Fundamentals of Fluid Flow in Porous Media

 

Chapter 2

Relative Permeability

Two Phase Relative Permeability Literature Survey: Relative Permeability Simulations

During the past forty years, many investigators tried to simulate the capillary and transport phenomena in porous media. Many different methods were used. These methods are classified as macroscopic approaches or pore level (microscopic) approaches.

Greenkom (1981) gives a review of the theoretical advances in the study of flow through porous media and discusses the phenomenological approaches for phenomena that occur in a porous medium under steady state conditions. He also provides an extensive list of references. According to Dullien (1979) and Chatzis (1980), the early models that deal with the porous media are classified as:

• Phenomenological models (i.e. Carman-Kozeny’s ‘Hydraulic Radius Theory’),
• Geometrical models (i.e., serial type, parallel type, and serial-parallel type capillaric models), and
• Statistical models, “cutting and random rejoining models”, (Haring and Greenkom (1970)).

Macroscopic approaches published include Slattery (1968), Casulli and Greenspan (1982), Gilman and Kassemi (1983) for the case of naturally fractured reservoirs, and Ramakrishnan and Wasan (1984) in connection with the effect of capillary number.

The pore level or network model approaches are based on the pioneering work ofFatt (1956), who stated that a network of tubes is a valid model of porous media. He also was the first to state that the relative permeability characteristics of porous media are a direct consequence of the network structure of these media. Later, the network principles were combined with the aspects of percolation theory and gave the stochastic network models.

This approach is the basis of the work of Chatzis (1976) (1980), Chatzis and Dullien (1978) (1982) (1982B), Larson et al (1981), Mohanty et al (1980), Koplik (1982), Heiba et al (1982) (1984), Mohanty and Salter (1982), Diaz (1984), and Kantzas (1985). The various models have many similarities but some crucial differences. Details on the above models are given below.

Theoretical Developments Pertinent to Relative Permeability Studies the Network Approach for Modelling Porous Media

A porous medium can be represented as a random network’of pores. The construction of such a network must follow some theoretical considerations (e.g., porosity, pore to pore coordination number, pore shapes and pore sizes, etc.). Many of these aspects are based on the percolation theory and its applications to flowing porous media. Some introductory information about percolation theory concepts is given in the sections that follow. For more details on percolation theory and its applications in porous media, see Shante and Kirkpatrick (1971), Kirkpatrick (1973), Chatzis (1976), (1980), Larson (1977), and Larson et al (1981).