Scaling and Correlation Functions to Map and Understand the Heterogeneity of the Productive Layer



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One of the most challenging problems in the development stage of a field is the prediction of the fluid type as well as lateral and vertical heterogeneities in the reservoir away from the well-location. This multi-scale approach, both downscaling and upscaling to the solution is a two-step process based on the Pair Correlation Function (PCF) approximation method that takes into account the effect of scattering by considering the interactions between any two points of a heterogeneous medium. The amplitude of the correlations of fluctuations are estimated for various combinations of measured and calculated physical properties like velocity, density, porosity, and elastic stiffness tensors. The fluctuations will be higher if the medium is heterogeneous due to sudden changes in lithology or if the properties of the inclusions are drastically different from the matrix, as in the case of a productive layer and so we expect higher values for amplitude.

The first step is to detect the heterogeneous layer from the well-logs for a range of frequencies. Hermite Distributed Approximating Functionals (HDAFs) and Simple Moving Average (SMA) are used as the averaging or upscaling methods for calculating the amplitude of the fluctuations. The results show that to detect the productive layers at lower frequencies that corresponds to seismic data, HDAF gives better results. The second step is downscaling where logs are predicted from the seismic data using scaled functions, which are then used to identify and map the heterogeneous layer and predict future well locations. This methodology is also applied to study the heterogeneity in a meandering fluvial channel fill using well–logs in the clastic Tertiary sediments of northern part of South Marsh Island in the Gulf of Mexico (GoM).



Downscaling, Seismic, Pair-correlation function, Rock physics, Well logs