Non-Gaussianity effects in petrophysical quantities

It has been proved that there are many indicators (petrophysical quantities) for the estimation of petroleum reservoirs. The value of information contained in each indicator is yet to be addressed. In this work, the most famous and applicable petrophysical quantities for a reservoir, which are the gamma emission (GR), sonic transient time (DT), neutron porosity (NPHI), bulk density (RHOB), and deep induced resistivity (ILD), have been analyzed in order to characterize a reservoir. The implemented technique is the well-logging method. Based on the log-normal model defined in random multiplicative processes, the probability distribution function (PDF) for the data sets is described. The shape of the PDF depends on the parameter λ2 which determines the efficiency of non-Gaussianity. When non-Gaussianity appears, it is a sign of uncertainty and phase transition in the critical regime. The large value and scale-invariant behavior of the non-Gaussian parameter λ2 is an indication of a new phase which proves adequate for the existence of petroleum reservoirs. Our results show that one of the indicators (GR) is more non-Gaussian than the other indicators, scale wise. This means that GR is a continuously critical indicator. But by moving windows with various scales, the estimated λ2 shows that the most appropriate indicator for distinguishing the critical regime is ILD, which shows an increase at the end of the measured region of the well.