Porosity Bayesian inference from multiple well-log data

Luiz Lucchesi Loures


This paper reports on an inversion procedure for porosity estimation and uncertainty analysis in well locations from a series of well-logs consisting of neutron, sonic (compression and shear wave) and density logs. The inversion procedure is based on the Bayesian methodology of inference. The inversion formulation considers log data uncertainties and information from rock physics, which include the effects of clay content and pressure. The main goal of this methodology is to reduce the uncertainties associated with each type of well-log, within the estimated porosity model.

The Bayesian formulation developed assumes that all uncertainties can be described by Gaussian pdfs and we consider the variances of the well-log datasets to be unknown parameters. The posterior pdf is marginalized for the variances and the final posterior pdf is one for the interval porosity. The methodology is implemented using a moving window, which computes one posterior of the interval porosity for each interval of the discrete well.

Examples with synthetic data are produced to show how this methodology works. Tests performed with different well-log combinations have provided a way to analyze the contribution of each type of log data towards increased reliability of the estimated porosity. Tests with a real dataset are presented. The results of these tests are compared with a porosity model derived from laboratory experiments on a core sample.

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