Extending the Application of a Shale Volume Estimation Formula Derived from Factor Analysis of Wireline Logging Data
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Extending the Application of a Shale Volume Estimation Formula Derived from Factor Analysis of Wireline Logging Data Norbert P. Szabó · Mihály Dobróka
Received: 18 April 2012 / Accepted: 8 February 2013 © International Association for Mathematical Geosciences 2013
Abstract A multivariate statistical procedure is developed for the estimation of shale volume in clastic sedimentary formations. The method offers an alternative for extracting the shale content from borehole geophysical measurements. Factor analysis of various well-logging data types generates a new well log that correlates with the shale content of shaly-sandy rocks. The mathematical relationship between shale volume and factor scores is represented by a nonlinear equation, which seems to be applicable for data sets originating from different sedimentary basins. A comparative study is made between three different data sets originating from Hungary and the United States of America in order to check the validity of the proposed empirical formula. Shale volumes predicted from factor analysis are confirmed by estimates from independent deterministic and inverse modeling. Petrophysical information derived by factor analysis of logs recorded in deep wells can be used for a more accurate and reliable estimation of effective porosity and absolute permeability of reservoir rocks, for decreasing the estimation error of inversion estimates and for reducing the ambiguity in the solution of the well-logging inverse problem. Keywords Shale volume · Factor log · Scaled factor · Deterministic procedure · Inverse modeling
1 Introduction Petrophysical properties of shaly sand formations can be extracted from borehole geophysical data either by deterministic or inversion procedures. The former ones N.P. Szabó · M. Dobróka () Department of Geophysics, University of Miskolc, 3515, Miskolc-Egyetemváros, Hungary e-mail: [email protected] N.P. Szabó e-mail: [email protected]
Math Geosci
substitute data to explicit equations in order to determine the petrophysical properties separately. There are several kinds of deterministic methods for the estimation of porosity, shale volume, mineral composition of rock matrix, water saturation, and other nonmeasurable properties of sedimentary formations (Serra 1984; Asquith and Krygowski 2004). Wireline logging data can also be evaluated by using an appropriate inversion method, which assumes a known relationship, called the probe response function, between the observed data and the parameters of the petrophysical model. The solution of the inverse problem is given by fitting a theoretical data set calculated by the response equations to the measured data. As a result of the inversion procedure, the most probable set of model parameters with estimation errors is specified (Menke 1984). The theory of the inverse problem of borehole geophysics and its practical implementation are detailed in Mayer and Sibbit (1980), Alberty and Hashmy (1984), Ball et al. (1987). Factor analysis is a multivariate statistical method, whi
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