Mathematical Modelling of Reservoir Rock Properties
Authors: Bennion D.W. , Hope A.C.A. 
Published: March 2010

Abstract
The 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. A1ltocorrelation 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 sampling distribution of the time series and for 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 the performance of a hydrocarbon-bearing reservoir it is desirable to have information pertaining to the distribution of its rock 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 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 are obtained at points which can be assigned a depth within a well. Flow tests usually give average properties of the well's drainage volume.
From an engineering point of view, reservoir's 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 horizontal neighbourhood of that point. In a correlated stratified reservoir. the rock properties at a point are dependent on the rock properties within a vertical and horizontal neighbourhood of that point. In a non-correlated stratified field, the value at a point depends only on the points in a vertical neighbourhood of that point. In this type of classification the strata are usually one foot to several feet in thickness rather than the very small micro strata that occur in many rocks. At the present time, well logging tools are not available for measuring the properties of these micro strata.
The object of this paper is to present a method toclassify reservoirs into one of these three groups. The technique assumes that the data obtained from well logs and core analysis can be regarded as a statistical time-series, with a pseudo time assignment to each depth. The development of time-series analysis methods has been reported in the literature(1–30 but its application has been limited mainly to meteorological(3), seismological(5), chemical processing(2)) and economic data(2); some efforts have also been made to apply it to geological data(6–8). This study will use four time-series tools: autocorrelation, cross correlation, power spectrum and filtering.