Monday, February 27, 2006

US Addiction to Oil


My two last posts were trying to forecast future oil exportation for Saudi Arabia and Iran based on a population driven growth of domestic demand. I believe that demographic pressure is ultimately determining the long term trend in oil consumption (assuming a constant lifestyle). The US is the top oil importer with imports near 15 mbpd in 2004. Like most of the western countries, the US population growth is modest with a fertility rate around 2.0 and a population that could reach 420 million in 2050 (Note that Hispanics count for almost one-half of population growth) [1].

Fig 1. US population trend (src: UN)

If we look at the quantity of oil consumed per capita (Figure 2), the trend seems to be linear since the 80s with 24.5 barrels/capita/year and a slight increase of 1.5 barrels/capita/year every 15 years (the oil comsumption data is from the 2004 BP energy review [3]).

Fig 2. Oil consumption per capita per year. The dotted lines are two possible trends.

Problem is that the US domestic oil production is declining rapidly since the 1970 production peak predicted by King Hubbert. On Figure 3, we added the result of the Particle Filtering based on a Stochasctic Bass Model (SBM-PF) which gives an Ultimate Recoverable Ressource around 230 Gb (logistic growth rate K=6%).

Fig 3. US oil production: actual data plus the result of the SBM-PF model.

If we combine the first order model for the consumption per capita (Figure 2) and the predicted US production on Figure 3 we can try to predict future importation levels (Figure 4).
Fig 4. US production, consumption and importation forecast.

If oil consumption stays strong in the US and grows to 22 mbpd in 2010, the oil imports could reach 17 mbpd (80%) in 2010 and 20 mbpd in 2015 (85%).
Fig 5. Oil importation and exportation shares for the US.

Now, what would happen if only part of the oil imports can be satisfied? the result is shown on Figure 6 and demonstrate how dramatic the fall could be for different change levels in imports. Just for a 25% decrease in imports, the consumption per capita could become flat.

Fig 6. Collapse of the oil consumption per capita/year if only a fraction of the oil imports is available. The population model is the UN medium variant.

Nobody knows what are the consequences implied by a fall in the oil consumption per capita but historically we can observe a significant correlation between the GDP per capita variations and the oil consumption per capita variations as shown on Figure 7.

Fig 7. Annual Variations (year-to-year relative change in %) for the US GDP and the oil consumption per capita. The estimated correlation coefficient is 0.68. The GDP per capita is derived from the real GDP data of chained 2000 dollars [4].

Friday, February 24, 2006

Iran's Ability to Export Oil

In this post, I repeat the same exercise I did for Saudi Arabia and try to predict the growth of Iran domestic oil consumption based on the predicted population growth. Iran was the fourth world oil exporter with a net export of 2.55 mbpd in 2004. Compared to Saudi Arabia, Iran faces less population pressures with a fertility rate of 2.1 children per woman. However, Iran's oil consumption is growing rapidly as shown on Figure 1.


Fig 1. Iran's oil consumption (millions of barrels per day, src: BP)

The annual population growth rate is about 1.2% for 2005 and is expected to stay constant for the next 10 years ([1]). The population was 69.5 million in mid-2005 and is expected to reach 102 million in 2025 (Population Reference Bureau). If we divide the oil consumption by the population numbers, we can see that the oil consumption is not mature and is expanding quickly at about 1 barrel/capita/year every ten years (see Figure 3). It is difficult to predict at which level the oil consumption per capita will stabilize. For now, we assume that the observed growth pattern will continue and could potentially reach European levels of consumption (about 10 barrels/capita/year) within 20 years.

Fig 2. Iran population trend (src: UN)

Fig 3. Number of barrels consumed per capita per year.

Based on the linear growth model (black dotted line on Figure 3) we predict Iran's future oil consumption based on the UN population forecast shown on Figure 2. The result is shown on Figure 4 for the three population model variants. The oil production forecast for Iran was derived from the SBM-PF model. We can observe that the oil exports will stay flat a few years around 2.8 mbpd before going down. The fraction of oil exports will fall below 60% after 2010 (Figure 5). This forecast is somewhat optimistic on future production levels with an URR around 188 Giga-barrels and a peak production at 5 mbpd around 2025. we also assume that the domestic oil consumption will continue to grow at the same pace which is a reasonable assumption knowing that fuel prices are heavily subsidised in Iran (Diesel at 1 US cent/liter, super gasoline at 9 US cents/liter in 2004!).

Fig 4. Projected oil consumption based on the population growth and a linear growth for the consumption per capita per year (1 additional barrel/capita/year every decade).

Fig 5. Projected share of the oil exports for the different population scenario.


References:

[1] PRB Country Profiles: Iran
[2] Population Division of the Department of Economic and Social Affairs of the United Nations Secretariat, World Population Prospects: The 2004 Revision and World Urbanization Prospects: The 2003 Revision

[3] www.internationalfuelprices.com

Sunday, February 19, 2006

Saudi Arabia's Ability to Export Oil

Saudi Arabia is the top world oil exporter with a net export of 8.73 mbpd in 2004. Saudi Arabia faces a number of challenges in rising production from its aging oil fields. Also, Saudi Arabia faces population pressures from a large, young population; fertility rates of almost 6 children per woman; high population growth; and a large expatriate population. One question is how this demographic pressure will drive the domestic oil consumption which has been rising rapidly :


Fig 1. Saudi Arabia oil consumption (millions of barrels per day, src: BP)

The annual population growth rate is about 2.3% for 2005 and is expected to stay constant for the next 10 years ([1]). The Total Fertility Rate (average no. of children born to a woman during her lifetime) is very high at almost 6 children per woman. The population was 24 million in 2002 and is expected to reach 41 million in 2025 (Population Reference Bureau). If we divide the oil consumption by the population numbers, the consumption per capita is remarkably stable around 25 barrels/capita/year (see Figure 3). This high number (in comparison to 21 for the US) can be explained by the fact that Fuel prices are subsidised at the expense of the country's energy sector. The average price for a liter of gasoline was only 24 cents in 2003 [3].

Fig 2. Saudi Arabia population trend (src: UN)

Fig 3. Number of barrels consumed per capita per year.

If we assume that the number of barrels/capita/year will remain constant around 25 we can predict Saudi Arabia's future oil consumption based on the population forecast shown on Figure 2. The result is shown on Figure 4 (red line). The oil production forecast for Saudi Arabia was established in the last post. We can observe that the oil exports will peak a few years before the total production. The fraction of oil exports will fall below 85% from 2010 (Figure 5).

Fig 4. Projected oil consumption based on the population growth and a constant consumption per capita of 24.8 barrels per year (red curve)..

Fig 5. Projected share of the oil exports for the different population scenario.

Edit: 02/20/2006 10:44 am: corrections of a few mistakes about the color coding employed for the different variants (sorry about that!).

References:

[1] PRB Country Profiles: Saudi Arabia
[2] Population Division of the Department of Economic and Social Affairs of the United Nations Secretariat, World Population Prospects: The 2004 Revision and World Urbanization Prospects: The 2003 Revision

[3] www.internationalfuelprices.com

Saturday, February 18, 2006

The 4 Biggest Oil Exporters (Revisited)

Last time, we applied the Hubbert linearization technique on the four top oil exporters in order to predict future production. The results were not satisfactory because of the difficulty to fit a logistic curve on the multimodal profiles of Russia, Iran and Saudi Arabia. This time, we revisit that exercise by using the SBM-PF method instead. We also model the Ultimate Recoverable Resource (URR) with a prior probability distribution function derived from a range of different estimates. The shape of the prior will be a triangular distribution inspired by the USGS approach. The different reserve and discovery estimates are taken from the following sources:

MEES
EIA
USGS

For the USGS, we added together the mean discovery estimate for oil fields and Natural Gas Liquids (NGL). All the volumes given below are in billions of barrels (Gb). The production profiles are from the 2004 BP statistical review.

Saudi Arabia









SourceReservesYearCumulativeYTFUltimate
BP Statistical Review262.730Year-End 2004
113.8
NA376
Oil & Gas Journal266.810January 1, 2006117NA384
World Oil262.075Year-End 2004
113.8
NA376
IHS 219Year-End 2002
106.2
34332-460
USGS261.4Year-End 199685.8136
483
ASPO194200110314300

The uncertainty about the URR is modeled by a triangular distribution shown on the figure below:



Iran









SourceReservesYearCumulativeYTFUltimate
BP Statistical Review132.460Year-End 200457.2NA190
Oil & Gas Journal132.460January 1, 200659NA192
World Oil130.800Year-End 200457.2NA188
IHS101Year-End 2002
54.3
6161-250
ASPO68Year-End 2002548130
USGS 92.6Year-End 19964667206



Russia









SourceReservesYearCumulativeYTFUltimate
BP Statistical Review72.277Year-End 2004130NA202
Oil & Gas Journal60.000January 1, 2006133NA193
World Oil67.138Year-End 2004130NA197
IHS59Year-End 200212726202-239
USGS 55Year-End 1996
110
115280
ASPO60Year-End 200212723210


Norway









SourceReservesYearCumulativeYTFUltimate
BP Statistical Review9.673Year-End 200419.5NA29
Oil & Gas Journal7.705January 1, 2006
20
NA28
World Oil9.863Year-End 200419.5NA29
IHS15Year-End 2002177
39-43
USGS11.6Year-End 19969.915
37
ASPO14Year-End 200116.31.432



We apply the curve tracking algorithm on each country separately and we sum all the results. The SBM-PF method was applied with 1,500 particles and the predicted curve was based on the propagation of the ten best particles.

Fig. 1. Results of the curve modeling on the 1930-2100 time period.


Fig. 2. Zoom-in on the 1985-2025 time period.










CountryCumulative (2004) Gb
URR (Gb)
qPeak Date
Saudi Arabia114 (29%)381
5.1%
2018-2022
Iran
57 (30%)
1883.7%
2024-2029
Russia
130 (58%)
224
5.8%
2005-2009
Norway
20 (56%)
35
13.8%
2001


The total production seems to reach a plateau between 2006 and 2009 before declining. The Saudi Arabia production is probably optimist reaching 14 mbpd in 2015. Russia is shown to decline in the next few years. Another factor is the growth of the domestic consumption that could further reduce their ability to export oil.

Monday, February 13, 2006

commenting and trackback have been added to this blog.

The USGS World Petroleum Assessment 2000

The USGS World Petroleum Assessment 2000 has been criticized by many peak oil advocates mainly because its predictions are very high compared to other studies as shown on Figure 1. However, very few have seriously looked into it and try to understand why the estimates are so high. This post is a suggestion of JD (peakoildebunked.com) which has posted a couple of interesting posts, along with Rembrandt Koppelaar, about the USGS approach (233. THE REAL USGS PREDICTION, 232. INTERPRETING THE USGS STUDY).


Fig. 1: Repartition of the Different URR estimates by year [1]


The USGS WPA is a huge undertaking and is a bottom up approach where the oil/gas/NGL volumes are estimated on elementary assessment units which are then aggregated in Total Petroleum Systems (TPS), regions, provinces, countries up to the entire world. All the data and documentation are available on their website (USGS Digital Data Series - DDS-60).


Fig .2: description of the Total Petroleum System map (TPS)

The overall procedure is described on Figure 3 below. I won't go into all the details of the method, I rather focus on the Monte-Carlo procedure that has been used.


Fig. 3: USGS Procedure

At the heart of the resource estimation is a Monte-Carlo calculation described on Figure 4.


Fig. 4: Steps involved in the Monte-Carlo procedure.

The Monte-Carlo procedure consists in estimating a marginal probability of the total volume v from the joint probability of the resource volume v and number of fields n:





Fig. 5: Monte Carlo Simulation

The Monte-Carlo method (Figure 5) assumes that it is possible to obtain a large number of N independent random samples distributed according to a law p(n). In our case, we want to estimate a marginal distribution p(v) of the total oil volume v from a joint distribution of the total volume and the number of unknown fields n:

The distribution for the field size p(s) is an truncated log-normal function detailed in the appendix I , page 17 (COMPUTATION OF THE FIELD-SIZE FREQUENCY DISTRIBUTIONS):



The different parameters can be estimated from the maximum, minimum and median value of the field-size distribution. I reproduced part of the algorithm in Matlab using the input contained in the input.tab file for the Assessment Unit Code 10150101 (Supra-Domanik Carbonates/Clastics, Volga-Ural Region, Former Soviet Union):


Fig. 6: Result of a Monte-Carlo integration using 1,000 runs, the red line on the top figure indicates the current number of oil fields value (~350) which fix the number of points on the field-size distribution. Note that only integer values are allowed for the field size.

Once the volume distribution has been sampled (bottom plot on Figure 6), different Coproduct ratios (gas to oil ratio, GOR; NGL to gas ratio; and liquids to gas ratio, LGR) are randomly applied in order to estimate volumes of undiscovered gas, NGL and oil. The Matlab code that produced this result is the following:

a= 100; % Minimum Number Of Undiscovered Oil Fields
b= 350; %
Median Number Of Undiscovered Oil Fields
c= 700 % Maximum Number Of Undiscovered Oil Fields
aS= 1; % Minimum Size of Undiscovered Oil Fields (MMBO)
bC= 2.5; % Median Size of Undiscovered Oil Fields (MMBO)
cS= 100; % Maximum Size of Undiscovered Oil Fields (MMBO)

h= 2.0 / (c - a);
vTriangularDistributionPDF(a:b)= h ./ (b - a) .* ([a:b] - a);
vTriangularDistributionPDF(b+1:c)= h ./ (c - b) .* (c - [b+1:c]);
vTriangularDistributionCDF= cumsum(vTriangularDistributionPDF);

fGamma= aS;

fMu= log(bC - fGamma);
fSigma= (log(cS - fGamma) - fMu) / icdf('normal',0.999,0,1);
vSizeofUndiscoveredOilFieldsCDF(aS:cS)= logncdf(aS:cS,fMu,fSigma);
% The distibution is truncated so we have to renormalized
vSizeofUndiscoveredOilFieldsCDF= vSizeofUndiscoveredOilFieldsCDF ./ vSizeofUndiscoveredOilFieldsCDF(end);

% Number of points
N= 1000;


% Monte-Carlo Integration
for i=1:N,
r= rand(1,1);
idx= find(vTriangularDistributionCDF >= r(1));
vN(i)= idx(1);
vVolume(i)= 0;
% Sampling of field-size distribution

for j=1:vN(i),
r= rand(1,1);
idx= find(vSizeofUndiscoveredOilFieldsCDF >= r(1));
vVolume(i)= vVolume(i) + idx(1);
end

end


The Monte-Carlo used is a brute force algorithm and requires many points to converge (The USGS used 50,000 points). There are many other ways to reach the same result using the Metropolis-Hastings and the Gibbs sampler algorithm. Jean Lahèrrere has written an article about the USGS approach [1] and has criticized the use of the truncated log-normal distribution for the field-size distribution:
The USGS claims that it uses a truncated log-normal distribution. But it evidently confuses the natural log-normal distribution of the total notional amounts in the ground with those that are recoverable subject to economic constraints. A better approach would have been to distinguish the two categories.
The USGS estimate seems to have been inflated by too many small uneconomical fields that should have been cut off.

[1] Jean Lahèrrere, Is USGS 2000 Assessment Reliable?


Friday, February 10, 2006

Russia

Russia is a difficult case because of the recent rebound in production in the late 90s resulting in a bimodal production profile. I applied the Stochastic Bass Model based Particle Filter I proposed yesterday (SBM-PF in short) assuming the following initial parameters:



All the SBM parameters are stochastics and updated at each iteration based on uniform transition probabilities:




For the production data, I used the 2005 BP statistical review for the period 1965-2004 completed with data (1930-1965) taken from a Jean Lahèrrere graph. I also added an unofficial estimate 0f 9.44 mbpd for 2005. The results are shown on the figures below:


Fig. 1. Simulated production profile using the SBM-PF technique


Fig. 2. Observed variations of the beta parameter.




Fig. 3. Resulting URR distribution using the SBM-PF technique. 95% of the values are above 226 Gb.

It's interesting to compare these results in a P/Q vs. Q representation (Hubbert Linearization):


Fig. 4. Result of the SBM-PF approach in the P/Q vs Q representation. The green line is the logistic model resulting from a fit based on the observed data only which gives an URR around 150 Gb. The red line is the fit using the SBM-PF projection.

The Fig. 4 seems to indicate a phenomenon similar to what has been observed with the North Sea production. The green line is mainly influenced by the first production peak whereas the red line fits the second peak better. From my dataset, the observed cumulative production is 142.2 Gb in 2005. Therefore, according to Fig. 3 there is a 95% probability that the Russian reserve is above 83.8 Gb. Published reserve estimates seem to be within the range 60-70 Gb:







SourceReserves (Gb)
BP Statistical Review
End 2004
72.277
Oil & Gas Journal
January 1, 2006
60
World Oil
End 2004
67.138
ASPO
End 2002
63


Below is the production forecast from the ASPO:




Thursday, February 02, 2006

How to Track an Oil Production Curve

Last time we explained how to build a logistic oil production profile using a Stochastic Bass Model which can be seen as a stochastic equivalent of the logistic curve used by peakoilers. This post is an attempt to apply this stochastic model so as to literally "track" the production curve and then project future production for the coming years. An interesting framework within which this goal can be achieved is called the particle filtering technique. Particle filtering can be seen as a generalization of the Kalman filter and is sometimes encountered under various names such as the bootstrap filter, the condensation method, the Bayesian filter or the sequential Monte-Carlo Markov Chain (MCMC). These techniques have been very sucessful in many applications such as the visual tracking of targets.

Particle filtering is quite a complex technique and there is a fairly large body of literature on it. I don't wish to flood this post with equations rather try to provide some intuitive insights. In order to explain the particle filtering, I will use the following simple analogy:

Imagine that you are in a totally dark room looking for a wall switch for the lights. The best way to find it is to randomly sample the walls with your hands in order to find an object that has a similar feeling under the touch. Of course, you have some prior knowledge on where to find the switch, its shape and your trajectory will probably evolve along the walls.

Well, particle filtering is exactly the same. The equivalent of the particles are the random sampling of the wall with your hands around your current position. The information you are getting with your hands is the equivalent of the particles' importance weights.

Now, let's look at some equations. Each particle will be an hypothetical oil production profile evolving according to a stochastic Bass model (SBM):


Note that only the SBM growth rate (or adoption rate) will be a random variable. We also need to discretize the production growth so that it can only grow by a fix amount of oil (ex 0.1 Gb/year).

The particle filtering is an iterative procedure where each iteration is composed of the following four steps:
  1. Sampling step: we randomly choose N candidate particles from a proposal distribution (i.e. I choose random positions on the wall where to put my hands)
  2. Reweighting step: we weight each particle with an importance weight (i.e. do I feel something under my hands?)
  3. Resampling step: this step is optional but gives better results and avoid degeneracy of the particles.
  4. Filtering step: we finally compute a mean state based on the new particle set (Monte-Carlo integration)
The design of the proposal distribution for the sampling step is a delicate task and can be simplified by equating the proposal distribution to the Markovian transition probability of the SBM. In that case, the particle filter is called Bayesian Bootstrap Filter. Consequently, each particle n is independently evolving according to the following equations:
The weighting step consists in assigning an importance weight to each particle according to their fit compared to the observed data:
where Prod(t) is the observed production at time t. One hurdle is how to extend the tracking for future production where there is no data available. For now, we simply replace the particle weights by an uniform weight which is equivalent to simulate a stochastic Bass model.

The resampling step consists in redistributing in place the initial set of particles according to their weight so that particles with bigger weights will be eventually duplicated. Once the particles have been resampled, we can estimate the mean state using a Monte-Carlo approach:
The two figures below give an example of curve tracking on the US production using N=1,000 particles (alpha=5e-5, m= 223 Gb). Because the growth rate is the only stochastic parameter it has to fluctuate widely in order to follow closely the oberved curve variations.


Fig. 1 Proposed method applied to the US production (EIA data) where the dark dots are the actual data, the thick orange line is the mean state of the particles and the two blue lines delineate the one sigma of the various particles' positions.


Fig. 2 The growth rate beta_t is the only parameter of the particles which is stochastic and reflects how particles have to accelerate production growth in order to match the data. Production seemed to have grown faster in the 50s. After 2005, we have no data so the growth rate stays around its mean value.

In summary, we are proposing to use a sequential Monte-Carlo Markov Chain for the modeling of the oil production.
  • The algorithm allows for a dynamic adaptation of the production parameters (growth rate and URR) instead of a static and global view of the parameters as in traditional curve fitting.
  • production shocks can be modeled.
  • the underlying Markov process is still based on a logistic model but a stochastic one.

There are many improvements possible in particular around the design of the proposal distribution and the choice of the priors for the URR and the growth rate.

For a good overview on particle filtering techniques:

M. Sanjeev Arulampalam, Simon Maskell, Neil Gordon, and Tim Clapp, A Tutorial on Particle Filters for Online Nonlinear/Non-Gaussian Bayesian Tracking, IEEE TRANSACTIONS ON SIGNAL PROCESSING, VOL. 50, NO. 2, FEBRUARY 2002.