Microstructures, percolation thresholds, and rock physical properties

Abstract

The physical properties (transport properties and mechanical properties) of porous/cracked rocks are mainly functions of their microstructure. In this connection the problem of critical (threshold) porosity for transport, elasticity and mechanical strength is especially important. Two dominant mathematical formalisms — effective medium theory (EMT) and percolation theory — pretend to give answers to this problem. Some of the EMT models do not predict any threshold (differential effective medium). Other EMT models (self-consistent models) do predict thresholds, but it is shown that these thresholds are fictitious and result from an extension of a theory beyond its limit of validity. The failure of EMT methods at high pores/crack concentrations is the result of clustering effects. The appropriate formalism to correctly describe the phenomenon of clustering of pores and cracks and the behaviour of a system close to its critical porosity is percolation theory. Percolation thresholds can be predicted in that case from classical site or bond percolation on regular or random lattices. The threshold values depend on the density and average size of pores/cracks so that porosity is not sufficient in general to characterize the threshold for a specific physical property. The general term ‘critical porosity’ should thus be used with caution and it is preferable to specify which property is concerned and what kind of microstructure is present. This term can be more safely used for a population of rocks which have an identical average shape of pores/cracks and for a given physical property.