RESCALING RELATIONS BETWEEN 2-DIMENSIONAL AND 3-DIMENSIONAL LOCAL POROSITY DISTRIBUTIONS FOR NATURAL AND ARTIFICIAL POROUS-MEDIA

Local porosity distributions for a three-dimensional porous medium and local porosity distributions for a two-dimensional plane-section thro ugh the medium are generally different. However: for homogeneous and i sotropic media having finite correlation lengths, a good degree of cor respondence between the two sets of local porosity distributions can b e obtained by rescaling lengths, and the mapping associating correspon ding distributions can be found from two-dimensional observations alon e. The agreement between associated distributions is good as long as t he linear extent of the measurement cells involved is somewhat larger than the correlation length, and it improves as the linear extent incr eases. A simple application of the central limit theorem shows that th ere must be a correspondence in the limit of very large measurement ce lls, because the distributions from both sets approach normal distribu tions. A normal distribution has two independent parameters: the mean and the variance. If the sample is large enough, local porosity distri butions from both sets will have the same mean. Therefore correspondin g distributions are found by matching variances of two- and three-dime nsional local porosity distributions. The variance can be independentl y determined from correlation functions. Equating variances leads to a scaling relation for lengths in this limit. Three particular systems are examined in order to show that this scaling behavior persists at s maller length-scales.