P ratio as the amount of production left. Therefore you will intuitively think that R/P ratios are going to decline with production.

On the other hand you can also see the R/P ratio as a measure of efficiency. It indicates how efficient you produce your reserves.

If you have a field of size R you can produce P with standard production methods.

If you introduce technology, which facilitates production but not increases reserves (like water lifting), your production (P) will increase and the R/P ratio will fall.

If you decide to cap some of your production to save your reserves for later (like OPEC did) your production (P) will fall and the R/P ratio will rise.

If your oil is harder to produce (complex reservoirs), production will be relatively low and the R/P ratio relatively high.

This appears to be the case in South and Central America.

For instance in Venezuela the extra heavy oil reserves are very large. However the production of these fields is very complex and slow. Therefore such a field will have an extremely high R/P ratio.

If you use this definition you can understand why a R/P ratio can rise despite falling production. The decreasing R/P ratios from the ordinary fields are counteracted by the addition of new fields with very high R/P ratios.

[Ender]

I’ve been thinking about that myself since I noticed that R/P ratios in S&C America where increasing despite falling production. I came to the conclusion that R/P ratios can run higher despite falling production.

If you use this definition you can understand why a R/P ratio can rise despite falling production. The decreasing R/P ratios from the ordinary fields are counteracted by the addition of new fields with very high R/P ratios.

The other possibility is that the reserves figures are bogus to begin with and/or not updated. Those reserves figures remaining the same year after year despite flat-out production stretches credibility a bit far....

(In relation to the original point, without really looking at the figures, I think assuming the 3% continuous decline might be flawed. It might initially decline at that rate but should slow down. A trickle of oil will be produced for many years to come)

[pup55]

Do us a favor and re-run your model using "zero" reserves growth, and re-figure the peak.

Seems to me like "reserves growth" is related to somebody's estimate of the ability of new technology to find new oil in existing holes, therefore the number is "soft", that is, it might be overly optimistic and/or pessimistic. It would be interesting to know the sensitivity of the peak to this number.

[Aaron]

I think that these reserve revisions are based on past experience with technology increasing ultimate recoverable. While certainly true for the past, the assumption that new technology will continue this trend is suspect.

It's similar to estimating new discoveries based on past trends... these historic estimates fail to account for the impact of these historic finds on possible future finds.

[DoctorDoom]

In the last paragraph you said, “unless growth increases”. So are you factoring in the world demand increase? Maybe that would account for the difference in the dates.

The model assumed 2% annual demand growth until the peak hits, at which point further growth is, by definition, impossible. Obviously bumping this up to 2.5% would change the scenario considerably.

I think that these reserve revisions are based on past experience with technology increasing ultimate recoverable. While certainly true for the past, the assumption that new technology will continue this trend is suspect.

100 Gb of yet-to-find is in line with the pessimistic view (Deffeyes, Campbell) that we've found 90% of the world's endowment; in fact the figure I hear most is 150 Gb of yet-to-find. 100 Gb of reserve growth is probably conservative; remember the USGS is using a number in the 700 range, 100 from Saudi Arabia alone! I admit it's a bit seat-of-the-pants. The growth doesn't have to come from technology; it's more likely to come from revisions of estimates. After all, by definition 1/2 of the P50 estimates should prove out, right? What I'd rather do is take the weighted average of world-wide P50 estimates, divided by 2, and subtract the P90 numbers. I'm pretty sure the net number for probable reserve growth would be greater than my "plug" figure of 100. I'd like to have hard numbers but I don't know where I'd get them.

If your oil is harder to produce (complex reservoirs), production will be relatively low and the R/P ratio relatively high.

Yes indeed. This is why I modelled the Venezuelan heavy oil separately. In fact, I'm cursing BP for throwing the Canadian tar sands into the overall reserves; I'd like to back that out and include them with the heavy, but I don't have the number.

Do us a favor and re-run your model using "zero" reserves growth, and re-figure the peak.

Well, we found 6 Gb through discovery last year, even the most hardened pessimist wouldn't think we will find nothing next year, nor that none of the P50 estimates will prove out. But OK, I'll put yet-to-find down to 10 Gb (less than what's thought to be in ANWR) and reserve growth at 10, plateau 2010-2015, decline at 3% until R/P 15. It's pretty grim:

Code: Select all

      Production     USA       Reserves   Conv
Year  Conv  Hvy    mbd w% ef%  Conv  Hvy  R/P
2005    80    0     20 25   0  1126  100   38
2006    81    0     20 24   1  1107  100   37
2007    83    0     20 24   3  1076  100   35
2008    84    0     20 23   5  1046  100   34
2009    86    0     19 23   7  1014  100   32
2010    86    0     19 23   9   983  100   31
2011    86    0     19 23  10   952  100   30
2012    86    0     19 23  12   920  100   29
2013    86    0     19 22  13   889  100   28
2014    86    0     19 22  14   857  100   27
2015    86    0     19 22  16   826  100   26
2016    83    0     19 23  17   796   99   26
2017    80    1     19 24  18   767   98   26
2018    78    2     19 24  19   738   97   25
2019    76    2     19 25  20   710   96   25
2020    73    3     19 25  21   684   94   25
2021    71    4     19 25  24   658   92   25
2022    69    4     19 26  26   633   90   25
2023    67    4     18 26  28   608   87   24
2024    65    4     18 26  30   584   85   24
2025    63    4     18 27  33   561   83   24
2026    61    4     18 27  35   539   81   24
2027    59    4     17 28  36   518   79   24
2028    57    4     17 28  38   497   77   23
2029    56    4     17 28  40   476   74   23
2030    54    4     16 28  42   457   72   23
2035    46    4     14 28  50   367   61   21
2040    40    4     14 32  49   290   50   19
2045    34    4     14 38  49   224   39   18
2050    29    4     14 43  49   167   28   15
2055    23    4     14 53  49   120   17   14


[notacornucopian]

Great work DD !

Regarding the Alberta tars sands number, the EUB report says 174 billion barrels remaining established recoverable, if that helps. The initial endowment is over a trillion barrels but the ultimate recoverable is noted as just over 300 billion barrels. Check this link if you want to look at it further www.eub.gov.ab.ca/bbs/products/STs/st98-2004.pdf
( the numbers above are found in the first few pages )

I wouldn't place a lot of value in the USGS numbers for yet to discover, either. If you have ever seen their yet to discover number plotted from where historical discovery leaves off, the " median " number they use for estimating future finds is completely implausible. I don't think I would use anything beyond their P90 number for future discovery in a model of this kind.

[smiley]

Doctordoom

I've been thinking some more on your model. A while back I tried to derive a simple model using two gaussians for exploration and production. Using gausians means that you only have to worry about two parameters and the area under the peak will be allways equal.

It works fine and if you fit it to production data you get a peak around 2000. It is essentially the same that Hubbert did. Only the oil crisis in the 70's is messing things up.

But it gives you a basic idea how the different parameters should behave. From that you can calculate the R/P ratios (Integral of exploration minus production) divided by production).

However if you start using the BP data you get a total mess and the peak shifts to 2060-2080. That is because the exploration data provided by Campbell and Laherre peak in the 60's. The reserve growth in the BP-data has not yet peaked.

In fact according to them the world R/P ratio has hovered around 40 for 20 years, which means that each year we find 40 times as much oil as we produce.

Perhaps if you cut the reserves by 20% (the Shell factor) you'll find that the need for a plateau disappears.

[DoctorDoom]

Regarding the Alberta tars sands number, the EUB report says 174 billion barrels remaining established recoverable, if that helps.

Yeah, I've seen that number, but it doesn't help because unless I misread it the BP report gives 77 Gb for all of Canada, so if I subtract it, it means that Canada has negative reserves. Something's not adding up!

In fact according to them the world R/P ratio has hovered around 40 for 20 years, which means that each year we find 40 times as much oil as we produce.

No - you only have to find as much as you use, + 40 times the amount of the year-over-year growth. So, if you used 24 Gb during a particular year, and the next year it's 25 Gb, you don't need to find 1000 Gb to hold the R/P at 40, you just need to find 25 + 40 = 65.

[Aaron]

DD.

Sent you an email...

received?

[pup55]

So the two changes you made, namely the reserves growth and the estimate of discoverable only really changed the "plateau" by a year or so, if I am seeing it correctly.

So the next question is, what magnitude of change in reserves growth/discoveries would give you a plateau at some comfortable time out into the future, say for example, 2050 or so? How much new oil would we need to find and/or obtain by improved technology to get us out that far, given the current consumption rate?

[smiley]

Aaron wrote

No - you only have to find as much as you use, + 40 times the amount of the year-over-year growth. So, if you used 24 Gb during a particular year, and the next year it's 25 Gb, you don't need to find 1000 Gb to hold the R/P at 40, you just need to find 25 + 40 = 65.

Yeah you're right. I messed up there. I wanted to write: ....40 times as much as we produce extra.