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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 S_w,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 S_w,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 S_w,irr.

Introduction

When immiscible fluids co-exist in the pore space of granular materials, capillarity determines the fluid configuration at the pore scale in many applications. The fluid configuration, in turn, strongly affects macroscopic properties such as relative permeability and electrical resistivity. For example, disconnection of a fluid phase during displacement causes the phenomenon of residual phase saturations and alters the topology of a fluid phase. These changes have a profound influence on macroscopic properties of the phase.

The coarsest measure of the fluid configuration is phase saturation, and this is described by drainage and imbibition capillary curves. These curves also have a considerable influence on several processes of environmental interest. An increasingly important example comes from observations of methane hydrate deposits in sediments below permafrost or below the seabed. The mechanism by which hydrates form is not well understood, and it would be valuable to be able to examine the drainage of gas into the hydrate stability zone (from a presumed accumulation below the zone) and the subsequent interaction between gas and residual brine. Predictive models of drainage and imbibition are thus of great utility in subsurface science and engineering.