

Because reserve growth is generally occurring as soon as the first producing well is put in place, the reserve growth G(t) is the result of the convolution of h Fallow ,h Build and h Growth :



This linear filtering of initial discoveries simulates the response of the oil production infrastructure to new oil discovery D(t) . Last time we have shown that this impulsional response was approximated by a Gamma function (in green on Figure 6) therefore simulating lagging effect and spreading reserve additions over time. The fourth convolution by h Growth makes the impulsional response larger with a heavier tail as shown in blue on Figure 6. The area under the blue curve is greater than one hence simulating reserve growth.





Fig 6. Effect of the reserve growth on the system impulsional response. The Modified Arrington CGF is used here.

Start

Start



Fig 7. Global annual discoveries of both oil and condensate, as reported in

1994 and 2005, together with oil production in billion of barrels (Gb) The difference

reported discoveries is the reserve growth. Source: Based on data from IHS Energy,

ASPO and Oil & Gas Journal (from Robelius [3], page 71).

Start

Ref

Init

The USGS is forecasting 612 billion barrels (mean estimate) for conventional oil between 1996 and 2025. Albrandt et al. (USGS) conclude that approximately 28% percent or 171 billion barrels of the forecasted 612 billion barrels for conventional oil had been added to the reserve pool between 1996 and 2003. 2005 resource growth in pre-2005 discoveries was only 8 Gb.

discovery data is the ASPO backdated (1932-2004) so t Ref =2004 . pre-1932 total discovery is 30 Gb (mainly US) post-2004 discovery forecast is based on a logistic decline. lambda= 3 years.

Peak URR (Gb) Total Reserve

Growth 1996-2025 Reserve

Growth 1996-2003 Reserve

Growth

2005 Reserve Growth Pre-2005

Reserve Growth Logistic 2005 @ 25.2 Gb 2023 0 0 0 0 0 SHM 2005 @ 26.9 Gb 1962 0 0 0 0 0 Modified Arrington

t Init = 1 2036 @ 36.8 Gb 3937 1976 704 146 21 427 Modified Arrington

t Init = 15 2017 @ 28.7 Gb 2616 655 230.8 59 7.7 236 Modified Arrington

t Init = 20 2015 @ 28.1 Gb 2500 538 191 50 6.5 204 West Siberia Growth

t Init = 1 2018 @ 29.3 Gb 2603 640 293 40 10.6 144 Table I. Peak estimates for crude oil + condensate derived from various model. The logistic fit was obtained using the Hubbert Linearization technique (1983-2006).

t

Init

=1

discoveries

t

Init

= 15

t

Init

=1



Fig 8. World producion forecast (C&C) produced by the HSM assuming the modified Arrington model for the reserve growth .



Fig 9. World producion forecast (C&C) produced by the HSM assuming Verma's model (West Siberia) for the reserve growth .



Fig 10. Reserves to production ratio values. Proven reserves are from BP. The corrected reserves account for anomalous Middle-East reserve revisions.

HSM (US) and HSM (West Siberai) are the production curve shown on Figures 8 and 9.

Conclusions

The interest of the Shock Model approach resides in its capacity to exploit the discovery data, the production profile and the reserve growth models. The URR is not an output of the model as it is the case for the Hubbert Linearization but results directly from the discovery curves and the application of reserve growth models. The HSM is a nice way to inject prior information about the URR. The method can potentially deal with difficult multi-modal production profiles such as Saudi Arabia. The logistic case can be seen as a particular case of the HSM when the extraction of total resource (URR) is instantaneous.

Using a fourth convolution function derived from empirical Cumulative Growth Factors, I was able to derive an estimate close to the USGS forecast on reserve growth. Note that we don't know how much true reserve growth is included in the 171 Gb figure. However, the reserve growth in 2005 for pre-2005 discoveries was only 8 Gb, it should have been 21.5 Gb (171/8). If we assume that 8 Gb per year is the true reserve annual addition we get 64 Gb for 1996-2003. In my opinion, peak oil proponents should pay more attention to reserve growth issues. Very often, the argument is only focus on new discoveries but reserve growth is poorly understood and may have a significant contribution especially within a high oil prices environment. Using the West Siberia reserve growth factor and a decreasing number of new discoveries, I estimate the peak to be at most in 2018 for conventional oil. The interesting thing is that it seems to match the 8 Gb in 2005. This result assumes that reserve growth related technologies will be applied aggressively and extensively. Also, the two CGFs that I used are for onshore fields and they are probably very different for offshore fields (new discoveries to come will be increasingly offshore). Therefore, I consider this result as being an upper bound on conventional production. It will be very important to watch reserve growth estimates for the year 2006 in order to confirm (or infirm) a decrease in reserve growth that was observed in 2005 (8 Gb). In particular, a collapse in reserve growth (2-3 Gb) could indicate that the peak for crude oil + condensate is likely to be in 2005-2006. It's important to note that the CGF model (5) is significantly different between large fields and small fields [1]. Because new discoveries are likely to be small fields, reserve growth post-2005 is likely to be smaller.

References:

1900-1959: API Facts and Figures Centennial edition 1959.

1960-2006: EIA data (includes tar sands production from Canada and Venezuela).

Code:

ShockModel_Part2.txt

The tricky part is to find an appropriate value for. It seems logical thatshould depend on the discovery age because the discovery curve already includes an unknown amount of reserve growth. The chart below is taken from Robelius PhD thesis [3] and is showing how much reserve growth we have experienced in the 1994-2005 period and how it has affected the shape of the discovery curve. It's pretty obvious that reserve growth cannot be neglected and that a static view of oil production will underestimate future production levels. Also, there is no obvious correlation between discovery age and the amount of reserve growth. The amount of reserve growth between 1994 and 2005 is an astonishing 427 billion barrels (Gb). However, only 170-190 Gb seems to be genuine reserve growth (see Rembrandt post ).I assume the following model forwhereis the reference year for which the backdated discovery curve has been issued andis a general offset that gives us a better control on the model. Below are a few claims that may help us calibrate our algorithm:In the simulations below, I made a few assumptions:The result of the SHM + Modified Arrington withyear (third row in Table I) is shown on Figure 8 and replicates closely the rosy USGS/DOE/CERA view of future production with a large amount of reserve growth to come. We can see clearly the effect of the relation (8) with a ramp up of reserve growth prior to 2004 and a huge input of reserve growth on newpost 2004. The SHM + Modified Arrington withyears and the SHM + Russian growth () give similar results with a peak in 2017-2018 and a URR around 2.6 trillion barrels. For the peak date to be before 2015, reserve growth should be around 6-7 Gb for 2006 and decrease afterward.On Figure 10, we can see that the HSM + Modified Arrington (in orange) fits the proven reserves from BP but does not fit with the recent record prices. The HSM + West Siberia CGF (in green) is closed to the corrected BP reserve numbers except since 2001. However the green curve is going down precisely when prices started their climb which makes me think that the proven reserve increases for 2001 and 2002 are probably bogus.About the Hybrid Shock Model:About reserve growth:Of course, this is a work in progress and more tests are needed. The US, Norway and the UK should constitute a nice benchmark for the HSM (maybe in a part III). By the way, if anyone has discovery datasets, please contact me [1] M. K. Verma and G. F. Ulmishek, Reserve growth in Oil fields of West Siberian Basin, Russia. Ulmishek of the United States Geological Survey. pdf [2] M.K. Verma, Modified Arrington Method for Calculating Reserve Growth—A New Model for United States Oil and Gas Fields, U.S. Geological Survey Bulletin 2172-D, pdf [3] Giant oil fields and their importance for future oil production, Fredrik Robelius, PhD Thesis The data for the world production of crude oil + condensate is composed of:The code is available in R language, the windows version of R software is available here . You will need to install the Matlab package (go in "Packages/Install Package(s)" then choose a CRAN site and select Matlab from the package list). To execute the program, open the file () and click on "Edit/Run all".