Application of Power Spectral Analysis and Digital Filtering in Evaluating the Distribution of Rock Properties
Authors: Bennion D.W. , Hope A.C.A. 
Published: December 2007

This paper was prepared for the 47th Annual Fall Meeting of the Society of Petroleum Engineers of AIME, to be held in San, Antonio, Tex., Oct. 8–11, 1972 Permission to copy is restricted to an abstract of not more than 300 words. Illustrations may not be copied. The abstract should contain conspicuous acknowledgment of where and by whom the paper is presented. Publication elsewhere after publication in the JOURNAL paper is presented. Publication elsewhere after publication in the JOURNAL OF PETROLEUM TECHNOLOGY or the SOCIETY OF PETROLEUM ENGINEERS JOURNAL is usually granted upon requested to the Editor of the appropriate journal, provided agreement to give proper credit is made. provided agreement to give proper credit is made. Discussion of this paper is invited. Three copies of any discussion should be sent to the Society of Petroleum Engineers Office. Such discussions may be presented at the above meeting and, with the paper, may be considered for publication in one of the two SPE magazines.

Abstract
Object of this paper is to present a mathematical technique for reservoir classification. Four tools of time series analysis are employed: autocorrelation, cross correlation, power spectrum, and filtering. Autocorrelation is used to classify the reservoir as random or stratified, cross correlation is used to determine if the strata can be correlated in the reservoir. Power spectrum is used to determine the frequency distribution of the time series and for picking the sampling interval for digitizing well picking the sampling interval for digitizing well logs or sampling cores. It is also used for determining the frequencies to be filtered out.
The paper presents the theory, sample calculations and applies the data to a sandstone reservoir. The reservoir is stratified and the strata can be correlated from well to well.

Introduction
To calculate reserves and predict performance of a hydrocarbon bearing reservoir performance of a hydrocarbon bearing reservoir it is desirable to have information pertaining to the distribution of its rock pertaining to the distribution of its rock properties. It is necessary to know the porosity properties. It is necessary to know the porosity distribution to determine reserves and the variations of permeability to calculate the flow rates. With the increased use of numerical simulations to predict reservoir performance it is necessary to develop better performance it is necessary to develop better methods of determining the spatial variations of rock properties. There are three generally accepted ways of sampling a reservoir to determine these properties: well logging coring, and flow tests. In well logging and coring data is obtained at points which can be assigned a depth within a well. Usually flow tests give average properties of the well's drainage volume.
From an engineering point of view, reservoirs can be classified in three ways: random, correlated strata, and non-correlated strata. The rock properties at a point in a random reservoir do not depend on the properties within the vertical or horizontal properties within the vertical or horizontal neighborhood of that point. In a correlated stratified reservoir the rock properties at a point are dependent on the rock properties point are dependent on the rock properties within a vertical and horizontal neighborhood of that point.