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Geostatistical Analysis of permeability data

Georgousakis Konstantinos

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Summary

Properties such as porosity and permeability are of utmost significance in petroleum industry. They are important parameters for both reservoir engineering and reservoir modelling, since they constitute the basis upon which hydrocarbon reserves, as well as hydrocarbon flow characteristics are determined. For that reason, accurate estimation of these properties has been the subject of continuous studies.For the purposes of this thesis, the porosity and permeability data provided by the 10th SPE benchmark reservoir model were used. This model is part of the PUNQ Complex Model and is a highly heterogeneous model, consisting of two parts: A relatively permeable Tarbert formation on top and an Upper Ness formation at the bottom. The latter comprises of permeable anastomosed channels laid on a non–permeable background. The data were analysed using visualization, statistical and geostatistical techniques, in order to investigate the statistical properties and to subsequently quantify and evaluate their spatial correlation and variability.The exploratory analysis was carried out using classical statistics (e.g., histograms, statistical moments, distribution fitting and scatter plots). However, the main results were derived using geostatistical methods. Geostatistical analysis included the calculation of various variograms (i.e., directional, anisotropic, omnidirectional and 3D variograms), and their subsequent fitting with appropriate theoretical variogram models. In addition to this analysis, an upscaling of the reservoir model was performed by implementing the Simplified Renormalization method to both porosity and permeability data.Various conclusions were drawn from this project concerning the behaviour and spatial correlation of the reservoir, as well as the general implementation of the geostatistical methods. The most important outcome was the confirmation of the high heterogeneity and anisotropy characterizing the entire reservoir model. An equally significant observation was that results depend greatly on the number and locations of data included. More specifically, considering more data across the horizontal plane increases the interpretable information of variogram analysis, while considering more data along the vertical direction increases the variability. Finally, upscaling leads to coarse–grained versions of the reservoir model; such reduced dimensionality models should be further evaluated by means of subsequent flow simulation.

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