Three‐dimensional, randomized, network model for two‐phase flow through porous media

Abstract

A structural model for a porous medium in the form of a randomized, three‐dimensional network is developed that can be used to calculate permeability, capillary pressure as measured under static conditions and during steady‐state flows, and relative permeabilities as measured during steady‐state flows. This randomized network model, expressed in terms of seven free parameters, can be employed to correlate for a given system the single‐phase permeability, the drainage and imbibition capillary pressure curves, and the two drainage relative permeability curves. The subsequent portions of the hysteresis loops for capillary pressure and for the relative permeabilities then can be predicted. The limited data available from the literature for unconsolidated packed beds have been successfully correlated: 100 to 200 mesh sand and uniform 181 μm glass spheres. Data for a bed of sintered 200 μm glass beads also has been successfully described.

Migrations of Fines in Porous Media

“…The connectivity of pore space can be precisely characterized by Betti numbers (Sahimi,1995b). A reasonable estimate of an average coordination number for sandstones is between 4 to 8 (Lin and Slattery, 1982;Yanuka et aI., 1984). An average coordination number representing the connectivity between constrictions to chamber is an important parameter.…”

“…Networks can be two-or threedimensional. While most of the network models have used cylindrical tubes for bonds, tubes with sinusoidally varying cross sections have been used in a few applications (Lin and Slattery 1982;Dias and Payatakes, 1986;Hopkins and Ng, 1986). As mentioned previously, the interconnectivity of the pore space is a major structural property of porous media.…”

The Coupled Effect of Fines Mobilization and Salt Precipitation on CO2 Injectivity

“…In this work, the pore chambers and throats were represented as individual non-interacting tubes. The average coordination number in sandstones is between 4 and 8 [44,45]. The pore size distribution in Figure 4 compares favorably with this range of coordination numbers.…”

The difference between steady-state and unsteady-state relative permeabilities

“…Lin and Slattery (1982) have summarized the available literature relevant to the functional forms taken by the capillary pressure and the relative permeabilities. Lin and Slattery (1982) have summarized the available literature relevant to the functional forms taken by the capillary pressure and the relative permeabilities.…”

“…We choose not to use the more realistic, three-dimensional, randomized network of more than 2000 pores employed by Lin and Slattery (1982) for two reasons. First, we estimated that the numerical problem of displacement in such a network was too large for the computer available to us at the beginning of this study.…”