Effect of the variance of pore size distribution on the transport properties of heterogeneous networks

Abstract

The goal of this paper is to evaluate the effect of the variance of pore size distribution on the transport properties of rocks. Several heterogeneous network realizations with very broad, uniform, or log uniform pore size distributions were constructed. A series of networks were then derived deterministically from these initial networks by repeatedly applying a shrinking operator to the pores of the original realizations. This operator was devised in such a way as to maintain the mean pore size constant while changing the variance of the pore size distribution, therefore allowing its effect on the transport properties to be isolated. We thus assessed the validity of several permeability models from the literature as a function of the variance of the pore size distribution. We found that the product of the permeability by the electrical formation factor was proportional to the square of the critical radius as proposed in the Katz‐Thompson model [ Katz and Thompson , 1986]. However, we observed that the dramatic flow localization occurring at high pore size variance was not restricted to the backbone of the critical subnetwork (or critical path) as assumed in the Katz‐Thompson model. We propose that a better justification of the relation mentioned above arises from the underlying percolation problem of the viscous‐inertial transition observed in harmonic flow as a function of frequency. In addition, we appraised the stochastic Bernabé‐Revil model [ Bernabé and Revil , 1995]. We found that this model was more and more difficult to implement as the pore size variance was increased. A possible interpretation could be that at high levels of pore‐scale heterogeneity, very large pore size fluctuations occur and the flow pattern is so strongly and determimstically related to these extreme fluctuations that a stochastic description becomes inadequate.