Discovery Process Modeling - Creaming

Every study based only on the so-called proved reserves should be discarded as useless following the principle GIGO: Garbage In, Garbage Out.
Laherre, 2006

A discovery process model

The term "creaming" (short for "creaming off") was coined in Shell Intnl. in the seventies when the work of Arps and Roberts (1958) and Drew (1974) became known. The idea is that the exploration process in a basin "creams off" the best prospects first, gradually having to consider more risky prospects. One could imagine that the large anticlines are so conspicuous that they are easier to find than the smaller more subtle closures. After that, fault traps against one fault and eventually more risky traps bounded by several faults would be drilled. In reality the process will be less organized, but in many basins the general trend is obvious.

There are various graphs that can be made to show the discovery process:

From a statistical point of view, the exploration process is a sampling without replacement from a finit population of exploration prospects. Without geology and geophysics this sampling may be random. However, even if the basin is drilled at random locations, the prospects with a larger 2-dimensional size have a slightly better chance to be found first. So even in that theoretical case there would be some creaming effect. The bias in the sampling will be still larger if geological insight, seismic and other surveys and geochemistry become involved. As the prospects portfolio becomes depleted we see that both the mean of and the variance of the population of the remaining prospects are decreasing.

Here is an example of cumulative discovery vs. cumulative number of exploration wells:

The part of the globe represented by this graph is "World Outside Communist Areas and North America". It is outdated in two respects: it was made in 1989 and the ultimate recoveries of the field discovered in say the last ten years of the graph will have changed. Nevertheless, there is considerable creaming.

In a recent article by E.Smith Llimás (2017) in the AAPG Explorer, a graph of yearly number of new Field Wildcats drilled and yearly discovery of conventional oil and gas in terms of barrels oil equivalent (BOE). It shows that since 2008, both drilling and discovery volume has declined considerably, suggesting a rather gloomy situation for conventional oil and gas, which is true, of course, with regard to the exploration activity. However, both declines are mainly influenced by economics at low oilprices, not geology! To show this I used the data extracted from the graph to construct a creaming curve of cumulative discovery versus cumulative exploration wells. This shows that the success rate in terms of BOE was high before 1980, and a little less since then, but there is no suggestion at all for a decline in recent decades. A good example to stress the importnace to work with exploration effort instead of years.

The data allow even a split into the amounts of oil and gas discovery separately, so the oil and gas creaming curves are as shown below. Both show no decline in discovery rate since 1980.

An important change is that in this period a significant change occurs from oil to gas as the predominant HC found. This is shown by the percentage of oil in the HC mix discovered, here against the cumulative number of wells, but a similar picture is obtained if we simply put years at the X-axis.

At the country and basin scale there are many examples of the creaming process, a striking example is from Laherre (2006) for Saudi Arabia. This shows that the creaming of the number of discoveries is not present, but rather the reverse, possibly due to improved seismic techniques and the cumulated geological knowledge. But very strong creaming in terms of volumes discovered is observed.

The "classic" creaming curve is from the Denver-Julesberg basin, cum. discovery up to a billion barrels against cum. number of exploration wells:

Various attempts to make extrapolations for forecasting have been made over the years, e.g. Meisner & Demirmen (1981) have developed a bayesian approach to creaming. I used this for a forecast of UK offshore production made in the early 80ies by UKOOA. Extrapolation of the creaming process allowed a probabilistic estimate of the undiscovered fields.

Forman & Hinde (1985) used a log-linear decline function for the discovery rate. Later Forman et al. (1995) further developed their creaming method, involving estimated areas of closure and reserves per area.
A new bayesian method was developed by Sinding-Larsen and Jingzhen Xu (2005).

Most of the more simple creaming forecasting schemes do not take the areal spread of exploration in time into account. Such "higher dimensional" creaming might improve forecasts. If exploration effort is not randomly spread over an area, but spreads out from a starting point incrementally, it matters if a new wildcat is drilled in the already known area, or in a virgin part of the province. In this way the discovery process may show "sub-creaming curves", a common feature of many creaming curves.

There a few practical point about creaming methods worth mentioning:

Estimating the number of discoveries that can be made in a play

When a play has n prospects, each with its own ,POS, it is fairly easy to obtain a distribution of the number of successes if we drill all the prospects. The procedure uses the binomial distribution not with a single fixed probability, but the various POS values for the prospects. For n < 14 it is possible to enumerate all possible permutations and extract the distribution of numbers of discoveries. The logic becomes clear if we use an example of only 3 prospects. Then the number of possibilities is 2^3 = 8 (and , in general 2^n). The 8 possible combinations are listed in the 8 rows in the left three columns of the table. The last two columns show the resulting number of discoveries for each cobination and the probability that a combination will occur.

Prospect 1Prospect 2Prospect 3Number
POS = 0.35POS = 0.12POS = 0.55  
0 0 0 0 0.2574
1 0 0 1 0.1386
0 1 0 1 0.0351
0 0 1 1 0.3146
1 1 0 2 0.0189
1 0 1 2 0.1694
0 1 1 2 0.0429
1 1 1 3 0.0231
SUM =1.0000

The probabilities are derived by multiplication ( this assumes independence of the prospects). For instance, In the first permutation, only prospect 1 is a success (indicated by a "1"). The probability of this result from three prospects drilled is p1 * (1- p2) * (1 - p3) = 0.35 * (1 - 0.12) * (1 - 0.55) = 0.2574.
Now by assembling the probabilities for 0,1, 2 and 3 discoveries we get:

0 0.2574
1 0.4883
2 0.2312
3 0.0231

For larger n an approximation based on the normal distribution can be used, then based on the average of the prospect probabilities.

This analysis of probabilities also plays a role in hindsight analysis of prospect appraisals.