Creaming and the Likelihood of Discovering Additional Giant Petroleum Fields
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Creaming and the Likelihood of Discovering Additional Giant Petroleum Fields Jostein Lillestøl1
· Richard Sinding-Larsen2
Received: 2 April 2016 / Accepted: 24 September 2016 © International Association for Mathematical Geosciences 2016
Abstract The applied context of this paper is the exploration for petroleum resources, like petroleum accumulations in different deposits, where the most promising deposits are likely to be drilled first, based on some size indicators, so-called creaming. The paper explores creaming models in the context of sampling with probabilities in proportion to size, for which a lognormal size distribution has nice analytical features. It departs from the traditional paradigm in petroleum resource assessment. Instead of conceiving a finite population being depleted over time in a decaying fashion with respect to size, the situation is studied within the framework of independent observations (infinite population) and an exploration maturity-dependent creaming factor. The theoretical and practical consequences for inference on the parent population and the probabilities and expectations linked to future discoveries are studied. The theory applies to the issue of remaining sizes of petroleum resources to be found within different future discovery horizons on the mature part of the Norwegian Continental Shelf. The aim is to obtain reasonable and useful predictions, and not to provide the best possible explanation of the exploratory behavior itself. Keywords Lognormal distribution · Sampling proportional to size · Resource prediction
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Jostein Lillestøl [email protected]
1
Department of Business and Management Science, Norwegian School of Economics, Helleveien 30, 5045 Bergen, Norway
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Department of Geology and Mineral Resources Engineering, Norwegian University of Science and Technology, Sem Sælands vei 1, 7491 Trondheim, Norway
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Math Geosci
1 Introduction This work is dealing with the opportunities offered by the lognormal distribution for predicting remaining recoverable petroleum deposit sizes. It is well known that observed size distributions from various regions, for example Mexican Gulf and Norwegian Continental Shelf (NCS), are well fitted by a lognormal distribution. However, the fitted distribution cannot directly be used for prediction purposes, since the observations are not randomly sampled from the assumed unknown parent distribution. By plotting the size of discoveries in sequence, one typically see a declining pattern, consistent with the behavior of exploring for the most promising fields first, so-called creaming. Figure 1 shows the consecutive sizes for existing and potential development projects on the mature part of Norwegian Continental Shelf, since the first drilling in 1966, measured in million Standard cubic meter oil equivalents (MSm3o.e.). By the mature part of the Norwegian Continental Shelf, hereafter named M-NCS, is meant The North Sea and The Norwegian Sea, excluding other Norwegian areas not yet open for wide exploration. The source for the da
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