## Saturday, August 18, 2007

### Hurricane Dean Update (2007/08/18 - 120:00 UTC)

An update on Dean, now a strong category 4 hurricane, using the last forecasts available (12:00 UTC). From, Dr. Jeff Masters' WunderBlog:

Texas and Louisiana
Things are looking much brighter for Louisiana, as the GFDL model has come in line with all of the other models in predicting a landfall in Southern Texas or Northern Mexico. It now appears likely that Mexico's Yucatan Peninsula will knock Dean down a category or two before it can approach the Texas coast. The upper level low that was forecast by the GFDL to potentially steer Dean northwards appears to be weakening and moving westwards, out of the way of Dean. You can watch this upper level low on water vapor satellite loops. It is the counter-clockwise spinning region that has moved west off the Florida coast into the eastern Gulf of Mexico. If this low continues to weaken and move westwards, it will not be able to swing Dean northwestwards towards northeast Texas and Louisiana.

The green bars are representing 2005 oil production (blue bars for gas production, see here for more explanations). The yellow track is the GFDL hurricane model which had the best tracking performance on Rita/Katrina. Click to Enlarge

Same as above but with an overlay of the potential wind impact (analysis performed by Chuck Watson ). Click to Enlarge

Zoom in on the GFDL model and associated wind impacts. Click to Enlarge

These images were obtained using Google Earth using the tools given here.

Update (1007/08/18 - 11:30 UTC):

The new forecast is almost a perfect straight line running through Jamaica and the Yucatan peninsula:

Click to Enlarge

## Friday, August 17, 2007

### Hurricane Dean Update (2007/08/17)

The green bars are representing 2005 oil production (blue bars for gas production). Click to Enlarge

The blue dots are representing the major oil platforms. Click to Enlarge

This image was obtained using Google Earth using the tools given here.

## Thursday, August 16, 2007

### Tracking Hurricane Dean on Google Earth

Google Earth is a wonderful tool for the integration and visualization of different georeferenced datasets. With Hurricane Dean approaching the Gulf of Mexico, damage to the Gulf of Mexico oil and gas infrastructure is likely. Below, I give some useful Google Earth add-ons that will enable you to visualize the latest storm forecasts/imagery along with data about the Gulf of Mexico Oil&Gas production (click on the various links to install the individual tools or download this kmz file that will install a Hurricane folder in google Earth containing all the tools below):

Forecasts:

Weather data:

Imagery:

Oil and gas data (Gulf of Mexico)

Once all the packages installed, you should get something like this:

Gulf coast oil operation insight, with Ted Falgout, Port Fourchon port director; Daniel Yergin, CNBC global energy analyst (src: CNBC).

"Delays and rising costs are now the name of the game". Daniel Yergin

### Hurricane Dean, a repeat of Katrina?

Dean is becoming strong and well organized:

Some models are predicting that Dean will be a repeat of Katrina.

GFDL (Geophysical Fluid Dynamics Laboratory) result for August 21 (+126 h).

However, the model average is forecasting a landfall on the Yucatán peninsula:

Five Day Forecast Map (src: Wunderground)

## Monday, August 13, 2007

### US Temperature Revision

A few charts showing NASA's revision of the average U.S. temperatures since 1882 (see RealClimate for explanations). The revision has a significant impact on the years 2000-2005. Unfortunately, this event has been grossly distorted by some news media.

Click to Enlarge.

The data before correction is coming from the web.archive.org (see data). Click to Enlarge.

Click to Enlarge.

Click to Enlarge.

Update (2007/08/15):

The data before correction is coming from the web.archive.org (see data). Click to Enlarge.

Click to Enlarge.

### A Positive Feedback in the Arctic

The Artic sea ice extent is shockingly small this summer and may become ice free sooner than expected (condition not observed for at least a million years):

Sea ice cover (src: NCEP). The image itself displays the ice concentration in intervals. Special colors are pale purple ('weather'), darker purple (no data), gray (too much land near the cell for reliable ice concentrations), and black (land). Red indicates low concentrations (16 to 28 percent), while blues indicate high ice concentrations (over 85%).

It's not surprising knowing that sea surface temperatures in the Artic have been 3 to 5 deg. higher than normal:

Sea Surface Temperature Anomaly (src: UNISYS).

The last three points in the chart below seem to indicate a significant departure from the the linear model used until now. This departure may suggest that a non linear model is maybe more appropriate indicating a possible acceleration of the melting sign of a self-enhancing or positive feedback process ( greater loss of sea ice and albedo (the degree of reflecting ability), brings about more warming, leading to greater loss of arctic ice).

Trends in ice extent anomalies show how the expanse covered by ice is changing from year to year for a given month. Anomalies are given in percentage difference from the mean extent for that month. The mean is calculated using the period 1979-2000 (src: NSIDC).

It seems to confirm the most pessimistic forecasts:

(a) Northern Hemisphere sea ice extent in September from one integration of the Community Climate System Model version 3 (CCSM3) with observations from the satellite era shown in red. The light blue line is a 5-yr running mean. The three lower panels show the September ice concentration (ice floes are separated by open water) in three select decades. (src: RealClimate and "Future abrupt reductions in the summer Arctic sea ice" (Holland et al.)).

## Wednesday, August 08, 2007

### EIA August Update

The EIA has updated its production numbers yesterday up to May 2007.

CategoryMay 2007May 200612 MA12007 (5 Months)2006 (5 Months)SharePeak DatePeak Value
All Liquids 84.18 84.09 84.49 84.1784.20
100.00%2006-07 85.39
Crude Oil + NGL 81.00 80.82 81.32 81.2181.21 96.23%2005-05 82.04
Other Liquids 3.17 3.26 3.17 2.96 2.99 3.77%2006-08 3.55
NGPL 7.94 7.76 7.85 7.937.75 9.43%2007-02 7.98
Crude Oil + Condensate 73.06 73.06 73.47 73.2973.46 86.80%2005-05 74.27

Production figures are in mbpd (million barrels per day)1Moving Average.2the tar sand production numbers are from Statistic Canada.

Below is the Crude oil + NGL production along with the compilation of 13 forecasts (see this post for the details).

## Tuesday, August 07, 2007

### Another Ethanol Debate

Debating whether ethanol is a good alternative or whether it's just a scam, with Lou Ann Hammond, editor-in-chief of Carlist.com; Jeff Goodell, Rolling Stone writer; and CNBC's Larry Kudlow (source: CNBC). Check also Robert Rapier's blog which has contributed to the Rolling Stonte's article. There is also a story by Robert on TheOilDrum.

## Friday, July 13, 2007

### Pickens on Oil and China

Boone Pickens, BP Capital CEO sets his sights on China, with CNBC's Becky Quick (src: CNBC).

## Wednesday, July 11, 2007

### The New IEA Forecast for Saudi Arabia

The following is derived from a comment posted on The Oil Drum thread about the new Medium Term Oil Market Outlook from the IEA.

Page 26 of the report, Saudi Arabia oil demand will grow almost +4.3% per year reaching 2.8 mbpd in 2012:

At this rate, domestic demand could reach 5 mbpd in 2025! this is far more bullish that my prediction of 4 mbpd in 2050 based on a constant consumption per capita of 24.8 barrels/capita/year. Also, the productive capacity forecast for Saudi Arabia (blue dashed line noted "IEA, 2007") is not very different from the previous forecasts (very close to the 2005 and 2006 forecast) with a productive capacity reaching 12 mbpd around 2012:

Click to Enlarge.

This is a nice case for Jeff Brown export land model.

## Tuesday, July 10, 2007

### Steve Andrews (ASPO) on CNBC

Steve Andrews, ASPO co-founder, is discussing the last IEA report with John Kilduff (Man Financial energy analyst).
src: CNBC.

### Net Oil Exports and the "Iron Triangle"

By: Jeffrey J. Brown

As Matt Simmons pointed out several years ago, the critical problem with post-peak exporting regions is that we would have two exponential functions (declining production and generally increasing consumption) working against net exports. From the point of view of importers, it is quite likely that we are facing a crash in oil supplies. In my opinion, what I have described as the “Iron Triangle” is doing everything possible to keep this message from reaching consumers.

In an essay posted on The Oil Drum blog in January 2006, I warned of an impending net oil export crisis, and I used what I called the Export Land Model (ELM) to illustrate the detrimental effect on net oil exports of declining production and increasing consumption. Figure One is a simple graph that illustrates the ELM.

Figure One

Until recently, I had never quantified what percentage of remaining Ultimate Recoverable Reserves (URR) on the ELM would be exported. Note that the ELM is a simple mathematical model for a hypothetical exporting country, but the model is based on actual producing regions.

Also note that the percentage of production that goes to consumption at the start of a production decline has a significant effect on when a net exporter becomes a net importer.

For example, the top five net exporters, in 2006 (Saudi Arabia, Russia, Norway, Iran and the UAE), consumed about 25% of their total liquids production. Offsetting this, many of the top exporters, based on our mathematical models, are at fairly advanced stages of depletion, especially the top three (Saudi Arabia, Russia and Norway), which showed a combined 3.8% decline in net oil exports from 2005 to 2006 (EIA, Total Liquids).

In any case, the answer to the question of how much oil would be exported from the ELM follows (I based URR on Texas URR versus peak production):

Assumptions:

1. URR 38 billion barrels (Gb), peaking at 55% of URR (approximately same range as Texas and Saudi Arabia, based on the premise that Saudi Arabia has peaked);
2. Post-peak production decline rate of 5% per year (approximately the same range as Texas, historically, and Saudi Arabia, currently);
3. Post-peak rate of consumption increase of 2.5% per year (less than half the current rate of increase in consumption for top exporters).

Results:

1. Net exports go to zero in nine years (note that the UK went from peak exports to zero exports in about six years).
2. From Year Zero and Peak Exports on the ELM, only about 10% of remaining recoverable reserves would be exported.

Given the accumulating evidence for declining net oil exports worldwide, it’s useful to remember what the conventional wisdom is regarding world net export capacity, i.e., basically an infinite rate of increase in the consumption of a finite energy resource base. While many economists don’t have a problem with this, back in the real world an infinite rate of increase tends to be hard to sustain.

Figure Two

Figure Two shows Total US Crude Oil and Petroleum Product Imports, which have increased at about 5% per year since 1990.

In my opinion, we will see an epic collision between the conventional wisdom expectations of a continued exponential rate of increase in net oil exports, versus the rapidly developing new reality of an exponential decline in net oil exports.

My frequent coauthor, “Khebab,” is presently working on some mathematical models for production, consumption and net exports by the top net oil exporters. Based on the data that I have seen so far, it will not be a pretty picture. I suspect that the models may show that not much more than 25% of the remaining URR in the top net exporting countries will be exported.

In regard to discussions of Peak Oil and Peak Exports, I have described what I call the “Iron Triangle,” which consists of: (1) Some major oil companies, some major oil exporters and some energy analysts; (2) The auto, housing and finance group and (3) The media group.

If one resides in the oil industry leg of the Iron Triangle, and if one has concluded that Peak Oil is upon us, or extremely close, does one say, "We cannot increase our production," and thereby encourage massive conservation and alternative energy efforts, or does one say "We choose not to increase production and/or we are temporarily unable to increase production for the following reasons (fill in the blank)?"

The latter course of action would tend to discourage emergency conservation efforts and alternative energy efforts, and it would encourage energy consumers to maintain their current lifestyles, perhaps by going further into debt to pay their energy bills, and it would in general have the net effect of maximizing the value of remaining reserves.

I always find it interesting that people like Matt Simmons (who are encouraging energy conservation) are widely blamed by some critics for high oil prices, while some major oil companies, some major oil exporters and some energy analysts are--in effect--encouraging increased energy consumption.

The prevailing message from some major oil companies, some major oil exporters and some energy analysts can be roughly summarized as follows “Party On Dude!”

Meanwhile, over on the other two legs of the Iron Triangle, the auto, housing and finance group is focused on selling and financing the next auto and house, and the media group just wants to sell advertising to the auto, housing and finance group. The media group is only too happy to pass on the “Party On Dude” message to consumers.

To some extent, what we are seeing across the board, from large sectors of the energy industry to the auto/housing/finance industry, media and beyond, is the "Enron Effect," i.e., many people know that we have huge problems ahead, but their paychecks are dependent on the status quo.

The suburbanites are caught in the middle of this, although they have a strong inclination to believe the prevailing message from the "Iron Triangle." As in the movie "The Sixth Sense," for most of us the automobile based suburban lifestyle is dead, but we just don't know it yet, and we see only what we want to see.

However, it is increasingly difficult for many suburbanites to ignore reality as it slowly dawns on them that Jim Kunstler was right when he said, “Suburbs represent the biggest misallocation of resources in the history of the world.” We shall probably soon see that hell hath no fury like a Formerly Well Off suburbanite who just had his SUV repossessed and his McMansion foreclosed.

At least those of us trying to warn of what is coming can try to be ready with a credible plan to try to make things "Not as bad as they would otherwise be,” when it becomes apparent to a majority of Americans that we cannot have an infinite rate of increase in the consumption of a finite energy resource base. How's that for a campaign slogan?

I recommend FEOT--Farming + Electrification Of Transportation (EOT), combined with a crash wind + nuclear power program.

Alan Drake has written extensively on EOT issues, for example in Electrification of transportation as a response to peaking of world oil production.”

In simplest terms, we are soon going to need jobs for hordes of angry unemployed males, and in my opinion “FEOT” is a way to put them into productive jobs.

On an individual basis, I would also recommend “ELP,” which is summarized in the following article: “The ELP Plan: Economize; Localize and Produce.

Good luck to all of us. We are going to need it.

Jeffrey J. Brown is an independent petroleum geologist in the Dallas, Texas area. His e-mail is westexas@aol.com.

## Monday, July 09, 2007

### Oil's Next Stop

Debating whether oil will go to $60 or$80, with John Kilduff, Man Financial; Phil Dodge, Stanford Group energy analyst; and CNBC's Bill Griffeth (src: CNBC).

Best quote: "we are choking on oil right now!", John Kilduff

## Monday, June 18, 2007

### In Defense of the Hubbert Linearization Method

By: Jeffrey J. Brown

The Hubbert Linearization (HL) method (the Hubbert Linearization term was coined by Stuart Staniford, with The Oil Drum) is essentially based on the mathematical observation that a parabolic (bell shaped) curve can be plotted as a line, when we plot P/Q versus Q, where P = annual production and Q = cumulative production to date. The parabolic curve assumption is based on the premise that we tend to find the big fields first. In essence, "Peak Oil" is the story of the rise and fall of the big fields. The parabolic HL model suggests that the world and Saudi Arabia are both probably now in terminal decline. While the overall world decline may be quite gradual, the impact on world oil exports will probably be very severe. See the following article for more information on the HL method: Texas and US Lower 48 Oil Production as a Model for Saudi Arabia and the World.

Note that if the Ghawar Field in Saudi Arabia is in long term decline, which I believe that it is, it is my understanding that every single field that has ever produced one million barrels per day (mbpd) or more of crude oil (crude + condensate) is now in decline. Saudi Arabia has one field coming on line that might make one mbpd, although a lot of people have their doubts. The only real confirmed one mbpd and larger field on the horizon is Kashagan, which probably won't break the one mbpd mark until 2020 at the earliest.

As many people know, Kenneth Deffeyes predicted, using the HL method, a world crude oil peak between 2004 and 2008, most likely in 2005. (He observed that world production apparently peaked in 2000, but he never backed away from his mathematical model that the probable peak was between 2004 and 2008.)

In any case, in the above referenced Texas/Lower 48 article, we supported Deffeyes' work, and we added the Texas model. I observed that Texas peaked at a later stage of depletion than the Lower 48. Post-peak, Texas declined at a faster rate than the overall Lower 48. This was the basis of my warning a year ago that the world and Saudi Arabia were on the verge of a decline in crude oil production. It may be a coincidence, but relative to monthly peaks in 2005, world crude oil production is down more than one percent and Saudi crude oil production is down about 11% (EIA data, crude + condensate).

Note that the initial Lower 48 decline was quite gradual, less than 1% per year for the first two years. Also note that the world has the benefit of the non conventional tar sands production that was not a factor in the Lower 48.

A key piece of data in support of an involuntary decline for the world and Saudi Arabia is the price of oil. The average monthly Brent crude oil price in the 20 months prior to 5/05 was $38 per barrel. The average monthly Brent crude oil price after 5/05 has been about$62, within a range of $54 to$74. Again, we saw this pattern of higher oil prices and lower production in the Texas and the Lower 48 in the Seventies.

The Lower 48 peaked in 1970. Based only on production through 1970, the Lower 48 was right at the 50% of Qt mark in 1970 (Qt is a mathematical estimate of URR for a region).

Russia peaked on a broad plateau centered on 1984. Based only on production through 1984 Russia was right at the 50% of Qt mark in 1984. Russia made from just above 11 mbpd to just below 11 mbpd for five years on both sides of 1984.

At my request, Khebab generated a post-1970 production profile for the Lower 48 and a post-1984 production profile for Russia, using only production data through 1970 for the Lower 48 and through 1984 for Russia to generate the models.

The post-1970 cumulative Lower 48 production, through 2004, was 99% of what the model predicted it would be, see Figure One, Hubbert Linearization technique applied to the Lower-48. Only the data between 1942 and 1970 (green points) are used to perform the fit (red curve).

The post-1984 cumulative Russian production, through 2004, was 95% of what the model predicted it would be. In other words, Russia was "underproduced" through 2004, see Figure Two, Hubbert Linearization technique applied to Russia. Only the data through 1984 (green points) are used to perform the fit (red curve).

In 2006, Russia "caught up" to where it should be. Now, as Russia has approached the 100% mark (100% of what it should have produced based on the HL model), its year over year increase in production has been slowing appreciably, and since October, 2006, the EIA has been showing basically flat production for Russia.

By the way, based on data through 1999 and 2005 respectively, both the North Sea and Mexico started declining right at their respective 50% of Qt marks.

Now, a lot of claims that the HL method is inaccurate are based on a misuse of the method. In most cases, we don't get an accurate Qt estimate until we get a P/Q intercept in the 5% to 10% range. For example, a lot of people use the UK as an example of where the HL method doesn't work, but this is based on wildly improbable early P/Q intercept of 30%.

A lot of the disbelief/denial about a World/Saudi peak is very similar to the reaction that we saw in the Lower 48/Texas in the Seventies. Probably 9 out of 10 Texas oilmen were shocked that Texas didn't show increasing production after the Texas RRC went to a 100% allowable in 1972.

But the bottom line is that we are using a fairly objective method that takes the two pieces data that we have the most confidence in, annual and cumulative production, to generate mathematical models. And many large producing regions--Texas; Lower 48; Total US; North Sea; Russia and most recently Mexico and the world--have shown production patterns that are consistent with the HL models.

The most common response I get to all of this is simply denial. The reserve situation "can't be that bad."

All I can tell you is what the mathematical models are telling me. In a nutshell, I think that the reserve situation is that bad, and I think that we are facing the near certainty of rapidly declining net export capacity worldwide.

While reasonable people can disagree on what the annual and monthly production data are telling us about our proximity to Peak Oil, in my opinion it is a virtual certainty that Peak Oil, from the point of view of importers, is here. This virtual certainty is due to the absolutely lethal combination of flat to declining crude oil production in exporting countries and the (sometimes rapidly) rising domestic consumption in exporting countries, resulting in sometimes catastrophic declines in oil exports. For example, based on EIA data, net total liquids exports by the UK dropped at an annual rate of 60% per year from 2000 to 2005.

In effect, in my opinion the very lifeblood of the world industrial economy is draining away in front of our very eyes. The only question is how fast the patient is bleeding to death.

Sorry to be the bearer of bad news, but you wuz warned.

Jeffrey Brown is an independent petroleum geologist in the Dallas, Texas area. His e-mail address is westexas@aol.com.

## Tuesday, May 29, 2007

### Russian Car Sales & Net Oil Exports

THE VIEW FROM EUROPE
Russian car boom catches eye of Japan, Germany

By JOCHEN LEGEWIE

Excerpt:

Oil boom's impact

All in all, the maximum output capacities of plants operated or planned by overseas automakers is approaching 1 million cars per year. Clearly, something is up in mother Russia.

To put matters simply, Russia is experiencing a good old-fashioned oil boom. Its deepening ties with European energy suppliers, along with rising prices of crude oil and other resources, has created a steady stream of revenue. Having gone through a major economic crisis as recently as 1998, the country has made a complete about face and is now prudently stockpiling funds for future rainy days.

It has also been generous with its citizens. Income tax in Russia is levied at an across-the-board rate of 13 percent, making it the lowest of the major industrialized nations. Combined with extremely low utility costs, as well as pent-up demand for goods after decades of state rule, and the deepening thirst for cars comes as no surprise.

Furthermore, car ownership in Russia is still at a relatively low level of less than 20 percent. Compare that with Germany, where it's over 50 percent, or Japan, which has 44 percent. And the average age of a car in Russia is approaching 10 years, which means many car owners will soon be looking for a replacement. All of these factors add up to a steeply growing market, especially for foreign makes.

In 2002, only 112,000 foreign cars were sold in Russia. This year, the VDA is forecasting that 1,350,000 foreign vehicles will be sold — a 12-fold increase. Conversely, sales of Russian-produced cars have been on a steady decline, from 857,000 in 2002 to a forecast of 750,000 in 2007.

This is a perfect example of the “Export Land” Model, where rising domestic consumption in exporting countries can overwhelm increases in oil production, resulting in lower net oil exports. As I warned in January, 2006 (see my article, “Net Oil Exports Revisited), net oil exports by the top three net oil exporters (Saudi Arabia, Russia and Norway) fell from 2005 to 2006 (EIA data). Based on the captioned article, since 2002, foreign car sales in Russia have been increasing at the rate of about 50% per year (doubling about every 1.4 years). I wonder what effect this will have on gasoline consumption in Russia?

By the way, my Net Oil Exports article appears to be quite popular on the web. Out of about 1.8 million listings for Net Oil Exports on Google, the article is consistently in the top five, and it is generally #1. (I should point out that I built on work done by Matt Simmons and Kenneth Deffeyes, et al, using "Khebab's" graphs.)

This graph shows a hypothetical oil exporting country where a 5% annual decline rate in oil production and a 2.5% annual rate of increase in domestic oil consumption results in a 50% decline in net oil exports in 4.5 years (a decline rate of 16% per year).

As production actually starts declining, many exporting countries will show double digit declines in net exports. For example, from January, 2006 to April, 2007, Mexican oil exports declined 18%, a decline rate of 16% per year, on a month to month basis.

In my opinion, because of the Export Land Model, the ongoing decline in world crude oil production, relative to May, 2005, will look more like a crash from the point of view of importing countries.

Based on our mathematical models (Hubbert Linearization), Russia, at least their mature basins, is at about the same stage of depletion as the United States, in the vicinity of 85% depleted. This suggests that when Russian oil production turns down again (no later than next year, in my opinion), it will be a very sharp decline.

Jeffrey J. Brown

## Tuesday, April 17, 2007

### The Shock Model (Part II)

This story was initially published on TheOilDrum.

This post is the second part of a review of the Shock Model that was introduced in part I. The shock model was developed by WebHubbleTelecsope and aims at modeling oil production based on the backdated oil discovery data. In the first part, we proposed to apply a bootstrap filter in order to estimate the shock function that was previously manually set by the user. We also observed that the predictive ability was limited because of a too conservative projection of future extraction rate values.

In this second part, I propose a modification of the extraction rate function in order to improve the predictive ability of the model. This modification is based on the observation that the extraction rate function is linearly dependent to the ratio of the cumulative production to the cumulative shifted discovery. The new formulation is similar to the logistic differential equation at the difference that the Ultimate Recoverable Resource (URR) is replaced by the cumulative shifted discovery.

I look also at the modelisation of reserve growth which is an important aspect of modern oil production that is often overlooked in the peak oil community.

The code in R language is provided at the end of this post.

Printer friendly version in pdf.

### Unification of the Logistic Model and the Shock Model

The shock model can be summarized by the following equation:
where QT(t) is the cumulative filtered oil discovery, Q(t) is the cumulative production and E(t) the extraction rate function (or shock function). I note t1 the last year of our baseline (i.e. the last year of available production data). One issue with this formulation is that E(t) remains constant and equals to E(t1) in predictive mode when t>t1. We have shown last time (see Figure 8) that this behaviour makes the predicted production follow the reserve profile R(t) leading to an immediate peak most of the time.

For the logistic model, the extraction rate is proportional to the cumulative production and all the oil is available for extraction at time t0:

In equation (2) there is no notion of reserves, it implicitly assumes that all the available oil has been discovered and brought online during the first year (t=t0). By combining equations (1) and (2), we can derive a hybrid shock model by modifying the extraction rate:

The extraction rate (or shock function) is then linearly dependent on the cumulative production as a fraction of the cumulative gross reserve addition:

Note that K is no longer a constant as in the logistic model (2) but becomes the shock function. In predictive mode ( t>t1), E(t) will still evolve thanks to the ratio Q(t)/QT(t) giving a logistic-like behaviour to the forecast.

Is the relation (4) observed in reality? the response is yes as shown on Figure 1 for the years 1985-2006.

Fig 1. Estimated Shock function E(t) versus the cumulative production as a fraction of the cumulative gross reserve additions.
World production for crude oil + condensate from 1985 to 2006. The red line has a slope equals to K=0.0598.

I call Hybrid Shock Model (HSM) this model defined by the relation (3). If I repeat my last time experiment, we can see that predictions are better behaved. In particular, the forecast based on the 1900-1990 baseline gives a 2006 production close to the actual number.

Fig 2. Comparison of the two models for different baselines.

Compared to logistic curves derived from the Hubbert Linearization for different time ranges (1983-1990,1983-2000,1983-2005). We can see that the HSM is better behaved mainly because the logistic curve is unable to account for the 1970-1980 production bump.

Fig 3. Comparison of the logistic curves and the HSM for different baselines.

On Figure 4, the estimated HSM shock function for the baseline 1900-2006 is close to the one given by the SM except in the predictive part where we can see clearly the convergence of E(t) toward K(t).

Fig 4. Estimated shock functions for the HSM and SM using the 1900-2006 baseline .

### Modeling Reserve Growth

Reserve growth is probably one of the most contentious and complex aspect of peak oil (see Rembrandt's posts for a great overview). A quick definition from Verma et al. [2]:

Reserve growth is a term used to refer to estimated increases in the total technically and economically recoverable petroleum reserves of a field that commonly occur through time because (1) additional reservoir and geologic information leads to increases in estimates of hydrocarbons in-place of existing reservoirs or pools; (2) new reservoirs or pools are discovered in existing fields; and (3) improvements take place in the hydrocarbon recovery factor owing to better understanding of reservoir characteristics and behavior through use of 3D/4D seismic interpretation, better geophysical logging tools, and improved reservoir simulation techniques. Additionally, application of horizontal-well drilling technology and enhanced recovery methods improve the hydrocarbon recovery factors significantly, resulting in increased estimates of reserves, particularly in oil reservoirs.

Unfortunately, reserve growth is also very sensitive to the reserve booking and reporting requirements in each country. For the US, reserve growth has been spectacular and is believed to follow a kind of parabolic curve spanning over 95 years. The recent modified Arrington Cumulative Growth Function (CGF) proposed by Verma [2] is forecasting an increase of 0.42% per year for oil fields (onshore) between 1996 and 2030 for the US onshore fields:

with α=1.75752 and β=0.30050 and t in the 1-95 years range (CGF=1 for t=0). This reserve growth model has also been observed on West Siberia by Vermak and Ulmishek [1] with the parameters α=1.56639 and β=0.36060. I'm proposing to model reserve growth using also a linear filtering derived from the above parabolic curve, the filter is the following:

where tStart is the initial reference year where we assume growth is taking place (i.e. the initial discovery number is including some reserve growth, up to tStart years of equivalent growth). The growth filter impulsional response (6) is shown on Figure 5 for tStart= 20 years.

Fig 5. Proposed linear filter response (bottom) for the modeling of reserve growth derived from the empirical CGF function (top).

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 hFallow,hBuild and hGrowth:

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 hGrowth 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.

The tricky part is to find an appropriate value for tStart. It seems logical that tStart should 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).

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).

I assume the following model for tStart:
where tRef is the reference year for which the backdated discovery curve has been issued and tInit is a general offset that gives us a better control on the model. Below are a few claims that may help us calibrate our algorithm:
1. The USGS is forecasting 612 billion barrels (mean estimate) for conventional oil between 1996 and 2025.
2. 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.
3. 2005 resource growth in pre-2005 discoveries was only 8 Gb.
In the simulations below, I made a few assumptions:
1. discovery data is the ASPO backdated (1932-2004) so tRef =2004.
2. pre-1932 total discovery is 30 Gb (mainly US)
3. post-2004 discovery forecast is based on a logistic decline.
4. lambda= 3 years.

 Peak URR (Gb) Total ReserveGrowth 1996-2025 ReserveGrowth 1996-2003 ReserveGrowth Pre-2005Reserve Growth 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 ArringtontInit= 1 2036 @ 36.8 Gb 3937 1976 704 146 21 427 Modified ArringtontInit= 15 2017 @ 28.7 Gb 2616 655 230.8 59 7.7 236 Modified ArringtontInit= 20 2015 @ 28.1 Gb 2500 538 191 50 6.5 204 West Siberia GrowthtInit= 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).

The result of the SHM + Modified Arrington with tInit=1 year (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 new discoveries post 2004. The SHM + Modified Arrington with tInit= 15 years and the SHM + Russian growth (tInit=1) 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.

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.

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.

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

1. The interest of the Shock Model approach resides in its capacity to exploit the discovery data, the production profile and the reserve growth models.
2. 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.
3. The method can potentially deal with difficult multi-modal production profiles such as Saudi Arabia.
4. The logistic case can be seen as a particular case of the HSM when the extraction of total resource (URR) is instantaneous.
1. 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.
2. 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.
3. 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.
4. 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.
5. 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.
6. 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.

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.

### References:

[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:
• 1900-1959: API Facts and Figures Centennial edition 1959.
• 1960-2006: EIA data (includes tar sands production from Canada and Venezuela).

### Code:

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 (ShockModel_Part2.txt) and click on "Edit/Run all".