Core Sample Permeability Estimation Using Statistical Image Analysis

摘要

The statistical description of pore space seen in a 2-D section has been successfully applied for the characterization of the pore structure of different types of porous media using 1)the optical porosity and 2)the spatial distribution of porosity,which can be described by the autocorrelation function(ACF)of pore space seen in 2-D space.Statistics obtained from images include the image porosity,specific surface area,and a length scale obtained from the integral of the image autocorrelation function.The number of images required to predict the permeability of a core sample accurately,using the porosity($,)and the integral scale of the autocorrelation function for an image(Ii),is adressed in this paper.The following phenon~enological permeability model was found to describe the behavior of many samples: k=A<Φ1>~B~c.where k is the predicted absolute permeability of the sample,<$,> and are the average porositv and average integral scale of ACF of all images respectively,while A,B,and C are parameter values determined by fitting experimentally determined permeabllities of tested core samples.The proposed correlation accounts not only for reservoir porosity,but also the pore structure characteristics of the medium as determined from statistics of 2-D images.The proposed form of permeability correlation is more robust than other similar methods.Furthermore,at least 10 randomly taken images from a section are required to make a reasonable estimate of the permeability of a core sample.The permeability distribution at the scale of 512 by 512 pixels with 1.5 microns resolution can be estimated using Monte Carlo trials if the number of images taken for any given sample is 40 or greater.