Some nations have a "double peak", for one reason or another. Maybe they have two fields that deplete at different rates, maybe there are other reasons.
So I composed a "double verhulst model" that consists of 2 sub-peaks, which can be used to model this phenomenon. If the peaks are close together, they look like one broad peak. If far apart, two little peaks. Peak size, orientation, width and ratio can be adjusted by adjusting the parameters of the sub-peaks.
I'll post the result of the Qatar peaks below. There is some funny stuff going on with them, by the way. It looked like they were going to peak out in about 2000, but somehow, some way, they managed to crank up the oilwells in 2003 for one more good pumping year. It will be interesting to see whether this was a death spasm or not by inspection of the 2004 data.
Also, they claim to have had 15 gb "ultimately recoverable" according to BP, but the model fits a little better if you assume lower.
Maybe SL will be nice to us and graph it for all to see.
- Code: Select all
Peak 1 Peak 2
n 7 12
qinf 8.00 7.00
t(1/2) 26 52
k 0.25 0.6
Actual predicted
1960 0.06
1961 0.06 0.06
1962 0.07 0.07
1963 0.07 0.09
1964 0.08 0.10
1965 0.09 0.11
1966 0.11 0.13
1967 0.12 0.14
1968 0.12 0.15
1969 0.13 0.16
1970 0.14 0.17
1971 0.16 0.18
1972 0.18 0.18
1973 0.21 0.19
1974 0.19 0.19
1975 0.16 0.18
1976 0.17 0.18
1977 0.16 0.18
1978 0.18 0.18
1979 0.19 0.17
1980 0.17 0.17
1981 0.16 0.16
1982 0.12 0.16
1983 0.11 0.15
1984 0.13 0.15
1985 0.12 0.14
1986 0.13 0.14
1987 0.12 0.14
1988 0.13 0.13
1989 0.15 0.13
1990 0.16 0.13
1991 0.15 0.12
1992 0.18 0.12
1993 0.17 0.13
1994 0.16 0.14
1995 0.17 0.16
1996 0.21 0.19
1997 0.25 0.23
1998 0.27 0.27
1999 0.29 0.31
2000 0.31 0.33
2001 0.31 0.34
2002 0.29 0.34
2003 0.33 0.33
2004 0.32
2005 0.31
2006 0.30
2007 0.28
2008 0.27
2009 0.26
2010 0.25
2011 0.24
2012 0.23
2013 0.22
2014 0.21
2015 0.20
2016 0.19
2017 0.18
2018 0.17
2019 0.16
2020 0.16
2021 0.15
2022 0.14
2023 0.14
2024 0.13
2025 0.12
2026 0.12
2027 0.11
2028 0.11
2029 0.10
2030 0.10
2031 0.09
2032 0.09
2033 0.09
2034 0.08
2035 0.08
2036 0.07
2037 0.07
2038 0.07
2039 0.07
2040 0.06
2041 0.06
2042 0.06
2043 0.05
2044 0.05
2045 0.05
2046 0.05
2047 0.05
2048 0.04
2049 0.04
2050 0.04