Multifractal analysis of the pore space of real and simulated sedimentary rocks

Abstract

It is well known that sedimentary rocks having same porosity can have very different pore size distribution. The pore distribution determines many characteristics of the rock, among which its transport properties are often the most useful. Multifractal analysis is a powerful tool that is increasingly used to characterize the pore space. In this study, we performed multifractal analysis of pore distribution on simulated sedimentary rocks using the relaxed bidisperse ballistic deposition model (RBBDM). The RBBDM can generate a 3-D structure of sedimentary rocks of variable porosity by tuning the fraction p of particles of two different sizes. We also performed multifractal analysis on two samples of real sedimentary rock to compare with the simulation studies. One sample, an oolitic limestone is of high porosity (40 per cent) while the other is a reefal carbonate of low porosity, around 7 per cent. 2-D sections of X-ray microtomographs of the real rocks were stacked sequentially to reconstruct the real rock specimens. Both samples show multifractal character. The results from analysis of real rock agree quite well with the simulated structure of low porosity. The simulated rock of high porosity showed a weak multifractal nature though the real rock sample of similar porosity was found to be strongly multifractal. We propose a ‘structure parameter’ ξ which is a function of porosity and the generalized dimensions, and controls the transport properties of the rock.