Infinite-Acting Physically Representative Networks for Capillarity-Controlled Displacements

Abstract Drainage/imbibition simulations are traditionally performed on finite regular lattices. If physically representative networks are used instead, the spatial correlation of pore space features inherent in granular materials is automatically accounted for. However, even these networks are obtained from finite samples, and conditions must be specified on the boundaries. Making the conditions correspond to physically realistic situations is difficult, especially for simulations of phase trapping. This paper presents a method of constructing infinite-acting model rocks, in which a well-defined criterion for phase trapping is possible that is independent of boundary conditions. The foundation of the model is computer generated dense random periodic packings of spheres. We illustrate the method with simulations of drainage and irreducible wetting phase saturations. To eliminate possible confounding effects from grains being arranged differently, we compare simulations in infinite-acting networks with simulations in the finite network taken from the unit cell of the periodic packing. Wetting phase connectivity is assessed globally and accounts for all phase morphologies, including pendular rings. This enables a physically rigorous method of identifying clusters of trapped pores: A "wrap-around" cluster of wetting phase is effectively infinite, and drainage of one or more pores in the cluster is deemed possible. All other clusters of wetting phase cannot undergo further drainage. Qualitatively different behavior is observed than when local connectivity criteria are used for trapping. The nonwetting phase percolation threshold and the drainage endpoint are not sensitive to the choice of inlet pores in infinite-acting networks. For a finite network the percolation threshold was similarly insensitive, but the drainage endpoint was highly sensitive to the number and location of the exit pores. Comparison with experiments showed that a strict criterion of wetting phase connectivity (pores connected only by throats filled with wetting phase) cannot account for typical values of Sw,irr and that connectivity must persist via pendular rings. Typical laboratory experiments and simulations in finite networks yield drainage curves that approach irreducible wetting phase saturation Sw,irr gradually, with large changes in capillary pressure inducing only small changes in saturation. Simulations in infinite-acting networks do not exhibit this behavior. We argue that these simulations are more representative of behavior in the field, and that typical laboratory measurements underestimate the value of Sw,irr.