Optimization, uncertainty analysis and upscaling of rock-physics models

During the last years, geomodel to seismic 3D and 4D feed back loops are becoming a new industry standard in geoscience. These loops are basically suited for automatic geomodel updating and history matching where the discrepancies between seismic data and geomodel petrophysical infilling are detected. One of the most important components of this type of loops where the synthetic seismic data computation is a compulsary step is the Rock-Physics (RPM) or Petro-Elastic Model (PEM). RPMs are widely used in geoscience for different reasons: 1) modelling of the elastic logs to provide different fluid scenarii; 2) quantitative lithoseismic interpretation and supervised seismic facies classifications; 3) 3D and 4D loops. In this paper we address several aspects: 1) different issues of RPM optimization at log scale; 2) uncertainty assessment of the RPM modelling results; 3) different approaches for RPM upscaling / recalibration at geological grid scale. The problem of RPM optimization and upscaling is an inverse nonlinear problem where around 20 of non-correlated coefficients in shale and sand compaction depth trend laws need to be found. Optimization is carried out with the means of global optimization tool based on simulated annealing algorithm. During the optimization the choice of the cost function is of a high importance. The uncertainty analysis is basically performed to assess the quality of the optimization and to establish some thresholds above which the results of modelling are qualified. Our methodology was applied for a turbiditic West African offshore field. The result shows that such optimization methodology can reduce significantly the differences between observed P, S-impedances data and modelled ones from the optimized RPM compared to the base RPM. The results of forward modelling in elastic domain match better the 3D inverted seismic data with around 15% reduction of residuals due to only RPM recalibration. From our observations, an upscaling of the RPM remains a delicate task which is of a second order importance compared to the fine tuning of the RPM at log scale. When the RPM is used for the forward seismic modelling, correct restitution of the elastic properties contrasts by the RPM is of high importance.