The Use of Capillary Tube Networks in Reservoir Performance Studies: 1. Equal-Viscosity Miscible Displacements
Authors: Simon Ralph , Kelsey F.J. 
Published: December 2007

Abstract
This paper concerns the use of network principles to study displacement phenomena in porous media. The information presented is for equal-viscosity, equal-density miscible displacements. The paper explains the reasons for using an interconnected network of capillary tubes to model the interconnected network of pores in a reservoir rock. A method is presented for defining the heterogeneity of a presented for defining the heterogeneity of a network of tubes based on tube-size and tube-location distribution functions. A technique is described for constructing a network whose heterogeneity models the heterogeneity of pores in a reservoir rock. The use of networks to provide information which can be used in the solution of reservoir engineering problems is illustrated with example calculations of the effect of heterogeneity on fingering, breakthrough, and selective plugging in linear systems, and the effect of heterogeneity on areal sweep efficiency in a five-spot pattern.

Introduction
Oil in a reservoir is contained in an interconnected three-dimensional network of pores. Direct evidence of the nature of this network of pores comes from examination of petrographic thin sections and three dimensional Scanning Electron Microscope (SEM) pictures of the pores.
The SEM pictures show that the pores in a reservoir rock are channels through which flow can occur. These channels have highly irregular configurations so irregular that it is not practical at this time to calculate flow behavior through individual channels or through the interconnected network of the channels. It is practical, however, to use a computer to calculate flow behavior in an interconnected network of capillary tubes and several investigators have studied the problem of using a network of tubes to model a network of pores. pores. Fatt pioneered the idea of using a network of cubes model for reservoir engineering studies. He demonstrated that capillary pressures, relative permeabilities, and electrical resistivities permeabilities, and electrical resistivities calculated for a network model have the same characteristics as those measured for real pores in reservoir rocks. From this, Fatt concluded that the network of tubes is a valid model of real porous media.
Rose reinforced Fatt&apos;s conclusion and showed that computers can be used to study the displacement characteristics of networks and to obtain results "…which can be supposed to have a direct bearing on the mechanics of petroleum recovery…"
This paper takes two steps beyond the work of Fatt and Rose. First, it describes a technique for constructing a network whose heterogeneity models the heterogeneity of natural pores. This is done by matching calculated equal-viscosity miscible displacement behavior in the network with measured behavior in a laboratory core. Second, it illustrates the use of the network model for calculating the effects of heterogeneity on fingering, breakthrough, and plugging in linear systems and areal sweep efficiency in a five-spot pattern.
The networks used in the studies in this paper consist of several hundred interconnected capillary tubes of different sizes. Four different types of connections or configurations were investigated and are shown below. These configurations are discussed in detail later in the paper.
SPEJ
P. 99