Capillarity - Permeability - The Network Model of Porous Media - I. Capillary Pressure Characteristics

This paper proposes the network of tubes as a model more closely representing real porous media than does the bundle of tubes. Capillary pressure curves are derived from network models and pore size distributions are calculated from these curves. In this way is shown the difference between the true and calculated pore size distributions when the capillary pressure curve is used to obtain pore size distribution for porous media. INTRODUCTION Despite the technological importance of the laws governing flow through porous media, many of these laws have not yet been clearly formulated. This is especially true of the laws governing multiphase flow. The static properties, such as the capillary pressure curve, are also not at present interpretable correctly in terms of the pore size distribution and other structural properties of porous media. In the absence of any well founded theoretical description of fluid flow through porous media, many empirical descriptions have been proposed. In addition to the strictly empirical flow equa- tions, some equations have been developed rigorously from simple geometrical models of the pore spaces. These equations are only as valid as is the model used in their development. The two models used in the past, the sphere pack and the bundle of tubes, have been too simple, and as a result, the equations derived from them have failed to predict the observed properties. Agreement between theory and observation has been achieved for these models by inserting parameters of doubtful physical significance. The work to be reported here was undertaken in the belief that the study of a model more closely resembling most real porous media than does the sphere pack or bundle of tubes would yield useful information concerning the structure of real porous media and the relation between structure and flow properties. There was no intention of developing any calculational procedures, as for example calculating relative permeability from capillary pressure data. The objective of the study was instead to develop a better qualitative understanding of the relation between the various measurable properties of porous media. The model chosen for study is the network of tubes in which each tube represents a pore space in the porous medium. Microscopic observations leave no doubt that sandstones and clastic carbonates are three-dimensional irregular networks of irregularly shaped pores. The irregularity of these structures makes any accurate theoretical study of their properties impossible. Results from an oversimplified model such as the bundle of tubes are worthless when applied to real systerns. The sphere pack model, on the other hand, not