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Geostatistical analysis of porosity, permeability and production data from Burbank Oil Field (Oklahoma, USA)

Tsepetakis Ioannis

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Summary

This thesis focuses on the analysis of data from a hydrocarbon reserve located in Burbank, Oklahoma. The study is based on the analysis of porosity, thickness and permeability data of a reservoir. Parameters were calculated for empirical models which relate the porosity and the permeability in porous media. Spatial analysis was also performed, based on two methods of linear spatial interpolation. One method belongs to the Kriging family and the other was the inverse distance weighting (IDW) method. These were applied with a view to estimating oil supplies in the reserve under normal conditions (OOIP) for specific flow units of the reservoir. In this thesis, the following units were examined: FU3, FU5, FU8, FU9 and FU10. The FU5 flow unit is extensively analysed and the others are presented in the Annex. Understanding of the spatial sequence is expected to improve plans for oil field development. It can provide a better picture of the financial risks at an early stage, and is therefore able to be of use when making investment decisions.The first part of the thesis concerns the investigation of empirical formulae, namely the Kozeny-Carman, Timur and Coates models. Comparison of the models was per- formed on the basis of their adaptation to existing data. As performance criteria, the root mean square error (RMSE) and the Spearman’s rank correlation coeffi- cient were used. Based on these measures, the Timur model demonstrated better adaptation to porosity - permeability data.In the second part, geostatistical analysis of the reservoir thickness in a flow unit was undertaken. Thickness combined with porosity make a contribution to the cal- culation of reserves and optimal exploitation planning. Different variogram models were examined and it was found that the spherical model was optimal. Point inter- polation was applied to the data and the ordinary kriging stochastic interpolation algorithm was used. This methodology is the most reliable method of linear esti- mation when enough data is available. At the other extreme, there is the inverse distance weighting (IDW) method which uses an empirical exponent for the distance (it usually takes arbitrary values between 1 and 3). The IDW method is a quicker way of estimating specific drillings in the same flow unit.The results of the spatial interpolation were evaluated using statistical validation measures. The IDW method resulted in better spatial estimation than the kriging based on the RMSE. Lastly, the OOIP was determined on the basis of an empir- ical formula that relates porosity to thickness and the technical characteristics of the reservoir (e.g : porosity, water saturation ”Sw” or oil formation volume fac- tor ”Bo”). Using both the Kriging and the IDW methods, volumetric calculations showed 10,484,000 barrels for the first method and 9,565,300 barrels for the other method, respectively. The comparison of the methods was based on the (RMSE) between kriging and IDW total Oil in place (OOIP) results. Unlike IDW, Kriging provides the ability to construct uncertainty maps of point estimates.Under suitable assumptions on the priors, kriging gives the best linear unbiased prediction of the intermediate values. In future projects with a similar theme, it is recommended that simulation also be used, to ensure better control of spatial variations.

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