Every study based only on the so-called proved reserves should be discarded as useless following
the principle GIGO: Garbage In, Garbage Out.
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:
Cumulative volume discovered vs years on the horizontal axis.
Cumulative volume discovered vs number of exploration wells
Cumulative number of discoveries vs number of exploration wells
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 It is outdated in two respects: it was made in 1989 and the ultimate recoveries of the field discovered in say the last ten years of the graph will have changed.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.
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:
Experience with growth of reserves of fields shows that there is considerable appreciation of reserves, at least in the first 6 or 7 years after first production tests. In a study of field reserves of some 600 fields outside the USA, I found a growth factor of over two after 7 years. From year zero to year seven the increase was roughly linear. Of course, this growth is the average of many fields. Some are initially overstimated, others underestimated. However, underestimation is the rule. Especially if reserve data refer to "proven" reserves (P90) the chances of growth are high. An extreme example of growth is the Groningen gas field in the Netherlands:
Other examples of the revision of Ultimate Recovery estimates are given for UK and Norway by Hermanrud et al. (1996).
Significant growth means that a reserves creaming needs correction to the last, say ten years, otherwise the creaming process will severely underestimate the undiscovered reserves as well.
The definition of the province, basin, or play that is analysed is very important. Each subdivision may have its own creaming curve. For instance, technical limitations have prevented deepwater exploration in earlier days. Also maximum depth of exploration plays a role. Then gradually prolific areas become available later, partly because of technical reasons. Especially creaming against a time scale rather than against number of exploration wells would become unreliable. So, areas for creaming have to be defined carefully on the basis of both geological and technical grounds.