## Monday, February 13, 2006

### 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?