Updated Verhulst model

by **pup55** » Thu 16 Jun 2005, 09:39:31

With the arrival of the new BP data, we can update the Verhulst model we did last year. Maybe someone friendly with a website can graph this for us (I am still too thrifty).

Since we are a lot smarter than we were a year ago, I have put in the following changes: The historical data is extended back to 1900, and the little forecast we calculated yesterday for 2005 through 2008 are included (since we are better able to adjust the current data for changes based on current news stories ex: Iraq not able to grow, etc. etc.). Also, I now have MS-Solver available, so as to take a little of the subjectivity out of the estimates. I have constrained the model so that the cumulative production equals the actual production for 1900-2008, and the 2008 forecast and model values are equal. I have let the variables k, n, T-50 and Q-inf float so as to minimize the standard error.

Commentary:

1. Based on this model, Q-inf, the “Original Oil in Place” value is 2,461 gb. This is a little bigger than the estimates we had last year. Cumulative production (1900-2008) is 1,273 gb, which leaves the BP estimate of 1,188 gb remaining. The historical data therefore suggests that we are past the 50% depletion midpoint.

2. This new model predicts a peak of 32.6 gb in 2014. This is about 91 mbo/d, which, as we discussed yesterday, is about what the “demand” is forecast to already be in 2007, therefore the world will be in the position in which oil usage will be geologically constrained, really, from now on.

3. The 2030 value (28 gby) will be just about what the 1996 value was. In the world of 2030, according to our population estimate from last year, there will be about 9.3 billion people, compared to 5.7 billion, therefore, somebody is going to have to do without oil, or else we are going to have to share.

4. The really steep part of the decline curve is between 2030 and 2050. If this form of modeling is correct, there will be a 2/3 decrease in supply during that time. Between now and then it will be a nuisance, but probably liveable.

5. What could change that would affect this model? Well, the assumptions we made yesterday are key, namely that Russia, Iraq and Saudi are not able to grow over and above what they are now producing for the next 3-4 years, but everybody else is able to increase or deplete at the same rate as they did in 2004. Also, any new countries that go into depletion (such as Iran, Mexico or Venezuela) may change the short-term forecast, which would in turn change the model a lot. Also, any discoveries that radically change the estimate of Q-inf would be important, and also, any economic screwup, such as we had in the early 80’s that killed demand prematurely would be important and extend the nominal peak some distance into the future.

Here is the data:

n 0.149454128
qinf 2,461.82
t(1/2) 106.8467633
k 0.039628337

by **pup55** » Thu 16 Jun 2005, 09:41:37

units are gbo/y

Code: Select all: year prod model 1900 0.20 1901 0.24 1.08 1902 0.27 1.12 1903 0.31 1.17 1904 0.35 1.22 1905 0.38 1.26 1906 0.42 1.32 1907 0.45 1.37 1908 0.49 1.42 1909 0.53 1.48 1910 0.56 1.54 1911 0.60 1.60 1912 0.64 1.66 1913 0.67 1.73 1914 0.71 1.80 1915 0.75 1.87 1916 0.78 1.94 1917 0.82 2.02 1918 0.85 2.10 1919 0.89 2.18 1920 0.93 2.26 1921 0.96 2.35 1922 1.00 2.45 1923 1.00 2.54 1924 1.29 2.64 1925 1.57 2.74 1926 1.86 2.85 1927 2.14 2.96 1928 2.43 3.08 1929 2.71 3.20 1930 3.00 3.32 1931 3.20 3.45 1932 3.40 3.58 1933 3.60 3.72 1934 3.80 3.86 1935 4.00 4.01 1936 4.20 4.17 1937 4.40 4.33 1938 4.60 4.49 1939 4.80 4.66 1940 5.00 4.84 1941 5.20 5.02 1942 5.40 5.21 1943 5.60 5.41 1944 5.80 5.61 1945 6.00 5.82 1946 6.20 6.04 1947 6.40 6.26 1948 6.60 6.50 1949 6.80 6.74 1950 7.00 6.99 1951 7.30 7.24 1952 7.60 7.51 1953 7.90 7.78 1954 8.20 8.06 1955 8.50 8.35 1956 8.80 8.65 1957 9.10 8.96 1958 9.40 9.28 1959 9.70 9.61 1960 10.00 9.94 1961 10.32 10.29 1962 10.64 10.65 1963 10.96 11.01 1964 11.29 11.39 1965 11.61 11.78 1966 12.62 12.18 1967 13.55 12.58 1968 14.76 13.00 1969 15.93 13.43 1970 17.54 13.87 1971 18.56 14.32 1972 19.59 14.77 1973 21.34 15.24 1974 21.40 15.72 1975 20.38 16.21 1976 22.05 16.70 1977 22.89 17.21 1978 23.12 17.72 1979 24.11 18.24 1980 22.98 18.77 1981 21.73 19.30 1982 20.91 19.85 1983 20.66 20.39 1984 21.05 20.95 1985 20.98 21.50 1986 22.07 22.06 1987 22.19 22.63 1988 23.05 23.19 1989 23.38 23.75 1990 23.90 24.32 1991 23.83 24.88 1992 24.01 25.44 1993 24.11 25.99 1994 24.50 26.54 1995 24.86 27.08 1996 25.51 27.61 1997 26.34 28.13 1998 26.86 28.64 1999 26.40 29.13 2000 27.36 29.61 2001 27.31 30.07 2002 27.17 30.50 2003 28.12 30.92 2004 29.29 31.31 2005 29.83 31.67 2006 30.58 32.01 2007 31.49 32.31 2008 32.58 32.58 2009 32.82 2010 33.02 2011 33.18 2012 33.30 2013 33.38 2014 33.42 2015 33.41 2016 33.35 2017 33.25 2018 33.09 2019 32.89 2020 32.64 2021 32.34 2022 31.98 2023 31.58 2024 31.13 2025 30.63 2026 30.08 2027 29.49 2028 28.86 2029 28.18 2030 27.46 2031 26.71 2032 25.92 2033 25.10 2034 24.26 2035 23.39 2036 22.50 2037 21.59 2038 20.67 2039 19.74 2040 18.81 2041 17.88 2042 16.95 2043 16.02 2044 15.11 2045 14.21 2046 13.33 2047 12.47 2048 11.63 2049 10.82 2050 10.04 2051 9.29 2052 8.57 2053 7.88 2054 7.23 2055 6.61 2056 6.02 2057 5.47 2058 4.96 2059 4.48 2060 4.04 2061 3.63 2062 3.25 2063 2.90 2064 2.58 2065 2.29 2066 2.03 2067 1.79 2068 1.57 2069 1.38 2070 1.20 2071 1.05 2072 0.91 2073 0.79 2074 0.68 2075 0.59 2076 0.51 2077 0.43 2078 0.37 2079 0.32 2080 0.27 2081 0.23 2082 0.19 2083 0.16 2084 0.14 2085 0.11

by MD » Thu 16 Jun 2005, 09:49:15

What are the assumptions for Saudi Arabia through 2015? Flat at 9mbd? Increasing to 15mbd as they promise? Depleting to 6mpd as feared by some?
What about the rest of OPEC and their suspicious reporting?

I guess I am really asking about the entire model as I wasn't here last year

by **pup55** » Thu 16 Jun 2005, 10:06:00

Code: Select all: assumptions for Saudi Arabia

The assumptions we made yesterday were constant production of 10.5 mbd through 2008. After 2008, the model is "global", that is to say, not broken out by individual countries. Also, I assumed that the production for Iraq was what the BP review said it was, which was 2 mbd. Both of these numbers might be "generous".

ASPO's model might or might not be better in this respect since it is the sum of individual models for each of the producing countries. If I get crazy later on, I may do a similar model/forecast on this basis, so we can break out some individual countries and note any important differences.

The weaknesses of this forecasting method (mathematical modeling) are discussed at length by Lahererre in one of the papers on the dieoff.org website. This stuff is still kind of fun, though, and should be looked at as one more data point, among many, in the study of this issue.

by **khebab** » Thu 16 Jun 2005, 13:02:37

The PO date seems to correspond to the one given by the French report (2013): Oilcast #7: French government examines `peak oil` theory

Figure 1

{edit: sorry, correction on the graph}

by **pup55** » Thu 16 Jun 2005, 13:10:07

Thanks, Khebab for the excellent graph.

by **MicroHydro** » Thu 16 Jun 2005, 13:35:31

Excellent work. But I share the concerns of Simmons and MD. Most of these models assume well managed fields ~Prudhoe Bay. There seems to be more potential for downside surprises from abused fields collapsing than upside surprises from new techniques for quaternary recovery increasing URR.

by **khebab** » Thu 16 Jun 2005, 14:05:44

If we add the demand prediction you made (New Forecast):

pup55 wrote: Well, if you do exactly the same thing with global consumption, you get the following:

Year Prod Demand/Cons
2004 act 80.2 80.7
2005 est 81.7 83.7
2006 est 83.7 86.7
2007 est 86.3 90.6
2008 est 89.3 94.5

we obtain the following graph:

Figure 2
Demand should exceed supply at the end of next year!

by MD » Thu 16 Jun 2005, 15:32:33

THE WORLD PETROLEUM LIFE-CYCLE
Richard C. Duncan and Walter Youngquist

does anyone know what happened to thsi series of studies? The last one I found was from 2000 and they had mentioned continuing. Has the program continued to anyones knowledge?

by **pup55** » Thu 16 Jun 2005, 21:23:30

does anyone know what happened to thsi series of studies

?

Check with Jake, the ASPO guy. Maybe he has a contact with the authors.

by **khebab** » Thu 16 Jun 2005, 23:35:45

A technical question about Q-inf:

is Q-inf the “Original Oil in Place” or the "Ultimate Resource Recoverable"? because the curve is about production, the area under the curve should converge toward the URR. am I wrong?

by **pup55** » Fri 17 Jun 2005, 08:50:29

You are quite right. The area under the curve should be Q-inf. I am no longer capable of doing it myself, but if you go back to the original Verhulst equation in the paper by Roper, and solve for y, you might be able to calculate the integral and arrive at an approximation of Q-inf, and also, by setting the first derivative to zero, you should be able to arrive at the peak.

The value of Q-inf is critical to the calculation of the curve. If the Q-inf value above were greatly higher or lower, the shape of the curve, and therefore the peak prediction, would be completely different.

When we did the exercises a year ago, in the "peak mart" thread, we ran through a lot of calculations, and did some "blind" tests where softlanding gave us some partial curves, and we tried to predict the peak, and what we found out was that we needed to be at least in the ballpark on Q-inf in order to be close to the correct curve shape. What we also found out is that there is an "inflexion point" on the curve, which is about 2/3 of the way up on the left side of the curve. This is the point at which the "tangent line" slope, if you will, goes to infinity. If you have data past that, it is also helpful.

So the ramifications of this, as it applies to us, is that the value of remaining reserves needs to be pretty well known in order to do a good job on peak prediction. Therefore this whole issue of "reserves transparency" is critical to being able to make this type of model. Also, if you think you are "close to the peak", you can do a pretty good job of fitting the curve to the existing data.

After that, it becomes an issue of resolution, that is, to what level of accuracy are you satisified that you have made an accurate prediction of the peak? If you have a hundred years of data, and you can predict the peak within 5 years, is your methodology good enough? We were never really able to answer that question to any degree of satisfaction.

This applies directly to the work of Hubbert himself, plus Lahererre and others. If you have data of a given quality, and they predict a peak value of 2000, or 2009, or whatever, is there enough accuracy in this methodology to be able to make plans and/or policy decisions on that basis?

So, I think the real answer is to use many sources of data, and also refine the predictions when new data comes in, to see whether or not the world is going to end, and not take any one prediction too seriously (including those of ASPO and others, and especially, the amateur pup55).

This is annoying to people who do not understand this type of modeling, because they expect some kind of easy-to-digest number. This is the very thing that Michael Lynch criticizes Campbell for all the time, because as new data comes in, you have to recalculate everything again, and this results in a change in the peak prediction, and so the less-enlightened people consider this "waffling" or whatever. Deffeyes has solved the problem by picking a peak date kind of tongue-in-cheek, but he freely admits that this is just a guess, and also, he has been around long enough and does it with enough of a sense of humor that he does not aggravate people and they kind of accept it.

Sorry to have gotten longwinded on this, but some background is in order for those who joined us recently and are reading up on this. For further edification, feel free to go back to the "peak mart" thread and read up on what we did a year ago. Also, the links to the original equations are in there for those calculus-proficient to go back and view.

Also, I am still happy to have an ongoing test of this curve-fitting ability. Anybody who wants to can submit some partial production curves for any country, and I will calculate the curve using this method, and predict the peak. Then, easy to compare with the actual peak and see if I predicted the peak accurately. That way, you can test our proficiency.

by **khebab** » Fri 17 Jun 2005, 09:53:50

Thank you for your response, I'm going to read the thread "peak mart" to get more info.

Question:
What kind of software are you using for your simulation (Excel, Matlab)?

I was thinking about putting together a little open source Matlab package on the different curve models and estimation techniques so that people can play with it and eventually improved the models.

pup55 wrote:So the ramifications of this, as it applies to us, is that the value of remaining reserves needs to be pretty well known in order to do a good job on peak prediction. Therefore this whole issue of "reserves transparency" is critical to being able to make this type of model. Also, if you think you are "close to the peak", you can do a pretty good job of fitting the curve to the existing data.

Usually in Physics, we perform sensitivity or error analysis on the model in order to evaluate the impact of the different parameters on the outcome. For instance, if you put an error interval on Q-inf you get an interval on the PO data. I was wondering if you have already performed such an analysis. It's also a question of intelectual honesty to put a confidence interval on your predictions. That fact always bothered me about the ASPO estimation.

pup55 wrote:This is annoying to people who do not understand this type of modeling, because they expect some kind of easy-to-digest number. This is the very thing that Michael Lynch criticizes Campbell for all the time, because as new data comes in, you have to recalculate everything again, and this results in a change in the peak prediction, and so the less-enlightened people consider this "waffling" or whatever.

This technique of curve fitting reminds me a little bit of tracking techniques (ex: Kalman filter) were you track a target based on a model but where the estimate is always recalculated each time a new observation comes in.

by **pup55** » Fri 17 Jun 2005, 11:01:10

What kind of software are you using for your simulation

MS-excel. I will send you the spreadsheet if you want. PM your email address and I will send it off to you.

I was wondering if you have already performed such an analysis. It's also a question of intelectual honesty to put a confidence interval on your predictions

.

This is a good idea. I will tinker with it and post the results.

Edit: added the last sentence. I hit the "submit" button too soon.

by **pup55** » Fri 17 Jun 2005, 11:38:42

Okay, here are three scenarios:

The USGS is the USGS estimate of estimated 3000 gbo remaining, rosy scenario, Q-inf=4173 gb. The peak is 2024. The "max" is a 20% increase in Q-inf (2953 gb) and "min" is a 20% decrease in Q-inf (1968 gb). The peak estimates are 2011 and 2017 respectively.

You do not want to be in the 20% decrease scenario, because the curve, in this case, really is like a cliff.

Code: Select all: USGS Max min 1901 0.96 1.04 1.17 1902 1.00 1.09 1.22 1903 1.04 1.13 1.26 1904 1.09 1.18 1.31 1905 1.13 1.22 1.36 1906 1.18 1.27 1.41 1907 1.23 1.33 1.47 1908 1.28 1.38 1.52 1909 1.34 1.44 1.58 1910 1.39 1.49 1.64 1911 1.45 1.55 1.70 1912 1.51 1.62 1.76 1913 1.58 1.68 1.83 1914 1.64 1.75 1.90 1915 1.71 1.82 1.97 1916 1.79 1.90 2.04 1917 1.86 1.97 2.12 1918 1.94 2.05 2.20 1919 2.02 2.14 2.28 1920 2.10 2.22 2.37 1921 2.19 2.31 2.46 1922 2.28 2.40 2.55 1923 2.38 2.50 2.65 1924 2.48 2.60 2.74 1925 2.58 2.70 2.85 1926 2.69 2.81 2.95 1927 2.80 2.92 3.06 1928 2.91 3.04 3.18 1929 3.03 3.16 3.29 1930 3.15 3.29 3.42 1931 3.28 3.42 3.54 1932 3.42 3.55 3.67 1933 3.56 3.69 3.81 1934 3.70 3.84 3.95 1935 3.85 3.99 4.10 1936 4.01 4.14 4.25 1937 4.17 4.30 4.40 1938 4.33 4.47 4.56 1939 4.51 4.65 4.73 1940 4.69 4.83 4.90 1941 4.87 5.01 5.08 1942 5.07 5.20 5.27 1943 5.27 5.40 5.46 1944 5.47 5.61 5.65 1945 5.69 5.82 5.86 1946 5.91 6.04 6.07 1947 6.14 6.27 6.29 1948 6.37 6.51 6.51 1949 6.62 6.75 6.75 1950 6.87 7.01 6.99 1951 7.13 7.27 7.24 1952 7.40 7.54 7.49 1953 7.68 7.81 7.76 1954 7.96 8.10 8.03 1955 8.26 8.39 8.31 1956 8.56 8.70 8.60 1957 8.87 9.01 8.90 1958 9.19 9.33 9.21 1959 9.53 9.67 9.53 1960 9.87 10.01 9.86 1961 10.22 10.36 10.19 1962 10.57 10.72 10.54 1963 10.94 11.09 10.90 1964 11.32 11.47 11.26 1965 11.71 11.86 11.64 1966 12.10 12.27 12.03 1967 12.51 12.68 12.43 1968 12.92 13.10 12.84 1969 13.35 13.53 13.26 1970 13.78 13.97 13.69 1971 14.22 14.42 14.13 1972 14.67 14.88 14.58 1973 15.13 15.34 15.04 1974 15.60 15.82 15.51 1975 16.07 16.31 15.99 1976 16.55 16.80 16.49 1977 17.04 17.30 16.99 1978 17.53 17.81 17.50 1979 18.03 18.33 18.02 1980 18.53 18.86 18.56 1981 19.04 19.39 19.09 1982 19.56 19.92 19.64 1983 20.08 20.46 20.20 1984 20.60 21.01 20.76 1985 21.12 21.55 21.33 1986 21.64 22.10 21.90 1987 22.17 22.66 22.48 1988 22.69 23.21 23.06 1989 23.22 23.76 23.64 1990 23.74 24.31 24.23 1991 24.26 24.86 24.81 1992 24.78 25.41 25.40 1993 25.29 25.95 25.97 1994 25.80 26.49 26.55 1995 26.30 27.01 27.11 1996 26.79 27.53 27.67 1997 27.28 28.04 28.22 1998 27.76 28.54 28.75 1999 28.22 29.03 29.26 2000 28.68 29.50 29.75 2001 29.12 29.95 30.23 2002 29.55 30.39 30.67 2003 29.97 30.81 31.09 2004 30.37 31.21 31.47 2005 30.76 31.59 31.81 2006 31.13 31.95 32.12 2007 31.49 32.28 32.38 2008 31.82 32.58 32.58 2009 32.14 32.86 32.74 2010 32.44 33.12 32.83 2011 32.72 33.34 32.86 2012 32.98 33.53 32.82 2013 33.22 33.69 32.70 2014 33.44 33.82 32.50 2015 33.64 33.91 32.22 2016 33.81 33.98 31.85 2017 33.97 34.01 31.38 2018 34.10 34.00 30.81 2019 34.21 33.96 30.13 2020 34.30 33.88 29.34 2021 34.37 33.77 28.44 2022 34.42 33.62 27.43 2023 34.44 33.44 26.30 2024 34.45 33.23 25.05 2025 34.43 32.98 23.68 2026 34.40 32.70 22.20 2027 34.34 32.38 20.62 2028 34.26 32.04 18.93 2029 34.16 31.66 17.15 2030 34.05 31.26 15.30 2031 33.91 30.82 13.39 2032 33.76 30.36 11.45 2033 33.59 29.88 9.51 2034 33.41 29.37 7.60 2035 33.21 28.84 5.77 2036 32.99 28.29 4.07 2037 32.76 27.72 2.57 2038 32.52 27.13 1.34 2039 32.26 26.53 0.46 2040 31.99 25.91 2041 31.71 25.28 2042 31.41 24.65 2043 31.11 24.00 2044 30.80 23.35 2045 30.48 22.69 2046 30.14 22.04 2047 29.81 21.38 2048 29.46 20.72 2049 29.11 20.06 2050 28.75 19.40 2051 28.39 18.75 2052 28.02 18.11 2053 27.65 17.47 2054 27.28 16.84 2055 26.90 16.22 2056 26.52 15.61 2057 26.14 15.01 2058 25.76 14.42 2059 25.37 13.85 2060 24.99 13.28 2061 24.60 12.73 2062 24.22 12.20 2063 23.83 11.68 2064 23.45 11.17 2065 23.07 10.68 2066 22.69 10.20 2067 22.31 9.74 2068 21.94 9.29 2069 21.56 8.86 2070 21.19 8.45 2071 20.82 8.04 2072 20.46 7.66 2073 20.10 7.29 2074 19.74 6.93 2075 19.38 6.58 2076 19.03 6.26 2077 18.68 5.94 2078 18.34 5.64 2079 18.00 5.35 2080 17.66 5.07 2081 17.33 4.81 2082 17.01 4.55 2083 16.68 4.31 2084 16.36 4.08 2085 16.05 3.86

by **khebab** » Fri 17 Jun 2005, 12:33:59

Figure 3

by **pup55** » Fri 17 Jun 2005, 12:40:27

Cool.

The size of the OOIP does not make too much difference on what the peak is, but it sure does make a lot of difference on what the shape of the downslope is like!

by **khebab** » Fri 17 Jun 2005, 13:04:06

If we calculate the depletion rate from the first derivative, the error on Q-inf has more impact:

Figure 4

by **nth** » Fri 17 Jun 2005, 14:18:56

this is awesome.

so PO in 2014 according to this.

by **khebab** » Fri 17 Jun 2005, 15:30:59

nth wrote:this is awesome.

so PO in 2014 according to this.

Yes, +/- 3 years depending on the uncertainty on the value of Q-inf. What's interesting is that a significant change in Q-inf does not affect much the position of the peak but rather the steepness of the depletion afterward.

Updated Verhulst model

Updated Verhulst model

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