Abstract

We discuss the influence of different statistical models in the prediction of porosity and litho-fluid facies from logged and inverted acoustic impedance (Ip) values. We compare the inversion and classification results that were obtained under three different statistical a-priori assumptions: an analytical Gaussian distribution, an analytical Gaussian-mixture model, and a non-parametric mixtu re distribution. The first model assumes Gaussian distributed porosity and Ip values, thus neglecting their facies-dependent behaviour related to different lithologic and saturation conditions. Differently, the other two statistical models relate each component of the mixture to a specific litho-fluid facies, so that the facies-dependency of porosity and Ip values is taken into account. Blind well tests are used to validate the final predictions, whereas the analysis of the maximum-a-posteriori (MAP) solutions, the coverage ratio, and the contingency analysis tools are used to quantitatively compare the inversion outcomes. This work points out that the correct choice of the statistical petrophysical model could be crucial in reservoir characterization studies. Indeed, for the investigated zone, it turns out that the simple Gaussian model constitutes an oversimplified assumption, while the two mixture models provide more accurate estimates, although the non-parametric one yields slightly superior predictions with respect to the Gaussian-mixture assumption.

Highlights

  • The Bayesian approach combines the prior knowledge about the model properties with the likelihood function of the data with the aim to estimate the posterior probability distributions of the subsurface properties of interests given the observed data [1,2]

  • At a first glance we note that the acoustic impedance and the porosity values decrease moving from shale to brine sand and to gas sand

  • The decrease of the Ip values moving from shale to sand is caused by the different elastic properties of the mineral matrices that are associated to the two litho-facies

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Summary

Introduction

The Bayesian approach combines the prior knowledge about the model properties with the likelihood function of the data with the aim to estimate the posterior probability distributions of the subsurface properties of interests given the observed data [1,2]. The estimation of petrophysical reservoir properties (i.e., porosity, shale content, fluid saturation) and litho-fluid facies around the target area is a common, highly ill-conditioned problem that is often casted into a Bayesian framework [3,4,5,6]. In this context, both analytical and numerical methods have been extensively applied [7,8,9,10,11,12]. The input data to the estimation and classification processes can be logged data

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