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Some benefits of seismic using in geostatistical porosity mapping, Case study from Drava depression

Clastic reservoir include much uncertainties, depends on lithology heterogeneity. There is several geostatistical direct and indirect methods (e.g. Kriging, Cokriging), and all of them solve the general problem of prediction inter-well area values with variable known at the well locations. Cokriging and Kriging with external drift use information produced by an auxiliary variable in relation or correlated with the interpolated variable. It is very often to combine seismic attributes (usually amplitudes) with porosities averaged at well locations to interpolate porosity map. Some authors, from theoretical point of view, point out (Collocated) Cokriging approach as better than the external drift method. The advantage of Collocated Cokriging is that the actual level of correlation between the auxiliary variable (seismic) and the variable of interest is taken into account. The better this correlation, the more weight is given to the auxiliary variable as compared to Kriging based on wells only. Analyzed oil field is located in northeastern part of Drava depression, with reservoir in Badenian (mostly calcitic) breccia (massive reservoir type). There is totally 106 well trajectories, and interpolated 3D seismic sections from which is derived six attributes. Reliable porosity averaging though reservoir interval is done at 14 well locations. Spearman rank correlation led to the highest correlation coefficient (R=-0.64) given for pair porosity-reflection strength. Advantage of rank correlation is that normal distribution is not any more necessary condition for correlation, what could be useful in case of small input dataset. The field porosity is characterised with slightly expressed anisotropy, shown though variogram ellipsoid with ranges of 1750x1500 m. Variogram axes follow the structural field axes. Variograms were inputs for Ordinary Kriging (OK) and Collocated Cokriging (CC) maps. These geostatistical maps were compared with Inverse Distance Weighting (IDW) results, via cross-validation results or uncertainties maps. The results acquired through IDW and OK methods differ very slightly, i.e. on both maps remain so-called “ bull eyes effect” . Cross-validation results (or Mean Square Error/MSE/values) for both methods are also very close (IDW=2.78, OK=2.97). The Kriging based exclusively on autocorrelation of the primary variable (porosity) did not show improvement regarding mathematically simpler IDW method. By introducing the secondary variable (reflection strength) the more advanced geostatistical algorithm of Collocated Cokriging was tested. MSE value was approx. 25 % lower (CC=2.19) than results acquired by IDW and OK. Geological differences in inter-well spatial porosity distribution could be searched and recognized at uncertainty maps. Such map, resulted from IDW and OK comparison, pointed out reservoir NE edge as the most “ problematic” prediction area (due to data missing). Uncertainty map, as difference of OK and CC maps, is more homogenous, with smaller “ background” differences scattered around entire reservoir. SGS simulations are recognized as the most appropriate tool for mapping inter-well area uncertainties. Based on 4 SGS simulations (small but representative set for qualitative mapping, due to low MSE differences) areas characterised with high uncertainties in porosity prediction are clearly outlined. References: Davi, B. (1987): Uses and Abuses of Cross Validation in Geostatistics. Mathematical Geology, v.19, no.3, 241-248, Dordrecht. Dubrule, O. (1998): Geostatistics in Petroleum Geology, AAPG Education Course Note, Series #38. Kelkar, M. & Perez, G. (2002): Applied Geostatistics for Reservoir Characterization. Society of Petroleum Engineers, Richardson, p. 264. Malvic, T. & Djurekovic, M. (2003): Application of methods: Inverse distance weighing, ordinary kriging and collocated cokriging in porosity evaluation, and comparison of results on the Benicanci and Stari Gradac fields in Croatia. Nafta, 54/9, 331-340. Smoljanovic, S. & Malvic, T. (2004): Improvements in reservoir characterization applying geostatistical modelling (estimation & stochastic simulations vs. standard interpolation methods), Case study from Croatia. Proceedings of World Petroleum Congress, 1st Youth Forum / Committee (ur.). Peking, Kina : Chinese National Committee for WPC, 1054-1061. Xu, W., Tran, T.T., Srivastava, R.M., Journel, A.G. (1992): Integrating Seismic Data in Reservoir Modelling: The Collocated Cokriging Alternative, SPE 24742.

Geostatistical mapping; Kriging; Cokriging; porosity; seismic

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