Discussion of the Use of Capillary Tube Networks in Reservoir Performance Studies
Authors: Claridge E.L. 
Published: December 2007

Abstract
The paper is presented as a discussion of the work of Simon and Kelsey on the use of capillary tube networks in reservoir performance studies. The author believes that calculation of oil recovery by the method outlined by Simon and Kelsey will give predictions that are too optimistic for reservoir-scale predictions that are too optimistic for reservoir-scale flooding processes, particularly when the mobility ratio is unfavorable. The reason for this is that the networks are too small to permit proper scaling of longitudinal and transverse dispersion effects. Hence, as early a breakthrough as will occur with fully developed viscous fingers is not observed.

Introduction
It appears to us that calculation of oil recovery by the method outlined by Simon and Kelsey will give predictions which are much too optimistic for reservoir-scale flooding processes, particularly when the mobility ratio is unfavorable. We believe that the principal reason for this is that the Simon-Kelsey networks are too small to permit proper scaling of longitudinal and transverse proper scaling of longitudinal and transverse dispersion effects. Hence, the authors do not observe as early a breakthrough as will occur with fully developed viscous fingers. Since the authors oil recovery predictions are too optimistic for any given degree of heterogeneity, but decrease with increasing heterogeneity, Simon and Kelsey have attributed too great a degree of heterogeneity to some of the laboratory models involved in previously reported work in attempting to match the observed recovery data. Data derived from the models themselves indicate a much lesser degree of heterogeneity.

MODELLING OF PORE STRUCTURE AND THE H FACTOR
The mathematical model of reservoir displacement processes described by Simon and Kelsey is related processes described by Simon and Kelsey is related to the capillary network model of pore structure devised by Fatt. However, Fatt intended his model to describe the capillary pressure and relative permeability properties of small samples of reservoir rock, rather than large-scale oil reservoirs. Fatt emphasized the relationship between the form of the network as expressed by his connectivity number, 8, and the degree of similarity of the capillary pressure and relative permeability curves for his model to those of typical reservoir rocks. Fatt found that similarity required a value of 8 in the interval from 7 to 25. This is the average number of other tubes connected to the two ends of a given tube. It means that from 4 to 13 flow channels meet at each junction, on the average. For this reason, Fatt favored the use of a triple hexagonal network (B = 10) in which six tubes meet at each junction. This judgment of natural rock pore structure is supported by more recent scanning electron microscope studies. Simon and Kelsey used the double hexagonal network (B = 7) in part of the work reported in Ref. 1; but the remainder and the second article are based on a diamond grid (B = 6). Fact also found that a reciprocal relationship between tube radius and tube length was required to simulate actual rock permeability-porosity relationships. Simon and Kelsey permeability-porosity relationships. Simon and Kelsey have instead used tubes of constant length. A wide distribution of cube radii was found by Fatt to be necessary to simulate the capillary pressure curves of consolidated porous media. Pore radius distributions are typically log-normal, and the distributions used by Fatt were of this shape. They are not flat-topped distributions such as that used by Simon and Kelsey to define a heterogeneity factor, H, as the ratio of the maximum to the minimum channel radius. However, it is easy to derive for such a flat-topped distribution that the fractional average deviation for a total number of flow channels, N, is given by the following equations:
............(1a) ............(1b)
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