Infinite-Acting Physically Representative Networks for Capillarity-Controlled Displacements

Abstract

Summary 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 computergenerated 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. The drainage endpoint for a finite network was highly sensitive to the number and location of the exit pores; while using the infinite-acting network, we removed this latter sensitivity. 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.