Fractal and cumulative trace analysis of wire-line logs from a well in a naturally fractured limestone reservoir in the Gulf of Mexico

We found that the wire-line well logs measured in a naturally fractured limestone reservoir show fractal behavior, and that the fractal parameters are correlated with the petrophysical properties. Based on neutron porosity, bulk density, gamma ray, P-wave transit time, shallow and deep resistivity logs, five strata were distinguished corresponding to the Tithonian and Kimmeridgian Jurassic (JST, JSK); Upper, Middle and Lower Cretaceous (KS, KM, KI). Each of these strata has different fractal dimensions. Using the BENOIT software we obtained average fractal dimensions for the logs by modeling them as fractional Brownian motion (fBm). For the neutron porosity log D=1.70 (KS), D=1.66 (KM), D=1.75 (KI), D=1.84 (JST), D=1.67 (JSK). We conclude that the fractal geometry of the pore space controls the log fluctuations as well as the fractal dimensions of the logs in each geological unit. Cumulative trace analysis has provided further insight, including zonation of the five main units.