Simulación condicional de variables regionalizadas y su aplicación al comportamiento de la porosidad efectiva en un yacimiento fracturado-poroso

 José Quintín Cuador-Gil^1* y Arelys Quintero-Silverio²

Departamento de Informática, ²Departamento de Matemática, Universidad de Pinar del Río, Martí, No. 270, Pinar del Río, 20100, Cuba.

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Abstract

In geosciences, it is very frequent to find spatially distributed variables. Nowadays, different estimation and/or simulation procedures are used to study this type of variables. From a set of samples taken from some location over the domain of the phenomenon, which are considered representative of the reality (reality that generally is always unknown), these procedures allow its description or characterization in two different ways: the first one gives estimated values in the location of interest where no samples were taken, and the second one generates values with the same characteristic dispersion of the original data.

Particularly in geology and mining, the kriging estimation proposed by geostatistics has been widely used. This is certainly the best possible estimation, as it provides the Best Linear Unbiased Estimator. This fact is confirmed by the increasing number of geostatistical applications that are presently carried out in earth sciences, especially in the mining industry, as well as in oil industry, environmental studies, cartography, climatology, etc. The geostatistical estimation, according to the mathematical condition from which it is obtained, gives a smooth image of the elements under study, in the same way as the wide group of other known interpolators. This estimation shows no fluctuation of its contents. An alternative for this situation is to simulate the behavior of the variable. Considering these variables as random functions it is possible to obtain a realization with the same variability and correlation characteristics of the original data, which can be used to represent the subject under investigation. These characteristics are revealed from the available information by the calculation of semivariograms and the fitting of theoretical models. The simulation process should not be considered better than the estimation process, but as an alternative to obtain the level of description needed. The objectives of these procedures are different, but they together could improve the knowledge of the regionalized variable.

In this paper, we present the fundamental elements of the conditional simulation theory that uses kriging in the conditioning process, and introduce an algorithm of simulation in one dimension, which can be extended for two and three dimension. Finally, we show an example of the simulation of the effective porosity in the productive horizon Tobas Gruesas in the fractured-porous reservoir Pina situated in the province of Ciego de Ávila in Cuba.

Keywords: Geostatistics, semivariogram, Kriging, conditional simulation, random function, algorithm.