Assessment of reservoir heterogeneities and hydrocarbon potential zones using wavelet-based fractal and multifractal analysis of geophysical logs of Cambay basin, India

Abstract

The scaling behaviour of physical properties of the earth's subsurface e.g. porosity, permeability, density, etc significantly influence reservoir characteristics. The characterization of the parameters, by analysing nonlinear geophysical logs using the application of linear and traditional empirical relations, is very tedious, complicated, and yields less accurate results. In this perspective, wavelet-based fractals and multifractals techniques provide effective insights into local and global characteristics of heterogeneity of reservoir parameters. The results from the numerical experiment on simulated synthetic data reveal that the wavelet-based fractal and multifractals are more useful to delineate the shorter fluctuations in signal and heterogeneities of the reservoir. The scaling exponent and fractal density, a component of fractal analysis, have been estimated for each sample from power law relationship that facilitates the understanding of the local characteristics of the subsurface formation. On the other hand, the multifractal spectrum, a generalization curve of the hurst exponents, provides the global nature of heterogeneities corresponding to reservoir parameters. We analyse gamma ray, density, and neutron logs of three wells (well-204, 203, and 172) of the Limbodara oil field of Cambay Basin, India. The fractal density curve of gamma ray log is found like the low-pass filtered version of the original signal, and map the lithologies by clustering their similar values while the scaling exponent curve on either side of 0.5 of scaling exponent demarcates the lithological boundaries at the intersection points. The scaling exponent curve highlights the finer variations embedded in the signal and is feasible to enhance the thin layers of the reservoir. The multifractal spectrum of gamma-ray logs across three wells encompasses three major formations emphasizing that the Kalol formation exhibits higher degree of heterogeneity than other formations (Tarapur and Olpad). The multifractal spectrum of neutron and gas corrected log for each well of Kalol formation shows the greater influence on well-203 and lowest influence on well-172, indicating the effective hydrocarbon bearing zones of the former well than the latter. This evidence that an increase in lithological heterogeneity enhances the quality of hydrocarbon reservoir as well as reduces the multifractality of porosity logs.